Conference Proceedings of 2022 2nd International Joint Conference on Energy, Electrical and Power Engineering [1060, 1 ed.] 9789819943333, 9789819943340

Table of contents :
Contents
Energy Consumption Analysis and Optimization of Comprehensive Energy System in Fishery Park
1 Introduction
1.1 Development Status
2 Analysis of Energy Consumption in Fishery Production
2.1 High Energy Consumption Equipment for Fishery Production
2.2 Heat Pump Model
3 Energy Saving Analysis of Equipment Motor
4 Conclusion
References
Decision Tree Ensembles for Smart Sewage Treatment: An Intelligent Dosing Model for Removing Phosphorus
1 Introduction
2 Problem Definition
2.1 Training a Phosphorus Removal Prediction Model
2.2 Dosage Suggestion with the Trained Model
3 Intelligent Dosing Model with Decision Tree Ensembles
3.1 Phosphorus Removal Prediction with Decision Tree Ensembles
3.2 Intelligent Dosing Model for Phosphorus Removal
4 Experiments
4.1 Data Preparation and Preprocessing
4.2 Evaluation on the Phosphorus Removal Prediction with Decision Tree Ensembles
4.3 Evaluation on the Chemical Consuming Reduction with the Intelligent Dosing Model
5 Conclusion
References
Failure Mechanism Analysis on Single Pulse Avalanche for SiC MOSFETs
1 Introduction
2 Single UIS Experiments
3 Failure Mechanism
3.1 Junction Temperature Estimation
3.2 Parasitic BJT Latch-Up
3.3 Metal System Damage
3.4 TCAD Simulation
4 Conclusion
References
Research on the Scale of Multi-regional Networking to Improve the Interoperability Benefits of Power Systems
1 Introduction
2 Characteristics of Regional Power Grid
2.1 Scale and Characteristics of Electricity Consumption
2.2 Power Supply Structure
2.3 Subject to Electrical Characteristics
3 Benefit of Interconnection
3.1 Installation Substitution Benefits
3.2 Clean Energy Consumption Benefits
3.3 Economic Benefits
3.4 Marketization Benefits
4 Network Scale Measurement Method
5 Network Scale Analysis
6 Conclusion
References
P2P Optimization Strategy for Integrated Energy Operators Based on Nash Negotiation
1 Introduction
2 Coordination Scheduling Model Considering Multi-agent Game
2.1 The Constraint
3 The Nash Bargaining Model of Multi-agent Cooperative Operation
3.1 Nash Bargaining Model
3.2 Problem Equivalent Conversion
4 Example Analysis
5 Conclusion
References
Three Phase O-Z-Source Inverter
1 Introduction
2 Analysis and Modeling of O-Z-Source Inverter
2.1 Steady-State Model
3 Experiment Results
3.1 Experimental Analysis
4 Conclusion
References
Recognition of Tunneling Boring Machine Operating Status Based on the Time Series Analysis
1 Introduction
2 Methodology
2.1 Time Series Segmentation
2.2 Feature Extraction and Selection of Time Series
2.3 Recognition of TBM Operating Status
3 Experiments
3.1 Experiment Setting
3.2 Results and Analysis
4 Conclusion
References
Flow Pulsation Optimization of Peristaltic Pump Based on Surrogate Model
1 Introduction
2 Peristaltic Pump
3 Digital Model
4 Surrogate Modeling
4.1 Experiment Design
4.2 Surrogate Model Comparison
4.3 Basic Theory of RSM Surrogate Model
5 Design Optimization
5.1 Optimization Equation
5.2 Optimization Algorithm and Results
5.3 Validation of Results
6 Conclusions
References
Dispatch Strategy for Transmission Overload Based on Safe Reinforcement Learning
1 Introduction
2 Problem Formulation
2.1 MDP Modelling
2.2 Power System Constraints
3 Methodology
4 Case Study
4.1 Test Case Preparation
4.2 Performance Validation
5 Conclusion
References
Research on Power Source Schemes in High Proportion of Renewable Energy HVDC System
1 Introduction
2 Basic Research Ideas
3 Evaluation Index System of Power Source Scheme
4 Ningxia Case
4.1 DC Sending End Power Source Scheme Design
4.2 Demonstration of Power Source Scheme
5 Conclusion
References
Experimental Study on the Influence of Voltage Sag Characteristic Parameters on the Dynamic Performance of SSTS
1 Introduction
2 Structure and Performance Indexes of SSTS
2.1 Working Principle of SSTS
2.2 Voltage Sag Detection
2.3 SSTS Switching Dynamic Characteristic Indexes
3 Experiment Design
3.1 Experiment Platform
3.2 Purpose and Procedure
3.3 Parameters Setting
4 Results and Analysis
4.1 Influence of Sag Magnitude on SSTS Switching Dynamic Performance
4.2 Influence of Sag Duration on SSTS Switching Dynamic Performance
4.3 Influence of Sag Initial Phase Angle on SSTS Switching Dynamic Performance
4.4 Influence of Sag Change Rate on SSTS Switching Dynamic Performance
5 Conclusion
References
Non-invasive Measurement Method for DC-Side Energy Storage Capacitance of Single-Phase Bridge Uncontrolled Rectifiers
1 Introduction
2 The Working Principle of the Single-Phase Bridge Uncontrolled Rectifier
2.1 Filtering Principle
2.2 Output Voltage Calculation
3 The Calculation Model of DC-Side Energy Storage Capacitance
4 Simulation Analysis
4.1 Simulation Parameter Setting
4.2 Output Voltage Simulation Analysis
4.3 Simulation Analysis of DC-Side Energy Storage Capacitance
5 Conclusion
References
Application of Generalized Predictive Control in Buck Converter
1 Buck Controller Design Ideas
2 Generalized Prediction PID Control Strategy
2.1 PID Control
2.2 Generalized Predictive PID Control
3 Verification by Experiment
3.1 Experimental Results
References
Sliding Mode Control of PMSM Based on Double Power Reaching Law
1 Introduction
2 Double Power Approach Law
3 Sliding Mode Controller Design
4 The Simulation Verification
5 Conclusion
References
Distinguishment of Power Quality Disturbances Using Segmented Adaptive S Transform
1 Background
2 Segmented Adaptive S Transform
2.1 S Transform
2.2 Adaptive S Transform Strategy
2.3 Segmented S Transform Strategy
3 Case Study
4 Conclusion
References
Robust Predictive Rotor Current Control of DFIGs Based on an Adaptive Ultra-local Model
1 Introduction
2 Dynamic Mathematical Model of the DFIG
3 Proposed Robust Predictive Rotor Current Control
3.1 Rotor Current Reference Value Acquisition
3.2 Ultra-local Model Updating and Delay Compensation
3.3 Calculation of Required Rotor Voltage
4 Simulation Verification
5 Conclusion
References
Multi-region V2G Optimal Scheduling Strategy Based on Region Division
1 Introduction
2 EV Travel Chain Model
2.1 Trip Probability Function
2.2 Daily Travel Chain Structure
2.3 The Related Model of EVs Models
3 Multi-region Optimal Scheduling Strategy
3.1 Objective Function
3.2 Constraint Condition
3.3 Multi-objective Optimization Model
3.4 Scheduling Strategy
4 Example Analysis
4.1 Example Description
4.2 Example Solution
4.3 Result Analysis
5 Conclusion
References
Maximum Power Point Tracking Control of Wind Power Generation System Without Inductance Decoupling
1 Introduction
2 Maximum Power Point Tracking
3 LADRC Controller
4 Inner Current Loop Control
5 Simulation Results
6 Conclusion
References
A Cluster-Based Dynamic Grouping Population Replication Strategy for Bilevel Multi-objective Optimization
1 Introduction
2 The Proposed Algorithm
3 Experiment Results
3.1 The Experimental Setups
3.2 The Comparisons with Other Approaches
4 Conclusion
References
Study on Multi-objective Scheduling Strategy for Electric Vehicle to Absorb Wind Power Considering Dynamic Time-of-Use Price
1 Introduction
2 Time Division of the DTOU Price
3 Dispatching Strategy Considering the DTOU Price
4 Multi Objective Optimal Scheduling Model
4.1 Objective Function
4.2 Binding Conditions
5 Example Analysis
5.1 Data Description
5.2 Results and Analysis
6 Conclusion
References
Thermal Effect Analysis of Three-Level Inverter Power Module Based on Single Cycle Loss Calculation
1 Introduction
2 Electro-Thermal Model of Inverter
2.1 Power Module Loss Model
2.2 Thermal Model of Inverter
3 Electro-Thermal Analysis of the Power Module
3.1 Loss Calculation
3.2 Junction Temperature Analysis
4 Thermal Simulation and Experiment
5 Single Cycle Heat Equalization
6 Conclusion
References
Secondary Authentication Method Suitable for 5G-Based Power Terminals and Formal Analysis
1 Introduction
2 Secondary Authentication Scheme
3 Formal Analysis
3.1 Protocol Description
3.2 Formal Model
3.3 Analysis of Results
4 Conclusion
References
Research on Multi-scale Space-Time Planning and Allocation Method of Energy Storage System Under New Energy Structure
1 Introduction
2 The Planning Model of the Energy Storage System
3 A Double-Layer Optimization Model Based on Improved Adaptive Genetic Algorithm
4 Example Analysis
4.1 Example Validation Based on IEEE-33 Node Distribution Network
5 Summary
References
FPGA-Based Servo Control for a Dual Three-Phase Permanent Magnet Synchronous Motor
1 Introduction
2 Mathematical Models of the Dual Three-Phase PMSM
3 Servo Control Design with Three Closed Loops
4 FPGA Implementation
5 Experimental Verifications
6 Conclusions
References
Measurement and Control System of Planetary Roller Screw Transmission Efficiency Test Bench Based on LabVIEW
1 Introduction
2 Transmission Efficiency Measurement Method
3 Structure of Test Bench and the Measurement and Control System
4 Software Design of Measurement Control System
5 Test Results
6 Conclusion
References
Improved Damping Ratio Control of Virtual Synchronous Generators with Multiple Parameter Coordination
1 Introduction
2 Multi-parameter Cooperative Adaptive Control of VSG
2.1 The System is Affected by VSG Parameters
2.2 Cooperative Adaptive Selection Strategy of Controlling Parameters
3 Simulation Analysis
4 Conclusion
References
Hybrid Time Step Day-Ahead Optimal Scheduling of the PV-Cascade Hydro Complementary Power Plant Based on PV Output Forecast
1 Introduction
2 LSTM Forecasting Model
3 Introduction
4 Mathematical Model for Optimal Scheduling of Cascade Water-Light System
4.1 Objective Function
4.2 The Constraint
4.3 Model Solving Method
5 A Case Study
5.1 Data
5.2 Forecast Results
5.3 Scheduling Result
6 Conclusion
References
GRU Network-Based Load Allocation for Hydro Units
1 Introduction
2 The Basic Theory of GRU Neural Networks
2.1 Gated Circulation Units
3 Unit Load Allocation Model Based on GRU Networks
3.1 Model Evaluation Indicators
4 Application Examples
4.1 Data Clustering Results
4.2 Parameter Setting and Training Process
4.3 GRU Model Load Allocation Results
5 Conclusions
References
A Novel Multi-fidelity Surrogate Model with Two-Stage Ensemble
1 Introduction
2 Methodology
2.1 Stage 1: Construction of MFS Model Library
2.2 Stage 2: Ensemble of MFS Models
3 Numerical Examples
3.1 The Investigation for the Parameter α
3.2 The Performance Analysis of the TSE-MFS Model
4 Conclusion
Appendix A: 20 Test Functions
References
A Fault Diagnosis Method for Molecular Pump Based on Dictionary Learning
1 Introduction
2 Methodology
3 Molecular Pump Fault Diagnosis Method
3.1 Signal Sparse Representation Based on DCT Denoise
3.2 Signal Sparse Representation Based on DCT Denoise
4 Results and Discussion
4.1 Vacuum Leakage Experimental Test
4.2 Compassion of Proposed Method and Traditional Method
5 Conclusion
References
Development of Comprehensive Training Platform for Power Electronics Teaching in Smart Grid and Renewable Energy
1 Introduction
2 Development of the Experimental Platform
2.1 Power Circuit Module
2.2 Circuit Control Module
2.3 Software Design
3 Teaching Experiment Platform Applications
3.1 Platform Construction
3.2 Teaching Experiment
4 Conclusion
References
Rotor Position Deviation Active Control of High Speed Magnetic Levitation Permanent Magnet Motor
1 Introduction
2 Control Strategy
3 Simulation
4 Experiment
References
Research on Risk Prevention and Control of Distribution Network Based on Knowledge Graphs
1 Introduction
2 Construction of Knowledge Graphs for Risk Prevention and Control of Distribution Network
2.1 Knowledge Graphs Construction Process
2.2 Basic Data and Graph Types
2.3 Knowledge Graph Construction Technology
3 Risk Prevention and Control Process of Distribution Network Based on Knowledge Graph
4 Application of Knowledge Graph for Risk Prevention and Control of Distribution Network
4.1 Incorporate Risk Control to the Auxiliary Decision-Making Knowledge Graph Application
4.2 Application Case
5 Conclusion
References
sDFT Based IRP Detection of the Electrical Excited Synchronous Machine
1 Introduction
2 Rotor Position Angle Detection Principle
3 Principles of sDFT
4 Detection Method Based on sDFT
5 Experiment Results
6 Conclusion
References
A Unified Startup Control Strategy for Modular Multilevel Converter with the Supercapacitor Energy Storage System
1 Introduction
2 Basic Analysis of the MMC-SCESS
3 The Precharge Strategy of the MMC-SCESS
3.1 Uncontrollable Precharge Stage of MMC-SCESS
3.2 Closed-Loop Precharge Stage of the MMC-SCESS
3.3 Precharge Method of the MMC-SCESS Supercapacitor
4 Simulation and Analysis of Precharge Strategy
5 Conclusion
References
Coordinated Operation for Honeycomb Active Distribution Network with Multi-microgrids
1 Introduction
2 Problem Formulation
2.1 Structure of HADN
2.2 Operation Model of Microgrids
2.3 Operation Model of Distribution Network
2.4 Collaborative Operation Model of HADN
3 Solution Algorithm
3.1 ADMM with RF Heuristics-Based Model
3.2 Solution Process
4 Numerical Results
5 Conclusion
References
Primary Frequency Modulation Control of Doubly-Fed Wind Turbine Based on Optimal Coordination of Pitch and Energy Storage
1 Introduction
2 Energy Storage and Pitch Angle Coordination Modes
2.1 Standby Energy Storage Cooperative Mode of Pitch Angle Load Reduction
2.2 Limited Power Energy Storage Collaborative Mode
3 Limited Power Mode in Minimum Wind Power
4 Seek the Optimal Limited Power Mode
5 Conclusion
References
Analysis of Harmonic Characteristics of Magnetic Controllable Transformer
1 Introduction
2 Harmonic Generation Mechanism
3 Principle Calculating Harmonic Content of Primary Current by FFT
4 Simulation Model and Parameters
5 Conclusion
References
Investigation of Pumped Storage Power Station Construction Conditions in Guangdong Province
1 Research Background
2 Investigation Principles
2.1 Compliance with Environmental, Ecological, Water Source, Cultural Heritage and Other Protection Requirements
2.2 Close to Electricity Load Centers
2.3 Decentralized Layout
2.4 Good Access System Conditions
2.5 Facilitating Multi-energy Complementarity and the Consumption of New Energy [8, 12–15]
2.6 Taking into Account the Needs of Economic Development in Both Eastern and Western Areas
2.7 Excellent Construction Conditions of the Site [9]
3 Investigation
3.1 Service Objects
3.2 Site Conditions
3.3 External Environment
3.4 Economy
4 Conclusion
References
Integrated Charger Topology and Control Strategy with Single-Phase and Three-Phase Charing Functions for Electric Vehicle
1 Introduction
2 Charger Topology
3 Control Strategy
3.1 Control Strategy for the Front-End AC–DC Converter
3.2 Control Strategy for the Back-End DC–DC Converter
4 Experimental Verification
4.1 Three-Phase Charging Mode
4.2 Single-Phase Charging Mode
5 Conclusion
References
Research on Short-Circuit Fault of High-Speed Maglev Traction Linear Motor
1 Introduction
2 Dynamic Mathematical Model
2.1 Motor Equivalent Model and Parameters
2.2 Armature WindingShort-Circuit Current
2.3 Excitation Short Circuit Current
3 Short Circuit Simulation Verification
4 Conclusion
References
A Designable Stability-Improving Control Method Based on Eigenvalue Sensitivity for Three-Phase Grid-Following Converter
1 Introduction
2 Small-Signal Model of Three-Phase Grid-Following Converter Considering the Nonlinear Characteristic of PLL
3 Designable Stability-Improving Method Based on Eigenvalue Sensitivity
3.1 Eigenvalue Sensitivity
3.2 Basic Idea of Stability-Improving Control Method Based on Eigenvalue Sensitivity
3.3 The Additional Inverter-Side d-Axis Inductor Current Feedback Control Derived by Eigenvalue Sensitivity
4 Simulation Verification of the Derived Stability-Improving Control Strategy
4.1 Simulation Verification
4.2 The Stability-Improving Effect of AIdCF Control in the Grid-Following Converter
5 Conclusion
Appendix
References
An Intuitionistic Time-Domain Stability Analysis Method Based on Floquet Theory for Three-Phase Grid-Following Converter
1 Introduction
2 Time-Domain Model and Stability Analysis of TGFC
2.1 The Topology of the TGFC
2.2 Time-Domain Model of the GFC
3 Time-Domain Stability Analysis
4 Simulation Verification
5 Conclusion
Appendix
References
Locational Marginal Price Model Considering Customer Directrix Load
1 Introduction
2 Customer Directrix Load Line
3 Locational Marginal Price
4 Case Analysis
5 Conclusion
References
Analysis of the Steady State Fluid Force and Flux of Nuclear Pressure Safety Valves Based on Surrogate Models
1 Introduction
1.1 A Subsection Sample
2 Pressure Safety Valves
3 Numerical Methods
4 Building Surrogate Nodel
4.1 Design of Experiments
4.2 Comparison of Surrogate Model
5 Validation of the Surrogate Model
6 Analysis of Parameter Sensitivity
7 Conclusions
References
Study on Mathematical Model and Dynamic Compensation of Oil Down-Hole Pressure Sensor Based on BP Neural Network
1 Introduction
2 Analysis of the Influence of the Specialized Buffer Device on the Dynamic Characteristics of the Pressure Sensor
3 Modeling and Compensation Method Based on Neural Network
4 Modeling and Compensation Practice of the Typical Pressure Sensor Based on BP Neural Network
5 Conclusion
References
Model Predictive Current Control of Three-Phase Voltage Source Rectifier Based on Optimal Space Trajectory
1 Introduction
2 Traditional Model Prediction Algorithm
3 Proposed OST-MPC Control Algorithm
3.1 Gradient Calculation of Switching Sequence
3.2 Calculation of Vector Action Time
3.3 Duty Cycle Calculation
4 Simulation Result
4.1 Steady State Performance Comparison
4.2 Dynamic Performance Comparison
5 Conclusion
References
A Novel Current-Limiting Hybrid DC Circuit Breaker
1 Introduction
2 Topology and Theoretical Analysis of the Proposed HCB
3 Simulation Verifications
4 Conclusion
References
Study on Motor Parameters of PMSM Based on the Principle of Adjustable Leakage Flux
1 Introduction
2 Motor Structure and Flux Weakening Principle
3 Analysis of the Influence of the Motor Parameters on the Electromagnetic Torque Ripple
3.1 The Influence of Air Gap and Current on Electromagnetic Torque Ripple
3.2 The Influence of Magnetic Conductor on Electromagnetic Torque Ripple
3.3 The Influence of Permanent Magnet on Electromagnetic Torque Ripple
3.4 The Influence of Coil Turns on Electromagnetic Torque Ripple
4 Torque-Speed Performance
5 Conclusion
References
The Coordination of FCL and Relay Protection: A Review
1 Introduction
2 Working Principle of FCL
3 Influence of FCL on Relay Protection
3.1 Distance Protection
3.2 Current Protection
3.3 Longitudinal Differential Protection
4 Coordination of FCL and Relay Protection
4.1 Distance Protection
4.2 Current Protection
4.3 Differential Protection
5 Conclusion
References
Research on Three-Phase Unbalance Compensation of Magnetic Control Transformer
1 Introduction
2 Principle of Magnetic Control Transformer and Balancing Compensation Principle
2.1 Principle of Magnetic Control Transformer
2.2 Balancing Compensation Principle
2.3 Simulation Analysis
3 Conclusion
References
Automatic Protective Relay Testing on Real Time Simulator
1 Introduction
2 Preparation of Automatic Testing on RTDS
3 Runtime Script Record/Playback Feature
4 An Application Example of Script Run in Relay Testing
5 Conclusion
References
Research on Harmonic Optimization of Magnetically Controlled Transformer
1 Introduction
2 Harmonic Optimization Based on Multistage Magnetic Valve Structure
2.1 Harmonic Problems of a New Type of Magnetically Controlled Reactance Transformer
2.2 Harmonic Mathematical Model
2.3 Harmonic Mathematical Model
2.4 Optimized Results
2.5 Mulation Experiment of Magnetically Controlled Transformer with Multi-stage Magnetic Valve Structure
3 Conclusion
References
Grasping Operation of Irregular-Shaped Objects Based on a Monocular Camera
1 Introduction
2 Methods of Image Processing
2.1 Image Segmentation and Contour Detection
2.2 Calculation of Rotation Angle
3 Experiments
4 Conclusions
References
Design and Development of an Unmanned Excavator System for Autonomous Mining
1 Introduction
2 Unmanned Excavator System (UES)
2.1 Autonomous Excavation Process
2.2 Overall Framework of UES
3 Numerical Experiments
3.1 The Experimental Equipment
3.2 Autonomous Digging
4 Conclusion
References
Research on the Switching Frequency Variation of Predictive Control Based on Circular Boundary-Limited Form
1 Introduction
2 Boundary Circle Confined Model Predictive Current Control
2.1 Voltage Vector Switching Trigger Mechanism
2.2 Optimal Voltage Vector Selection Strategy
3 Mechanism of Motor Speed Affecting Switching Frequency
4 Simulation Results
4.1 Results of MPC Simulation
4.2 Switching Frequency Variation at Different Speed
5 Conclusion
References
Electric Power Balance Contribution Calculation Based on Power Traceability
1 Introduction
2 Power Traceability Principle of Radiation Distribution Network
2.1 Proportional Sharing Principle (PSP)
2.2 Power Traceability of a Single Line
3 Electric Power Balance Contribution Calculation
3.1 Electric Power Balance Indices
3.2 Index Contribution Calculation Method
4 Case Study
4.1 Introduction of Basic Situation
4.2 Result and Discussion of Index SAF
4.3 Result and Discussion of Index VOF
5 Conclusion
References
Distributionally Robust Self-scheduling of Small-Scale Virtual Power Plants Considering Seasonal Variations
1 Introduction
2 Framework of the SVPP Self-scheduling Model
3 Framework of the SVPP Self-scheduling Model
3.1 Deterministic Self-scheduling Formulation for SVPP
3.2 Seasonal Variation-Based Ambiguity Set Description
3.3 The SDR Optimization with the Worst-Case Distribution
4 Case Study
5 Conclusion
References
Model-Free Predictive Control Strategy for PMSM Drives Based on Recursive Extended Least Square
1 Introduction
2 Conventional PCC Strategy
3 Modeling and Estimation for CAR
3.1 Modeling Process
3.2 Modeling Process
4 Validations
4.1 Tracking Performances
4.2 Robustness Verify
4.3 Performances with Different Orders
5 Conclusions
References
Power Optimization Control with Tracking Differentiator for Interior Permanent-Magnet Synchronous Motor
1 Introduction
2 Preliminary
2.1 Loss Model
2.2 MTPA Principle
2.3 LMC Principle
3 Proposed Power Optimization Control
3.1 Adaptive MPTA Principle
3.2 Adaptive LMC Principle
4 Results and Discussion
5 Conclusion
References
Full Life Cycle Prediction of Nuclear Bearings Based on Digital Twin Hybrid Model
1 Introduction
2 Method
2.1 Digital Twin
2.2 Artificial Intelligence Methods
3 Experiments
3.1 Data Processing
3.2 Deep Learning Methods
4 Conclusion
References
Simulation of Position Impedance Control for Single Leg of Electric Drive Legged Robot
1 Introduction
2 Single Leg Structure and Kinematic Modeling
2.1 Single Leg Structure
2.2 Kinematic Modeling
3 Simulation Analysis of Control Strategy
3.1 PID Closed-Loop Control Based on Single Joint
3.2 Position Impedance Control Based on Cartesian
4 Conclusion
References
Research on Distribution Transformer Quality Sampling Assessment Model Based on Entropy Weight Method
1 Introduction
2 Quality Sampling Test Data
3 EWM Analysis and Results
3.1 EWM Method Principle
3.2 Quality Sampling Assessment Model of Distribution Transformer
4 Conclusion
References
A Novel DC Energy Dissipation Topology and Control Method
1 Introduction
2 Proposed Concentrated Energy Dissipation Arm
3 Simulation Verifications
4 Conclusion
References
A Dual Inverter Topology Based on Quasi-Isolated Power Supply and Its Control Strategy
1 Introduction
2 The Proposed Topology and Its Mathematical Model
3 Control Strategy
3.1 Modulation Method
3.2 System Control Block Diagram
4 Simulation Verification
4.1 Simulation Parameters
4.2 Simulation Results and Analysis
5 Conclusion
References
The LCL Type Three-Phase Grid-Connected Inverter Active Damping Design Based on Capacitor Current Feedback
1 Introduction
2 Active Damping of Three-Phase LCL Filter
2.1 A Mathematical Model of the LCL Three-Phase Grid-Connected Inverter
2.2 Design of Capacitance Current Feedback Coefficient
3 Design Example
4 Conclusion
References
Peer-to-Peer Trading Among Prosumers Based on Cooperative Game
1 Introduction
2 A Cooperative Game-Based P2P Trading Model for Prosumers
2.1 Model
2.2 Shapley Value-Based Benefit Allocation Strategy
3 ADMM-Based Distribution Scheduling for Prosumers
4 Example Analysis
4.1 Model Parameters
4.2 Result Analysis
5 Conclusion
References
Second-Order Cone Based Dynamic Reconfiguration of Distribution Networks
1 Introduction
2 Distribution Network Reconfiguration Model
3 Second Order Cone Programming Model
4 Case Simulation
5 Conclusion
References
Research on Energy System Planning Method Considering Carbon Trading
1 Introduction
2 Planning Model
2.1 Objective Function
2.2 Models and Constraints
3 Case Study
3.1 Capacity and Economy Analysis
3.2 Environment Benefit Analysis
3.3 Sensitivity Analysis
4 Conclusion
References
Research on Influence of Buried Sand on Cable Temperature Rise Characteristics in Tunnel
1 Introduction
2 Model Building
2.1 Basic Assumptions When Building the Model
2.2 Model Parameter Settings
2.3 Heat Loss
3 Influence of Buried Sand on Temperature Rise Characteristics of Cables
4 The Influence of Other Conditions on the Temperature Rise Characteristics of the Cable
5 In Conclusion
References
A Innovative Three-Phase Unbalanced Compensation Range Evaluation for the Combination D-STATCOM
1 Introduction
2 Principle of the Combination STATCOM
2.1 Circuit Topology
2.2 Three-Phase Unbalanced Compensation Range Evaluation
3 Analysis and Control
4 Evaluation of Operating Range
5 Simulated Results
6 Conclusion
References
Parameter Optimization of the Three-Coil Wireless Power Transmission System Based on Genetic Algorithm
1 Introduction
2 Three-Coil System Model Analysis
3 The Implementation of the Genetic Algorithm
4 The Simulation and Experimental Verification
5 Conclusion
References
Analysis of Abnormal Working Conditions Influence Over a Self-switching LCC-LCC/S-Based WPT System with CC and CV
1 Introduction
2 Analysis of the Working Principle and Characteristics of Hybrid Topology
3 Analysis of the and Characteristics of Hybrid Topology
4 Simulation and Experiment
5 Conclusion
References
Design of Wide Voltage Range DC–DC Converter Based on SiC MOSFET
1 Introduction
2 Topology of DC–DC Converter
2.1 BOOST Converter
2.2 LLC Converter
3 Design for DC–DC Converter
3.1 BOOST Converter
3.2 LLC Converter
4 Experimental Verification
5 Conclusion
References
Study on Oscillation Characteristic Test and Data Fitting of DC Transfer Switch
1 Introduction
2 Oscillation Circuit Analysis
2.1 Equivalent Circuit
2.2 Test Error Analysis
3 Test Experiments
4 Data Fitting Method
5 Conclusion
References
Rolling Bearing Fault Diagnosis Method Based on Attention Mechanism Stacking
1 Introduction
2 Continuous Wavelet Transform
3 Attention Mechanisms Stacking Network
3.1 Convolutional Layer
3.2 Pooling Layer
3.3 Attention Mechanism
3.4 Inception Module
3.5 Optimizer
3.6 Overall Model Structure
4 Experimental Results and Analysis
4.1 Experimental Data
4.2 Experimental Results
5 Result
References
Optimal Design of Torque Ripple of External Rotor Permanent Magnet Synchronous Motor Based on Particle Swarm Optimization
1 Introduction
2 PMSM Analysis
3 Finite Element Simulation
4 Optimization of Motor Structure Parameters Based on Particle Swarm Optimization
5 Joint Simulation Results and Analysis
6 Conclusion
References
Study on Inertia-Resistant Disturbance Speed Control of Permanent Magnet Synchronous Motor Based on Exponential Integral Time-Varying Sliding Mode
1 Introduction
2 PMSM Mathematical Model
3 Inertia Identification
4 EITSMC Design
5 Simulation Verification
6 Conclusion
References
Torque Ripple Reduction of Permanent Magnet Synchronous Motor Based on Least Mean Square Algorithm
1 Introduction
2 PMSM Harmonic Analysis
3 LMS Filtering Algorithm
4 Design of Harmonic Suppressor Based on d-q Axis LMS Algorithm
5 Experimental Verification
6 Conclusion
References
Research on Multi-operating Control Strategy of Vehicle Motor Based on ALO
1 Introduction
2 Motor Voltage Equation
3 Ant Lion Algorithm
3.1 Algorithmic Principles
3.2 Basic Idea of Controller
4 Simulative Validation
5 Conclusion
References
Correction Method for Harmonic Measurement of Capacitor Voltage Transformer Based on Frequency Response Characteristics
1 Introduction
2 Experimental Test of Frequency Response of CVT
2.1 High Voltage Experimental Test Platform
2.2 Experimental Test Results
3 Key Parameter Identification
3.1 Impedance Model and Frequency Response Analysis of CVT
3.2 Key Parameter Optimal Identification
4 Parameter Identification Results and Correction
5 Conclusion
References
Design of Aviation AC/DC Contactor Life Test System Based on PXI-2204 and CPCI-7434
1 Introduction
2 Hardware Design
2.1 Main Circuit
2.2 Acquisition and Conditioning Circuit
2.3 Drive Circuit
2.4 Power Supply Circuit
3 Software Design
4 Experiment Platform and Results
5 Conclusion
References
MTPA Control Strategy of BLDCM Based on Back-EMF Orientation
1 Introduction
2 Selection of Conduction Mode Under MTPA Control
3 Difficulties of Traditional Transformation in MTPA
4 MTPA Control Strategy Based on Back-EMF Orientation
5 Experimental Verification
6 Conclusion
References
Torque Ripple Suppression Based on a New Multi-level DTC Strategy
1 Introduction
2 Multi-level DTC System
2.1 DTC System
2.2 Four-Level DTC During Non-commutation
2.3 Six-Level DTC During Commutation
3 System Simulation and Experimental Verification
4 Conclusion
References
Study of an IPT System Based on Configurable Charging Current and Charging Voltage
1 Quotes
2 A Constant-Current, Constant-Voltage, Self-switching IPT System with Configurable Charging Current and Charging Voltage
2.1 Analysis of the Constant Current Mode with Configurable Charging Current
2.2 Analysis of the Constant Voltage Mode with Configurable Charging Voltage
3 Parameter Settings
4 Simulation Validation
4.1 Simulation Analysis of a Constant Current and Constant Voltage IPT System with Configurable Charging Current
4.2 Simulation Analysis of a Constant-Current, Constant-Voltage IPT System with Configurable Charging Voltage
5 Summary
References
Impedance Remodeling Method of Single-Phase Grid-Connected Inverter Under Weak Grid
1 Introduction
2 Establishment of Impedance Model of Grid Connected Inverter
2.1 The Control Method of LCL Single Phase Grid Connected Inverter Mathematical Model
2.2 Impedance Model of Inverter
3 Impedance Remodeling Scheme Based on Low-Pass Filter
4 Second Order Low-Pass Optimized Impedance Remodeling Scheme
5 Simulation Results
6 Conclusion
References
Path Planning of Substation Inspection Robot Based on Improved Ant Colony Algorithm
1 Introduction
2 Environment Modeling
3 Traditional ACO
3.1 Basic Principle of ACO
3.2 Probability Selection
3.3 Rules for Pheromone Updating
4 Improvement of ACO
4.1 Uneven Distribution of Initial Pheromone Concentration
4.2 Improvement of Heuristic Function
4.3 Improvement of Pheromone Updating Rules
4.4 Improved Algorithm Process
5 Algorithm Simulation and Analysis
6 Conclusion
References
Research on Optimization Design of GaN Device Active Gate Drive Circuit
1 Introduction
2 Data Analysis of the Device Switching Process
2.1 Analysis of the Current Rise Phase in the Turn-On Process
2.2 Analysis of the Current Drop Phase During Turn Off
3 The Method of Driving a Current Source Gate Circuit
4 Simulation Results of the Active Gate Driving Strategy
5 Conclusion
References
Applications and Prospects of Online Insulation Monitoring Technique Based on Broadband Frequency Response for Transformers in Voltage Source Converter System
1 Introduction
2 Broadband Frequency Response from Offline to Online
2.1 Basic Principle
2.2 Challenges and Solutions of Online Implementation
3 Prospect of Non-invasive Technique Based on Online Broadband Frequency Response
3.1 Monitoring Principle
3.2 Evaluation Model
3.3 Technical Difficulties and Possible Solutions
4 Conclusion
References
Path Planning for Electric Power Inspection Robot Based on the Fusion of Improved A* and DWA Algorithm
1 Introduction
2 Path Planning Based on the Improved A* Algorithm
2.1 Traditional A* Algorithm
2.2 A* Algorithm Improvement Strategy
3 Animate Window Arithmetic
3.1 Robot Motion Model
3.2 Sampling Speed
3.3 Design of the Evaluation Function
4 Fusion Algorithm
5 Experiment and Analysis
5.1 Environment Model Description
5.2 Improved A* Algorithm Simulation Experiment
5.3 Fusion Algorithm Simulation Experiment
5.4 Experiment
6 Conclusion
References
Tunneling Operational Data Imputation with Radial Basis Function Neural Network
1 Introduction
2 Methodology
3 Experiments
3.1 Experimental Setup
3.2 Results and Analysis
4 Conclusion
References
A Novel IoT Based Multi-modal Edge Computing Optimization Method
1 Introduction
2 Analysis of Key Technical Points for Multi-source Information Feature Extraction
3 Multi-source Data Feature Extraction Based on Power Grid IoT and Deep Learning
3.1 Multi-source Information of Power Grid
3.2 Multi-source Information Extraction Method
3.3 Deep Convolutional Computation Model
4 Conclusion
References
An Advanced IoT Based Edge Computing Forecasting Framework
1 Introduction
2 Application of CPS in Power Internet of Things
2.1 Power System Layer
2.2 Sensor and Control System Layer
2.3 Communication Network
2.4 Application Layer
3 Implementation Technology
3.1 Communication Protocol
3.2 Data Management
3.3 Service
3.4 Application
4 Conclusion
References
A Novel Data Merging Intelligent Method for Whole System IoT
1 Introduction
2 Knowledge Extraction from Multiple Sources of Heterogeneous Data
3 Knowledge Multi-source Heterogeneous Data Fusion Based on Model Integration
4 Experiment
4.1 Data Sets and Evaluation
4.2 Experimental Results
5 Conclusion
References
Research on Model of Buck-Boost Converter Based on Digital Twin
1 Introduction
2 Mathematical Model of Buck-Boost Converter
2.1 Mosfet On
2.2 Mosfet Off
2.3 Mathematical Model
3 Runge-Kutta Method to Solve the Model
4 Experimental Verifications
5 Conclusion
References
A Hybrid Carrier-Based DPWM Strategy with Variable Clamp Region and Controllable NP Voltage
1 Introduction
2 T-type Three-Level Inverter and Its CB-DPWM Strategy
2.1 Topology for T-type Three-Level Inverter
2.2 CB-DPWM Strategy
3 NP Voltage Control Strategy for Variable Clamp Region
3.1 DPWM Strategy with Variable Clamping Area
3.2 Hybrid Carrier-Based DPWM (HCB-DPWM)
4 Simulation Verification
5 Conclusion
References
A Novel Multi-robot Path Planning Algorithm Considering Dynamic Environmental Information
1 Introduction
2 Fusion Path Planning Algorithm
2.1 Global Adaptive Improved A* Algorithm Considering Environmental Information
2.2 Local Path Planning Algorithm Based on Rolling Window Method
3 Simulation Experiments
3.1 Simulation Experiment I
3.2 Simulation Experiment II
3.3 Analysis of Experimental Results
4 Conclusion
References
A Method of Constructing Admittance Matrix for Power Flow Correction in Complex AC Systems Suitable for Equivalent Simplification
1 Introduction
2 Power Flow Data Calculation
3 Element Equivalence Simplification
3.1 Element with Weak Correlation Between Equivalent Parameters and Power Flow Change
3.2 Element with Strong Correlation Between Equivalent Parameters and Power Flow Change
3.3 The Admittance Calculation of Complex Combination Elements such as Converter Station
4 Construction of Node Admittance Matrix of Complex AC System
4.1 System Node Admittance Construction Based on Power Flow Variation and Component Equivalence Model
5 Example Simulation and Verification Based on Admittance Matrix Simplification
5.1 IEEE9 Node System Verification
6 Conclusion
References
Research on Pricing Strategy of Electricity Selling Company Based on Electricity Characteristics of Different Industry
1 Introduction
2 Research on Electricity Consumption Characteristics of Subdivided Industries
2.1 Evaluation of Industrial Load Power Consumption Characteristics
2.2 Evaluation of Commercial Load Power Consumption Characteristics
2.3 Evaluation of Residential Load Power Consumption Characteristics
3 Basic Electricity Selling Business System of the Electricity Selling Company
3.1 Fixed-Rate-Type of Electricity Price Package
3.2 Variable Rate Type of Electricity Price Package
3.3 Demand Response Type Electricity Price Package
3.4 Volume and Price Linkage Package
4 Research on the Influencing Factors of Electricity Selling Pricing of Electricity Selling Companies
4.1 Selection of Industrial Load Electricity Sales Package
4.2 Selection of Commercial Load Electricity Sales Package
5 Conclusion
Authors’ Background
References
Credit Risk Evaluation of Power Users in Power Sales Package Recommendation
1 Introduction
2 Risk Evaluation Index System of Credit Scoring for Power Consumers on the Electricity Sales Side
2.1 Design Principles of Credit Evaluation System for Power Users
2.2 Construction of Credit Evaluation System for Power Users
2.3 Using Logistic Regression to Create Credit Score Cards
3 Construction of Specific Evaluation Indicators
3.1 Logistic Regression Model
3.2 Mixed Matrix
3.3 ROC Curve and Statistics
4 Comprehensive Evaluation Method of Credit Model
4.1 Data Indicators
4.2 Evaluation Index Weighting Determination
4.3 Metrics for Comparing the Performance of Credit Decision Models
4.4 Data Pre-processing
4.5 Dividing Boxes
4.6 Effectiveness of Credit Model Based on Logistic Regression
5 Conclusion
References
Operating Low Frequency Wind Power System in Variable Voltage Mode
1 Introduction
2 Control Methods of Variable Voltage LFWPS
2.1 Variable Voltage Control Method of the Onshore AC–AC Station
2.2 Dynamic Minimum DC-Bus Voltage of WECS
2.3 Simulation Results
3 Loss Studies
3.1 Converter Losses of WECS
3.2 Transmission Line Losses
3.3 Generator Losses
4 Fault Transient Study
5 Conclusion
References
Extended Kalman Filtering Power System Dynamic State Estimation Based on Time Convolution Networks
1 Introduction
2 Dynamic State Estimation Model Based on EKF
3 TCN Model Principle
4 TCN-EKF Dynamic State Estimation Model
4.1 TCN Model Constructing
4.2 TCN-EKF Algorithm
5 Example Analysis
5.1 TCN Offline Training
5.2 TCN-EKF Estimation Accuracy Analysis
6 Conclusion
References
A Capacitive Wireless Power Transfer System with LCLC Resonant Network
1 Introduction
2 Introduction CPT System with Unilateral LCLC-S Resonant Network
2.1 CPT System
2.2 Equivalent Analysis of Coupling Capacitor
2.3 LCLC-S Resonant Network
3 Results
3.1 Simulation Results
3.2 Experiment Results
4 Conclusion
References
Cost Performance Analysis of the Typical Electrochemical Energy Storage Unit
1 Introduction
2 Model of Electrochemical Energy Storage Cost
3 Cost Performance Analysis
4 Conclusion
References
Remaining Useful Life Prediction of Multi-sensor Data Based on Spatial-Temporal Attention Network
1 Introduction
2 Preliminaries and Problem Statement
3 Methods
3.1 STAnet Method Architecture
3.2 Spatial-Temporal Attention Module
3.3 Feature Extraction Module
3.4 Information Reinforcement Module
4 Experiment
4.1 Data Description
4.2 Data Preprocessing
4.3 Performance Evaluation Metrics
4.4 Comparisons with Other Approaches
5 Conclusion
References
Model-Free Predictive Current Control Strategy Considering Noise Error Compensation
1 Introduction
2 Basic Principles of MFPCC
3 Error Compensation Based on Second-Order Generalized Integrator
4 Simulation
4.1 Simulation Comparison of Model Parameter Mismatch
4.2 Simulation Results of Prediction Effect
5 Conclusion
References
An Improved Sub-pixel Corner Detection Algorithm
1 Introduction
2 Principle of Algorithm
2.1 Image Preprocessing
2.2 Extract Poor Corners
3 Improved Sub-pixel Corner Detection Algorithm
4 Experimental Results and Analysis
4.1 Sub-pixel Corner Point Detection Simulation
4.2 Sub-pixel Corner Point Detection Accuracy Simulation
5 Conclusion
References
Research on Information Interaction Technology for Mobile Energy Storage
1 Introduction
2 Information Interaction Logic of Energy Storage Vehicle
2.1 Emergency Power Protection Task
2.2 Virtual Power Plant Tasks
2.3 Virtual Power Plant Tasks
3 Research on Collaborative Information Interaction of Energy Storage
3.1 Simulation Scenario 1
3.2 Simulation Scenario 2
3.3 Simulation Scenario 3
4 Experimental Test
5 Conclusion
References
A QPSO-ELM Based Method for Load Model Parameters Identification
1 Introduction
2 Load Model Structure
3 Case Study
4 Conclusion
References
A Finite Time Cooperative Control Strategy for Energy Storage Systems in DC Microgrids
1 Introduction
2 A Unified Distributed Cooperative Control
3 A Robust Finite Time Voltage Observer
4 Simulation Validation
4.1 Bus Load Step Response
4.2 Local Load Step Response
5 Conclusion
References
Wide Input and Output Voltage in Bidirectional DC-DC Converter
1 Introduction
2 Wide Input and Output High Current Bidirectional DC/DC Converter
2.1 Bidirectional DC/DC Converter Design Difficulties
2.2 Selection of Bidirectional DC/DC Converter Topology
2.3 Buck/Boost Topology Analysis
2.4 LLC-DCX Topology Analysis
3 Bidirectional DC-DC Converter Control Strategy
3.1 Buck/Boost Control
3.2 LLC-DCX Control
4 Experimental Verification
4.1 Prototype Main Parameters and Device Selection
4.2 Interleaved Parallel Buck/Boost Experimental Verification
4.3 LLC-DCX Experimental Verification
4.4 Experimental Verification of 5 kW Bidirectional DC-DC Converter
5 Conclusions
References
Active and Reactive Power Optimization Based on Soft Open Points
1 Introduction
2 Reactive Power Optimization Model Based on SOPs
2.1 Topology and Modeling of SOPs
2.2 Minimum Power Loss Model
3 Case Studies and Analysis
3.1 Results and Analysis of Optimal Power Flow
3.2 Results and Analysis of Optimization Model
3.3 Comparisons Between Different Methods
4 Conclusion
References
Permanent Magnet Synchronous Linear Motor Based on Disturbance Compensated Flux Observer Sensorless Control
1 Introduction
2 Mathematical Model of PMSLSM
3 Design of Flux Observer
3.1 Conventional Flux Observer
3.2 Design of Disturbance Compensation Flux Observer
4 Simulation Verification
4.1 Verification of Correctness
4.2 Validation
5 Conclusion
References
Peak Clipping Control Strategy Based on Inverter Air Conditioner and Electric Vehicle Power Compensation
1 Introduction
2 Flexible Load Classification of Intelligent Community
3 Control Characteristics and Potential Evaluation of Variable Frequency Air Conditioning Cluster
3.1 Equivalent Thermal Parameter Model of Air Conditioning
3.2 Potential Evaluation Model of Variable Frequency Air Conditioning Cluster
4 Load Control Characteristics and Potential Evaluation of Electric Vehicle Cluster
4.1 Electric Vehicle Charging and Discharging Model
4.2 Electric Vehicle Charge and Discharge Probability Calculation Model
4.3 Electric Vehicle Cluster Potential Assessment Model
5 Intelligent Community Peak Cutting Control Strategy
5.1 Peak Elimination Response Process
5.2 Peak Cutting Optimization Model
5.3 Constraint Condition
5.4 Peak Shaving Income Distribution
6 Analysis of Examples
6.1 Example Parameter
6.2 Analysis of Polymerization Accuracy
6.3 Analysis of Peak Clipping Results
7 Conclusion
References
A Data Center Energy Storage Economic Analysis Model Based on Information Decision Theory and Demand Response
1 Introduction
2 The Data Center Valuation Model
2.1 The Modeling Inherent Energy Consumption of Data Center Equipment
2.2 The Way Data Centers Participate in Demand Response
2.3 The Value Evaluation Model of Energy Storage
3 Information Gap Decision Theory
3.1 IGDT System Model
3.2 Algorithm Implementation
3.3 Algorithm Process
4 The Example Analysis
5 Conclusion
References
Simulation Analysis of Conducted Electromagnetic Interference in Excitation Power Cabinet of Giant Hydraulic Turbine Unit Based on Time Domain Finite Integration Method
1 Introduction
2 Analysis Method
2.1 Time Domain Finite Integration Method
2.2 Conducted Electromagnetic Interference Principle
2.3 Simplification and Setting of the Model
3 Simulation Analysis
3.1 Parameter Extraction
3.2 Analysis of Results
4 Conclusion
References
Research on the Wind Farm Layout Optimization Considering Different Wake Effect Models
1 Introduction
2 Wake Effect Modeling
2.1 Jensen Wake Model
2.2 AV Wake Model
3 Wind Speed Modeling of Wind Farm Considering Multiple Wake Effects
3.1 Calculation Model of Multiple Wake Effects
3.2 Calculation of Occlusion Area When Wind Direction Is Determined
3.3 Coordinate Transformation of Turbines if the Wind Direction Changes
4 Wind Farm Layout Optimization Based on the AV Model and Genetic Algorithm
4.1 Genetic Algorithm
4.2 Optimization of the Wind Farm Layout
5 Conclusion
References
A Hierarchical Fast Model Predictive Control for Cascaded H-Bridge SVG
1 Introduction
2 System Predictive Model
2.1 A Subsection Sample
3 Proposed FCS-MPC for CHB-SVG
3.1 Model Predictive Current Control
3.2 Model Predictive Phase Voltage Balancing Control
3.3 Module Voltage Balancing Control
4 Simulation Result
5 Conclusion
References
Speed Fluctuation Suppression Strategy of PMSM Based on Improved Linear Active Disturbance Rejection Control
1 Introduction
2 Establishment of PMSM Mathematical Model
3 The ILADRC Is Proposed
4 Experimental Verification
4.1 No Load Experimental Verification
4.2 Loading Experiment Verification
5 Conclusion
References
An Improved Distributed Wind Farm MPPT Control Based on Wake Propagation Prediction
1 Introduction
1.1 A Subsection Sample
2 System Model
2.1 Wind Farm Model
2.2 Wake Predictive Model
3 MPPT Control of a Wind Farm
3.1 Distributed Control Structure
3.2 Cooperative MPPT Control Using Wake Prediction
4 MPPT Control of a Wind Farm
5 Conclusion
References
Probabilistic Power Flow Computation Considering the Uncertainty of New Energy Access
1 Introduction
2 Probabilistic Models of Power System Components
2.1 Wind Turbine Probabilistic Model
2.2 Photovoltaic Generator Probabilistic Model
2.3 Load Probability Models
3 Cumulants Method Combined with Gram–Charlier Series
3.1 Cumulant
3.2 Gram–Charlier Series Expansion
4 Case Study
4.1 Speed and Accuracy of the Algorithm
4.2 Impact of New Energy Access
5 Conclusions
References
Modelling and Simulation of Demand Response in Frequency Modulation Markets
1 Current Status of Demand Response Research
1.1 The Development of Foreign Markets
1.2 The Development of Domestic Markets
2 Basic Framework of the FM Market
2.1 FM Auxiliary Services
2.2 FM Clearance Rules
2.3 Demand Response Participation in FM Markets
3 Construction of Demand Response Model in FM Market
3.1 Objective Function
3.2 Constraints
4 Analysis of the Algorithm
4.1 Parameter Setting
4.2 Clearance Results
5 Conclusion
References
Pitch Control Strategy for Wind Turbine Considering Operation Efficiency
1 Introduction
2 Wind Turbine Modeling
3 Control Policy
3.1 Unit Operating Characteristics
3.2 Bearing Life
3.3 Economic Model Forecast
3.4 Optimization of Genetic Algorithm
4 Objective Functions and Constraints
5 Example Analysis
6 Conclusion
References
Study on Sliding Mode Method of Five-Phase Permanent Magnet Synchronous Motor
1 Introduction
2 Ideal Module of Five-Phase PMSM
3 Design a New Type Velocity Controller
4 Analysis of System Based on MATLAB
5 Conclusion
References
Open-Circuit Fault Diagnosis for Wave Energy Converters with Support Vector Machine
1 Introduction
2 Fault Current Analysis
2.1 System Topology
2.2 Current Path
3 Diagnosis of WEC Based on SVM
3.1 Analysis of SVM
3.2 Fault Diagnosis of Switch Current in WEC
4 Simulation Results
5 Conclusion
References
Design and Implementation of 4G-Based Crop Rotation Soil Information Monitoring System
1 Introduction
2 Sensor Node Design
2.1 Sensor Node Hardware Design
2.2 Sensor Node Software Design
2.3 Design of Internet Access Module
3 Intelligent Monitoring and Processing Center
3.1 Monitoring and Processing Center
3.2 The Realization of Intelligent Monitoring and Processing Center
4 Conclusions
References
Comparison and Analysis of Different Overvoltage Suppression Circuits for Low-Voltage Solid-State Circuit Breakers
1 Introduction
2 Different Overvoltage Suppression Circuits
2.1 Solid-State Circuit Breaker with MOV
2.2 Solid-State Circuit Breaker with RC+MOV
2.3 Solid-State Circuit Breaker with RCD+MOV
3 Simulation and Experimental Results for 375 V Solid-State Circuit Breakers
3.1 Comparison of Three Types of Overvoltage Suppression Circuits
3.2 Analysis of the Influence Rule of Snubber Circuit Parameters
3.3 Experimental Test
4 Conclusion
References
Research on Resonance Problem of DC Feed in AC System
1 Introduction
2 S-domain Node Admittance Matrix Method
2.1 Formation of Node Admittance Matrix in S Domain
2.2 Resonant Structure of S Domain Node Admittance Matrix Method
3 Analysis of Resonance in DC Feed in AC System
4 Simulation Result
5 Conclusion
References
Online Estimation of the Variable Inertia of DFIG Units Via an Improved Least Squares Method
1 Introduction
2 Modeling of Virtual Inertia Control for the DFIG
2.1 Virtual Inertia Control
2.2 Analysis of Variable Inertia
3 Evaluation Method
3.1 Identification Model
3.2 Least Squares Algorithm
4 Examples and Simulations
4.1 Real-Time Data Curve
4.2 Real-Time Evaluation Curve
5 Conclusion
References
Modeling of 12-Pulse LCC Converter Station Based on Harmonic State Space Theory
1 Introduction
2 HSS Impedance Model of 12 Pulsating LCC Converter Station
2.1 Open Loop Time-Domain Mathematical Model of Pulsating LCC Converter Station
2.2 HSS Open-Loop Impedance Model of 12 Pulsating LCC Converter Station
2.3 HSS Closed-Loop Impedance Model of 12 Pulsating LCC Converter Station
3 Simulation Verification
3.1 Open Loop HSS Impedance Model Verification
3.2 Verification of Closed Loop HSS Impedance Model
4 Conclusion
References
CTM-Based Collaborative Optimization of Power Distribution Network and Urban Traffic Network with Electric Vehicles
1 Introduction
2 Framework of the Coordinated Operation of PTN and UTN
3 Proposed Coordinated Operation Model of PTN and UTN
3.1 CTM-Based UTN Model
3.2 Second Order Cone Relaxation Based UTN Model
4 Example Analysis
4.1 Traffic Congestion Analysis
4.2 Distribution Network Optimization Analysis
5 Conclusion
References
Optimal Design of Laminated Busbar for Three Level Inverter Based on Multiple Weakening Method
1 Introduction
2 Theoretical Analysis of Conducted Interference Paths
3 Three Dimensional Modeling of Laminated Busbar
4 Extraction of Parasitic Parameters
5 Magnetic Field Analysis of Conducted Interference
6 Experiments and Tests
7 Conclusion
References
Simulation and Experimental Research on Low Voltage DC Switching Fast Repulsion Mechanism
1 Introduction
2 Design of Electromagnetic Repulsion Mechanism
2.1 Principle of Electromagnetic Repulsion Mechanism
2.2 Mathematics Model of the Electro-magnetic Repulsion Mechanism
3 Modeling and Simulation of Electromagnetic Repulsion Mechanism
3.1 Simulation Model of Electromagnetic Repulsion Mechanism
3.2 Simulation Analysis
4 Breaking Test of Electromagnetic Repulsion Mechanism
5 Conclusion
References
Research and Application of Green Power Market Operation Evaluation System in Beijing
1 Introduction
2 Green Power Market Operation Evaluation Index System
2.1 Beijing Green Power Market Structure
2.2 The Operating Results of the Green Power Market in Beijing in Recent Years
3 Green Power Market Operation Evaluation Index System
3.1 Analysis on the Status Quo of Green Power Market Operation Evaluation
3.2 O-SCP Green Power Market Evaluation Index System
4 Evaluation Model Based on CRITIC Weight Method
4.1 Evaluation Steps
4.2 Weight Determination Method
5 Case Analysis
6 Conclusion
References
Market Research on Electric Auxiliary Services with the Participation of Massive Distributed Power Sources
1 Introduction
2 Analysis of Mass Distributed Power Participating in Auxiliary Services
2.1 Analysis of Frequency Modulation Performance of Massive Distributed Resources
2.2 Analysis of Peak Shaving Performance of Massive Distributed Resources
3 Mass Resources Participate in the Market Model of Peak Shaving Auxiliary Services
3.1 Objectives
3.2 Constraints
4 Solution
5 Numerical Results
5.1 System Introduction
5.2 Analysis
6 Conclusion
References
Safety Constrained Economic Scheduling Model with Mass Distributed Generation Participation
1 Introduction
2 Massive Distributed Power System
2.1 Massive Distributed Resources
2.2 Participation in Economic Dispatch of Massive Resources
3 Safety Constrained Economic Dispatch Model
3.1 Equipment Model of Massive Distributed Power System
3.2 Objectives
3.3 Uncertainty Output
3.4 Restrictions
4 Particle Swarm Algorithm Solution Process
5 Numerical Analysis
5.1 Introductions
5.2 Economic Analysis
6 Conclusion
References
A Power Spot Market Transaction Support System Adapted to the Participation of Massive Distributed Energy Sources
1 Introduction
2 Characteristics of Mass Distributed Resources Based on Virtual Power Plant
3 Mass Resource Market Transactions of Virtual Power Plants
3.1 Overview of Virtual Power Plant Participation in Market Transactions
3.2 Principles of Virtual Power Plants Participating in Spot Market Transactions
4 Spot Market Transaction Support System
4.1 Transaction Model
4.2 Trading System Architecture
4.3 Key Technology
4.4 Transaction Process Architecture Design
4.5 Transaction Application Implementation
5 Conclusion
References
Intelligent Management and Control System of Power Safety Tools Based on Power Big Data
1 Introduction
2 Full Life Cycle Electrical Safety Tools
2.1 Requirements for the Control of Electrical Safety Tools
2.2 Key Data Analysis
3 Power Internet of Things Big Data Key Technology
3.1 RFID Technology
3.2 Java Web Technology
4 System Function Design
4.1 Overall System Design
4.2 Overall System Architecture
4.3 System Network Architecture
5 Functional Module
5.1 Operation Inbound and Outbound Management
5.2 Cycle Test Management
5.3 Defect Management
5.4 Scrap Management
5.5 Real Time Monitoring
6 Application Analysis
7 Conclusion
References
Research on Application of 3D GIS Technology in Enterprise Management Visualization
1 Introduction
2 Systematic Design
2.1 Overall Architecture
2.2 Business Application Architecture
2.3 Platform Model Data Construction
3 System Function Realization
3.1 Visualization of Enterprise Assets
3.2 Employee Management Visualization
3.3 Visualization of Operational Decisions
3.4 Product case Visualization
4 Application Innovation and Effect Presentation
4.1 Application Innovation
4.2 Effect of Platform
5 Conclusion
References
Control Algorithm of Working Frequency for Ultrasonic Motor Used in Space Environment
1 Introduction
2 Working Principle of Ultrasonic Motor
2.1 Composite of Ultrasonic Motor
2.2 Temperature Influence on Ultrasonic Motor
3 Control Algorithm for Working Frequency
4 Test Under High Temperature
5 Conclusion
References
Functional Safety Verification and Validation Platform for Electric Drive System Based on X-in-the-Loop
1 Introduction
2 EDS and ITEM Definition
3 Functional Safety for EDS
4 Introduction of the X-in-the-Loop
5 Fault Injection Test Method
5.1 Motor Over Temperature Fault Injection
5.2 Motor Demagnetization Fault Injection
5.3 Motor Resolver Fault Injection
5.4 DC Voltage Wire Break
6 Conclusion
References
Research on Frequency Selection Bandpass Filter Based on MRCWP
1 Introduction
2 Frequency Selection Filter Based on MRC
3 Variable Frequency Selection Filter Based on MRCWPT
4 Conclusion
References
Effect of Secondary Sintering on the Performance of Zinc Oxide Varistors
1 Introduction
2 Experimental Steps
3 Experimental Results and Discussion
3.1 Change of Electric Parameters
3.2 Energy Tolerance Test
3.3 Accelerated Aging Test
4 Conclusion
References
Optimization Control of Flexible Interconnection Distribution Network for High-Proportion Integration of Renewable Energy
1 Introduction
2 Structure of Flexible Interconnection Distribution Network
3 Optimization Control Based on Harmonic Virtual Resistor
4 Simulation Verification
5 Conclusions
References
Three-Phase Unbalanced Condition and Power Loss Optimization Using Soft Open Points
1 Introduction
2 Three-Phase Optimization Model Using SOPs
2.1 Structure and Model of Sops
2.2 Minimum Three-Phase Unbalanced Condition and Power Loss Model
3 Case Studies and Analysis
3.1 Results and Analysis of Newton Raphson
3.2 Results and Analysis of Optimization Model
3.3 Comparisons Between Different Methods
4 Conclusion
References
Open-Circuit Fault Diagnosis for Three-Phase Voltage Source Inverter Based on Multi-source Information Fusion
1 Introduction
2 Fault Diagnosis Model Based on Multi-source Data-Level Fusion and 1D-CNN
2.1 Multi-source Data-Level Fusion
2.2 1D-CNN
3 Simulation Validation
3.1 Simulation Setup and Data Description
3.2 Build 1D-CNN Model
3.3 Results and Discussion
4 Conclusions
References
A Sliding Mode Observer-Based Open-Switch Fault Diagnosis for Bidirectional DC-DC Converter
1 Introduction
2 Mathematical Model of BDDC
2.1 Mathematical Model of BDDC
3 Open-Switch Fault Diagnosis
3.1 Design of State Observer
3.2 Open-Switch Fault Diagnosis
4 Simulation Validation
5 Conclusions
References
A SiC MOSFET Current Balancing Technique Based on the Gate Driver with a Multi-channel Output Stage
1 Introduction
2 Dynamic Current Sharing Model
2.1 SBL Connection
2.2 iMBL Connection
3 Simulation Results
4 Experiment Verification
5 Conclusion
References
The Parametric Array Speaker: A Review
1 Introduction
2 Topologies for Parametric Speaker
3 Implementation of the Parametric Speaker
4 Future Work
5 Conclusion
References
Realization of PT Controlled Buck Converter Using Switchable Memristor Based Pulse Generator
1 Introduction
2 MR Based Pulse Train Generator
3 ICF-PT-Controlled Buck Converter
4 Simulation Verification
5 Conclusions
References
A High-Robust Control Scheme for the Dual-Active-Bridge-Based Energy Storage Unit
1 Introduction
2 The Proposed High-Robust Control Scheme
3 Verification
4 Conclusion
References
Optimized Design of High Torque Density Permanent Magnet Synchronous Motor with Halbach Magnet
1 Introduction
2 Influence of Halbach Magnet Design
2.1 Permanent Magnet Thickness
2.2 Permanent Magnet Magnetization Angle
3 The Optimized Design of FSCW PMSM
3.1 Multi-objective Differential Evolution Algorithm
3.2 Analysis of Optimization Results
4 Conclusion
References
Author Index

Citation preview

Lecture Notes in Electrical Engineering 1060

Cungang Hu Wenping Cao   Editors

Conference Proceedings of 2022 2nd International Joint Conference on Energy, Electrical and Power Engineering

Lecture Notes in Electrical Engineering Volume 1060

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Napoli, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, München, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, University of Karlsruhe (TH) IAIM, Karlsruhe, Baden-Württemberg, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Dipartimento di Ingegneria dell’Informazione, Sede Scientifica Università degli Studi di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, Department of Mechatronics Engineering, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Intrinsic Innovation, Mountain View, CA, USA Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, Hunan, China Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Subhas Mukhopadhyay, School of Engineering, Macquarie University, NSW, Australia Cun-Zheng Ning, Department of Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Department of Intelligence Science and Technology, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Genova, Genova, Italy Bijaya Ketan Panigrahi, Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Federica Pascucci, Department di Ingegneria, Università degli Studi Roma Tre, Roma, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, University of Stuttgart, Stuttgart, Germany Germano Veiga, FEUP Campus, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Haidian District Beijing, China Walter Zamboni, Department of Computer Engineering, Electrical Engineering and Applied Mathematics, DIEM—Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA Kay Chen Tan, Department of Computing, Hong Kong Polytechnic University, Kowloon Tong, Hong Kong

The book series Lecture Notes in Electrical Engineering (LNEE) publishes the latest developments in Electrical Engineering—quickly, informally and in high quality. While original research reported in proceedings and monographs has traditionally formed the core of LNEE, we also encourage authors to submit books devoted to supporting student education and professional training in the various fields and applications areas of electrical engineering. The series cover classical and emerging topics concerning: • • • • • • • • • • • •

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Cungang Hu · Wenping Cao Editors

Conference Proceedings of 2022 2nd International Joint Conference on Energy, Electrical and Power Engineering

Editors Cungang Hu School of Electrical Engineering and Automation Anhui University Hefei, Anhui, China

Wenping Cao School of Electrical Engineering and Automation Anhui University Hefei, Anhui, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-4333-3 ISBN 978-981-99-4334-0 (eBook) https://doi.org/10.1007/978-981-99-4334-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Contents

Energy Consumption Analysis and Optimization of Comprehensive Energy System in Fishery Park . . . . . . . . . . . . . . . . . . . Zhao Dong, Yang Wang, and Quanwu Ge

1

Decision Tree Ensembles for Smart Sewage Treatment: An Intelligent Dosing Model for Removing Phosphorus . . . . . . . . . . . . . . Chunhua Zhang, Fang Yuan, Wei Xu, and Guojian Cheng

9

Failure Mechanism Analysis on Single Pulse Avalanche for SiC MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haoyang Fei, Lin Liang, and Ziyang Zhang

19

Research on the Scale of Multi-regional Networking to Improve the Interoperability Benefits of Power Systems . . . . . . . . . . . . . . . . . . . . . . Xinmiao Liu, Xun Lu, Huilai Wang, Yuanyuan Lou, Junlei Liu, and Qiao Wang P2P Optimization Strategy for Integrated Energy Operators Based on Nash Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kejun Dong and Yang Wang Three Phase O-Z-Source Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Luo, Xinghui Chen, Zhongzheng Zhou, and Kun Xia Recognition of Tunneling Boring Machine Operating Status Based on the Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Pang, Yitang Wang, Shuai Zhang, Suhang Wang, Xueguan Song, and Wei Sun Flow Pulsation Optimization of Peristaltic Pump Based on Surrogate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fu wen Liu, Qing ye Li, Shuo Wang, Yanfeng Zhang, and Xueguan Song

32

39 51

57

63

v

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Contents

Dispatch Strategy for Transmission Overload Based on Safe Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hang Zhou, Hongqin Zhu, and Han Cui Research on Power Source Schemes in High Proportion of Renewable Energy HVDC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao Huo, Hong Yang, Naixin Duan, Xiuting Rong, Xiaoyang Wang, Haiwei Li, Juan Zhao, and Xuliang Li

73

82

Experimental Study on the Influence of Voltage Sag Characteristic Parameters on the Dynamic Performance of SSTS . . . . . Qi Cui, Mingxing Zhu, Huaying Zhang, Yadong Jiao, and Min Gao

89

Non-invasive Measurement Method for DC-Side Energy Storage Capacitance of Single-Phase Bridge Uncontrolled Rectifiers . . . . . . . . . . Zhibo Yang, Mingxing Zhu, Huaying Zhang, and Min Gao

101

Application of Generalized Predictive Control in Buck Converter . . . . . Fei Song, Lusheng Ge, and Kuang Wang Sliding Mode Control of PMSM Based on Double Power Reaching Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kai Zhou, Lusheng Ge, and Kuang Wang Distinguishment of Power Quality Disturbances Using Segmented Adaptive S Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fang Fang, Zhensheng Wang, Tianhong Pan, Jun Tao, and Huaying Zhang Robust Predictive Rotor Current Control of DFIGs Based on an Adaptive Ultra-local Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin He, Shengnan Li, Junpeng Li, Xian Meng, Yong Cheng, Yongchang Zhang, and Tao Jiang Multi-region V2G Optimal Scheduling Strategy Based on Region Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gao Pengcheng, Zhang Chun, Wu Lingchen, Wu Shuang, Tong Zejun, and Li Haoyu Maximum Power Point Tracking Control of Wind Power Generation System Without Inductance Decoupling . . . . . . . . . . . . . . . . . Yu Wang, Shicheng Zheng, Mingjin Lu, Wei Qiu, Dengji Tian, and Jiahong Lang A Cluster-Based Dynamic Grouping Population Replication Strategy for Bilevel Multi-objective Optimization . . . . . . . . . . . . . . . . . . . . Wanyue Hu, Erqian Ge, Fei Li, and Hao Shen

111

117

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129

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Study on Multi-objective Scheduling Strategy for Electric Vehicle to Absorb Wind Power Considering Dynamic Time-of-Use Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuang Wu, Chun Zhang, Zejun Tong, Pengcheng Gao, and Haoyu Li

vii

161

Thermal Effect Analysis of Three-Level Inverter Power Module Based on Single Cycle Loss Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shi-Zhou Xu, Xi Yang, Min Feng, and Tian-Yi Pei

169

Secondary Authentication Method Suitable for 5G-Based Power Terminals and Formal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xin Hu, Yu Jiang, and Aiqun Hu

178

Research on Multi-scale Space-Time Planning and Allocation Method of Energy Storage System Under New Energy Structure . . . . . . Hui Peng, Ye Liao, Rong Huang, Xiang Chen, Weili Long, and Yingying Fang

186

FPGA-Based Servo Control for a Dual Three-Phase Permanent Magnet Synchronous Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qingqing Yuan, Chenming Zhong, Kun Xia, Xu Hu, and Shuo Dong

195

Measurement and Control System of Planetary Roller Screw Transmission Efficiency Test Bench Based on LabVIEW . . . . . . . . . . . . . Kexin Zhu, Kun Xia, Xiao Fu, Qingqing Yuan, and Wei Luo

202

Improved Damping Ratio Control of Virtual Synchronous Generators with Multiple Parameter Coordination . . . . . . . . . . . . . . . . . . Bixing Ren, Qiang Li, Zhiyuan Fan, Xiaoming Zou, Zhenhua Lv, Chenggen Wang, and Yichao Sun Hybrid Time Step Day-Ahead Optimal Scheduling of the PV-Cascade Hydro Complementary Power Plant Based on PV Output Forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kun Zheng, Dacheng Li, Xv Li, Tianze Song, Di Wu, Yun Tian, and Su Guo GRU Network-Based Load Allocation for Hydro Units . . . . . . . . . . . . . . . Xiaonan Zheng, Xu Li, Dacheng Li, Hong Pan, Yun Tian, Di Wu, and Fang Feng A Novel Multi-fidelity Surrogate Model with Two-Stage Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuai Zhang, Yong Pang, Peng Li, Xueguan Song, and Wei Sun A Fault Diagnosis Method for Molecular Pump Based on Dictionary Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kai Jia, Ming Jiang, Guizhong Zuo, Zuchao Zhang, Jilei Hou, and Xiaolin Yuan

207

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Development of Comprehensive Training Platform for Power Electronics Teaching in Smart Grid and Renewable Energy . . . . . . . . . . Yuying Wang, Quanzhu Zhang, Bo Ao, and Weining Xue

249

Rotor Position Deviation Active Control of High Speed Magnetic Levitation Permanent Magnet Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dan Zhang and Diju Gao

255

Research on Risk Prevention and Control of Distribution Network Based on Knowledge Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nan Yang, Yi Wang, Yu Si, and Zishuo Ai

260

sDFT Based IRP Detection of the Electrical Excited Synchronous Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiao Fu and Kun Xia

269

A Unified Startup Control Strategy for Modular Multilevel Converter with the Supercapacitor Energy Storage System . . . . . . . . . . . Song Han, Tianbai Deng, Tao Yuan, Qianlong Zhu, Jun Tao, Huaying Zhang, and Qing Wang Coordinated Operation for Honeycomb Active Distribution Network with Multi-microgrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jianzhong Wang, Qingfeng Wang, Lang Shen, and Zhenhua Jiao Primary Frequency Modulation Control of Doubly-Fed Wind Turbine Based on Optimal Coordination of Pitch and Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Longqing Zhao, Zhen Xie, and Liusheng Zhang Analysis of Harmonic Characteristics of Magnetic Controllable Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lingyun Gu, Feiyan Zhou, Wenchao Dong, Wenpeng Gao, Yu Dong, and Yan Wu

279

288

297

305

Investigation of Pumped Storage Power Station Construction Conditions in Guangdong Province . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Youkun Luo, Xiong Xiao, Ying Yuan, Xueyuan Deng, and Sujuan Luo

313

Integrated Charger Topology and Control Strategy with Single-Phase and Three-Phase Charing Functions for Electric Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaonan Chen, Linlin Sun, Xize Jiao, Heng Song, Yazhao Ren, and Xinsheng Dong

323

Research on Short-Circuit Fault of High-Speed Maglev Traction Linear Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinmai Gao, Yanxiao Lei, Weitao Han, Lvfeng Ju, and Zhou Ying

333

Contents

A Designable Stability-Improving Control Method Based on Eigenvalue Sensitivity for Three-Phase Grid-Following Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zexi Zhou, Hong Li, Jinchang Pan, Kai Li, Zhichang Yang, and Xiaoge Liu An Intuitionistic Time-Domain Stability Analysis Method Based on Floquet Theory for Three-Phase Grid-Following Converter . . . . . . . . Hong Li, Jinchang Pan, Zexi Zhou, Xu Shangguan, Zhichang Yang, and Xiaoge Liu Locational Marginal Price Model Considering Customer Directrix Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiangrong Han, Bin Han, Jingsong Zhu, and Wenjuan Niu Analysis of the Steady State Fluid Force and Flux of Nuclear Pressure Safety Valves Based on Surrogate Models . . . . . . . . . . . . . . . . . . Ao Zhang, Weihao Zhou, Chaoyong Zong, Qingye Li, and Xueguan Song Study on Mathematical Model and Dynamic Compensation of Oil Down-Hole Pressure Sensor Based on BP Neural Network . . . . . . Fan Yang, Chuanrong Zhao, Hongzhen Zhu, and Deren Kong Model Predictive Current Control of Three-Phase Voltage Source Rectifier Based on Optimal Space Trajectory . . . . . . . . . . . . . . . . . Xiaolei Sun, Tao Rui, Cungang Hu, Wenping Cao, Ke Zhang, and Weixiang Shen A Novel Current-Limiting Hybrid DC Circuit Breaker . . . . . . . . . . . . . . . Yiqi Liu, Bingkun Li, Junyuan Zheng, Tianshi Guo, Laicheng Yin, and Zhaoyu Duan Study on Motor Parameters of PMSM Based on the Principle of Adjustable Leakage Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qiu Chu, Chunyan Li, Yu Wang, Fei Guo, and Tao Meng The Coordination of FCL and Relay Protection: A Review . . . . . . . . . . . Zhiying Xue, Yue Yu, Yudong Sun, Yuankun Zheng, Jiawei Liu, and Guangchen Ma Research on Three-Phase Unbalance Compensation of Magnetic Control Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yaoliang Yan, Ming Fan, Hong Zhang, Lei Wang, Zhenqi Ma, Bengang Sui, Kun Peng, Jingtao Bai, Mingzhou Zheng, Tengda Wang, Yewei Jie, Wenhui Shi, and Wenchao Dong Automatic Protective Relay Testing on Real Time Simulator . . . . . . . . . . Xinyi Zhou, Xiaonan Han, Jiaohong Luo, Tao Huang, and Xiyang Tao

ix

339

348

356

364

374

380

387

392 398

404

409

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Contents

Research on Harmonic Optimization of Magnetically Controlled Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yaoliang Yan, Ming Fan, Hong Zhang, Lei Wang, Zhenqi Ma, Bengang Sui, Kun Peng, Jingtao Bai, Mingzhou Zheng, Tengda Wang, Yewei Jie, Wenhui Shi, and Wenchao Dong Grasping Operation of Irregular-Shaped Objects Based on a Monocular Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiantao Sun, Yinming Yang, Wenjie Chen, Weihai Chen, and Yali Zhi Design and Development of an Unmanned Excavator System for Autonomous Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tao Fu, Tianci Zhang, Guang Li, Jianqiang Qiao, Gang Sun, Haifeng Yue, and Xueguan Song Research on the Switching Frequency Variation of Predictive Control Based on Circular Boundary-Limited Form . . . . . . . . . . . . . . . . . Xin Qi, Yi Deng, Joachim Holtz, Deming Xu, Jiashi Ren, and Jianing Zhang Electric Power Balance Contribution Calculation Based on Power Traceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liang Ding, Jianjun Wang, Wei Ru, Zibo Xu, Pengcheng Sa, and Wei Jiang Distributionally Robust Self-scheduling of Small-Scale Virtual Power Plants Considering Seasonal Variations . . . . . . . . . . . . . . . . . . . . . . Yifan Deng, Guangnan Shi, Wei Jiang, Peng Li, Lizong Zhang, and Pengcheng Sa Model-Free Predictive Control Strategy for PMSM Drives Based on Recursive Extended Least Square . . . . . . . . . . . . . . . . . . . . . . . . . Yao Wei, Zhehan Ke, Dongliang Ke, and Fengxiang Wang Power Optimization Control with Tracking Differentiator for Interior Permanent-Magnet Synchronous Motor . . . . . . . . . . . . . . . . . Kunkun Zuo, Long He, Fengxiang Wang, Ralpha Kennel, and Marcelo Lobo Heldwein Full Life Cycle Prediction of Nuclear Bearings Based on Digital Twin Hybrid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chunyi Han, Yuanjun Guo, Zhile Yang, Wei Feng, Yanhui Zhang, Huanlin Chen, and Weihua Chen Simulation of Position Impedance Control for Single Leg of Electric Drive Legged Robot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaocan Wang, Shuai Wang, Huafeng Jiang, Zeliang Xiong, Qinggui Zheng, and Xianglin Chen

418

423

430

439

447

457

466

479

491

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Contents

Research on Distribution Transformer Quality Sampling Assessment Model Based on Entropy Weight Method . . . . . . . . . . . . . . . . Yanzhao Niu, Hanwu Xiong, Zhengbo Liang, Jin Zhang, Chao Peng, and Tian Yuan A Novel DC Energy Dissipation Topology and Control Method . . . . . . . Yiqi Liu, Laicheng Yin, Bingkun Li, Mingzhe Sun, Meiru Chen, and Tianshi Guo A Dual Inverter Topology Based on Quasi-Isolated Power Supply and Its Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chuanhao Liu, Jiaxing Lei, Yiyang Xiao, and Xinzhen Feng The LCL Type Three-Phase Grid-Connected Inverter Active Damping Design Based on Capacitor Current Feedback . . . . . . . . . . . . . Yuhang Zhu, Cungang Hu, Tao Rui, Wenping Cao, Ke Zhang, and Weixiang Shen

xi

504

511

517

523

Peer-to-Peer Trading Among Prosumers Based on Cooperative Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guowei Hu, Xiaodong Chen, Guiyuan Xue, Yin Wu, and Chen Wu

532

Second-Order Cone Based Dynamic Reconfiguration of Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinjie Sun, Jiangping Jing, Zhangliang Shen, and Liudong Zhang

542

Research on Energy System Planning Method Considering Carbon Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yongwei Fan, Guotao Song, and Tianze Song

553

Research on Influence of Buried Sand on Cable Temperature Rise Characteristics in Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jinli Fan, Yaping Deng, Qian Wang, and Qiming Xu

565

A Innovative Three-Phase Unbalanced Compensation Range Evaluation for the Combination D-STATCOM . . . . . . . . . . . . . . . . . . . . . . Maosong Zhang, Chunsheng Guan, Xiuqin Wang, Jun Tao, Xian Wu, Huaying Zhang, and Qunjing Wang Parameter Optimization of the Three-Coil Wireless Power Transmission System Based on Genetic Algorithm . . . . . . . . . . . . . . . . . . . Dazhuang Liang, Yunhu Yang, Han Xu, Ruofei Hong, Weina Jia, Yu Li, and Jianzhi Xue Analysis of Abnormal Working Conditions Influence Over a Self-switching LCC-LCC/S-Based WPT System with CC and CV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weina Jia, Yunhu Yang, Dazhuang Liang, Yu Li, Jianzhi Xue, and Zhi Yang

571

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Design of Wide Voltage Range DC–DC Converter Based on SiC MOSFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinying Wang, Xiaofeng Tao, Leilei Zhan, Xin Tang, Yonghao Sun, Yibo Sun, Chaohui Cui, Haoran Li, Cungang Hu, Ke Zhang, and Weixiang Shen Study on Oscillation Characteristic Test and Data Fitting of DC Transfer Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuo Shi, Lei Rao, Shaochong Li, Hechong Chen, Xin Tong, and Yifan Wang Rolling Bearing Fault Diagnosis Method Based on Attention Mechanism Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhen-Bi Li, Xue-Yan Feng, Jin-Yang Xie, and Yi-Chen Xie Optimal Design of Torque Ripple of External Rotor Permanent Magnet Synchronous Motor Based on Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Houying Wang, Fang Xie, and Shilin Ni Study on Inertia-Resistant Disturbance Speed Control of Permanent Magnet Synchronous Motor Based on Exponential Integral Time-Varying Sliding Mode . . . . . . . . . . . . . . . . . Shilin Ni, Fang Xie, and Houying Wang

594

603

609

620

629

Torque Ripple Reduction of Permanent Magnet Synchronous Motor Based on Least Mean Square Algorithm . . . . . . . . . . . . . . . . . . . . . Mengyuan Shen, Fang Xie, Wenyu Zhang, and Jinqiang Zhang

638

Research on Multi-operating Control Strategy of Vehicle Motor Based on ALO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wenyu Zhang, Fang Xie, Mengyuan Shen, and Jinqiang Zhang

647

Correction Method for Harmonic Measurement of Capacitor Voltage Transformer Based on Frequency Response Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhu Mingxing, Jiao Yadong, Zhang Huaying, Gao Min, Wang Qing, and Cui Qi

654

Design of Aviation AC/DC Contactor Life Test System Based on PXI-2204 and CPCI-7434 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siyang Liang, Run Dong, Siyi Yang, and Weilin Li

665

MTPA Control Strategy of BLDCM Based on Back-EMF Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mengting Chang, Qihang Sun, Yicheng Jia, Qingquan Jia, and Zhenguo Li

675

Contents

Torque Ripple Suppression Based on a New Multi-level DTC Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boran He, Mengting Chang, Yicheng Jia, Qimeng Han, and Zhenguo Li Study of an IPT System Based on Configurable Charging Current and Charging Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . YongGao Zhang, WeiWei Yang, Peng Liu, and ShangHai Liu Impedance Remodeling Method of Single-Phase Grid-Connected Inverter Under Weak Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liyan Zhang, Wenping Cao, Tao Rui, Xinyu Ma, Weixiang Shen, Cungang Hu, and Ke Zhang Path Planning of Substation Inspection Robot Based on Improved Ant Colony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xiaoming Wang, Shuo Shang, Daojin Yao, Chao Liang, Yu Pei, and Zunbin Xu Research on Optimization Design of GaN Device Active Gate Drive Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinyu Ma, Cungang Hu, Wenjie Zhu, Liyan Zhang, Weixiang Shen, and Ke Zhang Applications and Prospects of Online Insulation Monitoring Technique Based on Broadband Frequency Response for Transformers in Voltage Source Converter System . . . . . . . . . . . . . . . Geye Lu, Dayong Zheng, and Pinjia Zhang

xiii

681

687

699

710

717

730

Path Planning for Electric Power Inspection Robot Based on the Fusion of Improved A* and DWA Algorithm . . . . . . . . . . . . . . . . . . WeiMing Huang, Ping Chen, and JiaJun Xie

748

Tunneling Operational Data Imputation with Radial Basis Function Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yitang Wang, Yong Pang, Xueguan Song, and Wei Sun

756

A Novel IoT Based Multi-modal Edge Computing Optimization Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiajun Song, Jiayan Wang, Hui Lu, Zhixin Suo, Huijun Hong, Youfei Lu, Shirong Zou, and Xueqing Liang An Advanced IoT Based Edge Computing Forecasting Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhixin Suo, Youfei Lu, Huijun Hong, Shirong Zou, Jiajun Song, Hui Lu, Jiayan Wang, and Yu Zhang A Novel Data Merging Intelligent Method for Whole System IoT . . . . . . Huijun Hong, Hui Lu, Jiayan Wang, Yu Zhang, Zhixin Suo, Shuaihui Ren, Jiajun Song, and Yixuan Wang

761

768

775

xiv

Contents

Research on Model of Buck-Boost Converter Based on Digital Twin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Wan, Cungang Hu, Wenjie Zhu, Haitao Wang, Wenping Cao, Weixiang Shen, and Ke Zhang A Hybrid Carrier-Based DPWM Strategy with Variable Clamp Region and Controllable NP Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Huajian Zhou, Cungang Hu, Wenjie Zhu, Jixuan Zhang, and Wenping Cao A Novel Multi-robot Path Planning Algorithm Considering Dynamic Environmental Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiahao Zhang, Chengke Wu, Lan Cheng, Wei Feng, Yuanjun Guo, Zhile Yang, and Rui Yang

782

791

800

A Method of Constructing Admittance Matrix for Power Flow Correction in Complex AC Systems Suitable for Equivalent Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maolan Peng, Lei Feng, DaChao Huang, Hang Liu, Xilin Yan, Fangqun Liao, Jialin Wang, Junpeng Ma, and Shunliang Wang

807

Research on Pricing Strategy of Electricity Selling Company Based on Electricity Characteristics of Different Industry . . . . . . . . . . . . Zining Wang, Sheng Bi, Haotian Xu, Ciwei Gao, and Hao Ming

814

Credit Risk Evaluation of Power Users in Power Sales Package Recommendation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Xia, Sheng Bi, Ciwei Gao, Meihui Jiang, and Hao Ming

825

Operating Low Frequency Wind Power System in Variable Voltage Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Xingang, Xiong Xuejun, Du Zhaoxin, Zhang Yajun, Wang Qiming, and Jia Feng Extended Kalman Filtering Power System Dynamic State Estimation Based on Time Convolution Networks . . . . . . . . . . . . . . . . . . . Xundong Gong, Fei Hu, Li Jiang, Ming Chen, Yu Zhang, Shaolei Zong, and Qiu Miu A Capacitive Wireless Power Transfer System with LCLC Resonant Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zixuan Guo, Zhaodi Li, Jinli Zhang, Siyang Liang, Fan Pu, and Weilin Li Cost Performance Analysis of the Typical Electrochemical Energy Storage Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Wang and Jianye Zhu

837

844

856

864

Contents

Remaining Useful Life Prediction of Multi-sensor Data Based on Spatial-Temporal Attention Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yawei Hu, Xuanlin Li, Huaiwang Jin, Zhifu Huang, Jing Yu, and Yongbin Liu Model-Free Predictive Current Control Strategy Considering Noise Error Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yao Wang, Tao Rui, Wenping Cao, Ke Zhang, Cungang Hu, and Weixiang Shen An Improved Sub-pixel Corner Detection Algorithm . . . . . . . . . . . . . . . . . Junhua Wu and Lusheng Ge Research on Information Interaction Technology for Mobile Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinzhen Feng, Chen Zhou, Fan Yang, Shaojie Zhu, and Xiao Qian A QPSO-ELM Based Method for Load Model Parameters Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Baojun Xu, Yanhe Yin, Junjie Yu, Guohao Li, Zhuohuan Li, and Duotong Yang A Finite Time Cooperative Control Strategy for Energy Storage Systems in DC Microgrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tianyu Shi, Zhiqian Zhang, Qi Wang, Cungang Hu, Shiming Liu, and Zhenbin Zhang Wide Input and Output Voltage in Bidirectional DC-DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yibo Sun, Leilei Zhan, Xiaofeng Tao, Xinying Wang, Chaohui Cui, Haoran Li, Cungang Hu, Ke Zhang, and Weixiang Shen Active and Reactive Power Optimization Based on Soft Open Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiekai Fu, Chenglin Li, Qin Yan, Haoxiang Li, Tianxiang Huang, Yan Zhang, Kezhou Li, and Yurou Jiang

xv

873

883

890

897

905

911

919

932

Permanent Magnet Synchronous Linear Motor Based on Disturbance Compensated Flux Observer Sensorless Control . . . . . . Zhonggang Yin, Tong Liu, Cong Bai, and Yixuan Gao

939

Peak Clipping Control Strategy Based on Inverter Air Conditioner and Electric Vehicle Power Compensation . . . . . . . . . . . . . . . Yuan Tao, Wenyuan Xu, Ji Xu, Siqi Qiu, Yuan Luo, and Jianye Zhu

946

A Data Center Energy Storage Economic Analysis Model Based on Information Decision Theory and Demand Response . . . . . . . . . . . . . . Siqi Qiu, Wenyuan Xu, Yuan Tao, Yin Sheng, Ji Xu, and Wenhan Zhang

962

xvi

Contents

Simulation Analysis of Conducted Electromagnetic Interference in Excitation Power Cabinet of Giant Hydraulic Turbine Unit Based on Time Domain Finite Integration Method . . . . . . . . . . . . . . . . . . . Geng Zhang, Xiangtian Deng, Quanwen Wang, Qian Wang, and Qiannan Liu

974

Research on the Wind Farm Layout Optimization Considering Different Wake Effect Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yining Gong and Zhicong Wang

981

A Hierarchical Fast Model Predictive Control for Cascaded H-Bridge SVG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Han He, Qianli Xing, Zhenbin Zhang, Zhen Li, Zhiqiang Guo, Rong Ye, and Zhi Li

993

Speed Fluctuation Suppression Strategy of PMSM Based on Improved Linear Active Disturbance Rejection Control . . . . . . . . . . . 1002 Yangyang Cui, Zhonggang Yin, Peien Luo, and Yanping Zhang An Improved Distributed Wind Farm MPPT Control Based on Wake Propagation Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1008 Fenglin Miao, Yi Fan, and Zhen Li Probabilistic Power Flow Computation Considering the Uncertainty of New Energy Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Yan Li, Decheng Wang, Darui He, Yifei Fan, Qun Zhang, and Qingshan Wang Modelling and Simulation of Demand Response in Frequency Modulation Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025 Guiyuan Xue, Chen Wu, Ming Zhang, Yin Wu, Chen Chen, Wenjuan Wu, and Longpeng Ma Pitch Control Strategy for Wind Turbine Considering Operation Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033 Biao Huang, Lawu Zhou, Han Zhao, and Leyun Long Study on Sliding Mode Method of Five-Phase Permanent Magnet Synchronous Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046 Weifa Peng, Tao Lin, and Jun Liu Open-Circuit Fault Diagnosis for Wave Energy Converters with Support Vector Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1052 Xinqing Zhang, Zhen Li, Zhenbin Zhang, Rong Ye, and Zhi Li Design and Implementation of 4G-Based Crop Rotation Soil Information Monitoring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 Shuangxi Li, Shumei Cai, Naling Bai, Hanlin Zhang, Juanqin Zhang, Haiyun Zhang, Xianqing Zheng, Weiguang Lv, and Shipu Xu

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Comparison and Analysis of Different Overvoltage Suppression Circuits for Low-Voltage Solid-State Circuit Breakers . . . . . . . . . . . . . . . 1065 Xin Wu, Chuangchuang Tao, Yifei Wu, Wenxin Yang, Qiong Kang, Jingshuai Wang, and Liting Yan Research on Resonance Problem of DC Feed in AC System . . . . . . . . . . . 1076 Maolan Peng, Lei Feng, Dachao Huang, Hang Liu, Xilin Yan, Fangqun Liao, Shiding Zhou, and Shunliang Wang Online Estimation of the Variable Inertia of DFIG Units Via an Improved Least Squares Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1083 Ye He, Guangzeng You, Wei Guo, Peng Sun, Yixuan Chen, Run Huang, and Wuqi Zhang Modeling of 12-Pulse LCC Converter Station Based on Harmonic State Space Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093 Maolan Peng, Hang Liu, Lei Feng, Dachao Huang, Yuan Zhao, Yang Xie, Shunliang Wang, and Junpeng Ma CTM-Based Collaborative Optimization of Power Distribution Network and Urban Traffic Network with Electric Vehicles . . . . . . . . . . . 1101 Wenpei Li, Yan Wang, Guanghui Song, Fan Yang, Han Fu, Dongying Zhang, and Shiwei Xia Optimal Design of Laminated Busbar for Three Level Inverter Based on Multiple Weakening Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1110 Shi-Zhou Xu, Min Feng, Xi Yang, and Tian-Yi Pei Simulation and Experimental Research on Low Voltage DC Switching Fast Repulsion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118 Chuangchuang Tao, Jiahao Guo, Mingming Shi, Xin Wu, Yifei Wu, Yi Wu, and Ziteng Kang Research and Application of Green Power Market Operation Evaluation System in Beijing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127 Xiaochun Cheng, Hong Cheng, Qin Wang, Xingcun Wang, Chenda Zhang, and Yuxuan Zhang Market Research on Electric Auxiliary Services with the Participation of Massive Distributed Power Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140 Li Bo, Zhao Ruifeng, Xin Kuo, Lu Jiangang, Shi Zhan, and Pan Kaiyan Safety Constrained Economic Scheduling Model with Mass Distributed Generation Participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Jiangang Lu, Li Bo, Wenjie Zheng, Xin Kuo, Haixiang Gao, and Pan Kaiyan

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A Power Spot Market Transaction Support System Adapted to the Participation of Massive Distributed Energy Sources . . . . . . . . . . . 1159 Li Bo, Lu Jiangang, Zheng Wenjie, Huang Jinhua, Zhang Jian, and Pan Kaiyan Intelligent Management and Control System of Power Safety Tools Based on Power Big Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1168 Tiebin Hu, Jinbiao Ren, Jianxin Zeng, Da Wang, and Manlu Chen Research on Application of 3D GIS Technology in Enterprise Management Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1178 Xiaonan Hu, Weidong Wang, Hanzhi Li, Jingyu Li, and Pengcheng Li Control Algorithm of Working Frequency for Ultrasonic Motor Used in Space Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189 Cong Sheng, Biao Li, Congfa Zhang, Fanxin Sun, and Wu Zhang Functional Safety Verification and Validation Platform for Electric Drive System Based on X-in-the-Loop . . . . . . . . . . . . . . . . . . . 1195 Wang Bin, Wang Fang, Ma Kai, Huang Xin, Xie Kun, and Ren Shan Research on Frequency Selection Bandpass Filter Based on MRCWP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204 Weifa Peng, Tao Lin, and Jun Liu Effect of Secondary Sintering on the Performance of Zinc Oxide Varistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209 Yangfan Liu, Minxin Liu, Haibo She, Pengfei Zhai, Yayun Liu, and Bing Tian Optimization Control of Flexible Interconnection Distribution Network for High-Proportion Integration of Renewable Energy . . . . . . 1219 Yingying Zhao, Shaojie Liu, Bingbing Lu, Jianqiao Zhou, Gang Shi, and Jianwen Zhang Three-Phase Unbalanced Condition and Power Loss Optimization Using Soft Open Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1224 Jiekai Fu, Chenglin Li, Qin Yan, Haoxiang Li, Tianxiang Huang, Yan Zhang, Kezhou Li, and Yurou Jiang Open-Circuit Fault Diagnosis for Three-Phase Voltage Source Inverter Based on Multi-source Information Fusion . . . . . . . . . . . . . . . . . . 1232 Li Xiang, Li Shaojian, Wang Yu, Zhang Zijun, Luo Hui, Chu Jian, Wei Jie, and Huang Yong A Sliding Mode Observer-Based Open-Switch Fault Diagnosis for Bidirectional DC-DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239 Li Xiang, Li Shaojian, Wang Yu, Zhang Zijun, Luo Hui, Chu Jian, Wei Jie, and Huang Yong

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A SiC MOSFET Current Balancing Technique Based on the Gate Driver with a Multi-channel Output Stage . . . . . . . . . . . . . . . 1246 Zekun Li, Bing Ji, and Wenping Cao The Parametric Array Speaker: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . 1254 Shangming Mei, Hui Xu, Yihua Hu, Mohammed Alkahtani, and Yangang Wang Realization of PT Controlled Buck Converter Using Switchable Memristor Based Pulse Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1272 Jingjing Yu and Xiaotong Zhou A High-Robust Control Scheme for the Dual-Active-Bridge-Based Energy Storage Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1281 Shiqing Ji Optimized Design of High Torque Density Permanent Magnet Synchronous Motor with Halbach Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . 1292 Jiye Sun, Chenwei Yang, Xiaoyan Huang, Yi Wang, Zhaokai Li, and Huifan Yang Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1301

Energy Consumption Analysis and Optimization of Comprehensive Energy System in Fishery Park Zhao Dong1,4 , Yang Wang2,4(B) , and Quanwu Ge3,4 1 National Innovation Center for Digital Fishery, China Agricultural University, Beijing 100083,

China [email protected] 2 Key Laboratory of Smart Farming Technologies for Aquatic Animal and Livestock, Ministry of Agriculture and Rural Affairs, China Agricultural University, Beijing 100083, China [email protected] 3 Beijing Engineering and Technology Research Center for Internet of Things in Agriculture, China Agricultural University, Beijing 100083, China [email protected] 4 College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China

Abstract. In aquaculture, the temperature regulation of aquaculture water consumes a huge amount of energy. At present, driven by the national dual carbon goal, clean and renewable energy has become a new trend for aquaculture energy supply. In large fishery parks, the comprehensive use of multiple energy sources has become the norm. Under the premise of ensuring the temperature regulation requirements of aquaculture workshops, giving priority to the use of low-cost energy and renewable energy is a green strategy to reduce the cost of aquaculture. According to the fishery park scenario, this research constructs the key modules of the fishery park, analyzes the energy consumption of the comprehensive energy system of the fishery park, and optimizes the energy consumption of the system. Keywords: Fishery production equipment analysis · Energy consumption analysis · System energy saving optimization · Lemon Yang Können

1 Introduction 1.1 Development Status China is a big country in aquaculture, and aquaculture production accounts for more than 60% of the world’s total aquaculture products [1]. In 2020, the output of artificially cultured marine products will reach 21.353 million tons, and the output of artificially cultured freshwater products will reach 30.8889 million tons [2]. The development of fishery industrialization is an important development path for the transformation of traditional fishery management to modern fishery in my country [3]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1–8, 2023. https://doi.org/10.1007/978-981-99-4334-0_1

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In 2017, farming and fishing accounted for 46.98% of the embodied carbon emissions of various fishery sectors, making it the primary industry for embodied carbon emissions in fisheries [4]. For factory farming in northern my country, it takes about 4–6 months every year to warm up the water body [5]. Usually, factory waste hot water, boiler heating or electric heating are used. Research shows that the cost of traditional energy such as coal and electricity accounts for 31.20% of the total cost of factory farming enterprises, the energy cost of nursery farms accounts for 36.33% of the total cost, and the energy consumption of boilers It accounts for 92.78% of the total energy consumption of the nursery, and the sea water pump consumes the largest amount of electricity, accounting for 70.59% of the total power consumption [6]. The low-carbon development of the fishery economy is an inevitable choice for the sustainable development of China’s fishery. The use of various clean energy sources has been explored at home and abroad. For example, Spain has studied the use of hydrogen energy in the breeding process, which can save about 30% of energy [7]; Norwegian salmon farm adopts battery energy storage system, reducing total diesel consumption of fish farm by 60% [8]; Domestic use of ground source heat pump and geothermal well technology can reduce the energy consumption of aquaculture by 34% compared with the traditional farming mode [9]. At present, the comprehensive technical efficiency of aquaculture in my country is generally low, and there is room for improvement in both pure technical efficiency and scale efficiency. Extensive farming is not suitable for industrial farming. The comprehensive utilization of energy, such as complementary fishing and light, complementary wind and solar, provides new ideas for industrial farming to save energy [9]. In industrialized aquaculture, such as in fishery parks, the quality of energy utilization and management directly determines the benefits of aquaculture. To sum up, this research takes the fishery park as the object, and develops the comprehensive energy system and electrical equipment of the fishery park, aiming to optimize the dispatch of the comprehensive energy of the fishery park, reduce energy waste, and contribute to the dual-carbon goal.

2 Analysis of Energy Consumption in Fishery Production 2.1 High Energy Consumption Equipment for Fishery Production Aerator model. The performance of aeration equipment is mainly reflected by indicators such as saturated dissolved oxygen, oxygen mass transfer coefficient, oxygen increasing capacity and oxygen utilization rate. The basic equation for oxygen mass transfer is [10]: dC = KLa (C∞ − C0 ) dt

(1)

KLa is the oxygen transfer rate in units of h−1 ; C∞ is the saturated dissolved oxygen concentration, the unit is mg/L; C0 is the initial dissolved oxygen concentration, in units of mg/L. The factors that affect the oxygen transfer rate mainly include water quality, water temperature and air pressure. The standard oxygen transfer rate is under the conditions of 20 °C and a standard atmospheric pressure, and in the process of

Energy Consumption Analysis and Optimization of Comprehensive

3

aquaculture, the water temperature will change to adapt to fish life. The formula is as follows. KLa(T ) = KLa × 1.024(T −20)

(2)

R is the amount of oxygen added, the unit is kg/h; V is the volume of the aeration tank, the unit is m3 . The oxygen-enhancing capacity of the aerator is: R=

dC · V = KLa · C∞ · V × 10−3 dt

(3)

Due to the flow of water in the process of fishery production, and the flow rate of water will affect the utilization rate of oxygen in aeration, the relationship between the oxygen increase and the aeration flow rate is generally linear, but when the aeration flow rate is large, the oxygen increase The increment with the aeration flow rate is generally smaller than the increment with the bottom velocity aeration. Considering that the theoretical flow rate is 0 m/s, the oxygen increment is 0 kg/h. Since the oxygen supply rate is related to the aeration flow rate, the constraints are as follows:  Ugmax 1 EdUg , 0.6 ≤ h ≤ 1.2, −1 ≤ θ ≤ 1 (4) arg max E(E) = max η,ϕ,h,θ Ug − Ugmin Ugmin In the formula, Ugmax , Ugmin are the maximum and minimum aeration flow rates when the aeration device is working, in units of m/s. h is the aeration depth, the unit is m; θ is the aeration angle. 2.2 Heat Pump Model Heat sources in heating systems include electric heat pumps (EHP) and thermal energy storage (TES). A typical central heating system is shown in Fig. 1. Pump

Cistern

Water treatment room

Heat Exchanger

Water source heat pump

Backwater

Water supply

Fig. 1. Workshop circulating water model.

The heat production process of the electric heat pump can be simplified as the following formula: EHP EHP EHP = pi,t · COPi,k , pfi,tEHP = pfNEHP , ∀i ∈ I EHP , ∀t ∈ T qi,t

(5)

EHP is the heat production power of the electric heat pump, the unit is MW; pEHP is qi,t i,t EHP is the energy the power consumption of the electric heat pump, the unit is MW; COPi,k

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efficiency coefficient; pfi,tEHP is the power factor of the electric heat pump; it reflects the induction characteristics of the heat load undertaken by the electric heat pump; pfNEHP is the rated power factor; I EHP is the set of EHP nodes connected in the thermal network. The storage and release of heat by the heat storage device depends on whether the supply and demand of heat source heating and fish pond heating consumption are in balance at the current moment. The heat release of is used to meet the heating demand of users, so the mathematical model of the heat storage device can be expressed as: TES,stor CHS,char TES,stor = qi,t · ηTES,stor + qi,t−1 qi,t

∀i ∈ I TES , ∀t ∈ T

(6)

TES,stor qi,t is the thermal storage power of the thermal storage device, the unit is MW; CHS,char qi,t is the difference between the supply and demand of thermal power of the heating system, the unit is MW; ηTES,stor is the heat storage coefficient of the heat storage device; I TES is the set of nodes connecting TES in the thermal network.

3 Energy Saving Analysis of Equipment Motor The motors of fishery production equipment are mostly three-phase asynchronous induction motors, and the main loss of the induction motor is the resistance loss of the copper wire on the stator side PCu1 , eddy current loss of iron core on stator side PFe1 , rotor side copper wire resistance loss PCu2 , mechanical friction loss Pfw , stray loss P . Various power profiles are shown in Fig. 2.

WLS Stator stray losses P1 Input Power

PFe Iron loss

PM electroma gnetic power

PCu1 Stator losses

Stator side

WLR PMx Rotor stray Mechanical losses P2 power Output Power Pfw PCu2 mechanical loss Rotor losses Rotor side

Fig. 2. Induction motor power distribution.

According to the figure, the following formula can be obtained: P1 = PCu1 + PFe1 + PM

(7)

In the formula P1 = ms Us Is cos ϕ; PCu1 = ms Is2 Rs ; PFe1 = mr Im2 Rm ; ms is the number of stator phases, mr is the rotor phase number, cos ϕ is the stator power factor. From this it can be deduced that the electromagnetic power PM : PM = ms Ir2 r2 = ms Ir2

Rs s

(8)

Energy Consumption Analysis and Optimization of Comprehensive

5

The mechanical efficiency of an induction motor can be expressed as: η=

P2 P2  × 100% × 100% = P1 P2 + P

(9)

The stray loss of the motor is about 0.5% of the output power [11]. By selecting the appropriate voltage-frequency ratio k, the purpose of reducing the loss of the induction motor, saving energy and adjusting the speed, and improving the utilization rate of electric energy can be realized [12]. The voltage-to-frequency ratio is the ratio of the rms value of the voltage at the power supply end to the frequency k can be expressed by the following formula: k=

U1 fs

(10)

The total impedance of the T-equivalent circuit of an induction motor is: Z = Zs +

Zm Zr Zm + Zr

(11)

The output power of the motor can be expressed as:    Zm kfs 2 1 − s  Rr P2 = 3 (Zm + Zr )Z  s

(12)

n = 60fs (1 − s)/np

(13)

n is the motor speed. According to the above formula, the motor torque can be derived as:    Zm kfs 2 30np   Rr T2 = 3 (14)  (Zm + Zr )Z p(60fs − nnp ) When the load torque is constant, the light-load step-down operation has an optimal voltage ratio, and the efficiency is the highest at this time. The case in this article is based on Shandong Mingbo Aquatic Products Company. The power model and motor parameters of its large-scale electrical equipment are shown in Table 1. Table 1. Power models of large electrical equipment. Device name

Motor power (kW)

Voltage (V)

Frequency (Hz)

Circulating pump

5.5

380

50

Microfilter

5.5

380

50

Aerator

2.2

380

50

Centrifugal pump

4.0

380

50

Typical motor parameters: Rs is 0.531 , Rr is 0.408 , Ls , Lr , Lm are 0.00252 H, 0.00252 H and 0.00847 H, Is is 4.9 A, Us is 380 V, PN is 2.2 kW.

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4 Conclusion First, a simple three-phase squirrel-cage asynchronous motor model is established with Simulink, and the analysis is carried out according to the model, as shown in Fig. 3.

4

Continuous

powergui Rectified output Ref_01 P

Uref

Ref_02

unit conversion

Tm

Ref_03 T-e

A m B

L A

a

A

IM

g

+

+

B

b

A

Filter capacitor

B

Motor measurement

Vb

B

D11Y c C

Vc

C

Three-phase asynchronous motor

+

+

Va

-

C

C

Three-phase bridge rectifier

Three-phase bridge inverter

+ -

v

+ -

v

+ -

v

Vab

Vbc

Vca

Inverter output

Fig. 3. Three-phase asynchronous motor model.

According to the data model of the motor in Table 2, carry out modeling analysis, and by changing the starting frequency of the motor, the comparison is shown in Fig. 4. The simulation results of the motor running state are shown in Fig. 4, and the motor speed is reduced from 1500 r/ min to 900 r/ min. When the load torque is 20 N · m, the electromagnetic torque comparison diagram after changing different frequencies is Fig. 4. The speed, voltage and power of the motors at different frequencies are compared and sorted as shown in Table 2. Observing the data and simulation curves in the table, it can be concluded that under the condition of constant voltage-frequency ratio control, reducing the operating frequency of the motor can effectively reduce the speed and output power. In recirculating aquaculture and fishery production, the rational design and motor control operation of various electrical equipment in the integrated energy system can effectively save resources, reduce unnecessary waste, contribute to the sustainable development of fisheries, and achieve national carbon neutrality goals.

Energy Consumption Analysis and Optimization of Comprehensive

7

1600

1400

1200

1000

n/r/min

800

600

400

200

0

-200 0

100

200

300

400

500

600

t/ms

Fig. 4. Motor speed and electromagnetic torque comparison diagram. Table 2. Comparison of simulation results of variable frequency ratio speed regulation f (Hz)

50

30

n (r/ min)

1400

900

U (V)

380

235

P (kW)

4.03

2.42

Acknowledgement. This research was financially supported by the National Key Research and Development Program of China: National Innovation Center for Digital Fishery, and Beijing Engineering and Technology Research Center for Internet of Things in Agriculture. The authors also appreciate constructive and valuable comments provided by reviewers.

References 1. FAO: The State of World Fisheries and Aquaculture 2018: Meeting the Sustainable Development Goals. United Nations 2. Zhang, C., Meng, Q., et al.: Analysis of marine aquaculture status and Bohai Sea aquaculture governance in China. J. Mar. Environ. Sci. 40(06), 887–894 (2021) 3. Sheng, C., Zhu, J., et al.: Industrialization of China’s fishery: development model, efficiency enhancement mechanism and international experience. J. Econ. Issues 06, 47–54 (2021)

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4. Li, C., Li, H., et al.: Structural characteristics of implied carbon emissions in fishery production system and decomposition of driving factors. J. Resour. Sci. 43(06), 1166–1177 (2021) 5. Zhao, P., Li, X., et al.: Investigation and analysis of energy consumption and new energy application of seawater factory aquaculture. J. Fish. Mod. 38(02), 21–26 (2011) 6. Wang, F., Lei, J.: Energy value evaluation of factory circulating aquaculture mode of semislippery tongue squid. J. Eng. Sci. China 17(01), 4–10 (2015) 7. THE FISH SITE: Hydrogen energy being tested in the Spanish aquaculture sector. https://thefishsite.com/articles/hydrogen-energy-being-tested-in-the-spanish-aquacu lture-sector (2020) 8. RENEWABLE ENERGY MAGAZINE: Fish farm utilizes storage system to become more sustainable. https://www.renewableenergymagazine.com/storage/fish-farm-utilizes-storagesystem-to-become-20191112 (2020) 9. Song, X., Wang, J., et al.: Status quo of renewable energy utilization and emission reduction measures in marine aquaculture. J. Energy Environ. 02, 58–60 (2022) 10. ASCE: Standard Measurement of Oxygen Transfer in Clean Water. American Society of Civil Engineers, Virginia (2007) 11. Lu, S., Jia, W., et al.: Analysis and study of stray loss of asynchronous motor. J. Daily Electr. Appl. 06, 42–47 (2017) 12. Shan, L.: Application and promotion strategy of energy-saving technology for motor frequency conversion control. J. China Equip. Eng. 04, 190–191 (2019)

Decision Tree Ensembles for Smart Sewage Treatment: An Intelligent Dosing Model for Removing Phosphorus Chunhua Zhang1(B) , Fang Yuan2 , Wei Xu2 , and Guojian Cheng3 1 College of Software Engineering, Southeast University, Suzhou 215123, China

[email protected]

2 General Water of China Co., Ltd., Beijing 100022, China

{yuanf,xuw}@cecgw.com

3 Center for Energy and Environment, Institute for Process Modeling and Optimization, Jiangsu

Industrial Technology Research Institute, Southeast University - Monash University Joint Research Institute, Suzhou 215123, China [email protected]

Abstract. Removing phosphorus is an essential part of the sewage treatment process, which requires adding the corresponding treating chemical to the sewage. Currently, the dosage of the treating chemical is mainly determined by subjective experience of operators, which tends to result in subjective errors and more seriously, the excessive usage of the treating chemical. Excessive usage not only causes the waste of treating chemicals with more economic cost, but also brings additional pollution to the treated sewage. To overcome these difficulties, we propose an intelligent dosing model for removing phosphorus. Our intelligent dosing model includes two key steps. First, in the view of the non-linear mapping characteristic between the input and output of the phosphorus removal process, we propose using the powerful and explainable decision tree ensembles – Random Forest (RF) and Gradient Boosting Decision Tree (GBDT) – to accurately mimic the phosphorus removal process, i.e., predict the phosphorus removal effect according to the input sewage quality parameters and the used dosage of the treating chemical. Second, with the well-trained phosphorus removal prediction model, we can suggest the optimal treating chemical dosage with a fast binary search strategy, making the treating chemical sufficient to achieve a qualified phosphorus removal effect yet not overused. The experimental results show that compared with the strategy based on subjective experience, our proposed intelligent dosing model can reduce the use of phosphorus treating chemicals significantly while guaranteeing high-quality phosphorus removal. Keywords: Decision Tree · Random Forest · Gradient Boosting Decision Tree · Data mining · Removing phosphorus

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 9–18, 2023. https://doi.org/10.1007/978-981-99-4334-0_2

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1 Introduction Removing phosphorus is an essential part of sewage treatment. If the unphosphorized sewage is discharged directly, it will lead to serious eutrophication of water, which stimulates the proliferation of algae and ultimately endangers aquatic organisms [1, 2]. According to statistics, about 245,000 km2 of marine ecosystems have been affected by eutrophication, which poses a serious threat to biodiversity. In addition, the overgrowth of algae produces large amounts of harmful bacteria and organic matter, which impairs water quality and the health of residents [3, 4]. For the sake of environmental protection and human health, countries have made clear provisions on the phosphate discharge standard. The EU suggests that the concentration of total phosphorus discharged should be less than 2 mg/L, and member states formulate stricter standards based on their water characteristics, economic and technological conditions [5]. The United States Environmental Protection Agency (USEPA) recommends that the concentration of phosphorus in the treated water entering the lakes or reservoirs should not exceed 0.05 mg/L, and 0.1 mg/L in other streams [6]. This also means that effective phosphate removal has become an urgent issue in sewage treatment around the world. Chemical precipitation is currently the most widely used phosphorus removal method, by putting metal salt agents into the sewage to generate phosphate precipitates, which are ultimately removed by filtration or other mechanical methods [7]. Most enterprises use manual methods to control the dosage of phosphorus removal agents [8]. Operators directly determine the dosage according to the effluent total phosphorus in combination with experience. However, the process from dosing to measuring the effluent total phosphorus requires multiple processes, coupled with water quality changes in real time. Therefore, this judgment ignores errors caused by not only artificial experience but also delayed disturbance. Moreover, excessive dosages are often adopted to make the total phosphorus meet the national standard, affecting effluent quality and increasing drug consumption and treatment costs. Consequently, in water treatment, it is urgent to develop effective methods for predicting the reasonable dosage of phosphorus removal agents. In this paper, based on the historical data of a large water plant, Decision Tree and its two ensemble variants – Random Forest (RF) and Gradient Boosting Decision Tree (GBDT) are applied to the intelligent suggestion on the used amount of the phosphorusremoving chemical. The performance is verified using real sewage treatment data. The remainder of this paper is structured as follows. We define the research problem formally in Sect. 2 and detail the proposed intelligent dosing model in Sect. 3. In Sect. 4, we conduct an extensive empirical study to verify the efficacy of the proposed model. Finally, we conclude this paper in Sect. 5.

2 Problem Definition The objective of the proposed intelligent dosing model is to suggest the most feasible dosage of treating chemicals for removing phosphorus. To achieve this, we shall work on two tasks: 1) training a phosphorus removal prediction model and 2) dosage suggestion with the trained model.

Decision Tree Ensembles for Smart Sewage Treatment

11

2.1 Training a Phosphorus Removal Prediction Model For training the prediction model, we can access a collection of historical data on phosphorus removal, where the dosage of the treating medical is determined by the operators’ experience. The training data includes the quality parameters of sewage in n1 time slots Qtr ∈ Rn1 ×m , where m is the number of sewage quality parameters, together with the dosage of the used treating chemical dtr ∈ Rn1 and the concentration of phosphorus after the treatment ytr ∈ Rn1 . We aim to train a phosphorus removal prediction model f : Rm+1 → R, where the input feature x ∈ Rm+1 is composed of the sewage quality parameters x 1…m and the used dosage of the treating chemical x m+1 , the output f (x) is the predicted concentration of phosphorus in the treated sewage. 2.2 Dosage Suggestion with the Trained Model Given the trained phosphorus removal prediction model f , our objective is to suggest the dosage of the treating chemical for the test sewage in the coming n2 time slots with quality parameters Qte ∈ Rn2 ×m . The corresponding dosage of the treating chemical to be suggested is denoted as dte ∈ Rn2 . For each test sewage x ∈ Rm+1 with quality parameter x1···m ∈ Qte , our objective is to search the minimal used dosage of the treating chemical xm+1 ∈ dte , making the predicted concentration of phosphorus after sewage treatment f(x) no larger than a legal standard y˜ , i.e., f(x) ≤ y˜ . As the suggestion should be responded in a short time, the search should be conducted with small running time cost.

3 Intelligent Dosing Model with Decision Tree Ensembles In this section, we detail our proposed intelligent dosing model for phosphorus removal. The proposed intelligent dosing model consists of two components: 1) learning a phosphorus removal effect predictor with decision tree ensembles and 2) searching for the most reasonable dosage of the treating chemical with the learned phosphorus removal effect predictor. 3.1 Phosphorus Removal Prediction with Decision Tree Ensembles We use the decision tree regression as the base learner to predict the phosphorus  effect.  Given a set of training sewage examples  (1) (1)   removal x , y , x(2) , y(2) , . . . , x(n1 ) , y(n1 ) , decision tree regression traverses all feature dimensions and all possible values to find a split that divides the original sample set into two subsets with minimal intra-set discrepancy: ⎡ ⎛ ⎞2 1 ⎢ (i) ⎠ ⎝ (i) − min⎣ (j,s) y (j,s) y (j,s) x(i) ∈R1 x(i) ∈R1 j,s R1 ⎛ ⎞2 ⎤ (i) ⎠ ⎥ ⎝ (i) − 1 (1) + ⎦ (j,s) y (j,s) y (j,s) x(i) ∈R2 x(i) ∈R2 R2

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where j iterates overall feature dimensions, i.e., overall possible   j ∈ 1 . . . m+1, s iterates (j,s) (j,s) (1) (2) (n1 ) , and R1 and R2 values in the jth feature dimension, i.e., s ∈ xj , xj , . . . , xj are the split sewage sample sets according to j and s: (j,s)

R1

(i)

(j,s)

= {x(i) |xj ≥ s, i ∈ 1 . . . n1 }, R2

(i)

= {x(i) |xj ≥ s, i ∈ 1 . . . n1 }

(2)

Then the subsets are divided in accordance with the above step until the preset termination conditions are reached. When a new sewage sample comes, following the trained subset division criteria, it flows down from the root node to its split subsets until a leaf node with no splits, the mean concentration of phosphorus in the subset on the leaf node is taken as the predicted concentration of phosphorus for the new sewage sample.

Fig. 1. Decision ensemble strategies of GBDT and RF.

Ensemble learning is an effective strategy to boost the performance of base learners. In this paper, to predict the phosphorus removal effect, we use two decision tree regression ensemble variants – Gradient Boosting Decision Tree (GBDT) and Random Forest (RF) – that are respectively based on the Boosting and Bagging techniques. Their ensemble strategies are illustrated in Fig. 1. GBDT generates trees iteratively, which calculates residuals of the input samples after constructing a decision tree, and then retrains the next tree according to residuals. Iterating is stopped when the number of trees reaches a predetermined value. Finally, the predictions of all decision trees are accumulated as the predictions of the GBDT model. In contrast, RF adopts a parallel approach to generate decision trees. Through the put-back sampling method, multiple training sets containing the same amounts of samples are generated, and different trees are trained on these training sets. The RF prediction is constructed by voting on the predictions of all decision trees. Through ensemble, not only the prediction error caused by the bias of base learners is reduced significantly, but also model prediction stability and generalization ability can be greatly improved.

Decision Tree Ensembles for Smart Sewage Treatment

13

3.2 Intelligent Dosing Model for Phosphorus Removal After the phosphorus removal effect prediction model f is trained with the GBDT/RF, we take it as a virtual simulator to infer the concentration of phosphorus in the sewage after adding an amount of dosage of the treating chemical to the sewage with measured parameters. Taking the prediction as an accurate reference, we search the most feasible dosage of the treating chemical, which can effectively reduce the concentration of phosphorus in the sewage to a legal level while having a minimal amount to avoid unnecessary waste and additional pollution. Though the dosage takes continuous values, in practice, only a finite number of discrete dosages can be taken with limited precision. The set of candidate dosage values to search over is denoted as a list Cd , with the minimal value Cd [0] being 0, the maximal value being the dosage upper bound B. The values between the minimal and maximal dosages are the evenly binned dosages with a precision step . Given the sewage quality parameters x1 . . . m, to perform the suggestion about the dosage of the treating chemical to be used, we shall search the minimal dosage xm+1 among the dosage candidates so that the predicted concentration of phosphorus f (x) reaches to a qualified standard, i.e., f (x) ≤ y˜ . A straightforward search strategy is to exhaust every dosage candidate. However, it will consume a long running time, making it not suitable for real-world sewage treatment plant, which require a response in a relatively short time range. To do the dosage search much faster, we propose using the binary search strategy, which can reduce the search space logarithmically through choosing a half range  of candidates to  |C | search at each iteration. The time complexity is O N · d · log2 d , where N is the number of the decision tree base learners in GBDT/RF and d is the average depth of the decision trees. The algorithm can be conducted very efficiently to deliver fast dosage suggestions.

4 Experiments We conduct experiments on real-world sewage treatment data to verify the effectiveness of the proposed intelligent dosing model for phosphorus removal. 4.1 Data Preparation and Preprocessing We study on the sewage treatment data generated by a large anonymous water plant from October 1, 2020 to July 20, 2021. According to the previous studies, four main sewage factors have high correlations with the effect of removing phosphorus [9]. We consider them as the sewage quality parameters x 1…m in our model: – Orthophosphate (MI3PO4): As the main form of phosphorus in sewage, it directly affects the dosage of phosphorus-removing chemicals. – Inlet Water Flow (Q): It is the amount of sewage required to remove phosphorus per unit time. Changes in the inlet water flow will have a great impact on the flocculation and precipitation process [10].

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– pH: When pH in water varies, the charge carried by floc particles will be influenced, thus affecting the dosage of phosphorus removal agents required to make floc particles collide and aggregate [11]. – Water Temperature (TEMP): Water temperature is also an important factor for flocculation and precipitation. Water temperature affects the hydrolysis reaction speed and the strength of the Brownian motion [12] (Fig. 2).

Fig. 2. Data acquisition schematic.

The model also includes the dosage of the phosphorus-removing chemical determined by subjective experience used for removing phosphorus from each sewage sample, and the concentration of the phosphorus after the phosphorus removing treatment. The sewage quality parameters, the used chemical and the concentration of the phosphorus after treatment are recorded every specific time step, a day or an hour. Due to the time delay caused by the reaction between the sewage and the phosphorus removing chemical, the recorded data is misaligned. After aligning the data, we obtained 4,106 records. We use it to test the accuracy of the proposed decision tree model, and the amount of the saved phosphorus removing chemical delivered by the proposed intelligent dosing model. 4.2 Evaluation on the Phosphorus Removal Prediction with Decision Tree Ensembles Baseline Methods. We propose using decision tree ensembles – RF and GBDT – to predict the concentration of phosphorus from sewage quality parameters and the used phosphorus-removing dosage. To evaluate the effectiveness of RF and GBDT for phosphorus removal predicting, we compare them with four competitive baseline methods: – Linear Regression (LR), which builds a linear transformation from the input sewage features and the treating chemical dosage to the output concentration of phosphorus. The squared loss is used by LR. – Support Vector Regression (SVR) [13], which is actually a variant of LR, where hinge loss is used to train the prediction model.

Decision Tree Ensembles for Smart Sewage Treatment

15

– Back Propagation Neural Network (BPNN) [14] captures the nonlinear relationship between the input and output of the phosphorus removal process. We use two hidden layers in the implementation. – Decision Tree Regression (DT) is the base learner of RF and GBDT, with no ensemble techniques leveraged. The above four methods have been used to study non-linear dosing processes in sewage treatment and they obtained good feedback in some scenarios. Their experimental results are compared with RF and GBDT to verify the advantage of the decision tree ensembles for phosphorus-removing effect prediction. All methods are tested with the 5-fold cross validation. Performance Comparison. Table 1 compares the phosphorus-removing performance of different methods, where the average results and standard deviations on 5-fold cross validation are reported for MSE, MAE and R2 . To figure out the rates of the recalled test samples, for which the concentration of phosphorus after treatment is correctly predicted with a tolerance, we also use the accuracy with a tolerance (Acc@e) metric:  n2   i=1  yi − yi ≤ e (3) Acc@e = n2 where (·) is the indicator function, if the input Boolean statement is true, it has value 1, otherwise 0. In our experiments, we evaluate the metrics of [email protected] and [email protected], by taking the values of 0.1 and 0.05 for e. For each metric, the best and second performers are respectively highlighted by boldface and underline respectively; we also conduct paired t-test between the best performer and other competitors and use • to denote that the best performer is significantly better than the competitor at 5% confidence level. From Table 1, we can see that the decision tree ensemble methods – RF and GBDT – achieve the best prediction performance on all evaluation metrics. Due to the non-linear relation between the input and output of the phosphorus-removing process, the linear methods – LR and SVR – cannot achieve satisfactory performance. Though the BPNN has the ability to capture non-linear relations, the hidden-layer representation overrides the contribution of key input factors, making the model hard to perform well and to be interpreted. In comparison, DT provides an explainable approach to capture the nonlinear relation between the input and output of the phosphorus-removing process, which can not only exert the power of indicative input factors, but also leverage the interacting effects of different input factors for more accurate prediction. To boost the performance of DT further, we propose using its two ensemble variants, RF and GBDT to perform phosphorus-removing effect prediction. With an effective voting strategy, the decision tree ensemble methods achieve the best prediction performance. 4.3 Evaluation on the Chemical Consuming Reduction with the Intelligent Dosing Model As the decision tree ensemble methods, RF and GBDT can accurately predict the phosphorus-removing effect. We can use them to infer a feasible amount of the used phosphorus-removing chemical. In this section, we perform a comparison on the actually used and the suggested dosage of the phosphorus-removing chemical. The suggested

16

C. Zhang et al. Table 1. Performance comparison for phosphorus removing prediction.

Methods

MSE (%)↓

MAE (%)↓

R2 (%)↑

[email protected] (%)↑

[email protected] (%)↑

LR

0.534 ± 0.056•

5.502 ± 0.202•

20.126 ± 1.502•

78.465 ± 1.014•

91.328 ± 0.916•

SVR

0.656 ± 0.045•

6.350 ± 0.166•

3.664 ± 1.814•

71.620 ± 1.397•

85.725 ± 1.109•

BPNN

1.036 ± 0.071•

7.394 ± 0.355•

31.492 ± 1.898•

50.767 ± 2.127•

71.352 ± 0.744•

DT

0.244 ± 0.050•

3.132 ± 0.180•

68.350 ± 3.969•

91.060 ± 0.890•

97.564 ± 0.385•

RF

0.188 ± 0.048

2.722 ± 0.174

69.542 ± 6.082•

93.447 ± 0.798•

98.222 ± 0.485

GBDT

0.236 ± 0.056•

2.706 ± 0.222

72.004 ± 5.677

95.664 ± 0.479

98.952 ± 0.390

dosage of the phosphorus-removing chemical is inferred by the proposed intelligent dosing model. According to the international standard, the concentration of phosphorus in sewage after treatment is 0.5 mg/L. To tolerate the prediction errors and achieve the safe removal of phosphorus, we set the expected concentration of phosphorus in the treated sewage y˜ as 0.4 mg/L. For each test set of the 5-fold cross validation, which contains 822 sewage samples over 30 days, we suggest the dosage of the phosphorus-removing chemical to be used according to the proposed intelligent dosing model. Table 2 compares the suggested and actually used dosages of the phosphorus-removing chemical. Table 2. The comparison on the phosphorus-removing chemical dosage (m3 ). Test set

Actual usage

RF

GBDT

Suggestion

Reduction

Suggestion

Reduction

1

62.755

48.837

13.918

39.125

23.630

2

65.565

48.956

16.609

36.691

28.874

3

62.342

48.201

14.141

41.183

21.159

4

65.584

52.401

13.183

43.121

22.463

5

66.983

51.966

15.017

42.302

24.681

Average

64.646

50.072

14.574

40.484

24.162

As shown in Table 2, both RF and GBDT suggest a much smaller dosage of phosphorus-removing chemical for sewage treatment. Different from RF that ensembles decision trees trained parallelly on multiple samples training sets, GBDT ensembles decision trees trained on prediction residuals, which has better extrapolating ability. Because of this, GBDT can more accurately suggest the most feasible dosage of the phosphorusremoving chemical to make sure that the concentration of phosphorus can reach the qualified error, while the treating chemical will not be overused. From Table 2, we can find that, GBDT can save more phosphorus-removing chemicals than RF. Together with its accurate phosphorus-removing effect prediction performance, in practice, GBDT is expected to be an effective tool to suggest a feasible amount of phosphorus-removing chemical for high-quality sewage treatment.

Decision Tree Ensembles for Smart Sewage Treatment

17

For this water plant, if we use the GBDT model to suggest the used dosage of phosphorus-removing chemical for sewage treatment, from the obtained data, we can estimate that it will save about 24.2 m3 chemicals per month and 290.4 m3 chemicals per year, which is of great environmental and economic value. The saved chemical not only greatly reduces the secondary pollution caused by the total phosphorus residue in the water, but also reduces the process cost, promoting the green and sustainable development of the traditional wastewater treatment industry.

5 Conclusion The phosphorus-removing process in sewage treatment is characterized by non-linear mapping, time-delay perturbation, multi-parameters, etc. Traditional linear regression approaches cannot effectively capture the non-linear relations between the input and output of the process, while artificial neural network methods are hard to train with limited data. Therefore, based on historical data from water plant production, we proposed an intelligent dosing model for removing phosphorus using powerful and explicable decision tree ensembles. The performance of the proposed model is verified through comparative experiments. We have the following conclusions: (1) The decision tree algorithm can achieve excellent performance for predicting the phosphorus-removing effect, which is much better than commonly used linear regression and nonlinear BP neural networks. With well explainability, this model has met the general needs of engineering applications. In addition, its performance can be further improved through the ensemble strategy. It has been proved that the decision tree ensemble variant GBDT performs best in predicting the concentration of phosphorus after sewage treatment. (2) Integrated with the proposed intelligent dosing model, GBDT can help suggest the most reasonable amount of phosphorus-removing chemical for sewage treatment, providing a better chemical saving strategy for water plants, which can largely avoid secondary water pollution and capital waste caused by overdosing. The good performance shows its broad application scopes of the proposed decision tree ensemble based intelligent dosing model. In the future, we try to use some advanced algorithms like dynamic programming, to better train decision trees, to save more chemicals and funds, and boost the proposed intelligent dosing model to be applied in more real-world water plants. Acknowledgments. The authors acknowledge the financial support by Important Projects in the Scientific Innovation of CECEP (Grant No. cecep-zdkj-2020-005).

References 1. Dodds, W.K., Smith, V.H.: Nitrogen, phosphorus, and eutrophication in streams. Inland Waters 6(2), 155–164 (2016) 2. Norah, M., et al.: Impacts of untreated sewage discharge on water quality of middle Manyame River: a case of Chinhoyi town, Zimbabwe. Int. J. Environ. Monit. Anal. 3(3), 133–138 (2015)

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3. Tibugari, H., et al.: Worrying cadmium and lead levels in a commonly cultivated vegetable irrigated with river water in Zimbabwe. Cogent Biol. 6(1), 1802814 (2020) 4. Wurtsbaugh, W.A., Paerl, H.W., Dodds, W.K.: Nutrients, eutrophication and harmful algal blooms along the freshwater to marine continuum. Wiley Interdiscip. Rev. Water 6(5), e1373 (2019) 5. Kallis, G., Butler, D.: The EU water framework directive: measures and implications. Water Policy 3(2), 125–142 (2001) 6. Loganathan, P., et al.: Removal and recovery of phosphate from water using sorption. Crit. Rev. Environ. Sci. Technol. 44(8), 847–907 (2014) 7. Melgaçco, L., et al.: Phosphorus recovery from liquid digestate by chemical precipitation using low-cost ion sources. J. Chem. Technol. Biotechnol. 96(10), 2891–2900 (2021) 8. Al-Shandah, B.T., Ali, S.F.: Reduction turbidity of water in Tikrit drinking water treatment plant by using alum which was quantified by a jar test apparatus, with limnological study of treated and raw water. Indian J. Public Health 10(8) (2019) 9. Ghiasi, M.M., Zendehboudi, S.: Application of decision tree-based ensemble learning in the classification of breast cancer. Comput. Biol. Med. 128, 104089 (2021) 10. James, O.O., Cao, J.S., Lu, X.G.: The use of simulation modelling for optimisation of phosphorus removal in sewage treatment under varying influent loading. Res. J. Appl. Sci. Eng. Technol. 6(24), 4663–4670 (2013) 11. Tian, C., Zhao, Y.-X.: Dosage and pH dependence of coagulation with polytitanium salts for the treatment of Microcystis aeruginosa-laden and Microcystis wesenbergii-laden surface water: the influence of basicity. J. Water Process Eng. 39, 101726 (2021) 12. Brehar, M.-A., et al.: Influent temperature effects on the activated sludge process at a municipal wastewater treatment plant. Stud. Univ. Babes Bolyai Chem. 64 (2019) 13. Zaharia, C., et al.: Textile wastewater treatment in a spinning disc reactor: improved performances—experimental, modeling and SVM optimization. Processes 9(11), 2003 (2021) 14. Xiong, P., Dai, A.: Biological treatment process of urban wastewater based on BP fuzzy neural network control. J. Adv. Oxid. Technol. 21(2) (2018)

Failure Mechanism Analysis on Single Pulse Avalanche for SiC MOSFETs Haoyang Fei, Lin Liang(B) , and Ziyang Zhang State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China {M202171928,lianglin}@hust.edu.cn

Abstract. The avalanche failure mechanism of 1200 V 40-m planar silicon carbide (SiC) metal-oxide-semiconductor-field-effect transistor (MOSFET) is investigated in this article. Unclamped inductive switching (UIS) test is performed and the junction temperature is extracted by an accurate model to illustrate the relationship between failure temperature and avalanche current. The failure temperature shows little dependence on current and a critical temperature window around 980 K ~ 1100 K is found. The probability of the latch-up of parasitic bipolar junction transistor (BJT) and metal system damage is studied by an analytical model and the thermal diffusion equation. With further theoretical analysis and validation, the failure mechanism is demonstrated as the metal system damage because the high-temperature transition exceeds the sustainable time of SiC MOSFETs. TCAD simulation is also used to verify this mechanism and the temperature evolution suggests that aluminum is likely to melt during the avalanche. Keywords: Avalanche · Failure mechanism · Melting of metal system · Parasitic bipolar junction transistor (BJT) · SiC MOSFET

1 Introduction Silicon carbide (SiC) is considered a promising material in high-voltage device applications due to its superior properties such as wide bandgap, high thermal conductivity, and high critical electric field strength [1]. Over the past 10 years, commercial SiC MOSFETs have been comprehensively studied and adopted in power electronic fields to optimize system performance. Such devices can operate at high-switching frequency with high blocking voltage and small chip size, which makes them experience high temperature and even causes reliability problems especially in short-circuit and avalanche events. Therefore, to prevent catastrophic device destruction, it is vital to evaluate the avalanche capability and understand the avalanche failure mechanisms of SiC MOSFETs. Some applications with inductive components, such as power supply circuits, gasoline or diesel injection and automotive applications, may drive SiC MOSFETs to avalanche mode and then generate voltage spikes [2]. The typical method to analyze avalanche mode is the unclamped inductive switching (UIS) test. With this test, extensive research has been conducted to demonstrate the process of avalanche breakdown and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 19–31, 2023. https://doi.org/10.1007/978-981-99-4334-0_3

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some assumptions of failure mechanism have been proposed. In [3–5], experiments and electro-thermal simulations focused on the possibility of activation of channel owing to the significant decrease in the threshold voltage. However, by applying a higher negative gate bias, it was found that inhibiting the channel from turning on couldn’t substantially improve the avalanche capability of SiC MOSFETs [6, 7]. Furthermore, parasitic bipolar junction transistor (BJT) latch-up mechanism, which was generally reported in Si devices, was studied by an established electro-thermal model in SiC MOSFETs [8, 9]. Based on that model, literature [10] suggested that the BJT turn-on could be triggered at low temperature for SiC MOSFETs designed with shallow P+ body and high Ohmic contact resistance. However, the effective method to verify this mechanism still remains to be developed because the latch-up is difficult to be confirmed by experiments. Another failure mechanism for avalanche is the metal system damage. Power devices usually require some metals for contacts and passivating materials which may be destroyed by sharp temperature transition [11]. For example, according to [12], aluminum is prone to degrade before reaching the intrinsic temperature of 4H-SiC close to 1570 K, since its melting point is only 933 K. Decoupled UIS tests were carried out with various values of load inductors and devices produced by different manufacturers. The results showed that there was a critical temperature window, leading to the failure of metallization [12]. This mechanism was further verified by UIS experiments under different case temperatures [13]. In fact, it is difficult to distinguish these modes and find the real failure mechanism. One of the reasons is that the turn-on temperature of parasitic BJT may be close to the melting point of aluminum, though calculated by an advanced numerical model [14]. As a result, there is few experimental evidence of the latch-up mechanism and the verification method is required. Besides, the actual junction temperature could not be derived directly during the avalanche transition and the conventional method is complex. Consequently, this article aims to give a practical method to distinguish these mechanisms based on the analyses on their characteristics. The relationships between failure temperature and avalanche current are different in various mechanisms. The dependence of temperature on avalanche current is more serious in latch-up mechanism than in other conditions. And the method to identify the avalanche failure mechanism of SiC MOSFET could be established based on this feature, where the avalanche current is also included in the temperature estimation. In this article, the avalanche capability of 1200-V SiC MOSFET was presented by performing UIS tests under different conditions. The junction temperature is extracted by an accurate method and the influence of avalanche current on failure temperature is studied, which can clarify the failure mechanism. Finally, thermal diffusion equation and TCAD electrothermal simulation are used to validate the occurrence of metal systems damage.

2 Single UIS Experiments UIS tests are conducted and the simplified circuit schematic is shown in the inset of Fig. 1(a). In this study, SiC MOSFETs from CREE (C3M0040120D) are tested. The auxiliary device S and DUT are initially turned on to increase the current and inductor

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energy until desired value. To avoid disturbance, S is turned off prior to DUT, and the current path shifts to the SiC diode D. Once DUT is turned off, the avalanche mode occurs inside it. The inductor induces high voltage between drain and source to dissipate its stored energy, as shown in Fig. 1(a). The voltage waveform has a clear rise caused by high junction temperature. Moreover, after the peak point, junction temperature sightly drops until the end of avalanche mode.

(a)

(b)

Fig. 1. (a) UIS typical waveform and UIS test circuit (inset). (b) Avalanche energy E av shown with respect to avalanche current I av , with different inductors.

In this test, the charging time is gradually extended to control the avalanche current and also the energy until exceeding the avalanche capability of SiC MOSFET and finally the device is burned out. After that, in this study, devices were tested at higher avalanche current conditions to detect its influence on failure. Figure 1(b) shows the results where the energy is calculated by (1):  (1) E = VDS (t) · IDS (t)dt It is obvious that the device can withstand single avalanche events and operate normally before the maximum energy is reached. And the maximum values of tolerable energy are different when different inductors are used. Beyond this energy tolerance, a small increase of avalanche current could destroy SiC MOSFET though the stored energy is not totally released. When the current was significantly increased, for example, increased by 80% from 51.15 A to 90.92 A in the test with a 1 mH inductor, only 54% of the maximum energy could be dissipated, which indicates that there is another restriction existing such as temperature limitation or BJT latch-up. Once the limitation is reached, device breakdown occurs in spite of low energy.

3 Failure Mechanism 3.1 Junction Temperature Estimation To summarize, the junction temperature is of vital importance to explain the physics mechanism of avalanche failure while it is difficult to be directly obtained. However, previous studies have observed a positive temperature coefficient of breakdown voltage

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behavior in 4H-SiC, and it has been identified as a powerful tool to evaluate the junction temperature [15–17]. On the other hand, according to [18], the avalanche voltage of semiconductor is caused by not only the temperature-dependent breakdown voltage but also the voltage drop due to the space charge resistance, which can be expressed by (2): Vav = VB0 {1 + α(T − T0 )} + I ρsc

(2)

where V av is the actual avalanche voltage, V B0 is the breakdown voltage at T 0 , α is the temperature coefficient of the breakdown voltage, and ρ sc is the space charge resistance. With this equation, the junction temperature can be derived from the variety of avalanche voltage, as shown in (3): Vav = β(T − T0 ) + ρsc I

(3)

where V av is the difference of the voltage at the start point and the point whose temperature is T, β = αV B0 can be measured as a whole, and I is the current change between the two points. When using this method, previous articles usually ignored the second term, for example in [13] or involved complex steps when calculating ρ sc , for example in [10]. To enable a practical approach, a simplified process of this method is developed to acquire the parameters with this accurate model. First, breakdown voltages at different temperatures were measured by B1505A from which β could be obtained, as shown in Fig. 2(a). Then devices were tested at different avalanche current conditions and the initial avalanche voltages were recorded to get ρ sc . Its value slightly varies with devices because of process and manufacturing variability, as shown in Fig. 2(b). This plan is much easier because it’s not necessary to control the case temperature, while ensuring the accuracy. Figure 3(a) shows the waveforms when devices fail with 1 mH inductor. V DS increases rapidly and suddenly becomes zero while the avalanche current still remains, suggesting the DUT is out of control. It should be noted that when higher avalanche current is applied, the peak value of avalanche voltage is also higher, though the avalanche time is shorter. When Device3 failed, the temperature induced voltage reached 1858.8 V while the peak value of Device1 was just 1808.6 V. This phenomenon suggests that the temperature is similarly severe in all cases. Besides, the zoom-in plot in Fig. 3(a) shows that the initial avalanche voltage is significantly increased by higher current. Therefore, the voltage drop caused by the avalanche current should not be ignored in junction temperature evaluation. This could provide guidance for other work. The extracted junction temperatures from the data of Fig. 3(a) are shown in Fig. 3(b), respectively. At a higher avalanche, the junction temperature increased faster because higher power dissipation was generated. As a result, all tested devices experienced extremely high temperature before failure, and their peak values were within a small range which was between 1060 K and 1090 K. In fact, Device2 and Device3 with higher current suffered a little higher temperature than Device1, though the avalanche time decreased from 18.7 µs to 3.4 µs. The results reveal that the metal system had degraded for the junction temperature was far higher than the melting point of aluminum. It is also worth pointing out that Device1 didn’t fail at the highest temperature, but at a lower value where the junction

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Fig. 2. (a) Breakdown voltages as functions of temperature. Leakage current (inset). (b) Initial avalanche voltages as functions of current.

Fig. 3. (a) Three typical voltage waveforms of failure events at different current values with 1 mH inductor. The voltage change caused by current is significant (inset). (b) The extracted evolution of junction temperature from (a).

temperature has begun sightly dropping. One possible reason is that there is a delay between the temperature evolutions of Al metallization and SiC, so when the temperature of the semiconductor begins decreasing, the temperature of Al metallization may still remain rising. 3.2 Parasitic BJT Latch-Up Avalanche failure of power MOSFET is usually caused by parasitic BJT turning on and the intrinsic temperature limit in Si devices [19]. SiC MOSFET has a similar structure to Si MOSFET, which might bring the same problem, as shown in Fig. 4. Usually, the parasitic BJT is designed to be suppressed by the short-circuit between P+ and N+ region using source metal. However, when avalanche mode occurs, intensive impact ionization happens and generated hole current flows through base region which caused voltage drop across the base resistance Rb . The BJT would be activated if this voltage drop is higher than the built-in voltage of base-emitter junction. This destructive failure is likely to take place in Si devices because of its low built-in voltage which is around 0.6 ~ 0.7 V.

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Although 4H-SiC has a higher value of built-in voltage, SiC MOSFET undergoes high temperature and high current, which may also lead to latch-up. Source

Gate Ohmic Contact

I

Rb

N+ Pwell

N-

Drain

Fig. 4. Simplified MOSFET half-cell structure with the parasitic BJT and avalanche current path.

Obviously, the latch-up of parasitic BJT has a high dependence on current, which can be described by the analytical model established in [8, 10]. The base resistance includes the resistance of P implanted region and the Ohmic contact resistance, so the voltage drop caused by avalanche current can be expressed by (4): VBE = Iav ·

1 ρc L ( + ) A/p Lc qμp NB h

(4)

where A is the die area, p is the length of half-cell, ρ c is the Ohmic contact resistance, L c is the length of the region between Pwell and source metal, L and h are the length and height of the base, N B is the base doping concentration, and μp is the mobility of holes in the base of the BJT. μp is temperature-dependent, indicating that the base resistance rises with the increase of temperature: μp = μp,max Bp(N) = (

T βp Bp(N) ( 300 )

T βp +αp 1 + Bp(N) ( 300 )

1 + ( NNpg )γp μp,max ) −1 μp,max − μp,min ( NN )γp

(5)

(6)

pg

where μp,max , μp,min , N pg , γ p , α p , and β p depend on type of material and N is the doping concentration of the Pwell region. The built-in voltage of base-emitter junction is expressed by (7): ϕbi =

NB NE kT ln( 2 ) q ni

(7)

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where ϕ bi is the built-in voltage, k is the Boltzmann constant, N E is the emitter doping concentration, and ni is the intrinsic carrier concentration. For 4H-SiC, the temperature-dependence of intrinsic carrier concentration is illustrated by (8): ni = 1.70 × 1016 T 3/2 e−(2.08×10

4 )/T

(8)

When V BE exceeds ϕ bi , the BJT is turned on and failure occurs. Apparently, avalanche current and junction temperature have a profound impact on latch-up. When a high avalanche current is applied, the voltage drop (V BE ) across Rb would be increased by it; when high temperature emerges, Rb is increased and the built-in voltage (ϕ bi ) is lowered. And the relationship between failure temperature and avalanche current is calculated by this BJT latch-up model, as shown in Fig. 5. Theoretical results suggest that the failure temperature caused by BJT has a dependence on avalanche current. As the avalanche current increases, the failure temperature decreases. Although temperature is only 900 K, failure may still occur with a current high enough (≈ 120 A). This trend is consistent with the result simulated by accurate TCAD model in [20], which is also displayed in Fig. 5. Although some parameters are measured experimentally, some typical parameters are also used, which means that the model could not represent the true structure of the cell. However, these limited differences may change the specific value, but cannot change the negative correlation here.

Fig. 5. Calculated results of the BJT model, data from literature and experiment results.

However, this negative correlation was not observed in experiments. The maximum junction temperatures were derived from experiments and are also shown in Fig. 5. As can be seen, the maximum junction temperatures of failure cases are all higher than 933 K, and the avalanche current just has little impact on the failure temperature. SiC MOSFET failed at 1062 K and 1076 K when avalanche current is 51.15 A and 90.92 A, respectively. Higher current cannot make devices fail earlier before the critical

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temperature is reached. In fact, the junction temperatures are very similar even slightly increase with increased current, which is exactly contrary to the expectation of the BJT mechanism. In other words, avalanche failure in SiC MOSFET shows little dependence on current. This evident difference between these two trends implies that the parasitic BJT is unlikely to turn on in SiC MOSFET during avalanche. In practice, advanced fabrication techniques usually assert a deeply implanted P+ region to Pwell region and use high doping concentration at the Pwell /N-junction, which makes latch-up difficult to happen in mentioned experiments [21, 22]. 3.3 Metal System Damage Within the observed temperature window exceeding 933 K, the metal system suffers from unavoidable damage. Under this severe situation, aluminum would become molten and unstable. The thermally induced surface roughness and nano-cracks caused by the agglomeration of aluminum at 875 K were reported in [23], which resulted in the degradation of metal/SiC interface. The instability of the metal system and the contact under high temperature might provoke the formation of mesoplasma and make the device collapse. Devices do not fail immediately at the moment the melting point of aluminum is reached. Metal interconnect could sustain this temperature for a short period and break down at a higher failure threshold [24]. Therefore, during avalanche, SiC MOSFET may sustain a temperature value above the melting point and cool down until the end of avalanche mode without failure. However, if it lasts longer than the sustainable time, the device would fail because of continuous damages. Moreover, if the temperature proceeds to increase, which can cause severer damage, SiC MOSFET fails faster.

Fig. 6. (a) Junction temperature evolution of failure test and the last before failure. (b) The relationship between maximum temperature and avalanche time of all failure tests.

As can be seen from Fig. 6(a), for I av = 49.60 A, SiC MOSFET can dissipate the energy and withstand such a temperature for 18.26 µs without failure. However, at a little higher temperature, this time is reduced to 13.73 µs, so the device fails. The relationship between the maximum junction temperature and the avalanche time before failure is shown in Fig. 6(b). When the temperature is high enough, the device fails in

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a very short time. On the other hand, when the avalanche time is long enough to make the metal system degrade totally, the device could also be destroyed at a relatively low temperature. In short, the results demonstrate that SiC MOSFET is highly likely to fail because of the metal system damage caused by the critical temperature window above the melting point of aluminum. To ensure this mechanism, the junction temperature results should be verified. To validate the temperature during avalanche transition, the thermal diffusion equation can be used, which can be expressed as follows [25]: ρc

∂T(x,y,z,t) = ∇ 2 (κ · T ) + Q(x,y,z,t) ∂t

(9)

where ρ, c, κ are material density, thermal capacity, thermal conductivity of SiC, and Q is the generated heat. It can be solved by using Green function, which is performed in [13, 25]. The solution can be expressed in (10): Q T (0, t) = T0 + ρc

tav dτ 0

y z x ) · erf ( √ ) · erf ( √ ) · erf ( √ 4 DSiC τ 4 DSiC τ 4 DSiC τ

(10)

where DSiC = κ/ρc. Here, the maximum temperature point is considered the center point of the surface. Since the measured parameters of SiC MOSFET are so large that the erf can be regarded as 1. Therefore, the junction temperature can be calculated by (11): T (t) = T0 +

Q Pt = T0 + √ ρc S(Wdrift + DSiC t)ρc

(11)

where P is the power dissipated, S is the active region of the chip, and W drift is the width of drift region. This theoretical method can describe the evolution of temperature during the transition despite small deviation caused by idealization. For example, the cool-down process is not taken into account, which may lead to a steady increase of temperature and an overrated value as a result. However, this deviation is acceptable, because the approximate temperature range is to be verified instead of the specific value here. The calculated results as well as previous extracted results are shown in Fig. 7. The former results are basically in accordance with the latter, indicating that the metal damage induced by the critical temperature window is possible. This temperature range is around 980 K ~ 1100 K theoretically and experimentally. This temperature range is far lower than 1570 K, the intrinsic temperature of 4H-SiC, indicating that intrinsic temperature limit is not the direct failure mechanism. This verified avalanche failure mechanism of SiC MOSFET could give feedback on device design. As for the metal system damage, the thermal stability of metal contact

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Fig. 7. Extracted temperature results from experiments and calculated by the diffusion equation.

should be further improved to realize better avalanche robustness. Besides, according to (11), bigger chip size is also an effective way to relieve the heat accumulation in this transition. 3.4 TCAD Simulation To estimate the temperature evolution during avalanche, calibrated electrothermal model in TCAD Sentaurus is developed. Models including self-heating, interface mobility degradation, doping- and temperature-dependent mobility, incomplete ionization and adjusted Okuto–Crowell are used [26]. It should be noted that the area factor is optimized in terms of real size to get more reasonable results. Besides, the top metallization is added, which actually also has a nonnegligible influence as a heat capacitor [27]. The thickness of aluminum layer is 3.9 µm, and the thickness of SiC material is 18 µm. The calibrated structure is not exactly identical to the actual device, but it can be taken as a general case study.

Fig. 8. (a) Simulated maximum temperature evolution of top metallization and the mixed-mode simulation circuit (inset). All the results exceed 933 K. (b) Location of maximum temperature at increase phase (left) and decrease phase (right). It shifts from semiconductor to metal.

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Three typical failure cases at different current values are simulated and Fig. 8(a) shows the temperature evolution of top metallization. The simulated temperatures are all around the melting point of aluminum which has a good agreement with experiments. The temperature limitation can be clearly demonstrated. Besides, with calibrated parameters, in all events, the parasitic BJT doesn’t turn on for a relatively low current density. The simulation results of lattice temperature distribution at the increase and decrease phase of temperature are shown in Fig. 8(b). When high power dissipation is generated in the drift region, the semiconductor has the highest temperature. After the maximum point is reached, 4H-SiC cools down first, so the metallization holds a higher temperature. As a result, the metal system may still fail when the junction temperature has already decreased. This could explain the occurrence of failure after the peak temperature, which can be seen in Fig. 3(b). On the other hand, the temperature of metallization in Fig. 8(b) is so high (> 1000 K) that aluminum would be damaged.

4 Conclusion In this article, the avalanche capability of 1200 V 40-m planar SiC MOSFET is evaluated by performing single UIS test. The junction temperature is extracted by using a model of avalanche voltage. The influence of current in this model is discussed, which turns out to be an important factor. A method is developed to distinguish the failure mechanisms by focusing on the relationship between current and failure temperature. And the extracted results of failure temperature show little dependence on avalanche current and actually gather in a critical temperature range which is 980 ~ 1100 K. Three mechanisms are analyzed theoretically and experimentally. The possibility of the latch-up of parasitic BJT is evaluated by using an analytical model. By comparing the results of it with the experimentally observed results of the failure temperature with current, the latch-up turns out to be less likely. On the other hand, the metal suffers from unavoidable degradation because this temperature window is higher than its melting point (≈ 933 K). When the duration of high-temperature exceeds the sustainable time of SiC MOSFETs, devices break down. Metal system damage is also validated by the thermal diffusion equation and TCAD simulation. Besides, this temperature range is far lower than 1570 K, without reaching the intrinsic temperature limitation. Similarly, when the failure mechanism of a product is ambiguous and uncertain, the method formulated here provides a practical and simple method to verify the mechanism while the accuracy is considered. Currently, researchers usually focus on the failure temperature which may lead to some mistakes when the failure events happen in a temperature range where more than one mechanism could be effective. By considering the relationship between current and failure temperature, this confusion could be removed. Acknowledgment. This work was supported by JCJQ Program (2020-JCJQ-ZD-105).

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Research on the Scale of Multi-regional Networking to Improve the Interoperability Benefits of Power Systems Xinmiao Liu1 , Xun Lu1 , Huilai Wang2 , Yuanyuan Lou1 , Junlei Liu1 , and Qiao Wang2(B) 1 Guangdong Power Grid Corporation, Guangzhou 510000, China 2 Central Southern China Electric Power Design Institute, Wuhan 43000, China

[email protected]

Abstract. In 2022, power rationing will occur to different degrees in many parts of the country. The state requires that the advantages of large power grids be brought into play and that cross-provincial and inter-regional power cooperation be strengthened to enhance power security capacity. In this paper, taking largescale grid A and grid B as examples, the stochastic production simulation of power system is adopted, to study the benefits of grid A and B power mutual assistance such as installation substitution, peak shaving, accident support, clean energy consumption, etc. The research method of network scale based on seasonal mutual benefit and installed substitution benefit is put forward to provide reference for future cross-regional and inter-provincial network project research. Keywords: Complementary characteristic · Mutual benefit · Production simulation · Installation substitution · Scale of networking

1 Introduction The National Power Plan points out that the development of regional power markets will be explored, power resources will be optimally allocated nationwide and clean energy will be given priority. At present, the state is promoting the construction of electricity market in an all-round way, and will gradually form a market system with full competition, open and orderly development, and gradually explore the realization of market-oriented inter-provincial and inter-regional electricity trading, play the role of large power grid resource allocation [1–5]. At present, DC back-to-back interconnection is often adopted in the asynchronous network among the neighboring provinces of our country, including three back-to-back interconnection forms [6]: conventional DC, flexible DC and both include. Function positioning includes power transmission, safety and stability, power mutual help and so on. For example, back-to-back in Lingbao City, back-to-back in Cao Lanh, back-toback in China and Russia and back-to-back in Heihe, while back-to-back in Luxi and Chongqing and Hubei focus on power supply to keep the power grid safe and stable Back-to-back, Fujian and Guangdong mainly play the role of electric power mutual aid. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 32–38, 2023. https://doi.org/10.1007/978-981-99-4334-0_4

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The development of inter-provincial and regional power grid power cooperation is conducive to realizing the optimal allocation of inter-regional power resources, reducing the installation of thermal power in the system, improving the regulatory capacity of the power grid and promoting the large-scale absorption of clean energy. it is of great significance to promote the high-quality development of the power system by enhancing the power grid’s support capacity under emergency, building a cross-regional power market trading platform and saving the cost of the whole society’s electricity consumption.

2 Characteristics of Regional Power Grid 2.1 Scale and Characteristics of Electricity Consumption (1) Annual load characteristic The annual load characteristics of grid A showed a single peak, with the load rate above 0.9 from May to September, and the maximum load occurs in August in summer, while the load rate was relatively small in winter. The load characteristics of grid B showed double peak in summer and winter and the annual maximum load occurred in July and August in summer. The annual load characteristic curves of grid A and B are shown in Fig. 1.

Fig. 1. Load characteristic curve of grid A and grid B.

(2) Typical daily load characteristics Summer: there are two load peaks in grid A, the daily maximum load appears at 11:00, the afternoon peak appears at 15–17:00, the load rate is 0.97. The peak load of power Grid B in central China is about 21:00 in the evening and about 13:00 in the afternoon, with a load rate of 0.98. The typical daily load characteristic curves of grid A and B in summer are shown in Fig. 2. Winter: there are two load peaks in grid A. The daily maximum load appears at 11:00 and the afternoon peak appears at 17–19:00. The load rate is 0.98. Grid B shows double peak characteristics. The maximum load appears in the evening peak at 18–20 o’clock, noon peak appears at about 13 o’clock. The typical daily load characteristic curves of grid A and B in winter are shown in Fig. 3. Based on the annual load characteristics and typical daily load characteristics of grid A and grid B, it can be seen that there are no seasonal complementary characteristics in summer, but there are intraday complementary characteristics, and there are seasonal complementary characteristics in winter.

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Fig. 2. Load characteristic curve of grid A and grid B in summer.

Fig. 3. Typical daily load curves of grid A and grid B in winter.

2.2 Power Supply Structure As shown in Fig. 4, in terms of power supply structure, grid A and B have good complementary characteristics, while in terms of output characteristics, the hydropower of grid A and B belong to different basins, and there are complementary characteristics between basins, and the new energy output characteristic also has the certain difference.

Fig. 4. Power installation structure.

2.3 Subject to Electrical Characteristics Grid A and grid B are both energy-deficient areas, both are large-scale power-receiving areas, but there are great differences in the characteristics of receiving power, in which grid a mainly receives power from hydropower, including some thermal power. Power Grid B by power to thermal power, new energy-based, but also part of hydropower.

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3 Benefit of Interconnection 3.1 Installation Substitution Benefits Carry out mutual assistance between grid A and grid B through two-way mutual assistance of electricity. Grid B supports grid a in May in spring, grid a supports grid B in winter, and two-way intra-day mutual assistance is implemented in summer, up to 200% of the installed replacement benefits can be achieved. That is the construction of 2,000 MW network projects can replace grid A, grid B 2,000 MW each, a total of 4,000 MW of main power supply installed. 3.2 Clean Energy Consumption Benefits The mutual cooperation of power grid A and B can provide a platform for the optimal allocation of peak-shaving resources. Through the spring and autumn, summer and winter to achieve the full use of peak regulation resources, promote the development of new energy and consumption. Taking the 2,000-MW (GW) grid as an example, grid A and grid B could increase the scale of new energy development by 4 GW and reach a total of 8 GW respectively, which would be conducive to increasing the amount of non-water renewable energy, achieve the “3060” target as soon as possible. 3.3 Economic Benefits The substitution benefit of power grid A and B is up to 200%, which has obvious economic advantage compared with the self-built power supply scheme. According to preliminary estimates, about 3 billion yuan will be invested in 2,000-MW interconnection projects and access lines, and about 12.8 billion yuan will be invested in building 2,000MW coal-fired power plants in grid A and grid B, respectively, the investment of the network project is only about 23% of that of the coal power project and the economic benefit is very significant. In addition, the mutual cooperation of power grid A and B is beneficial to increase the hours of thermal power utilization, improve the efficiency of thermal power utilization and promote the economic operation of power system. 3.4 Marketization Benefits It is also possible to realize spot market trading of carbon emission rights in a large area by mutual help of Power Grid A and B. Clean power sources, such as solar, wind, hydropower and nuclear power, will be the main sources and direct trading of carbon emission rights will be achieved through grid-connected projects, thus promoting the green and low-carbon development of the power grids A and B. we will accelerate the pace of carbon neutrality and carbon peaking, contributing to the early realization of the “3060” target nationwide.

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4 Network Scale Measurement Method On the basis of the analysis and demonstration of the benefits of the network in the front, the construction scale of the network project is studied and determined according to the main methods of the comprehensive evaluation of technology and economy by comprehensively considering various influencing factors. The power profit and loss of Grid A and B during the profit and loss control period of the first month are αi and βi million kW. αj = αmin = min{α1 , α2 , αi , . . . α12 } i = 1, 2, 3, . . . , 12

(1)

βk = βmin = min{β1 , β2 , βi , . . . β12 } i = 1, 2, 3, . . . , 12

(2)

From the point of view of grid B, the maximum network scale that can achieve 100% substitution benefit is (αk − αmin )/2 million kW. From the point of view of grid A, the maximum network scale that can achieve 100% substitution benefit is (βj − βmin )/2 million kW. λ = min(

αk − αmin βj − βmin , ) 2 2

(3)

Considering the characteristics of the power systems in grid A and grid B, if only seasonal mutual benefits and installation substitution benefits are taken into account, the scale of grid B and grid A interconnection is about λ million kW.

5 Network Scale Analysis (1) Recently As can be seen from Table 1, the maximum power gap of A and B appears in summer afternoon peak and winter evening peak respectively. In summer and winter, the gap between the profit and loss of grid A is about 6.64 million kW (in winter, the gap can exceed 10 million kW if the overhaul arrangement is optimized) and that of grid B is about 4.45 million kW. If only the seasonal mutual benefit is considered, the grid A and the grid B will be connected at a scale of about 2.25 million kW, which can achieve better installed substitution benefits. If the intra-day mutual benefit is considered in summer, the network scale can be further increased. (2) Forward The maximum power gaps of forward grid A and B occur in May and winter respectively during the dry flood alternating period. In May and winter, the gap between the profits and losses of grid A was about 6.55 million kW, and the optimized maintenance arrangements would result in a gap of 10 million kW, while the gap between the profits and losses of grid B was more than 10 million kW. From the perspective of bi-directional substitution of two provinces, the scale of Grid A and grid B is up to 5 million kW, which can achieve better substitution efficiency.

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Table 1. Comparison of power balance results between grid A and grid B (recently) Month

Grid A Profit and loss control period

Grid B Profit and loss for power

Profit and loss control period

Profit and loss for power

Jan.

19

367

18

298

Feb.

19

380

20

1132

Mar.

19

429

18

2486

Apr.

19

302

18

3417

May

15

−283

20

3198

Jun.

11

286

22

3213

Jul.

11

−1

21

1396

Aug.

11

−290

21

430

Sep.

19

407

17

2111

Oct.

19

358

18

3880

Nov.

19

341

18

1854

Dec.

19

374

18

−15

6 Conclusion In this paper, the complementary characteristics of the adjacent large power grid in the aspects of power consumption characteristics, power supply structure and receiving characteristics are analyzed, the benefits such as substitution of installed power, absorption of clean energy, economy, marketization, disaster prevention and reduction are studied. The research method of reasonable network scale based on seasonal mutual benefit and installation substitution benefit is put forward. The research shows that it is appropriate to consider the scale of grid A and B connection at 200–300 MW in the near future and at about 500 MW in the long term.

References 1. Huang, M., Chen, G.: Reliability evaluation and characteristic analysis in inter-region power system interconnection. Electr. Power 34(7), 35–39 (2001) 2. Huang, M., Li, P.: Benefit analysis of interconnecting the northwest power system with the Chuanyu power system. Electr. Power 34(4), 31–36 (2001) 3. Wang, S.H.: Potential benefit analysis of interconnecting north China power system with central China power system. Power Syst. Technol. 24(9), 31–34 (2000) 4. Wang, S.H., Liu, J., Zheng, Y., Lin, T.: Calculation of benefit from interconnecting north China power system with central China power system and analysis of required tie line capacity. Power Syst. Technol. 1, 38–42 (2001)

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5. Zheng, Y., Du, Z.H.: Analysis on interconnection between southern joint running power network and central China power network. Electr. Power 7, 61–64 (2000) 6. Cai, D., Zhou, K., Dong, H., Liu, H., Cao, K.: Influence of back-to-back VSC-HVDC project on the operation characteristic of Hubei power grid. Hubei Electr. Power 41(1), 9–13 (2017)

P2P Optimization Strategy for Integrated Energy Operators Based on Nash Negotiation Kejun Dong1,2,3,4 and Yang Wang1,2,3,4(B) 1 National Innovation Center for Digital Fishery, China Agricultural University, Beijing 100083,

China [email protected] 2 Key Laboratory of Smart Farming Technologies for Aquatic Animal and Livestock, Ministry of Agriculture and Rural Affairs, Beijing 100083, China 3 Beijing Engineering and Technology Research Center for Internet of Things in Agriculture, China Agricultural University, Beijing 100083, China 4 College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China

Abstract. The integrated energy system containing electric heating and gas uses electricity and natural gas as energy sources, it is a new multi energy integration system. In recent two years, peer-to-peer (P2P) energy trading has become an important new energy trading method. Integrated energy operators provide users with power supply, heat and other energy supplies, and also further absorb new energy. Therefore, studying the energy transaction between multiple integrated energy operators can improve the economy. Aiming at this problem, based on Nash bargaining theory, a cooperative game model of comprehensive energy operators considering P2P mode is established, which is decomposed into benefit maximization subproblem and energy transaction payment subproblem to solve the two subproblems in turn. Compared with other traditional models, this method improves the capacity of renewable energy and reduces the operating costs of integrated energy operators. Keywords: P2P energy transaction · Nash negotiation · Integrated energy operator

1 Introduction The integrated energy system (IES) can convert various forms of energy such as renewable energy into demand side energy, which can realize the two-way flow of multi-energy system and the complementary and mutual energy sources [1]. Integrated energy system can improve the absorption rate of new energy and ensure the supply of energy [2]. In the energy Internet, there are multiple integrated energy operators for users. The interconnection between operators not only improves the economy, but also improves the flexibility of energy supply [3, 4]. Therefore, the comprehensive utilization of multiple energy systems has become a research hotspot and focus [5]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 39–50, 2023. https://doi.org/10.1007/978-981-99-4334-0_5

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At present, the research on P2P power trading mainly focuses on the power trading of individual users with distributed power in microgrid and multi microgrid groups with independent microgrid as the main transaction subject. Literature [6] analyzed the market transaction model of photovoltaic microgrid clusters, established a cooperative game model between multiple microgrids, and studied the power and revenue distribution of the alliance between microgrids. Literature [7] proposes an optimal scheduling model based on game theory in combination with game analysis methods. From an economic point of view, taking solar storage microgrids as an example, this paper analyzes the optimal allocation schemes of different investment entities under the competitive game mode. Literature [8] aims at the lowest operating cost, considers the demand response based on interruptible load, optimizes the power of the internal controllable unit of the microgrid, obtains the optimal strategy and completes the demand response at the distribution network level. Literature [9] explained the physical meaning of Nash equilibrium, and obtained the conditions and influencing factors of transactions between microgrids. Literature [10] established a game model based on Nash. Most of the studies in the above literatures focus on the power transaction in the game between microgrid and users and between multiple microgrid groups, and the research on the influence of each subject in the game optimization multi-energy optimization strategy is not in-depth enough. The research described above has laid a certain foundation, but the following issues still need to be considered: First, currently P2P is mostly used for transactions between electric energy as a single energy field, and less consideration is given to transactions between different energy sources. Second, compared with other traditional modes, new energy generation is not considered in order to achieve low-carbon economy, Therefore, it is necessary to consider the output of wind power and photovoltaic. This paper proposes a multi-agent optimal scheduling model, which takes into account the relevant constraints of the coupling devices, and optimizes the energy of the entire system, and conducts cooperation between various entities based on the Nash negotiation theory. Each IES has an independent integrated energy operator. The optimal operation of IES requires comprehensive consideration of the interests of each operator, determining the power required by each operator, and the best operation plan for achieving a low-carbon economy. Research on operation optimization of IES is of great significance to realize multi-energy complementarity, energy mutual benefit and reduce IES operating cost.

2 Coordination Scheduling Model Considering Multi-agent Game P2P energy trading emerged as a new type of transaction in integrated energy. Its concept is that energy is directly traded through a point-to-point approach, thereby increasing the flexibility, and realizing the resource sharing of operators. On the premise of not reverse transmission, with the increasing of distributed power supply, integrated energy operators equipped with distributed power generation can rely on renewable energy in their own regions to generate power, and in the case of meet their demand can be surplus electricity energy through the P2P direct deal to sell to other comprehensive energy operator. At this time, the transaction price of the operator will be lower than that purchased from the power grid, so that while ensuring that electricity

P2P Optimization Strategy for Integrated Energy Operators

41

can always be transmitted to consumers, it can also increase the revenue of each operator (Fig. 1).

IES1

IES1

IES1

Fig. 1. Schematic diagram of P2P energy trading network between interconnected integrated energy.

2.1 The Constraint Energy Storage Model. The relationship between the charged state of the electric energy storage device and its charge and discharge power is as follows: SOC(t + 1) = (1 − σ )SOC(t) +

ηch Pch,i,t t Pdis,i,t t − ηess ηdis ηess

(1)

where, SOC(t) represents the state of charge at time t; σ is self-discharge coefficient; Pch,i,t and Pdis,i,t respectively represent the charge and discharge power at time t; ηch and ηdis respectively represent the charge and discharge efficiency; ηess indicates the rated capacity of energy storage. Add zero-one state variable to constrain the charging and discharging power of energy storage as shown below:  min ≤ P max Kess Pch,i,t ch,i,t ≤ Kess Pch,i,t (2) min max (1 − Kess )Pdis,i,t ≤ Pdis,i,t ≤ (1 − Kess )Pdis,i,t min where, Kess is the state variable; 0 represents discharge and 1 represents charging; Pch,i,t max min and Pch,i,t respectively represent the maximum and minimum charging power; Pdis,i,t max respectively represent the maximum and minimum discharging power. and Pdis,i,t The state of charge of energy storage also considers the upper and lower limit constraints, as follows

SOCmin ≤ SOC(t) ≤ SOCmax

(3)

where, SOCmin and SOCmax represent the minimum and maximum values of the state of charge. Combined Heat and Power Model. Combined heat and power (CHP) unit model mainly consists of gas turbine and heat recovery steam generator. The gas turbine is driven by burning natural gas to generate electricity, and the high-temperature gas discharged is

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recovered and converted into heat energy by waste heat boiler, which supplies energy for heat load through hot water pipeline. Its model is as follows:  Hchp,i,t = cchp Vchp,i,t (4) Pchp,i,t = ηchp Vchp,i,t  min max Pchp,i,t ≤ Pchp,i,t ≤ Pchp,i,t (5) min max Pchp,i,t ≤ Pchp,i,t ≤ Pchp,i,t where, Hchp,i,t and Pchp,i,t represent the heating power and generating power of CHP unit; Vchp,i,t represents the natural gas consumption power of CHP unit; cCHP and min and ηCHP respectively represent the energy conversion efficiency of CHP unit; Pchp,i,t max min Pchp,i,t respectively represent the minimum and maximum discharge power; Pchp,i,t max and Pchp,i,t respectively represent the minimum and maximum climbing power of CHP unit. Load Constraints. Flexible load is an important resource for demand response. This paper considers transferable electrical and thermal loads, and reduces electrical and thermal loads. The characteristic of shaving load is to reduce the load to a certain extent when the system allows it, thereby reducing the power consumption. The specific formula is as follows:  min max Pcut,i,t ≤ Pcut,i,t ≤ Pcut,i,t (6) min max Hcut,i,t ≤ Hcut,i,t ≤ Hcut,i,t min and P max are the critical power that can reduce the electrical In the formula, Pcut,i,t cut,i,t min and H max are the critical power that can reduce the heat load. load; Hcut,i,t cut,i,t The characteristic of transferable load is to ensure that the total amount of electricity and heat load remains unchanged before and after the dispatch, and can be transferred to each other at different time periods. The specific formula is as follows: ⎧ T ⎪ Pzhuan,i,t = 0 ⎪ ⎪ t=1 ⎪ ⎪ ⎪ e ⎨ −α load e ≤ Pzhuan,i,t ≤ α e load e i i,t i i,t (7) T ⎪ ⎪ H = 0 ⎪ zhuan,i,t ⎪ t=1 ⎪ ⎪ ⎩ h h −αih loadi,t ≤ Hzhuan,i,t ≤ αih loadi,t

where, −αie and αie are the proportions of transferable electrical load and thermal load; −αih and αih are the proportions of transferable electrical load and thermal load. Power Balance Constraints ⎧ Pchp,i,t + Pwind ,i,t + Ppv,i,t + Pdis,i,t − Pch,i,t ⎪ ⎪ ⎪ ⎪ J ⎨ e e e = Pzhuan,i,t + Pcut,i,t + loadi,t + qe j=1 ij,t ⎪ ⎪ J ⎪ ⎪ h h ⎩ Hchp,i,t = Hzhuan,i,t + Hcut,i,t + loadi,t + qij,t j=1

(8)

P2P Optimization Strategy for Integrated Energy Operators

43

Electricity Price Model. Electricity price is an important factor in determining the operating cost of the system. The three-stage time-of-use electricity price model is now used as follows: ⎧ ⎪ ⎨ bottom : 0.35CNY /kWh 0.75CNY /kWh (9) Ce_price = flat : ⎪ ⎩ peak : 1.25CNY /kWh where Ce_price represents the time-of-use electricity price. IES Operating Costs. This paper takes the total operating cost F of each integrated energy operator as the goal, and mainly considers energy purchase cost C1 , energy sales revenue C2 , load transfer cost C3 , load reduction cost C4 , transaction cost of each operator C5 , and Internet connection cost C6 . Then there are: min F = C1 + C2 + C3 + C4 + C5 + C6

(10)

Energy Purchase Cost C1 =

J T  

Ce_price Pbuy,j,t

(11)

t=1 j=1

where, Pbuy,j,t is the electricity purchased by each integrated energy operator; Ce_price is the electricity purchase price of each operator. Energy Sold Cost C2 =

T  J 

Ce_sell Psell,j,t

(12)

t=1 j=1

where, Psell,j,t is the electricity sales of each integrated energy operator; Ce_sell is the electricity sales price of each operator. Transfer Load Cost C3 =

J T  

e e h h (θj,t Lj,t + θj,t Lj,t )

(13)

t=1 j=1 e and θ h represent the transfer load coefficient; Le and Lh respectively where, θj,t j,t j,t j,t represent the transfer amount of transferred electrical load and heat load.

Cut Load Cost C4 =

J T  

e e h h (σj,t Yj,t + σj,t Yj,t )

(14)

t=1 j=1 e and σ h represent the load reduction coefficient; Y e and Y h respectively where, σj,t j,t j,t j,t represent the transfer amount of reduced electrical load and thermal load.

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Transaction Cost C5 =

T  J 

e e h h (pij,t qij,t + pij,t qij,t )

(15)

t=1 j=1 e and ph represent the electricity price and heat price traded by each operator; where, pij,t ij,t e and qh is the electricity and heat traded by each operator. qij,t ij,t

Internet Connection Cost C6 =

J T  

e e h h (∂ij,t qij,t + ∂ij,t qij,t )

(16)

t=1 j=1 e and ∂ h represent the conversion coefficient of the internet connection cost; where, ∂ij,t ij,t e h respectively represent the electricity and heat traded by each operator. qij,t and qij,t

3 The Nash Bargaining Model of Multi-agent Cooperative Operation 3.1 Nash Bargaining Model Integrated energy operators have the right to choose to trade energy with other operators. It is assumed that integrated energy operators can negotiate with other operators, and achieve the goal of further enhancing the interests of each operator by setting corresponding energy transaction volumes and transaction prices. Then the problem that each entity can maximize the income of all entities through the transaction of electric energy and heat energy can be regarded as a Nash bargaining model, and its mathematical expression is: ⎧  J

⎪ ⎨ max C ∗ − C j j (17) j=1 ⎪ ⎩ s.t. C ∗ ≥ C j j The solution of maximizing the product of the above formula is the equilibrium solution of the game problem, and the goal is to maximize the benefits of all cooperative entities. Cj∗ is the negotiation breakdown point, that is, the optimal operating cost without P2P mode. In the P2P model to obtain the benefit of the appreciation. Cj∗ − Cj is the improvement value of benefits obtained in P2P mode. 3.2 Problem Equivalent Conversion Since the above expression is a non-linear problem, the following will convert it into and decompose it into the benefit maximization sub-problem and the energy transaction payment sub-problem to achieve the sequential solution of the two sub-problems.

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45

According to the mean value inequality, when Eq. (17) achieves the maximum value, it should satisfy: ⎡

 ⎤J J

 ∗−C C j J

⎥  ⎢ j=1 j ⎢ ⎥ Cj∗ − Cj = ⎢ ⎥ ⎣ ⎦ J

(18)

j=1

Since the trading volume of integrated energy operators is negative to each other and the trading price is the same, the transaction costs can offset each other in the accumulation, that is C5 = 0, the objective function can be transformed into: ⎤J ⎡ J J  1 ⎣ ∗ Cj − Cj0 ⎦ max (19) J j=1

j=1

where, Cj0 is the optimal cost of cooperative energy transaction without considering, and the objective function is transformed into: min

J 

Cj0

(20)

j=1

Formula (20) is the operating cost minimization problem 1 of integrated energy operator transactions. Taking the logarithm of this formula, the product problem is transformed into a summation problem, and the sum of strictly convex functions is obtained. Through the optimal solution in sub-problem 1, the formula (20) is further transformed into: min −

J 

In(Cj∗ − Cj0 − C5 )

(21)

j=1

By formula (21), the optimal electricity price and heat price of the transaction among the comprehensive energy operators are solved.

4 Example Analysis In a certain area, there are three integrated energy operators with distributed power sources as operators A, B, and C. Among them, IES1 and IES3 contain distributed photovoltaics, and IES2 contains a large number of distributed wind turbines. Figures 2 and 3 give the forecast of load demand, wind power and photovoltaic power generation. The data in this article are taken from a comprehensive demonstration area in northern China. The output and operation cost of IES renewable energy under different dispatching modes are compared. Assume that the transaction price between the entities is 70% of the electricity purchase price, and the selling price is 50% of the purchase price [11]. We use YALMIP to build the mathematical model of IES, and use the CPLEX solver in MATLAB (R2016b) to complete the solution. The division of electricity prices in different periods is shown in Table 1.

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K. Dong and Y. Wang Table 1. Time division.

Time category

Specific division

Peak time

09:00 ~ 12:00, 18:00 ~ 23:00

Normal time

13:00 ~ 17:00, 24:00

Valley time

01:00 ~ 08:00

Fig. 2. Electric/heat load prediction curve of main body A, B and C.

Fig. 3. Maximum output prediction curve of renewable energy.

Without considering the P2P model, the three integrated energy operators can only trade energy through their superiors to meet their own requirements. As can be seen from Fig. 4, in P2P mode, the surplus electricity can be sold to other operators during the day, and at night because the distributed photovoltaic of operator B cannot provide power, electricity can be purchased from operators A and C. At the same time, operator B also has similar purchases and sales of electricity. Operator C has abundant energy, so operator C can sell its surplus to other operators to obtain higher profits. Also in the heat transaction in Fig. 4, effective treatment and resource utilization have been realized.

P2P Optimization Strategy for Integrated Energy Operators

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Fig. 4. Electricity/heat energy transactions of various operators in the P2P mode.

As shown in Table 2, compared with the operating costs without mutual transactions, the costs of the operators through the point-to-point direct transaction method have been effectively reduced. Compared with the direct transaction of the superior, the total operating costs of service providers A, B and C respectively decreased by 2579.93 CNY, 2492.31 CNY and 1222.36 CNY. Table 2. Comparison of operation results before and after cooperative bargaining. Type

Operator A

Operator B

Operator C

Consider mutual transactions/CNY

17644.37

19111.56

7935.12

Mutual transaction not considered/CNY

20224.30

21601.87

9157.48

Fig. 5. Operator A optimal electricity/heat load in P2P mode.

The running results in P2P mode are shown in Fig. 5. The results show that during peak energy consumption hours, operator A’s electricity load has certain wind power, load reduction, and transferable load relief. In addition, since the cost of purchasing

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electricity through other operators is lower than directly purchasing electricity from the upper grid, it is not enough. Part of it will be borne by other operators. In the low peak period of energy consumption, operators include distributed power generation to meet their own needs, and at the same time they can sell excess electricity load to obtain their own profits. In addition, the optimal electricity and heat loads of operators B and C are as shown in Figs. 6 and 7.

Fig. 6. Operator B optimal electricity/heat load in P2P mode.

Fig. 7. Operator C optimal electricity/heat load in P2P mode.

As shown in Fig. 8 is the electricity and thermal energy transaction prices specified by each operator through bargaining, and the prices of each operator’s transaction are lower than the market price. Therefore, operators can reduce the cost of purchasing electricity and heat through bargaining transactions.

P2P Optimization Strategy for Integrated Energy Operators

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Fig. 8. Electricity/thermal energy transaction price of each operator under P2P mode.

5 Conclusion This chapter mainly expounds the design of P2P energy transaction mechanism among multiple integrated energy operators, and converts it into two easy-to-solve sub-problems of benefit maximization and electric energy transaction price. Under the P2P model, all operators can reduce operating costs through negotiation and cooperation. The lower the price of each operator’s mutual transaction, the more obvious the transaction effect through cooperation, and each operator achieves the best benefits. Each operator can increase its own revenue, and at the same time can alleviate the pressure of superiors, so as to gather into a sustainable new integrated energy system. The simulation results further verified the energy efficiency and economic benefits compared to the non-P2P mode, indicating that the application of P2P energy trading is effective and feasible. Acknowledgements. This research was financially supported by the National Key Research and Development Program of China: Sino-Malta Fund 2019 “Research and Demonstration of Realtime Accurate Monitoring System for Early-stage Fish in Recirculating Aquaculture System” (AquaDetector, Grant No. 2019YFE0103700), Major Science and Technology Innovation Fund 2019 of Shandong Province (Grant No. 2019JZZY010703), Overseas High-level Youth Talents Program (China Agricultural University, China, Grant No. 62339001), National Innovation Center for Digital Fishery, and Beijing Engineering and Technology Research Center for Internet of Things in Agriculture. The authors also appreciate constructive and valuable comments provided by reviewers.

References 1. Yu, B., Sun, Y.B., Xiang, T.C.: Planning design method of integrated energy system. Electr. Power Constr. 37(02), 78–84 (2016) 2. Yu, X.D., Xu, X.D., Chen, S.Y.: A brief review to integrated energy system and energy internet. Trans. China Electrotech. Soc. 31(01), 1–13 (2016). https://doi.org/10.19595/j.cnki. 1000-6753.tces.2016.01.002 3. Jia, H.J., Mu, Y.F., Yu, X.D.: Thought about the integrated energy system in China. Electr. Power Constr. 36(01), 16–25 (2015)

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4. Li, P., Yang, Y.L., Huang, Y.H.: Wind power integration in provincial power grid under electricity and heating load control. J. Xi’an Jiaotong Univ. 48(02), 69–73+117 (2014) 5. Sun, H.B., Guo, Q.L., Wei, Z.L: Energy strategy and energy internet. J. Glob. Energy Interconnect. 18(06), 7–8 (2020) 6. Liu, N., Zhao, J., Wang, J.: A trading model of PV microgrid cluster based on cooperative game theory. J. Trans. China Electrotech. Soc. 33(08), 1903–2191 (2018) 7. Chen, J., Liu, Y.T., Zhang, W.: Optimal sizing analysis of multilevel micro grids in distribution network based on game theory. J. Autom. Electr. Power Syst. 45–52 (2016) 8. Chen, H.Y., Huang, S.J., Fan, Z.H.: Demand response of multi-microgrid based on game theory. J. Southern Power Syst. Technol. 11(02), 34–40 (2017). https://doi.org/10.13648/j. cnki.issn1674-0629.2017.02.006(2017) 9. Zhao, M., Shen, C., Liu, F.: A game-theoretic approach to analyzing power trading possibilities in multi-micro grids. J. Proc. CSEE 35(04), 848–857 (2015) 10. Cheng, S., Shang, D.D., Wei, Z.B.: Hierarchical and distributed coordination and optimization of micro grid with CSS IS based on Nash bargaining game. Electr. Mach. Control 26(05), 86–95 (2022). https://doi.org/10.15938/j.emc.2022.05.010(2022) 11. Liu, N., Cheng, M., Yu, X.: Energy-sharing provider for PV prosumer clusters: a hybrid approach using stochastic programming and Stackelberg game. IEEE Trans. Ind. Electron. 65(8), 6740–6750 (2018)

Three Phase O-Z-Source Inverter Wei Luo1(B) , Xinghui Chen1 , Zhongzheng Zhou2 , and Kun Xia1 1 Department of Electrical Engineering, University of Shanghai for Science and Technology,

Shanghai, China {luowei,xiakun}@usst.edu.cn, [email protected] 2 Department of Electrical Engineering, Northwestern Polytechnical University, Xi’an, China [email protected]

Abstract. In this article, a novel three phase O-Z-source inverter (O-ZSI) with buck and boost capabilities is proposed. Compared with classic Z-source inverters (ZSIs), the O-ZSI utilizes fewer circuit elements through magnetic coupling, thus allowing considerably reduced volume and weight. Detailed modeling of steadystate, transient-state operations are performed to facilitate the O-ZSI design. In addition, a comparison with other typical ZSIs is included and shows that the proposed O-ZSI can considerably decrease the capacitor voltage stress as well as the starting inrush current. Moreover, a laboratory prototype of the O-ZSI was built, and its effectiveness was validated by the experimental results. Keywords: O-Z-source inverter · Z-source · T-Z-source · Circuit modeling · Small signal analysis

1 Introduction The voltage-source inverters (VSIs) can provide only a buck-type power conversion rather than a buck-boost conversion, which restricts their use in applications requiring a wide input or output voltage range [1]. Additionally, the necessary dead time introduced in the modulation of VSIs to avoid short-through failures leads to increased harmonics and distortion in the output voltage [2]. To address these problems, different solutions are proposed [3–5]. Among them, the Z-source inverter obtained by introducing an impedance network can solve the above two problems and has received extensive attention [6]. Two inductors and two capacitors of traditional Z-source inverter topology are cross connected to provide the inverter with boost capability, thus allowing the voltage of the power source to operate within a larger range. At the same time, the current-limiting capability of the inductors enables the inverter to work even when the upper and lower arms form a short circuit, which improves the robustness of the system and avoids the distortion problem associated with dead time [7–10]. However, a traditional Z-source inverter offers a relatively low boost capability, and the boost ratio depends heavily on the shoot-through duty ratio, which will inevitably affect the quality of the output waveforms. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 51–56, 2023. https://doi.org/10.1007/978-981-99-4334-0_6

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An inverter topology based on O-shaped impedance network (O-Z source) is proposed. Firstly, the topological structure of O-Z source inverter is analyzed, and the state space model and dynamic model of O-Z source inverter are established. In addition, the characteristics of classical ZSI, classical transformer ZSI (T-ZSI and -ZSI) and new O-ZSI are compared. Finally, an experimental prototype is constructed to verify the validity of the topology.

2 Analysis and Modeling of O-Z-Source Inverter The topology of a three phase O-ZSI is shown in Fig. 1, where the O-Z-source impedance network by diode D, capacitor C and a pair of coupled inductance coils. The turns ratio of the primary and secondary windings of the coupling coil is γ = W 1 /W 2 .

Fig. 1. O-Z-source inverter topology.

Figure 2 shows the equivalent circuit of O-ZSI in these two working states; vW 1 and vW 2 are the primary side voltage and secondary side voltage of the transformer respectively; the voltage and current of each component are in the reference direction. The coupled coil is equivalent to a magnetizing inductance L m connected in parallel with an ideal transformer. To simplify the analysis, L m is connected in parallel with the secondary coil, and the leakage inductance is ignored. At this time its inductance is equal to the self-inductance of the secondary coil, and the ideal transformer turns ratio is γ . When the upper and lower power switches of the same bridge arm of the inverter are turned on at the same time, the O-ZSI works in a through state, its load port is shortcircuited, and the output voltage is zero. At the same time, the coupling coil is subjected to a positive voltage, and the voltage difference superimposed on the capacitor voltage will apply a negative voltage to the diode D to turn it off. The power supply charges the capacitor C and the inductor L m , storing energy to increase the bus voltage. When the O-ZSI works in the non-transmitting state, that is, the zero vector state (only the upper switch of the inverter bridge is short-circuited or only the lower switch is short-circuited) or the non-zero vector (effective vector) state, the magnetizing inductance L m will bear the reverse voltage Reset, the coupling coil will also withstand the reverse voltage. At this time, the O-Z source network is closed due to the conduction of the diode, and the bus voltage is also boosted due to the superposition of the power supply voltage and the primary coil voltage. The following sections discuss the modeling and analysis of an O-ZSI with its equivalent circuit.

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Fig. 2. Equivalent circuit of the O-Z-source inverter during the (a) shoot-through state and (b) non-shoot-through state.

2.1 Steady-State Model Shoot-through state: By applying Kirchhoff’s voltage law, the equivalent circuit shown in Fig. 2(a), the circuit equation can be obtained:   dim        Lm 0 0 −1 im 1 0 vin dt = + (1) dvC vC io 0 C −1 0 00 dt where im is the magnetizing current of the magnetizing inductor of the coupling coil, and io is the total output current of the inverter in the non-penetrating state. Non-shoot-through state: In this state, the circuit works normally, and L 1 and L 2 are turned on, which satisfies the ideal transformer equation: iW W1 vW1 =− 2 = =γ vW2 iW1 W2 As shown in Fig. 2(b), the circuit equation can be described as:  (1 − γ )Lm didtm = vC (1 − γ )C dvdtC = −im + γ io The matrix form of (2) is as follows:        dim   1 0 1−γ 0 0 vin Lm 0 i m dt = −1 + γ dvC 0 0 v io 0 C C 1−γ 1−γ dt

(2)

(3)

(4)

If the PWM switching period is T s and the shoot-through time is T 0 , the shootthrough duty ratio is d 0 = T 0 /T s . According to (1) and (4), and using the state space averaging method, the period average model of the O-Z-source circuit can be obtained:       dim  Lm 0 im vin dt = A + B (5) dvC v io 0 C C dt where the left side of the equation represents the average voltage across the magnetizing inductance L m and the average current flowing through capacitor C. In the steady state, both expressions are zero, so the model of the O-ZSI in the steady state is:         0 0 D0 + 1−D D0 0 Im Vin 0 1−γ + = (6) (1−D0 )γ 0 0 V i 0 −D0 − 1−D 0 C o 1−γ 1−γ

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where V in , V C , I m , and D0 represent the input voltage, capacitor voltage, magnetizing current, and shoot-through duty ratio under steady state, respectively, and io represents the output current in the non-shoot-through state. According to (6), the expressions of the capacitor voltage and magnetizing inductance current in the steady state can be expressed as  0 )γ Im = (1−D 1−γ D0 io (7) D0 (γ −1) VC = 1−γ D0 vin

3 Experiment Results 3.1 Experimental Analysis To verify the operating effectiveness of an O-ZSI, the experimental prototype shown in Fig. 3 was built. The control circuit adopts dSPACE platform with hardware in the loop. To avoid electromagnetic interference, the dSPACE output control signal is transmitted to the drive circuit via an optical fiber, and the IGBT power switches are controlled via drive circuits. The experimental results are shown in Fig. 4. O-ZSource

Inverter

RL Load Diode Transformer Drive circuit

Fig. 3. Experimental platform of O-Z-source inverter.

Figure 4(a) shows the input voltage, the DC-link voltage, unfiltered AC voltage and the output current. Substituting these values vi = 150/(1 − 2 × 0.2) = 250 V. This is consistent with the DC-link voltage measured by an oscilloscope. When the output peak AC voltage of each phase is 83 V, the output peak AC current is 4.15 A. Figure 4(b) shows the O-ZSI experimental waveforms under boost mode. The O-ZSI DC-link will have a higher voltage peak when the shoot-through state and the non-shoot-through state are switched, which is consistent with observations in other magnetically coupled types of ZSIs. Figure 4(b) shows the relationship between the currents on both sides of the winding, which is consistent with the theoretical analysis of O-ZSI steady-state model.

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Fig. 4. (a) O-ZSI experiment waveforms. (b) O-ZSI under boost mode.

4 Conclusion This paper presents a novel three-phase O-Z source inverter. It is proved by theoretical analysis and experiments that the proposed O-ZSI has the following characteristics 1) By allowing adjustment of the transformer turns ratio, the new topology has a stronger boost capability and is suitable for applications requiring a high output voltage. 2) The new topology can effectively reduce voltage stress on the capacitor and suppress the inrush current during startup. Finally, This new inverter can be applied to photovoltaic and fuel cell systems, which will be further discussed in future work.

References 1. Tang, Y., Xie, S., Zhang, C., Xu, Z.: Improved Z-source inverter with reduced Z-source capacitor voltage stress and soft-start capability. IEEE Trans. Power Electron. 24(2), 409–415 (2009) 2. Pan, L.: L-Z-source inverter. IEEE Trans. Power Electron. 29(12), 6534–6543 (2014) 3. Zhu, M., Yu, K., Luo, F.L.: Switched inductor Z-source inverter. IEEE Trans. Power Electron. 25(8), 2150–2158 (2010) 4. Kikuchi, J., Lipo, T.A.: Three phase PWM boost-buck rectifiers with power regenerating capability. IEEE Trans. Ind. Appl. 38(5), 1361–1369 (2002) 5. Moschopoulos, G., Zheng, Y.: Buck-boost type AC-DC single-stage converters. In: Proceedings of IEEE International Symposium on Industrial Electronics, July 2006, pp. 1123–1128 6. Peng, F.Z.: Z-source inverter. IEEE Trans. Ind. Appl. 39(2), 504–510 (2003) 7. Loh, P.C., Vilathgamuwa, D.M., Lai, Y.S., Chua, G.T., Li, Y.W.: Pulse-width modulation of Z-source inverters. IEEE Trans. Power Electron. 20(6), 1346–1355 (2005) 8. Liu, J., Hu, J., Xu, L.: Dynamic modeling and analysis of Z-source converter—derivation of AC small signal model and design-oriented analysis. IEEE Trans. Power Electron. 22(5), 1786–1796 (2007)

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9. Sen, G., Elbuluk, M.E.: Voltage and current-programmed modes in control of the Z-source converter. IEEE Trans. Ind. Appl. 46(2), 680–686 (2010) 10. Rajakaruna, S., Jayawickrama, L.: Steady-state analysis and designing impedance network of Z-source inverters. IEEE Trans. Ind. Electron. 57(7), 2483–2491 (2010)

Recognition of Tunneling Boring Machine Operating Status Based on the Time Series Analysis Yong Pang, Yitang Wang, Shuai Zhang, Suhang Wang, Xueguan Song(B) , and Wei Sun Dalian University of Technology, Dalian, China [email protected]

Abstract. The automation and intelligence of tunnel boring machine (TBM) are of great significance to ensure the construction personnel safe and the construction proceeding normally. Establishing an accurate operating state recognition model is an important part of TBM automation and intelligence. For this issue, the method of TBM time series segmentation, time series feature extraction and selection, and establishment of status recognition classifier is adopted. Firstly, the key attributes of the whole time series of TBM are segmented by the time series segmentation algorithm, so that each segment can represent an independent status. Then feature extraction and selection methods are used to extract features from time series segments, and feature selection is carried out based on the correlation between features and classification objectives. Finally, the decision tree model is established with the selected feature and corresponding objectives. The experimental results show that the accuracy, precision, and recall of the TBM status classifier established by this method is more than 95%, which can accurately identify the operating status of the TBM. Keywords: Status recognition · Tunnel boring machine · Time series segmentation · Feature extraction and selection · Decision tree

1 Introduction With the progress of science and technology, tunneling boring machine (TBM) gradually replaces the traditional tunneling method and is widely used in tunnel construction projects [1]. The automation and intelligence of TBM are very important to ensure the construction progress and the personal safety of construction personnel, which inevitably requires the introduction of a lot of data and many data mining models [2]. These models are often applied to the construction data of TBM in a single operating status in order to recognize the patterns from the operating data to predict and even optimize the important operating parameters of TBM. Before applying the intelligent model, the operating status usually needs to be identified from a complete TBM time series. This task is mainly divided into two processes. The first process is to segment the complete TBM time series into different segments © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 57–62, 2023. https://doi.org/10.1007/978-981-99-4334-0_7

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so that each of them can represent a single operating status of the TBM. The second part is to automatically recognize the specific operating status according to the different characteristics of the time series data segments. For the first process, the time series segmentation algorithm is often used to automatically segment the TBM time series. In recent years, the time series segmentation algorithm has been studied a lot [3, 4]. Given the segment of TBM with unknown operating status, its automatic identification is of great significance to the intelligence of tunnel construction and the big data analysis of TBM. Therefore, it is necessary to establish an effective status recognition model for the time series segments. This paper proposed a method to analyze TBM operating status with time series segmentation and status recognition, which are introduced in detail in the following sections.

2 Methodology 2.1 Time Series Segmentation Assuming TBM multivariate time series is T = { t i |1 < i < n}, where t i is a m dimension vector obtained in ith time point. The time series segmentation algorithm divides the time series into k consecutive segments, and each segment can be expressed as     (1) Tj aj , bj = t aj , t aj +1 , . . . , t bj (1 < j ≤ k) where aj and bj are the boundaries of the jth segment. The time series segmentation   ˆ and bˆ = , a ˆ , . . . , a ˆ algorithm is to find the optimal segmentation boundaries a = a ˆ 2 3 k   bˆ 1 , bˆ 2 , . . . , bˆ k−1 by constructing an objective function of time series segmentation and solving it by the optimization algorithm. This paper adopts the algorithm proposed in [5] to segment the time series of TBM.

Fig. 1. An example of time series segmentation of TBM data.

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In the process of tunnel construction, a lot of time series data is collected. The time series segmentation only requires the key attributes of TBM for the operating status recognition of TBM. Figure 1 shows an example of TBM time series segmentation with three key attributes of TBM: speed of cutter head (R) torque of cutter head (T) and propulsion force (F). The time series is segmented into five segments and four statuses by the algorithm in [5], which are shutdown status, start status, loading statues, and tunneling status, which are labeled as A, B, C, and D in Fig. 1. These four operating status of TBM are four classes that requires recognition. 2.2 Feature Extraction and Selection of Time Series The feature extraction and selection of time series segments in this paper are mainly based on FRESH method in [6]. The mapping relation of feature extraction of time series is Rnt → R where nt is the number of samples of the time series segment. More feature extraction methods refer to [7, 8]. After feature extraction, a large number of features need to be refined. Taking a binary classification problem as an example, if a feature X has different conditional probability density functions with respect to different classification objective y1 and y2 , this feature is said to be related to this classification objective. Feature X is related to the objective Y , if and only if ∃y1 , y2 : fX |Y =y1 = fX |Y =y2

(2)

Therefore, for any feature Xϕ , the hypothesis test of whether there is a correlation between Xϕ and Y can be set as   ϕ H0 = fX |Y =y1 = fX |Y =y2 , ϕ H1 = fX |Y =y1 = fX |Y =y2 ϕ

(3) ϕ

H0 means that the feature is not related to the Y while H1 means that the feature is related to the Y . Kolmogorov–Smirnov test method is used for continuous feature data [9], while Fisher’s test method is used for discontinuous feature data [10]. Based on these methods, q most related features are selected as the input of the classifier. 2.3 Recognition of TBM Operating Status Since the classification objective of TBM data has multiple categories and the features in classification models are expected to be analyzed, the decision tree model is adopted. Decision trees are typically constructed using top-down rules. Selecting the optimal feature is the key to the construction of a decision tree. The CART [11] model is used in the work. The purity of dataset D can be measured by the Gini value as Gini(D) = 1 −

|Y |

j=1 pj

(4)

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|Y | is the number of the categories of the data. pj is the probability of the data belonging to jth class. Under the condition that dataset D is partitioned by feature c, the Gini index is |c| i| (5) Gini(D, c) = i=1 |D |D| Gini(Di ) |c| is the number of the categories of D with respect to c, Di represents the ith subset of D. |Di | is the number of the samples of Di . In the feature selection of CART, the feature with the smallest Gini index is selected each time for partitioning by aˆ = argmina∈A Gini(D, a)

(6)

3 Experiments 3.1 Experiment Setting The real TBM operating time series is used in this work with three key attributes (R, T, and F), which is from a subway construction project in a city in China. The time series is segmented into four classes by the algorithm in [5]. Three evaluation metrics are used to test the performance of the classifier, which are accuracy, precision, and recall. The k-fold cross-validation is used in the feature date to make full use of the limited data. k different classifiers will be generated from the k group data by k-fold cross-validation. The mean result of different classifiers was taken as the result of one run. The final result is obtained based on 5 runs of the experiments. 3.2 Results and Analysis After the segmentation of the TBM time series, a total of 200 segments were obtained. Since there were four statuses, the sample size of each category is 50. Feature extraction is conducted for these 200 time series segments. On the one hand, in order to improve efficiency, the 9 most basic features of the TBM time series as shown in Table 1 are extracted for selection, which is named the simplified experiment. Because time series consists of three attributes, 27 features were extracted in the simplified experiment in total. On the other hand, in order to make full use of the potentially useful information in the time series, 787 features in the FRESH method were extracted from the TBM time series, and the total number of features with three attributes was 2361. This experiment was called the comprehensive experiment. The k is set to 10 in k-fold cross-validation and the significance level α is set to 0.01 in feature selection. Table 2 shows the number of the selected features in one experiment for simplified and comprehensive experiments. Through the mean value of 5 experiments, it is found that the number of the selected features in simplified experiments is about 10, indicating that several simple features of time series are still related to the classification objective. Since they are more intuitive and easier to explain, it is more convenient to analyze the TBM time series by these features. The number of features selected by the comprehensive experiment is about 400, which

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Table 1. Basic features of the TBM time series. No.

Feature

No.

Feature

No.

Feature

1

Maximum

4

Mean

7

Standard deviation

2

Minimum

5

Sum

8

Variance

3

Medium

6

Length

9

Root mean square

Table 2. The number of the selected features. The number of the selected features in one experiment 1 Simplified

2

12

3 8

4 9

12

5

6 9

11

7 12

8 13

9

Mean of 5 runs 10

9

12

10.7

Comprehensive 394 396 387 392 428 403 406 389 383 387 396.5

is much larger than that of the simplified experiment. This indicates a large number of features are related to the classification objective, which provides more choices for the construction of the appropriate classifier. The results of classification are shown in Table 3, where the results of accuracy, precision, and recall in both the simplified experiment and the comprehensive experiment are more than 0.95. This indicates the classifiers established by simple features and complex features can accurately identify the operating status of the time series segments and the method proposed in this paper is very effective. Table 3. The classification results by decision tree. Type of experiment

Class

Accuracy

Precision

Recall

Simplified

Class 1

–

0.976

0.993

Class 2

–

0.993

0.978

Class 3

–

0.967

0.951

Class 4

–

0.958

0.967

Mean result

0.972

0.974

0.972

Class 1

–

0.982

0.993

Class 2

–

0.984

0.974

Class 3

–

0.937

0.945

Comprehensive

Class 4

–

0.971

0.949

Mean result

0.970

0.969

0.965

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4 Conclusion This paper proposed an analysis method for the TBM operating status with the TBM time series. First, the TBM time series is segmented by an algorithm according to its operating status. Then, the feature data is extracted and selected from the time series segments. Finally, a classifier is built to recognize the operating status of the TBM. The experimental results show that the accuracy, precision, and recall of the classifier established by this method are above 0.95 in both simplified and comprehensive experiments, indicating the excellent capacity of the proposed algorithm to recognize the operating status of TBM. Acknowledgement. This research is supported by the National Key Research and Development Program of China (No. 2018YFB1702502) and Dalian Science and Technology Innovation Fund Project (2020JJ25CY009).

References 1. Sun, W., Shi, M., Zhang, C., Zhao, J., Song, X.: Dynamic load prediction of tunnel boring machine (TBM) based on heterogeneous in-situ data. Autom. Constr. 92, 23–34 (2018) 2. Pang, Y., Shi, M., Zhang, L., Song, X., Sun, W.: PR-FCM: a polynomial regression-based fuzzy C-means algorithm for attribute-associated data. Inf. Sci. 585, 209–231 (2022) 3. Lovri´c, M., Milanovi´c, M., Stamenkovi´c, M.: Algorithmic methods for segmentation of time series: an overview. J. Contemp. Econ. Bus. Issues 1(1), 31–53 (2014) 4. Jamali, S., Jönsson, P., Eklundh, L., Ardö, J., Seaquist, J.: Detecting changes in vegetation trends using time series segmentation. Remote Sens. Environ. 156, 182–195 (2015) 5. Pang, Y., Shi, M., Zhang, L., Sun, W., Song, X.: A multivariate time series segmentation algorithm for analyzing the operating statuses of tunnel boring machines. Knowl.-Based Syst. 242, 108362 (2022) 6. Christ, M., Kempa-Liehr, A.W., Feindt, M.: Distributed and parallel time series feature extraction for industrial big data applications. arXiv preprint arXiv:1610.07717 (2016) 7. Fulcher, B.D., Jones, N.S.: Highly comparative feature-based time-series classification. IEEE Trans. Knowl. Data Eng. 26(12), 3026–3037 (2014) 8. Nun, I., Protopapas, P., Sim, B., Zhu, M., Dave, R., Castro, N., Pichara, K.: Fats: feature analysis for time series. arXiv preprint arXiv:1506.00010 (2015) 9. Massey, F.J., Jr.: The Kolmogorov–Smirnov test for goodness of fit. J. Am. Stat. Assoc. 46(253), 68–78 (1951) 10. Fisher, R.A.: On the interpretation of χ2 from contingency tables, and the calculation of P. J. R. Stat. Soc. 85(1), 87–94 (1922) 11. Loh, W.Y.: Classification and regression trees. Wiley Interdiscip. Rev. Data Min. Knowl. Discov. 1(1), 14–23 (2011)

Flow Pulsation Optimization of Peristaltic Pump Based on Surrogate Model Fu wen Liu1 , Qing ye Li1 , Shuo Wang1 , Yanfeng Zhang2 , and Xueguan Song1(B) 1 Dalian University of Technology, Dalian 116024, China

[email protected] 2 Hebei Province Fluid Precision Transmission Technology Innovation Center, Baoding Lead

Fluid Technology Co., Ltd., Baoding 071000, China

Abstract. Peristaltic pump is widely used in pharmaceutical, medical and other industries because of its advantages of no pollution and high transmission accuracy. The fluid medium is conveyed by the rollers alternately squeezing and relaxing the hose, so when the rollers away from the hose as the rebound of the hose will cause the backflow of liquid, thus forming the flow pulsation. The more serious the flow pulsation, the more difficult it is to control the output flow, the peristaltic pump flow pulsation reduction is of great importance for the improvement of its transmission accuracy. For exploration and optimization of mechanism design, a response surface methodology (RSM) model based mechanism optimization method is proposed. Two peristaltic pump parameters were chosen as the primary design variables for the surrogate model, with the objective of minimizing the instantaneous flow ratio of the peristaltic pump flow curve. With the two design variables, Optimal Latin hypercube sampling (OLHS) based design of experiments (DoE) were carried out, with which different Fluid-Structure-Interaction (FSI) numerical model were developed to calculate the instantaneous flow rate ratio the Peristaltic pump flow curve, thereby the RSM model was constructed to establish the relationship between the design variables and the flow pulsation performance. Based on the RSM model, Peristaltic pump design optimization was performed with the help of genetic algorithm (GA). Finally, a peristaltic pump design scheme that may effectively lessen the flow pulsation was obtained. To verify the results, another simulation was performed and compared the results with those generated by the optimization, achieving good agreement and demonstrating the feasibility of an optimal design approach. Keywords: Peristaltic pump · RSM surrogate model · Design optimization · Flow pulsation

1 Introduction The peristaltic pump, also known as the constant flow pump, is a modern industrial pump that has no pollution, high transmission accuracy, cleaning, low shear, and other significant advantages. It is frequently used to transport media that is viscous, highly corrosive, requires a high degree of purity, and contains certain granular materials [1–3]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 63–72, 2023. https://doi.org/10.1007/978-981-99-4334-0_8

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Drug coating granulation and pharmaceutical liquid dispensing are inseparable from the help of peristaltic pumps, peristaltic pumps in blood analysis, stool analysis, hemodialysis, surgical ablation, liposuction, etc. also play a significant role, its to a certain extent to promote the progress of the pharmaceutical and medical industries. There are many types of peristaltic pumps, with the most common is the three-roller type peristaltic pump, through the three rollers alternately squeeze and release the hose to pump the medium. An obvious disadvantage of peristaltic pumps, when the roller release hose, the bouncing of the hose causes the backflow of the liquid, thus forming the flow pulsation. The more serious the flow pulsation, the more difficult to control the accuracy of the output flow [4, 5]. The instantaneous flow ratio, i.e., the percentage of the maximum instantaneous flow rate exceeding the average flow rate, is one of the indicators to evaluate the degree of flow pulsation. It is important to study how to reduce the flow pulsation of peristaltic pump and improve the transmission accuracy. To properly reduce the instantaneous flow ratio, lower the flow pulsation, probe the effect of vital parameters, numerous studies have been conducted in recent years. Various methods have been used in these studies, such as analytical, numerical and experimental methods, where the numerical method of which has proven to be a more suitable approach [6–8]. Although the method of numerical simulation has the advantages of economy, convenience and accuracy, it requires a lot of time for model reconstruction and calculation for each simulation. For the purpose of improving the efficiency of computing and saving computing resources, a more efficient method is needed to develop a model for the relationship between peristaltic pump design variables and flow pulsations. The surrogate model which is a method for quickly and efficiently construct input and output relationships for complex systems using limited sample data, and is also a common optimization method in engineering problems. The accuracy of different surrogate models was compared, and the response surface model has the highest accuracy, therefore, it was used in this work. A special study was conducted on the flow pulsation characteristics of a typical threeroller type peristaltic pump in order to investigate the pulsation mechanism and design optimization in the paper. The remaining chapters of this paper contains: Sect. 2 is an introduction to the peristaltic pump; From Sect. 3 to Sect. 5, the FSI model, experimental design, surrogate model and optimization design are then presented respectively. Finally, a summary of the findings in present study is presented in Sect. 6.

2 Peristaltic Pump

Table 1. Value ranges of key peristaltic pump parameters Parameter

Definition

Value range (mm)

A

Diameter of the working circle of the block

47.90–82.50

B

Inner diameter of rubber hose

3.00–7.30

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Figure 1 shows the structure of a peristaltic pump with three rollers. It is composed of fundamental functional components including the pump heads, motor case, rubber hose, pressure block, trigger bar, rollers and hose clamps. The most important functional components including the rubber hose, the pressure block, the rollers, and the pressure block is located above the rubber hose during operation, and the rollers cooperate to squeeze the hose, and the three rollers rotate to alternately squeeze and release the rubber hose to transport the medium, and the simplified model of the peristaltic pump is shown in Fig. 2. For the optimal design of the peristaltic pump, two main parameters of the peristaltic pump are defined, respectively, the diameter of the working circle of the pressure block and the inner diameter of the rubber hose. The definition of the two main parameters and the specific range of values are shown in Table 1.

Fig. 1. Schematic diagram of typical peristaltic pump.

Fig. 2. Model simplification of peristaltic pumps.

3 Digital Model The FSI numerical model is established in this paper to solve the flow-solid interaction problem to obtain the basic data for the analysis of flow pulsation and the surrogate model, as shown in Fig. 2.

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Fig. 3. FSI model for peristaltic pump calculation.

The model of fluid-solid interaction mainly consists of rollers, rubber hose, block, and fluid domain, and to improve the efficiency, the block and rollers are replaced by rigid facets, a 1/2 model is developed instead of a full model, as demonstrated in Fig. 3. The ANSYS WORKBENCH, a commercial software, was used to perform numerical simulations [9, 10]. As illustrated in Fig. 4, Speed of the roller is set to 1 RPM, the movement of the rollers is divided into two steps. First, the rollers move up to the specified position, then rotate around the center at a uniform speed. Fluid domain inlet and outlet are set to a pressure of 0 MPa, laminar flow model is selected, dynamic mesh technology with spring smoothing and mesh reconstruction is used, the timestep of 0.1 s. Reconstruction and calculation of peristaltic pump models with different parameters can be carried out using the modeling method described above, providing data for the subsequent construction of the surrogate model and optimization of the design.

4 Surrogate Modeling 4.1 Experiment Design As mentioned before, there were 2 main variables were defined in this paper for flow pulsation study of peristaltic pumps. With the aim of obtaining samples data for the surrogate model, 20 train points and 9 test points were generated using the optimal Latin hypercube sampling (OLHS) method [11]. The 2-D spatial distribution of the train and test points is shown in Fig. 5. The different peristaltic pump models are reconstructed with the generated train/test points, which are numerically simulated to obtain the flow curve of the peristaltic pump and then calculate the instantaneous flow percentage. Results of all simulations combined with DoE data that will be applied to construct alternative models and validate the accuracy of the models. 4.2 Surrogate Model Comparison The accuracy of the surrogate model generated is higher, the more accurate its predictions will be. The simulation results of the simple points were used to construct three

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Fig. 4. FSI model for peristaltic pump setup.

Fig. 5. Design variables of the peristaltic pump.

mathematical models that can express design variables in relation to the response of the peristaltic pump flow pulsation characteristics, i.e., response surface methodology (RSM) model, radial basis function (RBF) model, and orthogonal polynomial (OPM) model, and to quantify the accuracy of each model using the error index R2 (as shown in Eq. 1). As illustrated in Fig. 6, the RSM surrogate mode has the highest accuracy with error indexes of R2 = 0.89 (the closer the value of R2 is to 1, the higher the accuracy of the model), as can be seen by comparing, and indicates that the RSM surrogate model has good reproducibility. So, the RSM surrogate model was selected for the optimal design of the peristaltic pump.

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Error index R2 : n 

R2 = 1 −

i=1 n  i=1

(yi − yˆ i )2 (1) (yi − yi )2

where the n is the number of test points, the yi (x) are the true values obtained by numerical calculation, the yˆ i (x) are the predictions produced by surrogate model, the yi (x) are the average values.

Fig. 6. Accuracy comparison of surrogate models.

4.3 Basic Theory of RSM Surrogate Model Response surface analysis, a method that fits the design space by means of a multiple quadratic regression equation. The response surface method can approximate the function relationship more precisely in the local range by fewer experiments and show it with simple algebraic expressions, simple calculation, bringing great convenience to design optimization. A better visualization of the generated RSM model can be obtained from Fig. 7. As known above, the error index obtained from the instantaneous flow percentage surrogate model validation is R2 = 0.89, indicating that the RSM surrogate model has good reproducibility. Other than that, a more direct validation was performed, comparing the results obtained from the RSM surrogate model and the validation simulation as show in Fig. 8. It can be seen a good agreement between the prediction results of the surrogate model and the simulation analysis results, and it confirms the ability of surrogate model of RSM in predicting the degree of peristaltic pump flow pulsation.

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Fig. 7. Influence of key parameters on the flow pulsation characteristics of peristaltic pumps.

Fig. 8. Verification of the accuracy of the agent model based on test points.

5 Design Optimization 5.1 Optimization Equation The flow pulsation degree of the peristaltic pump can be expressed as the percentage of the instantaneous flow rate of the flow curve. Peristaltic pump flow pulsation is smaller, the peristaltic pump outlet flow is easier to control, and transmission accuracy is higher, Therefore, the peristaltic pump flow curve is expected to have the smallest instantaneous flow percentage.

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Based on the above analysis, a relatively straightforward optimization scheme is proposed in this paper, namely, finding an optimal combination of design variables to minimize the instantaneous flow percentage, as shown in Eq. 2. ⎧ min IFPFC ⎪ ⎨  (2) 47.90 ≤ A ≤ 82.50 ⎪ ⎩ s.t. 3.00 ≤ B ≤ 7.30 where the IFPFC is the instantaneous flow rate percentage of the flow curve. 5.2 Optimization Algorithm and Results The Genetic algorithm (GA) is a global optimization stochastic search algorithm, searching from the population, with potential parallelism, to facilitate distributed computation and speed up the solution. The Genetic Algorithm uses a probabilistic mechanism for iteration, featuring stochasticity and avoiding local optimal [12–14]. Therefore, it was used a genetic algorithm (GA) to obtain the best design solution for the peristaltic pump. An optimum peristaltic pump design (A and B equal to 78.00 mm, 5.20 mm, respectively) was obtained after convergence of the optimization solution, where the instantaneous flow percentage is 50%. The instantaneous flow percentage of the original structure peristaltic pump is 103%, and the instantaneous flow percentage of the new structure peristaltic pump is significantly lower than the original structure peristaltic pump, the flow pulsation degree has been greatly reduced. 5.3 Validation of Results Aiming to verify the accuracy of the results of optimization, an additional FSI simulation was performed by bringing the optimal design parameters found by the genetic algorithm into the finite element model. The calculation results are shown in Fig. 9, the peristaltic pump’s flow rate curve for one operating cycle before and after optimization was demonstrated, and the corresponding instantaneous flow percentages can be calculated. The difference between the simulation results and the optimization results is found to be 4% (for Instantaneous flow rate percentage), showing that the design optimization work carried out in this paper for the RSM agent model, genetic algorithm and numerical peristaltic pump model has good capability. In Fig. 9, fluctuations in the optimized peristaltic pump curve can be clearly seen to be significantly lower and the flow rate more stable.

6 Conclusions From the perspective of reducing the flow pulsation and improving the transmission accuracy, the flow pulsation design optimization research was carried out for peristaltic pumps widely used in medical and pharmaceutical industries. For the purpose of establishing the relationship between the design variables and the degree of peristaltic pump flow pulsation, the DOE of OLHS, the numerical model of FSI and the modeling method

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Fig. 9. Comparison of flow curves before and after optimization.

of RSM agent were used successively. The Genetic algorithm is used for design optimization to obtain the optimal peristaltic pump design scheme. It is concluded that the analysis and conclusions of this study are summarized as follows. (i) An FSI model was built to solve the fluid-solid interaction of the peristaltic pumps, so that the peristaltic pump outlet flow curve under actual operating conditions was obtained, and thus the instantaneous flow percentage that characterizes the degree of flow pulsation can be obtained. (ii) Based on the DOE and FSI simulation results, the RSM, OPM and RBF surrogate models were developed, and the RSM surrogate model with the highest accuracy was selected by comparing the error index R2 of the three models. The error index for the instantaneous flow percentage is equal to 0.89, indicating that the RSM surrogate model has good ability to predict the flow pulsation characteristics of peristaltic pumps. (iii) Through the optimization of genetic algorithm, the optimal peristaltic pump design scheme (namely, parameters of A, B equal to 78.00 mm, 5.20 mm, respectively) was obtained, which can significantly reduce the instantaneous flow percentage and reduce the degree of flow pulsation.

References 1. Faria, M., Liu, Y., Leonard, E.F.: Particle spallation in a microfluidic blood processing device: the problem of using peristaltic pumps and silicon-based microfilters. Int. J. Artif. Organs 589–593 (2017) 2. Deiringer, N., Friess, W.: Proteins on the rack: mechanistic studies on protein particle formation during peristaltic pumping. J. Pharm. Sci. 111(5), 1370–1378 (2022) 3. Krautbauer, K., Sparrow, E., Gorman, J.: A structural and fluid-flow model for mechanically driven peristaltic pumping with application to therapeutic drug delivery. J. Fluids Eng. 139(11) (2017)

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4. Wang, B.C., Wang, Y.L.: The research on flow pulsation characteristics of axial piston pump. In: Seventh International Conference on Electronics and Information Engineering, vol. 10322. SPIE (2017) 5. Yang, F., et al.: Analysis of timing effect on flow field and pulsation in vertical axial flow pump. J. Mar. Sci. Eng. 9(12), 1429 (2021) 6. Marinaro, G., Frosina, E., Senatore, A.: A numerical analysis of an innovative flow ripple reduction method for external gear pumps. Energies 14(2), 471 (2021) 7. McIntyre, M.P., van Schoor, G., Uren, K.R., Kloppers, C.P.: Modelling the pulsatile flow rate and pressure response of a roller-type peristaltic pump. Sens. Actuators A Phys. 325, 112708 (2021) 8. Zahoor, R., Bajt, S., Šarler, B.: A numerical investigation of micro-jet characteristics in different pressure environments. Int. J. Hydromechatron. 4(4), 368–383 (2021) 9. He, F., Hua, L., Guo, T.T.: Fluid–structure interaction analysis of hemodynamics in different degrees of stenoses considering microcirculation function. Adv. Mech. Eng. 13(1), 1687814021989012 (2021) 10. Kitson, R.C., Cesnik, C.E.: Fluid–structure–jet interaction modeling and simulation of highspeed vehicles. J. Spacecr. Rocket. 55(1), 190–201 (2018) 11. Mohammadi Amin, M., Kiani, A.: Multi-disciplinary analysis of a strip stabilizer using bodyfluid-structure interaction simulation and design of experiments (DOE). J. Appl. Fluid Mech. 13(1), 261–273 (2020) 12. Xu, Y.W., Renteria, A., Wang, P.F.: Adaptive surrogate models with partially observed information. Reliab. Eng. Syst. Saf. 225, 108566 (2022) 13. Hüner, E., Toylan, H.: Design optimization with genetic algorithm of open slotted axial flux permanent magnet generator for wind turbines. Int. J. Green Energy 1–9 (2022) 14. Kandilli, C., Mertoglu, B.: Optimisation design and operation parameters of a photovoltaic thermal system integrated with natural zeolite. Int. J. Hydromechatron. 3(2), 128–139 (2020)

Dispatch Strategy for Transmission Overload Based on Safe Reinforcement Learning Hang Zhou1 , Hongqin Zhu1 , and Han Cui2(B) 1 Nanjing Power Supply Company of State Grid Jiangsu Electric Power Company,

Nanjing 210000, China 2 Southeast University, Nanjing 210000, China

[email protected]

Abstract. Active power dispatch is one of the major operation tasks for power system that keeps the power generation and consumption in a real-time balance. Real-time decisions for active power dispatch can be seen as a modification on the Day-ahead OPF (DAOPF) and are constrained by power system safety rules. Consequently, active power dispatch focuses mainly on the perspective of operation safety which is influenced by renewable generation power fluctuation, load variation and maintenance. It is impossible to incorporate these stochastic factors in a DAOPF problem. To solve this problem, active power dispatch is formulated into a CMDP problem, where the target is to optimize the dispatch policy that maximize the reward without breaching the safety constraints. Risk of blackout arises from the violation of safety constraints and potential human and property damage would be enormous, which makes the problem different from common RL task. To handle this problem, IPO algorithm, which belongs to safe RL, is adopted. In IEEE 14-bus system, the proposed method is implemented to show the advantages from full aspects. Keywords: Active power dispatch · Operational constraints · Safe reinforcement learning

1 Introduction Nowadays, significant efforts have been devoted to renewable energy for both environmental factors and energy supply security reasons. Despite the effect of COVID-19, newly installed renewable energy capacity exceeds 260 GW in 2020 [1]. However, the rapid growth introduces more uncertainty, volatility and intermittency to power system, which intensifies the transmission congestion. During unexpected high/low renewable power generation period, local load cannot match up with the power generation. Consequently, transmission lines have to undertake power out of/into this region, which might exceeds the thermal limit of transmission lines [2]. Previous work has predominately employed model-based optimization approach to regulate active power dispatch [3–6]. An optimization problem is typically formulated with an objective function and is subjected to various constraints under known system © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 73–81, 2023. https://doi.org/10.1007/978-981-99-4334-0_9

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conditions and models, resulting in an optimal solution derived from known system dynamics. However, this type of approach exhibits a significant drawback: once the real-word system condition has changed, the employed system model for optimization becomes inaccurate, which deteriorates the effectiveness of the dispatch decisions. This paper proposes a novel real-time active power dispatch strategy based on the interior-point policy optimization (IPO) algorithm [7]. IPO belongs to the paradigm of safe deep RL, in which the dispatch problem is formulated as a Constrained Markov Decision Process (CMDP), where the uncertainties arisen from renewable power generation, load and network topology are considered to formulate realistic training scenarios. The control objective is to compute the constrained topology adjustment and generation rescheduling strategies so that the overloading of the transmission lines can be removed. The IPO method does not require any knowledge on the distribution of uncertainty as well as the constraints. Different from existing deep RL methods, IPO promises direct fulfillment of action-related constraints, without the need to employ some designated penalty terms and tune the associated penalty factors for the constraints’ satisfaction, ensuring the action’s feasibility while improving its optimality at the same time. Furthermore, the proposed approach is tailored to align with the nature of the problem by establishing it in multi-dimensional state and action spaces. A dedicated deep neural network is designed to approximate the active power dispatch policy and trained by IPO, facilitating more efficient learning in mixed discrete and continuous action space.

2 Problem Formulation The goal of transmission congestion dispatch is to avoid breaching line thermal limits while maintaining balance between power supply and power consumption, where randomness of renewable generation, volatility of load, scheduled maintenance and power system operational constraints are taken into consideration. In this research, transmission congestion dispatch, which belongs to preventive control in power system industry, is real-time decision to rectify the day-ahead optimal power flow that deviates from security region due to uncertainties. A successful dispatch would keep all lines operating at low load rate. In this context, power system security is more emphasized so that the economic cost is eliminated from the optimization objective function. The transmission congestion dispatch is considered to be a CMDP problem in that it meets both criterion: 1) The state transition in transmission congestion dispatch is MDP. 2) Power system operational rules make the problem constrained. Detailed explanations are as following: 2.1 MDP Modelling Subsequent paragraphs, however, are indented. According to classical tuple model of MDP, the MDP problem model is fully established once (S, A, P, R, γ) are determined, which is shown in Fig. 1. In the tuple, S stands for the whole set of different states: A covers all actions; P is a transition matrix that quantify the probability of state transition given the current state and the action to take; R is the reward from state transitions that

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Fig. 1. CMDP of transmission overload dispatch.

is closely connect with optimization target; γ is discount factor that sum up all rewards from beginning to end. 1) State: State of power system contains 4 types of variables: Pload , Pgen , ρline and Tline . Pload is indexed with bus number. Pgen is indexed with generator number. ρline and Tline are indexed with line number. In actual power system dispatch, these state variables can be fetched from SCADA.   1 G 1 L 1 L St = P1load , . . . , PN load , Pgen , . . . , Pgen , ρline , . . . ρline Tline , . . . , Tline 2) Action: Generator power dispatch and line status dispatch are two types of actions in this problem. For thermal power plant, power dispatch can be done continuously between ramp limits, which can alter the power flow in a delicate way. Line status dispatch is a discrete action that choosing the connection bus for each transmission lines, which alters the topology of power grid.   1 2 L , a , a , . . . , a At = a1gen , a2gen , . . . , aG gen line line line To simplify the problem, line status dispatch is set to be a one-hot coded vector that only 1 line can be dispatched at one step. 3) State Transition Matrix: From the perspective of probability, element in P can be written in the form P(St+1 |St , At ), which is the conditional probability of St+1 given that current state is St and the action to take is At . In active power dispatch, uncertainty of renewable energy and load are main factors for the state transition randomness. Apart from that, the state transition follows the physics laws of power system, which are embed in the power system simulator. 4) Reward: From the perspective of dispatcher, it would be better that ρ is below 1 in a wide gap when other operational conditions are satisfied. In this problem, reward is defined as R = 1 − ρ. It can be seen that R is solely dependent on ρ. When 0.9 < ρ < 1, the line is operating near the thermal limit and certain dispatch actions need to be taken to prevent the potential overload. As the ρ > 1, the thermal limit is breached so that more severe punish are imposed.

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5) Discount factor: Power system operates in a continuous time sequence so that every dispatch action has effect on future steps. γ is the discount factor to sum up all time steps considering the time effect that more distant actions have less  on current  impact state. Consequently, the total discount reward is defined as G = Ti=0 γi × Ri . To maximize G, it is necessary to optimize the policy π, which is the conditional probability of choosing action given current state, denoted as P(a|s). For an intelligent dispatch agent, this policy enables it to make dispatch decisions based on the real-time observation. 2.2 Power System Constraints As a physical system, power system operates under the governance of physics laws, such as Ohm’s law, law of inertia, law of thermodynamics etc., which are fully built in the simulation model. Apart from that, many artificial rules should be adopted. In active power dispatch, two types of artificial rules are introduced: regular constraints and safety constraints. Regular constraints. In many existing researches, cost-oriented power system dispatch sets a list of constraints contain bus voltage, line current, generator output power and so on. Similarly, these regular constraints are defined in active power dispatch. Safety constraints. From the perspective of security, the mentioned regular constraints only ensure the power system be effective at common scenarios. Once a disturbance happens, power system might undergo severe blackouts without the security constraints. Based on investigations on actual power system dispatch department, the following constraints are proposed: a) busbar switching shall not be implemented at more than one substation; b) connectivity of substations must not be reduced by m in the whole system.

3 Methodology To realize intelligent active power dispatch, it is the core issue to optimize the dispatch policy. As is summarized in introduction, both optimization algorithms and RL algorithms is applicable to policy optimization. Compared to existing RL-based research, security constraints are more focused so that IPO algorithm is implemented to improve the model performance with these constraints. Both the optimization solution and IPO algorithm are shown as follows. IPO algorithm, which belongs to safe RL, is proposed based on the idea of interiorpoint method, which uses barrier function to substitute the inequality constraints. The policy update mechanism of IPO is inherited from PPO so that trust region property is retained. As a first-order algorithm, derivative calculation is easy to perform compared to CPO, which is a second-order algorithm.

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Objective function of IPO is consisted of two parts: clipped surrogate objective of PPO and barrier function in the interior-point method. The constraints can be written as the inequality expression so that active power dispatch problem is defined as: maxθ LCLIP (θ) π

s.t. JCiθ ≤ i 

π

π

The constraints can be reduced by introducing a new term that JCiθ = JCiθ − i . For 

π

each JCiθ , indication function is defined to form a unconstrained MDP problem.   π I JCiθ = 





0,

π

JCiθ ≤ 0



π

−∞, JCiθ > 0

  π The I JCiθ is an ideal barrier function that handles the safety constraints perfectly, which, however, is not a first-order differentiable function. Since IPO leverages firstorder derivative to optimize the policy, it is compulsory to find an approximation  funcπ tion, which is both first-order differentiable and suitable as the barrier, for I JCiθ . An logarithm-based barrier is proposed that   θ   lg −Jπ Ci π φ JCiθ = t 



where t > 0 is a hyperparameter   to be chosen that larger t corresponding to a more π precise fit to ideal barrier I JCiθ . IPO inherits the policy gradient method from PPO, which is proposed by Schulman in 2017. As a model-free method, policy gradient was firstly proposed by Sutton to solve MDP problems in 2000. 

4 Case Study To verify the proposed intelligent dispatch method, a test case on IEEE-14 bus system is demonstrated. Firstly, the test system and CMDP problem are introduced. Then, the IPO-based method is compared to the theoretical best solution to verify the optimization performance. Typical cases are also included so that the dispatch decisions can be understood from a more specific viewpoint.

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4.1 Test Case Preparation The IEEE-14 bus system contains 5 generators, 20 transmission lines and 11 load access points. Nuclear power plant at bus 1 operates at a fixed level constantly. Output power of renewable generators at Bus 2 and 3 is in a random fluctuation pattern due to weather factors. Only thermal generators at Bus 6 and 8 are dispatchable in a continuous action space, which can be represented using a 2-dimension vector. Each one of the 20 transmission lines can be connect/disconnect at a time step, which can be coded with a one-hot 20-dimension vector. Load curve in this problem is a given condition that must be satisfied. A one-year span of load data that considering season and time factors are used in the RL training and test. Detailed data can be found in Grid2op. All calculation and simulations are performed on a computer with a NVIDIA 1080Ti GPU and i5-7600K CPU. 4.2 Performance Validation Active power dispatch is a MINLP problem, which is solved by Gurobi solver in this research. Two critical reasons make it impractical to use Gurobi performing the realtime dispatch: 1) Randomness of renewable power and load are not known to the MINLP model. 2) Optimization time for a single day reaches 10 min. Although the optimization solver cannot be applied online, the results can be used to assess the RL agent since the solver gives the theoretically optimal solution. It can be seen in Fig. 2 that IPO approaches the benchmark in each of the months. The total reward during a year is up to 93.2% of the theoretical best.

Fig. 2. Comparison between the proposed method and theoretical benchmark.

Since the renewables are intermittent and random, the transmission lines might overload when the power from wind/solar farms send too much power. In Fig. 3, the dispatch on thermal generators relief the overload on transmission lines. By reducing the power generation of generators, renewable power can be consumed by local load without sending out.

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Fig. 3. Dispatch strategy against uncertain renewables.

In the power grid, residence and industry regions show different load profiles. The spatial imbalance across regions might cause transmission overload. It can be seen in Fig. 4 that by conducting the dispatch strategy of the proposed method, the reward is higher than no dispatch actions.

Fig. 4. Dispatch for cross-regional power consumption imbalance.

In power grid, transmission lines might need maintenance for better operation. In such scenarios, the proposed method can also give proper dispatch actions, as in Fig. 5. When line 7 and 15 are under maintenance, the IPO method also solve the overload problem.

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Fig. 5. Dispatch strategy for line maintenance.

5 Conclusion In this paper, we propose a safe-RL method for active power dispatch. Which belongs to CMDP problem. Randomness of renewable generation, variety of load profile and power system maintenance are considered in the CMDP problem formulation. It is the safety constraints of power system operation that distinguish this research from others research that mainly focused on economic cost. Corresponding to these safety constraints, IPO algorithm is adopted to transform the constraints into a differentiable barrier function, which can be optimized together with reward using policy gradient method. Test on the IEEE 14-bus system have proven that the intelligent dispatch agent reaches the 93.2% level of theoretically optimal solution. By showing the typical cases of transmission overload, the proposed method handles the scenarios well. Acknowledgment. This work is funded by State Grid Jiangsu Electric Power Company Key Technology Project J2021138.

References 1. Zheng, H., Song, M., Shen, Z.: The evolution of renewable energy and its impact on carbon reduction in China. Energy 237, 121639 (2021) 2. Li, X., Zhang, X., Wu, L., Lu, P., Zhang, S.: Transmission line overload risk assessment for power systems with wind and load-power generation correlation. IEEE Trans. Smart Grid 6(3), 1233–1242 (2015) 3. Abbas, A.Y., Hassan, M., Abdelrahim, H.: Transmission lines overload alleviation by generation rescheduling and load shedding. J. Infrastruct. Syst. 22(5), A4016001 (2016) 4. Ding, L., Hu, P., Liu, W., Wen, G.: Transmission lines overload alleviation: distributed online optimization approach. IEEE Trans. Ind. Inform. 17(5), 3197–3208 (2021) 5. Zeng, L., Chiang, H.: Toward an online minimum number of controls for relieving overloads. IEEE Trans. Power Syst. 33(2), 1882–1890 (2018)

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6. Jin, X., et al.: Alleviation of overloads in transmission network: a multi-level framework using the capability from active distribution network. Int. J. Electr. Power Energy Syst. 112(11), 232–251 (2019) 7. Liu, Y., Ding, J., Liu, X.: IPO: interior-point policy optimization under constraints. Proc. AAAI Conf. Artif. Intell. 34(04), 4940–4947 (2020)

Research on Power Source Schemes in High Proportion of Renewable Energy HVDC System Chao Huo1 , Hong Yang2(B) , Naixin Duan1 , Xiuting Rong1 , Xiaoyang Wang2 , Haiwei Li2 , Juan Zhao2 , and Xuliang Li2 1 Northwest Power Grid Co., Ltd., Xi’an 710048, China 2 Northwest Electric Power Design Institute Co., Ltd., Xi’an 710075, China

[email protected]

Abstract. In order to achieve carbon peaking and carbon neutrality goal and promote the construction of new power system based on renewable energy, China requires the construction of a high proportion of renewable energy HVDC projects with renewable energy accounting for not less than 50% of the total electricity at the sending-end grid. In this paper, a research method of matching power source scheme for high proportion of renewable energy HVDC system is proposed. This method provides an evaluation index system of matching power source schemes and a calculation method of electrovalence, which can be used to evaluate the rationality of corresponding power source schemes and provide the economic evaluation of HVDC projects. In this paper, the matching power source schemes for Ningxia ± 800 kV HVDC project are discussed and the recommended scheme is put forward. The research method and evaluation index system of matching power source schemes proposed in this paper provide a beneficial reference for the development of similar projects in the future. Keywords: Novel power system · Renewable energy · HVDC · Evaluation index system of matching power source scheme · Electrovalence competitiveness

1 Introduction The proposal of the “carbon peaking and carbon neutrality” goal has promoted the transformation of the novel power system dominated by renewable energy. As an important way to realize large capacity and long-distance transmission, ultra-high voltage direct current (UHVDC) transmission will become the pivotal carrier of large-scale renewable energy power transmission [1–6]. In order to support the task of achieving carbon peak, Ningxia plans to build a 10 million kW integrated power supply for wind, photovoltaic, coal and storage, which rely on Tengger desert base. The generated power will be delivered to the central and eastern regions of China through UHVDC. In 2021, China requires the proportion of renewable energy electricity in the transmission channel should not be less than 50% in principle, and priority should be given to planning and building channels with a higher proportion. How to determine the supporting power supply capacity of UHVDC and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 82–88, 2023. https://doi.org/10.1007/978-981-99-4334-0_10

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the ratio of various power supplies reasonably is very important to improve the channel utilization and ensure the safe and reliable operation of the DC system. Reference [7] proposed an analysis method for bundled power supply of thermal power, wind and photovoltaic power when the power transmission curve is given. Literature [8] proposed an optimal operation of wind-thermal-storage combined power generation system, and processed and optimized the operation simulation of hydropower units. Reference [9] provided a method and system for optimizing the matching ratio of UHVDC power supply. Most existing papers focus on the optimal operation and dispatching of power systems with high proportion of renewable energy, while corresponding evaluation mechanism or screening criteria to analyze the structure and proportion of DC matching power source scheme to determine the optimal scheme are still deficient. This paper mainly proposes a research method and evaluation index system for containing high proportion of renewable energy ultra-high voltage DC matching power source schemes. The annual 8760 h power production simulation calculation is carried out for each scheme by using the production simulation calculation program. The proportion of renewable energy electricity, the utilization rate of renewable energy, and other technical indicators are derived. The optimal power source scheme is recommended in combination with the power source comprehensive feed-in tariffs.

2 Basic Research Ideas The basic research ideas of this paper are shown in Fig. 1.

Fig. 1. Basic research ideas of high proportion renewable energy UHVDC power source scheme.

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3 Evaluation Index System of Power Source Scheme The evaluation index system of matching power source scheme includes 4 dimensions and 8 indexes (see Fig. 2 for details), so as to evaluate the production simulation calculation and electrovalence calculation results of multi-power source scheme.

The proportion of annual electricity transmission of renewable energy : ≥50%

Green and LowCarbon

Utilization rate of renewable energy Peak regulation quantity of electricity required from the main

Peak Regulation Demand

network (with 95% utilization rate of renewable energy)

Confidence of power supply during peak hours The necessary power support from the main network (with 95% confidence of power supply) The necessary electric quantity support from the main network (with 95% confidence of power supply)

≤ 5% of the DC power transmission ≤2000MW Safe and Reliable

Safe and stable

Comprehensive on-grid price of power source at the sending end

Economically Reasonable

Fig. 2. Evaluation index system of high proportion renewable energy UHVDC matching power source scheme.

(1) Dimension 1: Green and Low-Carbon. The main indicator of low-carbon is the proportion of annual electricity transmission of renewable energy. The proportion of annual power transmission of renewable energy in the DC channel shall not be less than 50% on the premise that meeting the requirements of safe, stable and reliable power transmission. (2) Dimension 2: Peak Regulation Demand. Including 2 indicators: 1) Utilization rate of renewable energy Without considering the peak regulation support of the main network, the renewable energy utilization rate should be as high as possible, that is, the power discarding rate should be as low as possible.

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2) Peak regulation quantity of electricity required from the main network In order to meet the renewable energy utilization rate is not less than 95%, the main network is generally required to provide peak regulation support. The less peak regulation quantity of electricity required from the main network, the better the power source scheme performs. (3) Dimension 3: Safe and Reliable. Including 4 indicators: 1) Confidence of power supply during peak hours The proportion of the time that the matching power source can meet the power transmission demand during the annual DC power transmission peak period is called power supply confidence. The annual power supply confidence of the high proportion renewable energy matching power source scheme will not reach 100%, and the main network is required to provide power support in some periods. 2) The necessary power support from the main network If the confidence level of power supply during peak hours more than 95% is required, the main network is generally required to provide power support. For DC system with rated design capacity of 8000 MW, the supportive power is considered as not more than 2000 MW. 3) The necessary electric quantity support from the main network In order to ensure that the confidence level of power supply during peak hours is not less than 95%, the main network is required to provide electric quantity support, and the annual quantity of electricity support is considered as not more than 5% of the DC power transmission. 4) Safe and stable Check whether the power source scheme can meet the safe and stable operation requirements of the DC transmission system under different operation modes. In particular, attention should be paid to the possibility that renewable energy may cause interlocking high-voltage disconnection in the over-voltage transient process after DC fault. (4) Dimension 4: Economically Reasonable. The main indicator is the comprehensive on-grid price of power source at the sending end. The comprehensive on-grid price of power source is determined by the power source scheme and the proportion of various electric quantity. In order to ensure the profitability

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of the power transmission projects, the comprehensive on-grid price of power source should be competitive.

4 Ningxia Case 4.1 DC Sending End Power Source Scheme Design In 2020, China proposes to strengthen the development and utilization of renewable energy and cultivate a number of clean energy bases and continues to increase the construction of transmission channels such as power transmission from the west to the east, and improve the development philosophy such as clean power transmission capacity, providing new opportunities for Ningxia’s external transmission. Ningxia plans to give priority to the use of coal power in stock, build a 10 million kW renewable energy power installation based on the Tengger Desert Base, and send it to southern Hunan through the UHVDC channel. Based on the above research methods and evaluation index system of matching power source scheme, this paper focuses on the supporting thermal power and energy storage configuration scheme. The proposed power source comparison scheme is shown in Table 1. 4.2 Demonstration of Power Source Scheme For the above proposed power source schemes, the production simulation calculation program is used to conduct a detailed analysis of the annual supply and demand of 8760 h. The calculation results are shown in Table 1. According to the evaluation index system of matching power source schemes and the calculation results, it can be seen that: 1) The proportion of annual power transmission of renewable energy in the channel shall be more than 50%. Power source scheme II A (49%) and power source scheme III (46%) are slightly lower than 50%. 2) Without considering the peak regulation power of the main network, the utilization rate of renewable energy in scheme I is superior to scheme II and III. 3) To ensure that the utilization rate of renewable energy is not less than 95%, scheme I (A, B) and scheme II (B) meet the requirement that the peak regulation power of the main network is not higher than 5% of the DC power transmission. 4) The confidence level of power supply during peak hours in scheme III is obviously better than scheme I and scheme II. In order to ensure that the confidence level of power supply during peak hours is not less than 95%, the power and electric quantity supply support provided by the main network is required. The supporting power required of scheme II and scheme III are not higher than 2 GW. The supporting electric quantity required of scheme II and scheme III are not higher than 5% of the DC power transmission. 5) The comprehensive on-grid price of power source at the sending end is the lowest (0.293 yuan/kWh) in scheme II A and the highest (0.325 yuan/kWh) in scheme I B. In summary, in order to meet the requirements of all indicators, it is recommended to adopt the medium thermal power configuration scheme, namely Scheme II B.

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Table 1. Power matching scheme and results of production simulation. Items

Scheme I

Scheme II

Scheme III

Plan A

Plan B

Plan A

Plan B

1. Coal power (GW)

2

2

4

4

6

2. Wind power (GW)

4

4

4

4

4

3. Photovoltaic (GW)

9

9

9

9

9

4 (4 h)

2 (2 h)

2 (4 h)

0

4. Electrochemical energy storage (GW) 4 (2 h) Indexes of evaluation system Green and low-carbon

Proportion of annual 53 electricity transmission of renewable energy (%)

55

49

51

46

Peak regulation demand

1. Utilization rate of renewable energy (%)

90

94

84

88

78

2. Peak regulation quantity of electricity required (billion kWh)

1.34

0.3

2.73

1.88

4.33

Safe and reliable

1. Confidence of power 70 supply during peak hours (%)

75

86

88

92

2. The necessary power 4.41 support from the main network (GW)

4.35

2.00

1.00

0.53

3. The necessary electric quantity support (billion kWh)

7.36

6.33

1.24

0.93

0.27

4. Safe and stable

✓

✓

✓

✓

✓

0.325

0.293

0.306

0.306

Economically reasonable

Comprehensive on-grid 0.299 price of power source at the sending end (yuan/kWh)

5 Conclusion The renewable energy plays a leading role in the novel power system, in which how to build a matching power source scheme with high proportion of renewable energy to transmit power has become an important issue. The research method and evaluation index system of UHVDC matching power source scheme proposed in this paper carding the research process of matching power source scheme and proposes a comparatively comprehensive index system, which can be conveniently applied to the integrated configuration scheme of wind, photovoltaic, thermal and storage power source at the UHVDC

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sending end. The physical concepts of this scheme are clear, scientific and reasonable, simple and feasible, which is worth popularizing and applying in a large number of similar projects in the future.

References 1. Liu, Z., Zhang, Q., Dong, C., et al.: Efficient and security transmission of wind, photovoltaic and thermal power of large-scale energy resource bases through UHVDC projects. Proc. CSEE 34(16), 2513–2522 (2014) 2. Xin, S., Zhang, Y., Bai, J.: Study on power regulation scheme of large-capacity and longdistance DC transmission for wind power. Electr. Power 46(6), 70–74 (2013) 3. Ye, X., Zhang, X., Ouyang, X.: A power source capacity optimization method for wind, photovoltaic and hydro power integrated sending-end power system considering different UHVDC operation mode. Renew. Energy Resour. 37(5), 707–713 (2019) 4. Mehdi, T., Edris, P., Jafar, A., Radu, G., João, P.: Load-frequency control in a multi-source power system connected to wind farms through multi terminal HVDC systems. Comput. Oper. Res. (2018) 5. Ludin, G., Nakadomari, A., Yona, A., Mikkili, S., Rangarajan, S., Collins, E.: Technical and economic analysis of an HVDC transmission system for renewable energy connection in Afghanistan. Sustainability (2022) 6. Ostadzad, A.: Innovation and carbon emissions: fixed-effects panel threshold model estimation for renewable energy. Renew. Energy (2021) 7. Xia, Y., Song, W., Zhang, Z.: Study on the matching scheme of ultra-high voltage DC wind power, photovoltaic and thermal power supply. In: Proceedings of 2015 Annual Academic Conference of Gansu Institute of Electrical Engineering, pp. 60–68 (2015) 8. State Grid Xinjiang Electric Power Co., Ltd.: A method and system for optimizing the matching ratio of UHV DC power supply: CN202010362406.X[P] (2021) 9. He, J., Zhuang, W., Xu, T., et al.: Study on cascading tripping risk of wind turbines caused by transient overvoltage and its countermeasures. Power Syst. Technol. 40(6), 1839–1844 (2016)

Experimental Study on the Influence of Voltage Sag Characteristic Parameters on the Dynamic Performance of SSTS Qi Cui1 , Mingxing Zhu1 , Huaying Zhang2 , Yadong Jiao1 , and Min Gao1(B) 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui,

China [email protected] 2 New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid, Shenzhen Power Supply Co., Ltd., Shenzhen 518020, Guangdong, China

Abstract. Voltage sag is the main power quality problem in the application of solid state transfer switch (SSTS). Different sag characteristic parameters indicate different impacts on the switching performance of SSTS, which have not been fully investigated in existing researches. Given this, this paper quantifies the influence of four voltage sag characteristic parameters on the dynamic performance of SSTS through experimental study. Firstly, the basic structure and working principle of SSTS are analyzed. Secondly, the dynamic performance indexes of SSTS are introduced. Then, taking a brand SSTS product as the research object, an experimental test platform is built without knowing the specific internal structure of the equipment. Based on the principle of single variables, the switching performance of SSTS is tested and analyzed for four voltage sag characteristic parameters. The results show that different sag characteristic parameters are obviously correlated with the dynamic performance of SSTS switching. The quantitative research results provide help for the actual installation scheme of SSTS, provide data support for the research of higher performance SSTS, and also provide reference for the dynamic performance evaluation of SSTS. Keywords: Solid state transfer switch · Sag magnitude · Sag duration · Sag initial phase angle · Sag change rate · Dynamic performance

1 Introduction With the development of power electronics technology, a large number of nonlinear power electronic devices and equipment are widely used in the power grid. They have caused serious pollution and damage to the power system, and the power quality problems are becoming increasingly serious [1]. There are tens of billions of dollars losses a year in USA due to power quality problems [2]. A lot of equipment, such as precision experimental instruments, the IT industry, new medical devices, and the semiconductor manufacturing industry, can-not work properly due to these problems. According to a survey, more than 72% of power quality complaints are caused by voltage sags and short-term power outages [3]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 89–100, 2023. https://doi.org/10.1007/978-981-99-4334-0_11

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To solve power quality problems in modern power systems, customized power technology based on smart grid technology, computer technology, communication technology, and modern power electronics technology has emerged. It aims to provide a stable and reliable power supply for specific users. Solid state transfer switch (SSTS) is an important part of it [4]. SSTS can realize the fast switching of main and standby power supply. Its superior performance has attracted wide attention in related fields since it was proposed. Compared with the traditional automatic transfer switch (ATS), SSTS has the advantages of short switching time, good controllability, simple structure, and “no arc” due to the use of the thyristor switch. Replacing ATS with SSTS will effectively solve the inherent problems of traditional mechanical switches. Meanwhile, it can meet the stringent requirements of sensitive and critical loads for power supply reliability and power quality. At present, SSTS is the most economical and effective measure to solve voltage sag and temporary power-off [5]. The dynamic performance of SSTS is an important index. It has a certain reference significance for selecting appropriate SSTS products for different loads, which can prevent the decline in switching performance due to special circumstances, and improve the high-quality power supply. Additionally, a certain reference value can be provided for researchers to further study shortening the SSTS switching time and improving the performance of existing SSTS devices. However, at present, the research on SSTS at home and abroad mainly stays at the thyristor commutation and control [6, 7], voltage-sharing of thyristor series [8], switching surge current suppression [9], reduce signal transmission time by fuzzy control to reduce STSS switching time [10, 11], and so on. Reference [12] studied the switching ability of SSTS devices under different power quality disturbances through experiments, but did not carry out relevant experimental research on the dynamic performance of SSTS. The effect of voltage sag on the dynamic performance of SSTS is studied experimentally in this paper. In the laboratory environment, the effects of different voltage sag characteristic parameters (magnitude, duration, initial phase angle, change rate) on SSTS switching dynamic performance (switching time, transfer time) are tested and analyzed. Thus, the influence of voltage sag characteristic parameters on SSTS switching dynamic performance is quantified. The rest of this paper is organized in the following form. Section 2 introduces the basic structure, principle, and dynamic performance indexes of SSTS. Section 3 introduces the scheme design of this experiment, including the construction of the experimental platform, the experimental steps, and the parameter setting. The experimental results and analysis are conducted in Sect. 4. Section 5 summarizes the full study and looks forward to future works.

2 Structure and Performance Indexes of SSTS 2.1 Working Principle of SSTS A typical structure of SSTS is shown in Fig. 1. The basic working principle of SSTS is described as follows. Under normal operating conditions, the load is powered by the main power supply by the fast mechanical switch PS1, and the heat generation is small

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due to the small contact resistance of the metal contact of the fast mechanical switch. When the main power supply circuit fails, the main power side disconnects the fast mechanical switch PS1 and triggers the thyristor valve TS1 at the same time, at which time the current of the main power supply loop is transferred to the thyristor branch. When the main power circuit current reduces to zero, the thyristor valve TS1 is naturally turned off. Then the thyristor valve TS2 on the standby power supply side is triggered. After several cycles, the system stabilizes, closes the fast mechanical switch PS2, stops triggering the thyristor valve TS2, and the commutation process ends. The whole process of fast mechanical switch PS1, PS2 turn off and close when the voltage is almost 0, so the whole commutation process is ‘no arc’. Standby power

Main power PS1

PS2

TS2

TS1 Load

VS1

UV

VS2 Voltage transducer

Voltage phase difference detection

Voltage transducer

φ

UL θ

Switching judgment

Switching instruction

Switching operation

Fig. 1. SSTS detection and control topology.

2.2 Voltage Sag Detection

θ ua ub

Virtual threephase voltage

uc

-sin cos abc dq

Threshold value

ud

LPF

udα

uq

LPF

uqα

Sag magnitude

Switch

N Y

Trigger signal

Voltage signals

PLL

Comparator

At present, the voltage sag detection commonly used in SSTS is based on the method of dq conversion, which includes signal construction, abc/dq conversion, low-pass filtering, and tidal sag magnitude calculating, as shown in Fig. 2.

Fig. 2. Dq transformation flow chart of constructing virtual three-phase voltage.

Taking the single-phase voltage Ua as an example, it is delayed by 60° to get −Uc , and then the three-phase voltage is constructed according to Ub = −Ua − Uc . At the same time, through the phase locked loop (PLL), the phase of phase A is obtained. After abc/dq transformation, the Ud and Uq components of three-phase voltage can be gained. After these two components pass through the low-pass filter, the DC components Ud α

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and Uqα are obtained. Finally, the effective value of voltage is calculated. The abc/dq transformation of voltage is expressed as 

ud uq



⎡ ⎤       ua  2π 2 cos θ cos θ − 2π cos θ + 3  3  ⎣u ⎦   = b sin θ + 2π 3 sin θ sin θ − 2π 3 3 uc

The amplitude of voltage is calculated as √ 3 2 2 U = ud α + uqα 3

(1)

(2)

2.3 SSTS Switching Dynamic Characteristic Indexes Switch time T1 and transfer time T2 are two indexes to characterize SSTS switching dynamic performance [13]. Switch time T1=te-tds

Time of sag occurrence tds Switching end time te Switching start time tcs Transfer time T2=te-tcs

Fig. 3. SSTS switching dynamic characteristics characterization indexes definition.

Switch time T1 refers to the time from the abnormal power supply voltage to load transfer to the standby power supply, including detection time, setting time, and transfer time. Transfer time T2 refers to the time from the device control system issuing the switching instruction to the completion of the load transfer. Their specific meanings are shown in Fig. 3.

3 Experiment Design 3.1 Experiment Platform Given the above overview of the structure, control, and detection principle of SSTS, this paper selects the SSTS product of a manufacturer for field application. Then the experimental platform is built as shown in Fig. 4(a) with only the nameplate parameters known. During the experiment, the programmable power supply (main power supply) and the three-phase 380 V urban power network (standby power supply) are connected to the input end of the SSTS through a circuit breaker. Besides, the output end is connected to a load cabinet with a maximum of 60 kW (resistive) through a circuit breaker.

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I2

city power Standby Power K1

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U2

SSTS

I3 U3

K3

I1 U

Load

1

Main power Programmable power

(a) Experiment platform

Measuring device

(b) Wiring diagram

Fig. 4. Experiment platform and wiring diagram.

In addition, the multi-channel data acquisition device is used to synchronously test and record the voltage and current waveform signals of the two power supplies and the load side during the test. The test circuit is composed of a programmable power supply, SSTS, load cabinet, multi-channel data acquisition device and test auxiliary accessories. The voltage and current waveform signals of the two power supplies and the load side during the test are synchronously tested and recorded. The test wiring diagram is shown in Fig. 4(b). The SSTS switching threshold voltage is 216 V in this experiment. 3.2 Purpose and Procedure Four characteristic parameters of voltage sag are detected in the laboratory environment, including sag magnitude, duration, initial phase angle, and change rate, which respectively affect the dynamic characteristics of SSTS switching. The test steps are shown in Fig. 5. The Magnitude represents the percentage of the effective value of the initial voltage after the occurrence of the sag. The Duration refers to the total duration time from the occurrence of the sag to the end. The Initial Phase Angle refers to the voltage phase angle of phase A at the time of the occurrence of the sag, and the Change Rate refers to the speed of the change of the effective value of the voltage at the time of the sag. Start Control the main power supply voltage sag

Magnitude

Duration

Initial phase angle

Record switching data for SSTS

Update parameters

N

Are all sag characteristic parameters tested ? Y End

Fig. 5. Test steps.

Change rate

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3.3 Parameters Setting The setting values of voltage sag characteristic parameters during the experiment are shown in Table 1. To strictly follow the principle of single variables, when studying the influence of a characteristic parameter on the dynamic performance of SSTS, the other parameters are set to fixed values. Table 1. Characteristic parameters setting value. Sag characteristic parameters

Setting value

Magnitude

0.7 p.u.

Duration

200 ms

Initial phase angle

0°

Change rate

3000%/s

4 Results and Analysis 4.1 Influence of Sag Magnitude on SSTS Switching Dynamic Performance The sag magnitude refers to the root mean square (RMS) value difference of steadystate voltage after the end of the sag transition relative to that before the occurrence, expressed as a percentage of the nominal voltage ratio. To reflect the influence of the sag magnitude on the dynamic characteristics of SSTS switching, the test can be carried out by changing the magnitude. The results are shown in Table 2 and Fig. 6. Table 2. Results of SSTS dynamic characteristics under different sag magnitude. Magnitude/p.u.

Transfer time/ms

Switch time/ms

0.8

10.2593

34.2419

0.7

10.1891

13.6496

0.6

10.125

13.5

0.3

10.1991

13.4404

According to the results, the magnitude of voltage sag does not affect the transfer time of SSTS. As the sag magnitude decreases from 0.8 p.u. to 0.7 p.u., the switch time decreases from about 30 ms to about 13 ms. Then the sag magnitude decreases to 0.3 p.u., the switch time decreases slightly, but still maintains at the level of 13 ms. It can be seen that the sag magnitude will affect the switch time of SSTS. On the one hand, the sag magnitude affects the sag detection time of the SSTS device. On the other hand, after the detection time is changed, the time node that meets the switching

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95

Transfer time Switch time

30

T/ms

25 20 15 10 5

0.8

0.7

0.6

0.3

Voltage sag magnitude/p.u.

Fig. 6. Dynamic performance of SSTS under different magnitudes.

condition will also change, eventually leading to a change in the switch time. However, the transfer time of SSTS is the intrinsic parameter of SSTS, so the change of external conditions will not affect it. 4.2 Influence of Sag Duration on SSTS Switching Dynamic Performance Duration is defined as the time from occurrence to end of sag, which is one of the most important characteristic parameters of sag. For voltage sag duration less than switch time and greater than switch time, the tested SSTS response is shown in Table 3. Table 3. Results of SSTS dynamic characteristics under different durations. Duration/ms

SSTS state

Transfer time/ms

Switch time/ms

5

Switchover

10.0309

13.6994

10

Switchover

10.1449

13.6584

20

Switchover

10.0758

23.7016

30

Switchover

10.1812

13.3927

50

Switchover

10.0526

17.0742

100

Switchover

10.0908

13.5134

200

Switchover

10.1757

13.5402

Based on Table 3 and Fig. 7, the following conclusions can be drawn: (1) When the duration is less than the switch time, the voltage has returned to normal before the SSTS switching, but the SSTS still switches to the standby power. The minimum duration of the voltage sag in the test is 5 ms, indicating that the ‘detection + setting’ time is less than 5 ms. According to the switch time and transfer time recorded in the test, it can be preliminarily inferred that the ‘detection + setting’ is about 3.6 ms. Therefore, voltage sags lasting beyond this value will cause SSTS switching.

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Transfer time Switch time

30

T/ms

25 20 15 10 5

5

10

20

30

50

100

200

Duration time/ms

Fig. 7. Dynamic performance of SSTS under different durations.

(2) With the extension of voltage sag duration, the transfer time of SSTS is not affected and always maintains at 10 ms. (3) The extension of duration will lead to an increase in switch time in some experiments, but there is no specific rule. For example, in the duration of 20 ms and 50 ms, the corresponding switch time reaches 23 ms and 17 ms, but the ‘detection + setting’ time does not exceed its corresponding duration, solid-state switches are effectively switched. It can be seen that the SSTS ‘detection + tuning’ time is short, but the switch time is long. This is because the existence of low-pass filters in the system will lead to a large time delay and the transfer time is long. 4.3 Influence of Sag Initial Phase Angle on SSTS Switching Dynamic Performance The initial phase angle of voltage sag refers to the phase angle of the voltage at the moment before the sag occurs. The phase angle of the first point in the transition process is calculated by using the zero crossing point before the sag occurs as the reference. The randomness of the occurrence of voltage sag is also reflected in the initial phase angle of the sag, which is determined by the operating state of devices in the power grid. To study its influence on the SSTS switching dynamics, phase A is used as the control phase, and the interval is 45°. The situation from 0° to 360° is tested one by one, and the results are shown in Table 4. According to the experimental data record results, draw its polar coordinates contrast diagram, as shown in Fig. 8. The following conclusions are obtained. (1) The closed-loop curve formed by the SSTS transfer time at different voltage sag starting angles approaches a positive circle, indicating that the voltage sag initial angle does not affect the transfer time of the test SSTS, which is always maintained at about 10 ms. (2) The closed-loop curve formed by the switch time of the test SSTS at different voltage sag onset angles tends to be elliptical. These rules can be summarized as follows: (a) When the initial phase angle of the sag is at 0° and 180°, the corresponding switch time is the longest, which is about 26.5 ms;

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(b) When the initial phase angle of the sag is at 90° and 270°, the corresponding switch time is the shortest, which is about 21.7 ms; (c) When the sag initial phase angle is 45°, 135°, 225°, and 315°, the corresponding switch time is between (a) and (b).

Table 4. Results of SSTS dynamic characteristics under different initial phase angles. Initial phase angle/°

Transfer time/ms

Switch time/ms

0

10.0479

26.8122

45

10.0202

24.3146

90

9.9626

21.7767

135

9.7116

23.922

180

10.1465

26.4676

225

10.1134

22.818

270

10.2482

21.764

315

10.2227

24.1237

90

Transfer time/ms Switch time/ms

135

180

45

8

225

12

16

20

24 28

0

315

270

Fig. 8. Dynamic performance of SSTS under different initial phase angles.

The above results show that the initial sag angle has influences on the switch time of SSTS. This is also due to the different time required for SSTS devices to reach the nodes that meet the commutation conditions after the initial angle change of the sag, so the switch time of SSTS is also different. 4.4 Influence of Sag Change Rate on SSTS Switching Dynamic Performance The change rate of voltage sag is a measure of the decline of the effective value of voltage in unit time when the voltage sag occurs. It aims to describe the speed of voltage decline. To quantify the influence of the sag change rate on the dynamic characteristics of SSTS switching, the experiment is carried out by changing the size of the sag change rate. The test results are shown in Table 5 and Fig. 9.

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Change rate/%

Transfer time/ms

Switch time/ms

3000

10.3173

26.4903

2000

9.3588

33.7539

1000

9.2845

33.7299

500

10.2128

100

10.2384

10

10.002

57.0493 147.518 1040.16

35

10

4

Switch time/ms

Transfer time/ms

30 25 20 15

10

10

3

2

10 5

10

100

500

1000

2000

Change rate/%/s

a

SSTS transfer time

3000

10

1

10

100

500

1000

2000

3000

Change rate/%/s

b SSTS switch time

Fig. 9. Dynamic performance of SSTS under different change rates.

According to the experimental results, the change rate of voltage sag does not affect the transfer time of SSTS, but the corresponding switch time is obviously affected. With the increase of the change rate, the switch time decreases rapidly (the change rate is less than 1000%/s), and then decreases slowly (the change rate is greater than or equal to 1000%/s). The test results show that when the voltage sag occurs, the faster the effective value of the voltage changes, the shorter the switch time, and vice versa.

5 Conclusion This paper quantifies the effects of four different sag characteristic parameters on the dynamic performance of SSTS experimentally. The main conclusions of this study can be summarized as follows: (1) The transfer time of the SSTS is its inherent characteristic, which is maintained in a constant value state and is not affected by the voltage sag characteristic parameters. In the test, the transfer time of the SSTS is about 10 ms. (2) With the decrease of voltage sag amplitude, the switch time is shortened, and the shortening is significant in the range of 0.8 p.u. to 0.7 p.u., and the shortening time is in the nanosecond level after 0.7 p.u., which has little effect.

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(3) The sag duration has no effect on the switch time of SSTS in general, but in some experiments, the switch time will increase for a specific duration time, but this phenomenon has no specific rule and is worthy of attention. (4) For different initial phase angles of sag, the switch time of SSTS presents an ‘oval’ rule, that is, when the initial phase angle is at 0° and 180°, the corresponding switch time is the longest. When the initial phase angle of sag is at 90° and 270°, the corresponding switch time is the shortest, and the switching time corresponding to other angles is between the two. (5) With the increase of the change rate of sag, the switch time first decreases rapidly, then slowly decreases, and finally stabilizes. That is, the faster the RMS of the voltage that is temporarily dropped changes, the shorter the switch time, and vice versa. However, different manufacturers of SSTS products by the parameters, structure and algorithm may be slightly different in the experimental results, but the same manufacturer of products should be roughly the same conclusion. The next step of the research will consider the impact of different load types on the dynamic performance of SSTS, the reason why different durations can randomly prolong SSTS switching time, and the impact of other power quality issues on the performance of SSTS. Acknowledgment. This research was supported by the Science and Technology Project of China Southern Power Grid (090000KK52190169/SZKJXM2019669).

References 1. Gao, Z., Zhang, K., Zhou, X., Ma, Y.: The discussion on power quality technology. In: IEEE International Conference on Mechatronics and Automation, pp. 569–574. IEEE, Harbin, China (2016) 2. Wang, Y., He, H., Fu, Q., Xiao, X., Chen, Y.: Optimized placement of voltage sag monitors considering distributed generation dominated grids and customer demands. Front. Energy Res. 9, 1–13 (2021) 3. Gao, T., Cao, J., Xu, Y., Zhang, H., Yu, P., Yao, S.: From power quality to power experience. In: 4th International Conference on Networking and Distributed Computing, pp. 116–120. IEEE, Hong Kong, China (2013) 4. PhDessay Homepage: https://phdessay.com/custom-power-devices-and-the-benefits-oftheir-application/. Accessed 15 Sept 2018 5. Mollik, M.S.: Review on solid-state transfer switch configurations and control methods: applications, operations, issues, and future directions. IEEE Access 8, 182490–182505 (2020) 6. Tsai, M.J., Zhou, J., Cheng, P.T.: A forced commutation method of the solid-state transfer switch in the uninterrupted power supply applications. In: 8th International Power Electronics Conference (IPEC-Niigata)/Energy Conversion Congress and Exposition, pp. 1609–1617. IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, Niigata, Japan (2018) 7. Cui, X., Zhang, Z., Zhao, H., et al.: SSTS-based soft transfer control method of motor load under different residual voltage condition. In: IEEE Energy Conversion Congress and Exposition, pp. 1075–1080. IEEE, Montreal, Canada (2015) 8. Pan, G., Chun-en, F., Nanxun, Z., Wei, L., Xiao, R.: Research of grading for series-connected thyristor valves of solid-state transfer switch. In: 4th International Conference on Electric Power Equipment-Switching Technology, pp. 444–447. IEEE, Xian, China (2017)

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9. Cheng, P.T., Chen, Y.H.: An in-rush current suppression technique for the solid-state transfer switch system. In: 4th Power Conversion Conference, pp. 1698–1705. IEEE, Nagoya, Japan (2007) 10. Sebastian, G., et al.: A novel PSO based fuzzy controller for robust operation of solid-state transfer switch and fast load transfer in power systems. IEEE Access 10, 37369–37381 (2022) 11. Arsad, A.Z., et al.: Rule-based fuzzy controller for solid state transfer switch towards fast sensitive loads transfer. IEEE Trans. Ind. Appl. 58(2), 1888–1898 (2022) 12. Huo, X., Lv, J., Guo, B., Li, K.: Experimental study on power quality disturbance tolerance and performance of SSTS. In: 2021 Power System and Green Energy Conference, pp. 558–564. IEEE, Shanghai, China (2021) 13. DL/T 1226-2013: Solid state transfer switch technical specification (2013)

Non-invasive Measurement Method for DC-Side Energy Storage Capacitance of Single-Phase Bridge Uncontrolled Rectifiers Zhibo Yang1 , Mingxing Zhu1 , Huaying Zhang2 , and Min Gao1(B) 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui,

China [email protected] 2 New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid, Shenzhen Power Supply Co., Ltd., Shenzhen 518020, Guangdong, China

Abstract. Single-phase bridge uncontrolled rectifiers are widely used in power electronic devices. Their DC-side energy storage capacitors play a key role in filtering, stabilizing the output voltage, and so on. In practice, it is difficult to measure the DC-side energy storage capacitance of rectifiers inside the device directly. Therefore, this paper gives an idea about a non-invasive measuring method for DC-side energy storage capacitance of single-phase bridge uncontrolled rectifiers. First, the single-phase bridge uncontrolled rectifier is modeled and analyzed considering the network impedance. Then, the DC-side energy storage capacitance is calculated by measuring the data of the source-side. Finally, the simulation analysis is conducted, and the calculated values are compared with the actual values. The results show that the capacity of the capacitor which calculated by the method put forward in this article is close to actual capacitance, which validates the availability of this method. This method has advantages of convenient calculation and engineering significance. Keywords: Non-invasive measurement · Uncontrolled rectifier · Energy storage capacitors

1 Introduction During the past few years, proportion of power from switching power supplies is gradually increasing in power delivered by the power supply system. The application of single-phase bridge uncontrolled rectifiers in switching power supplies is very common. At present, the rectification part of many microcomputers, televisions, and other household appliances used in the switching power supply is the single-phase bridge uncontrolled rectifier [1]. This electrical circuit constitutes one of main sources of power supply for DC power supplies, so it is necessary to analyze the single-phase bridge uncontrolled rectifier. Single-phase bridge uncontrolled rectifiers can turn AC into pulsating DC. To alleviate the pulsation degree of output voltage, energy storage capacitors are often added © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 101–110, 2023. https://doi.org/10.1007/978-981-99-4334-0_12

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to the output of circuits. It has the ability to stabilize energy exchange between input and the output, and stabilize the output voltage and inhibit the harmonic voltage on the output side [2]. In addition, the capacity of the energy storage capacitor in the rectifier also affects the ripple current of the capacitor itself, which in turn has an impact on the service life of the capacitor [3]. For the single-phase bridge uncontrolled rectifier, as the capacitance increases. Consequently, the ripple current that flows through the energy storage capacitor will increase, so that capacitor loss will increase to the pole and then gradually decrease [4]. It is noticeable that the DC-side energy storage capacitance will have a certain impact on the whole circuit, so we need to focus on the DC-side energy storage capacitance in rectifiers. For single-phase bridge uncontrolled rectifiers, the nominal value of the capacitor in the circuit may be known, but the capacitance will change with the influence of prolonged placement and environmental factors. Therefore, measuring the DC-side energy storage capacitance is indispensable. The existing researches mainly involve the selection of capacitance in rectifiers and the influence of the size of capacitance on circuit performance. Reference [5] analyzes the charging and discharging process of the single-phase uncontrolled rectifier, and obtains the design basis of the minimum capacitance based on the voltage fluctuation across the capacitor in the steady state. In [6], a calculation method for the design and selection of filter capacitors is given by the requirements of ripple voltage. Reference [7] analyses different operating modes of three-phase uncontrolled rectifiers which have a DC power supply. The average current value of the DC-side and root mean square (RMS) value of the AC-side current in every mode are derived by building a corresponding model. In [8], the expression of the output voltage is derived from different circuit models considering the network impedance. It is verified by simulation that the output voltage pulsation changes significantly when the filter capacitance increases in a certain range, but the average value of the output voltage remains unchanged. Reference [9] presents the theoretical and practical discussion of full bridge rectifiers which has a capacitor filter, and the mathematical expressions of peak current and voltage are obtained. In the above researches, Refs. [5, 6] provide criteria for the selection of the DC-side capacitance in rectifiers, but the calculation of capacitance is not involved. Although Refs. [7–9] involve the calculation of some physical quantities in the rectifier, the calculation process is complex and not practical. According to the above analysis, we know that the DC-side energy storage capacitance of the single-phase bridge uncontrolled rectifier has a large impact on the performance of this circuit, and the capacitance is prone to change. To address the abovementioned problems, this article suggests a non-invasive measurement method for DC-side energy storage capacitance of single-phase bridge uncontrolled rectifiers. Since it is difficult to measure the component parameters inside the circuit in practice, this method obtains the parallel network parameters of the circuit and calculates the DC-side energy storage capacitance by modeling. Effectiveness of this measurement method is proved by comparing calculated value with actual value through simulation analysis. The surplus part of this article is set in the following form. The working principle of single-phase bridge uncontrolled rectifiers is narrated in Sect. 2. Section 3 derives the

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relevant equations by modeling. The effectiveness of this paper’s method is proven by simulation in Sect. 4. The contributions of this paper are finally concluded in Sect. 5.

2 The Working Principle of the Single-Phase Bridge Uncontrolled Rectifier 2.1 Filtering Principle The topology of the single-phase bridge uncontrolled rectifier is illustrated in Fig. 1. It is assumed that the circuit works in the steady state. Since the average DC consumed by the post-stage circuit as a load in the steady state is certain, the resistor R is used as the load in the analysis. I2 VD1

RT

us

VD3

Id

LT

uo

u2 VD2

VD4

Fig. 1. The topology diagram of the single-phase bridge uncontrolled rectifier.

The working principle of the circuit is described as follows. When u2 lies in a positive half-cycle and the amplitude is higher than uc that across the capacitor, VD1 and VD4 conduct. At this time the AC power supply charges the capacitor C and provides energy to load R. Without considering the internal resistance of the diodes, the voltage across the capacitor uc is the same as u2 , as shown in section ab in Fig. 2. When u2 reaches its peak and starts to fall, the capacitor discharges through the load R by the time constant RC as an exponential function. And the two trends are basically equal, as shown in section bc in Fig. 2. On account of the capacitor discharges as an exponential function, when both decline to a certain extent, the decline rate of uc is lower than that of u2 . When uc is greater than u2 , the diodes VD1 and VD4 turn off, after which the capacitor C keeps discharging to R. And uc decreases as the exponential scale, which is shown in the cd section in Fig. 2. While the amplitude of the negative half-cycle waveform of u2 is greater than uc , another pair of diodes VD2 and VD3 conduct because of adding positive voltage, and u2 charges the capacitor C again. When uc reaches the peak of u2 , it starts to drop, and after dropping to a certain degree, VD2 and VD3 turn off, the capacitor C discharges to the load R. Then uc decreases according to the exponential scale, and the diodes VD1 and VD4 conduct after discharging to a certain degree, and the above process is repeated later.

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uo

π

ωt

2π

Fig. 2. Output voltage waveform at ideal conditions.

2.2 Output Voltage Calculation If the on-state resistance of the diode is taken into account, the output voltage uo is represented in Fig. 3, where shaded parts represent the on-state voltage drop of the diode.

uo

π

ωt

2π

Fig. 3. Output voltage waveform when considering the internal resistance of the rectifier.

When considering the diode internal resistance, the output voltage waveform of the rectifier is difficult to be described by an expression. Thus, an approximate calculation is used to equate the waveform shown in Fig. 3 to a sawtooth waveform, which is shown in Fig. 4. uo

U O max U O min

π T 2

2π

3π

ωt

Fig. 4. Approximate waveform when considering the internal resistance of the rectifier.

√ Assuming that the capacitor reaches the peak of u2 each charge, that is UO max = 2u2 , and it drops linearly with the initial slope of the RC discharge. The voltage

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expression of the capacitor discharge in the RC parallel circuit is: −t

uc (t) = UO max · e RC

(1)

The derivation of (1) to t can be obtained by: −t

uc (t) = UO max · e RC · −

1 RC

(2)

Substituting t = 0 into (2) gives the initial slope of − UORCmax when the capacitor is disO max , charged, and the slope of the straight line L can be obtained from Fig. 4 as UO min −U T 2

so it is obtained by: UO min − UO max T 2

=

−UO max RC

(3)

The mean value of the output voltage is expressed as: UO(AV ) =

UO max + UO min UO max − UO min = UO max − 2 2

(4)

Substituting (3) into (4) yields: UO(AV ) = UO max (1 −

√ T T ) = 2U2 (1 − ) 4RC 4RC

(5)

It can be seen from (5) that when the circuit is unloaded, i.e. the load resistance R = ∞, the discharge time constant of the energy storage capacitor is infinite, the √ average value of the output voltage is UO(AV ) = 2U2 . The time constant RC is usually made RC ≥ 3∼5 2 T at design time, and at this point the average value of the output voltage is calculated as UO(AV ) ≈ 1.2U2 .

3 The Calculation Model of DC-Side Energy Storage Capacitance To obtain the DC-side energy storage capacitance, the voltage source parameters, network impedance, diode parameters, source-side active power, the source-side’s current and voltage of single-phase uncontrolled rectifiers need to be known. When considering the internal resistance of the diode, the equal circuit shown by Fig. 1 is modeled as Fig. 5.

RT

us

LT

rT uo

Fig. 5. Equivalent circuit model when considering diode internal resistance.

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The network resistance power loss is calculated by: 2 ∗ RT PTR = I2RMS

(6)

where I2RMS represents the source-side current and RT is the network resistance. The diodes power loss in one cycle is:   I2RMS 2 × rT (7) PVD4 = 4 × √ 2 where rT is the diode resistance. Ignoring the capacitor power loss, the active power loss of the load is obtained according to the active power balance: Pd = P1 − PTR − PVD4

(8)

where P1 is the real power of the power source. Considering the no-load condition, the equivalent resistance of the circuit is: Rsum = RT + 2 ∗ rT

(9)

The equivalent impedance of the circuit is:  Zsum = R2sum + XT2

(10)

where XT is the network inductance, XT = 2π ∗f ∗LT , and LT is the network inductance. The port voltage is: √ (11) Ud 0 = 2 ∗ U20 − 2 ∗ VF where VF is the diode on-state voltage drop. Under the load condition, we have: ⎧  ⎨ UO(AV ) = Ud 0 ∗ (1 − Zsum ) 2∗R 2 ⎩ R = UO(AV )

(12)

Pd

The average output voltage UO(AV ) and load resistance can be obtained by (12), and the capacitance C can be obtained by substituting the obtained UO(AV ) and R into (5). In summary, the flow chart for measuring DC-side energy storage capacitance of single-phase uncontrolled rectifiers is shown in Fig. 6. The detailed steps include: (1) Determine the network impedance, active power, and the current and voltage of source-side; (2) Calculate the network resistance loss and diodes power loss based on the measured data; (3) Derive the load active power by establishing the active power balance; (4) Calculate the average value of the output voltage and the size of the load resistance; (5) Calculate the DC-side energy storage capacitance according to the input-output relationship. The above analysis shows that if the RMS value of the source-side, the network impedance, the RMS value of the source-side active power, the voltage and current of the source-side are known, the capacitance can be determined.

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Fig. 6. The flow chart for measuring DC-side energy storage capacitance.

4 Simulation Analysis 4.1 Simulation Parameter Setting To verify this method’s effectiveness, the model shown in Fig. 1 is built by MATLAB/Simulink. The concrete parameters are listed in Table 1. 4.2 Output Voltage Simulation Analysis The output voltage is changed by changing the DC-side energy storage capacitance. The output voltage calculated by (5) is compared with the actual output voltage obtained by simulation, and the comparison diagram is shown in Fig. 7. It can be seen from Fig. 7 that in the rectifier, the output voltage’s average value obtained from (5) has a small error compared with the actual output voltage value when the DC-side energy storage capacitor C is in a certain range. 4.3 Simulation Analysis of DC-Side Energy Storage Capacitance The effect of DC-side energy storage capacitance on source-side active power is shown in Fig. 8.

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Parameters

Value

Frequency of the voltage source f/Hz

50

RMS value of the voltage source U20 /V

25

Network resistance RT /

0.26

Network inductor LT /mH

0.73

Diode on-state voltage VF /V

0.8

Diode slope resistance rT /

0.055

Load resistance R/

1.82

Filter capacitor C/µF

16500

22.6 22.5

U o (V)

22.4 22.3

The calculated output voltage The output voltage obtained by simulation

22.2 22.1 22 16500 17000 17500 18000 18500 19000 19500 20000

C ( F)

Fig. 7. Calculated and actual values of output voltage for different capacitance values. 364 362

1

P (W)

360 358 356 354 352 15000 20000 25000 30000 35000 40000 45000 50000

C(

F)

Fig. 8. Source-side active power at different capacitance.

Figure 8 shows that as the DC-side energy storage capacitance increases, the sourceside active power decreases gradually. Thus it has the necessity to calculate the energy storage capacitance accurately.

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The single-phase bridge uncontrolled rectifier model is built by MATLAB/Simulink, and the simulation parameters are the same as Table 1. The proposed method in this article is used to calculate the DC-side energy storage capacitance and compare it with the actual capacitance. Firstly, the real power P1 of the source-side is 363.2 W, the effective value of the source-side current I2RMS = 16 A, and the effective value of voltage U2RMS = 20 V. Then, indicators on the DC-side are obtained according to the formulas in Sect. 4 and compared with the actual values, and the results are shown in Table 2. Table 2. The comparison results between the calculated value and the actual value. Id /A

UO(AV ) /V

R/ 

C/µF

Calculated value

11.91

22.42

1.87

15400

Actual value

11.25

22.16

1.82

16500

Error (%)

5.86

1.17

2.74

−6.67

It is seen in Table 2 that the output voltage deviation obtained by the proposed method is within 2%, the load current error is within 6%, the load resistance error is within 3%, and the capacitance error is about 7%. According to the National Standard of the People’s Republic of China GB2693-86, the measurement accuracy of the capacitance is required to 10% of the nominal capacitance deviation. It is proved that the method used in this article meets the capacitance measurement standard and has a certain application value in practice.

5 Conclusion This article presents a non-invasive measurement approach for DC-side energy storage capacitance of single-phase bridge uncontrolled rectifiers. Firstly, the working principle of the single-phase uncontrolled rectifier is analyzed. The output voltage is analyzed considering the internal resistance of diodes, then the formula of the output voltage is deduced. The DC-side energy storage capacitance can be calculated by measuring the source-side data. Finally, the calculated output voltage, load current, and capacitance are compared with the real values by simulation software. The results indicate the errors of the results calculated by the proposed method are small, which validates the high accuracy of the proposed method. In practice, it is competent to calculate the DC-side energy storage capacitance of single-phase uncontrolled rectifiers. Acknowledgment. This research was supported by the Science and Technology Project of China Southern Power Grid (090000KK52190169/SZKJXM2019669).

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References 1. Mohan, N., Undeland, T.M., Robbins, W.P.: Power electronics-converters, applications, and design, 3rd edn. Wiley, New York, NY (2003) 2. Khan, M.A., Pavel, A.A., Khan, M.R.: Design of a single phase rectifier with switching on AC side for high power factor and low total harmonic distortion. In: Region 5 Technical Conference, pp. 289–292. IEEE, Fayetteville, AR (2007) 3. Stevens, J.L., Shaffer, J.S., Vandenham, J.T.: The service life of large aluminum electrolytic capacitors: effects of construction and application. IEEE Trans. Ind. Appl. 38(5), 1441–1446 (2002) 4. Xu, L.G., Chen, Q.H., Zhu, X.: Mathematical model and analysis of ripple current of single phase rectifier filter capacitor. Power Electron. 43(3), 107–143 (2009) 5. Huang, J.F.: Design of single phase bridge rectifier filter capacitor. Electr. Switchgear 45(3), 2 (2007) 6. Dong, Z.Q., Zhao, W.H., Liu, Y.H.: Research on design and selection method of rectifier filter capacitor. Electron. Des. Eng. 20(14), 3 (2012) 7. Gerlando, A.D., Foglia, G.M., Iacchetti, M.F.: Comprehensive steady-state analytical model of a three-phase diode rectifier connected to a constant DC voltage source. IET Power Electron. 6(9), 1927–1938 (2013) 8. Wang, Y.N., Du, S.J., Liu, X.N.: Voltage analysis of capacitor-filtered three-phase bridge rectifier circuit. J. Hefei Univ. Technol. (Nat. Sci.) 28(5), 4 (2005) 9. Doval-Gandoy, J., Castro, C., Martinez, M.C.: Line input AC-to-DC conversion and filter capacitor design. IEEE Trans. Ind. Appl. 39(4), 1169–1176 (2003)

Application of Generalized Predictive Control in Buck Converter Fei Song, Lusheng Ge(B) , and Kuang Wang School of Electrical and Information Engineering, Anhui University of Technology, Maanshan 243032, China [email protected]

Abstract. In order to solve the problems of poor dynamic performance and low steady-state accuracy of switching converters by traditional frequency domain methods, a method combining predictive control and Buck converter is proposed. First, analyze the control idea of the Buck converter. Secondly, double closed-loop PI (Proportional Integral) controller is designed, and Simulink model is used to simulate the double closed-loop PI control Buck converter, and the control system can dynamically adjust the time and adjust the speed when switching load. Then the algorithm design of GPCPID-PI (Generalized Predictive Control Proportional Integral Derivative) controlled Buck converter is carried out. Keywords: PI controller · Buck converter · GPCPID-PI control · Voltage fluctuation

1 Buck Controller Design Ideas Buck circuit in the military, space and life and other charging and discharging field has a very important position, and in order to make the system get a stable output voltage, usually with a variety of circuits or controllers to complement the cooperation, so in this study are based on the Buck circuit research [1]. Typically, a step-down DC/DC converter topology consists of an input voltage source, a power switching device, a filter network RLC, and a freewheeling component [2]. Buck controller overall block diagram as shown in Fig. 1, respectively, Buck circuit, drive circuit, GPCPID controller, PI controller and other parts, the specific control idea is: the outer ring is controlled by the GPCPID controller, its output signal is sent to the current inner ring, the inner ring is controlled by the traditional PI, and then converted to the drive circuit, thereby controlling the Buck circuit. This can be composed of GPCPIDPI cascade control, the control block diagram shown in Fig. 1. The generalized prediction of the PID output value is used as the reference value of the inner loop PI, not the output voltage of the Buck converter, so the Buck converter is controlled by the inner loop controller. Therefore, it is necessary to treat the PI controller and Buck converter as a whole when obtaining the mathematical model of the converter.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 111–116, 2023. https://doi.org/10.1007/978-981-99-4334-0_13

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L Vin

Q1 C

Q2

Driver circuit

1

u (k )

PI controller

iref

R

iL GPCPID controller

Vref

Fig. 1. GPCPID-PI cascade control structure block diagram.

2 Generalized Prediction PID Control Strategy 2.1 PID Control When the load is switched or the components change, the overall model of the switching power supply will change, and the ideal operating effect cannot be achieved if only the open-loop control is used. Therefore, it is necessary to change the control method and use digital closed-loop control to carry out real-time feedback correction, so as to meet the actual control needs. The PID control algorithm is simple, wide application range, mature technology, can meet the system requirements. It is easy to know from the literature that the PID transfer function is as follows [3] (1): GC (S) = KP + W +W

KP = KC WZZ1 WZZ2 ; Ki = KC ; Kd = 1 2 the gain value.

Ki + Kd S S

KC WZ1 WZ2 ,

(1)

WZ1 , WZ2 is the zero point and KC is

2.2 Generalized Predictive PID Control The objective function of a generalized predictive control algorithm is generally taken as the following Eq. (2): J =

N  j=1

[w(k + j) − y(k + j)]2 +

Nu 

λ[u(k + j − 1)]2

(2)

j=1

where N represents the predicted time domain, Nu represents the control time domain, w(k + j) represents the expected output value, y(k + j) represents the predicted output value, and λ is the weighted coefficient, and w(k + j) = αw(k + j − 1) + (1 − α)c, α is the softening coefficient, α ∈ [0, 1], c is the set value and k is the current moment. The following Eq. (3) is a controlled autoregressive model: A(z −1 )y(k) = B(z −1 )u(k − 1) +

C(z −1 )ξ(k) 

(3)

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where, A(z −1 )C(z −1 ) and B(z −1 ) represent the n and m order polynomials of z −1 , z −1 represents the backward operator,  is the differential operator, the system output value y(k), the control system input u(k) together constitute the upper equation, ξ(k) represents the white noise sequence, and the following theoretical derivation process of the white noise sequence value will be regarded as 0. Combining the generalized predictive control (GPC) algorithm and the PID control algorithm [4], the objective function of the GPCPID control algorithm is the following Eq. (4):   N N u   Ki [e(k + j)]2 + Kp [e(k + j)]2 λ(u(k + j − 1))2 (4) + J (k) = 2 2 +K [ e(k + j)] d j=1 j=1 e(k) = e(k) = 2 e(k) = 0, λ represents the weighted coefficient, Kp , Ki , Kd represent the term coefficients of the ratio, integral and differential of PID, e(t + j) = w(t + j) − y˜ (k + j). Introduce a set of Diophantine equations and make C(z −1 ) = 1 possible to get the Eq. (5):  1 = Ej (z −1 )A(z −1 ) + z −j Fj (z −1 ) (5) Ej (z −1 )B(z −1 ) = Gj (z −1 ) + z −j Hj (z −1 ) Multiply the left and right ends of formula (4) by Ej qj at the same time to obtain the following Eq. (6): Ej Ay(k + j) = Ej Bu(k + j − 1) + Ej ξ(k + j)

(6)

From formula (6), it can be transformed into the following formula: 1 − z −j Fj (z −1 ) = Ej (z −1 )A(z −1 )

(7)

Substituting Eq. (6) into Eq. (5) can obtain the following equation: y(t + j) = Ej Bu(t + j − 1) + Fj y(t) + Ej ξ(t + j)

(8)

Since ξ(t + j) is random noise, it can be ignored, so the optimal prediction output of the system at time k + 1 is as follows: y˜ (k + j) = Gj u(t + j − 1) + Fj y(t) + Hj u(t − 1)

(9)

f (t + j) = Fj y(t) + Hj u(t − 1)

(10)

Definition:

Then the optimal prediction output is: y˜ (k + j) = Gj u(t + j − 1) + f (t + j)

(11)

e(t) = [w(t) − f (t)] − Gj u(t − 1), j = 1, 2, 3 . . . , N

(12)

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e(t + j) = [w(t + j) − f (t + j)]−   Gj u(t + j − 1) − Gj u(t + j − 2)

(13)

e2 (t + j) = [2 w(t + j) − 2 f (t + j)] − [Gj u(t + j − 1) −2Gj−1 u(t + j − 2) + Gj−2 u(t + j − 3)], j = 3, 4 . . . , N

(14)

In order to facilitate the later theoretical derivation, the matrix is introduced: ⎡

g0 ⎢ g1 ⎢ ⎢ ⎢ g2 ⎢ Ga = ⎢ . ⎢ .. ⎢ ⎢ ⎣ gN −2 gN −1 ⎡

g0 g1 − g0

⎢ ⎢ ⎢ ⎢ g2 − g1 ⎢ Gp = ⎢ .. ⎢ . ⎢ ⎢ ⎣ gN −2 − gN −3

0 g0

0 0

g1

g0

g2 .. .

··· ··· .. .

. g1 . . .. . . . .

⎤

0 0 .. . 0

g0 gN −2 gN −3 · · · gN −Nu

0 g0

0 0

g1 − g0

g0

g2 − g1 .. .

g1 − g0 .. .

gN −1 − gN −2 gN −2 − gN −3 gN −3 − gN −4

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(15)

N ×Nu

··· ··· .. .

0 0 .. .

.

0

..

..

⎤

. g0 · · · gN −Nu − gN −Nu −1

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ N ×Nu

(16) ⎡ ⎢ ⎢ ⎢ ⎢ Gj = ⎢ ⎢ ⎢ ⎣

g0 g1 − g0 g2 − 2g1 + g0 .. . gN −1 − 2gN −2 + gN −3

⎤

··· 0 ⎥ .. .. ⎥ . . ⎥ ⎥ .. ⎥ . 0 ⎥ ⎥ .. ⎦ . g0 · · · gN −Nu − 2gN −Nu −1 + gN −Nu −2 N ×N

(17)

u

where gi is the coefficient of the term of z −i in Gj (z −1 ). Therefore, the following formula (18) can be obtained: ⎧ ⎪ ⎨ e = w − f − Ga U e = w − f − Gp U (18) ⎪ ⎩ 2 2 2  e =  w −  f − Gj U In Eq. (18), U is the input vector, and by substituting Eq. (18) into Eq. (5), we can obtain: J = Ki eT e + Kp eT e + Kd 2 eT 2 e + λU T U

(19)

Application of Generalized Predictive Control in Buck Converter

In order to find the optimal solution, let can be obtained as follows (20), (21):

∂J ∂U

115

= 0, after simplification, the control law

U = Hp (w − f ) + Hi (w − f ) + Hd (2 w − 2 f )

(20)

Hp = e1T (λI + Kp GPT Gp + Ki GiT Gi + Kd GdT Gd )−1 Kp GPT Hi = e1T (λI + Kp GPT Gp + Ki GiT Gi + Kd GdT Gd )−1 Ki GiT

(21)

Hd = e1T (λI + Kp GPT Gp + Ki GiT Gi + Kd GdT Gd )−1 Kd GdT In the above formula, e1T = [1, 0, 0, . . . , 0]TNu ×1 , I is the identity matrix, and the formula (21) is the control law for generalized prediction of PID.

3 Verification by Experiment The control parameters of GPCPID controller include PID parameter, predictive time domain, control time domain and weighted coefficient. When designing the GPCPID controller, the transfer function model of the controlled system must be obtained first. The output value of the GPCPID controller is used as a reference value for the internal loop PI. Therefore, the PI controller and Buck converter should be considered as a whole. According to control theory knowledge, the transfer function can be written as: G(s) =

LCRs3

RKpi Vin s + RKii Vin + (L + RCKpi Vin )s2 + (R + Kpi Vin + RCKii Vin )s + Kii Vin

(22)

According to the above Eq. (14), the output response fitting method of the controlled system is adopted [5]. The proportional integral controller of the inner ring is changed to the proportional controller [6], that is, Kpi in Eq. (22) is changed to Kp , and the value of Kii is zero. Then the generalized controlled object is simplified as Eq. (23): G(s) =

RKP Vin LCRs2 + (L + RCKP Vin )s + R + KP Vin

(23)

Then by discretizing the above formula, the expression after discretization is the following formula (24): G(z) =

c1 z + c0 z 2 + b1 z + b0

(24)

3.1 Experimental Results The platform of lice suborder was built and verified by experiment. To verify this, switch the load resistance back and forth between 0.5  and 0.25 . When the load current is 5–10, the voltage fluctuation is 730 mV. When the load current is transitioning from 10 A to 5 A, the adjustment time of the output voltage is 300 us and the fluctuation of the output voltage is 980 mV. As can be seen from the voltage fluctuation and adjustment

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time in the figure, the double closed-loop control algorithm designed in this paper can control the DC/DC Buck converter, but it has some shortcomings such as overvoltage and long adjustment time, and the dynamic performance cannot meet the expectations. Under the GPCPID control algorithm, the output voltage can be stabilized at about 2.5 V. When the load current jumps from 5 A to 10 A, the voltage fluctuation is 530 mV; When the load current jumps from 10 A back to 5 A, the maximum fluctuation voltage of the output voltage is 690 mV. Compare with the experimental results of the double closed-loop PI controller, as shown in Table 1. Table 1. Experimental comparison results. Way

Algorithm PI

GPCPID-PI

Contrast value

Adjustment time (us)

Volatility (mV)

Adjustment time (us)

Volatility (mV)

Adjustment time (us)

Volatility (mV)

5 A → 10 A

260

730

130

530

↓ 130

↓ 200

10 A → 5 A

300

980

150

690

↓ 150

↓ 290

References 1. Ren, J., Chen, Z., Sun, M., Sun, Q., Wang, Z.: Proportion integral-type active disturbance rejection generalized predictive control for distillation process based on grey wolf optimization parameter tuning. Chin. J. Chem. Eng. 49 (2022) 2. Shiravani, F., Cortajarena, J.A., Alkorta, P., Barambones, O.: Generalized predictive control scheme for a wind turbine system. Sustainability 14(14) (2022) 3. Li, M., Lang, J., Zhang, C., Cui, C., Xu, L.: Decentralized composite generalized predictive control strategy for DC microgrids with high PV penetration. Int. J. Robust Nonlinear Control 32(14) (2022) 4. Franco, R.A.P., Cardoso, Á.A., Filho, G.L., Vieira, F.H.T.: MIMO auto-regressive modelingbased generalized predictive control for grid-connected hybrid systems. Comput. Electr. Eng. 97 (2022) 5. Sun, G., Chen, J., Yong, Y., Li, Y.: Generalized predictive control of spacecraft attitude with adaptive predictive period. Int. J. Adapt. Control Signal Process. 36(3) (2021) 6. Cheng, C., Peng, C., Zhang, T.: Fuzzy K-means cluster based generalized predictive control of ultra supercritical power plant. IEEE Trans. Ind. Inf. 17(7) (2021)

Sliding Mode Control of PMSM Based on Double Power Reaching Law Kai Zhou, Lusheng Ge(B) , and Kuang Wang School of Electrical and Information Engineering, Anhui University of Technology, Maanshan 243032, China [email protected]

Abstract. A sliding mode controller using double power reaching law is proposed to address the issues of large overshoot and poor robustness in traditional sliding mode control (SMC) for permanent magnet synchronous motors (PMSM). The controller contains two power-law terms, with the smaller power law term dominating when the system approaches the sliding mode surface and the larger power-law term dominating when the system moves away from the sliding surface, thus accelerating the convergence rate in different stages. The designed controller is compared with exponential approach law and PI controller under stable and perturbed conditions. The results indicate that the designed controller reduces overshoot by 12.5% and 8.4% compared to the PI controller and exponential approach law, respectively. The designed controller achieves zero overshoot tracking under sudden load changes. Simulation results demonstrate that this control strategy effectively reduces overshoot and enhances the robustness of the system. Keywords: PMSM · Speed control system · SMC · Double power approach law

1 Introduction To address the challenge of traditional control methods failing to meet the demands of complex control, experts and researchers worldwide have applied modern control theory to PMSM vector control systems [1]. While many researchers have developed reaching laws that effectively reduce chattering [2], but each reaching law has its own shortcomings in its application. According to the finite-time convergence theorem, it is apparent that the exponential approach law takes a considerable amount of time to converge, whereas the high convergence rate of the isokinetic reaching law does not effectively minimize chattering. In literature [3], the conventional variable exponential term and pure power reaching law are merged to accelerate the approach speed when the system is distant from the sliding surface. This method exhibits significant chattering during motor startup, which should be minimized as much as possible in practical applications. In Ref. [4], the speed at which the system state variable approaches is connected to the switching function of the sliding surface, which allows for dynamic regulation of the approach speed. This results in a decrease in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 117–122, 2023. https://doi.org/10.1007/978-981-99-4334-0_14

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the response time of the controller and a more effective reduction of chattering. Nevertheless, the approach law involves numerous intricate parameters, which fails to address the issue of stable control effect under disturbance. In Ref. [5], a double power approach law has been designed. The switching of two power terms makes the system keep fast approaching speed all the time. Currently, numerous papers [6] aim to reduce system overshoot by utilizing novel reaching laws to mitigate chattering in sliding mode control. Building on the aforementioned literature, this paper applies the double power approach law to PMSM control. Theoretical analysis indicates that, in comparison to traditional control methods, sliding mode control utilizing the double power approach law exhibits superior performance under diverse conditions. The steady state is reached faster than the traditional control method after the disturbance, which strengthens the robustness of the system.

2 Double Power Approach Law To form a double power approach law, a term with power greater than 1 is incorporated into the traditional power reaching law, as shown below. •

α β S = −k1 |S| sgn(S) − k2 |S| sgn(S)

(1)

In the formula, α > 1, 0 < β < 1, k1 > 0, k2 > 0. The second term of the approach law is the conventional power approach law, while the first term features a higher power term than the traditional power approach law. The integration of these two terms guarantees that the system state can maintain a rapid movement speed, whether it is distant from or near the sliding surface.

3 Sliding Mode Controller Design Define the PMSM state variables:



x1 = ωref − ωm •

•

x2 = x1 = − ωm

(2)

In the formula: ωref is the set speed of the motor, and ωm is the actual speed measured by the motor sensor. Combining Eq. (2), we can obtain: ⎧ 3pn ψf 1 • • ⎪ iq ) ⎨ x1 = − ωm = (TL − J 2 (3) ⎪ ⎩ x• = − ω•• = − 3pn ψf i• 2 m q 2 •

Let u = iq , D = can be written:

3pn ψf 2

, according to Eq. (3), the state space equation of the system 

•

x1 • x2



=

01 00





0 x1 + u x2 −D

(4)

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The sliding surface function is defined as s = cx1 + x2 where: c > 0 is the sliding surface parameter. Partial differentiation of Eq. (7) can be obtained as follows: •

•

•

•

s = c x1 + x2 = cx2 + x2 = cx2 − Du

(5)

Using the double power approach law to solve the controller expression is:  1 iq = [cx2 + k1 |s|α sgn(s) + k2 |s|β sgn(s)] dt D

(6)

4 The Simulation Verification The simulation model is constructed in the MATLAB/SIMULINK environment, and the system’s control block diagram is depicted in Fig. 1. Anti-park iq

ref

SMC

+

m

idref=0

PI

dq +

+

PI

-

u

ud

+

i

ia

dq

id Decoupling module

threephase inverter

SVPWM

-

iq

Speed calculation

udc u

uq

+

i Park Position and speed sensors

ib ic abc Clarke

PMSM

Fig. 1. Structure of control system.

Table 1 displays the motor parameters. According to Eq. (6), the output expression of the sliding mode controller, which is based on the traditional exponential approach law, is as follows:  1 iq = (7) [c1 x2 + μsgn(s) + qs] dt D The following simulation are designed to illustrate the effect of the double power approach law on reducing system overshoot and enhancing system robustness.

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Parameter

Value

Polar logarithm

4

Stator inductance/mH

8.5

Stator resistance/

2.875

Flux linkage/Wb

0.175

Inertia/(kg • m2 )

0.003

Viscous damping/N • m • s

0.008

Simulation conditions: Set the simulation duration to 0.4 s, target speed to 1000 rad/s, start with load and load at 0.2 s. PI control parameters: speed ring KP = 0.14, Ki = 7, speed ring output limit is −30 ∼ 30, current ring KP = 9350, Ki = 3162, speed ring output limit is −161 ∼ 161. The control parameters of the exponential approach law are: c1 = 60, μ = 200, q = 300, and the output limit is −30 ∼ 30. Double power approach law control parameter: c = 1000, k1 = 0.7, k2 = 100, α = 1.1, β = 0.85. When the motor starts with load and suddenly increases load during operation, the speed and torque response waveforms of the three control methods are shown in Fig. 2. It can be seen from Fig. 2(a) that when the motor runs to 0.2 s, the load suddenly increases, the double power approach law control method can achieve no overshoot tracking when the load is suddenly added. The adjustment time for the traditional PI control to attain the target speed is 0.025 s, while the exponential approach law is 0.018 s, and the double power approach law is 0.002 s. The double power approach law control technique retains outstanding dynamic performance even during the motor’s loaded start. Compared with traditional PI control, the overshoot of sliding mode control using double power approach law is reduced by 12.5%, and that of sliding mode control using exponential approach law is reduced by 8.4%. It shows that the dynamic performance and robustness of the motor controlled by the double power approach law are obviously better than the traditional exponential approach law control and PI control, no matter in the on-load starting or sudden load during operation. As depicted in Fig. 2(d), it is evident that during the motor’s load starting, the output torque is strictly controlled within a narrow range, when sudden loading, double exponential approach law control motor acceleration time is shorter, to reach the target speed is faster, and reach the target output torque after speed overshoot will be smaller.

Sliding Mode Control of PMSM Based on Double Power Reaching Law

(a) Speed response under three control strategies

(b) PI control torque response when starting with load and suddenly adding load

(c) The exponential approach law controls the torque response in the case of starting with load and suddenly adding load

(d) The torque response is controlled by the double power approach law in the case of starting with load and suddenly adding load Fig. 2. Simulation waveform when the motor is started with load and suddenly loaded.

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5 Conclusion In this paper, the sliding surface is designed with the error between the target speed and the actual rotation and the acceleration of the speed as state variables. The operation of the motor with load starting and sudden increase of load is compared with the traditional PI control and sliding mode control using exponential approach law. According to the simulation results, it can be seen that the sliding mode control using the double power approach law is better than other control methods, which is mainly manifested in smaller overshoot and stronger robustness, no matter when the motor is started with load or when the motor is suddenly increased during operation.

References 1. Liu, Y.: Review of research on sliding mode variable structure control. J. Shanghai Dianji Univ. 19(02) (2016) 2. Yu, C., Kang, E.: Design of fuzzy sliding mode speed controller for permanent magnet synchronous motor. Electr. Mach. Control 26(7) (2022) 3. Dai, P., Xu, N., Xie, H., Lv, Y.: PMSM sliding mode control based on fast power reaching law. Electr. Mach. Control 21(11) (2017) 4. Pan, X., Zhao, S., Yang, X., Xiao, P.: Research on sliding mode control of PMSM based on asymptotic reaching law. Small Spec. Electr. Mach. 50(5) (2022) 5. Zhang, H., Fan, J., Meng, F., Huang, J.: A new double power reaching law for sliding mode control. Control Decis. 28(2) (2013) 6. Yue, C., Yu, H., Meng, X.: Decouple sliding mode control for underactuated systems based on novel reaching law. Control Eng. China 22(05) (2022)

Distinguishment of Power Quality Disturbances Using Segmented Adaptive S Transform Fang Fang1 , Zhensheng Wang1 , Tianhong Pan1(B) , Jun Tao1 , and Huaying Zhang2 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui,

China [email protected] 2 New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid (Shenzhen Power Supply Co., Ltd.), Guangdong 518020, Shenzhen, China

Abstract. With the development of microgrids and distributed power sources, a large number of non-linear loads are connected to the grid, which increasingly cause serious problems of power quality. It is important to distinguish and deal with the power quality disturbances. In order to compensate for the shortcomings of current power quality disturbance classification, a segmented adaptive S transform is proposed in this work. Firstly, various adjustment factors are introduced into the S transform Gaussian window function, which can adjust the width of window function more flexibly. Then, the signal is divided into different frequency bands. Different adjustment factors are selected to process the signal according to different segments, which reduces the difficulty of parameter selection. The test of power quality disturbance shows that the proposed segmented adaptive S transform algorithm improves the accuracy of power quality disturbance classification and is suitable for the accurate and fast detection of disturbance signals in power systems. Keywords: Power quality disturbances · S transform · Segmented adaptive strategy

1 Background More and more users, especially high-end manufacturing users, have put forward high requirements for power quality. At the same time, a large number of new energy sources are connected to the power grid [1], which leads to the increasingly complex problems of power quality. The management of power quality is imminent, and how to distinguish the power quality disturbances is a key issue. The detection of power quality disturbances is mainly divided into two steps: feature extraction and pattern recognition. In the feature extraction stage, the time-frequency analysis methods, such as short-time Fourier transform (STFT) [2], wavelet transform (WT) [3], S transform (ST) [4] have been used. The ST uses a Gaussian window function and the window width is proportional to the reciprocal of frequency, which alleviates the disadvantage of the fixed window width function to some extent. And the feature © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 123–128, 2023. https://doi.org/10.1007/978-981-99-4334-0_15

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extracted by ST is not sensitive to noise. So, the ST has been widely used to analyze power quality problems. Although the Gaussian window of the traditional ST varies with frequency, its property of being inversely proportional to frequency makes it still relatively fixed. It is difficult to perform in places where the time-frequency resolution requirements are more flexible, which results in poor time-frequency resolution. For this reason, Liang et al. [5] proposed other windows (such as the Kaiser window) to improve the time-frequency resolution. Xu et al. [6] proposed an incomplete ST which significantly reduces the computational effort of the ST and enables it to meet the real-time requirements. Sejdi´c et al. [7] proposed a generalized ST, in which the window’s width corresponding to each frequency point is controlled. In this study, a segmented adaptive S transform (SAST) is proposed. Firstly, various adjustment parameters are introduced into the ST, which can adjust the width of Gaussian window more flexibly. In addition, a segmentation mechanism is proposed to segment the ST, and the optimal value of the width of Gaussian window is determined by matching the interval of the main value of the disturbance signal spectrum. The proposed method reduces the difficulty of parameter selection and computational complexity, and realizes the fast and accurate identification of the disturbance signal of power quality.

2 Segmented Adaptive S Transform 2.1 S Transform The ST is a non-destructive reversible signal time-frequency analysis method proposed by Stockwell et al. [8] based on the improvement and development of WT and STFT. The ST uses a Gaussian window as the window function, which not only solves the difficulty of choosing a fundamental function for WT, but also overcomes the defect of fixed window function of STFT to a certain extent. The ST has shown very good performance in processing feature extraction and classification of non-stationary signals, and has been applied by a large number of scholars in feature extraction and classification of EMG signals, EEG signals and power quality signals. The one-dimensional continuous ST of signal x(t) is given by [9]:  +∞ x(t)w(τ − t, σ )e−i2π ft dt (1) S(τ, f ) = −∞

where w(τ − t, σ ) is a general Gaussian window function, which affects the timefrequency resolution of ST directly defined as: w(τ − t, σ ) = √

1 2π σ

e−(τ −t)

2 /2σ 2

(2)

where τ is a translation factor in time, σ is the dilation factor about frequency f as σ (f ) =

1 |f |

(3)

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2.2 Adaptive S Transform Strategy As can be seen from Eq. (3), the width of window function is inversely related to the frequency. So, it is still relatively fixed at the same sampling frequency. Even for different types of disturbed signals at the same frequency point, the corresponding time-frequency resolution is same. This leads to poor time-frequency resolution in places where timefrequency resolution requirements are more flexible. So, the signal detection accuracy still needs to be improved. In order to manipulate the window width of ST more flexibly, an adaptive ST strategy is proposed. The standard deviation of window function is defined as σ (f ) =

λ α + |f |β

(4)

where α, β, and λ are adjustment parameters. Three parameters can be set to different values to adjust the width of the window function and achieve more flexible control. The modified S transform formula is  +∞ α + |f |β −(τ −t)2 α+|f |β 2 /2λ2  −i2π ft x(t) √ e dt (5) e S(τ, f ) = 2π λ −∞ where λ is the scale adjustment factor. The parameter α has a translational relationship with the frequency. The parameter β depends exponentially on the frequency, which can control the rate of change of the width of the window function and take the range [0, 1]. 2.3 Segmented S Transform Strategy Yang et al. [10] changed the ST further into the form of a segmented function. The frequency band above 100 Hz is defined as the high frequency band region. Although the method can analyze the signal better, the segmented region is too few. For this reason, a new segmentation strategy is proposed in this work. According to the general rule of signal frequency distribution of power quality, the analysis frequency domain is divided into three parts: ➀ 0–100 Hz is the low frequency band; ➁ 100–600 Hz is the middle frequency band; and ➂ above 600 Hz is the high frequency band. The different frequency bands correspond to different regulation factors. ⎧  +∞ α1 + |f |β1 −(τ −t)2 α1 +|f |β1 2 /2λ2  −i2π ft ⎪ ⎪ 1 e x(t) √ e dt f < 100 Hz ⎪ ⎪ ⎪ 2πλ1 −∞ ⎪ ⎪ ⎪ ⎨  +∞ α2 + |f |β2 −(τ −t)2 α2 +|f |β2 2 /2λ2  −i2π ft 2 e SSAST (τ, f ) = x(t) √ e dt 100 Hz < f < 600 Hz ⎪ 2πλ2 ⎪ −∞ ⎪ ⎪  +∞ ⎪ ⎪ α3 + |f |β3 −(τ −t)2 α3 +|f |β3 2 /2λ2  −i2π ft ⎪ ⎪ 3 e ⎩ x(t) √ e dt f > 600 Hz 2πλ3 −∞

(6) where αi , βi , λi , (i = 1, 2, 3) are the modulation factors for the low, medium, and high frequency bands respectively. The effect of parameters αi , βi and λi (i = 1, 2, 3) on the window function is shown in Fig. 1. Three parameters are individually influenced on the window function.

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Compared with αi and λi , the influence of βi on the Gaussian window is stronger. The adaptive multi-factor adjustment strategy proposed in this study can adjust the timefrequency resolution of the ST in a more detailed way. According to the Heisenberg uncertainty principle, the time domain resolution increases and the frequency domain resolution decreases when the amplitude of window function increases. Conversely, the frequency resolution of the window function increases and the time resolution decreases. Therefore, the SAST can be adjusted by different parameters to meet the requirements of the different frequency resolutions of the disturbed signal.

Fig. 1. Influence of αi , βi and λi to the window shape.

Notes: Three adjustment factors of the segmented adaptive window are determined through extensive experiments and are α1 = 0.5, β1 = 1.05, λ1 = 1 in the low frequency band, α2 = 0.5, β2 = 1.05, λ2 = 1 in the middle frequency band and α3 = 0, β3 = 1, λ3 = 1 in the high frequency band, which can be flexibly adjusted to obtain better time-frequency information when dealing with composite signals.

3 Case Study In most cases, the power quality problem is the superposition of multiple power disturbances. The characteristics of such composite power quality problems are seriously mixed. Compared with single power quality problems, the identification and feature extraction of composite power quality problems are more difficult and more demanding. In this study, harmonic with swell is selected as composite disturbance to verify the accuracy of ST and SAST. Harmonic with swell mathematical model is [11]: x(t) = A{1 + a[u(t2 ) − u(t1 )]} cos(ωt) + α3 cos(3ωt) + α5 cos(5ωt) + α7 cos(7ωt)

(7)

where a = 0.3, t1 = 0.02, t2 = 0.06, α3 = 0.05, α5 = 0.06, α7 = 0.12, A is the standard voltage amplitude, valued 1. The harmonic with sag signal and the results of the disturbed signal after the ST and the SAST were shown in Figs. 2 and 3 respectively. The ST processed signal does not confirm the starting and ending moments of the signal well. But the SAST has a stable starting and ending moment in the apparently falling interval. So, the extracted eigenvalues are closer to the original signal. A comparison of the time-frequency analysis was shown in Table 1. The initial time error of ST is 0.014 and the termination time error is 0.025, while the initial time error

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127

Fig. 2. Harmonic with sag disturbance.

Fig. 3. ST and SAST analysis results.

of SAST is only 0.0016 and the termination time error is 0.00123. It can be shown that the feature values extracted by SAST are very close to the original signal and can restore the original signal to the greatest extent. The SAST has a higher time-frequency analysis accuracy in the face of complex perturbations. It can better detect the relative error of disturbance and harmonic amplitude in the composite disturbance. Table 1. Composite disturbance detection. Methods

Initial value error

Termination value error

SAST

0.0016

0.00123

ST

0.014

0.025

4 Conclusion The traditional ST window function is inflexible and cannot meet the high time-frequency resolution. In this study, an improved segmented adaptive S-transform is proposed to increase the accuracy of perturbation feature extraction. Multiple adjustment factors are

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introduced into the Gaussian window function to adjust the window size more carefully. And the signal is divided into different frequency bands according to the signal frequency and frequency band analysis requirements. Different adjustment factors are selected for each frequency band to reduce the difficulty of adjustment factor selection. The simulation results show that the SAST proposed in this study improves the accuracy of time-frequency analysis of power quality disturbances, and has high detection accuracy in the detection of power system disturbances. Acknowledgement. This work is supported by Science and Technology Project of China Southern Power Grid under Grant 090000KK52190169/SZKJXM2019669s.

References 1. Hao, W., Xu, J., Tong, G., Zhang, W., Liu, Y., Tong, N.: Research on control strategy of PV-energy storage system connected to low voltage distribution network. In: Hu, C., Cao, W., Zhang, P., Zhang, Z., Tang, X. (eds) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 899, pp. 659–674. Springer, Singapore (2022) 2. Li, L., Cai, H., Han, H., et al.: Adaptive short-time Fourier transform and synchro squeezing transform for non-stationary signal separation. Signal Process. 166(7), 107231–107246 (2020) 3. Kumar, A., Tomar, H., Mehla, V.K., et al.: Stationary wavelet transform based ECG signal denoising method. ISA Trans. 114(4), 251–262 (2021) 4. Dharmapandit, O., Patnaik, R.K., Dash, P.K.: A fast time-frequency response based differential spectral energy protection of AC microgrids including fault location. Prot. Control Mod. Power Syst. 2(1), 1–28 (2017). https://doi.org/10.1186/s41601-017-0062-0 5. Liang, C., Teng, Z., Li, J., et al.: A Kaiser window-based S-transform for time-frequency analysis of power quality signals. IEEE Trans. Ind. Inf. 18(2), 965–975 (2021) 6. Xu, L.W., Li, K.C., Luo, Y.: Classification of complex power quality disturbances based on incomplete S-transform and gradient boosting decision tree. Power Syst. Prot. Control 47(6), 24–31 (2019) 7. Sejdi´c, E., Djurovi´c, I., Jiang, J.: A window width optimized S-transform. EURASIP J. Adv. Signal Process. 20(4), 1–13 (2008) 8. Stockwell, R.G., Mansinha, L., Lowe, R.P.: Localization of the complex spectrum: the S transform. IEEE Trans. Signal Process. 44(4), 998–1001 (1996) 9. Ray, P.K., Mohanty, S.R., Kishor, N.: Disturbance detection in grid-connected distributed generation system using wavelet and S-transform. Electr. Power Syst. Res. 81(3), 805–819 (2011) 10. Yang, J., Jiang, S., Shi, G.: Classification of composite power quality disturbances based on piecewise-modified S transform. Power Syst. Prot. Control 47(9), 64–71 (2019) 11. Liu, N., Gao, J., Zhang, B., et al.: Time-frequency analysis of seismic data using a three parameters S transform. IEEE Geosci. Remote Sens. Lett. 15(1), 142–146 (2017)

Robust Predictive Rotor Current Control of DFIGs Based on an Adaptive Ultra-local Model Xin He1 , Shengnan Li1 , Junpeng Li1 , Xian Meng1 , Yong Cheng1 , Yongchang Zhang2 , and Tao Jiang2(B) 1 Electric Power Research Institute of Yunnan Power Grid Co., Ltd., Kunming 650200, China 2 School of Electrical and Electronic Engineering, North China Electric Power University,

Beijing 102206, China [email protected]

Abstract. In the control strategy of doubly fed induction generators (DFIGs), the traditional control method usually uses too much machine parameters, which leads to a serious decline in the control performance when the parameters mismatch, a robust predictive rotor current control (RPRCC) based on an adaptive ultralocal model for DFIGs is proposed in this paper. The ultra-local model can be updated in real time through the sampling rotor currents and stored rotor voltages. When the machine parameters change, by timely estimating the disturbance and bringing it into the closed-loop feedback system, so the influence of disturbance can be quickly eliminated. Because the proposed method does not require any machine parameters and the control model is updated in real time during operation, the proposed method can greatly improve the robustness of the DFIG system. Simulation results show that the method is effective. Keywords: Doubly fed induction generator · Robust control · Predictive current control

1 Introduction As a kind of renewable energy, wind energy can replace fossil fuels to a certain extent, thus reducing carbon dioxide emissions and protecting the environment [1]. With the increasing demand for the quality and consumption of electric energy in the power system, the control strategies of wind power technology in the process of power generation, transmission and distribution, and use need to be continuously optimized and updated. Recently, scholars have proposed various robust control methods [2–5] to improve the system robustness. In [2], based on the concept of parallel distributed compensation in fuzzy control, the system maintained stable operation under the condition of inaccurate parameters. In [3], an H∞ robust current controller was used to improve the robustness and enhance the harmonic suppression of the system. The mutual inductance of the motor was estimated online in [4], thus avoiding the influence of parameter changes on © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 129–137, 2023. https://doi.org/10.1007/978-981-99-4334-0_16

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the control target. In [5], to improve the system robustness, a structured linear system was used to simulate the motor to quickly respond to external inputs. In addition, model-free predictive current control [6–9] has attracted more and more attention because it does not require any motor parameters. So far, it has been applied in power converters and motor drives. In [6], the stator current difference corresponding to different voltage vectors at each moment was detected and stored, and then the cost function was used to determine the next switch state. Since no machine parameters are used, this method has strong robustness. However, this method suffers from the stagnant updating of the current difference, especially at high speeds. In [7], the goal of using no parameters in control was achieved by relying only on the collected current as the input of the ultra-local model and then obtaining the output voltage of the corresponding inverter. In [8], the prediction of the grid side current was realized by the ultra-local model of the voltage source rectifier. In recent years, the use of model-free methods in DFIGs has become more widespread [9, 10]. However, the ultra-local model in [7–9] uses a fixed gain for the input voltage and a complicated differential algebraic method to estimate the total disturbance, which requires some tuning work and has a relatively high computational burden. In this paper, the ultra-local model is updated online by using the rotor currents/voltages in the past periods to accurately estimate the total disturbance of the system and the gain for the input voltage. By using this online updated ultra-local model and the principle of deadbeat current control, the required rotor voltage can be calculated. Once the reference voltage vector is calculated, to fix the switching frequency, switching state of the converter can be obtained by the space vector modulation (SVM). Because the system disturbance can be estimated in real time without any machine parameters, the robustness of the proposed RPRCC is improved. In this paper, a simulation model has been built in MATLAB/Simulink to verify the method, and the simulation results show that the proposed RPRCC is effective.

2 Dynamic Mathematical Model of the DFIG Equation (1) shows the dynamic mathematical model of a DFIG in synchronous coordinate system, where the d-axis of the reference frame is aligned with the grid voltage [11]. ⎧ dψ ⎪ us = Rs is + dt s + jωg ψ s ⎪ ⎪   ⎨ dψ ur = Rr ir + dt r + j ωg − jωr ψ r (1) ⎪ ψ = L i + L i s s m r ⎪ s ⎪ ⎩ ψ r = Lm is + Lr ir In (1), the subscripts g , s and r are abbreviations of grid side, stator side and rotor side, respectively; ψ, i and u are the complex vector of flux, current and voltage, respectively; L and R are the inductance and resistance parameters of the DFIG; Lm and ωr are the mutual inductance parameter and electric angular velocity of the rotor. According to the definition of instantaneous power, the DFIG stator side power can be written in the form of complex power as [11]: S=

3 ∗ i us = Ps + jQs 2 s

(2)

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where the symbol ∗ stands for the conjugate of the variable; Ps and Qs are the stator side active power and reactive power, respectively. According to Ref. [12], a single-input single-output system (SISO) can be described by the ultra-local model, and the order of the system can be reflected in the ultra-local model. For example, a first-order system with u as input and y as output can be described as: y = αu + F

(3)

where F represents the total disturbance of this first-order system, including the disturbance caused by known or unknown factors; and α represents the input gain, which is generally constant and is used to match orders of magnitude between αu and F [9]. According to the dynamic mathematical model of DFIG (1), with the goal of controlling the rotor current, the corresponding ultra-local model can be written as: d ir = αur + F dt

(4)

Theoretically, the relationship between the ultra-local mode and the mathematical model is as follows:  α = λLs     F = −λLm us − Ris − jωg ψ s − λLs Rr ir + j(ωg − ωr )ψ r where λ = 1 (Ls Lr − L2m ).

3 Proposed Robust Predictive Rotor Current Control This paper focuses on the control of rotor-side converter of DFIG, proposes a robust predictive control, and applies adaptive ultra-local model to solve the problem of weakened control effect under the condition of mismatching system parameters. The control structure diagram of the proposed RPRCC method is shown in Fig. 1. The whole control structure is mainly composed of three parts: rotor current reference value acquisition, updating the ultra-local model and delay compensation, and obtaining the required rotor voltage vector. 3.1 Rotor Current Reference Value Acquisition Because the d-axis of the synchronous coordinate system is aligned with the voltage vector of the power grid and the voltage drop on the stator resistance can be ignored, usd = |us | and ψsd = 0. Combing (1) and (2), the relationship between the dq axis rotor current and the active/reactive powers of the stator side can be obtained: ⎧ 3L ⎪ ⎪ Ps = − m usd ird ⎨ 2Ls (5) 3(ψ ⎪ sq − Lm irq ) ⎪ ⎩ Qs = − usd 2Ls

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Fig. 1. Control diagram of robust predictive rotor current control.

Based on (5), the reference value of rotor current is obtained from the tracking error of power through PI controller, while avoiding the use of machine parameters. Because the stator inductance and mutual inductance of DFIG are approximately equal, the proposed power loop is as follows: ⎧   

⎨ iref = − 3 P ref − Ps Kp + Ki rd 2|us | s (6)  

ref ⎩ irq = 2|u3 s | Qref − Qs Kp + Ksi

3.2 Ultra-local Model Updating and Delay Compensation As introduced in Sect. 2, the values of parameters α and F can be determined by the DFIG mathematical model in theory. Therefore, in the process of system operation, the parameters α is always a constant. F is the sum of all items except the items that contain ur , and it changes accordingly with the operation state of the system. In the proposed RPRCC method, because the rotor current and rotor voltage at each moment can be detected and stored, parameters α and F can be estimated by relying on the data of these past moments. According to (4), the ultra-local model of DFIG in the past two control periods can be obtained as:   k ir − irk−1 = Tsc αurk−1 + Fk  (7) irk−1 − irk−2 = Tsc αurk−2 + Fk−1 where Tsc indicates the sampling period, the superscripts k, k − 1 and k − 2 indicate the kth moment, the (k − 1)th moment, the (k − 2)th moment, respectively.

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When the sampling frequency is high enough, it can be assumed that the total disturbance F of the system remains unchanged in the adjacent control period under steadystate conditions. This means Fk ≈ Fk−1 . Therefore, the estimated value of α can be derived from (7) as: ik − ik−1

 Tsc urk−1 − urk−2

αˆ =

(8)

where ik = ikr − irk−1 , ik−1 = irk−1 − irk−2 and the superscript ^ means the variable is estimated. Because the parameter α is constant and has been accurately estimated, it can be substituted into (7) as a known quantity to estimate the variable Fk : ik − αu ˆ rk−1 Fˆ = Tsc

(9)

Thus far, two important parameters of the ultra-local model that can describe the system have been estimated based on the operating state of the system in the past. There is a computational delay in digital processing just like any other predictive control [13], so it is necessary to compensate for the impact of one-step delay and predict the rotor current and disturbance at the next sampling point. Due to the short sampling interval, it can be considered that the total disturbance at the next time is approximately equal to the total disturbance at the current time. Then, based on (7), the predicted value of rotor current at the next sampling point can be obtained as: irk+1 = ikr + (αukr + Fk )Tsc

(10)

3.3 Calculation of Required Rotor Voltage In this paper, according to the idea of deadbeat control, the final required rotor voltage is obtained, which ensures the fast dynamic response of the system and also has satisfactory steady-state performance. After discretizing (4) and substituting the variable after delay compensation, it can be obtained ref

ur

=

k+1 ref ir − irk+1 Fˆ − αT ˆ sc αˆ

(11)

And by (10), (11) can be further simplified as ˆ sc ir − ikr − 2FT − ukr αT ˆ sc ref

ref

ur

=

(12)

To facilitate the design of the filter in the circuit and reduce the harmonics in the current, this paper uses the seven-stage space vector modulation technology to convert the required rotor voltage into switching signals.

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4 Simulation Verification To test the effectiveness of the proposed method, a grid-connected model of DFIG controlled by rotor side converter was built in MATLAB/Simulink environment. The DC bus voltage is provided by a DC source, which is set as 100 V in this paper. The grid voltage is a three-phase 50 Hz sine wave with 150 V RMS of phase voltage. The simulation step was set to 2.5 μs, and the sampling interval was set to 100 μs. Parameters of DFIG and control system are shown in Table 1. Table 1. Simulation system parameters Parameters

Symbol

Value

Rated resistance at stator side

Rs

2.719 

Rated resistance at rotor side

Rr

2.208 

Rated stator side inductance

Ls

176 mH

Rated rotor side inductance

Lr

176 mH

Rated mutual inductance

Lm

168 mH

Machine pole pairs

Np

3

Stator/rotor turn ratio

Nk

2.93

Proportional factor of power loop PI controller

Kp

0.00008

Integral factor of power loop PI controller

Ki

0.5

Figure 2 shows the simulation results of the proposed RPRCC method while the machine parameters remain unchanged, where dashed line represents the reference value for corresponding channel variable. In Fig. 2(a), when the rotor speed is stabilized at 700 rpm by prime mover, the power can be tracked without error, and the power fluctuation is small and the stator/rotor currents remain sinusoidal. From Table 2, it can be seen that the THD of the stator and rotor currents is quite small at the steady-state operating points at different speeds. Table 2. THD of stator and rotor currents at different speeds 700 rpm

800 rpm

900 rpm

1100 rpm

1200 rpm

1300 rpm

isa

1.54%

1.45%

1.20%

1.09%

1.29%

1.38%

ira

1.19%

1.08%

0.91%

0.83%

0.98%

1.12%

The dynamic response results of the proposed method are shown in Fig. 2(b) and Fig. 2(c). When the active power reference value steps, the actual power can track the reference value quickly within 0.05 s, while the actual reactive power is basically unchanged. It indicates that the proposed method has good power decoupling property.

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On the other hand, when the speed increases from 700 to 1300 rpm, no significant change in power tracking effect and the rotor current can achieve a smooth transition. The dynamic simulation show that the proposed method can achieve fast and accurate tracking in the dynamic process.

Fig. 2. Simulation results of the proposed RPRCC method while the machine parameters remain unchanged. (a) Steady state. (b) Active power step. (c) Speed variation.

To highlight the robustness of the proposed method, Fig. 3 shows the rotor current loop tracking results of the two methods in case of mutual inductance mismatch. At 0.06 s, the mutual inductance parameter of the DFIG is artificially changed from 168 to 126 mH (reduced by 25%). The components of rotor current reference value on the dq axis were set as 2 A and 5 A for both methods. At the moment of mutual inductance mutation, the dq axis current based on the mathematical model method will generate a large disturbance, and the disturbance cannot be completely eliminated. There is tracking error in dq-axis current, and the error in q-axis is more obvious. But in Fig. 3(b), under the same conditions, the proposed control method based on the adaptive ultra-local model will quickly converge back to the reference value when the d-axis is disturbed, and the tracking performance of the q-axis is almost not affected. By comparing the control effects of the two methods, it is obvious that the proposed method has stronger parameter robustness. Similar to Fig. 3, the mutual inductance parameter of the DFIG in Fig. 4 decreased by 25% from the original rated value in 0.05 s. In the traditional predictive control

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Fig. 3. Current loop tracking effect of two methods under mutual inductance mismatch. (a) Predictive rotor current control based on mathematical model. (b) Proposed RPRCC method.

Fig. 4. Simulation waveforms of two methods under actual inductance variation. (a) Predictive rotor current control based on mathematical model. (b) Proposed RPRCC method.

method, tracking static error exist for both active power and reactive power. However, the active power tracking of the proposed method is hardly affected, the reactive power can quickly track its reference value when disturbed. Therefore, in the case of DFIG parameter mismatch, the proposed method has a satisfactory control effect both on the current loop and the whole control structure.

5 Conclusion This paper combines adaptive ultra-local model with predictive rotor current control, which does not rely on machine parameters. The method has an excellent system robustness and a satisfactory control effect in an ideal grid. The input gain and total disturbance of the ultra-local model are re-estimated and continuously updated in each control cycle. Through one-step delay compensation and based on deadbeat control principle, the final required rotor voltage can be obtained. Then, the corresponding switching signal is obtained by SVM, which fixes switching frequency.

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Firstly, the proposed method has a good control effect when the machine parameters are matched. Secondly, when the machine parameters are not matched, the proposed RPRCC method control performance is almost unaffected compared with the traditional predictive control. These has been verified by the simulation results provided in this paper.

References 1. Nehrir, M.H., et al.: A review of hybrid renewable/alternative energy systems for electric power generation: configurations, control, and applications. IEEE Trans. Sustain. Energy 2(4), 392–403 (2011) 2. Kamal, E., Oueidat, M., Aitouche, A., Ghorbani, R.: Robust scheduler fuzzy controller of dfig wind energy systems. IEEE Trans. Sustain. Energy 4(3), 706–715 (2013) 3. Wang, Y., Wu, Q., Gong, W., Gryning, M.P.S.: H∞ robust current control for dfig-based wind turbine subject to grid voltage distortions. IEEE Trans. Sustain. Energy 8(2), 816–825 (2017) 4. Bhattarai, R., Gurung, N., Ghosh, S., Kamalasadan, S.: Parametrically robust dynamic speed estimation based control for doubly fed induction generator. IEEE Trans. Ind. Appl. 54(6), 6529–6542 (2018) 5. Cai, R., Zheng, R., Liu, M., Li, M.: Robust control of pmsm using geometric model reduction and μ-synthesis. IEEE Trans. Ind. Electron. 65(1), 498–509 (2018) 6. Lin, C., Liu, T., Yu, J., Fu, L., Hsiao, C.: Model-free predictive current control for interior permanent-magnet synchronous motor drives based on current difference detection technique. IEEE Trans. Ind. Electron. 61(2), 667–681 (2014) 7. Zhang, Y., Jin, J., Huang, L., Xu, W., Liu, Y.: Model-free predictive current control of pmsm drives based on ultra-local model. In: Proceedings of the 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–5. IEEE Press, Harbin (2019) 8. Zhang, Y., Liu, X., Liu, J., Rodriguez, J., Garcia, C.: Model-free predictive current control of power converters based on ultra-local model. In: IEEE International Conference on Industrial Technology (ICIT), pp. 1089–1093. IEEE Press, Buenos Aires (2020) 9. Zhang, Y., Jiang, T., Jiao, J.: Model-free predictive current control of a dfig using an ultra-local model for grid synchronization and power regulation. IEEE Trans. Energy Convers. 35(4), 2269–2280 (2020) 10. Zhang, Y., Jiang, T., Jiao, J., Xu, W.: Model-free predictive current control of doubly fed induction generator. In: Proceedings of the 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–5. IEEE Press, Harbin (2019) 11. Zhang, Y., Zhang, S., Jiang, T., Jiao, J., Xu, W.: A modified model-free predictive current control method based on an extended finite control set for dfigs applied to a nonideal grid. IEEE Trans. Ind. Appl. 58(2), 2527–2536 (2022) 12. Michel, L., Join, C., Fliess, M., Sicard, P., ChÃcriti, A.: Model-free control of dc/dc converters. In: IEEE 12th Workshop on Control and Modeling for Power Electronics (COMPEL), pp. 1–8. IEEE Press, Boulder, CO (2010) 13. Zhang, L., Hu, C., Zhu, W., Jiao, J.: Predictive control method for secondary ripple suppression of two-stage single-phase inverter. In: Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering (CoEEPE), pp. 165–177. Springer Nature Singapore, Singapore (2022)

Multi-region V2G Optimal Scheduling Strategy Based on Region Division Gao Pengcheng , Zhang Chun(B) , Wu Lingchen , Wu Shuang , Tong Zejun , and Li Haoyu School of Electrical Engineering, Anhui Polytechnic University, Wuhu, Anhui, China [email protected]

Abstract. In order to improve the schedulability of electric vehicles (EVs), a multi-region V2G optimal scheduling strategy based on region division is proposed. Firstly, the travel start time, end time and travel distance are simulated, and the region where the user’s destination is in is counted. Secondly, according to the main load properties of these regions, regions are divided into business areas, residential areas and industrial areas. At the same time, considering the new energy power generation and the participation of EVs in scheduling in each region, the multi-region optimal scheduling strategy of EVs is established. Finally, according to the load power, new energy generation power and the amount of EVs that can participate in scheduling in each region in a day, the objective function is established to minimize the mean square deviation of power-interaction between the multiregion system and the large power grid and to minimize the V2G scheduling cost. The optimal scheduling result is obtained by the Particle Swarm OptimizationArtificial Bee Colony (PSO-ABC) algorithm. The simulation results show that this strategy can effectively complete the task of peak shaving and valley filling, improve the flexibility of EVs participating in multi-region system scheduling. Keywords: V2G · Travel chain · Regional division · PSO-ABC algorithm

1 Introduction In order to promote the clean and low-carbon transformation and high-quality development of electric energy, China strongly supports the development of new energy EVs. EVs can not only be used as an elastic load, but also as a mobile energy storage power supply, so as to realize the two-way interaction between power grid and EVs [1]. At present, the relevant research on the participation of EVs in scheduling has been studied by some scholars. In [2], a daily scheduling strategy is proposed for EVs that took into account the needs of users and both sides of the grid. In [3], the travel demand model of EVs is built based on the travel chain, and the power consumption model is built based on the travel demand. Based on the two models, the schedulable capacity of the EV cluster is obtained and a price incentive scheduling model is established. In terms of solution, in [4, 5], the Non-dominated Sorting Genetic algorithm (NSGA-II) and the multi-objective Particle Swarm Optimization algorithm (MOPSO) based on pareto optimal solution set have been used respectively to solve the proposed model. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 138–147, 2023. https://doi.org/10.1007/978-981-99-4334-0_17

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It can be seen from most of the current literatures that most studies only considered the time model of EVs, focused on the schedulable period of EVs and ignored the impact of the spatial movement of EVs. What’s more, according to the real-time electric quantity, PSO-ABC algorithm is used to solve the EVs scheduling, so as to lessen the cost of scheduling as much as possible, reduce the peak-valley difference and power fluctuation of power-interaction with the large power grid, improve the flexibility of EVs participating.

2 EV Travel Chain Model Generally speaking, there are certain rules for the daily travel of EVs, it can be roughly divided into four types, they are shown in Table 1. 2.1 Trip Probability Function The probability curve of the travel time of EVs conforms to the normal distribution [2]. In this paper, a day is divided into 96 time periods with 0.25 h as the time interval, and the travel time probability function and the probability function of EV travel distance is shown in [3, 5]. 2.2 Daily Travel Chain Structure The types of travel activities are shown in [6]. Table 1. Travel chain structure table. Type

Route

1

a–b–a

2

a–c–b–a

3

a–b–a–b–a

4

c–b–a–c

Taking the region where the earliest travel time is located as the starting point of the travel chain, the travel chain of EVs is shown in Table 2. In the table, residential area, business area and industrial area respectively are represented by a, b and c. After confirming the travel chain, the parameters can be set. Specific values are shown in Tables 2, 3 and 4. In these Tables, the mean and standard deviation parameters is respectively represented by the first number and the second number. The travel of EVs is used to monte Carlo method to simulate in this paper. Random selection of EVs travel steps by Monte Carlo method is in [7].

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Type

1

2

3

4

1

0.1,20

2

0.1,30

–

–

–

0.1,10

0.1,25

3

0.1,20

–

–

–

4

0.1,10

0.1,25

0.1,30

–

Table 3. The start of travel relevant parameters. Type

1

2

3

4

1

–

0.1,70

–

–

2

–

0.1,70

0.1,72

–

3

–

0.1,46

–

0.1,70

4

0.1,34

0.1,36

–

–

Table 4. The end of travel relevant parameters. Type

1

2

3

4

1

0.1,34

–

–

–

2

0.1,34

–

–

–

3

0.1,34

–

0.1,58

–

4

–

–

0.1,82

–

2.3 The Related Model of EVs Models The electric quantity model of EVs is shown in [8]. The scheduling cost of EVs is consisted of incentive cost and loss cost. The compensation cost of battery loss is shown in [7].

3 Multi-region Optimal Scheduling Strategy In this paper, the schedulable power of EVs in the current period is obtained by simulating the travel status of EVs. EVs are scheduled. 3.1 Objective Function In this paper, the minimize the quantity of power-interaction between each region and the large power grid and the minimum scheduling cost are taken as goals.

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The quantity of power-interaction between internal and external power in residential area, business area and industrial area is shown in the Eq. (1). ⎧ ⎪ ⎨ Pyz,i = Pxnyz,i + Pfdz,i − Pfhz,i − Pcdz,i Pys,i = Pxnys,i + Pfds,i − Pfhs,i − Pcds,i (1) ⎪ ⎩ Pyg,i = Pxnyg,i + Pfdg,i − Pfhg,i − Pcdg,i Taking the residential area as an example, Pyz,i , Pxnyz,i , Pfdz,i , Pfhz,i , Pcdz,i are respectively the quantity of power-interaction (kW), new energy generation power (kW), discharging power of EVs (kW), load power (kW) and charging power of EVs (kW) between the residential area and the outside at time i. We set that the power is supplied by the residential area to the outside is a positive value. Pys,i and Pyg,i are similar to the above. The objective function is established as follows: ⎧ T  2

 ⎪ ⎪ ⎪ Pddw,i − Pddw ⎨ i=1 (2) F1 = min s2 = ⎪ T ⎪ ⎪ ⎩ Pddw,i = Pyz,i + Pys,i + Pyg,i where, Pddw,i is the power-interaction between the system and the large power grid at time i (kW), Pddw,i = Pyz,i +Pys,i +Pyg,i . Pddw is the average power-interaction between the system and the large power grid at all times (kW). About the V2G scheduling cost, the objective function is established as:  (3) F2 = min C = min Cjl + Csh + Cmmg + Cbuy + Csale where: Cjl Csh Cmmg Cbuy Csale are the price transaction cost to encourage users to participate in V2G (¥), the compensation cost of EVs battery loss, the power scheduling cost between regions, the power purchase cost of the system from the large power grid and the cost of power sold by the system to the large power grid. 3.2 Constraint Condition Power balance constraints are: Pddw,i = Pyz,i + Pys,i + Pyg,i The charging and discharging power of EVs constraints are:  0 ≤ Pcd ,min ≤ Pcd ≤ Pcd ,max 0 ≤ Pfd ,min ≤ Pfd ≤ Pfd ,max

(4)

(5)

where, Pcd ,min , Pcd ,max are the minimum and maximum charging power (kW) of EVs respectively. Pfd ,min , Pfd ,max are the minimum and maximum discharging power (kW) of EVs. Pcd and Pfd are respectively the charging and discharging power of electric vehicles (kW).

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The overcharge and overdischarge protection constraints of EVs are: Emin ≤ E(t) ≤ Emax

(6)

where: Emin and Emax are respectively the minimum and maximum value of the remaining electric power of EVs (kW · h). E is the electric power of EVs. The selection rules of time nodes are set as shown in the Eq. (7).  a ≤ Ts (t) ≤ b, Ts (t) = a (7) a ≤ Te (t) ≤ b, Te (t) = b where: a and b are the two integers closest to the start or end of the trip respectively. Ts and Te are the starting time and the ending time. EVs can only be in one of the charging or discharging states at any time, that is: τc + τf ≤ 1

(8)

τc , τf are the charging and discharging state parameters respectively, taking 0 or 1. 3.3 Multi-objective Optimization Model The multi-objective function is weighted by the linear weighting method. In addition, the homogenization weighting process is required, as shown in the Eq. (9). min F = r1 ×

F1 F2 + r2 × F1n F2n

(9)

where: F1n is the power-interaction between the system and the large power grid when EVs do not participate in the scheduling (kW). F2n is the transaction price cost (¥) generated when EVs do not participate in the scheduling. r1 and r2 are the weight coefficients of the two objective functions, satisfying r1 + r2 = 1. To maximize the benefits of the two objectives, r1 and r2 are set as 0.5 [3]. 3.4 Scheduling Strategy When the new energy power generation can’t meet the load demand in one area, the EVs in the current area are discharging, if it still can’t meet the demand, the EVs in other areas are discharging, and transmit power to the area. When the EVs have sufficient discharge capacity in one area, they can also transmit power to the area with insufficient power preferentially. The specific scheduling strategy is shown in Fig. 1. Pfh is the load power (kW). Pxny is the power generated by new energy (kW). In this paper, PSO and ABC algorithm are combined to obtain the global optimum solution in the Eq. (9). Figure 2 is a flowchart of PSO-ABC algorithm. Firstly, some local optimal solutions are obtained through PSO algorithm in the early stage, and jump out of the local optimal solution through ABC algorithm in the middle stage, finally the global optimal solution is obtained quickly through PSO algorithm.

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Start Charging electric vehicles

The original data such as load is input, power generation, time-of-use price, etc

Pfh >=Pfd max +Pxny Y

N Pxny >=Pcdmax+Pfh

According to the travel chain of electric vehicles, the regions where electric vehicles are located are divided The electric vehicle remains in its current state

SOC status of electric vehicles in each region are obtained and prepare for scheduling

Is there excess power in other regions?

Y N

Do other regions need power supply?

Power transmission among regions

Whether the electric vehicle satisfies the discharging demand? Y

Whether the N electric vehicle satisfies the charging demand?

N

Pfh >=Pxny Y

Whether the inter regional scheduling satisfies the power demand?

Selling electricity to large power grid

Y

N

Y Power transmission among regions

Y N

N

N

Power is Purchased from large power grid

Y

The charging and discharging power of electric vehicles is adjusted and optimized according to time-of-use price, inter-regional scheduling cost, V2G compensation cost, etc

Discharging electric vehicles

Y

End

Fig. 1. Flow chart of scheduling strategy.

Start The particles are initialized and divided into N independent groups

PSO

N optimal solutions as n initial honey sources of Artificial Bee Colony

ABC

Iterative updating of Artificial Bee Colony algorithm

Speed and position are updated of the first group iteration

Speed and position are updated of the second group iteration

Speed and position are updated of the No.N group iteration

The optimal solution is obtained from the first group

The optimal solution is obtained from the second group

The optimal solution is obtained from the No.N group

The obtained optimal solution is regarded as the global optimal solution of Particle Swarm Optimization

PSO

The optimal solution is obtained by Particle Swarm Optimization End

Fig. 2. Flow chart of PSO-ABC algorithm.

4 Example Analysis 4.1 Example Description In order to verify the superiority of the proposed scheduling strategy, the scenarios are set as follows: (1) The battery capacity of EVs is 32 kW·h, the power consumption is 0.195 kW·h/km, and the daily starting power consumption of users is 28 kW·h. (2) The charging device is set with a maximum charging and discharging power of 9 kW and a variable power charging and discharging mode. The upper and lower limits of the remaining battery capacity are 4 and 28 kW·h respectively. (3) In this paper, 500 EVs are set to travel according to the travel chain rules. (4) Time-of-use power price is shown in [9]. (5) The time-of-use incentive charging and discharging price is shown in Table 5.

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(6) According to the main load types in the region, the region is divided into three types, namely, industrial area, business area and residential area. The load power curve and new energy generation power curve are shown in Fig. 3.

(a) Business area

(b) Industrial area

(c) Residential area

Fig. 3. Relevant power curve of each region.

Table 5. Time-of-use incentive charging and discharging price. Price type

Time interval

Purchase price/(¥/kW·h)

Selling price/(¥/kW·h)

Valley time

1–11, 40–54, 89–96

0.34

0.30

Flat time

12–17, 36–39, 55–58, 67–77, 87–88

0.80

0.80

Peak time

18–35, 59–66, 78–86

1.20

0.96

4.2 Example Solution In this paper, PSO–ABC algorithm is used to solve the problem. And it is compared with PSO and ABC algorithms. The iterative process of the above three algorithms is shown in Fig. 4.

Fig. 4. Algorithm iteration process.

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Fig. 5. Daily power-interactive curve of system and large power grid.

4.3 Result Analysis In this paper, the multi-region scheduling strategy of EVs, i.e., orderly charging and discharging, and, the situation when EVs do not participate in the scheduling, i.e., disorderly charging will be compared. The daily power-interactive curve is shown in Fig. 5. As is shown in Fig. 5, We set that the power is supplied by the system to the large power grid is a positive value. As can be seen that the proposed scheduling strategy can achieve the goal of peak shaving and valley filling.

(a) Industrial area

(b) Business area

(c) Residential area

Fig. 6. Comparison curve of power balance in different regions with multi-region scheduling strategy and disordered charging.

The importance of power balance in each region is set as industrial area > business area > residential area, it means that priority is given to scheduling EVs in the area with low importance. The power balance comparison curve of three areas during orderly charging and discharging and disordered charging is shown in Fig. 6. It can be seen that the peak-valley difference of daily power between the industrial area and the business area has been significantly improved. The importance of regional power balance is set as residential area > business area > industrial area, related data are shown in Table 6. In the Table 6, the reduction of peak-valley difference of daily power and reduction of mean square error in the residential area increases by 1895 kW and 0.1896 × 107 , with the increase ratio of reduction being about 35.57% and 73.83% in the residential area. The reduction of peak-valley difference of daily power and the reduction of mean square

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Index

Before

After

Peak-valley difference in industrial area/(kW)

26620

26476

Variance in industrial area/(× 107 )

4.1146

4.0123

Peak-valley difference in business area/(kW)

8253

8297

Variance in business area/(× 107 )

6.5034

5.8028

Peak-valley difference in residential area/(kW)

3902

7335

Variance in residential area/(× 107 )

0.1199

0.1871

error is reduced by 1557 kW and 0.3611 × 107 , with the decrease ratio of reduction being about 91.53 and 77.92% in the industrial.

5 Conclusion In the paper, a multi-region scheduling strategy of EVs based on region division is proposed in V2G mode. According to the case analysis, the following conclusions can be drawn. Compared with disordered charging, the strategy proposed in this paper can effectively reduce the peak-valley difference and the mean square error of power fluctuation of power-interaction with large power grids. And compared with other orderly charging and discharging strategies, the multi-region scheduling strategy proposed in this paper can observe the charging and discharging status of EVs in each region more intuitively. The multi-region scheduling strategy of EVs has more prominent advantages in the emphasis and flexibility of regional management, compared with the non-regional scheduling.

References 1. Luo, W., Chang, X., Fu, R., et al.: Charging and discharging scheduling strategy for electric vehicles considering supply and demand). Proc. CSU-EPSA 34(07), 106–112 (2022) 2. Li, Y., Zhang, S., Xiao, X., et al.: Charging and discharging scheduling strategy of EVs considering demands of supply side and demand side under V2G mode. Elect. Power Autom. Equip. 41(03), 129–143 (2021) 3. Wang, M., Lu, L., Xiang, Y.: Coordinated scheduling strategy of electric vehicles for peak shaving considering V2G price incentive. Elect. Power Autom. Equip. 42(04), 27–85 (2022) 4. Yu, W., Liu, S., Chen, Q., et al.: Multi-objective optimization scheduling for PV microgrid considering electric vehicle charging and demand response. Proc. CSU-EPSA 30(01), 88–97 (2018) 5. Yang, X., Guo, X., Wang, H.: Collaborative optimization scheduling of wind and photovoltaic generation and electric vehicle charge and discharge. J. Sichuan Univ. Sci. Eng. 34(05), 55–61 (2021) 6. Chen, L., Nie, Y., Zhong, Q.: A Model for electric vehicle charging load forecasting based on trip chains. Trans. China Electrotechn. Soc. 30(04), 216–225 (2015)

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7. Li, B.: Monte Carlo Method-Based Prediction of Charging Load of Large-Scaled Electric Vehicles. Ningxia University, Ningxia (2018) 8. Liu, X., Zhao, M., Wei, Z., Lu, M.: Economic optimal allocation of photovoltaic energy storage system based on quantum particle swarm optimization algorithm. In: Cao, W., Hu, C., Huang, X., Chen, X., Tao, J. (eds.) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 916. Springer, Singapore (2021) 9. Wang, B.: The Strategy and Price Research of EV Charging and Discharging Based on Demand Response. North China Electric Power University, Beijing (2015)

Maximum Power Point Tracking Control of Wind Power Generation System Without Inductance Decoupling Yu Wang, Shicheng Zheng(B) , Mingjin Lu, Wei Qiu, Dengji Tian, and Jiahong Lang Anhui University of Technology, Ma’anshan, China [email protected]

Abstract. This paper proposes a new maximum power point tracking (MPPT) control for improving generation efficiency of PMSG based on inductance-free decoupling. The outer speed loop adopts the linear active disturbance rejection control (LADRC) to achieve MPPT combining with the optimal blade speed ratio. Considering the idea of synthetic vector, the inner current loop adopts no inductance decoupling control to realize the current decoupling in the synchronous rotating dq coordinate system, and reduces the influence of input inductance value. Simulation results verify validity and feasibility of the proposed method. Keywords: Maximum power point tracking (MPPT) · Linear active disturbance rejection control (LADRC) · No inductance decoupling control

1 Introduction Wind power has been paid more and more extensive attention because it has green and important renewable characteristics. Nowadays, countries in the world have increased the exploitation of wind energy. With increasing development of wind industry, people put forward higher demand on the security and reliability of wind generator system. As the core of wind power system, how to control generator with high efficient is essential to the whole system. However, wind turbine system is nonlinear, strong coupling and complex, and the wind velocity is stochastic and changes with time. In addition, the parameters of the motor, inductance saturation and other factors are hard to measure, so the accurate mathematics model of wind turbine system is hard to obtain, which brings great challenges. Reference [1] designed a sliding mode power regulator for wind power system based on power exponential reaching law, which suppressed the chattering of power tracking when wind speed fluctuates and enhances the accuracy of the control system. Reference [2] designed an adaptive output feedback regulator without speed sensor, which effectively improved the power tracking control ability. These control methods for PMSG are mainly devoted to improving system stability and anti-interference ability. However, these methods are hard to apply to engineering practice due to their large amount of calculation and complex structure. Most of the control algorithms are based on the known © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 148–153, 2023. https://doi.org/10.1007/978-981-99-4334-0_18

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system parameters. However, it is often difficult to accurately aquire system model in actual application. Aiming at these characteristics of system, a more detailed and general control method is designed to solve the interference and nonlinearity problems of system, which has great meanings for the safety and reliability operation of system and the realization of maximum power tracking.

2 Maximum Power Point Tracking According to the aerodynamics, the wind turbine blade absorbs wind energy and converts it into mechanical power, which has the following functional relationship. Po =

1 ρπ R2 Cp (λ, β)v3 2

(1)

where, Po is wind turbine output; ρ is air density; R is wind blade radius; Cp is rotor power coefficient; λ is blade tip velocity ratio; β is pitch angle; v is wind velocity. Cp is a nonlinear formula of λ and β, which can be expressed as follows [1]. ⎧   ⎨ C (λ, β) = 0.5173 ∗ 116 − 0.4β − 5 e −21 γ + 0.0068 ∗ λ p γ (2) 1 ⎩1 = − 0.035 3 γ

λ+0.08β

β +1

Known from Eq. (2) that Cp is only related to λ and β, and has nothing to do with the wind speed v. It can be seen from Eq. (2) that when pitch is fixed, though the wind speed changes, the blade can operate in optimal blade tip speed ratio state by adjusting blade speed. At this time, wind power coefficient can achieve maximum. There is a fixed relationship between wind speed and rotational speed when maximum power tracking is realized. ω∗ =

λopt v = Kopt v R

(3)

where, ω∗ represents optimal speed of wind turbine at current wind speed, which is a given value; λopt represents the best tip velocity ratio; Kopt represents optimal wind speed ratio.

3 LADRC Controller As the core of alternating current speed control system, outer speed loop should have the characteristics of fast dynamic response, wide adjustment range and strong antiinterference ability. LADRC can real-time observe and compensate of these disturbances. Therefore, outer speed loop will use LADRC control. Generally, considering second-order system [3]: y¨ = −a1 y˙ − a2 y + w + bu

(4)

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where, u is input;y is output, y˙ and y¨ respectively represent the first derivative and the second derivative of y;w represent external disturbance; a1 and a2 represent system parameters; b is control gain and has b0 ≈ b. According to the reference [4], the generalized disturbance of the system can be set as f (y, y˙ , w) = −a1 y˙ −a2 y +w +(b − b0 )u, and function f contains internal uncertainty and external disturbance of system. If x1 = y, x2 = y˙ is set, function f can be extended to x3 = f (y, y˙ , w). System state equation can be shown as follows. ⎧ x˙ 1 = x2 ⎪ ⎪ ⎨ x˙ 2 = x3 + b0 u (5) ⎪ x˙ 3 = h ⎪ ⎩ y = x1 where, x1 , x2 and x3 are system state variables; h represents the first derivative of function f , and that is h = f˙ (y, y˙ , w). So, LESO can be established as follows. ⎧ ⎨ Z˙ 1 = Z2 − β1 (Z1 − y) (6) Z˙ = Z − β2 (Z1 − y) + b0 u ⎩ 2 ˙ 3 Z3 = −β3 (Z1 − y) Selecting suitable β1 , β2 , β3 , LESO can realize the real-time tracking of each variable of Eq. (6). The PD controller is designed as follows [5]. u0 = kp (V − Z1 ) − kd Z2

(7)

where, V is a given signal; kp and kd represent controller gains. In summary, Eqs. (4)–(7) constitute LADRC controller. The structure is shown in Fig. 1. v

+

kp

−

+ −

−

1 b0

kd 1 s

y

G (s)

b0

+

β1

+ 1 s

+

+ +

β2 1 s

+ −

β3

Fig. 1. Structure of LADRC controller.

4 Inner Current Loop Control The inner current loop determines fast tracking performance of system. In this paper, a current inner loop control without inductance parameter decoupling is proposed.

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In the dq rotating coordinate system, composite vector mdq and scalar md , mq can be expressed as follows [6]. mdq = md + jmq

(8)

Therefore, the synthetic vector equation of SPMSM in dq rotating coordinate system can be expressed as: udq = L

didq + Rs idq + edq dt

(9)

Rotating differential operator ddtχ + jωe is used to replace stationary differential operator ddtχ , and the model of SPMSM can be obtained as follows. udq

 dχ + jωe idq + Rs idq + edq =L dt

(10)

The Laplace transform of Eq. (10) can be acquired: 

1

idq = udq − edq L s + (Rs /L + jωe )

(11)

According to the transfer function G(s) = kp + ksi of PI controller, the current decoupling PI controller on account of synthetic vector is designed as follows.    ki 1 (12) H (s) = kp 1 + + jωe × kp s Combining Eqs. (11) and (12), traditional current inner loop with double input and double output can be transformed into a single input and single output system as shown in Fig. 2. (a). The following relation can be gained from Fig. 2. (a).   ∗ udq = H (s) idq − idq + edq (13) The rotor flux linkage direction is defined as the d axis of the dq rotating coordinate system, and there is ed = 0, eq = ωe /ωf . Combined with Eq. (8), ed and eq , Eq. (13) can be reduced to a scalar as follows. ⎧ 

   ωk  ⎨ ud = kp + ksi id∗ − id − es p iq∗ − iq    (14)

 ⎩ uq = kp + ki i∗ − iq + ωe kp i∗ − id + ωe ψf q d s s According to Eq. (14), the decoupling inner current loop control block diagram without inductance value is established in Fig. 2. (b).

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(a)

jω

iq

idq* + −

kp

ki kp

ki kps

kp − id

+

+

1 s

+

edq +

+ +

ud −

ωe s

udq

ωe

+

s iq −

iq* +

ki kps

kp

+ + +

uq

+

ωeψ f

Fig. 2. (a) Current inner loop decoupling block diagram based on synthetic vector. (b) Noninductance decoupling current inner loop control block diagram.

(a)

(b)

Fig. 3. (a) Wind speed tracking curve. (b) Direct current bus voltage curve.

5 Simulation Results Aiming to verify the proposed control method, simulation is carried out on Matlab. This paper set the basic wind as an example of the system modeling and simulation. Comparing with the traditional PI control, the superiority of the proposed algorithm is proved. Figure 3. (a) shows the comparison curve of LADRC and traditional PI speed tracking ability under the basic wind speed. It is obvious from the diagram that LADRC controller achieves stable maximum power tracking at 0.09 s, traditional PI controller achieves stable maximum power tracking at 0.1 s. Obviously, LADRC controller basically achieves anti-interference and fast-tracking characteristics. Figure 3. (b) is the direct current bus voltage comparison curve of proposed control and traditional control. It is evident that the direct current bus voltage stabilization time under the control proposed is 0.1 s, while that of traditional control is 0.15 s. The direct current bus voltage under proposed control has faster stability and smaller overshoot. Figure 4. (a) is the system current waveform under the traditional vector control method, Fig. 4. (b) is the system current waveform under the improved control method proposed, that is combination of LADRC and inductance free decoupling method. It can be seen that the stabilization time of Fig. 4. (a) is longer than that of the improved method in Fig. 4. (b), and the current overshoot in Fig. 4. (a) is larger, which means that the impact on the system is greater, while the overshoot of the current in Fig. 4. (b) is smaller, which can make the system more stable.

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(a)

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(b)

Fig. 4. (a) Traditional vector control. (b) Improved control method.

6 Conclusion This paper proposes a new MPPT control for wind power system based on inductancefree decoupling. For the outer speed loop, the LADRC controller is proposed to improve the anti-interference and fast-tracking ability of system. For the inner current loop, a decoupling method without inductance value is proposed to reduce the dependence on SPMSM generator inductance parameters. Finally, by simulation the validity and feasibility of proposed control method are verified. Simulation results show that the method proposed can effectively suppress interference of external factors such as wind speed, and realize fast and stable maximum power point tracking. Acknowledgements. This paper is supported by Postgraduate Research Projects in Anhui Province YSJ20210347.

References 1. Wang, Y.R., Mao, J.F., Zhang, Z.M., et al.: Power index approaching sliding mode control of wind power generation system based on maximum electric power. Renew. Energy 38(6), 852–858 (2019) 2. Eimagria, A., Giri, F., Besancon, G., et al.: Sensor less adapt output feedback control of wind energy systems. Control Eng. Pract. 21(4), 530–543 (2013) 3. Li, J., Zhang, K., Li, S., et al.: Maximum power point tracking control with active disturbance rejection controller based on the best tip speed ratio. Elect. Mach. Control 19(12), 94–100 (2015) 4. Hou, L.M., Ren, Y.F.: Permanent magnet synchronous motor slip based on speed sensorless modular self disturbance control. J. Syst. Simul. 31(5), 963–970 (2019) 5. Zeng, Y.N., Zhou, B., Zheng, L., et al.: Design of 1st-order linear active disturbance rejection controller for PMSMs. Control Eng. China 24(9), 1818–1822 (2017) 6. Chen, Y., Zhong, Y.: Study on the current control for voltage source PWM rectifier using complex vectors. Proc. CSEE 26(2), 143–148 (2006)

A Cluster-Based Dynamic Grouping Population Replication Strategy for Bilevel Multi-objective Optimization Wanyue Hu1,2 , Erqian Ge1,2 , Fei Li1,2(B) , and Hao Shen1,2 1 Anhui University of Technology, Ma Anshan 243032, China

[email protected], [email protected], [email protected] 2 Anhui Province Key Laboratory of Special Heavy Load Robot, Ma Anshan 243032, China

Abstract. Many problems encountered in engineering design and business decision-making can be solved by the bilevel optimization method. There are two optimization tasks in the bilevel optimization problems (BL-MOPs), in which each upper feasible solution corresponds to a lower optimal solution set to a lower-level optimization problem. However, rigidly using nested methods to solve bilevel optimization problems often leads to more evaluations at the upper and lower levels. This paper proposes a grouping-based replication optimization strategy for lower populations for BLMOPs, called BLEMO-PR. Individuals in the upper level of the offspring directly use the lower population of the closest individual to the parent in the upper level as the initial population. To improve the convergence and distributivity of the algorithm, we follow the already proposed dual populations lower-level search strategy. The difference is that when updating the lower-level populations, we use a new iterative selection strategy that considers the neighborhood individuals of non-dominated solutions more likely to be optimal in the next iteration. Experimental results demonstrate that the proposed algorithm maintains better convergence and diversity with fewer evaluations. Keywords: Bilevel optimization · Migration optimization strategy · Evolutionary multi-objective optimization · NSGA-II · Dual population

1 Introduction The upper-level optimization problem and the lower-level optimization problem together form a bilevel optimization problem (BLOP) [1, 2]. Considering that both the upper level and lower level optimization problems are conflicting multi-objective optimization problems, a Pareto front can be obtained for each level in the optimization process. It is obvious that in bilevel optimization, the lower-level optimization must run more frequently than the upper-level optimization because we must first satisfy the constraints of the upper-level optimization problem. For these reasons, it is crucial to lowering the computational complexity of both the upper-level and lower-level optimization as well as to shorten the algorithm’s overall running time. To this end, we use a population © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 154–160, 2023. https://doi.org/10.1007/978-981-99-4334-0_19

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replication-like strategy to replicate an initial set of optimal solutions for the initial lowerlevel population, thus speeding up the convergence and optimization of the lower-level population. The nested evolutionary algorithm has the advantage of solving the lower-level optimization problem corresponding to each upper-level member [4], to reduce the computational complexity of the pre-evolutionary algorithm, we added clustering to the optimization process of individuals at the upper level. The order is as follows for the remaining parts of this essay. In Sect. 2, we first give the fundamentals of formulating bilevel problems. Additionally, we offer dual population techniques. In Sect. 2, the algorithm suggested in this study is described in depth. Section 3 contains the experimental research and discussions. Finally, Sect. 4 brings this essay to a close.

2 The Proposed Algorithm Algorithm 1 represents the whole framework of our proposed algorithm. It consists of the following major aspects: first, we initialize the population. Then, crossover and mutation of the upper-level individuals produces the upper-level offspring individuals. Finally, update and refine the search for upper-level populations. Algorithm 1 BLEMO-PR 1: Input: nu , nl 2: Output: output_1   3: upop, lpop, output, Archive, RPs, output_1 ← Initilizing(upop, lpop) 4: whileNotTerminationdo 5: [SQ, RQ] ← Reproduce(upop, lpop) 6: Mergetheparentsandoffspringofthelowerpopulationandupdatethelower populationusingnon − dominancerelationships 7: UpdatingtheupperpopulationandArchive 8: Withoutrepeatingtheselectionoftheupper − levelindividualsthathavebeen UL − SelectionandArchivetodifferentialevolutionwithindividualsinArchive 9: Mergingoffspringandparentpopulations, usingenvironmentalselectionfor mergedpopulations 10: Nondominatedindividualsareemployedtoupdateoutput1, RP, andArchive 11: endwhile

In the initialization, we divide the upper-level populations into four groups, and the lower-level populations are generated randomly. Each initialized upper-level individual corresponds to two lower-level populations RP i and SP i . In the first iteration, SP i are generated randomly, RP i are replicated from SP i , and SQi are the offspring of SP i . Then the two population and offspring are merged and filtered using a reference-points-based non-dominated sorting method according to their lower-level objective value.

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In order to balance the convergence and diversification of the lower-level solutions, Wang et al. [3] develop an evolutionary algorithm that exploits dual populations in the lower-level search process. It is worth noting that for the parent individual of the iterative optimization process of the lower population RP, we choose the neighbouring individual of the nondominated solution to increase the convergence of the underlying individual. This is because the likelihood of an individual becoming the Pareto-optimal solution for the following generation is higher for descendants who are closest to the parent’s answer. Algorithm 2 Reproduction   1: Input: u_pop = u_pop1 , . . . , u_popk , l_pop 2: Output: SQ, RQS   3: qu ← GA u_poprandi ; 4: Deletethesameupperlevel vectorsfromquasinlpop ; 5: Deleteduplicateupperlevel vectorsinqu; 6: Calculatethedistancebetweenquandu_poptofindthequclosesttou_popi ; 7: for gl = 1 : max(i) do 8: Usingkmeans togroupthesamegroupofquagain, qusharesthelower populationofu_popi ; 9: {SQi , RQsi } ← LLsearchDPL_2 10: end for

The optimization process of the upper-level population is carried out, and we use the GA operator to generate the offspring of the upper decision variables and group the offspring according to the Euclidean distance between the offspring and the parent (K-means clustering method) and replicate the lower-level populations of the upperlevel parent to the lower-level population of the offspring closest to them. This is due to we believe that the initial individuals of the lower-level population of the children’s individuals can be replaced by the lower-level individuals corresponding to the parent’s upper-level individuals closest to them, which can provide the lower-level population of the children’s individuals with an initial population closest to their Pareto frontier, thus reducing the number of iterations and evaluations of the lower-level optimization. The maximum number of groups we limit to 20. Finally, the upper environment selection and refinement search will be performed. In addition, we create an external archive as output, which is used to store non-dominated individuals before the termination condition is reached.

3 Experiment Results The benchmark test sets used in this section’s experimental research are the TP (TP1– TP2) [5] and DS (DS1, DS4–DS5) [6] test suites, each of which has five test questions. We demonstrate the excellent properties of our algorithm by comparing it with the nested strategy (NS) and a state-of-the-art hybrid bilevel evolutionary multi-objective optimization algorithm (H-BLMEO) [5] as well as the knowledge migration-based dynamic variable decomposition approach (BLMOCC) [7].

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3.1 The Experimental Setups For a fair comparison, the parameters are set the same as indicated in the article [8], The number of TP1, TP2, DS4, and DS5 upper-level members is set to 5, the number of TP1 lower-level members is set to 12, the number of TP2 lower-level members is set to 60, and the number of DS4 and DS5 lower-level members is set to 40. 3.2 The Comparisons with Other Approaches We evaluate the H-BLEMO [5], BLMOCC [7], and MOBEA-DPL algorithms in this section using their lower evaluation counts, IGD [9], and HV [10] measures. Table 1 shows the values of the four algorithms on the average HV metrics after 21 independent runs. In all test problems, except DS1, BLEMO-PR performs exceptionally well in terms of HV values compared to the other algorithms. The tremendous overall performance of the BLEMO-PR algorithm on the HV metric proves the correctness of our determination method of regional optimality in the optimization of the lower-level individuals, which notably will increase the diversity of the lower-level folks whilst making sure the convergence of the lower-level highest quality solution. Table 2 indicates the ratio of the BLEMO-PR algorithm to the three algorithms. According to the acquired data, it can be proved that we can velocity up the convergence of the algorithm by using the use of the replication approach of the decrease layer populace in the decrease layer optimization process.

4 Conclusion The clustering and population replication approach are the two primary parts of BLEMOPR. In BLEMO-PR, populations are grouped by clustering to reduce the number of upper-level evaluations in the early stage of algorithm optimization. The population replication strategy can give an initial optimal population at the beginning of lowerlevel optimization, which speeds up the convergence of lower layer optimization and makes the number of lower layer evaluations reduced. In this study, we demonstrate the effectiveness of this algorithm in solving the computational complexity involved in the bilevel multi-objective problem with the help of two types of test problems.

3.306E-01(4.080E-03)

1.895E-01(1.980E-03)

1.012E+00(2.630E-03)

9.994E-01(1.520E-02)

8.634E-01(1.990E-02)

TP1

TP2

DS1

DS4

DS5

NS

9.158E-01(3.180E-02)

1.076E+00(2.250E-02)

1.089E+00(3.760E-02)

2.028E-01(2.210E-03)

3.614E-01(2.250E-03)

H-BLEMO

9.416E-01(3.310E-03)

1.122E+00(2.960E-03)

1.152E+00(3.360E-03)

2.264E-01(3.680E-03)

3.632E-01(3.690E-03)

BLMOCC

2.329E+00(2.447E-01)

2.273E+00(2.710E-01)

0.000E+00(0.000E+00)

5.440E-01(1.796E-03)

5.554E-01(1.750E-02)

BLEMO-PR

Table 1. Mean and standard deviation value of HV obtained by four algorithms on five test instances.

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5.186E-02

2.969E-02

6.308E-01

3.300E-02

1.404E-02

TP2(5+60)

DS1(20+20)

DS4(5+40)

DS5(5+40)

2.176E-01

3.931E-01

8.339E+00

1.567E+00

7.510E-01

8.896E-03

1.965E-02

2.606E-01

1.881E-02

3.418E-02

1.096E-01

2.059E-01

2.492E+00

7.654E-02

5.340E-01

Total LL FEs

Total UL FEs

Total ULFEs

Total LL FEs

BLMOOC(Med ) Saving : BLEMO−PR(Med )

H −BLEMO(Med ) Saving : BLEMO−PR(Med )

TP1(5+12)

Problem

3.863E-01

1.177E+00

1.444E+01

6.358E-01

4.895E-01

Total UL FEs

4.125E-01

1.151E+00

2.830E+01

1.490E+00

2.031E+00

Total LL FEs

) Saving : MOBEA−DPL(Med BLEMO−PR(Med )

Table 2. The ratios of median function evaluations spent by BLEMO-PR over H-BLEMO, BLMOCC, and MOBEA-DPL.

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Acknowledgements. The authors are supported by the National Natural Science Foundation of China under 61903003, 62273006 and Supported by Open Project of Anhui Province Key Laboratory of Special and Heavy Load Robot (Grant TZJQR001-2021) and Scientific Research Projects in Colleges and Universities of Anhui Province (Grant KJ2019A0051) and the Nature Science Research Project of Anhui province (Grant NO. 2008085QE227).

References 1. Vicente, L.N., Calamai, P.H.: Bilevel and multilevel programming: a bibliography review. J. Glob. Optim. 5(3), 291–306 (1994) 2. Colson, B., Marcotte, P., Savard, G.: An overview of bilevel optimization. Ann. Oper. Res. 153(1), 235–256 (2007) 3. Wang, W., Liu, H.-L., Shi, H.: A multi-objective bilevel optimisation evolutionary algorithm with dual populations lower-level search. Connect. Sci. 34(1), 1556–1581 (2022) 4. Sinha, A., Malo, P., Frantsev, A., Deb, K.: Finding optimal strategies in a multi-period multileader–follower stackelberg game using an evolutionary algorithm. Comput. Oper. Res. 41, 374–385 (2014) 5. Deb, K., Sinha, A.: An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary local-search algorithm. Evolut. Comput. 18(3), 403–449 (2010) 6. Deb, K., Sinha, A.: Constructing test problems for bilevel evolutionary multi-objective optimization. In: Proceedings of the 2009 IEEE Congress on Evolutionary Computation, pp. 1153–1160. IEEE (2009) 7. Cai, X., Sun, Q., Li, Z., Xiao, Y., Mei, Y., Zhang, Q., Li, X.: Cooperative coevolution with knowledge-based dynamic variable decomposition for bilevel multiobjective optimization. IEEE Trans. Evolut. Comput. (2022) 8. Storn, R., Price, K.: Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997) 9. Zhou, A., Jin, Y., Zhang, Q., Sendhoff, B., Tsang, E.: Combining model-based and geneticsbased offspring generation for multi-objective optimization using a convergence criterion. In: Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, pp. 892–899. IEEE (2006) 10. While, L., Hingston, P., Barone, L., Huband, S.: A faster algorithm for calculating hypervolume. IEEE Trans. Evolut. Comput. 10(1), 29–38 (2006)

Study on Multi-objective Scheduling Strategy for Electric Vehicle to Absorb Wind Power Considering Dynamic Time-of-Use Price Shuang Wu1,2

, Chun Zhang1,2(B) , Zejun Tong1,2 and Haoyu Li1,2

, Pengcheng Gao1,2

,

1 College of Electrical Engineering, Anhui Polytechnic University, Wuhu, Anhui 241000,

People’s Republic of China [email protected] 2 Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, Anhui, People’s Republic of China

Abstract. By right of the load transferability and energy storage characteristics of electric vehicles, the energy consumption period of users can be guided to change by dynamic time-of-use (DTOU) price, Further improvement of the charging and discharging power of EVs. Simultaneously, the load peak-valley deviation can be decreased by DTOU price, which increases the wind power consumption as well. Then the DTOU price model is established in this paper, with the proposed start-stop control strategy of electric vehicles. Regarding the minimum system cost and carbon emissions as the objective functions, a multi-objective optimal scheduling model is generated. By means of comparing the operation results of three scenarios, it is shown that the realization of coordinated scheduling, increase of wind power consumption, reduction of total operation cost and carbon emissions as well as enhancement of system operation economy can be completed by the proposed strategy. Keywords: DTOU price · EVs · V2G · Absorb excess wind power

1 Introduction With the proposal of “double carbon” goal and a large number of new energy sources connected to the grid, the development of power system is facing huge challenges [1]. Taking advantage of the load transferability of electric vehicles and the fluctuation of wind energy, the joint scheduling of wind energy and electric vehicles becomes a measure to optimize energy consumption [2, 3]. At present, there has been a great deal of researches on wind power consumption and electric vehicle load participation in optimal scheduling at home and abroad. According to the real-time operation status of the charging station, the literature [4] proposes a method for setting peak-to-peak charging tariffs to achieve orderly charging control in charging stations. In the literature [5], time-of-use (TOU) price mechanism and energy © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 161–168, 2023. https://doi.org/10.1007/978-981-99-4334-0_20

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storage technology are incorporated into the wind power consumption model. The literature [6] proposes a coordinated scheduling strategy for EV peak shaving with V2G price incentive. This paper starts from the benefit of wind power consumption, makes full use of the load transferable characteristics of electric vehicles, establishes a DTOU price model, guides users to change the energy consumption period of electric vehicles through the price mechanism, so as to transfer part of the load, so as to absorb more excess wind power, and constructs an electric vehicle optimal dispatching strategy guided by the DTOU price; At the same time, considering the economy and sustainable development of the power grid, the dispatching optimization is carried out with the goal of minimum total system operating costs and minimum carbon emissions; Finally, the effectiveness of this scheduling strategy is verified by arithmetic examples.

2 Time Division of the DTOU Price First, calculate the predicted power load and wind power data, get the equivalent load and calculate the average value; Then calculate the peak valley difference of the whole dispatching period, and determine the division period of electricity price according to the average value of equivalent load and peak valley difference. The DTOU price model is established as follows: ⎧ ⎨ (1 + β)e0 , Peq (t) ≥ Pav + αPh (1) e(t) = e0 , Pav − αPh ≤ Peq (t) ≤ Pav + αPh ⎩ (1 + β)e0 , Peq (t) ≤ Pav − αPh Peq (t) = Pload (t) + Pwf (t) Ph =



(2)

Peq,max − Peq,min

(3)

T 1 Peq (t) T

(4)

t∈[1,T ]

Pav =

i=1

where, e0 is the daily electricity price; β is the fluctuation range coefficient of high and low electricity prices based on the electricity price in normal time; T is the number of scheduling cycle periods; Peq (t) is the equivalent load of electric load and wind power; Pload (t) is the system electrical load; Pwf (t) is the forecasted output of wind power; Peq,max and Peq,min are the maximal and minimal values of the equivalent load, respectively; Ph is the peak-to-valley difference of the equivalent load; Pav is the mean value of the equivalent load.

3 Dispatching Strategy Considering the DTOU Price In this paper, the dispatch center is responsible for the output regulation of each power supply unit, wind power forecast, electric vehicle and electric load.

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Since the introduction of electric vehicles as energy storage equipment has changed the structure of the traditional energy supply network, the coordinated operation strategy between the unit and the electric vehicle should be studied, aiming at the optimal production cost and the lowest carbon emission, and guide customers to change the energy consumption period of electric vehicles through the DTOU price mechanism, so as to transfer part of the load, so as to absorb more excess wind power. Considering the elimination of abandoned air, the improvement of energy supply efficiency and cost effectiveness of the system, and the reduction of unnecessary energy transfer, the start and stop control strategy of abandoned air shall be adopted for electric vehicle V2G, that is, the start and stop of electric vehicle V2G shall be determined according to whether there is abandoned air. Whether there is abandoned air is judged as follows:  1 PGASF (t) + PCONF (t) > Pload (t) − Pwf (t) (5) k1 = 0 PGASF (t) + PCONF (t) ≤ Pload (t) − Pwf (t) where, k1 = 1 means there is wind power abandonment; k1 = 0 means no wind power abandonment; PGASF (t) is the forced output of gas unit at time t; PCONF (t) is the forced output of thermal power unit at time t. In this paper, a dispatching strategy based on the DTOU pricing is constructed with reference to price-based demand response means to guide load shifting. Study of the loadside with the participation of EVs, and a dispatching strategy considering the DTOU pricing is established, as illustrated in Fig. 1. System Control Center

Giving instructions

Upload information

Coordinated operation of electric power

Main control objective: Guide load transfer through dynamic time of use tariff

Upload information

Power monitoring Wind power monitoring

Control rules

Charge and discharge control of electric vehicle

Stabilize load fluctuation

Giving instructions

Main control objective: Minimum system operation cost Minimum carbon emissions Load

Common electrical load

Optimizati on method

Load transfer

Control requirements

Load distribution Power dispatching

Electric Vehicle V2G and load transfer

V2G air abandonment start stop control

Minimum cost and carbon emissions Maximum wind power consumption

Fig. 1. Block diagram of dispatching strategy considering DTOU price.

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4 Multi Objective Optimal Scheduling Model 4.1 Objective Function In this paper, a scheduling cycle is set as 24 h, which is separated into 24 scheduling periods. Taking 1 h as the scheduling subsection, the scheduling optimization is carried out with the objective of the lowest total operation cost and minimum carbon emissions of the whole cyclic network. The objective function is established as follows: ⎧ T T T    ⎪ ⎪ Vbuy (t) + a2 FCON (t) + a3 PV 2G (t) ⎨ f1 = a1 t=1 t=1 t=1 (6) N  T  ⎪ CO2 ⎪ ⎩ f2 = λc Pc (t)t n=1 t=1

For the objective function f1 . Where a1 , a2 and a3 are unit natural gas price, unit coal price and unit discharge power operation cost of electric vehicle respectively; Vbuy (t) is the natural gas purchase volume during the period; FCON (t) is the coal consumption of pure condensing fire motor unit during the period; PCON (t) is the discharge power of electric vehicle during the period. For the objective function f2 . Where N is the number of carbon emission devices; λc is the carbon emission coefficient of the c-th carbon emission device; PcCO2 (t) is the output of the c-th carbon emission device at time t; t is the duration of the scheduling period. 4.2 Binding Conditions Energy Balance Constraint PGAS (t) + PCON (t) + Pw (t) = Pload (t) + k1 PV 2G (t)

(7)

where, PGAS (t) is the electric power output of gas turbine unit at time t; PCON (t) is the electric power output of thermal power unit at time t; Pw (t) is the electric power output of wind turbine unit at time t. Electric vehicle constraints are described as dis char Pmax ≤ PV 2G (t) ≤ Pmin

(8)

Smin ≤ S(t) ≤ Smax

(9)

Smin = d1 NV 2G Sev max

(10)

Smax = d2 NV 2G Sev max

(11)

char is the minimum charging power; P dis is the maximum discharge power; where, Pmin max Smin and Smax are the minimize and maximize values of residual power of on-board battery respectively; Sev max is the maximum value of the average capacity of a single electric vehicle; d1 and d2 are the proportion of the minimum and maximum electricity that should be retained by each electric vehicle respectively. In this paper, the model is solved using an improved particle swarm algorithm [7].

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5 Example Analysis 5.1 Data Description The system in this paper includes a thermal power plant, a thermal power plant (four thermal power units) and a wind farm (installed capacity of 250 MW). Table 1 shows the DTOU price. The initial battery power of electric vehicles is 50%, and the detailed parameters are illustrated in Table 2. Figure 2 indicates the curve of wind power predicted output and electric load power. The system dispatching cycle is 24 h and the dispatching interval is 1 h. In order to verify the efficiency and economy of the studied energy scheduling strategy, we set 3 study scenarios. Scenario 1: The system is not equipped with any device to restrict air abandonment. Scenario 2: The system is equipped with V2G equipment but does not implement the tou strategy. Scenario 3: The system is equipped with V2G equipment and implements TOU pricing strategy.

Fig. 2. Wind power predicted output and electric load power curve.

Table 1. Dynamic time of use price Period

Time

Electricity price (¥/kWh)

Peak hours

10:00–15:00

1.18

18:00–20:00 Usual period

06:00–10:00

0.87

15:00–18:00 20:00–23:00 Valley hours

23:00–06:00

0.41

5.2 Results and Analysis In order to analyze the role of this scheduling strategy in reducing the peak-to-valley difference and relieving the pressure on power system supply, the following analysis is

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Parameter

Value

Battery capacity (kWh)

18

Charging power (kW)

3.6

Discharge power (kW)

2.5

conducted accordingly. Figure 3 shows the change curve of electric vehicle charge and discharge power before and after the implementation of the strategy. Figure 4 shows the load power change curve before and after the implementation of the strategy. From the comparison of wind power output data in Figs. 2 and 3, it can be seen that after the DTOU price division, the load is transferred by implementing the dispatching strategy based on the updated electricity price. As can be observed from Fig. 4, after the implementation of the strategy, EVs will transfer the charging load from the peak load period to the low load period, effectively lessening the peak-to-valley load difference.

Fig. 3. Change curve of electric vehicle charging and discharging power before and after implementation of the strategy.

Fig. 4. Load power change curve before and after strategy implementation.

The electric power scheduling results of Scenario 3 is indicated in Fig. 5. Comparing Fig. 5 with Figs. 2 and 3, it can be observed that the charging time of electric vehicles is allocated to the period of high wind power generation and low load after scheduling, which effectively reduces the power consumption cost of users and consumes excess wind power. Figure 6 shows the predicted output of wind power and wind power on grid power curve under different scenarios, Table 3 illustrates the total system cost and total carbon emissions under the three scenarios.

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As can be seen from Fig. 6 and Table 3, compared with Scenario 1, the total cost of Scenario 3 is reduced by 2.60% and the total carbon emission is reduced by 4.01%, realizing the economic optimization. In the meantime, the wind power consumption is increased, effectively relieving the power supply pressure of the power system during the high load period. Thereby, the feasibility of the proposed electric vehicle scheduling strategy is verified.

Fig. 5. Scenario 3 electric power dispatching results.

Fig. 6. Wind power predicted output and wind power on grid power curve under different scenarios.

Table 3. Total system cost and total carbon emissions under three scenarios. Scenario

Total cost (yuan)

Total carbon emissions (kg)

Scenario1

6719473.06

38074.18

Scenario2

6604238.49

37016.40

Scenario3

6544689.73

36545.91

6 Conclusion For the sake of improve the wind power consumption of the power system and avoid the influence of centralized charging of electric vehicles on the power grid, a multiobjective scheduling strategy for regional energy system with V2G is proposed by using the transferable characteristics of electric vehicle loads and combining with the DTOU price. By setting the threshold value, whether there is wind rejection in the system

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can be judged and the system operation efficiency can be improved. The comparative scheduling results under three scenarios prove the effectiveness of the tactics proposed in this paper, which not only has a good effect of eliminating wind, but also can reduce the system operation cost and carbon emissions.

References 1. Yang, J., Qing, W., Shi, W.: Two-stage optimal dispatching of regional power grid based on electric vehicle participating in peak load regulation pricing strategy. Trans. China Electrotechn. Soc. 37(01), 58–71 (2022) 2. Li, J., Zhang, L., Yang, A., Zhang, Q., Chen, X.: An artificial intelligence-based fusion method for wind power prediction. In: Cao, W., Hu, C., Huang, X., Chen, X., Tao, J. (eds.) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 916. Springer, Singapore (2022) 3. Zhang, N., Tang, Z.: Multi-objective optimization strategy considering collaborative scheduling of electric vehicles and wind power under V2G. Elect. Measur. Instrum. 55(12), 54–87 (2018) 4. Xu, Z., Hu, Z., Song, Y.: Orderly charging strategy of electric vehicle charging station based on dynamic time-of-use price. Proc. CSEE 34(22), 3638–3646 (2014) 5. Song, Y., Tan, Z., Li, H.: Joint optimization model of generation side, energy storage and demand side to promote wind power consumption. Power Syst. Technol. 38(03), 610–615 (2014) 6. Wang, M., Lv, L., Xiang, Y.: Cooperative dispatching strategy of electric vehicle peak shaving considering V2G price incentive. Elect. Power Autom. Equip. 42(04), 27–85 (2022) 7. Yang, K.: Combined Electricity-Heat-Cooling Scheduling Method for Gas-Steam Combined Cycle Units. Harbin Institute of Technology, Harbin (2018)

Thermal Effect Analysis of Three-Level Inverter Power Module Based on Single Cycle Loss Calculation Shi-Zhou Xu1,2 , Xi Yang1(B) , Min Feng1 , and Tian-Yi Pei1 1 Department of Electronic and Electrical Engineering, Henan Normal University, 46 Jianshe

East Road, Xinxiang 453000, China [email protected] 2 Henan Key Laboratory of Optoelectronic Sensing Integrated Application, 46 Jianshe East Road, Xinxiang 453000, China

Abstract. Three-level inverters have been widely used, but hot faults of power modules often occur. The power module generates a lot of heat during operation. If the heat is not dissipated in time, the performance of the module will be affected. In serious cases, the power device will be damaged and burned. To solve this problem, this paper advances a fast loss algorithm of inverter based on single cycle loss calculation, and analyzes the thermal effect of power module. Firstly, the mathematical model of insulated gate bipolar transistors (IGBT) power module is established, the single-cycle loss is calculated by IPOSIM software, and the thermal model is established and simulated by ANSYS Icepak. The single cycle loss is defined as the thermal source of the cooling plate to improve the design the power module, during which process a single cycle heat equalization principle is proposed. Then the heat dissipation of the power module is analyzed, and the fins of the heat sink are modified and optimized to improve heat dissipation efficiency of the heat sink to enhance thermal stability of IGBT power module. Finally the simulation and experiment results demonstrate the effectiveness and feasibility of the proposed method. Keywords: IGBT module · Electro-thermal analysis · Icepak · Thermal equilibrium

1 Introduction As a key component in the new energy conversion system, IGBT power module has the advantages of strong short-circuit resistance, simple driving circuit and low steady loss. However, if the temperature of the IGBT module is too high or exceeds the junction temperature, it will cause bond connection fusing, solder failure and other faults, which will reduce the service life of the device. Therefore, the thermal analysis and heat dissipation analysis of IGBT power module are principal for device reliability. For the thermal analysis of electronic devices, many domestic and foreign experts have done plenty of analysis and research. An air cooling system for IGBT module under © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 169–177, 2023. https://doi.org/10.1007/978-981-99-4334-0_21

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modular multilevel converters (MMC) operation conditions is proposed in [1], which has low lost. An electro-thermal model based on mixed-logical-dynamic (MLD) is proposed in [2], it can quickly observe thermal characteristics of power devices in the converter under normal conditions and open circuit (OC) faults. A method is presented in [3] to solve the electro-thermal problem of power electronic components by using the enhanced RC network model. According to the characteristics of different time scales, a multi-time scale prediction model (MTPM) of IGBT junction temperature is proposed in [4], but this method is computationally heavy. An analytical model is presented in [5] for calculating the mean current and root mean square current of IGBT and anti-parallel diode (APDs) hard switching operation using bus clamp pulse width modulation (BCPWM), but this is too complicated. Thermosensitive electrical parameters (TSEP) method is presented in [6] to extract the IGBT junction temperature. However, the accuracy is not high. The radiator with various fin combinations under natural convection conditions conducts a comparative study in [7], but the heat capacity of the radiator is not analyzed. An IGBT junction temperature estimation algorithm is proposed in [8], which the calculation of loss is optimized. The plastic strain variation of IGBT power module is related to the thickness of baseplate and DBC in [9]. A method to calculate IGBT junction temperature using machine learning algorithm is proposed [10], but this is only for photovoltaic inverters. Therefore, this paper analyzes a fast loss algorithm and proposes a heat balance principle. The remaining of this paper is mainly as below. In Sect. 2, the electric-thermal model of the inverter is discussed, and the loss distribution and junction temperature of power module are analyzed. In Sect. 3, the loss and junction temperature of IGBT and diode are simulated and analyzed by simulation software. In Sect. 4, the finite element analysis of the power module is carried out to obtain the temperature distribution of IGBT and diode. In Sect. 5, the heat dissipation analysis of power module is optimized and the principle of single cycle heat equalization is proposed.

2 Electro-Thermal Model of Inverter 2.1 Power Module Loss Model Neutral Point Clamped (NPC) three-level topology is one of the most widely used multilevel topologies. Compared with the two-level structure, the three-level structure has the advantages of better output waveform, reduced loss, and increased switching frequency. The power loss of IGBT and diode in inverter is divided into two parts: the power loss of IGBT power device includes conduction loss and switching loss; the power loss of diode includes conduction loss and reverse recovery loss. The power losses of IGBT power devices and diodes can be calculated as [11–13]: Ploss_I = Pcon_I + Psw_I

(1)

Ploss_D = Pcon_D + Pre_D

(2)

The conduction loss of IGBT and diode is able to represent as [11–13]: Pcon_I =

I2 I2 1 I I (VCE0 ∗ + r ∗ ) + m cos φ ∗ (VCE0 ∗ + r ∗ ) 2 π 4 8 3π

(3)

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Pcon_D =

1 I I2 I I2 (VT 0 ∗ + rd ∗ ) − m cos φ ∗ (VT 0 ∗ + rd ∗ ) 2 π 4 8 3π

171

(4)

V CE0 is constant voltage drop of IGBT, r is slope resistance of IGBT, V T0 is constant voltage drop of diode, r d is slope resistance of diode, ϕ is phase difference between the output signal and the current, m is modulation ratio, I is amplitude of load current. In a period T, the switching loss of IGBT can be given as [13, 14]: Psw_I =

1 i Vdc ∗ fsw ∗ (Eon (Ib , Vb ) + Eoff (Ib , Vb )) ∗ ∗ π Ib Vb

(5)

E on is turn-on energy losses of the IGBT at each pulse, E off is turn-off energy losses of the IGBT at each pulse, i is bridge arm currents of each phase, I b is nominal current of the IGBT, V b is nominal voltage of the IGBT, V dc is DC side voltage. The reverse recovery loss of the diode is able to express as [13]: Pre_D =

1 I Vdc ∗ fsw ∗ (Ere (Ib ) ∗ (0.45 ∗ + 0.55) ∗ π Ib Vb

(6)

f sw is switching frequency, E re is reverse recovery loss of diode. 2.2 Thermal Model of Inverter The internal structure of the power device is depicted in Fig. 1. The internal structure includes chip, direct bonded copper (DBC), base plate and radiator. The thermal network model is proposed to realize the measurement of junction temperature [15–18]. In this paper, the RC equivalent thermal model is used to calculate junction temperature of power devices. The equivalent thermal model of IGBT power module is depicted in Fig. 2. chip

RthJC

copper ceramic

ΔTJ C

copper layer base plate

ΔTCH

RthCH radiator

ΔTHA

RthHA Fig. 1. Internal structure of the power device.

Through RC equivalent thermal model, the junction temperature of IGBT and diode can be obtained [14]: Tj_IGBT = TH + (RthJC_IGBT + RthCH _IGBT ) ∗ Ploss_IGBT

(7)

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Fig. 2. Equivalent thermal model of power module [19].

Tj_Diode = TH + (RthJC_Diode + RthCH _Diode ) ∗ Ploss_Diode

(8)

TH = Ta + (Ploss_IGBT + Ploss_Diode ) ∗ RthHA

(9)

RthJC_IGBT is thermal resistance of junction of IGBT to case, RthJC_Diode is thermal resistance of junction of diode to case, RthCH_IGBT is thermal resistance of case of IGBT to the radiator, RthCH_Diode is thermal resistance of case of diode to the radiator, RthHA is thermal resistance of radiator to the environment, T H is junction temperature of radiator, T a is temperature of the surrounding environment, T j_IGBT is junction temperature of IGBT, T j_Diode is junction temperature of diode.

3 Electro-Thermal Analysis of the Power Module 3.1 Loss Calculation In this paper, the IPOSIM software developed by Infineon is used to simulate the FF450R17ME4 power module. Because of the symmetrical structure of each phase of NPC three-level inverter, only power loss of the A-phase upper bridge arm is being studied. The loss distribution of inverter phase A is shown in Fig. 3. Under the same parameters, compared with other power devices, switch I1 has the largest loss. The reason for this phenomenon is that the switch I1 in the inverter state is in the high frequency state and the switching loss is greater. The switch I2 is in the power frequency state and only bears the conduction loss. 3.2 Junction Temperature Analysis The simulation platform of Infineon is used to analyze the A-phase upper bridge arm of NPC three-level inverter. The junction temperature fluctuation results of each power device are depicted in Fig. 4. It indicates that the junction temperature of S1 is about 1 °C higher than that of S2. The junction temperature of D1 and D2 is 2–3 °C lower than that of the switch tube. The junction temperature of D5 is about 0.5 °C different from S1.

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35.8

35 26.71 24.32

30 25 20

19.72

18.6117.19 13.49

15 10 5

6.23 1.770.43 2.2

2.39

0 Switch I1 / I4 Diode I1 / I4 Switching loss W

0 0.430.43

Switch I2 / I3 Diode I2 / I3 FWD D5 / D6 Conduction loss(W) Total loss(W)

Fig. 3. Loss distribution of inverter phase A.

Fig. 4. Junction temperature distribution in phase A upper bridge arm.

4 Thermal Simulation and Experiment In this paper, Icepak software is used to conduct thermal simulation analysis of IGBT power module. Firstly, the 3D model of a single IGBT power module is established in Icepak, as shown in Fig. 5(a). After the 3D model is established, the material parameters of the model structure need to be set. The material and its thermal conductivity are shown in Table 1. After simulation analysis, the temperature distribution cloud diagram of IGBT module is depicted in Fig. 5(b). Figure 5(b) exhibits that the highest temperature is at the IGBT chip. The IGBT temperature finally stabilizes at about 57.9 °C, which is about 3.5 °C different from the obtained in the previous section, and the error is within 6%. The temperature of diode is stable at about 48 °C, which is about 2 °C different from the obtained in the previous section, and the error is within 5%. In order to further verify the accuracy of the simulation results, the power module is tested by fiber sensing and thermal imaging. The fiber is fixed in the baseplate of

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Fig. 5. (a) Structure diagram of 3D model; (b) Temperature distribution cloud image of single IGBT module. Table 1. Materials and their thermal conductivity. Name

Materials

Thermal conductivity (W/m*k)

Chip

Si

100

DBC (ceramic layer)

Al2 O3

Base plate

Cu

Solder

SnAg3.5

Thermally conductive silicone grease

Organic silicone

25 380 28 2

Fig. 6. Experiment temperature of power module.

the power module, which can test the temperature of IGBT. Figure 6 indicates that the experiment temperature is 2.6 °C higher than the simulation one, and the error rate is 4.2%, which is acceptable in engineering.

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5 Single Cycle Heat Equalization The IGBT power module generates a large amount of heat during operation. The heat needs to be transferred by the radiator in time to avoid affecting the normal operation of the IGBT. A single cycle heat equalization method is proposed to verify the heat dissipation effect of radiator. Convective radiant heat resistance of the radiator is [20]: Rhs,cr =  1−

Nf Af At

1   1 − ηf At h

(10)

N f is number of fins, Af is fin heat dissipation area, h is heat transfer coefficient of the radiator, ηf is fin efficiency, At is total heat dissipation area of radiator. The total heat flow of radiator is [20]:    Nf Af  Tb − T∞ 1 − ηf At h(Tb − T∞ ) = 1− Qhs = (11) Rhs,cr At T b is wing base temperature, T ∞ is ambient temperature. Combined with the expression of the total heat flow of radiator, it can be concluded that the total heat flow of the radiator is 36.3 W. The calculated total heat flow rate of the radiator is slightly lower than the total power of IGBT module. Therefore, the fin parameters of the radiator are modified to improve the heat dissipation. The fin heat transfer considering the convection and radiation of the wing top is approximately equivalent to a fin with an adiabatic wing top and a slightly longer length. The additional length makes the surface area of the fin increase equal to the area of the wing top. This in effect converts the heat dissipation area at the top of the wing to the side. The corrected fin length is [20]: Lc = L +

Ac P

(12)

L is the length of the fin, Ac is cross sectional area along the wing height, P is perimeter of cross section.Before correction, L is 0.015 m. After the modification of the length of the radiator fin, L c is 0.016 m. Comparison with the results before correction, the total heat flow of the radiator is increased to 39.6 W, and all heat generated by the IGBT module can be released, which realizes the heat balance and ensures the system is not overheated and finally thermal stability. The results of comparing the total heat flow of the radiator before and after the fin length modification are shown in Fig. 7.

6 Conclusion In this thesis, the loss model and thermal model of inverter are proposed, moreover the loss and junction temperature distribution of the IGBT and diode are analyzed. The highest junction temperature appears at the IGBT chip. Finally the simulation and experiment results are similar to Icepak simulation results, and the error is 4.2%, which is acceptable in engineering.

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IGBT module power W Total heat flow rate of radiator 38

39.6 W 38

36.3 36 34 L=0.015m

Lc=0.016m

Fig. 7. Total heat flow rate of radiator before and after correction.

At the same time, a single cycle heat equalization principle is proposed. By modifying the fin length, the optimal scheme is finally obtained, which enables the radiator to transfer all the heat generated by the module in time to ensure that the system does not overheat and realize the thermal stability of the system. Acknowledgments. The authors would like to thank Henan science and technology project, Grant Number 202102210299; Science and technology project of Xinxiang, Grant Number GG2020005; Henan Engineering Laboratory of Additive Intelligent Manufacturing.

References 1. Wang, B., et al.: Air-cooling system optimization for IGBT modules in MMC using embedded O-shaped heat pipes. IEEE J. Emerg. Select. Top. Power Electron. 9(4), 3992–4003 (2021) 2. Yang, C., et al.: MLD-based thermal behavior analysis of traction converters under faulty conditions. IEEE Trans. Transp. Elect. 7(3), 1058–1073 (2021) 3. Shahjalal, M., et al.: An analysis of the thermal interaction between components in power converter applications. IEEE Trans. Power Elect. 35(9), 9082–9094 (2020) 4. Liu, B., et al.: A multi-timescale prediction model of IGBT junction temperature. IEEE J. Emerg. Select. Top. Power Electron. 7(3), 1593–1603 (2019) 5. Islam, M.M., Rahman, M.A., Islam, M.R.: Power loss and thermal impedance modeling of multilevel power converter with discontinuous modulation. IEEE Trans. Energy Conver. 36(1), 36–47 (2021) 6. Zhang, J., et al.: IGBT junction temperature measurements: inclusive of dynamic thermal parameters. IEEE Trans. Dev. Mater. Reliabil. 19(2), 333–340 (2019) 7. Charles, R., Wang, C.: A novel heat dissipation fin design applicable for natural convection augmentation. Int. Commun. Heat Mass Transf. 59, 24–29 (2014) 8. Lim, H., et al.: A Study on Real Time IGBT Junction Temperature Estimation Using the NTC and Calculation of Power Losses in the Automotive Inverter System. Sensors 21(7), 2454 (2021) 9. Ren, Z., Zhao, Y., Liu, Z., Wang, Z., Wang, N.: Plastic strain analysis of IGBT solder layer. In: Hu, C., Cao, W., Zhang, P., Zhang, Z., Tang, X. (eds.) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 899. Springer, New York (2021) 10. Zhang, B., Gao, Y., Li, T., Hu, X., Yang, E.: Optimal PV system capacity ratio and power limit value selection based on a novel fast calculation method of IGBT junction temperature and IGBT annual damage analysis. Energy Rep. 8(S13), 348–355 (2022)

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11. Wang, Y., Liu, D., Chen, Z., Liu, P.: A hierarchical control strategy of microgrids toward reliability enhancement. In: Proceedings of the 6th IEEE International Conference on Smart Grid, pp. 123–128 (2018) 12. Rohner, S., et al.: Modulation, losses, and semiconductor requirements of modular multilevel converters. IEEE Trans. Ind. Elect. 57(8), 2633–2642 (2010) 13. Infineon Technical Documentation. Dimensioning program IPOSIM for loss and thermal calculation of infineon IGBT modules 14. Wang, Y., et al.: Enhanced hierarchical control framework of microgrids with efficiency improvement and thermal management. IEEE Trans. Energy Conver. 36(1), 11–22 (2021) 15. Musallam, M., Johnson, C.M.: Real-time compact thermal models for health management of power electronics. IEEE Trans. Power Electr. 25(6), 1416–1425 (2010) 16. Chen, M., Hu, A., Yang, X.: Predicting IGBT junction temperature with thermal network component model. In: APPEEC, Wuhan, Hubei Province, China, pp. 1–4 (2011) 17. Gachovska, T.K., Tian, B., Hudgins, J.L., Qiao, W., Donlon, J.F.: A real-time thermal model for monitoring of power semiconductor devices. IEEE Trans. Ind. Appl. 51(4), 3361–3367 (2015) 18. Bahman, A.S., Ma, K., Ghimire, P., Iannuzzo, F., Blaabjerg, F.: A 3-D-lumped thermal network model for long-term load profiles analysis in high-power IGBT modules. IEEE J. Em. Sel. Top. P. 4(3), 1050–1063 (2016) 19. Yang, Y., Wang, H., Blaabjerg, F., Ma, K.: Mission profile based multi-disciplinary analysis of power modules in single-phase transformerless photovoltaic inverters. In: Proceedings of the 2013 15th European Conference on Power Electronics and Applications (EPE), Lille, pp. 1–10 (2013) 20. Younes, S.: Heat Transfer. Taylor and Francis; CRC Press, New York (2011)

Secondary Authentication Method Suitable for 5G-Based Power Terminals and Formal Analysis Xin Hu1,2 , Yu Jiang1,2(B) , and Aiqun Hu1,2 1 School of Cyber Science and Engineering, Southeast University, Nanjing, China

[email protected] 2 Purple Mountain Laboratories, Nanjing, China

Abstract. In the 5G network, the access method of IoT terminals is mainly wireless access. Aiming at the high authentication cost in massive access scenarios, this paper proposes a secondary authentication method based on aggregate signcryption for the secondary authentication of 5G-based power terminals. This method not only ensures the security, but also has the characteristics of less computation and storage consumption, and high operation efficiency. At the same time, it avoids the certificate management problem in traditional public key cryptosystem and the key escrow problem in identity-based public key cryptosystem. In this paper, 5G EAP-TLS authentication protocol suitable for this method is studied. 5G EAP-TLS protocol is mainly used for authentication and key agreement in 5G private networks or IoT scenarios. This paper constructs the 5G EAP-TLS protocol model based on TS 33.501 document, uses ProVerif verification tool to verify the security attributes of the protocol, and proposes a modification scheme. Keywords: 5G-based power terminals · Secondary authentication · Aggregated signcryption · Formal analysis

1 Introduction With the advent of 5G, new prospects and opportunities have emerged for the development of the power Internet of Things. On the other hand, the challenge of device security access is even more severe. In order to meet the high security requirements of vertical industries, the 5G network proposes a secondary authentication architecture [1], which adopts the Extensible Authentication Protocol (EAP) to realize the secondary authentication between the user terminal and the data network to meet the security requirements of different services. In the massive access scenario, the devices connected to the Internet of Things are of different nature and large in number, and each terminal needs to be authenticated one by one, which brings about the problems of high authentication cost and low efficiency. The concept of signcryption was proposed by Zheng in 1997 [2].With the development of signcryption technology, the first certificateless signcryption scheme was © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 178–185, 2023. https://doi.org/10.1007/978-981-99-4334-0_22

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proposed by Barbosa et al. in 2008 [3]. Through the aggregation signature technology, each Internet of Things device can sign and encrypt the collected data and send the ciphertext after signing to the specified device. The device aggregates the received symbolic encrypted ciphertext with the aggregation algorithm and then obtains the ciphertext with a very small length and sends it to the processing center. Finally, the processing center authenticates and decrypts the signed and encrypted ciphertext to authenticate the identity of the device and the reliability of the sent data. As the first defense line of mobile communication network security, authentication protocol security research has always been an important field of concern in the industry. Some researchers use formal methods to analyze the security of authentication protocols. Broek et al. used ProVerif to comprehensively analyze the privacy of user identifier IMSI in 2G, 3G and EPS AKA protocols, found a vulnerability caused by plaintext transmission of IMSI, and proposed an alternative to IMSI [4]. Cheval et al. used DeepSec to verify the unlinkability of EPS AKA protocol and found a linkability attack against this protocol [5]. Basin et al. used Tamarin to model and verify the confidentiality and authentication of the 5G-AKA protocol and found an identity vulnerability caused by the lack of integrity protection of service network names [6]. This paper proposes a secondary authentication method suitable for 5G-based power terminals, which introduces certificateless aggregated signcryption technology in the secondary authentication process of 5G-based power terminals. Compared with the traditional public key cryptosystem, this method has the characteristics of low consumption of computing and storage space and high operating efficiency. For the 5G EAP-TLS protocol used in the authentication and key negotiation of the power Internet of things, the formal verification is carried out with the ProVerif tool, and the potential loopholes are found and the correction scheme is proposed.

2 Secondary Authentication Scheme In order to overcome the defects of high authentication cost and low efficiency in the prior art, a secondary authentication method based on aggregated signcryption suitable for secondary authentication of 5G-based power terminals is proposed. A secure channel for key transmission is established based on an efficient passwordauthenticated key agreement protocol under the standard model. After receiving a specific event trigger, the secondary authentication trigger module checks whether the primary authentication has passed. In the hybrid networking architecture of 5G and power communication network, there is no local traffic path between the enterprise’s proprietary 5G equipment and the Internet server. Therefore, the traffic must reach the UPF in the operator’s edge cloud, and then return to the enterprise through a private line to communicate with the enterprise LAN. Devices to communicate. The MEC that provides 5G application services for 5G devices in the enterprise is located in the mobile operator edge cloud. Therefore, the authentication request message enters the UPF of the operator’s core network through the access network and the bearer network for traffic offloading, and then is sent to the DN-AAA server of the enterprise intranet. The DN-AAA server responds to the message, generates a challenge code based on random numbers and timestamps, uses a certificateless signcryption scheme based

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on elliptic curve finite fields to signcrypt, and sends the signcrypted message to the 5G-based power terminal. The secondary authentication module of the 5G-based power terminal decrypts the signcryption to obtain a challenge code, and judges whether the network identity authentication of the DN-AAA server has passed. After the identity authentication is passed, the 5G-based power terminal signs the challenge code and the identity authentication code of the 5G-based power terminal using a certificateless signcryption scheme based on elliptic curve finite fields. The signcrypted message enters the local UPF through the access network and bearer network for traffic offloading, and then is sent to the MEC device for aggregation processing. According to different business types, different business flows are formed. Processed by the MEC/UPF deployed in the core network, the business in the Internet region and the low-bandwidth non-real-time business in the management region are returned to the AAA server through the EAP channel of the 5G network. The high-bandwidth, lowlatency, and high-reliability services in the production control area and the management information area are processed by the MEC/UPF deployed at the power grid plant and station, and then returned to the AAA server through the 5G network EAP channel through the forward and reverse isolation devices. The DN-AAA server performs aggregation de-signcryption, and determines whether the identity authentication of the 5G-based power terminal is passed. After the identity authentication is passed, the DN-AAA server sends an identity authentication success statement to the 5G-based power terminal and the 5G-based power terminal successfully establishes a connection to the data network. The process is shown in Fig. 1. Establish a secure channel for key distribution using a passwordbased authenticated key agreement protocol Confirm that the main certification is passed The 5G terminal sends an authentication request message, which enters the UPF of the operator's core network for traffic offload and sends it to the DN-AAA server The DN-AAA server generates an identity authentication challenge code, and obtains the password of the power 5G terminal as a shared key, and encrypts the challenge code

Secondary certification

The authentication server performs certificateless signcryption on the challenge code and identity authentication code, and sends the message to the 5G terminal The 5G terminal decrypts the signcryption. and the DN-AAA server authentication passes 5G terminal performs certificateless aggregate signcryption on challenge code and identity authentication code The 5G terminal sends the signcrypted message to the MEC, and the processing center on the MEC aggregates the message and sends it to the DN-AAA server The DN-AAA server aggregation de-signcryption The DN-AAA server sends an authentication success statement to the 5G terminal Establish a 5G terminal to establish a connection to the data network

Fig. 1. Process of secondary authentication method based on aggregated signcryption.

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In order to enhance the security of key transmission between the key generation center KGC, the 5G-based power terminal, and the authentication service server during the secondary authentication process, an efficient password-based authentication key agreement protocol under the standard model is used to establish a secure channel for key transmission. After assigning simple passwords to KGC, 5G terminals, and authentication service servers in an out-of-band manner, the password authentication key exchange (PAKE) protocol is used to enable users who share low-entropy passwords to securely generate shared high-entropy session passwords through insecure public channels. Key to establish a secure channel for key transmission. The steps of key exchange between KGC and 5G terminal through the key agreement protocol include: 1. The 5G terminal selects a random number and uses the public parameter calculation message to send to the KGC. 2. After KGC receives the message from the 5G terminal, it selects a random number, uses the public parameters to calculate the message and sends the authentication information to the 5G terminal. 3. After the 5G terminal receives the message and the authentication information, it verifies the authentication information. It calculates messages received by 5G terminals with common parameters and compares the resulting values with authentication information. After the verification is passed, the confirmation message and the highentropy session key sk are calculated and the confirmation message is sent to the KGC. The key sk is used as the session key shared with the KGC. 4. After KGC receives the confirmation message, it verifies the confirmation message with the previous calculation result. After the verification is passed, the high-entropy session key sk is calculated using the public parameters. 5. Using the high-entropy session key sk, a secure channel can be established between the KGC and the 5G terminal to transmit the key. Aggregate signcryption adopts a certificateless signcryption scheme based on finite fields of elliptic curves. The aggregated signcryption consists of multiple signers, a signcryption aggregator, and a verifier. The participants here are the 5G terminal, the aggregation center on the MEC, and the DN-AAA server. The steps of the aggregation signcryption stage include: 1. The key generation center KGC performs system initialization. KGC selects a random number as the master key and calculates the master public key. 2. KGC broadcasts to select the public parameters involved in the operation. 3. The 5G terminal, aggregation center, and DN-AAA server select a random number as the long-term private key, calculate the corresponding public key according to the public parameters, obtain a public-private key pair, and send the public key to the KGC through the established secure channel for register. 4. KGC calculates part of the private key of the 5G terminal according to the public parameters, and sends it to the corresponding terminal through the established secure channel. Similarly, KGC calculates part of the private key of the aggregation center and DN-AAA server, and sends it to the terminal through a secure channel. 5. The 5G terminal signs the challenge code and the identity authentication code. 6. Signcryption messages are aggregated.

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7. The DN-AAA server decertifies the reply returned by the 5G terminal. This method introduces certificateless aggregated signcryption technology in the secondary authentication process of 5G-based power terminals. It has the characteristics of less computing and storage space consumption and high operating efficiency while ensuring security. In order to strengthen the security of key transmission between the key generation center KGC, the 5G-based power terminal, and the authentication service server during the key distribution process, the password-based authentication key agreement protocol is used to generate a shared high-entropy session key, thereby establishing Secure channel for key transfer.

3 Formal Analysis 3.1 Protocol Description TS33.501 describes three different authentication protocols, namely, 5G AKA, 5G EAPAKA’, and 5G EAP-TLS. The 5G EAP-TLS protocol is mainly used for authentication and key negotiation in 5G private networks or IoT scenarios. This protocol is based on the TLS protocol, contains multiple key negotiation modes, and has four parties: UE (user device), SEAF (security anchor function), AUSF (authentication server), and ARPF (authentication certificate storage and processing). 3.2 Formal Model Using formal analysis tools to analyze security protocols can more effectively discover protocol design flaws. This paper uses the formal analysis tool ProVerif [7] to model and analyze the 5G EAP-TLS process. The overall structure of ProVerif consists of three parts: protocol input, analysis verification and result output, as shown in Fig. 2. The formal modeling of the 5G EAP-TLS protocol in ProVerif requires the interaction process of the modeling protocol and the description of the attributes that need to be verified. According to the protocol flow of 5G EAP-TLS, the channel is modeled: C1 represents the common channel for communication between UE and SEAF, C2 represents the private channel between AUSF and SEAF, and C3 represents the private channel between AUSF and ARPF. Then, UE, SN and HN processes are modeled respectively. Based on some security requirements described by 3GPP, the following security properties are modeled through the analysis of the protocol flow and security requirements [8]: Authentication properties: A1: Agreement on the pre-master key Rprekey. A2: Agreement on the identity of each other. Confidentiality Properties: S1: Confidentiality of Rprekey of the honest user. S2: Confidentiality of Ksession of the honest user. S3: Confidentiality of the identity of the honest user SUPI.

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Attributes need to be verified: confidentiality, authentication, etc.

Automatic translation module

Describing Security Protocols with Horn Clauses

Describing security protocol properties with Horn clauses

Protocol analysis

Safety

ExistIng attack

Fig. 2. Overall structure of the ProVerif tool.

Proverif makes the following queries to check the confidentiality of the pre-master key Rprekey, the session key Ksession and the user identity SUPI: query attacker (Rprekey). query attacker (Ksession). query attacker (SUPI). 3.3 Analysis of Results The result of running the program is shown in Fig. 3.

Fig. 3. Operation result.

The results show that all confidentiality properties (S1, S2, and S3) are satisfied, while authentication properties (A1 and A2) are violated. The output also contains the derivation process for violating the authentication properties, as shown in Fig. 4.

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Fig. 4. Process of violation of the authentication attribute.

According to the possible attack path of the attacker, a possible repair scheme is proposed, which encrypts the message used for authentication between the user and the home network to avoid the attacker intercepting and forging the message and simulates the home network to establish a connection with the user [9]. At the same time, a challenge-response mechanism is added in the process of establishing the pre-master key between the home network and the user to avoid man-in-the-middle attacks.

4 Conclusion Secondary authentication is a new architecture proposed by 3GPP to meet the high security requirements of vertical industries. How to further improve the security and availability of 5G services is an urgent problem to be solved. This paper proposes a secondary authentication method suitable for 5G-based power terminals. This method introduces certificateless aggregated signcryption technology in the secondary authentication process of the 5G-based power terminals. Compared with the traditional public key cryptosystem, this method can ensure security while ensuring security. It has the characteristics of less computing and storage space consumption and high operating efficiency. For the 5G EAP-TLS protocol suitable for the authentication and key negotiation of the power Internet of Things, the ProVerif tool is used for formal verification, to find out potential loopholes and propose a repair plan. Acknowledgment. This work is supported in part by Jiangsu key R&D plan BE2019109, the National Natural Science Foundation of China under Grant 61941115, 62001106, Natural Science Foundation of Jiangsu Province under Grant BK20160692, BK20200350, BK20200352, Jiangsu Provincial Key Laboratory of Network and Information Security No. BM2003201, Project of State Key Laboratory of Mobile Communication, Southeast University No. 2020B05 and the Purple Mountain Laboratories for Network and Communication Security.

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References 1. 3GPP TS 33.501 V15.4.0: Security Architecture and Procedures for 5G System (Release 15). USA: 3 GPP. https://www.3gpp.org/ftp/Specs/archive/33_series/33.501/ (2019) 2. Zheng, Y.: Digital Signcryption or How to Achieve Cost (Signature and Encryption) 0 ⎨ J0 + kJ ω  dt dt (6) J = ⎪ ⎪ ⎩ J0 , ω · d ω ≤ 0 dt KP = KP0 + kω · |ω|

(7)

In the formulas, J 0 and K P0 are the virtual inertia and droop modulus of VSG fixed parameters, respectively; k J is modulus of inertia variation; kω is the adjustment modulus of the droop modulus. The coordinated control design of droop modulus, virtual inertia and damping modulus is carried out. This damping modulus D design under the correlation can be obtained:  1 EU − KP (8) D = 2ξ J ωN X ωN Based on automatic control theory, in order to keep the system in the optimal control operation state, ξ can be set to 0.707.

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3 Simulation Analysis To validate the control strategy proposed in this paper, this paper builds an improved VSG system model on the MATLAB/Simulink platform, and the corresponding control factors are listed in Table 1. Table 1. The corresponding control factors of VSG. Factor

Numerical value

Factor

Numerical value

Nominal voltage on AC grid ug (V)

380

Filter inductor L abc (mH)

0.8

Rated voltage on DC side Udc (V)

800

Filter capacitor C abc (uF)

10

Nominal active power (W) 50,000

Initial value of virtual inertia J 0 (kg·m2 )

1.127

Nominal reactive power (Var)

Initial value of droop modulus K P0

5000

0

The simulation model is connected to the large grid with a simulation time of 2 s, and the initial steady state is assumed, and rated frequency value is equivalent to grid frequency value; For the purpose of simulating the change of load, the load power increases by 10 kW at 1 s, and the reactive power is always 0 kVar during this period. For the verification of superiority of this proposed control mode, it is compared with coordinated inertia damping (ξ = 0.707) and J & D coordinated control respectively. The frequency change is shown in Fig. 2.

Fig. 2. Frequency variation under different control strategies.

Figure 2(a) shows the variation of the system frequency, and a partial enlarged view can be seen in Fig. 2(b). In Fig. 2, the coordinated inertia damping (ξ = 0.707) control strategy is adopted—when the parameters are fixed, the maximum volume of the fluctuation reaches 0.17 Hz, and it takes about 0.3 s to reach the steady state; When using J and D coordinated adaptive control, the maximum volume of fluctuation of frequency

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is shortened to 0.133 Hz, and the adjustment time is about 0.22 s; When the multiparameter cooperative adaptive control mode is adopted in this work, the maximum volume of fluctuation of frequency is 0.123 Hz, and the adjustment time is 0.22 s.

4 Conclusion In this paper, the existing J and D coordinated adaptive control is optimized. The P/ω droop modulus and virtual inertia can be adjusted according to the system frequency state timely, and the damping modulus can be changed cooperatively according to the corresponding relationship. The reliability of the proposed multiple-arguments cooperative adaptive control mode has been checked by simulation. Acknowledgement. This work is supported by State Grid Corporation of China under Grant J2021177.

References 1. Zhong, Q.C., Nguyen, P.L., Ma, Z., et al.: Selfsynchronized synchronverters: inverters without a dedicated synchronization unit. IEEE Trans. Power Elect. 29(2), 617–630 (2014) 2. Du, W., Jiang, Q., Chen, J.: Design and application of reactive power control system for wind farm. Autom. Elect. Power Syst. 35(23), 26–31 (2011) 3. Ren, H., Chen, Q., Zhang, L., et al.: Parameter adaptive strategy for virtual synchronous generator control. Control Theory Appl. 37(12), 2571–2580 (2020) 4. Wang, F., Zhang, L., Feng, X., et al.: An adaptive control strategy for virtual synchronous generator. IEEE Trans. Ind. Appl. 54(5), 5124–5133 (2018) 5. Alipoor, J., Miura, Y., Ise, T.: Power system stabilization using virtual synchronous generator with alternating moment of inertia. IEEE J. Emerg. Select. Top. Power Elect. 3(2), 451–458 (2015) 6. Zhou, P., Meng, J., Wang, Y., et al.: Influence analysis of the main control parameters in FVSG on the frequency stability of the system. High Voltage Eng. 44(4), 1335–1342 (2018) 7. Yang, Y., Mei, F., Zhang, C., et al.: Coordinated adaptive control strategy of rotational inertia and damping coefficient for virtual synchronous generator. Elect. Power Autom. Equip. 39(3), 125–131 (2019) 8. Li, D., Zhu, Q., Lin, S., et al.: A self-adaptive inertia and damping combination control of VSG to support frequency stability. IEEE Trans. Energy Conver. 32(1), 397–398 (2017) 9. Li, Z., Yang, M., Zhang, J., Liu, H.: Research on the cooperative adaptive control of VSG inertia and damping. J. Elect. Power Syst. Autom. 14, 1–8 (2022) 10. Shao, Y.: Research on Energy Storage Inverter Control Based on Virtual Synchronous Generator. Zhejiang University, Zhejiang (2021) 11. Zhang, G., Yang, J., Wang, H., Xie, C., Fu, Y.: Coordinated frequency modulation control strategy of wind storage system based on virtual synchronous machine technology. J. Electrotech. Technol. 37(S1), 83–92 (2022)

Hybrid Time Step Day-Ahead Optimal Scheduling of the PV-Cascade Hydro Complementary Power Plant Based on PV Output Forecast Kun Zheng1 , Dacheng Li2 , Xv Li3 , Tianze Song1 , Di Wu2 , Yun Tian3 , and Su Guo1(B) 1 Hohai University, Nanjing, China

[email protected]

2 POWERCHINA Guiyang Engineering Corporation Limited, Guiyang, China 3 Huaneng Lancang River Hydropower Inc., Kunming, China

Abstract. Accurately forecast of photovoltaic output and a PV-cascade hydro complementary power plants are important means to make up for the fluctuation of PV power. First, LSTM is formed to estimate the power output of the PV plant. Second, a hybrid time dispatching step model is obtained according to the time-frequency characteristic of the power curve in the whole dispatching cycle, which is used for the optimal dispatching of PV-cascade hydro complementary power plants. Third, considering that the frequent changes of units will affect the service life of units, aiming at improving the operation stability of hydro unit. The optimal dispatching model of the complementary power plant is used and solved by differential evolution algorithm. The analysis show that the hybrid dispatch step model can preferentially reduce the operation time and hydropower unit fluctuation. Keywords: PV output forecasting · The PV-cascade hydro complementary power plant · Day-ahead scheduling optimization · Differential evolution algorithm

1 Introduction Fossil energy depletion and environmental pollution aggravate the transformation of energy industry structure and the development of renewable energy generation process. Therefore, the development of clean and renewable energy, mainly hydropower and photovoltaic power generation, has attracted extensive attention [1]. However, photovoltaic power generation has strong volatility and low controllability, and photovoltaic resources and load characteristics are inversely distributed. In addition, the proportion of regulating power in our power structure is low, and grid connected photovoltaic power will bring great hidden trouble to the safe operation of the system [2]. How to safely and effectively connect large-scale photovoltaic power stations to the grid becomes an urgent problem to be solved. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 212–219, 2023. https://doi.org/10.1007/978-981-99-4334-0_27

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This paper adopts Hilbert-Huang Transform (HHT) to estimate the PV output prediction curve. Then, an efficient hybrid time-step model (HTSM) is formed to conduct day-ahead optimization operation for the cascade hydro-PV complementary system. A day-ahead optimal dispatching model for the complementary power generation system is established to increase the synthesized performance of the complementary plant.

2 LSTM Forecasting Model Long Short-Term Memory (LSTM) neural network is a variant structure of RNN prediction model. LSTM not only has the state h sensitive to the short-term input, but also adds the unit state c which saves the long-term.

3 Introduction The HHT is a method that can deal with the time-frequency characteristics of complex signals, which can estimate the instantaneous frequency of signals. The primary output signal can be shown by every component:  N    j 2π ωi (t)dt ] [ s(t) = Re (1) Ai (t)e n=1

Equation (1) is the original output curve expression. Ai (t) and ωi (t) are the amplitude and instantaneous frequency of each IMF component during t period. The scheduling model of different time periods is calculated as follow. t =

α (ω + β)2

(2)

where t expresses the time step in the calculation period; α and β represent two constants.

4 Mathematical Model for Optimal Scheduling of Cascade Water-Light System Photovoltaic power generation is not adjustable, but it has obvious price advantage when it is connected to the Internet. To improve the system economy and photovoltaic utilization rate, the photovoltaic power generation in the short-term optimization scheduling is all online. Due to the powerful control ability of the cascade hydropower plants, the power output of hydropower unit changes constantly during the dispatching operation, which may cause the frequent start and stop of hydraulic unit and the crossing of the vibration zone of the hydropower unit to damage the life of the unit. The day-ahead optimal objective of the complementary power generation system is to improve the operation stability of hydro unit and reduce the influence of photovoltaic grid-connected in the complementary system on hydropower units.

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4.1 Objective Function Mei-Wang Fluctuation index [3], which combines the standard deviation of the power curve and the rotation angle of the power curve, is proposed to calculate the quantitative changes and contour changes of the power output, so as to reflect the fluctuation characteristics of the output power. Figure 1 shows the diagram of rotation angle. ⎧ arctan|kt | t = 1, or, T ⎪ ⎪ ⎪ ⎪ 1 ≤ t ≤ T − 1, ⎨ arctan kt − arctan kt−1 (3) θt = and , kt × kt−1 ≥ 0 ⎪ ⎪ 1 ≤ t ≤ T − 1, ⎪ ⎪ ⎩ arctan|kt | − arctan|kt−1 | and , kt × kt−1 < 0  Pt+1 −Pt 1≤t ≤N −1 (4) kt = tt+1 −tt t=N kN −1

 T 1  α= × (Pm,n,t − Pm,n ) (5) T t=1

β=

T 

(exp(θm,n,t ) − 1))

(6)

t=1

F = min(

M  N 

(α × β))

(7)

m=1 n=1

Fig. 1. Rotation angle diagram

In the formula, θt and kt respectively mean the rotation angle of forecasted PV power at t time; Pm,n,t (MW) means the average power output of nth unit in mth plant during t period. 4.2 The Constraint 1. Power balance constraint Ppv,t +

M  N  m=1 n=1

Pm,n,t = Pload ,t

(8)

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2. Water balance constraint in out Vm,t+1 = Vm,t + (Qm,t − Qm,t )t

out = Qm,t

N 

g

cur Qm,n,t − Qm,t

(9)

(10)

n=1

3. Reservoir capacity constraint Vm ≤ Vm,t ≤ Vm

(11)

4. Water flow delay constraint flow

in out Qm+1,t = Qm,t−τ + Qm+1,t

(12)

eco out out Qm,t ≤ Qm,t ≤ Qm,t

(13)

5. Ecological flow constraints

6. Generation flow constraint g

g

0 ≤ Qm,n,t ≤ Qm,n,t

(14)

In the formula, Ppv,t and Pload ,t (MW) respectively mean the output and load requirements of photovoltaic power stations at the time t; Pm,n,t means the power of nth unit in mth station at the time of t; Vm,t (m3 ) means the mth reservoir volume at the time t; Vm , in , Q out and Vm respectively mean the upper and lower limits of reservoir capacity; Qm,t m,t cur (m3 /s) respectively mean the average inflow flow, average outflow flow and average Qm,t flow

abandoned water flow of mth reservoir at the time of t; Qm+1,t means interval runoff of eco means the Minimum ecological discharge of (m + 1)th reservoir at the time of t; Qm,t mth station. Ecological flow is the minimum discharge of the lower river under the condition that ecological environment does not deteriorate and can guarantee the ecological discharge in dry season. According to the method of determining ecological discharge in the previous literature, the average annual flow of 10% was selected as the ecological discharge of g out means the maximum out flow rate of mth station. Q g the reservoir. Qm,t m,n,t , Qm,n,t th th respectively mean the generation flow and its upper bound of n unit in m power station at the time of t. 4.3 Model Solving Method The Differential evolution algorithm, as a kind of heuristic algorithm, is based on population differences. It uses difference strategy to realize individual variation and has strong searching ability. It is an very effective ways to solve the nonlinear and very complex high-dimensional problems, and is mostly used to solve the global optimal solution in multi-dimensional space.

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5 A Case Study 5.1 Data The total installed capacity of cascade water-light complementary power generation system is 4270 MW, photovoltaic capacity is 1200 MW, and the total capacity of the cascade hydropower plants is 3070 MW, and the load of the system is a constant 3000 MW. 5.2 Forecast Results The photovoltaic output results predicted by the LSTM prediction model under three typical weather conditions are shown in Fig. 2. In sunny days, the output curve fluctuates little and has a certain rule, and the prediction result has a high accuracy. Cloudy output curve has great fluctuation, strong uncertainty, great difficulty in forecasting, and low prediction accuracy. 5.3 Scheduling Result To verify the advantage of hybrid time-step model applied to the short-term optimized operation of complementary power system, the performance of the two conventional unified time step model (UTSM) and HTSM in the optimal operation of the complementary system were compared. The UTSM 1 and UTSM 2 steps are 60 and 15 min, respectively. Figure 3 shows the optimal dispatching results of the three models under three kinds of weather in 10% runoff year. The mixed time step model adopts a 20-min scheduling step at 6–9 and 15–17, which improves the deviation degree of output and load in USTM 1 and improves the scheduling efficiency of USTM 2. The amount of PV curtailment and load power loss in USTM 1 are significantly increased than UTSM in Table 1. The maximum increase of PV curtailment and load power loss is 162.25 and 127.05%, respectively. The minimum reduction of hydropower unit fluctuation and calculation time is 2.19 and 8.80% in the better scenario. Compared with the HTSM, the amount of light abandoned and load power shortage generated by USTM 2 scheduling are slightly reduced. In the best scenario set, the minimum reduction of light discard and load power deficiency is 7.74 and 1.94%, respectively, and in the worst scenario set, the maximum reduction is 43.83 and 14.42%, respectively. Compared with the hybrid time-step model, USTM 2 has a sharp increase in hydropower unit fluctuation and computation time. In the best scenario set, the maximum increase in fluctuation and calculation time of hydropower units is 70.43 and 935.61%, respectively, and the minimum increase in the worst scenario set is 56.23 and 838.05%.

6 Conclusion A hybrid time-step model is established for the optimal dispatching of the cascade hydroPV complementary power plant. The following conclusions are obtained by analyzing the calculation examples: 1. In this paper, LSTM is used for day-ahead PV output prediction. LSTM long and short-term memory neural network can well process long data series, avoid long-term dependence problem, and achieve high prediction accuracy.

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(a)

Fig. 2. (a) Sunny day. (b) Cloudy day. (c) Rainy day

2. The different scheduling step sizes were used according to the fluctuation coefficient of the PV curve, and a hybrid scheduling time step model was established for shortterm optimization scheduling. 3. Two unified time step models with a step of 60 and 15 min were set as the comparison group. Light loss, load shortage, fluctuation coefficient of hydropower unit and running time are selected as the comparison indexes.

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Fig. 3. Comparison of scheduling results of three scheduling models under sunny weather Table 1. Scenario analysis results Indicators

Light loss

Load power loss

Fluctuation coefficient

Computation time

USTM 1

162.25%

62.28%

− 2.19%

− 8.80%

USTM 2

0.91%

− 1.94%

43.11%

935.61%

Cloudy day

USTM 1

87.10%

58.89%

− 25.83%

− 14.27%

USTM 2

− 7.74%

− 14.50%

69.04%

885.17%

Rainy day

USTM 1

− 20.18%

− 7.88%

− 19.23%

USTM 2

29.75%

70.43%

769.56%

Sunny day

127.05% 6.17%

Acknowledgements. This work was supported in part by the Science and Technology Project of Huaneng Group Headquarters under Grant HNKJ20-H20, and in part by the Fundamental Research Funds for the Central Universities of China under Grant B210202069.

References 1. Liu, Z., Zhang, Z., Zhuo, R., et al.: Optimal operation of independent regional power grid with multiple wind-solar-hydro-battery power. Appl. Energy 235, 1541–1550 (2019) 2. Xiong, H., Egusquiza, M., Alberg Østergaard, P., et al.: Multi-objective optimization of a hydro-wind-photovoltaic power complementary plant with a vibration avoidance strategy. Appl. Energy 301, 117459 (2021) 3. Majidi, M., Nojavan, S., Zare, K.: Optimal stochastic short-term thermal and electrical operation of fuel cell/photovoltaic/battery/grid hybrid energy system in the presence of demand response program. Energy Conver. Manag. 144, 132–142 (2017) 4. Zhang, J., Cheng, C., Shen, J., et al.: Short-term joint optimal operation method for high proportion renewable energy grid considering wind-solar uncertainty. Proceed. Chin. Soc. Elect. Eng. 40(18), 5921–5931 (2020)

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5. Zhao, M., Wang, Y., Wang, X., et al.: Flexibility evaluation of wind-PV-hydro multi-energy complementary base considering the compensation ability of cascade hydropower stations. Appl. Energy 315, 119024 (2022)

GRU Network-Based Load Allocation for Hydro Units Xiaonan Zheng1 , Xu Li2 , Dacheng Li3 , Hong Pan1(B) , Yun Tian2 , Di Wu3 , and Fang Feng4 1 Hohai University, Nanjing 211100, China

[email protected]

2 Huaneng Lancang River Hydropower Inc, Kunming 650200, China 3 PowerChina Guiyang Engineering Corporation Limited, Guiyang 550000, China 4 Shanghai Aircraft Design and Research Institute, Shanghai 200000, China

[email protected]

Abstract. For the current problems of non-linearity and complexity of hydropower unit load allocation, traditional algorithms or intelligent optimization methods have the problems of slow and insufficient accuracy in finding the best, and the adaptability of the model is low. It is suggested to use a GRU neural network-based load allocation system for hydropower plants. The historical data of the hydropower unit head and external load are utilized as sample inputs for neural network training after the GRU network has been set up, and the load allocation of hydropower units may be resolved and predicted once the training is complete. The average operating efficiency of the hydropower plant solved under each PV scenario can reach over 93%, according to the results of training and testing using data from a power plant. For instance, the results show that the GRU neural network can significantly improve the efficiency of the solution. This is supported by a large amount of historical data. The accuracy and reliability of the model can be continuously improved, which can better adapt to the development trend of today’s hydropower plants. The method has some practical value for solving the load allocation of hydropower units. Keywords: GRU neural network · Hydropower unit load allocation · In-plant economic operation · Artificial neural network

1 Introduction Unit load allocation and unit combination issues are at the heart of the operation process in the short term for optimal hydropower unit scheduling and in-plant profitable hydropower plant operation. A reasonable load allocation can reduce unit operating losses, maintain long-term stable operation, and reduce turbine wear and tear, thus reducing the maintenance and repair costs of the whole unit and improving economic efficiency [1, 2]. Therefore, how hydropower units’ loads are distributed is important. For this problem, the traditional solution idea is to establish the corresponding mathematical model combined with the actual engineering and then use mathematical means © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 220–229, 2023. https://doi.org/10.1007/978-981-99-4334-0_28

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to simplify it according to the characteristics of the model, and finally study the corresponding solution algorithm. Many models have been put forth during the research process by earlier researchers: Shen Jianjian et al. [3], proposed a mixed integer nonlinear programming model for the allocation of unit loads in hydropower stations on the same day and verified the accuracy of the model; Yang Kan et al. [4], given the high and non-linear characteristics of the economic operation of large hydropower plants, a spatial load allocation and temporal unit combination optimization coupled with each other is proposed as a Spatio-temporal economic operation model. The classic algorithms for unit load allocation solutions essentially consist of the prioritizing approach, linear programming method, dynamic programming method [5, 6], etc. Long-used intelligent algorithms include the genetic algorithm and the ant colony algorithm [7]. Despite the above method, the problem of “dimensional explosion” still exists as the amount of data continues to increase, resulting in the slow speed of some traditional swarm intelligence optimization algorithms and insufficient solution accuracy [8–10] to meet the load allocation requirements. The complex problem of unit load allocation can now be solved more effectively thanks to machine learning techniques, which have powerful feature extraction and learning capabilities. These techniques can also be trained on a large amount of historical decision data and continuously improved over time. Therefore, this paper applies the GRU (gated recurrent unit) neural network method to solve the load allocation of hydropower units, and establishes the GRU load allocation model. Using the June data of a leading hydropower station in a basin as a reference, the results and indicators of load allocation are obtained and compared with traditional mathematical methods to verify the effectiveness of the algorithm for large volumes of data.

2 The Basic Theory of GRU Neural Networks GRU neural networks are based on recurrent neural networks (RNN), which are widely used in the analysis and processing of serial data. The output of a neuron at a certain point in time can be used as input to the neuron again. This single-chain cascade structure can effectively store the connections between data, which has obvious advantages in the analysis and processing of sequential data [11]. In practice, RNN often faces training challenges, especially as the number of layers in the network grows deeper, making them unable to handle the dependencies between neural units over longer distances [12]. The computational complexity of the product of matrices often shows an exponential increase or decrease, resulting in a weakening of the RNN network’s ability to handle time-series data. 2.1 Gated Circulation Units Since RNN produces “gradient disappearance” or “gradient explosion” when analyzing longer dimensional temporal series. Cho et al. proposed the GRU neural network in 2014. The gated recurrent unit (GRU) replaces the three gates of the LSTM network by using reset gates and update gates while merging the data units and hidden layer states, which can well solve complex non-linear problems [13].

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Fig. 1. GRU structure diagram.

The basic structure of the GRU is shown in Fig. 1. The GRU structure includes only two gates, the update gate and the reset gate, which are calculated as follows [14]. Updating the door zt = σ (Wz xt + Uz ht−1 )

(1)

where zt is the update gate, t is the moment, σ is the sigmoid activation function, xt is the input matrix of neurons at the current moment, and ht−1 is the hidden state of the unit at the previous moment, and Wz is the weight matrix from the input layer to the update gate at the current moment, and Uz is the weight matrix from the hidden state at the previous moment to the update gate at the current moment. Reset the door rt = σ (Wr xt + Ur ht−1 )

(2)

where Wr is the weight matrix from the input layer to the reset gate, and Ur is the weight matrix from the hidden layer to the reset gate. Candidate hidden status hˆ t = tanh(xt Wxh + (rt  ht−1 Whh ))

(3)

where hˆ t is the candidate hidden state, Wxh is the weight matrix from the input layer to the candidate hidden state, and Whh is the weight matrix from the hidden layer at the previous moment to the hidden layer at the next moment. Output values ht = zt  ht−1 + (1 − zt )  hˆ t

(4)

where ht is the output of the GRU unit at the current moment and is a linear combination of the previous moment’s hidden state ht−1 and the current candidate hidden state hˆ t .

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3 Unit Load Allocation Model Based on GRU Networks The overall structure of the GRU unit load allocation model developed in this paper can be divided into three main parts: the input layer, the hidden layer, and the output layer. The input set or test set samples include both head and external load characteristics, so the input layer of the network is set as a 2-dimensional fully connected layer. The hidden layer is a single GRU layer, which contains several memory units. The output data is the output of each unit, so the output layer has the same dimension as the number of units in the power station. Before the data samples enter the input layer, they need to be normalized to eliminate the influence of the dimension caused by the different rated outputs of each unit. Within the GRU layer, to prevent the occurrence of overfitting, a Dropout layer can be added for adjustment to improve the training speed and prediction accuracy of the model. The flowchart is shown in Fig. 2.

Fig. 2. Flow chart of load allocation of hydro units based on GRU network

3.1 Model Evaluation Indicators To facilitate the evaluation of how well the proposed GRU model solves the load allocation results and the error of the model prediction, Mean Absolute Error (MAE), Mean Square Error (MSE), and Root Mean Square Error (RMSE) are used to evaluate. The formulae of the three indicators are as follows [15, 16]: 2 1  MSE = yˆ i − yi n n

i=1 n 

  1 yˆ − y  i i n i=1   n 1   2 RMSE =  yi − yˆ i n MAE =

(5)

(6)

(7)

i=1

where the number of samples is n, and yˆ i , yi denoting the predicted and label values of the i sample model, respectively.

4 Application Examples Referring to the above method, a GRU network-based unit load allocation is carried out for a leading hydropower station in a basin as an example. The data covered in this paper are real data provided by hydroelectric power stations, which come from the operation of real units. The relevant power station parameters are as follows in Table 1.

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Unit parameters

Data

Rated head

246 m

Maximum head

282.6 m

Maximum efficiency

96.29%

Rated flow rate

194.8 m3 /s

Rated output

442 MW

4.1 Data Clustering Results The number of clustering centers is determined to be 3. The K-means algorithm is used to calculate the clustering categories. And set the maximum number of iterations of the algorithm to 300, each cycle starts from the initial clustering center. The collected sample data is entered as a sample with a unit head and external load for clustering. The clustering results are shown in Fig. 3.

Fig. 3. Clustering results.

As can be seen from Fig. 3: the first category of data has a small external load, between 300 and 800,000 kW, with a total of 3524 samples. The second category of data has an external load between 800 and 1.9 million kW, with a total of 4397 samples. The third category of data has the largest external load, between 1.9 and 2.7 million kW, with a total of 3594 samples. And all samples have an operating head between 180 and 280 m. 4.2 Parameter Setting and Training Process Several parameters are used to build the model, such as Batch_size, Epoch, Dropout and the selection of the loss and activation functions. Batche_size is the number of data

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passed to the program for training in a single pass. Epoch defines as the single training iterations for all batches in the forward and backward propagation, meaning that one cycle is a single forward and backward pass of the entire input data. The definition of Dropout is the probability that a neural network unit will be temporarily discarded from the network during the training of the deep network. The loss function defines as the error between a single training sample and the true value. The activation function is a function that runs on the neurons of an artificial neural network and is responsible for mapping the inputs of the neurons to the outputs. Based on the clustering results of the above three categories, three GRU neural network models are established respectively. But the number of hidden layer neural units needs to be determined first. Taking the third category as an example, the relevant parameter settings are shown in Table 2. Table 2. Hidden layer node-seeking parameters. Parameters

Value

Dropout

0.1

Training set Batch_size

80

Number of training epochs

300

Input matrix dimension (input_shape)

(4397*2, 1, 4397*6)

Test sample dimension (test_shape)

(72*2, 1, 72*6)

Output matrix dimension (output_shape)

(72*6)

Backward propagation loss function loss

MSE

Maximum number of iterations epochs

300

Gating activation functions

Sigmoid

Merit search interval

50–300 at 20 intervals

Optimization algorithms

Adam

After repeated tests and error analysis, the number of neurons inside the GRU layer is selected as 210, and the number of neurons in the other two categories of the hidden layer is 200 and 210 respectively. When the above parameters were determined, the GRU network model is trained. The relevant training parameters were set as follows: the number of training data batches was 80, the maximum number of training cycles was 400, the validation set data accounted for 10% of the training set data, the loss function was MSE, the training algorithm was Adam, and the gating activation function was Sigmoid. During the GRU model training, the model’s total loss (MSE) increases and then decreases, stabilizing around 0.11 after about 200 iterations. The loss value of the test set also tends to be stable after 200 iterations. When the maximum number of iterations is 400, the value is stable at around 0.125. After 400 iterations of training, the parameters of this GRU network model stabilized.

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4.3 GRU Model Load Allocation Results The parameters related to the training of the other two GRU network models were set in the same way as the third type. First, determine which class each sample belongs to based on the Euclidean distance between each test set sample and each cluster centre, and then use the corresponding GRU model to make predictions. The test set samples are the data of the leading hydropower station during June. And input is the head and external load of the hydropower units under each PV output scenario (cloudy, rainy, sunny). The output is the respective output of six units. And the allocation results are shown in Fig. 4.

Fig. 4. GRU model unit load allocation results graph.

As can be seen from Fig. 4, units 2–6 have more or less output at each time slot in the three PV scenarios. With units producing more output at moment 9 and moments 18–21, and almost equal output at the rest of the time, with little fluctuation. There is a gap between the unit load allocation results calculated by the GRU network model and the traditional calculation results and other methods. In some hours, units that should not be working are still allocated a certain amount of capacity. To better evaluate the effect of the GRU network on unit load allocation and to compare the differences between the calculated results. Table 3 gives the corresponding indicators for the load allocation results. As can be seen from Table 3, the total water consumption of the unit increases in all scenarios. The proportion of non-economic operation zones increases in sunny and

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Table 3. Load allocation indicators for GRU model units. Scenarios

Indicators Total water consumption (m3 )

The Proportion of non-economic operating areas (%)

Number of starts and stops

Maximum output volatility %

Average efficiency %

Sunny day

65,013,447

4.36

0

2.1437

93.12

Cloudy days

70,337,136

3.21

0

1.6706

93.22

Rainy day

65,192,409

14.21

0

2.4947

93.11

cloudy scenarios and decreases in rainy scenarios. There is no start-up and shutdown operation of the unit during the whole load allocation process; the maximum output fluctuation rate of the unit increases little and the average operating efficiency does not change much. Although the load allocation results obtained from the GRU network model are somewhat different from those of the traditional method, all the indicators of the load allocation results are within the reasonable range of unit operation, except for the difference in the economics of hydropower plant operation. Considering the reason for this phenomenon, the initial guess is that it is due to the small amount of training data for the GRU network model. To this end, the existing training set was divided and the number of samples in the training set was gradually increased to observe the change in the error metrics predicted by the model. The relevant network parameters were set as follows: the number of data in the training set was increased from 5000 to 11,000 with a step size of 1000, and the rest of the parameters are the same as before.

Fig. 5. Effect of training set sample size on GRU network.

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As shown in Fig. 5, with the increase in the number of samples in the training set, the error metrics of the GRU model decreased, which is most obvious when the number of samples is 5000–7000. And after several iterations, all three error metrics decreased by about 50%. After training 9000 samples, the error metrics continue to decrease. Finally, when all the training samples have been collected, the error metrics reach their minimum values and the overall decrease is obvious. Therefore, the reason for the discrepancy between the results obtained by the GRU unit load allocation model and by the traditional mathematical method is most likely that the number of samples in the training set is too small and that led to the model has not been able to fully and comprehensively learn the unit output allocation under the head and external load conditions of each unit. However, it also shows that GRU performs better and better on the test set as the amount of data in the training set increases, which verifies the excellent performance of this method in solving the load allocation of hydropower units under massive data.

5 Conclusions This paper proposes a unit load allocation method based on a GRU network. By establishing a GRU neural network and innovatively applying it to the calculation of the solution of unit load allocation, the following conclusions are drawn: (1) Compared with traditional algorithms, the GRU neural network can use the accumulated historical decision-making solutions to guide the load allocation. And as the amount of data grows, the GRU network becomes more and more effective in solving the load allocation, which is well suited to the current situation where the scale of hydropower plants is expanding and the number of units is increasing. (2) The number of training samples has a great influence on the GRU network model. If historical data is lacking or the number of samples is too small, it will cause the neural network to learn insufficiently, thus making the results of unit load allocation deviate from other calculation methods. However, as time goes by and the number of training samples increases, the error indicators of the prediction results of the test set have a significant trend of decreasing, and the accuracy and reliability of the model continue to improve. In this example, the prediction error has decreased by 50% when the number of samples increases by 2000, which can well confirm this conclusion. (3) Compared with the LSTM network, the GRU network has a faster solving efficiency. The prediction results show that the average operating efficiency of the hydropower units can also reach over 93% under each PV output scenario. The method is an excellent solution to the unit load allocation problem and has strong practicality and certain reference value. Funding. This work was supported by the National Key R&D Program Key Project of Intergovernmental International Science and Technology Innovation Cooperation under Grant 2019YFE0105200, in part by the Science and Technology Project of Huaneng Group Headquarters under Grant HNKJ20-H20, and in part by the Multi-Dimensional Fault Diagnosis Method of Hydropower Unit Based on Improved Deep Learning Strategy under Grant 51809082.

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References 1. Shi, S.F., Wu, J.Q., Zheng Jiao, T.: Study on unit load distribution of Shuibuya Hydropower Station based on unit operation safety. Hydropower Power Gener. 40(3), 1579 (2014) 2. Pan Hong, F., Hang Chenyang, S., Zheng Yuan, T.: Simulation study of hydraulic turbine regulation system based on improved gravitational search algorithm. Drain. Irrigat. Mach. J. Mech. Eng. 25(09), 1–7 (2022) 3. Shen Jianjian, F., Zhang Xiufei, S., Wang Jian, T., et al.: A mixed integer nonlinear programming model for solving optimal daily load allocation of hydropower plants. Power Syst. Autom. 42(19), 34–40 (2018) 4. Yang Kan, F., Chen Wei, S., Li Hao, T.: A model for the overall spatial and temporal economic operation of large hydropower plants and its algorithm. J. Huazhong Univ. Sci. Technol. 43(09), 117–122 (2015) 5. Li Jinghua, F., Lan Fei, S.: A review of models and algorithms for the unit combination problem. Mod. Electr. 28(6), 1–10 (2011) 6. Chu Qinghe, F.: Study on the economic operation of hydropower plants based on recursive preference method. Hydropower Energy Sci. 29(8), 159–161 (2011) 7. Hu Fei, F., Zhang Dehu, S., Yang Xiaochun, T., et al.: Optimization of AGC unit combination and load allocation based on ant colony algorithm. Hydroelect. Energy Sour. Sci. 30(12), 147 (2012) 8. Labadie, J.W.: Optimal operation of multi-reservoir systems: state-of-the-art review. J. Water Resour. Plan. Manag. 130(2), 93–111 (2004) 9. Cheng Chuntian, F., Shen Jianjian, S., Wu Xinyu, T.: Practical solution strategies and methods for large-scale complex hydropower optimal scheduling systems. J. Water Resour. 43(07), 785–802 (2012) 10. Zhang Rui, F., Zhou Jianzhong, S., Xiao Ge, T., et al.: Analysis of the compensation benefits of joint scheduling of the lower Jinsha River and Three Gorges hydropower plant groups. Power Grid Technol. 37(10), 2738–2744 (2013) 11. Yang, L.F., Wu, Y.X., Wang, J.L., et al.: A review of recurrent neural network research. Comput. Appl. 38(S2), 1–26 (2018) 12. Bengio, Y.F., Simard, P.S., Frasconi, P.T.: Learning long-term dependencies with gradient descent is difficult. IEEE Trans. Neural Netw. 5(2), 157–166 (1994) 13. Cho, K.F., Van Merrienboer, B.S., Bahdanau, D.T., et al.: On the properties of neural machine translation: encoder-decoder approaches. arXiv preprint arXiv: 1409.1259 (2014) 14. Li Lin, F.: Research on the Application of Crude Oil Futures Price Forecasting Model Based on EEMD-GRU Neural Network. Beijing Jiaotong University, Beijing (2021) 15. Zheng Jianfei, F., Mou Hanxiao, S., Hu Changhua, T., et al.: Residual life prediction of degraded equipment considering the correlation of multiple performance indicators. Harbin J. Harbin Eng. Univ. 05, 1–10 (2022) 16. Qinglin Zhao, F., Lianchao Zhang, S., Yuhong Cai, T., et al.: Load forecasting based on improved long short-term memory artificial neural network. In: Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering, vol. 899, pp. 393–405 (2021)

A Novel Multi-fidelity Surrogate Model with Two-Stage Ensemble Shuai Zhang, Yong Pang, Peng Li, Xueguan Song(B) , and Wei Sun School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, China [email protected]

Abstract. In the engineering optimization, High-fidelity (HF) information is typically more precise than low-fidelity (LF) information. Nevertheless, LF tends to be more computationally efficient than HF. In order to fully integrate the benefits of both HF and LF information, this work proposes a novel multi-fidelity surrogate (MFS) model with two-stage ensemble. In the first stage, multiple scale factors are determined by the feasible region to further build the MFS model library. Then, in the second stage, the weight coefficient is determined based on cross validation error, so as to realize the construction of ensemble MFS model. The performance of proposed MFS model is evaluated across twenty test functions. The findings indicate that the proposed MFS model exhibits excellent prediction accuracy and robustness. More importantly, in comparison to other MFS models, the developed model demonstrates a higher priority. Moreover, the study examines the impact of critical parameters on the proposed model’s performance. The research presents a novel approach to reduce simulation cost in the engineering design and optimization. Keywords: Multi-fidelity surrogate · Ensemble approaches · Multiple scale factors

1 Introduction Numerical simulation has become an indispensable technical means in engineering design and optimization. Nonetheless, HF simulation is usually time-consuming in complex systems, leading to substantial computational expenses when utilized in design optimization. In order to solve this problem, low-cost surrogate models such as kriging (KRG) [1], moving least squares [2], and artificial neural networks [3] have replaced HF simulation. Although the surrogate model saves a lot of costs, it still needs sufficient HF simulation to ensure sufficient accuracy. Especially in the case of high-dimensional problems, the required costs are often unbearable. Therefore, some scholars have proposed MFS model to solve this problem. MFS model is constructed by integrating LF and HF information. The HF samples used in MFS have greater precision but require more computational resources than the LF samples. On the contrary, while the LF samples may lack the precision of the HF samples, they do effectively capture the changing trend of the physical system. Additionally, an © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 230–238, 2023. https://doi.org/10.1007/978-981-99-4334-0_29

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adequate amount of LF samples can be acquired at low cost. The scale function-based MFS method has been widely studied due to its straightforward structure and broad applicability. This method is mainly divided into three categories. (1) Multiplicative method involves using the scaling function to multiply the LF surrogate model to create the MFS [4]. (2) Additive method constructs the MFS model by adding the LF surrogate and discrepancy function [5]. (3) Comprehensive method can significantly improve the accuracy by combining multiplicative method and additive method [6]. In scale function-based MFS method, the selection of scale factor has an important impact on the performance of model. Thus, in order to avoid the selection of poor scale factors, this work proposes a novel MFS model with two-stage ensemble (TSE-MFS).

2 Methodology 2.1 Stage 1: Construction of MFS Model Library In this study, the comprehensive method is adopted to create the MFS model, 

ym (x) = ρyl (x) + δ (x) 



(1)

where yl (x) and ym (x) are the LF and MFS model, respectively. ρ is a scaling factor. δ (x) represents discrepancy function and can be computed by,       (2) δi xih = yh xih − ρyl xih 







    f h xih is the response corresponding to the HF sample xih . δi xih is the discrepancy at xih . Based on this discrepancy, δ (x) is constructed using surrogate model. However, we need to determine the scale factor ρ before the obtained δ (x). The usually approach for determining ρ consists in minimizing the difference between the scaled LF model and the HF samples, 



find ρ min e =

N      2  ρ yˆ l xih − yh xih

(3)

i=1

where N represents the size of the HF samples. Using Eq. (3), we can get the scale factor denoted as ρ1 . To obtain the best scale factor, we set a feasible region [ρ1 − d , ρ1 + d ]. Then, a series of scale factors are determined by step h, and the MFS model’s library yl are further constructed, which can be expressed as, 



yl = {ym1 , ym2 , · · · , ymn }

(4)

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2.2 Stage 2: Ensemble of MFS Models Cross-validation (CV) errors are often adapted to calculate the weight of model. Therefore, the work calculates the CV errors of the δ (x) to obtain the weight of MFS model [7]: 

CV =

N     2 1   h h y xi − ρyl xih − δ −i xih N 



(5)

i=1



Corresponding to yl , the CV errors can be written as, CV = {CV 1 , CV 2 , · · · , CV n } The weight of the k-th MFS model can be calculated as follows, n wk = wk∗ / wj∗ j=1

(6)

(7)

where wk∗ = 1/(CV k + αE) E=

1 n CV j j=1 n

(8) (9)

where α is a parameter of weight. The constructed ensemble MFS model ym can be written as, 

ym = yl w T =





n+1 



wi ymi

(10)

i=1

3 Numerical Examples This part uses some test functions to evaluate the effectiveness of TSE-MFS model. These test functions are presented in Appendix A. In addition, the TSE-MFS model is compared with following MFS models: (1) ME-MFS model in which the scale factor is determined by minimizing difference between the LF model and HF samples. (2) MLS-MFS is proposed by Wang et al. [8]. (3) RBF-MFS is proposed by Song et al. [9]. (4) CoKriging is proposed by Forrester et al. [10]. The coefficient of R2 is often employed to assess the predictive precision of a model. Consequently, in this study, this metric is utilized to evaluate the performance of TSEMFS model, 2

 yj − yj j (11) R2 = 1 −  2 j yj − y 



where yj , y, and yj are the prediction value, mean value, and actual response, respectively. Design of experiments (DoE) is implemented to produce surrogate model samples. To mitigate the impact of randomness, the DoE procedure was repeated 20 times for each test function, and the outcome represents the average of 20 randomized outcomes.

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3.1 The Investigation for the Parameter α α is the key parameter of the ensemble strategy, which directly determines the weight of the MFS model. As a result, selecting the appropriate value for parameter α becomes imperative. For this paper, the parameter range is established to be between 0 and 1. Figure 1 shows the impact of α on the performance of TSE-MFS model. The results show that smaller values of α can improve the predictive precision of TSE-MFS model. More importantly, a small α means that the TSE-MFS has better robustness than other case. Therefore, the value of parameter α recommended in this paper is 0.1.

Fig. 1. The impact of α on the performance of TSE-MFS model.

3.2 The Performance Analysis of the TSE-MFS Model Figure 2 illustrates the comparison between TSE-MFS and other MFS models, demonstrating that the TSE-MFS model outperforms the other MFS models in terms of prediction accuracy, as indicated by its mean of R2 value of 0.88. Additionally, the TSE-MFS model exhibits greater robustness than the other MFS models, as evidenced by its smaller standard deviation (Std) of R2 . In short, TSE-MFS model has better prediction accuracy and robustness than other MFS models. In order to improve the reliability, a boxplot is drawn, as shown in Fig. 3. We obtain results similar to those in Fig. 2. It shows that the TSE-MFS model has the superior prediction accuracy and robustness. It is further to verify the performance advantages of TES-MFS model over other models.

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Fig. 2. Comparison of TSE-MFS and other models.

Fig. 3. Comparison of TSE-MFS and other models under 20 test functions.

4 Conclusion The present study introduces a novel MFS model approach, namely TSE-MFS. First, MFS model library is established by the feasible region. Then, multiple MFS models in the library are combined to obtain the final TSE-MFS model. To evaluate the proposed model, twenty test functions are employed, and the results demonstrated that the TSEMFS model exhibits good prediction accuracy and robustness. More importantly, the TSE-MFS model shows a higher priority than other MFS models. This study provides a promising approach to reduce simulation cost in the engineering design and optimization.

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Acknowledgment. This research is funded by the Dalian Science and Technology Innovation Fund Project (2020JJ25CY009) and National Key Research and Development Program of China (No. 2018YFB1702502).

Appendix A: 20 Test Functions No

Test functions

1

HF yh = (6x − 2)2 sin(12x − 4)

2

HF yh = sin(2π (x − 0.1)) + x2

LF yl = 0.5yh + 10(x − 0.5) − 5 LF yl = sin(2π (x − 0.1)) 3

HF yh = xsin(x)/10 LF yl = xsin(x)/10 + x/10

4

HF yh = cos(3.5π x)exp(−1.4x) LF yl = cos(3.5π x)exp(−1.4x) + 0.75x2

5

6

6 HF yh = 4 − 2.1x41 + 13 x1 + x1 x2 − 4x22 + 4x24 LF yl = 4 − 0.5x41 + 0.04x61 + 0.5x1 x2 − 1.96x22 + 0.96x24 HF y = [x − 1.275 x1 2 + 5 x1 − 6]2 + 10(1 − 1 )cos(x ) 2 1 h π π 8π     2 LF y = 1 [x − 1.275 x1 2 + 5 x1 − 6] + 10 1 − 1 cos(x ) + 10 1 l π π 2 2 8π

7

HF yh = [1 − 2x1 + 0.05sin(4π x2 − x1 )]2 + [x2 − 0.5sin(2π x1 )]2

8

LF yl = [1 − 2x1 + 0.05sin(4π x2 − x1 )]2 + 4[x2 − 0.5sin(2π x1 )]2

HF yh = 2i=1 xi4 − 16xi2 + 5xi

LF yl = 2i=1 xi4 − 16xi2

9

HF yh = 16 [(30 + 5x1 sin(5x1 ))(4 + exp(−5x2 )) − 100]   LF yl = 1 [(30 + 5x1 sin(5x1 )) 4 + 2 exp(−5x2 ) − 100] 6

5

10 HF yh = cos(x1 + x2 )exp(x1 x2 ) LF yl = cos[0.6(x1 + x2 )]exp(0.6x1 x2 ) 11 HF y = [x − 1.275 x1 2 + 5 x1 − 6]2 + 10(1 − 1 )cos(x ) 2 1 h π π 8π   LF y = 1 [x − 1.275 x1 2 + 5 x1 − 6]2 + 5 1 − 1 cos(x ) + 10 1 l π π 2 2 8π 

2  12 HF −1 yh = 1 − exp 2x2   2300x13 + 1900x12 + 2092x1 + 60 / 100x13 + 500x12 + 4x1 + 20 (continued)

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(continued) No

Test functions LF yl = 1 [yh (x1 + 0.05, x2 + 0.05) + yh (x1 − 0.05, x2 + 0.05) + 8 yh (x1 + 0.05, max(0, x2 − 0.05)) + yh (x1 − 0.05, max(0, x2 − 0.05)) − 5x1 − 7x12 ]

13 HF yh = x12 + 2x22 − 0.3cos(3π x1 ) − 0.4cos(4π x2 ) + 0.7 LF yl = 0.5yh + 100rand(1) 4 14 HF yh = (4 − 2.1x21 + 13 x1 )x12 + x1 x2 − (4 + 4x22 )   LF yl = yh (0.8x1 , 0.8x2 )[1 + sin x1 + x2 + x1 x2 − 10] 2

15 HF



yh = 105 x12 + x22 − x12 + x22

2

 4 + 10−5 x12 + x22

LF yl = 0.5yh + 10000rand(1) 16 HF yh = (x1 − 1)2 + (x1 − x2 )2 + x2 x3 + 0.5 LF yl = 0.2yh − 0.5x1 − 0.2x1 x2 − 0.1 2  17 HF yh =100 x12 − x2 + (x1 − 1)2 2  + (x3 − 1)2 + 90 x32 − x4 + 10.1(x2 − 1)2 + (x4 − 1)2 + 19.8(x2 − 1)(x4 − 1) LF yl = yh − 1.5(5x1 2 + 4x2 2 + 3x3 2 + x4 2 )



2 4 18 HF yh = 6i=1 xi2 + ( 6i=1 0.5ixi ) + ( 6i=1 0.5ixi )



2 4 LF yl = 2.5[( 6i=1 0.5ixi ) + ( 6i=1 0.5ixi ) ]

19 HF yh = 2i=1

LF yl = 2i=1

10 20 HF yh = 10 i=1 exp(xi )[A(i) + xi − ln( k=1 exp(xk ))] A = [−6.089, − 17.164, − 34.054, − 5.914, − 24.721, − 14.986, − 24.100, − 10.708, − 26.662, − 22.662, − 22.179]

10 LF yl = 10 i=1 exp(xi )[B(i) + xi − ln( k=1 exp(xk ))] B = [−10, − 10, − 20, − 10, − 20, − 20, − 20, − 10, − 20, − 20] No 1

HF

D

Domain

1

[0,1]D

1

[0,1]D

1

[0,10]D

LF 2

HF LF

3

HF LF

(continued)

A Novel Multi-fidelity Surrogate Model with Two-Stage Ensemble (continued) No 4

HF

D

Domain

1

[0,1]D

2

[−2,2]D

2

[−5,0; 10,15]

2

[0,1]D

2

[−2,2]D

2

[0,1]D

2

[0,1]D

2

[−5,10]D

2

[0,1]D

2

[−100,100]D

2

[−3 − 2;3 2]D

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[−20,20]D

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[0,1]D

4

[−1,1]D

6

[−5,10]D

8

[0,1]D

10

[−2,3]D

LF 5

HF

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HF

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HF

LF LF LF 8

HF LF

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LF LF 11

HF LF

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HF LF

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LF LF 18

HF LF

19

HF

20

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LF LF

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References 1. Bouhlel, M.A., Martins, J.R.R.A.: Gradient-enhanced kriging for high-dimensional problems. Eng. Comput. 35(1), 157–173 (2019) 2. Wang, B.: A local meshless method based on moving least squares and local radial basis functions. Eng. Anal. Bound. Elements 50, 395–401 (2015) 3. Basheer, I.A., Hajmeer, M.: Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Methods 43(1), 3–31 (2000) 4. Haftka, R.T.: Combining global and local approximations. AIAA J. 29(9), 1523–1525 (1991) 5. Gano, S.E., Renaud, J.E., Martin, J.D., Simpson, T.W.: Update strategies for kriging models used in variable fidelity optimization. Struct. Multidiscip. Optim. 32(4), 287–298 (2006) 6. Zhang, Y., Kim, N.H., Park, C., Haftka, R.T.: Multifidelity surrogate based on single linear regression. AIAA J. 56(12), 4944–4952 (2018) 7. Zhang, S., Liang, P., Pang, Y., Li, J.J., Song, X.G.: Multi-fidelity surrogate model ensemble based on feasible intervals. Struct. Multidiscip. Optim. 65(8), 1–13 (2022) 8. Wang, S., Liu, Y., Zhou, Q., Yuan, Y., Lv, L., Song, X.: A multi-fidelity surrogate model based on moving least squares: fusing different fidelity data for engineering design. Struct. Multidiscip. Optim. 64(6), 3637–3652 (2021). https://doi.org/10.1007/s00158-021-03044-5 9. Song, X., Lv, L., Sun, W., Zhang, J.: A radial basis function-based multi-fidelity surrogate model: exploring correlation between high-fidelity and low-fidelity models. Struct. Multidiscip. Optim. 60(3), 965–981 (2019). https://doi.org/10.1007/s00158-019-02248-0 10. Forrester, A.I., Sóbester, A., Keane, A.J.: Multi-fidelity optimization via surrogate modelling. Proc. R. Soc. A Math. Phys. Eng. Sci. 463(2088), 3251–3269 (2007)

A Fault Diagnosis Method for Molecular Pump Based on Dictionary Learning Kai Jia1,2(B) , Ming Jiang1,2 , Guizhong Zuo3 , Zuchao Zhang3 , Jilei Hou3 , and Xiaolin Yuan3 1 Key Laboratory of Advanced Perception and Intelligence Control of High-end Equipment,

Anhui Polytechnic University, Wuhu 241000, China [email protected] 2 School of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China 3 Institute of Plasma Physics, Chinese Academy of Science, Hefei 230031, China

Abstract. The molecular pump fault results in a vacuum leakage and lead to accidents in a fusion device. The fault diagnosis for molecular pump can provide an early warning and avoid a greater loss in a fusion device. This paper proposed an innovative fault diagnosis method for molecular pump based on dictionary learning. Firstly, discrete cosine transform (DCT) is used to perform noise reduction. Then, the k-singular value decomposition (K-SVD) is used to train an over-complete dictionary of normal state signal and decomposed other state signal on the dictionary of normal state signal. Finally, the orthogonal matching pursuit (OMP) is used to reconstruct the signal and compare the reconstructed signal with the original signal, the molecular pump fault diagnosis is realized by the sparse representation error. The superiority of the proposed method in molecular pump fault diagnosis are shown by the experimental results. Compared with the traditional method, this approach is 8.79% more accurate. Our analyses also indicate that the proposed method can be used in fault diagnosis of molecular pump for EAST. Keywords: Fault diagnosis · Molecular pump · Dictionary learning

1 Introduction Nowadays, the radical solution of ecological and energy problems of the Earth is associated by scientists with the development of nuclear fusion. Nuclear energy has attracted widespread attention, the purpose of studying controlled nuclear fusion is to build a fusion device with good economic performance [1]. Experimental Advanced Superconducting Tokamak (EAST) is a fusion device for high-parameter plasma physics experiments under long pulse conditions [2]. The molecular pump is mainly providing a high vacuum environment for EAST. However, the molecular pump fault results in a vacuum leakage that can lead to accidents in EAST [3]. The fault diagnosis for molecular pump can provide an early warning and avoid a greater loss in EAST. Vibration signal contains lots of information about the state of molecular © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 239–248, 2023. https://doi.org/10.1007/978-981-99-4334-0_30

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pump and the vibration signal is often used for mechanical fault diagnosis [4–6]. Traditional fault diagnosis method commonly use time and frequency domain analysis to extract signal features [7, 8]. Cai [9] proposed a novel signal feature extraction method for gear fault diagnosis based on generalized S transform, the reversibility of generalized S transform can represent the time-frequency energy of gear vibration signal, in addition, the time-frequency domain noise can be removed by constructing time-frequency filtering factors. Zhi [10] described a motor bearing fault diagnosis based on time domain and frequency domain feature extraction approach, the new feature vector dataset is used to train and test the Classification and Regression Tree (CART) algorithm. Lu [11] presents an ensemble empirical mode decomposition (EEMD) method to decomposed signals and obtain the detailed time-frequency characteristics of the signal. Meng [12] proposed a novel gear fault diagnosis method based on accommodative random weighting theory to reduce the total mean squared error, this approach can adaptively adjust the difference between current measurement and historical measurement. This paper present a molecular pump fault diagnosis method based on dictionary learning, Firstly, discrete cosine transform (DCT) is used to perform noise reduction. Then, the k-singular value decomposition (K-SVD) is used to train an over-complete dictionary of normal state signal and decomposed other state signal on the dictionary of normal state signal. Finally, the orthogonal matching pursuit (OMP) is used to reconstruct the signal and compare the reconstructed signal with the original signal, the molecular pump fault diagnosis is realized by the sparse representation error. The superiority of the proposed method in molecular pump fault diagnosis are shown by the experimental results. Our analyses also indicate that the proposed method can be used in fault diagnosis of molecular pump for EAST.

2 Methodology Sparse representation has attracted a lot of attention in signal processing, pattern recognition and other fields. To improve the performance of signal sparse decomposition, it is necessary to consider the characteristics of the signal [13]. Suppose a training set is Y = {y1 , y2 , ..., ym }. Firstly, the training set is used to identify the model and get a dictionary, if the model bias ε is known, considering the following optimization problem: ⎧ m  ⎨ xi 0 minm D,{xi }i=1 i=1 (1) ⎩ s.t.yi − D · xi 2 < ε, 1 ≤ i ≤ m The unknow dictionary D and the sparest representation vector xi is used to represent each training sample yi . Then, find the appropriate sparse representation vector and dictionary in the joint domain. A viable model will be found if each sparse representation vector in the solution contains P or fewer nonzero elements. Restricting the sparsity, then obtained the best match, Eq. (1) can be rewritten as: ⎧ m ⎨ min  y − D · x 2 i i 2 D,{xi }m (2) i=1 i=1 ⎩ s.t.xi 0 ≤ P, 1 ≤ i ≤ m

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In Eqs. (1) and (2), the number and order of the atoms in dictionary D are uncertain. Zhang [14] points out that if the number and order of atoms in the dictionary is fixed, then at least for ε = 0, the solution is unique. Suppose exist a dictionary D0 and a sufficiently large set of training samples, each of training samples can be represented by at most 0) P < spark(D atoms, then in the case of determining the number and order of atoms, D0 2 is the only dictionary that can makes all training samples sparse representation possible. Aharon [15] proposed a new dictionary update rule that progressively processes each atom in the dictionary D. This approach is called K-SVD. The aim of K-SVD is to obtain the dictionary by learning, then perform a sparse representation of the training samples. Set the number of iterations k = 0, construct the initialized dictionary D(0) ∈ Rn∗m , then normalizing the columns of D(0) , while k increase from 1. In the sparse encoding step, the tracking algorithm is used to estimate the solution:   2  xi = arg minyi − D(k−1) · x2 (3) s.t.x0 ≤ k0 For 1 ≤ i ≤ M to obtain each sparse representation x˜ i , these sparse representation vectors form the matrix X (k) , In the dictionary update step of K-SVD, the following procedure is repeated for j0 = 1, 2, ..., m respectively, define the index set of samples that use atom αj0 :

 j0 = i|1 ≤ i ≤ M , X(k) j0 , i = 0 (4) Calculate the residual matrix: Ej0 = Y −

j=j0

αj · xjT

(5)

where xjT denotes the j-th row of X(k) . The residual matrix Ej0 is restricted by selecting the columns corresponding to j0 , then obtained the restricted matrix EjR0 . Apply SVD decomposition to EjR0 , i.e., EjR0 = U · S · V T . Update the dictionary atom αj0 = u1 is the first column of U , update the sparse representation coefficient xjR0 = S[1, 1] · v1 , where v1 is the first column of V . Stop the iteration when the transformation of Y − A(K) · X(K) 2F is small enough, otherwise start the next loop iteration, and finally get the desired dictionary A(k) .

3 Molecular Pump Fault Diagnosis Method 3.1 Signal Sparse Representation Based on DCT Denoise Signal sparse representation is very important to achieve fault diagnosis for rotating machinery. However, the vibration signal is generally not sparse in the time domain. If the original signal is directly used as the input of K-SVD algorithm, the reconstruction result is not satisfactory. Therefore, a method based on DCT is proposed to reduce the influence of noise. The original data Xoriginal = {x1 , x2 , ..., xm } is transformed to another spatial domain to get

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Fig. 1. (a) normal state sparse representation error; (b) mild vacuum leakage sparse representation error; (c) severe vacuum leakage sparse representation error.

the coefficient matrix Tβ = ˜t1 , ˜t2 , ..., ˜tm . Set the Tβ value to 0 if it lower than 2% peak-to-peak value and get matrix Tδ . Then, using inverse DCT method to obtain the denoised signal Xδ = {˜x1 , x˜ 2 , ..., x˜ m }. Finally, Xδ will be the input of K-SVD algorithm and obtain a denoised sparse representation dictionary Dδ . To compare the effectiveness of this method for signal reconstruction, introduced reconstruction error to measure the advantages of proposed method:   N  (6) φ= (xi − x˜ i )2 i=1

xi is the i-th point of the original signal and x˜ i is the i-th point of the reconstructed signal. In Fig. 1, the normal state signal average reconstruction error after DCT is 1.09 and the average reconstruction error of the original normal state signal is 2.54, the reconstruction error is reduced 57.09%; the mild vacuum leakage state signal average reconstruction error after DCT is 1.3 and the average reconstruction error of the mild vacuum leakage state original signal is 3.46, the reconstruction error is reduced 62.14%; The severe vacuum leakage state signal average reconstruction error after DCT is 1.37 and the average reconstruction error of the severe vacuum leakage state original signal is 3.15, the reconstruction error is reduced 56.51%. 3.2 Signal Sparse Representation Based on DCT Denoise According to the novel method of signal sparse representation mentioned in the previous section, the vibration signal has the smallest sparse representation error on the dictionary of the corresponding state. Therefore, this advantage can be used to realized molecular pump fault diagnosis in different vacuum leakage conditions. The sparse representation error is calculated as Eq. (7). ∼

ξ = X − Dnormal · λi 

(7)

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Table 1. Different sparse representation error in the normal dictionary. Fault type

Direction

Sparse representation error

Normal

X direction

0.24

Y direction

0.32

Z direction

0.33

X direction

0.55

Y direction

2.24

Z direction

0.73

X direction

0.89

Y direction

2.20

Z direction

0.59

Mild vacuum leakage

Severe vacuum leakage

∼

Equation (7) include parameters X , Dnormal , λi which are original signals, the dictionary trained by the normal state signal and different states signal sparse representation error on the normal dictionary. In Table 1, the average sparse representation error in three directions of the normal state signal are 0.24, 0.32, 0.33, respectively. Compared with the mild vacuum leakage state, the sparse representation error of the normal state signal on the normal dictionary is reduced by 0.31, 1.92, and 0.4 in the X, Y and Z direction, respectively. Compared with the severe vacuum leakage state, the sparse representation error of the normal state signal on the normal dictionary is reduced by 0.31, 1.92, and 0.4 in the X, Y and Z direction, respectively. In other words, only the normal state signal has the smallest sparse representation error on the normal dictionary, and there is obviously difference in the sparse representation error of other fault signals. • In this paper, we proposed a fault diagnosis method for molecular pump based on dictionary learning. The process is shown in Fig. 2. The fault diagnosis steps for molecular pump are as follows: Obtained the molecular pump different states vibration signals and use the normal state signal as training samples. • DCT signal denoising and K-SVD algorithm is used to train the over-complete dictionary Dnormal . • The signals of normal state, mild vacuum leakage state and severe vacuum leakage state are sparsely decomposed on the over-complete dictionary Dnormal , using OMP algorithm to reconstruct signals, calculate the sparse representation error of different states. • divide the sparse representation error into the training set and the test set, the training set is used as input to the classification algorithm to build the diagnostic model and the test set is used to evaluate the model’s performance.

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Normal state signal samples

Molecular pump vacuum leakage fault diagnosis

Signal reconstitution and error calculation

Signal noise reduction

Training set

Sparse representation error

Machine learning classification algorithms DCT noise reduction & K-SVD method

Reconstitution signals in normal dictionary Reconstitution algorithm

Normal state dictionary

Test set

Fault diagnosis model

Signals sparse representation coefficient in normal dictionary OMP algorithm

Other status signals

DCT noise reduction

Normal status

Mild leakage

Severe leakage

Fig. 2. The schematic view of fault diagnosis process for molecular pump.

Table 2. Description of the vacuum leakage fault datasets. Fault type

Vacuum degree (Pa)

Training samples

Test samples

Number of each sample

Normal

5.2 × 10−4

2048

512

512

Mild vacuum leakage

120

2048

512

512

Severe vacuum leakage

400

2048

512

512

4 Results and Discussion 4.1 Vacuum Leakage Experimental Test The molecular pump vacuum leakage experiments can verify the effectiveness of the proposed fault diagnosis method, the signal sampling frequency is 10kHz and the experimental system is shown in Fig. 3. The total number of signals contained in each state is 1048576, the sample dataset is shown in Table 2. The molecular pump vacuum experimental system mainly consists of pumping system, vacuum chamber, vacuum gauge, needle control valve and upper monitor. The pumping system consists of molecular pump and vacuum pump, the experimental steps are as follow: when the vacuum degree of vacuum chamber is under normal air pressure, open the vacuum pump for pumping at first; after turning on the vacuum pump, open the molecular pump for pumping when the vacuum degree of vacuum chamber drops to 10 Pa; after the stable operation of the pumping system for a period of time, when

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Fig. 3. (a) Molecular pump vacuum leakage experimental system; (b) The location of sensor.

Fig. 4. Visualization of sparse representation error.

the number of the vacuum gauge is 5.2 × 10–4 Pa it means that the experimental system has reached the high vacuum state. Due to the vacuum leakage fault, the molecular pump in EAST will be in a high load working state, if the molecular pump works in this high load state for a long time, the performance will be degraded or even damaged. To prevent vacuum leakage, using the experimental system to simulate the vacuum leakage fault of EAST molecular pump. Specifically, open the needle control valve when the experimental system is in a vacuum state, which will cause the vacuum degree of

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vacuum chamber to be destroyed, and molecular pump will work in a high load state, the vacuum leakage fault can be divided into mild vacuum leakage and severe vacuum leakage. The molecular pump will have different performance under different degrees of vacuum leakage fault. 4.2 Compassion of Proposed Method and Traditional Method The K-SVD algorithm is used to train the normal samples to obtain the sparse representation error of different signals. The quantity of atoms is set to 1024, the sparsity is set to 10 and the number of loops is set to 20. The sparse representation errors were calculated for different signals at 10 decomposed atoms and the result are shown in Fig. 4. There is a clear distinction between the sparse representation errors of different signals, which is the basis for the classification algorithm to accurately identify different faults. To visually represent the difference between different signals after sparse decomposition on Dnormal , the sparse representation coefficients of different signals are reconstructed according to the dictionary Dnormal . The reconstructed signals are compared with the original signals as shown in Fig. 5. In order to compare the performance of proposed method and traditional feature extraction methods for molecular pump fault diagnosis, using traditional feature extraction method extract the mean value, variance value, standard deviation value, root mean square value, skewness value, waveform factor, impulse factor and margin factor of the original signal, the accuracy rate and false alarm rate are introduced to judge the results of the classification model, where the accuracy rate represents the ratio of the number of correctly identified samples to the total number of samples, and the false alarm rate represents the ratio of the number of incorrectly identified samples to the total number of samples. The results are shown in Fig. 6, the average accuracy rate of the proposed method on different classification algorithms is 99.9%, while the average accuracy rate of the traditional feature extraction method on classification algorithms is 91.11%, and the average accuracy rate is improved by 8.79%. In terms of the false alarm rate, the average false alarm rate of the proposed method is 0.16%, and the average false alarm rate of the traditional feature extraction method is 10.64%, the average false alarm rate reduced 10.48%, it proves the effectiveness of the proposed method in this paper.

5 Conclusion In this study, a novel approach based on dictionary learning is proposed to achieve the fault diagnosis of molecular pump. The main conclusions can be drawn as follows: DCT noise reduction method and K-SVD algorithm is used to train the over-complete dictionary Dnormal ; the normal state signal, mild vacuum leakage signal and severe vacuum leakage signal are sparsely decomposed on the over-complete dictionary Dnormal , then used OMP algorithm to reconstruct signals, calculate the sparse representation error of different states; divide the sparse representation error into the training set and the test set, the training set is used as input to the classification algorithm to build the diagnostic model, and the test set is used to evaluate the model’s performance. Molecular pump vacuum leakage experiments demonstrate the effectiveness of this method, compared

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Fig. 5. Reconstruction of different signals in Dnormal .

Fig. 6. Accuracy rate and missing alarm rate of traditional methods and proposed methods on different classification algorithms.

with the traditional feature extraction methods, the identification accuracy is increased by 8.79% and the missing alarm rate is reduced by 10.48%. As a result, the proposed method improved the safety of molecular pump. To achieve more accurate molecular pump fault diagnosis, it is still a challenge to obtain more fault signals. In the future, we plan to continue to explore the impact of molecular pump fault on EAST and guarantee the safety of fusion device.

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References 1. Zelensky, V.F.: Fusion of light atomic nuclei in vacuum and in solids and two ways of mastering nuclear fusion energy. J. Cond. Matter Nucl. Sci. 24, 146–167 (2017) 2. Hu, J.S.: Vacuum and wall conditioning system on EAST. Fusion Eng. Des. 84(12), 2167– 2173 (2009) 3. Liu, S.Q.: Multi-feature fusion for fault diagnosis of rotating machinery based on convolutional neural network. Comput. Commun. 173, 160–169 (2021) 4. Jia, Z.: Review on engine vibration fault analysis based on data mining. J. Vibroeng. 23(6), 1433–1445 (2021) 5. Kafeel, A.: An expert system for rotating machine fault detection using vibration signal analysis. Sensors 21(22), 7587 (2021) 6. Zhang, D.: A multi-feature fusion-based domain adversarial neural network for fault diagnosis of rotating machinery. Measurement 200, 111576 (2022) 7. Van Hecke, B.: A new spectral average-based bearing fault diagnostic approach. J. Fail. Anal. Prevent. 14(3), 354–362 (2014) 8. Zhang, M.: Rolling bearing fault diagnosis based on time-frequency feature extraction and IBA-SVM. IEEE Access 10, 85641–85654 (2022) 9. Cai, J.H.: Gear fault diagnosis based on time–frequency domain de-noising using the generalized S transform. J. Vibrat. Control 24(15), 3338–3347 (2018) 10. Zhi, L.: Anti-noise motor fault diagnosis method based on decision tree and the feature extraction methods in the time domain and frequency domain. In: Proceedings of the 2021 International Conference on Communications, Information System and Computer Engineering, pp. 71–75. IEEE (2021) 11. Lu, N.: A zero-shot intelligent fault diagnosis system based on EEMD. IEEE Access 10, 54197–54207 (2022) 12. Meng, Z.: A gear fault diagnosis method based on improved accommodative random weighting algorithm and BB-1D-TP. Measurement 195, 111169 (2022) 13. Zhang, Z.: A survey of sparse representation: algorithms and applications. IEEE Access 3, 490–530 (2015) 14. Zhang, J.: L2-norm shapelet dictionary learning-based bearing-fault diagnosis in uncertain working conditions. IEEE Sens. J. 22(3), 2647–2657 (2021) 15. Aharon, M.: K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)

Development of Comprehensive Training Platform for Power Electronics Teaching in Smart Grid and Renewable Energy Yuying Wang, Quanzhu Zhang(B) , Bo Ao, and Weining Xue North China Institute of Science and Technology, Yanjiao, China [email protected]

Abstract. This paper introduces an advanced experimental platform based on power electronics. The platform is a multi-link (AC/DC/AC1-AC2/DC/AC) power conversion circuit based on power electronics technology, which can realize the adjustment of output AC voltage and frequency. The platform can be used in the teaching experiment of power electronic technology course and electric drive control system course, and advanced control algorithm can be realized through DSP control board. The design and experience shared in this paper will benefit many researchers who need such a platform. So far, more than 100 undergraduate students have been taught courses, which plays a positive role in the course teaching of power electronics. Keywords: Power electronics · DSP · Teaching platform · PWM control

1 Introduction With increasing interest in smart grid and renewable energy, significant investments have been allocated to promote related studies. To meet the demands of both teaching and research, a lot of universities increase investment in related area to initiate/redevelop a new or strengthen the existing power program. Since power systems and power electronics studies are application oriented, it is desirable to have an experimental platform for both teaching and research purposes, especially for the highly experimental studies of power electronics. Since such experimental platforms are not commercially available, developing is usually the only option [1, 2]. “Power Electronics Technology” is a professional basic course for undergraduate majors of electrical engineering and automation in higher engineering colleges. It is also the most active field in modern electrical technology and a marginal discipline of power, electronics and control, with strong theory, practicality and application [3]. The rapid development of power electronics and power transmission technology is rapidly changing people’s way of life, such as high-speed rail technology, smart grid and electric vehicles [4]. At present, such experimental courses are mostly traditional verification experimental projects under set conditions, equipped with general experimental equipment purchased from the department. Such equipment is generally finalized products, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 249–254, 2023. https://doi.org/10.1007/978-981-99-4334-0_31

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and students’ problem-solving ability, subjective initiative and innovation ability are limited [5]. Power electronics research is applied research, which requires an experimental platform for both teaching and research purposes. In recent years, more and more scholars have carried out research on such experimental platform. According to the latest development direction of inverter technology, inspired by the power electronics experiment platform developed by The School of Electrical Engineering, Zhejiang University in literature [5], our college built a power electronics discipline comprehensive training platform based on DSP control (multi-link single-three-phase voltage frequency converter experiment platform) [6–8]. Through this platform, students can conduct various experiments of multi-link single-three-phase inverter, including high-frequency DC/DC converter, three-phase SPWM inverter, multi-link AC/DC/AC1AC2/DC/AC power converter, voltage/frequency/phase/phase number multi-parameter converter and so on. The experimental content of the design is closely combined with the theoretical knowledge students have learned, which helps to strengthen students’ intuitive understanding of the knowledge points they have learned, and improve their sense of innovation and operational ability. The strong electric part of the experimental platform is protected with high security and suitable for students to operate. This paper first introduces the hardware structure and software implementation process of the platform, and then verifies the experimental teaching function of the experimental platform. The results show that the platform enriches the experimental teaching content of power electronics course, and can improve and enhance the experimental teaching quality of power electronics course.

2 Development of the Experimental Platform 2.1 Power Circuit Module The power circuit adopts two levels of “AC/DC/AC1 - AC2/DC/AC” circuit. The circuit structure was stable, and achieved the electrical isolation of input and output, and completed the requirements of the output. At the same time, the high frequency transformer is added to the circuit, which can save a lot of forming machine volume. Although the use of two-stage “AC/DC/AC1 - AC2/DC/AC” makes the circuit structure complex, the use of multi-link AC/DC/AC transformation, and the front and back stages are different, as teaching experiment equipment, is conducive to teaching experiment. Figure 1 shows the Schematic diagram of Power circuit. The input AC 220 V/50 Hz is processed by a singlephase rectifier and a single-phase inverter to output high-frequency AC power. Then through the high-frequency transformer boost, fast rectifier and three-phase inverter, output three-phase AC380 V. 2.2 Circuit Control Module The control system structure diagram, as shown in Fig. 2. It consists of SPWM drive circuit, HMI (Human-machine interface), voltage sampling, current sampling, temperature sampling module and fault signal, etc. It used TMS320F28335 as the core of the controller to generate six-way center symmetric SPWM, three-phase waveform 120

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Fig. 1. Schematic diagram of power circuit.

degrees of mutual difference, LCD display waveform parameters (frequency, amplitude), through the keyboard to set the frequency value, through the dial switch to select the type of compensation curve to be applied, finally in oscilloscope to observe the waveform generated.

Fig. 2. Construction diagram of the control system.

Fig. 3. The program flow chart.

2.3 Software Design The program flow chart mainly consists of main program, waveform generator interrupt program, external fault interrupt program, CAN interrupt program and timer interrupt service program, as shown in Fig. 3. The main program to complete the initialization variable interrupt Settings and open interrupt function. Waveform generator interrupt

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service program mainly completes the cycle register and duty cycle update, duty cycle calculation and SPWM wave generation output. The external fault interrupt program mainly deals with the decision of the faulty circuit module. CAN interrupt program mainly completes information interaction between LCD and controller. The timer interrupt service program mainly completes the following tasks: (1) the signal sampling of the external terminals, the signal sampling of the start and stop of the power supply, the reset signal of the CPU, and the output fault signal. (2) Sampling and calculation of voltage, current and temperature. (3) Complete the calculation of automatic voltage stabilization, dead zone compensation, waveform generator cycle register value, phase accumulation value, overload and current, etc.

3 Teaching Experiment Platform Applications 3.1 Platform Construction In order to verify the designed power electronics discipline comprehensive training platform, oscilloscope is used to collect and analyze the experimental data. The power electronics discipline comprehensive training platform and Physical drawing of hardware circuit are shown in Fig. 4(a).

Fig. 4. Teaching and experimental platform

Currently teaching experiment platform as shown in Fig. 4(b), the deficiencies are students can’t direct contact with the lab equipment, and engineering, due to the analog circuit parameters change with environment, students debugging time is long and hard to get target effect, students’ experiment ability, through the research is shown in Fig. 4(a) teaching platform to provide a development platform for students interested in, in order to avoid the student beginning ability is insufficient, At the same time, because the experimental platform is highly targeted and has a clear application background, it can improve students ‘interest in learning.

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3.2 Teaching Experiment On the basis of the original teaching experiment platform, four teaching experiments can be added to the training platform, including high-frequency DC/DC converter experiment, three-phase SPWM inverter experiment, voltage/frequency/phase/phase number multi-parameter converter experiment, and multi-link AC/DC/AC1-AC2/DC/AC power converter experiment. Figure 5 show High-frequency transformer output voltage waveform, the inverter outputs SPWM waveform, Sinusoidal Waveform. The feasibility of the platform development is verified through experimental waveforms.

(a)High-frequency transformer output waveform (b) The inverter output waveform (c) Sinusoidal Waveform

Fig. 5. Oscillogram waveform

4 Conclusion (1) The circuit design adopts modularization, according to the function and characteristics of the circuit, as well as the principle of convenient testing, observation and experiment, the circuit adopts modularization design, which is easy to replace, upgrade, expand and redevelop. (2) Each module of the device design adopts fully open structure, which is very convenient for students to learn circuit, data and waveform measurement. Students can learn circuits and devices from the component level, through the circuit module level, and then to the system level. (3) The control circuit of the power converter is constructed with DSP F28335 as the core. Combined with voltage and current sampling circuit, display circuit and CAN bus data communication circuit, the power electronics discipline integrated training platform is constructed. The voltage closed-loop PWM control method is applied to realize the continuous voltage and frequency conversion from single phase to three phase. (4) It combines with the needs of experimental teaching in colleges and universities, which is targeted and practical. As a typical application of power electronics power conversion technology, this system can be further developed as application equipment, and can also be used as experimental teaching and research platform reference study in the field of power electronics technology and motor drive control.

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(5) At present, the platform has benefited more than 100 undergraduates and played an active role in the teaching of power electronics. In particular, it has played a positive role in the implementation of “Education and Training program for Excellent Engineers in Automation”. Acknowledgments. The authors would like to thank the Fundamental Research Funds for the Central Universities of China (No. 3142018049) and the project of Hebei Higher Education Association of China, research on the effect of Education and Training program for Excellent Engineers in Automation Program on talent Cultivation (GJXHZ2017-05) project fund for valuable contributions during the preparation of this paper.

References 1. Liu, W., Kim, J., Wang, C., et al.: Power converters based advanced experimental platform for integrated study of power and controls. IEEE Trans. Industr. Inf. 14(11), 4940–4952 (2018) 2. Guerrero, J.M., Vasquez, J.C., Matas, J., et al.: Hierarchical control of droop-controlled AC and DC microgrids—a general approach toward standardization. IEEE Trans. Industr. Electron. 58(1), 158–172 (2011) 3. Yang, T., Yang, C.: Research on power electronics virtual simulation experimental platform based on Matlab. Exp. Technol. Manag. 35(07), 152–154 (2018) 4. Bi, D., Guo, R., Chen, H.: Design of power electronics and power transmission DSP-HIL teaching experiment platform. Exp. Technol. Manag. 36(01), 226–229 (2019) 5. Zhao, J., Pan, Z., Lu, H., et al.: Construction of experimental platform for single-phase inverter system innovation. Lab. Res. Explor. 36(03), 196–199 (2017) 6. Ma, H., Deng, Y., Gan, J.: Several experimental projects of developing power electronic system with real—time simulation software. J. North China Inst. Sci. Technol. 17(02), 119–124 (2020) 7. Zhang, Q., Jing, C., Deng, Y.: Design of driving circuit of SiC-MOSFET charger for mine. J. North China Inst. Sci. Technol. 17(06), 59–64 (2020) 8. Zhang, Q., Chen, H.: Study on the scheme of switching from single phase AC to three phase AC. J. North China Inst. Sci. Technol. 15(03), 98–101 (2018)

Rotor Position Deviation Active Control of High Speed Magnetic Levitation Permanent Magnet Motor Dan Zhang(B) and Diju Gao Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai 201306, China [email protected]

Abstract. The abstract should summarize the contents of the paper in short terms, the magnetic suspension system includes displacement sensor, power amplifier, rotor, coil, magnetic bearing, electromagnet and controller. According to the magnetic force supply mode, magnetic bearing can be divided into active magnetic bearing (AMB), passive magnetic bearing (PMB) and hybrid magnetic bearing (HMB). Due to the existence of active control, AMB has the characteristics of controllable stiffness and damping, and compensate rotor unbalance vibration. The system and the reliable operation of permanent magnet motor is in highspeed rotating magnetic field. As the outer control loop, the position controller converts the rotor position signal detected by the position sensor into the current command required by the success rate amplifier. As the inner control loop, the power amplifier uses the differential control mode to make two electromagnets produce a pair of opposite forces. The rotor is suspended by changing the magnitude of the electromagnetic force to maintain the balance position. In order to make the magnetic bearing work stably, the active magnetic suspension control method is adopted and simulated in MATLAB. Finally, the correctness of the proposed method is verified by experiment. Keywords: Active magnetic bearing · Unbalance vibration · Suspension

1 Introduction There is no contact and friction between the stator and rotor of high speed magnetic levitation motor, which can greatly improve the equipment efficiency. The rotor speed is generally above 10,000 r/min. The products developed based on this key technology, such as magnetic suspension blower and magnetic suspension compressor, have gradually matured and achieved good energy-saving effect in industrial applications. Magnetic levitation bearing is a new type of high-performance bearing, which uses controllable magnetic force to suspend the rotor in the air, so as to realize non-contact support between the stator and rotor. According to the way of magnetic force generation, magnetic bearings can be divided into three categories, namely, active magnetic bearing (AMB), passive magnetic bearing (PMB) and hybrid magnetic bearing (HMB). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 255–259, 2023. https://doi.org/10.1007/978-981-99-4334-0_32

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Among them, AMB is a typical mechatronics product based on closed-loop feedback control. Due to the existence of active control, AMB has the characteristics of controllable stiffness and damping, and can compensate rotor unbalance vibration. Therefore, it is the most widely used in industrial applications. At present, it is mainly used in turbine machinery, machining, aerospace, artificial heart, nuclear power generation and other fields. AMB used position sensors and electroniccircuits that control electromagnets to achieve stable levitation of the rotating element in [1, 2]. A design of this bearing system is currently being constructed and tested in [3]. Aiming at the rotor mass unbalance and the vibration generated by sensor runout, time domain iterative learning control [4], multiresonance control [5], repetitive control [6], sliding-mode control [7], etc. have been proposed to suppress harmonic currents. In the rotating machinery, due to the material uniformity, processing error and other reasons, coupled with the high cost of high-precision dynamic balancing, it is a common phenomenon that the rotor has unbalance, which is the main reason for the vibration of rotating machinery. Many control methods have been proposed to improve the stability of active magnetically suspended rotor. Zheng et al. [8] proposed a tracking compensation control for the whirling motion of gyroscopic effects rotors. In order to suppress the influence of precession effect on magnetically suspended control and sensitive gyroscope, a novel parallel control method of PID and band stop filtering based on differential cross feedback was proposed [9]. The unbalanced magnetic pull is studied by finite element analysis and experimental in 3-D hybrid air-gap eccentricity cases [10]. Rotor position deviation of high speed magnetic levitation permanent magnet motor based on active control method in this paper. The proposed method is validated by simulation and experiment.

2 Control Strategy An eddy current displacement sensor with high sensitivity is used to accurately measure the eccentricity displacement of the rotor. The transfer function of displacement sensor can be expressed as a first-order inertial link, as shown in Eq. (1). Gs (s) =

ks 1 + τs s

(1)

where, ks is the amplification factor of the sensor; τs is the time constant of the sensor. As the important part of the magnetic levitation control system, power amplifier provides current to the electromagnet, which can provide power to the high-speed magnetic levitation rotor. The power amplifier adopts the output mode of current differential control. The transfer function of the power amplifier is expressed by the first-order inertial link, as shown in Eq. (2). Gpa (s) =

kpa 1 + τpa s

(2)

where, kpa is the amplification factor of the power amplifier; τpa is the time constant of the power amplifier.

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The transfer function of controller is expressed by Eq. (3).   1 + τd s Gc (s) = kp 1 + τi s

257

(3)

where, kp is the proportionality coefficient; τi is the integral time constant; τd is the differential time constant.

3 Simulation The simulation model of the proposed active control of the magnetic levitation bearing is built in Matlab/Simulink. The relevant simulation parameters are shown in Table 1. Table 1. Simulation parameters of MLS Name

Parameter

μ0

4π × 10−7 N/A2

Name

Parameter

x0

0.4 mm

n

50

m

30 kg

A

700 mm2

kmi

27.49 N/A

i0

3.5 A

kmx

210.46 N/mm

Rotor air gap position (mm)

The reference value of the rotor’s air gap position in the magnetic levitation bearing is defined as 0.4 mm. The simulation result of the rotor’s air gap position without active control is shown in Fig. 1. The rotor’s air gap position appears obvious divergence without position control, and the magnetic levitation bearing can not be stable.

Time (s)

Fig. 1. Simulation result of rotor air gap position without active control.

The simulation result of the rotor’s air gap position with active control is shown in Fig. 2. The rotor’s air gap position can be stabilized at 0.4 mm by using active control.

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Time(s)

Fig. 2. Simulation result of rotor air gap position with active control.

4 Experiment The experimental result is shown in Fig. 3. When the magnetic suspension bearing is started, it can maintain stability after a short fluctuation. The rotor shaft deviation signal is detected by the position sensor. After receiving the signal, the controller is calculated to output the control signal. The coil current is controlled by the power amplifier to adjust the size of the electromagnetic force, so that the rotor is stably suspended in the working position.

Floating state

Voltage(2V/step)

Static state

Rotor vibration

Time(1s/step)

Fig. 3. Experimental result.

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References 1. Sobhan, P.V.S., Kumar, G.V.N., Amarnath, J.: Rotor levitation by active magnetic bearings using fuzzy logic controller. In: Proceedings of the International Conference on Industrial Electronics, Control and Robotics (IECR), pp.197–201 (2010) 2. Khoo, W.K.S., Kalita, K., Garvey, S.D., et al.: Active axial-magnetomotive force parallelairgap serial flux magnetic bearings. IEEE Trans. Magn. 46(7), 2596–2602 (2010) 3. Bachovchin, K.D., Hoburg, J.F., Post, R.F.: Stable levitation of a passive magnetic bearing. IEEE Trans. Magn. 49(1), 609–617 (2013) 4. Bi, C., Wu, D., Jiang, Q., et al.: Automatic learning control for unbalance compensation in active magnetic bearings. IEEE Trans. Magn. 41(7), 2270–2280 (2005) 5. Peng, C., Sun, J., Song, X., et al.: Frequency varying current harmonics elimination for active magnetic bearing system via multiple resonant controllers. IEEE Trans. Ind. Electron. 64(1), 517–526 (2017) 6. Cui, P., Zhang, G.: Modified repetitive control for odd-harmonic current suppression in magnetically suspended rotor systems. IEEE Trans. Ind. Electron. 66(10), 8008–8018 (2019) 7. Kandil, M., Dubois, M., Bakay, L.: Application of second-order sliding mode concepts to active magnetic bearings. IEEE Trans. Ind. Electron 65(1), 855–864 (2018) 8. Zheng, S.Q., Yang, J.Y., Song, X.D., et al.: Tracking compensation control for nutation mode of high-speed rotors with strong gyroscopic effects. IEEE Trans. Ind. Electron. 65(5), 4156– 4165 (2018) 9. Yin, Z.Y., Cai, Y.W., Ren, Y., et al.: A precession effect suppression method for active magnetically auspended rotor. IEEE Trans. Ind. Electron. 69(6), 6130–6139 (2022) 10. He Y.L., Sun, Y.X., Xu, M.X., et al.: Rotor UMP characteristics and vibration properties in synchronous generator due to 3D static air-gap eccentricity faults. IET Electr. Power Appl. 14(6), 961–971 (2020)

Research on Risk Prevention and Control of Distribution Network Based on Knowledge Graphs Nan Yang, Yi Wang, Yu Si, and Zishuo Ai(B) Hebei Key Laboratory of Distributed Energy Storage and Micro-grid, North China Electric Power University, Baoding 071003, China [email protected]

Abstract. With the application of high proportion of power electronic equipment and the access of high proportion of renewable energy, the fault patterns of distribution network are increasingly complex, and the risk associated data are also more complex and diverse. To effectively improve the data perception ability and risk response ability of distribution network, this paper combines the traditional risk prevention and control of distribution network with the knowledge graph technology with interconnected, structured, and visualized knowledge, and proposes a risk prevention and control method of distribution network based on knowledge graph. The top-down and bottom-up graph construction method is adopted to construct the graph from two aspects: pattern layer and data layer, and it is divided into distribution network entity graph, the auxiliary decision-making graph, and case graph. The critical construction technologies of knowledge graph are analyzed, and ideas are provided for the realization of each link of the risk control process. Finally, combined with the actual digital twin case of distribution network, the auxiliary decision-making graph in the actual fault situation is demonstrated. The consequence show that this method can swiftly and efficiently realize the power loss recovery of the distribution network, and realize multi-dimensional data perception and human-computer interaction. Keywords: Knowledge graph · Distribution network risk prevention and control · Digital twin · Artificial intelligence

1 Introduction With the advent of the era of artificial intelligence, smart grid has become an inevitable trend in the development of power grid technology [1]. Facing the background of big data development, knowledge graph, a new cognitive method developed by artificial intelligence technology, has gained development space in the field of electric power, and a large number of research workers have applied knowledge graph in the field of power grid scheduling [2–4]. At the same time, with the development of artificial intelligence, the massive data of the power system can be used as input, and the digital twin model of the new power system can be effectively established by directly mining © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 260–268, 2023. https://doi.org/10.1007/978-981-99-4334-0_33

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the potential connections between the data [5–8]. However, at present, there are many technical challenges in the application research of knowledge graph in power system, especially the knowledge extraction and graph construction from mixed data, as well as the cognitive reasoning and related auxiliary decision-making under the grid topology. The construction and research of knowledge graph in the field of distribution network risk prevention and control are not yet mature. In this paper, we address these issues on the basis of existing research, put forward the distribution network risk control method based on the knowledge graph, from the distribution network build process of the risk prevention and control knowledge graph, graph classification and relationship, the main building technology and power distribution network fault recognition based on knowledge graph isolation for process and other aspects in detail, Finally, combined with the actual case, the graph is displayed and applied, and the application of the knowledge graph to cope with the operation risk of the distribution network, improve the staff scheduling ability, optimize the data management and so on are actively explored.

2 Construction of Knowledge Graphs for Risk Prevention and Control of Distribution Network 2.1 Knowledge Graphs Construction Process The knowledge graph is a technical method that uses a graph model to describe the relationship between knowledge and everything in the modeling world. Each node represents an entity, and the edges connecting the nodes correspond to the relationship between the entities. The expression of the graph maps human beings. The way of cognition of the world, knowledge graph is very suitable for integrating unstructured data, discovering knowledge from scattered data, and building various knowledge points, data, business, and analysis relationships [3, 4]. This paper establishes a knowledge graph for the risk prevention and control of intelligent distribution network. The existing knowledge can be used to realize the topdown construction of the knowledge graph. At the same time, determining some elements of the graph will involve various types of semi-structured and non-structured Structured information, for example, system stability requirements, post-fault operation mode, fault handling points, etc. To ensure the completeness of the knowledge graph ontology, this paper adopts a top-down and bottom-up ontology construction method, which can not only fully apply the historical experience and traditional cases of risk prevention and control in the distribution network, but also consolidate and update the existing knowledge. Through the steps of data model construction, knowledge extraction, knowledge fusion, and knowledge processing, the original knowledge or data is formed into a knowledge graph. Firstly, based on the existing knowledge, including traditional power system knowledge and other structured knowledge about risk prevention and control of distribution network, a top-down method is used to construct the model layer to form a data model for risk prevention and control of distribution network. Meanwhile, in order to obtain standard knowledge, it is necessary to process structured data such as real-time

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operating data of distribution network and semi-structured unstructured data through knowledge extraction and knowledge fusion, and other steps; the standard knowledge refines or modifies the data model, and then realizes the bottom-up construction of the schema layer. When a certain distribution network risk treatment is added to the noncompletely structured data such as the newly identified data of the relevant knowledge, the content of the auxiliary decision-making in the data model will be updated. For the data layer, to form the knowledge expression of the same structure of interconnection, special technical means are needed to unify the data of different structural forms, and then according to the data model defined by the schema layer, the knowledge is assigned to the corresponding category, and then form a standard knowledge representation, and then through technical means such as knowledge processing, a knowledge graph is formed. When the corresponding information (such as entities, attributes, etc.) changes, the knowledge graph needs to be updated with knowledge update technology. According to the formed grid risk prevention and control knowledge graph data platform, the intelligent risk prevention and control auxiliary decision-making application of the distribution network can be realized. 2.2 Basic Data and Graph Types In the established distribution network risk prevention and control knowledge graph, structured data refers to the database in the power grid, including the real-time and historical operation data of the power grid, the attributes of the power grid equipment and its topology, and other information. Semi-structured data mainly refers to incompletely structured and fragmented data to be processed in depth, including distribution network risk data, risk level early warning data, etc. Unstructured data mainly refers to text data, including power generation scheduling, maintenance, and transfer plans, and historical emergency response plans in case of failure.

Correction Prior knowledge Traditional power knowledge system

Case graph Data model

Form

Information Str ucture

Knowledge base Guidance Semi/Unstructur ed data Unit combination, power generation scheduling, maintenance plan

Form

Concept mapping

Entity mapping Entity quer y

Str uctured data Form Transformer Property par ameters Transformer wor king condition

Str uctured data Case base

Relevant decisions

Emer gency Management Pr ogram

Gr id existing database

Auxiliary Decision-making graph Transfer Risk program

Knowledge extr action and recording

Distribution networ k entity graph Trans1 Switch 1 Load 1

Bus 1

New energy power generation Load 2

Entity

Line 1 Bus 3

Bus Trans2 2 Relationship

Update

Real time oper ation data

Line 2

Fig. 1. Required data and classification of knowledge graph of risk prevention and control of distribution network.

Based on the above analysis, this paper divides the distribution network risk prevention and control knowledge graph into three types: auxiliary decision-making graph,

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distribution network equipment entity graph, and case graph. The relationship between the graphs is shown in Fig. 1. The auxiliary decision-making graph defined in this paper corresponds to the risk control link. It is the core technical content in the risk control process. The purpose is to reduce the probability or severity of the risk by implementing early warning control and emergency management on the basis of risk identification and assessment. In the whole process of fault occurrence, development, control, recovery, and disposal, it provides dispatchers with a dispatching decision-making basis, suggestions, and prompts. Reduce the system from a high-risk state to a lower-risk state to prevent further deterioration of the system’s security posture. Incorporating emergency management into the last link of the power grid security risk management and control system can provide an effective supplement to the grid risk control work to deal with emergencies, and reduce the probability or severity of risks by implementing early warning control and emergency management. Based on the auxiliary decision-making knowledge base, it provides auxiliary decision-making schemes such as fault area, power loss range, transfer path, and recovery status. The distribution network entity graph represents the network topology of the actual distribution network. The entities in the power grid such as transformers, lines, switches, converters and other power distribution equipment are used as entities in the knowledge graph, and the connections between the devices are represented by the relationships in the knowledge graph. Information such as voltage, power, and frequency of electrical equipment are stored in the database in the form of attributes, and then linked to the knowledge graph. The data required for the establishment process comes from the structured database of the distribution network, and the entities, relationships, and attributes in the formed distribution network entity graph are constantly updated with the changes in information such as the update of equipment and device connections in the actual power grid and changes in the connection relationship of components. The case graph is to use information extraction technology to record and save each risk treatment, mainly to extract the time, data collection, risk identification, level assessment, early warning mechanism, and other data in the risk treatment process, and to represent the historical scheme in the form of characteristic keywords and stored in the structured case database. The update of the case is automatically generated by the machine. When handling a new case, it automatically searches and matches relevant records, pushes risk handling history and handling suggestions, and forms the historical association and multi-angle analysis of a single troubleshooting task. 2.3 Knowledge Graph Construction Technology The application technology mainly includes knowledge extraction, knowledge fusion, knowledge processing, and knowledge update. Knowledge extraction is mainly oriented to text data. It extracts available knowledge units through information technology that combines automation and semi-automation. It is a technical means to convert semi/unstructured data into structured data. Knowledge fusion aims to obtain a highquality comprehensive knowledge graph. The purpose of knowledge fusion is to clean and integrate it, so as to ensure the quality of knowledge. It is a process of aligning, correlating, and merging large amounts of data and knowledge, and removing ambiguity and redundancy [9].

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After knowledge fusion knowledge processing should be carried out. Knowledge processing is the further integration and refinement of the extracted information to form a relatively complete knowledge system. The equipment, devices, and network topology in the regional distribution network are in a state of continuous updating, and the corresponding knowledge of distribution network operation procedures, risk assessment, and fault transfer is also increasingly enriched. Therefore, knowledge updating is the process of extending or changing all kinds of knowledge information in the knowledge graph. In addition, the update of the schema layer means that new concepts are acquired after data is added, and new concepts need to be automatically added to the existing concept graph to ensure that the knowledge graph keeps pace with the times.

3 Risk Prevention and Control Process of Distribution Network Based on Knowledge Graph In this paper, the application of the knowledge graph to realize the risk prevention and control function of distribution network is presented in Fig. 2. Firstly, based on the existing grid entity data of the distribution network, it is converted into a power grid entity graph and recorded into the database. At the same time, during the operation of the distribution network, the entity graph of the distribution network is updated in realtime. Then, data generation, machine learning, deep learning, feature extraction, and other technologies are applied to the distribution network entity graph to automatically extract the key information of the distribution network. Combined with the structured knowledge network obtained by knowledge extraction, knowledge fusion and knowledge processing of textual data such as historical cases and fault transfer schemes, the risk prevention and control knowledge graph is initially formed. Humancomputer interaction

Intelligent information display

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Key information on distribution network Equip Voltage Distributed -ment level energy Automatic generated Grid entity graph Graphs update Historical records

Auxiliary formation

Form Operation data

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Operating Guidelines

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Trend forecast

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Data processing calculation

Database

Rule support Case record

Display of command results

Transfer Analysis Recommendation s

Intelligent recommendation of maintenance strategy Knowledge application

Knowledge reasoning Result analysis Running state

Fault link

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Fig. 2. Distribution network risk prevention and control knowledge graph disposal flow chart.

In practical application scenarios, by using human-computer interaction technology, related device push the information and evaluation knowledge of the power grid intelligently. On this basis, the management personnel can carry out auxiliary operations,

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so as to build a detailed and specific knowledge graph of the auxiliary decision-making of the distribution network. In addition, the knowledge graph stores a large amount of scheduling operation history and experience, which has certain reference significance for personnel scheduling and disposal operations. On the one hand, the scheduler can evaluate the operation hints online to help the machine update its knowledge and improve its analysis and decision-making ability. On the other hand, according to the experience stored in the knowledge base, the machine can also give evaluation and risk hints to the dispatcher’s operation, so as to realize two-way improvement between the machine and the machine. The graph displays knowledge structurally through rich semantic content, and dispatchers can query historical fault cases at any time for historical review and experience summary. Especially for new dispatchers, the access and learning of the whole process of historical faults can quickly improve the dispatching experience, and with the gradual accumulation of power grid fault cases and experience knowledge, the machine decision-making accuracy can be gradually improved.

4 Application of Knowledge Graph for Risk Prevention and Control of Distribution Network According to the mentioned above graph build processes and building technology, selection of Hebei north one regional actual new energy distribution network, with the grid database and the guidelines for the urban distribution network operation level and the power supply capability evaluation of unstructured knowledge as a data base, build the region distribution network digital twin system, improve the risk prevention and control knowledge graph. 4.1 Incorporate Risk Control to the Auxiliary Decision-Making Knowledge Graph Application The auxiliary decision-making graph is combined with the power grid entity graph and risk relationship knowledge graph, and based on power grid equipment entity relationship, risk analysis results, regional distribution network support emergency plan and fault handling business process, the dynamic reasoning and analysis technology of knowledge graph is used to establish power grid fault auxiliary decision-making application, as shown in Fig. 3. As shown in Fig. 3, first of all, after the power grid failure, the result of digital twin extrapolation is input into the grid equipment entity graph, use of entity concept mapping and mapping technology, setting on the risk assessment results, the feeder terminal equipment status code, with the electronic station will feeder terminal equipment status code as input, using an intelligent algorithm for fault section risk point and fault localization. After that, the risk source is determined by the inference query technique based on the risk relation graph, and the power loss range is analyzed. Based on power loss analysis, the optimization mathematical model is established with the objective function of minimizing the number of switching operations and the comprehensive index of network loss to analyze all the power supply paths of the load lost due to faults. Combined

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Fault area and outage range

Digital twin deduction data

AH #2 Bus #1

DL

BL

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GH #1

D O

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SY main

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LO

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DT

Auxiliary decisionmaking Locating the fault area

M PF Inference query power loss range and transfer path

SB Analysis of optimization calculations and recovery situations

Fig. 3. Auxiliary decision-making knowledge graph application.

with the fault isolation switch, the feasible set of fault diversion paths is analyzed. Based on the knowledge base of auxiliary decisions and the analysis and evaluation of the power grid security situation, the optimal switching scheme is determined. Finally, based on the auxiliary decision knowledge base and network security situation analysis and evaluation, complete breakdown for analysis, to determine the optimal transfer for a solution. 4.2 Application Case Fault details. Due to the line fault of GH line 1, GH line 2 and AH line, three lines were cut off, and then a large area of power loss occurred, leading to the power loss of YD station. LH line 1, LH line 2, LH line 3, LH line 5, GY line 1, GY fourth line, HX contact line No. 1, HX contact line No. 2, 110 kV AX substation, GPS/GJHS and HXGY#2 open and close stations lost power, generating relevant data in the distribution network twin. System loss statistics are as follows: HXGY#2 opening and closing station #1FOP lighting load loss is 427.5 kW, ZXP8 box body is 55.59 kW, The box body of #2FOP is 427.5 kW, ZXP13 is 55.59 kW, ZXP5 is 25.41 kW, ZXP9 is 55.59 kW and so on, a total of 18 sets, the total loss of 2951.6 kW. Fault Isolation and Recovery. By using the graph shown in Fig. 3 and inputting real data, the fault isolation and recovery process of the distribution network in this region is shown in Fig. 4. First of all, using the knowledge of the graph query function, complete the data collection, data preprocessing to distribution network twin body work, by identifying a single point of failure, the failure of multipoint, regional different fault types, auxiliary decision-making graph according to the construction of the digital model, power supply

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Risk Profile and Data

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GH#1line ... AH#1 line caused power outage on three lines due to line failure Twin body failure display part

Distribution network entity graph

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Auxiliary Decision-making Graph (Schematic,Part)

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Key information extraction of distribution network Urban distribution network, substation level, new energy grid connection etc The closed switches include 527 switch of 110kV AX substation...etc

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Risk Analysis D ata Requirements Checklist(Part) Require Syste Dep. Use ment m EPI

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The closed equipment includes 511 switch and 512 switch of 220kV GYS substation #527 switch of 110kV AX substation. System solution part

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Fig. 4. Application example of risk prevention and control knowledge graph in distribution network.

network topology information, respond to lose electric analysis and auxiliary decisionmaking plan. The auxiliary decision analyzes the line outage from the perspective of power loss risk and determines the closed isolation range. Further analyze the risk level, affected location, power loss, and solution of each faulty line. In the part of the recovery scheme, it is necessary to determine the transfer scheme, decide the optimal scheme, and judge the ring-closing and ring-breaking switch. That is, isolating the faulty line switch and using the power supply mode of the normal line or the standby line to restore the power supply of the lost box transformer, lighting system, and substation. The scheme given in the final graph is shown in system. The next step is to analyze the recovery situation, such as the recovery rate, the degree to which the recovered electricity users reach the standard, the electricity records of the users who have not returned, and other related indicators, complete the risk treatment, and feedback to the digital twin of the power grid for display. Finally, the relevant information is extracted and stored in the case graph. By using the human-computer interaction technology, the staff can easily and quickly query the information of any link in the fault isolation and recovery, and achieve the depth and efficiency of the risk prevention and control work.

5 Conclusion In this paper, the knowledge data model of knowledge graph is applied to the field of distribution network risk prevention and control, this paper proposes a distribution network risk control method based on the knowledge graph, from the graph building, evaluation process, graph application three aspects has carried on the train of thought and method is discussed in detail, combined with the related application cases, knowledge graph in distribution network is discussed the role of risk prevention and control, it

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provides ideas to deal with the risks of the new form of power grid under the background of “double high” power grid. At the same time, it also has certain positive significance to improve the security and reliability of distribution network, and realize the artificial intelligence of power system combined with digital twin technology.

References 1. Ju, P., Zhou, X., Chen, W., et al.: “Smart grid plus” research overview. Electr. Power Autom. Equip. 38(5), 2–11 (2018) 2. Qiao, J., Wang, X., Bai, S., et al.: Framework and key technologies of knowledge-graph-based fault handling system in power grid. Proc. CSEE 40(18), 5837–5948 (2020) 3. Li, X., Xu, J., Guo, Z., et al.: Construction and application of knowledge graph of dispatching automation system. Electr. Power 52(2), 70–77 (2019) 4. Lin, X., Bai, X., Wang, L., et al.: Review and trend analysis of knowledge graphs for crop pest and diseases. IEEE Access 7, 62251–62264 (2019). https://doi.org/10.1109/ACCESS.2019. 2915987 5. Yu, S., Xi, Y., Peng, B., et al.: Research on comprehensive evaluation of distribution network based on knowledge graphs. In: 2021 IEEE 2nd China International Youth Conference on Electrical Engineering (CIYCEE) (2021) 6. Medjroubi, W., Müller, U.P., Scharf, M., Matke, C., Kleinhans, D.: Open data in power grid modelling: new approaches towards transparent grid models. Energy Rep. 3, 14–21 (2017) 7. Bikel, D.M., Miller, S., Schwartz, R., et al.: Nymble: a high-performance learning name-finder. In: Proceedings of the Fifth Conference on Applied Natural Language Processing Stroudsburg: Association for Computational Linguistics, pp. 194–201 (1997) 8. Passos, A., Kumar, V., Lexicon, M.A.: Infused phrase embeddings for named entity resolution. In: Proceedings of the Eighteenth Conference on Computational Natural Language Learning, pp. 78–86. Association for Computational Linguistics, Baltimore, MD, USA (2014) 9. Lin, H., Wang, Y., Jia, Y. et al.: Network big data oriented knowledge fusion methods: a survey. Chin. J. Comput. 40(1), 1–21 (2017)

sDFT Based IRP Detection of the Electrical Excited Synchronous Machine Xiao Fu1(B) and Kun Xia2 1 Public Experiment Center, University of Shanghai for Science and Technology,

Shanghai 200093, China [email protected] 2 School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Abstract. The advantages of electrical excited synchronous motors (EESM) are adjustable power factor, high efficiency, controllable excitation current and small moment of inertia, thus they are widely used in high-power industrial applications, such as mine hoisting and steelmaking. Now they are also favorable in the highperformance electrical vehicles. In the vector control of the EESM, the detection accuracy of the initial rotor position (IRP) directly decides whether the motor can start correctly and smoothly. The traditional pure integral stator flux linkage model has problems such as integrator drift and saturation due to DC offset. In this paper, the fundamental component of the induced voltage was extracted by the sliding discrete Fourier transform (sDFT). An sDFT-based method for detecting the IRP of the EESM was designed. The method could effectively extract the fundamental signals, so as to accurately detect the rotor initial position angle of the synchronous motor. Experimental results confirmed the detection accuracy of the rotor initial position angle for the synchronous motor vector control system. Keywords: Sliding discrete Fourier transform · Electrical excited synchronous motors · Initial rotor position detection

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 269–278, 2023. https://doi.org/10.1007/978-981-99-4334-0_34

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1 Introduction EESM have been widely used in the high-power industries. The traditional applications are mining and steelmaking [1–3]. Now they are also favourable in the high-performance electrical vehicles [4, 5]. In the vector control system of EESM, the IRP detection accuracy of the directly decides whether the motor staring performance. With an inaccurate IRP, the starting performance of the system will be reduced due to the inaccurate observation of the stator flux linkage at the motor starting state, and sometimes the EESM will even fail to start. Therefore, it is necessary to accurately detect the IRP of the EESM. The basic principle of the initial positioning of the traditional EESM is that when the stator winding is not energized, a step excitation voltage is applied to both ends of the rotor winding. Induce the electromotive force, use the traditional voltage model to integrate the potential to obtain the stator flux linkage, and calculate the magnitude of the magnetic flux and the position angle of the flux linkage. Since the stator is not energized during positioning, the air-gap magnetic flux at this time is the rotor magnetic flux [6, 7], and the obtained magnetic flux electrical angle can truly reflect the rotor magnetic pole position. Although the traditional pure integral stator flux linkage model is relatively simple in form, there are the following problems in practical applications: a) A small DC offset or drift in the voltage/current measurement channel may cause saturation of the integrator [8, 9]; b) The initial value of the integral makes the observed flux linkage amplitude DC offset; c) The high frequency interference introduced by the PWM converter. All the above problems will lead to errors in the observation of the IRP. To solve the above problems, this paper improves the traditional initial positioning method, which adopts the method of passing AC sinusoidal current excitation into the static rotor winding, and uses the existing voltage sensor in the speed control system to detect the induced voltage in the three-phase winding of the stator, and constructs an improved IRP method.

2 Rotor Position Angle Detection Principle The rotor of the three-phase squirrel-cage asynchronous motor is symmetrical in all directions, so the d-axis can be defined in any direction, and no initial positioning is required. The EESM is different, the d axis is on the axis of the excitation winding, so the synchronous motor vector control system requires that the rotor position must be determined first before the motor starts. Estimation methods of the IRP for the permanent-magnet synchronous motor (PMSM) have been extensively reported, such as PLL [10] high-frequency harmonics injection [11] extended Kalman filter [12] and extended-EMF [13]. Since the rotor flux of PMSM is almost constant, the rotor cannot be controlled, and the rotor position needs to be calculated by the stator voltage and the stator current. However, it’s very difficult to directly measure the motor state voltage, and this will introduce calculation errors. As a comparison, the control of rotor flux of the EESM is much easier, since it can be separately controlled by the rotor excitation system. The existence of rotor exciting coils offers a great flexibility in adjusting the rotor flux and the induced stator back EMF. For

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EESM, a DC step excitation signal was used by the traditional IRP detection methods. But if the rotor is suddenly excited by DC, the voltage induced by the stator winding will decay quickly, and in the actual system, the pure integral flux linkage observer cannot eliminate the integral initial value. Therefore, in order to obtain an accurate IRP signal, the rotor winding is fed with a constant sinusoidal AC excitation, and the pure integral link is improved. During the initial positioning, the rotor winding is fed with a constant sinusoidal AC voltage, and the three-phase winding of the stator induces a sinusoidal voltage. After reaching a steady state, the voltages of the three-phase windings of the stator are different. Ideally, the motor stator voltage vector should be perpendicular to the stator flux linkage. But when there is a DC error, the relationship between the observed induced voltage, flux linkage and rotor position angle is esβ = ±b · cos θ + βsβ esβ = ±b · cos θ + βsβ

(1)



a sin θ + βsα T ω  b = esβ dt = ± sin θ + βsβ T ω

ψsα = ψsβ

esα dt = ±

ϕ = arctan

ψsβ ψsα

(2) (3)

where, β sα and β sβ is the unknown DC residual compensation error, a and b represents the voltage amplitude, θ and ω are the angle and angular frequency of the induced voltage cosine component, respectively, T is the integration period. In the actual system, a  β sαβ , However, due to the existence of the pure integral link, the small error will still lead to the offset of the integral flux linkage, so it must be eliminated. When θ = π, 2π, 3π, …, esα = 0. At the zero-crossing point of the β-axis voltage, the α-axis stator flux linkage is ψsα = βsα Tz

(4)

where, T z is the period of voltage zero-crossing. Similarly, when the voltage of the α-axis is zero, the flux linkage of the β-axis becomes ψsβ = βsβ Tz

(5)

The DC offset error and high-frequency noise will affect the detection of the IRP. Besides, since the rotor winding is controlled by the H-bridge converter, the excitation current is affected by the dead zone and the nonlinearity of the PWM converter, which makes the induction in the stator winding. As a result, the voltage waveform is distorted, which affects the detection accuracy of the IRP. In this paper, to accurately extract the fundamental signal waveform from noise, DC offset, PWM dead zone and other nonlinearity factors, the sDFT method is used.

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3 Principles of sDFT Define x(n) as a finite-length sequence with length N, and its discrete Fourier transform is X (k) = DFT [x(n)] =

N −1 

x(n)WNnk , (0 ≤ k ≤ N −1)

(6)

n=0

where, WN = e−j2π/N . Expanding (6) we can get X (k) = x(0) + x(1)e−j

2π k N

+ x(2)e−j

2π k∗2 N

+ · · · + x(N − 1)e−j

2π k∗(N −1) N

(7)

The graphical representation of x(n) is shown in Fig. 1, where x 0 represents the first set of data, x 1 represents the following sampling point, and the corresponding Fourier transforms of the two sets of data are X 0 (k) and X 1 (k), where X0 (k) = x(0) + x(1)e−j

2π k N

+ x(2)e−j

2π k∗2 N

+ · · · + x(N − 1)e−j

X1 (k) = x(1) + x(2)e−j

2π k N

+ x(3)e−j

2π k∗2 N

+ · · · + x(N )e−j

2π k∗(N −1) N

2π k∗(N −1) N

(8)

Combine (8) and Fig. 1, we can get X1 (k) = [X0 (k)0 − x(0)]ej

2π k N

+ x(N )e−j

= [X0 (k) − x(0) + x(N )]ej

2π k N

2π k(N −1) N

(9)

x0

0

1

N -1

2

N

N+1

N+2

x1

Fig. 1. Data diagram of the sDFT.

From the above formula, to calculate the discrete Fourier transform X 1 (k) of data x 1 , it is only necessary to subtract x(0) plus x through X 0 (k) of the previous data x 0 (N), and finally calculate the phase shift of the result to obtain X 1 (k). Therefore, to calculate the Fourier transform of x 1 , you only need to know X 0 (k), and then perform 2 real additions and 1 complex multiplication. This method is sliding DFT (sDFT). It can be shown that the ratio of FFT to sDFT computation is (log 2N)/2, especially when N is large, sDFT can improve the computational efficiency more [14–16]. Because the computational complexity of sDFT is quite small, it can accurately reproduce the fundamental signal. Therefore, in order to suppress the influence of DC drift and high-frequency signal interference caused by sampling, this paper uses sDFT to restore the fundamental voltage waveform induced in the stator winding, and for the rapidity of sDFT calculation, DSP programming is used to detect the IRP.

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4 Detection Method Based on sDFT The rotor is fed by a sinusoidal excitation method to avoid the problem of rapid attenuation of the rotor sudden DC excitation voltage; and based on the sDFT principle, the DC error caused by sampling and the stator induced voltage distortion can be suppressed. For this reason, based on the sDFT principle, this paper detects the IRP of EESM. The diagram of the main circuit is shown in Fig. 2. Inverter

ud

ua ub

udcf if*

PR Regulator

-

H Bridge

SM

+ -

if Fig. 2. Main circuit diagram of the IRP detection.

Because the air-gap flux fields passes through the sinusoidal excitation current, the induced stator voltage and flux linkage will also change according to the sinusoidal law, so the sign of the fundamental wave flux linkage is exactly opposite before and after the zero-crossing point in one cycle, and the detected rotor position angle will generate a zero point at this time. Drift. In order to avoid zero drift affecting the detection of the rotor position angle, the quadrant of the position angle should be judged. First, sample the flux linkage values in the first half cycle of the fundamental wave flux linkage ψ sα and ψ sβ . According to the symbols of the flux linkage ψ sα and ψ sβ , the quadrant of the rotor position angle and the values of the symbols A and B can be determined, as shown in Table 1 shown. Table 1. Quarters of the rotor angle position and signs. Magnet signs

Quadrant

Symbol signs

ψ sα > 0, ψ sβ > 0

1

A = 0, B = 1

ψ sα < 0, ψ sβ > 0

2

A = 1, B = − 1

ψ sα < 0, ψ sβ < 0

3

A = − 1, B = 1

ψ sα > 0, ψ sβ < 0

4

A = 0, B = − 1

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Then the fundamental flux linkage amplitude output by sDFT |ψ sα | and |ψ sβ | and A and B Send it to the arctangent calculation module; Then the rotor initial position angle ϕ is    (10) ϕ = A · π + B · atan2 |ψsα |, ψsβ  The software block diagram is shown in Fig. 3.

esα

ua

3s/2s Transfo rm

ub

Amplitude Calculation Quadrant Calculation

esβ

sα

1 s

sα

A B

sβ

sDFT

sβ Equ(10)

Fig. 3. Flowchart of the control algorithm.

5 Experiment Results The experimental platform is shown as Fig. 4(a), and its parameters is shown in Table 2. The proposed sDFT-based detection method is experimentally verified on this platform. In the experiment, the rotor current if uses an H-bridge inverter to supply power to the rotor winding, and the rotor is fed with a sinusoidal excitation current, whose peakto-peak value is 1A, the frequency is 5Hz, and the number of sDFT points is 128. The excitation current waveform is shown in Fig. 4(b) (CH1), and the induced voltage waveform of the stator A-phase winding is shown in Fig. 4(b) (CH2). It can be seen from Fig. 4(b) (CH2) that due to the sampling error and noise affecting the stator induced voltage waveform, it cannot directly participate in the rotor position angle detection, and further processing is required. When the actual rotor position angle is 60°, the fundamental wave flux linkage ψ sα and ψ sβ waveforms restored by sDFT are shown in Fig. 5. The detection result of the IRP is shown in Fig. 6 (CH1). Figure 6 (CH2) shows the IRP drift caused by the arctangent calculation when the flux linkage crosses the zero axis. Using the actual value of the

sDFT Based IRP Detection of the Electrical Excited Synchronous Exciting current(1A/div)

Load Machine

Synchronous Machine

275

Stator voltage(10V/div)

t(100ms/div)

(a) test platform

(b) tested waveform

Fig. 4. Waveforms of the exciting current and induced voltage in the stator.

Table 2. Parameters of the experimental system. Module

Rating

Power module

1700 V/650 A

Voltage sensor

LV28-P/600 V

Current sensor

LT508/500 A

Exciting coils power module

600 V/50 A

Exciting coils voltage sensor

LV28-P/600 V

Exciting coils current sensor

LA28-NP/25 A

Synchronous motor

JT-50/50 kW

Encoder

1024 incremental

Motor load

40 kW induction motor

Control chip

TMS320F28335

IRP as the abscissa, and the detected value and error of the rotor position angle as the ordinate, the experimental result curve is shown in Fig. 7. From the error curve in Fig. 7, it’s shown that the linearity between the detected value of the IRP and the actual value is good, and the IRP error is limited within the range of ± 1° (electrical angle), which meets the requirements of the synchronous motor vector control system when starting.

X. Fu and K. Xia

Ψ(5Wb/div)

-axis flux

-axis flux

t(100ms/div)

Detected initial rotor angle

Fig. 5. sDFT filtered fundamental stator flux.

Proposed method

Zero drift

t(25ms/div)

Detected angle(deg)

Fig. 6. Detected IRP by sDFT.

Error(deg)

276

Actual rotor postion angle(deg)

Fig. 7. Results of the IRP detection.

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6 Conclusion A sDFT-based EESM IRP detection method was designed. To solve the pure integrator problem of the tradition DC step method, the rotor winding was fed with a constant sinusoidal AC excitation, thus the steady state values were used, compare to the previous transient decay signals. Since the fundamental voltages were mixed with noise, the sDFT method was used to get the fundamental signals in the stator induced voltages. The accuracy of the designed method was verified by experiments results.

References 1. Gieras, J.F.: Electrical Machines: Fundamentals of Electromechanical Energy Conversion. CRC Press (2016) 2. Long, Q., Zhou, Z., Lin, X., Liao, J.: Investigation of a novel brushless electrically excited synchronous machine with arc-shaped rotor structure. Energy Rep. 6(9), 608–617 (2020) 3. Yang, Q., Pang, L., Shen, H., Qin, H., Zhao, C.: Influence of excitation current on electromagnetic vibration and noise of rotor magnetic shunt hybrid excitation synchronous motor. Energy Rep. 8(10), 476–485 (2022) 4. BMW high-performance excitation synchronous motor system won the “innovative technology” award. In: World New Energy Vehicle Congress. Beijing (2022) 5. Xu, D., Li, N., Li, Q., Kong, Y., Lin, M.: Investigation on the field regulation capacity in a hybrid excited axial field flux-switching permanent magnet machine for EV application. Energy Rep. 8(15), 696–703 (2022) 6. Jain, A.K., Ranganathan, V.T.: Modeling and field oriented control of salient pole wound field synchronous machine in stator flux coordinates. IEEE Trans. Industr. Electron. 58(3), 960–970 (2011) 7. Feuersänger, S., Pacas, M.: Enhanced estimation of the rotor position of MV-synchronous machines in the low speed range. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 4481–4487 8. Lee, S., Kim, H., Lee, K.: Current measurement offset error compensation in vector-controlled SPMSM drive systems. IEEE J. Emerg. Sel. Top. Power Electron. 10(2), 2619–2628 (2022) 9. Bi, G., Wang, G., Zhang, G., Zhao, N., Xu, D.: Low-noise initial position detection method for sensorless permanent magnet synchronous motor drives. IEEE Trans. Power Electron. 56(6), 7032–7043 (2020) 10. Yu, L., Wang, D., Liu, Z., Zheng, D., Li, W.: A DPS-PLL based rotor position estimation method for permanent magnet wind turbine. Energy Rep. 7(6), 502–507 (2021) 11. Kozakura, T., Nimura, T., Doki, S.: The improvement of initial rotor position estimation method with extended-EMF available at overall speed range by exciting with speed and signal injection. In: 2020 23rd International Conference on Electrical Machines and Systems (ICEMS) 12. Nicola, M., Nicola, C.-I.: Sensorless control of PMSM using fractional order SMC and extended Kalman observer. In: 2021 18th International Multi-Conference on Systems, Signals and Devices (SSD) 13. Kyung-Rae, C., Jul-Ki, S.: Pure-integration-based flux acquisition with drift and residual error compensation at a low stator frequency. IEEE Trans. Ind. Appl. 45(4), 1276–1285 (2009)

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14. Jacobsen, E., Lyons, R.: The sliding DFT. IEEE Signal Process. Mag. 20(2), 74–80 (2003) 15. Jacobsen, E., Lyons, R.: An update to the sliding DFT. IEEE Sig. Process. Mag. 21(1), 110–111 (2004) 16. Chen, D., Lin, Y., Xiao, L., Xu, Z., Lian, H.: A harmonics detection method based on improved comb filter of sliding discrete Fourier for grid-tied inverter. Energy Rep. 6(9), 1303–1311 (2020)

A Unified Startup Control Strategy for Modular Multilevel Converter with the Supercapacitor Energy Storage System Song Han1 , Tianbai Deng1(B) , Tao Yuan1 , Qianlong Zhu1 , Jun Tao1 , Huaying Zhang2 , and Qing Wang2 1 School of Electrical Engineering and Automation, Anhui University, Hefei 232000, People’s

Republic of China [email protected] 2 New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid, Shenzhen Power Supply Co., Ltd., Shenzhen 518000, People’s Republic of China

Abstract. Renewable energy sources have developed rapidly, presenting higher demands on grid development and construction. Modular multilevel converters with the supercapacitor energy storage system (MMC-SCESS) can compensate the impact of active power, and suppress the oscillation and power fluctuation to maintain the stability of the power grid. This paper analyzes the working principle and control methods of the MMC-SCESS under different operating modes. Then a precharge control strategy for MMC-SCESS is proposed. The strategy can realize the constant current charging of MMC-SCESS in ac-side. Under the proposed control strategy, the MMC-SCESS can complete the startup steadily and quickly with different initial conditions and component parameters of the supercapacitor. Finally, the feasibility of the proposed startup control strategy is verified by simulation. Keywords: Modular multilevel converter with the supercapacitor energy storage system (MMC-SCESS) · Closed-loop startup control · Constant power control

1 Introduction New energy sources have developed rapidly in recent years, and renewable energy sources are widely used. However, the uncertainty and fluctuation of new energy sources limit the efficiency of electric energy utilization. Adding energy storage devices can improve the efficiency of electric energy utilization, and inhibit high-power shocks and grid oscillations [1–3]. Compared with batteries, the supercapacitor is an energy storage element with higher power density and higher cycle times [4], which can be applied in scenarios with frequent charging and discharging. It is observed that the characteristics of SCESS meet the needs of new energy systems. The modular multilevel converter (MMC) is flexible and modular and can adapt to various voltage levels, which has a wide range of applications in the field of medium and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 279–287, 2023. https://doi.org/10.1007/978-981-99-4334-0_35

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high voltage [5–7]. Before entering the steady-state operating mode, a startup strategy is needed to boost the voltage of submodule capacitance to the rated operating range and avoid damage to components such as IGBTs. The current research on self-excited starting has been more mature. The MMC absorbs energy from the DC side or AC side by controlling submodules method, such as charging one by one, charging in groups, or gradually reducing the number of submodules [8–10]. These methods limit the charging current magnitude but do not control the charging current. In [11], a closed-loop controlled constant-current pre-charging strategy was proposed, which has good robustness and anti-interference capability. The MMC with the supercapacitor energy storage system has further expanded the application scope of MMC, and its control strategy and optimization strategy have also been studied [12–14]. However, the startup strategy for MMC-SCESS has not received too much attention. This paper proposes a closed-loop-based MMC-SCESS startup control strategy. The DC side of MMC-SCESS explored in this paper has no active system supply, so the capacitor can only be charged through the AC side, as the DC side startup method is not studied. Section 2 analyzes the operation control mode of MMC-SCESS. Section 3 analyzes the closed-loop control of MMC-SCESS startup and the constant power control of the bidirectional DCDC converter. Section 4 verifies the effectiveness of the MMCSCESS startup strategy through Simulink. Section 5 concludes this article.

2 Basic Analysis of the MMC-SCESS The MMC-SCESS can realize power compensation to the grid and the circuit topology of a typical MMC-SCESS is shown in Fig. 1.

Icabc

SM1

SM1

SM1

Ipa

Ipb

Ipc

SMn

SMn

SMn

R0

R0

R0

L0

L0

L0

R0

R0

R0

L0

L0

L0

SM1 Ina

SM1

SM1

Inb

Inc

SM

SM S1

SMn

SC

S3 + CSM _

S2 SMn

DC/DC Converter

S4

+ _CSC

SMn

Fig. 1. Topology of the MMC-SCESS.

Each arm of MMC-SCESS contains N half-bridge submodules, and U sm is the voltage of submodule capacitance. To ensure that active power can flow in both directions,

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a supercapacitor is connected in parallel on the DC side of each submodule through a bidirectional DC/DC converter. Considering that the voltage of the supercapacitor is lower than the voltage of the submodule supercapacitor, the supercapacitor is on the low-voltage side of the bidirectional DC/DC converter to improve the utilization of the supercapacitor [11]. Each submodule can be considered as a distributed power module. The basic control strategy of MMC-SCESS is divided into inner loop control and outer loop control, as shown in Fig. 2(a). The outer loop control provides the reference current for the inner loop control. The outer loop control takes the active and reactive components as input signals. The active component can be the DC side voltage or AC grid frequency, or the active power can be used as the active component. The reactive component contains the grid AC voltage or the reactive power. The active component and reactive component selected in the paper are active power and reactive power. During active power regulation, the submodule capacitor exchanges power with the supercapacitor through a bidirectional chopper circuit, and the capacitor voltage is maintained in a stable range. The control diagram is shown in Fig. 2(b). + Usd Pref

+ -

Qref

+

Gp_PI

Icdref + Icd -

P

Icq Q Gp_PI

Icqref

+

GPId

+

Udiffdref -

L L GPIq

Usm_ref

+

GPI 1

Isc_ref +

GPI 2

dsc

-

-

Udiffqref

+

+

Usm_ave

Isc

+ Usq (a)

(b)

Fig. 2. (a) Current control block diagram of MMC; (b) control diagram of bidirectional DC–DC converter.

U smref denotes the reference voltage value of the submodule capacitor. U smave denotes the average value of the same phase upper and lower arm module capacitance voltages. I sc denotes the supercapacitor current.

3 The Precharge Strategy of the MMC-SCESS The charging process can be divided into the uncontrolled charging stage and the closedloop precharge stage. 3.1 Uncontrollable Precharge Stage of MMC-SCESS The MMC-SCESS uncontrolled charging phase has all submodules in the blocked state. As all submodules of the arm are bypassed, the forward charging current is through diode S2, and the reverse current flows out of this module through S1. As shown in Fig. 3, the upper arm of the highest AC side voltage phase is in the bypass state and the other phases are charged. The lower arm of the lowest AC side voltage phase is in the bypass state and the submodule of other phases is charging, where Rslim is the uncontrolled charging current limiting resistor. All submodule capacitors are connected to the main

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circuit in parallel. There is a maximum charging upper limit for the capacitor voltage of each submodule: √ 3Us (1) USM _uc = N

p3

+

p2

+

p1

Ipcharge R sl im Uc1

Us1

Uc2

Us2

Uc3

Us3

S1 n3

n2

+

n1

+ Incharge

Csm

S2

Fig. 3. Uncontrolled startup of the MMC-SCESS (U s1 > U s2 > U s3 ).

The charging current will drop rapidly as the submodule capacitor voltage rises, and the charging efficiency will decrease. In most cases, the voltage of the submodule capacitor is lower than the rated operating voltage at this time, and the MMC-SCESS needs to be further charged. 3.2 Closed-Loop Precharge Stage of the MMC-SCESS After the uncontrolled charging phase, the AC side voltage of MMC is consistent with the grid voltage. To further improve the capacitor voltage of the submodule, it is necessary to control the MMC submodule to change the AC side voltage. The ideal active precharge is that MMC can absorb constant active power. When the active power input of the MMC-SCESS is constant, the d-axis icharged current is constant, and the q-axis current is 0. The closed-loop reference current of MMC SCESS is: icharged =

2 qchargeref 3 ucd

(2)

Similar to the uncontrolled charging stage, the upper and lower arm charging in closed-loop charging stage also follows the principle that the upper arm of the highest phase voltage is blocked, and the lower arm of the lowest phase voltage on the AC side

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is blocked. The blocked submodule current does not charge the submodule capacitor. Therefore, there are different control logics in the control process of the upper and lower arms during the active pre-charging process. Make the voltage at the AC side of U c1 the highest and the voltage at the cross-current side of U c3 the lowest. At this time, all the submodules of the upper arm of the highest voltage phase U p1 are controlled to be in the locked state. The charging current flows through the locked p1 arm. The current is diverted to the bypass submodules of the p2 and p3 arm pairs for charging. At the same time, all submodules of the U s3 phase lower arm are locked. The current is shunted from the locked U s3 lower arm to the n1 and n2 arms to charge the submodules of the bypass. The generation logic of modulated signal is shown in Table 1. Table 1. Calculation formula of the arm reference voltage. Voltage of upper arm

U p1

U p2

U p3

Reference voltage

0

U cp1 −U cp2

U cp1 −U cp3

Voltage of lower arm

U n1

U n2

U n3

Reference voltage

U cn1 −U cn3

U cn2 −U cn3

0

U cni , U cni (i = 1, 2, 3) denotes the reference voltage value of closed-loop control

3.3 Precharge Method of the MMC-SCESS Supercapacitor The precharge process of the MMC-SCESS supercapacitor is carried out simultaneously with the active pre-charge process. The charge power of the MMC-SCESS is determined and controllable. The constant power charging control strategy of the supercapacitor can improve the flexibility of power distribution. The constant power control strategy is shown in Fig. 4. Pscref

+

Psc

-

Usc Isc

×

PI

Iscr ef Isc

V3

V3 V4

+

CSC

+

PI d

PWM

V4

Fig. 4. Structure of constant power control for DC–DC converter.

The constant power controller uses the double closed-loop control method. The inner loop of inductance current and the outer loop of power. At the initial moment of supercapacitor charging, because the voltage of the supercapacitor is low, the amplitude of the supercapacitor charging current is high and changes rapidly. The supercapacitor withstands a great impact.

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At the initial moment, the calculated I scref generated by the outer loop control is too large. Therefore, slope control is introduced to limit the size and change rate of the charging current of the supercapacitor to avoid the supercapacitor to withstand a large impulse current.

4 Simulation and Analysis of Precharge Strategy In this paper, the MMC-SCESS model is built using Matlab/Simulink software to verify the charging strategy proposed in the previous article. The detailed parameters of the simulation are shown in Table 2. Table 2. Parameters of the MMC-SCESS. Parameter

Value

Parameter

Value

Number of SMs per arm N

4

SC capacitance C CS /F

2

Arm resistor R0 /Ω

0.02

DCDC inductor L/H

2 × 10–3

Arm inductor L 0 /H

4 × 10–2

SM capacitance Rslim /

20

SM capacitance C SM /F

5 × 10–2

Reference charging current Iac/A

400

As shown in the simulation, the starting charging current is limited to about 700 A with the current limiting resistor. At t = 0.8 s, the current limiting resistor is bypassed, and the submodule capacitor charging current rises rapidly. When the capacitor voltage of the submodule increases, the voltage difference between the MMC-SCESS and the main circuit decreases, which leads the charging current and the charging speed to a decrease. t = 5.219 s, the capacitor voltage of the submodule reaches the maximum voltage of the uncontrolled charging theory, and the uncontrolled charging phase ends. The supercapacitor is not charged at this stage, and the voltage and current are both 0. Upper arm current

400

400

200

200

0

0

-200

-200

-400

-400

-600

0

2

4

6 t/s

8

Lower arm current

600

Inj/A

Ipj/A

600

10

12

-600

0

2

4

6 t/s

8

10

12

Fig. 5. Startup performance of charge currents.

At time t ∈ [5.428 s, 11.807 s], the controller operates on the closed-loop charging stage. The main circuit current during active charging is the sum of the upper

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UAsc/kV

6 4 2 0 0

2

4

6 8 t/s

10

12

UBsc/kV

6 4

2 0 0

2

4

6 8 t/s

10

6 4 2 0 0

2

4

6 8 t/s

10

1.2 0.8 0.4 0 0

4

6 8 t/s

10

12

2

4

6 8 t/s

10

12

2

4

6 8 t/s

10

12

0.8

0.4

1.2 0.8 0.4 0 0

12

2

1.2

0 0

12

UCsc/kV

UBsm/kV

UBsm/kV

UAsm/kV

and lower arm currents, and the upper and lower arm capacitor charging is carried out simultaneously. As shown in Fig. 5, the upper and lower arm currents are I ac /2. At time t ∈ [5.428 s, 6.428 s], the controller operates on the slope control stage. Figures 6 and 7 are the voltage of capacitance and supercapacitor charging current. The rising rate of the supercapacitor voltage is lower than the voltage of the submodule capacitor, and the charging current of the supercapacitor is about 600 A. At time t = 6.2 s, the constant current charging power is the same as the constant power charging power, and the charging mode is switched to constant power charging mode. At t = 11.813 s, the submodule capacitor and the supercapacitor get the rated operating voltage, and the MMC-SCESS pre-charging is completed.

0 2 4 6 8 10 12 t/s (a)

0 2 4 6 8 10 12 t/s

IAnsc/A

IApsc/A

6

8 10 t/s

8 10 t/s

12

6

8 10 t/s

12

6

8 10 t/s

12

6

8 10 t/s

12

600 400 200 0

12

600 400 200 0 6

600 400 200 0

12

600 400 200 0

0 2 4 6 8 10 12 t/s 600 300 0 -300 -600

8 10 t/s

IBnsc/A

600 300 0 -300 -600

6

ICnsc/A

600 300 0 -300 -600

ICnsm/A

ICpsm/A

0 2 4 6 8 10 12 t/s

600 400 200 0

0 2 4 6 8 10 12 t/s

IBpsc/A

600 300 0 -300 -600

IBnsm/A

IBpsm/A

0 2 4 6 8 10 12 t/s

600 300 0 -300 -600

ICpsc/A

600 300 0 -300 -600

IAnsm/A

IApsm/A

Fig. 6. Startup performance of arm SM capacitor voltages.

600 400 200 0

(b)

Fig. 7. (a) Start-up performance of arm SM capacitor currents; (b) start-up performance of arm supercapacitor currents.

There is no imbalance between the submodule capacitor voltage and supercapacitor voltage in each phase and arm during the MMC-SCESS start-up. The maximum grid

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charging current is about 700 A and the maximum IGBT charging current is near 800 A, which is in line with the actual application limits. In summary, it can be seen that the MMC-SCESS startup is feasible and can complete the pre-charging process in a stable and fast manner.

5 Conclusion This paper developed a startup control strategy for MMC-SCESS, which not only retains the advantages of a stable and fast MMC closed-loop control strategy but also has good adaptability for supercapacitor. This control strategy of MMC-SCESS can achieve stable and effective startup under different element parameters. Acknowledgments. This work was supported by the Science and Technology Project of China Southern Power Grid(090000KK52190169/SZKJXM2019669). The authors would like to appreciate thank to all the members of the team.

References 1. Guo, Z., Wei, W., Chen, L., Dong, Z.Y., Mei, S.: Impact of energy storage on renewable energy utilization: a geometric description. IEEE Trans. Sustain. Energy 12(2), 874–885 (2021). https://doi.org/10.1109/TSTE.2020.3023498 2. Mohammadi, F., Gholami, H., Gharehpetian, G.B., Hosseinian, S.H.: Allocation of centralized energy storage system and its effect on daily grid energy generation cost. IEEE Trans. Power Syst. 32(3), 2406–2416 (2017). https://doi.org/10.1109/TPWRS.2016.2613178 3. Chai, H., Zhang, X., Li, M., et al.: Mechanism for photovoltaic generation system suppressing power system oscillations. Power Syst. Technol. 45(5), 1809–1817 (2021) (in Chinese) 4. Grbovíc, P.J.: Ultra-Capacitors in Power Conversion Systems: Analysis, Modeling and Design in Theory and Practice (2013) 5. Liu, X., Lv, J., et al.: A novel STATCOM based on diode-clamped modular multilevel converters. IEEE Trans. Power Electr. (2017) 6. Freytes, J., et al.: Dynamic analysis of MMC-based MTDC grids: use of MMC energy to improve voltage behavior. IEEE Trans. Power Delivery 34(1), 137–148 (2019). https://doi. org/10.1109/TPWRD.2018.2868878 7. Xia, B., et al.: Decentralized control method for modular multilevel converters. IEEE Trans. Power Electron. 34(6), 5117–5130 (2019). https://doi.org/10.1109/TPEL.2018.2866258| 8. Das, A., Nademi, H., Norum, L.: A method for charging and discharging capacitors in modular multilevel converter. Proc. Conf. IEEE Ind. Electron. Soc. 1058–1062 (2011) 9. Xue, Y., Xu, Z., Tang, G.: Self-start control with grouping sequentially precharge for the C-MMC-based HVDC system. IEEE Trans. Power Del. 29(1), 187–198 (2014) 10. Li, B., et al.: Closed-loop precharge control of modular multilevel converters during start-up processes. IEEE Trans. Power Electron. 30(2), 524–531 (2015) 11. Zhang, G., Tang, X., Zhou, L., et al.: Research on complementary PWM controlled buck/boost Bi-directional converter in supercapacitor energy storage. Proc. CSEE 31(6), 15–21 (2011) 12. Arunkumar, C.R., Manthati, U.B., Punna, S.: Supercapacitor voltage based power sharing and energy management strategy for hybrid energy storage system. J. Energy Storage 50, 104232 (2022)

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13. Cui, G., et al.: Supercapacitor integrated railway static power conditioner for regenerative braking energy recycling and power quality improvement of high-speed railway system. IEEE Trans. Transp. Electrif. 5(3), 702–714 (2019) 14. Lei, L.I., Jun, T.A.O., Mingxing, Z.H.U., et al.: Control strategy for MMC based on supercapacitor energy storage. Electr. Power 53(11), 15–22 (2020)

Coordinated Operation for Honeycomb Active Distribution Network with Multi-microgrids Jianzhong Wang(B) , Qingfeng Wang, Lang Shen, and Zhenhua Jiao State Grid Jiaxing Power Supply Company, Xiuzhou Branch, Jiaxing, China [email protected], [email protected], [email protected]

Abstract. Honeycomb active distribution network (HADN) is a new morphology of distribution network which provides intelligent interconnection for microgrid clusters and a promising scheme for large-scale integration and consumption of distributed renewables. However, the coordinated operation of distribution network and the microgrids in HADN is not clear. Hence, this paper proposes a distributed operation model for HADN based on the alternating direction multiplier method (ADMM) with relax and fix (RF) heuristics, where the operation schemes of microgrids and the distribution network are cooperatively optimized. Numerical results on a HADN with 7 microgrids demonstrate the effectiveness and efficiency of the proposed model and the quantitative comparison of HADN and radial active distribution network (RADN) operations are performed by using the proposed model. Keywords: Honeycomb active distribution networks (HADN) · Microgrids · Optimal operation · Alternating direction multiplier method (ADMM)

1 Introduction With the access of large-scale distributed generations (DGs) and the application of various types of flexible power devices based on power electronics, the distribution networks have become more and more massive and complex, and the safety and stability issues are becoming more prominent [1]. The difficulty and cost to solve these problems in the current radial active distribution networks (RADN) are getting higher, hence new morphology of distribution network needs to be studied. Microgrids, as an effective way to utilize distributed energy sources in the power systems, can realize large-scale and multi-type renewables for local consumption and plug-and-play. Since the increasing deployments of microgrids, the efficient and largescale application of microgrids in distribution networks needs to be studied. Some studies have shown that microgrids can be configured in series or parallel in current RADN [2, 3]. However, the low level of intelligence and ability of autonomous operation under this structure not only limits the large-scale application of microgrids but also brings challenges to the operation of the distribution networks. To this end, Ref. [4] proposes a new morphology of distribution network called the honeycomb active distribution network (HADN). Reference [5] proposes a networking © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 288–296, 2023. https://doi.org/10.1007/978-981-99-4334-0_36

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scheme for HADN and introduces its composition. Specifically, each microgrid constitutes an autonomous small power system through a standardized configuration of source, grid, load, and energy storage, which can achieve local consumption of renewables and self-balancing of supply and demand. In addition, the HADN has many advantages, such as strong network architecture, efficient consumption of renewables, flexible operation characteristics, and support for power market transactions. To further study the advantages of HADN, Ref. [6] clarified the three central features of HADNs. Reference [7] proposed a control strategy for HADN. Reference [8] studied an ES-VSC-MTDC-based energy hub for HADN. Reference [9] established a two-stage energy dispatching model based on conditional value-at-risk for HADN. Despite the existing research on HADN, there are still research gaps including (1) the coordinated operation of microgrids and the distribution network in HADN is not clear. (2) The quantitative comparison of HADN and RADN operations has not been studied. Such research gaps make it difficult to exploit the potential advantages of HADN and hinder the application of HADN. Hence, it is necessary to figure out whether HADN is effective for cooperative operation of muti-microgrids, and improving system performances by filling the above research gaps. This paper proposes an alternating direction multiplier method (ADMM) with relax and fix (RF) heuristics-based optimal operation model for HADN. Thus, the flexible operation characteristics of HADNs are effectively utilized to coordinate the load demand of different microgrids and improve the system performances. Meanwhile, autonomous management and the requirement of preserving privacy information for different entities are also realized. Furthermore, the quantitative comparison of HADN and RADN operations is performed by using the proposed model.

2 Problem Formulation 2.1 Structure of HADN The topological structure of the HADN is shown in Fig. 1, where the hexagonal areas represent the microgrids. Adjacent microgrids are interconnected with smart power/Information exchange stations (SPIES) based on power electronics and energy storage systems (ESSs) through their points of common coupling (PCC) by which the HADN is formed. Under normal operations, the internal power generations (including energy storage power supply) of each microgrid supply the local load demand. When abnormal operation or failure in a microgrid occurs, corresponding SPIES can detect the abnormal conditions and take remedial action swiftly, such as imposing power support to the abnormal microgrids and cutting off the abnormal microgrids. Therefore, the HADN can combine a series of advantages, such as high reliability of power supply, flexible operation, and efficient integration of renewables, which are difficult to be achieved simultaneously in the traditional distribution networks. 2.2 Operation Model of Microgrids The microgrids in HADN are autonomous operation systems, where the output of distributed generators and the interactions of neighboring microgrids are optimized to meet

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Microgrid 1

SPIES

viD, PiD

Microgrid 6

PCC

viM, PiM Microgrid 2

Microgrid 5

Microgrid 7

Microgrid 3

Microgrid 4

Fig. 1. Topological structure of the HADN.

the local load demand and maximize their objectives. The operation model of microgrid m is stated as follows [10]. ⎛ ⎞    CDG ME ⎠ ⎝ min (1) ag Pg,t + bi Pi,t t∈T

g∈G m

i∈C m

Subject to G ≤ PgG,max PgG,min ≤ Pg,t

(2)

G QgG,min ≤ Qg,t ≤ QgG,max

(3)

   CDG UDG M LOAD L Pg,t +Pi,t + Pg,t = Pi,t + Pi,t

(4)

g∈G i

   CDG UDG M LOAD L Qg,t +Qi,t + Qg,t = Qi,t + Qi,t

g∈G i L Pi,t =



pij,t −



j∈C i

(6)

k∈Pi

j∈C i L Qi,t =



pki,t − rki lki,t

(5)

qij,t −



qki,t − xki lki,t

(7)

k∈Pi



 M M vi,t − vj,t = 2 rij pij,t + xij qij,t − rij2 + xij2 lij,t    2pij,t     2qij,t  ≤ lij,t + vM i,t   l − v  ij,t i,t

(8)

(9)

where t, g, and m are the indices of time, distributed generator, and microgrid, respectively. i, j, and k are the indices of buses. ag , Pg CDG , and Qg CDG are production cost

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and active and reactive output of controllable DGs (CDGs) g, respectively. Pg UDG , and Qg UDG are the active and reactive output of uncontrollable DGs (UDGs) g, respectively. bm and Pi M , and Qi M are import price and active and reactive power from distribution network, respectively. Pi D and Qi D are active and reactive loads on bus i. Pi L and Qi L are active and reactive power injections on bus i. pij and qij are active and reactive power flow on line ij, respectively. Rij and x ij are resistance and reactance of line ij, respectively. vi and l ij are squares of voltage on bus i and current on line ij, respectively. (1) denotes that the microgrid minimizes its cost during the horizon, where the first and second terms are the cost of generations and import power from other microgrids, respectively. (2) and (3) are the active and reactive output constraints of generator g, respectively. (4) and (5) show the active and reactive power balance on bus i, respectively. (6) and (7) show the active and reactive injection power on bus i, respectively. (8) presents the voltage difference between bus i and bus j. (9) shows the power flow constraint on line ij, respectively. 2.3 Operation Model of Distribution Network In HADN, SPIES are operated to coordinate the power exchange among microgrids and maintain the security operation of distribution network. The operation model of distribution network is stated as follows.  ct PtSS (10) min t∈T

Subject to CH CH ,max 0 ≤ Pe,t ≤ RCH e,t Pe

(11)

DC DC,max 0 ≤ Pe,t ≤ RDC e,t Pe

(12)

DC RCH e,t + Re,t ≤ 1

(13)

CH Se,t = Se,t−1 + ηeCH Pe,t −

DC Pe,t

ηeDC

(14)

Semax ≤ Se,t ≤ Semin

(15)

   DC CH D SS L Pe,t +Pi,t − Pe,t + Pi,t = Pi,t

(16)

e∈ESS i D T L + Qi,t = Qi,t Qi,t L Pi,t =

 j∈C i

pij,t −



pki,t − rki lki,t k∈Pi

(17) (18)

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 j∈C i



qki,t − xki lki,t

qij,t −

(19)

k∈Pi



 D D − vj,t = 2 rij pij,t + xij qij,t − rij2 + xij2 lij,t vi,t    2pij,t     2qij,t  ≤ lij,t + vD i,t    l − vD  ij,t i,t

(20)

(21)

where ct and Pt SS denote the electricity price and power from the transmission network, respectively. Pe,t CH and Pe,t DC are charging and discharging power of ESS e in SPIES, respectively. Re,t CH and Re,t DC are binary variables and denote the charging and discharging states of ESS e, respectively. i M denotes the set of microgrids that connect to bus i in the distribution network. S e,t denotes the state of charge of ESS e. ηe CH and ηe DC are charging and discharging efficiency of ESS e, respectively. Pi D , and Qi D are active and reactive power injecting to microgrids, respectively. (10) denotes that the distribution network minimizes the cost of buying electricity from the transmission network. (11) and (12) are charging and discharging constraints of ESS e, respectively. (13) shows that the ESS e cannot be charged and discharged at the same time. (14) shows the state of charge of ESS e between two consecutive periods. (15) shows the limit of state of charge (SOC) of ESS e. (16) and (17) show the active and reactive power balance on bus i, respectively. (18) and (19) show the active and reactive injection power on bus i, respectively. (20) presents the voltage difference between bus i and bus j. (21) shows the power flow constraint on line ij, respectively. 2.4 Collaborative Operation Model of HADN The distribution network tends to coordinate with microgrids to obtain the optimal operation schemes during the horizon. Hence, considering all the controllable devices in distribution network, the collaborative operation model of HADN is as follows. ⎛ ⎞   G ⎝ ag Pg,t + ct PtSS ⎠ (22) min t∈T

g∈G

Subject to (2)−(9) and (11)−(21)

(23)

M D vi,t = vi,t , ∀m, ∀i ∈ C m

(24)

M D Pi,t = Pi,t , ∀m, ∀i ∈ C m

(25)

where (22) denotes that the HADN minimizes the total operation cost. (23) denotes that the constraints in microgrids and distribution network should be satisfied. (24) and (25) specifies the equality of coupling variables from the perspective of microgrids and distribution network, as illustrated in Fig. 1.

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3 Solution Algorithm 3.1 ADMM with RF Heuristics-Based Model ADMM is a distributed algorithm for solving optimization problems. It decomposes the original problem into sub-problems and thus performs distributed alternate solutions [11]. Let the set m denote the feasible region of microgrid m, i.e. (2)–(9) and set  denote the feasible region of distribution network, i.e. (11)–(21). To facilitate the application of ADMM, (3) is rewritten as the following compact form:  fmM (xm ) + f DN (y) (26) min xm ∈m ,y∈

m∈M

Subject to 

Am xm = By

(27)

m∈M

where x m denotes all decision variables of microgrid m and y denotes all decision variables of distribution network. (26) shows that the collaborative objective function is optimized. (27) denotes the coupling constraint of microgrids and distribution network. The augmented Lagrange function of (4) is as follows. L(x, y, λ) =



⎛ fmM (xm ) + f DN (y) + λT ⎝

m∈M



m∈M

2       ρ  Am xm − By⎠ +  A x − By m m   2  M ⎞

m∈

2

(28) where λ is the Lagrangian multiplier and ρ is the penalty factor. By applying RF heuristics [12], the binary variables are relaxed to continuous variables. So the variables are updated as follows.

u+1 u (29) = arg min L x1u , · · · , xm , · · · , xM , y u , λu , xm xm ∈mR

  yu+1 = arg min L xu+1 , y, λu ⎛ λu+1 = λu +ρ ⎝

y∈R



(30) ⎞

u+1 Am xm − Byu+1 ⎠

(31)

m∈M

where u is the iteration number during the solution process.  R and R are the relaxed feasible region of microgrids and distribution network, respectively. The stopping criteria include that the primal and dual residuals are small enough.  2     u 2   u u ξ  =  A x − By m m   ≤ ε1 2 m∈M  2

(32)

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 2  u 2   ζ  =  ρdiag AT1 , . . . , ATM B λu − λu−1  ≤ ε2 2 2

(33)

where ξ and ζ are primal and dual residuals, respectively. ε1 and ε2 represent allowable errors for primal and dual residuals, respectively. The small enough primal and dual residuals indicate the convergence of the algorithm. After the iterations, the relaxed variables of microgrids and distribution network are enforced to binary variables one by one. When the binary variables are fixed, the operation scheme of HADN is obtained. 3.2 Solution Process The microgrids can solve local operation problems in parallel when adopting the ADMM-based model. After interacting information in each iteration, the distribution network and microgrids update decision variables, respectively. The residual is calculated by the distribution network at each iteration. The solution process is stated as follows. Step 1: Distribution network and microgrids initialize their decision variables x, y, λ, and ρ, respectively, and let u = 0. Step 2: Distribution network and microgrids update iteration number, u = u + 1. Step 3: Microgrids use (29) to update decision variables x and send the updated x to the distribution network. Step 4: Distribution network use (30) and (31) to update decision variables y and dual variables λ. And send the updated y and λ to microgrids. Step 5: The distribution network calculates the residual. Step 6: If (32) is satisfied, the distribution network announces the end of the iteration and the relaxed solution of HADN operation is obtained, otherwise, go to step 2. Step 7: The relaxed variables are enforced to binary variables using RF heuristics in [12] and the operation schemes of HADN with muti-microgrids are obtained. Because each microgrid interacts energy with the distribution network, the variables of multi-microgrids are not coupled. Although multi-microgrids solve their subproblems as shown in (29), these problems can be considered as an integrated problem and solved at once mathematically. Hence, problem (4) is essentially a two-block case for ADMM solution. In addition, by using RF heuristics, the iterative solution of ADMM would converge because the problem is convex.

4 Numerical Results As illustrated in Fig. 1, a HADN with 7 microgrids is simulated to validate the proposed model. The power exchanges between microgrids and distribution network are shown in Fig. 2(a), where a positive number indicates that the generation in the microgrid is greater than the load and thus it supplies power to the distribution network and a negative number indicates that the microgrid absorbs power from the distribution network. Microgrids 6 and 7 output power to the distribution network from 10:00 to 18:00. Other microgrids absorb power from the distribution network because the DG output is less than the local

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load. Hence, the proposed operation model coordinates the power of each microgrid and the renewable energy is consumed through the interaction between microgrids. The SOCs of ESSs in corresponding SPIESs are illustrated in Fig. 2 (b), which shows that ESSs are discharged from 12:00 to 19:00 when electricity prices are high. Hence, the proposed model can coordinate the operation of the microgrids and the distribution network, and support the operation of the transmission network by responding to the electricity price.

(a)

(b)

Fig. 2. Operation of HADN: (a) Power exchanging between microgrids and distribution network; (b) SOCs of ESSs.

(a)

(b)

Fig. 3. Comparison of HADN and RADN operations: (a) bus voltages; (b) total SOC.

The proposed model for HADN and RADN operations are compared in Fig. 3. The comparison of bus voltages in HADN and RADN shows that the voltages of bus 4 of microgrid 3 and bus 1 of microgrid 4 in HADN are above 0.97 p.u. during the 24 h. The bus voltages are relatively low in RADN and the voltage of bus 4 of microgrid 3 reaches the lower limit from 18:00 to 21:00. This shows that the HADN is effective for improving the voltage profiles. The comparison of total SOCs in HADN and RADN shows that the ESSs in HADN are charged from 0:00 to 6:00 when the electricity prices are low and discharged from 12:00 to 18:00 when electricity prices are high. Hence, the HADN operation has enough flexibility to support the transmission network operation by responding to the electricity prices. However, the ESSs in RADN have to be discharged from 17:00 to 21:00 to eliminate bus voltage violations. HADN has a larger operation margin than that of RADN.

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5 Conclusion This paper proposes an ADMM with RF heuristics-based model for operations of HADN with multi-microgrids. The operation schemes of microgrids and distribution network are cooperatively optimized. Furthermore, the comparison of HADN and RADN operations is studied by using the proposed model, which shows that the HADN is effective in improving bus voltage profiles, balancing line flows, and the flexibility of the system compared to those performances in RADN. Hence, the proposed method has engineering significance, which is to improve the operation performance of the distribution networks with renewable generations. Future works would study the economics of HADN to clarify the specific scenarios for HADN applications.

References 1. Wang, C., et al.: A highly integrated and reconfigurable microgrid testbed with hybrid distributed energy sources. IEEE Trans. Smart Grid 7(1), 451–459 (2016) 2. Li, Z., Shahidehpour, M., Aminifar, F., Alabdulwahab, A., Al-Turki, Y.: Networked microgrids for enhancing the power system resilience. Proc. IEEE 105(7), 1289–1310 (2017) 3. Shahidehpour, M., Li, Z., Bahramirad, S., Li, Z., Tian, W.: Networked microgrids: exploring the possibilities of the IIT-Bronzeville grid. IEEE Power Energy Mag. 15(4), 63–71 (2017) 4. Ji, H., et al.: An enhanced SOCP-based method for feeder load balancing using the multiterminal soft open point in active distribution networks. Appl. Energy 208, 986–995 (2017) 5. Ruan, C., et al.: Reliability calculation based on honeycomb distribution grid. In: 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC), pp. 1–6 (2018) 6. Wang, L., Zu, G., Xu, W., Zhu, W., Luo, F.: Honeycomb distribution networks: concept and central features. In: 2022 International Conference on Energy, Electrical and Power Engineering, pp. 629–633 (2022) 7. Xiao, X., Hu, P., Fang, Y., Jiang, D., Zhang, Y.: A control strategy for honeycomb distribution network. In: 2020 Asia Energy and Electrical Engineering Symposium (AEEES), pp. 543–549 (2020) 8. Yan, Y., Yu, B., Zhu, D., Geng, L., Peng, Y., Jiang, W.: ES-VSC-MTDC based energy hub for honeycomb distribution network. In: 2021 IEEE Sustainable Power and Energy Conference (iSPEC), pp. 3355–3360 (2021) 9. Zhu, N., Jiang, D., Hu, P., Yang, Y.: Honeycomb active distribution network: a novel structure of distribution network and its stochastic optimization. In: 2020 IEEE Conference on Industrial Electronics and Applications, pp. 455–462 (2020) 10. Farivar, M., Low, S.H.: Branch flow model: relaxations and convexification—part I. IEEE Trans. Power Syst. 28(3), 2554–2564 (2013) 11. Boyd, S., Parikh, N., Chu, E., Peleato, B., et al.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011) 12. Toledo, C.F.M., da Silva Arantes, M., Hossomi, M.Y.B., França, P.M., Akartunalı, K.: A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems. J. Heuristics 21(5), 687–717 (2015). https://doi.org/10.1007/s10732-015-9295-0

Primary Frequency Modulation Control of Doubly-Fed Wind Turbine Based on Optimal Coordination of Pitch and Energy Storage Longqing Zhao, Zhen Xie(B) , and Liusheng Zhang School of Electrical Engineering and Automation, Hefei University of Technology, Hefei, China [email protected], [email protected]

Abstract. With the increase of the capacity of wind turbine assembly machines in the future, the proportion of new energy continues to increase, which puts forward higher requirements for wind turbines to connect to the grid. Conventional wind turbines are difficult to meet the essential needs of the grid and users at high penetration rates. In this paper, through the analysis of energy storage control and pitch angle control, the coordinated control of energy storage and pitch angle is explored to achieve a stable primary frequency regulation effect considering the minimum wind power limiting power. On the basis of the coordinated control of limited power, the main factors affecting the cost of wind power are analyzed, and the optimal power limit mode is sought by establishing the optimal objective function, which satisfies the economy of frequency modulation while completing the primary frequency regulation goal. Keywords: Doubly fed induction generator (DFIG) · Primary frequency modulation · Energy storage · Pitch control

1 Introduction With the continuous increase of wind turbine grid-connected capacity, new energy power generation systems put forward higher requirements for wind power to participate in frequency regulation. However, conventional doubly-fed wind turbine control is difficult to meet the frequency requirements of the system, and there are problems such as the lack of inertia support for the grid frequency and the weak ability to regulate the frequency of the primary frequency [1, 2]. Usually most wind turbines are not in the MPPT power generation state, but in the standby or power limited operation state, which will lead to an increase in curtailment power. In order to make better use of the curtailment power, consider the pitch angle and energy storage to work together to obtain a constant primary frequency regulation state. While meeting the frequency modulation needs, maximize the economic benefits of frequency modulation.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 297–304, 2023. https://doi.org/10.1007/978-981-99-4334-0_37

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2 Energy Storage and Pitch Angle Coordination Modes In order to enable the wind turbine to simulate the demand for thermal power frequency regulation, it is expected that the wind turbine will fail at the time of frequency regulation, and it is expected that at the current fault moment, 10% of the unit rated power will be issued. This control scheme puts forward higher requirements for the traditional wind turbine to participate in frequency regulation, using paddle pitch angle reservation mode or limited power mode, because the wind power is difficult to meet this demand with the continuous fluctuation of wind speed, so it is necessary to be equipped with a certain energy storage synergy. However, the equipment of energy storage and the different operating states of energy storage and pitch angle synergy output will involve economic problems, so it is required to seek a relatively excellent operating state to ensure economic optimization while meeting the needs of primary frequency regulation. This article will start from different wind power limit power operating states, and seek the optimal limited power operation mode under the premise of meeting the frequency regulation of 10% of the rated power at the time of failure. At present, there are two modes of pitch angle and energy storage cooperation, which are the cooperative mode of standby energy storage and the cooperative mode of limited power energy storage at the pitch angle. Based on the wind power prediction in the next 5 min, this paper is based on the precondition that the fault occurs while the current wind power is still running, and it is expected that at the current fault moment, the rated power of the unit will be increased by 10% for a frequency modulation [3–5]. The specific principles of the two control modes are as follows. 2.1 Standby Energy Storage Cooperative Mode of Pitch Angle Load Reduction As shown in Fig. 1, the blue line area is the load shedding standby power area, the orange line is the energy storage operation area, the maximum power curve of the fan Pmppt , and the load shedding standby coefficient d %. At different wind speeds, in order to make the power after load reduction is (1 − d %)Pmppt , check the table to get the corresponding reference pitch angle. Reserve the corresponding load reduction power according to the different load reduction coefficient d %, so that the fan runs on the (1 − d %)Pmppt curve. When the frequency fails at any time, the energy storage output level can be calculated according to the power reserved by the current wind power, ensuring that a constant 10%Pn power can be issued at the moment of failure.

10%Pn+(1-d%)Pmppt

Pmppt (1-d%)Pmppt

Fig. 1. Standby energy storage cooperative mode of pitch angle load reduction.

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2.2 Limited Power Energy Storage Collaborative Mode As shown in Fig. 2, the blue line area is the limited power frequency modulation power, the red line area is the energy storage output area, and the green line area is the curtailment power area.

Pmppt 10%Pn+ Plimit

Plimit

Fig. 2. Limited power energy storage collaborative mode.

According to the above description, it can be obtained as shown in Fig. 3 of the energy storage + pitch angle reservation + rotor kinetic energy and energy storage + limited power + rotor kinetic energy two optimization coordination scheme. In view of the limited power energy storage collaborative mode described above, based on the premise of wind power forecasting in the next 5 min, the following three prerequisites are assumed: Condition 1: The fault point corresponds to the power that is multiple in the current power state at the time; Condition 2: Suppose that the paddle pitch angle reserved in advance is fully released at the time of frequency failure; Condition 3: The maximum power class equipped for energy storage is the rated wind turbine power.

Fig. 3. Control block diagram of energy storage pitch angle cooperative mode.

3 Limited Power Mode in Minimum Wind Power Based on the above principles and discussion analysis, this paper will take the minimum point power of future wind power as the power limit point, explore how to control the power limit and energy storage in this minimum wind power limit mode, and explore

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the size of the four power costs of wind power cost and wind power curtailment power cost, energy storage battery output power cost, and standby power cost, and adjust the proportion of frequency regulation benefits of various power costs according to the size of the wind probability. The minimum wind power limiting mode is shown in Fig. 4.

Fig. 4. Schematic diagram of minimum wind power limit.

As shown in Fig. 4, when the minimum wind power point is the limited power, the green line area is the energy storage output power, the red line area is the curtailment power, and the blue is the load reduction standby power provided by the paddle pitch angle energy. When the wind power Pmppt is greater than 10%Pn +Plimit , the pitch angle is enough to participate in a frequency regulation, and the energy storage does not contribute to a frequency regulation. When the wind power Pmppt is less than 10%Pn + Plimit , the power of the limited power release and the energy storage output are controlled in synergy, and when the power failure occurs at the minimum power point, the maximum power is released at this time. According to the figure above, due to the continuous fluctuation of wind power, assuming that the minimum wind speed is just in the t0 to t3 time period, the power cost of each stage can be derived [6]. a) The cost of curtailed wind power The cost of curtailment power mainly refers to the power greater than Plimit :  t   W1 = t03 Pmppt − Plimit dt Pmppt > Plimit

(1)

b) The cost of energy storage output The cost of energy storage output is the 10%Pn power that cannot be emitted in the power limit:  t   W2 = t13 Plimit + 10%Pn − Pmppt dt (2) Plimit + 10%Pn > Pmppt c) The cost of load-reducing backup power costs The cost of load-shedding standby power mainly refers to the existence of power limiting, and part of the power will belong to the active power of load-shedding frequency regulation:  t1  t3   −Plimit + Pmppt dt (3) W3 = (10%Pn ) dt + t0

t1

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Due to the volatility of wind power, the power operating curves of the curtailed wind power, energy storage output, and standby power cost function are different similar N N N    W1 , W2 , W3 . to the t0 to t3 time periods: N =1

Then the total cost function is:

max COC = −α ·

N =1

N  n=1

N =1

W1 + β ·

N  n=1

W2 + γ ·

N 

W3

(4)

n=1

Among them, α, β, γ represent the weights of the curtailed wind power. Based on the above description, the simulation is shown in Fig. 5. In figure (a), the orange line represents the wind power curve, the red line represents the curtailment power curve, the blue line represents the standby power curve, and the green line represents the power curve of the energy storage output. The area of red shadow in figure (b) is the curtailment power cost. The area of green shadow in figure (c) is the energy storage power cost, and the area of green shadow in figure (d) is the load-reduced standby power cost. According to the above simulation diagram, the red area is 3.29e6 J, the green area is 4.34e5 J, and the blue area is 2.06e6 J. Assuming that the proportion of wind curtailment benefit weight α is 0.4, the proportion of energy storage frequency modulation benefit weight is 0.4, and the proportion of load reduction frequency regulation benefit weight is 0.2, the total cost function COC = − 7.21e5 J is obtained by counting. When the minimum wind power is used as the power limiting point, the overall cost function of frequency modulation of this control scheme is negative, and this control scheme should seek the optimal power limit mode due to the large economic loss of frequency regulation caused by the large cost of curtailment at high wind speed.

Fig. 5. Frequency modulation benefit diagram of minimum wind power limit mode.

4 Seek the Optimal Limited Power Mode Based on the above principles and discussions, this chapter aims to solve the limitations of the limited power mode with minimum wind power and explore the optimal power limit mode with the lowest cost function as the goal. And to meet the fault instantaneous can increase the constant 10%Pn power demand, coordinate energy and pitch angle to participate in a frequency regulation, is committed to adapting to various working conditions to operate, and to meet the maximum benefits of frequency regulation, can achieve positive frequency modulation gain, minimize the economic loss of frequency modulation. The optimal power limit mode is shown in Fig. 6.

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Fig. 6. Optimal power limit power pattern diagram.

As shown in Fig. 6, the green line area is the energy storage output power, the red line area is the curtailment power, and the blue is the load reduction backup power provided by the pitch angle. When the wind power Pmppt is greater than 10%Pn + Plimit , the pitch angle is enough to participate in a frequency regulation, and the energy storage does not contribute to a frequency regulation. When the wind power Pmppt is less than 10%Pn +Plimit , the power released by the limited power and the energy storage output are controlled cooperatively. When wind power Pmppt is between the limiting power curves Plimit and 10%Pn + Plimit , the energy storage and limiting power are produced together. When the wind power curve Pmppt is less than the limit power Plimit , the entire energy storage system is fully output. According to the figure above, due to the continuous fluctuation of wind power, it is assumed that the minimum wind speed is just in the t0 to t3 time period, and the power state of the wind power and the limited power of the t0 to t3 time period is intercepted, the power cost of each stage can be obtained. a) The cost of curtailed wind power   t3   Wa = t0 Pmppt − Plimit dt Pmppt > Plimit b) The cost of energy storage output   t2   Wb = Plimit + 10%Pn − Pmppt dt + t1

(5)

t3

(10%Pn ) dt

(6)

t2

c) The cost of load-reducing backup power costs  t1  t2   −Plimit + Pmppt dt Wc = (10%Pn ) dt + t0

(7)

t1

Due to the volatility of wind power, the power operating curves of the curtailed wind power, energy storage output, and standby power cost function are different similar to N N N    the to time periods: Wa , Wb , Wc . N =1

N =1

The total cost function is:

max COC = −α ·

N =1

N  n=1

Wa + β ·

N  n=1

Wb + γ ·

N  n=1

Wc

(8)

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Based on the above description, the simulation is shown in Fig. 7. The area of red shading in figure (b) is the curtailed power cost in different power limiting modes. The area of green shadow in figure (d) is the energy storage power cost in different power limit modes, and the area of green shadow in figure (f) is the load-reducing standby power cost in different power limit modes. Assuming that the wind power and minimum power modes use the same set of data, as shown in Fig. 7 of the simulation, it is assumed that the proportion of the curtailment benefit weight α is 0.4, the energy storage frequency modulation benefit weight β is 0.4, and the load reduction frequency modulation benefit weight γ is 0.2.Through simulation, it can be found that when the power limit point is set to 8.29e5 points, the red area is 5.56e5 J, the green area is 2.00e6 J, and the blue area is 4.99e5 J, at this time the total cost function reaches the maximum, the maximum frequency modulation benefit cost is max COC = 6.77e5 J, compared with the minimum limited power mode, which increases the economy of frequency modulation. The overall cost function of frequency modulation in this control scheme is positive, which can achieve positive frequency modulation benefits. Therefore, the limitation of the minimum power point as the limited power point can be overcome.

Fig. 7. Frequency modulation benefit diagram of different power limit modes.

5 Conclusion This paper starts from the coordinated control of energy storage and pitch angle. Taking the minimum point power of future wind power as the power limit point, and explore how to control the power limit and energy storage synergy in this minimum wind power limit mode, and analyzes the size of the four power costs. At the same time, on the basis of this research, the optimal limited power energy storage mode is explored, and the optimal power limit mode is sought according to different wind power curves, so as to achieve economic optimal control while meeting the frequency regulation requirements.

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References 1. Li, J., Feng, X., Yan, G., et al.: Overview of power system frequency modulation research under high wind power penetration rate. Power Syst. Protect. Control 46(2), 163–170 (2018) 2. Zhou, X., Wang, Z., Ma, Y., Gao, Z.: An overview on development of wind power generation. In: 2018 IEEE International Conference on Mechatronics and Automation (ICMA), pp. 2042– 2046. Changchun, China (2018) 3. Fan, L., Guo, H., Gu, W., Jiang, P.: Wind power fluctuation suppression based on control coordination between energy storage and pitch angle. Electr. Power Autom. Equip. 36(09), 100–105 (2016) 4. Tang, X., Yin, M., Shen, C., Xu, Y., Dong, Z.Y., Zou, Y.: Active power control of wind turbine generators via coordinated rotor speed and pitch angle regulation. IEEE Trans. Sustain. Energy 10(2), 822–832 (2019) 5. Prasad, R., Padhy, N.P.: Synergistic frequency regulation control mechanism for DFIG wind turbines with optimal pitch dynamics. IEEE Trans. Power Syst. 35(4), 3181–3191 (2020) 6. Jiang, Y., Bian, X., Li, D., Zhou, Q.: Research on doubly fed induction generator participation in microgrid frequency modulation based on variableload shedding ratio over-speed control. Electr. Mach. Control Appl. 36(09), 100–105 (2016)

Analysis of Harmonic Characteristics of Magnetic Controllable Transformer Lingyun Gu1 , Feiyan Zhou1 , Wenchao Dong2 , Wenpeng Gao1 , Yu Dong2(B) , and Yan Wu2 1 Beijing Key Laboratory of Distribution Transformer Energy-Saving Technology, China

Electric Power Research Institute, Beijing 100192, China 2 School of Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

Abstract. Magnetically controlled transformer is a new kind of transformer based on core saturation principle, which can not only change voltage but also output reactive power stably. However, high harmonics will be produced in the process of dynamic reactive power output, which seriously affects the power quality of power system. The harmonic generation mechanism of magnetic control transformer is studied and analyzed. It is found that the harmonic content is related to the area and length of magnetic valve. The simulation model of single-stage magnetron reactor is established in Finite element simulation software, the theoretical value of harmonic content of single-stage magnetron transformer primary current is derived, and the Fast Fourier Transformation (FFT) algorithm is used to verify and calculate the harmonic content of transformer primary current. The research results can provide technical reference for the design of magnetic transformer. Keywords: Magnetically controlled reactor · FFT · Core saturation · Reactive compensation · Magnetic valve

1 Introduction The current urban distribution network cabling rate is higher and higher, distribution network of reactive power compensation problem from most of the past perceptual reactive power compensation to compensate the capacitive reactive power [1]. Magnetic control transformer is a kind of magnetic valve type distribution transformer based on magnetic saturation working principle of iron core. The device can not only complete the function of transformer, but also output a certain capacitive reactive power, which saves the cost of external controllable reactor. It has good economy and is a good choice to solve the problem. High harmonics will be generated in the process of dynamic reactive power output of magnetic transformer. The larger the reactive power rated capacity of the magnetically controlled transformer is, the larger the harmonic current output is. Therefore, it is necessary to analyze the mechanism of its harmonic generation, so as to reduce the harmonic content as much as possible in the design [2]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 305–312, 2023. https://doi.org/10.1007/978-981-99-4334-0_38

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2 Harmonic Generation Mechanism The basic structure of the magnetic control transformer is shown in Fig. 1. The common transformer requires the core to work in the unsaturated region, but the magnetic transformer requires the core to work in the saturation region and the unsaturated critical point, by adding dc excitation winding to control the magnetic saturation of the core, to achieve the excitation reactance regulation. The single-phase magnetic control transformer is taken as an example. The single-phase split core transformer structure is adopted. The left two columns are iron core, the low-voltage primary winding, the high-voltage secondary winding and the DC excitation control winding are wound on the iron core, and the right column is side yoke to provide a loop for the excitation flux. In addition, the two cores each have a small section, called the magnetic valve. The input voltage of the primary winding of the transformer is U1, and the output voltage of the secondary winding is U2. The DC excitation control winding is externally connected with first-class voltage source Uk, and is cross-connected.

Fig. 1. Schematic diagram of magnetic transformer.

Magnetic transformer can adjust the excitation inductance because of the nonlinear saturation characteristics of soft magnetic materials [3]. When the magnetic saturation of the core increases, the magnetic conductivity μ decreases gradually. According to the principle of circuit and magnetic circuit, it can be deduced that the excitation inductance Lm of magnetically controlled transformer is the same as that of iron core reactor, which meets the following requirements: Lm =

μN 2 A l

(1)

By piecewise linear magnetic permeability of the simplified model to simulate the magnetization curve of magnetic transformer work in the stage of magnetic saturation magnetization characteristics, it ignored the hysteresis effect of ferromagnetic materials and eddy current effect, and assumes that when its core saturated permeability instantaneous value is equal to the air permeability.

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Figure 2 shows that when the magnetic induction intensity of the magnetic valve segment is in the magnetic saturation region, the magnetic field intensity H is much higher than that in the unsaturated region, so the excitation reactance decreases sharply in the magnetic saturation region.

Fig. 2. Magnetization curve.

Under rated voltage, the magnetically controlled transformer has no DC bias and the small magnetic valve is in the critical saturation state [4]. When reactive power is required from the magnetron transformer, adjust the DC voltage lift B curve, the maximum magnetic induction B1 of the core is greater than Bt. At this time, there will be a magnetic saturation interval in the magnetic valve section within a power frequency cycle β. This magnetic saturation interval β. It is defined as magnetic saturation of magnetic valve and its calculation formula is expressed as follows: β = 2 arccos

Bt − Bd Bt

(2)

When the magnetic induction strength of the magnetic valve section is in the magnetic saturation range, the magnetic field strength H is much larger than the value in the unsaturated range, so the excitation reactance decreases sharply when the magnetic saturation occurs [5]. Magnetic saturation interval β The larger the transformer, the longer the operation time of the transformer under the condition of small excitation reactance, the greater the inductive reactive power output.

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The harmonic generation mechanism of single-stage solenoid transformer is studied here. The relationship between core excitation current and primary current and secondary current is as follows. N1 i0 = N1 i1 + N2 i2

(3)

Based on the principle of circuit and magnetic circuit, the fundamental component of excitation current, the harmonic components of each order and the value of DC excitation current can be derived.   1 Bt lt1 1 1 i0(1) = − (4) (β − sin β) 2π μ0 μ1 m N1   1 Bt lt1 1 1 i0(2k+1) = − ×g (5) (2k + 1)π μ0 μ1 m N1 In equation: 

 sin kβ sin(k + 1)β − 2k 2(k + 1)     Bt lt1 β β β 1 1 sin − cos = − μ0 μ1 m Nk π 2 2 2 g=

ik(0)

(6) (7)

From the above formula, it is known that with the increase of the magnetic saturation of the core of the magnetron transformer, the fundamental component of the excitation current increases according to the sinusoidal relation, and the harmonic component is the smallest when the magnetic saturation is π and 2π .

3 Principle Calculating Harmonic Content of Primary Current by FFT In this paper, fast Fourier transform (FFT) is used for harmonic analysis of primary current of magnetron transformer [6]. FFT decomposes a finite length discrete signal y(n) into the sum of two sequences of even and odd numbers [7–9]. y(n) = y1 (n) + y2 (n)

(8)

A sequence of even and odd numbers of which the length is N/2 respectively. N 2

Y (k) =

−1  n=0

N

y1 (n)WN2nk

+

2 

n=0

(2n+1)k

y2 (n)WN

(9)

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There are: N 2

Y (k) =

−1 

N 2

y1 (n)WN2nk

+ WNk

n=0

=e

N 2

Y (k) =

n=0

y2 (n)WN2nk

(10)

n=0

WN2nk −1 

−1 

−j 2π N 2nk

= WNnk/2

(11)

N 2

y1 (n)WNnk/2

+ WNk

−1 

y2 (n)WNnk/2 = Y1 (k) + WNk Y2 (k)

(12)

n=0

Equation 12 can be obtained from Eq. 11. In Eqs. (9)–(12), k = 0, 1, …, N − 1. Y1 (k) and Y2 (k) are the discrete Fourier transforms of y1 (n) and y2 (n) at point N/2, respectively. Since both Y1 (k) and Y2 (k) take k+N /2 N/2 as the cycle. and WN = −WNk , following equation can be obtained: X (k) = X1 (k) + WNk X2 (k)

(13)

  N X k+ = X1 (k) − WNk X2 (k) 2

(14)

Based on the above formula, the FFT calculation program is built in MATLAB software, and the harmonic calculation results will be shown in the next section.

4 Simulation Model and Parameters In order to obtain the current waveform value of the primary side of the magnetic control transformer, a simulation model of single-phase magnetic control distribution transformer based on Finite element simulation software is constructed. The voltage ratio of the simulation model is 400/32 V. The core structure of the magnetic control transformer is shown in Fig. 3. The area of the magnetic valve is 900 mm2 and the length is 50 mm [10–12]. When the magnetic control transformer works approximately when the magnetic saturation is π, its output voltage, current and reactive power are shown in the following Figs. 4, 5 and 6 respectively. It can be seen that the magnetron transformer can stably output reactive power on the basis of completing the voltage rise and fall function. Taking the third harmonic as an example, from Eq. (14) and Eq. (15): 1 2 sin β − sin 2β i0(3) = × i0(1) 6 β − sin β

(15)

When the magnetic saturation is approximately π, the ratio of the third harmonic content to the fundamental content of the magnetic control transformer is approximately zero, which is consistent with the basic harmonic content calculated by FFT in Fig. 7.

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Fig. 3. Structure diagram of magnetic control transformer.

Fig. 4. Voltage waveform of magnetic control transformer.

Fig. 5. Current waveform of magnetic control transformer.

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Fig. 6. Reactive power output diagram of magnetic control transformer.

Fig. 7. Harmonic content of transformer primary side current.

5 Conclusion Based on Finite element simulation software, the single stage magnetron transformer is modeled, and the harmonic generation principle and formula are deduced. The harmonic current of primary side current of transformer is calculated by FFT algorithm. The simulation results are consistent with the theoretical analysis, which verifies the correctness of the simulation model and method. It can provide technical reference for the design of magnetic control transformer. Acknowledgements. Open Fund of Beijing Key Laboratory of Distribution Transformer EnergySaving Technology (China Electric Power Research Institute) (No. PDR51202102015).

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References 1. Liang, W., Liu, Y., Shen, Y.: Active power control integrated with reactive power compensation of battery energy stored quasi-Z source inverter PV power system operating in VSG mode. IEEE J. Emerg. Sel. Top. Power Electron. 1 (2021) 2. Wang, C., Tian, C., Cheng, H., Zhao, Z.: Control strategy of parallel unidirectional controlled rectifiers for reactive power compensation. In: PCIM Asia 2019; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, pp. 1–7 (2019) 3. Mestriner, D., Labella, A., Bonfiglio, A., Benfatto, I., Li, J., Ye, Y., Song, Z.: ITER reactive power compensation systems: analysis on reactive power sharing strategies. In: 2019 IEEE International Conference on Environment and Electrical Engineering and 2019 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe), pp. 1–6 (2019) 4. Koeppe, H., Fernandez, J.P.M., Engel, B.: Technical and economical comparison of reactive power provision with variable renewable energy power plants and compensation systems. In: NEIS 2018; Conference on Sustainable Energy Supply and Energy Storage Systems, pp. 1–6 (2018) 5. Vegunta, S.C., Barlow, M.J., Stapleton, S.: Reactive power compensation solutions and reactive power source priority impact on wind farm losses. In: 2017 IEEE Manchester PowerTech, pp. 1–5 (2017) 6. Ramaswami, A., Kenter, T., Kühne, T.D., Plessl, C.: Efficient ab-initio molecular dynamic simulations by offloading fast Fourier transformations to FPGAs. In: 2020 30th International Conference on Field-Programmable Logic and Applications (FPL), pp. 353–354 (2020) 7. Apriono, C., Firmansyah, M.D., Zulkifli, F.Y., Rahardjo, E.T. Near-field to far-field transformation of cylindrical scanning antenna measurement using two dimension fast-Fourier transform. In: 2017 15th International Conference on Quality in Research (QiR): International Symposium on Electrical and Computer Engineering, pp. 368–371 (2017) 8. Zhou, H., Li, B., Tang, M., Feng, Z., Fu, S., Shum, P.P., Liu, D.: A fast and robust blind chromatic dispersion estimation based on fractional Fourier transformation. In: 2015 European Conference on Optical Communication (ECOC), pp. 1–3 (2015) 9. Yang, Y.H., Wang, L.: The online detection of faulty insulator using fast Fourier transformation. In: The 2014 2nd International Conference on Systems and Informatics (ICSAI 2014), pp. 175–179s (2014) 10. Suto, J., Oniga, S., Hegyesi, G.: A simple fast Fourier transformation algorithm to microcontrollers and mini computers. In: IEEE 18th International Conference on Intelligent Engineering Systems INES 2014, pp. 61–65 (2014) 11. Ismail, N., Syahrir, W.M., Zain, J.M., Tao, H.: Fabric authenticity method using fast Fourier transformation detection. In: International Conference on Electrical, Control and Computer Engineering 2011 (InECCE), pp. 233–237 (2011) 12. Kara, S., Guven, A., Okandan, M.: Diagnosing mitral and tricuspid stenosis with the help of artificial neural networks built on the fast Fourier transformation sonogram. In: First International IEEE EMBS Conference on Neural Engineering, 2003. Conference Proceedings, pp. 340–343 (2003)

Investigation of Pumped Storage Power Station Construction Conditions in Guangdong Province Youkun Luo1 , Xiong Xiao2 , Ying Yuan3(B) , Xueyuan Deng3 , and Sujuan Luo4 1 Strategy and Planning Department of CSG Power Generation Co., Ltd, Guangzhou, China

[email protected]

2 CSG Power Generation Co., Ltd, Guangzhou, China 3 Planning Branch of Guangdong Hydropower Planning and Design Institute Co., Ltd,

Guangzhou, China {yuan.y,deng.xy}@gpdiwe.com 4 Production Operation Department of Guangdong Hydropower Planning and Design Institute Co., Ltd, Guangzhou, China [email protected]

Abstract. With the determination of China’s “carbon peaking and carbon neutrality goals”, a large number of pumped storage power stations will be planned to be built in Guangdong Province in the next 10–15 years. This paper determines the investigation principles of pumped storage in Guangdong Province, typical sites were selected analyzed and compared in terms of service objects, site conditions, external environment and economics. The advantages and disadvantages of each site was summarized and the conclusion would provide technical support for the following planning and construction of pumped storage power stations. After comparative analysis, it can be seen that Zhongdong and Sanjiangkou are closer to the load center, with higher head, less environmental constraints, and better economical efficiency. All indicators of Zhongdong and Sanjiangkou are excellent and belong to the first echelon of the rare high-quality sites in Guangdong province. Guangdong Province is rich in energy storage site resources, and more excellent sites can be selected in the preliminary stage based on the abovementioned construction conditions investigation method. In addition to the above factors, the final economics of the site is also affected by non-technical factors such as specific scheme design, future tariff policy, investor’s decision and local government coordination. Keywords: Pumped · Storage · Construction · Conditions investigation · Guangdong

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 313–322, 2023. https://doi.org/10.1007/978-981-99-4334-0_39

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1 Research Background In recent years, pumped storage power of Guangdong Province develop very rapidly, and large pumped storage power stations (PSPS) such as Guangzhou PSPS, Huizhou PSPS, Qingyuan PSPS, and Shenzhen PSPS, etc. have been built [1]. At present, Guangdong’s power system has formed a diversified power supply system with coal power as the main source, and a combination of nuclear power, electric power from the western region, gas power, hydropower, pumped storage, wind power and other types of power sources. And the grid has a large peak-to-valley difference. With the increasing proportion of nuclear power, electric power from the western region and new energy power, the peak load regulation requirements of power grid are enhanced. Also, the demand for reliable power supply is increasing as well, the power system requires more adequate and highquality peak-shaving power supply [1–3]. The construction of reasonable scale of peakshaving power supply is an important means to solve the peak-shaving problem of the power grid, ensure the safety of power grid operation and promote the economic operation of various power sources. Therefore, it is particularly important to investigate the construction conditions of pumped storage sites in Guangdong Province.

2 Investigation Principles Based on the previous experience of pumped storage investigation, it is determined that the investigation principles of this pumped storage include the following aspects. 2.1 Compliance with Environmental, Ecological, Water Source, Cultural Heritage and Other Protection Requirements The construction of PSPS should comply with the requirements of laws, regulations and local policy documents, and the selection of project sites should give priority to avoiding environmentally sensitive areas such as ecological protection red lines, nature reserves and drinking water source protection zones [4–6]. 2.2 Close to Electricity Load Centers One of the main functions of pumped storage is peak and frequency regulation [1, 3, 7]. In the site selection stage, the site should be considered close to the load center [8, 9]. 2.3 Decentralized Layout In order to achieve safe, stable and economic operation of the power system, pumped storage power stations should be decentralized as much as possible, which is conducive to improving the speed of system recovery after power failure and avoiding large inflow and outflow of power.

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2.4 Good Access System Conditions The distance of power grid access point should be taken into account in the selection of pumped storage sites [10, 11]. Generally, the smaller the distance, the less the investment in accessing the grid. At the same time, the distribution of power flow should be considered, and the site selection should comply with the power flow distribution. 2.5 Facilitating Multi-energy Complementarity and the Consumption of New Energy [8, 12–15] Guangdong Province has a diverse energy structure, including coal and oil resources, hydro energy resources, nuclear power, wind power, photovoltaic and other new energy resources. With the social and economic development of Guangdong Province, the future demand for newly increased electricity in Guangdong will mainly rely on new energy and nuclear power to meet the increasingly urgent demand for peak-shaving power supply. The construction of pumped storage power stations is conducive to multi-energy complementarity and new energy consumption, and is an important means to achieve the double carbon goal [16, 17]. Site selection should be as close as possible to the new energy surrounding areas, and in line with the power flow distribution, which is conducive to saving power grid investment. 2.6 Taking into Account the Needs of Economic Development in Both Eastern and Western Areas In the future, the Pearl River Delta city cluster will promote infrastructure integration, the east and west areas will take the development of port industries as a breakthrough, vigorously cultivate pillar industries, accelerate the development of the eastern Guangdong town cluster with Shantou as the center and the western Guangdong town cluster with Zhanjiang as the center, form a coastal industrial belt, and build a new pattern of regional economy. Therefore, the economic development of the east and west areas will be on the fast track. The construction of pumped storage power plants should be coordinated with the economic development and guarantee the development. 2.7 Excellent Construction Conditions of the Site [9] Construction conditions should be selected according to local conditions, the construction conditions of the station site should be fully considered. Try to take into account the following factors (1) favorable geological conditions; (2) good load regulation performance; (3) head variation ratio (maximum lift/minimum head) within a reasonable range; (4) appropriate distance to height ratio; (5) good conditions for reservoir formation; (6) less land acquisition and migration; (7) good water source conditions; (8) convenient transportation.

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3 Investigation According to the investigation principles, the construction conditions should be determined by comparing the service objects, station site conditions, external environment, and economics. According to the power grid structure of Guangdong Province, the province can be divided into the Eastern and Western areas. PSPS sites are compared and selected within Guangdong province in line with the investigation principles. The sites include Zhongdong, Centian, Meizhou PSPS II, Sanjiangkou and Longchuan in eastern area; Shuiyuanshan, Langjiang, Hecheng, Huangmaogang, Yangjiang PSPS II, Zoumaping and Xinfeng in western area. The comparison of construction conditions of each site is shown in Fig. 1.

Fig. 1. Watershed area of reservoir at each site.

3.1 Service Objects From the perspective of service objects, the distance between each station site in the Eastern area and the load center of the Pear River Delta is within 100–200 km, with little difference. From the perspective of distance to nearby offshore wind plant, Zhongdong and Sanjiangkou are better than Meizhou PSPS II, Centian and Longchuan. From the perspective of distance to the nearest substation, Zhongdong, Centian and Sanjiangkou are better. For sites in the western area, only Shuiyuanshan is within 100 km to the load center of the Pear River Delta, while other sites are not much different. From the perspective of distance to the nearby offshore wind plant, Yangjiang PSPS II and Mainlining are better. From the perspective of the distance to the nearest substation, all sites are within 50 km (Fig. 2).

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From the perspective of the service objects, the focus of each site is different. Shuiyuanshan, Zhongdong and Sanjiangkou are relatively close to the load center of the Pear River Delta, which facilitates peak-shaving regulation. Yangjiang PSPS II and Zoumaping are close to the offshore wind power plant, which can play a great role in absorbing western area’s offshore wind power.

Fig. 2. Distance of each station site.

3.2 Site Conditions The site conditions are mainly compared in terms of geological characteristics, head, hydraulic arrangement, etc. The geological conditions of each station site are not very different, and the geological lithology is mainly granite.The comparison of geologica conditions of each site is shown in Table 1. From the aspect of average head, Zhongdong and Sanjiangkou in eastern area, Yangjiang PSPS II in western area are more favorable, with an average head of more than 600 m (Fig. 3). From the aspects of main dam length and dam height, indexes of the upper and lower reservoirs are better at Zhongdong and Centian in the eastern area and Xinfeng in the western area. For Longchuan in the eastern area, Shuiyuanshan, Langjiang and Zoumaping in the western area, the dams have higher heights. 3.3 External Environment The external environment is mainly compared from the aspects of land acquisition and resettlement, relocation population, ecological red line and nature reserve. From the perspective of land acquisition and resettlement, Yangjiang PSPS II and Meizhou PSPS II basically do not involve the issue of land acquisition and resettlement. The indicators of Zoumaping and Centian are just so so due to involving more than 900 mu of arable land acquisition and 700 people migration. Other sites involve relatively less arable land and population (Fig. 4).

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Fig. 3. Length, height and average head of the main dam at each station site.

From the perspective of the ecological red line, Zhongdong, Meizhou PSPS II, Sanjiangkou, Langjiang and Yangjiang PSPS II basically do not involve the ecological red line, while other sites do (Table 2).

Fig. 4. Comparison of permanent and temporary land acquisition and farmland by station site.

3.4 Economy Site economics are mainly compared in terms of investment per kW, economic internal rate of return and static investment per kWh. Because Yangjiang PSPS II and Meizhou PSPS II do not involve investment in major building projects, the investment per kW is small, only 2909 and 3424 Yuan/kW respectively. The investment per kW of other sites are as following: Sanjiangkou (4915 Yuan/kW), Zhongdong (5033 Yuan/kW), Shuiyuanshan (5222 Yuan/kW), Centian (5229 Yuan/kW), Xinfeng (5339 Yuan/kW), Longchuan (5383 Yuan/kW), Langjiang (5713 Yuan/kW),and Zoumaping (RMB 5828/kW).

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The investment per kWh varies widely among these sites, excluding Meizhou PSPS II and Yangjiang PSPS II, whose investments per kWh are small because of no major building investments. For the other sites, Sanjiangkou has the smallest investment of 534 Yuan/kWh, Longjiang has the largest of 935 Yuan/kWh, followed by Zoumaping with 828 Yuan/kWh (Fig. 5).

Fig. 5. Comparison of investment for each station site.

Table 1. Comparison of the geological lithology of each station site. Site name Zhongdong

Centian

Meizhou PSPS phase II

Sanjiangkou

Longchuan

Shuiyuanshan

Geology and lithology

Granite

Granite, taconite

Granite

Tuff, quartz porphyry, volcanic breccia, etc

Granite

Granite

Site name

Langjiang

Yangjiang PSPS phase II

Zoumaping

Zoumaping

Xinfeng

Geology and lithology

Granite, sandstone

Granite and migmatite

Granite

Granite

Granite

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Table 2. Comparison of each station site on red lines and environmentally sensitive areas. Site name

Zhongdong Centian

Meizhou Sanjiangkou Longchuan Shuiyuanshan PSPS phase II

Whether it No involves ecological red line

Yes

No

No

Yes

Yes

Whether it No involves environmental sensitive areas such as natural protection area, water source area, etc

Municipal No forest park

No

Municipal nature reserve

No

Site name

Langjiang

Yangjiang PSPS phase II

Zoumaping

Zoumaping

Xinfeng

Whether it involves ecological red line

No

No

Yes

Yes

No

Whether it involves environmental sensitive areas such as natural protection area, water source area, etc

No

No

County forest park

Drinking water source protection area, district level protection area, county forest park

No

4 Conclusion Through comparison of some sites in Guangdong province in terms of service object, station conditions, external environment and economy, these site are divided into different echelons, which providing some technical basis for each investor and government’s preliminary work. After comparative analysis, it can be seen that Zhongdong and Sanjiangkou are closer to the load center, with higher head, less environmental constraints, and better economical efficiency. All indicators of Zhongdong and Sanjiangkou are excellent and belong to the first echelon of the rare high-quality sites in Guangdong province. For Centian, Shuiyuanshan and Xinfeng sites, most of the indicators are quite good, while individual indicators are so so, so they belong to the second echelon sites.

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The indicators of Longjiang and Zoumaping are so so in all aspects, but the locations are good and meet the construction conditions, they belong to the third echelon. Guangdong Province is rich in energy storage site resources, and more excellent sites can be selected in the preliminary stage based on the above-mentioned construction conditions investigation method. In addition to the above factors, the final economics of the site is also affected by non-technical factors such as specific scheme design, future tariff policy [1, 18, 19], investor’s decision [17, 20], and local government coordination. Therefore, the construction conditions investigation method in this paper can only be used as an important basis for preliminary work, not the only basis.

References 1. Kong, Y., Kong, Z., Liu, Z., et al.: Pumped storage power stations in China: the past, the present, and the future. Renew. Sustain. Energy Rev. 71, 720–731 (2017) 2. Feng, J., Bo, Y., Wu, S., et al.: Research on the function orientation of pumped-storage plant in China. IOP Conf. Ser. Earth Environ. Sci. 52, 012043 (2017) 3. Ming, Z., Junjie, F., Song, X., et al.: Development of China’s pumped storage plant and related policy analysis. Energy Policy 61, 104–113 (2013) 4. Blakers, A., Lu, B., Stocks, M.: 100% renewable electricity in Australia. Energy 133, 471–482 (2017) 5. Sovacool, B.K., Dhakal, S., Gippner, O., et al.: Halting hydro: a review of the socio-technical barriers to hydroelectric power plants in Nepal. Energy 36(5), 3468–3476 (2011) 6. Lu, Z., Gao, Y., Zhao, W.: A TODIM-based approach for environmental impact assessment of pumped hydro energy storage plant. J. Clean. Prod. 248, 119265 (2020) 7. Li, J., Yi, C., Gao, S.: Prospect of new pumped-storage power station. Global Energy Interconnect. 2(3), 235–243 (2019) 8. Zhou, J., Du, X., Zhou, X.: New situation and assignments of China’s hydropower development in the new phase. Hydropower Pumped Storage 7(04), 1–6 (2021) 9. Qu, Y., Chen, Q., Liu, Z.: Planning review and development potential analysis of Jilin Province pumped-storage power station under the new situation. J. Hydropower Pumped Storage 7(06), 49–52 (2021) 10. Wu, Y., Zhang, T., Xu, C., et al.: Optimal location selection for offshore Wind-PV-seawater pumped storage power plant using a hybrid MCDM approach: a two-stage framework. Energy Conver. Manag. 199, 112066 (2019) 11. Shao, M., Han, Z., Sun, J., et al.: A review of multi-criteria decision making applications for renewable energy site selection. Renew. Energy 157, 377–403 (2020) 12. Zhou, J., Du, X., Zhou, X.: Situation analysis, prediction and countermeasures of hydropower development during the 14th five-year period. Hydropower Pumped Storage 7(01), 1–5 (2021) 13. Sun, K., Li, K.-J., Pan, J., et al.: An optimal combined operation scheme for pumped storage and hybrid wind-photovoltaic complementary power generation system. Appl. Energy 242, 1155–1163 (2019) 14. Sun, H., Rungrojsuwan, S.: Parental involvement in students’ English writing competence: a model at Chinese junior middle school. Asian Cult. Hist. 11(1), 41 (2019) 15. Gong, Y., Tan, C., Zhang, Y., et al.: Peak shaving benefits assessment of renewable energy source considering joint operation of nuclear and pumped storage station. Energy Proc. 152, 953–958 (2018) 16. Zhou, J., Li, S., Gao, J.: Technical and economic analysis of water energy storage to promote new energy development. J. Hydroelect. Eng. 41(6), 1–10 (2022)

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17. Zhang, B.: Vigorously developing pumped storage is an urgent matter to realize China’s dual carbon goal. J. Hydropower Pumped Storage 7(06), 1–10 (2021) 18. Zhang, S., Andrews-Speed, P., Perera, P.: The evolving policy regime for pumped storage hydroelectricity in China: a key support for low-carbon energy. Appl. Energy 150, 15–24 (2015) 19. Hongjun, L., Chengren, L., Weijun, W.: Analysis on current tariff-sharing issues for pumped storage power plants. Energy Technol. Econ. 22(9), 38–42 (2010) 20. Huang, H., Yan, Z.: Present situation and future prospect of hydropower in China. Renew. Sustain. Energy Rev. 13(6–7), 1652–1656 (2009)

Integrated Charger Topology and Control Strategy with Single-Phase and Three-Phase Charing Functions for Electric Vehicle Xiaonan Chen1(B) , Linlin Sun1 , Xize Jiao2 , Heng Song3 , Yazhao Ren4 , and Xinsheng Dong4 1 State Grid Smart Internet of Vehicles Co., Ltd., Beijing, China

[email protected]

2 State Grid Jiangsu Electric Power Co., Ltd., Nanjing, China 3 State Grid Jiangsu Electric Power Co., Ltd. Taizhou Power Supply Company, Nanjing, China 4 SGCC Smart Energy and Electric Transportation Technology Innovation Center (Suzhou) Co.,

Ltd., Nanjing, China

Abstract. In this paper, an integrated on-board charger (OBC) with single- and three-phase operation capabilities is presented. The on-board charger has the ability of bidirectional energy flow in both operation modes. When in single-phase charging mode, the spare bridge arm can be configured as a power decoupling circuit to eliminate the inherent ripple power. The proportional resonant (PR) controller is used in the current inner-loop for the front-stage AC/DC converter with harmonic compensation module, which can effectively eliminate the specific harmonic and implement grid frequency adaptation. After phase angle compensation, the frequency and phase of power grid can be effectively locked when the frequency of power grid fluctuates. In addition, variable DC-link bus voltage control is proposed to make the switching frequency of the CLLLC converter close to the resonant frequency to improve the charging efficiency for the backend CLLLC converter. Finally, a small power platform of the proposed on-board charger is built. The correctness of the proposed charger topology and the control strategy are verified by experiments. Keywords: Charger topology · Control strategy · Electric vehicle

1 Introduction With the increasing application of electric vehicles (EV), different charger topologies have been developed in recent years [1–7]. The literatures [8, 9] analyze, summarize and prospect the development trend of on-board chargers (OBCs) system for EVs. A novel OBC topology converter is proposed for EVs in [10], and the multiple working modes such as OBC, V2G and LDC modes, can be implemented. The safety of non-isolated charging is studied in [11], and the motor windings and power converters are used as the energy storage inductance and charging topology. A multi-functional OBC with high-grade vehicle-to-vehicle (V2V) capability for EV is proposed in [12], which could © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 323–332, 2023. https://doi.org/10.1007/978-981-99-4334-0_40

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improve the charging flexibility effectively. An integrated single-phase charger has been proposed in [13], and multiphase machines windings are used as filtering inductors, but the additional switching relay are required for modes switching. A series electrical drive system including reluctance generator and reluctance motor is proposed for PHEV [14], and the motor stator winding and power converter are used to realize the rectification and charging functions. In [15], the (G2V/V2G) bidirectional energy flow capability is realized. The CLLLC converter is employed as the DC/DC converter to implement the electrical isolation and variable voltage function. However, the second-order voltage ripple in the single-phase charger is not considered. With the proposed rectifier topology in [16], high switching frequency and low harmonic grid current are realized. What’s more, different topological structures and corresponding control schemes of OBCs are studied in [17–20]. In this article, a multifunctional converter topology with driving and charging functions is proposed. The traction battery can be charged with low DC-link bus voltage pulsation and high-power factor in both single- and three-phase charging modes. The highperformance control strategy for the integrated converters also is proposed to implement different charging functions.

2 Charger Topology

Three-phase grid ua ub uc Q1

1 1

J

u1 2 Single-phase 2 grid

Q3

Q7

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Q9 C7

La

D1

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D5

Lb

udc Q2

Caux

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ub

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(b) Front-end Q1

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Single-phase full bridge

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D5

T

D13

D11

Lr2

Ctra

Cr2

utra

Q14

Q12

C12 D12

C14 D14

Active filter

(c)

Fig. 1. Charger topology (a) proposed topology (b) three-phase mode (c) single-phase mode

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Table 1. Working modes of the charger Position of relay J

Operation mode

Function

1

Three-phase mode

G2V

2

Single-phase mode

G2V and active filter

Figure 1(a) shows the proposed EV charger topology. And the front-end AC/DC converter is mainly composed of switches Q1 ~ Q6 , AC filter inductors L a , L b , L c and capacitors C dc , C aux . The back-end DC/DC converter is CLLLC resonant converter and mainly composed of switches Q7 ~ Q14 , inductors L r1 and L r2 , capacitors C r1 , C r2 and C tra , and high frequency transformer T. Power relay J is used to switch the operating mode of the charger. When J switches to position “1”, the system works in three-phase charging mode, and its topology is shown in Fig. 1(b). When J switches to position “2”, the system works in single-phase charging mode, and its topology is shown in Fig. 1(c). The front-end converter is a full-bridge converter, and the spare bridge arm can be configured as an active power decoupling circuit to eliminate the inherent two-frequency ripple power. This topology can realize bidirectional energy flow regardless of working in three-phase mode or single-phase mode. Table 1 lists the position of relay J and the corresponding operation modes of the proposed charger.

3 Control Strategy

Fig. 2. Control scheme for the charger

Figure 2 illustrates the control diagram for the OBC. The red loop is the control part of the outer-loop voltage. The green loop is the inner-loop current control part. The blue loop is the control part of the CLLLC converter. The variable DC-link bus voltage control is adopted. When the traction battery voltage is below the upper threshold (360 V), the constant-current charging strategy is adopted. When the traction battery voltage is higher than the threshold value, the constant voltage control is employed. The detailed design process is given below.

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3.1 Control Strategy for the Front-End AC–DC Converter

Fig. 3. Control strategy (a) The front-end AC–DC converter (b) Structure of the current controller

The PR controller is employed for the current inner-loop control. The SOGI is employed for the resonant part of the controller, and the orthogonal output of the SOGI is used as the grid synchronization signal, which is inputted into the DSOGI-PLL. The phase of the power grid voltage can be obtained after proper phase angle compensation without the need of the voltage sensor. Meanwhile, the DSOGI-PLL has good frequency adaptive ability, and can accurately lock the frequency and phase of the grid voltage when the grid frequency fluctuates. In addition, the PR controller is coupled with harmonic compensators (HC), which can effectively improve the anti-interference ability of the system. Figure 3 shows the proposed control scheme in this paper. In Fig. 3(a), i* d and i* q are the given reference values of the current inner-loop. i* d is the output of the voltage outer-loop PI controller, and i* q is usually set to 0 to eliminate the reactive power. The reference values i* α and i* β of the current inner-loop in the two-phase stationary coordinate system are obtained by inverse Park transformation of i* d and i* q . The reference values are compared with the actual values iα and iβ to obtain the current error values iα and iβ , and then the current errors are respectively sent to the PR + HC controllers. The PR + HC controller Gc (s) can be expressed as:  s s + kr,m 2 ) 2 2 s +ω s + (mω)2 N

Gc (s) = kp (1 + kr

(1)

m=2

where k p is the proportional gain, k r represents the resonant gain, N is the highest harmonic order, m represents the harmonic order, and k r,m is the compensation coefficient of the mth harmonic. The structure diagram of the inner-loop current controller is illustrated in Fig. 3(b). Ginv (s) and Gp (s) are the transfer functions of the converter and the AC side line and inductor respectively, which can be expressed as: Ginv (s) = e−s1.5T Udc Gp (s) =

1 sL + R

(2) (3)

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When the external disturbance is considered, I x (s) can be expressed as: Ix (s) = Ix∗ (s)

Ugrid (s)Gp (s) Gc (s)Ginv (s)Gp (s) − 1 + Gc (s)Ginv (s)Gp (s) 1 + Gc (s)Ginv (s)Gp (s) ωg Ugrid (s) = 2 Ugrid s + ωg2

(4) (5)

where ωg and U grid are the angular frequency and amplitude of the grid voltage respectively.

eα

SOGI

vα qvα

eβ

SOGI

vβ qvβ

vq+

vα +

vβ

+

αβ/dq

vd +

∫

PI n

Fig. 4. Structure diagram of DSOGI-PLL

iLc*

PI

LPF * uCaux uCaux

ir

PR

iLc

Q5 Q6

Fig. 5. Control strategy of the active power decoupling circuit

The structure diagram of DSOGI-PLL is illustrated in Fig. 4. It uses the orthogonal SOGI-QSG to realize the 90-degree phase angle offset of the input signal, and then realizes the extraction of its positive sequence component. When the grid voltage is unbalanced, it can still accurately lock the phase. The output frequency of the PLL is taken as the resonant frequency of the SOGI-QSG and the current PR controller. When the frequency of the grid changes, the PLL can accurately lock the frequency and phase with good adaptation ability. For the single-phase charging control, another bridge arm can be used as an active power decoupling circuit to eliminate the inherent two-frequency ripple of DC-link bus voltage. Assuming that the ripple power is absorbed by the power decoupling circuit, and there is no ripple power on the DC-bus, then the DC bus voltage remains constant. The average current ir flowing through the decoupled circuit can be expressed as [9]: ir =

Pr −Pk × sin(2ωt − 2ϕ + φ) = Uc Uc

(6)

where the ϕ is the phase difference between phase voltage and current. The block diagram of the control strategy for the power decoupling circuit is shown in Fig. 5. The reference value iLc * is composed of two parts, one is the ripple current ir , which is calculated by Eq. (6), and the other is the output value of PI controller, which is used to regulate the voltage of C aux . Since the ir is a double frequency AC quantity, the PR controller is used.

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3.2 Control Strategy for the Back-End DC–DC Converter

Battery voltage Converter gain 1.212 400V

1.212

G ai n

DC-bus voltage

0.848

550V

330V

1

280V

0.848

Normalized frequency

(a)

(b)

Fig. 6. Traditional control strategy (a) Gain of CLLLC converter (b) Frequency range of CLLLC converter

During the charging process, the voltage variation range of the traction battery is large, which would cause the switching frequency of the CLLLC converter to deviate from the resonant frequency. When the input voltage V in of the CLLLC converter is 550 V, the battery voltage V out varies from 280 to 400 V during the charging process, which is shown in Fig. 6(a). The variable ratio of the high-frequency transformer is n = 5/3, and the gain of the CLLLC converter is: G=

N1 Vout nVout = Vin N2 Vin

(7)

Figure 6(b) shows the gain variation range of the CLLLC converter. When the traditional control strategy with constant bus voltage is adopted, the gain variation of the CLLLC converter is relatively large, ranging from 0.848 to 1.212, which leads to a large change in the switching frequency, as shown in Fig. 7(b). In this case, k = 3 and Q = 0.3. The blue area represents the variation range of switching frequency of the CLLLC converter to achieve the above gain. To reduce the variation range of switching frequency of CLLLC converter, this paper adopts variable DC-link bus voltage control, that is, the DC-link bus voltage changes with the battery voltage. When the charger works in single-phase mode, the gain of the converter is shown in Fig. 7(a). When the battery voltage is at the lowest value of 280V, the bus voltage is controlled at about 467V by the front-end AC–DC converter, and the gain of the converter is 1. After that, the bus voltage rises synchronously with the battery voltage until the voltage reaches to 600 V. During the whole charging process, the gain of the converter varies from 1 to 1.111. The red area in Fig. 7(b) shows the switching frequency range. The switching frequency of the converter changes within a small range and remains close to the first resonant frequency.

Integrated Charger Topology and Control Strategy with Single-Phase Battery voltage 400V

1

360V

600V

Converter Gain 1.111

1.111

Gain

DC-bus voltage

329

1

1

280V

467V

Normalized frequency

(a)

(b)

Fig. 7. Variable DC-link bus voltage control (a) Gain of CLLLC converter (b) Frequency range of CLLLC converter Capacitor

Heat sink

M57962AL Inductor

Voltage sensor

SI8273 driver

Mosfet

Current sensor

Sensor

DSP controller board

Emulator

AD7606

(a)

Resonant inductor

high-frequency Resonant transformer capacitor

(b)

Fig. 8. The protype platform (a) AC/DC converter (b) CLLLC converter

4 Experimental Verification To verify the proposed converter topology and control strategy, the protype of the integrated OBC for EV is shown in Fig. 8. The protype platform includes AC/DC and CLLLC converters shown in Fig. 8(a) and (b), respectively. The M57962AL and SI8273 are the driver for the power switches. TI DSP TMS320F28335 is used as the main controller and implement the control strategy and algorithm. LEM voltage and current sensors are adopted to sense the voltage and current. 4.1 Three-Phase Charging Mode The experiment waveforms when the DC-link bus voltage changes in three-phase charging mode is shown in Fig. 9. It can be noted that the DC-link bus voltage drops from 600 to 550 V. The active power output of the charger is reduced from 3300 to 2700 W, and the reactive power remains 0, as shown in Fig. 9(b). Currently, the CLLLC converter is in a quasi-resonant state, and its switching frequency is close to the resonant frequency. The primary and secondary resonant currents are sinusoidal with peak values of 14.4 and 17 A as shown in Fig. 9(a) and (b).

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t:(100ms/div)

udc

P

ua Q

ia CH1:200V/div,CH2:600Vdiv,CH3:15A/div

CH1:2000W/div,CH2:2000Var/div

(a) t:(2

s/div)

(b) t:(2

uGS7

s/div)

iLr2

uDS7

uDS11

iLr1

iD11 utra

CH1:25V/div,CH2:550V/div,CH3:30A/div

CH1:40A/div,CH2:280V/div,CH3:25A/div,CH4:550V/div

(c)

(d)

Fig. 9. Experimental waveforms when the DC-link bus voltage changes (a) phase A voltage, current and DC-link bus voltage (b) load power (c) primary waveforms (d) secondary waveforms

4.2 Single-Phase Charging Mode t:(20ms/div)

t:(20ms/div)

udc

udc

u

u

i

i

CH1:500V/div,CH2:500V/div,CH3:35A/div

(a)

CH1:500V/div,CH2:500V/div,CH3:35A/div

(b)

Fig. 10. Experimental waveform of grid voltage with 9th harmonic (a) traditional control strategy (b) improved control strategy

For single-phase charging mode, when the grid voltage contains 10% 9th harmonic, the experimental waveforms using the traditional and the improved control strategies are shown in Fig. 10(a) and (b), respectively. It can be seen that when the traditional control strategy is adopted, the output current is significantly distorted by the influence of higher harmonics. When the improved control strategy is adopted, the output current distortion is small, and the improved control strategy can effectively suppress the interference of higher harmonics in the single-phase charging mode. Figure 11 shows the experimental waveform when the DC-link bus voltage changes. The DC-link bus voltage rises from 470 to 550 V, and the peak value of the grid output current rises from 14 to 21 A, and the load power rises from 2100 to 3300 W. During this process, the CLLLC converter is in quasi-resonant operation state. Figure 12 shows the efficiency curves of the proposed charger under three-phase and single-phase charging modes, using the traditional and proposed control methods. Compared with the traditional control method, the overall efficiency of the proposed

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331

t:(100ms/div)

t:(100ms/div)

udc

P

u

Q

i CH1:550V/div,CH2:600V/div,CH3:35A/div

(a)

CH1:2000W/div,CH2:2000Var/div

(b)

Fig. 11. Experimental waveforms when the DC-link voltage is changed (a) DC-link bus voltage change (b) load power

(a)

(b)

Fig. 12. Experiment efficiency (a) three-phase charging mode (b) single-phase charging mode

control method is improved. As shown in Fig. 12(a) and (b), the maximum efficiencies of the proposed control method reach to 94.7 and 95.5%, respectively.

5 Conclusion In this article, an integrated vehicle charger with single- and three-phase operation capability is proposed. The PR + HC controller is used in the inner-loop current for the front-end AC–DC converter, which can effectively suppress the specific harmonics. The output of the resonant term of PR controller is taken as the input signal of the DSOGI-PLL with phase angle compensation to eliminate the voltage sensors. The variation DC-link bus voltage control is employed to make the switching frequency of the CLLLC converter close to the resonant frequency to improve the charging efficiency. In addition, the active power decoupling circuit is used to eliminate the ripple power when the charger works in single-phase mode. By adopting the proposed control strategy, the maximum efficiencies of the proposed control method reach to 94.7 and 95.5% for the three-phase and single-one modes. Acknowledgement. This research is supported by the State Grid Corporation of China science and technology project: 5400-202218161A-1-1-ZN.

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References 1. Khaligh, A., D’Antonio, M.: Global trends in high-power on-board chargers for electric vehicles. IEEE Trans. Vehicul. Technol. 68(4), 3306–3324 (2019) 2. Kim, S., Kang, F.-S.: Multifunctional onboard battery charger for plug-in electric vehicles. IEEE Trans. Ind. Elect. 62(6), 3460–3472 (2015) 3. Verma, A., Singh, B., et al.: Multi-objective reconfigurable three-phase off-board charger for EV. IEEE Trans. Ind. Appl. 55(4), 4192–4203 (2019) 4. Khaligh, A., Antonio, D.M.: Global trends in high-power on-board chargers for electric vehicles. IEEE Trans. Vehicul. Technol. 68(4), 3306–3324 (2019) 5. Semsar, S., Soong, T., et al.: On-board single-phase integrated electric vehicle charger with V2G functionality. IEEE Trans. Power Electr. 35(11), 12072–12084 (2020) 6. Park, M.H., Baek, J., Jeong, Y., Moon, G.W.: An interleaved totem-pole bridgeless boost PFC converter with soft-switching capability adopting phase-shifting control. IEEE Trans. Power Elect. 34(11), 10610–10618 (2019) 7. Shah, S.S., Bhattacharya, S.: A simple unified model for generic operation of dual active bridge converter. IEEE Trans. Ind. Electr. 66(5), 3486–3495 (2019) 8. Wang, Y., Zhang, Y., et al.: A dual-active-bridge with half-bridge submodules DC solid-state transformer for DC distribution networks. IEEE J. Emerg. Select. Top. Power Electr. 9(2), 1891–1904 (2021) 9. Nazib, A.A., Holmes, D.G., McGrath, B.P.: Self-synchronising stationary frame invertercurrent-feedback control for LCL grid-connected inverters. IEEE J. Emerg. Select. Top. Power Electr. 9(1), 1–12 (2021) 10. Cheng, H., Wang, W., Liu, H., Yang, S.: Integrated multifunctional power converter for small electric vehicles. J. Power Electr. 21(11), 1633–1645 (2021). https://doi.org/10.1007/s43236021-00308-7 11. Xiao, Y., Liu, C., Yu, F.: An integrated on-board EV charger with safe charging operation for three-phase IPM motor. IEEE Trans. Ind. Electr. 66(10), 7551–7560 (2019) 12. Taghizadeh, S., Hossain, M.J., Poursafar, N., Lu, J., Konstantinou, G.: A multifunctional single-phase EV on-board charger with a new V2V charging assistance capability. IEEE Access 8, 116812–116823 (2020) 13. Subotic, I., Bodo, N., Levi, E.: Single-phase on-board integrated battery chargers for EVs based on multiphase machines. IEEE Trans. Power Electr. 31(9), 6511–6523 (2016) 14. Hassan, T., Cheema, K.M., Mehmood, K., Tahir, M.F., Milyani, A.H., Akhtar, M.: Optimal control of high-power density hybrid electric vehicle charger. Energy Rep. 7, 194–207 (2021) 15. Cheng, H., Wang, L., Xu, L., Ge, X., Yang, S.: An integrated electrified powertrain topology with SRG and SRM for plug-in hybrid electrical vehicle. IEEE Trans. Ind. Electr. 67(10), 8231–8241 (2020) 16. Patil, D., Agarwal, V.: Compact onboard single-phase EV battery charger with novel lowfrequency ripple compensator and optimum filter design. IEEE Trans. Vehicul. Technol. 65(4), 1948–1956 (2016) 17. Ali, A., Jiang, C., Zhou, Y., Salman, H., Khan, M.M.: An efficient soft-switched vienna rectifier topology for EV battery chargers. Energy Rep. 8, 5059–5073 (2021) 18. Semsar, S., Soong, T., Lehn, P.W.: On-board single-phase integrated electric vehicle charger with V2G functionality. IEEE Trans. Power Electr. 35(11), 12072–12084 (2020) 19. Nassary, M., Orabi, M., Ghoneima, M.: Discussion of single-stage isolated unidirectional AC– DC on-board battery charger for electric vehicle. In: Proceedings of the IEEE 4th Southern Power Electronics Conference (SPEC) (2018) 20. Han, Y., et al.: Design considerations of asymmetric step-up/down dual-resonator charger for lithium-ion battery applications. Energy Rep. 8, 696–704 (2022)

Research on Short-Circuit Fault of High-Speed Maglev Traction Linear Motor Xinmai Gao(B) , Yanxiao Lei, Weitao Han, Lvfeng Ju, and Zhou Ying National Engineering Research Center for High-Speed Trains, CRRC Qingdao Sifang Co., Ltd., Qingdao, China [email protected]

Abstract. The short-circuit fault of the traction linear motor has the most serious impact on the high-speed maglev vehicle. In order to evaluate vehicle and track structural strength, it is necessary to calculate the traction force and current impact in the fault condition. In this paper, on the basis of analyzing the fault types and short-circuit equivalent models of high-speed maglev traction linear motors, the short-circuit current impact and the suspension and traction forces caused by fault condition are calculated through the single electromagnet finite element as the equivalent model of traction linear motor. Numerical calculation and model derivation of short-circuit fault of traction linear synchronous motor mutually confirm the reliability of the analysis. Keyword: Linear synchronous motor · Short-circuit fault · High-speed maglev

1 Introduction The EMS high-speed maglev vehicle tracked by a long stator synchronous linear motor [1, 2]. The stator of the propulsion motor is arranged along the left and right sides of the track, and the mover is assembled on the suspension frame. In this way, contactless suspension and traction are achieved. The structure relationship of the traction linear motor stator and stator is shown in Fig. 1(a), and the relationship of the traction motor in the high-speed maglev system is shown in Fig. 1(b). Stator Winding

Stator core Rail part

Vehicle part Armuture Magnet

Suspension core

a)

Excited winding

Cross section of propulsion motor

b) propulsion motor position in system

Fig. 1. Propulsion motor structure and installed position.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 333–338, 2023. https://doi.org/10.1007/978-981-99-4334-0_41

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2 Dynamic Mathematical Model 2.1 Motor Equivalent Model and Parameters A 5-marshalled maglev vehicle has a about 130 m length traction motor. When the rear end and the front of the vehicle are short-circuited at same time, and the rear of the vehicle posited the star connected node, the back-EMF of the vehicle is the largest and the short-circuit loop impedance is the smallest, so the short-circuit current is the largest, as shown in Fig. 2. Armature resistance and indutance EMF

Line resistance and inductance

One electromagnet

U

Star-connected node short with ground

V W Un-coverage

Part armature of vehicle coverage, about 130miter

Short point

Fig. 2. Worst short-circuit condition.

The back EMF and the impedance of short-circuit loop are proportional to the speed of the vehicle. When the reactance of the short-circuit loop is much larger than the loop resistance (the speed is high enough, about 20 m/s), the magnitude of the short-circuit current has no matter with the speed. The short-circuit current can be equivalent to an electromagnet short-circuit, and the traction motor parameters are shown in Table 1. Table 1. High-speed maglev traction motor parameters. Traction motor parameters

Value

Armature resistance

0.27 /km

Armature inductance

4 mH/km

Armature leakage inductance

2.6 mH/km

D-axis mutual inductance

3.8 mH/one

EMF factor

0.2822 V/m/s/m

D-axis mutual inductance

3.8 mH/one electromagnet

The voltage and magnetic circuit equations [3–7] of the traction motor are shown in (1) and (2). ⎤ ⎡ ⎤ ⎡ ⎤⎡ ⎤ ⎡ ⎡ ⎤ −ωψ q ψd rd 0 0 id ud ⎣ uq ⎦ = p⎣ ψq ⎦ + ⎣ 0 rq 0 ⎦⎣ iq ⎦ + ⎣ ωψ ⎦ (1) d uf ψf if 0 0 rf 0

Research on Short-Circuit Fault of High-Speed Maglev Traction

⎤ ⎡ ⎤⎡ ⎤ ψd xd 0 xmd id ⎣ ψq ⎦ = ⎣ 0 xq 0 ⎦⎣ iq ⎦ xmd 0 xf ψf if

335

⎡

(2)

where p is the differential operator, u, ψ, i are represent the terminal voltage, flux linkage and winding current respectively, and the subscripts d, q, f represent the d-axis, q-axis and excitation components. 2.2 Armature WindingShort-Circuit Current A. Steady current before short circuit It is Consider that the active current before the short circuit is the maximum active current, and the reactive current is zero, that is iq0 = 2800A, id 0 = 0. B. Armature Short circuit current The magnitude of the short-circuit current is related to the moment when the shortcircuit occurs at ud0 = 0, uq0 = Em , the short-circuit current is the largest. The voltage boundary condition is brought into Eq. (1), and the Laplace transformation of (1) and (2) is performed to obtain the current in the frequency domain, ignoring the stator winding resistance. 1 1 Em   × × id (s) = − (3) 1 1 s s + 1 xd (s) s 2 + rs + xd (s)

iq (s) = −

s 2 + rs



1 xd (s)

xq (s)

1  × + xq1(s) s + 1 xq (s)

Em

(4)

It is necessary to carry out the inverse Laplace on (3) and (4), in order to obtain the time-domain current. 

 1 Em − Tt 1 1 − Tt  e d + + (5) id (t) = −Em − e a cosωt xd  xd xd xd  t Em (6) iq (t) = − e− Ta sinωt xq The formulas (5) and (6) are transformed with the rotation coordinates. The phase winding current in stationery coordinates can be expressed as (7). 

 1 1 − Tt 1 d + e cos(ωt + θ0 ) − iu (t) = − Em xd xd xd



Em − Tt 1 1 Em − Tt 1 1 cosθ0 + cos(2ωt + θ0 ) + e a  + e a  − (7) 2 xd xq 2 xd xq v, w phase winding current in the stationery coordinates can be deduced as u phase. The short-circuit current includes the fundamental component decayed with the excitation winding time constant, the DC component and the secondary component attenuated with the armature winding time constant, and the steady-state short-circuit magnitude is related to the short-circuit steady-state impedance.

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2.3 Excitation Short Circuit Current According to the superposition theorem, when the traction motor is short-circuited, the excitation winding current is composed of the steady-state current before the short-circuit and the impulse current caused by the zero excitation voltage after the short-circuit.   t uf −T xmd − Tt f if (t) = Em e − e d cos(ωt + θ0 ) + (8) xd rf The short circuit excitation current of the traction motor includes a DC component decayed with the excitation time constant, a fundamental wave component and a steadystate DC component attenuated with the armature winding time constant.

3 Short Circuit Simulation Verification There are two simulation condition. The motor operates in the 600 km/h constant speed, and the maximum acceleration capacity operation. To compare the two working conditions, the vehicle speed is set 600 km/h when acceleration condition is simulated. When a short-circuit fault occurs in the traction motor, the regulation effect of the excitation current controller is ignored. A. Uniform motion at 600 km/h.

a)

Armature winding short circuit current

b) short circuit traction

c)short-circuit excitation current d) short-circuit suspension force

Fig. 3. The impact of short-circuit fault current and force when the vehicle is running at uniform motion.

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When the high-speed maglev vehicle runs 600 km/h, the armature winding current amplitude is 1 kA, the short-circuit impulse current is 12.7 kA, as shown in Fig. 3 a). The decay period of the periodic armature winding current component is about 13 ms. The non-periodic short-circuit current component generated traction and suspension force with the short-circuit armature winding current. The maximum traction force is 14.1 kN, as shown in Fig. 3 b). The equivalent impact traction of the whole vehicle is 225 kN. Figure 3 c) The excitation winding current contains periodic and anti-periodic components when the armature is short-circuited. The periodic component decays as the armature winding time constant, and the anti-periodic component attenuated as the excitation winding time constant. The stable short-circuit current of the armature decreased the main field, which has a great influence on the suspension force, as shown in Fig. 3d). B. Accelerated operating conditions.

a)

Armature winding short circuit current

C) short-circuit excitation current

b) short circuit traction

d) short-circuit suspension force

Fig. 4. The impact of short-circuit fault current and force when the vehicle is running at accelerated operation.

The stator winding stable operating current amplitude is 2.8 kA, when the highspeed maglev vehicle occurs short-circuit fault in acceleration condition. The shortcircuit current peak value is 15.9 kA, as shown in Fig. 4 a). The impact traction force reaches 20.1 kN, which is 321 kN when converted to the impact traction force of the entire vehicle. The attenuation and properties of the short-circuit current are the same as those in the uniform operation, however the short-circuit current, the traction force and suspension force caused are larger than those in the uniform operation.

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4 Conclusion The traction linear motor short-circuit current components are deduced through shortcircuit operation impedance and mathematical analysis. The correctness is verified by FEA simulation. The short-circuit current reaches more than 20 kA, and the traction impact force reaches 320 kN. Since the high-speed maglev traction synchronous linear motor has no damping winding, there is no super-transient component in the shortcircuit current. The number of turns and the magnetic leakage of the excitation winding is large, which reduces the impact of the short-circuit current, however the decay period of the excitation short-circuit current is too long, which affects the suspension control performance. Acknowledgement. Project supported by special funding for key research and development of Qingdao Science and Technology Plan, project number: 21-1-2-9-cl.

References 1. Creppe, R.C., de Souza, C.R., Simone, G.A., Serni, P.J.A.: Dynamic behavior of a linear induction motor. In: MELECON’98 9th Mediterranean Electrotechnical Conference. Proceedings (Cat. No.98CH36056), Tel-Aviv, Israel, vol. 2, pp. 1047–1051 (1998). https://doi.org/10.1109/ MELCON.1998.699389 2. Higuchi, T., Abe, T., Oyama, J., Yoshida, T., Hirayama, T.: Short-armature selfexcitation type linear synchronous motor for transport system. In: Proceedings of the 2007 International Conference on Electrical Machines and Systems (ICEMS), Seoul, Korea (South), pp. 1513–1516 (2007). https://doi.org/10.1109/ICEMS12746.2007.4412280 3. Sun, Z., Gao, J., Ma, W., Lu, J., Xu, J.: Impedance matrix and parameters measurement research for long primary doublesided linear induction motor. IEEE Trans. Plasma Sci. 47(5), 2703–2709 (2019). https://doi.org/10.1109/TPS.2019.2909112 4. Sakamoo, T.: Guidance control characteristics for Maglev vehicle with dynamic compensator. In: Proceedings of the 2000 26th Annual Conference of the IEEE Industrial Electronics Society. IECON 2000. 2000 IEEE International Conference on Industrial Electronics, Control and Instrumentation. 21st Century Technologies, Nagoya, Japan, vol. 4, pp. 2285–2290 (2000). https://doi.org/10.1109/IECON.2000.972353 5. Howard, D.F., Habetler, T.G., Harley, R.G.: Experimental study on the short-circuit contribution of induction machines. In: Proceedings of the 2013 International Electric Machines and Drives Conference, Chicago, IL, USA, pp. 960–967 (2013). https://doi.org/10.1109/IEMDC.2013. 6556213 6. Liu, F., Mecrow, B., Smith, A.C., Alvarenga, B., Deng, X.: A fault tolerant induction motor drive. In: Proceedings of the 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA, pp. 1616–1622 (2019). https://doi.org/10.1109/ECCE.2019.8912575 7. Zhao, W., Cheng, M., Ji, J., Cao, R., Du, Y., Li, F.: Design and analysis of a new fault-tolerant linear permanent magnet motor for Maglev transportation applications. IEEE Trans. Appl. Supercond. 22(3), 5200204 (2012). https://doi.org/10.1109/TASC.2012.2185209

A Designable Stability-Improving Control Method Based on Eigenvalue Sensitivity for Three-Phase Grid-Following Converter Zexi Zhou1 , Hong Li1(B) , Jinchang Pan1 , Kai Li1 , Zhichang Yang2 , and Xiaoge Liu2 1 Beijing Jiaotong University, Beijing, China

[email protected] 2 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., Beijing, China

Abstract. For a three-phase grid-following converter, the system may run unstably due to the improper parameters of phase-locked loop (PLL) and the controller under the weak grid. This paper for the first time presents a designable stability-improving control method based on eigenvalue sensitivity for threephase grid-following converters. Firstly, the small-signal model of the three-phase grid-following converter considering the nonlinear characteristic of PLL is established; next, the mechanism of the proposed designable stability-improving control method for the grid-following converter based on eigenvalue sensitivity is introduced; further, using the proposed stability-improving control method, an additional inverter-side d-axis current feedback (AIdCF) stability-improving control strategy is derived, whose effectiveness is also verified by simulation. This paper not only provides a stability-improving control strategy for the three-phase grid-following converter, but also the method to generate the stability-improving control strategies. Keywords: Three-phase grid-following converter · Designable stability-improving control method · Eigenvalue sensitivity analysis

1 Introduction Grid-following converter is widely applied in renewable energy conversion system such as wind power generator [1]. The synchronization between grid-following converters and power grid is realized based on the PLL. However, in the case of weak power grid, sideband oscillations and loss of synchronization (LOS) [2] will occur due to the inaccuracy grid voltage phase estimated by PLL. At the same time, high-frequency harmonic oscillation will occur when the control parameters of current controller are unsuitable [3]. These stability problems appeared in many practical projects [4] and seriously endangered the normal operation of the power grid. Currently, there are two main ways to improve the small signal stability of gridfollowing converters. One is to improve the converter system stability under specific © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 339–347, 2023. https://doi.org/10.1007/978-981-99-4334-0_42

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working conditions by tuning the parameters of PLL and current controller [5]. However, this approach is closely related to all the possible working conditions of the system. When the working conditions of the converter system changes, the corresponding control parameters need to be reset manually. Another is to change the controller of grid-connected converter to achieve stability improvement. In [6], to solve the sideband oscillation problem caused by PLL, the virtual impedance was added into the PLL model to eliminate the characteristic of the weak power grid and make the PLL track an equivalent strong power grid. Most of the existing methods proposed to improve the small-signal stability of grid-following converters only focus on solving a specific stability problem in real application. However, these methods are difficult to be extended into other converters with different controllers and different stability problems. Therefore, this paper proposes a designable stability-improving control method based on eigenvalue sensitivity analysis and time-domain model for deriving the required controller, it is to freely solve different stability problems in practice.

2 Small-Signal Model of Three-Phase Grid-Following Converter Considering the Nonlinear Characteristic of PLL The basic three-phase grid-following converter system is shown as Fig. 1 below. The main circuit of the grid-following converter system includes the inverter bridge, LCL filter, and power grid. Power Grid L1 I1a LCL Filter I2a L2 Lg Rg Vg I2b L2 Lg Rg Vg L1 I1b b Vdc I2c L2 Lg Rg Vg c L1 I1c Ica Icb Icc S4 S6 S2 vca vcb vcc [Vpcc_abc] Inverter Bridge C C C g1 g2 g3 g4 g5 g6 abc RC RC RC abc PLL

S1 S3 S5 a

N

SPWM

vId vIq

+ +k

ii

+ +k

dq kpi

xd

∫

kpi

ii

xq

∫

i2d + i Idref -

-

2q

+

Iqref

dq

θPLL

vαβ αβ vgd dq vgq θPLL

kpPLL kiPLL

SRF-PLL

+ ωg Δω ∫ Φ+ + ωPLL PLL +

∫

θPLL

vPCC_abc αβ abc

Fig. 1. Structure of basic three-phase grid-following converter system including PLL and inner current controller.

The controller of the grid-following converter system includes PLL and current controller. In the synchronous coordinate system, all three-phase AC components can be converted into DC components on the d and q axes. The current i1a , i1b , i1c , i2a , i2b , i2c , and voltage vca , vcb , and vcc in stationary coordinate system correspond to i1d , i1q , i2d , i2q , vcd , and vcq in synchronous coordinate system. For the three-phase grid-following converter, all controllers control the DC component in synchronous coordinate system. The differential equation in synchronous coordinate system of three-phase inverter with current controller can be obtained as introduced in [7].

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Under the weak grid, there is a difference δ = θ PLL − θ g between the output phase of PLL and the phase of the grid. At this time, the d and q axis components of grid voltage in the synchronous coordinate system are vgq = −V g sin(δ) and vgd = V g cos(δ), respectively. The nonlinear differential equation of PLL in synchronous coordinate system is shown as (1). It can be seen that there is nonlinear term with a sine function for the state variable δ as sin(δ). At the same time, there are product terms between state variables such as ω(t)i2d (t). Therefore, the differential equation of PLL under weak grid shows strong nonlinear characteristics. dδ = f9 = ω dt ⎡

d ω = f10 dt

⎤  di2q   di2d d 2 i2q  ⎢ kpPLL Lg dt 2 + kiPLL Lg + kpPLL Rg dt + kpPLL Lg ω + ωg dt ⎥ ⎥ ⎢ ⎦ ⎣   dvgq +kpPLL + kiPLL ω + ωg Lg i2d + kiPLL Rg i2q + kiPLL vgq dt = 1 − kpPLL Lg i2d (1)

By combining the differential equation of the three-phase inverter with current controller in [7] with the nonlinear differential equation of PLL shown in (1), the whole nonlinear differential equation of the grid-following converter under weak grid can be obtained. The nonlinear differential equation of the whole system as shown in Fig. 1 can be expressed as (2). T

(2) x˙ = f (x) x = i1d i1q i2d i2q vcd vcq xd xq δ ω Then the small-signal Jacobian matrix J of the grid-following converter can be derived by small-signal linearization at an equilibrium point in synchronous coordinate system as described in [8]. The derived small-signal Jacobian matrix is shown below as (3). In the Jacobian matrix (3), I 1d , I 1q , I 2d , I 2q , V cd , V cq , and δ s are the stable values of the system at an equilibrium point. As (3) is a constant matrix, the small-signal stability of the grid-following converter system can be judged by the position of the eigenvalues of Jacobian matrix in complex plane [8]. ⎤ ⎡ Rc Vdc kpi Vdc kii 1 − L1 ωg RL1c − 2L 0 − 0 0 0 I 1q L 2L 1 1 1 ⎥ ⎢ Vdc kpi Rc dc kii ⎢ −ωg − RL c 0 − 2L 0 − L11 0 V2L 0 −I1d ⎥ L 1 1 1 1 ⎥ ⎢ R +R V sin δ 1 ⎢ Rc − L2c +Lgg ωg 0 0 0 Lg2 +Lgs I2q ⎥ ⎥ ⎢ L2 +Lg 0 L2 +Lg ⎥ ⎢ Rc +Rg Vg cos δs Rc 1 ⎥ ⎢ 0 −ω − 0 0 0 −I g 2d ⎥ L2 +Lg L2 +Lg L2 +Lg L2 +Lg ⎢ ⎥ ⎢ 1 1 J =⎢ C 0 −C 0 0 ωg 0 0 0 Vcq ⎥ ⎥ ⎢ 1 1 ⎢ 0 0 −C −ωg 0 0 0 0 −Vcd ⎥ C ⎥ ⎢ ⎢ 0 0 −1 0 0 0 0 0 0 0 ⎥ ⎥ ⎢ ⎢ 0 0 0 −1 0 0 0 0 0 0 ⎥ ⎥ ⎢ ⎣ 0 0 0 0 0 0 0 0 0 1 ⎦ J2 J3 J4 J5 J6 0 J7 J8 J9 J1 (3)

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3 Designable Stability-Improving Method Based on Eigenvalue Sensitivity 3.1 Eigenvalue Sensitivity For a given system, the first-order Jacobian matrix eigenvalue sensitivity of the ith eigenvalue λi to a certain parameter b in matrix can be expressed as (4) introduced in [9]. ⎧ T ⎨ J · i = λi i ∂λi T ∂J J · i = λ i i =  (4) i i ∂b ∂b ⎩ T i i = 1 where, Ψ i and Φ i are the standardized left and right eigenvector of the i-th eigenvalue. According to the eigenvalue sensitivity of the system Jacobian matrix, the influence of the system parameter’s changing on the system stability can be obtained [10]. 3.2 Basic Idea of Stability-Improving Control Method Based on Eigenvalue Sensitivity

Fig. 2. Flowchart of designable stability-improving control method based on eigenvalue sensitivity.

As seen in Fig. 2, a perturbation element needs to be added to a certain position in the Jacobian matrix. Then the sensitivity of the added element to the eigenvalues of the modified Jacobian matrix J b will be calculated. If the added element is beneficial to the system stability, namely the real part of the eigenvalue sensitivity to the added element is less than zero. It is necessary to transfer the added element to current control row of Jacobian matrix. By this matrix similarity transformation, the actual stability-improving control strategy that can be implemented in practice will be obtained.

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3.3 The Additional Inverter-Side d-Axis Inductor Current Feedback Control Derived by Eigenvalue Sensitivity The grid-following converter system parameters used later are shown in Table 1 below. Table 1. Parameters of three-phase grid-following converter system Main circuit parameters

Control parameters

V dc = 800 V, L 1 = 1.6 mH, L 2 = 1 mH, C = 20 uF, Rc = 2 , Rg = 0.01 , L g = 5 mH

k pi = 0.04, k ii = 5, k ppll = 0.566, k ipll = 50.776

The additional perturbation element is first added to the first row and first column of the Jacobian matrix as (5). When −5/L 1 is added, according to (4), the eigenvalues sensitivity of the grid-following converter can be obtained as shown in Table 2. From Table 2, the real part of the eigenvalue sensitivity of −5/L 1 to all the eigenvalues are negative. Therefore, the system stability can be improved when −5/L 1 is added. Table 2. Eigenvalues sensitivity of parameter b. Sb λ1,2

Sb λ3,4

Sb λ5,6

Sb λ7,8

Sb λ9,10

− 786.9 ± 77i

− 407.4 ± 298i

− 383.2 ± 389i

− 2.75 ± 2.66i

17.9 ± 10i

Since the main purpose of this paper is to improve the system stability without changing the parameters and structure of the main circuit, it is necessary to transfer the row where the disturbance element −b/L 1 is located to the current control row. Jb = ⎡ Rc − L1 − Lb1 ωg ⎢ ⎢ −ωg − RL1c ⎢ Rc ⎢ 0 ⎢ L2 +Lg ⎢ R c ⎢ 0 L2 +Lg ⎢ ⎢ 1 0 ⎢ C ⎢ 1 ⎢ 0 C ⎢ ⎢ 0 0 ⎢ ⎢ 0 0 ⎢ ⎣ 0 0 J2 J1

Rc L1

−

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0 R +R

− L2c +Lgg −ωg − C1 0 −1 0 0 J3

− L11

0

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0

− L11

1 L2 +Lg

− L2c +Lgg

0

0 − C1 0 −1 0 J4

0 −ωg 0 0 0 J5

0 Rc L1

−

Vdc kpi 2L1

ωg

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0

0

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0

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0 0 0 0 0 0

0 0 0 0 0 J7

ωg 0 0 0 0 J6

Vg sin δ L2 +Lg Vg cos δ L2 +Lg

0 0 0 0 0 J8

I1q

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⎥ −I1d ⎥ ⎥ I2q ⎥ ⎥ ⎥ −I2d ⎥ ⎥ ⎥ Vcq ⎥ ⎥ −Vcd ⎥ ⎥ 0 ⎥ ⎥ 0 ⎥ ⎥ 1 ⎦ J9 (5)

The similarity transformation matrix Pb is the matrix that the first row of unit matrix times −2b/(V dc k ii ) then adds to the seventh row. Similarly, transformation matrix Pb−1

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is the matrix that the seventh column times 2b/(V dc k ii ) then adds to the first column. After matrix similarity transformation Jb  = Pb Db Pb−1 , perturbation elements b can be transformed into d-axis current control row. The Jacobian matrix after similarity transformation is shown as (6) below, where the new elements transferred to the d-axis current control line are:   2bωg 2Rc − Vdc kpi b 2Rc b , A2 = , A3 = , A1 = − Vdc L1 kii Vdc kii L1 Vdc kii 2bI1q 2b 2b Vdc b A4 = , A5 = − , A6 = , A7 = . Vdc kii Vdc kii L1 Vdc L1 Vdc kii As shown in (6) below, for the seventh line namely d-axis current control line of Jb , it can be concluded that the added elements after similarity transformation A1 -A7 is the same as all the elements in the first line after multiplying a coefficient 2b/(V dc k ii ). Jb  = ⎡ Rc Vdc kpi − L1 ωg RL1c − 2L 1 ⎢ ⎢ −ωg − RL1c 0 ⎢ R +R ⎢ Rc − L2c +Lgg ⎢ L2 +Lg 0 ⎢ Rc ⎢ 0 −ωg L2 +Lg ⎢ ⎢ 1 0 − C1 ⎢ C ⎢ 1 ⎢ 0 0 C ⎢ ⎢ −A1 −A2 −1 − A2 ⎢ ⎢ 0 0 0 ⎢ ⎣ 0 0 0 J2 J3 J1

− L11

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Vdc kii 2L1

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− L11

1 L2 +Lg

− L2c +Lgg

0

0 − C1 −A3 −1 0 J4

0 −ωg −A4 0 0 J5

0 Rc L1

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Vdc kpi 2L1

ωg

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0 0 −A5 0 0 0

0 0 0 0 0 J7

ωg 0 0 0 0 J6

Vg sin δ L2 +Lg Vg cos δ L2 +Lg

0 0 0 0 0 J8

I1q

⎤

⎥ −I1d ⎥ ⎥ I2q ⎥ ⎥ ⎥ −I2d ⎥ ⎥ (6) ⎥ Vcq ⎥ ⎥ −Vcd ⎥ ⎥ −A6 ⎥ ⎥ 0 ⎥ ⎥ 1 ⎦ J9

The first line of Jb  is the derivation of inverter-side d-axis current. Therefore, the control strategy equivalent to adding perturbation element at first row and first line of system original Jacobian matrix J can be deduced as an additional inverter-side daxis current feedback (AIdCF) control. The specific deduced stability-improving control strategy is shown in Fig. 3. dxd 2b di1d dxd  2b = − ⇒ xd  = xd − i1d dt dt Vdc kii dt Vdc kii

(7)

4 Simulation Verification of the Derived Stability-Improving Control Strategy 4.1 Simulation Verification A simulation model of grid-following converter system with the same PLL is built in Simulink and its main circuit parameters are given in Table 1. The stability-improving effect of the derived AIdCF control with b = 5 is shown in Fig. 4. When the PI parameters

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S5 L1 L1 b vb c L1 vc S6 S2 S3

g1 g2 g3 g4 g5 g6

I1a I1b I1c Ica Icb Icc v abc ca vcb vcc dq C C C RC RC RC i1d N

Lg Rg Vg Lg Rg Vg Lg Rg Vg

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abc θPLL [Vpcc_abc] dq abc dq

[vpccd,vpccq] i2d PLL kpi + x' + xd ∫ Idref kii d i2q I kpi qref + x kii q ∫

-2b/(Vdckii)

vId

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I2a L2 I2b L2 I2c L2

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vIq

+

+

Fig. 3. Grid-following converters system with AIdCF control.

of current controller is k pi = 0.003,k ii = 5, it will lead to loss of synchronization (LOS). At 0.2s the AIdCF is switched in the system, it can be seen that the grid current I 2abc changes from the original LOS to stability. Further, when the PI parameters of current controller is k pi = 0.04, k ii = 50, high-frequency harmonic oscillation will occur in this three-phase grid-following converter. Similarly, the AIdCF is switched in the system at 0.2s, and the grid current I 2abc changes from the original high frequency harmonic oscillation to stability.

100

100 50

50

I2abc/(A)

I2abc/(A)

Add additional feedback control b=5

Add additional feedback control b=5

0

-100 0.1

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-50

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0.2

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0.22 0.24 0.26 0.28

0.3

0.1

0.12 0.14

0.16 0.18

0.2 t/(s)

0.22 0.24 0.26 0.28

0.3

(b)

Fig. 4. Stability-improving effect of the additional inverter-side d-axis current feedback control (AIdCF) (a) k pi = 0.003, k ii = 5 (b) k pi = 0.04, k ii = 50.

4.2 The Stability-Improving Effect of AIdCF Control in the Grid-Following Converter Concluded from Fig. 5 (a) shown below, the eigenvalues of the Jacobian matrix of gridfollowing converter system will move to left half plane when b is increasing. The root locus proves that the stability of the grid-following converter system can be improved by the additional control. Known from Fig. 5 (b), the stable region of the PI parameters of current controller will significantly enlarge when b is 5. An equivalent area of the blue region bounded by the stable boundary and the k p and k i axes can be calculated. The area of blue region after additional control added is 7.31. However, the area of stable region in yellow before additional control added is 4.5. The area of the stable region of the PI

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parameters of current controller has been enlarged 62% of that before adding additional control. The enlargement of the stable region of PI parameters proves the robustness enhancement of the grid-following converter system. λ1

8000 6000

λ3

4000 2000 0

-2000 -4000

250

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b=0

-6000

150

λ9λ7 λ10λ

λ6

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b=0 b=5

200

0

500

0 0

0.01

0.02

0.03

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Fig. 5. Stability-improving effect of additional inverter-side d-axis current feedback control (AIdCF). (a) Eigenvalue locus of Jacobian matrix of grid-following converter when b is increasing. (b) Stable region of PI parameters of current controller.

5 Conclusion The proposed designable stability-improving control method can be used to derive a new stability-improving control strategy by adding one or more elements into the Jacobian matrix of the grid-following converter system. In this paper, an additional inverter-side d-axis current feedback (AIdCF) control is proposed, which can significantly improve the parameter robustness of the grid-following converter, and make the stable region of the PI parameters have been increased by 62%. The high-frequency harmonic oscillation and loss of synchronization (LOS) are both effectively suppressed by the AIdCF control. Acknowledgements. This work was supported by Key Program of National Natural Science Foundation of China under grant number 52237008, and State Grid Corporation of China under the headquarter science and technology project “Synchronization stability research of weak grid connected converter of flexible ac transmission system based on voltage synchronization scheme (Project No.: 5100-202158354A-0-0-00)”.

Appendix The elements in the last row of Jacobian matrix (3) of three-phase grid-following converter are shown below.   Rc Lg Rc + Rg J1 = − kpPLL ωg , J3 = kpPLL ωg Lg − Rg L2 + Lg L2 + Lg kpPLL Lg ωg Rc Vdc kii   , J7 = kpPLL Lg J5 = − L2 + Lg 2L1 L2 + Lg

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J2

J4

J6 J8

   R c Rc + R g R2c 1 −   =kpPLL Lg −  2 +  L1 L2 + Lg C L2 + Lg L2 + Lg  Rc  + kiPLL Lg + kpPLL Rg L2 + Lg     Rc + R g 2 Rc Vdc kpi R2c 1  −  +  =kpPLL Lg −  L2 + Lg L1 L2 + Lg 2L1 L2 + Lg C L2 + Lg     Rc + R g + kiPLL Rg + kiPLL Lg + kpPLL Rg − L2 + Lg     kiPLL Lg + kpPLL Rg Rc + Rg Rc   + = − kpPLL Lg 2 + L2 + Lg L1 L2 + Lg L2 + Lg     Rc + R g V g Vg =kpPLL Lg −  sin δ 2 cos δ − ωg L2 + Lg L2 + Lg   + kiPLL Lg + kpPLL Rg

J9 =

kpPLL Lg

−Rc I1d L2 + Lg

Vg cos δ − kiPLL Vg cos δ L2 + Lg    + Rc + Rg I2d − Vcd + Vg cos δ − kpPLL Rg I2d − kpPLL Vg cos δ

References 1. Taul, M.G., Wang, X., et al.: An overview of assessment methods for synchronization stability of grid-connected converters under severe symmetrical grid faults. IEEE Trans. Power Electr. 34(10), 9655–9670 (2019) 2. Wang, X., Taul, M.G., et al.: Grid-synchronization stability of converter-based resources: an overview. IEEE Open J. Ind. Appl. 1, 115–134 (2020) 3. Wang, X., Blaabjerg, F.: Harmonic stability in power electronic-based power systems: concept, modeling, and analysis. IEEE Trans. Smart Grid 10(3), 2858–2870 (2019) 4. Liu, H., et al.: Subsynchronous interaction between direct-drive PMSG based wind farms and weak AC networks. IEEE Trans. Power Syst. 32(6), 4708–4720 (2017) 5. Wen, B., Boroyevich, D., Burgos, R., Mattavelli, P., Shen, Z.: Analysis of D-Q small-signal impedance of grid-tied inverters. IEEE Trans. Power Electr. 31(1), 675–687 (2016) 6. Suul, J.A., et al.: Impedance-compensated grid synchronization for extending the stability range of weak grids with voltage source converters. IET Gener. Transm. Distrib. 10(6), 1315– 1326 (2016) 7. Kroutikova, N., et al.: State-space model of grid-connected inverters under current control mode. IET Elect. Power Appl. 1(3), 329–338 (2017) 8. Slotine, J., Li, W.P.: Applied nonlinear control. China Machine Press, Beijing (1991) 9. Condren, J.E., Gedra, T.W.: Eigenvalue and eigenvector sensitivities applied to power system steady-state operating point. In: The 2002 45th Midwest Symposium on Circuits and Systems, pp. 1–683, Tulsa, OK (2002) 10. Li, H., Liu, C., Zou, Y., Jiang, X.: A stability improvement method based on parameter sensitivity for grid-connected inverter. In: IECON 2020 the 46th Annual Conference of the IEEE Industrial Electronics Society, pp. 4649–4654, Singapore (2020)

An Intuitionistic Time-Domain Stability Analysis Method Based on Floquet Theory for Three-Phase Grid-Following Converter Hong Li1(B) , Jinchang Pan1 , Zexi Zhou1 , Xu Shangguan1 , Zhichang Yang2 , and Xiaoge Liu2 1 Beijing Jiaotong University, Beijing 100044, China

[email protected] 2 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., Beijing, China

Abstract. Due to the unreasonable control parameters, when the three-phase inverter system is connected to the weak grid, the converter system may oscillate or even collapse. The traditional frequency-domain stability analysis method has limitations in the stability analysis of three-phase grid-following converter (TGFC) due to the complexity of the closed-loop transfer function. In this paper, the small-signal time-domain model of the TGFC with considering phase-locked loop (PLL) is firstly established, and following an intuitionistic time-domain stability analysis method of the TGFC based on the Floquet theory is proposed. Finally, the simulation test on a 12 kVA TGFC system is carried out to verify the correctness of the proposed method, which provides a new perspective to analyze the TGFC stability fast and accurately. Keywords: TGFC · Stability analysis · Floquet theory · Time-domain

1 Introduction With the march of distributed generation (DG) technology, TGFC have been served as important interface devices between converter system and the grid. On account of the scattered distribution of renewable energy, there are long transmission lines and more transformer equipment between DG and the grid, so the grid gradually has weak grid characteristics which is represented by L g and Rg in Fig. 1 [1]. Under the control parameters with small stability margin, according to the literature, TGFCs are more prone to meeting the synchronous oscillation and frequency collapse problems in real applications when connected to the weak grid [2, 3], which endanger the safty of GFC and the weak grid. Therefore, it is of great significance to accurately analyze the stability of the GFC and well design their control parameters. At present, the analysis methods of the stability of the TGFC mainly in the frequencydomain [4]. In the stability analysis of it, the matrix impedance model in frequencydomain is usually established with the dq axis [5]. In [6, 7], A series of norm criteria are © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 348–355, 2023. https://doi.org/10.1007/978-981-99-4334-0_43

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proposed based on the return ratio matrix which is the product of power output impedance and load input admittance. So far, the norm criterion which through the Gershgorin theorem in matrix theory theorem to estimate the position of matrix eigenvalues, thus simplifying the stability judgment. It is the most popular criterion for analyzing the stability of DC–AC converter system and guiding the parameter design. However, norm criterion is not a sufficient or necessary condition for judging stability, that is, systems that satisfy the criteria must be stable, but not all of the systems are consistent with the criteria are stable. So, there are some stable systems that do a system judged by the criterion to be unstable, and the probability that this occurs rate is defined as the conservative nature of the criterion and the region of the negative domain of the criterion related. In addition, the derivation of impedance matrix of the system is also too difficult to analyze the stability. And the time-domain stability method has been proposed in recent years [8]. In [9], a time-domain stability analysis method for a single-phase gridconnected inverter with PR control based on Floquet theory is proposed which can avoid deriving the complex transfer function of the system and has good accuracy on stability analysis. The time-domain analysis provides a new perspective for stability analysis of the TGFC system, but the PLL is not modeled and considered in [9]. However, for the TGFC used in weak grid, PLL is an indispensable part. So, in this paper, a full order timedomain model of three-phase converter connected to the weak grid with considering PLL is established, and an intuitionistic stability analysis method based on Floquet theory is proposed.

2 Time-Domain Model and Stability Analysis of TGFC 2.1 The Topology of the TGFC

S1

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van

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Three-phase LCL filter I1_a I2_a L2 I1_b I2_b L2 I2_c L2 I1_c Ica Icb Icc vca vcb vcc C C C RC RC RC

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+

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vPCCd vPCCq dqabc

θPLL

∫

i2q

kp

+

θPLL

Iqref

+

∫

Fig. 1. Commonly topology of TGFC.

Phase-locked loop

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The commonly used topology of TGFC is shown in Fig. 1, it is always connected to the grid with an LCL filter. To describe the weak grid characteristics, an inductor L g from the grid is provided here, since the toughness of the grid is often evaluated according to the short circuit ratio (SCR) [10]. Table 1 shows the parameters used in the paper. Table 1. Main circuit parameters and PLL control parameters Main circuit parameters

PLL control parameters

V dc = 800 V V g = 311 V idref = 80 A iqref = 0 A L 1 = 1.6 mH L 2 = 1 mH C = 20 uF RC = 2  L g = 5 mH Rg = 0.01  ωg = 100 π

k pPLL = 0.566 k iPLL = 50.776

2.2 Time-Domain Model of the GFC Before analyzing the stability, the mathematical model of the entire system has firstly been established. The entire GFC system consists of four parts: three-phase LCL filter, current loop, PLL and inverter bridge. This chapter will introduce the modeling process of these four parts. Part 1: Time-Domain Model of the LCL Filter The LCL filter is one of the main parts of the GFC system, whose time-domain model is established in the dq coordinate system as (1): di1d (t) dt di1q (t) dt di2d (t) dt di2q (t) dt dvcd (t) dt dvcq (t) dt

vdN RC 1 L1 i2d − L1 vcd + L1 v RC RC = −ωPLL i1d − L1 i1q + L1 i2q − L11 vcq + LqN1 R +R 1 1 C = LgR+L i1d − LCg +L2g i2d + ωPLL i2q + Lg +L vcd − Lg +L vgd 2 2 2 R +R 1 1 C = LgR+L i1q − ωPLL i2d − LCg +L2g i2q + Lg +L vcq − Lg +L vgq 2 2 2 1 = C1 (i1d − i2d ) + ωPLL vcq   = C11 i1q − i2q − ωPLL vcd

= − RLC1 i1d + ωPLL i1q +

(1)

Part 2: Time-Domain Model of the Current Loop In the current loop, in this paper, the integral output x 2d of the PI controller is defined as the state variable which can fully describe the time-domain behavior of the loop. Then, the current loop can be modeled as (2): dx2q dx2d = −i2d + Idref = −i2q + Iqref dt dt

(2)

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Part 3: Time-Domain Model of PLL The PLL collects the voltage of the Point of Common Coupling (PCC) to realize the phase synchronization of the grid-connected current and the grid voltage. The basic structure of PLL is shown in Fig. 1. In this paper, the nonlinear differential equation time-domain model of PLL is established in (3). dδ dt

= ω

d ω dt

⎤

⎡

 di2q d 2 i2q  di2d ⎥ ⎢ kpPLL Lg + kpPLL Lg ωPLL + kiPLL Lg + kpPLL Rg ⎢ 2 dt dt dt ⎥ ⎥ ⎢ ⎦ ⎣ dvgq + kiPLL ωPLL Lg i2d + kiPLL Rg i2q + kiPLL vgq +kpPLL dt = 1−kpPLL Lg i2d

(3)

where, δ = θPLL − θg

(4)

θ PLL and θ g are respectively of the output of the PLL and the grid. Part 4: Time-Domain Model of Inverter Bridge According to the state space averaging method [9], the amplification factor of the inverter bridge is V dc /2, so the dq-axis component of the fundamental wave of the inverter bridge can be obtained as (5).     vId = ki x2d + kp Idref − i2d vIq = ki x2q + kp Iqref − i2q

 

  (5) vdN = V2dc ki x2d + kp Idref − i2d vqN = V2dc ki x2q + kp Iqref − i2q Time-Domain Small Signal Model of the GFC According to (1)–(5), the dynamic behavior of the GFC system can be described. However, in this case, the dq-axis value of the grid voltage are no longer described by ωg , but the ωPLL , so the dq-axis component of grid can be define in (6). vgd = Vg cos(δ) vgq = −Vg sin(δ)

(6)

Therefore, a large-signal nonlinear full-order time-domain model of the GFC under weak grid has been established with (1)–(6). ZSdq (s) and YLdq (s) respectively denote the output impedance of the source subsystem and the input admittance of the load subsystem. The system stability is determined by return ratio L(s) which is the product of ZSdq (s) and YLdq (s). Combining the GNC with Gershgorin theorem, the stability of the converter system can be analyzed in frequencydomain. Let the differential equation in (1)–(5) be 0, and the steady-state solution or the equilibrium point of the system of the system is obtained. Applying the small-signal linearization method at equilibrium point, the small-signal differential equation of the

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Laplace Transfomation

Linearize at the equilibrium point Jacobi matrix of the system

Return ratio L(s)=ZSdq (s)YLdq(s) Multiple Input Multiple Output

Floquet theory Time domain stability criterion

Generalized Nyquist criterion Gershgorin theorem

Time domain

A series of norm criterion Frequence domain[6]

Fig. 2. Time-domain and frequency-domain modeling and stability analysis steps.

GFC system under weak grid is obtained. Further, the Jacobi matrix of the system can be obtained as (7) (where the values of A1 –A10 are given in the appendix): ⎡

− RL1c

⎢ ⎢ −ωg ⎢ ⎢ RC ⎢ L2 +Lg ⎢ ⎢0 ⎢ ⎢ J = ⎢ C1 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎢0 ⎢ ⎣0 A1

ωg − RL1c

Rc L1

−

Vdc kp 2L1

0 R +R

0 Rc L1

−

Vdc kp 2L1

− L11

0

Vdc ki 2L1

0

− L11

1 L2 +Lg

0

− LC2 +Lgg

ωg

RC L2 +Lg

−ωg

− LC2 +Lgg

0

0 − C1 0 −1 0 A4

0 −ωg 0 0 0 A5

0 1 C

0 0 0 A2

− C1 0 −1 0 0 A3

R +R

0

0

0

Vdc ki 2L1

0

0

0

0

1 L2 +Lg

0

0

0 0 0 0 0 A7

0 0 0 0 0 A8

ωg 0 0 0 0 A6

Vg sin δs L2 +Lg Vg cos δs L2 +Lg

0 0 0 0 0 A9

I1q

⎤

⎥ −I1d ⎥ ⎥ I2q ⎥ ⎥ ⎥ −I2d ⎥ ⎥ ⎥ Vcq ⎥ ⎥ −Vcd ⎥ ⎥ ⎥ 0 ⎥ ⎥ 0 ⎥ ⎦ 1 A10 (7)

Finally, according Floquet theory, the stability analysis can be carried out in timedomain. From Fig. 2, compared with the frequency-domain modeling and stability analysis process in [6], the proposed time-domain method can avoid complex product of matrix and greatly reduce the complexity of modeling and analysis.

3 Time-Domain Stability Analysis According to [8], it can be known that if the maximum eigenvalue of the state transition matrix D(t) = eJT is < 1, the system is stable, where J means the Jacobi matrix of a periodic system and T means the system’s period. In this section, the stability of the GFC is carried out. And the stability analysis results with different PI controllers’ parameters are shown in Fig. 3. Where, the eigenvalues distribution of the D(t) versus the control parameters are shown in Fig. 3(a) and (b).

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With the increase of PI parameters of k p and k i , the maximum eigenvalues will be out of the unit circle and the system is being unstable, as shown in detail in Fig. 3(c) and (d). Eigenvalues

Unstable

0.5

Stable

1 Stable

-0.5 -1

Stable

0.5

-1.5 -1 -0.5 0 0.5 1 1.5 Real (a) Keep ki=30 increase kp

0

-0.5 -1

-1.5 -1 -0.5

0 0.5 1 Real (c) kp =0.034 ki=30

-1.5 -1 -0.5 0 0.5 1 1.5 Real (b) Keep kp=0.03 increase ki

Stable

0.5

0 0.5 -1

0 0.5 -1

Unstable

1

Image

0

Eigenvalues

Unstable

Image

1

Image

Image

0.5

Eigenvalues

Eigenvalues

Unstable

1

-1.5 -1 -0.5 0 0.5 1 1.5 Real (d) kp =0.03 ki=82

1.5

Fig. 3. Distribution of eigenvalues when increase k p and k i .

4 Simulation Verification To verify the correctness of the proposed method, a 12 kVA TGFC simulation platform was built in simulink. The simulation parameters are the same with those in Table 1. From Fig. 4(a), it can be seen that the grid-connected current of the converter is stable when k p = 0.033. However, the same with the theoretical analysis in Fig. 4(b), there are high frequency oscillations in the grid-connected current when k p = 0.034, in this case, its THD achieves 10.22%, far more than the maximum value 5% in IEEE1547 [11]. From Fig. 4(c), it can be seen that the grid-connected current of the converter is stable when k i = 81. However, the same with the theoretical analysis in Fig. 4(d), there are high frequency oscillations in the grid-connected current when ki = 82, in this case, its THD achieves 5.43%, which also cannot satisfy the IEEE1547.

-100 2.9 2.92 2.94 2.96 2.98 t/(s) (a) kp=0.033 ki=30

3

0 -50

-100 2.9 2.92 2.94 2.96 2.98 t/(s) (b) kp=0.034 ki=30

3

i2abc/(A)

0

-50

100 100 50 50 0 0 -50 -50 -100 -100 2.9 2.92 2.94 2.96 2.98 3 2.9 2.92 2.94 2.96 2.98 3 t/(s) t/(s) (c) kp=0.03 ki=81 (d) kp=0.03 ki=82

i2abc/(A)

50

i2abc/(A)

100

50

i2abc/(A)

100

Fig. 4. Grid-connected current when increase k p and k i .

Table 2 shows the stable region of the TGFC system, it is obvious that the simulation results are the same with the theoretical analysis, which verifies the effectiveness of the time-domain model and stability analysis way.

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The type of stability analysis

Stable ranges

Floquet theory

k i = 30, k p ≤ 0.033 k p = 0.03, k i ≤ 81 k i = 30, k p ≤ 0.033

Simulation

k p = 0.03, k i ≤ 81

5 Conclusion In this paper, an intuitionistic time-domain model and time-domain stability analysis method of the TGFC system is proposed by deriving the time-domain model of the system with considering PLL. According to the theoretical and simulation results, the accuracy of the proposed method are verified. Compared with the frequency-domain method in [6], the proposed method has good accuracy on stability analysis and greatly reduce the complexity of modeling and stability analysis. Therefore, a new way for analyzing the stability of TGFC is being proposed in this paper. Acknowledgements. This work was supported by Key Program of National Natural Science Foundation of China under grant number 52237008.

Appendix A1 –A10 appearing in the Jacobi matrix J of the small signal model:

RC + Rg kpPLL ωg RC Lg kpPLL Lg ωg A5 = − A1 = − A3 = kpPLL Lg − Rg L2 + Lg L2 + Lg L2 + Lg     RC RC + Rg R2C 1 −   A2 =kpPLL −  2 +  L1 L2 + Lg C L2 + Lg L2 + Lg   + kpPLL Rg + kiPLL Lg 

RC L2 + Lg

A7 = 0



RC + Rg 2 RC Vdc kp 1  −  +  A4 =kpPLL Lg −  L2 + Lg L1 L2 + Lg 2L1 L2 + Lg C L2 + Lg

  RC + Rg + kiPLL Rg + kpPLL Rg + kiPLL Lg − L2 + Lg     kiPLL Lg + kpPLL Rg RC + Rg RC  +  + A6 = −kpPLL Lg L2 + Lg L2 + Lg L1 L2 + Lg R2C

A8 = kpPLL Lg

RC Vdc ki   2L1 L2 + Lg

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  RC + Rg Vg ωg Vg A9 =kpPLL Lg −  sin δs 2 cos δ − L2 + Lg L2 + Lg   Vg + kpPLL Rg + kiPLL Lg cos δ − kiPLL Vg cos δs L2 + Lg A10 =

   kpPLL Lg

−RC I1d + RC + Rg I2d − Vcd + Vg cos δs − kpPLL Rg I2d − kpPLL Vg cos δs L2 + Lg

References 1. Wang, X., Blaabjerg, F.: Harmonic stability in power electronic based power systems: concept, modeling, and analysis. IEEE Trans. Smart Grid 10(3), 2858–2870 (2018) 2. Zhao, J., Huang, M., Zha, X.: Nonlinear analysis of PLL damping characteristics in weakgrid-tied inverters. Circ. Syst. II Exp. Briefs IEEE Trans. 67(11), 2752–2756 (2020) 3. Taul, M.G., Wang, X., Davari, P., et al.: An overview of assessment methods for synchronization stability of grid-connected converters under severe symmetrical grid faults. IEEE Trans. Power Electr. 2019, 1 (2019) 4. Sun, J.: Impedance-based stability criterion for grid-connected inverters. IEEE Trans. Power Electr. 26(11), 3075–3078 (2011) 5. Wen, B., Boroyevich, D., Burgos, R., et al.: Analysis of D-Q small-signal impedance of grid-tied inverters. IEEE Trans. Power Electr. 31(1), 1–1 (2015) 6. Fangcheng, L., Jinjun, L., Haodong, Z., et al.: G-norm and sum-norm based stability criterion for three-phase AC cascade systems. Proc. CSEE 34(24), 4092–4100 (2014) 7. Zeng, L., Jinjun, L., Weihan, B., et al.: Infinity-norm of impedance-based stability criterion for three-phase AC distributed power systems with constant power loads. IEEE Trans. Power Electr. 30(6), 3030–3043 (2015) 8. Yin, W., Xiong, L., Zhao, T.: Review of stability analysis methods of grid-tied inverter power generation systems. Southern Power Syst. Technol. 13, 14–26 (2019) 9. Li, H., Liu, C., Jiang, X., Zeng, Y., Guo, Z., Zheng, T.Q.: A time-domain stability analysis method for grid-connected inverter with PR control based on floquet theory. IEEE Trans. Ind. Elect. 68(11), 11125–11134 (2021) 10. Xin, H., Gan, D., Ju, P.: Generalized short circuit ratio of power systems with multiple power electronic devices: analysis for various renewable power generations. Proc. CSEE 40(17), 5516–5527 (2020) 11. IEEE 1547–2003: IEEE standard for interconnecting distributed resources with electric power systems. Institute of Electrical and Electronics Engineers Inc (2003)

Locational Marginal Price Model Considering Customer Directrix Load Xiangrong Han1 , Bin Han2(B) , Jingsong Zhu2 , and Wenjuan Niu3 1 State Grid Nanjing Electric Power Company, Nanjing 210000, China 2 School of Electrical Engineering Company, Jiaozuo 454002, China

[email protected] 3 Electric Power Research Institute of State Grid Jiangsu Electric Power Company,

Ninjing 210000, China

Abstract. This paper proposes a locational marginal price model considering large-scale demand response, which also takes into account the uncertainty of renewable energy. The influence of renewable energy access to distribution network on node margin is analyzed and modeled, and a demand response model suitable for large-scale scenarios is established, which can fully mobilize the flexible load on the load side to absorb as much renewable energy as possible in real time. This paper establishes a locational marginal price model node with minimum active power loss, and the constraint conditions are taken into account. Finally, IEEE6 node model is used to simulate the example, and the validity of the model is verified. Keywords: Demand response · Locational marginal price · Customer directrix load · Renewable energy

1 Introduction Due to the exploitation and use of a large number of fossil energy, the shortage of global warming resources and other problems are becoming increasingly serious. New clean and renewable energy sources, such as solar and wind energy, are developing rapidly and will gradually replace non-renewable resources as the main mode of power generation. However, the output of renewable energy is easily affected by unstable factors such as season and climate, with obvious volatility and randomness, and poor controllability [1]. Traditional supply and demand balance adjustment methods mainly rely on controllable units or a large number of wind and light abandoning, high cost, low efficiency, has been unable to adapt to the current access to a high proportion of new energy grid. In the ongoing reform of the electric power system, the flexible load on the user side has become an important alternative regulation resource in the electric power system [2]. The concept of demand response was first proposed in the United States. Meanwhile, demand response in our country has also got advance by leaps and bounds development. Dispatching center, in order to maintain the grid supply and demand balance, as far as possible according to electricity by the user’s behavior, set prices or excitation signal to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 356–363, 2023. https://doi.org/10.1007/978-981-99-4334-0_44

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guide users to change behavior after the implementation of demand response, electricity power system can reduce power generation cost and to improve the reliability of power grid operation, was used as a power system in recent years, the first choice for energy conservation and emissions reduction plan. The traditional demand response mode is divided into price demand response and incentive demand response [3]. Price-type demand response is an involuntary user adjustment method, which is not user-friendly for rigid load and weak decision-making ability, and is not conducive to attract massive user participation, so it can only be applied in small-scale systems [4]. However, when the incentive demand response is faced with large-scale promotion demand response, the communication and calculation pressure faced by the dispatching center is huge, which may lead to the inaccuracy of the calculation results [5]. Therefore, the concept of Customer Directrix load (CDL) is proposed [6]. The ideal load curve shape which can well smooth the fluctuation generated by high proportion of renewable energy power generation equipment is defined as load directivity. This systemlevel load directionality is the target of load curve shaping for all users participating in demand response. However, users do not have to adjust according to this curve, and make decisions autonomously after weighing the cost of changing power consumption behavior and the incentives obtained. Based on the demand response of load alignment, the dispatching center only needs to publish the load alignment of the next day every day, without collecting massive user load data and calculating [7]. The existing results put forward the concept of load directivity and established the response mechanism of load directivity, which provides a new idea for large-scale user resource aggregation to participate in renewable energy consumption. The CDL calculates an electricity consumption curve that is best suited to the consumption of renewable energy. However, when users adjust their consumption behavior according to the CDL, they may encounter blocked lines. Therefore, this paper calculates Locational Marginal Price (LMP) based on the load of users’ participation in demand response adjustment, so as to reflect the power supply and demand of each node after the implementation of CDL scheme, and correctly guide the power generation and consumption. This paper presents an LMP model considering demand response. Firstly, considering the uncertainty of renewable energy, the CDL demand response that can effectively absorb renewable energy is established by adjusting the flexible load of users. Secondly, the LMP model aiming at minimizing the active power loss is established, and the constraints are taken into account. Finally, an example of IEEE6 node model is simulated to verify the effectiveness of the proposed model.

2 Customer Directrix Load Line The mechanism of CDL is to use the flexible load on the user side to stabilize the load fluctuation on the system side. So, the principle of this mechanism can be concluded as “adjustable resources balance non-adjustable”. Therefore, the objective function of

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CDL is divided into two parts, one is to minimize the operating cost of the system, and the other is to minimize the cost of wind curtailment. The objective function specific to the mathematical expression can be written as: min

NG  T  

   2 ai PG,i (t) + bi PG,i (t) + ci + CR PR,max (t) − PR (t)

(1)

t=1 i=1

In formula (3): PG,i (t) represents the output of traditional generating units i; NG is the number of traditional generating units; PR (t) represents the total new energy output at time t; PR,max (t) represents the upper limit of new energy output at time t, this data is usually achieved by day-ahead prediction; ai , bi , ci is the cost coefficient of the i-th traditional generator set; CR is the penalty factor of wind curtailment. To discard wind, C r should be set to an appropriate value to ensure that new energy can be consumed as much as possible. In the CDL model, the power supply and demand balance constraints in the power system are no longer considered and replaced by the form of “adjustable resources” balance “non-adjustable resources”. NG 

PG,i (t) − Pd∗ (t)Pd ,flex = Pd ,fix (t) − PR (t)

i=1

(2)

t = 1, 2, · · · , T In formula (4): Pd∗ (t) is standard unit value for DR load line; Pd ,fix (t) is the fixed load at t period; Pd ,flex is the total flexible load of all users in the period. The remaining constraints are as follows: T 

Pd∗ (t) = 1

(3)

t=1

0 ≤ Pd∗ (t) ≤ 1

t = 1, 2, · · · , T

Pimin · Ii,t ≤ PG,i ≤ Pimax · Ii,t 0 ≤ PR (t) ≤ PR,max (t)

t = 1, 2, · · · , T t = 1, 2, · · · , T

(4) (5) (6)

Equations (3) and (4) indicates that the CDL mechanism only shifts the flexible load, the total power consumption of the user is constant; Eq. (5) limits the output range of traditional generator sets, Pimin and Pimax is the upper and lower limit of the output of the traditional generator set, respectively, Ii,t is a 0–1 variable, represents whether the traditional generator set i is in operation at time t; Eq. (8) is the new energy output range constraint. The CDL curve is independent of the order of magnitude of the load, but only provides the optimal power consumption decision. It is applicable for all DR users and is easy to implement.

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3 Locational Marginal Price Locational marginal price (LMP) is defined as the marginal cost of the system to meet the new load demand of nodes. It can reflect the temporal and spatial distribution characteristics of power supply and demand, and is a widely adopted pricing method in the centralized power market. In this paper, when each node changes its load according to the CDL line shape, the calculation of LMP can immediately reflect the power supply and demand of each node and guide generators and users to effectively generate and consume electricity. To calculate the LMP of the distribution network, assume that the Lagrange function of node i is k . For active and reactive LMP, it can be calculated by the following formula:  ∂ k kt τtiP = (7) ∂Pti  ∂ k kt Q τti = (8) ∂Qti Q

where τtiP , τti is active and reactive LMP respectively; Pti , Qti are the active power and reactive power injected by unit I in time period t. LMP is obtained by solving the optimal power flow. Depending on the LMP of different time periods, peak-to-valley differences and costs can be reduced through demand response. The objective of LMP is: min cG PG − cD PD

(9)

In formula (7), cG represents the generator cost coefficient curve; PD is the node load. The constraints are as follows: KD PD − KP PG = 0

(10)

SF(KP PG − KD PD ) ≤ PLmax

(11)

−SF(KP PG − KD PD ) ≤ PLmax

(12)

0 ≤ PD ≤ PD max

(13)

Vt,i Vt,j Yij cos(θij − δt,i +δt,j )

(14)

Vt,i Vt,j Yij sin(θij − δt,i +δt,j )

(15)

Pi,t =

N  i=1

Qi,t =

N  i=1

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Where, K D and K P are bus-generator and bus-load incidence matrix; PL max is the allowable maximum power flow; PDmax is the maximum node load limit; Pi,t , Qi,t are the active and reactive loads of node i at time period t, respectively; Vt,i , Vt,j are respectively the voltages of nodes i and j in time period t; Yij , θij are the admittance and admittance angle of line ij, respectively; δt,i , δt,j are the phase. Thus, it can be deduced that the user’s profit is: S=

NT 

(PD0 (t) × Pm (t) − PD (t) × τtP )

(16)

t=1

where, PD0 (t), PD (t) are the original demand at time period t and the demand after response; Pm (t), τtP are respectively the original electricity price at time period t and the electricity price after demand response.

4 Case Analysis This section will validate the feasibility of the model.A IEEE6-bus power system with a high proportion of renewable energy sources is constructed in Fig. 1, and suppose that a large amount of users involve in the response event. This section uses the load data of 500 residential users published by the US Department of Energy’s Open Energy as the initial load. As for new energy, a typical day’s new energy output is selected, which is counted by PJM, as shown in the Fig. 2. The electricity purchase cost is shown in Fig. 3.The program in this article is run on MATLAB 2021a, using Yalmip optimizer and the GUROBI solver. G1

Load

G2 bus2

bus1

L2

L1 L3

bus3 T1 P1

L4

L7 bus5

bus4 L5 DG

T2

L6

bus6 G3

Load

Fig. 1. IEEE-6bus system.

In this example, the system demand response load accounts for 20% of the total load. The CDL of each load node is calculated according to the parameters of controllable unit, renewable energy generator unit, controllable load and flexible load. Compare Fig. 2 with Fig. 4, it can be seen that the line shape of CDL is consistent with the output shape of renewable energy, which proves that CDL can effectively absorb renewable energy in real time. Assuming that the user can adjust exactly according to the CDL profile, we

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Fig. 2. Day-ahead prediction renewable energy.

Fig. 3. Initial price.

can calculate the load adjustment at each moment, to simplify, we choose the peak and valley time of load respectively to verify the effect of CDL on LMP. Table 1 shows the load adjustment at the peak and valley time. In the following, the calculation is performed for the LMP, the results are shown in Tables 2 and 3. It can be found by comparing Tables 2 and 3, when the load in the line is in the normal range, the LMP does not change, because the line is not blocked and the unit does not need to adjust its output. On the contrary, when the line is in the blocked state, the output of generators 1 and 2 is reduced, thereby alleviating the overall blocking situation and LMP is changed accordingly. By calculating the LMP of 24 h with this method, we can calculate the profit obtained by users. The total cost before demand response is 1758$, and the total cost after demand response is 1583$, reducing the cost by 9.9%. At the same time, it can be seen from Fig. 5 that CDL plays a great role in promoting the consumption of renewable energy.

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Fig. 4. CDL profile.

Table 1. Load adjustment Time/h

5

18

Adjustment/MW

316.8

388.5

Table 2. LMP calculation results at valley time Generators

System electricity price($/MW·h)

LMP($/MW·h)

Gen 1

34.7

34.7

Gen 2

34.7

34.7

Gen 3

34.7

34.7

Table 3. LMP calculation results at peak time Generators

System electricity price($/MW·h)

LMP($/MW·h)

Gen 1

34.7

31.1

Gen 2

34.7

31.7

Gen 3

34.7

36.2

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Fig. 5. RE output.

5 Conclusion The aim of this article is to utilize the CDL in the electric power system to integrate new energy mostly, at the same time, the LMP of nodes is considered to minimize the dynamic cost in the distribution network. The LMP is calculated according to the load adjustment calculated by CDL, which can provide economic signals to users and maximize user revenue. At the same time, CDL can also effectively promote the integration of new energy. Acknowledgement. This work was supported by State Grid Jiangsu Electric Power Company (“Research on electricity market mechanism adapting to energy structure transformation”).

References 1. Shu, Y., Zhang, Z., Guo, J., et al.: Study on key factors and solution of renewable energy accommodation. Proc. CSEE 37(01), 1–9 (2017) 2. Zhang, Z., Wang, W., Zhang, X.: Renewable energy capacity planning based on carrying capacity indicators of power system. Power Syst. Technol. 45(02), 632–639 (2021) 3. Deng, T., Lou, S., Tian, X., et al.: Optimal dispatch of power system integrated with wind power considering demand response and deep peak regulation of thermal power units. Autom. Elect. Power Syst. 43(15), 34–41 (2019) 4. Bitaraf, H., Rahman, S.: Reducing curtailed wind energy through energy storage and demand response. Sustain. Energy 9(1), 228–236 (2019) 5. Liu, T., Zhang, Q., He, C.: Coordinated optimal operation of electricity and natural gas distribution system considering integrated electricity-gas demand response. Proc. CSEE 41(05), 1664–1677 (2021) 6. Fan, S., Li, Z., Yang, L., He, G.: Customer directrix load-based large-scale demand response for integrating renewable energy sources. Electr. Power Syst. Res. 181, 106175 (2020). https:// doi.org/10.1016/j.epsr.2019.106175 7. Fan, S., Jia, K., Wang, F., et al.: Large-scale demand response based on customer directrix load. Autom. Elect. Power Syst. 44(15), 19–27 (2020)

Analysis of the Steady State Fluid Force and Flux of Nuclear Pressure Safety Valves Based on Surrogate Models Ao Zhang, Weihao Zhou, Chaoyong Zong, Qingye Li, and Xueguan Song(B) Dalian University of Technology, Dalian 116024, China [email protected]

Abstract. Pressure safety valves (PSVs) maintain the safety and stability of the pressure systems used in nuclear power plants. However, it may show dynamic instabilities under extreme conditions, such as flutter or low-frequency cycling. To explore the underlying mechanism of these undesirable behaviors, an in-depth analysis on the fluid force and flux is essential. As a complex nonlinear system, the fluid disk force and flux are affected by many factors, such as pressure, temperatures and so on. To overcome this, a surrogate model-based method which can account for all of these factors were adopted to establish the relationship between valve design parameters and steady state characteristics. Among the used surrogate modeling methods, the RBF was identified as the optimal model. With the RBF model, Sobol’s method was used to identify key parameters for the fluid disk force and flux, based on which, the effect of the identified key parameters on the valve static performance were analyzed. The method proposed in this paper can not only used to valve behavior predictions, but also available for the mechanism exploration of dynamic instabilities. Keywords: Spring-loaded nuclear safety valve · Surrogate model · Steady state characteristics · Fluid disk force · Flux

1 Introduction 1.1 A Subsection Sample As a significant basic configuration in modern industry, valves are generally used in many energy fields such as oil gas, coal chemical and nuclear power. The valve researched in this paper is mainly used in the pressure control of nuclear power system, which is a crucial component to ensure the safe operation of nuclear power plants. The safety state of nuclear power plant plays a vital role in ensuring the normal operation of energy system [1–4]. In practical applications, PSVs may experience failures such as valve jamming and flutter, which can lead to catastrophic consequences for the pressure system [5]. To explore the mechanisms that generate these undesirable behaviors, it is necessary to conduct an in-depth analysis of the fluid disk force and flux. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 364–373, 2023. https://doi.org/10.1007/978-981-99-4334-0_45

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Substantial research on the fluid disk force and flux of PSVs have been conducted by domestic and foreign scholars in recent years [6–11]. With the development of computational methods and capability, the numerical method has been proved to be a suitable method. Although the numerical method improves the computational efficiency compared to other methods, the fluid disk force and flux are influenced by many factors such as pressure, temperature and flow field shape, any change in valve parameters requires re-modeling, which is clearly inefficient for the study of PSVs with multiple parameters. To comprehensively consider the influence of all parameters on the fluid disk force and flux, improving the computational efficiency, the surrogate model method is used to establish the relationship between valve design parameters and research objects. The surrogate model is a method that can quickly build the relationship between the system response and design parameters using limited sample data, which has the advantages of high efficiency, economy and applicability [12, 13]. Firstly, the numerical model of the PSV is established based on CFD, and the surrogate model is constructed by using CFD simulation data as the generation tool of the base sample points. And then the computational capability of different surrogate modeling methods in terms of the fluid disk force and flux of the PSV is compared, the optimal surrogate model is obtained, and its computational accuracy is verified. To further analyze the influence of valve design parameters on the fluid disk force and flux, the sensitivity of system parameters is studied based on the Sobol’s method, and the key parameters affecting the fluid disk force and flux are obtained. On this basis, the influence law of the key parameters on the steady state characteristics of the valve is analyzed.

2 Pressure Safety Valves The PSV is designed to overcome the pressure of the medium by adjusting the spring force to achieve sealing. Figure 1 shows the structure of a PSV, the structure of the valve disk as well as the local details are enlarged at the right-hand side of Fig. 1. To facilitate subsequent analysis, nine valve parameters are defined, as shown by A to I. The meanings and specific values of these nine parameters are shown in Table 1.

3 Numerical Methods To obtain the sample data for surrogate model construction, a numerical model based on CFD is developed. Because of the axisymmetric geometry of this PSV, a 2-D axisymmetric mesh model is constructed firstly. And considering the computational efficiency, a 1/8 3-D numerical model is also developed, as shown in Fig. 2. To improve the mesh quality, the fluid region of this PSV is decomposed into three parts: the central sub-domain, the pipe sub-domain and the external atmosphere subdomain, different subdomains are connected by interfaces, as shown in Fig. 3. The central sub-domain is the whole of the valve disc and the end of the valve nozzle, in which the obvious flow phenomena such as flow shear and separation occur. Aside from the interface boundary, the boundary conditions in this paper also set up four parts of inlet, outlet, symmetry plane and valve disc wall of the fluid region. Among them, the

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Fig. 1. Schematic diagram of a typical PSV.

Table 1. Value ranges of key valve parameters. Parameter

Definition

Value range

A

Radius of the outer circle of valve disc

10.00–11.00 mm

B

Radius of the inner circle of valve disc

8.00–9.00 mm

C

Radius of valve nozzle

5.50–6.50 mm

D

Radius of the outer circle of adjustment ring

9.00–11.00 mm

E

Valve opening

0.20–3.60 mm

F

Height of adjustment ring

2.50–4.00 mm

G

Valve disc edge depth

1.00–2.00 mm

H

Static pressure of the valve inlet

1.00–5.00 bar

I

Radius of the valve inlet

6.0 m

Fig. 2. 2-D and 3-D models of the PSV.

inlet and outlet of the fluid region are defined as the pressure inlet and pressure outlet respectively, the static pressure of the pressure outlet is specified as 0 bar.

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Structural grid

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Non-structural grid

Fig. 3. Method of fluid domain decomposition [9].

The correctness of the above numerical modeling scheme has been verified in the authors’ previous work [14]. Using this numerical modeling scheme, the valve models with different parameters are reconstructed and calculated, thus providing the original data for the construction and validation of subsequent surrogate models.

4 Building Surrogate Nodel 4.1 Design of Experiments For the valve design parameters A–H listed in Table 1, the Optimal Latin Hypercube Sampling (OLHS) method is adopted and a total of 80 (10 N) sample and 24 (3 N) validation points are generated to obtain the initial training and validation data of surrogate model. The spatial distribution of sample points and validation points is shown in Fig. 4.

Fig. 4. Sample and validation points distribution for experimental design.

Figure 4 shows the sample points and validation points are evenly distributed and have good space filling. Due to the magnitude difference of the values of different design parameters, in order to facilitate the construction of the surrogate model, all design parameters and predicted values are normalized. As shown by Eq. (1). xNor =

x − xMin xMax − xMin

(1)

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4.2 Comparison of Surrogate Model With the normalized data, the surrogate model was constructed by Polynomial regression surface (PRS), Kriging (KRG), Radial basis function (RBF) and Support Vector Regression (SVR) [15–18], aiming at the fluid disk force and flux of the PSV. It can be seen from Table 2 that structures and correlations functions of the above different models. Table 2. Surrogate modeling method used in this research. Model PRS

yˆ (x) b0 +

Correlation function n 

n n  

bi xi +

i=0

n  n n  

–

bij xi xj +

i=1 j=1

bijk xi xj xk

i=1 j=1 k=1

KRG

ˆ βˆ + r T (x)R−1 (y − f β)

RBF

ns 

SVR

i=1 ns  i=1

R(xi , xj ) = exp(− 

n dv

j

k=1

θk |xki − xk |2 )

λi ϕ(r(xi , x))

ϕ(r(xi , x)) =

x − xi 2 + c2

(ai − ai∗ )k(xi ∗ x) + b

k(x, x ) = exp(− x−x2 )

 2

2σ

In addition, the global and local prediction accuracy of the proposed model were evaluated by four indexes. The global prediction accuracy index mainly includes MeanSquare-Error (MSE), Root-Mean-Square Error (RMSE), R Square (R2 ) and so on. And the Maximum-Absolute-Percentage-Error (MAPE) is commonly used as the index of local prediction accuracy. The four indexes are shown by Eqs. (2)–(5). (1) MSE: 1 (yi − yˆ i )2 n n

MSE =

(2)

i=1

(2) RMSE:   n 1  RMSE =  (yi − yˆ i )2 n

(3)

i=1

(3) R2 : n (yi − yˆ i )2 R = 1 − ni=1 2 i=1 (yi − y i ) 2

(4)

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(4) MAPE:



|yi − yˆ i | MAPE = max yi

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(5)

The n is the number of the validation points, the yi and yˆ i are the true values corresponding to the validation points and the predicted values of the model, respectively. 1.01

0.0020

Force Flux

1.00

R2

MSE

0.99 0.98 0.97 0.96

Force Flux

0.0016 0.0012 0.0008 0.0004

PRS

RBF

KRG

SVR

0.0000

PRS

(a) R²

SVR

0.8

Force Flux

0.04

Force Flux

0.6

0.03

MAPE

RMSE

KRG

(b) MSE

0.05

0.02

0.4 0.2

0.01 0.00

RBF

PRS

RBF

KRG

SVR

0.0

PRS

(c) RMSE

RBF

KRG

SVR

(d) MAPE

Fig. 5. Comparison of accuracy of different surrogate models. Table 3. Accuracy assessment of different surrogate models. Predictive value

Indicators

PRS

RBF

KRG

SVR

F

R2

0.9882

0.9906

0.9724

0.9884

MSE

0.0006

0.0005

0.0015

0.0006

RMSE

0.0254

0.0227

0.0388

0.0251

MAPE

0.1060

0.0821

0.1944

0.1227

R2

0.9959

0.9964

0.9965

0.9967

Q

MSE

0.0002

0.0002

0.0002

0.0002

RMSE

0.0141

0.0132

0.0130

0.0127

MAPE

0.4394

0.4368

0.6426

0.4392

The comparison of prediction accuracy of different surrogate models and the specific values of each evaluation index are shown in Fig. 5 and Table 3. Among them, F and

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Q represent the fluid disc force and flux of the PSV. Among the four models, the one constructed by RBF method has the highest coefficient of determination and reasonable local prediction accuracy in terms of the fluid disc force and flux. Considering the values of other global accuracy evaluation indexes, RBF is the best method to construct the steady state characteristic surrogate model of the PSV.

5 Validation of the Surrogate Model In order to verify the calculation ability of the constructed RBF model in terms of the fluid disk force and flux of the PSV, the simulation data of the verification sample points selected in the experimental design were compared with the calculation data of the corresponding surrogate model, and the specific deviation of each sample point was quantified. The results are shown in Fig. 6.

(a) Fluid disk force

(b) Flux

(c) Deviation of fluid disk force

(d) Deviation of flux

Fig. 6. Accuracy validation for RBF model.

Figure 6 (a) and (b) show the comparison between the predicted and verified values of the surrogate model established by RBF in terms of the fluid disk force and flux, respectively. Among them, the abscissa is the 24 verification sample points. Figure 6 (c) and (d) show the specific values of the error between the CFD simulation value corresponding to each sample points and the calculated value of the surrogate model, and the calculation method of the error is shown in Eq. 6. Error =

VCFD − VSM × 100% VCFD

(6)

For the fluid disk force, the deviation of only 5 sample points is greater than 5%, but the maximum deviation is still 5%, most are concentrated in the working condition with small valve opening. The large deviation value is caused by the small basic flow rate, and the absolute deviation is still small. So the RBF method has high accuracy in the calculation of the fluid disk force and flux.

6 Analysis of Parameter Sensitivity For PSVs with multiple design parameters, changes in any of design parameters may have a great influence on the system characteristics. Therefore, it is necessary to conduct sensitivity research on the system parameters. In this section, based on the surrogate model of the steady state characteristics of the PSV established in Sect. 4, the Sobol’s method was used to analyze the parameter sensitivity. The Sobol’s method determined the sensitivity of the parameters by the ratio of the model partial variance and the total variance [19]. The results are shown in Figs. 7 and 8.

(a) Fluid disc force

(b) Flux

Fig. 7. Results of the sensitivity analysis.

(a) Fluid disc force

(b) Flux

Fig. 8. Fluid disc force and flux predicted by the surrogate models.

It can be concluded from the analysis results that static pressure of the valve inlet (Parameter H in the Table 1) had the greatest influence on the fluid disc force, followed by the valve opening (Parameter E in the Table 1), and the other valve parameters had little influence. For the flux, the valve opening had the greatest influence, followed by the static pressure of the valve inlet, the valve nozzle radius (Parameter C in the Table 1) also had a slight effect, and the effects of the remaining parameters can be ignored.

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7 Conclusions In this paper, the fluid disk force and the flux studies were conducted on the PSVs which are broadly used in electrical, energy and other industrial fields. To construct the relationship between design parameters and research variables, a numerical model was constructed, four methods of PRS, RBF, KRG and SVR were used to develop the surrogate model, and the model accuracy was compared and verified. Lastly, sensitivity analysis of valve parameters was carried out. The conclusions obtained from this research are summarized as follows: (1) A numerical model based on CFD has been established for the research of the PSV, and the accuracy of the model has been verified, the fluid force and flux of the PSV with different structural parameters were obtained. (2) Based on the CFD simulation results, the surrogate model was studied. The results shown that RBF was the optimal method for building surrogate model for the steady state characteristics of the PSV. And the calculation ability of the optimal surrogate model RBF in the steady state response of the PSV was analyzed, the surrogate model constructed by the RBF method had high accuracy in the calculation of the fluid force and flux. (3) Sensitivity analysis of the valve parameters shown that the static pressure of the valve inlet and the valve opening had the greatest influence on the fluid disk force and the flux. Therefore, when analyzing the steady state characteristics of the PSV, we should first pay attention to the influence of the static pressure of the valve inlet on the fluid disk force, so as to select the appropriate stiffness of the spring for balancing the fluid force; when designing the flux of the PSV, we should pay primary attention to the valve opening, and select a reasonable valve structure to ensure the discharge efficiency of the system.

References 1. Yang, L., Wang, Z.J., Dempster, W.M., et al.: Experiments and transient simulation on springloaded pressure relief valve under high temperature and high pressure steam conditions. J. Loss Prevent. Process Ind. 45, 133–146 (2017) 2. Daryush, M., Mahmood, R., Reza, K.: Hydro-mechanical response in polymeric pipes assuming interaction of fluid. Int. J. Hydromechatr. 3(4), 334–348 (2020) 3. Xiang, X., Wang, R., Zheng, F., et al.: Flow forces prediction of a spring-loaded pressure safety valve with numerical models. In: IEEE 8th International Conference on Fluid Power and Mechatronics, pp. 444–451. FPM, IEEE (2019) 4. Qian, J., Wei, L., Zhu, G., Chen, F., Jin, Z.: Transmission loss analysis of thick perforated plates for valve contained pipelines. Energy Conver. Manag. 109, 86–93 (2016) 5. Zheng, F., Zong, C., Dempster, W., et al.: A multidimensional and multiscale model for pressure analysis in a reservoir-pipe-valve system. J. Pressure Vessel Technol. 141, 1–14 (2019) 6. Song, X.G., Wang, L., Park, Y.: Transient analysis of a spring-loaded pressure safety valve using computational fluid dynamics (CFD). J. Pressure Vessel Technol. 132(5), 054501– 054505 (2010)

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7. Zong, C., Wang, R., Zheng, F., et al.: Experimental analysis of the lift force discontinuity of a spring-loaded pressure safety valve working in pneumatic service. J. Pressure Vessel Technol. 142(6), 064501–064505 (2020) 8. Brouwer, K., McNamara, J.: Surrogate-based aeroelastic loads prediction in the presence of shock-induced separation. J. Fluids Struct. 93, 102838 (2020) 9. Scuro, N., Angelo, E., Angelo, G., et al.: A CFD analysis of the flow dynamics of a directlyoperated safety relief valve. Nucl. Eng. Des. 328, 321–332 (2018) 10. Zhang, H., Zhao, L., Peng, S., et al.: Thermal-fluid-structure analysis of fast pressure relief valve under severe nuclear accident. Nucl. Eng. Des. 371, 110937 (2021) 11. Geng, K., Hu, C., Yang, C., Rong, R.: Numerical investigation on transient aero-thermal characteristics of a labyrinth regulating valve for nuclear power plant. Nucl. Eng. Des. 382, 111369 (2021) 12. Song, X.G., Sun, G., Li, G., et al.: Crashworthiness optimization of foam-filled tapered thinwalled structure using multiple surrogate models. Struct. Multidiscip. Optim. 47(2), 221–231 (2013) 13. Lv, L., Zong, C., Zhang, C., et al.: Multi-fidelity surrogate model based on canonical correlation analysis and least squares. J. Mech. Des. 143, 2 (2021) 14. Zong, C., Zheng, F., Chen, D., et al.: Computational fluid dynamics analysis of the flow force exerted on the disk of a direct-operated pressure safety valve in energy system. J. Pressure Vessel Technol. 142(1), 011702 (2020) 15. Gunst, R.: Response surface methodology: process and product optimization using designed experiments. J. Stat. Plan. Infer. 59, 185–186 (1997) 16. Gholampour, A.: Nonlinear modelling of the dynamic response of pipe conveying fluid coated with FRP under seismic load: comparison of RSM and kriging approach. Int. J. Hydromechatr. 3(1), 26–37 (2020) 17. Hardy, R.: Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res. 76(8), 1905–1915 (1971) 18. Gunn, S.: Support vector machines for classification and regression. ISIS Tech. Rep. 14, 85–86 (1998) 19. Sobol, I.: Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Math. Comput. Simul. 55(1), 271–280 (2001)

Study on Mathematical Model and Dynamic Compensation of Oil Down-Hole Pressure Sensor Based on BP Neural Network Fan Yang1 , Chuanrong Zhao2(B) , Hongzhen Zhu1 , and Deren Kong3 1 Wuxi University, Wuxi 214105, China 2 Anhui University of Technology, Ma’anshan 243002, China

[email protected] 3 Nanjing University of Science and Technology, Nanjing 210094, China

Abstract. During down-hole perforation and fracturing, there are always strong mechanical vibration and impact that affect dynamic pressure measurement. In order to overcome the influence, a specialized buffer device was designed for the dynamic pressure sensor. Based on the double-diaphragm shock tube, we researched the influence of the specialized buffer device on the dynamic characteristics of the pressure sensor. Based on BP neural network, a mathematical model was built to characterize the pressure sensor with the buffer device, and the method was studied to implement dynamic compensation of the pressure sensor. According to the results of dynamic calibration and compensation for the typical piezoelectric pressure sensor with the buffer device, the specialized buffer device can greatly reduce the working bandwidth of the pressure sensor. The method of dynamic compensation based on BP neural network can not only effectively widen the working bandwidth of the piezoelectric dynamic pressure sensor, but also improve the accuracy of dynamic measurement. Keywords: Oil down-hole pressure · BP neural network · Mathematical model · Dynamic compensation

1 Introduction Nowadays, the most important way to ensure oil and gas resources is to exploit and utilize the deep oil-gas resources through the technological innovation. During the oil exploitation, down-hole perforation and fracturing can generate instantaneous high-pressure shock signal [1], which can easily damage the wall of the well and even lead to the oil well scraped. Therefore, it is necessary to measure the pressure to ensure the safety and smooth going of oil exploitation. The instantaneous high-pressure shock signal during the down-hole perforation and fracturing has a steep rising edge and wide effective bandwidth whose upper limit can reach to tens of kHz [2]. In order to ensure the undistorted measurement in engineering, the working bandwidth of the pressure sensor is required to completely cover the effective bandwidth of the perforation pressure signal. Therefore, the pressure sensor © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 374–379, 2023. https://doi.org/10.1007/978-981-99-4334-0_46

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needs to be dynamically calibrated to study its dynamic characteristics. If the working bandwidth of the sensor cannot cover the effective bandwidth of the pressure signal, it should be dynamically compensated to reduce the measurement error and improve the measurement accuracy. The mathematical model of the pressure sensor is the basis of dynamic compensation, so it is necessary to study the modeling method. Traditional algorithms for modeling mainly include least square method and maximum likelihood estimation method [3]. However, these two algorithms are easy to lead to local minima, and all based on the assumption of the linear time-invariant system. In the dynamic characteristic compensation method, the dynamic performance of the sensor can be improved by designing a compensation model and connecting with the sensor in series connection [4]. System modeling and compensation can be realized by not only traditional algorithms but also intelligent optimization algorithms. The neural network algorithm appeared at the end of the 20th century is one of the most representative intelligent algorithms [5]. Wherein, BP neural network is widely researched and applied in recent years, which is be commonly considered to be the most mature neural network algorithm [6]. Based on the double-diaphragm shock tube, we carried out a dynamic calibration test on a typical piezoelectric pressure sensor with a buffer device, obtained the step response of the pressure sensor, and studied the modeling and compensation method based on BP neural network, which has great importance to improve the dynamic performance of the dynamic pressure sensor and the measurement accuracy.

2 Analysis of the Influence of the Specialized Buffer Device on the Dynamic Characteristics of the Pressure Sensor During the down-hole perforation and fracturing, the dynamic pressure measurement is accompanied with the parasitic effect of strong mechanical vibration and impact. In order to restrain the mechanical vibration and impact, a specialized buffer device was designed to improve the measurement accuracy [7]. The structure of the sensor with the buffer device is shown in Fig. 1.

Fig. 1. The structure of the sensor with the buffer device.

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The double-diaphragm shock tube contains a high-pressure chamber, a mediumpressure chamber and a low-pressure chamber. Compared with the one-diaphragm shock tube, the breaking time of double diaphragms of the double-diaphragm shock tube is controllable. The dynamic calibration system is mainly composed of the gas source, the shock tube, the pressure sensor, the signal conditioner and the data acquisition system, as shown in Fig. 2.

Fig. 2. The composition of the dynamic calibration system.

Considering that pressure amplitude has little influence on the dynamic characteristics of the pressure sensor, it is unnecessary to install a standard pressure sensor. Therefore, we installed the calibrated sensor at the center of the end of the shock tube. The original and 100 kHz low-pass filtered step responses of the typical piezoelectric pressure sensor PCB113B with the buffer device are shown in Fig. 3.

Fig. 3. The step response in the dynamic calibration test.

The dynamic characteristics of the pressure sensor PCB113B with the buffer device is shown in Fig. 4. Comparing that the natural frequency of the bare PCB113B sensor is about 120 kHz, the buffer device obviously influences the dynamic characteristics and narrows the working bandwidth. Considering that the upper limit of the effective bandwidth of the perforation pressure signal is usually higher than 10 kHz [2], the working bandwidth of the pressure sensor is not enough to cover the effective bandwidth of the measured signal. Therefore, dynamic compensation is necessary to reduce the distortion and improve the measurement accuracy.

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Fig. 4. The dynamic characteristics of the typical pressure sensor.

3 Modeling and Compensation Method Based on Neural Network BP neural network, composed of several neural nodes, contains the input layer, the hidden layer and the output layer, includes the forward propagation of the signal and the back propagation of the deviation. There are usually two kinds of neural network models, the forward parallel model and the forward series-parallel model. When the initial coefficients are not clear, the forward series-parallel model [8] is more preferred. The nonlinear forward series-parallel model of the pressure sensor can be constructed as shown in formula (1). y[k] = f (y[k − 1], . . . , y[k − n], . . . , x[k], . . . , x[k − n])

(1)

where, y[k] is current output value, y[k − 1], . . . , y[k − n] are past output values, x[k] is current input value, x[k − 1], . . . , x[k − n] are past input values, and n is the order. Based on the dynamic calibration of the double-diaphragm shock tube, taking the ideal step signal values as input values [9] and the step response signal values output from the pressure sensor as output values, the input layer can be constructed by current input values, past input values and past output values. Meanwhile, the output layer can be constructed by current output values. Similar to the neural network modeling method of the pressure sensor, the dynamic compensation model of the pressure sensor is shown in formula (2).   (2) x [k] = g x [k − 1], . . . , x [k − n], . . . , y [k − n], . . . , y [k − n] where, x [k] is current output value, x [k − 1], . . . , x [k − n] are past output values, y [k] is current input value, y [k − 1], . . . , y [k − n] are past input values, and n is the order. To comprehensively train the weights of the compensation model based on BP neural network, we set the output step response signal values derived after the ideal step signal passing through the established neural network model as input values, rather than the step response values output in the dynamic calibration test. Moreover, we set the ideal step signal values as output values. Current input values, past input values and past output values build the input layer. And current output values form the output layer.

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4 Modeling and Compensation Practice of the Typical Pressure Sensor Based on BP Neural Network Based on the dynamic calibration test, the neural network model of the typical pressure sensor can be established first. We set the quantity of hidden layers as 1, the model order as 7, the quantity of neural nodes as 7, took the quantity of iterative calculation steps as 100, and the calculation standard as the model error approaching 0. The input-output neural network model of the pressure sensor was established. An ideal step signal passes through the neural network model to get the step response. The original step response from the dynamic calibration test and the step response from the neural network model are shown in Fig. 5. Two curves have good consistency, and the neural network model of the typical pressure sensor has high accuracy and reliability.

Fig. 5. The original step response and the step response from the neural network model.

Fig. 6. The original step and the step signal from the neural network model.

Based on the neural network model, the neural network dynamic compensation model can be established. Similarly, the quantity of hidden layers of the neural network is set as 1, the model order as 5, the quantity of neural nodes as 5, the quantity of iterative calculation steps as 100, and the calculation standard as the model error approaching 0. The comparison between the original ideal step signal and the step signal restored by the neural network dynamic compensation model is shown in Fig. 6. The coincide of two curves proves the effectiveness of the dynamic compensation model of the typical pressure sensor.

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5 Conclusion In this paper, the double-diaphragm shock tube was selected as the calibration device to calibrate the typical piezoelectric pressure sensor with the buffer device. The results show that the buffer device can significantly narrow the working bandwidth of the oil downhole pressure sensor. To solve the problem, based on BP neural network, the mathematical model with good accuracy and robustness was constructed to compensate the dynamic characteristics of the pressure sensor. The neural network dynamic compensation model of the pressure sensor can effectively improve the dynamic performance and expand the working bandwidth of the sensor to improve the accuracy of pressure measurement.

References 1. Zhang, H., Cui, C., Tiehua, M.A.: Oil well perforation pressure test instrument. Instrument Tech. Sens. 08, 26–28+32 (2015) 2. Xiao W.: The Design and Research of Oil-Gas Well Perforating Fracturing Pressure Test System. Taiyuan, North University of China (2015) 3. Ghaedi, M., Ghaedi, A.M., Hossainpour, M., et al.: Least square-support vector (LS-SVM) method for modeling of methylene blue dye adsorption using copper oxide loaded on activated carbon: Kinetic and isotherm study. J. Ind. Eng. Chem. 20(4), 1641–1649 (2014) 4. Wang, J., Cao, J., Yao, C., et al.: Force sensor model identification and dynamic compensator design. Des. Res. 07, 85–88+91 (2018) 5. Georgieva, P., Azevedo, S.D.: A neural network based approach for measurement dynamics compensation. Appl. Artif. Intell. 16(06), 423–442 (2002) 6. Li, Y.-P., Zhao, D.: Thermal zero drift compensation of pressure sensor based on data mining and BP neural network. In: Liu, S., Ma, X. (eds.) ADHIP 2021. LNICSSITE, vol. 416, pp. 94–104. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-94551-0_8 7. Li, C., Kong, D., Shang, F., et al.: Simulation test study on sensor installation structure of ground reflection pressure measurement. J. Test Measurement Technol. 30(05), 442–449 (2016) 8. Liu, H.: Research on Shock Wave Test System and Dynamic Characteristic Compensation. Taiyuan, North University of China (2017) 9. Matthews, C., Pennecchi, F., Eichstädt, S., et al.: Mathematical modelling to support traceable dynamic calibration of pressure sensors. Metrologia 51(3), 326–338 (2014)

Model Predictive Current Control of Three-Phase Voltage Source Rectifier Based on Optimal Space Trajectory Xiaolei Sun1 , Tao Rui2 , Cungang Hu1(B) , Wenping Cao1 , Ke Zhang3 , and Weixiang Shen4 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected]

2 School of Internet, Anhui University, Hefei, China 3 Jiangsu Dongrun Zhilian Technology Co., Ltd, Jiangsu, China 4 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, Australia

Abstract. The traditional two-level rectifier model predictive control only uses a single voltage vector in the control cycle, which makes the current ripple larger. The voltage source rectifier model predictive current control approach based on optimal space trajectory (OST-MPC) is suggested as a solution to the aforementioned issues. By rearranging the vector switch sequences and selecting the switch sequences with the smallest value function as the optimal sequence combination, the problem of uneven frequency spectrum distribution of the traditional predictive control current is solved by applying it to the next control cycle. The deadbeat method is used to calculate the vector action time, which improves the steady state accuracy of current and reduces the aberration of the current; Optimization of the control set results in a smaller system computation. Compared with the traditional three vector model prediction algorithm, The outcomes of the experiments support the efficacy of this approach. Keywords: Voltage source rectifier (VSR) · Model predictive current control · Optimal space trajectory

1 Introduction The previous years, predictive control (MPC) has been used to research because of its intuitive concept, easy modeling, fast dynamic response and support for multi-objective control [1–3]. References [4, 5] determines the optimal switch sequence that can satisfy multiple control objectives by setting two value functions for quadratic optimization. In references [6, 7], the steady-state value of the system state variable is weighted and introduced into the value function to optimize the selection of the switching sequence when the circuit operates in a transient state. Reference [8] proposes a dynamic weight factor calculation method, which improves the dynamic performance. In essence, the above methods only © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 380–386, 2023. https://doi.org/10.1007/978-981-99-4334-0_47

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take the momentary forecast blunder at the conclusion of the switching cycle as the only standard to evaluate the effect of the switch sequence, but the prediction error at a single point in the control cycle cannot accurately evaluate the effect of the whole switch sequence. This study provides an effective spatial trajectory-based predictive current control method (OST-MPC) for a voltage source rectifier model. This work proposes a vector time computation approach based on inexact computing and optimizes the switching sequence. The suggested technique can lessen current ripple. By acting on multiple vectors in one cycle. Ultimately, modeling and experimentation are used to validate the method’s viability and efficacy.

2 Traditional Model Prediction Algorithm This paper mainly studies two-level rectifier. Figure 1 shows its physical structure.

e

o

L

R i a

S1

S3

a

ib ic S2

S5

b S4

c

C

RL udc

S6

N

Fig. 1. A voltage source rectifier’s schematic.

VSR at α, β The following is an expression for the mathematical model in the reference frame: eαβ = Rs iαβ + L

d iαβ + vαβ dt

(1)

where vα , vβ is the component of AC measurement input signal of rectifier on axis α, β; iα , iβ is the component of grid current on axis α, β; eαβ = [eα , eβ ]T is the grid voltage. R is the line impedance, representing the line’s resistance to current. Formula (1) is obtained after forward Euler discretization: iy (z + 1) = iy (z) +

Ts (ey (z) − Riy (z) + vy (z)) L

(2)

where, y = [α, β] the variable x(z) represents the amount of the variable at that time. And Ts represents discrete time. The prediction process of traditional MPC is shown in Fig. 2.

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The predicted current calculated by formula (2) is brought into formula (3) for judgment, and the vector of the smallest amount is finally selected as the optimal vector vop . G = (i∗α (z + 1) − iα (z + 1))2 + (i∗β (z + 1) − iβ (z + 1))2

(3)

where, [iα∗ (z + 1), iβ∗ (z + 1)] is the given current at next time.

Fig. 2. Prediction process of MPC.

3 Proposed OST-MPC Control Algorithm The proposed control strategy mainly includes the following parts: 1. Gradient calculation of switching sequence 2. Calculation of the vector action time 3. Generation of the duty cycle. 3.1 Gradient Calculation of Switching Sequence In this paper, the 6-Sector 7-segment vector switching sequence shown in Table 1 is adopted. The vectors in Table 1 are uniformly numbered in the following form according to the order of action: {vi0 , vin , vim , vi0 , vim , vin , vi0 }. Where i represents the ith switch sequence, and 0, n and m are the numbers corresponding to each vector in the switch sequence. The prominent advantage of the fixed vector combination method used in this paper is that the switching cost is small. Table 1. Vector combination table. Number

Switch order

I

v0 , v1 , v2 , v7

II

v0 , v3 , v2 , v7

III

v0 , v3 , v4 , v7

IV

v0 , v5 , v4 , v7

V

v0 , v5 , v6 , v7

VI

v0 , v1 , v6 , v7

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Transform formula (1) to obtain the current change gradient generated by each vector: f vαβk =

d iαβ 1 = (eαβ − vk − iαβ R) dt L

(4)

where, vk , k ∈ {0 · · · 7} represents eight vectors in Fig. 2. f vαβk , k ∈ {0 · · · 7} represents the two corresponding current gradients. The current trace is shown in Fig. 4. Assuming that the vector action time is known, the following current prediction formula can be obtained according to the vector action sequence shown in Fig. 3; pre

iy (k + 1) = iy (k) + 2(fvy1 t1i + fvy2 t2i + 2fvy0 t0i )

(5)

where, y = [α, β], txi , x ∈ {0, 1, 2} represents the action time of vectors 1, 2 and 0 in the ith vector combination.

Fig. 3. Inductance current trace.

3.2 Calculation of Vector Action Time The ideal vector action time of each potential vector switching sequence is determined by reducing the sum of squares of current tracking errors in order to achieve the inductor current reference tracking that best suits the control cycle. ref

pre

ref

G(tin , tim ) = (iαpre (z + 1) − iα (z + 1))2 + (iβ (z + 1) − iβ (z + 1))2

(6)

By solving formula (6), the optimal vector duration t 0 , t 1 and t 2 are respectively: ⎧ Eα (fβim − fβi0 ) + Eβ (fαi0 − fαim ) Ts (fαim fβi0 − fαi0 fβim ) ⎪ ⎪ tin = + ⎪ ⎪ 2A 2A ⎨ Eα (fβi0 − fβin ) + Eβ (fαin − fαi0 ) Ts (fαi0 fβin − fαin fβi0 ) (7) tim = + ⎪ ⎪ ⎪ 2A 2A ⎪  ⎩ ti0 = (Ts 2 − tin − tim ) where, Eα = iα∗ (z +1)−iα (z), Eβ = iβ∗ (z +1)−iβ (z) A = fαi0 fβin −fαi0 fβim +fαin fβim − fαin fβi0 + fαim fβi0 − fαim fβin .

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The output waveform may be further improved, the quality is raised, and the stability of the entire system is ensured, and the time is computed using this approach with an extraordinarily high degree of tracking precision. 3.3 Duty Cycle Calculation According to the vector action sequence given in Table 1 and the vector action time calculated by formula (7), the following optimal duty cycle calculation formula can be obtained: ⎧ ⎪ ⎨ da,op = 2(Sa,opn topn + Sa,opm topm + top0 )/Ts db,op = 2(Sb,opn topn + Sb,opm topm + top0 )/Ts (8) ⎪ ⎩ dc,op = 2(Sc,opn topn + Sc,opm topm + top0 )/Ts where: dop is the calculated three-phase optimal duty ratio,Sop is the three-phase switching state of vector n in the selected optimal switching sequence, top is the action time corresponding to the selected n, m and 0 vectors.

4 Simulation Result Using a simulink simulation environment, the algorithm’s efficacy is confirmed.The simulation parameters are: DC bus voltage 300 V, line resistance 0.02 , filter inductance 7 mH, grid voltage 100 V, sampling frequency 10 kHz, dead time 2 μs. 4.1 Steady State Performance Comparison To evaluate the OST-MPC algorithm’s performance, The new method is compared to the conventional three vector approach in Fig. 4, which shows their quiescent current performance.

Fig. 4. Current waveforms of two algorithms.

The sample current data was exported from the oscilloscope and loaded into the workspace as Excel to compare the FFT evaluation findings of the power backend current. The data was imported into Simulink through the from workspace module in Simulink for FFT analysis, and the analysis results were obtained. Figure 4 shows the three-phase current waveforms of the network side under different control strategies when the reference current is 5A and the sampling frequency is 10 kHz. The network side current THD of the

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traditional three vector control strategy is 1.47%. In accordance with the control method suggested in this study, by optimizing the switching sequence and the value function, the thd is reduced to 0.96%. It is clear that the strategy suggested in this research has a favorable impact on raising the system’s constant-state performance. This enhancement enhances power consumption quality and current performance significantly. 4.2 Dynamic Performance Comparison Figure 5 displays the findings of the experiment with dynamic switching of the grid side current when the reference current changes from 5 A to 10 A. When the traditional three vector strategy is adopted, the grid connected current regulation time of the system is 876 μs. Under the oss-mpc strategy, the regulation time of grid connected current is 512 μs. It is clear that the oss-mpc technique suggested in this study performs well in terms of quick dynamic reaction. This is because the method refines the evaluation index of the switch sequence, and can more accurately select the optimal switch sequence when it changes dynamically, thus improving the fluctuating performance of the system, which confirms the efficiency of the technique suggested in this study in further detail.

Fig. 5. Simulation waveform of traditional double vector algorithm.

5 Conclusion An optimal spatial trajectory model predictive control strategy (OST-MPC) is proposed. Based on multi vector synthesis, the minimum number of switches in the current cycle and adjacent cycles is realized to optimize the switch sequence, so as to increase the system’s control precision. By examination of simulation and experimental data from the OST-MPC algorithm and conventional three vector control approach, the benefits of the control approach suggested in this study in terms of constant-state performance and fluctuating performance are confirmed,which provides an idea for the algorithm design of multi vector model predictive control. The requirement of a realistic time calculation in the process of numerous vectors is successfully demonstrated in this research. The

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vectors can only be correctly synthesized after a fair amount of calculating time. Of course, beat compensation or two-step prediction can also be thought of as improvement methods if the performance still has to be improved. Acknowledgments. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation) - Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

References 1. Xing, N., Qi, X., Cao, W., Huang, X.: Novel adaptive control strategies for permanent magnet synchronous generator based wind power generation. In: Cao, W., Hu, C., Huang, X., Chen, X., Tao, J. (eds.) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 916. Springer, Singapore (2022). https://doi.org/10.1007/978-981-19-3171-0_48 2. Li, L., et al.: Multi-time scale optimal dispatch for AC/DC distribution networks based on cluster partition. In: Hu, C., Cao, W., Zhang, P., Zhang, Z., Tang, X. (eds.) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol. 899. Springer, Singapore (2022). https://doi.org/10.1007/ 978-981-19-1922-0_30 3. Xiaohe, W., Dan, S.: Three-vector-based low complexity model predictive direct power control strategy for doubly fed induction generators. IEEE Trans. Power Electron. 32(1), 773–782 (2017) 4. Vazquez, S.V., Acuna, P., Pou, J., et al.: Model predictive control for single-phase NPC converters based on optimal switching sequences. IEEE Trans. Industr. Electron. 63(12), 7533–7541 (2016) 5. Vazquez, S.V., Marquez, A., Aguilera, R., et al.: Predictive optimal switching sequence direct power control for grid-connected power converters. IEEE Trans. Industr. Electron. 62(4), 2010– 2020 (2015) 6. Machado, O., Martín, P., Francisco, J., et al.: A Neural Network-based dynamic cost function for the implementation of a predictive current controller. IEEE Trans. Industr. Electron. 33(10), 10068–10078 (2022) 7. Mora, A., Cardenas, R., Aguilera, R.P.: Predictive optimal switching sequence direct power control for grid-tied 3L-NPC converters. IEEE Trans. Industr. Electron. 68(9), 8561–8571 (2021) 8. Xicai, L., Libing, Z., Jin, W., et al.: Robust predictive current control of permanent-magnet synchronous motors with newly designed cost function. IEEE Trans. Power Electron. 35(10), 10778–10788 (2020)

A Novel Current-Limiting Hybrid DC Circuit Breaker Yiqi Liu, Bingkun Li(B) , Junyuan Zheng, Tianshi Guo, Laicheng Yin, and Zhaoyu Duan Northeast Forestry University, Harbin 150040, China [email protected]

Abstract. The hybrid DC circuit breaker (HCB) plays a vital role in the flexible DC grid by providing fault isolation on the DC side. However, with the rise of DC grid capacity, the fault current levels have become higher, and most current HCB topologies lack the ability to limit the fault current. In light of this, this paper proposes a novel current-limiting HCB topology that can change the branch’s series and parallel structure to achieve current limiting, thus ensuring faster fault isolation. This paper conducts a detailed analysis and theoretical deduction of the working process of the proposed HCB. Additionally, a single-end equivalent is built in PSCAD/EMTDC for simulation verification. Simulation results reveal that the proposed HCB outperforms the ABB HCB in fault isolation speed, with a 21.4% increase and energy consumption reduced by 73.2%. The simulation comparison further demonstrates the feasibility and superiority of the HCB. Keywords: Hybrid DC circuit breaker · Current limiting · Fault isolation

1 Introduction The technology of flexible DC transmission has gained widespread attention due to its advantages in connecting large-scale renewable energy grids and transmitting power over long distances [1, 2]. However, flexible DC grids are characterized by low impedance and inertia, which can lead to rapid increases in fault current in the event of a DC fault, posing serious safety risks to the power grid. Therefore, timely fault isolation is crucial [3]. As the voltage level and capacity of the DC grid continue to improve, fault current levels are also increasing, making it necessary to develop new high-capacity devices with fault current limiting capabilities. The conventional HCB lacks such capabilities, making it necessary to explore new solutions. Reference [7] proposed a fault current limiter topology that can be used with the HCB for fault isolation. In addition, a multibranch current-limiting HCB has been proposed that limits fault current by converting the current-limiting inductance of each branch from parallel to series, but it requires more IGBTs, which increases costs [8].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 387–391, 2023. https://doi.org/10.1007/978-981-99-4334-0_48

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To address these issues, this paper proposes a new current-limiting HCB topology that improves overall performance and meets the demands of large-capacity and large-scale DC grids. The paper first analyzes the proposed topology of the HCB and then theoretically deduces its working process. Finally, simulation verification and performance comparison analysis are carried out in PSCAD/EMTDC.

2 Topology and Theoretical Analysis of the Proposed HCB As shown in Fig. 1, The main breaker module is comprised of three branches. Branch 1 is made up of ultra-fast disconnector (UFD) and load commutation switch (LCS). Branch 2 consists of diodes and IGBTs, and diode rectifier bridges and IGBTs provide bidirectional fault isolation. Branch 3 consists of Metal oxide arresters (MOVs), which provide circuit protection and dissipate the fault energy. The breaker module is made up of two branches, UFD and LCS used primarily to carry current during normal operation, and diode rectifier bridges and IGBTs providing bidirectional fault isolation. The current limiting circuit is composed of the current limiting inductor (L), energy dissipating resistor (Rd ), and diode rectifier bridge.

Fig. 1. The topology of the proposed HCB.

The operation process of the HCB is divided into five states: (1) Normal working (t 0 –t 1 ), as shown in Fig. 2a with the red line indicating the current path. R1 and R2 represent the equivalent resistances of the breaker module and the main breaker module, respectively, while L 0 denotes the line inductance. R0 and RS represent line resistance and load impedance, respectively, and L is the currentlimiting inductance with an equivalent resistance of RL . U dc denotes the DC voltage. Using Kirchhoff’s Voltage Law (KVL), the system current I can be expressed as: I=

Udc R0 + R + Rs

(1)

A Novel Current-Limiting Hybrid DC Circuit Breaker

389

Fig. 2. The current path of the equivalent circuit: (a) t 0 < t < t 1 ; (b) t 1 < t < t 2 ; (c) t 2 < t < t 3 ; (d) t 3 < t < t 4 ; (e) t 4 < t < t 5 ; (f) t 5 < t.

where R is the equivalent resistance of the proposed HCB. R1 t1

(6) (7)

The resistance and inductance determine the time constant τ, and I N represents the rated current. (3) Current commutation (t 2 –t 4 ): As illustrated in Fig. 2c, the LCS receives the trip signal at t 2 . The UFD is fully disconnected at t 3 , and the IGBT blocking in the main breaker module as shown in Fig. 2d. The MOV reaches its operating voltage, R3 and R4 represent the equivalent resistances of the IGBT and diode that are turned on in the breaker module and main breaker module, respectively.

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(4) Current limiting (t 4 –t 5 ): At t 4 , three parallel branches are turned into a series, as shown in Fig. 2e. According to KVL, the following formula can be obtained: Udc = (R0 + 2R3 + 3RL )I + (L0 +3L) I=

dI dt

t−t Udc Udc − 4 + (It3 − )e τ1 R0 + 2R3 + 3RL R0 + 2R3 + 3RL

τ1 = (L0 + 3L)/(R0 + 3R3 + 3RL ), t > t4

(8) (9) (10)

After fully turning off the main breaker module, the parallel current limiting inductance is switched to series, which causes the fault current in the system to rise at a lower rate. This indicates the effectiveness of the proposed HCB in limiting the current. (5) Fault isolation(t 5 < t): At t 5 , the IGBT blocking in the main breaker module and the fault current are discharged to zero via the MOV. As a result, fault isolation is achieved, and the equivalent circuit diagram at this stage is shown in Fig. 2f.

3 Simulation Verifications To confirm the effectiveness of the proposed HCB, a simulation model system was created using PSCAD/EMTDC and compared to an ABB HCB. The simulation results are displayed in Fig. 3. DC voltage U dc , load resistance Rs , line resistance R0 , current limiting inductance L, and line inductance L 0 are 320 kV, 320 , 10 , 100 mH and 100 mH, respectively.

Fig. 3. Simulation results: (a) System current I; (b) The current waveform of each branch; (c) Fault current comparison with ABB HCB; (d) Energy absorption of MOV comparison with ABB HCB.

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Figure 3a, b display the results of the simulation verification. At t 1 , a fault occurs. At t 2 , the HCB receives a trip signal, which blocks the LCS and causes the IGBTs in both the main and breaker modules to conduct. At t 3 , the UFD is fully opened, the IGBT blocks in the main breaker module and the MOV dissipates fault current energy. At t 4 , the main breaker module is fully disconnected, and the parallel branches are switched to series. The HCB then performs its current limiting function, resulting in a reduced growth rate of the fault current. At t 5 , the IGBT in the breaker module is disconnected, and the fault is completely isolated after the energy of the MOV is consumed. Figure 3c, d show that the ABB HCB lacks the current limiting ability, causing the fault current to rise at a higher rate after a fault occurs. Moreover, the proposed HCB achieves a 21.4% faster fault separation speed than the ABB HCB, consuming 73.2% less energy.

4 Conclusion To address the need for higher technical and economic performance in larger capacity and scale DC grid systems, this paper proposes a new topology for a current limited HCB. This paper analyzes the working process and principle of the proposed HCB and carries out simulation and verification in a single-end equivalent system. Compared to the ABB HCB, this paper proposed HCB achieves a 21.4% faster fault isolation speed and consumes 73.2% less energy. Simulation results demonstrate the feasibility and superiority of the proposed HCB.

References 1. Flourentzou, N., Agelidis, V.G., Demetriades, G.D.: VSC-based HVDC power transmission systems: an overview. IEEE Trans. Power Electron. 24(3), 592–602 (2009) 2. Wang, Y., Zhu, J., Zeng, Q., Zheng, Z.: Frequency regulation method for HVDC system with wind farm. In: Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, vol. 899. Springer, Singapore (2022) 3. Liu, G., Xu, F., Xu, Z., et al.: Assembly HVDC breaker for HVDC grids with modular multilevel converters. IEEE Trans. Power Electron. 32(2), 931–941 (2016) 4. Li, S., Xu, J., Lu, Y., et al.: An auxiliary DC circuit breaker utilizing an augmented MMC. IEEE Trans. Power Deliv. 34(2), 561–571 (2019) 5. Guo, Y., Wang, G., Zeng, D., et al.: A thyristor full-bridge-based DC circuit breaker. IEEE Trans. Power Electron. 35(1), 1111–1123 (2019) 6. Zhang, S., Zou, G., Wei, X., et al.: Diode-bridge multiport hybrid DC circuit breaker for multiterminal DC grids. IEEE Trans. Industr. Electron. 68(1), 270–281 (2020) 7. Nie, Z., Yu, Z., Gan, Z., et al.: Topology modeling and design of a novel magnetic coupling fault current limiter for VSC DC grids. IEEE Trans. Power Electron. 36(4), 4029–4041 (2020) 8. Xu, J., Feng, M., Zhao, X., et al.: A topology of clamped single module type reciprocating high voltage DC circuit breakers with current-limiting capability. Proc. CSEE 39(18), 5565–5574 (2019)

Study on Motor Parameters of PMSM Based on the Principle of Adjustable Leakage Flux Qiu Chu1 , Chunyan Li1(B) , Yu Wang2 , Fei Guo1 , and Tao Meng1 1 Heilongjiang University, Harbin 150080, China

[email protected] 2 Nanyang Explosion-Proof Electrical Research Institute, Nanyang 473000, China

Abstract. The magnetic field of the permanent magnet cannot be adjusted and the flux-weakening speed range of permanent magnet synchronous motor (PMSM) is small. To solve this problem, a PMSM based on the principle of adjustable leakage flux is proposed. The magnetic conductor in the rotor can move in the slot according to the rotating speed. The magnetic conductor is fixed when operates below rated speed. Once the motor speed exceeds rated speed, the magnetic conductor will slide along the slot to outward of the rotor until the forces keep balance again. The leakage flux is greater with higher speed, and the air-gap magnetic flux becomes smaller. On the basis of introducing the rotor structure, the fluxweakening principle of the motor is described. The influence of motor parameters on electromagnetic torque ripple of the motor with rated load is analyzed. The torque-speed performance is calculated. The simulation results are in agreement with the theoretical results, and the validity of wide flux-weakening range of this PMSM based on the principle of adjustable leakage flux is verified. Keywords: Permanent magnet synchronous motor · Flux weakening · Adjustable leakage flux · Electromagnetic torque ripple

1 Introduction High efficiency and energy-saving PMSM is widely used in various fields such as textile, electric vehicles, numerical control machine tools and military industry [1]. However, PMSM is excited by permanent magnet (PM) that cannot be adjusted, and it limits the application of PMSM in wide speed field. Based on this, scholars at home and abroad have done a lot of research on the flux weakening (FW) of PMSM [2].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 392–397, 2023. https://doi.org/10.1007/978-981-99-4334-0_49

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Scholars at home and abroad have proposed some special rotor structures to expand the FW speed range of PMSM. A PMSM with conical rotor is proposed in [3]. The memory motor scheme by changing the magnetization state of the PM is proposed in [4]. The composite rotor is proposed in [5]. The segmented PM is proposed in [6]. The d-axis inductance is increased by the magnetic bridge formed by the PM segments to widen the FW range. In addition to the special motor structure, the scholars also achieve the FW by optimizing the control method. There are mainly vector control and direct torque control methods. For examples, the leading angle FW control method is proposed in [7]. The direct torque method based on the given improved torque can make the motor meet the requirement of the current and voltage limits simultaneously to realize high-speed and stable operation in [8, 9]. Based on above analysis, a PMSM based on the principle of adjustable leakage flux is proposed. This method is new in that it belongs to the adaptive passive FW method. The motor speed is adjusted automatically by the movement of the MC according to its own force on it. The motor structure and the FW principle are introduced in Sect. 2. The influence of motor parameters on electromagnetic torque ripple is studied in Sect. 3. The torque-speed performance is analyzed in Sect. 4 to verify the effectiveness of the FW.

2 Motor Structure and Flux Weakening Principle The stator structure is the same with the common PMSM. The rotor is composed of PM, spring, magnetic conductor (MC), slide slot and iron core, as shown in Fig. 1. The MC is fixed in the slot for low speed, and its position is shown in Fig. 1a. In this case, the inter-pole leakage flux is the same as that of the common motor. The MC starts to move in the slot toward the rotor outer once speed exceeds rated speed. It moves until to achieve the force balance and operates at the new location steadily. The maximum movement of the MC is shown in Fig. 1b. In this case, a lot of the magnetic flux produced by the PM is closed inside the rotor through the MC. The movement distance of the MC is bigger with higher motor speed. It results in greater inter-pole rotor leakage flux, and the air-gap magnetic field control of the motor is realized. a Magnetic conductor

permanent magnet

core N

S

shaft

2

spring

slide slot

1

b

spring core

N 2

S

Magnetic conductor

1 3

3 N

4

permanent magnet shaft slide slot

S

Operation at or below the rated speed

N

4

S

Operation above the rated speed

Fig. 1. (a) Rotor operated at or below the rated speed; (b) rotor operated above the rated speed.

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3 Analysis of the Influence of the Motor Parameters on the Electromagnetic Torque Ripple The motor parameters and simulation results are shown in Table 1. Table 1. Motor parameters and simulation results. Rated parameters

Simulation results

Rated power

750 W

Output power

752.6 W

Rated torque

4.22 Nm

Electromagnetic torque

4.36 Nm

Rated speed

1700 r/min

Rated speed

1700 r/min

Maximum speed

4500 r/min

Maximum speed

> 5100 r/min

3.1 The Influence of Air Gap and Current on Electromagnetic Torque Ripple The electromagnetic torque ripple versus the air-gap length and winding current is shown in Fig. 2. The small air-gap length is conducive to improving the electromagnetic torque and slightly increasing the torque ripple due to large magnetic flux density. From the aspect of the torque ripple, it should be selected as large as possible on the premise of meeting the electromagnetic torque. In this paper, 0.4 mm was chosen. The variation range of torque fluctuation with different current is very small.

a

b

12 11 10 9

10.1 Troque ripple/%

Torque ripple/%

13

0.2

0.3 0.4 Air-gap length/mm

0.5

10.05 10 9.95 9.9 1.15

1.3

1.45

1.6

Current/A

Fig. 2. (a) Torque ripple versus air gap length; (b) torque ripple versus current length.

3.2 The Influence of Magnetic Conductor on Electromagnetic Torque Ripple The MC moves in the slot to regulate the inter-pole leakage flux. The MC width varies from 3.5 mm to 4.8 mm with unchanged other parameters. We change the MC width while keeping the magnetic bridge 1 mm constant. In the model, the PM length should be reduced to increase the MC width. At the same time, the PM thickness should be increased to keep the total area of PM unchanged. The effect of the MC on the electromagnetic torque ripple is shown in Fig. 3. The torque fluctuation generally shows a slight downward trend with the increase of the MC width.

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Torque ripple/%

12 11 10 9 8

3.5

4 4.5 MC width/mm

4.8

Fig. 3. The effect of the MC on the electromagnetic torque ripple.

3.3 The Influence of Permanent Magnet on Electromagnetic Torque Ripple The influence of length and thickness of the PM on torque ripple is shown in Fig. 4. Longer and thicker PMs can provide more PM flux, at the same time, it also causes larger torque fluctuations. Iron saturation of the motor leads to the decrease of the effective flux increasing per unit PM thickness. The torque fluctuation has a downward trend for the reason of motor saturation when the thickness of the PM exceeds 5 mm. 12 10.5 9 7.5 6

11

b Torque ripple/%

Torque ripple/%

a

15

19 23 PM length/mm

29

10.5 10 9.5 9 8.5

2

3 4 5 PM thickness/mm

6

Fig. 4. (a) Torque ripple versus PM length; (b) torque ripple versus PM thickness.

3.4 The Influence of Coil Turns on Electromagnetic Torque Ripple In order to maintain the same current density, the winding current is reduced while the number of turns is increased. In this case, the stator current and no-load back electromotive force (EMF) also changes with the number of turns. The electromagnetic torque ripple under the condition of equal current density is calculated as shown in Fig. 5. The electromagnetic torque with different turns is close to the same under same current density, that is, the turns have little influence on the electromagnetic torque and torque ripple. At the same time, under the condition of the same current density, the current needed to get the same torque decreases with the increase of the turns, and the increase of turns is also restricted by the value of no-load back EMF.

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11

b Torque ripple/%

Current/A

a

38

40 42 Number of turns

10.6 10.2

44

9.8 9.4 9

38

40 42 Number of turns

44

Fig. 5. (a) Current versus coil turns; (b) torque ripple versus coil turns.

Torque/(N·m)

4.5 3 1.5 0

800

2600 4400 Speed/(r/min)

6200

Fig. 6. The electromagnetic torque versus motor speed.

4 Torque-Speed Performance The relation between electromagnetic torque and speed in full speed range of the motor can be obtained by successively calculating each speed, as shown in Fig. 6. The maximum speed of the motor shall be increased to at least 3 times of the rated speed.

5 Conclusion The PMSM based on the principle of adjustable leakage flux provides a new way to solve the flux weakening problem of PMSM. The simulation results are consistent with the theoretical analysis, which verifies the effectiveness of the flux weakening of this motor. The maximum speed can reach 3 times of the rated speed. The motor parameter designed principle for reducing torque ripple is determined by qualitative analysis and quantitative calculations. Acknowledgements. This work was supported by the Heilongjiang Natural Science Foundation under Grant LH2021E100.

References 1. Giang PT, Ha VT: Drive control of a permanent magnet synchronous motor fed by a multilevel inverter for electric vehicle application. Eng Technol Appl Sci Res 12(3), 8658–8666 (2022)

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2. Mubarok MS, Liu T: An adjustable wide-range speed control method for sensorless IPMSM drive systems. IEEE Access (10), 42727–42738 (2022) 3. Chai, F., Zhao, K., Li, Z., Gan, L.: Flux weakening performance of permanent magnet synchronous motor with a conical rotor. IEEE Trans. Magn. 53(11), 8208506 (2017) 4. Yang, H., Rui, T., Lin, H., Niu, S., Lyu, S.: Investigation of balanced bidirectional-magnetization effect of a novel hybrid-magnet-circuit variable-flux memory machine. IEEE Trans. Magn. 58(2), 8102506 (2022) 5. Ayub, M., Jawad, G., Kwon, B.: Consequentole hybrid excitation brushless wound field synchronous machine with fractional slot concentrated winding. IEEE Trans. Magn. 55(7), 8203805 (2019) 6. Duan, S., Zhou, L., Wang, J.: Flux weakening mechanism of interior permanent magnet synchronous machines with segmented permanent magnets. IEEE Trans. Appl. Supercond. 24(3), 0510005 (2014) 7. Bon-Gwan, G., Choi, J.-H., Jung, I.-S.: Simple lead angle adjustment method for brush less DC motors. J. Power Electron. 14(3), 541–548 (2014) 8. Zhang, K., Fan, M., Yang, Y., Zhu, Z., Garcia, C., Rodriguez, J.: Field enhancing model predictive direct torque control of permanent magnet synchronous machine. IEEE Trans. Energy Convers. 36(4), 2924–2933 (2021) 9. Lin, X., Huang, W., Jiang, W., Zhao, Y., Dong, D., Xu, W.: Direct torque control for three-phase open-end winding PMSM with common DC bus based on duty ratio modulation. IEEE Trans. Power Electron. 35(4), 4216–4232 (2020)

The Coordination of FCL and Relay Protection: A Review Zhiying Xue1 , Yue Yu1 , Yudong Sun2(B) , Yuankun Zheng2 , Jiawei Liu2 , and Guangchen Ma2 1 State Key Laboratory of Power Grid Safety and Energy Conservation (China Electric Power

Research Institute), Beijing 100000, China 2 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

Abstract. With the increase of electricity demand and the development of power grid scale, the short-circuit current level of the power grid is increasing, which seriously endangers the security and stability of the power system. Traditional current limiting methods have certain limitations in terms of economy and reliability. The fault current limiter (FCL) has been widely studied due to their low impedance during normal operation and high impedance during faults, and are expected to solve the problem of short-circuit current breaking. However, many complex relay protection devices may be affected by the FCL. Therefore, this paper summarizes the research status of the existing coordination of FCL and relay protection. Keywords: FCL · Relay protection · Coordination

1 Introduction With the continuous expansion of the scale of our country’s power system, the shortcircuit current level of the power grid continues to rise, making the short-circuit current of the power grid in some areas reach or even exceed the breaking capacity of the circuit breaker [1]. Conventional current limiting methods include power system level methods and power equipment level methods [2], but there are certain limitations in economy and reliability. The FCL has the characteristics of low impedance under normal conditions and high impedance during faults [3], which is expected to solve the problem of shortcircuit current interruption. However, due to the impedance change of the FCL during faults, the total impedance of the whole system increases, causing the relay protection devices to malfunction or refuse to operate [4]. Therefore, in recent years, scholars at home and abroad have made a lot of research on the coordination of FCL and relay protection, which can be mainly divided into distance protection, current protection and longitudinal differential protection.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 398–403, 2023. https://doi.org/10.1007/978-981-99-4334-0_50

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2 Working Principle of FCL As an effective device to limit the short-circuit current of the power system, the FCL works as shown in Fig. 1. In normal operation, low impedance has no effect on system operation, and high impedance at fault time effectively limits the rise of short-circuit current. During faults, τ and δ need to be very short [5]. Z

ZFCL

τ

Impedance Change Multiple

response time

ZFCL kfcl = Zfcl

recovery time ρ

Zfcl Before fault

t0

t1

After fault removal

t

Fig. 1. The basic operating principle of FCL.

3 Influence of FCL on Relay Protection 3.1 Distance Protection The FCL can be equivalent to a resistance component or a reactive component, which will cause different changes in the parameter characteristics of the transmission line, resulting in refusal to move or misoperation. Reference [6] explored the influence of resistive and inductive FCLs on distance protection, and demonstrated it with a directional circle impedance action characteristic diagram, as shown in Fig. 2. Z'X

XSFCL XSFCL

ZM

jXM

ZM

RSFCL

ZX

Z'X RM

(a)

ZX

RSFCL

(b)

Fig. 2. (a) Influence of resistive FCL on distance protection, (b) influence of inductive FCL on distance protection.

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3.2 Current Protection Due to the installation of a FCL, in the event of a fault, the short-circuit current is reduced, which may lead to an extended operating time limit of the protection device, a refusal to operate the protection or a reduction in sensitivity. 3.3 Longitudinal Differential Protection After adding the FCL, since the impedance of the current limiter is much smaller than the impedance of the transmission line, it has little effect on the electrical quantity at both ends, so it has basically no effect on the longitudinal differential protection.

4 Coordination of FCL and Relay Protection 4.1 Distance Protection Reference [7] proposed a method for modifying the setting value of the distance protection section I, which can be calculated by (1):  = Zzd + ZSFCL Zzd

(1)

By adding the impedance value of the FCL to the set impedance value, so that the measured impedance can be within the characteristic circle of the set impedance when a fault occurs, as shown in Fig. 3a. However, considering that when the FCL is installed downstream of the protection, reference [8] proposed a combination method of impedance circle characteristic offset. The action characteristic impedance circle was added up along the jX axis, and the two together constituted the protection action characteristic area and expanded the protection range, as shown in Fig. 3b. ZAB D2

Z zdref 2 D1

Z ' zd

ZFCL

ZAD1 = ZFCL

Zzd Z SF

Z zdref 1

Z 'J

CL

ZlAB

ZJ

A

(a)

(b)

Fig. 3. (a) Directional circular action characteristics after re-tuning, (b) The operating characteristics of the impedance circle offset combination method.

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References [9, 10] pointed out that the measured impedance of phase-to-ground distance protection was more complex than that of phase-to-phase distance protection. By changing the wiring form of the relay, applying voltage and current, the measured distance was the sum of the superconducting fault current limiter (SFCL) impedance and the transmission line impedance from the relay to fault location. 4.2 Current Protection Reference [11] studied the coordination between SFCL and current protection in power distribution system, and proposed to modify the impedance value of SFCL to meet the requirements of coordination with current protection. Reference [12] proposed to modify the setting value and action time of the current protection section I, which can be calculated by (2): Eϕ Zs min + ZSFCL I t = 0 + tSFCL = tSFCL

I I = Krel × Iset

(2)

As in [13], the simulation analysis of SFCL’s time-definite and inverse-time overcurrent protection was carried out. And the use scenarios and coordination strategies of the two protections were also given respectively. Reference [14] developed a resistive SFCL model in PSCAD/EMTDC, the optimal value of the shunt resistance was found through simulation analysis, which can effectively solve the problems of the resistive SFCL and current protection. 4.3 Differential Protection Reference [15] proposed a new principle of longitudinal protection based on the current transient change. This principle can still have absolute selectivity when dealing with the fault transition resistance between the DC lines impact, etc. Reference [16] proposed a DC line longitudinal protection based on a resistive SFCL. It utilized the voltage direction at both ends of the SFCL to determine whether the fault in the area or outside the area. Take the SFCL1 for example, as shown in Fig. 4. When the voltage USFCL1 is greater than 0, we can conclude that the fault is in the area. Otherwise, outside the area. SFCL2

SFCL1

DC AC

DC AC

K1

K2

DCCB1 DCCB2

DC AC

Fig. 4. Structure of Nan’ao flexible DC system.

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5 Conclusion Although some research progress has been made in the coordination of fault current limiter and relay protection, it is only limited to the theoretical research stage, and there is a lack of practically verified and widely adopted protection configuration schemes, standards about the coordination of fault current limiter and relay protection, and the practical application feedback is yet to be explored. The future development direction may be towards the use of the electrical quantity characteristics of the fault current limiter for rapid fault identification and protection acts immediately. Also the use of artificial intelligence algorithms for coordination of fault current limiter and protection is also an important development direction. With the wide application of the fault current limiter, coordination of fault current limiter and relay protection will become an important backing for the stability of the power system in the future, and relevant technical standards and protection schemes will be finally promulgated. Acknowledgements. This work was supported by Open Fund of State Key Laboratory of Power Grid Safety and Energy Conservation (China Electric Power Research Institute) (JBB51202101688).

References 1. Yuan, J., Zhang, C., Zhou, H.: Current situation and development of AC saturated iron core fault current limiter. Electric Power Autom. Equip. 40(05), 209–221 (2020) 2. Han, G., Han, L., Wu, L.: Application and development of methods on limiting power grid’s short-circuit current. Power Syst. Protection Control 38(1), 141–144 (2010) 3. Yuan, J., Hong, Y., Zhang, C., Zou, C., Ye, C.: A multifunctional saturated iron core fault limiter with mixed excitation. Proc. CSEE 42(17), 6471–6480 (2022) 4. He, Y., Chen, X., Tang, Y., Yang, Z., Zhang, H.: Influence of SFCL on automatic reclosing and relay protection. High Voltage Technol. 10, 2190–2194 (2008) 5. Hao, X., Wang, P., Sun, H.: Analysis and characterization of DC fault current limiter working principle. Power Grid Technol. 43(12), 4414–4424 (2019) 6. Xia, Y., Liu, J.: Influence of SFCL on power system relay protection and transient stability. New Technol. Electrical Eng. 02, 45–48+58 (2007) 7. Wei, F., Li, H., Lin, X., Li, Z., Ke, D., Muhammad, S., Owolabi, S.: Distance protection setting method considering dynamic process of TCSC type FCL. Chin. J. Electrical Eng. 37(08), 2279–2290 (2017) 8. Liu, H., Jiang, D., Chen, G., Zhang, P.: Improvement method of distance protection setting after installing solid-state short-circuit current limiter. Autom. Electric Power Syst. 02, 90–95 (2006) 9. Shi, T.: Research on the Coordination Between 220kV Saturated Iron Core SFCL and Transmission Line Distance Protection. Lanzhou Jiaotong University (2018) 10. Li, B., Li, C., Guo, F.: Application studies on the active SISFCL in electric transmission system and its impact on line distance protection. In: 2015 IEEE Transactions on Applied Superconductivity, pp. 1–9 (2015) 11. Moon, G., Wi, Y., Lee, K.: Fault current constrained decentralized optimal power flow incorporating. IEEE Trans. Appl. Supercond. 21(3), 2157–2160 (2010)

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12. Kim, J., Kim, J., Lim, S.: Study on protection coordination of a flux-lock-type SFCL using switches. IEEE Trans. Appl. Supercond. 26(4), 1–4 (2016) 13. Li, B., Li, C., Guo, F., Xin, Y.: Overcurrent protection coordination in a power distribution network with the active superconductive FCL. In: 2014 IEEE Transactions on Applied Superconductivity, pp. 1–4 (2014) 14. Chen, Y., Li, S., Sheng, J.: Experimental and numerical study of co-ordination of resistivetype superconductor FCL and relay protection. J. Supercond. Nov. Magn. 26, 3225–3230 (2013) 15. Dong, Q., Wang, J., Shi, B.: Research on the coordination between FCL and transmission line longitudinal protection. Electr. Eng. 6, 18–23 (2014) 16. Xiao, L., Sheng, C., Luo, P.: Vertical protection method of DC line based on resistive Superconductive fault current limiter. Guangdong Electric Power 33(8), 11–17 (2020)

Research on Three-Phase Unbalance Compensation of Magnetic Control Transformer Yaoliang Yan1 , Ming Fan1 , Hong Zhang2 , Lei Wang1 , Zhenqi Ma1 , Bengang Sui2 , Kun Peng1 , Jingtao Bai1 , Mingzhou Zheng1 , Tengda Wang1 , Yewei Jie1 , Wenhui Shi1 , and Wenchao Dong3(B) 1 State Grid Jia Xing Power Supply Company, Jia Xing 314001, China 2 Jia Xing Heng Guang Electric Power Construction Co., Ltd., Bin Hai Branch, Bin

Hai 300450, China 3 School of Engineering and Automation, Wuhan University, Wuhan 4300724, China

[email protected]

Abstract. A three-phase unbalance compensation system based on magnetic control transformer is proposed, changes the three-phase system from unbalance to balance. Firstly, the working principle of the magnetic control transformer and the balance compensation principle based on the magnetic control transformer are analyzed. Secondly, the situation of three-phase unbalanced load is analyzed. The three-phase unbalanced system at the low voltage side becomes balanced at the grid side, and the power factor of the system is compensated to 1. Finally, a three-phase unbalance simulation model was built in Matlab, the simulation results show that the combination of the magnetic control transformer and the fixed capacitor bank can effectively eliminate the negative sequence current, compensate the reactive power of the system, improve the power factor, and balance the three-phase current. Keywords: Magnetic control transformer · Three-phase imbalance · Negative-sequence current

1 Introduction With the improvement of people’s living standards, power consumption increasing, easy to cause the low voltage distribution network in the three phase unbalanced three-phase imbalance degree of increase will seriously affect the power quality and increase the loss of power system, affect power supply reliability [1, 2]. At present, the following schemes are mainly used to solve the three-phase unbalance problem [3]. In the literature [4], a combined TCR and TSC compensation device was developed to achieve continuous compensation of reactive power and negative sequence current compensation in the distribution network. The paper [5] proposed a TCR + FC type SVC with 12-pulsation technique to achieve dynamic negative sequence reactive power compensation and reduce harmonic content. The literature [6] analyzed the load unbalance problem of three-phase four-wire low-voltage distribution network by connecting capacitors between the neutral © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 404–408, 2023. https://doi.org/10.1007/978-981-99-4334-0_51

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line and any two phases to reduce the current on the neutral line to 0. But at this time, the three phases are still asymmetric, and then the active power is transferred by connecting capacitive inductors between phases to make the three-phase current balanced and the power factor is 1. The literature [7] proposed to use two-stage saturated magnetron and fixed capacitor Cooperate with the negative sequence and reactive power integrated management, and at the same time can greatly reduce the harmonics emitted by the reactor. In this paper, the magnetic control transformer and fixed capacitor bank are used to dynamically and smoothly regulate the reactive power to change the three-phase unbalanced system on the low-voltage side to balanced on the grid side and to compensate the power factor of the system to 1.

2 Principle of Magnetic Control Transformer and Balancing Compensation Principle 2.1 Principle of Magnetic Control Transformer Figure 1 shows the schematic diagram of the magnetic control transformer. The main principle is to adjust the size of the DC control current by changing the trigger angle of K1 and K2, thus changing the saturation degree of the core and changing the size of the core permeability, so that the size of the equivalent excitation inductance of the transformer can be adjusted smoothly.

B1

i1

B2

A +

N1

U1 primary side

a

i2

X

+ N2 l

Nk

U2 secondary side

-

D

lt K1

K2

iron core I

iron core II

x

Fig. 1. Schematic diagram of a new magnetic control transformer.

2.2 Balancing Compensation Principle The power supply voltage is generally symmetric, so most of the unbalance of the threephase system is caused by the unbalanced load of the three-phase current imbalance, three-phase load imbalance will generate negative sequence current and zero sequence current in the line. Therefore, if we compensate the negative sequence current in the line

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current, we can change the three-phase line current from unbalanced to balanced. At the same time, we can compensate the reactive component of the positive sequence current, which can improve the power factor of the power system and improve the utilization rate of power resources [8–10]. Suppose that the supply voltage is symmetrical and connected with three-phase load, the analysis diagram of balanced compensation circuit based on magnetic control transformer can be drawn, as shown in Fig. 2.

IA

IAX

ILA

n:1

ICa

YLA

IB

IBX

ILB YLB

IC

ICX

ILC YLC

n:1

ICb

n:1 ICc

Ia

Ya

Ib

Yb

Ic

Yc

Fig. 2. Three-phase load balancing compensation circuit analysis diagram.

2.3 Simulation Analysis Three phase unbalance simulation model is built in Matlab/Simulink, as shown in Fig. 3. Connecting an unbalanced inductive load on the load side, the three-phase current waveform is shown in Fig. 4, and the parameters in the circuit are shown in Table 1. From Table 1 and Fig. 4, it can be seen that the three-phase current is the smallest in phase A and the largest in phase C. The three-phase currents are not equal to each other, the power factor of phase A and phase C is only about 0.5, and the three-phase current imbalance is 40.26%.

Fig. 3. Simulation model.

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Fig. 4. Three phase current waveforms before compensation.

Table 1. Parameters before compensation Parameter

Effective current value/A

Degree of unbalance (%)

Power factor

A phase

7.56

40.26

0.58

B phase

14.33

40.26

0.90

C phase

16.07

40.26

0.53

The compensation device is put in to compensate the unbalanced load, The threephase current waveform after compensation is shown in Fig. 5 and the parameters in the circuit are shown in Table 2. From Table 2 and Fig. 5, we can see that the three phase currents are basically equal in size after compensation, the phase power factor rises to 1, and the negative sequence component of the current basically drops to 0.

Fig. 5. Three phase current waveforms before compensation.

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Parameter

Effective current value/A

Degree of unbalance (%)

Power factor

A phase

8.80

0.11

1

B phase

8.79

0.11

1

C phase

8.81

0.11

1

3 Conclusion This paper mainly researches the three-phase unbalance compensation based on magnetic control transformer, using the cooperation of magnetic control transformer and fixed capacitor bank to compensate the negative sequence current and reactive power of the unbalanced system, changing the three-phase system from unbalanced to balanced, which can effectively eliminate the negative sequence current, compensate the system reactive power, improve the power factor and balance the three-phase current.

References 1. Ghaeb, J.A., Aloquili, O.M.: High performance reactive control for unbalanced three-phase load. Int. Trans. Electrical Energy Syst. 20(6), 710–722 (2010) 2. Youssef, T.A., Elsayed, A.T., Berzoy, A., et al.: Power quality enhancement for nonlinear unbalanced loads through improved active power filter control. In: The 40th Annual Conference of the IEEE Industrial Electronics Society, Dallas, pp. 5202–5207 (2014) 3. Saeed, Y., Mahmoud, E., Seyed, H.T.: Presents a new topology for parallel compensator to improve the load unbalance in electrical energy distribution network. In: The 20th Conference on Electrical Power Distribution Networks Conference (EPDC), Zahedan, pp. 246–253 (2015) 4. Das, S., Chatterjee, D., Goswami, S.K.: Tuned-TSC based SVC for reactive power compensation and harmonic reduction in unbalanced distribution system. In: IET Generation Transmission & Distribution (2017) 5. Dan, W., Yang, C., Xin, Z., et al.: Research on application of TCR+FC typed SVC in power quality integrated management for power traction system. In: International Conference on Sustainable Power Generation & Supply, IET (2013) 6. Liu, J., Zheng, Y., Li, L., et al.: Research on the control method of three-phase four-wire STATCOM. In: 2012 IEEE International Conference on Oxide Materials for Electronic Engineering (OMEE), IEEE (2012) 7. Li, X.-C., Wang, X., Ge, D.-X.: Study on two-stage saturable magnetically controlled reactor to improve power system based on negative sequence current. In: Equipment Manufacturing Technology (2014) 8. Zheng, W., Huang, W., Hill, D.J.: A deep learning-based general robust method for network reconfiguration in three-phase unbalanced active distribution networks. Int. J. Electrical Power Energy Syst. 120 (2020) 9. Wang, S., Etemadi, A., Doroslovaˇcki, M.: Adaptive cascaded delayed signal cancellation PLL for three-phase grid under unbalanced and distorted condition. Electric Power Syst. Res. 180 (2020) 10. Montoya-Mira, R., Blasco, P.A., Diez, J.M., Montoya, R., Reig, M.J.: Un-balanced and reactive currents compensation in three-phase four-wire sinusoidal power systems. Appl. Sci. 10(5) (2020)

Automatic Protective Relay Testing on Real Time Simulator Xinyi Zhou, Xiaonan Han(B) , Jiaohong Luo, Tao Huang, and Xiyang Tao State Grid Changzhou Electric Power Supply Company, Changzhou City 213004, Jiangsu Province, China [email protected]

Abstract. Real-time digital simulators (RTS) have been widely used in the electric power industry for over two decades. The main advantage of RTS is creating a work environment to test the equipment as if it is installed in the real power system. In the simulation environment, the users can do tests of severe faults, which is impossible to be done in real-time systems. Today, many important devices are tested on RTS before it is installed in the real power system. One popular application is to use RTS for closed-loop testing protective relays. These simulators provide continuous, hard real-time, Electro-Magnetic Transient (EMT) simulation results. EMT simulation provides the instantaneous value results, which can be sent to protection relays directly as if the relay received the fault signals from the real power systems. Over the years, the hardware and software of RTS has been significantly improved since they were first introduced commercially in the early 1990s. Many advanced functions have been developed to improve the performance of the RTS. This paper introduces an automatic testing procedure that can significantly increase the testing productivity for manufacturers and utility engineers. Keywords: Real time digital simulators (RTS) · Automatic testing · Closed-loop testing · Traveling wave

1 Introduction Real-time simulators based on Electro-Magnetic Transient (EMT) theory [1] provide the most comprehensive means available for testing protective relays. Closed-loop testing offers several important advantages compared to open-loop (i.e. COMTRADE playback) testing. Firstly, since closed-loop testing is run in real-time, the work efficiency is very high compared to performing a sequence of tests using COMTRADE playback, which typically requires scenarios to first be simulated with off-line programs. Secondly, a real-time operation can model a realistic grid with multiple protection relays connected to it. The interactions between the relays and their operating grid can be investigated in a close loop. In fact, close loop testing is the only way to fully test and evaluate the interaction and he coordination of multiple relays (e.g. double-ended twin circuit line protection involves the interaction of four relays) [2]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 409–417, 2023. https://doi.org/10.1007/978-981-99-4334-0_52

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When conducting closed-loop protective relay testing, or any closed-loop testing, the real time digital simulator acts as the power system. As described above, the simulator provides low-level analogue outputs (e.g. ± 10 V) to amplifiers connected to the device under test. The low-level signals are proportional to the instantaneous value of the signal being represented (e.g. voltage, current, etc.). Voltage and current amplifiers convert the simulator’s analogue outputs to the secondary values normally seen by the relays in service (typical nominal values are 115 Vrms ph-ph and 1 Arms or 5 Arms). The simulator also has output contacts so that breaker status can be provided to the relays at auxiliary/station level voltage. Since all the standard inputs are provided to the relays, they behave as if installed in the actual network. The relay should trip if a simulated fault is applied in the protection zone. To close the test loop, the relay output contacts are connected to the simulator to provide various signals such as trip, reclose, etc. Both single-phase and three-phase tripping schemes can be tested. Since the power system is being simulated, various faults, including evolving faults, can easily be applied using controlled and repeatable network conditions to evaluate the performance of the protection [3]. Automated testing is on of advantages in using real time simulation to test protective relays. The Real-time simulators will normally offer a facility to create automated test sequences. For example, scripts can be created for the simulator using a combination of special simulator commands and C programming. Nested loops allow very extensive and adaptive testing with thousands of cases to be conducted and documented automatically [4]. By using automatic testing, the users can design a complete list of testing scenarios and validate the relays in every possible circumstance in power systems. The list of tests will be executed automatically, so it significantly reduces the demand for manpower in the testing work. This paper introduces the automatic testing function on RTDS real time simulator, which uses a script file to run multiple cases and collect the simulation results.

2 Preparation of Automatic Testing on RTDS An automatic testing script for RTDS is a file containing a series of commands for the simulator. These commands control the operation of the simulator and collect and analyze data. The script file is automatically generated and does not require direct user interaction. A record/playback feature is provided to assist in creating the script file. The user can expand the script based on the recorded commands. This section will explain the procedure of developing a script for an automatic run based on a simple example. The first step is to record the commands that will be used in the script file. To do this, the user can use the record/playback feature. This feature allows the user to record the commands that will be used in the script file and then play them back. The user can then expand the script file based on the recorded commands. The next step is to write the commands that will be used in the script file. These commands should be written in professional English. The commands should be written in a way that is easy to understand and follow. The user should also ensure that the commands are correct and will work correctly when the script is run. After the commands have been written, the user should test the script file. This can be done by running.

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We use a script file to realize “Automatic Multiple Run” or “Batch Mode Operation”, in which many different simulation cases can be run automatically. During such operation, the users do not need to monitor the entire process. Often it is run at nighttime when the simulator is not used for other work. The script can steer the procedure and record the simulation results for all the cases. This style of simulation is very useful for protective relay testing. For instance, the distance protection needs to be validated for faults or different types of faults, with various fault resistors at all possible locations along a transmission line. Preprocessor variables are special variables that can be changed from the RunTime window of RSCAD software suite. In RunTime window, the change of any preprocessor can induce the software to perform a re-compile automatically. It does not need to return to the Draft window. We will use an example case to show the automatic script run. The simple example case is illustrated in Fig. 1, which consists of an infinite bus supplied by a voltage source, a transmission line of 100 km and a load at the receiving end of the line. We will demonstrate the Script Run by modelling a movable fault bus on the line. In the meantime, we will change the fault types and fault resistors.

Fig. 1. Example circuit.

The real time simulation relies on the highly efficient design of the computation technique. A normal procedure is to compile every case then to download the binary code on simulation hardware. On RTDS simulation, Draft is used to prepare the case and to compile it to highly efficient machine code, which will be downloaded to the simulator by RunTime. When some circuit structure changes, such as moving the fault location, the case needs to be stopped, compiled and started. The operations switch back and forth between Draft and RunTime, which restricts the multiple runs of multiple simulation cases. In order to streamline the multiple runs, the preprocessor variable function was developed. The RunTime can directly recompile and run the case again when any preprocessor variable is changed. With this function, the automatic run can be achieved in Runtime only instead of switching back and forth between Runtime and Draft. In order to model the fault on the transmission line, a bus is created in the middle of the transmission line. The transmission line in the circuit of Fig. 1 is modified by two transmission lines, which have a total distance equal to the length of the original line. When the length of the two transmission lines changes respectively (total length remains the same), the faults bus moves along the line. Theoretically, the faults can be applied at any location along the line. The transmission line model can be Bergeron traveling wave model with distributed parameters, in which the transpose can also be

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represented. Figure 2 shows the method to model the faults on an arbitrary location on the transmission line, which provides a practical foundation to test protective relays.

Fig. 2. Faults on transmission line.

The changing of the fault resistor can also be done by a preprocessor variable. We can add a preprocessor in Draft and give it a draft variable name as in Fig. 3a. This draft name is then specified in the fault model in Fig. 3b, with $ character being preceded in the front of the variable name. An example is shown in a red circle in Fig. 3. In the fault component menus, the preprocessor variable name $Ron represents the each phase to the grounding point.

Fig. 3. a, b Defining a preprocessor variable.

Figure 4 shows the menu of a Draft variable component icon (rtds_draft_var), in which the name of the variable is given as Ron, and the initial value is set to 0.2 as an example. The maximum and minimum values are given in the menu too. Based on the information in the menu, a slider will be generated in the RunTime window. The draft variable component is available in the “Fault & Breaker” library of the Draft. The compiler maps the slider and the draft variable by the name; therefore, the identical name should be used. The name convention of a draft variable and a normal variable are similar, except the draft variable starts with the $ sign. The RunTime window is established as in Fig. 5. By changing the fault location, fault type and fault resistors, the relay under testing can be validated with different possible fault scenarios.

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Fig. 4. Draft variable slider and parameters.

Fig. 5. RunTime operators control setup.

3 Runtime Script Record/Playback Feature RunTime has the script record function, which can create the initial script file by running various operations in RunTime window. This function is extremely helpful for beginners in learning the script language. Upon pushing the record button, a record session starts, and the user can perform the operations. A script file will be written that record all the operations since starting this record session. For instance, if a simulation is started during a record session, the command “Start” will be recorded in the script file. By selecting Script → New from the RunTime Toolbar, the users can start a script session, in which a script file can be generated. We will use an example file name called rec_play.scr in the following context. If the user push the record script button from the Script Toolbar as shown in the red circle in Fig. 6, an example script file labelled rec play.scr is now recorded. As an example, the following operations are performed during this record session [5], • start the case • set the switch (AG) to 1, representing A phase to ground fault • set the switches (BG & CG) to 0, representing No B and C phase to ground fault

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• set the slider FLTDUR to 0.1 s, to adjust the fault duration • Press the Fault Push Button, to apply the fault • Terminate the case The record session can be terminated by pushing the stop button in the script tool bar. The above operations will be written into a script file once the record session is completed. A script file names rec_play.scr is created in this example. To view the contents of the rec_play.scr file, select the edit button from the script toolbar shown in the green circle in Fig. 6. An example recorded script file is displayed below. SUSPEND 1.5; Start; SUSPEND 5.0 SetSwitch ”Subsystem #1: CTLs: Inputs: AG” = 1; SUSPEND 1.2; SetSwitch ”Subsystem #1: CTLs: Inputs: BG” = 0; SUSPEND 1.4; SetSwitch ”Subsystem #1: CTLs: Inputs: CG” = 0; SUSPEND 8.5; SetSlider ”Subsystem #1: CTLs: Inputs: FLTDUR” = 0.1; SUSPEND 2.0; PushButton ”Subsystem #1: CTLs: Inputs: Fault”; SUSPEND 0.1; ReleaseButton ”Subsystem #1: CTLs: Inputs: Fault”; SUSPEND 2.5; Stop; The above script file can be run directly. However, it is more often used as a base to develop a more organized and comprehensive script file. We will briefly introduce how to improve and expand the script file using the script edit facility. The purpose of Script mode operation is to run multiple simulation cases automatically without any direct involvement of the user. The recorded script files can be reorganized and expanded to achieve such purposes by using a script command set like ‘C’ programming language. This example makes a script, which will perform 27 simulations according to the flow chart in Fig. 7.

Fig. 6. Flow chart showing the script operations.

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It is often to start a script file by the record feature. A base script can be generated by the record function of the script tool bar. The base script can then be modified to operate according to the flow chart in Fig. 7. In the following example, we will show a script file with the list of operations below. (1) Define the value of the draft variable slider “length”; (2) Define the value of the fault resistance; (3) Enable the A phase to ground fault switch (AG); (4) Enable the B and C phase to ground fault switches (BG & CG); (5) Run the simulation case; (6) Perform the fault by pressing the Fault Push Button; (7) Update the current plot; (8) Terminate the simulation case. An organized script file according to the flow chart in Fig. 6 is shown as below in Fig. 7.

Fig. 7. The edited script file.

After the script file is edited as above, the user can conduct the automatic run by playing back the script. The fprintf message will be output in the Runtime message window when the script is running. This example script can conduct multiple runs containing 27 different simulation cases. In this example, the simulation automatically runs the simulation cases of line faults with different fault locations, various faults, and different fault resistors. In the real world, more variables can be included, such as different strengths of the AC system, faults on different point of wave, etc. Those features can be included by modifying the script files described above. The line protective relay can be tested by close loop simulation. Using the script file, the relay can be automatically tested in all possible fault scenarios.

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4 An Application Example of Script Run in Relay Testing Figure 8 shows a power system circuit often used to test the line protection. The circuit models a two parallel transmission line that connects a generator to large power system. The generator is modelled by detail Park equations and the associated excitation control and governor control, so that all the dynamics of the power plant will be included in the simulation. The large power system is modelled as an infinite bus behind a system impedance, which is adjustable to model a strong or weaker power systems. The impedance based relays are installed on the lines. By varying the location of the faults, the faults occurring time, type of faults, and fault resistances, the transients of all scenarios can be simulated. The simultaneous faults and evolute faults can also be modelled by the scripts. The protective relays can be thoroughly tested and validated if they work properly in all possible circumstances. The simulation results of all the cases are monitored in Runtime as in Fig. 9. The performance of protective relay is recorded in a file through the script file. Once the testing started by script, it can automatically proceed and complete without need of additional man power input. Therefore, the productivity is significantly increased.

Fig. 8. Circuit for line protection testing.

Fig. 9. Runtime window for automatic testing of line protection.

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5 Conclusion The paper introduced automatic testing procedures of protective relays on RTDS realtime simulator. Automatic testing is an effective way to validate the relays in various operation circumstances. The procedure helps to ensure the relays will work properly before they are installed in real power systems.

References 1. Dommel, H.W.: Digital computer solution of electromagnetic transients in single- and multiphase networks. IEEE Trans. Power Apparatus Syst. PAS-88(4), 388–399 (1969) 2. Forsyth, P., Ouellette, D., Peters, C., Desjardine, M.: A Real Time Environment for ClosedLoop Testing of PMU-based WACS Schemes, Cigre Canada 2013, paper 235, September 2013 3. Plumptre, F., Brettschneider, S., Hiebert, A., Thompson, M., “Venkat” Mynam, M.: Validation of Out-of-Step Protection With a Real Time Digital Simulator, Western Protective Relay Conference 2006, Spokane, Washington, 17–19 October 2006 4. Testing a Protection System using the RTDS Batch Mode Facility. In: Proceedings. IPST 2001, Rio de Janeiro Brazil, pp. 447–452, June 2001 5. RTDS Tutorial Manual, RTDS Technologies (2019)

Research on Harmonic Optimization of Magnetically Controlled Transformer Yaoliang Yan1 , Ming Fan1 , Hong Zhang2 , Lei Wang1 , Zhenqi Ma1 , Bengang Sui2 , Kun Peng1 , Jingtao Bai1 , Mingzhou Zheng1 , Tengda Wang1 , Yewei Jie1 , Wenhui Shi1 , and Wenchao Dong3(B) 1 State Grid Jia Xing Power Supply Company, Jia Xing 314001, China 2 Jia Xing Heng Guang Electrc Power Construction Co., Ltd., Bin Hai Branch, Bin Hai 300450,

China 3 School of Engineering and Automation, Wuhan University, Wuhan 4300724, China

[email protected]

Abstract. With the progress and development of productivity, people are increasingly demanding the reliability of power supply [1, 2]. Although the magnetically controlled equipment has the characteristics of wide adjustment range of excitation inductance and strong regulation ability, the high content of harmonic current in the actual operation of the magnetically controlled equipment also limits its use [3–5]. Therefore, this paper studies the problem of harmonic optimization of magnetron transformer. Harmonic generated by different magnet valves under multi-stage solenoid valve structure can cancel each other out to suppress harmonic generated by magnetron transformer. The harmonic mathematical model of magnetron transformer with multi-stage solenoid valve structure is established, the expression of each harmonic content of excitation current is derived, and the fundamental wave and harmonic component of excitation current of multi-stage solenoid core structure are analyzed theoretically. On this basis, the objective function of optimization is determined, and the harmonic is optimized by particle swarm optimization (PSO), which has the characteristics of small adjustment parameters and fast convergence speed. The optimization parameters of all levels of solenoid valves are obtained, and the correctness of harmonic optimization by using multi-stage solenoid valve structure is proved by simulation experiments. Keywords: Magnetically controlled transformer · Multi-stage magnetic valve · Harmonic optimization

1 Introduction Because of the advantages of simple production, easy control, convenient transmission, green cleaning and high utilization, electric energy has become an indispensable energy in modern life [6]. Harmonics generated by magnetically controlled equipment cause additional losses of power grid components, which are easy to reduce power generation efficiency and transmission and distribution efficiency, and result in local temperature rise of transformers, resulting in insulation aging of equipment and greatly shortening service life of equipment [7–9]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 418–422, 2023. https://doi.org/10.1007/978-981-99-4334-0_53

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In order to give consideration to the content of harmonic voltage in the power grid and the cost of governance, this paper studies the problem of optimizing the harmonic generated by the magnetic control transformer by using the multi-stage magnetic valve structure [10, 11]. The harmonic generated by different magnetic valves under the multistage magnetic valve structure can offset each other. This feature can suppress the harmonic generated by the magnetic control transformer. The particle swarm optimization algorithm [12, 13], which is characterized by high maturity and fast convergence, is used to optimize the harmonics, and the optimization parameters of the magnetic valves at all levels are obtained. The simulation results verify the correctness of the harmonic optimization using the multi-level magnetic valve structure [14, 15].

2 Harmonic Optimization Based on Multistage Magnetic Valve Structure 2.1 Harmonic Problems of a New Type of Magnetically Controlled Reactance Transformer The new magnetron transformer is based on the principle of core magnetic saturation to regulate excitation reactance, so harmonics will occur during the adjustment process. Generally, the nominal fundamental current is used as the reference value to represent the magnitude of each harmonic current. The expression of each harmonic component of excitation current is as follows:   sin(k + 1)β sin kβ 1 ∗ − k = 1, 2, 3, . . . (1) i0(2k+1) = 2k 2(k + 1) (2k + 1)π In the range of 0 to 2π, the nth harmonic has n zeros and (n − 1) extreme points, and the extreme points are symmetrically distributed, with the symmetry center being β = π point, the maximum per unit value of each harmonic is also at β = Near the π point. 2.2 Harmonic Mathematical Model The core structure of magnetron transformer with multi-stage magnetic valve structure is shown in Fig. 1. The magnetic valve of the iron core is composed of several small sections with different areas and lengths. In Fig. 2, As1 , As2 … Asn are the areas of the magnetic valves at all levels of the iron core, and l1 , l 2 … ln are the lengths of the magnetic valves at all levels of the iron core, where As1 is not less than 1/3 of the area of the iron core Ab , Asn is not more than Ab , and the sum of the lengths of all sections is l. The magnetic valves at all levels are equivalent to the iron core structure with the length equal to the original magnetic valve section, the area equal to the iron core section Ab , and the equivalent magnetic field strength of H s1 , H s2 … H sn respectively. Then the whole magnetic valve section is equivalent to the magnetic circuit with the length of l, the area of Ab , and the equivalent magnetic field strength of H e .

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l1 l2

…

As2

Ab

Ab

ln

1 1

HS1

l1 l2

Hs2

ln

Hsn

He

1

Fig. 1. Cross-sectional view of core of magnetron transformer with multi-stage magnetic valve structure.

According to the equivalent structure in Fig. 2, He l =

n 

Hsk lk

(2)

k=1

The magnetic saturation of the magnetron transformer with multi-stage solenoid valve structure is only related to the section area of each stage solenoid valve and is independent of the length of the solenoid valve. This conclusion is of great significance for the subsequent harmonic optimization. 2.3 Harmonic Mathematical Model It can be seen that the harmonic magnitude is determined by the length of the solenoid valve hi and the magnetic saturation β i , and magnetic saturation β i can be calculated from the section area ratio sn , so the harmonic content is determined by both the section area of the valve and the length of the valve.The formula for calculating the minimum harmonic content can be derived as  iopt = f (x) (3) X ∈ S = {X |1 ≤ S(X ) ≤ 3, j = 1, 2, . . . , n } where, f(x) is the objective function of harmonic optimization, and S(X) is the constraint condition. The objective function f(x) of harmonic optimization for magnetron transformer with multi-stage solenoid valve structure is non-linear, so it is a non-linear programming problem. In this paper, particle swarm optimization is used. 2.4 Optimized Results Particle Swarm Optimization (PSO) is used to optimize the magnetron transformer with multi-stage solenoid valve structure. The final fitness function is programmed in MATLAB according to the above PSO process. The optimization results are shown in Table 1. The harmonic content of the magnetron transformer with multi-stage solenoid valve structure can be reduced to 2.64%, and the change of the harmonic content is smaller and smaller with the increase of series of solenoid valves.

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Table 1. Optimum parameters of magnetic control transformer solenoid with multi-stage solenoid valve structure. Magnetic valve stage S 1 S 2

S3

S4

S5

S6

S7

Fitness(%)

2

1

1.6425

4.13

3

1

1.6425 1.9947

3.19

4

1

1.6426 1.9947 2.2840

2.79

5

1

1.6425 1.9948 2.2839 2.6394

2.66

6

1

1.6425 1.9948 2.2840 2.6393 2.8956

2.64

7

1

1.6425 1.9948 2.2841 2.6395 2.9169 2.9612 2.64

2.5 Mulation Experiment of Magnetically Controlled Transformer with Multi-stage Magnetic Valve Structure The models of magnetron transformer with multi-stage solenoid valve structure are built, and the harmonic distributions are obtained, as shown in Fig. 2.

3nd 5th 7th

3nd 5th 7th

(a) Three stage magnetic valve;

(b) Five stage magnetic valve;

Fig. 2. Simulation waveform of magnetically controlled reactor transformer with different magnetic valve structures.

From the simulation waveform, it can be seen that the harmonic content of each order simulated by magnetron controlled transformer with different series of magnetic valves is not significantly different from the theoretical value.

3 Conclusion This paper discusses the harmonic optimization problem of the magnetic control transformer, and adopts the multi-level magnetic valve structure to suppress the harmonic generated by the magnetic control transformer.. The simulation results show that the multi-level solenoid valve structure can effectively reduce the harmonic content, and verify the correctness of the harmonic optimization of the magnetic control transformer using the multi-level solenoid valve.

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References 1. Zhai, H., Zhuo, F., Zhu, C.Z., et al.: An optimal compensation method of shunt active power filters for system-wide voltage quality improvement. IEEE Trans. Industr. Electron. 67(2), 1270–1281 (2020) 2. Xue, W., Yunguang, G., Lingyan, L., et al.: Research status and prospect of active power filter. Power Syst. Protection Control 47(1), 177–186 (2019) 3. Yin, Z., Liu, H., Wang, S., et al.: Optimum design of distributed small section of MCR based on ANSYS. Diangong Jishu Xuebao/Trans. China Electrotechnical Society 30(10), 204–211 (2015) 4. Ramos-Carranza, H.A., Medina, A.: Single-harmonic active power line conditioner for harmonic distortion control in power networks. IET Power Electron. 7(9), 2218–2226 (2014) 5. Grady, W.M., Samotyj, M.J., Noyola, A.H.: Minimizing network harmonic voltage distortion with an active power line conditioner. IEEE Trans. Power Deliv. 6(4), 1690–1697 (1991) 6. Grady, W.M., Samotyj, M.J., Noyola, A.H.: The application of network objective function for actively minimizing the impact of voltage harmonics in power systems. IEEE Trans. Power Deliv. 7(3), 1379–1386 (1992) 7. Ji, Y.Q., Yuan, J.X.: Overhead transmission lines sag and voltage monitoring method based on electrostatic inverse calculation. IEEE Trans. Instrumentation Measure. 71 (2022) 8. Chang, W.K., Grady, W.M., Samotyj, M.J.: Meeting IEEE-519 harmonic voltage and voltage distortion constraints with an active power line conditioner. IEEE Trans. Power Deliv. 9(3), 1531–1537 (1994) 9. Chen, H.C., Yuan, J.X., et al.: A novel fast energy storage fault current limiter topology for high-voltage direct current transmission system. IEEE Trans. Power Electron. 37(5), 5032– 5046 (2022) 10. Zhikang, S., An, L., Wenji, Z., et al.: Study on the size and optimal location of shunt active power filter. Proc. CSEE 29(13), 92–98 (2009) 11. Chen, B., Chen, W.: Analyses of harmonics and overvoltage limitation characteristics of EHV controlled reactor. Proc. CSEE 17(2), 122–125 (1997) 12. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE Conference on Neural Networks, Perth, Australia 1942–1948 (1995) 13. Shuai, Z., Luo, A., Tu, C., et al.: Optimal placement of hybrid active power filter. Proc. CSEE 28(27), 48–55 (2008) 14. Zhou, H., Yuan, J.X., et al.: Hybrid-material based saturated core FCL in HVDC system: modeling, analyzing and performance testing. IEEE Trans. Industr. Electron. 68(12), 11858– 11869 (2021) 15. Chang, W.K., Grady, W.M.: Minimizing harmonic voltage distortion with multiple current constrained active power line conditioners. IEEE Trans. Power Deliv. 12(2), 837–843 (1997)

Grasping Operation of Irregular-Shaped Objects Based on a Monocular Camera Xiantao Sun1 , Yinming Yang1 , Wenjie Chen1(B) , Weihai Chen2 , and Yali Zhi1 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China

[email protected] 2 School of Automation Science and Electrical Engineering, Beihang University,

Beijing 100191, China

Abstract. At present, the small and medium-sized enterprises have a large number of irregular-shaped workpiece grasping operations, which require a vision system to cooperate with a robotic gripper. However, the existing visual grasping systems are difficult to be widely deployed due to cost or accuracy issues. To solve this problem, this paper proposes a vision system based on a cheap monocular camera, which can complete the detection of the position and posture of the target workpiece. Firstly, the light intensity of the environment is measured by the light sensor, and then it is input into the parameter prediction network to obtain the color segmentation parameters under the light intensity. After that, the system adopts these parameters to complete image segmentation by the HSV color segmentation method and uses the Canny edge detection with the area filter to obtain contour. Then, the system processes the contour features by the Douglas-Puck algorithm and calculates the posture angle of the workpiece. Finally, the position and posture of the workpiece relative to the robot arm can be obtained by hand-eye calibration. The experimental results show that the vision system can conduct the automatic recognition of the workpiece and the calculation of the position and posture. Keywords: Position and posture detection · Irregular-shaped workpiece grasping · Monocular camera · Image segmentation

1 Introduction With the rapid development of automation technology, the robot industry has become increasingly prosperous, and more and more operating robots are widely deployed in the industry to replace workers for some repetitive and cumbersome grasping tasks. To improve the grasping accuracy of the robot, machine vision [1] is introduced to help the robot obtain more grasping information. At present, robot visual grasping has become one of the hotspots in robot research [2, 3]. The robot vision system is mainly composed of object detection and pose estimation.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 423–429, 2023. https://doi.org/10.1007/978-981-99-4334-0_54

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In terms of object detection, Lower [4] used the SIFT algorithm to extract the scaleinvariant features of objects and completed object detection by matching the invariant features. With the introduction of deep learning into computer vision, convolutional neural networks have attracted extensive attention in the field of object detection [5, 6]. He et al. [7] proposed a residual network model RestNet, which can further increase the number of network layers and prevent gradients from disappearing, thereby improving object recognition accuracy. Although there are many methods for object detection, the technology for estimating object pose based on object detection information is still immature. Zhang et al. [8] used a convolutional neural network to achieve object detection and then processed the depth image to complete the acquisition of object position coordinates. Song Wei et al. [9] added a 3D template library of parts to the robot vision system, completed the pairing between the image and the template through the Chamfer distance matching algorithm, and then extracted the pose information from the matched template. Song et al. [10] used the method of obtaining the smallest rectangular frame of the object to complete the estimation of its rotation angle and realized the grasping and assembly of the mobile phone case. At present, the monocular camera vision system commonly used in the industry can only obtain the position information of the part, but cannot obtain the specific posture of the part. Part of the improved monocular camera vision system can roughly estimate the rotation angle of the object, and then rotate the corresponding angle through the wrist joint of the robotic arm, and use the two-fingered manipulator to grasp. However, the detection error of the rotation angle will cause the two-fingered manipulator to apply extra torque to the part during the grasping process [11], which is easy to cause grasping failure or even damage the part. Considering the above questions, this paper proposes a visual grasping system based on a monocular camera, which can obtain feature points of the workpiece and calculate the rotation angle.

2 Methods of Image Processing 2.1 Image Segmentation and Contour Detection As the “eyes” of the robot, the vision system detects the parts and informs the robot of the specific position and posture of the parts to be grasped. Therefore, the accuracy of obtaining the part information from the image is the premise to ensure the success of the grasping operation, and it is particularly important to complete the accurate segmentation of the part in the image. The environment for the grasping operation in this paper is the workbench in the production workshop of small and medium-sized enterprises. In this environment, the images captured by the camera do not have too many interference factors, and the color difference between the parts and the workbench is obvious. Based on the above reasons, the HSV color segmentation method, which is more sensitive to the perception of color changes, is used to perform preliminary operations on the image. Ferone et al. [12] have verified that the color image can be accurately segmented in the HSV color space, but this method is greatly affected by illumination. Even under the same lighting conditions, because the texture and roughness of the part surface are not the same, their reflection characteristics to the light are different, so the HSV value

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between the pixels of the part image will be different. In the environment, the light intensity at different periods will also change. To reduce the influence of illumination on the visual capture system, it is necessary to obtain accurate HSV color segmentation parameters under different illumination environments. Therefore, a neural network is added to predict the segmentation parameters in this environment before segmenting the image. The network structure of parameter prediction based on the BP neural network is shown in Fig. 1. The first layer is the input layer, the middle is the hidden layer, and the last layer is the output layer. The input of the network is the real-time light intensity. The outputs of the network correspond to the HSV color segmentation parameters one by one.

Fig. 1. Parameter prediction network structure diagram.

The specific steps for the grasping system to use the HSV color segmentation method to complete the segmentation of the part image are as follows: • Collect part images with the workbench as the background under the illumination environment of 50–600 lumens, and extract the segmentation parameters of each image. • The illumination intensity and segmentation parameters are uniformly encoded into a dataset which is used to complete the training of the network. • Detect the light intensity of the environment where the grasping system is located, and input it into the parameter prediction network, and obtain the HSV color segmentation parameters H max , H min , S max , S min , V max , and V min in the current environment. • Set H max , S max , and V max predicted in the previous step be the upper thresholds, and H min , S min , and V min be the lower thresholds. Each pixel value in the part image is filtered, and it is regarded as a part pixel within the threshold range, and the pixel is initialized to black when it is outside the threshold range.

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The Canny edge detection algorithm uses the method of non-maximum suppression and hysteresis threshold, which has an excellent effect on the extraction of image edges. Therefore, the visual grasping system in this paper uses the Canny operator to extract the edge contour. To eliminate interfering contours, a filter with contour area as the judgment condition is added after Canny detection. The area of the interfering contour is much smaller than that of target part contour. The filter uses 0.85 times and 1.15 times the area of the part contour in the template image as the thresholds, which can filter most of the interference contours. The specific operations are as follows: first, a 3 × 3 Gaussian kernel is used to perform Gaussian filtering on the segmented image, and then Canny edge detection is performed on the processed image, where the lag thresholds are 25 and 75 respectively. Secondly, the contour area S of the parts in the template image is calculated, and the upper and lower thresholds of the contour filter are set to 0.85S and 1.15S, respectively. Then, the contour within the threshold is extracted by the filter, and the Hu invariant moment is calculated. Finally, the results are compared with the Hu invariant moments of the part contour in the template image to determine whether the obtained contour is the target part contour. 2.2 Calculation of Rotation Angle The contour of the target part is a set P containing n pixels in the image. The coordinates of the centroid point pc of the part can be obtained by weighting the X coordinate value and the Y coordinate value of each pixel in the point set P respectively. Determining the rotation angle of the part in the image is a necessary condition for obtaining the part attitude, and the determination of the rotation angle also requires the vertex position of the workpiece. When the edges and corners of the part are relatively clear, the Harris corner algorithm is a very suitable method for the vertex detection of the part contour, but it is not effective for vertex detection of some abnormal parts. The visual grasping system of this paper uses the Douglas-Puck algorithm to obtain the vertex position. First, the system uses the Douglas-Puck algorithm to fit the workpiece into a polygon (as shown in Fig. 2). Then, the system judges the vertex of the workpiece according to the distance to the centroid point. The specific method is as follows: • Connect the first point a and the last point b in the set of contour points. • The point c with the largest distance from the line segment is detected in the contour, and the distance from point c to the line segment is calculated as L, which is compared with the set threshold L t . • When L is greater than L t , connect point a with point c, and point b with point c, and repeat the previous step for line ac and line bc until all distances are less than the threshold L t . • Connect all segmentation points to form a polygon fitting the contour of the workpiece. • The distance from each vertex of the polygon to the centroid point is calculated and compared with the distance from the vertex of the part to the centroid point in the template image, and then the vertex py of the contour of the target part is selected.

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The threshold Lt is set to 0.02 times the length of the target contour, which can not only adapt to the image contour changes caused by different positions of the parts, but also prevent the contour from being over-segmented. The characteristic point where the centroid point extends 100 pixels along the positive direction of the X-axis of the image is pr , which connects the centroid point, pr and the centroid point, vertex respectively. At this time, the slope of the two lines is K 1 and K 2 , so the rotation angle of the part is shown in Eq. (1)    K1 − K2   (1) θ = arctan 1 + K1 · K2 

c L>Lt L>Lt

e L 5 s) to obtain the optimal output. The signal injection control [17] and virtual signal injection control [18] methods suffer from a relatively slow dynamic performance because they rely on search-based schemes to converge on MTPA operating points. Look-up table (LUT) based POC methods require a lot of preliminary work and might be affected by material and temperature variations [10]. Even though the methods mentioned above are widely researched, some potential issues still need to be addressed. To overcome these issues and improve control quality, this paper presents an adaptive POC strategy. Depending on the analysis of loss power, the optimization problems of MTPA and LMC are converted to extremum problems. Then, novel objective functions are respectively designed for MTPA and LMC to guarantee performance. This paper is the first to introduce the tracking differentiator into power optimization problems to design an intuitive optimization algorithm. The proposed method is notable because it not only does not need accurate prior knowledge of motor parameters but avoids the complex control structure. The comparative results verify that the proposed method achieves excellent performance.

2 Preliminary 2.1 Loss Model The losses of IPMSM mainly include copper loss (stator winding resistance loss), iron loss (hysteresis loss and eddy-current loss), and mechanical loss. Generally, the mechanical loss is quite small and cannot be effectively controlled with control algorithms. Hence, this research towards reducing electrical losses, such as copper loss and iron loss.

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Fig. 1. Equivalent circuit of IPMSM including losses.

Taking the copper loss and iron loss into account, the equivalent circuit with the series-parallel structure of IPMSM is depicted in Fig. 1. Wherein ud and uq denote daxis and q-axis voltages, respectively; id and iq denote d-axis and q-axis stator currents, respectively; iod and ioq denote active currents; icd and icq denote iron loss currents; Ld and Lq denote d-axis and q-axis inductances, respectively; Rs is the phase resistance and RFe is the equivalent iron loss resistance; ψPM is the permanent magnet flux linkage; ωe is the electrical angular speed. Based on the equivalent circuit in d-q axis, the stator current equations can be characterized as

icd = −

id = iod + icd , iq = ioq + icq

(1)

ωe Lq ioq ωe Ld iod + ωe ψPM , icq = − RFe RFe

(2)

Then, the copper loss power PCu and iron loss power PFe can be obtained.      ωe Lq ioq 2 3 ωe (Ld iod + ψPM ) 2 PCu = Rs iod − + ioq + 2 RFe RFe PFe =

2 3 ωe2  Lq ioq + (Ld iod + ψPM )2 2 RFe

(3) (4)

2.2 MTPA Principle In IPMSM, the stator current interacts with magnetic field ψPM to produce electromagnetic torque Te . Te =

 3

p ψPM iq + (Ld − Lq )id iq 2

(5)

From (5), Te is a first-order binary function of d-axis current id and q-axis current iq by ignoring the variation of motor parameters. Therefore, each torque has one pair of d-q current components that minimize the current amplitude, thereby minimizing copper loss power and improving power efficiency. Using the Lagrange multiplier method, the relation between id and iq for MTPA is 2 ψPM ψPM (6) + iq2 − id = − 4(Ld − Lq )2 2(Ld − Lq )

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2.3 LMC Principle Ignoring the mechanical loss, the total electrical loss power Ploss is defined as 2  2 3 Rs  R i − ω L i + R i + ω i + ψ (L ) Fe e q oq Fe oq e PM od d od 2 R2Fe 2 3 ωe2  Lq ioq + (Ld iod + ψPM )2 + 2 2 RFe

Ploss =

(7)

At certain rotating speed and load torque, it can be proved that the Ploss is a convex function with respect to active current iod . This means that there is only one minimum point to make ∂Ploss ∂iod = 0. Omitting the mathematical derivation, the optimal iod that minimizes the total electrical loss Ploss is   2 L (R + R ) −ωe Rs RFe Te Ld − Lq − ωe2 ψPM Fe d s opt

 iod = (8) 2 2 np ψPM Rs RFe + ωe2 Ld (Rs + RFe ) Given stator current equations of IPMSM, the relation between id and iq for LMC is id =

ωe2 Ld Lq + R2Fe R2Fe

opt

iod +

ωe2 Lq ψPM R2Fe

−

ωe Lq iq RFe

(9)

3 Proposed Power Optimization Control 3.1 Adaptive MPTA Principle The purpose pursued by MTPA is to minimize the current amplitude I in the constant torque region to reduce the copper loss. Since stator current amplitude I is positive in electrical mechanical, the optimization problem of I can be equivalently converted to the optimization problem of I 2 . The relation between I 2 and id can be found by rewriting (5). I2 =

4Te2 2

  2 + id  9p2 ψPM + Ld − Lq id

In addition, the partial derivative of I 2 of id is   −8Te2 Ld − Lq ∂I 2 =

 3 + 2id  ∂id ψPM + Ld − Lq id

(10)

(11)

  Herein id = ψPM Lq − Ld is a singularity. For the general salient pole PMSM, except for some extreme operating conditions

 that may destroy the drive system, Lq always greater than Ld . Hence, ψPM Lq − Ld is positive. From (10) and (11), when

  id < ψPM Lq − Ld , I 2 is a convex function of id and only has one available point that

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makes ∂I 2 ∂id = 0. Obviously, the optimal id that minimizes the I 2 also minimizes I . Therefore, the MTPA is reformulated to a local minimum problem of I 2 . In this way, the designed MTPA is min I 2 = id2 + iq2    3

Te = p ψPM iq + Ld − Lq id iq 2  s.t. Ilim ≥ id2 + iq2

  id < ψPM Ld − Lq

(12)

id keeps zero or Ilim is the current limitation determined by system constraints.

 Generally,  negative in the motor drive system. Therefore, id < ψPM Ld − Lq does not affect control progress. Control engineering always avoids differentiating a given signal because sampled signals, such as stator current and rotating speed, are prone to corruption by high-frequency sampling noise. For example, the proportion integration differentiation (PID) is simplified to PI controller in the real control system to eliminate the differentiation’s influence. In order to differentiate sampling noise and large derivative along with the given signal, various approaches have been studied to design the desired differentiator, such as high-gain observer [19], sliding mode observer [20], singular perturbation technique [21], discrete time optimal control [22], and Fhan [23]. Considering the complexity and control performance of the system while avoiding the influence of nonlinear control on the differential signal, this work adopts a linear tracking differentiator [23]. The utilized tracking differentiator fl (v, t) is  x˙ 1 = x2 (13) x˙ 2 = −r 2 (x1 − v) − 2rx2 wherein r determines the convergence speed. Instead of directly differentiating the given signal, (13) uses x1 to track v and x2 to approximate the derivate of v. In this way, the influence of high-frequency sampling noise is dampened. Depend on this TD, the  derivative of I 2 of time t, fl I 2 , t , is  x˙ I 2 1 = xI 2 2 (14)   x˙ I 2 2 = −r 2 xI 2 1 − v − 2rxI 2 2 In this function, xI 2 1 tracks the I 2 , and the

disturbance caused by high-frequency noise is eliminated. Therefore, xI 2 2 tracks dI 2 dt. In a similar way, the derivative of id with respect to time t, fl (id , t), can be presented as  x˙ id 1 = xid 2 (15)   x˙ id 2 = −r 2 xid 1 − v − 2rxid 2 According to (14) and (15), the partial derivative of I 2 of id is derived from

∂id = xI 2 2 xid 2 . However, the derivatives of I 2 and id are prone to chatter

due to various disturbances. Meanwhile, it is noteworthy that ∂I 2 ∂id has a dramatic

∂I 2

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change when did dt is close to 0. To improve the steady-state performance, an adaptive convergence speed is designed as =

kv x2 ,v = I 2 1 + |v| xid 2

(16)

wherein k is positive and determines the convergence speed.  → k when v → ∞, and  → 0 when v → 0. With this strategy, the convergence process is limited to a suitable speed that improves the system’s insensitivity against random noise signals. While the convergence speed gradually shrinks to 0 when the output is close to the minimum to  ref pre pre avoid chattering. Then, the d-axis reference current is id = id − dt. id is the preset value of d-axis current, and always set to 0. In summary, the whole control process of proposed MTPA is ⎧ xI 2 2 ⎪ ⎪ ⎨v = x id 2  (17) v ⎪ ref pre ⎪ ⎩ id = id − k dt 1 + |v| The proposed MTPA method enables the drive system to achieve the minimum current amplitude by designing an adaptive convergence method. There is no need for any motor’s parameter to ensure that the drive system has better robustness against parameter mismatches in control progress. 3.2 Adaptive LMC Principle Although model-based and model-free LMC methods have proposed some strategies to obtain the optimal current components reference, these methods generally need accurate motor parameters or complex algorithms. In order to avoid these vulnerable and tedious control strategies, the proposed LMC algorithm indirectly estimates Ploss and adopts tracking differentiator to structure an optimization method. In (7), ωe is determined by speed reference, ioq is related to torque-generated current iq , and motor parameters, such as Rs and RFe , can be regarded as constant variables during a short enough control episode. Ploss , therefore, is a convex function with respect to iod . From (1), id is the positive linear project of iod in steady state. Hence, Ploss also is a convex function of id . Similar to the MTPA optimization problem, there is only one minimum point that makes ∂Ploss ∂id = 0. However, in the real system, the total electrical loss Ploss is hard to be obtained directly. According to the conservation of energy, the input power of motor system is the sum of output power and loss power. Pin = IU = Pco + PCu + PFe + PMe + Ps + Pout

(18)

Pco stands for the converter loss and does not need to be considered since it has little influence on the drive system [24]. Ps is the sum of various loss power that cannot be modelled, and generally ignored in control process because it is relatively small. The mechanical loss PMe is proportional to the square of rotor speed ωe , PMe = km ωe2 . km is the mechanical loss coefficient. Then, the total electrical loss Ploss is given by ploss = PCu + PFe = Pin − Pout − Pco − PMe − Ps

(19)

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wherein Pco and are Ps ignored. The optimization problem of LMC is min Ploss    3

Te = p ψPM iq + Ld − Lq id iq 2  s.t. Ilim ≥ id2 + iq2

(20)

ωe does not directly relate to stator current and can be regarded as a constant when the motor operation is steady. Therefore, km ωe2 is eliminated in the derivative progress. Hence, the partial derivative of Ploss with respect to id is rewritten as    

∂ IU − 1.5Pωe ψPM iq + Ld − Lq id iq ∂Ploss = (21) ∂id ∂id The proposed LMC method is summarized as ⎧ xp2 ⎪ ⎪ ⎨w = x id 2  w ⎪ ref pre ⎪ ⎩ id = id − k dt 1 + |w|

(22)

The proposed LMC method is freed from dependence on system knowledge and estimates the total loss power depending on the input and output power. Then, an optimization method is tailored to simplify the control process.

4 Results and Discussion An IPMSM test bench utilizes a dSpace to verify the effectiveness of proposed MTPA and LMC methods. This experimental platform comprises a 2.1 kW IPMSM test bench, a dSpace DS1007 controller, and a power analyzer YOKOGAWA WT1800E, as shown in Fig. 2. The dSpace is a core part of the platform system, which is used to carry out control algorithms. The WT1800E power analyzer samples and stores the current and power data to evaluate the controlled performance. All methods are programmed using a function block in MATLAB/Simulink, which is implemented experimentally using the DS1007 controller. The control frequency of dSpace is set to 10 kHz, and the sampling frequency of WT1800E is 70 Hz. To ensure the fairness of all comparative tests, outerloop’s PI coefficients of all methods and parameters of proposed method throughout experiments are kept the same. This work uses a continuous model predictive current control [25–27] as every algorithm’s inner-loop (current loop) controller. The current amplitude of all methods is sampled in different operation conditions, as shown in Fig. 3. Compared with id = 0, model-based MTPA and the proposed method both exhibit smaller current amplitude. With the increase in torque and speed, modelbased MTPA and proposed method illustrate better performance than id = 0. Moreover, the obtained results show the proposed method’s effectiveness to attain smaller stator current amplitude.

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Fig. 2. Test bench.

Fig. 3. The current amplitude of all methods.

The current amplitude comparison of id = 0, MTPA and the proposed method were conducted under different torque and speeds. The mean of 300 sampled tested values under certain conditions is stored to compose a performance matrix to avoid the sample noise. Based on this matrix, the control performance of all methods is exhibited in Fig. 4. Since model-based MTPA and proposed method utilize optimization method, the stator current is lower than id = 0 (under 900 rpm with 100% load torque, the stator current of id = 0 is 5.01 A, model-based MTPA is 4.44 A, and proposed method is 4.42 A). To better quantify the improvement of the proposed method, a comparison between the model-based MTPA and proposed MTPA method is carried out, as shown in Fig. 5. Model-based MTPA and proposed method both obtain lower current amplitude than the id = 0 method. In contrast, the proposed method obtains better performance because the ref optimization strategy adaptively converges on the optimal id to minimize the current amplitude. The power efficiency of the drive system with all methods are performed by operating at different speed and load torque, as shown in Fig. 6. In this study, id = 0, modelbased LMC and the proposed LMC are carried on the test bench to evaluate control performance. It is observed that the power efficiency of all methods gradually improves with the increases of rotating speed. Model-based LMC exhibits a slight improvement

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Fig. 4. The contour of stator current amplitude (left: id = 0; medium: Model-based MTPA; right: Proposed MTPA).

than id = 0 in power efficiency. Compared with other methods, the proposed method is observed to have a higher and smoother power efficiency.

Fig. 5. The reduced amplitude of stator current.

Fig. 6. The power efficiency of all methods.

To entirely comparative the control performance of all methods, comparison against id = 0 and model-based LMC is carried out, as shown in Fig. 7. Although all methods obtain the smallest power efficiency at 300 rpm rotating speed with 100% torque load, the proposed LMC achieves the better results than other methods (the efficiency of id = 0 is about 70%, model-based LMC is about 71%, and proposed method is 72%). As the speed is increases, the power efficiency gradually improves and can obtain higher efficiency when rotating speed rises to 900 rpm (the efficiency of id = 0 is 86%, model-based

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Fig. 7. The contour of power efficiency (left: id = 0; medium: Model-based LMC; right: Proposed LMC).

LMC is about 86.5%, and proposed method is 87%). The contour map of test results shows that the highest power efficiency can be achieved in high speed and low torque load. However, it can be observed that the contour line of 91% of the proposed method is longer than other methods, which means the proposed method obtains a more high power efficiency zone. Compared with id = 0, the test results of increased power efficiency of modelbased LMC and proposed method are presented in Fig. 8. Model-based LMC performs comparatively small and irregular improvement since the iron loss resistance varies with frequency. The proposed method exhibits better results on every test point. It should be noted that the proposed method achieves the best improvement under low speed and high load torque.

Fig. 8. Improved power efficiency under different operations.

5 Conclusion In this paper, a novel power optimization strategy is proposed for MTPA and LMC methods. Based on the analysis of loss power, the proposed method transfers traditional power optimization problems into extremum problems. An adaptive optimization method is tailored by using the derivation of a given signal to quickly and theoretically converge on the optimal point. Proposed POC methods have been evaluated on an IPMSM test bench with good results. The proposed method will be combined with field weakening

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and optimization problems in future work, especially the weighting factor optimization problem. Acknowledgements. This research was partly supported by the National Natural Science Foundation of China: 52277070 and partly by the Science and Technology Program of Fujian Province 2022T3061, 2021T3062, and 2020T3003, partly by the Science and Technology Plan Project of Fujian Province under Grant 2021I0039, 2021T3064, and 2021T3035, partly by the STS Plan in Fujian Province under Grant 2020T3024, and partly by the project 2022G026.

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16. Butt, C., Hoque, M., Rahman, M.: Simplified fuzzy-logic-based mtpa speed control of ipmsm drive. IEEE Trans. Industr. Appl. 40(6), 1529–1535 (2004) 17. Antonello, R., Carraro, M., Zigliotto, M.: Maximum-torque-per-ampere operation of anisotropic synchronous permanent-magnet motors based on extremum seeking control. IEEE Trans. Industr. Electron. 61(9), 5086–5093 (2014) 18. Chen, Q., Zhao, W., Liu, G., Lin, Z.: Extension of virtual-signal-injection-based mtpa control for five-phase ipmsm into fault-tolerant operation. IEEE Trans. Industr. Electron. 66(2), 944– 955 (2019) 19. Chitour, Y.: Time-varying high-gain observers for numerical differentiation. IEEE Trans. Autom. Control 47(9), 1565–1569 (2002) 20. Davila, J., Fridman, L., Levant, A.: Second-order sliding-mode observer for mechanical systems. IEEE Trans. Autom. Control 50(11), 1785–1789 (2005) 21. Wang, X., Chen, Z., Yang, G.: Finite-time-convergent differentiator based on singular perturbation technique. IEEE Trans. Autom. Control 52(9), 1731–1737 (2007) 22. Zhang, H., Xie, Y., Xiao, G., Zhai, C., Long, Z.: A simple discrete-time tracking differentiator and its application to speed and position detection system for a maglev train. IEEE Trans. Control Syst. Technol. 27(4), 1728–1734 (2019) 23. Han, J.: From pid to active disturbance rejection control. IEEE Trans. Industr. Electron. 56(3) (2009) 24. Abrahamsen, F., Blaabjerg, F., Pedersen, J., Thoegersen, P.: Efficiency-optimized control of medium-size induction motor drives. IEEE Trans. Industr. Appl. 37(6), 1761–1767 (2001) 25. Wang, F., Li, S., Mei, X., Xie, W., Rodriguez, J., Kennel, R.M.: Model-based predictive direct control strategies for electrical drives: An experimental evaluation of ptc and pcc methods. IEEE Trans. Industr. Informatics 11(3), 671–681 (2015) 26. Ke, D., Wang, F., He, l., Li, Z.: Predictive current control for PMSM systems using extended sliding mode observer with Hurwitz-based power reaching law. IEEE Trans. Power Electron. 36(6), 7223–7232 (2021) 27. Hu, H., Liu, K., Wei, J., Wang, H.: Multirate model predictive current control of a permanent magnet synchronous machine for a flywheel energy storage system. Energy Rep. 8, 11579– 11591 (2022)

Full Life Cycle Prediction of Nuclear Bearings Based on Digital Twin Hybrid Model Chunyi Han1,2 , Yuanjun Guo3(B) , Zhile Yang3 , Wei Feng3 , Yanhui Zhang3 , Huanlin Chen1 , and Weihua Chen1 1 State Key Laboratory of Nuclear Power Safety Monitoring Technology and Equipment,

Shenzhen, China 2 Hebei University, Hebei, China 3 Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences Shenzhen,

Shenzhen, China [email protected]

Abstract. With the development of Industry 4.0, there is an increasing demand for industrial digital transformation. As a clean energy source with high efficiency, nuclear power is confronting new challenges of safety and digital and intelligent operational stability. One of these issues is the accurate prediction of the life of nuclear power equipment. In this paper, a hybrid model based on data-driven digital twin and deep learning prediction is established for nuclear power safety issues. First, a digital twin model of nuclear power equipment is established, driven by nuclear power bearing data, and the health factor curve is obtained by data cleaning and smoothing of the original data. Then the full life cycle of nuclear power equipment is modeled using the deep learning prediction method. Finally, simulations using real bearing data demonstrate the effectiveness of the proposed hybrid model. Keywords: Nuclear power bearings · Digital twin · Full life cycle · Deep learning · LSTM · RNN · GRU · Transformer

1 Introduction With the development of Industry 4.0, various industries such as the Internet, artificial intelligence technology, and new energy have entered a new stage of development [1]. Traditional industries such as nuclear power and petroleum have an increasingly profound impact on social development. Bearings are used in a variety of equipment and instruments in traditional industries and are also one of the main components of nuclear power equipment. However, due to impact, wear, and other effects, nuclear power bearings will inevitably fail and degrade, which will not only seriously affect the production efficiency and safe operation of the equipment, but also bring unnecessary economic losses [2].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 491–497, 2023. https://doi.org/10.1007/978-981-99-4334-0_61

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A digital twin (DT) is a digital model of a physical entity based on sensors and is mapped in a virtual space to reflect the entire life cycle process of the corresponding entity [3]. In recent years, DT is already being applied in the oil and gas industry to predict emergencies and accident prevention, etc. [4]. With the development of digital technology, it is possible to apply DT to effectively manage the whole life cycle of nuclear power plant equipment [5]. Currently, DT has demonstrated significant performance gains in the aerospace, automotive, and construction industries. It has also been proposed for use in individual life cycle stages in the construction industry [6]. However, few studies have applied DT to the full life cycle prediction of nuclear power bearings. In this paper, a digital twin-based prediction model for the full life cycle of nuclear power bearings is proposed. The model takes the vibration acceleration signal as input and combines a variety of deep learning methods to achieve the purpose of prediction. First, a digital model of the real physical bearing is established, and the real bearing data is uploaded to the digital model at the same time. Then, the deep learning methods in the digital model are used to simulate the whole life cycle of nuclear power bearings, and the final experimental results prove the effectiveness of the proposed method.

2 Method In this section, the method of full life cycle prediction of nuclear bearing based on the digital twin hybrid model is mainly discussed. For the full life cycle of bearing life, traditional deep learning methods such as Long short-term memory (LSTM) and Gate recurrent unit (GRU) can accurately predict it. However, the traditional prediction process is separate and cannot display the results in real-time. Thus, the proposed method combines artificial methods with digital twin technology to establish a hybrid model, which can optimize the prediction process of the full life cycle of nuclear power bearings and reduce the time required for prediction. 2.1 Digital Twin The concept of the digital twin was first proposed by Dr. Michael Grieves of the University of Michigan [7]. The digital twin is to establish a virtual model of a physical object. With the help of historical data, real-time data, and algorithm models, it can realize real-time analysis, prediction, improvement, and optimization of physical objects. The digital twin, which integrates the virtual world with the real world, is the next generational development theme of cutting-edge technology. The proposed nuclear power bearing digital model is shown in Fig. 1. To establish the digital twin model, the acceleration signals of the bearing are collected to build the health index (HI) of the whole life cycle. Then the data in the physical space and the virtual space are synchronized. Finally, deep learning methods are used to make full life cycle predictions and the results are shown in virtual space synchrony.

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Fig. 1. Nuclear power bearing digital model.

2.2 Artificial Intelligence Methods For the prediction of the full life cycle of nuclear power bearings, four artificial intelligence methods are selected: recurrent neural network (RNN), LSTM, GRU, and Transformer. These four methods are integrated into the proposed digital model of nuclear power bearing. In this section, these four AI methods are introduced. RNN is a recurrent neural network designed to process sequence data especially. LSTM is a special RNN network that can solve the long-term dependency problem [8]. The structure of LSTM is shown in Fig. 2. xt is the input of the current time, ht−1 is the output of the hidden layer of the previous layer, W is the input dimension multiplied by the output dimension, b is the output dimension. First, xt and ht−1 passes sigmoid unit to determine whether history information needs to be retained or discarded. Then, the update information is determined by a sigmoid unit and a tan-h layer. Finally, the dot product of Ot and tanh(Ct ) may be used to produce the output ht , the formulas are as follows. The structure of GRU is similar to that of LSTM [9]. The difference is that GRU has one less “gate” inside and has fewer parameters than LSTM, but it can also achieve the same function as LSTM.     (1) ft = σ Wf · ht−1 , xt + bf     ot = σ Wo · ht−1 , xt + bo

(2)

ht = ot ∗ tanh(Ct )

(3)

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Fig. 2. Structure of LSTM.

The transformer is generated to resolve issues that cannot be parallelized. The structure of attention is used to completely replace the RNN part, and the effect is better [10]. Encoder and decoder are the two components that make up the transformer, and Fig. 3 depicts how it is constructed. The transformer uses positional encoding to add relative position information to the input. This information can be gained in one of two ways: via learning or by directly computing the sin and cos functions of various frequencies, as illustrated in Eqs. (4) and (5). The Encoder’s primary area of emphasis is the multi-head attention network. As shown in Eq. (6), “Multi-Head” refers to the projection of the embedding vectors q, k, and v across several linear transformations of the head.   (4) PE(pos,2i) = sin pos/10002i/dmodel   PE(pos,2i+1) = cos pos/10002i/dmodel  T qk Attention(q, k, v) = softmax √ · v dk

(5) (6)

Fig. 3. Structure of transformer.

3 Experiments 3.1 Data Processing The experimental data were collected on a platform designed to evaluate bearings for accelerated deterioration [11]. The load in this experiment is 4000 N, and the speed is 1800 rmp, according to the vibration acceleration signal data of the operating state of

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this data set. From 08:33:00 to 15:08:41, this collection of data is gathered every 10 s at a sampling frequency of 25.6 kHz for 0.1 s at a time, that is, 2560 points per sample will be obtained.

Fig. 4. The original data and the processed data.

As shown in the left half of Fig. 4, the y-axis is the vibration acceleration signal unit of the bearing in g, and the x-axis is the time series. First, the experimental data is downsampled from 600000 to 5000. Then, median filtering is performed on the experimental data, where kernel_size = 111. Finally, the HI curve is obtained after data processing, as shown in the right half of Fig. 4. When a new bearing enters the working state, it goes through the healthy stage, the degradation stage, and the critical stage, which is the full life cycle of the bearing [12]. The division of health stages is based on the following principles: the range of HI < 0.5 is regarded as the healthy stage, the range of 0.5 < HI < 0.8 is regarded as the degradation stage, and the range of HI > 0.8 is regarded as the critical stage. 3.2 Deep Learning Methods Four deep learning methods were used in this experiment, and the experimental results are shown in Fig. 5. Results between 1200 and 1500 and 4800 and 4900 are zoomed in, black is the real data, yellow, green, purple, and red are the HI curves of the predicted data trained by RNN, GRU, LSTM, and Transformer networks, respectively. Some parameters to evaluate the quality of the model are shown in Table 1. MSE, RMSE, MAE, and R2 are crucial metrics for assessing the efficacy of prediction models. The more closely the created model matches the actual data and the smaller the values of MSE, RMSE, and MAE as well as the higher the value of R-square, the more accurate the model is. As can be seen from Table 1, the LSTM prediction model outperforms the other three models, according to the evaluation metrics. LSTM may be more efficient for the whole life cycle prediction of nuclear power bearings, even though the findings of the four models’ predictions are all valid.

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Fig. 5. The true value and the prediction results of the four models.

Table 1. The results of the difference comparison between the predicted value and the true value of the four methods. NAME

MSE

RMSE

MAE

R2

GRU

0.0012

0.0355

0.0133

0.9780

LSTM

0.0009

0.0310

0.0126

0.9836

RNN

0.0011

0.0339

0.0131

0.9800

Transformer

0.0017

0.0415

0.0185

0.9700

4 Conclusion Digital twins provide fresh viewpoints for full-life-cycle prediction as a technique for achieving unification between the real world and its digital representation. This paper uses the digital twin modeling method, combined with the artificial intelligence deep learning method, to predict the full life cycle of nuclear power bearings. The experimental results demonstrate that by segmenting the different stages of the nuclear power bearing life cycle and analyzing the raw data during the experiment to produce the HI curve, it is possible to utilize artificial intelligence to predict the full life cycle of nuclear power bearings. The whole life cycle of a piece of equipment may be precisely predicted by intelligent algorithms based on digital twins. Digital twins will be widely employed through nuclear industries in the future to achieve nuclear intelligence and raise the operatiional effectiveness of nuclear power plants. Acknowledgment. This work was supported by the State Key Laboratory of Nuclear Power Safety Monitoring Technology and Equipment under grant K-A2021.422, China NSFC under grants 52077213 and 62003332, Natural Science Foundation of Guangdong Province under grants 2018A030310671 and outstanding young researcher innovation fund of SIAT, CAS (201822).

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References 1. Tao, F., Qi, Q., Wang, L., et al.: Digital twins and cyber-physical systems toward smart manufacturing and industry 4.0: correlation and comparison. Engineering 5(4), 653–661 (2019) 2. Qin, Y., Chen, D., Xiang, S., et al.: Gated dual attention unit neural networks for remaining useful life prediction of rolling bearings. IEEE Trans. Industr. Inf. 17(9), 6438–6447 (2020) 3. Zheng, Y., Yang, S., Cheng, H.: An application framework of digital twin and its case study. J. Ambient. Intell. Humaniz. Comput. 10(3), 1141–1153 (2019) 4. Abdrakhmanova, K.N., Fedosov, A.V., Idrisova, K.R., et al.: Review of modern software complexes and digital twin concept for forecasting emergency situations in oil and gas industry. In: IOP Conference Series: Materials Science and Engineering, vol. 862 no. 3, p. 032078. IOP Publishing (2020) 5. Arzhaev, A., Makhanev, V., et al.: NPP unit life management based on digital twin application. In: E3S Web of Conferences, vol. 209, p. 03006. EDP Sciences (2020) 6. Opoku, D.G.J., Perera, S., Osei-Kyei, R., et al.: Digital twin application in the construction industry: a literature review. J. Build. Eng. 40, 102726 (2021) 7. Jones, D., Snider, C., Nassehi, A., et al.: Characterising the digital twin: a systematic literature review. CIRP J. Manuf. Sci. Technol. 29, 36–52 (2020) 8. Huang, R., Wei, C., Wang, B., et al.: Well performance prediction based on long short-term memory (LSTM) neural network. J. Petrol. Sci. Eng. 208, 109686 (2022) 9. Raza, M.R., Hussain, W., Merigó, J.M.: Cloud sentiment accuracy comparison using RNN, LSTM and GRU. In: 2021 Innovations in Intelligent Systems and Applications Conference (ASYU), pp. 1–5. IEEE (2021) 10. Sun, Z., Cao, S., Yang, Y., et al.: Rethinking transformer-based set prediction for object detection. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 3611–3620 (2021) 11. Nectoux, P., Gouriveau, R., Medjaher, K., et al.: An experimental platform for bearings accelerated degradation tests. In: Proceedings of the IEEE International Conference on Prognostics Health Manage, pp. 1–8 (2012) 12. Lei, Y., Li, N., Guo, L., et al.: Machinery health prognostics: a systematic review from data acquisition to RUL prediction. Mech. Syst. Signal Process. 104, 799–834 (2018)

Simulation of Position Impedance Control for Single Leg of Electric Drive Legged Robot Xiaocan Wang1 , Shuai Wang2(B) , Huafeng Jiang1 , Zeliang Xiong1 , Qinggui Zheng2 , and Xianglin Chen2 1 Xiamen University of Technology, Xiamen 361024, China 2 Quanzhou Institute of Equipment Manufacturing Haixi Institutes, Chinese Academy of

Sciences, Jinjiang 362216, China [email protected]

Abstract. The electric drive legged robot has the advantages of fast torque response, light weight, energy saving, and low noise. For the single-leg bounce motion control problem of the electric drive legged robot, the single-leg structure is equivalent to a two-link mechanical structure, and an application is combined. The position impedance control adapted for high-speed response and high-precision motion control method, achieved the single leg more stable in bouncing and more adaptable to complex terrain. Simulation results show that the control method proposed in this paper can realize the stable bouncing and two-dimensional motion of the electric drive leg under multi-road conditions. Keywords: Legged robot · Electric drive · Position impedance control

1 Introduction Legged robots have developed from hydraulic drives to electric drives [1–5].In the single leg motion control system, in order to make the single-leg motion run on the expected trajectory, improve the stability of the system, and reduce the trajectory deviation, a closed-loop control strategy is added to the control structure, and the expected value of the motor is used as the ideal input, and the feedback value of the motor As the actual output, the expected and actual errors are reduced, thereby improving the control accuracy [6–9]. In the research of link-type robot, the control strategies can be classified into position control and force control [10, 11]. The position control of the robot focuses on how to control each joint of the robot to reach the specified position, which is the basis of the robot’s motion control. The position control of the link-type robot can be divided into the position control of the joint space and the position control of the Cartesian space. In this paper, the position impedance control is selected for the single-leg of the electric drive legged robot, and the PID closed-loop control strategy based on joint space and the position impedance control method based on Cartesian space are tested and compared respectively, and the closed-loop simulation is carried out.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 498–503, 2023. https://doi.org/10.1007/978-981-99-4334-0_62

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2 Single Leg Structure and Kinematic Modeling 2.1 Single Leg Structure The basic components of the single-leg structure is shown in Fig. 1. Both hip and leg use same brushless DC motors. The motor has a built-in driver, which control the position, speed, and torque of the motor. The motor rotor outputs power through a planetary reducer with a reduction ratio of 6:1. The power output end of the hip motor is fixedly connected to the end cover of the leg motor, and the mechanical connecting rod of the hip motor is fixed on the stator of the lap motor, and rotates with the rotation of the stator of the lap motor; the power output end of the lap motor and the knee joint are equipped with a gear ratio of 19:30 synchronous wheel, the two synchronous wheels are connected by a nylon belt, and the lap motor rotates to drive the lap link to swing.

Fig. 1. 3D structure of single leg.

Fig. 2. Two-link plan in D-H system.

2.2 Kinematic Modeling 1. Positive Kinematics Modeling The electric drive single leg model is simplified to a two-link structure for analysis, and its kinematics modeling is built by D-H coordinate method. The coordinate system of each joint is shown in Fig. 2, where x_0-y_0-z_0 is the spatial coordinate system, which is located at the hip joint; x_1-y_1-z_1 is the rotating coordinate system at the hip joint, and x_2-y_2-z_2 and x_3-y_3-z_3 are the motion coordinate systems of the knee and foot respectively. Since the single leg movement is only performed in the two-dimensional space, the z-axis component is always 0, z-axis is not shown in Fig. 2.

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Link

ai

αi

di

ϑi

1

L1

0

0

ϑ1

2

L2

0

0

ϑ2

According to the Table 1, the D-H matrix of each link can be obtained, respectively A1 , A2 , A3 , according to the positive kinematics of the robot, the position of the foot end can be obtained as: T20 = A1 A2

(1)

Since each link is rotational, the two joints of a single leg have the same homogeneous transformation matrix: ⎤ ⎡ c1 −s1 0 Li ci ⎢ s1 c1 0 Li si ⎥ ⎥ (2) =⎢ Ai−1 i ⎣ 00 10 ⎦ 00

01

where i = 1, 2. According to the positive kinematics equation: ⎡

c12 −s12 ⎢ s12 c12 T20 (q) = A01 A12 = ⎢ ⎣ 0 0 0 0

⎤ 0 L2 c12 + L1 c1 0 L1 s12 + L1 s1 ⎥ ⎥ ⎦ 1 0 0 1

(3)

Which c1 represents cosϑ1 , s1 represents sinϑ1 , c12 represents cos(ϑ1 + ϑ2 ), s12 represents sin(ϑ1 + ϑ2 ), T20 represents the position of the foot end of a single leg in the space coordinate system of the hip joint. 2. Inverse Kinematics Modeling In the process of single leg movement, the deflection of the hip motor ϑ1 and the lap motor ϑ2 need to be solved in real time according to the position constraints of the foot, and adjusted in real time according to the deflection angle and the feedback of the foot trajectory, so that the foot trajectory and the ideal motion trajectory can be adjusted in real time, in order to achieve the best follow-up effect. The foot position T is: ⎡

nx ⎢ ny T =⎢ ⎣ nz 0

ox oy oz 0

ax ay az 0

⎤ px py ⎥ ⎥ pz ⎦ 1

(4)

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where the joint angle is ϑ2 , T = A1 A2 and calculated with (4), it can be obtained: ⎤ ⎡ ⎤⎡ nx ox ax px c1 s1 0 −L1 ⎢ −s1 c1 0 0 ⎥⎢ ny oy ay py ⎥ ⎥ ⎢ ⎥⎢ A2 = A−1 1 T = ⎣ 0 0 1 0 ⎦⎣ n o a p ⎦ z z z z 0 0 0 1 0 0 0 1 ⎡ ⎤ t11 t12 t13 c1 px + s1 py − L1 ⎢ t21 t22 t23 −s1 px + c1 py ⎥ ⎥ =⎢ ⎣ t31 t32 t33 ⎦ pz 0 0 0 1

501

(5)

calculated with (4) and (5) to obtain: L2 c2 = c1 px + s1 − L1 L2 s2 = −s1 px + c1 py

(6)

The deflection of the lap motor can be obtained from the arc tangent function ϑ2 : ϑ2 = arctan 2(c2 , s2 )

(7)

3 Simulation Analysis of Control Strategy 3.1 PID Closed-Loop Control Based on Single Joint The simulation results are shown in Fig. 3, the foot end trajectory is set to satisfy the position constraint x_f = 0, y-axial is used as the analysis point. In Fig. 3a, the error exist when the foot end moves, but it varys accoding to time, and the smoothness of the actual trajectory meet the design, which is to prevent the foot oscillation, to ensure the stability and gradual change of the single leg movement. The performance of the hip motor in Fig. 3b is like the foot, because the motor angle and the foot trajectory have forward and inverse kinematics transformation, and the motor position is directly affecting the foot. The error is also reflected in the foot. If the hip motor obtains a good effect, the foot also obtains a good result due to its kinematic transformation, and optimization of PID parameters will further reduce the position error. In Fig. 3c shows the speed slip of the actual position has a high frequency oscillation, and the speed error rate is maintained within 2% in a steady state. 3.2 Position Impedance Control Based on Cartesian The foot-end trajectory as the control reference point is the most intuitive control for single leg movement because the movement performance of a single leg is directly affected by the position of the foot end. To build an impedance controller in the joint space, it is necessary to establish the control systems of the hip motor and the leg motor respectively. The impedance control block diagram of Cartesian space is shown in Fig. 4.

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(a)Position of the foot end

(b) Position of the hip motor (c)Speed & error rate of the hip motor

Fig. 3. PID simulation results

Fig. 4. Position impedance control of single leg.

(a)Position of the foot end

(b) Position of the hip motor (c)Speed & error rate of the hip motor

Fig. 5. Impedance control simulation results.

During single leg movement, the swing end is not connected with the external object, so f is 0. If the single leg is jumping with load, or an external force is applied on it, and then item f is not zero. The position impedance control simulation results shown in Fig. 5, the foot position, motor position and speed performance following very well with the theoretical control strategy, and actual deviation cannot be seen in the same figures. In the characteristic analysis, the expectation and the actual are derived separately, from the angle of error and error rate. In Fig. 5a it only has a large error in the initial stage, but the tracking error will be reduced to 10% within 0.1 s, and the foot error in the steady state is maintained within 3%. It can ensure that the foot end position moves smoothly according to the expected trajectory. The rotation angle is converted from the foot position in Cartesian space to the joint space through inverse kinematics. The following characteristics of the motor rotation angle will have the most direct impact on the foot following characteristics. It can be seen from Fig. 5b that the tracking error of the motor angle balance state is maintained within 2%. The excellent position tracking characteristics of the motor ensure accurate tracking of the foot position.

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The motor speed is the derivative of the motor position in Fig. 5c, and the expected speed characteristics in the position-type impedance control ensure the fast response of position tracking and the fast adjustment of position error. According to the comparison of simulation results, the impedance control has higher control accuracy and faster speed response than PID closed-loop control.

4 Conclusion The position impedance control based on Cartesian space is to add an impedance control law on the basis of the PID control strategy of the two joint motors. According to the position deviation of the foot end, the position compensation amount is calculated and then acts on the two joint spaces. PID controller. Compared with the PID closed-loop control strategy based on joint space, the impedance control in the simulation produces smaller position and speed errors, and responds quickly, so as to achieve rapid adjustment of position errors. It can be seen that in the PID closed-loop with impedance position control can realize high precision control of single leg motion, so that single leg can move according to the designed trajectory, and provide an expected control strategy basis for single legged robot control and even quadruped robot control.

References 1. Seok, S., Wang, A., Chuah, M.Y..: Design principles for energy-efficient legged locomotion and implementation on the MIT cheetah robot. IEEE/ASME Trans. Mechatron. 20(1), 1117– 1128 (2015) 2. Park, H.W., Park, S., Kim, S.: Variable-speed quadrupedal bounding using impulse planning: untethered high-speed 3D running of MIT Cheetah 2. In: IEEE International Conference on Robotics and Automation, pp.5163–5170. Seattle, WA (2015) 3. Wensing, P.M., Wang, A., Seok, S., Otten, D., Lang, J., Kim, S.: Proprioceptive actuator design in the MIT cheetah: Impact mitigation and high-bandwidth physical interaction for dynamic legged robots. IEEE Trans. Rob. 33(1), 509–522 (2017) 4. Zhai, S., Jin, B., Cheng, Y.: Mechanical design and gait optimization of hydraulic hexapod robot based on energy conservation. Appl. Sci. 10(11), 3884–3894 (2020) 5. Runbin, C., Yangzhen, C., Wenqi, H.: Trotting gait of a quadruped robot based on the time-pose control method. Int. J. Adv. Rob. Syst. 10(1), 323–330 (2013) 6. Brinker, J., Corves, B. and Takeda, Y.: Kinematic performance evaluation of high-speed delta parallel robots based on motion/force transmission indices. Mech. Mach. Theory 125(2), 111–125 (2018) 7. Li, P., Xu, X., Yang, S., Jiang, X.: Open circuit fault diagnosis strategy of PMSM drive system based on grey prediction theory for industrial robot. Energy Rep. 9(1), 313–320 (2023) 8. Loro, J.A.R.: Robust position control of SM-PMSM based on a sliding mode current observer. Int. J. Electr. Electron. Eng. Telecommun. 9(5), 337–341 (2020) 9. Ba, K.-X., Yu, B., Ma, G.-L., Zhu, Q.-X., Gao, Z.-J., Kong, X.-D.: A novel position-based impedance control method for bionic legged robots’ HDU. IEEE Access 6(2), 55680–55692 (2018) 10. Xu, Q.: Robust impedance control of a compliant microgripper for high-speed position/force regulation. IEEE Trans. Indus. Electron. 62(2), 1201–1209 (2015) 11. Sato, R., Hiasa, S., Wang, L., Liu, H., Meng, F., Huang, Q., Ming, A.: Vertical jumping by a legged robot with upper and lower leg Bi-articular muscle–tendon complexes. IEEE Robot. Autom. Lett. 6(4), 7572–7579 (2021)

Research on Distribution Transformer Quality Sampling Assessment Model Based on Entropy Weight Method Yanzhao Niu1 , Hanwu Xiong1 , Zhengbo Liang2(B) , Jin Zhang2 , Chao Peng2 , and Tian Yuan2 1 Material Department, State Grid Corporation of China, Beijing, China 2 China Electric Power Research Institute, Wuhan, China

[email protected]

Abstract. Distribution transformer is an important equipment in power system. Power grid companies purchase a large number of distribution transformers every year to satisfy the social electricity demand. At present, there are many manufacturers producing distribution transformers. Different manufacturers produce distribution transformers due to different processes, leading to differences in the performance of distribution transformers. Therefore, it is an urgent problem for power grid companies to select the optimal distribution transformer. Based on entropy weight method, a transformer quality assessment model based on factory test data is studied in this paper. By analysing the open-circuit loss, on-load loss, average temperature rise of HV winding and average temperature rise of LV winding, a distribution transformer quality assessment model is constructed. Based on the above model, the distribution transformers of different manufacturers are scored and the optimal distribution transformer manufacturer is extracted. This study can provide reference for power grid companies to purchase distribution transformers in the future. Keywords: Quality sampling test · EWM · Distribution transformer

1 Introduction With the increasing social demand for electricity, the quantity of distribution transformers purchased by power grid companies increases sharply, which puts forward higher requirements for the quality and reliability of distribution transformers [1]. Because different manufacturers of the same model, specifications of the distribution transformer manufacturing process are different, the performance of the distribution transformer produced by the difference, the selection of excellent performance of the distribution transformer is very important to maintain the reliability of electricity. Distribution transformer delivery test is an effective means to verify its performance [2, 3]. The most important measurement items in this test include open-circuit loss, on-load loss, average temperature rise of high-voltage winding and average temperature rise of low-voltage winding. In the assessment model of distribution transformer, the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 504–510, 2023. https://doi.org/10.1007/978-981-99-4334-0_63

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objective evaluation method based on entropy weight method (EWM) can effectively distinguish the performance of distribution transformer [4–6]. EWM is a method to determine the weight assignment completely based on objective data and rules, and its essence is to analyse the variability of different evaluation indicators to judge the impact of each indicator on the overall degree. This method can effectively avoid the decision errors caused by the subjective will of decision makers in the subjective weighting method, and is widely used in mathematical statistics, financial big data analysis and other fields. However, at present, there are many manufacturers of distribution transformers purchased by each provincial company of State Grid Corporation, and the quality of distribution transformers is uneven. It is urgent to put forward an assessment model for the quality of distribution transformers of each manufacturer. This paper constructs a distribution transformer quality assessment model based on EWM according to quality sampling test data. Based on this model, the distribution transformers of each manufacturer are scored, and the manufacturer with the best performance of distribution transformer is selected.

2 Quality Sampling Test Data The quality sampling test of 10 kV and 400 kVA silicon steel sheet oil-immersed transformers produced by different companies was carried out. The test included open-circuit loss, on-load loss, HV and LV winding temperature rise. Part of results are shown in Table 1 and Fig. 1.

3 EWM Analysis and Results 3.1 EWM Method Principle EWM method is an objective weight assignment method which includes six steps [7]. First, construct decision matrix X. If there are m evaluated indexes which has n levels, the decision matrix X is a matrix with m rows and n columns, which is shown in Eq. (1), where x ij represents the ith evaluated index and jth level.   x11   x21  X = .  ..  x m1

x12 · · · x1n x22 · · · x2n .. . . .. . . . xm2 · · · xmn

        

(1)

m×n

Secondly, the evaluation index in matrix X is processed dimensionless. If higher x ij value represents better performance, x ij ’ = x ij /x j * , where x j * is the maximum of evaluation index. Otherwise, x ij ’ = x j * /x ij , where x j * is the minimum of evaluation index. Eventually, characteristic decision matrix X ’ = (x ij ’ ) m*n is established, where each index is in the range of 0 and 1, and higher value represents better performance.

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Fig. 1. Quality sampling test of 400 kVA, 10 kV Silicon steel sheet oil-immersed transformer.

Thirdly, by normalizing characteristic Eq. (2). ⎛ b11 ⎜ b21 ⎜ B=⎜ . ⎝ ..

decision matrix X ’ , matrix B is established in b12 b22 .. .

··· ··· .. .

⎞ b1n b2n ⎟ ⎟ .. ⎟ . ⎠

bm1 bm1 · · · bmn

(2) m×n

Then, the information entropy of each index is calculated. For the same index, the index values of different evaluation objects differ greatly, indicating that the index contains abundant effective information and has obvious influence on the evaluation object. The calculation formula of information entropy is shown in Eq. (4). If bij = 0 or 1, denoting bij lnbij = 0. m bij ln bij (3) Ej = i=1 ln m The deviation degree of each index is calculated by Eq. (4). dj = 1 − Ej

(4)

Finally, the deviation degree of each index is normalized, and the deviation degree after normalization is shown in Eq. (6). At this time, the deviation degree is the objective

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Table 1. Quality sampling test of distribution transformer from different manufacture. Manufacture

Open-circuit loss (kW)

On-load loss (kW)

HV winding temperature rise (°C)

LV Winding temperature rise (°C)

A

0.399

3.435

47.84

53.26

0.401

3.441

49.37

54.23

0.406

3.439

51.25

55.06

0.408

3.448

47.2

53.8

B

C

D

0.409

3.502

48.5

55.2

0.394

3.526

51.4

55.8

0.384

3.532

51.4

53.4

0.393

3.532

51.6

55.8

0.398

3.43

51.3

53.6

0.385

3.568

51.3

52.4

0.391

3.508

57.6

56

0.386

3.476

54.8

54.9

0.394

3.481

52.4

55.5

0.384

3.467

58.8

59.9

0.393

3.489

60.6

59.5

0.396

3.505

53.3

52.2

0.391

3.502

45.2

49.2

0.396

3.460

51.9

51.1

0.382

3.455

52.8

51.5

0.385

3.461

52.9

51.8

weight of the evaluation system. The calculation of information entropy and deviation degree of each evaluation index in decision matrix X based on entropy weight method can effectively avoid the decision error caused by subjective weighting method. Usually, the normalized deviation degree is taken as the objective weight of each index. dj µj = n

j=1 dj

SCORE = X  · µj

(5) (6)

3.2 Quality Sampling Assessment Model of Distribution Transformer Based on the factory test, this paper selects four indexes of open-circuit loss, on-load loss, average temperature rise of high-voltage winding and average temperature rise of

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low-voltage winding as the evaluation index system of distribution transformer. Taking an oil-immersed silicon steel sheet distribution transformer with a capacity of 400 kVA and a voltage level of 10 kV as an example, the average value of distribution transformers delivered by four manufacturers was selected for evaluation. The indicators are divided into four levels: excellent, good, medium and poor. The specific parameters of each indicator are shown in Table 2. First, the decision matrix X is constructed in Eq. (8). Since lower value of the four indexes represent better performance, the characteristic decision matrix is shown in Eq. (9). By normalizing X , matrix B is obtained in Eq. (10). Table 2. Evaluation Index. Classification

Index Open-circuit loss (kW)

On-load loss (kW)

HV winding temperature rise (°C)

LV winding temperature rise (°C)

Excellent

0.38

3.49

50

50

Good

0.39

3.53

54

54

Normal

0.4

3.57

57

57

Poor

0.41

3.61

60

60

   0.38 3.49 50 50     0.39 3.53 54 54    X =   0.4 3.57 57 57   0.41 3.61 60 60     1.000 1.000 1.000 1.000     0.974 0.989 0.926 0.926   X  =    0.950 0.978 0.877 0.877   0.927 0.967 0.833 0.833     0.519 0.508 0.549 0.549     0.506 0.503 0.508 0.508    B=   0.493 0.497 0.481 0.481   0.481 0.492 0.457 0.457 

(7)

(8)

(9)

The information entropy and deviation degree of each evaluation index are shown in Eqs. (10) and (11). Normalized deviation degree, which is objective weight, is shown in Eq. (12). The results show that the four parameters of quality sampling test are equally important.   (10) Ej =  −1.000 −1.000 −0.998 −0.998 

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  dj =  2.000 2.000 1.998 1.998 

(11)

  µj =  0.250 0.250 0.250 0.250 

(12)

The calculated results of quality scoring model based on entropy weight method are shown in Eq. (13), and the results show that distribution transformer of manufacturer A is the best, followed by D, and manufacture C gets the lowest score.

 SCORE (A, B, C, D) = 95.1 93.5 91.8 95.0 (13)

4 Conclusion Distribution transformer is an important equipment in power system. Power grid companies purchase a large number of distribution transformers every year to satisfy the social electricity demand. This paper studies the distribution transformer quality assessment model based on EWM. The results and conclusions are as follows: (1) Quality sampling test data is an important method to evaluate distribution transformer quality produced by different manufactures, but different distribution transformer from different manufactures has its own advantages in some quality sampling test item. Thus, it is hard to judge which distribution transformer has the best operation performance. (2) Entropy weight method is an objective evaluation method. By constructing a quality sampling assessment model, the operating performance advantage of distribution transformers can be quantified. Therefore, the operating performance of distribution transformers can be scored and evaluated. (3) The quality sampling assessment model based on EWM can also be used to analyse other types of transformers produced by different manufactures, only the number of parameters and boundary values need to be changed. The research results of this paper can provide reference for power grid companies to purchase equipment. Acknowledgements. This work was supported by “Research on key technologies for improving resilience of power grid material supply chain under novel power system” of Headquarters Management Science and Technology Project Funding of State Grid Corporation of China. (5108-202218280A-2–187-XG).

References 1. Yan, W.U., Lan, L.I.U., Changkai, S.H.I., Kui, M.A., Yang, L.I., Haibao, M.U.: Research on measurement technology of transformer no-load loss based on Internet of Things. In: 2019 IEEE 8th International Conference on Advanced Power System Automation and Protection (APAP), pp. 150–153, Xi’an, China (2019)

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2. IEEE approved draft standard for general requirements for liquid-immersed distribution, power, and regulating transformers. In: IEEE PC57.12.00/D2.2, August 2021, pp. 1–70 (2021) 3. IEEE standard test code for liquid-immersed distribution, power, and regulating transformers and IEEE guide for short-circuit testing of distribution and power transformers. In: ANSI/IEEE Std C57.12.90–1987, pp. 1–80 (1988) 4. Wang, J., Gu, C., Liu, K.: Anomaly electricity detection method based on entropy weight method and isolated forest algorithm. Front. Energy Res. (2022) 5. Zhou, S.: Research on safety evaluation of nuclear power plant based on entropy weight method. Can. Soc. Sci. 17(4) (2021) 6. Wang, Y., Yaling, J., Yang, J., Tang, Y., Zhou, P., Chen, C.: Research on power grid infrastructure investment distribution model based on entropy weight method. In: E3S Web of Conferences, p. 253 (2021) 7. Liang, H.F., Lin, D.S.: Research on the transformer condition assessment based on the entropy weight method. Adv. Mater. Res. 2481(732–733) (2013)

A Novel DC Energy Dissipation Topology and Control Method Yiqi Liu, Laicheng Yin(B) , Bingkun Li, Mingzhe Sun, Meiru Chen, and Tianshi Guo Northeast Forestry University, Heilongjiang 150040, China [email protected]

Abstract. A DC energy dissipation arm(EDA) structure with coupled transformer is proposed to solve the problem of DC voltage rise caused by AC voltage sag fault in offshore wind power generation systems; The proposed method reduces the cost of the high-voltage wall bushing and improves the economy of the equipment by reducing the voltage at both ends of the energy dissipation resistors; According to the calculation, the cost of high-voltage wall bushing can be reduced by 23 ~ 28% under 230 kV condition; The IGBT overvoltage caused by inconsistent turn-off time was successfully avoided by connecting IGBT and MOV in parallel, and reduce the volume of converter station caused by excessive capacitance; The proposed control strategy successfully dissipates surplus energy. At the same time, a fault operation control strategy is proposed, in which the device can cooperate with the receiving end converter(REC)in the case of partial IGBT faults and continue to operate at a specific power. Keywords: Energy dissipation · Transformer · Surplus energy

1 Introduction The voltage source converter based on high voltage direct current transmission (VSCHVDC) has been widely used in offshore wind power generation due to its characteristics of long-distance support and large capacity [1]. When the ground fault occurs at the AC side of the receiving end converter (REC), the AC voltage sag will reduce the power transmission capacity of the REC [2, 3]. If the wind turbine and the sending end converter (SEC) do not respond, the DC side voltage will rise and exceed the range that the MMC can withstand. It will cause damage to the converter, seriously threatening the system’s safe and stable operation. There are two effective methods that exist to solve the AC side grounding fault of the REC in the offshore wind power generation system. One is to raise the frequency or reduce the voltage of the offshore wind turbine to reduce its output power, and the other is to invest in a dissipative device for dissipated energy in the system [4].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 511–516, 2023. https://doi.org/10.1007/978-981-99-4334-0_64

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Among them, the concentrated energy dissipation arm(C-EDA) has the following advantages compared with several other energy dissipating methods: 1. Compared with the method of limiting the power of the wind turbine, the energy dissipation arm (EDA) on the DC side does not need to communicate with the wind turbine, which improves the reliability of the system, and does not need to consider the power recovery problem after the wind turbine failure; 2. Compared with the AC energy dissipation method, the fault ride through (FRT) method of the DC side concentrated EDA does not need to build the offshore platform, which reduces the construction difficulty and maintenance cost. 3. Compared with the distributed energy dissipation arm, the concentrated energy dissipative arm does not require a water-cooling system, significantly reducing construction and maintenance costs. 4. Compared with adding distributed energy dissipation resistors inside the converter, the EDA at the DC side can avoid effects on the converter caused by the heat generated by the energy dissipation resistors [5].

2 Proposed Concentrated Energy Dissipation Arm The most direct way to control the power of the energy dissipation resistor is to prevent the on-off time of full-control power devices. And the DC link voltage in the high-voltage DC system is higher, and many fully controlled devices need to be connected in series to share the DC link voltage. The shutdown transient process of each switch in the arm is not consistent, which is easy to cause serious voltage imbalance. This study use a switching module that connects the switching device in parallel with a metal oxide varistor(MOV). Each switch module in the arm is formed by a parallel connection of IGBTs, diodes, and MOVs to achieve modularity. This structure uses the voltage threshold characteristics of the MOV to avoid the voltage imbalance problem during the series connection of the IGBT when the state of the IGBT in the arm is inconsistent during the shutdown process. And the volume of energy dissipation stations is effectively reduced compared to other methods. The voltage characteristics are shown in Fig. 1.

1.00 0.50

Shutdown signal

2.00 Without protection device

Safe voltage

0.25

With protection capacitor

Voltage(p.u.)

Voltage(p.u.)

2.00 1.50

With MOV

1.50 1.00 0.50

0.50

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1.25

1.50

Shutdown signal

Safe voltage

Without MOV T1

T1

T1

T1 With MOV

1.00

2.00

3.00 4.00 Time(µs) (b)

5.00

6.00

Fig. 1. The voltage of the IGBTs with MOV.

The resistors of C-EDA need to be arranged outdoors, far away from the power devices in the arm. Therefore, many high-voltage wall bushings are necessary to connect the energy dissipation resistors with other devices in the arm. The cost of high-voltage wall bushings increases significantly with the voltage levels at both ends of the resistance. This paper proposes a combination of a concentrated energy dissipation resistor and transformer, which reduces the voltage at both ends of the concentrated energy dissipation resistor while retaining the advantages of the traditionally C-EDA, as shown in

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Fig. 2. The secondary side of the coupling transformer passes through the outer wall of the building through the high-voltage wall bushing and is connected to both ends of the energy dissipation resistance. The proposed structure greatly reduces the cost of highvoltage wall bushing and improves the overall economy of the shore energy dissipation station [6].

Fig. 2. The structure of the energy dissipation arm.

When a voltage rise on the DC side is detected in the system, the IGBTs in A1, A2 is controlled by a PWM signal. By contrast, the opposite PWM signal is applied to B1, B2 causing alternating current to be generated on the secondary side of the transformer. Then applies voltage to both ends of the energy dissipation resistance. The value of resistance should meet formula (1). Rdiss is the value of the energy dissipation resistor, U dc is the DC side voltage, k u is the unit value of the DC voltage, k t is the transformer ratio coefficient, Pwind is the output power of the SEC. Rdiss = (Udc · ku )2 /kt · Pwind /2

(1)

The power of sending end convert is consistent with that of the wind power generation equipment. The power of wind turbines and SEC Pwind can be shown in the formula(2), I v is the effective value of rated current, U v is the effective value of line voltage, δ is the power angle. √ Pwind = 3IV UV cos δ (2) When the fault occurs on the AC side of the REC, the U v decreases, and the output power of the converter decreases. In this case, increasing the output current appropriately can compensate for the output power reduction caused by AC voltage sag. Thus, an appropriate increase in the output current can maintain the output power at a safe level during the fault to achieve FRT and ensure that the arm device is within a safe voltage range. When other devices do not participate in fault handling, the lowest fault voltage that MMC can achieve by its own regulation ability is shown in formula(3). U vmin is the

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minimum fault voltage, U v is the effective value of rated voltage, I v is the effective value of rated current, I smax is the maximum current that the arm of the MMC can withstand. √ (3) Uvmin = Uv · Iv /(Is max − Idc )/ 2 When the voltage of the AC side of the REC falls below U vmin , the output current must exceed I smax to achieve FRT. Therefore, FRT cannot be achieved by the converter itself without other equipment. The new type of DC-EDA adopts DC voltage and energy dissipation resistance current double closed-loop control. When U dc exceeds the setting value U safe and U v is lower than U vmin , the EDA is put into operation, and the energy dissipation resistance current value I R_exp is calculated according to the surplus power in the system during the fault. When the resistance current I R_diss value is less than I R_exp and U dc is greater than the U safe , the duty cycle increases. When I R_diss is larger than I R_exp and U dc is smaller than U safe , the duty cycle is reduced. To ensure the rapid response of the EDA after the failure, the duty cycle frequency is set as 20kHz. In this structure, when the switch tube is damaged, a series of switch tubes cannot be put into service. In order to improve the reliability of the EDA, the fault operation strategy is implemented when a switch tube is damaged. Only the switch tubes of B1 and B2 are controlled when the switch tube of A1 and A2 is faulty. The duty cycle is adjusted according to the I R_diss and U dc . At this time, the energy dissipation resistance cannot work at full power, and the negative input of the transformer primary current cannot be realized. To ensure that the EDA can cope with higher fault grade in the semi-input fault state, the REC is controlled to adjust the output current to the maximum extent within a safe range and share the surplus energy dissipation pressure of the EDA when the EDA is in the semi-input state. This control method dramatically improves the system’s overall reliability.

3 Simulation Verifications Simulation results are shown in Fig. 3. The change in AC side voltage of the REC after the fault is shown in Fig. 3a. After the fault occurs, the AC side voltage is changed from 1.0 p.u. drops to 0.6 p.u.. Figure 3b shows the average current of the energy dissipation resistance after it is put into the circuit after the system fails at 1s. Figure 3c shows the operating power of the REC and the SEC before and after the system failure. When the system failure occurs at 1s, the power of the SEC does not change, and the power of the REC is limited to 0.6p.u. Figure 3d shows the change of DC voltage before and after the proposed EDA input. It can be seen that after the e EDA input, the DC side voltage is well suppressed, always within ± 0.05, and the protection inside the converter is well realized.

4 Conclusion A novel DC-EDA structure has been proposed to reduce the voltage at both ends of the energy dissipation resistance through a transformer to meet the reliability and economy of future large-scale and higher voltage class offshore wind power systems. And the

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Fig. 3. Simulation results (a) three-phase voltage of REC (b) mean current of energy dissipating resistor (c) power of SEC and REC (d) DC voltage.

structure and control method are analyzed and elaborated, built the simulation model simultaneously, and the feasibility is simulated and verified. The overvoltage problem caused by the inconsistent turn-off time of the power switching device is effectively avoided by connecting the power switching device in parallel with the MOV; The proposed structure of the DC-EDA can effectively reduce the cost of the high-voltage wall bushing by 23 ~ 28% compared with the traditionally C-EDA in view of the 230 kV currently used on the DC side of offshore wind farms. And when the voltage level is further increased, the cost saved will be further increased. Furthermore, it can continue to operate with a specific power when a power switch device in the EDA is faulty, further improving the system’s overall reliability.

References 1. Zhang, H., Xiang, W., Zhou, M., et al.: Cooperative strategy of active energy control and AC energy dissipation device for flexible direct grid-connected offshore wind power system. Proc. CSEE 42(12), 4319–4330 (2022) 2. Li, Z., Zhou, Y., Zhang, N., et al.: Energy diverting converter topology using unidirectional current H-Bridge submodules for VSC-HVDC transmission system. IEEE Trans. Power Electron. 37(5), 5299–5308 (2021) 3. Kirakosyan, A., El Moursi, M.S., Khadkikar, V.: Fault ride through and grid support topology for the VSC-HVDC connected offshore wind farms. IEEE Trans. Power Delivery 32(3), 1592– 1604 (2016) 4. Nanou, S., Papathanassiou, S.: Evaluation of a communication-based fault ride-through scheme for offshore wind farms connected through high-voltage DC links based on voltage source converter. IET Renew. Power Gener. 9(8), 882–891 (2015) 5. Wu, S., Zhang, X., Jia, W., et al.: A modular multilevel converter with integrated energy dissipation equipment for offshore wind VSC-HVDC system. IEEE Trans. Sustain. Energy 13(1), 353–362 (2021)

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6. Li, F. et al.: Summary of research on phase shifting transformer. In: Cao, W., Hu, C., Huang, X., Chen, X., Tao, J. (eds) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Lecture Notes in Electrical Engineering, vol 916. Springer, Singapore (2022)

A Dual Inverter Topology Based on Quasi-Isolated Power Supply and Its Control Strategy Chuanhao Liu1(B) , Jiaxing Lei1 , Yiyang Xiao2 , and Xinzhen Feng3 1 Southeast University, Nanjing 210096, Jiangsu Province, China

[email protected]

2 Southwest Jiaotong University, Chengdu 611756, Sichuan Province, China 3 State Grid Shanghai Energy Interconnection Research Institute Co., Ltd., Nanjing, China

Abstract. The open-end winding motor (OEWM) driven by dual inverters has superior control performance, and there are two main topological forms. However, the independent DC bus needs to use two DC power supplies, the common DC bus generates zero sequence current (ZSC) in the load. To solve this problem, this paper proposes a new dual inverter topology based on quasi-isolated power supply, the DC bus voltage of inverter 1 is passed through the auxiliary converter to output the DC bus voltage of inverter 2. The mathematical model of load zero-sequence component and auxiliary converter is established. Then, the control strategy of the whole system is proposed. The ratio of DC bus voltage can be adjusted, the ZSC can be effectively suppressed, and only using one DC power supply can achieve the same performance as independent DC bus. Finally, the effectiveness of the proposed topology and control strategy is verified by Matlab/Simulink simulation model. Keywords: OEWM · Dual inverter · PWM modulation

1 Introduction The OEWM opens the neutral point of the traditional star-connected winding, and both ends of the winding are respectively connected to an inverter [1]. It not only has the advantages of traditional permanent magnet brushless motor, but also further improves the utilization rate of DC bus voltage and the reliability of the drive system. It has the advantages of fault tolerance [2]. From the perspective of output voltage, dual inverters can be equivalent to multilevel inverters, but they use fewer power devices and have simpler structure and higher reliability [3]. Currently, there are two topologies of widely used dual inverters [4], which are common DC bus and independent DC bus. The dual inverter with independent DC bus is shown in Fig. 1a. The power supply of the two inverters is independent of each other, and there is no ZSC. The output line voltage has a maximum of five levels, but two DC power supplies are needed, which is costly and difficult to achieve in most cases [5]. The © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 517–522, 2023. https://doi.org/10.1007/978-981-99-4334-0_65

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dual inverter with common DC bus is shown in Fig. 1b, which uses only one DC power supply and has low cost. However, the common DC bus provides a loop for the output common mode voltage(CMV), which leads to the abnormal operation of the motor and generates ZSC, and increases the system loss [6].

Fig. 1. Two traditional dual inverter topologies.

Considering the characteristics of two traditional dual inverter topologies, in order to make full use of their advantages, this paper proposes a new topology. The DC bus voltage of inverter 1 is output to the DC bus voltage of inverter 2 through the auxiliary converter, the ZSC can be effectively suppressed by controlling the auxiliary converter. The same effect can be achieved with only one DC supply as with two DC supplies.

2 The Proposed Topology and Its Mathematical Model The topology of the proposed dual inverter is shown in Fig. 2. The DC power supply udc1 provides energy for the entire system.

Fig. 2. The proposed dual inverter topology.

Supposing that the resistance of each phase of the load OEWM is R and the inductance is L, the zero sequence equation can be obtained from Kirchhoff voltage law: (uA1 − uA2 ) + (uB1 − uB2 ) + (uC1 − uC2 ) = R(iA + iB + iC ) + L

d(iA + iB + iC ) dt (1)

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Supposing the CMVs of inverter 1 and 2 are ucm1 and ucm2 respectively. According to the definition of CMV and ZSC [7, 8], Formula (1) can be arranged as follows: (ucm1 − ucm2 )/3 − uO2O1 = Ri0 + L

di0 dt

(2)

where uO2O1 is the voltage between the neutral points of the two inverters. The mathematical equation describing the auxiliary converter can be obtained from Fig. 1 and Kirchhoff’s law: u2 = udc2 + Lf

dif dudc2 , if = i2 + Cf dt dt

(3)

3 Control Strategy 3.1 Modulation Method (1) Modulation of dual inverter For the dual inverter, the load phase voltage is the difference between the phase voltages of the two inverters. For the load reference phase voltage uA * , uB * , uC * , decompose them into the difference of phase voltages between inverter 1 and 2:   ∗ ∗ ux∗ =udc1 ux∗ /(udc1 + udc2 ) − −udc2 ux∗ /(udc1 + udc2 )=ux1 − ux2 , (x = A, B, C) (4) The first and second terms at the right end of the equal sign in Formula (4) are the modulated signals of inverter 1 and 2 respectively. After the modulation signals of the two inverters are obtained, space vector pulse width modulation(SVPWM) is applied to them respectively [9]. (2) Modulation of auxiliary converter To control the ZSC to be zero, the right end of the equal sign of Formula (2) should be equal to zero, so the reference value of uO2O1 is: ∗ uO2O1 = (ucm1 − ucm2 )/3

(5)

And uO2O1 is the voltage on the switch tube S34 , when S33 is on, its value is udc1 , when S34 is on, its value is zero. u2 is the voltage difference between the two bridge arms, and its reference value can be obtained by closed-loop control of udc2 . So for a given reference voltage uO2O1 * and u2 * , there is: ∗ D33 = uO2O1 /udc1 ,u2∗ = (D31 − D33 )udc1

(6)

where D31 and D33 are the duty cycle of switch tubes S33 and S31 , respectively. In this way, the four switch tubes of the auxiliary converter can be controlled to realize the control of the ZSC i0 and the output voltage udc2 .

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3.2 System Control Block Diagram The control block diagram of the proposed topology is shown in Fig. 3. For the dual inverter, the current closed-loop control is adopted. With the reference current, the actual load dq axis current is fed back, and the expected load dq-axis voltage is obtained through PI controller and cross decoupling. And then the load reference phase voltages uA * , uB * , uC * are obtained. The modulated signals of the two inverters can be obtained from Formula (4). The reference voltage signal uO2O1 * can be obtained from Formula (5), which can be used for the modulation of the auxiliary converter. For auxiliary converter, voltage and current double closed-loop control is adopted [10]. The outer loop is the output voltage, the reference value of the inductance current is obtained through the PI controller. The inner loop is the inductance current, the reference value u2 * of the bridge arm voltage is obtained by combining the PI controller with Formula (3). The modulation signal of the H-bridge of the auxiliary converter can be obtained from Formula (6).

Fig. 3. Control block diagram of dual inverter and auxiliary converter.

4 Simulation Verification 4.1 Simulation Parameters The proposed dual inverter and its control model are built in Matlab/Simulink. The simulation time is 0.2s, id * is always zero. And iq * increases from 8 to 12 A at 0.5s, increases from 12 to 17 A at 0.15 s.The ratio of DC bus voltage is 3:1 at 0 ~ 0.1 s, is 2:1 at 0.1 ~ 0.2 s. The main parameters of the system are shown in Table 1. 4.2 Simulation Results and Analysis Figure 4 shows the simulation results. The output voltage of the auxiliary converter is shown in Fig. 4a, it can quickly reach the set value and remain stable, with the increase of load, its low order harmonic component will increase. The load current is shown in Fig. 4b, its sinusoidal degree is very high, and it can quickly follow the command signal, the proposed modulation method can suppress the impact of low order harmonics of udc2 on the load current. The ZSC is shown in Fig. 4c, it can be approximately zero, and its amplitude increases slightly with the increase of the load current, which is about 0.7% of the load current amplitude. The line voltage of the dual inverter is shown in Fig. 4d, it can be output to four or five levels through modulation.

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Table 1. Main parameters. Parameters

Value

Parameters

DC bus voltage of inverter 1/V

450

PWM switching frequency/kHz

Load resistance/

20

Filter inductance of auxiliary converter/mH

Load inductance/mH

15

Filter capacitor of auxiliary converter/µF

Value 16 1 120

Fig. 4. Simulated results.

5 Conclusion In this paper, a dual inverter topology based on quasi-isolated power supply is proposed, and its control strategy is studied. The proposed topology combines the advantages of traditional dual inverters. By controlling the output voltage of the auxiliary converter, the dual inverter can output four or five levels. By controlling the difference between the CMVs of two inverters, the ZSC can be effectively suppressed. Simulation results show the effectiveness of the proposed topology and control strategy. Acknowledgment. This work was supported by the National Key Research and Development Project of China under Grant 2020YFF0305800.

References 1. Takahashi, I., Ohmori, Y.: High-performance direct torque control of an induction motor. IEEE Trans. on Ind. Appl. 25(2), 257–264 (1989) 2. Zhang, X., Xu, C.: Second-time fault-tolerant topology and control strategy for the openwinding PMSM system based on shared bridge arm. IEEE Trans. Power Electron. 35(11), 12181–12193 (2020)

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3. Zhong, L., Hu, S.: Reference voltage self-equalization-based modulation strategy for openend winding PMSM fed by dual three-level inverters with common DC bus. IEEE J. Emerg. Sel. Top. Power Electron. 10(1), 196–206 (2022) 4. Liu, C., Shang, J.: Three-dimension space vector based finite control set method for OWPMSM with zero-sequence current suppression and switching frequency reduction. IEEE Trans. Power Electron. 36(12), 14074–14086 (2021) 5. Chai, N., Hu, W.: A fault-tolerant scheme against the open-switch failure in open-end winding PMSM system with isolated DC bus. IEEE Trans. Energy Convers 6. Yuan, X., Zhang, S., Zhang, C., Degano, M., Buticchi, G., Galassini, A.: Improved finite-state model predictive current control with zero-sequence current suppression for OEW-SPMSM drives. IEEE Trans. Power Electron. 30(5) (2020) 7. Liu, C., Lei, J., Hua, W., Zhang, H., Xi, Y., Wang, S.: A modulation scheme to suppress common-mode voltage of four-level dual inverter. In: 2022 IEEE 5th International Electrical and Energy Conference (CIEEC), pp. 3613–3619 (2022) 8. Hu, W., Nian, H., Sun, D.: Zero-sequence current suppression strategy with reduced switching frequency for open-end winding PMSM drives with common DC bus. IEEE Trans. Ind. Electron. 66(10), 7613–7623 (2019) 9. Shu, Z., Tang, J., Guo, Y., Lian, J.: An efficient SVPWM algorithm with low computational overhead for three-phase inverters. IEEE Trans. Power Electron. 22(5), 1797–1805 (2007) 10. Yin, Y., et al.: Advanced control strategies for DC–DC buck converters with parametric uncertainties via experimental evaluation. IEEE Trans. Circ. Syst. I Regul. Pap. 67(12), 5257– 5267 (2020)

The LCL Type Three-Phase Grid-Connected Inverter Active Damping Design Based on Capacitor Current Feedback Yuhang Zhu1 , Cungang Hu1(B) , Tao Rui2 , Wenping Cao1 , Ke Zhang3 , and Weixiang Shen4 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected]

2 School of Internet, Anhui University, Hefei, China 3 Jiangsu Dongrun Zhilian Technology Co., Ltd., Nantong, China 4 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, VIC 3122, Australia

Abstract. Distributed generation systems based on renewable energy are one of the important ways to cope with the energy crisis and environmental pollution. As an energy conversion interface between renewable energy generation units and the grid, the LCL type grid-tied inverter converts direct current into highquality alternating current and feeds it into the grid. However, LCL grid-connected inverter has obvious attenuation effect on high-frequency harmonics, but there is a resonance problem, and solving this problem is of great significance for the safe, stable and efficient operation of RE-DPGS. Capacitor current feedback active damping can effectively reduce the resonant peak of the LCL filter, which is equivalent to combining a resistor on the filter capacitor under analog control. In this paper, by analyzing the error of steady-state grid-connected current, as well as the phase margin and amplitude margin of the system, the capacitor current feedback coefficient value range that meets the above requirements is obtained. Keywords: Three-phase grid-connected inverter · LCL filter · Active damping

1 Introduction Today’s world is facing a severe situation of energy depletion and environmental pollution. In this context, renewable energy represented by wind and solar which has received a lot of attention because of their rich reserves and environmental friendliness. Distributed grid-connected power generation is one of the main ways of using renewable energy. Grid-connected inverters are interface devices between distributed sources and the grid, and their role is to convert electrical energy from distributed sources into AC energy acceptable to the grid. In order to reduce the harmonics generated by the turn-on and off of the inverter power switch, a filter needs to be added between the grid-connected inverter and the grid. These commonly used filters are L-type filters, the LC-type filter, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 523–531, 2023. https://doi.org/10.1007/978-981-99-4334-0_66

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and the LCL filter. But the LCL filter is widely used because it can obtain better harmonic suppression performance than the previous two filters in the case of low switching frequency and small inductance [1]. However, the LCL filter has a third-order characteristic, and the frequency response has a resonant peak at the resonant frequency, and the phase will jump −180, which will cause the oscillation of the grid-connected inverter to be unstable, so it needs to be damped to reduce this resonance spike [2, 3]. The damping methods for the resonant peaks of LCL filters can be classified into two types: undamped, passive damping, and active damping [4, 5]. Passive damping methods are usually done by connecting resistors in series or parallel across a filter inductor or capacitor. However, the inductor series resistance on the inverter side reduces the lowfrequency band gain, while the shunt resistance reduces the filter’s ability to filter out high-frequency harmonics [6, 7]. The series resistance of the filter capacitor also reduces the ability of the filter to suppress high-frequency harmonics, and heat loss is generated across the resistor [8, 9]. Adding active damping is the introduction of appropriate state variables for feedback, to reduce resonant peaks, such as the voltage or current of the filter inductor or filter capacitor, with no additional passive components and no additional energy loss [10]. In this article, capacitor current is used as the state quantity of feedback. When the capacitor current feedback coefficient is too small, the LCL filter is less effective in damping the resonant peak. If the capacitor current feedback coefficient is too large, the resonant peak can be effectively suppressed, but at the same time the phase margin of the system will be significantly reduced. Therefore, this paper first establishes the mathematical model of LCL three-phase grid-connected inverter, obtains the PI parameters through the undamping test, and then determines the value range of the capacitor current feedback coefficient according to the requirements of system steady-state error, phase edge and amplitude edge.

2 Active Damping of Three-Phase LCL Filter 2.1 A Mathematical Model of the LCL Three-Phase Grid-Connected Inverter As shown in Fig. 1, the grid voltage phase is obtained from the actual sampled grid side voltage (Ea, Eb, Ec) through the three-phase phase-locked loop (PLL) phase locking. The Icd and Icq are obtained by abc/dq transformation of three-phase capacitor currents (ICa, ICb, ICc). The actual instantaneous active current Id_fdb and reactive current Iq_fdb can be obtained by the transformation of the network current (Ia, Ib, Ic) through the abc/dq coordinate system. After we give a reference current value, the error between active reference current Id_ref, reactive reference current Iq_ref and actual value Id_fdb and Iq_fdb is subtracted by the PI controller, Icd and Icq multiplied by feedback coefficient Hi, and then the reference voltage Ud_out,Uq_out in the dq coordinate system are output. Ud_out and Uq_out obtain the given values of the modulation strategy of three-phase grid-connected inverter Ua_out, Ub_out and Uc_out through the transformation of the dq/abc coordinate system, and then generate the switching signals S1, S2, S3, S4, S5 and S6 of each power device of three-phase grid-connected inverter through the modulation strategy.Its basic control principle is shown in Fig. 2.

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Fig. 1. LCL three-phase grid-connected inverter and its control structure.

Fig. 2. Control block diagram.

In the case of three symmetry, Fig. 2 shows the control block diagram of a three-phase grid-tied inverter with an LCL filter. This article ignores the parasitic parameters of the filter inductor and filter capacitor. The inverter uses the sine pulse width modulation (SPWM) strategy. Ginv is the transfer function of the modulation wave to the output voltage of the inverter bridge, and Gi(s) is the transfer function of the grid-tied current regulator. Hi is the capacitor current feedback coefficient. Phase-locked loop (PLL) by detecting grid voltage crossing zeros. The grid connected the current closed-loop regulator Gi (s) adopts a PI regulator. The transfer function is: Gi (s) = Kp +

Ki s

The resonant frequency fr of the LCL filter is:  1 L1 + L2 fr = 2π L1 L2 C

(1)

(2)

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A simplified control block diagram can be obtained by the equivalent transformation of the control block diagram shown in Fig. 2, as shown in Fig. 3. Gxl (s) = Gx2 (s) =

Ginv Gi (s) + sCGinv Hi + 1

(3)

s2 L1 C + sCGinv Hi + 1 + s2 L2 CHi Ginv + s(L1 + L2 )

(4)

s2 L1 C

s3 L1 L2 C

Fig. 3. Equivalent block diagram of control block diagram.

The loop gain of the system T(s) is T (s) = Gx1 (s)Gx2 (s) Ginv Gi (s) = 3 2 s L1 L2 C + s L2 CHi Ginv + s(L1 + L2 )

(5)

Grid-connection current Ig (s) is T (s) Gx2 (s) Iref (s) − Ug (s) 1 + T (s) 1 + T (s) = Ig1 (s) + Ig2 (s)

Ig (s) =

(6)

Ig (s) is represented by the sum of Ig1(s) and Ig2(s). Ig1 (s) =

T (s) Iref (s) 1 + T (s)

Ig2 (s) = −

Gx2 (s) Ug (s) 1 + T (s)

(7) (8)

2.2 Design of Capacitance Current Feedback Coefficient The design of the capacitance current feedback coefficient will make changes in phase margin and amplitude margin and the amplitude gain TFO at the fundamental frequency Fo of the grid connected inverter system, which will be discussed below. It should be noted that the following discussion is based on the unit power factor operation mode of grid connected inverter.

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According to Eq. (5), Fig. 4 is the Bode diagram of the system loop gain before compensation (i.e., Gi (s)) when the capacitance current feedback coefficient Hi is different. The relevant parameters of the system are given in Table 1. It can be seen from Fig. 4 that the greater Hi, the better the damping effect on the resonance peak of the system loop gain; Hi has little influence on the amplitude frequency characteristics of the low frequency band and the high frequency band, but it has obvious influence on the phase frequency characteristics of the system near fr, which makes the phase angle of the system before fr decrease.

Fig. 4. Bode diagram of system loop gain.

The cutoff frequency fc of a closed-loop grid-tied inverter is usually between 0 and 10% of the switching frequency. In order to better reduce the switching harmonics and make the system have better dynamic response characteristics, the resonant frequency fr of the LCL filter is generally designed at 25–50% of the switching frequency. Since the cutoff frequency is relatively small, when the system is below the cutoff frequency, the branch of the filter capacitor can be ignored, and the LCL filter can be simplified to a single-L filter with an inductor value of L1 + L2. According to Eq. (5), the approximate loop gain t (s) can be obtained as: T (s) ≈

Ginv Gi (s) s(L1 + L2 )

(9)

Since at the cutoff frequency fc, the amplitude of the system loop gain is equal to 1, according to Eq. (9):     Ginv Kp  |T (j2π fc )| = 1 ≈  (10) j2π fc (L1 + L2 )  Equation (10) can be rewritten as Kp ≈

2π fc (L1 + L2 ) Ginv

(11)

From Eq. (11), KP determines the system cutoff frequency fc. The larger the Kp, the higher the fc, the faster the dynamic response speed of the system, and the higher the low-frequency gain. However, when fc is close to the resonance frequency fr of the LCL filter, the stability margin of the system will be smaller.

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Since the phase frequency curve of the loop gain of the system crosses −180 at the resonant frequency fr of the LCL filter, the reciprocal of the loop gain amplitude at the resonant frequency is the amplitude edge of the system. At the shear frequency Wc, the phase angle that is added to make the system reach a stable critical state is the phase angle edge of the system.Strictly speaking, to obtain a stable system, the phase angle margin PM needs to be positive, and the amplitude margin needs to meet GM > 1. In order to meet the requirements of system amplitude margin GM , there are: −20 lg|T (j2π fr )| ≥ GM

(12)

(Where GM is in dB.) For the sake of accuracy, the system loop gain T(s) near fr is expressed by the Eq. (5), which is substituted into Eq. (12), and GI (s) is replaced by Kp, and the expression of KP is Eq. (11), then: Hi ≥ 10

GM 20

2π fc L1 Ginv

(13)

After the Kp and Ki parameters that can make the system stable are obtained by trial and error method, fr can be obtained by Eq. (11). To ensure the requirements of system phase margin PM, it is required to meet: ◦

180 +  T (j2π fc ) ≥ PM Substituting formula (5) into formula (14) and finishing, we can get:   2π L1 fr2 − fc2 Ki arctan − arctan ≥ PM Hi1 Ginv fc 2π fc Kp

(14)

(15)

After trying out Kp and Ki parameters that make the system stable, the cut-off frequency fc is determined by Eq. 11. It can be seen from Eq. (15) that the system phase margin PM is related to Hi, and the larger the Hi, the smaller the PM. Therefore, the value range of hi is obtained when the phase angle margin condition is satisfied.

3 Design Example Table 1 shows the relevant parameters of LCL three-phase grid connected inverter. By trial and error, the grid connection current is stabilized at the Kp and Ki parameters of the given value without participating in the grid connection of the three-phase inverter without active damping. Kp = 0.005, Ki = 1。The Kp = 0.005 substitution formula (11) can obtain fc = 0.56 kHz, and the L1 = 0.8 mH and L2 = 0.2 mH substitute formula (2) can obtain fr = 1.78 kHz. During design, it is expected that the phase margin PM of the closed-loop system is more than 45° and the amplitude margin GM is more than 3dB, so as to ensure that the system has ideal dynamic response performance and stability margin.

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Table 1. Relevant parameters of LCL three-phase grid connected inverter. Parameters

Value

Bus voltage

700 V

Grid voltage

220 V

Output power

100 kW

Fundamental frequency

50 Hz

Switching frequency

4 kHz

Inverter side inductance

0.8 mH

Grid side inductance

0.2 mH

Filter capacitor

50 uF

Carrier amplitude

1V

Bus voltage

700 V

Substituting Kp, Ki, fc, and fr into Eqs. (13) and (15) respectively yields the range of values for Hi: [0.0056, 0.03267].Hi takes 0.006, the change of harmonic distortion rate with active damping and no active damping can be verified by simulation. (The given value of the grid-connected current phase current peak is 250 A) (Figs. 5 and 6).

Fig. 5. Grid-connected current waveform and its harmonic distortion without active damping.

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Fig. 6. Grid-connected current waveform and its harmonic distortion with active damping

By setting the appropriate active damping coefficient calculated to add active damping, compared with the harmonic distortion rate without active damping, it is obvious that after the addition of suitable active damping, the harmonic distortion rate decreases significantly, thus verifying the feasibility of the above method.

4 Conclusion Through calculations and example verification, it can be seen that this method is suitable for finding the active damping coefficient in the case of the known current loop Kp and Ki of the three-phase grid-connected inverter. Acknowledgement. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation)—Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

References 1. Bao, C., Ruan, X., Wang, X.: LCL type grid-connected inverter closed-loop parameter design based on PI regulator and capacitor current feedback active damping. Proc. CSEE 32(25), 133–142 (2012). (in Chinese) 2. Yue, Z., Liu, L., Tian, Y.: LCL type grid-connected converter AC/DC double-sided status feedback active damping optimization control. High Voltage Technology (2022)

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3. Nan, G.: An active damping control strategy for current-source grid-connected inverter. J. Northeast Normal Univ. (Nat. Sci. Edi.) 53(1), 77–84 (2021) 4. Liserre, M., Blaabjerg, F., Hansen, S.: Design and control of an LCL-filter-based three-phase active rectifier. IEEE Trans. Ind. Appl. 41(5), 1281–1291 (2005) 5. Yang, D., Ruan, X., Wu, H.: Adaptable virtual impedance approach on improving LCL type grid-connected inverter to weak power grids. Proc. CSEE 34(15), 2328–2335 (2014). (in Chinese) 6. Liserre, M., Aquila, A.D., Blaabjerg, F.: Genetic algorithm-based design of the active damping for an LCL-filter three-phase active rectifier. IEEE Trans. Power Electron. 19(1), 76–86 (2004) 7. Dannehl, J., Fuchs, F., Hansen, S., et al.: Investigation of active damping approaches for PIbased current control of grid-connected pulse width modulation converters with LCL filters. IEEE Trans. Ind. Appl. 46(4), 1509–1517 (2010) 8. Twining, E., Holmes, D.: Grid current regulation of a three-phase voltage source inverter with an LCL input filter. IEEE Trans. Power Electron. 18(3), 888–895 (2003) 9. Blasko, V., Kaura, V.: A novel control to actively damp resonance in input LC filter of a three-phase volage source converter. IEEE Trans. Ind. Appl. 33(2), 542–550 (1997) 10. Dannehl, J., Wessels, C., Fuchs, F.: Limitations of voltage-oriented PI current control of grid-connected PWM rectifiers with LCL filters. IEEE Trans. Ind. Electron. 56(2), 380–388 (2009)

Peer-to-Peer Trading Among Prosumers Based on Cooperative Game Guowei Hu1 , Xiaodong Chen2(B) , Guiyuan Xue1 , Yin Wu1 , and Chen Wu1 1 Economic and Technological Research Institute of State Grid Jiangsu Electric Power Co. Ltd,

Nanjing, China 2 College of Energy and Electrical Engineering, Hohai University Nanjing, Nanjing, China

[email protected]

Abstract. With the massive access to renewable energy and the change in power system operation, users change from traditional energy consumers to prosumers with electricity production/consumption. In this context, we introduce the cooperative game into peer-to-peer (P2P) trading of prosumers to achieve optimal energy management and rational benefit distribution. Firstly, a P2P trading model is established based on cooperative game for prosumers. Secondly, the alternating direction multiplier method (ADMM) is adopted to realize P2P trading in a distributed manner. Finally, Shapley value method is used to allocate the profit of prosumers. The simulation analysis of three prosumers verifies the effectiveness of the P2P trading and proves that the proposed model can effectively reduce the cost of prosumers. Keywords: Prosumer · Peer-to-peer · ADMM · Cooperative game

1 Introduction Nowadays, in the context of a large number of distributed energy access and the development of the electricity market, more and more energy consumers are gradually transforming into prosumers that take into account both electricity production and consumption [1]. Prosumers generally consist of distributed renewable energy, heating, ventilation, air conditioning (HVAC) systems, battery energy storage (BES) and other resources aggregated, with dual attributes of electrical source and load, which are notably characterized by a high degree of integration and interaction between electricity and information [2]. At present, domestic and foreign scholars have achieved many research findings in the energy management and market-based trading of prosumers. The energy sharing mechanism is employed to optimize the scheduling of large-scale prosumer groups in References [3, 4]. Reference [5] studies the demand response of prosumers in a centralized trading model. Reference [6] evaluates the centralized power trading between prosumers through “Source-Load-Storage” cooperative scheduling. However, References [3–6] only consider a single interaction between prosumers and the external grid, and

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 532–541, 2023. https://doi.org/10.1007/978-981-99-4334-0_67

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each prosumer only has energy interaction with main grid, which makes insufficient use of the complementary characteristics and lacks in the optimal utilization of the overall resources. In fact, since the electricity consumption behavior and patterns of multiple prosumers have good complementary characteristics and interactive nature, the research on the trading strategy of prosumers should not be limited to between prosumers and main grid, but should also gradually move towards energy sharing among prosumers. Cooperative game is currently widely used in the coordination and optimization of prosumers, as it can accurately reflect the characteristics of the interactions between prosumers and effectively promote intelligent decision-making. Reference [7] designs a benefit allocation scheme applicable to a cooperative model with the participation of a large number of prosumers. Reference [8] proposes a leasing model for shared energy storage dynamic capacity based on the cooperative relationship between energy storage systems, where the benefits are distributed using Nash bargaining. Reference [9] coordinates the scheduling of multiple prosumers through the park platform to maximize the economic benefits of the park, and Shapley value is adopted to allocate benefits to each user. References [10, 11] investigate the energy sharing strategy of prosumers based on cooperative game and apply the Shapley value method to allocate the cooperative surplus. However, the adoption of centralized management in the above references requires full mastery of information related to electricity consumption resources of prosumers, which involves the issue of user information security. These problems can be avoided through peer-to-peer (P2P) trading, which has attracted widespread attention in recent years. Reference [12] designs a decentralized transaction mechanism of prosumers based on P2P mode to reduce the risk of information exposure. Reference [13] proposes a supply demand ratio method for setting intra-park tariffs, which can coordinate generation or consumption users. In recent years, the alternating direction method of multipliers (ADMM) [14, 15], which transmits less information and iterates faster, has been widely used for P2P trading. References [14, 15] apply ADMM to share resources under the premise of ensuring the privacy and security of participating subjects to achieve secure and economic operation of multiple subjects. Based on previous researches, the distributed transactions between prosumers have been studied a lot, but the profit distribution is not complete. We establish an energy sharing model for prosumers based on the cooperative game with Shapley method, and make a reasonable profit distribution among prosumers. Firstly, the P2P trading model based on cooperative game is established under the premise of energy sharing, then ADMM is used to realize the P2P trading between prosumers to protect the privacy and security of devices. Finally, the profit of prosumers is reasonably allocated according to Shapley value method. On this basis, the effectiveness of the model proposed in this paper is verified through the analysis of three prosumers.

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2 A Cooperative Game-Based P2P Trading Model for Prosumers 2.1 Model In this paper, the P2P trading framework is shown in Fig. 1. Prosumers are connected to the main grid to purchase and sell electricity. The P2P platform is responsible for the P2P transactions between prosumers and the profit distribution. These prosumers contain renewable energy sources, HVAC systems, BESs and basic loads. Prosumer 1 WT

BES

HVAC

Load

P2P Platform

Main grid Prosumer 3

Prosumer 2 PV

BES

PV

BES

HVAC

Load

HVAC

Load

Energy flow

Information flow

Fig. 1. The framework of P2P trading among prosumers.

When prosumers cooperate with each other, a fair and reasonable benefit distribution scheme is an important factor influencing prosumers to join cooperative alliances. The cooperative game emphasizes collective rationality, and the core problem of the study is how the participating subjects carry out cooperation and distribute the benefits obtained from cooperation. In this paper, the objective function of prosumers is to minimize the total cost, which is described as follows:  grid Cn + CnHVAC + Cnbes (1) min n∈N grid

In the formula: Cn , CnHVAC and Cnbes are the cost of purchasing power from the grid, the discomfort cost according to HVAC systems and BES degradation cost of prosumer n. ⎧ grid  grid ,buy buy grid ,sell sell ⎪ Cn = λn,t Pn,t − λn,t Pn,t ⎪ ⎪ ⎪ ⎪ t∈T ⎪ ⎪ ⎨ HVAC  ref in Cn = αn (Tn,t − Tn )2 (2) ⎪ t∈T ⎪ ⎪  ⎪ ⎪ bes ch dis ⎪ λbes ⎪ n (Pn,t + Pn,t ) ⎩ Cn = t∈T

Peer-to-Peer Trading Among Prosumers Based on Cooperative Game grid ,buy

535

grid ,sell

In the formula: λn,t and λn,t are the purchasing price and selling price from the main grid; αn is the coefficient for the discomfort cost; λbes n is the given coefficient buy sell are the for the degradation cost of charging and discharging of BES; Pn,t and Pn,t in and purchased power and selling power from the main grid of prosumer n at time t. Tn,t ref

ch Tn represent the indoor temperature and the comfortable temperature respectively; Pn,t dis are the BES charge and discharge power of prosumer n at time t. and Pn,t Prosumers also need to satisfy the following operational constraints: ch 0 ≤ Pn,t ≤ Pnch,max

(3)

dis 0 ≤ Pn,t ≤ Pndis,max

(4)

bes bes ch dis Sn,t = Sn,t−1 + ηnch (Pn,t ) − (Pn,t )/ηndis

(5)

bes Snbes,min ≤ Sn,t ≤ Snbes,max

(6)

bes bes Sn,T ≥ Sn,0

(7)

in Tn,t = (1 −

1 1 ηHVAC HVAC in out )Tn,t−1 + Tn,t − n P Gn Rn Gn Rn Gn n,t in,min in,max in Tn,t ≤ Tn,t ≤ Tn,t

buy

res dis sell load HVAC ch Pn,t + Pn,t + Pn,t = Pn,t + Pn,t + Pn,t + Pn,t +

(8) (9)



Pn,m,t

(10)

m∈N \n

Pn,m,t + Pm,n,t = 0

(11)

In the formula: Pnch,max and Pndis,max are the maximum charge and discharge power of bes , S bes,min and S bes,max are the storage capacity, minimum storage capacity and BES; Sn,t n n maximum storage capacity; ηnch and ηndis are the efficiency of charge power and discharge power; Gn and Rn are the thermal capacity and resistance of HVAC systems; ηnHVAC is HVAC is the energy consumption of the energy conversion efficiency of HVAC systems; Pn,t in,min in,max HVAC systems; Tn,t and Tn,t are the minimum and maximum indoor temperature res is the renewable energy output of prosumer n at time t; P load is the of prosumer n; Pn,t n,t basic load of prosumer n at time t; Pn,m,t is the exchanged power between prosumer n and prosumer m at time t.

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2.2 Shapley Value-Based Benefit Allocation Strategy Shapley value method is an equitable revenue allocation method in cooperative game [16]. In this paper, Shapley value is used to allocate the profit of each prosumer. This method can fully consider the marginal contribution of each prosumer, and the P2P trading gain of prosumer n can be expressed as: xn =

 (|S| − 1)!(n − |S|)! · Mn N!

(12)

n∈S S⊂N

Mn = v(S) − V (S\{ n}) n ∈ S, S ⊂ N

(13)

In the formula: M n indicates the marginal contribution of prosumer n to the alliance S; |S| is the number of prosumers in S; and |N| represents the total number of prosumers in the game. x n is the profit distributed by prosumer n.

3 ADMM-Based Distribution Scheduling for Prosumers When multiple subjects collaborate to optimize, important information within each subject cannot be fully shared. A centralized scheduling not only makes it difficult to describe the energy interaction process among subjects, but also poses the risk of privacy leakage. In this paper, we adopt ADMM to decouple the coupling between prosumers and obtain the optimal energy interaction value through iterative interaction. To address the coupling constraint Eq. (11), we reformulate it in the following standard ADMM form by introducing an auxiliary variable Pˆ n,m,t . Pn,m,t = Pˆ n,m,t

(14)

Pˆ n,m,t + Pˆ m,n,t = 0

(15)

Then we establish the augmented Lagrangian for the problem as follows: ⎧ ⎡ ⎤⎫  ⎨ grid   λn,m,t (Pn,m,t − Pˆ n,m,t ) ⎬ ⎣ τ ⎦ F= + CnHVAC + Cnbes + C 2 ⎭ ˆ ⎩ n (P − P ) + n,m,t n m=n t 2 n,m,t

(16)

In the formula: λn,m,t is the dual variable and τ is the penalty parameter. The ADMM solution contains three steps. The first step is prosumer n updating its own scheduling policy in the k + 1 iteration: ⎧ ⎡ ⎤⎫ k ⎨ λkn,m,t (Pn,m,t − Pˆ n,m,t ) ⎬   grid ⎣ τ ⎦ min Cn + CnHVAC + Cnbes + k 2 ⎭ ˆ n,m,t ⎩ (17) (P − P ) + n,m,t t m=n 2 s.t. (3) − (10)

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The second step is P2P platform updating the auxiliary variable in the k + 1iteration:     τ k+1 k+1 λkn,m,t (Pn,m,t min − Pˆ n,m,t ) + (Pn,m,t − Pˆ n,m,t )2 2 (18) n∈N m=n t s.t.(16) The third step is P2P platform updating the dual variable in the k + 1iteration: k+1 k+1 k+1 λn,m,t = λkn,m,t + τ (Pn,m,t − Pˆ n,m,t )

(19)

The convergence criteria of the model are that the primal residuals and dual residuals are less than the thresholds.    k+1 k+1 k+1  rn,m,t = Pn,m,t − Pˆ n,m,t (20)  ≤ εr     k+1 k+1 k sn,m,t = Pn,m,t − Pn,m,t  ≤ εs

(21)

The specific flow of the proposed solution is shown in Algorithm 1. Algorithm 1 1: Initialize k = 1, τ = 0.01, λn,m,t = 0; 2: repeat 3: Each prosumer updates its schedule by (18); 4: Update axillary variables by (19); 5: Update dual variables by (20); 6: k = k + 1; 7: until r(k + 1) < ε r and s(k + 1) < εs 8: Distribute profits of prosumers according to (12); 9: Output results: scheduling strategies

4 Example Analysis 4.1 Model Parameters In this paper, simulation tests are performed on the three prosumers shown in Fig. 1. These prosumers contain renewable energy sources, HVAC systems, BESs and basic loads. Prosumer 1 is equipped with wind turbine, and Prosumers 2 and 3 are equipped with PV. The HVAC system parameters are given as follows: Gn = 1.5kWh/°C, Rn = 1.33°C/ kWh and ηn = 0.15. The indoor comfort temperature is set at 20–25 °C for all prosumers. The maximum charge and discharge power of BES is 20 kW and the storage level is limited to [20, 120] kWh. The ADMM penalty parameters is set as 0.001 and the criterion for convergence of primal and dual residuals is set as 0.01 (Fig. 2).

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4.2 Result Analysis Figures 3 and 4 illustrate the energy trading profiles of prosumers with the main grid without P2P trading and with P2P trading. Note that a positive power indicates that prosumers purchase electricity from the main grid; otherwise, they sell electricity. Without P2P trading, prosumers purchase energy directly from the main grid for energy shortages and sell energy to the main grid for energy surpluses, and prosumers interact relatively frequently with the main grid. It can be seen from Fig. 4 that with P2P trading, prosumers significantly reduce the amount of electricity exchanged with the main grid. The comparison results show that the proposed approach can lessen the energy dependency of prosumers on the main grid.

100

Prosumer1 Prosumer2 Prosumer3

Power/kW

50 0 -50 -100 -150

0

2

4

6

8

10

12 14 Time/t

16

18

20

22

24

Fig. 2. Profiles of energy trading with the main grid without P2P trading.

40

Power/kW

20 0 -20 Prosumer1 Prosumer2 Prosumer3

-40 -60 -80

0

2

4

6

8

10

12 14 Time/t

16

18

20

22

24

Fig. 3. Profiles of energy trading with the main grid with P2P trading.

Figure 4 shows the energy flow profile of P2P trading between prosumers. Combined with Fig. 3, when there is a shortage or surplus of energy, prosumers prefer to trade energy with neighboring prosumers to meet energy balance. Prosumer 1, which is equipped with wind turbine, generates high levels of wind power in the early morning and evening, and transmits energy to Prosumers 2 and 3 after meeting its own demand for electricity.

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During daytime hours, Prosumer 1 chooses to purchase electricity from Prosumers 2 and 3 to make up the energy deficit.

Fig. 4. Energy flow profile of P2P trading.

In this paper, Prosumers 1, 2 and 3 are taken as participants in the cooperative game and are numbered from 1 to 3 respectively. There are 7 sub-alliances in the game, which is shown in Table 1. In order to verify the economic benefits of P2P trading, Table 2 shows the cost comparison between prosumers participating in P2P trading and those not participating in P2P trading. It can be found that P2P energy sharing reduces the operating costs of participating prosumers, where Prosumer 1 makes the highest profit for its contributing the most renewable energy to the P2P trading. Table 1. Prosumer portfolio income. Serial number

S

Portfolio income/$

Serial number

S

Portfolio income/$

1

{1}

95.3

5

{1, 3}

−24.8

2

{2}

−156.4

6

{2, 3}

−368.0

3

{3}

−212.8

7

{1, 2, 3}

−130.4

4

{1, 2}

24.6

Table 2. Cost comparison with and without P2P. Prosumer1

Prosumer2

Prosumer3

Cost without P2P energy sharing/$

−95.3

156.4

212.8

Cost with P2P energy sharing/$

−172.5

124.9

178.0

Cost reduction/$

77.2

31.5

34.8

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A schematic diagram of the convergence of primal and dual residuals of the model is given in Fig. 5. We observe from Fig. 5 that the ADMM algorithm takes 37 iterations to converge and the running time is in 50 s. So the model is verified to have good convergence. 10

Primal residual Dual residual

Residuals

1 0.1 0.01 0.001 1E-4 1E-5

10

20

30

40

50 60 Iterations

70

80

90

100

Fig. 5. Convergence of primal and dual residuals.

5 Conclusion In this paper, a P2P trading model based on cooperative game for prosumers is established. The model is solved in a distributed manner based on the ADMM algorithm, and the profit is allocated to the prosumers according to Shapley value method. The simulation test shows that the P2P trading between prosumers can reduce the cost of electricity, and the distribution of the cooperative surplus based on Shapley value method is reasonable, which is conducive to stable cooperation. The proposed model, which is solved in a distributed solution, protects the internal equipment privacy of each prosumer in the P2P transaction, and the model converges well. Acknowledgements. This work was supported by Science and Technology Project of State Grid Jiangsu Electric Power Co., Ltd., (J2021143).

References 1. Ren Hongbo, W., Qiong, L.J.: Economic optimization and energy assessment of distributed energy prosumer coupling local electricity. Proc. CSEE 38(13), 3756–3766 (2018) 2. Qianya, H., Zhenjia, L., Haoyong, C., et al.: Bi-level optimization based two-stage market clearing model considering guaranteed accommodation of renewable energy generation. Prot. Control Mod. Power Syst. 7(3), 433–445 (2022) 3. Yizhou, Z., Zhinong, W., Guoqiang, S., et al.: A robust optimization approach for integrated community energy system in energy and ancillary service markets. Energy 148, 1–15 (2018) 4. Zhao, Y., Xin, A.: Distributed optimal scheduling for integrated energy building clusters considering energy sharing. Power Syst. Technol. 44(10), 3769–3778 (2020)

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5. Jiang, T., Li, Z.N., Jin, X.L., et al.: Flexible operation of active distribution network using integrated smart buildings with heating, ventilation and air-conditioning systems. Appl. Energy 226, 181–196 (2018) 6. Wang, F., Zhou, L.D., Ren, H., et al.: Multi-objective optimization model of source-loadstorage synergetic dispatch for a building energy management system based on TOU price demand response. IEEE Trans. Ind. Appl. 54(2), 1017–1028 (2018) 7. Changsen, F., Jiajing, S., Chongjuan, Z., et al.: Cooperative game-based coordinated operation strategy of smart energy community. Electr. Power Autom. Equip. 41(4), 85–93 (2021) 8. Shuai, X., Wang, X., Wu, X., et al. Shared energy storage capacity allocation and dynamic lease model considering electricity-heat demand response. Autom. Electr. Power Syst. 45(19), 24–32 (2021) 9. Jiechen, W., Xin, A., Yan, Z., et al.: Day-ahead optimal scheduling for high penetration of distributed energy resources in community under separated distribution and retail operational environment. Power Syst. Technol. 42(6), 1709–1717 (2018) 10. Wenshi, R., Hongjun, G., Youbo, L., et al.: Optimal day-ahead electricity scheduling and sharing for smart building cluster. Power System Technol. 43(7), 2568–2577 (2019) 11. Paudel, A., Chaudhari, K., Long, C., et al.: Peer-to-peer energy trading in a prosumer-based community microgrid: a game-theoretic model. IEEE Trans. Industr. Electron. 66(8), 6087– 6097 (2019) 12. Xiupeng, C., Gengyin, L., Ming, Z., et al.: Distributed optimal scheduling for prosumers in distribution network considering uncertainty of renewable sources and P2P trading. Power Syst. Technol. 44(9), 3331–3340 (2020) 13. Nian, L., Cheng, W., Jinyong, L.: Power energy sharing and demand response model for photovoltaic prosumer cluster under market environment. Autom. Electr. Power Syst. 40(16), 49–55 (2016) 14. Wang, C., Wei, W., Wang, J.H., et al.: Convex optimization based distributed optimal gaspower flow calculation. IEEE Trans. Sustain. Energy 9(3), 1145–1156 (2018) 15. Mu, C.L., Ding, T., Qu, M., et al.: Decentralized optimization operation for the multiple integrated energy systems with energy cascade utilization. Appl. Energy 280, 115989 (2020) 16. Ali, L., Muyeen, S.M., Bizhani, H., et al.: Optimal planning of clustered microgrid using a technique of cooperative game theory. Electric Power Syst. Res. 183, 106262 (2020)

Second-Order Cone Based Dynamic Reconfiguration of Distribution Networks Xinjie Sun(B) , Jiangping Jing, Zhangliang Shen, and Liudong Zhang State Grid Jiangsu Electric Power Co., Ltd., Nanjing Power Supply Branch, Nanjing 210019, Jiangsu Province, China [email protected]

Abstract. Distribution network reconfiguration is a part of power system automation, Distributed generation (DG) in distribution network with distributed the increase of the proportion of the active power distribution network faces significant power fluctuations and uncertainty, dynamic reconfiguration technology in balance the system load distribution network, improve the quality of node voltage, reduce the loss of network plays an important role in aspects such as, can satisfy the operating requirements, It can effectively improve the operating parameters of distribution network with less economic cost. This paper studies the distribution network reconfiguration model and method based on second-order cone programming, and establishes a mixed-integer second-order cone programming model for distribution network reconfiguration, considering the uncertainty output of multitime sections of distributed power supply. The validity of the model is verified by testing and calculating the IEEE33 node system. Keywords: Distribution network · Second order cone optimization · Dynamic reconfiguration

1 Introduction The emergence of DG makes the distribution network not only play the role of electric energy distribution in the power system, but further become a new type of electric power interaction system with energy collection, regulation and detection, information interaction and multi-energy complementarity. However, the access of a large number of DGS also brings many challenges to the operation and regulation of distribution networks. In this regard, how to balance the spatio-temporal correlation, improve the decisionmaking ability of distribution network optimization, and then improve the economy of distribution networks has become a concern. Distribution network reconfiguration (DNR) is one of the commonly used measures for optimal operation of distribution network. DNR refers to the control strategy of optimizing single or multiple operation indexes of distribution network by changing the section switch and tie switch on the line to change the network topology under certain operation conditions [1–3]. Different power grid operating indicators, such as minimizing active power loss, balancing distribution network load, increasing the reliability and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 542–552, 2023. https://doi.org/10.1007/978-981-99-4334-0_68

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quality of the power supply, etc., can be chosen for the optimization target of DNR [3–7]. DNR models fall under the following groups from the standpoint of mathematical models: mixed integer nonlinear programming model, mixed integer linear programming model, mixed integer second-order cone programming model, etc. Reference [8] created a nonlinear reconfiguration model of a three-phase unbalanced distribution network and used piecewise linear technology to convert the nonlinear model into a linear model, successfully reducing network loss and voltage variation. A mixed integer second-order cone reconfiguration model of the distribution network was developed in Reference [9], and the reconfiguration technique significantly decreased network loss and maintenance expenses. The DNR model can be classified into single-objective optimization models and multi-objective optimization models according on the objective function. Active power network loss, load balancing, voltage offset, and others are some of the common objective functions in the single objective optimization model, whereas the optimization objective in the multi-objective optimization model is made up of two or more single optimization objectives. Reference [10] establishes a DNR model with minimum network loss, and uses an improved adaptive search algorithm to solve the model. In reference [11], a multi-objective DNR model was created with the least amount of network loss and voltage offset, and the model was then solved using a harmonic search algorithm. Reference [12] established a fuzzy reconfiguration model considering load uncertainty, transformed the equality constraints into fuzzy expressions, and established the membership function of the load according to the reliability measure. In reference [13], a three-phase balanced distribution network was given a static robust reconfiguration model, and the quadratic term was linearly relaxed using piecewise linearization. On this basis, the main problem and sub-problems were decomposed and iteratively solved the reconfiguration scheme. At present, most distribution network reconfiguration problems are established as mixed integer nonlinear programming models, and then solved by intelligent algorithms. Intelligent algorithms have been widely used because of their excellent applicability and modeling convenience. The intelligent class solution technique does, however, have a drawback in that it cannot reliably guarantee that the solution outcome is the overall optimal answer. Because the clever algorithm continuously iterates until it finds the optimal answer, but the result of each optimization has a certain randomness and is easy to fall into local optimization, which also brings some obstacles to the practical application of intelligent algorithm. Although some methods have made corresponding improvements in the iterative mechanism, the local optimization problem still exists. In recent years, more and more analytical algorithms can solve this problem. By changing the model, the analytical method may guarantee that the result is the global optimal result, which has significant benefits for solution stability. This research analyzes the dynamic reconfiguration of the distribution network with the limit of switching times in light of the aforementioned circumstances using the second-order cone model. Establishes a dynamic reconfiguration model with distributed power generation, taking the optimal network loss as the objective function. Finally, carry out the simulation analysis by using the IEEE33 node system, which verifies the validity of the model and algorithm in this paper.

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2 Distribution Network Reconfiguration Model The conventional distribution network reconfiguration model is a mixed integer nonlinear programming model that comprises an objective function, a power flow equation, an equality constraint, a constraint on the voltage amplitude, a constraint on the line capacity, and other constraints. Among these, the active power loss is a significant indicator of the distribution network’s operation and is directly related to the cost of the network’s operation. The active power loss on the line of the distribution network can be successfully decreased by modifying the topology of the distribution network and changing the distribution of the power flow of the distribution system. The specific mathematical model is as follows: min

n 

Pi

(1)

i=0

where, n represents the total number of nodes in the system; Pi Represents the active component of the injected power at the node i. The equation constraint of power flow equation contains quadratic term, so its mathematical form is nonlinear. The specific form of active power injection constraint is as follows:     αij gij Vi2 − Vi Vj gij cos θij + bij sin θij Pi = j∈N (i)

= PDGi − PDi , i = 1, . . . , n

(2)

where, αij represents the connection status of the line ij, αij = 0 represents the disconnection status of line ij and αij = 1 represents the connection status of line ij; θij represents the voltage phase angle difference between node i and j; gij represents the conductance of the line ij; bij represents the susceptance of the line ij; Vi represents the voltage of the node i; PDGi represents the active part of the distributed power supply connected to node i that provides power to the distribution system; PDi represents the active power of the electric load connected to node i. Reactive power injection constraints are as follows:     Qi = αij −bij Vi2 − Vi Vj bij cos θij − gij sin θij j∈N (i)

= QDGi − QDi , i = 1, . . . , n

(3)

where, QDGi represents the distributed power supply component of the access node i that supplies power to the distribution system; QDi represents the reactive power of the electric load connected by the node i. The voltage range must be managed during the distribution network’s regular operations in order to minimize major voltage deviations. The voltage amplitude can neither be too low nor cross the boundary.

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The specific form of voltage amplitude constraint is as follows: Vi min ≤ Vi ≤ Vi max

(4)

where, Vi min and Vi max are the allowable minimum and maximum values of node voltage respectively. It is required to limit the current carrying capacity of the line in order to prevent overloading.

3 Second Order Cone Programming Model Second order cone is an important research direction in mathematical analysis. It has a wide range of applications and a large diversity of application scenarios. Dealing with similar issues across diverse professions is important. It covers many different topics, including as control, finance, machine learning, combinatorial optimization, and other interdisciplinary areas. Second-order cone programming is a technique for maximizing or minimizing a linear function defined by the intersection of a radial subspace and the Cartesian product of a finite number of second-order cones. It is connected to both linear programming and semidefinite programming and is situated between them. Applications for second-order cone programming, a specific example of the symmetric cone programming issue, are quite varied. First, a cone is described as a vector space V and its subset C if and only if the product of any point X and any positive number an in the subset C still belongs to the subset C. A standard cone is shown in Fig. 1:

Fig. 1. Cone diagram.

Moreover, cones are divided into convex cones and non convex cones. The specific definition about convex cone is that if any two points X and Y and any two positive numbers a and B in a cone C have AX + BY belonging to C.

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A standard cone needs to meet the following forms:   C = (x, t)|x ≤ t, x ∈ C n−1 , t ∈ V

(5)

The second-order cone is equivalent to the standard cone’s affine transformation. In geometry, affine transformation, also known as affine mapping, denotes the transformation of one vector space into another vector space via a linear transformation followed by a translation. Ax + b2 ≤ cT x + d

(6)

In fact, cone programming can be regarded as a general linear programming model with nonlinear constraints x ∈ C. Where C needs to be a convex cone. A kind of programming problem with the above conditions is called conic optimization, and its form is as follows: ⎧ T c x ⎪ ⎪ ⎪ ⎨ Ax ≤ r c (7) min 

⎪ x ∈ 1x , ux ⎪ ⎪ ⎩ x∈C where, A is the constraint matrix, x is the decision variable, and c is the cost coefficient of the objective function. Vectors 1x and ux are the upper and lower limits of decision variable x. In order to transform the mixed integer nonlinear programming model into a secondorder cone programming model, several variables ui , Rij , Tij are newly defined. These variables themselves have no physical significance and are only used for the transformation of the model. They are used to replace the nonlinear terms in the original model. The newly defined variables are as follows: √ (8) ui = Vi2 / 2 Rij = Vi Vj cos(θi − θj )

(9)

Tij = Vi Vj sin(θi − θj )

(10)

After reintroducing the newly defined variables into the original power flow equation restrictions, the following new active and reactive power injection equations can be obtained:  Pij = PDGi − PDi , i = 1, ..., n (11) PIi = j∈N (i)

QIi =



j∈N (i)

Pij =

Qij = QDGi − QDi , i = 1, ..., n √

2gij ui − gij Rij − bij Tij

(12) (13)

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√ Qij = − 2bij ui + bij Rij − gij Tij

(14)

2ui uj ≥ R2ij + Tij2 , Rij ≥ 0

(15)

It can be seen that after the substitution, the original nonlinear power flow equation has become a linear form containing only variables ui , Rij , and Tij . On the basis of the second-order substitution of the power flow equation, it is also necessary to add the integer variable indicating the disconnection of the line in the distribution network reconfiguration to the power flow equation. Therefore, it is essential to define two new voltage variables uil , ujl to connect the switching variables αl and the power flow equation. i and j of the variables uil and ujl are the first node and the end node of the line l respectively. Substituting the newly determined voltage for and in the original power flow equation, and the power flow equation is transformed into the following form: √ (16) Pij = 2gij uil − gij Rij − bij Tij √ Qij = − 2bij uil + bij Rij − gij Tij

(17)

2uil ujl ≥ R2ij + Tij2 , Rij ≥ 0

(18)

In addition to the constraints of power flow equation, due to the definition of new variables, several constraints need to be added to establish the relationship between switching variables αl and power flow equation. The new constraints are as follows: Vi2max 0 ≤ uil ≤ √ αl 2

(19)

Vj2max 0 ≤ ujl ≤ √ αl 2

(20)

Vi2max 0 ≤ ui − uil ≤ √ (1 − αl ) 2

(21)

Vj2max 0 ≤ uj − ujl ≤ √ (1 − αl ) 2

(22)

The dynamic reconfiguration of distribution network involves optimization in two dimensions, time and space. The solution process needs to take the actual constraints into account, such as switching operations while considering the changes of various uncertain parameters in the entire reconfiguration period. Segment a period of time, collect the changes of power, load or other parameters in each period, perform static reconfiguration processing in each time period, and then coordinate the reconfiguration results. Some results with the same topology can be initially merged, and then topological merging in adjacent time sections can be performed through some loss reduction indicators. In

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order to reduce the loss of switching operation or reduce the cost of switching operation, it can be dealt with by using the number of switching operation constraints. The number of switching constraints are as follows: ⎧ N    ⎪ ⎪ αij,n+1 − αij,n  ≤ Ts ⎨ n=1

(23)

nb  N    ⎪ ⎪ αij,n+1 − αij,n  ≤ Tt ⎩ l=1 n=1

Among them, Ts is the limit of the number of operations of a single switch, and Tt is the limit of the total number of operations of all operable switches in the system.

4 Case Simulation The IEEE-33 node distribution network system was taken as the test system, and the DICOPT solver was used to solve the above traditional distribution network reconfiguration basic model (MIQCP) based on GAMS optimization platform. The calculation example of 33-node distribution network system includes 33 system nodes, 32 lines equipped with segmented switches, and 5 lines equipped with contact switches. The total active load size of the system is 3715kW, and the total reactive load size is 2300kvar. The initial disconnections are 24–28, 32–17, 8–14, 7–20, and 11–21. The power reference value is set as 10000 kVA, and the line voltage reference value is set as 12.66 kV. The grid structure of IEEE-33 node is shown in Fig. 2:

23

24

26

27

28

25

1

2

4

5

3

19

7 6

20

21

30

31

32

33

11

12

13

14

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8

10 9

16 15

17 18

22

Fig. 2. Grid structure of IEEE-33.

After second-order cone reconfiguration and optimization of IEEE-33 system, the obtained reconfiguration strategy is connected line 7–20, disconnected line 6–7, connected line 8–14, disconnected line 8–9, connected line 11–21, disconnected line 13–14, connected line 17–32, and disconnected line 31–32. The initial active power loss of the distribution network is 202.68 KW, and the active power loss after reconfiguration is 139.55 kW. It can be seen from the results that after the second-order cone reconfiguration optimization, the active power loss of the distribution network has been effectively reduced, and the economy of the system operation has been improved.

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The comparison results of voltage amplitude before and after static reconfiguration are shown in Fig. 3.

Fig. 3. Voltage comparison before and after Reconfiguration.

As shown in Fig. 3, by comparing the voltage amplitude before and after the reconfiguration of distribution network system, it can be seen that the voltage quality has been significantly improved. The node with the lowest voltage before system reconfiguration is node 17, and its voltage amplitude is 0.9131 p.u. The node with the lowest voltage after the distribution network reconfiguration is node 31, and the voltage amplitude is 0.9381 p.u. The results show that the voltage conditions of the majority of system nodes are improved after the optimization of the second-order cone programming, while the voltage conditions of a small number of nodes deviate. The voltage stability and power quality of the distribution network are also generally improved. The above is the result of the static reconfiguration of the system. Divide a day into 24 time sections with an interval of 1h. Add distributed power generations to each time section, and set different distributed power output conditions according to historical data. Respectively, The load on each time section is dynamically processed and change the load demand on different time sections. The distributed power generations are connected to nodes 3, 4, 6, 7, 9, 10, 13, 14, and 16. After adding the switch constraints, perform the dynamic reconfiguration of the distribution network. The dynamic reconfiguration results are shown in Table 1: After the dynamic reconfiguration and optimization of the IEEE-33 node system, the obtained reconfiguration strategy combines 24 time sections into 5 reconfiguration sections, which are t1 ~ t5; t6; t7 ~ t9; t10 ~ t11; t12 ~ t24. Among them, the total number of actions of a single switch does not exceed 3 times, and the total number of switch actions in dynamic reconfiguration does not exceed 20 times. The voltage amplitude comparison results after dynamic reconfiguration are shown in Fig. 4. As shown in the figure above, From the dynamic reconfiguration results of the IEEE33 node system, it can be seen that the voltage results in the two dynamic reconfiguration periods of t6 and t7 ~ t9 are not satisfactory. The voltage results of the remaining three dynamic reconfiguration periods are better, because the output of distributed energy

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Reconstructed section

Disconnected switch

t1 ~ t5

3–4,7–8,10–11,14–15,32–33

t6

9–10,13–14,14–15,32–33,8–21

t7 ~ t9

7–8,9–10,13–14,14–15,8–21

t10 ~ t11

3–4,7–8,9–10,13–14,8–21

t12 ~ t24

3–4,9–10,14–15,32–33,33–34

Fig. 4. IEEE-33 node voltage amplitude Comparison.

resources fluctuates greatly during this period, but it is still within the acceptable deviation range; in the face of such fluctuations, if only static The result will greatly increase the number of switching actions, which will seriously affect the life of the switch and the economics of the distribution network.

5 Conclusion The operation of the traditional distribution network’s power flow distribution and dispatching will be impacted by the access of DG. The purpose of this research is to investigate the impact of dynamically changing DG and load on distribution network reconfiguration and to examine the economics of distribution network in the mixed integer nonlinear distribution network model. By using the second-order cone programming technology, this paper transforms the mixed integer nonlinear optimization model into a mixed integer second-order cone model, and deduces the specific process of model transformation. The IEEE-33 node example test demonstrates the effectiveness of the second-order cone programming model in addressing the issue of distribution network reconfiguration. The findings of

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the calculation example demonstrate that the active power loss of the distribution network can be significantly reduced after the reconfiguration, which also improves the voltage quality of the distribution system and increases the minimum voltage amplitude of the node. Based on the IEEE-33 node system, adding distributed energy modeling, establishing a distribution network optimization model with uncertain output of distributed power generation, dynamic reconfiguration is implemented by limiting the number of switching activities. This calculation example demonstrates how dynamic reconfiguration can reduce active power loss and increase distribution network economics. The penetration rate of DG in the distribution network is on the rise. How to reasonably consider the robustness and conservatism of the distribution network while ensuring the economy needs further research. In the future, robust dynamic reconfiguration can be considered in the reconfiguration method in this paper to ensure higher robustness. Acknowledgement. This work was supported by State Grid Jiangsu Electric Power Co., Ltd. Science and Technology Project (J2021004):Research and Demonstration Application of Key Technologies for Network Source Coordination in Medium and Low Voltage Distribution Networks Based on Operation and Distribution Information Fusion.

References 1. Liu, W., Guo, Z.: Research on security indices of distribution network. Proc. CSEE 23, 85–90 (2003) 2. Bi, P., Liu, J., Liu, C., Zhang, W.: Improved genetic algorithm for distribution network reconfiguration. Autom. Electr. Power Syst. 57–61 (2002) 3. Liu, H., Cheng, L., Huang, J.: Islanding of multi period active distribution network considering intermittent DG and load response. Electr. Power Construbtion 39(2), 50–57 (2018) 4. Liu, L., Chen, X.: Reconfiguration of distribution networks based on fuzzy genetic algorithms. Proc. CSEE 20(2), 66–69 (2000) 5. Fang, J., Li, Z., Zha, W., et al.: Prediction based two-stage fault recovery strategy for isolated active distribution network operation with large number of photovoltaic power supplies. Smart Power 46(11), 47–52 (2018) 6. Wang, X., Wei, Z., Xun, G.: Multi-objective distribution network reconfiguration with distributed power and load uncertainties. Electr. Power Autom. Equip. 116–121 (2016) 7. Yi, H., Zhang, B., Wang, H.: Distribution network dynamic reconfiguration method for improving distribution network’s ability of accepting DG. Power Syst. Technol. 1431–1436 (2016) 8. Wu, Z., Cheng, S., Zhu, C., Xu, J.: Reconfiguration of three-phase unbalanced active distribution network based on linear approximation model. Autom. Electr. Power Syst. 134–141 (2018) 9. Wang, F., Wang, Z.: An optimum reconfiguration method for distribution networks with DG based on mixed integer second-order cone programming. Power Syst. Prot. Control 24–30 (2016) 10. Wu, P., Cheng, H., Liu, Y., Xiong, W.: Distribution network reconfiguration method considering closed loop constraints. Autom. Electr. Power Syst. 163–168 (2017) 11. Li, Y., Zhang, K., Zhang, G., Wang, Y.: Multi-objective integrated optimization of distribution network based on improved harmony search algorithm. Power Syst. Clean Energy 82–86 (2017)

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12. Popovic, D.S., Popovic, Z.N.: A risk management procedure for supply restoration in distribution networks. IEEE Trans. Power Syst. 221–228 (2004) 13. Haghighat, G., Bo, Z.: Distribution system reconfiguration under uncertain load and renewable generation. IEEE Trans. Power Syst. 2666–2675 (2016)

Research on Energy System Planning Method Considering Carbon Trading Yongwei Fan1 , Guotao Song2 , and Tianze Song2(B) 1 Shanghai Energy Technology Development CO.LTO, Shanghai, China 2 College of Energy and Electrical Engineering, Hohai University, Nanjing, China

[email protected]

Abstract. In order to achieve the national strategic goal of non-fossil energy consumption, China has formulated the renewable energy consumption guarantee payment and the implementation of the green card trading system. It is necessary to take the green card trading system into account in the integrated energy system (IES) planning. Therefore, this paper establishes an IES planning model considering carbon trading, takes the costs and benefits brought by green card trading into account in the economic objective function, and obtains the optimal capacity allocation. At the same time, the impact of different green card trading prices (GCTPs) on the planning results is analyzed. The results show that compared with the IES planning model without considering green card trading, the system economy is improved by 10% and the carbon emission is reduced by 31%; The total system cost will not decrease with the increase of GCTP, and the carbon emission will continue to decrease. Through the method of data fitting, the functional relationship between planning cost, carbon emission, power curtailment ratio and GCTP is obtained, which provides a reference for evaluating the performance of IES planning model under different GCTPs in the future. Keywords: Integrated energy system · Carbon trading · Green card trading price · Capacity planning

1 Introduction With the development of society, the problem of environmental pollution is becoming more and more serious. China has put forward the goals of “30 and 60” to make an important contribution to the global environment. The transformation of energy system structure is an important measure for this goal. As a new and excellent energy structure, the integrated energy system (IES) couples a variety of energy forms and strengthens energy coupling, which can improve energy efficiency and reduce carbon emission [1]. In recent years, with the development of China’s renewable energy industry, the establishment of renewable energy quota system and green power card (green card) trading system is an important way for China to promote the development of renewable energy, promote the reform of energy system and achieve the goal of non-fossil energy consumption [2]. Before the large-scale implementation of the green card trading system in China, most of the carbon emissions in the IES were studied in the form of punishment factors. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 553–564, 2023. https://doi.org/10.1007/978-981-99-4334-0_69

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The literature [3, 4] proposed to add carbon emission punishment factors to the planning and operation model of IES to curb the carbon emissions, this sacrificing behavior from the IES to obtain emission reduction benefits is not conducive to the energy industry healthy development, but also damages the interests of the renewable energy industry. With the continuous development of carbon trading market, carbon trading is considered in much IES research. Qu et al. [5] taken the carbon trading price into account in the operation model of electrical interconnected IES, and analyzed the impact of carbon trading price on the operation cost. Literature [6] introduced the carbon trading mechanism into the scheduling model of electric heat gas IES, constructed a ladder carbon trading calculation model, and studied the low-carbon and economy performance. Literature [7] also introduced the stepped carbon trading cost into the IES planning model to study the sensitivity of carbon emissions to the changes of parameters of the stepped carbon trading mechanism. These studies provide a theoretical basis for the urban IES planning considering carbon trading.

2 Planning Model 2.1 Objective Function In the IES planning model, it is necessary to fully consider the factors such as investment income and green environmental protection, integrate the carbon emission behavior into the market economy behavior by introducing green card trading, and optimize the economy of IES planning through optimization theory. The objective function includes the following four aspects: investment cost, annual operation cost, wind and photovoltaic curtailment penalty and green card trading cost. min Ctotal = Cinv + Cope + Cw + Cgreen

(1)

where, Cinv is the annual investment conversion cost of equipment; Cope is the operation cost of equipment; Cw is the wind and photovoltaic curtailment penalty cost; Cgreen is the green card trading cost. Cinv = Cope



λ 1 − (1 − λ)−αi i    = Oi · dm Ei,m,t Ri · Capi ·

i

Cw = ψ ·

m

 t

(2) (3)

t

(Et,r − Et,r )

(4)

r

Cgreen = ffg − fwg

(5)

where, Ri represents the equipment unit capacity investment cost; Capi is the equipment capacity, which is also the decision variable in this study; λ is the discount rate; αi is the service life of the equipment; Oi is the equipment unit operation cost; dm is the operation days; Ei,m,t is the hourly output; ψ represents the penalty factor of wind and photovoltaic curtailment; Et,r and Et,r are the predicted output and actual output of wind and photovoltaic.

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2.2 Models and Constraints Equality constraint. The IES includes various energy demands of cold, heat and electricity. These demands need to be met in real time during planning to ensure the reliability of the system. Hchp,t + Heb,t − Hac,t = Hload ,t

(6)

Pchp,t + Pwt,t + Ppv,t + Ptp,t − Peb,t − Pec,t = Pload ,t

(7)

Cac,t + Cec,t = Cload ,t

(8)

where, Hload ,t , Pload ,t , Cload ,t represent the heat load, electric load and cooling load respectively, Hchp,t , Heb,t , Hac,t are CHP output thermal power, electric boiler output thermal power and thermal power consumption of absorption chiller, Pchp,t , Pwt,t , Ppv,t , Ptp,t are CHP, wind power plant, photovoltaic and coal-fired power plant power output, Peb,t and Pec,t are the power consumption of electric boilers and electric chiller, Cac,t , Cec,t are the output cooling power of absorption chiller and electric chiller. Combined heat and power unit. While generating electricity, the combined heat and power (CHP) unit extracts part of the steam from the steam turbine for heating, and the remaining steam works through the steam turbine to generate electricity [8]. Its mathematical expression is: min max Hchp ≤ Hchp,t ≤ Hchp

(9)

min and H max represent the minimum and maximum thermal output of CHP where, Hchp chp respectively. According to the operation mode of “determining electricity by heat” of CHP unit, the output range of electric power can be expressed as:   ⎧ min ⎪ − cv Hchp,t Pchp,t ≥ max cm Hchp,t − (cm + cv )Hchp,t + Pchp,t , Pchp ⎪ ⎨ max (10) Pchp,t ≤ Pchp − cv Hchp,t ⎪ ⎪ ⎩ Pchp,t ≤ Capchp min , P max respectively represent the minimum and maximum output of CHP where, Pchp chp unit under condensing gas condition; cm is the elasticity coefficient of electric power and thermal power when the CHP unit operates under back pressure. The electric and thermal power output of the unit is converted into the electric power under the pure condensing condition, and the climbing rate of the unit is required to be within a certain range. up

down ≤ (Pchp,t + cv Hchp,t ) − (Pchp,t−1 + cv Hchp,t−1 ) ≤ Pchp Pchp up

(11)

down are the upward and downward climbing limits of CHP unit where, Pchp and Pchp respectively.

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Wind power and photovoltaic model.

Pwt,t = Capwt · Pwt,t

(12)

0 ≤ Pwt,t ≤ Pwt,t

(13)





Ppv,t = Cappv · Ppv,t

(14)

0 ≤ Ppv,t ≤ Ppv,t

(15)



where, Pwt,t and Ppv,t are the unit value of predicted output of wind power and photovoltaic respectively; Pwt,t and Ppv,t are the predicted output respectively, Pwt,t and Ppv,t are the actual output respectively. Electric boiler, absorption chiller and electric chiller models. Heb,t = Peb,t · ηeb

(16)

Cac,t = Hac,t · COPac

(17)

Cec,t = Pec,t · COPec

(18)

where, ηeb is the thermal efficiency of electric boiler, COPac and COPec are the energyefficiency ratio of absorption chiller and electric chiller respectively. Capeb σeb ≤ Heb,t ≤ Capeb

(19)

Capac σac ≤ Cac,t ≤ Capac

(20)

Capec σec ≤ Cec,t ≤ Capec

(21)

where, σeb , σac and σec are the minimum load rate of electric boiler, absorption chiller and electric chiller. Green card trading model. For renewable energy, the proceeds from the sale of green cards are:

T Pwg,t · (1 − β) · Cg (22) fwg = t=1 Eg where, Pwg,t is the renewable energy output; β is the weight coefficient of renewable energy consumption responsibility; Eg is the renewable energy generation required for a single green card; Cg is the GCTP. For thermal power and CHP units, the cost of purchasing green card is:

T (Ptp,t + Pchp,t + cv Hchp,t ) · β ffg = t=1 · Cg (23) Eg

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Capacity constraint Capimin ≤ Capi ≤ Capimax

(24)

where, Capimax and Capimin are the upper and lower limits of the planned capacity of equipment respectively. To sum up, the objective function (1) and constraints (2) - (24) together constitute the IES planning model considering green card trading. The model is a mixed integer linear programming (MILP) model, which is solved by calling the commercial solver Gurobi on the MATLAB platform.

3 Case Study This paper selects a northern city as the research object, and its IES structure is shown in Fig. 1. The system load demand includes cold, heat and electricity. The annual load demand of the case is simulated by Monte Carlo method, as shown in Figs. 2 and 3. In order to reduce the difficulty of solution, this paper ignores the transmission process of power grid, heating network and cooling network. The parameters of equipment are shown in Table 1. In order to respond to the call for energy conservation and emission reduction and reduce the capacity of thermal power, this case sets a higher investment cost and operation cost of thermal power. The renewable energy power generation required by a single green card is set as 1MW, and the price of a single green card is 175 yuan. The weight coefficient of renewable consumption is 30%. In order to compare the planning results of IES considering green card trading, this case (Case 1) also sets a planning scenario without considering green card Trading (Case 2). The planning models of the two cases are only different in whether to consider green card trading model, and other parameters are consistent. Electrical load

WT PV EC TP

Cooling load AC

CHP Heating load EB

Fig. 1. IES planning case diagram.

The optimized cost and other indicators of the two scenarios are shown in Table 2. The equipment capacity configuration results are shown in Figs. 4 and 5. The carbon emissions in Table 2 can be calculated according to the carbon emission calculation formula proposed in document [9], as shown in formula (25). The power curtailment ratio can be calculated according to Eq. (26). Carbon =

T 

2 (α1 (Pchp,t + cv Hchp,t )2 + α2 (Pchp,t + cv Hchp,t ) + α3 + β1 Ptp,t + β2 Ptp,t + β3 )

t=1

(25)

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Fig. 2. Cooling, heating and electrical load.

Fig. 3. Per-unit value of photovoltaic and wind power output.

Table 1. Parameters of equipment. Equipment type

Maximum/minimum capacity(MW)

Investment cost(10,000¥/MW)

Operation cost(10,000¥/MW)

CHP

50/200

790

0.009

WT

50/300

600

0

PV

50/300

430

0

TP

0/200

700

0.03

EB

0/100

120

0

AC

0/100

122.8

0.0008

EC

0/100

250

0.0097

where, Carbon is the carbon emission; α and β are the carbon emission coefficient of CHP and coal-fired power plant. Curt =

T  (Pwt,t − Pwt,t + Ppv,t − Ppv,t ) t=1

Pwt,t + Ppv,t

(26)

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where, Curt is the renewable power curtailment ratio. 3.1 Capacity and Economy Analysis After considering the green card trading, the total planning cost of the system is 36.1762 million yuan less than that without considering the green card trading, a decrease of 10%. Although the overall cost has decreased, the investment cost has increased by 58.1917 million, an increase of 21%. This is because the renewable energy capacity has greatly increased and the investment amount has also increased sharply under the condition that the capacity of other equipment remains basically unchanged, However, due to the increase of renewable energy capacity and the reduction of operation output of other equipment, the operation cost decreased from 92.482831 million in case 2 to 55.717388 million yuan, a decrease of 40%. As the green card trading can bring certain benefits, the planning results will favor the construction of more renewable energy power generation equipment capacity. Among them, the system is more inclined to the construction of wind power because the investment cost of wind power is small and the local wind resources are good. In case 1, the capacity of wind power is 154MW more than that in case 2, and the photovoltaic capacity is 19mw more. The sharp increase of renewable energy capacity leads to a sharp increase in the phenomenon of renewable energy curtailment. The ratio of renewable energy curtailment increases from 2.045% in case 2 to 19.025%. The increase of the proportion of renewable energy also leads to the increase of the capacity of electric boilers. Electric boilers can absorb more renewable energy power generation, and their capacity increases by 26MW, an increase of 49%, At the same time, the planned capacity of thermal power decreased by about 4%. Due to the simple structure of the cooling system, it is not affected by the growth of renewable energy capacity, and the capacity of electric refrigerator and absorption refrigerator has not changed. At the same time, in both cases, CHP is the primary choice, which has reached the upper limit of the planned capacity. The main reason is that it’s wide operation range and high thermoelectric efficiency, although its planning and operation cost are high, it does not affect its excellent operation characteristics. Table 2. Comparison of optimization results. Index Total cost (10,000¥) Power curtailment ratio Carbon emission (ton)

Green card trading (Case 1) 33763.9282 19.025% 2539226.439

No green card trading (Case 2) 37381.55 2.045% 3706326.87

Investment cost (10,000¥)

33948.7401

28129.5654

Operation cost (10,000¥)

5571.7388

9248.2831

Green card trading expenses (10,000¥)

2951.2214

/

Green card trading income (10,000¥)

8815.6416

/

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Fig. 4. Comparison of capacity results under two optimization cases.

3.2 Environment Benefit Analysis After considering the green card trading, due to the increase in the proportion of renewable energy, its annual carbon emissions decreased from 3706326.87 tons in case 2 to 2539226.439 tons, reducing carbon emissions by 31%. The carbon emission of thermal power plant is 18882 tons, and the carbon emission of CHP system is 99991 tons; In case 2, the carbon emission of CHP is 2930134.0045 tons and that of thermal power is 776192.8654 tons. The carbon emissions of both equipment have been greatly reduced. Considering the green card trading, it will have a very far-reaching impact on the operation mode of the system. In order to further describe the impact of green card trading on the system, normalize the three indicators mentioned above: total system cost, carbon emission and power curtailment ratio. As shown in Table 2, considering that the system economy and environmental protection have been improved after the green card trading, but the power curtailment ratio has increased significantly, which requires decision makers to choose appropriate planning methods according to different indicators. 3.3 Sensitivity Analysis In order to further illustrate the impact of GCTP on IES planning, this study will study the impact of GCTP on three types of indicators by linearly increasing the price of green card, so as to analyze the impact of different GCTPs on IES planning. According to the China Green Power integer subscription platform, the trading price of wind power green card is up to 330 yuan/book, the lowest is 128.6 yuan/book, and the trading price of photovoltaic green card is up to 900 yuan/book, the lowest is 518.7 yuan/book. In the future, with the expansion of green card trading market, the price of green card will certainly increase further. The impact of GCTP on the total cost of IES planning, system carbon emission and renewable energy power curtailment ratio is shown in Figs. 5, 6, 7, and 8. In Fig. 5, as the GCTP rises from 100 yuan/book to 775 yuan/book, the total cost of the system continues

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to decline, and the relationship between the total cost and the GCTP is basically a cubic function. The specific expression is as follows: Cinv = 4.6751 × 10−5 x3 − 0.08293x2 − 9.7359x + 37593

(27)

where, x is the GCTP. According to the fitted formula, it can be predicted that when the GCTP reaches 823 yuan, the total cost is 0, that is to say, at this time, the investment cost and operation cost of the system offset each other with the income obtained from the green card trading. According to the current price in the green card market, there is still a certain distance at this stage, but the possibility of existence is not ruled out. In Fig. 6, with the increase of the GCTP, the annual carbon emission of the system continues to decline, but after the GCTP reaches 400 yuan, the annual carbon emission basically remains unchanged with the increase of the GCTP. The main reason is that the capacity of wind power photovoltaic in the model in this paper reaches the planning upper limit, and the GCTP cannot affect the operation state of CHP and thermal power by affecting the capacity of wind power and photovoltaic. The relationship between carbon emissions and GCTP can be fitted into a univariate quartic function as shown in formula (28). Carbon = 6.9449 × 10−6 x4 − 0.01878x3 + 18.961x2 − 8559.2x + 3.5478 × 106 (28) In Fig. 7, the rise of GCTP will aggravate the phenomenon of renewable energy curtailment. With the rise of GCTP from 100 yuan/book to 775 yuan/book, the curtailment ratio also increases from 12.7 to 37.7%, but its growth rate is decreasing. The main reason is that the wind power and photovoltaic capacity are gradually closed to the planned capacity, especially the wind power capacity. When the GCTP reaches 475 yuan, the wind power capacity reaches the planned maximum capacity, In the follow-up planning results, the growth is only the photovoltaic capacity, so the growth of power curtailment ratio slows down. The relationship between power curtailment ratio and GCTP is shown in formula (29). Curt = 8.0112 × 10−10 x3 − 1.8016 × 10−6 x2 + 0.0013967x + 0.0015931

(29)

4 Conclusion This study establishes the IES planning model, takes the green card trading into account in the planning model, studies and analyzes the impact of green card trading on the planning results of IES, and draws the following conclusions: (1) Compared with the IES planning method without considering green card trading, after considering green card trading, the total planning cost is reduced by 10% and the carbon emission is reduced by 31%. However, the power curtailment ratio of renewable energy is increased from 2.045 to 19.025%.

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Fig. 5. The impact of GCTP on total cost.

Fig. 6. The impact of GCTP on carbon emission.

Fig. 7. The impact of GCTP on power curtailment ratio.

(2) After considering the green card trading, the planned capacity of wind power photovoltaic will change greatly, and the system will be more inclined to plan and build more renewable energy power generation capacity. The planned capacity of wind power and photovoltaic will increase by 154 MW and 19 MW respectively. At the same time, on the premise of meeting the cooling, heating and electrical loads,

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Fig. 8. Change trend of three types of indicators with GCTP (normalization).

increasing the capacity of wind power photovoltaic will affect the capacity of electric boiler and thermal power unit. The planned capacity of electric boiler has increased by 26 MW and the thermal power planned capacity has decreased by 5.88 MW. (3) This paper studies and analyzes the impact of GCTP on the planning results of IES, and analyzes the impact of GCTP from three aspects: total cost, carbon emission and power curtailment ratio. The results show that with the linear increase of GCTP from 100 to 775 yuan/book, the total cost of system planning continues to decline. According to the fitted function relationship, it can be predicted that when the GCTP is 823 yuan, the total cost of system will be 0; With the increase of GCTP, carbon emissions continue to decrease, but after the GCTP reaches 400 yuan, carbon emissions basically remain unchanged; With the increase of GCTP, the power curtailment ratio continues to rise, but the rising rate continues to decline. At the same time, this paper fitted the relationship expressions between the total cost of system planning, carbon emissions, power curtailment ratio and GCTP respectively, so as to provide reference for follow-up research.

References 1. Jia, H., Wang, D., Xu, X., et al.: Research on some key problems related to integrated energy systems. Autom. Electr. Power Syst. 39(07), 198–207 (2015) 2. https://guangfu.bjx.com.cn/news/20181126/944275.shtml 3. Haitao, L.I.U., Hainan, Z.H.U., Fengshuo, L.I., et al.: Economic operation strategy of electricgas-heat-hydrogen integrated energy system considering carbon cost. Electr. Power Constr. 42(12), 9 (2021) 4. Qu, K., Huang, L., Yu, T., et al.: Decentralized dispatch of multi-area integrated energy systems with carbon trading. Proc. CSEE 38(3), 11 (2018) 5. Ting, Q., Huaidong, L., Jinqiao, W., et al.: Carbon trading based low-carbon economic dispatch for integrated electricity-heat-gas energy system. Autom. Electr. Power Syst. 42(14), 7 (2018) 6. Chen, Z., Hu, Z., Weng, C., et al.: Multi-stage planning of park-level integrated energy system based on ladder-type carbon trading mechanism. Electr. Power Autom. Equip. 41(9), 8 (2021) 7. Jing, R., Han, H., Lin, J.: Urban energy planning considering impacts of typhoon extreme weather. J. Glob. Energy Interconnection 20(02), 178–187. https://doi.org/10.19705/j.cnki.iss n2096-5125.2021.02.008

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8. Yin, B., et al.: An economy and reliability co-optimization planning method of adiabatic compressed air energy storage for urban integrated energy system. J. Energy Storage 40 (2021) 9. Yang, H., Zhou, M., Wu, Z., et al.: Optimal operation of electro-thermal energy systems with concentrated solar power plant. Power Syst. Technol. 1–12 (2022). https://doi.org/10.13335/j. 1000-3673.pst.2021.0825

Research on Influence of Buried Sand on Cable Temperature Rise Characteristics in Tunnel Jinli Fan(B) , Yaping Deng, Qian Wang, and Qiming Xu Xi’an University of Technology, No.58 Yanxiang Road, Xi’an 710054, China [email protected]

Abstract. In order to study the influence of buried sand conditions on the temperature rise characteristics of cables in the tunnel, a two-dimensional cable model was established in the finite element software COMSOL for simulation. Compare and analyze the temperature difference of cable core between buried sand cable and not-buried sand cable, and investigate the influence of air convection heat transfer coefficient and cable spacing on cable current carrying capacity. The results show that with the increase of the load, the temperature difference between the core of buried sand cable and the core of the not-buried sand cable also gradually increases. Although buried sand conditions will increase the temperature of the cable, the temperature difference under the load of the actual application is small, and the impact of buried sand on the current carrying capacity of the cable is also weak. Burying sand also has a strong fireproof effect, so it is necessary study the influence of buried sand conditions on the temperature rise characteristics of cables. Keywords: XLPE cable · Cable buried in sand · Finite element simulation · Temperature field analysis · Cable laying method

1 Introduction With the continuous improvement of voltage levels, cable transmission has become the main component of power transmission, and temperature is an intuitive indicator to judge its performance. If the temperature of the cable is too high, the copper core will heat up, accelerate its insulation aging, and greatly shorten the service life. If the temperature is too low, its characteristics will not be fully utilized [1, 2]. In order to make more effective use of high-voltage cable lines, it is of great significance to study the current carrying capacity and temperature under different laying environments for the load dispatching of power grid. Cables often cause fires due to excessive temperature. If the faulty cables are not solved in time, serious economic losses will be caused. At present, there are many studies on the influencing factors of the cable temperature rise characteristics in the tunnel [3, 4], and the corresponding solutions are also proposed, but most of these measures are limited to using a kind of materials with certain characteristics, and do not elaborate on a specific material. Therefore, in order to prevent cable fires more efficiently, we © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 565–570, 2023. https://doi.org/10.1007/978-981-99-4334-0_70

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think of adding some fireproof materials when the cables are initially laid. Based on the research content, we focus on sand. Sand is an insulator and does not absorb water. Although sand burying will reduce the current carrying capacity of cables, it is the best fire extinguishing material. In addition, this topic will also study the effect of buried sand conditions on the temperature rise characteristics of cables. The results show that its impact on the current carrying capacity is not as serious as expected. Compared with the heavy losses after the cable accident, it is still necessary to bury the sand in the early stage of cable laying.

2 Model Building The research target of this subject is XLPE cable, the model is ZR-YJLW03 1X630 64/110 kV. The structure and composition details of this type of cable are shown in Fig. 1 and Table 1.

Fig. 1. 110 kV XLPE cable structure section.

Table 1. 110 kV XLPE cable material dimensions. Serial number

Cable structure

Thickness (mm)

Size (mm)

➀

Conductor

30.0

30.0

➁

Strap

0.3

30.6

➂

Conductor shield

1.2

33.0

➃

XLPE insulation

16.5

66.0

➄

Insulation shield

1.0

68.0

➅

Semi-conductive resistance water tape + semi-conductive buffer water-blocking tape

3.3

74.6

➆

Corrugated Aluminum Sheath

2.0

87.7

➇

Semi-rigid flame retardant PVC sheath

4.5

96.7

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2.1 Basic Assumptions When Building the Model It is not practical to completely restore the actual structure of power cable and the current laying situation, so the following assumptions are made when establishing the model [5, 6]. • The outer layer of the cable structure adopts the method of natural convection, the heat generation is the same as the heat dissipation; • When the cable runs under load, the copper core of the cable is the only definite heat source and will not change; • The material properties filled in each layer of the cable structure are also fixed and will not change with temperature. 2.2 Model Parameter Settings Based on the actual situation of cable laying in the tunnel, the shape of the tunnel is defined as a simple rectangle, and the cables are placed near the tunnel wall and arranged in a three-phase “pin” shape. Since it is necessary to compare the actual current carrying capacity of the sand-buried cable and the not-sand-buried cable, the cables in the two cases are placed in the same tunnel space for easy observation and analysis. The width of the tunnel is set to 1500 mm and the height is set to 1800 mm. On the one hand, this size is conducive to laying more cables in the tunnel space, and on the other hand, it is also convenient for the staff to enter the tunnel, which is easy to inspect and troubleshoot. The tunnel is laid in the soil, and the infinite length of soil is infinite relative to the tunnel cross-section area, so the length is ignored and the width is considered, 40 mm of concrete filler is added outside the tunnel, and the basic model of the tunnel cable is completed. 2.3 Heat Loss The heat loss of the cable conductor mainly depends on its AC resistance. According to Ohm’s theorem, the Joule heat loss of the conductor core per unit length is: wc = I 2 R

(1)

where, the I refers to the load current flowing through the high-voltage cable; the R means the AC resistance per unit length at a certain temperature, (/m) Considering the influence of conductor skin effect and proximity effect, the calculation formula of AC resistance of cable conductor:   (2) R = R 1 + ys + yp where, the R is the AC resistance of the conductor at the working temperature; the R· means the DC resistance per unit length (/m) at a certain temperature; the ys means the skin effect factor; the yp means the cable proximity effect factor. The DC resistance of a conductor can be obtained as: R = R0 × [1 + ∂20 (θ − 20)]

(3)

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where, the R0 -DC resistance of cable conductor cores at 20 °C, (/m), Its value can be obtained by the cable manufacturer or by experiment; the α20 means resistivity temperature coefficient at 20 °C, (k −1 ); the θ means maximum operating temperature of conductor, (°C).

3 Influence of Buried Sand on Temperature Rise Characteristics of Cables The simulation diagram of the influence of buried sand conditions on the temperature rise characteristics of cables in the tunnel is shown in Fig. 2. Based on the actual situation of cables buried in sand, The shape of the buried sand should be as close as possible to the shape of the cable, and the sandbag should also have a certain height and width. In order to prevent the mutual influence of the two sets of three-phase cables, the distance between the two should be as far as possible.

Fig. 2. Comparative simulation model diagram of cable buried sand.

Based on the theoretical the thermodynamic parameters of sand are set as   reference, follows: density is 1400 kg/m3 , thermal conductivity is 1.29 (w/(m · k)), and constant pressure heat capacity is 920 (J/(kg · k)). Compared with air, thermal conductivity plays a major role in cable temperature rise characteristics. The external ambient temperature is set to 293.15 k, and the applied current varies from 200 to 900 A. The difference in the maximum temperature of the cable core between the sand-buried cable and the not-sand-buried cable under the same laying conditions is compared and analyzed when different loads are applied.

Fig. 3. Cable simulation temperature rise diagram at 200 A load.

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Figure 3 shows the two-dimensional temperature distribution characteristics of the cable under a load of 200 A. As can be seen from the figure, white indicates that the temperature of the heat distribution process is higher, and purple indicates that the temperature of the heat distribution process is lower. The abscissa and ordinate both represent the position distribution of the cable.

Fig. 4. Comparison of the maximum temperature of buried sand cables and not-buried sand cables under different loads.

It can be seen from the analysis of the above figure that when a certain load is applied, the temperature of the cable buried in the sand is higher than that of the cable not buried in the sand. In combination with Fig. 4, we can also learn that the temperature difference between the intermediate phase cable of buried and not-buried sand increases with the applied load. When the load changes from 200 to 900 A, the temperature difference gradually increases from 1 to 15 °C. There is also a temperature difference between the intermediate phase cable and the other two phases, and it increases with the increase of the load.

4 The Influence of Other Conditions on the Temperature Rise Characteristics of the Cable The effects of air convection heat transfer coefficient and cable spacing on cable current carrying capacity are explored through the control variable method, as shown in Figs. 5 and 6. Figure 5 shows that the current-carrying capacity of the cable increases with the increase of the air convection heat transfer coefficient. The rate of increase is relatively fast at first, and then gradually tends to grow steadily and smoothly. Figure 6 shows that as the distance between the two groups of cables increases, the current carrying capacity of the cables also increases.

5 In Conclusion In this paper, solid heat transfer, single-phase laminar flow and their coupling fields are added to analyze the cable state and the following conclusions are obtained: • The change in cable temperature rise is closely related to the thermal conductivity. The larger the thermal conductivity, the lower the temperature of the cable;

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Fig. 5. Influence of air convection heat transfer coefficient on cable current carrying capacity.

Fig. 6. Influence of cable spacing on cable current carrying capacity.

• Compared with the not-buried sand cable, the buried sand condition will increase the cable temperature. But the temperature difference between them is small under the actual application load. • The temperature of the cable core increases with the increase of the applied load. • With the increase of the distance between the cables, the current carrying capacity of the cable increases, the effect of air convection heat transfer has the same trend.

References 1. Zhang, S., Min, Y., Yuan, J., Ni, Z.: Insulation aging monitoring method of cross-linked polyethylene cable considering load characteristics. In: Cao, W., Hu, C., Huang, X., Chen, X., Tao, J. (eds) Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering. Springer, Singapore (2022) 2. Marie, T.F.B., Han, D., An, B. and Chen, X.: Photoelectric composite cable temperature calculations and correction of the parameters. Int. J. Power Electron. 15(2) (2022) 3. Guo, J.M., Wang, F.F.: Influence of cable temperature rise on PDC method test results of water tree aged cables. E3S Web Conf. 261 (2021) 4. Sedate, A., Leon, G.D.: Thermal analysis of power cables in free air: evaluation and improvement of the IEC standard capacity calculations. IEEE Trans. Nondelivery 29(5), 2306–2314 (2014) 5. Tykocki, J., Jordan, A.: Pareto—ABC analysis of high voltage single core cable temperature. Przeglad Elektrotechniczny 90(10) (2014) 6. Li, X.J., Yang, J., Yan, B.Q., Zheng, X.: Insulated cable temperature calculation and numerical simulation. MATEC Web Conf. 175 (2018)

A Innovative Three-Phase Unbalanced Compensation Range Evaluation for the Combination D-STATCOM Maosong Zhang1 , Chunsheng Guan1(B) , Xiuqin Wang1 , Jun Tao1 , Xian Wu2 , Huaying Zhang2 , and Qunjing Wang1 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China

[email protected] 2 New Smart City High-Quality Power Supply Joint Laboratory of China Southern Power Grid,

Shenzhen Power Supply Co., Ltd., Shenzhen 518020, China

Abstract. Some scholars have proposed a new combination multilevel converter topology composed of CMI and DC side common capacitors. In this combination D-STATCOM, the universal capacitor unit of DC side enables free exchange of active power between the three phase branches. In this paper, by properly distributing the output voltage of the CMI and the universal capacitor unit of DC side, the D-STATCOM achieves the command of the dc-link voltage balancing while reaching the three-phase unbalance compensation. And use the phase analysis, unbalanced compensation capability of the combination D-STATCOM has been quantitatively analyzed, simulation and semi-physical simulation on the combination D-STATCOM model to verify the accuracy of the analysis. Keywords: Active power exchange · Capability of three-phase unbalance compensation

1 Introduction As a crucial equipment in custom power technology, the Distribute Static Synchronous Compensator (D-STATCOM) forms a self-commutation converter through the proper on-off of power electronic switching devices such as IGBT, provide leading or lagging reactive power by altering the magnitude and phase of the output voltage dynamically. D-STATCOM has the advantages of fast response, small size, large capacity, and ideal output characteristics [1–3]. Among them, the D-STATCOM is highly valued and concerned because it is based on a series of cascaded H-bridge modules, high reliability, low waveform distortion rate, and the ability to connect directly to the AC gird through reactors [4]. In the current application of medium voltage distribution system, the main topology of dynamic reactive power regulation is cascaded D-STATCOM., which can be divided into the delta-connection and the star-connection. In [5], the cascaded STATCOM with delta-connection is introduced to compensate for the three-phase unbalance. The voltage © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 571–581, 2023. https://doi.org/10.1007/978-981-99-4334-0_71

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controller of droop control and var reserve control was introduced in delta-connected Hbridge STATCOM in [6]. A class of cascaded D-STATCOM with delta-connection and star-connection was proposed in [7] to achieve the compensation of three-phase unbalance. Due to the cost advantage, the cascaded D-STATCOM based with star-connection has received more attention and application. To realize the compensation of the three-phase unbalance by D-STATCOM, the topology of the DC-link common-capacitor inverter can be adopted in the low-voltage distribution network such as 0.38 and 0.69 kV. In the medium voltage distribution network, the breakthroughs of D-STATCOM should be presented in the theoretical technology and device manufacturing process. Reference [8] have proposed a similar new novel effective D-STATCOM configuration, which composed of several cascaded multilevel inverters (CMIs) and a universal capacitor unit of DC side. In this article, the basic principle of the combination D-STATCOM has analyzed, the ability to distribute the output voltage of the chain unit and the universal capacitor unit of the DC link is the biggest advantage of this topology. The active power exchange between each phase bridge arm is realized, and the DC-link voltage balance of the CMIs and the universal capacitor unit of DC side are realized. In the past, if the unbalance degree was beyond the compensation range, it must cause serious damage to the stable running of the device. Hence, the compensation range needs to be evaluated. The unbalanced compensation range of star-connected and delta-connected Static Var Generator (SVG) were analyzed and discussed in [9]. Still, the method of calculation for the injection of zero-sequence voltage/current was slightly complicated. In order to improve the accuracy of compensation and the speed of static synchronous compensator (D-STATCOM) under unbalanced load, a new linear active disturbance rejection controller is proposed by Reference [10]. In this paper, by properly distributing the output voltage of the CMI and the common capacitor unit of DC side, the combination D-STATCOM achieves the command of the DC-link voltage balancing while reaching the three-phase unbalance compensation of the distribution network. Then the compensation range of the topology is quantitatively analyzed, and the superior effectiveness and unparalleled accuracy of the proposed method are verified by simulation results and semi-physical simulation in RTLAB.

2 Principle of the Combination STATCOM 2.1 Circuit Topology The combination D-STATCOM based on hybrid multilevel topology is illustrated in Fig. 1, composed of three CMIs and a three-phase inverter with a common DC-link. One end of CMIs is directly connected in parallel to the power grid by interface inductor in the star-connection, and the other is connected to the common DC-link inverter. These CMIs can be grouped and named as the master inverter. The basic cell of the master inverter can be two-level H-bridge inverter, diode-clamped three-level inverter, T-type three-level inverter, or flying-capacitor three-level inverter.

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The three-phase inverter, named as the slave inverter. The common ground of these inverters is that they all have a common DC-link, which can be used for the device to exchange active power among its three-phase clusters. Especially, active power can be freely exchanged among the clusters of Modular multilevel converter (MMC), which can be regarded as having a virtual common DC-link.

Fig. 1. Circuit topology of the system configuration.

2.2 Three-Phase Unbalanced Compensation Range Evaluation The key to ensuring stable and reliable operation when compensating reactive and unbalanced loads is appropriately distributing the output voltages of the device between the master and slave inverters, making the output voltages of master inverter and compensation currents are perpendicular to each other respectively.

Fig. 2. Phasor diagram to explain the STATCOM.

Figure 2 shows a phasor-diagram explanation of the operation principle when compensating reactive and unbalanced loads, where V˙ x is the output voltage of the device (x = a, b, c). The subscript “p” and “q” represent the active and reactive component, and “ +” and “−” represent the positive-sequence and negative-sequence components,

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respectively. Phasors I˙x , V˙ sx , jwLI˙x , and V˙ mx are either perpendicular to each other or parallel to each other, as well as the phasors I˙xq+ , I˙xp+ , and U˙ x+ . The master inverter is controlled to generate the desired voltage V˙ mx , which is perpendicular to I˙x . As a result, there is no need to exchange active power among the three CMIs of the master inverter. The rest of V˙ x is generated by the slave inverter, expressed as V˙ sx . The phase angle of V˙ mx is fixed, in order to ensure that the projection of V˙ sx on I˙x is fixed, which results a certain active power that should be exchanged among three-phase clusters.

3 Analysis and Control As shown in Fig. 2, the system voltages and compensation currents can be written as  U˙ x = Ux  θux = U+  θx + U−  (−θx + θun ) (1) I˙x = Ix  θix = Ip+  θx + Iq+  (θx + θiq ) + I−  (−θx + θin ) where θx = 0, − 23 π, 23 π for x = a, b, c respectively, θiq = ± π2 . From (1), the average active power flowing into the three-phase clusters can be obtained as Px =Ux Ix cos(θux − θix ) = U+ Ip+ + U− I− cos(θun − θin ) + U+ I− cos(2θx − θin ) + U− Ip+ cos(−2θx + θun ) + U− Iq+ cos(−2θx + θun − θiq ) (2)

From (2), considering the difference of θx , the average active power can be divided into two parts, one is the same item Ps , the other is the different item Px , that is Px = Ps +Px

(3)

Ps =U+ Ip+ + U− I− cos(θun − θin )

(4)

Px = U+ I− cos(2θx − θin ) + U− Ip+ cos(−2θx + θun ) + U− Iq+ cos(−2θx + θun − θiq ) (5)

Ignoring the active power losses in the device, in the steady state, the total active power exchanged between the system and device should be zero, that is Pa + Pb + Pc = 0

(6)

According to (6), although there is an active power balance between the system and device, there is still an unbalance among the three-phase clusters because of the different item Px .

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Fortunately, the slave inverter has a common DC-link, which can be used to exchange the different item Px by appropriately distributing the output voltage, the average active power equations should be satisfied as (7).  Re[V˙ mx I˙x∗ ] = 0 (7) Re[V˙ sx I˙x∗ ] = Px where I˙x∗ is the conjugate value of I˙x . As shown in Fig. 2, the phase angle of V˙ mx is fixed, but the magnitude is unfixed, which results in many combinations of V˙ mx and V˙ sx . By adding the number of cascaded units, the voltage level of master inverter is easy to raise. Thus, the operating range is limited by the output voltage capability of the slave inverter. Based on (7), in order to get a minimized required output voltage, V˙ sx should be in parallel with I˙x . Thus, V˙ mx and V˙ sx can be expressed as follows. ⎧ ⎨ V˙ mx =Vmx  (θix − π ) 2 (8) ⎩ V˙ =V  θ sx sx ix From Fig. 2 and (8), the steady state model can be written as Vmx  (θix −

π )+Vsx  θix +jωLIx  θix =Ux  θux 2

From (9), voltage phasors can be easily got as ⎧ ⎨ V˙ mx =(ωLIx − Ux sin(θux − θix )) (θix − π ) 2 ⎩ V˙ =U cos(θ − θ ) θ = (P /I ) θ sx x ux ix ix x x ix

(9)

(10)

In general, quasi-proportional resonance (quasi-PR) control is used for the current control. Based on this, the reference value of device output voltage vx∗ can be obtained vx∗ =ux + GPR (s)(ix − ix∗ ) where GPR (s) = KP + ix∗

2K R ωc s , s2 +2ωc s+ω02

(11)

ω0 is the resonance frequency, ωc is the cut-off

frequency, is the instruction current. ∗ and the The reference value vx∗ is composed of the master inverter’s reference vmx ∗ ∗ ∗ ∗ slave inverter’s reference vsx . How to distribute vx between vmx and vsx is very important. For (11), ix is directly known by sampling. The reference value of device’s output voltage ∗ and v ∗ can be written as vmx sx ⎧ ∗ ∗ ∗ ⎪ ⎨ vmx =ux + GPR (s)(ix − ix ) − vsx (12) Px ∗ ⎪ ⎩ vsx = 2 ix |Ix |

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4 Evaluation of Operating Range As shown in Fig. 2, the output voltage magnitudes of the master inverter are close to the system voltages, while the magnitudes of the slave inverter are significantly varied because of the reactive- and negative-sequence currents. For the master inverter based on the cascaded topology, it is effortless to raise the voltage level by adding the number of cascaded units. Thus, the operating range is mainly limited by the slave inverter. From (10), the output voltage magnitudes of the slave inverter can be rewritten as Vsx =Ux (cos θux cos θix + sin θux sin θix )

(13)

In general, the unbalanced degree of the system voltage is minimal. To evaluate this operating range, the negative-sequence component of system voltage will be neglected  U− =0 (14) θux =θx From (1) and (14), it can be obtained that cos θix =

Iq+ cos(θx + θiq ) + I− cos(−θx + θin ) Ix

(15)

sin θix =

Iq+ sin(θx + θiq ) + I− sin(−θx + θin ) Ix

(16)

Substituting (13), (15), and (16) into (13) yields Iq+ cos(θx + θiq ) + I− cos(−θx + θin ) Ix Iq+ sin(θx + θiq ) + I− sin(−θx + θin ) + Ux sin θx Ix

Vsx =Ux cos θx

(17)

where Ix =  2 2 [Iq+ cos(θx + θiq ) + I− cos(−θx + θin )] + [Iq+ sin(θx + θiq ) + I− sin(−θx + θin )] . In the formula (17), it can be clearly seen that under certain system voltage, the output voltage magnitudes of the slave inverter vary not only with Iq+ and I− , but also on θin . To evaluate this dependence, the three-dimensional (3-D) plots show the general relationship of Vsx /Ux with respect to θin and I− /Iq+ . Using the method of numerical analysis, let |Vsx |/Ux = Zx , θin = N , I− /Iq+ = M , and θiq = π/2, from Eq. (17), we can obtain (18), (19), and (20) M cos N (18) Za = √ 1 + X 2 + 2M sin N √ 1 3 + M cos(N + 2 π ) √3 − 1 + M sin(N + 2 π ) 3 2 3 (19) Zb = − 2 − 2 Z+ 2 Z+

A Innovative Three-Phase Unbalanced Compensation Range √ 1 − 3 + M cos(N − 2 π ) √3 − 1 + M sin(N − 2 π ) 2 3 2 3 Zc = − + 2 Z− 2 Z−

577

(20)

 √ where Z+ = [ 23 + M cos(N + 23 π )]2 + [− 21 + M sin(N + 23 π )]2 , Z− =  √ [− 23 + M cos(N − 23 π )]2 + [− 21 + M sin(N − 23 π )]2 . According to (18), (19), and (20), the following are obtained through MATLAB plotting tools, As shown in Fig. 4(a), (b), and (c), they are the variations of the output voltages of the three-phase from the slave inverter with the negative sequence current initial phase θin and unbalance degree Ki = I− /Iq+ , respectively. According to these figures, when 0 < Ki < 1, as the proportion of the negativesequence current to be compensated increases, the output voltage from the slave inverter is also required to increase continuously. When the value of Ki is about 1, |Vsx |/Ux reaches the maximum value of 1, and after that, |Vsx |/Ux either stays near the maximum value or decreases (depending on θin ). In addition, |Vsx |/Ux alters periodically when θin changes. In this paper, max (|Vsx |, |Vsb |, |Vsc |)/U+ is used as a criterion for examining the negative-sequence current compensation capability of the structure. If the ratio is too large, the slave inverter will be over modulated because it cannot output the required voltage, that is, it will go beyond its compensation range. Similarly, Fig. 3(d) can be obtained by the MATLAB drawing tool. In the Fig. 3(d), it can be clearly seen that the result is similar to the change rule of single-phase, except that |Vsx |/Ux alters more frequently with periodicity when θin changes. Therefore, in practical application, according to Fig. 3(d), the appropriate DC-side voltage from the slave inverter can be selected under the condition of available load unbalance degree, and the unbalanced compensation range of the structure can be determined under the condition of known DC-side voltage of the slave inverter.

5 Simulated Results In this paper, a simulation model of 3300 V voltage class combination D-STATCOM is established, in the Simulink function of the software MATLAB, this model is based on the general topology of the multilevel, and its role is to verify the practical feasibility and treatment effectiveness of the combination topology applied to D-STATCOM to achieve the three-phase unbalance compensation. In this simulation model, the twolevel H-bridge inverter as the basic unit of the master converter, and the slave converter is a Neutral Point Clamped (NPC) inverter, is also the universal capacitor unit of DC side. The following Table 1, What it contains is the main simulation parameters of the combination D-STATCOM. Load parameters of the asymmetric load in the simulation are that:Ra = 2.4  and La = 7.2 mH, Rb = 0.6  and Lb = 9 mH, Rc = 2.4  and Lc = 10.8 mH. The positivesequence reactive current is compensated from t = 0.04 s, and the negative-sequence current is compensated from t = 1 s.

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(a) A-phase

(b) B-phase

(c) C-phase

(d) Slave inverter

Fig. 3. Slave inverter unbalance compensation capability analysis diagram.

Table 1. Parameters Parameters

Value

Three-phase system voltage/V

3300

Grid frequency/Hz

50

Cascade numbers of each phase of the master inverter/N

4

Reference value of the DC voltage of master and slave inverters/V

900

DC-link capacitor/F

0.0042

Reactive value of the connected reactor/H

0.002

Figure 4 is a summary of the system voltage and current waveforms. It can find that before t = 1 s, the system voltage and current cannot be in the same phase. After t = 1 s, the negative-sequence current is added into the compensating, so the system currents are balanced and in phase with the system voltages, that is, the reactive and the negative-sequence current are both compensated. Figure 5 are the DC-side’s voltage waveforms of the master and slave inverters. In these figures, both the master and slave inverters can be stabilized near the set value, thus it verifies the effectiveness of the DC-side voltage control strategy. In this simulation model, the initial phase angle of the negative-sequence current is θin = 94◦ , in this case, according to (18)–(20) and the above parameters, compensation range of the new topological can be obtained as follows: 0 < Ki < 0.33.

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Based on the load simulation parameters in Table 1, the actual unbalance degree of the compensation current is Ki = 0.324. For comparison, on the premise that the initial phase angle of the negative-sequence current is unchanged, the load is changed to change the unbalance degree of the compensation current. When t = 2 s, Ki = 0.324; when t = 3 s, Ki = 0.45, the simulation result is shown in Fig. 6.

Fig. 4. System current and voltage waveform.

(a) the master inverters

(b) the slave inverters

Fig. 5. DC-side voltage waveform of the inverters.

(a) DC-side voltage of the master inverter

(b) Modulation wave of the slave inverter

Fig. 6. The System characteristics after changing the unbalance degree.

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In the Fig. 6(a), it can be clearly seen that the DC-side’s voltage of the master inverter is also stable near the set value after t = 2 s, and the modulation ratio is < 1 at this time. However, when t = 3 s, Ki = 0.45, the DC-side voltage of the master inverter cannot be stable near the set value, even there is a significant difference. It can be clearly seen that the phase-to-phase unbalance problem of the DC-side voltage control is not well solved at this time. And the amplitude of the modulated wave of the slave inverter is > 1 as Fig. 6(b), which means that over modulation has appeared from the salve inverter, so the slave inverter cannot produce enough voltage for unbalance compensation. The above verifies the correctness of the theoretical calculation of the unbalanced compensation range in this paper.

6 Conclusion (1) Aiming at the combination D-STATCOM topology, the corresponding output voltage of the salve inverter is calculated. The matching closed-loop control strategy proposed can stabilize the DC-side voltage and it can make the compensation work more effective. (2) Through the quantitative analysis of the output voltage of the salve inverter, the unbalanced compensation capability range of the combination topology is determined. Results of the analysis provide an excellent theoretical basis for the system design and device selection of the combination D-STATCOM. Acknowledgments. This research was funded by Science and Technology Project of China Southern Power Grid, 090000KK52190169/SZKJXM2019669; Key Research and Development Program of Anhui Province, 202104a05020056.

References 1. Wei, X.L., Zhu, G.R., Lu, J.H., Li, W.J., Qi, E.J.: Improved reactive current detection method of SVG. Energies 10, 1374 (2017) 2. Akagi, H., Ogasawara, S., Kim, H.: The theory of instantaneous power in three-phase four-wire systems: a comprehensive approach. IEEE Trans. Ind. Appl. 1, 431–439 (1999) 3. Zhao, J.Q., Liu, X., Lin, C.N., Wei, W.H.: Three-phase unbalanced voltage/VAR optimization for active distribution networks. In: Proceedings of the IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA, 17–21 July 2016, pp. 1–5 (2016) 4. Chang, W.N., Liao, C.H.: Design and implementation of a STATCOM based on a multilevel FHB converter with delta-connected configuration for unbalanced load compensation. Energies 10, 921 (2017) 5. Blazic, B., Papic, I.: Improved D-STATCOM control for operation with unbalanced currents and volt-ages. IEEE Trans. Power Del. 21(1), 225–233 (2006) 6. Peng, F.Z., Wang, J.: A universal STATCOM with delta-connected cascade multilevel inverter. In: Proceedings of the 2004 35th Annual IEEE Power Electronics Specialists Conference. IEEE, Aachen, pp. 3529–3533 (2004) 7. Luo, R., He, Y.J., Liu, J.J.: Research on the unbalanced compensation of delta-connected cascaded H-bridge multilevel SVG. IEEE Trans. Ind. Electr. 65(11), 8667–8676 (2018)

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8. Zhang, M.S., Li, J.W., Chi, B.X., et al.: A novel generalized multilevel converter with the application in D-STATCOM. In: Proceedings of the 2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA) (2017) 9. Ji, Z.D., Sun, Y.C., Li, D.Y., et al.: Comparative analysis for unbalance compensation of cascaded H-bridge STATCOMs between star and delta configuration. High Volt. Eng. 41(7), 2435–2444 (2015) 10. Ma, Y.J., Jiang, X.Y., Zhou, X.S.: Research on application of innovative linear active disturbance rejection control in three-phase four-wire system DSTATCOM. In: Proceedings of the CoEEPE, pp. 495–509 (2021)

Parameter Optimization of the Three-Coil Wireless Power Transmission System Based on Genetic Algorithm Dazhuang Liang(B) , Yunhu Yang, Han Xu, Ruofei Hong, Weina Jia, Yu Li, and Jianzhi Xue School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243000, China [email protected]

Abstract. In three-coil systems, the two performance indexes of transmission efficiency and output power cannot simultaneously reach the maximum value under the same conditions. In order to solve the above problems, the coil turns, the side length of the central turn, the system frequency, the distance between the transmitting coil and the relay coil, and the distance between the relay coil and the receiving coil are taken as optimization variables in this paper, and the product of efficiency and output power is constructed as the objective function. Genetic algorithm is used to obtain the compromise between the efficiency and the output power, and the system parameters used for nonlinear constraints are optimized. Finally, the simulated and experimental results verify the correctness of the optimization methods. Keywords: Wireless power transmission · Three-coil · Genetic algorithm · Nonlinear constraints

1 Introduction The wireless power transmission system (WPT) can improve the flexibility and safety of electrical equipment due to the elimination of physical contact between the power source and the load. WPT playing an increasing role in fields such as electric vehicle battery charging [1–3]. In [4], a two-coil wireless power transfer system is introduced, and a genetic algorithm is used to optimize several parameters, but the output power is not considered. In [5], the parameters such as the resonant frequency, the coil turn, and the coil radius of the micro-robot capsule for wireless power transmission system are optimized by a modified genetic algorithm, but the distance between the coils is not considered as the optimization variable. In [6], only for the issue on the transmission efficiency increasement, the transmission efficiency, transmission distance, voltage gain and other indicators are used as the objective function, and the multi-objective optimization algorithm is used to optimize the system parameters. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 582–587, 2023. https://doi.org/10.1007/978-981-99-4334-0_72

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Due to the insufficiency of the above literature research, this paper takes the coil turn, the length of the center turn, the distance and the frequency as the optimization variables, and uses the genetic algorithm to calculate the maximum value of the product of the system efficiency and the output power to improve the system performance.

2 Three-Coil System Model Analysis Figure 1 presents the schematic diagram of the three-coil wireless power transmission system, U is the root mean square value of the inverter output voltage, R1 and R2 are the parasitic resistances of the transmitting circuit and the relay circuit respectively, and RL is the load. C 1 , C 2 and C 3 are the compensation capacitors of the transmitting coil, the relay coil and the receiving coil, respectively. I 1 , I 2 and I 3 are the root mean square values of the transmitting coil, relay coil and receiving coil current respectively. I1 U

I2 C1

I3 C3

C2 L1

L2

L3

RL

R2

R1

Fig. 1. The schematic diagram of three-coil wireless power transmission system.

Neglect the mutual inductance M 13 , the output power can be expressed as follows,  2 Pout = ˙I3  RL =

2 ω2 M 2 U 2 RL ω02 M12 0 23 2 + R R R + R ω 2 M 2 )2 (RL ω02 M12 1 2 L 1 0 23

(1)

The system efficiency can be expressed as: η =

2 ω2 M 2 RL ω02 M12 0 23 2 (RL ω02 M12

2 ))(R R + ω2 M 2 ) + R1 (R2 RL + ω02 M23 2 L 0 23

(2)

Three-dimensional visualization model related with the three-coil output power and efficient are established as shown in Fig. 2. It can be seen from Fig. 2(a) and (b) that the efficiency and output power cannot reach the maximum value under the same conditions. Therefore, in this paper, the optimized objective function is set as the product of the efficiency and output power.

3 The Implementation of the Genetic Algorithm The optimization objectives of the three-coil wireless power transmission system are as following: Min(−η ∗ Pout (N1 , N2 , N3 , a1 , a2 , a3 , f , D12 , D23 ))

(3)

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（ a ）The relationship between output power and mutual inductance M12, M23

（ b ）The relationship between efficiency and mutual inductance M12, M23

Fig. 2. Three-dimensional surface plot of efficiency and output power.

a1 , a2 and a3 are the coil side length of the transmitting coil, the relay coil and the receiving coil, respectively. N 1 , N 2 and N 3 are the coil turns of the transmitting coil, the relay coil and the receiving coil, respectively. D12 is the distance between the transmitting coil and the relay coil, D23 is the distance between the relay coil and the receiving coil. The farther away from the edge of the transmitting coil, the less the magnetic field distribution, Therefore, in order to avoid the loss of magnetic flux due to the large difference in the size of the three coils, the following nonlinear constraints on coil turns and the coil side length are added. ⎧ |N − N2 | ≤ 12 ⎪ ⎪ 1 ⎪ ⎨ |N − N | ≤ 12 2 3 (4) ⎪ |a1 − a2 | ≤ 0.06 ⎪ ⎪ ⎩ |a2 − a3 | ≤ 0.06 Finally, the optimal solution can be obtained as following: N 1 = 17.015, N 2 = 28.768, N 3 = 17.486, a1 = 0.18843, a2 = 0.24666, a3 = 0.19785, f = 89966, D12 = 0.19579, D23 = 0.1781, η*Pout = 129.43. Figure 3 shows the iterative curve of genetic optimization:

Fig. 3. The iterative curve of genetic optimization algorithm.

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4 The Simulation and Experimental Verification The parameters in the circuit can be obtained, as shown in Table 1. Table 1. The optimal and suboptimal solutions. Parameter

Quantity

Parameter

Quantity

L 1 , L 2 , L 3 /µH

115.2, 394.6, 128.8

M 12 , M 23 /µH

12.572, 16.611

C 1 C 2 C 3 /nF R1 R2 RL /

27.1, 7.9, 24.3

U/V

34

0.11, 0.24, 10

Figure 4 presents the experiment platform of the three-coil WPT.

Fig. 4. Experimental platform of the three-coil wireless power transmission system.

Through simulation, η*Pout = 123.23 W, where η = 0.8102, Pout = 152.10 W, which is consistent with the result calculated by the genetic algorithm. Figure 5 shows the correctness of the algorithm optimization through simulation and experiment. As can be seen from Fig. 5(a), when keep other variables unchanged and gradually reduce the distance D12 between the transmitting coil and the relay coil, η*Pout of the simulation and experiment decreases gradually. In Fig. 5(b), When keep other variables unchanged and gradually increase the distance D23 between the relay coil and the receiving coil, η*Pout of the simulation and experiment decreases gradually. As is the case in Fig. 5(c) and (d). The comparison of the data obtained from the above four simulation and experiments verifies that the distance between the coils is the optimal solution. As can be seen from Fig. 6(a), when N 1 reduces gradually, η*Pout decreases gradually in simulation and experiment. It can be seen from Fig. 6(b) that when the length a1 of the center turn of the transmitting coil increases gradually, η*Pout decreases gradually in simulation and experiment. It can be seen from Fig. 6(a) and (b) that the center turn length and the number of turns obtained by the genetic algorithm are optimal.

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Fig. 5. Experiment and simulation verification of the optimal solution of coil distance.

（a）Keep other conditions unchanged, increase N1

（b）Keep other conditions unchanged, increase a1

Fig. 6. Experimental and simulation verification in the case of the working frequency the coil turns and the side length of the central turn as the optimal solution.

5 Conclusion In this paper, an optimization model is established with parameters such as coil turns, coil side length, frequency and coil distance, then nonlinear constraints are added to simplify the model and maximize the use of magnetic vector lines. In order to achieve the overall optimization of the system, the product of efficiency and output power is taken as the optimization objective, and then the system model is calculated by a genetic algorithm. The simulation and experimental results show that the parameters calculated by the genetic algorithm are optimal and meet the requirements of practical applications.

References 1. Jeong, S., Jang, Y.J., Kum, D., Lee, M.S.: Charging automation for electric vehicles: is a smaller battery good for the wireless charging electric vehicles? IEEE Trans. Autom. Sci. Eng. 16(1), 486–497 (2019)

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2. Zhang, Z., Pang, H., Georgiadis, A., Cecati, C.: Wireless power transfer—an overview. IEEE Trans. Ind. Electr. 66, 1044–1058 (2019) 3. Zhang, J., Yuan, X., Wang, C., He, Y.: Comparative analysis of two-coil and three-coil structures for wireless power transfer. IEEE Trans. Power Electr. 32(1), 341–352 (2017) 4. Hassan, M.A., Hailat, N., Badawi, N., Hussein, A.A.: A wireless power transfer system with optimized circuit parameters using genetic. In: Proceedings of the 2017 8th International Renewable Energy Congress (IREC), pp. 1–4 (2017) 5. Li, M., Liu, D., Liu, X.Q.: Optimal design of wireless power transmission system for micro robotic capsules. J. South China Univ. Technol. 44(11), 78–83 (2016) 6. Liu, W., Li, Y.H., Wang, Y., Li, W.Y.: Parameter optimization of multi-objective genetic algorithm wireless power transfer system. For. Electr. Measur. Technol. 39, 86–90 (2020)

Analysis of Abnormal Working Conditions Influence Over a Self-switching LCC-LCC/S-Based WPT System with CC and CV Weina Jia, Yunhu Yang, Dazhuang Liang(B) , Yu Li, Jianzhi Xue, and Zhi Yang School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243000, China [email protected]

Abstract. A self-switching LCC-LCC/S-based WPT system with constant current (CC) and constant voltage (CV) is proposed in this paper. By switching the two switches on the secondary side, the proposed system can not only realize the CC/CV output, but also effectively deal with various abnormal working conditions. Keywords: Wireless power transfer · Constant current and constant voltage · Composite topology

1 Introduction At present, there are several ways to achieve CC/CV charging for WPT systems. The first one is the working frequency adjustment [1–3]. The second one is the duty cycle adjustment [4, 5]. The above three methods can achieve CC/CV charging with high control accuracy, but the closed-loop control is too complex. The fourth one is that an AC switch is added at the primary side or the secondary side. The literature [6] uses a variable structure LC-CLCL topology to achieve CC and CV charging, but the output current and the output voltage fluctuate greatly for the switch action duration, which will cause the battery shock and reduce the battery life. The literature [7] proposed a hybrid S/P-S/SP compensation topology. Although the circuit structure is simple, the voltage transient response on the AC switch is not analyzed. This paper proposed WPT system can not only achieve the segmented CC and CV charging, but also effectively improve the system safety under abnormal working conditions.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 588–593, 2023. https://doi.org/10.1007/978-981-99-4334-0_73

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2 Analysis of the Working Principle and Characteristics of Hybrid Topology The proposed LCC-LCC/S self-switching CC and CV composite topology is shown in Fig. 1. The IGBTs T 1 and T 2 are connected in reverse series to compose a AC switch as shown in Fig. 2.

Q1

CS

Q3 Cp L1

Vin

C1

Q2

Q4

iL1

. . M

LP ip

CS1

D1

CS2

LS

S1 iS

D2

L2 C2

Co

Ro

Vo

S2 iL2 D3

D4

Fig. 1. LCC-LCC/S self-switching constant current and constant voltage composite topology.

T1

T2

Fig. 2. AC switch with 2 IGBTs connected in reverse series.

The relationship between the switches state and charging mode is shown in Table 1. Table 1. The relationship between switching state and output mode. Working mode

Compensation topology

Switch status

CC mode

LCC-LCC

S 1 , S 2 on

CC mode

LCC-S

S 1 , S 2 off

Neglecting the parasitic resistance RS , the output current of the LCC-LCC topology can be expressed as M U˙ in I˙L2 = jωL1 L2

(1)

From the above equation, it can be seen that the LCC-LCC topology can achieve load-independent CC characteristics at the resonant frequency. Neglecting the parasitic resistance RS , the output voltage of the LCC-S topology can be expressed as M U˙ in U˙ o = L1

(2)

From the above equation, it can be seen that the LCC-S topology can achieve the load-independent CV characteristic.

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Therefore, The WPT system compounded the LCC-LCC topology with the LCCS topology can achieve CC-CV charging for two different duration by the rational parameter design. In order to make the output power little fluctuation for the two switches S 1 and S 2 switching duration, the following principle need be satisfied, Pout−CC = Pout−CV =

U˙ in2 LP LS R M 2 U˙ in2 R M2 × = 2 2 L1 L2 L21 (ω2 L2 + 2RRS ) L1 (R + RS )2

(3)

Taking the equivalent resistance R as variable and the other parameters in formula (3) as constants, the resistance R can be calculated to be 8.1 .

3 Analysis of the and Characteristics of Hybrid Topology During the charging process, abnormal working conditions such as secondary side missing, load open-circuit, load short-circuit may occur. Therefore, it is necessary to analyze the abnormal working conditions so that the system can timely deal with them to avoid the device damage. Figure 3 presents the simulated curves of I L1 , I C1 , and I P for the duration of the secondary side missing. The system can automatically cope with the secondary side missing during the charging process without any detection device.

Current (A)

IP

IS

Secondary side missing

Current (A)

IL1

IC1

Secondary side missing Time (s)

Fig. 3. The current of Ip, Is, I L1 , and I C1 for the duration of the secondary side missing.

Current A

Current A

Similarly there shows a current surge in the receiving coil, as shown in Fig. 4. IP

IS

Open load

IL1

IC1

Open load Time (s)

Fig. 4. The current of Ip, Is, I L1 , and I C1 in CC mode for the duration of the load open circuit.

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IP

IS

Load short circuit

IL1

IC1

Current

A

Current

A

The equivalent circuit diagram of the load open circuit in CV mode is the same as that of its secondary side missing, which is not interpreted repeatedly here. It can be seen that the input current I L1 and the receiving coil current I S increase rapidly for the duration of the load short-circuit in CV mode, and similarly I C1 increases rapidly, the simulated waveform is shown in Fig. 5.

Load short circuit Time (s)

Fig. 5. The current of Ip, Is, I L1 , and I C1 in CV mode for the duration of the load short circuit.

These two topologies can effectively cope with the secondary side missing, but the LCC-LCC topology cannot cope with the load open circuit, and the LCC-S topology cannot cope with the load short circuit. Therefore, when the load open circuit occurs in the CC mode, the WPT system requires switching the LCC-LCC topology to the LCC-S topology, and when the load short circuit occurs in the CV mode, the WPT system requires switching the LCC-S topology to the LCC-LCC topology. This topology switching can not only improve charging safety, but also avoid effectivity component damage under abnormal operating conditions.

4 Simulation and Experiment The experiment platform is shown in Fig. 6. DC source

Primary side compensation inductance

Secondary side compensation inductance

Rectifier

Load

Primary side drive Secondary side drive Inverter

Receiver coil

Oscilloscope

TMS320 F28335 Transmitter coil

TMS320 F28335

Fig. 6. Experimental platform.

The parameters of the experimental platform are shown in Table 2. It can be seen from Fig. 7 that the voltage is basically in phase with the current, it will not produce reactive energy and can realizes ZPA. It can be seen from the Fig. 8 that the efficiency in simulation is basically the same as that on experiment and with a high efficiency.

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Parameters

Value

Parameters

Value

Parameters

Value

U in (V) U output-max (V)

100

C 1 (nF)

94.7

L P (µH)

48.11

C S2 (nF)

115.3

48.92

C P (nF)

330.4

L S (µH)

55.07

C 2 (nF)

230.18

I output-max (A)

5.03

L 2 (µH)

15.20

L 1 (µH)

37.2

M(µH)

17.26

f (kHz)

85

C S1 (nF)

90

Uin=99.5V

I L1=2.65A

i L1(5A /div)

Uin=99.6V

I L1=2.57A

U in(150V /div)

i L1(5A /div) U in(150V /div)

Parameters

t(5μs/div)

t(5μs/div)

(a) Voltage and current output by inverter in CC mode

(b) Inverter output voltage and current in CV mode

Fig. 7. Experimental waveforms of inverter output voltage and current.

Efficiency

Experimental efficiency Simulation efficiency

8.1

Equivalent resistance R (Ω)

Fig. 8. The efficiency comparison between on experimental and in simulation.

It can be seen from the Fig. 9 that the current Ip of the transmitting coil remains basically unchanged for the duration of the secondary side missing, It is consistent with the results of both theoretical analysis and simulation analysis. The secondary side missing

The secondary side missing

IL1

I(10A/div)

I(10A/div)

IS

IC1 IP

t (20μs/div)

t (10μs/div)

(a) The current through the transmitter coils and (b) The current through the compensation capacitor the receiver coils C1 and the compensation inductor L1

Fig. 9. Experimental current waveform for the duration of the secondary side missing.

Analysis of Abnormal Working Conditions Influence Over

593

5 Conclusion A circuit model based on LCC-LCC/S composite topology is proposed to apply for a WPT system in this paper. By adding both two AC switches and an additional capacitor on the secondary side, the two-stage charging CC/CV mode is realized. The proposed system can effectively deal with the abnormal working including the secondary side missing, the load short circuit and the load open circuit during the charging process. At last, a self-switching LCC-LCC/S-based WPT system is fabricated to obtain the expected performance of safety, reliability and high efficiency.

References 1. Wang, M., Feng, J., Shi, Y., Shen, M.: Demagnetization Weakening and Magnetic Field Concentration with Ferrite Core Characterization for Efficient Wireless Power Transfer. IEEE Trans. Ind. Electr. 66(3), 1842–1851 (2019) 2. Li, Z., Zhu, C., Jiang, J., et al.: A 3kW wireless power transfer system for sightseeing car supercapacitor charge. IEEE Trans. Power Electr. 32(5), 3301–3316 (2017) 3. Wang, C.S., Stielau, O.H., Covic, G.A.: Design considerations for a contactless electric vehicle battery charger. IEEE Trans. Ind. Electr. 52(5), 1308–1314 (2005) 4. Wu, H.H., Gilchrist, A., Sealy, K.D., et al.: A high efficiency 5kW inductive charger for EVs using dual side control. IEEE Trans. Ind. Inform. 8(3), 585–595 (2012) 5. Wu, X., Hu, C., Du, J., et al.: Multistage CC-CV charge method for Li-ion battery. Math. Probl. Eng. 6(4), 23–34 (2015) 6. Liao, Z., Zhou, L., Wu, Z., et al.: An electric-field coupled power transfer system with CC and CC output based on changeable LC-CLCL resonant circuit. Proc. CSEE 41(17), 6039–6050 (2021) 7. Zhang, H., Wang, H., Li, H., et al.: Analysis on hybrid compensation topology circuit for wireless charging of electric vehicles. Autom. Elect. Power Syst. 40(16), 71–75 (2016)

Design of Wide Voltage Range DC–DC Converter Based on SiC MOSFET Xinying Wang1 , Xiaofeng Tao2 , Leilei Zhan3 , Xin Tang1 , Yonghao Sun1 , Yibo Sun1 , Chaohui Cui1 , Haoran Li1(B) , Cungang Hu1 , Ke Zhang4 , and Weixiang Shen5 1 School of Electrical Engineering and Automation, Anhui University, Hefei, People’s Republic

of China [email protected] 2 Anhui Provincial Department of Finance, Anhui, China 3 Towngas Energy Investment Limited, Quarry Bay, China 4 Jiangsu Dongrun Zhilian Technology Co., Ltd, Nantong, China 5 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, VIC 3122, Australia

Abstract. In order to realize the DC/DC converter with large current input and wide output voltage range, a design scheme of current sharing by multiple modules in parallel is proposed. Each module is composed of BOOST converter and LLC converter in cascade. SiC MOSFET is used as the switching devices in the converter. This design scheme can reduce voltage stress, current stress and circuit loss, and improve circuit efficiency. Calculate the parameters of key components in the circuit and complete the type selection design, build a single module prototype, and measure the reliability of the converter design. The experimental results show that the design scheme is reasonable and reliable, which is of great significance for the research of wide voltage range DC/DC converter. Keywords: DC/DC converter · High voltage input · Wide range · BOOST circuit · LLC circuit

1 Introduction DC/DC Converter is widely used in vehicle charger, wireless charging system, motor drive system and other fields [1–3]. Therefore, in order to adapt to the more and more extensive application fields, the research on wide input voltage range, wide output voltage range and high efficiency DC/DC converter is of great significance [4–6]. Studying the corresponding circuit topology and the selection of key components can further optimize the circuit structure and improve the circuit efficiency. To ensure the reliability of DC/DC converter, SiC MOSFET is used as the switching devices. Compared with traditional switching devices, SiC MOSFET can greatly improve the performance of the converter due to its wide band gap, high switching frequency, good thermal stability and other advantages [7]. According to its switching characteristics, many scholars have carried out research in related fields [8]. Due to the particularity of materials, SiC © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 594–602, 2023. https://doi.org/10.1007/978-981-99-4334-0_74

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MOSFET can work under high voltage, high frequency, high temperature and other severe conditions, so it has gradually become a popular choice for such converters [9]. In addition, the selection of components in the converter often affects the operation efficiency and application range of the converter. Therefore, it is also important to calculate the parameters of each component and select a reasonable type for improving the performance of the converter.

2 Topology of DC–DC Converter Wide input high-voltage DC–DC converter often brings problems such as high voltage stress, high current stress and high circuit loss. Therefore, this paper proposes a DC–DC converter structure that can be applied to wide voltage input range and large current. First, five modules are connected in parallel for voltage division to reduce the voltage stress borne by each module. The module connection mode is shown in Fig. 1. Secondly, in a single module, the circuit topology is divided into two parts, consisting of BOOST converter and LLC converter cascaded. BOOST converter adopts six interleaved parallel structures to reduce current ripple and harmonic effects. In the LLC converter, the transformer is used to isolate the low-voltage side and the high-voltage side. The primary side of the transformer is connected in series and the secondary side is connected in parallel. The working frequency is always kept near the resonance point, which can not only achieve two-way energy transmission, but also achieve high efficiency. The single module topology is shown in Fig. 2.

Fig. 1. Multi module parallel connection.

2.1 BOOST Converter Due to the large input current, some BOOST converter adopt a six channel interleaved parallel structure, and the phase difference between each channel is 60° in turn. This can not only reduce the impact of harmonics, but also reduce the current flowing through each circuit, reduce the current stress, expand the selection range of devices, reduce the cost of devices, reduce the circuit loss, and improve the efficiency of the converter. Among them, the switching devices in the circuit are all SiC MOSFET, the upper and lower switching devices are mutually connected, and the purpose of voltage transformation is achieved by adjusting the duty cycle.

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X. Wang et al. Q 21

36~60V L1

200~360V

100~180V

Q11

S3

S1

1:1 Lr

Q 22 L2

L3

L4 L5

*

*

Q 12 Q 23

S4

S2

Q 24

S7

S5

Q 13

Q 14

S8

Q15

M1 Cbus1

Lm M4

M2

1:1 *

Q 25

M3

*

Lm Cr

S6

Q 26 L6

Q16

BOOST converter

LLC converter

Fig. 2. DC/DC converter topology.

2.2 LLC Converter The LLC converter always works near the resonance point to improve efficiency and realize ZVS switching on and ZCS switching off. High voltage side and low voltage side are connected by transformer, and the transformer ratio is 2:1 to achieve isolated voltage rise. In order to solve the problem of high current at the low-voltage side, the transformer is connected in series with the primary side and in parallel with the secondary side. Similarly, SiC MOSFET is used for all switching devices in LLC converter.

3 Design for DC–DC Converter The above-mentioned five modules are connected in parallel to realize wide range voltage input. The five modules have the same circuit topology. Therefore, in the following parameter calculation and component selection, only one module is taken as an example. The module power is 5 kW, and the designs of other modules are the same. 3.1 BOOST Converter Considering the performance and limitations of different components, it is necessary to reasonably design each component parameter. The reference parameters of this prototype are as follows: Table 1. Parameters of BOOST circuit prototype. Variable

Parameter

BOOST circuit input voltage

36–60 V

BOOST circuit output voltage

100–180 V

BOOST circuit input current

84–140 A

Switching frequency

50 kHz

Design of Wide Voltage Range DC–DC Converter Based on SiC MOSFET

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According to Table 1, the range of duty cycle can be obtained, which is the minimum value of duty cycle and the maximum value of duty cycle: Dmax = 1 −

Vin min = 0.8 Vo max

(1)

Dmin = 1 −

Vin max = 0.4 Vo min

(2)

Vin min , Vin max , Vo min , Vo max are the minimum and maximum values of input voltage and the minimum and maximum values of output voltage respectively. According to the total input current of the circuit is 84–140 A, the current range of each circuit flowing through six parallel circuits is 14–24 A. A. Boost Inductance design Since the six parallel circuits are only different in phase, the circuit structure and component parameters are the same. The parameters of a single branch are calculated as follows. The inductance in the converter plays the role of energy storage. It stores energy when the upper switching device is turned off and the lower switching device is turned on, and releases energy when the upper switching device is turned on and the lower switching device is turned off. It is the key to boost the voltage of the converter. The inductance value is calculated as follows: L=

Vin max Dmin = 78.994 μH fs k1 Iin min _ sin gle

(3)

The ripple coefficient is taken as 0.42, Iin min _ sin gle is the minimum value of the current flowing through each circuit. After considering the error and margin, the circuit energy storage inductance value can be 80 µH. After considering the margin, the maximum value of the current flowing through the inductance of a single circuit is calculated as follows: IL_ max = Iin max _ sin gle 120% = 28 A

(4)

Iin max _ sin gle is the maximum value of the current flowing through each circuit. The inductance material shall be the PQ 50/28 magnetic core of DMEGC, and the magnetic material shall be DMR96. The effective sectional area of the magnetic core Ae = 349.8 mm2 , the effective volume V e = 26996 mm3 , and the window area Aw = 136.4 mm2 . Set inductance flux variation Bmax = 300 mT, the inductance turns are calculated as follows: NL =

LIL max =12.764 Ae Bmax

(5)

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X. Wang et al.

Take turns N L = 14. Under this condition, Bmax = 274 mT, less than the allowable maximum magnetic flux density of 300 mT, meeting the requirements. B. B. Selections of Power Devices In the two states of circuit operation, the current flowing through the switching devices is the same as the current flowing through the inductor. Therefore, considering the margin, the maximum current flowing through SiC MOSFET is as follows: IMOS_ max = IL_ max = 28 A

(6)

When the switching device is turned on, the voltage at both ends is very small. When the switching device is turned off, both ends will bear the power voltage. Therefore, after considering the margin, the maximum voltage at both ends of the switching devices is calculated as follows: VMOS_ max = Vin max × 120% = 216 V

(7)

To sum up, IPB156N22NFD of Infineon is selected as the switching devices. The maximum voltage of the MOSFET is 220 V, the maximum current is 65 A (at 75 °C), the on resistance Rds(on) = 18.5 m (at 60 °C), and the gate charging charge Qg = 66 nC. The selected components can meet the stress requirements with a certain margin. 3.2 LLC Converter The reference parameters of this prototype are shown in Table 2: Table 2. Parameters of LLC circuit prototype. Variable

Parameter

LLC circuit input voltage

100–180 V

LLC circuit output voltage

200–360 V

Switching frequency

150 kHz

A. Inductance design First, calculate the transformer turn ratio. Since the LLC converter operates in DCX mode, the turn ratio design should make the resonant cavity voltage gain 1, that is, the LLC converter operates at the resonant point, making the resonant waveform close to sine and the loss minimum. The calculation formula of transformer turn ratio n is: n=

Vbus =2 Vo

Vbus is the input voltage and Vo is the output voltage.

(8)

Design of Wide Voltage Range DC–DC Converter Based on SiC MOSFET

599

When the LLC converter works at the resonance point, during the dead time, the peak value of the excitation inductance current charges the junction capacitor of the switching devices that have just been turned off and discharges the junction capacitor of the switching devices that will be turned on, thus realizing the zero voltage turn on of the switching devices. Set the dead time t d = 250 ns. In order to achieve ZVS of the switching devices, the excitation inductance L m value needs to meet: Lm
0. The vibration signal of bearing fault is converted into time-frequency picture by using continuous wavelet transform: Assuming that the scale is a, the sampling frequency is fs, and the wavelet center frequency is fc, the actual frequency is fa = fc*fs/a; The scale sequence should be of the form c/totalscale, c/(totalscale-1),… c/2,c. Where totalscale is the length of scale sequence at wavelet transform, c = 2 * fc * totalscale.

3 Attention Mechanisms Stacking Network 3.1 Convolutional Layer By performing a convolution operation, the convolution layer can preserve the spatial relationship between pixels and extract image features. The convolutional layer consists of a certain number of convolution kernels. The features of the input region are extracted by sliding convolution with a specified step size, and the output results are obtained by activation function to obtain nonlinearity. Traditional convolution layer need to compute a large number of parameters, result in slow network speed, and the depthwise separable convolution compared with the conventional convolution layer can greatly reduce the number, at the same time can make the network can build deeper.

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Depth-separable convolution is a combination of depth-separable convolution and pointwise convolution, as shown in Fig. 1. Among them, one convolution kernel processes one channel in Depthwise Convolution, and only one convolution kernel convolves one channel at a time. The quantity of feature images produced by depth convolution corresponds to the quantity of channels in the input image. Convolution of channels one by one leads to the fact that it is unable to successfully use feature data from many channels in the same spatial location, so the feature map needs to be combined by pointwise convolution: convolution kernels of size 1 × 1 are weighted in the depth direction of the feature map.

Fig. 1. Depthwise seperable convolution

3.2 Pooling Layer The pooling layer is actually a kind of downsampling, which avoids a catastrophic rise in the parameters of the network structure by selecting the output of the features. A commonly used pooling layer is the maximum pooling layer, where the maximum value is taken for the selected region to represent the features in that region by dividing the input image into a number of rectangular regions and by assuming that the more important features have higher activity values. 3.3 Attention Mechanism Human eyes automatically filter out minor information when observing things and focus on the information with high importance first. The size of the target area can be decreased and information processing effectiveness can be significantly increased by concentrating attention on the more crucial information. By imitating the way human eyes process information, the attention mechanism highlights the key information in the input picture to increase its overall proportion and reduce the network’s attention to other information. In this paper, the input feature images are first convolved to further extract feature information, the original image information is stacked with the extracted feature images through the residual structure and then the feature images are fed into the Sigmoid activation function to map the elements in the feature images to between 0 and 1, and then multiplied with the corresponding position features of the original images to highlight the key features. Attention mechanism is shown in Fig. 2.

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Fig. 2. Attention mechanism

3.4 Inception Module The network’s ability to extract features can be enhanced by the inception model. By using 1 * 1, 3 * 3 and 5 * 5 convolution to extract multi-scale features from images, through information fusion, better image display capability for feature images. In addition to boosting the network’s capacity for generalization and structure expression, convolution kernels of various scales can also increase the network model’s nonlinearity, which facilitates the network’s capacity for feature learning. To enhance the network’s ability to extract features, we incorporate an attention mechanism in this research to draw attention to key characteristics in the inception block. The structure is shown in Fig. 3. There are three branches to the input feature map, and each branch uses a convolutional layer of 1 * 1, 3 * 3 and 5 * 5 respectively as its first layer, and each convolutional layer is followed by an attention mechanism with n layers, where n is an adjustable parameter.

Fig. 3. Attention mechanism stacking module

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3.5 Optimizer Convolutional neural networks optimize the loss function by using an optimizer to compute and update the training parameters of the model. Stochastic gradient descent (SGD) is a commonly used neural network optimizer that performs well when training large datasets, but the initial learning rate cannot be determined and easily falls into local optimum solutions. Compared with SGD, the adaptive moment estimation optimization algorithm (Adam) calculates the update step by considering the first-order and secondorder moment estimation of the gradient, and designs independent adaptive learning rates for various parameters. Using these methods, Adam dynamically adjusts the learning rate. Therefore, Adam is chosen as the optimizer of the network in this paper. 3.6 Overall Model Structure Figure 4 shows the overall structure of the model, whose input is a two-dimensional image transformed from time-frequency graph by continuous wavelet changes. In order to extract the first fault features from the image, the network is initially made up of a convolution layer, an activation function layer, and a pooling layer, and then followed by attention stacking layer, whose stacking times are a variable. The attention stacking layer highlights fault features in the model’s tail, which is made up of convolutional layers, activation function layers, and random inactivation layers. Finally, fault types are divided by the linear layer.

CWT

Fig. 4. Model overall process

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4 Experimental Results and Analysis 4.1 Experimental Data To verify the performance of the constructed fault diagnosis model, the rolling bearing fault dataset of Case Western Reserve University and the multi-service bearing fault data set of Jiangnan University are used as experimental data. Case Western Reserve University rolling bearing failure data set selected for experimental verification of basic drive-side acceleration failure data at 12 kHz sampling frequency, the speed of the motor is 1730 r/min, The fault diameters are 0.07, 0.14 and 0.21 mm, respectively. There are 10 kinds of vibration signals under each fault diameter, including inner ring failure, outer ring fault, rolling element fault and a fault-free signal; Jiangnan University bearing fault dataset is a multi-service fault dataset containing 600, 800 and 1000 r/min, and its sampling frequency is 50 kHz. The interception method of fault data is divided into a group of 2048 pieces of data, and the stride length is 2048. Training and test sets are split up into the data set in a 7:3 ratio. 4.2 Experimental Results The attention module and Inception module in the attention stacking network model are compared with different stacking times to explore the network model with the optimal bearing fault diagnosis performance. The results of the diagnostic tests are shown in Tables 1 and 2, respectively. When the attention module is stacked twice inside each Inception block in the attention stacking network model and the Inception block in the network is stacked only once, the overall performance of network performance is optimal, its fault diagnosis accuracy can reach 100 and 85.3%. Table 1. Results of the attention stacking experiment in CWRU Accuracy of diagnosis: % The number of attention mechanism stacks

Inception number of stack 1

2

3

1

98.9

99.4

100

2

100

98.9

99.4

3

21.1

97.8

96.7

To highlight the effect of the attention stacking mechanism, we conducted comparative experiments on the stacking model and the no stacking module on the CWRU and Jiangnan University bearing datasets, respectively. It is a comparative experiment with or without attention stacking in Fig. 4, the experimental results are shown in Fig. 5. The figure shows that the addition of attention to the stack has significantly improved the fault diagnosis ability of the model, diagnostic accuracy improved by 23.3% on CWRU datasets. For the multi-service bearing fault dataset of Jiangnan University, it still increased by 4.9%.

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Z.-B. Li et al. Table 2. Results of the attention stacking experiment in JN

Accuracy of diagnosis: %

Inception number of stack

The number of attention mechanism stacks

1

2

3

1

82.7

84.0

82.9

2

85.3

84.5

83.7

3

82.6

82.7

75.1

Fig. 5. Stack effect verification

Because Batch_Size values affect computer memory utilization as well as training oscillations, in order to further optimize the network parameters, the performance changes of the network were observed by selecting the above-mentioned excellent performance networks and conducting different Batch_Size on the CWRU bearing fault dataset. Batch_Size values are 16, 32, and 64, the network structure is one attention mechanism in each Inception module and two times in the network. The experimental results show that the network fault diagnosis performance is best when Batch_Size = 32, as shown in Fig. 6, and the test accuracy can be stable at 100%. To reflect the performance and noise immunity of the stacking model in bearing fault diagnosis problems, we have carried out the experimental comparison of the original fault data on different methods and the experimental comparison of the experimental data with 6db noise on different diagnosis methods, the experimental results are shown in Figs. 7 and 8 respectively. For the original data, stacked model diagnostic accuracy is at least 8.2% higher than that of other comparison methods, When 6db noise is added, the stacking model is also 11.65% higher than other comparison methods.

5 Result In this paper, the fault diagnosis model of rolling bearing is established by using the Inception Attention structure, the multi-scale convolution capability of the Inception model was used to extract the features of images, and through attention mechanism, the

Rolling Bearing Fault Diagnosis Method Based on Attention 1.0

test-accuracy

0.8

0.6

0.4

0.2

0.0 0

10

20

30

40

50

epoch

Fig. 6. Comparative experiments with the different batch_size

Fig. 7. Comparing experiments between different diagnostic models

Fig. 8. Comparison experiment between different diagnostic models under 6db noise

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key features of the picture are highlighted to strengthen the network learning effect. The main conclusions are as follows: (1) Utilise time series information between signals by transforming one-dimensional time series vibration signals into time-frequency maps using continuous wavelet transform. (2) The number of stacks of the attention mechanisms in the Inception module and the number of stacks of the Inception layer in the network are adjusted to create the best network model. Based on the experimental results, it can be seen that the attention mechanism is stacked twice in the Inception module, and the network performs best when the Inception layer is stacked just once in the network, achieving 100% diagnostic accuracy. (3) The stacked model has superior diagnostic performance and noise immunity when compared to other fault diagnosis techniques. Acknowledgement. This research is supported by the 2018 Bozhou College Natural Science Research Project (BYZ2018C01) and 2019 Anhui Provincial Department of Education Natural Science Key Research Project (KJ2019A1307).

References 1. Lei, W., Huang, X., Wen, G., et al.: Rolling bearing fault diagnosis based on ds-vmd and associated crags. J. Vibr. Measur. Diag. 41(01), 133–141+204 (2021) 2. Chen, Q., Dai, S., Xinle, B.I., et al.: A rolling bearing fault diagnosis method based on EEMD. Comput. Simul. 38(02), 361–364+369 (2021) 3. Zhang, D., Lu, G.: J. Vibr. Measur. Diagn. 41(02), 249–253+408 (2021) 4. Jiao, J., Zhao, M., Lin, J., Liang, K.: A comprehensive review on convolutional neural network in machine fault diagnosis. Neurocomputing 417, 36–63 (2020) 5. Shiza, M., Islam, M., Manjurul, M., Sohaib, M.: Deep learning aided data-driven fault diagnosis of rotatory machine: a comprehensive review. Energies 14(16), 5150 (2021) 6. Zhijiao, Z.H.A.O., Zhihong, Z.H.A.O., Shaopu, Y.A.N.G.: Rolling bearing fault disgnosis based on residual connection and 1D-CNN. J. Vibr. Shock 40(10), 1–6 (2021) 7. Zifei, X.U., Jiangtao, J.I.N., Chun, L.I.: New method for the fault diagnosis of rolling bearings based on a multiscale convolution neural network. J. Vibr. Shock 40(18), 212–220 (2021) 8. Yang, J., Wan, A., Wang, J.L., et al.: Aeroengine bearing fault diagnosis based on convolutional neural network for multi-sensor information fusion [J/OL]. Proc. CSEE 1–9 (2021-12-01) 9. Chen, B., Chen, X., Sheng, B., et al.: An application of convolution neural network and long short-term memory in rolling bearing fault diagnosis. J. Xi’an Jiaotong Univ. 55(06), 28–36 (2021) 10. Yufeng, J., Yao, M., Liu, X., et al.: Rolling bearing fault diagnosis model combining with residual network and attention mechanism. Mech. Sci. Technol. Aerosp. Eng. 39(06), 919–925 (2020) 11. Gu, Y.H., Zhu, T., Rao, W.J., et al.: Rolling bearing fault diagnosis based on EMD binarized image and CNN. J. Vibr. Measure. Diagn. 41(01), 105–113+203 (2021) 12. Wang, Z., Zhao, W., Du, W., et al.: Data-driven fault diagnosis method based on the conversion of erosion operation signals into images and convolutional neural network. Process Saf. Environ. Prot. 149(12), 591–601 (2021)

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13. Tong, Y., Pang, X.Y., Wei, Z.H.: Fault diagnosis method of rolling bearing based on GADFCNN. J. Vibr. Shock 40(05), 247–253+260 (2021) 14. Chen, Z., Mauricio, A., Li, W., Gryllias, K.: A deep learning method for bearing fault diagnosis based on cyclic spectral coherence and convolutional neural network. Mech. Syst. Signal Process. 140, 106683 (2020) 15. Kaplan, K., Kaya, Y., Kuncan, M., M˙inaz, M.R., Ertunç, H.M.: An improved feature extraction method using texture analysis with LBP for bearing fault diagnosis. Appl. Soft Comput. J. 87, 1568–4946 (2020)

Optimal Design of Torque Ripple of External Rotor Permanent Magnet Synchronous Motor Based on Particle Swarm Optimization Houying Wang1,2 , Fang Xie1(B) , and Shilin Ni1 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected] 2 National Engineering Laboratory of Energy-Saving Motor & Control Technology, Anhui

University, Hefei, China

Abstract. In order to reduce the torque ripple of outer rotor frameless permanent magnet synchronous motor, this paper adopts the structure of skewed slots to optimize the design of PMSM (permanent magnet synchronous motor). First, the equivalent magnetization method is used to analyze the key parameters that affect the torque ripple of the motor. Secondly, in view of the problem that the torque caused by the skewed slots is greatly reduced, the angle of the skewed slots is studied in this paper, and the structural parameters of the skewed slots are determined, so that the torque ripple is greatly reduced while the torque is slightly reduced. Thirdly, this paper establishes a fitting model based on the sample data generated by the key parameters and introduces particle swarm optimization algorithm to optimize the key parameters of the fitting model. Finally, joint simulation is used to verify the effectiveness of the optimization results. Keywords: Permanent magnet synchronous motor · Skewed slots · Torque ripple · Particle swarm optimization

1 Introduction Permanent magnet synchronous motor (PMSM) has the characteristics of low speed and large torque, and is widely used in machine arms, automobiles and other fields [1, 2]. Different from the general internal rotor motor structure, the external rotor permanent magnet synchronous motor has an external rotor and an internal stator, and the shaft remains fixed and the external rotor rotates during operation. This structure has the characteristics of low speed and high torque, but there is still the problem of high torque ripple [3]. The relatively large torque ripple will cause vibration and serious noise [4]. In some occasions that are sensitive to speed fluctuations, it will lead to irreversible losses. Therefore, reducing the torque ripple of the motor is still an urgent problem to be solved. To solve this problem, scholars at home and abroad have done a lot of research, which is mainly divided into two categories: one is to optimize the design of the motor body, the other is to improve the control strategy of the motor. In the motor body design, proper © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 620–628, 2023. https://doi.org/10.1007/978-981-99-4334-0_77

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slot pole matching, stator skewed slot or rotor skewed pole [5, 6], different slot width matching, permanent magnet blocking, optimization of magnetic steel eccentricity, pole arc coefficient, magnetic steel thickness [7, 8], etc. can inhibit cogging torque. The research on the skewed slots structure in the existing literature is mostly used in the internal rotor motor, because the external rotor motor will substantially reduce the torque ripple, but also greatly reduce the torque after adding the skewed slots structure. Therefore, this paper studies the external rotor skewed slots, and uses particle swarm optimization algorithm to optimize the structural parameters to reduce torque ripple.

2 PMSM Analysis During the operation of permanent magnet synchronous motor, due to the influence of harmonic magnetomotive force and cogging effect, it will produce strong torque ripple. The electromagnetic torque of permanent magnet motor is Tem = Tcog + Tavg + Tv

(1)

where, Tem is electromagnetic torque; Tcog Is the cogging torque; Tavg Is the average electromagnetic torque; Tv Is harmonic torque. According to Formula (1), the torque ripple of the motor can be reduced by reducing the cogging torque of the motor. The cogging torque can be expressed as the negative derivative of the magnetic field energy W in the motor relative to the relative position angle α of the fixed rotor without excitation. Tcog = −

∂W ∂α

(2)

Assuming that the magnetic conductivity of the fixed rotor ferromagnetic material tends to infinity, the magnetic field energy in the motor can be approximated by the sum of the air-gap magnetic field energy and the permanent magnet magnetic field energy.   ∂Wairgap+PM ∂ 1 ∂W ∫ B2 (θ, α)dV ≈ =− Tcog = (3) ∂α ∂α ∂α 2μ0 v In the equation, B(θ, α) is the distribution of air gap magnetic density along the rotor surface, and θ is the radian of rotor rotation. When considering the inclined groove, the tooth groove torque of the permanent magnet synchronous motor is Tcog

  ∞  Ns ts nQ1 Ns ts Lπ μ0  2 2 sin R − R2 = nGn F nQ1 sin nQ1 α + 2Ns ts 1 2 2 2p

(4)

n=1

where, L is the axial length of motor iron core, Q1 is the length of stator, and R1 and R2 are the inner diameter of rotor and outer diameter of stator respectively. The sinusoidal distortion rate of motor air gap flux density and the existence of high-order harmonics of no-load induced electromotive force will cause torque ripple of

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permanent magnet synchronous motor. The torque ripple coefficient is used to evaluate the overall torque ripple degree of the motor, It is defined as: Kmb =

Tmax − Tmin 2Tavg

(5)

where, Tmax , Tmin and Tavg is the maximum, minimum and average values of torque Respectively.

3 Finite Element Simulation After the external rotor PMSM is designed with a suitable skewed slots, the torque ripple will be reduced, but the torque will also be greatly reduced. Compared with the increase of torque, the reduction of torque ripple is more important. In this paper, the slanting angle of the pole is studied to obtain lower torque ripple at the expense of smaller torque. The finite element model and 3D model of PMSM designed with skewed slots is as follows (Fig. 1).

Fig. 1. The finite element model and 3D model of PMSM

It can be seen from Fig. 2 and Table 1 that when the inclination angle is a cogging, that is, 7°, the torque ripple will be reduced to the minimum. However, The torque reduction amplitude is too large at this time, so it is necessary to find other suitable angles. 00

Torque(mNm)

50 00 50 00 50 00

time(ms)

Fig. 2. Influence of different inclination angles on torque.

In order to find a suitable angle, Order, μ = K/T the bigger the μ , the larger the angle, the greater the torque ripple reduction rate is than the torque reduction rate. It can be seen from the Table 2 that when the tilt angle rises from 1° to 2°, the torque decreases by 0.6643%, K decreases by 48.751%, and the value of μ is the largest, representing the best effect on torque ripple suppression. so 2°is The most appropriate tilt angle.

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Table 1. Torque ripple at different tilt angles. Tilt angle (°)

1

2

3

4

5

K (%)

3.8071

1.9611

1.7678

1.1590

1.0603

Tilt angle (°)

6

7

8

9

10

K (%)

1.3825

0.8028

1.2642

1.7811

3.7367

Tilt angle (°)

11

12

13

14

15

K (%)

4.8401

3.9265

2.1344

1.7415

1.4337

Table 2. μ value table. 1° → 2° 2° → 3°

3° → 4°

4° → 5°

5° → 6°

6° → 7°

7° → 8°

3.4927

5.6271

8.1757

11.126

14.475

Percent 48.7510 9.3947 reduction in torque ripple (%)

34.4382

8.5160

− 30.3876 41.9313

− 57.4738

μ

9.8601

1.5134

− 3.7168

− 3.9705

Percent 0.6643 torque reduction (%)

1.8224

73.3870 5.1551

3.7688

8° → 9° 9° → 10° 10° → 11° 11° → 12° 12° → 13° 13° → 14° 14° → 15° Percent 18.21 torque reduction (%)

35.90

45.99

40.87

Percent − − − 29.5287 18.8756 reduction 40.8875 109.7973 in torque ripple

4506411

35.228

23.2271

μ

1.2713

0.7659

0.5683

− 2.2457

22.27

26.59

− 4.9303 − 1.1105

31.15

0.6060

It can be seen from the analytical formula (4) that the motor structure parameters such as the stator slot height, Hr pole arc coefficient, δ permanent magnet thickness, D stator outer diameter, Rm etc. of the permanent magnet synchronous motor will have a certain impact on the torque ripple and electromagnetic torque. The table of four factors and five levels is as follows (Table 3). There are 625 combinations of four factors and five levels. Use the finite element method to calculate the torque and torque ripple corresponding to each parameter combination, and establish the sample library as shown below.

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Parameter

Level 1

D/mm

1.83

Level 2 1.84

Level 3

Level 4

1.85

Level 5

1.86

1.87

Rm/mm

61.3

61.4

61.5

61.6

61.7

Hr/mm

8.1

8.2

8.3

8.4

8.5

δ

0.8

0.81

0.82

0.83

0.84

Table 4. Sample library. Serial No

Motor structure parameters

Torque

Torque ripple

δ

D/mm

Rm/mm

1

0.8

1.81

61.3

Hr/mm

T/N m

K/%

8.1

738.7522

2.8019

2

0.8

1.81

61.3

8.2

737.0580

2.8088

3

0.8

4

0.8

1.81

61.3

8.3

735.3219

2.8113

1.81

61.3

8.4

733.5297

2.8127

5

0.8

1.81

61.3

8.5

731.6843

2.8141

6

0.8

1.81

61.4

8.1

750.0462

3.6483

···

···

···

···

···

···

···

623

0.84

1.85

61.7

8.3

786.3193

8.6684

624

0.84

1.85

61.7

8.4

784.1556

8.7032

625

0.84

1.85

61.7

8.5

781.9632

8.7371

4 Optimization of Motor Structure Parameters Based on Particle Swarm Optimization The fitting model is established according to Table 4. Particle swarm optimization algorithm has achieved very good results in various multi-dimensional and multi-objective optimization problems due to its easy implementation, fast convergence, few adjustable parameters, strong global search ability, etc. In this paper, the particle swarm optimization algorithm is introduced to iteratively optimize the fitting model and solve the global optimal structural parameters of the motor. The specific steps are as follows (Figs. 3 and 4). The optimization iteration results are shown in the figure, and the comparison of parameters before and after optimization is shown in Table 5.

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Start

Set the size, initial position and initial speed of the particle swarm

Calculate the objective function of each particle, find the current individual extreme value of each particle, and find the current global optimal solution of the entire particle swarm

Update the speed and position of individual particles

Whether the termination conditions are met

Output optimal solution

End

torque ripple/%

Fig. 3. Flow chart of PSO

Genetic algebra

Fig. 4. Evolutionary process with PSO

Table 5. Comparison of structural parameters. Parameters D/mm

Initial parameters

Optimization parameters

1.85

1.8113

Rm/mm

61.7

61.3125

Hr/mm

8.1

8.0787

δ

0.8

0.8366

5 Joint Simulation Results and Analysis Joint simulation results and analysis in order to prove the correctness of the structural design and optimization, this paper based on the joint simulation of maxwell and simplorer to verify and analyze the experimental results. The module diagram built by Simplorer is as follows (Figs. 5 and 6).

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Fig. 5. Joint simulation model.

Torque ripple(%)

2°skewed slots 15°skewed slots Optimized straight slot Initial straight slot Optimized 2°skewed slot

Time(ms)

Fig. 6. Torque under different parameters

The figure contains the PMSM simulation waveform before and after optimization, and the analysis of experimental results is shown in the Table 6 and Fig. 7. Table 6. Torque and torque ripple under different parameters.

Initial straight slots

Torque ripple (%)

Torque (m Nm)

7.8233

798.2736

2° skewed slots

1.9511

791.6468

15° skewed slots

1.4337

410.1619

Optimized straight slots

2.6502

755.4991

Optimized 2° skewed slots

1.5449

748.3547

The analysis of the experimental results shows that 1) Compared with that before optimization, the torque ripple of the optimized outer rotor PMSM is greatly reduced, 2) The torque ripple of PMSM with 2°skewed slots is significantly reduced. The torque ratio of PMSM with 2°skewed slots is higher than that of PMSM with 15°skewed slots, and the torque ripple is lower than that of PMSM with straight skewed slots.

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Fig. 7. Comparison of torque and torque ripple under different parameters.

6 Conclusion In this paper, the structure and optimization design of the external rotor frameless permanent magnet synchronous motor are carried out. First, the causes of torque ripple and the influence of the skewed slots on the torque ripple are analyzed. Secondly, the different skew angles of the skewed slots are studied to find the appropriate skew angle, so that the torque reduction amplitude can be reduced while reducing the torque ripple. Thirdly, the particle swarm optimization algorithm is used to iteratively optimize the fitting model established by the sample library with the optimization goal of minimizing torque ripple, and obtain the global optimal motor structure parameters. Finally, the experimental optimization parameters are verified by the joint simulation based on Maxwell and Simplerer, which proves the effectiveness of the experiment. Acknowledgement. This work was supported by Natural Science Foundation of Anhui Province (2108085ME179), National Natural Science Foundation of China (51607002).

References 1. Ocak, O., Onsal, M., Aydin, M.: Development of a 7.5kW high speed interior permanent magnet synchronous spindle motor for CNC milling machine. In: 2018 XIII International Conference on Electrical Machines (ICEM), pp. 704–709 (2018). https://doi.org/10.1109/ICELMACH. 2018.8506701 2. Yu, L., et al.: IEEE 4th Advanced information management, communicates. Electr. Autom. Control Conf. (IMCEC) 2021, 792–796 (2021). https://doi.org/10.1109/IMCEC51613.2021. 9482043 3. Li, Z., Chen, J.-h., Zhang, C., Liu, L., Wang, X.: Cogging torque reduction in external-rotor permanent magnet torque motor based on different shape of magnet. In: 2017 IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pp. 304–309 (2017). https://doi.org/10.1109/ ICCIS.2017.8274792 4. Chen, J.: The study on source of vibration and acoustic noise of permanent magnet machines by inverter. IEEE Workshop Adv. Res. Technol. Indust. Appl. (WARTIA) 2014, 694–696 (2014). https://doi.org/10.1109/WARTIA.2014.6976359 5. Wang, S., Li, H.: Effects of rotor skewing on the vibration of permanent magnet synchronous motors with elastic-plastic stator. IEEE Trans. Energy Convers. 37(1), 87–96 (2022). https:// doi.org/10.1109/TEC.2021.3100285

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6. An, Y., et al.: Calculation model of armature reaction magnetic field of interior permanent magnet synchronous motor with segmented skewed poles. IEEE Trans. Energy Convers. 37(2), 1115–1123 (2022). https://doi.org/10.1109/TEC.2021.3123359 7. Xia, Y., Jiang, H., Yi, X., Wen, Z., Chen, Y.: Parameter optimization of hybrid excitation permanent magnet synchronous motor. In: 2018 21st International Conference on Electrical Machines and Systems (ICEMS), pp. 398–401 (2018). https://doi.org/10.23919/ICEMS.2018. 8549262 8. Zhao, X., Sun, Z., Xu, Y.: Multi-objective optimization design of permanent magnet synchronous motor based on genetic algorithm. In: 2020 2nd International Conference on Machine Learning, Big Data and Business Intelligence (MLBDBI), pp. 405–409 (2020). https://doi.org/ 10.1109/MLBDBI51377.2020.00086

Study on Inertia-Resistant Disturbance Speed Control of Permanent Magnet Synchronous Motor Based on Exponential Integral Time-Varying Sliding Mode Shilin Ni1,2 , Fang Xie1(B) , and Houying Wang1 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected] 2 National Engineering Laboratory of Energy-Saving Motor & Control Technology, Anhui

University, Hefei, China

Abstract. To enhance the dynamic performance of speed control when the moment of inertia changes during the operation of permanent magnet synchronous motor (PMSM), this paper investigates an anti-inertia disturbance method based on exponential integral time-varying sliding mode control (EITSMC). First, the paper analyzes the relationship between moment of inertia and motor speed using the mathematical analytical model of PMSM. Secondly, to track the change of the inertia moment immediately, the model reference adaptive system (MRAS) is applied to estimate the inertia change online and improve its tracking accuracy. Thirdly, To solve the issues of unstable motor speed under the sudden change of inertia, the sliding mode control method of exponential integration time variable is proposed, and the introduction of this method can not only better enhance the stability of motor speed, but also improve the fast performance of motor speed. Then, the identifiable moment of inertia is refreshed in real time to the exponentially integrated time-varying SMC, which realizes the adaptive speed control of the PMSM and satisfies the dynamic speed performance of the motor when the inertia changes. Eventually, the feasibility and effectiveness of the proposed method are verified by experiments. Keywords: Permanent magnet synchronous motor · Model reference adaptive system · Inertia recognition · Exponential integral time-varying sliding mode control

1 Introduction Because of his small size, high power and good speed regulation, PMSM has made many achievements in a lot of fields. However, in the actual operation of PMSM, the inertia often alters. This change in the servo system operation, will make the servo system before the operation of the motor control parameters and the controlled object does not match, resulting in servo control system speed stability and rapidity deterioration. In order to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 629–637, 2023. https://doi.org/10.1007/978-981-99-4334-0_78

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maintain a fast and stable response to the system, the servo control system needs to obtain the inertia information immediately, and adjust the motor control parameters in time according to the inertia parameter information to accommodate to the variation of inertia. At present, many researchers have proposed many methods in the anti-inertia perturbation. For example fuzzy control [1], sliding mode control [2], intelligent control [3, 4], predictive control [5–8] and adaptive control [9–11], etc. It is mainly divided into two categories: adding observers and not adding observers. There are many studies of anti-inertia perturbations without the addition of observers. Literature [1] proposes a PMSM fuzzy auto-tuning adaptive integral step control to overcome the trouble of inertial disturbance. Literature [2] proposes an adaptive nonsingular fast terminal sliding mode control method is used to a PMLSM, which reduces the influence of parameter or inertia changes on system control performance. Literature [3, 4] applies a neural network to a PMSM control system with inertia perturbation to achieve high servo accuracy under parameter changes. There are also many studies on the anti-inertia perturbation of the added observer, such as the Landau Observer designed based on the Landau discrete time recursion algorithm in literature [5, 6], the current value of the observed inertia is adjusted according to the partial model matching design method to adjust the velocity loop PI parameters. Literature [7, 8] proposes the gradient algorithm is applied to estimate the inertia online, and the PI parameters of the velocity ring are adjusted in real time according to the principle of pole configuration, the effectiveness of the proposed method is verified by experiments. Literature [9–11] based on the traditional perturbation observer improved by the variable gain algorithm, the identified inertia is updated to the improved perturbation observer, which can effectively enhance the anti-disturbance performance of the system, however the method has higher hardware requirements and is more difficult to implement. The above methods have achieved satisfactory results in experiments, but these results have been more complex and have not been popularized in engineering applications. This paper proposes a time-varying sliding mode control method based on the characteristics of the system inertia. Firstly, the inertia is observed by the model reference adaptive algorithm; Then, the inertia observation value is updated in real time to the exponential integration time-varying sliding mode controller; Finally, the speed response performance and stable performance of the system under inertia disturbance are studied and verified by experiments.

2 PMSM Mathematical Model The equations of mechanical motion for PMSM in the d-q coordinate system is shown as follows: J

d ωm = Te − TL − Bωm dt

(1)

Above ωm is the mechanical angular velocity; J is the inertia; B is the damping coefficient; TL is the load torque and Te is the electromagnetic torque.

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In the moment of inertia recognition algorithm, the damping coefficient of the system can be neglected. So the formula (1) can be reduced to:   J = (Te − TL ) d ωm dt (2) When studying the disturbance of the inertia on the motor speed, this paper sets the load torque to a fixed value, which avoids the effect of the load torque on the motor speed and improves the reliability of the experimental scheme.

3 Inertia Identification Via the discrete model reference adaptive theory, this paper uses Landau’s discrete-time adaptive algorithm to identify inertia in real time. Taking the motor mechanical motion equation as the reference model of Landau algorithm, the moment of inertia is selected as its identification coefficient, and then the accurate inertial identification value is obtained through the appropriate selection of adaptive gain. When the Landau algorithm’s sampling interval for velocity is sufficiently small, the motor mechanical motion equations can be simply discretized as:    (3) ωm (t) = ωm (t − 1) + Ts J [Te (t − 1) − TL (t − 1)] where Ts is the control period of Landau’s algorithm. In this paper, the angular velocity difference of the motor at the time of k and k−1 is used as the reference model of the Landau algorithm, and the reference model is shown in formula (4).    ωm (t) = 2ωm (t − 1) − ωm (t − 2) + Ts J [Te (t − 1) − Te (t − 2)] (4)  Make formula Ts J = b(t), Te (t − 1) − Te (t − 2) = Te (t − 1). This document designs a adjustable model based on the reference model as shown in Eq. (4). ˆ · Te (t − 1) ωˆ m (t) = 2ωm (t − 1) − ωm (t − 2) + b(t)

(5)



ˆ = Ts Jˆ , b(t) ˆ is the parameter to be identified, Jˆ is the inertial In the formula (5), b(t) identification value. Because Ts remains unchanged, the inertial recognition value can be calculated from the parameters to be identified. According to the discrete-time recursive parameter identification mechanism of Landau used in literature [2], the adaptive identification law of the moment of inertia can be obtained as follows: ˆ = b(t ˆ − 1) + β b(t)

Te (t − 1) 1 + β[Te (t − 1)]2

· ωm (t)

(6)

In formula (6), ωm (t) is the difference between the angular velocity of the motor of the reference model and the adjustable model; β is an adaptive gain.

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Fig. 1. Moment of inertia identification diagram

The value of the adaptive gain has a significant impact on the recognition convergence time and recognition accuracy of Landau’s algorithm. In this paper, three sets of adaptive gains are selected for comparative experiments, The adaptive gains selected in the inertia identification plot below are 10, 30, and 50. From Fig. 1, it can be seen that when the adaptive gain is taken to 50, the convergence time is shorter, but the over regulation amount is too large; When the adaptive gain is taken to 10, the overshoot amount is small, but the convergence time is the longest; When the adaptive gain is taken at 30, the over regulation is moderate, and the convergence time is shorter than that when the gain is 10, so the adaptive gain is selected in this paper with an adaptive gain of 30.

4 EITSMC Design The status variables that define the PMSM system are:  x1 = ωref − ωm x2 = x˙ 1 = −ω˙ m

(7)

where ωm is the actual speed, ωref is the motor reference mechanical angular velocity. Formula (8) can be obtained according to Formula (1) and formula (7) as follows: ⎧  1 ⎪ ⎨ x˙ 1 = −ω˙ m = TL − Kt iq J (8) ⎪ ⎩ x˙ = −ω¨ = − 1 K ˙i 2 m t q J ψf is the permanent magnet magnetic chain, Kt is where pn is the number of pole-pairs,  the torque constant and Kt = 3 2pn ψf . When defining the exponential integration of the system, the sliding surface is:  t s = x1 + c ex1 d τ + αe−βt (9) 0

where c, α, β are constant and c > 0.

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The new law of convergence uses a combination of exponential law of convergence and power approach law, is shown in formula (10): s˙ = −k1 |s|∂ sgn(s) − k2 s

(10)

where 1 > ∂ > 0,k1 > 0,k2 > 0 and sgn(s) is a symbolic function. According to the formula (8), formula (9), formula (10) can obtain the control rate of the anti-inertia disturbance index integral:

ˆ ˆiq∗ = J cex1 − αβe−βt + k1 |s|∂ sgn(s) + k2 s Kt

(11)

In order to verify the  stability of the new law of convergence, this paper selects the Liyaprov function:V = 1 2s2 . Substituting formula (8), formula (9) and formula (11) into the derivative of the Liyaprov function can be obtained:   ⎫ ⎧   ⎬ ⎨ TL − Jˆ − J cex1 Jˆ k1 |s|∂ sgn(s) + k2 s s˙s = s − − αβe−βt ⎭ ⎩ J J (12)   x 1 ˆ TL − J − J ce Jˆ Jˆ − · k1 |s|∂+1 − k2 s2 − αβe−βt · s ≤s· J J J It can be seen from the formula (12) that when the surface parameter c is    sliding   x 1 ˆ selected to be large enough, satisfy c > TL J − J e .According to the Liapunov stability principle, the sliding mode controller is progressively stable.

5 Simulation Verification To verify the efficiency of the time-varying sliding mode control method based on exponential integral in this paper on the anti-inertia disturbance of PMSM, the control performance of conventional SMC, conventional time-varying SMC and exponential integral time-varying SMC is compared and studied. Table 1 shows the relevant parameters of the simulation operation. When the system gives a reference speed, the following Figs. 2, 3, and 4 are the speed response waveforms under the three inertia changes of small, medium and large, respectively. The analysis of the experimental results shows that: (1) As shown in Fig. 2, when the inertia changes are the same, the overregulation amount and adjustment time of the motor speed at different given speeds are different. Given a low speed, the speed waveform under the SMC and TSMC methods has a small overshoot amount and adjustment time at startup, but the overshoot amount is too high when the inertia changes; At a given high speed, the speed waveform under the SMC and TSMC methods has a high overshoot and adjustment time at startup, and when the inertia changes, the overshoot amount is greatly reduced compared with

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Parameter

Numerical value

Slow-speed of revolution/rpm

300

Medium-speed of revolution/rpm

600

High speed of revolution/rpm

1200

Low rotation inertia/kg m2

0.0001

Medium rotation inertia/kg m2

0.001

High rotation inertia/kg m2

0.01

Fig. 2. Under the small inertia change, the rotation speed response waveform

the low speed period. However, regardless of the given low speed or high speed, regardless of the motor start or inertia change, the EITSMC lower speed waveform overshoot and the adjustment time are not much different. (2) As shown in Figs. 2, 3, and 4,when the system starts, the motor speed under different inertial changes maintains the same change under the three control methods, of which the SMC adjustment time is the longest, about 260 ms; TSMC overshoot was the highest, reaching 33%.When the moment of inertia changes, the motor speed under different inertial changes changes greatly under the three control methods, and under the small inertia changes, the speed overregulation of SMC and TSMC methods is extremely large, all of which exceed 100%, but the adjustment time is short; The speed overregulation of SMC and TSMC in the medium inertia change has dropped to about 70%, but the adjustment time has increased by about 140 ms; The speed

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Fig. 3. Under the medium inertia change, the rotation speed response waveform

Fig. 4. Under the large inertia change, the rotation speed response waveform

waveform of SMC and TSMC is directly out of control under large inertia changes. However, the EITSMC method has the best stable performance and fast performance when the motor is started or when the inertia changes.

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6 Conclusion To improve the stability and fast performance of the motor speed of the permanent magnet synchronous motor when the moment of inertia changes, this paper first identifies the inertia online through the model reference adaptive theory, and then updates the identification results to EITSMC in real time to improve the motor speed performance. By comparing the speed waveforms under the SMC, TSMC and EITSMC simulation experiments, it is found that regardless of whether the given reference speed is high or low, and the inertia change is large or small, the speed waveform under the EITSMC method has the lowest overshoot amount and the fastest adjustment time. The results of the simulation experiment effectively verify the reliability of the EITSMC method, and also verify that the EITSMC can respond quickly and accurately follow the given speed when the system inertia changes, with good dynamic response and strong robustness. Acknowledgement. This work was supported by Natural Science Foundation of Anhui Province (2108085ME179), National Natural Science Foundation of China (51607002).

References 1. Wang, W., Wu, J., Zhang, Y.: Fuzzy self-tuning adaptive integral backstepping control for permanent magnet synchronous motor. Trans. Chain Electrotech. Soc. 35(4), 724–733 (2020) 2. Fu, X., Zhao, X.: Adaptive nonsingular fast terminal sliding mode control for permanent magnet synchronous motor. Trans. Chain Electrotech. Soc. 35(4), 717–723 (2020) 3. Chaoui, H., Khayamy, M., Okoye, O.: Adaptive RBF network based direct voltage control for interior PMSM based vehicles. IEEE Trans. Vehic. Technol. 67(7), 5740–5749 (2018) 4. Zhang, C., Liu, G., Qin, J.: An adjustable control for inertia momentum wheel with disturbance compensation. In: 2012 8th IEEE International Symposium on Instrumentation and Control Technology (ISICT) Proceedings, pp. 320–323 (2012). https://doi.org/10.1109/ISICT.2012. 6291630 5. Chen, C., Luo, J., Jin, Z.: Research on control strategy of PMSM driving variable load with large inertia. In: 2020 IEEE International Conference on Artificial Intelligence and Information Systems (ICAIIS), pp. 514–518 (2020). https://doi.org/10.1109/ICAIIS49377.2020.919 4793 6. Wang, S., Yu, D., Wang, Z.: A novel inertia identification method for PMSM servo system based on improved particle swarm optimization. In: 2017 9th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), pp. 123–126 (2017). https:// doi.org/10.1109/IHMSC.2017.143 7. Liu, K., Hou, C., Hua, W.: A novel inertia identification method and its application in PI controllers of PMSM drives. IEEE Access 7, 13445–13454 (2019). https://doi.org/10.1109/ ACCESS.2019.2894342 8. Hou, Q., Ding, S.: Finite-time extended state observer-based super-twisting sliding mode controller for PMSM drives with inertia identification. IEEE Trans. Transport. Electrific. 8(2), 1918–1929 (2022). https://doi.org/10.1109/TTE.2021.3123646 9. Zhang, C., et al.: Research on the identification of the moment of inertia of PMSM for industrial robots. Chin. Autom. Congr. (CAC) 2020, 1329–1334 (2020). https://doi.org/10. 1109/CAC51589.2020.9327128

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10. Zhao, S., Cui, L., Liu, G., Chen, Y.: An improved torque feed-forward control with observerbased inertia identification in PMSM drives. In: 2012 15th International Conference on Electrical Machines and Systems (ICEMS), pp. 1–6 (2012) 11. Du, S., Zhao, s., Chen, Y.: Inertia identification for speed control of PMSM servo motor. In: 2011 International Conference on Electrical Machines and Systems, pp. 1–6 (2011). https:// doi.org/10.1109/ICEMS.2011.6073404

Torque Ripple Reduction of Permanent Magnet Synchronous Motor Based on Least Mean Square Algorithm Mengyuan Shen1,2 , Fang Xie1(B) , Wenyu Zhang1 , and Jinqiang Zhang1 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected] 2 National Engineering Laboratory of Energy-Saving Motor & Control Technology, Anhui

University, Hefei, China

Abstract. Current harmonic is one of the main causes of torque ripple in permanent magnet synchronous motor PMSM). Considering this problem, an adaptive filter is designed based on least square algorithm (LSM). Firstly, in order to better analyze the problem, this paper establishes the mathematical model of current harmonics, and establishes the mathematical relationship between current harmonics and torque. Secondly, the principle of the adaptive algorithm and the influence of the convergence coefficient on the filter are analyzed. Thirdly, an adaptive filter for current loop LMS algorithm is designed in synchronous rotating coordinate system. Finally, an experimental platform for harmonic suppression of PMSM is built to verify the effectiveness and feasibility of this method through experimental comparison. Keywords: Permanent magnet synchronous motor · Adaptive filter · Torque ripple · Harmonic suppression

1 Introduction With the development and application of permanent magnet material technology, PMSM has attracted more and more attention due to its small size, simple structure, fast dynamic response and other characteristics. It is widely used in household appliances, ships, automobiles, robots [1, 2].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 638–646, 2023. https://doi.org/10.1007/978-981-99-4334-0_79

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Due to the non-sinusoidal distribution of the motor winding, magnetic field distortion in the air gap, inverter dead-time effect and other reasons, it is inevitable that there will be a large number of current harmonics [3] and voltage harmonics in the PMSM control system. These harmonics can be divided into two categories, one is space harmonics, the other is time harmonics [4]. The space harmonics mainly come from the motor body structure, which can be solved by improving the design structure of the motor. For the suppression method of space harmonics, the rotor structure of permanent magnet motor can be optimized. The time harmonic mainly comes from the drive part of the motor, among which the dead time effect of the inverter is the main factor leading to the time harmonic. This part of the harmonic cannot be improved through ontology optimization, but can be suppressed through control strategies. When the motor manufacturing is completed, the control strategy becomes the main method to suppress the motor harmonic [5]. PI controller is often used in motor control system, but the control effect of PI controller on AC signal is far worse than that of DC signal, and cannot control the disturbance component. The repetitive controller [6] is used for motor harmonic suppression. In theory, repetitive control can eliminate harmonics of integer times of the given frequency, but repetitive control requires a certain storage space. When the harmonic frequency changes, the controller needs to be redesigned. Based on the principle of auto disturbance rejection, the PI controller in the current loop is replaced by the active disturbance rejection controller [7], and the relevant harmonic model is established, which can achieve the purpose of specific harmonic suppression. Some scholars also use resonance control to solve the harmonic problem of the motor, and use the infinite gain of resonance controller at a specific frequency to suppress current harmonic. The above method can reduce the harmonics in permanent magnet synchronous motor, but they are all for the suppression of specific harmonics. To solve these problems, an adaptive filter based current harmonic suppression method is designed, which not only suppresses a specific harmonic, but also suppresses the total harmonic. In this paper, the current harmonics in the stationary coordinate system are first transformed into the synchronous rotating coordinate system, and it is proved that current harmonic will affect torque through formula transformation. Secondly, in order to suppress current harmonics, a filter structure based on LMS algorithm [8] is designed in the current loop. Finally, the effectiveness of this method is verified by experiments.

2 PMSM Harmonic Analysis In the vector control system of PMSM, the current signal is very important, and its accuracy will affect the control effect of the motor. The controller in the current loop uses the traditional PI controller, which can control the DC component well. However, the harmonic component will become a disturbance component after coordinate transformation, and the PI controller cannot eliminate the harmonic in the current loop, so

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adaptive algorithm is added in this paper. Formula (1) gives the harmonic analysis model of phase current. ⎧ ia = I1 sin(ωe t) + I5 sin(−5ωe t) + I7 sin(7ωe t) ⎪ ⎪ ⎪ ⎪ ⎪ +I11 sin(−11ωe t) + I13 sin(13ωe t) + · · · ⎪ ⎪ ⎪ ⎪ ⎪ 2π 2π ⎪ ⎪ ) + I5 sin[5(−ωe t − )] ib = I1 sin(ωe t − ⎪ ⎪ ⎪ 3 3 ⎪ ⎪ ⎪ 2π 2π ⎪ ⎪ +I7 sin[7(ωe t − )] + I11 sin[11(−ωe t − )] ⎪ ⎪ ⎪ 3 3 ⎨ 2π (1) +I13 sin[13(ωe t − )] + · · · ⎪ ⎪ 3 ⎪ ⎪ ⎪ ⎪ 4π 4π ⎪ ⎪ ic = I1 sin(ωe t − ) + I5 sin[5(−ωe t − )] ⎪ ⎪ 3 3 ⎪ ⎪ ⎪ ⎪ 4π 4π ⎪ ⎪ +I7 sin[7(ωe t − )] + I11 sin[11(−ωe t − )] ⎪ ⎪ 3 3 ⎪ ⎪ ⎪ ⎪ 4π ⎪ ⎩ +I13 sin[13(ωe t − )] + · · · 3 In the formula (1), I1 , I5 , I7 , I11 and I13 are the amplitude values of fundamental. wave, 5th, 7th, 11th and 13th harmonics respectively, ωe representing the electrical angular velocity. After coordinate transformation, Formula (1) can be converted to synchronous rotation coordinate system (d-q), as shown in Formula (2).  id = Id + I5 sin[6(−ωe t)] + I7 sin 6(ωe t) + I11 sin[12(−ωe t)] + I13 sin(12ωe t) + · · · iq = Iq + I5 cos[6(−ωe t)] + I7 cos 6(ωe t) + I11 cos[12(−ωe t)] + I13 cos(12ωe t) + · · · (2) In the formula (2), id and iq represent d-q axis current, and Id and Iq are fundamental DC components under d-q coordinate axis. When = 0 is set, the formula of electromagnetic torque is as follows (3). Te = 1.5Piq ψf

(3)

In formula (3), Te electromagnetic torque, P represents the number of pole pairs and ψf represents the flux linkage. It can be seen from the formula that electromagnetic torque is affected by iq . In fact, d-q axis current contains a lot of harmonic components, which will cause torque ripple.

3 LMS Filtering Algorithm The implementation of adaptive filtering algorithm should include two parts, one is digital filter with adjustable parameters, the other is adaptive algorithm. Figure 1 shows the structure of the adaptive filter. In Fig. 1, x(n) and d(n) on the left of the figure are input signals and expected signals respectively. y(n) and e(n) on the right of the figure are output signals and error signals

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x ( n)

Parameter adjustable digital filter

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y ( n)

+

d ( n)

-

e( n )

Adaptive algorithm

Fig. 1. Structure of adaptive filter

respectively. As shown in the figure, the error signal e(n) is obtained by subtracting the output signal y(n) from the required signal d(n). Adaptive algorithm for adjusting filter coefficients of digital tunable filters, so that the error e(n)is continuously reduced, and the output will be closer to the expected value. e(n) = d (n) − X T (n)W (n)

(4)

W (n + 1) = W (n) + 2μe (n)X (n)

(5)

In formula (4) and formula (5), W(n) is the parameter responsible for adjustment, and X(n) represents the input signal vector. μe is Step size of adaptive algorithm. The size of μe determines the calculation speed of the adaptive algorithm. The larger the value is, the faster the calculation speed is, but it will reduce the stability of the algorithm. The convergence condition of LMS algorithm is related to the autocorrelation matrix of the input signal, as shown in (6). 0 < μe
0.5 ⎩ r(t) = 0 if rand ≤ 0.5

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where: cumsum is the cumulative sum; n is the maximum number of iterations set; t is the current number of iterations; and rand is a random number from 0 to 1. To guarantee that ants walk randomly within the prescribed scope, Eq. (5) is optimized to obtain the ant location update formula as follows   t Xi − ai × bi − cit t Xi = + ci (6) dit − ai where: ai is the minimum value of random walk of the i-dimensional variable, bi is the maximum value of random walk of i-dimensional variable. cit is the minimum value of the i-dimensional variable in the t-th iteration, dit is the maximum value of the i-dimensional variable in the t-th iteration. The existence of ant lion trap will affect the route of ants. Each ant will change its route based on the ant lion position (ALti ) in each iteration, as shown in the following formula  t ci = ALti + ct (7) dit = ALti + d t In the ant lion algorithm, the probability of the ant lion catching the ant is determined according to the fitness. In addition, once the ants enter the prey range of the ant lion, the ant lion will throw sand over the trap edge to restrict the ants from walking. At the same time, if the ant lion succeeds in catching ants, the ant lion will move to a new position. As shown in Formula (8) ⎧ t ⎪ ct = cI ⎪ ⎪ t ⎨ t d = dI (8) ⎪ I = 10ω · (t/T) ⎪ ⎪ ⎩ t ALi = Antit if f (Antit ) > f (ALti ) where: ω is a constant. I indicates the size of the ant lion construction snare, which increases with the number of iterations. T represents the maximum number of iterations. f is the fitness function, and Antit is the position of the i-th ant in the t-th iteration. The fittest ant lion is selected as the elite ant lion after each iteration. The ant position of iteration t is shown in Eq. (9) below Antit =

RtA + RtE 2

(9)

where: RtA is the random walk step size of ants selected by roulette wheel in iteration t, RtE is the step size of ants randomly walking in the elite ant lion circle in iteration t, while Ant ti is the i-th ant position of iteration t. 3.2 Basic Idea of Controller To make the motorfeatured fast dynamic response and high steady-state accuracy, a controller with proportional and integral terms of PI controller varying with error is

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designed. The scale term and integral term of the controller are determined according to the difference between the actual value and the reference value. The specific design method is: when the error is relatively large, the same goes for the scale item, and the error is rapidly reduced. When the error is small, in order to prevent overshoot and long adjustment time, the proportion term gradually decreases and the integral term works. In order to discover the optimal values of the proportional and integral terms of the controller under different errors, the ant lion algorithm is resorted to find the optimal proportional and integral coefficients. To sum up, the controller first optimizes the controller coefficients under different errors, and then adjusts the controller parameters in real time according to the current errors. The structure block diagram of the designed controller is presented in Fig. 2.

ref +

e

Controller

PM SM

ALO

Fig. 2. Controller based on ant lion algorithm.

4 Simulative Validation Table 1. Parameters. Parameter

Value

Voltage/V

380

Current/A

380

Power/kW

100

Polar

6

Speed/(rpm)

1500

D-axis inductance/mh

0.64

Q-axis inductance/mh

2.12

DC resistance/m

29.14

The motor parameters used in this simulation are shown in Table 1, and the rated speed of the motor is 1500 rpm. The simulation experiment is conducted under two working conditions. One is that the low speed enters the weak magnetic field area, and the speed is from 1000 to 2500 rpm. One is that the weak magnetic field area enters the low speed area, from 2000 to 500 rpm. Comparing the strengths and weaknesses of

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various approaches in the figure, the red curve is the PI control method, the green curve is the fuzzy control method, and the blue curve is the advantages and disadvantages of the ant lion-based control method.

Speed(rpm)

(1) 1000–2500 rpm

Time(s)

Fig. 3. 1000 rpm to 2500 rpm.

Figure 3 shows the waveform of the motor speed from 1000 to 2500 rpm. It can be discovered from the figure that the PI control method has large overshoot and long regulation time. The adjustment time of fuzzy control is the same as that of ALO control, but the overshoot of this method is smaller. (2) 2000–500 rpm

Speed(rpm)

PI control method Fuzzy control method Method based on ALO

Time(s)

Fig. 4. 2000 rpm to 500 rpm.

Figure 4 is the waveform diagram of the motor speed from 2000 to 500 rpm. According to the figure, the overshoot of fuzzy control is the same as that of PI control, but the adjustment time of fuzzy control is shorter. The control method in this paper is better than the other two methods in dynamic response.

5 Conclusion This paper proposes a control method based on the ant lion algorithm. On the basis of the traditional controller, according to different error sizes, the algorithm is employed to optimize the controller parameters, so that the current error can adapt to the controller parameters. Finally, the experiment shows that compared with other methods,

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this method has the such strengths as small overshoot, short adjustment time, good dynamic response and high steady-state accuracy. Acknowledgement. This work was supported by Natural Science Foundation of Anhui Province (2108085ME179),National Natural Science Foundation of China (51607002).

References 1. Meesala, R.E.K., Athikkal, S., Aruldavid, R.: Improved Direct torque controlled PMSM drive for electric vehicles. J. Inst. Eng. India Ser. B 103(1177–1188), 2016 (2022). https:// doi.org/10.1007/s40031-022-00716-8.Author,F.,Author,S.:Titleofaproceedingspaper.In:Edi tor,F.,Editor,S.(eds.)CONFERENCE2016,LNCS,vol.9999,pp.1-13.Springer,Heidelberg 2. Cao, B., Grainger, B.M., Wang, X., Zou, Y., Reed, G.F., Mao, Z.-H.: Direct torque model predictive control of a five-phase permanent magnet synchronous motor. IEEE Trans. Power Electron. 36(2), 2346–2360 (2021). https://doi.org/10.1109/TPEL.2020.3011312 3. Ma, X., Bi, C.: A technology for online parameter identification of permanent magnet synchronous motor. CES Trans. Electr. Mach. Syst. 4(3), 237–242 (2020). https://doi.org/10. 30941/CESTEMS.2020.00029 4. Zhu, S., Zhang, H.: Simplified model predictive current control strategy for open-winding permanent magnet synchronous motor drives. J. Power Electr. 21(6), 911–920 (2021). https:// doi.org/10.1007/s43236-021-00237-5 5. Author, F.: Contribution title. In: 9th International proceedings on proceedings, pp. 1–2. Publisher, Location (2010) 6. Liu, D., Wang, S., Zhang, Y., Wang, M., Wang, S.: Design of fuzzy adaptive PI control system for permanent magnet synchronous motor. Electric Tool (04), 4–6+26 (2020). https://doi.org/ 10.16629/j.cnki.1674-2796.2020.04.002 7. Bin, S., Wang Haixia, S., Tao, S.C., Xiaoran, L.: Nonlinear active disturbance rejection controller design and tuning for permanent magnet synchronous motor speed control system. Proc. CSEE 40(20), 6715–6726 (2020). https://doi.org/10.13334/j.0258-8013.pcsee.200018 8. Li, G., Ren, X., Ren, B.: Application of compound fuzzy-PI controller in PMSM. Mach. Tool Hydr 41(09), 51–53 (2013) 9. Li, H., Jican, L, Tang, H.: BP neural network based vector compound control of permanent magnet synchronous motor. Modern Electr. Tech. 42(11), 104–107+112 (2019). https://doi. org/10.16652/j.issn.1004-373x.2019.11.024 10. Zhuanzhe, Z., Zhang, Y., Yongming, L., Zhen, Z.: Statistic analysis of parameter efficiency of ant lion optimizer. Comput. Simul. 39(03), 330–334 (2022) 11. Sant, A.V., Rajagopal, K.R., Sheth, N.K.: Permanent magnet synchronous motor drive using hybrid PI speed controller with inherent and noninherent switching functions. IEEE Trans. Magn. 47(10), 4088–4091 (2011). https://doi.org/10.1109/TMAG.2011.2159831

Correction Method for Harmonic Measurement of Capacitor Voltage Transformer Based on Frequency Response Characteristics Zhu Mingxing1 , Jiao Yadong1 , Zhang Huaying2 , Gao Min1 , Wang Qing2 , and Cui Qi1(B) 1 School of Electrical Engineering and Automation, Anhui University, Hefei 230601, Anhui

Province, China [email protected] 2 Quality Power Supply Joint Laboratory of China Southern Power Grid, New Smart City High, Shenzhen Power Supply Co., Ltd, Shenzhen 518020, Guangdong Province, China

Abstract. Capacitor voltage transformers (CVTs) are widely used in high-voltage and ultra-high voltage power systems, and harmonic measurement cannot avoid its influence. The calibration of CVTs primarily consists of two steps: accurate frequency response measurement and precise parameter identification. In this paper, an intelligent high-voltage CVT harmonic frequency response test platform based on the sweeping frequency principle is established. The test results of several CVTs show that the frequency characteristics of CVTs manufactured with the same design parameters by the same manufacturer are very close. On this basis, to solve the minimum frequency regulation limitation of the test, the optimal identification model of key parameters is proposed by using the least square method to minimize the difference between the model simulation and the test results. The results show that the optimization model can identify the key parameters more accurately, which can be used as the basis future correction of CVTs. It further expands the ability of CVTs in harmonic measurement. Keywords: Capacitor Voltage Transformer · Test platform · Frequency response · Parameter identification · Correction Method

1 Introduction With the wide application of power electronics technology in the fields of HVDC and FACTS, PV Power stations, wind farms, high-speed rail, and rail transit, the harmonic pollution problem of the high-voltage system has become increasingly serious, which has attracted the high attention of transmission system operators [1–3]. In recent years, CVT has significantly improved its design and manufacturing level and product quality. With its many advantages in the application of high-voltage power system, CVTs are widely used in new and reconstructed 110 kV and above substations. CVTs can fully meet the requirements of the system in terms of measuring the accuracy of fundamental voltage and fundamental signal transformation of system protection and automatic © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 654–664, 2023. https://doi.org/10.1007/978-981-99-4334-0_81

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device [4]. However, the presence of capacitors, inductors, and other energy storage components in CVTs causes significant harmonic measurement inaccuracies. In some cases, variations of up to 200% or more can be seen [5]. At present, guiding documents such as IEC61869-5:2011, IEEE Std 1159-2009, and CIGRE C4.112 report do not recommend the direct use of CVTs to measure harmonics. This severely limits how high-voltage power networks are governed and monitored for power quality. Thus, the frequency response characteristics and critical parameters of CVTs are analyzed based on the high-voltage power grid’s operational status, which has significant theoretical relevance and practical usefulness to address the harmonic measurement inaccuracy generated by CVTs. The issue of measuring the CVT harmonic voltage has been covered in a number of studies. The voltage transformation ratio measured by CVTs at different frequencies are different, and the frequency response characteristics are different with the different parameters of CVT circuit. The lack of a unified quantitative rule challenges the accurate measurement of harmonics [6]. In order to compute the voltage value of the CVT’s high voltage side by measuring the capacitive current and the known voltage divider capacitance, it is also possible to connect two current sensors to the ground circuit of the device, so as to achieve the CVT harmonic measurement [7]. However, this method needs changes in the circuit configuration, which is not applicable to the CVT in operation, and there are problems such as accurate measurement of small signals and noise interference. Therefore, attempting to establish a CVT high-frequency harmonic impedance model, derive its transfer function, and correct the harmonics according to the CVT response at different frequencies. In reference [8] believes that this is a good method, but the key point of its realization is to accurately obtain the parameters of the model, which requires parameter identification on the offline CVT frequency response characteristics test results. At present, researchers from the Electric Power Research Institute of America apply low-voltage frequency varying voltage signals at the CVT input terminal to draw a broadband transmission characteristic curve. However, the low voltage input makes the output test result close to the noise level, which has a great impact on the measurement result, and it needs to be improved by inputting a high-voltage signal. At the same time, the CVT parameters produced by different manufacturers are different, and their frequency response measurements must be different. A lot of offline tests need to be carried out, and the impact of operating load and temperature on the frequency response characteristics cannot be ignored [9]. It is more necessary to bring the temperature coefficient and load size of each parameter into the simulation model based on the results of parameter identification, and finally obtain the frequency response characteristics consistent with the actual situation, to achieve harmonic measurement of CVTs. This paper develops an intelligent high-voltage CVT harmonic frequency response characteristic test platform based on the sweep frequency principle, on which several groups of 35–220 kV rated voltage CVTs are tested. According to the experimental findings, the frequency characteristics of CVTs made by the same manufacturer using the same design specifications are fairly similar, and the consistency of parameters creates conditions for identification. Given the minimum frequency regulation limit of the test, the least square method can be used to minimize the difference between the model

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simulation and the test results, and the equivalent resistance and stray capacitance of the compensation inductor and the stray capacitance of the intermediate transformer winding are used as the key parameters for identification. The optimal identification model of the key parameters is proposed. The identification results are more precise than the resonant frequency characteristics. Future harmonic correction of CVT might be based on the established parameters. The advancement and use of CVT must be strongly encouraged.

2 Experimental Test of Frequency Response of CVT 2.1 High Voltage Experimental Test Platform

Low-voltage variable frequency source DDS signal generator

Standard Adjustable step-up capacitive voltage transformer divider H

DAC digital to analog signal

Gear M adjuster

200kW power amplifier

EUT CVT

DSP Upper computer controller

Data acquisition

Data analysis FFT Harmonic analyzer

Fig. 1. Composition and principle of experimental test platform.

The platform is composed of an upper computer controller, low-voltage variable frequency source, adjustable step-up transformer, standard capacitor voltage divider, harmonic analyzer, and equipment under test (EUT). Its principle block diagram is shown in Fig. 1. The low-voltage variable frequency source can generate voltage of different amplitude and frequency. The step-up transformer can raise the low voltage to the rated voltage of EUT, and the standard capacitor is used as the comparison object for EUT output measurement. A field picture of the platform was given in Fig. 2.

(a)

(b)

(c)

Fig. 2. Field picture of the platform: (a) field wiring; (b) low-voltage variable frequency source; (c) upper computer controller.

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The technical requirements for each component of the platform are as follows: (1) Low-voltage variable frequency source: it adopts a DDS signal generator to realize multiple harmonic superposition signal output. Then, the high-precision DAC chip is used as the output amplitude regulator to adjust the amplitude output of each harmonic. Rated output capacity: 200 kW; output voltage range: 0–350 V; Harmonic adjustment range: 45–2500 Hz. (2) Adjustable step-up transformer: its iron core is made of an ultra-thin silicon steel sheet with a thickness of 0.2 mm to minimize the transformer’s short-circuit impedance. During the test, when the rated voltage of the test object is 66 kV or below, select the gear of 0.7/100 kV; For 110 kV and above, select 0.35/100 kV gear. (3) Standard capacitor voltage divider: the rated voltage is 100 kV, which is composed of high-voltage capacitor CH and low-voltage capacitor CL . Among them, CH uses stainless steel filled with SF6 gas, with a capacity of 100 pF; CL uses a mica capacitor, with a capacity of 100 nF, a partial voltage ratio of 1000, and a voltage measurement accuracy of ≤ 0.2%. 2.2 Experimental Test Results The low-voltage variable frequency source is controlled by the higher computer to produce the voltage of the “fundamental wave plus a specific harmonic” throughout the test, then the adjustable step-up transformer is used to boost the voltage to the rated voltage of the CVT to be measured, and then power the typical capacitor voltage divider and CVT. Finally, the response characteristics of the corresponding frequency are calculated according to (1) and (2) by synchronously outputting this harmonic voltage from the standard capacitor and the secondary side of CVT. The rated voltage sweep test of CVT can be realized by changing the frequency of the low-voltage variable frequency power supply’s output harmonic, and the frequency response characteristics within the frequency range of 2th –50th harmonics can be obtained.  amp(h) = HRUout (h) HRUin (h) (1) pha(h) = θout (h) − θin (h)

(2)

where HRU out (h) and θ out (h), are respectively the h harmonic voltage content (%) and phase (°) of CVT output; HRU in (h) and θ in (h) are respectively the h harmonic voltage content (%) and phase (°) of the standard voltage divider output; apm and pha are CVT amplitude-frequency characteristics and phase frequency characteristics. Conduct√frequency tests on multiple groups of CVTs with √ √ response characteristic √ 35/ 3, 66/ 3, 110/ 3, and 220/ 3kV rated voltage levels. Part of the test results of CVT frequency response characteristics are given in Fig. 3. Table 1 lists the frequency and value for the amplitude-frequency characteristics’ peak and valley points as well as the frequency and phase angle for the phase frequency characteristics’ lowest point. The test results show that CVTs with different rated voltages from the same manufacturer are manufactured according to different design parameters, and the corresponding frequency response characteristic points are different. Although CVTs manufactured with the same design parameters have different manufacturing tolerances, the frequency

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CVT type

√ TYD35/ 3-CVT1 √ TYD35/ 3-CVT2 √ TYD66/ 3-CVT1 √ TYD66/ 3-CVT2 √ TYD110/ 3-CVT1 √ TYD110/ 3-CVT2 √ TYD220/ 3-CVT1 √ TYD220/ 3-CVT2

Peak point

Valley point

Lowest point

frequency Amplitude frequency Amplitude Frequency Phase (Hz) (p.u.) (Hz) (p.u.) (Hz) (°) 500

3.71

600

0.22

550

-129.49

500

3.63

600

0.23

550

-129.85

350

2.34

450

0.2

400

-123.48

350

2.21

450

0.18

400

-124.6

250

2.03

350

0.26

300

-93.52

250

1.98

350

0.31

300

-88.36

400

3.56

500

0.2

450

-130.3

400

3.47

500

0.21

450

-126.99

response of CVTs is very close. The sample exhibits a maximum error of less than 0.13 p.u. for the measured amplitude-frequency characteristic and less than 5.16° for the measured phase-frequency characteristic. If the test is conducted under similar conditions, CVTs from the same manufacturer with the same design parameters can be identified through a limited number of tests, which can reduce the test workload.

3 Key Parameter Identification 3.1 Impedance Model and Frequency Response Analysis of CVT The harmonic impedance model of CVTs is constructed, as illustrated in Fig. 4, to identify the critical parameters and realize the simulation of the frequency response properties. In the figure, C 1 and C 2 are high and medium voltage partial capacitors. L c , Rc and C c are the inductance, equivalent resistance, and stray capacitance of the compensation inductor. The resistance and inductance of the intermediate transformer’s excitation winding are designated as Rm and Lm, respectively. RT,1 , L T,1 are the primary winding resistance and leakage inductance of the intermediate transformer. RT,2 , L T,2 are the winding resistance and leakage inductance of the secondary side converted from the intermediate transformer to the primary side. C p is the stray capacitance of the primary side winding of the intermediate transformer to the ground. RD and L D are equivalent resistance and inductance of secondary load converted to primary side. √ Table 2 shows the measured parameters of a model of CVT (TYD66/ 3). In combination with Fig. 4, the frequency response characteristics with and without stray parameters are compared through simulation. The simulation’s stray parameters are Cc = 750pF, Cp = 350pF, infinite excitation impedance, and no-load condition load. According to the comparison results shown in Fig. 5, when there is no distribution parameter, the CVT frequency response characteristic curve tends to be horizontal. However, the phase frequency characteristic curve and “peak” and “valley” points of the CVT

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3

-20

Phase-frequency

Amplitude-frequency

4

2

1

-40 -60 -80 -100

TYD35/ 3-CVT1 TYD35/ 3-CVT2 Calibrated divider

-120 0

5

10

15

20

-140

25

5

10

Harmonic order

1

-40 -60 -80 -100

TYD66/ 3-CVT1 TYD66/ 3-CVT2 Calibrated divider

0.5 -120 5

10

15

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Amplitude-frequency

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1.5

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Harmonic order

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Harmonic order 0

4 TYD220/ 3-CVT1 TYD220/ 3-CVT2 Calibrated divider

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Phase-frequency

Amplitude-frequency

15

Harmonic order

2

2

1

-40 -60 -80 TYD220/ 3-CVT1 TYD220/ 3-CVT2 Calibrated divider

-100 -120

0

25

-20

1.5

0

20

0 TYD66/ 3-CVT1 TYD66/ 3-CVT2 Calibrated divider

2

Phase-frequency

Amplitude-frequency

15

Harmonic order

2.5

0

659

5

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15

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-140

5

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Harmonic order

15

20

25

Harmonic order

(a)

(b)

Fig. 3. Frequency response characteristic test results of CVTs: (a) amplitude-frequency characteristics; (b) phase-frequency characteristics.

Lc

Rc

RT,1

LT,1

RT,2

Rd

C1 C2

LT,2

Cc

Cp

Rm

Lm Ld

Fig. 4. Impedance model of CVT.

amplitude-frequency characteristic curve exist when there are distribution parameters. Before reaching the amplitude “peak” point, the phase error increases, and the hysteresis increases, and then the phase error decreases and the hysteresis decreases.

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Parameter

Actual data

Parameter

Actual data

Parameter

Actual data

Parameter

Actual data

C 1 /nF

13.52

L c /H

162.00

RT,1 /

1427

RT,2 /

1570

C 2 /nF

38.79

Rc /

6000

L T,1 /H

26.33

LT,2 /H

11.68

0

4

3

With distributed parameters No distribution parameter

Series resonant point

Phase-frequency

Phase-frequency

With distributed parameters No distribution parameter

2

Parallel resonant point 1

0

5

10

15

20

25

-50

-100

-150

Harmonic order

5

10

15

20

25

Harmonic order

(a)

(b)

Fig. 5. Frequency response characteristic simulation results of CVT: (a) amplitude-frequency characteristics; (b) phase-frequency characteristics.

Based on the tiny secondary load capacity of the CVT, the influence of the intermediate transformer can be disregarded in order to further clarify the nonlinear generating mechanism of the CVT frequency response characteristic curve. Currently, it is possible to simplify the transfer function in the red shadow region of Fig. 2 as (3). 1 − 4π 2 f 2 Lc Cc U2 (f ) = U1 (f ) 1 − 4π 2 f 2 Lc (Cc + Cp )

(3)

According to (3), the peak point in Fig. 3 is the series resonant point, and the valley point is the parallel resonant point. The resonant frequency is shown in (4) and (5), that is, L c and C c have parallel resonance; The compensation reactor (including L c and C c ) has a series resonance with C p . fs =

1  2π Lc (Cc + Cp )

(4)

1 √ 2π Lc Cc

(5)

fp =

Therefore, the fundamental reason why CVT cannot measure harmonics is the resonance caused by distribution parameters. Various resonance locations are associated with various CVT distribution parameters, and the harmonic measurement error caused by frequency response characteristics will also be different.

Correction Method for Harmonic Measurement of Capacitor Voltage

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3.2 Key Parameter Optimal Identification The manufacturing parameters and stray parameters are among the CVT’s parameters. The manufacturing parameters have been determined according to the design requirements. Even if there is manufacturing tolerance, manufacturers will test their accurate values at the delivery stage. The capacitance effect between conductors leads to the distribution parameters of CVT, which is difficult to calculate or measure. If the resonant point position of CVT under harmonic conditions is accurately known, the key parameters C c and C p can be accurately calculated by using (4) and (5). Cc, Rc, and Cp are therefore important stray factors that will influence the frequency response. However, the minimum frequency adjustment interval (50 Hz) of the test power supply is limited, and the measured CVT frequency response characteristics can only identify the approximate distribution area of its resonant point, so using it to calculate the key parameters C c and C p will inevitably lead to large deviations. The comparison of the measured results of frequency response characteristics of a CVT at the minimum frequency regulation interval of 5 and 50 Hz are given in Fig. 6. 0 5Hz 50Hz

5Hz 50Hz

°

-20

2

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3 2.5

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-60 -80 -100

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5.5

6

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(a)

(b)

Fig. 6. Test results of frequency response characteristics of different minimum frequency regulation intervals: (a) amplitude-frequency characteristics; (b) phase-frequency characteristics.

The CVT frequency response characteristic curve of the 5 Hz interval test is smoother than that of the 50 Hz interval test, the curve change trend is closer to the real CVT frequency response characteristic, the position information of the series and parallel resonant points and their peak and valley point multiples are more accurate, and the calculation error is smaller according to the formula at this time., as shown in Table 3. However, in the test, if the frequency adjustment interval is set smaller, the performance of the harmonic generator is required to be higher, the overall operation process is complex, and the calculation is cumbersome. At the same time, the calculation method cannot obtain Rc . Consequently, As a result, the objective function is set using the least squares approach, with the objective criterion being the minimal value of the square cumulative sum of the difference between the measured value and the simulated value, as shown in (6). The optimization model is established to identify the key parameters of CVT. min f (Rc , Cc , Cp ) =

n    [Am (h) − As (h)]2 + [Pm (h) − Ps (h)]2 h=1

(6)

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Table 3. Calculation results of CVT parameters Cc and Cp under different frequency regulation intervals. Minimum frequency regulation interval (Hz)

Reactance value (H)

Series resonant point (Hz)

Parallel resonance point (Hz)

CC Calculated value (pF)

CP Calculated value (pF)

5

202.2

290

335

1117

374

300

350

1027

366

50

where Am (h) and Pm (h) are the amplitude and phase of the measured at the frequency of the h order harmonic, As (h) and Ps (h) are the amplitude and phase of the simulated at the frequency of the h order harmonic. It is advised to solve the optimization model using the particle swarm optimization (PSO) methodology in order to acquire a set of ideal key parameters that will minimize the error.

4 Parameter Identification Results and Correction √ The CVT of TYD 66/ 3 model is studied here. The manufacturing parameters are shown in Table 2. A group of key parameters can be calculated by using the frequency corresponding to the series and parallel resonant points in the amplitude-frequency characteristic measurement. By optimizing the model, one might also find a different collection of crucial variables. Table 4 compares the outcomes of parameter identification and computation. Table 4. Comparison of the key parameter identification results. Series resonance point (Hz) 350

Parallel resonance point (Hz) 450

Calculated parameters

Optimal parameters

C c (pF)

C p (pF)

C c (pF)

C p (pF)

Rs (k)

773

506

819.11

316.77

14.51

The comparison between the frequency response of the calculation parameters and the identification optimal parameters brought into the model simulation and the test results is shown in Fig. 7. Table 5 shows the maximum deviation between the model simulation frequency response of the two-parameter sources and the test results. The results show that the parameters identified by the optimization model established by the least square method can significantly reduce the deviation. The amplitude deviation can be reduced to 73.86%. The phase deviation can be reduced by 84.22%. It may be concluded from the comparison that this suggested strategy has two benefits. One is that it is possible to determine the compensated inductor Rs’s equivalent resistance. The second is that the identified key parameters overcome the minimum

Correction Method for Harmonic Measurement of Capacitor Voltage 0

3 Calculate Optimization Measurement

Calculate Optimization Measurement

-20

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Amplitude-frequency

2.5 2 1.5 1 0.5 0

663

-40 -60 -80 -100 -120 -140

5

10

15

20

25

5

10

15

20

25

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Harmonic order

(a)

(b)

Fig. 7. Comparison of frequency reponse: (a) amplitude-frequency characteristics; (b) phasefrequency characteristics.

Table 5. Maximum deviation of simulation value from measured value of different parameter sources Source of parameters

Maximum deviation of amplitude Maximum deviation of phase (°) (p.u.)

Parameters of calculated 0.88

58.49

Parameters of optimal

0.23

9.23

Optimization rate (%)

73.86

84.22

frequency regulation limit of the test power supply, and it is more accurate than the parameters calculated from the measured resonant frequency point. The experimental test comparison results in Fig. 3 lead to the conclusion that the frequency responses of CVTs made with the same design parameters exhibit a high degree of similarity. The labor of experimental testing can be greatly reduced by using the key parameter identification approach. At the same time, under the condition that the influence of temperature and secondary load is clear, the temperature coefficient and load size of each parameter can be directly brought into the simulation model to realize the correction of CVTs harmonic measurement error in actual field operation in the future.

5 Conclusion The comprehensive test results show that under similar environmental conditions, the frequency responses of CVTs made with the same design parameters show a significant degree of similarity. Through the comparison of CVTs frequency response characteristics measured on the test platform and simulated by the model, the optimization model of key parameter identification is established by using the least square method. The parameters determined from the resonant frequency point in the amplitude-frequency characteristic assessed by the 50 Hz minimum frequency regulation test are less accurate than the optimal identification result. This method can also reduce the workload of CVTs test with the same design parameters.

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Further research is needed to master the change rule of CVT component parameters under the influence of temperature, quantify the influence mechanism of secondary load capacity and power factor on frequency response characteristics, and identify the key parameters under corresponding conditions according to the frequency response characteristic curve provided by the manufacturer in the future, then bring the temperature coefficient and load size of each component parameter into the simulation model, and accurately correct the harmonic measurement. Acknowledgment. This research was supported by the Science and Technology Project of China Southern Power Grid (090000KK52190169/ SZKJXM2019669).

References 1. Guowei, Z.H.O.U., Yongdi, G.U., Jianping, Z.H.O.U., et al.: Analysis of non-characteristic harmonic in UHVDC system. Power Syst. Prot. Control 44(03), 122–128 (2016) 2. Bo, C., Guo, L., Shenghui, Y., et al.: A brief analysis of new energy and power quality. Power Syst. Clean Energy 28(06), 91–96 (2012) 3. Li,Y., Zhu, N., Jian, W., et al.: Analysis and control on harmonic of traction power supply system of heavy electrified railways. Power Capacitor React. Power Compensation 40(06), 123–129 (2019) 4. Zhang, F., Li, K., Chen, X., et al.: Error analysis of capacitor voltage transformer in the operation environment. In: IEEE international conference on high voltage engineering and application, pp. 1–4. IEEE, Chengdu, China (2016) 5. Meyer, J., Stiegler, R., Kilter, J.: Accuracy of voltage instrument transformers for harmonic measurements in Elering’s 330-kV-transmission network. In: IEEE Conferences on Electric Power Quality and Supply Reliability, pp. 85–90. IEEE, Tallinn, Estonia (2016) 6. Wang, R.: Research the Distortion of Applying CVT to Measure Harmonic. North China Electric Power University (2009) 7. Ghassemi, F., Gale, P., Cumming, T., et al.: Harmonic voltage measurements using CVTs. IEEE Trans. Power Deliv. 20(01), 443–449 (2005) 8. Ghassemi, F., Gale, P., Clegg, B., et al.: Method to measure CVT transfer function. IEEE Trans. Power Deliv. 17(4), 915–920 (2002) 9. Klatt, M., Meyer, J., Elst, M., et al.: Frequency responses of MV voltage transformers in the range of 50 Hz to 10 kHz. In: 14th International Conference on Harmonics and Quality of Power (ICHQP), pp.1–6. IEEE. Bergamo, Italy (2010)

Design of Aviation AC/DC Contactor Life Test System Based on PXI-2204 and CPCI-7434 Siyang Liang, Run Dong, Siyi Yang, and Weilin Li(B) Department of Automation, Northwestern Polytechnical University, Xi’an, China [email protected]

Abstract. The health status and operation life of aviation contactor are closely related to the safety of airborne power distribution system. This paper designs and builds a set of aviation contactor life test platform. The proposed circuit topology can perfectly realize the operation life test of contactor under different working conditions, and the invalid switching operations of the components are greatly reduced, so as to improve the contactor test experimental efficiency. The peripheral circuit adopts the driving circuit with CPCI-7434 digital I/O board, the signal acquisition and conditioning circuit with PXI-2204 data acquisition card and the power supply circuit. The full-automatic control life cycle test interface is designed by LabVIEW in order to collect and display the voltage and current signals of contactor contacts and coils. In addition, after system joint debugging, the whole set of life test platform successfully achieve designed functions, such as data output and storage in real time, ensure the visualization and operability of the whole test system on the premise of friendly human-computer interface. Keywords: Aviation CONTACTOR · Life test · Full-automatic working condition simulation · LabVIEW · Real-time output

1 Introduction Aviation contactor is a basic electrical component in aircraft electrical control system. As an essential equipment in aviation power distribution system, its health status and operation life directly affect the working condition of aircraft electrical system. It is of great significance to realize intelligent automatic control and working condition monitoring, which will greatly reduce or avoid accidents caused by faults or mis-operation, so as to ensure the safe start-up of aircraft and the normal completion of flight tasks. The overall aviation AC/DC contactors life test platform design framework is illustrated in Fig. 1. In this paper, a life cycle test system is designed, in which the master computer PC transmits commands to automatically control the contacts to complete various working conditions. On the premise of building a friendly human-computer interaction interface, the overall system can simulate different working conditions of the aviation contactor, and carry out real-time data acquisition, conditioning, output and storage [1]. Ensuring the visualization and operability of the overall test system, the physical platform is completely established after debugging the corresponding functions. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 665–674, 2023. https://doi.org/10.1007/978-981-99-4334-0_82

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Acquisition conditioning circuit PXI-2204 Data Acquisition Card

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KM3-6 Companion samples KM1-2

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KS1-2

Fig. 1. The overall framework of the life test platform.

In terms of hardware design, some innovations have been made in the research of existing scholars, and the previously selected adjustable power source is replaced by variable load. In the variable load test in the electrical life test, the companion test sample is frequently switching initially, and the main power supply and 1/6 times power supply switch each other to simulate the load change, which is directly designed to use the controllable simulated load instead [2]. By controlling the switching sequence of the contactor and the variable load, the load change can be directly simulated. On the premise of greatly reducing the invalid switching frequency of the test sample, the variable load test can be realized more efficiently and time saving.

2 Hardware Design The hardware design is mainly from two aspects of electrical life and mechanical life [3, 4]. The AC and DC contactors life test platform are carried out the closing, breaking, constant load, variable load and mechanical life tests, which is shown in Table 1. Table 1. Definition of contactor life test patterns. Test pattern

Action Sequence of Test Samples

Connection test

On-load closing, no-load breaking

Breaking test

No-load closing, on-load breaking

Constant load test

On-load closing and breaking. DC-3, AC-4

Variable load test

On-load closing and breaking. DC-5, AC-3

Mechanical life test

No-load closing and breaking

The constant load test means that when the contactor is closing or breaking, the current and voltage amplitudes of the contacts are the same. While in the variable load test, the closed current value is 6 times the rated current and the voltage is the rated voltage, but the breaking current is the same as rated current. Therefore, when designing the topology of the main circuit, a variable load is used to adjust the current and voltage

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values in the circuit to meet different working conditions under the corresponding test patterns. Besides, it still collects and extracts the characteristic parameters of the contactors, so as to provide reliable data support for the subsequent life health management of the contactors [5, 6]. 2.1 Main Circuit The main circuit of AC/DC contactor life test is divided into five parts: main power supply, companion test samples, test samples, variable load, voltage and current signal acquisition sensor. By placing the companion test contactor in the main circuit, the invalid switching operation frequency of the test contactor can be greatly reduced. Therefore, its switching state is necessary for the test (i.e. effective switching). Therefore, more useful information can be obtained and provide more real and powerful guaranteed data for the subsequent analysis of the aviation contactor life. DC Power supply

DC circuit

AC circuit

UA4 UB4 UC4

KS1

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KM5

Ia5 Ib5 Ic5

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Ia4 Ib4 Ic4

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Id3

Id4

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IA2 IB2 IC2

Id2

Id1

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KM6

Ia6 Ib6 Ic6

Current sampling

UD2

IA1 IB1 IC1

UD1

DC Power supply QF1

AC Power Supply

Current sampling

Internal wiring of main circuit Adjustable load

Fig. 2. Topology of the main circuit.

As indicated in Fig. 2, the main circuit topology of the AC/DC contactor life test has been built. KM1 and KM2 are AC relays, which are used as companion samples to control the AC channel power supply status of the main circuit. Cooperating with the other four AC contactor test samples KM3-KM6, the experiments under different working conditions with AC power supply can be realized completely [7]. KS1 and KS2 are DC contactors, which are powered by DC power supply to conduct the test of each DC contactor test samples separately, then complete the expected DC working condition test [8]. 2.2 Acquisition and Conditioning Circuit In the life test, the contactor characteristic signals to be collected are the current and voltage waveforms of the contactor contacts and coils [9]. The AC contactor contacts are connected to 115V/400 Hz AC aviation bus power supply, while the contactor coil and DC contactor contacts pass through 15 V DC power supply and 28 V DC aviation bus power supply respectively. When collecting and measuring the contactors’ voltage and current

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waveforms with the two different power supply modes, four different acquisition circuits are required: AC voltage acquisition, AC current acquisition, DC voltage acquisition and DC current acquisition. These four signals still need to be conditioned after acquisition, that is, the amplitude of the waveform is converted into an electrical signal that can be collected by the PXI-2204 data acquisition card in a certain proportion, and transmitted to the PC for display and storage. In this paper, precision resistor is selected to isolated from the main circuit through an isolation amplifier. The selected Hall sensor which with physical isolation effect is used to collect the current waveform. However, the amplitude range of the output signal cannot match the AD sampling range in the PXI-2204 card data acquisition channel. It is still necessary to input the collected signal into the card after a certain degree of proportional amplification and impedance matching through the operational amplifier circuit. The content above is illustrated in Fig. 3. Voltage signal acquisition

Isolation Proportional adjustment

Impedance matching

PXI-2204 Data acquisition

Current signal acquisition

Fig. 3. The block diagram of waveform acquisition and conditioning.

To sum up, the AC/DC current, voltage acquisition and conditioning circuit is integrated, the single ports are combined and transmitted to the 64 channels of PXI-2204 independently. There are 22 channels are designed for AC voltage and current signals respectively, 9 channels are remained for DC voltage and current signals respectively. As shown in Fig. 4(a).

(a)

(b)

(c)

Fig. 4. Three PCB boards. (a) Acquisition and conditioning circuit. (b) Drive circuit. (c) Power supply circuit.

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2.3 Drive Circuit The main function of the drive circuit is to drive the coil of the AC and DC contactor test samples and the companion test samples in the main circuit. It can change the switch state of the contactors through whether the coil is energized or not. AC relays like KM1 and KM2 is used to control the switching strategy of the companion test samples and test samples. By expanding more channels to carry out the switching design of the relay and contactor, the platform is able to complete the life test under different working conditions with corresponding regular pattern. Besides, the input and output signal can be isolated to prevent circuit failure or mis-operation from damaging the power supply. The driver circuit is mainly composed of two parts: digital output circuit and isolated driver circuit. In the design of digital output circuit, the PC independently controls each output level through the design program. The signal voltage is transmitted to the PCB of drive circuit by the CPCI-7434 card, and is used as the drive signal after passing through the Darlington transistor. During the design of the isolation drive circuit, the digital output signal after the overturned level is used as the final drive signal to control the switching status of the relay. The Fig. 4(b) illustrates the overall circuit and then jointly realize different working condition strategies. 2.4 Power Supply Circuit The power supply circuit is mainly composed of four parts, namely, civil power conversion to ± 28 V module, ± 15 V power conversion module, ± 5 V power conversion module, DC 2.5 V and DC 1.5 V power conversion module, as indicated in Fig. 4(c).

3 Software Design This section describes and analyzes the software control of AC/DC contactor based on the hardware design. In the design of the system software, through the comprehensive understanding and integrated analysis of the requirements, the LabVIEW software in the graphical development environment under the Windows operating system is finally build. The software design mainly includes the driver of CPCI-7434 digital I/O board and the data acquisition and display program control of PXI-2204 acquisition card, which is illustrated thoroughly in Fig. 5. The automatic control mode is divided into five working conditions: closing test, breaking test, constant load test, variable load test, and mechanical life test. The life tests of AC and DC contactors under different power supply modes are tested respectively. Under the dual modes of manual and automatic control, the control modes are more flexible and diverse, and more complex functions will be realized in the future. For the acquisition program, different forms of data from different channels can be displayed and saved in two ways: image and data. By setting the number of sampling points and sampling frequency, the software system can obtain more useful and precise waveform information. The maximum sampling rate of the PXI-2204 card can reach 3M/S. The sampling type setting choices, such as differential or floating signals and so

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CPCI-7434 DO port

Output drive circuit

Solid state relay

Current & voltage sensor

coil, contact Voltage & current

Signal acquisition circuit

Measured signal

AC, DC contactor coil

Board PXI-2204 AI port

Fig. 5. The overall software design process.

on, which are designed to adapt to various types of signals. The signals before and after filtering are displayed on two oscilloscope screens, and multiple sampling signals can be displayed on the same screen with lines of different colors for real-time comparison and output.

Fig. 6. The final overall software platform interaction interface.

The above software design has fully realized the expected functions, and the entire interface is shown in Fig. 6. The program design is perfectly combined with the above hardware circuit, which has laid a solid foundation for subsequent test and verification.

4 Experiment Platform and Results In this section, the life test platform of aviation contactor is debugged and verified. Firstly, the PCB board of acquisition circuit combined with PXI-2204 are used for acquisition, conditioning and debugging. Secondly, combined with the main circuit and the other three PCB boards, the AC and DC contactor life tests are carried out automatically, and the contact and coil voltage, current are synchronously collected, displayed and saved. The joint system is illustrated in Fig. 7. The current acquisition of the three-phase contact of AC contactor is divided into two parts: power on and power off, corresponding to the turn-on and turn-off of the contactor respectively. Figure 8 illustrates the original and partial magnified waveform of aviation three-phase AC contact current, at the moment of power on and power off when the acquisition card collects the frequency of 500 kHz.

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DC circuit

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AC circuit

PC with CPCI-7434 & PXI-2204 LabVIEW interface

Drive circuit power supply

Three PCB boards of peripheral circuit

28V DC power supply

115V/400Hz Constant AC power supply load

Variable load

Fig. 7. AC/DC aviation contactor life test physical system.

Different from the current acquisition, the voltage acquisition corresponds to the opposite state respectively. Figure 9 shows the acquisition voltage waveforms of the two parts respectively. After several parallel tests, the current waveform at the breaking moment of the contactor is more stable than the voltage waveform. Obvious distortion can be seen in the voltage waveform, and the jump during breaking process is much more serious than that during closing. 2.5

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2.5

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1.05

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3.5 104

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1

1.5

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(b)

Fig. 8. Current waveform of the aviation three-phase AC contacts. (a) Closing. (b) Breaking.

It is still necessary to take the same operations on the characteristic waveforms of the contactor coil. Especially locally amplify the waveform at the moment when the driving signal is triggered on and off. Figures 10 and 11 are the original current, voltage signals and local amplified waveforms when the acquisition board card collects the frequency of 500 kHz. It can be seen that in the process of coil power on and power off, the current waveform has dozens or even hundreds of times of pulse, and the pulse amplitude in the process of power off is much higher than that in the process of power on. The voltage waveform has obvious step signal in the power turn-on stage. The voltage drops instantly from positive amplitude to negative amplitude at the moment of power off, and keeps it for

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a while, then slowly rises to 0, completing the charging and discharging process in the power off stage. 0.45

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6000

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(b)

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Through the above collection of each type of signal, and by amplifying the partial waveform to conclude the dynamic change rules of current and voltage waveform at the moment of action. Then, by collecting and comparing the switching moments of the contactor, the causal relationship between the driving signal and characteristic waveforms can be seen more intuitively. Figure 12(a) shows the overall and partial real time waveforms of the four types of signals respectively during the switching process of AC contactor. By the comparison of the four characteristic waveform information at the same time, the working principle of the contactor can more comprehensively and intuitively understand, which provides a solid data theoretical basis for further analysis of the operation life of the contactor [11].

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(b)

Fig. 12. Overall characteristic waveforms of the. (a) Closing and breaking of aviation AC contactor. (b) Closing and breaking of aviation DC contactor.

The data acquisition process of DC contactor life test is similar to that of AC contactor. However, since there is only one channel current in the main circuit of DC contactor, the data acquisition is relatively simple compared with AC contactor. Therefore, each signal is collected independently according to the same AC measurement method, which will not be repeated in this paper. Figure 12(b) shows the overall and partial real time waveforms of the four types of signals respectively varying with time, during the switching process of DC contactor.

5 Conclusion In this paper, a set of AC/DC contactor life test platform is successfully built. Through the design of the main circuit topology, the platform achieves the best performance and the most complete functions. Under the joint debugging with the peripheral drive circuit and the operation interface of the life test platform built by LabVIEW, the real-time data acquisition and conditioning life test is finally successfully accomplished with different working conditions. The whole system control methods are composed of manual and automatic control this two aspects, so it provides great flexibility to design and improve the test strategy. Besides, the data display, output and storage are realized in the humancomputer interaction interface, providing a large number of reliable data support for subsequent life assessment.

References 1. Mützel, T., Hubrich, C., Tasch, J.: Impact of mechanical parameters on switching results of electro-mechanical contactors. In: 2021 IEEE 66th Holm Conference on Electrical Contacts (HLM), pp. 217–222 (2021). https://doi.org/10.1109/HLM51431.2021.9671118 2. Taylor, E.D., Eiselt, M., Tschiesche, R., Suresh, U., Brauner, T.: Electrical life of vacuum interrupters for load current switching. IEEE Trans. Plasma Sci. https://doi.org/10.1109/TPS. 2022.3175240 3. Sun, S., Wang, Q., Du, T., Wang, J., Li, S., Zong, J.: Quantitative evaluation of electrical life of AC contactor based on initial characteristic parameters. IEEE Trans. Instrumen. Measur. 70, 1–10 (2021). Art no. 3503510. https://doi.org/10.1109/TIM.2020.3031160

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4. Abirami, S., Ruthvik, S., Sathiq Ali, M., Sathish Kumar, R., Sujith Kumar, J.P.: AC contactor electrical health estimator model, IOP conference series: materials science and engineering. Mater. Sci. Eng. 1145 012070 5. Yang, C., Zheng, Z., Ren, W.: Investigation of making process and associated contact bounce behaviors for alternating current contactor. In: 2021 IEEE 66th Holm Conference on Electrical Contacts (HLM), pp. 165–170 (2021). https://doi.org/10.1109/HLM51431.2021.9671183 6. Zheng, Z., Ren, W., Wang, T.: Experimental investigation of the breaking arc behavior and interruption mechanisms for AC contactors. IEEE Trans. Plasma Sci. 49(1), 389–395 (2021). https://doi.org/10.1109/TPS.2020.3042545 7. Ruiz, J.R.R., Garcia, A., Cusidó, J., Delgado, M.: Dynamic model for AC and DC contactors— simulation and experimental validation. Simul. Model. Pract. Theory 19 1918–1932 (2011) 8. Fei, Y., Zhou, Z., Tao, Y., Li, Y., Li, W.: A novel bidirectional zsource solid-state circuit breaker for DC microgrid. In: 2021 IEEE 2nd China International Youth Conference on Electrical Engineering (CIYCEE), pp. 1–7 (2021) 9. Zheng, S., Niu, F., Li, K., et al.: Analysis of electrical life distribution characteristics of AC contactor based on performance degradation. IEEE Trans. on Compon. Packag. Manuf. Technol. 8(9), 1604–1613 (2018) 10. Zhang, B., et al.: A novel bidirectional Z-source DC circuit breaker for fuel cell related system,” IECON 2020. In: The 46th Annual Conference of the IEEE Industrial Electronics Society, Singapore, pp. 4981–4986 (2020) 11. Li, K., et al.: Electrical performance degradation model and residual electrical life prediction for AC contactor. IEEE Trans. Compon. Packag. Manuf. Technol. 10(3), 400–417 (2020). https://doi.org/10.1109/TCPMT.2020.2966516

MTPA Control Strategy of BLDCM Based on Back-EMF Orientation Mengting Chang1 , Qihang Sun2 , Yicheng Jia1 , Qingquan Jia1 , and Zhenguo Li1(B) 1 Key Lab of Power Electronics for Energy Conservation and Motor Drive of Hebei Province,

Yanshan University, Qinhuangdao, China [email protected] 2 Zhejiang University, Hangzhou, China

Abstract. Brushless DC motor (BLDCM) with ideal trapezoidal back electromotive force (back-EMF) can generate constant torque under square wave current, but it cannot achieve maximum torque per ampere (MTPA). In this paper non-square wave current is adopted. If the traditional transformation matrix is adopted, the d-axis and q-axis components of the back-EMF are not like the permanent magnet synchronous motor (PMSM), that is, the d-axis component of the back-EMF is not zero, thus achieving the decoupling control of the torque about d-axis and q-axis components in the PMSM. For this reason, this paper proposes a MTPA control strategy based on back-EMF orientation with non-square wave current adopted, it can realize decoupling control of torque by changing the rotation angle of transformation matrix. Torque ripple can be suppressed by inputting constant given torque. Finally, the feasibility and effectiveness of the proposed MTPA control strategy based on back-EMF are verified by DSP experiments. Keywords: BLDCM · MTPA · Torque ripple suppression · Rotation angle

1 Introduction BLDCM has been greatly applied to housekeeping appliance, automotive, aerospace and other fields with simple control and high power density [1–3]. Its torque ripple during commutation reach about half of the average torque [4]. Pursuing higher efficiency and torque ripple suppression has been concerned by relevant scholars. Now there are mainly three control strategies. The first strategy is proposing a new topology for regulating DC bus voltage, there are additional expenses. A strategy based on the quasi-Z source network was addressed in [5], different DC bus voltages are used during commutation and non-commutation. [6] balances the change rate of commutation current to suppress torque ripple during commutation. The second strategy is different modulation methods adopted to suppress torque ripple [7], with large amount of calculation. Besides them, the direct torque control has high performance characteristic [8], but it has low control accuracy.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 675–680, 2023. https://doi.org/10.1007/978-981-99-4334-0_83

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In order to suppress torque ripple and realize MTPA, this paper proposes a MTPA control strategy based on back-EMF orientation. By changing the rotation angle in the traditional coordinate transformation, the torque is only related to the q-axis current, so as to realize the decoupling control. The MTPA strategy of the surface-mounted BLDCM is realized by controlling the d-axis current, its control system of the BLDCM based on back-EMF orientation is constructed. The proposed strategy is verified to be feasible and effective by relevant digital signal processor (DSP) experiments.

2 Selection of Conduction Mode Under MTPA Control The MTPA strategy is to minimize the stator current under required torque, so as to reduce the motor copper loss. There are two main conduction modes, one is 120°and the other is 180°. The intention of this section is to select conduction mode. Take the B + C- conduction as an example, if the 120° conduction mode is adopted, where iA = 0, iB + iC = 0 and eB = −eB = E, E is the amplitude of back-EMF. The generated electromagnetic torque is T = 2k e iB , k e is the back-EMF waveform coefficient. iB can be obtained, and the square sum of three-phase current can be calculated as 2 iA + iB2 + iC2 =

T2 2ke2

(1)

In the same section, if the 180° mode is adopted, iA + iB + iC = 0, and the back-EMF of phase A is, eA = −6E. Where, θ is the rotor position. The torque is T = 2k e iB + (1 − 6θ /π)k e iA . iB can be obtained, and the square sum of three-phase current can be calculated as, T 1 6 T 1 6 + ( − 1)iA ]2 + [ + ( + 1)iA ]2 2ke 2 π 2ke 2 π   2 4T T 3 12 2 θ = 2 + ( 2 θ + 1) iA + 12 iA 2 2ke 2 π π ke 2θ +1

2 2 + iB2 + iC2 = iA +[ iA

(2)

π

During the B + C- conduction, θ ∈ [−30°, 30°]. The square sum of three-phase current under 180° conduction mode is smaller than that under 120° conduction mode, which means greater torque per ampere. ⎧ 4T ∀θ < 0 ⎨ 0 < iA < 12 −θ θ 2 +1 π k e π2 (3) ⎩ 0 > iA > 12 −θ2 π4Tk ∀θ ≥ 0 e π2

θ +1

Therefore, 180° conduction mode is adopted in this paper.

3 Difficulties of Traditional Transformation in MTPA When the three-phase back-EMF is transformed to the d-axis and q-axis back-EMF by traditional equal power transformation, the d-axis and q-axis back-EMF waveforms are shown in Fig. 1. At this time, the torque can be expressed as, T=

ed id + eq iq 

(4)

MTPA Control Strategy of BLDCM Based on Back-EMF

677

back-EMF 1.5E E 0.5E 0

eq ed - 150°

-90°

-30°

30°

150°

90°

θ

Fig. 1. Dq-axis EMF waveform in synchronous rotating coordinate systems.

The sinusoidal back-EMF of PMSM can realize decoupling control of torque. However, the trapezoidal back-EMF of BLDCM is transformed by Park transformation, ed is not zero, and eq is not a constant value, similar decoupling control cannot be achieved.

4 MTPA Control Strategy Based on Back-EMF Orientation To realize decoupling control of torque and high-performance constant torque control, d-axis back-EMF is required to be zero, this paper only changes the rotation angle in the tradition transformation matrix from θ to θ 1 . In order to meet the condition that the ed is 0, the conforming transformation matrix [C ], as shown in (5),

   2 1 − 21 −√21 cos θ1 sin θ1 √ · (5) C = − sin θ1 cos θ1 3 0 3 − 23 2

New rotation angle θ 1 can be expressed as, θ1 = arctan

eA − 21 (eB + eC ) √

3 2 (eC

− eB )

(6)

Therefore, the change of rotation angle achieves that the electromagnetic torque is only related to the q-axis current. D-axis current is set to zero, since the MTPA control strategy in the surface-mounted BLDCM. The torque ripple can be suppressed by inputting the given electromagnetic torque. According to the above theory, the MTPA control system block diagram based on back-EMF orientation can be constructed, as shown in Fig. 2. The database of the new rotation angle and the back-EMF waveform coefficient are obtained through offline test or finite element simulation. The database of new rotation angle is obtained by (6). The back-EMF waveform coefficient k e is obtained by (7):  1 2 1 1 1 [eA (θ ) − eB (θ ) − eC (θ )]2 + [eB (θ ) − eC (θ )]2 ke = (7)  3 2 2 2

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By inputting the given d-axis current and torque, the given d-axis and q-axis current are obtained, and they are transformed to three-phase currents through the proposed transformation. The given three-phase voltages can be gotten by PI controller, when the differences of actual and given three-phase currents respectively, and then voltages are input into the inverters through the PWM generator to drive the motor. iA* id*=0 T*

Inverse transformation

iq*

÷

PI controller

iB* PI controller iC* PI controller

θ1

ke

iA

θ1-θ database

uA* uB*

PWM generator

uC*

VT1 VT2 VT3 VT4 VT5 VT6

inverter

iB iC

θ

back EMF coeffcient

Position sensor

BLDCM

Fig. 2. Block diagram of MTPA control system based on back-EMF orientation.

5 Experimental Verification The actual back-EMF of BLDCM is not an ideal trapezoidal wave, the three-phase current of proposed strategy under the actual back-EMF through special parameter measurement experiments. The actual back-EMF and current are shown in Fig. 3. eA iA

Actual eA

0

Required iA eB iB

Actual eB

0 Required iB eC iC 0

Actual eC Required iC

-150°

- 90°

-30°

30°

90°

150°

θ

Fig. 3. Three-phase current of proposed control system under the actual back-EMF.

The torque ripple suppression under rated torque is obvious, and there is no commutation torque ripple. The torque ripple is about 7.1%. According to the comparison between Fig. 4. And Fig. 5, the ratio of average torque to q-axis current is 0.707 and 0.974 respectively, which significantly improves the efficiency of motor.

Torque N·m

2N· m

Duty cycle

MTPA Control Strategy of BLDCM Based on Back-EMF

0.25 0 2A 0

679

Current A

1N· m

Phase Voltage (V)

-2A 300V 150V 0

0

Phase Voltage (V)

Actually Given Torque current current N·m A A

Fig. 4. Experimental results under ideal square wave current control system at 600 rpm.

2N· m 1N· m

1.2A

1.2A

-0.4A

0.4A

-1.2A

0.4A

-0.4A -1.2A 300V 150V 0

Fig. 5. Experimental results under the proposed control system at 580 rpm.

6 Conclusion In this paper, a decoupling control of torque about d-axis and q-axis components are proposed by changing the rotation angle in traditional transformation. At the same time, the MTPA strategy is achieved by controlling the d-axis current to zero. Torque ripple can be suppressed by inputting constant given torque. Through experimental verification, the MTPA control increases motor efficiency by 37.8% and the torque ripple is less than 10%.

References 1. Liu, Y., Hu, J., Dong, S.: A torque ripple reduction method of small inductance brushless DC motor based on three-level DC converter. In: 2019 14th IEEE Conference on Industrial Electronics and Applications, pp. 1669–1674 (2019) 2. Jahns, T.M., Soong, W.L.: Pulsating torque minimization techniques for permanent magnet AC motor drives-a review. IEEE Trans. Industr. Electron. 43(2), 321–330 (1996) 3. Li, Z., Gao, X., Wang, J., et al.: Phase back-EMF space vector oriented control of brushless DC motor for torque ripple minimization. In: 2016 IEEE 8th International Power Electronics and Motion Control Conference (2016) 4. Bian, C., Duan, P.: A PWM scheme for regenerative braking of brushless DC motor. In: Proceedings of the CSEE , vol. 39, no. 17, pp. 5247–5256 (2019) 5. Xia, K., Zhu, L., Zeng, Y., et al.: Researches on the method of suppressing commutation torque ripple for brushless DC motors based on a quasi-Z-source net. In: Proceedings of the CSEE, vol. 35, no. 04, pp. 971–978 (2015)

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6. Shi, T., Guo, Y., Song, P., et al.: A new approach of minimizing commutation torque ripple for brushless DC motor based on DC–DC converter. IEEE Trans. Industr. Electron. 57(10), 3483–3490 (2010) 7. Carlson, R., Lajoie-Mazenc, M., Dos, S., Fagundes, J.C.: Analysis of torque ripple due to phase commutation in brushless DC machines. IEEE Trans. Ind. Appl. 28(3), 632–638 (1992) 8. Kang, S.J., Sul, S.K.: Direct torque control of brushless DC motor with non-ideal trapezoidal back-EMF. IEEE Trans. Power Electron. 10(6), 796–802 (1995)

Torque Ripple Suppression Based on a New Multi-level DTC Strategy Boran He, Mengting Chang, Yicheng Jia, Qimeng Han, and Zhenguo Li(B) Key Lab of Power Electronics for Energy Conservation and Motor Drive of Hebei Province, Yanshan University, Qinhuangdao, China [email protected]

Abstract. Under the traditional hysteresis control, three-level direct torque control (DTC), one voltage vector can be selected from only three voltage vectors in a direct torque control cycle of brushless DC motor (BLDCM), resulting in a large torque ripple. Therefore, this paper proposes a new inverter topology that can provide more levels. By analyzing all sorts of the equivalent circuits at different times, this new multi-level DTC strategy makes corresponding switching state selection tables during commutation and non-commutation, and adopts respectively four-level hysteresis and six-level hysteresis control. At the same time, the additional capacitors are adopted to supply power according to different switching states, and their voltages are equalized by selecting different switch states. The more levels due to capacitors can reduce the torque ripple of traditional scheme greatly, the new multi-level DTC strategy has good advantages of simple structure and easy implementation. The proposed control strategy is verified practicability and effectiveness by experiment and simulation. Keywords: Brushless DC motor (BLDCM) · Direct torque control (DTC) · Torque ripple suppression · Multilevel inverter topology

1 Introduction BLDCM is widely applied in automotive electronics, aerospace, and other fields due to its advantages of simple structure and high power density [1–3]. The 120° conduction mode is widely used because the theoretical torque ripple is less than other modes. However, its actual torque ripple is still largely due to the actual back electromotive force (back-EMF) and actual square current [4]. Among many control methods, DTC can directly control torque without complex coordinate transformation, so it has the advantages of fast torque response and great robustness. In [5], under a modified SEPIC converter, the desired DC bus voltage can be gotten by controlling the duty cycle. The new commutation torque ripple suppression strategy is proposed by constructing four types of switching vectors [6]. A proposed DTC strategy combined with Pulse Width Modulation (PWM), which reduces torque ripple due to using one voltage vector and low inductance. Meanwhile, different duty cycles were set to suppress torque ripple during commutation and non-commutation [7]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 681–686, 2023. https://doi.org/10.1007/978-981-99-4334-0_84

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To solve the disadvantage of the large torque ripple of traditional DTC strategy, in this paper, a new inverter topology is proposed and a multi-level DTC system is constructed. Firstly, the proposed strategy suppresses torque ripple decreases by half during the noncommutation. Meanwhile, the torque ripple during commutation is analyzed, and its hysteresis controller outputs six levels. The proposed strategy is verified to be effective by simulation and digital signal processor (DSP) experiments.

2 Multi-level DTC System 2.1 DTC System In the three-level DTC strategy, the commutation exists large torque ripples, because that strategy in a control cycle chooses a voltage vector from only three voltage vectors, the voltage is unable to change smoothly. And the phase inductance of the stator winding of the BLDCM is very small so the current and torque changes largely. To solve the traditional large torque ripple in the three-level DTC strategy, a new multi-level inverter topology is proposed in this paper as shown in Fig. 1. VD7 +

VT7 C1 VD9 VT1

VD1 VT3

VD3 VT5

VD2 VT4

VD4 VT6

VD5 R

L

Udc C2 -

VD10 VD8 VT 2

eA eB eC

N

VD6

VT8

Fig. 1. The proposed multi-level inverter topology.

2.2 Four-Level DTC During Non-commutation VD7 C1 VD9 VT1

VD1 VT3

VD3 VT5

VD5 R

+ VT7 L

Udc C2 -

VD10 VD8 VT 2

VT8

VD2 VT4

VD4 VT6

eA eB eC

VD6

C1 VD9 VT1 C2 -

VD10 VD8 VT 2

VD5 R

+ VT7

L

VD2 VT4

VD4 VT6

eA eB eC

VD6

NUdc -

C1 VD9 VT1

VD1 VT3

VD3 VT5

VD5 R

C2 VD10 VD8 VT

VD2 VT4

VD4 VT6

VD6

2

(b)+1non

C1 VD9 VT1

VD1 VT3

VD3 VT5

VD5 R

C2 VD10 VD8 VT

2

VD2 VD4 VT4 VT6

(d)0non

VD6

+ VT7 L

eA eB eC

C1 VD9 VT1

-

VD10 VD8 VT 2

VT8

eA eB eC

N

eA eB eC

N

VD7 VD1 VT3

VD3 VT5

VD5 R

NUdc C2

L

(c)+1non

VD7

VT7

VT8

VD3 VT5

VT8

VT8

(a)+2non

Udc

-

VD1 VT3

NUdc

VD7 +

VD7

VD7

+ VT7

VD2 VD4 VT4 VT6

(e)0non

VD6

+ VT7 L

eA eB eC

C1 VD9 VT1

VD1 VT3

VD3 VT5

VD5 R

NUdc C2 -

VD10 VD8 VT 2

VT8

VD2 VD4 VT4 VT6

L

VD6

(f)-2non

Fig. 2. Equivalent circuit during non-commutation.

The circuits of voltage vectors in +2non , +1non , 0non and −2non levels are shown in Fig. 2. During the non-commutation period, the four-level hysteresis controller is shown in Fig. 3, the switching table is shown in Table 1.

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non

2 1 -H non2 -Hnon1

0 Hnon1

Te

-2

Fig. 3. Diagram of four-level hysteresis controller during non-commutation.

Table 1. Switching table of multi-level DTC strategy during non-commutation. τnon

dnon

Sector I

II

III

IV

V

VI

+2

\

00100111

01100011

01001011

00011011

10010011

10000111

+1

1non

00100110

01100010

01001010

00011010

10010010

10000110

0non

00100101

01100001

01001001

00011001

10010001

10000101

0

\

000001xx

001000xx

010000xx

000010xx

000100xx

100000xx

−2

\

000000xx

000000xx

000000xx

000000xx

000000xx

000000xx

In Table 1, 1 means on, 0 means off, x means 0 or 1, 1non and 0non means that capacitor C1 , C2 is adopted for power supply. Symbol solidus (\) means that capacitor voltage equalizing signal dnon does not affect the overall result. 2.3 Six-Level DTC During Commutation BLDCM will inevitably lead to larger commutation torque ripples. Taking the commutation AB-AC as an example, the equivalent circuits are shown in Fig. 4. VD7 + VT7 C1 VD9 VT1

VD7 VD1 VT3

VD3 VT5

VD5 R

L

Udc C2 -

VD10 VD8 VT 2

VT8

VD2 VD4 VT4 VT6

eA eB eC

VD6

C1 VD9 VT1 C2 -

VD10 VD8 VT 2

VT8

VD7 C1 VD9 VT1 C2 -

VD8 VT 2

VD3 VT5

VD5 R

+ VT7 L

VD2 VD4 VT4 VT6

eA eB eC

VD1 VT3

VD3 VT5

VD5 R

VD2 VD4 VT4 VT6

VT8 (d)+1com

VD6

eA eB eC

C2

VD6

-

-

VD10 VD8 VT 2

VT8

VD8 VT 2

VT8

VD1 VT3

VD3 VT5

VD5 R

NUdc C2

VD10

VD2 VD4 VT4 VT6

(e)-2com

VD6

L

VD2 VD4 VT4 VT6

VD6

VD1 VD3 VT3 VT5

C1 VD9 VT1 eA eB eC

VD5 R

L

VD5 R

Udc

N

C2 -

VD10

VD2 VD4 VT4 VT6 VD6

VD8 VT 2

VT8

eA eB eC

N

eA eB eC

N

(c)+1com

+ VT7

C1 VD9 VT1

VD3 VT5

NUdc

(b)+2com

+ VT7 L

VD1 VT3

C1 VD9 VT1

VD7

Udc VD10

VD1 VT3

NUdc

(a)+3com

+ VT7

VD7

+ VT7

(f)-3com

Fig. 4. Equivalent circuit during commutation.

L

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The formula of phase voltage of BLDCM is, uA = RiA + L

diA + eA + uN dt

(1)

Since the variation of torque is only proportional to the variation of non-commutative current, transform the above equation, iA = uA − eA − uN

(2)

According to three-phase voltage like (1), phase voltages and back-EMFs at that time, where, uAg = U d , uBg = uCg = 0, eA = −eB = −eC = E, (2) becomes,   4E t 2Ud − (3) iA = 3 3 L It is concluded that +3com level is when the DC link provides two-thirds of the bus voltage for the inverter. Using the same analysis, +2com , +1com , −2com , −3com levels provide 1/3, 1/6, −1/3, −2/3 of bus voltage for the inverter respectively. Six-level hysteresis controller is shown in Fig. 5. Thus, the switching table during the commutation is obtained, as shown in Table 2. com

3 2 1 -Hcom2 -0.5H com1 0

H com1

Te

-2 -Hcom1

-3

-0.5(Hcom1+Hcom2 )

Fig. 5. Six-level hysteresis controller during commutation.

3 System Simulation and Experimental Verification The simulation results show that the torque ripple of the proposed system decreases by 50% compared with the three-level DTC system in Fig. 6 (a) and (b). And the effect of the experimental figure is the same as theoretical simulation. Considering the torque ripple during non-commutation and commutation, the different multi-level DTC hysteresis control is adopted respectively, which makes great achievements in Fig. 7 (a) and (b). It illustrates the commutation torque ripple is necessary greatly. Figure 7 (c) and (d) show that the proposed multi-level DTC strategy has the advantages of fast torque response and great robustness at rated torque.

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685

Table 2. Switching table of multi-level DTC strategy during commutation. τcom

dcom

Sector I

II

III

IV

V

VI

+3

\

10100111

01100111

01101011

01011011

10011011

10010111

+2

\

00100111

01100011

01001011

00011011

10010011

10000111

+1

1non

00100110

01100010

01001010

00011010

10010010

10000110

0non

00100101

01100001

01001001

00011001

10010001

10000101

0

\

001000xx

010000xx

000010xx

000100xx

100000xx

000001xx

−2

\

001000xx

010000xx

000010xx

000100xx

100000xx

000001xx

000000xx

000000xx

000000xx

000000xx

000000xx

000000xx

Torque N·m

Torque N·m

−3

1.5 1 0.5

1.5 1 0.5

1 0 -1

Level Current A

Level Current A

1 0 -1

1 0 -1

1 0 -1

0.1

0.11 0.12 0.13 0.14 (a)Three-level at 600rpm with 1.27Nm

0.15 time/ms

0.1

0.11

0.12

0.13

(b)Multi-level at 600rpm with 1.27Nm

0.14

0.15 time/ms

Curre Torque nt(A) (N·m)

Fig. 6. The simulation waveforms.

1N·m

0 1A 0 -1A

0 1A 0 -1A

State

+2 +1 0

(a)Four-level DTC at 600 rpm with 0.6N·m.

2N·m

(b)Multi-level DTC at 600rpm with 0.6N·m.

1N·m 0 2A 0 -2A +3 +2 +1 0 -2 -3

State

Curre nt(A)

Torque (N·m)

1N·m

(c)Multilevel DTC at 600rpm with 1.1N·m.

+3 +2 +1 0 -2 -3

2N·m 1N·m 0 2A 0 -2A +2 +1 0

(d)Multi-level DTC at 1000rpm with 1.1N·m.

Fig. 7. The experimental waveforms.

4 Conclusion This paper proposes a new multi-level inverter topology, deduces switching tables and provides the corresponding control strategy. The proposed strategy can reduce torque ripple greatly. In addition, the additional structure produces more voltage vectors to choose, providing more possibilities for better performance of the BLDCM at a low cost. Finally, the experimental results of the proposed control strategy verify its practicability.

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References 1. Liu, Y., Hu, J., Dong, S.: A torque ripple reduction method of small inductance brushless DC motor based on three-level DC converter. In: 2019 14th IEEE Conference on Industrial Electronics and Applications, Xi’an, China, pp. 1669–1674 (2019) 2. Sun, L., Yu Jun, J.: Design of vector control system for brushless DC motor based on hall sensor. In: 2018 International Symposium on Communication Engineering & Computer Science, Hohhot, China, pp. 416–422 (2018) 3. Shi, X., Wang, X., Xu, T., et al.: Self-optimization commutation correction strategy for highspeed brushless DC motor. Trans. China Electrotech. Soc. 3997–4005 (2019) 4. Zhu, C., Zeng, Z., Zhao, R.: Comprehensive analysis and reduction of torque ripples in threephase four-switch inverter-fed PMSM drives using space vector pulse-width modulation. IEEE Trans. Power Electron. 5411–5424 (2017) 5. Viswanathan, V., Seenithangom, J.: Commutation torque ripple reduction in BLDC motor using modified SEPIC converter and three level NPC inverter. IEEE Trans. Power Electron. 535–546 (2017) 6. Cao, Y., et al.: A commutation torque ripple suppression strategy for brushless DC motor based on diode-assisted buck–boost inverter. IEEE Trans. Power Electron. 5594–5605 (2018) 7. Li, Z., Zhang, S., Zhou, S., et al.: Direct torque control of brushless DC motor considering torque ripple minimization. Trans. China Electrotech. Soc. 139–146 (2014)

Study of an IPT System Based on Configurable Charging Current and Charging Voltage YongGao Zhang, WeiWei Yang(B) , Peng Liu, and ShangHai Liu East China Jiaotong University, Nanchang City 330013, Jiangxi Province, China [email protected]

Abstract. In order to improve the flexibility of configuring charging voltage and charging current for wireless charging systems, the paper is based on a combination of LCL-LCL/S and T-type compensation networks, adding two switches and a T-type compensation network to the secondary side circuit. The interconversion of the In addition, the solution has the following advantages: firstly, the input of reactive power is avoided in the process of constant current and constant voltage charging and the communication between the primary and secondary sides is eliminated, secondly a wireless charging IPT system can be configured for different charging currents and charging voltages and finally the output current or output voltage can be fixed unchanged to realise a wireless charging IPT system for multiple charging devices with constant current or constant voltage output configuration. In order to verify the feasibility of this scheme, an IPT system with four different charging voltages and charging currents is built. The experimental results show that the scheme can be flexibly configured with different charging currents and voltages and has good constant current and constant voltage output characteristics. Keywords: ZPA · Constant-current and constant-voltage charging · T-network

1 Quotes The current methods to achieve constant current and constant voltage charging are mainly divided into two categories: dynamic regulation methods and variable static compensation methods, of which variable static compensation methods include the addition of converters to the primary and secondary sides [1, 2], frequency control [3, 4], phase shift control [5] and so on. The variable static compensation method is mainly to recombine some basic compensation topologies into a composite compensation topology that can meet the constant current and constant voltage conditions. In [6], a constant current and constant voltage IPT system with configurable charging current is achieved by recombining a T-type circuit with an S-S-type circuit, but the charging voltage is not configurable, while in [7], a T/F variable structure constant current and constant voltage output with configurable charging current is achieved by switching on the transmitter side, eliminating the communication between the primary and secondary sides, but the charging voltage is not configurable and requires a complex control circuitry. Both the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 687–698, 2023. https://doi.org/10.1007/978-981-99-4334-0_85

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dynamic regulation method and the variable static compensation method do not allow for free configuration of the charging voltage and current and lack the flexibility of a constant current and voltage output. Based on this problem, this paper proposes a wireless charging IPT system with a variable secondary compensation structure, which allows free configuration of the charging current and voltage by switching to a different compensation topology and changing the parameters of the T-shaped compensation network elements.

2 A Constant-Current, Constant-Voltage, Self-switching IPT System with Configurable Charging Current and Charging Voltage Since the T, LCL-LCL type compensation network topology is a constant current output with an AC voltage source as the excitation, and the LCL-S type compensation network topology is a constant voltage output with an AC voltage source as the excitation, a constant current and constant voltage self-switching IPT system is given as shown in Fig. 1.

LP1 Q1 IE

Q3 Iin

E

M

Zin UP

. IS

. IP

Cp

Lp

1

LS 1

Q2

S2

Q4

CS ZT

2

S1

LS1

LS3

Lse T US CS2 Cse Icc S3 2

Req

D1 D3 IB

Iab Vab

Cf

RB

VB

D2 D4

ZT' LS1' CS2'

LS3' T'

Fig. 1. IPT system with constant current and constant voltage self-switching

2.1 Analysis of the Constant Current Mode with Configurable Charging Current When switch S1 is connected to contact 2, switch S2 is connected to contact 2 and switch S3 is closed, the system enters the constant current charging mode, when the T-shaped compensation network compound consisting of LCL-S and LS1 , CS2 and LS3 constitutes. The current flowing through the charging load of the system in constant current mode can be calculated as IB =

8EM ωCS2 π 2 LP1

(1)

The input impedance of the system in constant current mode is calculated to be Zin =

π 2 LP1 2 C R (8 + π 2 )ω4 M 2 CS2 P L

(2)

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From Eq. (1) it can be seen that the output current of the system in constant current mode is independent of the load and is only related to the DC regulated power supply E, the mutual inductance M, the primary side compensation inductor LP1 , the resonant angle frequency ω of the system, and the compensation capacitor CS2 in the T-shaped compensation network on the receiving side. In general LP1 , M, E and ω are not easily adjustable in a wireless charging IPT system and can be considered as fixed and constant. Adjusting the receive-side compensation capacitor CS2 to configure the magnitude of the required charging current. And from Eq. (2) it can be seen that the system input impedance is purely resistive, there is no reactive power input to the system and the system voltage and current can achieve ZPA. 2.2 Analysis of the Constant Voltage Mode with Configurable Charging Voltage When the load voltage rises to the threshold voltage for switching, switch S1 is connected to contact 1, switch S2 is connected to contact 1 and switch S3 is disconnected, the system enters the constant voltage charging mode, at which point the system consists of a composite LCL-LCL type compensation network and a T type compensation network consisting of LS1 , CS2 and LS3 . The voltage across the charging load can be found as VB =

8EMCse  π 2 LP1 CS2

(3)

The input impedance of the system in constant voltage mode can be calculated as Zin =

 R LP1 CS2 eq

CP3 M 2

=

2 R L (8 + π 2 )CS2 L P1

π 2 CP3 M 2

(4)

From Eq. (3), it can be seen that the output voltage of the system in constant voltage mode is independent of the charging load and is only related to the DC regulated power supply E, the mutual inductance M, the transmitting side compensation inductor LP1 , the receiving side compensation capacitor Cse, and the compensation capacitor CS2 in the T type compensation network. When the receiving side compensation parameters of the EV are fixed, i.e. the DC regulated power supply, the mutual inductance M between the transmitting and receiving coils, the resonant angle frequency ω and the transmitting measurement compensation inductor LP1 remain unchanged, it is still possible to adjust the magnitude of the charging load output voltage by adjusting the compensation capacitor CSe on the receiving side and the compensation capacitor CS2 in the T type compensation network. And from Eq. (4) it can be seen that the system input impedance is purely resistive, the system has no reactive power input, and the voltage and current can achieve ZPA. From Eqs. (1) and (3), it can be seen that when the compensation network system parameters are fixed, the output voltage and output current of the system are only related to the DC power supply E. In order to meet the demand for different levels of charging voltage and charging current for electric vehicles, the variable topology constant current and constant voltage IPT system shown in Fig. 4 can be connected in parallel to one

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inverter, which can realize free configuration for different charging voltages and charging currents, and the system circuit diagram for charging multiple systems by a single inverter is shown in Fig. 2. LP1

. ZT IS

. IP1 M

Cp1

1

CS1

2

LS11

S11

Cse1 LS1 LSe1

Lp1

US CS21

S

21 2

. Icc LS11' CS21'

LP2 Q1

Q3 Iin

E

. ZT IS

. IP2

Zin

M Cp2

UP

LS12

S12

Cse2 LS2 LSe2

Lp2

US CS22

Q4

S22

S2

2

. Icc LS12' CS22'

LPn

. ZT IS

. IPn M

1

Csen Cpn

Lpn

LSn

2

LS1n US CS2n

LSe3 S2n

2

LS32

VB1

D12 D32

Req2

IB2

IL

T2 Vab2

Cf2

RL2

VB2

D22 D42 LS3' T2'

LS3n

Reqn

D1n D3n IBn

IL

Tn S3n

. Icc LS1n'

Cf1

D21 D41

CSn

S1n

1

Sn

Vab1

RL1

LS31' T1'

S32

1

Q2

IB1

IL

T1

CS2

2

1

D11 D31

Req1

S31

1

S1

LS31

Vabn

Cfn

RLn

VBn

D2n D4n LS3' Tn'

CS2n'

Fig. 2. Circuit diagram of a single inverter to multi-system charging system

As can be seen from Fig. 2, switches S1 , S2 up to Sn determine whether a certain charging system charges the electric vehicle or not. In order to meet the demand of the electric vehicle for different charging current levels, the charging current of the electric vehicle can be freely configured by adjusting the T1, T2 up to Tn system parameters, and in order to meet the demand of the electric vehicle for different charging voltage levels, the charging voltage of the electric vehicle can be freely configured by adjusting the T1 , T2 up to Tn system parameters.

3 Parameter Settings Let the charging current of the wireless charging system in constant current mode be IB , the charging voltage in constant voltage mode be VB , the DC input voltage of the inverter be E, the resonant frequency of the system be ω, the self-inductance of the primary coil be LP , the self-inductance of the secondary coil be LS , and the mutual inductance between the primary and secondary coils be M. The values of L1 , CP and CS can be found separately as LP1 = LP CP =

1 ω2 LP

(5) (6)

Study of an IPT System Based on Configurable Charging

CS =

1 ω2 LS

691

(7)

The values of Cse and Lse can be found as Cse =

1 ω2 LS

Lse = LS

(8) (9)

The value of CS2 can be found as CS2 =

π 2 IB LP1 8EM ω

(10)

The value of CS2 can be found as  CS2 =

8EM π 2 ω2 LP1 VB LS

(11)

The values of LS1 , LS3 and LS1 , LS3 in the T-compensated network can be obtained as LS1 = LS3 = LS1 = LS3 =

8EM ωπ 2 IB LP1

(12)

π 2 LS VB LP1 8EM

(13)

4 Simulation Validation In order to verify the correctness of the theoretical analysis of the configurable charging current and configurable charging voltage IPT system, the simulation model was built in MATLAB environment. In this paper, two sets of simulation results of 48V2A and 48V3A are used to verify the theory of the configurable charging current IPT system, and two sets of simulation results of 36V3A and 48V3A are used to verify the theory of the configurable charging voltage IPT system, and the specific simulation parameters and system indicators are shown in the Appendix. 4.1 Simulation Analysis of a Constant Current and Constant Voltage IPT System with Configurable Charging Current From Figs. 3 and 4, it can be seen that no matter in constant current mode or constant voltage mode, the inverter output current and output voltage keep the same phase, and it can be considered that the system operates under unit power without reactive power input, which verifies the correctness of the theoretical analysis that the input impedance is purely resistive in constant current and constant voltage stages. In addition, as the

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UP

Iin

Iin

Time(s)

Time(s)

12Ω

24Ω

Fig. 3. Inverter output voltage UP and output current Iin waveforms in constant current mode for 48V2A system UP

UP

Iin

Iin

Time(s)

Time(s)

24Ω

200Ω

Fig. 4. Inverter output voltage UP and output current Iin waveforms in constant voltage mode for 48V2A system

internal resistance of the charging load increases in constant current mode, the system input impedance gradually decreases and the system output This corresponds to Eq. (2), which verifies the correctness of the theoretical analysis. In the constant voltage mode, as the internal resistance of the charging load increases, the input impedance of the system gradually increases and the output current of the system gradually decreases, which corresponds to Eq. (4) and verifies the correctness of the theoretical analysis.

40

CC

1.0

CV

35 30

0.5

25

Charging voltage

B

Charging current

45 1.5

VB

50

2.0

0.0 2.5

3.0

3.5

4.0

4.5

5.0

5.5

Charge load equivalent resistance natural log In(RB)

Fig. 5. Charging voltage and charging current curves with charging load for 48V2A system

From Fig. 5, it can be seen that the charging process of the variable topology wireless charging IPT system is mainly divided into two stages: constant current (CC) and constant

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voltage (CV). When the internal resistance of the charging load gradually increases from 12 to 24 , the charging current gradually decreases from 2.1 to 2.0 A, and the current change rate is 4.28%, the charging current is almost unaffected by the charging load, and the charging current basically remains unchanged. As the voltage across the charging load rises to the threshold voltage of 48 V for constant-current and constantvoltage switching, the constant-current mode switches to constant-voltage mode, and the internal resistance of the charging load continues to increase from 24 to 200 , and the charging voltage increases from 48 to 49.6 V, with a voltage change rate of 3.22%. At the same time, the system output current gradually decreases to the cut-off current (0.248 A), which ends the charging process. UP

Iin

Time(s)

8Ω

UP

Iin

Time(s)

16Ω

Fig. 6. Inverter output voltage UP and output current Iin waveforms in constant current mode for 48V3A system

UP

UP

Iin

Iin

Time(s)

Time(s)

16Ω

200Ω

Fig. 7. Inverter output voltage UP and output current Iin waveforms in constant voltage mode for 48V3A system

As the basic principle and charging process of the 48V3A system is similar to that of the 48V2A system, the description is not repeated here. Only the waveforms of the inverter output current and output voltage of the 48V3A system and the graphs of the charging current and charging voltage with the variation of the internal resistance of the charging load are given in Figs. 6, 7, and 8. The specific system parameters and system indicators are shown in Tables 1, 2 and 3.

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3

Charging current

45 40

2

35 1

30 25

0 2.0

2.5

3.0

3.5

4.0

4.5

5.0

Charging voltage V B

B

694

5.5

Natural logarithm of the equivalent resistance of the system charging load In(RB)

Fig. 8. 48V3A system charging voltage and charging current curves with charging load

4.2 Simulation Analysis of a Constant-Current, Constant-Voltage IPT System with Configurable Charging Voltage

UP

UP

Iin

Iin

Time(s)

Time(s)

6Ω

12Ω

Fig. 9. Inverter output voltage UP and output current Iin waveforms in constant current mode for 36V3A system

UP

Iin

Time(s)

12Ω

UP

Iin

Time(s)

200Ω

Fig. 10. Inverter output voltage UP and output current Iin waveforms in constant voltage mode for 36V3A system

As the 48V3A charging system has been given above, the simulated waveforms are not repeated here, only the waveforms of the inverter output current and output voltage of the 36V3A system and the graphs of the charging current and charging voltage with the variation of the internal resistance of the charging load are given in Figs. 9, 10 and 11. The specific system parameters and system indicators are shown in Tables 1, 2 and 3.

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CC

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25 20

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4.0

4.5

5.0

VB

35

Charging voltage

Charging current

B

40

15 5.5

Charge Load Equivalent Resistance Natural Log In(RB)

Fig. 11. Charging voltage and charging current curves with charging load for 36V3A system

5 Summary In this paper, based on two topological circuits, LCL-S and LCL-LCL, we propose to add three switches on the receiving side, switch the LCL-S type compensation network to the LCL-LCL type compensation network through the switching of the switches, and use the T type compensation network as the regulation system to adjust the charging current and charging voltage to achieve the interconversion of constant current and constant voltage, and at the same time, connect several configurable charging current and charging voltage The IPT system is connected in parallel to a single inverter for the purpose of freely configuring the charging voltage and charging current. In addition, the solution has the following obvious advantages: no need for transmitter-side and receiver-side communication and complex control circuitry, resulting in low system complexity, and secondly, almost no reactive input during constant-current and constant-voltage charging, which greatly improves the charging efficiency of the system. Finally, in the simulation results, both the charging current and charging voltage show good constant-current and constant-voltage characteristics, and the charging voltage and charging current can be freely configured, which fully satisfies the concept of charging multiple IPT systems with a single inverter and provides a reference for future configurable charging current and charging voltage IPT systems.

140

LP2 /μH

140

48V2A

Parameters

48V3A

LP1 /μH

Parameters

60

CP2 /nF

60

CP1 /nF

140

LP2 /μH

140

LP1 /μH

140

LS2 /μH

140

LS1 /μH

60

CS2 /nF

60

CS1 /nF

34.7

LS12 /μH

52.5

LS11 /μH

34.7

LS32 /μH

52.5

LS31 /μH

242

CS22 /nF

160

CS21 /nF

141.9

LS32 /μH 141.9

140 LS12 /μH

LS31 /μH 140

LS11 /μH

Table 1. Simulation parameters for 48V2A, 3 A configurable charging current IPT systems

59.2

CS22 /nF

60

CS21 /nF

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LP3 /μH

140

LP4 /μH

140

Parameters

36V3A

Parameters

48V3A

60

CP4 /nF

60

CP3 /nF

140

LP4 /μH

140

LP3 /μH

140

LS4 /μH

140

LS3 /μH

60

CS4 /nF

60

CS3 /nF

34.7

LS14 /μH

36.2

LS13 /μH

34.7

LS34 /μH

36.2

LS33 /μH

242

CS24 /nF

232

CS23 /nF

141.9

LS34 /μH 141.9

107.7 LS14 /μH

LS33 /μH 107.7

LS13 /μH

Table 2. 3A36V, 48 V configurable charging voltage IPT system simulation parameters.

59.2

CS24 /nF

78

CS23 /nF

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Table 3. Configurable charging current and charging voltage constant current and constant voltage IPT system specifications System indicators

Rate of change of voltage (%)

Rate of change of current (%)

Switching internal resistance ()

Range of internal resistance variation ()

Threshold voltage (V)

Cut-off current (A)

48V2A

3.22

4.28

24

12–200

48

0.248

48V3A

4.57

6.25

16

8–200

48

0.252

36V3A

5.76

3.84

12

6–200

36

0.191

48V3A

4.57

6.25

16

8–200

36

0.252

References 1. Li, H., Li, J., Wang, K., et al.: A maximum efficiency point tracking control scheme for wirelesspower transfer systems using magnetic resonant coupling. IEEE Trans. Power Electron. 30(7), 3998–4008 (2015) 2. Chen, G.: Study on current stability technology of contactless power transmission system. Chongqing University (2008) 3. Wang, C.S., Stielau, O.H., Covic, G.A.: Design considerations for a contactless electric vehicle battery charger. IEEE Trans. Industr. Electron. 52(5), 1308–1314 (2005) 4. Nagatsuka, Y., Ehara, N., Kaneko, Y., et al.: Compact contactless power transfer system for electric vehicles. In: The 2010 International Power Electronics Conference—ECCE ASIA, Sapporo, Japan. IEEE (2010) 5. Zhang, W., Qin, W., Song, J., Ji, L., Bi, L.: Development of constant-current and constantvoltage wireless charging system with primary-side mutual inductance recognition. Electr. Eng. Mag. 25(04), 52–60 (2021) 6. Zhang, Y.: Research on inductive wireless charging system with configurable charging current. Southwest Jiaotong University (2019) 7. Pingan, T., Jiawei, L., Tingyu, T., Bin, S., Yimeng, D.: Constant voltage/constant current wireless charging system based on transmit-side T/F variable structure compensation network. J. Electr. Eng. Technol. 36(02), 248–257 (2021)

Impedance Remodeling Method of Single-Phase Grid-Connected Inverter Under Weak Grid Liyan Zhang1 , Wenping Cao1,2(B) , Tao Rui2 , Xinyu Ma1 , Weixiang Shen3 , Cungang Hu1,2 , and Ke Zhang4 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected]

2 Engineering Research Center of Power Quality, Ministry of Education, Anhui University,

Hefei, China 3 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, VIC 3122, Australia 4 Jiangsu Dongrun Zhilian Technology Co., Ltd., Nantong, China

Abstract. The conditions of weak grid pose a threat to the safe operation of grid-working inverter. The second-order low-pass filter (LPF) in series before the phase-locked-loop (PLL) branch can effectively reduce high-frequency noise and improve the stability of grid-working inverter, but the fundamental wave signal will cause phase offset. Therefore, it is impossible to achieve unity power factor grid connection. In this paper, based on the second-order LPF, a new remodeling scheme is proposed, which can greatly improve the phase margin of inverter which operating in weak grid environment, and achieve unity power factor grid connection. Finally, the effectiveness of the proposed method is verified by Simulation. Keywords: Weak grid · Grid-connected inverter · Impedance characteristics · Current correction

1 Introduction As more distributed power supplies are parallel operation to the power system. However, under the influence of a long transmission line, the power grid will present a high impedance, showing a weak network state. In weak grid environment, the impedance of grid can be considered as inductance. In previous studies, some scholars found that the PLL can be equivalent to negative impedance. With the decrease of Short circuit ratio, the impedance of grid and the PLL are increasingly coupled, which will cause resonance, noise amplification and other phenomena. Thus, the safe operation of grid-working single-phase inverter is challenged.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 699–709, 2023. https://doi.org/10.1007/978-981-99-4334-0_86

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To learn the mechanism of inverter instability caused by grid impedance under weak grid conditions. Literature [1] proposed a highly robust phase-locked loop. Compared with the traditional, this one increases the negative power grid current feedforward component, thus improving the stability of the PLL under the weak current network. From the point of view of compensating the system phase margin, literature [2] reconstructs the inverter output impedance characteristics to improve the system stability. Literature [3] and [4] designed the PLL bandwidth with the constraints of grid impedance and phase margin, sacrificing the current dynamic tracking performance to improve the system stability. Literature [5] proposes a multi constrained second-order current correction amplifier based on the pre low-pass filter of phase-locked loop branch, which can improve its stability under the condition of weak current network. The pre-LPF can increase the phase at the impedance intersection, but it will affect the grid connected power factor angle. Based on the second-order LPF, this paper optimizes its transfer function, which not only improves the phase between voltage and current of the inverter. The converter can still maintain high phase margin and stable operation under greater grid impedance. Finally, the effectiveness of the proposed scheme is verified by simulation.

2 Establishment of Impedance Model of Grid Connected Inverter 2.1 The Control Method of LCL Single Phase Grid Connected Inverter Mathematical Model The topology and control of the single-phase LCL-type grid-connected inverter is shown in Fig. 1. L1 is the inverter-side inductor, L2 is the grid-side inductor, C is the filter capacitor, Udc is the DC input voltage, i1 is the inverter current, i2 is the grid-connected current, and ic is the capacitor current, pcc is the common coupling point between the grid and the grid-connected inverter. Upcc is the voltage at the pcc. The PLL enables the grid connection of the inverter by detecting the phase. Kad is the capacitive current feedforward coefficient to achieve active damping. Gc is the transfer function of the current regulator, in order to accurately track the fundamental current, this paper uses quasi-proportional resonant control. Kp is the proportionality factor, Kr is the resonance factor, ω0 is the fundamental angle frequency and ωc is the cut-off angle frequency. The transfer function is: Gc (s) = Kp +

s2

2Kr ωc s + 2ωc s + ω02

(1)

2.2 Impedance Model of Inverter The block diagram of inverter current loop is shown in Fig. 2. Kpwm is the gain, which can be approximately equivalent to the specific value of the UDC to the Utr . Gpll is the transfer function of SRF-PLL [6].

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Fig. 1. Structure block diagram of inverter

Fig. 2. Control block diagram

In frequency domain impedance analysis method, inverter can be divided into two parts. Without considering the influence of PLL [7], according to Norton equivalence theorem, the inverter can be equivalent to an ideal controlled current source in parallel with the output impedance, and the weak current network can be equivalent to an ideal controlled voltage source in series with the grid impedance.

Fig. 3. Norton equivalent circuit

However, with the deepening of research, some scholars found that the PLL and the current reference value will be mutually coupled and change the characteristics of the inverter [8]. Considering the influence of PLL, the inverter’s Norton equivalent model will be modified to the form of impedance affected by the current reference value. The

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Norton equivalent model of the two is shown in Fig. 3. Among them, Zout_ Pll is the inverter output impedance taking the disturb of PLL into account; Zg is the impedance of the power grid. The export impedance of inverter regarding the disturb of PLL is shown in the following formula [9]. Zout_pll =

L1 L2 Cs3 + L2 CHad Kpwm s2 + s(L1 + L2 ) + Kpwm Gc L1 Cs2 + CKpwm Had s − Kpwm Iref Gpll Gc + 1

(2)

The Bode diagram of power system impedance and export impedance regarding the influence of PLL is shown in Fig. 4. If the impedance of power system gradually increases, the intersection of Bode diagram shifts to low frequency. When the frequency is reduced to such that the phase margin is less than 30°, the safe operation of the inverter will be affected, mainly reflected in the distortion of Ig and Upcc . Therefore, it is important to reshape the impedance to enable it to operate stably under weak grid conditions.

Fig. 4. Bode diagram of impedance characteristics of inverter

3 Impedance Remodeling Scheme Based on Low-Pass Filter The second-order LPF’s transfer function is as follows: GL (s) =

ωh2 s2 + 2αωh s + ωh2

(3)

where, α Is the damping coefficient, ωh is the bandwidth. Under the weak grid environment, because to the increase of power grid impedance, the voltage harmonic at Upcc increases also, which will affect the accuracy of phase locking. The second-order LPF is added after the voltage detection link. By filtering the low-frequency noise with the LPF which mentioned earlier, the high frequency harmonics cannot pass the LPF and the fundamental wave can be effectively extracted [10], thus improving the accuracy of phase locking. The Bode diagram of the second-order LPF is shown in Fig. 5.

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Fig. 5. Bode diagram of LPF

When the PLL and LPF are connected in series with each other, the characteristics of the two affect each other. If the turning frequency is too small, the bandwidth of the PLL will be reduced, resulting in a slower phase-locked speed; If the turning frequency is too high, the filtering effect will become worse. Therefore, it is important to reasonably devise the turning frequency of the second-order LPF. This article selects ωh is 500, α is 1. The impedance characteristics of grid-working inverter before correction and the impedance characteristics after correction are shown in Fig. 6.

Fig. 6. Comparison of impedance characteristics before and after correction

The second-order low-pass filter under this parameter will produce 65° phase shift to the fundamental wave signal. Phase difference between voltage and current which resulting in the inverter transmitting reactive power to the power system which may cause the grid voltage to rise.

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4 Second Order Low-Pass Optimized Impedance Remodeling Scheme Adding a first-order integral link to the transfer function molecule of the second-order LPF can change the characteristic at the fundamental frequency. To reduce the gridconnected power factor angle, the following correction links are proposed in this paper, and their transfer functions are shown in the formula: Gco =

−A(s + ω2 ) s2 + Bs + ω12

(4)

where A and B are constants, ω1 is the turning angle frequency, ω2 is the angular frequency corresponding to the phase frequency characteristic of 45°. The Bode diagram of this correction link is shown as Fig. 7.

Fig. 7. Bode chart of correction link

The amplitude frequency characteristics of the correction link are:  A2 ω22 + A2 ω2 A(ω) = B2 ω2 + (ω12 − ω2 )2

(5)

The phase frequency characteristics of the correction link are: ϕ(ω) = arctan

Bω2 ω − ω(ω12 − ω2 ) −ω2 (ω12 − ω2 ) − Bω2

(6)

The method of designing the appliance is given in this paper. First of all, the gridworking inverter should achieve stable operation. After correction, the phase margin at the intersection frequency of grid impedance characteristics and grid connected inverter impedance characteristics should be greater than 40°, namely: arctan

Bω2 ωg − ω(ω12 − ωg2 ) −ω2 (ω12 − ωg2 ) − Bωg2

≥ 40◦

(7)

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Among them, ωg is the frequency that the grid impedance characteristic and the inverter export impedance characteristic intersect on the Bode diagram. Secondly, the grid connected inverter should achieve unity power factor grid connection, and the offset of the correction link to the fundamental wave phase angle should be small enough, that is: arctan

Bω2 ω0 − ω0 (ω12 − ω02 ) −ω2 (ω12 − ω02 ) − Bω02

≤ 1◦

(8)

Then, the low-frequency gain of the correction link shall not be greater than 0 dB, or the low-frequency noise will be amplified:  A2 ω22 + A2 ω32 20Lg ≤0 (9) B2 ω32 + (ω12 − ω32 )2 Finally, in order to facilitate analysis, the intersection point of Bode diagram of two impedance characteristics should still be one, namely: AZout_co (ω1 ) > AZg (ω1 )

(10)

The expression of correction links meeting the above conditions is: Gco =

−0.5(s + 3000π ) + 1.88s + (80π )2

s2

(11)

Connect the correction transfer function which meeting the above formula into the phase-locked loop branch in series as shown in Fig. 8, and the output impedance of the grid-working inverter is reshaped as: Zout_co =

L1 L2 Cs3 + L2 CHad Kpwm s2 + s(L1 + L2 ) + Kpwm Gc L1 Cs2 + CKpwm Had s − Kpwm Iref Gpll Gc Gco + 1

Fig. 8. String in mode of correction links

(12)

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As shown in Fig. 9, the phase frequency characteristic of output impedance is improved after the addition of the corrector. When the grid impedance is 12.8 mH, when it is not corrected, the phase margin of is 9.8°,which is far less than the engineering requirement of more than 40°. The grid-working inverter operates at resonance edge. After impedance remodeling, the phase of the cut-off frequency is increased to 42.3°, and the grid connected inverter can operate stably.

Fig. 9. Comparison of impedance characteristics before and after correction

According to Bode diagram, after the proposed correction link is connected in series, the mid frequency phase rise of the characteristics of grid-working inverter is greater than that of the traditional second-order LPF. Therefore, compared with the original scheme, the optimized correction has a larger scope.

5 Simulation Results In order to verify the effectiveness of the proposed scheme, the simulation is carried out in Matlab/Simulink, The simulation parameters are shown in Table 1. Table. 1 Single-phase inverter parameter table U dc

L1

C

L2

f

Switching frequency

400 V

1 mH

10 µF

0.5 mH

50 Hz

10 kHz

Simulation 1: when the grid impedance is 12.8 mH. At this time, the phase margin of cut-off frequency is 9.8°, the system is operating on unstable state, and the current of grid contains a million high-order harmonics. The current waveform is shown in Fig. 10.

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Fig. 10. Waveform of grid connected current before correction

The second order LPF and the optimal corrector are connected in the PLL branch as shown in Figs. 11 and 12, the waveform distortion of grid connected current has been improved, but compared with the optimized corrector, the second-order LPF appears phase shift.

Fig. 11. Waveform of grid connected current after LPF correction

Fig. 12. Waveform of grid connected current after optimization LPF correction

Experiment 2: Increase the grid impedance to 16mH, and the system’s phase margin continues to decrease. The grid-working inverter’s grid-connected current waveform is shown in Fig. 13. The second order LPF and the optimized corrector are connected in series respectively, and the current waves of the two are shown in Figs. 14 and 15 respectively. According to the current waveforms of the two filters, the optimal corrector has a wider application range than the second-order LPF.

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Fig. 13. Waveform of grid connected current before correction

Fig. 14. Waveform of grid connected current after LPF correction

Fig. 15. Waveform of grid connected current after optimization LPF correction

6 Conclusion Throughout the full paper, aiming at the shortcomings of the second-order LPF under the harsh working conditions of grid connected inverter, the form of transfer function is optimized based on it, and its parameters are designed from the aspects of phase margin, power factor, etc. The simulation shows that this link can improve the phase margin of grid-working inverter under the environment of weak grid, make it operate safely when the grid impedance is large, and have a larger correction range. However, the impact of adding correction link on the immunity of PLL has not been solved.

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Acknowledgement. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation) - Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

References 1. Yang, D., Ruan, X., Wu, H.: Virtual impedance method to improve the adaptability of LCL grid connected inverter to weak power grid. Chin. J. Electr. Eng. 34(15), 2327–2335 (2014) 2. Zhang, Y., Chen, X., Wang, Y., Gong, C.: Impedance phase angle dynamic control method of grid connected inverter under weak current network. J. Electrotech. Eng. 32(01), 97–106 (2017) 3. Xu, J., Bian, S., Qian, Q., Xie, S.: Single phase inverter phase-locked loop based on grid current feedforward under weak current grid. Chin. J. Electr. Eng. 40(08), 2647–2657 (2020) 4. Zhang, C., Wang, X., Blaabjerg, F., et al.: The influence of phaselocked loop on the stability of single-phase grid-connected inverter. In: 2015 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, Montreal, pp. 4737–4744 (2015) 5. Du, Y., Yan, M., Yang, X., Zhang, M., Sun, Q., Su, J.: Current correction method of inverter impedance under multi-objective constraints. Control Theor. Appl. 39(04), 701–710 (2022) 6. Han, Y., Luo, M., Zhao, X., et al.: Comparative performance evaluation of orthogonal-signalgenerators- based single-phase PLL algorithms: a survey. IEEE Trans. Power Electron. 31(5), 3932–3944 (2016) 7. Sang, S., Gao, N., Cai, X., et al.: Operation control and stability study of converters for battery energy storage under weak grid conditions. In: Proceedings of the CSEE, vol. 37, no. 1, pp. 54–63 (2017) (in Chinese) 8. Wu, H., Ruan, X., Yang, D.: Research on the stability caused by phase-locked loop for LCLtype grid-connected inverter in weak grid condition. In: Proceedings of the CSEE, vol. 34, no. 30, pp. 5259–5268 (2014) 9. Xu, J., Qian, Q., Zhang, B., et al.: Harmonics and stability analysis of single-phase gridconnected inverters in distributed power generation systems considering phase-locked loop impact. IEEE Trans. Sustain. Energy 10(3), 1470–1480 (2019) 10. Xu, J., Bian, S., Qian, H., et al.: Robust control and optimization of delay-based phase-locked loop of single-phasegrid-connected inverters under weak grid conditions. In: Proceedings of the CSEE, vol. 40, no. 7, pp. 2062–2070+2386 (2020)

Path Planning of Substation Inspection Robot Based on Improved Ant Colony Algorithm Xiaoming Wang, Shuo Shang, Daojin Yao(B) , Chao Liang, Yu Pei, and Zunbin Xu School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, China [email protected]

Abstract. At present, most of the substation inspection robots use ant colony optimization (ACO) to realize path planning, but the traditional ACO has deficiencies such as long planning path, slow convergence speed and blind search, therefore, an improved ACO is proposed in this paper. First, an initial path is planned using the A* algorithm; Second, introducing the cost of the target node in the heuristic function in order to speed up the algorithm’s search efficiency; Finally, the pheromone update rule is improved by conditioning factors to make the ants converge to the optimal path faster. Simulation experiments show that the proposed improved ACO has better merit-seeking ability and faster convergence speed. Keywords: Patrol robot · Path planning · A* algorithm · Improved ACO

1 Introduction As an important part of the power network, substations ensure the stability, reliability and safety of the power system [1, 2]. As a basic guarantee for the safe operation of power equipment, substation inspection is mainly to inspect the internal equipment of substations, including instruments and meters, to ensure the stable operation of equipment through regular inspection. The traditional manual inspection requires a lot of human resources, low efficiency and high danger. The use of robots for automated inspection can ensure safety and efficiency, but also overcome some of the problems and defects of the traditional manual inspection. Therefore, it is essential to study the path planning of inspection robots. So far, various path planning algorithms have been proposed by domestic and foreign scholars, including traditional algorithms such as Dijkstra’s algorithm [3], A* algorithm [4] and intelligent bionic algorithms such as ACO [5], GA [6] and simulated annealing method [7]. Different path planning algorithms have their own advantages and disadvantages. ACO is an intelligent search algorithm with parallel computing and positive feedback of information. However, the traditional ant colony algorithm converges slowly and searches blindly. To address these problems, domestic and foreign scholars have made corresponding improvements to the algorithm. The literature [8] makes the pheromone of the ACO Gaussian distributed, which can reduce the probability of collision with © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 710–716, 2023. https://doi.org/10.1007/978-981-99-4334-0_87

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obstacles and improve the robot’s search efficiency and obstacle avoidance ability. The literature [9] introduced a descent factor and adjusted the pheromone fluctuation factor by setting an iteration threshold to shorten the path length and planning time of the mobile robot.The literature [10] proposes an adaptive pheromone update method to avoid the ACO from falling into local optimal solutions. In response to the problems of traditional ACO such as slow convergence and low operational efficiency, this paper proposes an improved ACO for static environment planning. (1) The initial path is planned using the A* algorithm so that the pheromones are unevenly distributed. (2) Introducing the cost of the target point in the heuristic function in order to increase the purpose and direction. (3) Improving the pheromone update rule so that the optimal solution of the path can be found quickly. Simulation experiments show that the proposed improved ACO can effectively solve the above existing problems.

2 Environment Modeling This paper uses the raster map method for map environment construction due to its simplicity of creation, efficiency, accuracy and clear structure. Assume that the robot works in a 20 * 20 two-dimensional raster environment, as shown in Fig. 1, the white raster is the passable area; the black raster is the impassable obstacle area, and the obstacle is not satisfied with a raster by a black raster processing.

Fig. 1. Grid environment model.

The coordinates of each raster point are:  xi = d ∗ (mod(Gn , M ) − 0.5) yi = d ∗ (M + 0.5 − ceil(Gn /M ))

(1)

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where d denotes the raster edge length; Gn denotes the raster number; M denotes the raster dimension; mod(Gn ,M) denotes to obtain the remainder of Gn /M; ceil(Gn ,M) denotes to round backward to Gn /M; xi , yi denote the coordinates of each raster.

3 Traditional ACO 3.1 Basic Principle of ACO The ACO is an intelligent search algorithm that finds paths through the foraging activity of ant colonies. During foraging, the ants release pheromones while sensing the pheromones around them. The higher the concentration of pheromones, the shorter the path represented, which ensures that the entire colony is concentrated on the shortest path. At the same time, the pheromone concentration will slowly evaporate over time. 3.2 Probability Selection The movement of an ant from one node to the next depends on the pheromone concentration in this path. The state transfer probability equation is as follows: ⎧ β τijα (t)ηij (t) ⎨ , j ∈ allowedk  β k α (2) pij (t) = k∈allowedk τik (t)ηik (t) ⎩ 0, otherwise ηij (t) =

1 dij

(3)

where τij (t) is the pheromone concentration between i and j; α and β are the τij (t) and ηij (t) weights, respectively; allowedk is the set of optional nodes under ant k; and ηij (t) is the heuristic function. 3.3 Rules for Pheromone Updating The pheromone concentration at the next moment is shown in the following equation: τij (t + 1) = (1 − ρ)τij (t) + τij (t) τij (t) =  τijk (t)

=

m k=1

Q Lk ,

0,

τijk (t)

ant k from i to j otherwise

(4) (5)

(6)

where ρ denotes the volatility coefficient; Q denotes the total amount of pheromone.

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4 Improvement of ACO 4.1 Uneven Distribution of Initial Pheromone Concentration In this paper, we adopt a strategy of targeted and unbalanced pheromone allocation. Taking advantage of the fast global path planning capability of the A* algorithm and the ease of combining with other algorithms, the A* algorithm is combined with the ACO. A* algorithm is used in advance to plan a better initial path to avoid the blindness of the ant search path. 4.2 Improvement of Heuristic Function The heuristic function of the traditional ACO is 1/dij, which only considers the cost of i and j when performing path search, without considering the guiding role of the target point, leading to blindness in the algorithm search process. To address these defects, this paper improves the heuristic function of the ACO to improves the search purpose of the algorithm. At the same time, the weight adjustment factor is set for the node cost in the heuristic function, so that the heuristic function changes with the change of the search node. The improvements are as follows: ηij =

1 (1 − μ)dij + μdjG

(7)

djG D

(8)

μ=

where djG denotes the cost of j to the target location; μ denotes the path balance adjustment factor; and D denotes the path cost from the starting position to the target position. 4.3 Improvement of Pheromone Updating Rules Different treatments are adopted for different ants, and when the length of the path taken by ants is greater than the average length of all ants in each generation, the pheromone concentration of these ants is weakened, and vice versa, the pheromone concentration is increased so that subsequent ants gradually move towards the optimal path. The improved pheromone rules are as follows: τij =  θ=

θQ Lk

θ > 1, Lk < Lave θ < 1, Lk > Lave

(9) (10)

where θ denotes the regulator; Lave denotes the average path length of one generation of ants.

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Fig. 2. Flow chart of improved ACO.

4.4 Improved Algorithm Process The flow chart of the improved ACO is shown in Fig. 2.

5 Algorithm Simulation and Analysis The path planning is performed in a 20 × 20 raster map environment with the traditional ACO and the improved ACO. The black dot indicates the starting position and the red asterisk indicates the target position. Simulation comparison graph and simulation data are as follows (Figs. 3, 4 and Table 1).

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Fig. 3. Path planning and convergence curve of traditional ACO.

Fig. 4. Path planning and convergence curve of improved ACO.

Table 1. Simulation experiment data. Algorithm

Optimal path length

Iterations

Traditional ACO

30.38

43

Improved ACO

25.21

8

6 Conclusion The path planning of the substation inspection robot is studied and an improved ACO algorithm is proposed. First, the unbalanced allocation of initial pheromones avoids the blindness of the ants in the initial path finding; then, Second, introducing the cost of the target node in the heuristic function in order to improve the search efficiency of the algorithm; Finally, a pheromone adjustment factor is introduced to adjust the total amount of pheromones. Simulations were performed by Matlab, and the improved ACO

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has shorter path length and fewer iterations, as well as stronger search capability, which proves the feasibility of the improved algorithm. Acknowledgments. This work is supported by the Key Research and Development Plan of Jiangxi province (20212BBE51010, 20202BBE20005), in part by the Jiangxi Provincial Natural Science Foundation (20202BABL214027, 20202BABL214035, 20202BAB212007), and in part by the National Natural Science Foundation of China (52005182).

References 1. Wang, C., Li, H., Zhang, Z., Yu, P., Yang, L., Du, J., Niu, Y., Jiang, J.: Review of bionic crawling micro-robots. J. Intell. Robot. Syst. 105(3) (2022) 2. Li, L., Zhang, Y., Ripperger, M., Nicho, J., Veeraraghavan, M., Fumagalli, A.: Autonomous object pick-and-sort procedure for industrial robotics application. Int. J. Semant. Comput. 13(2) (2019) 3. Sun, J.: Study on Dijkstra path planning of sensor networks based on optimized ant colony algorithm. In: Proceedings of the 2018 8th International Conference on Mechatronics, Computer and Education Informationization (MCEI 2018) (2018) 4. Zhang, Z., Wan, Y., Wang, Y., Guan, X., Ren W., Li, G.: Improved hybrid A* path planning method for spherical mobile robot based on pendulum. Int. J. Adv. Robot. Syst. 18(1) (2021) 5. Yue, L., Chen, H.: Unmanned vehicle path planning using a novel ant colony algorithm. EURASIP J. Wirel. Commun. Netw. 2019(1) (2019) 6. Park, H., Son, D., Koo, B., Jeong, B.: Waiting strategy for the vehicle routing problem with simultaneous pickup and delivery using genetic algorithm. Expert Syst. Appl. 165 (2021) 7. Fan, C., Li, S., Guo, R., Wu, Y.: Analysis of AGV optimal path problem in smart factory based on genetic simulated annealing algorithm. In: Proceedings of 2018 4th Workshop on Advanced Research and Technology in Industry Applications (WARTIA 2018), pp. 175–179 (2018) 8. Li, C., Liu, Q., Song, S., Huang, T., Zhu, Q.: Path planning for mobile robots based on an improved ant colony algorithm with gaussian distribution. J. Phys. Conf. Ser. 2188(1) (2022) 9. Li, Y., Liu, F.: Path planning algorithm for mobile robot based on improved ant colony algorithm. J. Phys. Conf. Ser. 2083(4) (2021) 10. Xin, C., Luo, Q., Wang, C., Yan, Z., Wang, H.: Research on route planning based on improved ant colony algorithm. J. Phys. Conf. Ser. 1820(1) (2021)

Research on Optimization Design of GaN Device Active Gate Drive Circuit Xinyu Ma1 , Cungang Hu2(B) , Wenjie Zhu2 , Liyan Zhang1 , Weixiang Shen3 , and Ke Zhang4 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China 2 Engineering Research Center of Power Quality, Ministry of Education, Anhui University,

Hefei, China [email protected] 3 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, VIC 3122, Australia 4 Jiangsu Dongrun Zhilian Technology Co., Ltd, Nantong, China

Abstract. GaN devices are now widely used in high-frequency switching power supplies, communication radio frequency and other fields, and there are various losses in the topology circuit used, these losses are mainly in the process of device turn-on and turn-off and the loss when the device makes reverse switching. After analyzing the switching process, this paper proposes a new current source driving circuit for the switching loss and overlap loss in the typical half-bridge buck circuit to enhance the switching speed and reduce the oscillation, and finally verifies the results by PSpice simulation. Keywords: Active gate drive circuit · GaN · Driver circuit · VSD · CSD

1 Introduction The performance of traditional silicon-based power devices has approached or even reached its material limit, and researchers as well as the market are gradually turning to the third generation of wide-band semiconductor materials represented by GaN. Compared with silicon and silicon carbide, GaN has high broadband, high saturation electron drift rate, very small gate input charge, an input capacitance of no more than 100 pF, and a lower Miller capacitance effect. These excellent characteristics bring the possibility of miniaturization, high frequency and high power density of power electronics [1]. Nowadays, GaN devices are widely used in military electronics, the communication industry, fast charging sources, etc. Due to the fast switching speed of GaN devices, large dv/dt and di/dt will be generated during the switching process, coupled with the presence of spurious parameters in the circuit, the transient voltage and current of the device will generate large spikes and oscillations, which will endanger the safety of the device, on the one hand, making it necessary to leave a large margin in the device selection and increase the hardware cost, on the other hand, it will also increase the high-frequency electromagnetic interference of power electronics converters. The electronic converter of high-frequency electromagnetic interference [2]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 717–729, 2023. https://doi.org/10.1007/978-981-99-4334-0_88

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In practice, as the operating frequency increases, the traditional voltage source driver (VSD) drive loss and switching loss increase, while the parasitic parameters of the drive circuit will cause the drive voltage oscillation at high frequencies, so it is necessary to add a resistor in the drive circuit to limit the oscillation, and the size of the resistor resistance affects both the power device, Therefore, it is necessary to add a resistor in the driving circuit to limit the oscillation, and the resistor resistance value affects both the switching speed of the power device and the overshoot of the driving voltage [3]. On the other hand, in the traditional VSD circuit, the energy is eventually consumed in the resistive components of the drive circuit, increasing the loss and the overall heat of the PCB, and this loss increases with the increase of the switching frequency, so the traditional VSD drive is an energy-consuming drive method. Based on this drawback, the traditional VSD circuit is only suitable for use in lower-frequency applications [4]. Therefore, to solve the above problems in GaN applications and to meet the requirements of the driving waveform of power devices under high-frequency conditions, this paper proposes the application of a Current Source Driver (CSD) after analyzing the causes of voltage and current spikes and oscillations during the turn-on and turn-off of GaN devices [5]. The CSD can rapidly pull and inject current into the GaN device during the turn-on and turn-off process to suppress the voltage oscillation and current spikes during the switching process while achieving the goal of increasing the switching speed and thus reducing the switching loss [6]. The proposed active drive circuit has a simple structure and can improve the switching speed of GaN devices while taking into account voltage oscillations and current spikes, thus improving the driving quality of GaN devices.

2 Data Analysis of the Device Switching Process In order to explain the characteristics of GaN devices in turn-on and turn-off, this paper adopts the half-bridge topology test circuit as shown in Fig. 1, in which VDC is DC Bus voltage, CBUS is DC-regulated filter capacitor, L1 is an inductive load, in which GaNsystem’s GS-065-011-1-L is selected as the GaN devices, and its internal parasitic parameters are Cgd , gate drain capacitance is Cgs , gate source capacitance is Cds . According to the manual, the input capacitance Ciss = Cgd + Cgs , output capacitance Coss = Cgd + Cds , the input current of Q1 is IQ1, the input current of Q2 is IQ2, and the current flowing through the load inductor is I L . V th is the gate threshold voltage, Vpl is the gate step voltage, tcr is the current rise time, and tvf is the voltage fall time of DS (Figs. 2 and 3). In the switching process of the devices, During the on/off process of the device, T1 and T2 are mainly converted between the cutoff region to the non-saturation region of the switching tube. In the cutoff region, the current between the drain and source terminals of the switching tube is 0, while in the process of conversion, the switching tube passes through the saturation region, when the voltage and current between the drain and source terminals of the device are conducted, and the current is highly susceptible to the gate drive voltage Vgs. GaN switching tube turn-on process as shown in the figure, due to There is input capacitance Ciss and Miller capacitance Cgd , gate voltage does not stabilize quickly, As the current between the drain-source poles begins to rise, the gate drive voltage Vgs also continues to rise, which causes the current in the channel to

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CISS=70pF COSS=20pF CRSS=0.4pF

iQ1

CGD_Q1

CGS_Q1

CQ1

VDC

L1

VOUT+ IL

iQ2

CBUS

T1

CDS_Q1

G1

CGD_Q2 CDS_Q2

G2

T2

CGS_Q2

CQ2

VOUT-

Fig. 1. Half-bridge buck circuit

VDC IL

IDS

VGS Vpl

VDS PON

Vth

TVF

TCR

T

Fig. 2. Turn on process loss

VDC VDS IL IDS Vgs Vpl Poff

Vth TVR

TCF

T

Fig. 3. Turn off process losses

continue to rise as well. The Miller capacitor Cgd reduces the slope of the gate voltage rise curve, but the voltage drop time depends on the charge of the parasitic capacitor at the inverter switch output node. The part of power loss is divided into two parts, one is Eoss loss and overlap loss, Eoss loss is mainly affected by the output capacitance Coss, and overlap loss is mainly generated due to the transfer of voltage and current between the source and drain when the switching tube passes through the saturation region, Eoss loss is independent of the switching time [7]. The overlap loss is related to the switching

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time, and the gate current charge can be changed during the switching process to reduce the overlap loss. Similarly, the switching-off process principle is similar to the turn-on process, the current flow in the on-circuit circuit loop through the device’s saturation zone channel into the cut-off zone, that is, the circuit still generates commutation losses, similar to the turn-on process, the size of the loss value in the turn-off process also depends on the on voltage drop time of the switching tube and the voltage rise time at turn-off. 2.1 Analysis of the Current Rise Phase in the Turn-On Process As shown in Fig. 4. Before the drive voltage reaches the threshold voltage of the switching tube, the total charge of the parasitic capacitor at the output node in the loop is exceeded, and the loop load current also flows through the switching tube through the saturation region [8], resulting in the overlap of the charge to the capacitor and the current flowing through resulting in loss, which is calculated as the expression: PON = fsw EON

(1)

The total energy loss caused by the overlap can be calculated as: 1 VDC IL (tcr + tvf ) (2) 2 The turn-on and turn-off of GaN devices are similar to that of SiC devices in that the gate has a high input impedance, and a certain amount of charge is injected or pulled from the gate by the driver circuit to control the turn-on and turn-off of the switching tube device [9]. As shown in Fig. 4 the gate charge characteristics are divided into four main parts: Qgs(th) : the charge required to increase the gate voltage to the threshold voltage, Qgst : the charge required to increase the gate voltage from the threshold voltage to the step voltage, i.e., the charge required to satisfy the drain current ID , Qgd : the charge required to pull the drain voltage down from the cutoff state to zero, i.e., the charge required to satisfy the drain-source voltage VDS , When the switching device enters the linear operating region, the charge in the circuit satisfies the voltage Vds between the drain and source, assuming that the voltage and current across the drain and source of the switching device vary by VDS and ID during this period, and the other required parameters can be found in the official manufacturer’s datasheet [10].   Qgs Vgs(th) (3) Qgs(th) = Vpl EON =

Qgst = Qgs − Qgs(th)  Qgs = Qgst

ID ID

(4)

 (5)

According to the parasitic capacitance characteristics, since the total gate charge Qg and Qgd are related, it follows that:  VDC CRSS (vDS )dvDS (6) Qgd = 0

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400V 100V

6

Qg

Vgs/V

5 4

Gate Voltage

Vpl

3 2

Qgs Qgd Vgs(th)

1

Qgst Qgs(th)

0.5

1

1.5

Charge of the Gate

2

2.5

QG/nC

Fig. 4. Characteristics of gate charge versus voltage

Qg is then the amount of charge required to raise the switching tube from zero voltage to the rated gate voltage. The main process of conduction occurs when the current rises in the gate voltage and reaches the threshold voltage before it begins, and the current begins to flow when the drain-source voltage begins to convert, that is, to complete the action, the greater the swing of the current, the longer the time required and the loss increases. Determine the current conversion time of the charge Qgs , Under normal operating conditions, the time required to fill the internal capacitor with the total charge is: Q (7) t= I Assuming that the current I is constant during the charging and discharging time, the time tcr of the current rise phase is: tcr =

Qgs Igcr

(8)

The expression for the dynamic gate current Ig during the turn-on process is: Ig =

Vdrv − vgs Rg

(9)

Rgin is the GaN device’s internal gate resistance, Rgex is the gate loop applied resistance, and the gate loop gate resistance Rg is expressed as: Rg = Rgin + Rgex

(10)

During the switching process, the gate current varies with the gate voltage, and the average value of the current within the current rise phase, Igcr is expressed as:   V +V Vdrv − gs(th)2 pl (11) Igcr = Rg

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Voltage drop time tvf : tvf =

Qgd Igvf

(12)

The dynamic gate current Igvf during the in-channel transition is calculated as: Igvf =

Vdrv − Vpl Rg

(13)

The excess conversion current Icha in the trench during conversion is calculated as: Icha = gfs vgs vf + IL

(14)

The relationship between t_vf and the total displacement charge of the output node TQ1 + TQ2 is given by: tvf =

TQ1 + TQ2 1 2 (Icha

− IL )

=

2(TQ1 + TQ2 ) gfs vgsvf

The gate voltage vgsvf during conversion is given by:    Igvf CTQ1 + CTQ2 (VDC ) vgsvf ≈ gfs CRSS

(15)

(16)

Solving for the formulas (17) and (18) two equations gives the estimated value of the gate voltage rise calculated as: vgsvf ≈

1 2

+



Vdrv − Vpl Rggfs CRSS CTQ1 +CTQ2 (VDC )



(17)

Solving tvf with the previous equation yields the voltage drop time calculated as 

  2Rg CRSS TQ1 + TQ2 1 (18) + tvf ≈  gfs CTQ1 + CTQ2 (VDC ) Vdrv − Vpl

2.2 Analysis of the Current Drop Phase During Turn Off The previous section of the current rise formula can be calculated in the same way to calculate the expression of the current fall time, As shown in Fig. 3, when the conduction channel from the non-saturation region to the saturation region, as well as in the cut-off region completely closed, the average current of the gate in this period is calculated as follows:   Vpl +Vgs(th) − Vdrv 2 (19) Igcf = Rg

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Substituting the above equation for the duration of the conversion tcf equation is: tcf =

Qgst Igcf

(20)

The overlap loss EOFF during the current drop, The equation for this process is: EOFF =

1 tcf IL vDS− cf 6

(21)

To calculate the overlap loss at shutdown, the value of the change in VDS during the current drop time must be calculated:  tcf dvDS_Q1 vDS_cf = dt (22) dt 0 ≈

1 2 tCf IL

CTQ1 + CTQ2 (VDC )

(23)

The overlap loss of the shutdown process can be estimated from the current drop period transition duration and the above equation: EOFF ≈

1 2 12 (IL tcf )

CTQ1 + CTQ2 (VDC )

POFF = EOFF fsw

(24) (25)

As for the time of the voltage rise phase, it is mainly related to the inductor current IL and the output capacitance of TQ1 and TQ2, and the upper tube is in the cut-off zone without resistive overlap loss, so the voltage rise time is calculated by the formula: tvr =

TQ1 + TQ2 tcf − IL 2

(26)

From the analysis in Sects. 2.1 and 2.2 above, it is clear that the overlap loss during the switching of GaN devices is closely related to the timing of the current rise and current fall phases, and optimizing the rise and fall times can effectively reduce the loss in the topology circuit.

3 The Method of Driving a Current Source Gate Circuit From the analysis in the previous section, it is clear that during the current rise and current fall phases of the GaN device turn-on and turn-off process, the current can be injected and pulled to achieve fast turn-on and turn-off and reduce the voltage and current oscillations and spikes in the switching process by reducing di/dt. In this paper, we design a new active gate drive circuit that pulls current during the current rise phase of the gate drive turn-on of GaN devices and injects current during the current fall phase of the gate drive turn-off. The overall design adopts a separate

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design for turn-on and turn-off, to reduce the voltage and current spikes and oscillations during the turn-on and turn-off of GaN devices while improving the turn-on and turn-off speed. The separate design for turn-on and turn-off also takes into account the impact of the dead time on the device loss in the corresponding topology, and the optimized control of the dead time at high frequencies can effectively reduce the loss. The active gate driver circuit designed in this paper mainly consists of an input circuit, a push-pull circuit, a detection circuit, and an output control circuit, as shown in Fig. 5. The gate driver circuit is divided into a turn-on circuit and a turn-off circuit, and the two separated circuits contain different push-pull structures and output circuits. 1. Input circuit: gate signal isolation input, used to generate the drive voltage, and the input signal to do optical isolation, using the Avago model ACPL-W346 driver chip. 2. Gate opening circuit: gate opening circuit and gate closing circuit share a signal input, the signal through the 74VHC132MX on the input signal to do the reverse and dead adjustment into complementary PWM waveform, respectively, passed to the opening circuit and closing circuit, which for the dead time control is mainly composed of device C1 and device R1, the dead time calculation is as follows: Td = 2π R1 C1

(27)

After the drive signal is input through M1, M1 mainly realizes the fast shutdown function for the turn-on signal. The signal then passes through the push-pull circuit, which is mainly composed of devices Q1 and Q2 to control the positive voltage input of the gate drive signal and control device M2 to realize the final device turn-on. 3. The normal shutdown circuit is driven by the PWM wave input from the gate optocoupler, which forms a complementary and self-regulating deadtime with the opening PWM wave, and is transmitted to the M3 device by the push-pull circuit composed of Q3 and Q4 to control the GaN device shutdown process. The soft-off circuit is mainly transmitted from the drain of the GaN power switch to the D5 fast recovery diode, which controls the opening and closing of Q5 and then controls the pull-down grounding of the shutdown signal. 4. Output circuit: The output circuit mainly contains part of the turn-on circuit and part of the turn-off circuit, the general architecture is the same, but the specific devices are different. The turn-on circuit is mainly responsible for the positive voltage part, from the positive voltage VDD and GND by the push-pull circuit by the P-channel MOS M2 control on, turn-off circuit is mainly responsible for the negative voltage drive part, from the negative voltage VEE and VDD by the push-pull circuit by the N-channel MOS M3 control off. Table 1 summarizes the device parameters of the proposed gate drive loop. Compared with the existing active drive scheme, the structure is streamlined and easy to implement, and the cost is not very high. For different GaN devices, only the corresponding gate voltage needs to be changed in the process of use, which applies to most devices and is universal.

Research on Optimization Design of GaN Device Q1

VDD

Turn On

R6

R4

R3

C1

M1

R2

R1

R10

R7

R5

R8

Q2

M2 R9

VDD

R16

VEE

R11

Isolated Input

DSS

C2 D5

R18 C3

D4 R19 Q5

Q3

D3

D2

G SS

R17

DSS

S

R15

R13 M3 R14

Q4

Turn Off

D M4

GaN

R12 C4

VDD

VDD

D1

PWM

725

Turn Off

VEE

VDD

Fig. 5. Proposed current source gate drive circuit structure

Table 1. Active drive circuit parameters Circuit structure

Device model

Component parameters

Input circuit

ACPL-W346

–

Turn on circuit

74VHC132MX, MMBT4403, BC817

R1 = 2.4 k, C1 = 1 nF, R6 = 2 k, R7 = 100 , R8 = 2.2 K, R10 = 1.2 , VDD = 6 V

Turn-off circuit

74VHC132MX, IRF7317TRPBF, MMBT4403, BC817, IRF7317TRPBF

R12 = 100 , R13 = 2.2 k, R16 = R17 = 51 , R15 = 2.2 , VEE = − 3V

4 Simulation Results of the Active Gate Driving Strategy In order to verify the effect of the proposed current source driving circuit, the designed driving circuit is simulated and verified using Pspice simulation, and the results and parameters used in the simulation are shown in the following Table 2 and figures. Table 2. PSpice simulation parameters Parameters

Parameter values

DC bus voltage Vdc /V

400

Load inductor Lload /µH

0.3

Load resistor Rload / 

40

Switching frequency fsw /MHz

10

According to the simulation conditions in Table 3, the topology circuit is simulated using Pspice and the results of Figs. 6 and 9 can be obtained from condition I for the

X. Ma et al. Uds 410V

1ns

id

Ugs(5V/Div)

id(5A/Div) Uds(50V/Div)

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Ugs 1ns/Div

Ugs(5V/Div)

id(5A/Div) Uds(50V/Div)

Fig. 6. Turn off waveform by simulation condition I

490V Uds 7ns id Ugs 1ns/Div

Ugs(2V/Div) id(10A/Div) Uds(100V/Div)

Fig. 7. Turn off waveform by simulation condition II

450V 2ns

Uds

id Ugs 1ns/Div

Fig. 8. Turn off waveform by simulation condition III

device turn-off process and the device turn-on process, respectively. Similarly, Figs. 7 and 8 are the results of the turn-off process under conditions II and III, and Figs. 10 and 11 are the simulation results of the turn-on process under conditions II and III.

Ugs(2V/Div) id(10A/Div) Uds(100V/Div)

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Uds

id

10A

Ugs 5ns

5ns/Div

Ugs(2V/Div) id(10A/Div) Uds(100V/Div)

Fig. 9. Turn on waveform by simulation condition I

Uds

id

10.6A

Ugs 10ns 2ns/Div

Ugs(2V/Div) id(10A/Div) Uds(100V/Div)

Fig. 10. Turn on waveform by simulation condition II

Uds

id

10A

Ugs 7ns

10ns/Div

Fig. 11. Turn on waveform by simulation condition III

The results summarized in Table 4 show that the proposed current source drive circuit is better than the voltage source drive circuit in suppressing the voltage spike of 410 V and current spike of 10.6 A under the same simulation conditions, and the proposed current source drive circuit has a voltage oscillation time of 1 ns and a current oscillation time of 5 ns. Oscillation time of the proposed current source driver circuit is better than the voltage source driver circuit of 7 ns and 10 ns.

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Simulation condition Driving method

Drive resistor

I

Current source active drive

Ron = 1.5 , Roff = 2.2 

II

Conventional voltage source active driver Ron = 1.5 , Roff = 2.2 

III

Conventional voltage source active driver Ron = 10 , Roff = 2 

Table 4. Comparison of results under different conditions Condition

Voltage spike/V

Voltage oscillating time/ns

Current spike/A

Simulation condition I

410

1

10

Simulation condition II

490

7

10.6

Simulation condition III

450

2

10

Current oscillating time/ns 5 10 7

From the theoretical analysis of this paper and the results shown by Pspice simulation, it can be seen that the traditional voltage-source type driver circuit has the problems of a relatively slow switching process and easy oscillation of voltage and current. The newly proposed current-source driver circuit not only improves the turn-on and turn-off time of the device but also reduces the existence of voltage and current oscillation during the switching process, the proposed driver circuit achieves the preset functional purpose.

5 Conclusion This paper addresses the overlap losses and the voltage oscillations and current spikes that occur in the GaN switching process. After analyzing the generation mechanism, a current-source type drive circuit is proposed and the effectiveness of the proposed active drive circuit is verified in simulation. The simulation results show that the newly proposed current-source drive circuit not only improves the turn-on and turn-off time of the device but also reduces the voltage and current oscillations present in the switching process. Acknowledgments. The work is supported by the Outstanding Youth Project of the Natural Science Foundation of Anhui Province under Grant (2108085J24) and the Natural Science Foundation of Anhui Province (2108085QE239). The Policy Guidance Plan (International Scientific and Technological Cooperation) - Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

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References 1. Qi, Y., Li, Y., Wang, L.U.: The common-mode characteristics and loss of dual buck gridconnected inverter based on GaN devices. Trans. China Electrotech. Soc. 32(20), 133–141 (2017) 2. Dymond, H.C.P., Wang, J., Liu, D., et al.: A 6.7-GHz active gate driver for GaN FETs to combat overshoot, ringing, and EMI. IEEE Trans. Power Electron. 33(1), 581–594 (2018) 3. Zhang, X., Pan, S.: Optimal design of gallium nitride power device driving circuit. Electric Drive 52(05), 34–38 (2022) 4. Wang, X., Zhu, Y., Zhao, Q.M., et al.: Impact of gate-loop parameters on the switching behavior of SiC MOSFETs. Trans. China Electrotech. Soc. 32(13), 23–30 (2017) 5. Sang, X., Wang, Y., Xu, D.: Research on loss analysis and efficiency improvement of current source driver. Trans. China Electrotech. Soc. 36(S2), 610–618 (2021) 6. Feng, C., Li, H., Jiang, Y., et al.: Research on current injection active drive method of SiC MOSFET with transient voltage and current spike and oscillation suppression. Proc. CSEE 39(19), 5666–73+894 (2019) 7. Pan, S., Li, H., Feng, X., et al.: Design of gate drive scheme for 600 V depletion-mode GaN power devices. J. Power Sources 17(03), 57–63 (2019) 8. Okamoto, M., Ishibashi, T., Yamada, H., et al.: Resonant gate driver for a normally ON GaN HEMT. IEEE J. Emerg. Sel. Top. Power Electron. 4(3), 926–934 (2016) 9. Ren, X., Reusch, D., Ji, S., et al.: Three-level driving method for GaN power transistor. Trans. China Electrotech. Soc. 28(05), 202–207 (2013) 10. Lidow, A., De Rooij, M., Strydom, J., et al.: GaN Transistors for Efficient Power Conversion. Wiley, Hoboken (2019)

Applications and Prospects of Online Insulation Monitoring Technique Based on Broadband Frequency Response for Transformers in Voltage Source Converter System Geye Lu(B) , Dayong Zheng, and Pinjia Zhang State Key Lab of Security Control and Simulation of Power Systems and Large Scale Generation Equipment, Tsinghua University, Beijing 100084, China {ddgy2021,zday,pinjia.zhang}@mail.tsinghua.edu.cn

Abstract. Power electronic converters are widely applied in new power system. Converter transformers have a critical risk in safe and reliable operation due to the insulation ageing. At present, conventional transformer insulation monitoring methods are limited to low sensitivity, invasive sensors and sophisticated evaluation. The goal of this paper is to improve the performance of online insulation monitoring for converter transformers based on broadband frequency response. The significance of application promotion, the disadvantages of existing methods and the challenges from offline to online implementation are clarified. A novel technique based on inherent harmonics in voltage source converter system is investigated, which provides the prospect in improving the online monitoring performance with high reliability and non-invasiveness nature. Keywords: Broadband frequency response · Insulation · Online monitoring · Transformer · Voltage source converter

1 Introduction Electric power is crucial to the development of politics, economy and livelihood. Since the 21st century, zero carbon has transformed from a global political consensus into economic and technological goals [1]. Power system is undergoing significant changes as a result of worldwide energiewende. Renewable energy, represented by wind power and photovoltaic, is ushering in an accelerated development. According to the statistics of the International Energy Agency [2], the global wind power generation accounted for nearly 5% in 2018 and the global photovoltaic power generation accounted for nearly 3% in 2020. The average annual renewable energy is expected to 45% in total power generation by 2040 [3]. New power system is integrated with high proportion of renewable energy, where electrification diversification is promoted but the complexity is increased in power generation, transmission, distribution and consumption units. Power electronic converters are © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 730–747, 2023. https://doi.org/10.1007/978-981-99-4334-0_89

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widely applied to facilitate the operating efficiency and flexibility. Voltage source converters (VSCs) based on full-controlled semiconductor switching devices have apparent advantages compared with the converters based on thyristors [4]. From the perspective of power generation, the limitations of traditional fossil fuel option can be overcome, such as high carbon emission and low dispatch flexibility. From the perspective of power demand, the operation and management mode can be reshaped in residential, industrial and rail-transit applications, so that new power system is becoming clean, safe, intelligent and interactive. Figure 1 shows the framework of power system with high-proportion VSC integration, enabling the connection of traditional power units, renewable energy units and nonlinear loads. These transformers connected with VSCs are the key electric assets considering high producing cost and high operating risk [5]. Compared with traditional power transformers, converter transformers face a greater threat on insulation ageing, since they additionally suffer from a mass of voltage stresses and harmonic losses caused by DC polarity reverse and switching transients. Electrical ageing and thermal ageing are two of the most critical factors leading to transformer failures, as outlined in Table 1. Table 1. Insulation ageing caused by electrical and thermal ageing. Factor

Description

Evaluation

Electrical ageing

Voltage stresses are large as a result of switching transients (dv/dt) [6], harmonic voltages [7] and polarity reversal [8]

Dielectric properties of insulating materials are degraded, especially for insulating components at the line lead of the winding on the converter side

Thermal ageing

Stray loss and eddy current loss are increased as a result of harmonic currents [9] and magnetic leakage flux [10]

Insulating materials endure severe thermal fatigue due to the sharp temperature rise. The leakage flux leads to the hotspot and/or overheating winding

According to the IEC/IEEE Standards (IEEE Std C57.129-2007 and IEC/IEEE 60076-57-129:2017) [11, 12], offline routine and online implementation for insulation monitoring of converter transformers are the same with these for traditional power transformers. However, accident severity and financial loss of converter transformers are critical, as evidenced by multiple transformer failures in power electronic converter system. In recent years, the State Grid Corporation of China has experienced more than 30 failures. In April 2018, the transformer in ± 800 kV Tianshan Converter Station caught fire. In March and June 2019, the transformers in ± 800 kV Yinan Converter Station and ± 800 kV Yibin converter station burst into flames separately. In November 2019, the transformer in 1000 kV Jinan Quancheng Substation deflagrated, resulting in one death and two injuries. Hence, the existing monitoring configuration for converter transformers can hardly realize reliable failure prognosis and defect diagnosis at the initial ageing stage.

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Fig. 1. Framework of power system with high-proportion VSC integration

Ensuring the operating security and comprehensive management of electric assets has become a key technological challenge in building new power system. It is no longer limited to traditional failure isolation, but is more committed to online condition monitoring and preventive protection. The transformer failure, which is usually evolved from the insulation defect, generally has the latent characteristic. Especially for these transformers in power electronic system, insulating components are subject to severer and accelerated ageing due to harsher operating conditions. Hence, effective online monitoring for minor insulation defects is of great significance. In this paper, the conventional broadband frequency response is reviewed in Sect. 2, placing emphasis on the challenges and possible solutions of online implementation. Then, the prospect of improved broadband frequency response is investigated in Sect. 3, placing emphasis on the principle, the technical issues on online implementation.

2 Broadband Frequency Response from Offline to Online 2.1 Basic Principle With the severer ageing of a transformer insulating component, the inside charges have the larger concentration and freedom degree and the energy loss is increased. Under the voltage excitation (U) at a certain angular frequency (ω), the loss is equivalent to a complex capacitance (C), including the real part (C  ) for dielectric loss due to the polarization effect and the imaginary part (C  ) for resistive loss due to the conductance effect. On this basis, two indicators of dissipation factor and leakage current are further raised. The indicator performances are usually presented as broadband frequency spectrums, formulated by Complex Capacitance: C(ω) = C  (ω) − jC  (ω)

(1)

Dissipation Factor: tan δ(ω) = C  (ω)/C  (ω)

(2)

Leakage Current: I˙ (ω) = jωC(ω)U˙ (ω)

(3)

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Relaxation time of the oil-paper insulating system is experimentally clarified on the order of seconds [13]. Both C  and C  are sensitive to the ageing under the lowfrequency voltage excitation (typically below 1 Hz). In the middle and high frequency bands (typically over 1 kHz), they have the frequency-independency feature and the capacitance change caused by insulation ageing is not obvious. In practical applications, the broadband frequency response is carried out over the range from 0.1 MHz to 1 Hz. In Table 2, the advantages and disadvantages of three ageing indicators for broadband frequency response are summarized. They provide a powerful tool for insulation monitoring, with the advantages of non-invasiveness and definitive physical correlation of dielectric property. However, they have individual critical restrictions. In common, the broadband voltage excitation on the transformer should rely on additional injection devices, introducing the difficulties in online implementation. Hence, the evaluation based on complex capacitance and dissipation factor is limited to offline implementation. The root cause is that both C  and C  are too large to measure accurately in the operation, which are typically obtained offline via the Schering Bridge. The evaluation based on leakage current lack the sensitivity in incipient-ageing defect diagnosis, since only several milliamperes or even hundreds of microamperes are changed under the rated voltage with the ageing development. The challenge lies in leakage current measurement with high sensitivity and high signal-to-noise ratio (SNR). In addition, any small ambient interference, including electromagnetic noise, temperature, moisture and dynamic loads, can lead to the poor response performance. It is difficult to differentiate the response variation caused by insulation ageing from the interference. Table 2. Evaluation of broadband frequency response based on three indicators. Complex capacitance Advantages

Leakage current

Non-invasiveness, definitive physical correlation of dielectric property Detailed information

Disadvantages

Dissipation factor Geometry independency

Offline implementation

Online implementation Low sensitivity

Therefore, there are majorly three technical issues restricting online implementation of broadband frequency response, i.e., the hardware complexity in multi-frequency signal injection the low-sensitivity measurement of leakage current, and the effects of operating conditions. With the development of power electronic switching technology and current sensing technology in recent years, there have been prospective solutions to support the broadband frequency response toward online implementation, along with several challenges to be resolved. 2.2 Challenges and Solutions of Online Implementation Setups Complexity. In traditional power system, the excitation on transformer insulation is the operating voltage at the fundamental frequency. Online frequency response is the result based on the measured voltage and current at a single frequency. Figure 2 shows

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three setups for multi-frequency signal injection which are majorly discussed in existing researches. In Fig. 2 (a), the signal is injected via the neutral point of potential transformers. The potential voltage at this point usually remains at the low level under the normal operation. The isolation transformer serves for the electrical isolation between the signal generator and the high-voltage operating system. The responding current is measured at the neutral point of the transformer on the secondary side. In this schematic of test setups, the advantage lies in the convenience by using the equipped potential transformers. The disadvantage is the overvoltage threat on low-voltage test devices when the system is attacked by the asymmetric fault or the lightning strike. In addition, the setups involve high-voltage assets, so that the implementation lacks the flexibility and the extendibility. Hence, the reliability by this means is reduced in online transformer monitoring. In Fig. 2 (b), the signal is injected via the bushing tap. The responding current is measured at the neutral end of transformer winding on the same side. Effective electric isolation can be realized simply since the bushing itself is non-charged. The setups contain a protection circuit with air gap capable of preventing the low-voltage test system from the attack. The disadvantage is the individual phase injection. There is a synchronization problem caused by three-phase injection and measurement online. In addition, the dielectric property of the bushing itself is introduced in the response performance, increasing the difficulty in transformer insulation evaluation. Hence, this means is typically used to monitor the whole system consisting of transformer body and bushings. In Fig. 2 (c), the signal is injected via the power electronic converter with small capacity at the neutral end of transformer winding. First, in cases of external attack, the H bridge based on full-controlled switching devices can be blocked quickly, avoiding device damage. Second, the magnitude and frequency of injected signals can be controlled flexibly by changing the DC voltage, the switching frequency and the modulation strategy. Third, the converter is independent of the original operating system. The hardware setups can be applied in different in-service transformers in either single phase or three phases. The above three means realize multi-frequency signal injection into the high-voltage power system, capable of online insulation transformer monitoring based on broadband frequency response. However, additional setups for injection and protection can increase the topology complexity and cost, which becomes the first obstacle in online implementation. They have not been officially used in practical applications by compromising the pros and cons. Measurement promotion. The leakage-current-based frequency response supports the online monitoring of groundwall insulation. High-sensitivity measurement of leakage current over the broad frequency band is the basic for online implementation. It is important to promote the sensitivity of current sensing units at milliampere or microampere level and to promote the monitoring scope toward the incipient insulation defect in each phase. To achieve two promotion goals, a novel technology for high-sensitivity leakage current measurement has been developed [17–19], which relies on the electromagnetic modal decoupling principle and the optimizing magnetic shielding topology. First, based

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(a)

(b)

(c)

Fig. 2. Schematics of setups for multi-frequency signal injection. (a) Potential transformers [14], (b) bushing tap [15], (c) winding neutral [16]

on the electromagnetic modal decoupling principle, the condition of groundwall insulation can be monitored in either three phases or each phase, as shown in Fig. 3 (a) and (b), respectively. According to the Ampere Circuital Theorem, the magnetic field intensity (H) is determined by the current vector sum in cables. In Fig. 3 (a) and (b), the relationship can be expressed as     (4) I˙P + I˙leakP − I˙P = I˙leakA + I˙leakB + I˙leakC . Hd l = P = A/B/C



(a)

Hd l = I˙A + I˙leakA − I˙A = I˙leakA .

(5)

(b)

Fig. 3. Two measurement modes for leakage current. (a) Three phases [17], (b) single phase [18]

The advantage of this high-sensitivity leakage current measurement lies in electromagnetic mode decoupling. In both two modes of leakage current measurement, H is irrelevant to the load current and the magnetic field distribution (B) has the spatial characteristic dependent on the cable positioning. For the single-phase leakage current measurement, the inlet cable and the outlet cable are in a certain insulation distance. There are large magnetic field noises caused by the load current in hundreds of Amperes, leading to the low sensitivity of the leakage current measurement. The magnetic shielding

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topology can significantly filter the noises, with the magnetic field outside the shielding core dominated by the leakage current. The topologies for two developed high-sensitivity current sensors are shown in Fig. 4. In Fig. 4 (a), the topology serves for three-phase leakage current measurement. The three-phase cable goes across the shielding core with optimizing physical dimensions. A magnetic sensor based on the tunnel/giant magnetoresistance is used to measure the tangential magnetic field after the filtering. Figure 4 (b) shows a dual-core topology, consisting of the shielding core and the detection core. It serves for the single-phase leakage current measurement and the optimizing detection position on the outer core is the symmetry axis of two cables. Based on these two optimizing magnetic shielding topologies, the leakage current can be measured with high sensitivity and high signal-to-noise-ratio in large load noises. The effect of asymmetrical cable positioning can be significantly reduced. Therefore, this measurement promotion addresses the key bottleneck of online broadband frequency response, as the sensitivity of leakage current measurement is improved from Ampere level to milliampere level. Online groundwall insulation monitoring of many crucial electric assets can be covered in transformers, cables and motors.

(a)

(b)

Fig. 4. Two topologies for high-sensitivity current sensors. (a) Three phases [17], (b) single phase [18]

Effects of Operating Factors Temperature compensation. Dielectric properties of transformer insulating components are affected by the temperature. The rising temperature causes charge motivation and moisture migration from the paper/board towards the oil. To exclude this effect, offline tests usually require the transformer cooling down to the specified temperature. However, the effects of temperature derivation are hardly avoided online due to the changes in load current and ambient temperature. Hence, the compensation for such effects is essential to allow the response to be comparable. The effects of temperature derivation can be divided into the static and the dynamic [19]. The static effect results from ambient temperature differences in different tests considering the temperature being unchanged in one test duration. Many researches have investigated the compensation for static effect, which are in two main categories. First,

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the compensation is done using the moisture-equilibrium curves restored as the database in advance [20]. Second, the compensation is done based on the empirical Arrhenius equation [21]. The standard master curve can be structured and the response can be normalized with respective to the standard at the specified temperature. Both two categories are less intelligent since they are dependent on general rules obtained from a large number of experiments on insulating samples under specified test conditions. They usually offer limited information in field applications since insulation geometry of the transformer system makes the diverse performance in different transformer families. The dynamic effect results from the temperature derivation in one test duration. The response in the low-frequency band can be affected to a great extent. The compensation is of great significance in the on-site monitoring, but few researches have addressed effective solutions. In [20], the response in the low-frequency band is corrected by the iterative calculation of partial test data between 10 and 1 Hz. The compensation is done until the match is found. This approach is validated when the test temperature decreases or increases monotonically and uniformly, which is probably against temperature derivation on site. Therefore, due to this difficulty, effective online monitoring is hardly realized based on the response over the low frequency band. Speed-up test. The duration of the sweep frequency response test typically lasts dozens of hours with the lowest frequency of 0.1 mHz. In some field applications, such as the traction transformer [22], it is suggested to realize fast and convenient test in a few hours or even less for the out-of-service transformer, or directly conduct the test online. The long test duration makes the response vulnerable to varying operating factors. Speeding the test can provide an effective solution from this perspective. The widely-discussed method is based on the multi-frequency mixed excitation by replacing the single-frequency sweep excitation. The aliasing response is decomposed at each discrete frequency based on the data processing. In this way, the test duration can be reduced up to 73% with a satisfactory match between the conventional response and the speed-up response [23]. This method is assumed that there is no cross-frequency coupling of energy loss inside the insulating component. However, the effect of crossfrequency coupling cannot be neglected when the multi-frequency excitation is mixed at several low frequencies. The other popular method is to use inherent transient signals [24–27], such as the lightning strike and the protection switching. Online broadband frequency response can be obtained based on date in a short duration. In practical applications, there are several outweighing disadvantages. First, this method is destructive. Second, the transient signal typically lasts hundreds of nanoseconds. The response ranges up to several megahertz and measurement issues in accuracy and bandwidth are caused. Third, electromagnetic interferences, stray losses and lead connections have effects on the response at high frequencies above megahertz. Fourth, each transient signal is unique with individual frequency spectrum, leading to the difficulties in test repetition and result comparability.

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Therefore, the speed-up broadband frequency response is feasible in theory and not widely used in practice. Reducing the test duration to a few hours is still not immune to the effects of temperature derivation. The requirement of signal injection setups restrains online implementation. Another kind of methods based on inherent transient signals are not competent in transformer insulation monitoring, as a result of poor online performances. Robustness to system operation. Dynamic system operation leads to uncertainties in online results. The response is largely dependent on the changes in equivalent transformer parameters which are affected meanwhile by varying system operation conditions, especially considering the effects of unbalanced loads and the varying magnetizing operation of the core. Hence, minimizing the effects of system operation is crucial to the accomplishment of online implementation. Online in many researches is essentially in an energized way. The transformer is excited by power source with the secondary side unloaded. In fact, it is not the exact online monitoring since the transformer is not operated with connection to power system. To achieve this goal, the insulation indicators should be robust to dynamic operating conditions of power system. Conventional methods based on physical and chemical signals can possess this advantage. However, these physicochemical-based methods generally have the invasiveness nature. The signals are partial and minor, with a long duration for dispersion and propagation. The performance is highly dependent on the installation position and the sensitivity of sensing units. By contrast, the frequency response only uses measurement units of voltage and current. However, due to the intrinsic relation to electrical variable, the effects of dynamic operating conditions are hardly avoided, as the critical bottleneck of online implementation. In recent years, online broadband frequency response has been developed at designated frequencies over 1 kHz. The designation refers to the known high-order components from external injection or inherent harmonics in power system. There are three major advantage. First, the frequency band over 1 kHz is far away from the fundamental frequency ( f 0 ), minimizing the effects of system harmonics and simple data processing methods are sufficient. Second, the test duration is largely shortened, ruling out the dynamic effect of temperature derivation. Third, the transformer insulation system is capacitive and the equivalent impedance decreases at high-order frequencies. The sensitivity and SNR of leakage current measurement can be improved. Hence, the frequency response in high-order frequency band can provide a great potential with the robustness to dynamic system operation.

3 Prospect of Non-invasive Technique Based on Online Broadband Frequency Response A novel online insulation monitoring technology for converter transformers is investigated, based on inherent and characteristic harmonics in power electronic converter system, so as to achieve comprehensive diagnosis of multiple insulating components in quantitative and non-invasive manners.

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3.1 Monitoring Principle Converter Characteristic Harmonics. VSCs have several major topologies including two-level converter, three-level converter and modular multilevel converter (MMC). MMC is popularly applied in power electronic system [28]. As shown in Fig. 5 (a), several submodules in each bridge arm enables low frequency of switching devices and low harmonics of output voltage. In MATLAB/Simulink, the MMC system model is built and each bridge arm contains 20 submodules with the switching frequency ( f s ) of 800 Hz. The rated voltage on AC side is 10 kV. Characteristic harmonic frequencies ( f ch ) of the converter system can be expressed as fch = p · fm ± q · fs .

(6)

where two coefficients of p and q are related to converter topology and switching modulation strategy. f m represents the modulation frequency which is typically equal to f 0 . f s is 16 kHz in simulation. In Fig. 5 (b), the frequency spectrum (U Ag ) is shown in the range from 10 to 100 kHz. There are several characteristic harmonic bands at multiples of f s . These harmonics are mainly distributed in the middle-frequency range between several kilohertz to hundreds of kilohertz. Stray loss and electromagnetic interference can lead to high-frequency noises above megahertz coupling with the converter output voltage.

(a) diagram of MMC

(b) output voltage

Fig. 5. Illustration of the MMC system simulation.

Characteristic harmonic voltage components in VSC system can be divided into common mode (CM) and differential mode (DM). CM components are caused by specific switching states. Figure 6 (a) shows one of CM switching states. At this state, uAg (t) = uBg (t) = uCg (t) = Udc /2,

(7)

where t = t 1 . There is another switching state (t = t 2 ), the output voltage in each phase is equal to −U dc /2. In the frequency domain, the voltage phasor in each phase at each CM frequency ( f CM ) is equal to each other. CM CM CM = U˙ Bg = U˙ Cg . U˙ Ag

(8)

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As shown in Fig. 6 (b), the voltage component at f CM in each phase has the same amplitude and phase. DM components result from these switching states (t = t 1 and t = t 2 ). At the DM frequency ( f DM ), three-phase voltage phasors have the same amplitude and the phase difference of 120° in between, as shown in Fig. 6 (c).

(a) CM switching state

(b) CM components

(c) DM components

Fig. 6. Characteristic harmonics in converter output voltages.

There is a certain amount of DM harmonic currents in transformer windings, leading to harmonic pollution on AC grid side. By contrast, few CM harmonic currents can flow through transformer windings, with the same order of these in insulating components. CM voltage potential at the neutral point is nearly equal to CM component in uAg , so that few CM voltage drops on transformer windings. In other words, CM components contribute little to power transmission and are rarely affected by varying load conditions. Monitoring Frequency Selection. Figure 7 (a) shows the diagram of a three-phase transformer with the YN/yn winding connection. Converter output voltages contribute to the voltage distribution along transformer windings, driving leakage currents (ileak ) in various groundwall insulating components to the ground, as shown in Fig. 7 (b). In insulation ageing development, the voltage distribution is changed as well as the leakage current. On this basis, electrical variables of the test transformer are used to obtain the broadband frequency response.

(a) YN/yn transformer

(b) equivalent circuit of transformer system

Fig. 7. Schematics of the transformer system.

The monitoring performance lies in the effective selection of harmonic voltage components.

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It is less prone to use the fundamental frequency. The voltage components at f 0 change with system operating conditions, which makes the response vulnerable to the system operation. Moreover, the response at a single frequency provides limited information of complex transformer insulation system. Based on converter harmonic components, there are three major advantages. First, f ch can be accurately calculated out according to converter topology and switching modulation strategy [29]. f ch is typically far away from f 0 and these high-frequency noises, making the data processing easier in filtering and response calculation. Second, in the middle-frequency band, the permeability of transformer core is close to that of the air, leading to little inductive coupling among different coils in windings. The inductive effect is rather small in the equivalent circuit. The broadband frequency response can effectively characterize the changes of equivalent capacitances caused by insulation ageing. Third, these harmonic components of leakage current are increased at higher exciting frequency. The sensitivity and SNR of online measurement can be improved as a result. Hence, online insulation monitoring for converter transformers based on inherent characteristic harmonics in VSC system is promising. Two key difficulties are worthy of attention in practical applications. Effect of phase-to-phase insulation ageing. Due to the phase difference, there are DM voltage drops on phase-to-phase insulating components. By contrast, there are no CM voltage drops since voltage phasors in three phases are the same. Along the winding, DM leakage currents flow through interturn insulating components, the grounding insulating components and the phase-to-phase insulating components, as shown in Fig. 7 (b). Since CM components only flow through the former two types of insulating components, the ageing in phase-to-phase insulation can be reflected in the DM frequency response but against the CM frequency response. Effect of load fluctuation on AC grid side. DM currents in windings are subjected to the dynamically-varying load. For the transformer with delta or wye winding connection on the grid side, CM currents hardly flow into the grid, forming the path in transformer windings and insulating components. CM components are rarely affected by the load fluctuation. Hence, thought DM frequency response has the benefit in monitoring the phase-to-phase insulation ageing, ensuring the unvarying grid load condition is rigorous. By contrast, CM frequency response can be robust to load fluctuation on AC grid side. Developing CM broadband frequency response is more benefit to achieve insulation monitoring for the operating converter transformer in non-invasive and robust manners. For practical applications, conducting pre-analysis and selecting effective components are necessary to ensure high sensitivity and SNR of measurement and effective data processing. 3.2 Evaluation Model Two CM evaluation models are developed, so as to provide reference for related works. Due to CM characteristics, the equivalent circuit of three-phase converter transformer can be presented in the single-phase view, as shown in Fig. 8 (a). There are two assumptions of conventional N-ladder equivalent circuit. First, it covers three types of insulating

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components. Second, each type of insulating components is distributed uniformly along the winding. The same circuit parameters in different ladders are equal. Since the model serves for the monitoring based on CM broadband frequency response, circuit parameters should be refined in two aspects. One refers to the frequency-dependent feature in the wide frequency band. The other is the CM inductive coupling among different coils.

Fig. 8. Conventional N-ladder equivalent circuit [30].

The state equation in s-domain is expressed as   ˙ s2 C + sG + Γ Y(s) = 0.

(9)

where Y˙ is the column vector of CM node voltages in the size of 2(N + 1) based on Fig. 9 (a). C, G and Γ are the nodal capacitance matrix, the nodal conductance matrix and the inverse nodal inductance matrix, respectively. They are in the size of 2(N + 1) * 2(N + 1).

(a) node network

(b) CM voltage-ratio measurement

(c) CM impedance measurement

Fig. 9. Networks for transfer function measurement. CM = U ˙ , the rest of (2N Assuming that the converter output voltage is known as U˙ Ag 1 + 1) node voltages (Y˙  ) makes response to the excitation, which is equal to

˙ U˙ 1 (s) Y˙  (s) = W(s)

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−1 −1 −1 ˙ W(s)  −(s2 I + C  sG + C    )−1 C  (s2 C k + sGk + Γ k ),

(10)

˙ is the parameter matrix in the size of (2N + 1) * 1, only dependent on all where W circuit parameters and the exciting frequency. The derivation of W and the expressions of C, G, Γ , C k , Gk , and Γ k can refer to [31]. The amplitude-frequency performance of the (i + 1)-th node voltage can be calculated using the given excitation and the i-th element in W. Namely, ˙ i (s)U˙ 1 (s), U˙ i+1 (s) = W

(11)

where i = 1, 2, …, (2N + 1). Since the CM inductive coupling is minor and unchanged over kilohertzs, these matrices related to inductances can be considered as constants. Hence, these matrices related to capacitances and conductances determine the variations of W caused by insulation ageing. An increment of (G + s·C) raise when one insulating component is aged. The associated elements in C and G are changed, leading to the variation of the ˙ broadband voltage distribution along transformer windings. The parameter matrix (W) characterizing the ageing scenario can be formulated as −1 −1 −1 ˙ W(s) = −(s2 I + C  sG + C  Γ  )−1 C  (s2 C k + sGk + Γ k ).

(12)

Equation (10) describes the analytical model for CM broadband frequency response based on measured voltages. The differences of two parameter matrices in Eqs. (10) and (12) are determined by the ageing component and the ageing severity. Exploring the response performances under different ageing scenarios are enabled. In practice, it is difficult to obtain the voltage at each node of windings. The voltages at line leads and neutral ends of two-side windings are measured typically. The equivalent circuit can be further simplified to the four-node network, as shown in Fig. 9 (b). To monitor different types of transformer insulation, three transfer functions using different voltages are defined as Converter-side GW Insulation: TF1 = UN +1 /U1 = W2N +1 .

(13)

Grid-side GW Insulation: TF2 = U2(N +1) /UN +2 = W2N +1 /WN +1 .

(14)

Grid-side GW Insulation & HV-LV Insulation: TF3 = U2(N +1) /UN +1 = W2N +1 /WN .

(15)

To reduce harmonic currents into the grid, converter transformers are usually operated with the grounded neutral point on the grid side. In this case, the evaluation model based on Eq. (10) performs diversely. The node conductance matrix is modified by adding a circuit branch for the grounding resistance. According to Fig. 9 (c), the transfer function for CM impedance is defined as TF4 =

U1 U2(N +1) /R0

=

R0 † W2N +1

,

(16)

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† where R0 is the grounding resistance around several ohms. W2N +1 is the last element of the modified parameter matrix. TF 4 is namely the equivalent CM broadband impedance based on commercial broadband analyzer. From the perspective of online implementation, TF 4 is insensitive to the ageing in the grid-side GW insulation and mainly serves to monitor these components of HV-LV insulation. Equations (13)–(16) provides four transfer functions capable of monitoring different types of transformer insulation. With the ageing development of different insulating components, the shifts of resonance frequencies and the movement of measurement curves can be identified, as theoretical supporting to online monitoring.

3.3 Technical Difficulties and Possible Solutions Measurement and data processing. These components at f 0 occupy the majority in the converter output voltage. The amplitudes of harmonics at high frequencies are restrained due to power quality requirement. Equipped voltage transformers, which serve to measure the major fundamental-frequency component, hardly measure these high-order harmonic components with high sensitivity and high signal-to-noise ratio. This technical difficulty can be resolved in two ways. One possible solution relies on the analog filter circuit with considerations of monitoring frequency selection. Ineffective harmonics are filtered to achieve the measurement of specified harmonic components. It is suggested to parallel the analog filter circuit at the neutral point of transformer winding, considering the high-voltage electrical isolation. On the other hand, data processing based on artificial intelligence algorithms can facilitate noise reduction and feature extraction. Improved broadband circuit model. The conventional N-ladder model in Fig. 8 is applicable to the transformer winding with single-layer structure. However, in power electronic system, the transformer winding sometimes has multi-layer structure to increase power density. These insulating components between layer to layer can change the voltage distribution along the transformer winding and affect the broadband performance of transfer function measurement. Furthermore, circuit parameters should be featured in frequency dependency, especially for resistive parameters representing copper loss and core loss. In addition, inductive coupling among different coils should be carefully parameterized since resonant frequencies of transfer function measurement are dependent on these inductive parameters. Resistive parameters can be obtained via offline tests conducted on the winding and the core separately. However, the results hardly meet the online realities under VSC switching actions. Another approach relies on building the finite element simulation model, according to physical dimensions and material properties of the test transformer. Circuit parameters in different ladders can be calculated in the broadband frequency range. In the practical significance, it is not essential to develop the improved broadband circuit model for each test transformer. The improved model is benefit to explore the changing rules of transfer function measurement, caused by the effect of frequencydependent feature of each circuit parameter and the effect of ageing interlayer insulation. Low-frequency-response-based monitoring. According to the dielectric theory, the response at low frequencies smaller than 1 Hz is much more sensitive to insulation

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ageing compared with the response based on inherent characteristic harmonics. Based on active converter control, it is possible to obtain the low-frequency response and realize insulation monitoring in online and non-invasive manners. The low-frequency-response-based monitoring usually requires the test duration up to several seconds or even hundreds of seconds. To avoid the effects of system operation, the monitoring can be conducted before the converter transformer is normally put into operation, with the grid side unloaded and the converter side connected to the converter. The technical difficulty lies in identifying the low-frequency response representing insulating material properties. In existing researches, few have explored the response under the composite electrical field considering how the polarization effect caused by the low-frequency excitation interacts with that caused by converter harmonic voltages.

4 Conclusion New power system is developing with high proportion of power electronic converters. Converter transformers have a great risk in the operating safety and reliability. In this paper, several issues toward online insulation monitoring technique for converter transformers are discussed, including the specific ageing mechanism, the disadvantages of conventional monitoring methods, the technical difficulties in improving the online monitoring performance, and the prospect of advanced monitoring technique. (1) There are a mass of inherent harmonic voltages and currents in VSC system, resulting in severe electrical and thermal ageing of converter transformers. (2) A kind of methods based on broadband frequency response belong to offline implementation, which are difficult to apply online due to the complexity of testing device and the effects of system operation. Broadening the response frequency band from several to hundreds of kilohertz has a great potential in offline implementation. The test time can be greatly shorted and the effects of dynamic temperature change and varying load condition can be effectively minimized. (3) The prospect of online insulation monitoring technique lies in four aspects. First, the monitoring effectiveness and efficiency can be improved based on inherent characteristic harmonics. Second, measuring units can be installed non-invasively. DM and CM measurement of leakage current can promote the sensitivity of online insulation sensing. Third, the monitoring indicators can have intuitive physical meaning, avoiding complex signal processing and analysis. Fourth, the monitoring scope can cover multiple insulating types to localize the incipient defect and quantify the ageing degree. Acknowledgements. This work was supported in part by the National Natural Science Foundation of China under Grant 52207208, in part by the National Key R&D Program of China under Grant 2022YFE0102500, and in part by the National Natural Science Foundation of China under Grant 52225702.

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20. Wang, D.Y., Zhou, L.J., Wang, L.J., Zhu, S.B., Jiang, J.F.: Frequency domain dielectric response of oil gap in time-varying temperature conditions. IEEE Trans. Dielectr. Electr. Insul. 24(2), 964–973 (2017) 21. Oommen, T.V.: Moisture equilibrium charts for transformer insulation drying practice. IEEE Trans. Power Appar. Syst. 103(10), 3063–3067 (1984) 22. Zhou, L., Wang, D., Guo, L., Wang, L., Jiang, J., Liao, W.: FDS analysis for multilayer insulation paper with different aging status in traction transformer of high-speed railway. IEEE Trans. Dielectr. Electr. Insul. 24(5), 3236–3244 (2017) 23. Jaya, M., Geißler, D., Leibfried, T.: Accelerating dielectric response measurements on power transformers—Part I. IEEE Trans. Power Deliv. 28(3), 1469–1473 (2013) 24. Florkowski, M., Furgal, J., Pajak, P.: Analysis of fast transient voltage distributions in transformer windings under different insulation conditions. IEEE Trans. Dielectr. Electr. Insul. 19(6), 1991–1998 (2012) 25. Zhao, X., Yao, C., Zhao, Z., Abu-Siada, A.: Performance evaluation of online transformer internal fault detection based on transient overvoltage signals. IEEE Trans. Dielectr. Electr. Insul. 24(6), 3906–3915 (2017) 26. Coffeen, L., McBride, J., Cantrelle, D.: Initial development of EHV bus transient voltage measurement: an addition to on-line transformer FRA. In: Proceedings of EPRI Substation Equipment Diagnostics Conference, Mar 2008 27. Popov, M., van der Sluis, L., Paap, G.C., De Herdt, H.: Computation of very fast transient overvoltages in transformer windings. IEEE Trans. Power Deliv. 18(4), 1268–1274 (2003) 28. Kouro, S., et al.: Recent advances and industrial applications of multilevel converters. IEEE Trans. Industr. Electron. 57(8), 2553–2580 (2010) 29. Song, Q., Liu, W., Li, X., Rao, H., Xu, S., Li, L.: A steady-state analysis method for a modular multilevel converter. IEEE Trans. Power Electron. 28(8), 3702–3713 (2013) 30. Abu-Siada, A., Hashemnia, N., Islam, S., Masoum, M.A.S.: Understanding power transformer frequency response analysis signatures. IEEE Electr. Insul. Mag. 29(3), 48–56 (2013) 31. Kasturi, R., Murty, G.R.K.: Computation of impulse-voltage stresses in transformer windings. In: Proceedings of the Institution of Electrical Engineers, vol. 126, no. 5, pp. 397–400 (1979)

Path Planning for Electric Power Inspection Robot Based on the Fusion of Improved A* and DWA Algorithm WeiMing Huang(B) , Ping Chen, and JiaJun Xie School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, People’s Republic of China [email protected]

Abstract. Based on the real-time path planning needs of electric power inspection robot in substation environments, we propose a path planning algorithm using an improved A* and dynamic window approach (DWA). This addresses the issues of low search efficiency and numerous turning points associated with traditional A* algorithms. Firstly, we propose an adaptive dynamic weighting factor to enhance the evaluation function of the A* algorithm. Secondly, we integrate the dynamic window approach with the improved A* algorithm to achieve optimal path planning. The simulation results indicate that the fusion algorithm produces a smoother and more efficient path plan in comparison to the traditional A* algorithm. Moreover, field experiments demonstrate that the fusion algorithm is capable of generating smooth paths at corners while maintaining a safe distance from obstacles. The electric power inspection robot effectively navigates through obstacles during practical operations, thereby satisfying the imperative need for safe and efficient inspection practices in the electric power industry. Keywords: Electric power inspection robot · Path planning · Improved A* algorithm · Dynamic window approach · Algorithm fusion

1 Introduction Electric energy is an important energy to maintain the operation of modern society. With the growth of social electricity consumption, higher standards have been established for the quality of power inspection. At present, manual inspection is often used in substations in China. With the development of automation technology, some manual inspection work can be completed by electric power inspection robots [1]. Electric power inspection robot integrated many technologies, path planning is one of the most capital parts. Global Path planning algorithms including but not limited to Dijkstra algorithm, A* algorithm and intelligent bionic algorithm. There are many local path planning algorithms, the most representative of which include artificial potential field method [2], time elastic band method (TEB) [3], dynamic window approach (DWA) [4], etc. Among them, the A* algorithm can often effectively find the optimal path in static environments. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 748–755, 2023. https://doi.org/10.1007/978-981-99-4334-0_90

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However, if the scene is larger, the A* algorithm has problems such as long path distance, many inflection points, and low search efficiency and so on in practical applications. Therefore, many scholars have carried out research on algorithm improvement and fusion. A improved A* algorithm put forward by František D et al. has huge computational problems in the actual operation of complex real environment, so it cannot be used in a unknown regime environment [5]. Zhang H. M. et al. proposed to weight the evaluation function to ensure the security of the path generated by A* algorithm [6]. JI et al. added the road roughness information to the traditional A* algorithm, but the improved A* algorithm is deficient in search efficiency [7]. Aiming at the insufficient of A* algorithm, we put forward a fusion algorithm in this paper. Firstly, we propose some improvements to the traditional A* algorithm, and then apply the improved A* algorithm to the whole path planning of the power inspection robot, and then adopt the DWA method [8] is used to complete the local path planning in real time, which makes the path more reasonable and smooth. In view of the existing research, this paper has the following contributions: 1) The adaptive dynamic weighting factor is introduced to improve the A* algorithm, which improves the search yield of path planning and reduces the turning point; 2) The improved A* algorithm and the DWA algorithm are integrated, and the fusion algorithm is used to plan the path, making the path smoother. The rest part of this paper is organized as follows: Section 2 presents the A* algorithm improvement method based on adaptive dynamic weighting factors. Section 3 describes the DWA algorithm. Section 4 describes the algorithm fusion process. Section 5 discussion on the Application of Algorithm and verifies the credibility of the algorithm by experiments. Section 6 concludes the paper.

2 Path Planning Based on the Improved A* Algorithm 2.1 Traditional A* Algorithm As A typical heuristic search algorithm, A* algorithm is a potent search way for solving the shortest route [9]. The A* algorithm is start from the starting point to expand around, calculates the cost value of each surrounding node through the cost function, selects the minimum cost node as the next expansion node, and repeats this process until it can reaches the target point to generate the final path. The cost function f (n) of the A* algorithm is denoted by f (n) = h(n) + g(n)

(1)

In the above formula, f(n) indicates the all cost value of the present node n, h(n) symbolizes the approximated cost value from the target point to the current node n, and g(n) symbolizes the real cost value from the current node n to the starting node. For A* algorithm, the evaluation function h(n) determines its search efficiency. The effect of the algorithm under different weights (see Table 1), where h*(n) is the cost of the true path.

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Weight size

A* algorithm description

Effect

h(n) = 0

f(n) = g(n)

Short path, time consuming

h(n) = h*(n)

f(n) = g(n) + h(n)

Longer path, shorter time

h(n)  g(n)

f(n) = h(n)

Long path, short time

2.2 A* Algorithm Improvement Strategy Aiming at the problems of inefficiency and many kickpoints of traditional A* algorithm, an adaptive dynamic weight strategy is introduced. The basic idea is: introducing weights to provide algorithm search efficiency, and the weights can be adaptively adjusted according to different robot positions; through the attenuation of exponential function, the effect of balancing search efficiency and search path diversity is achieved. In the beginings of search, dynamic weight factor is used to speed up the search. When the search node gradually approached the target node, the weight factor gradually decreased. At this time, the algorithm expands more nodes and the diversity of path search increased. The improved evaluation function is denoted by:  (2) h(n) = eα (yn − yG )2 + (xn − xG )2 α=

|yn − yG | + |xn − xG | ∈ (0, 1) |yS − yG | + |xS − xG |

(3)

In the formula, eα is the introduced dynamic weight factor; xn is the current node’s abscissa; yn is the node’s current ordinate; xS is the initial node’s abscissa; yS is the ordinate of the starting node; xG is the abscissa of the target point; yG is the ordinate of the target point.

3 Animate Window Arithmetic 3.1 Robot Motion Model The Ackerman kinematics model used for the electric power inspection robot (see Fig. 1) [10]. Figure 1, XR OR YR represents the robot system of coordinate, and the coordinate origin coincides with the midpoint of the rear axle. Assuming that ωr (t) and vr (t) represent angular velocity the and linear speed of the back-shaft of the electric power inspection robot at time t, the kinematic state equation of this model robot is expressed as: ⎤ ⎤ ⎡ ⎡ ⎤ cos ϕ(t) 0 XR (t) ⎣ YR (t) ⎦ = ⎣ sin ϕ(t) ⎦ · vr (t) + ⎣ 0 ⎦ · ωr (t) 0 ϕ(t) 1 ⎡

(4)

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Fig. 1. Kinematics model of electric power inspection robot.

Among them, the relationship among angular velocity ωr (t) and yaw Angle ϕ satisfies: R = L/tan α(t)

(5)

ωr (t) = vr (t)/R

(6)

3.2 Sampling Speed There are infinitely many groups (vt , ωt ) in the velocity interspace, however, the sampling velocity span requires to be constrained as stated by the constraints of electric power inspection robot itself and the environment in the actual process. Vm = {(v, ω)|v ∈ [vmin , vmax ] , ω ∈ [ωmin , ωmax ]}

(7)

The velocity constraint brought by the addition and subtraction restraint existing in the motor drives during the dynamic window moving time interval is Vd = {(ω, v)|ω ∈ [ωc − ω˙ b t, ωc + ω˙ a t], v ∈ [vc − v˙ b t, vc + v˙ a t] }

(8)

In the equation, vc , ωc represents the current speed, v˙ a , ω˙ a represents the maximum accelerated speed of the electric power inspection robot, v˙ b , ω˙ b represents the maximum retardation of it. The braking distance constraint of the electric power inspection robot: When the electric power inspection robot avoiding obstacles in actual local environment, it is necessary to avouch the safety of the electric power inspection robot. Beneath the constraint of maximum retardation, the speed need to be able to reduced to 0 m/s before impact. Therefor, the robot’s braking restraint formula is formulation as follows:   (9) Vd = (v, ω)|(d (v, ω) ∗ v˙ b ∗ 2) 1/ 2 ≥ v, (2 ∗ d (v, ω) ∗ ω˙ b )1/ 2 ≥ ω In the formula, d (v, ω) behalf of the closest space between the trackway of (v, ω) robot and obstacles.

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3.3 Design of the Evaluation Function Under the premise of speed constraints, there are several practicable simulation trajectories in the sampled speed group. Therefore, the optimal trajectory is selected by lead-in an evaluation function to perfection local path planning. At the same time, the global of path planning informations are combined to ensure that the final dynamic planning path is the global of the best path. The designed formula of estimate function is given by G(v, ω) = σ (αh(v, ω) + βd (v, ω) + γ ve (v, ω))

(10)

In the formula, h(ω, v) represents the orientation angle assess sub-function of the electric power inspection robot—it represents the Angle departure between the terminal direction of the simulation track and the heading Angle of the global path; d (ω, v) behalf of the obstacle assess sub-function—the vertical dimension between the imitative track and the obstacle; ve (ω, v) behalf of the velocity evaluation sub-function—represents the velocity of simulation trajectory; σ is the smoothing parameter. α, β, γ are the coefficient of weight of each term.

4 Fusion Algorithm The improved A* algorithm can quickly plan a global path with short path and few turning points, but it has some shortcomings such as large turning Angle and too close distance with obstacles. Dynamic window approach can not achieve the global optimal path, likely fall into the local optimal trap, path finding success rate is low. In view of the above shortcomings, in the paper will improve the A* algorithm and DWA fusion. First, we use the improved A* algorithm above to plan whole path. Second, extracts the important points on the path as the temporary target points of the DWA algorithm to calculate the optimal trajectory. Finally, the fusion of the improved A* algorithm and DWA algorithm ensures the global path optimization while ensuring good obstacle keep away and moving effect in the local planning.

5 Experiment and Analysis 5.1 Environment Model Description The working environment of electric power inspection robot is viewed as a twodimensional plane, and use the grid method to construct its map (see Fig. 2). The area of obstacles in the actual environment is replaced by black, areas available for robot are replaced with white, than the electric power inspection robot is considered as a freely moving point on a plane. 5.2 Improved A* Algorithm Simulation Experiment Figure 3 shows optimized results for our method on the task, the track generated by our improved traditional of A* algorithm is shorter, than the track generated by the traditional of A* algorithm, the inflection points are fewer, and the smoothness is better, which is conductive to the robot smoothly executing the path trajectory to the target point.

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5.3 Fusion Algorithm Simulation Experiment The simulation experiment result of the fusion algorithm is shown in Fig. 4. The fusion algorithm combined with the global optimal path to extract the key point sequence, when close to the obstacle when local planning, so that the path is able to effectively achieve obstacles avoidance, and ultimately successfully reach the target point.

Fig. 4. Fusion algorithm simulation experimental result.

5.4 Experiment To validate the path programming ability of the fusion algorithm in reality environment, the Ubuntu 18.04 development host is built in the VMware Workstation virtual machine

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environment, and the electric power inspection robot is used for experiment. The electric power inspection robot is furnished with the Melodic Morenia version of the ROS robot operating system. The robot-side ROS node controller uses the Jetson Nano and STM32F103 open source controller, and is equipped with a lidar that enables SLAM map modeling and navigation to meet the requirements of this experiment. The experiment is carried out in a specific environment, using the fusion algorithm to plan the path. Figure 5 shows the trajectory chart of the electric power inspection robot after running on the path is created by the fusion algorithm. The picture can be seen that the track planned by the fusion algorithm is smooth at corner and has a certain safety distance from the obstacles. From the actual running trajectory, the motion path of the electric power inspection robot is smooth, and it always keep enough safety distance from the obstacle at the corner (see Fig. 6). Therefore, The path is safe and effective, and the algorithm can be used in practical applications.

Fig. 5. Fusion algorithm experimental result.

Fig. 6. Robot running diagram.

6 Conclusion Path planning problem of electric power inspection robot, we propose the fusion algorithm of improved traditional of the A* algorithm and the dynamic window approach of DWA algorithm to a new algorithm. This algorithm possesses the advantage of the traditional A* algorithm guarantee the global optimal path, avoid the planning path DWA algorithm may be trapped in local optimum. The experiments prove the fusion algorithm

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can juggle path length and smoothness, improve the operating efficiency of the electric power inspection robot. It is important for the development of electric power inspection robot. Acknowledgments. This work is supported by the Key Research and Development Plan of Jiangxi province (20212BBE51010, 20202BBE20005), in part by the Jiangxi Provincial Natural Science Foundation (20202BABL214027, 20202BABL214035, 20202BAB212007), and in part by the National Natural Science Foundation of China (52005182).

References 1. Wang, K.: Research and Implementation on the Key Technologies and System of Substation Inspection Robot. University of Electronic Science and Technology of China, Chengdu (2015) 2. Rasekhipour, Y., Khajepour, A., Chen, S.K., et al.: A potential field-based model predictive path-planning controller for autonomous road vehicles. IEEE Trans. Intell. Transp. Syst. 18(05), 1255–1267 (2017) 3. Rösmann, C., Hoffmann, F., Bertram, T.: Integrated online trajectory planning and optimization in distinctive topologies. Robot. Auton. Syst. 88, 142–153 (2017) 4. Fox, D., Burgard, W., Thrun, S.: The dynamic window approach to collision avoidance. IEEE Robot. Autom. Mag. 4(01), 23–33 (1997) 5. František, D., Andrej, B., Martin, K., et al.: Path planning with modified A star algorithm for a mobile robot. Procedia Eng. 96(96), 59–69 (2014) 6. Zhang, H.M., Li, M.L., Yang, L.: Safe path planning of mobile robot based on improved A* algorithm in complex terrains. J. Algorithms 11(4), 44–63 (2018) 7. Ji, X., Feng, S., Han, Q., et al.: Improvement and fusion of A* algorithm and dynamic window approach considering complex environmental information. Arab. J. Sci. Eng. 46, 7445–7459 (2021) 8. Seder, M., Petrovic, I.: Dynamic window based approach to mobile robot motion control in the presence of moving obstacles. In: IEEE International Conference on Robotics and Automation. IEEE, Piscataway, USA (2007). http://doi.org/10.1109/ROBOT.2007.363613 9. Korf, R.E.: Real-time heuristic search. Artif. Intell. 42(2/3), 189–211 (1990) 10. Ping, W., Lan, T., Kun, Y.: Ideal Ackerman steering angle research based on brush type model. In: Proceedings of 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SMTA2015), pp. 665–667. DEStech Publications, Paris, France (2015)

Tunneling Operational Data Imputation with Radial Basis Function Neural Network Yitang Wang, Yong Pang, Xueguan Song(B) , and Wei Sun Dalian University of Technology, Dalian, China [email protected]

Abstract. Missing data is an inevitable problem in operational data collecting of tunnel boring machine (TBM). Generally, incomplete data will reduce the quality and reliability of dataset and affect the progress of the project. The effective data processing method should be selected according to the data characteristics of TBM. In order to address this issue, we utilize the radial basis function neural network (RBFNN) to model and impute real-world tunneling data in this paper. In this study, the model parameters are solved firstly using the complete samples, followed by pre-imputing the incomplete samples, then the imputed samples are fed into the model, and finally the output values are used as the imputed values. To demonstrate the performance of the proposed method, incomplete datasets with different missing ratios from TBM operating dataset are used for experiments. Experimental results validate the effectiveness of the proposed method. Keywords: Tunnel boring machine · Data imputation · Data modeling · Missing value

1 Introduction Owing to the increasing demand for underground space development, tunnel boring machine (TBM) is gradually becoming the tool of choice for tunnel construction projects [1]. In recent years, with the rapid development of sensor measurement technology, TBM operation data can be collected in real time. Analyzing the mechanistic information contained in such data provides numerous opportunities for TBM optimization, control, and maintenance [2, 3]. However, missing values are inevitable in real-world datasets due to the equipment failure, limitation of data collection and errors in data storage, etc. These missing values undermine the integrity of the data and make data analysis more difficult. Therefore, it is a matter of concern how to deal with missing values in TBM data analysis. The treatment of missing data should be carefully considered, otherwise it may lead to erroneous analysis results. Nowadays, many imputation methods have been proposed and mainly include statistical based method [4, 5] and machine learning based methods [6, 7]. With the advancement of artificial intelligence technology, machine learning based methods have received wider attention from researchers. Neural network based method is one of the competitive methods and has been widely used in data imputations [8, 9]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 756–760, 2023. https://doi.org/10.1007/978-981-99-4334-0_91

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This type of method usually uses the existing attributes in the incomplete dataset to train the network parameters and imputes in the missing values of the incomplete samples with the constructed network models. Radial basis function neural network (RBFNN) is a feed-forward neural networks and has many advantages, such as faster convergence, higher reliability and so on [10]. Although RBFNN has been widely used in a variety of problems, its availability in TBM is a question to be proven. The correlation between TBM operating parameters and equipment performance is complex and variable, and there may be complex non-linear relationships. RBFNN can identify complex nonlinear relationships between inputs and outputs. So, we design a training scheme for RBFNN which can impute incomplete TBM dataset in this work. The rest of this paper is organized as follows. Section 2 introduces the methodology. Section 3 discusses the imputation performance through experiments. Section 4 presents the conclusions.

2 Methodology RBFNN consists of three layers, i.e. input layer, single hidden layer and output layer [11]. RBF is a function that is built into a distance criterion about the center for the hidden layer neurons. Given a dataset xi = [xi1 , xi2 , · · · , xis ]T , the neuron k computes the following function   xi − μk 2 (1) nik = exp − (1) , k = 1, 2, . . . , n(1) 2σk2 (1)

where nik is the kth output of xi , n(1) is the number of neurons in the hidden layer, µk is the center of such neuron and is the width of neuron. The only output of RBFNN is calculated by (1)

yij =

n 

(2) (1)

wkj nik , j = 1, 2, . . . , m

(2)

k=1 (2)

where wkj is the neuron weight. K-means clustering algorithm is employed at first to initialize the neurons in the network. Then, the centroid of the cluster is set equal to the center of the neuron. To prevent the radial basis function from being too sharp or flat, the width equal to the mean of N = 2 nearest neurons, as in σk =

dmax , k = 1, 2, . . . , n(1) N

(3)

where dmax is the maximum distance between center points. The number of K-means cluster is equal to n(1) and the initial centroids of cluster are random and different. The neurons are adjusted by successive iterations using the Euclidean distance until the neurons are unchanged.

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In the second stage,   the sample expectation output is used to calculate the neuron weight. Let D = dij n×m denotes the two-dimensional matrix composed of n input       (1) (2) samples and m desired outputs, G = nik , W = wkj (1) , Y = yij n×m , let (1) n×n

n

×m

the network output equal to the desired output. It can be formulated as Y = GW = D

(4)

The neuron weight can be calculated by GT GW = D

(5)



−1 W = GT G GT

(6)

After calculating the parameters by above steps, pre-impute the missing values with the mean values of corresponding variable in missing samples. Then, input the preimputed data to the trained RBFNN. After the samples are input to the hidden layer neurons, the distance between the samples and the centroids is measured to calculate the activation degree, which determines the contribution of each weight vector to the model output. The further the distance from the centroid, the lower the activation of the neuron, and conversely, the higher the activation. The final output impute value is a weighted sum of the weight values of the different hidden layer neuron weights.

3 Experiments 3.1 Experimental Setup The effectiveness of the proposed method is test on real complete TBM operational dataset. The construction diagram of TBM is shown in Fig. 1. The dataset contains 15 attributes and 869 records, which is from a metro construction project in China. We generate four incomplete datasets randomly at different missing ratios, and the missing ratios are set as 4, 8, 12 and 16%. And we use 70% of the complete samples for training and the rest for validation. In order to validate the imputation performance of the developed method, the root mean square error (RMSE) is used, and can be calculated by  2 1 num yt − yt (7) RMSE = t=1 num



where num is the total number of missing values, yt denotes the real value, and yt denotes the imputation value. The smaller the RMSE value, the better the imputation performance. The experiments were conducted on a PC with an Intel Core i7-10700 CPU at 3.8 GHz, 32G RAM.

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Fig. 1. TBM construction schematic

3.2 Results and Analysis In this section, experiments are conducted by imputing incomplete datasets composed of datasets at different missing rates, and five incomplete datasets are randomly generated at each missing rate, and the average value of RMSE is taken as the result. The number of clusters initialized by K-means clustering algorithm is set to 2, 3, 4 respectively. The results of imputation are shown in Table 1. It can be observed from the table, as the missing rate increases, the imputation performance decreases. But the results do not change much, indicating that the performance of the method is still relatively stable. It can also be seen that the imputation results are different under different number of clusters, indicating that the number of clusters has some influence on the filling performance. The reason for this phenomenon is that the working state of the TBM is variable, but the result of its clear division is unknown. This also shows that the proposed method has the ability of cluster analysis. In conclusion, the neural network is simple in structure and flexible in design, and can tap the potential information contained in the TBM data. It has application potential for TBM systems with complex structures. Table 1. The imputation results Missing ratio (%)

Clusters 2

4

8.325

3 7.996

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10.618

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10.225

12

12.243

11.928

12.077

16

13.907

13.345

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4 Conclusion In this paper, a RBFNN based method of data modeling and imputing is presented for TBM data. This method first solves the model parameters by modeling with the complete samples from the incomplete dataset, then pre-imputes the incomplete samples and brings the resulting complete samples to the model for training. Finally, the model output values are considered as the final imputed values. The proposed solution strategy can avoid the direct duplication of output to input and improve the imputing accuracy. The performance of the proposed method is verified by experiments on datasets with different miss ratios. Acknowledgement. This research is supported by the National Key Research and Development Program of China (No. 2018YFB1702502) and Dalian Science and Technology Innovation Fund Project (2020JJ25CY009).

References 1. Sun, W., Shi, M., Zhang, C., Zhao, J., Song, X.: Dynamic load prediction of tunnel boring machine (TBM) based on heterogeneous in-situ data. Autom. Constr. 92, 23–34 (2018) 2. Wang, Y., Pang, Y., Sun, W., Song, X.: Industrial data denoising via low-rank and sparse representations and its application in tunnel boring machine. Energies 15(10), 3525 (2022) 3. Pang, Y., Shi, M., Zhang, L., Song, X., Sun, W.: PR-FCM: a polynomial regression-based fuzzy C-means algorithm for attribute-associated data. Inf. Sci. 585, 209–231 (2022) 4. Andridge, R.R., Little, R.J.: A review of hot deck imputation for survey non-response. Int. Stat. Rev. 78(1), 40–64 (2010) 5. Hughes, R.A., Heron, J., Sterne, J.A., Tilling, K.: Accounting for missing data in statistical analyses: multiple imputation is not always the answer. Int. J. Epidemiol. 48(4), 1294–1304 (2019) 6. Raja, P.S., Thangavel, K.: Missing value imputation using unsupervised machine learning techniques. Soft. Comput. 24(6), 4361–4392 (2019). https://doi.org/10.1007/s00500-019-041 99-6 7. Razavi-Far, R., Farajzadeh-Zanjani, M., Saif, M., Chakrabarti, S.: Correlation clustering imputation for diagnosing attacks and faults with missing power grid data. IEEE Trans. Smart Grid 11(2), 1453–1464 (2019) 8. Choudhury, S.J., Pal, N.R.: Imputation of missing data with neural networks for classification. Knowl.-Based Syst. 182, 104838 (2019) 9. Lin, J., Li, N., Alam, M.A., Ma, Y.: Data-driven missing data imputation in cluster monitoring system based on deep neural network. Appl. Intell. 50(3), 860–877 (2019). https://doi.org/ 10.1007/s10489-019-01560-y 10. Girosi, F., Poggio, T.: Networks and the best approximation property. Biol. Cybern. 63(3), 169–176 (1990) 11. Buhmann, M.D., Levesley, J.: Cambridge monographs on applied and computational mathematics. Radial Basis Func.: Theory Implemen. 12, x–259 (2003)

A Novel IoT Based Multi-modal Edge Computing Optimization Method Jiajun Song, Jiayan Wang, Hui Lu, Zhixin Suo(B) , Huijun Hong, Youfei Lu, Shirong Zou, and Xueqing Liang Guangzhou Power Supply Bureau, China Southern Power Grid, Guangdong, China [email protected]

Abstract. Extracting information from the rich multi-source data of the power system is one of the keys to playing the role of the core production factors of the power grid. On the one hand, multi-source data fusion will facilitate an accurate and comprehensive analysis of various scenarios in all source, network, and load storage aspects. The fusion of multi-source information can complement and enhance each other, thereby effectively improving the accuracy of target perception. To this end, we propose a method based on the power Internet of Things and deep learning for feature extraction of multi-source information. Since traditional methods reveal hidden correlations between different morphologies of learned features through linear connections, it is difficult to obtain desirable results. Therefore, this paper proposes a deep learning computing model of DCCM, which further improves the feature extraction and fusion capabilities of rich multi-source data. Keywords: Multi-source data · Deep learning · IoT · Feature extraction · Power grid

1 Introduction With the rapid development of China’s socio-economic development, social production and life have higher requirements for the stability and efficiency of the power supply system [1]. In this context, the power network management and control system began to change gradually to intelligence and informatization. The rapid progress of computer science and the network undoubtedly brings the possibility of realizing this goal. The convergence of IoT technology and smart grids has emerged as a crucial trend in managing the entire power distribution system [2]. By leveraging information sensing equipment and distributed readout devices, power IoT can establish a network architecture that enables seamless communication and coordination among human operators and electromechanical devices, paving the way for more efficient, reliable, and sustainable power supply. The function of the power IoT is mainly reflected in the three levels, which are the perception layer, network layer, and application layer. It should be pointed out that IoT is an extension of the current Internet and will become an essential part of the Internet in the next generation of the Internet. The three-layer structure of IoT is shown in Fig. 1. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 761–767, 2023. https://doi.org/10.1007/978-981-99-4334-0_92

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The perception layer is responsible for perception control and communication extension, and gathers information from various sources. The network layer is in charge of transmitting data securely. The application layer encompasses infrastructure, middleware, and various application services, and enables analysis and processing of the data collected during the sensing process to meet visualization requirements and leverage the benefits of IoT technology in smart grids. However, with the continuous development of the power IoT, it faces hundreds of millions of massive terminal device access and data transmission [4, 5], and the representations of these information are various, such as images [6], texts [7], numbers [8], audio [9] and video [10]. Most of them are presented in heterogeneous data, with high dimension, different expression forms, and more redundant information, which brings severe challenges to the current various information processing systems. Utilizing information efficiently, uncovering latent patterns within data, unearthing potential worth, forecasting the progression of events, and allocating resources more reasonably will enhance the intellectual advancement of the power grid. As such, exploring the simultaneous use of diverse data sources and extracting impactful fusion characteristics from this multi-source information is an area that requires further research.

Fig. 1. The three layer architecture of power IoT.

Conventional techniques for reducing data dimensionality, such as Principal Component Analysis (PCA) [11] and Linear Discriminant Analysis (LDA) [12], alter the spatial structure of the original data and extract low-dimensional features from highdimensional data in order to achieve dimensionality reduction. However, this method will break the hidden internal links between the original information, the classification or regression tasks after extracting information features. I, deep learning (DL) methods have been widely used in industry and have effectiveness in various applications. Therefore, introducing the deep learning method into the power grid IoT is an effective way to improve the efficiency, reliability and safety of power grid operation and maintenance by extracting key information features for multi-modal data fusion and improving the manageability and controllability of each work link of the power grid.

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2 Analysis of Key Technical Points for Multi-source Information Feature Extraction A. Based on Traditional Machine Learning Method Convolutional Neural Network (CNN) is the most famous deep learning model, which is a hierarchical network composed of convolutional layers, pooling layers, and full connections. CNNs have attained the most advanced level of performance in tasks such as image classification and speech recognition. However, due to the complex multimodality and high heterogeneity of information in IoT, it is difficult for CNN to learn its highdimensional features. Specifically, CNN operates in a vector space and cannot represent the high-dimensional features inherent in multi-source information. B. Multi-modal Deep Learning Models With the ongoing advancements in deep learning, a multitude of models, including stacked autoencoders, deep convolutional neural networks, and their variations, have been introduced. These models have made significant strides in various domains, such as facial recognition, real-time retrieval, and speech recognition, in industrial applications. However, these methods are all based on a single data source or data with a single structure, which severely limits the feature of discovering and multi-source information in the industrial IoT. In order to solve these problems, a large number of scholars have begun to explore multimodal deep learning (MDL) models in recent years. The most popular graphical model-based representation method is the Deep Boltzmann machine (DBM), which is stacked from the restricted Boltzmann machine (RBM). However, the most significant defect of DBM is that it is challenging to train DBM, which not only consumes a lot of computation but also requires the use of nearly variational training methods. Generative adversarial networks (GAN) is an unsupervised method for learning data representations without labels, which greatly reduces the dependence on manual annotation. However, GAN is unsuitable for processing discrete-form data similar to text and is prone to instability and gradient disappearance during training. To summarize, these models fall short of achieving their anticipated performance as the connection characteristics of the shared space are insufficient in revealing the intrinsic nonlinear representation of the high-dimensional space. To this end, the article proposes a deep convolution computing model to solve these problems to describe the nonlinear correlation in multi-source heterogeneous space. This is a deep computational model for feature learning and profound representation of tensor space, which takes tensor autoencoder as the basic module of DCCM, which is one of DCM. At the same time, the error function is reconstructed by tensor distance better to describe the hierarchical nonlinear relationship in heterogeneous space.

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3 Multi-source Data Feature Extraction Based on Power Grid IoT and Deep Learning See Fig. 2.

Fig. 2. Multi-source information on the power grid.

3.1 Multi-source Information of Power Grid Under the construction of the power Internet of Things and digital grid, the power system data are multi-modal. Ulti-modal power system data are related to power business, coming from different domains, different loop segments, and different forms and configurations. Power system multi-modal data are available from a wide range of sources such as shown in Fig. 2, in terms of data types, multi-modal data of power systems has many data types. From the business domain perspective, the multi-modal data is divided into planning operation data, operation data, management data, non-electricity energy data and non-energy data, etc. In general, the power system more modal data in the data source, data types, and data structure has the characteristics of broad and diverse, abundant knowledge. It is necessary to give play to the role of the core factors of production by effective analysis and utilization. 3.2 Multi-source Information Extraction Method Aiming at the problem of multi-source unstructured data in the power grid, the DCCM framework proposed in this paper mainly includes multi-source data input, data preprocessing, feature extraction, feature assimilation, feature fusion and analysis. Multiple source data input: The in-network fusion input of the power system is multi-source input, which has various forms in data structure and time scale.

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When aligning structured data, high-sampling rate data is employed as the foundation for high-frequency reconstruction using point estimation or interpolation. Meanwhile, for unstructured or heterogeneous multi-modal data, time alignment methods can be utilized by selecting high-sampling data at the same or similar sampling time as the basis for effective fusion, based on the low-sampling frequency. Feature extraction: Feature extraction is the process of analyzing analyses data according to its format, physical meaning, and fusion purpose. DCCM which is an extension of the traditional CNN that can be used to complete this process. Feature assimilation: The multi-modal feature information obtained after different feature extraction has different other feature description spaces, so feature fusion cannot be performed directly. Hence, it is necessary to map each feature onto a shared space or coordinate system. This entails assimilating the multi-source feature vectors and subsequently conducting feature fusion in a mutual subspace or sub-coordinate system, which streamlines the classification of the extracted features. 3.3 Deep Convolutional Computation Model In this section, we will describe how DCCM completes feature extraction, as shown in Fig. 3, for the operation process of DCCM. Tensors, being high-dimensional arrays, find extensive applications in domains such as data mining, machine learning, and facial recognition, among others.

Fig. 3. The pipeline of DCCM

Tensors, being high-dimensional arrays, find extensive applications in domains such as data mining, machine learning, and facial recognition, among others. In mathematics, tensors are represented as higher-order expansions of vectors in the dimensions of space. For example, in the isomorphic sense, zero-order tensors are called scalars, vectors are called first-order tensors, and matrics are called second-order tensors. In Fig. 3(a), the convolutional layer of the model employs weight-sharing mechanism and local connectivity to effectively diminish the number of inter-layer connections and achieve position invariance for the representation of multi-source information. Figure 3(b) illustrates the tensor pooling layer, which further reduces the number of weights and links while ensuring translation invariance in high-dimensional space. Figure 3(c) demonstrates how the tensor fully connected layer maps multiple feature maps of the constrained network onto a total tensor for input classification, thereby uncovering hidden distributions between

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heterogeneous objects. And We use the HBP algorithm to train the DCCM, and the specific loss function is defined as follows:  1    n hθ x − yn 2 M

JDCCM =

(1)

n=1

Then perform forward propagation until the training is complete. Table 1. Classification accuracy of deferent model Model

Best accuracy

Worst accuracy

Mean accuracy

MDL

0.858

0.781

0.814

DCM

0.878

0.821

0.851

DCCM

0.901

0.840

0.862

As depicted in Table 1, the mean classification accuracy of DCCM stands at 86.2%, surpassing that of alternative models. Even in the poorest scenario, the classification accuracy of DCCM is slightly greater than that of disparate models, underscoring its efficacy.

4 Conclusion In the energy transformation domain, diverse data types such as dispatch, electricity, and maintenance generate during power grid operation, and contain valuable information on the power grid’s operating status. The reasonable exploration of this information can enhance the intelligence of power grid operations. Owing to spatial constraints, this article only examines the multi-source data of the power Internet of Things and briefly outlines the extraction technique of DCCM for multi-source features. Moreover, the acquisition, communication, and storage of multi-source data are also critical aspects that necessitate attention while extracting features from multi-source data of power systems. By doing so, the full potential of extensive data in the power grid can be harnessed, amplifying the information service capabilities of power grid companies while guaranteeing the secure and steady operation of the power grid. Acknowledgment. This paper is supported by “Research and Application of Key Technologies for Interconnection of Multi-Type Power Terminals-Project 1: Research on Key Technologies for Pan-Access and Intelligent Management of Massive Multi-source and Multi-state Heterogeneous Terminals” (Project code 080010KK52200001; Technology project code GZHKJXM20200005).

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References 1. Wang, C., Li, X., Liu, Y., et al.: The research on development direction and points in IoT in China power grid. In: 2014 International Conference on Information Science, Electronics and Electrical Engineering. IEEE (2014) 2. Liu, J., Li, X., Chen, X., et al.: Applications of Internet of Things on smart grid in China. In: 13th International Conference on Advanced Communication Technology (ICACT2011), pp. 13–17. IEEE (2011) 3. Chen, X., Liu, J., Li, X., et al.: Integration of IoT with smart grid. In: IET International Conference on Communication Technology and Application (ICCTA 2011), IET, pp. 723–726 (2011) 4. AlZubi, A.A., Abugabah, A., Al-Maitah, M., AlZobi, F.I.: DL Multi-sensor information fusion service selective information scheme for improving the Internet of Things based user responses. Measurement 185, 110008 (2021) 5. Jacob, I.J., Darney, P.E.: Design of deep learning algorithm for IoT application by image based recognition. J. ISMAC 3(03), 276–290 (2021) 6. Chae, B.K.: The evolution of the Internet of Things (IoT): a computational text analysis. Telecommun. Policy 43(10), 101848 (2019) 7. Hsueh, J.C., Chen, V.H.C.: An ultra-low voltage chaos-based true random number generator for IoT applications. Microelectron. J. 87, 55–64 (2019) 8. Shah, S.K., Tariq, Z., Lee, Y.: Audio IoT analytics for home automation safety. In: 2018 IEEE International Conference on Big Data (Big Data), pp. 5181–5186. IEEE (2018) 9. Chen, C.W.: Internet of video things: next-generation IoT with visual sensors. IEEE Internet Things J. 7(8), 6676–6685 (2020) 10. Daffertshofer, A., Lamoth, C.J.C., Meijer, O.G., et al.: PCA in studying coordination and variability: a tutorial. Clin. Biomech. 19(4), 415–428 (2004) 11. Yu, H., Yang, J.: A direct LDA algorithm for high-dimensional data—with application to face recognition. Pattern Recogn. 34(10), 2067–2070 (2001) 12. Doersch, C.: Tutorial on variational autoencoders. arXiv preprint arXiv:1606.05908 (2016) 13. Cho, K.H., Raiko, T., Ilin, A.: Gaussian-Bernoulli deep Boltzmann machine. In: The 2013 International Joint Conference on Neural Networks (IJCNN), pp. 1–7. IEEE (2013) 14. Nair, V., Hinton, G.E.: Rectified linear units improve restricted Boltzmann machines. ICML (2010)

An Advanced IoT Based Edge Computing Forecasting Framework Zhixin Suo, Youfei Lu, Huijun Hong, Shirong Zou, Jiajun Song, Hui Lu, Jiayan Wang, and Yu Zhang(B) Guangzhou Power Supply Bureau, China Southern Power Grid, Guangdong, China {Zx.suo,Yf.lu,Hj.hong,Sr.zou,jj.song,h.lu,Jy.wang}@gzpsb.csp.cn, [email protected]

Abstract. There are a lot of spatiotemporal data in the power grid, such as planning operation and maintenance data, operation data, management data and power data, etc. These data are often massive in volume. They constitute the impression of the real world in the virtual digital world, which contains a lot of wealth. However, the emergence of massive data in the power grid brings both opportunities and many challenges to the industry, one of which is the problem of computing power in the data analysis of the power grid. Due to the large volume of data, multimodality and heterogeneity, etc., it causes a huge computational load. Therefore, using distributed computing, heterogeneous computing and other technologies to accelerate the high-performance deployment of power grid big data analysis and applications has excellent practical application value and theoretical research value. According to the industrialization and informatization needs of modern power IoT, synergize the advantages of the cyber physical system (CPS) and power IoT, and establish an analysis and calculation engine based on CPS. This paper revolves around the four processes of CPS, namely status perception, real-time analysis, scientific decision-making and accurate implementation. An analysis and calculation engine based on the CPS system is developed around the terminal, information system and service platform of the power IoT. Keywords: Power IoT · Calculation and analyze engine · Cyber-physical system

1 Introduction In recent years, the rapid development of communication and computer technology has profoundly impacted our country and society. With the growing number of personal smart devices and the development of social networks, various data sources with status and time tags have flourished. Data with two attributes of time and space are collectively referred to as spatiotemporal data, such as power grid environmental data [1], economic policy data [2], and energy planning data [3]. These data sources reflect all aspects of smart grid information (Fig. 1). The original data faced by power grid data analysis is multi-source data, a data type with a large volume and complex structure. Through in-depth research and mining © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 768–774, 2023. https://doi.org/10.1007/978-981-99-4334-0_93

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Fig. 1. The three-layer architecture of IoT applications.

of massive spatiotemporal data, user experience, management efficiency, and resource waste can be significantly improved, which is of great significance to the intellectual development of the power grid with infinite possibilities. Big data is creating significant value for human society. The traditional power grid physical architecture, without fully integrating the information system, has been unable to meet the development needs of diversified scenarios and services of the power Internet of Things, such as distribution automation, distributed power access control, orderly charging of electric vehicles, smart home, horticultural equipment, industrial equipment, etc. [4]. But simply adding an information system to the traditional physical grid can easily lead to a separation of operation, control, and analysis of the grid. It cannot meet the needs of the global optimal dispatch and user satisfaction of the power grid, nor can it make the operation of the power Internet of Things achieve the expected results [5]. In recent years, the network physical system (CPS) [6] that is deeply integrated with the information and physical system has provided a new way for the information system to integrate into the traditional power grid truly. CPS is a next-generation intelligent system that realizes the close integration and coordination of computing and physical resources through the organic and deep integration of computing, communication and control technologies. Each subsystem of CPS works in coordination through wired or wireless communication technology and relies on the network infrastructure to realize real-time perception, remote coordination, precise and dynamic control and information services of physical and engineering systems. The most basic function of CPS consists of three parts: sensor, control actuator and logic control unit. In addition, CPS pays more attention to the rational allocation of system resources and the efficient optimization of system performance to fully meet users’ needs.

2 Application of CPS in Power Internet of Things In the practical application process, CPS interacts with other similar systems. Still, there are observed differences between them [7]: The difference between CPS and software systems is that CPS focuses on real-time control of each physical process, feedback

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information when necessary, and has a dynamic response process in information processing and interaction [8]. The application of CPS to the actual power grid is shown in Fig. 2.

Fig. 2. The application of CPS in real power grid working scenarios.

The CPS system comprises three parts [9–11]: the power system layer, sensor and control system layer, communication layer and application layer. A Cyber-Power-System with four layers and different functions is shown in Fig. 3. In addition, the connection of these devices also requires two major networks, a communication network and a transmission network, various data information is transmitted in the communication network, and different physical devices are connected in the transmission network, of which the main functional units are as follows. 2.1 Power System Layer It mainly refers to power equipment in the active distribution network, such as energy storage devices, distributed power sources, flexible loads, and sensitive load vehicles. The power system layer obtains the environment, equipment, system, and process status through the IoT terminal. These data elements are used to provide the basis for decisionmaking support for the power Internet of Things. After processing, it is transmitted outward through the network layer. 2.2 Sensor and Control System Layer Mainly data acquisition devices, including embedded data collectors and various sensors (such as PMUs), are used to monitor the status of the grid, such as voltage, phase, frequency, transmission line temperature and even wind speed. By cooperating with the actuator, the sensing system can collect sensing information and send the control information issued by the control system downward. The sensor and control system are used to receive the status information and data transmitted by the physical system [12],

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issue instructions to the physical system, change the state of the physical system, transmit the collection information and data of the terminal layer to the CPS intelligent service platform, and receive the instructions issued by the CPS intelligent service platform. 2.3 Communication Network It is composed of CPSNet and CPS local area network. CPSNet refers to the next generation communication network. Other components in the active distribution network are connected to CPSNet through communication lines, and CPSNet provides real-time services for the entire distribution network. The CPSNet local area network ensures the required low delay, is used for local information communication and real-time aggregation and can process the data uploaded by the collection node in real time to the local control centre for real-time processing. 2.4 Application Layer The application layer mainly monitors the status of terminal layer objects, centralized management, control and scheduling. The functions of the CPS intelligent service platform [13] also include collecting, parsing, and processing information and data and cleaning, integration and storage of information and data. In addition, it also provides business service configuration and service resource management, status monitoring of power Internet of Things systems, data analysis, auxiliary decision-making, control and dispatch and other enterprise applications.

Fig. 3. A cyber-power-system with four layers and different functions.

3 Implementation Technology 3.1 Communication Protocol In the smart grid environment, power operators and consumers monitor a large amount of high-precision power consumption data through smart meters, and confidential user data is continuously exposed to unauthorized access. In this traditional communication mode,

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intelligent meters’ fine-grained measurement of household users’ energy consumption poses severe privacy and security issues. At the same time, existing static access control methods do not satisfy the context-based dynamic access characteristics of smart grid environments. The access control scheme based on the Internet of Things communication protocol (MQTT protocol) [14] can be used to perform access control authorization, which is more suitable for the power Internet of Things network environment. The information system realizes the communication with the CPS intelligent service platform access layer through the acquisition and control interface based on MQTT communication. It is responsible for the data acquisition and decision instruction receiving tasks of the CPS information system. The CPS intelligent service platform access layer implements the data access and data transmission interface through MQTT communication. It is responsible for the access of terminal data and the issuance of decision-making instructions. The flexible communication method makes MQTT meet the closed-loop requirements of information and data and become the preferred communication method for power Internet of Things systems. 3.2 Data Management Data resources have become the fourth largest resource of power grid companies after human, financial and material resources. A deep understanding and study of the scientific connotation formed by data resources have become indispensable and essential work for developing and constructing power grid enterprises. The data management team of the CPS intelligent service platform is responsible for cleaning, integrating and storing IoT data. Mainstream database systems such as Mysql, MongoDB, Hbase, etc., are usually used. The process of data management design, one or more databases can be selected to establish a data management system according to the different characteristics and needs of the data. Through the whole process management of enterprise data and the continuous mining and application of the value of data resources, the transformation of data resources into useful information and business value can be realized, to improve the core business capabilities, expand the effective information resource chain, and optimize the enterprise data management system. 3.3 Service The service layer of the CPS intelligent service platform [15] includes power elements and business management services, platform resource management services, and also has service management and configuration functions. At present, the mainstream implementation technology of the service layer is microservices architecture, such as Docker-based microservices architecture. For the power Internet of Things, the CPS intelligent service platform contains the management, integration, coordination and dispatch of many elements and related business services required by the power Internet of Things, which can be regarded as an extensive system composed of many unit-level or system-level CPS information systems and can be decomposed into multiple subsystems that can operate independently through the microservice architecture design mode, and each subsystem can complete a task independently, or it can complete a task through coordination.

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3.4 Application The application layer of the CPS intelligent service platform provides monitoring, management, analysis, diagnosis, early warning, configuration, scheduling, and control interactive functions of power Internet of Things system. In application layer construction, you can choose a relatively suitable technical framework according to specific business characteristics. The power grid CPS has typical hybrid characteristics, integrating massive operation information, device information and external information. Relying on the information network and control terminals, the fusion model-based control method can cope with more complex and intelligent operating conditions.

4 Conclusion The power Internet of Things CPS has great economic potential and social influence and is of great significance to national competitiveness and social livelihood. Driven by the current trend of “Industry 4.0” and “Internet+”, the power grid CPS will not only achieve technological breakthroughs in its field but will also be the technical foundation for the formation of energy and industrial interconnection system centred on the power grid. The power grid CPS fusion modelling technology constitutes the research basis to reveal the fusion mechanism. Power grid cyber-physical system analysis provides methods and tools for exploring power grid operating characteristics under conditions of massive information and complex physical variables. Grid control based on the fusion model realizes the synchronous evolution of information control, the physical world, and intelligent network control. Formal verification based on the fusion model provides a method for verifying and evaluating the performance of static logic and dynamic systems. Breakthroughs in power grid CPS theory and practice will significantly promote the application and development of energy Internet and traditional power grid data analysis and calculation. Acknowledgment. This paper is supported by “Research and Application of Key Technologies for Interconnection of Multi-type Power Terminals-Project 1: Research on Key Technologies for Pan-Access and Intelligent Management of Massive Multi-source and Multi-state Heterogeneous Terminals” (Project code 080010KK52200001; Technology project code GZHKJXM20200005).

References 1. Eason, G., Noble, B., Sneddon, I.N.: On certain integrals of Lipschitz-Hankel type involving products of Bessel functions. Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955 (references) 2. Clerk Maxwell, J.: A Treatise on Electricity and Magnetism, 3rd ed., vol. 2, pp. 68–73. Clarendon, Oxford (1892) 3. Nicole, R.: Title of paper with only first word capitalized. J. Name Stand. Abbrev., in press 4. Yorozu, Y., Hirano, M., Oka, K., Tagawa, Y.: Electron spectroscopy studies on magnetooptical media and plastic substrate interface. IEEE Transl. J. Magn. Japan, 2, 740–741, August 1987 [Digests 9th Annual Conference Magnetics Japan, p. 301, 1982]

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5. Young, M.: The Technical Writer”s Handbook. University Science, Mill Valley, CA (1989) 6. Sridhar, S., Hahn, A., Govindarasu, M.: Cyber–physical system security for the electric power grid. Proc. IEEE 100(1), 210–224 (2011) 7. Khaitan, S.K., McCalley, J.D., Liu, C.C. (eds.): Cyber physical systems approach to smart electric power grid. Springer (2015) 8. Rajkumar, R., Lee, I., Sha, L., Stankovic, J.: Cyber-physical systems: the next computing revolution. In: Design Automation Conference, pp. 731–736. IEEE (2010) 9. Yu, X., Xue, Y.: Smart grids: a cyber–physical systems perspective. Proc. IEEE 104(5), 1058–1070 (2016) 10. Negri, E., Fumagalli, L., Macchi, M.: A review of the roles of digital twin in CPS-based production systems. Procedia Manuf. 11, 939–948 (2017) 11. Wang, F.Y.: The emergence of intelligent enterprises: from CPS to CPSS. IEEE Intell. Syst. 25(4), 85–88 (2010) 12. Amin, M., El-Sousy, F.F., Aziz, G.A.A., Gaber, K., Mohammed, O.A.: CPS attacks mitigation approaches on power electronic systems with security challenges for smart grid applications: a review. IEEE Access 9, 38571–38601 (2021) 13. Liang, X., Chen, H.: The application of CPS in library management: a survey. Library Hi Tech (2018) 14. Lee, J., Bagheri, B., Kao, H.A.: A cyber-physical systems architecture for industry 4.0-based manufacturing systems. Manuf. Lett. 3, 18–23 (2015) 15. Liu, X.Y.: Vehicular CPS: an application of IoT in vehicular networks. J. Comp. Appl. 32(04), 900 (2012)

A Novel Data Merging Intelligent Method for Whole System IoT Huijun Hong, Hui Lu, Jiayan Wang, Yu Zhang, Zhixin Suo, Shuaihui Ren, Jiajun Song, and Yixuan Wang(B) Guangzhou Power Supply Bureau, China Southern Power Grid, Guangdong, China {Hj.hong,h.lu,Jy.wang,y.zhang,Zx.suo,Sh.ren, jj.song}@gzpsb.csp.cn, [email protected]

Abstract. Big data technology based on Internet of Things technology has made a breakthrough in recent years. Still, with the widespread application of big data technology, the system generates massive, all-encompassing, multi-source, heterogeneous data resources. The ability to organise, query and analyse data effectively is key to achieving technological advances in IoT. The challenge of fusing heterogeneous data from multiple sources due to factors such as data privacy, data security and transmission restrictions cannot be ignored. This paper performs knowledge extraction and data fusion on numerous heterogeneous data sources generated by IoT systems. Firstly, for multi-source heterogeneous data, a knowledge extraction model combining lexical attention mechanism is proposed to extract and transform features from the data; secondly, a model-integrated multisource heterogeneous data fusion algorithm is proposed; finally, the algorithm is applied to multi-source heterogeneous data to achieve data fusion and deep mining of multi-source heterogeneous data. Keywords: Internet of Things · Data fusion · Knowledge extraction · Machine learning

1 Introduction In recent years, with the development of information technology and network technology, the era of big data has arrived. The rapid development of Internet of Things (IoT) technology, and urban sensing technology relying on this has also been a breakthrough. A large amount of data in various data types for the application and development of IoT technology has laid a solid foundation. In terms of data sensing, there has been an explosion of data with the emergence of various intelligent terminals and technologies, including smartphones, smart IoT [1], mobile social networks and cloud computing [2]. Regarding data collection, there are two main approaches: centralised and distributed. Centralised data collection is usually based on a cloud computing platform in a data centre, where the data is centralised in the cloud for fusion, and the data center’s powerful computing and storage capabilities are used to provide high quality data services to users. Centralised data collection requires all data to be transferred to the cloud, where the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 775–781, 2023. https://doi.org/10.1007/978-981-99-4334-0_94

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data is analysed and pushed, which consumes many transmission resources and causes delays. On the other hand, due to user privacy and physical transmission limitations, data silos can occur in reality and cannot support centralised data collection methods. With technological developments, distributed systems such as fog computing [3] also offer new opportunities to solve centralised data transmission challenges. With the rapid development of big data technology, data fusion [4, 5] based on machine learning theory and supported by perceptual data has become a popular research area. As an important part of knowledge management and knowledge engineering, knowledge fusion has received extensive attention from scholars in computer science, knowledge engineering and information science, and is gradually being applied and expanded in the fields of health care, finance and library intelligence. Knowledge fusion implementation paths usually include knowledge fusion algorithms, techniques, etc., which dominate the knowledge fusion research process. Most traditional knowledge fusion algorithms are derived from information fusion. They intersect with applied research to be implemented in domain-specific applications: Xu et al. [6] used a maximum entropy model to analyse the relationship between ontology-based knowledge elements and semantic relevance, applied the concept of fused knowledge degree and genetic annealing algorithms to the knowledge fusion process to improve population selection and genetic manipulation, and used information diffusion theory to evaluate the accuracy of knowledge fusion. Chen et al. [7] proposed a meta-model of structured knowledge representation based on the problems such as different descriptions of things caused by different knowledge backgrounds and individual perspectives in the Web 2.0 environment, and based on this, the cognitive views of group members on things were abstracted into different knowledge elements. Then, for attributes in all knowledge element versions where members disagree, the corresponding group argumentation task is designed to verify their consistency. Knowledge fusion is achieved in the Web 2.0 environment. In this paper, in order to solve the data fusion problem of multi-source heterogeneous data, a multi-source heterogeneous data fusion method based on multi-model deep learning is proposed to fuse and apply multi-source heterogeneous data from IoT systems. Experiments are conducted with fine-grained air quality index data in Beijing to verify the effectiveness of the method.

2 Knowledge Extraction from Multiple Sources of Heterogeneous Data In multi-source heterogeneous data, there is both structured data and unstructured data. This chapter will introduce a knowledge extraction model that combines lexical attention mechanisms to learn from three dimensions: lexical, morphological as well as semantic, using attention mechanisms to fuse lexical features with other features to help accurately understand the semantics of words in a sentence and improve the accuracy of entity information extraction tasks. The knowledge extraction model proposed in this chapter is an entity information extraction model combined with a linguistic attention mechanism. By introducing linguistic features, the model learns the components of words in terms of syntactic construction, which helps the model to obtain more accurate semantics, thus improving the

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accuracy of entity information extraction. The model consists of four main components a morphological feature extraction, a semantic feature extraction, a linguistic feature extraction, and a lexical feature fusion. The specific roles of each element are described below: (1) Morphological feature extraction section: The internal structure of the original words is studied, and the word prefixes and suffixes of the words are learned as characterlevel features of the model. (2) Semantic feature extraction section: The inter-word relationships of the original words are studied, and the meaning of the words in the sentence is learned so that the exact meaning of the words can be obtained. (3) Lexical feature extraction section: The linguistic properties of the original words are studied, and the patterns of linguistic transformations are learned as features of the original data in terms of syntactic construction. (4) Verbal feature fusion section: The relationship between linguistic features and other features is learned so that lexical features can help the model to obtain more accurate word meanings. Before the model is constructed, the raw unstructured data must first be pre-processed with data. The raw unstructured data is processed into sentences and words, and then the words, linguistic properties and their character composition in each sentence are further obtained. For the acquired words, the pre-training model is used to encode the acquired words and get the word vectors of the words. For the characters as well as the linguistic properties, random encoding is used to obtain the respective vector expressions. The model structure is shown in Fig. 1. After the model obtains the vector expressions of each part, the linguistic properties of the different words in the sentence are fed into a bidirectional RNN network to learn the properties and categories of the other words expressed in the particular context of the sentence, and the set of hidden layer vectors is used as the linguistic features of the sentence P, the set P consists of p1 , p2 , p3 , . . . , pn . Where pi denotes the lexical feature vector of the i th word in the sentence and n is the number of words in the sentence, also known as the sequence length. The comment characters are fed into a bidirectional LSTM network to learn the internal structure of each word in the sentence to obtain different morphological features, e.g. to learn the role of word prefixes in word interpretation. The encoded word vectors are concatenated with the morphological characteristics of the words to obtain a set S of initialised word vectors at different word character levels, which consists of s1 , s2 , s3 , . . . , sn . Where si denotes the initialised word vector for the i th word in the sentence. This vector contains the morphological features of the word and the encoded expressions of the different terms. The vectors in S are fed into the multi-layer bidirectional LSTM in order of position. When is fed into the multi-layer bidirectional LSTM network, its corresponding hidden layer vector is obtained as hi . The output of the LSTM is the hidden layer set H, which consists of h1 , h2 , h3 , . . . , hn . hi contains the morphological features of the word and the contextual semantic features of the word in the context of the sentence, and is fed together with the lexical set P is fed into the attention mechanism together with the lexical set P. The importance magnitude of different lexical pi on hi is learned, and the lexical P is weighted and spliced with si+1 to continue learning in the LSTM network. The hidden layer of the LSTM after splicing

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is defined as the set of output vectors O. The set of O consists of o1 , o2 , o3 , . . . , on . The output vectors are mapped to the label dimension by two fully connected layers, and finally, the distribution probabilities of the corresponding labels for each word in the sentence are obtained. The distribution probabilities are fed into the CRF layer, which constrains the label proximity transfer method to get the final label classification results.

Fig. 1. Data extraction model structure

3 Knowledge Multi-source Heterogeneous Data Fusion Based on Model Integration This chapter implements a higher accuracy urban air quality assessment system based on urban sensing data, using three knowledge extraction models to classify the different data, and then using an extreme learning machine to fuse the three sub-models. Urban sensing data is a collection of data consisting of multiple single-source sensing data. There are significant differences in sensing equipment, spatial and temporal distribution, cost and type of sensing data between different single-source sensing data. The overall framework of the data fusion model consists of three main parts: (1) homogeneous data aggregation, which mainly matches different source data through difference analysis, data analysis and relationship analysis to find a collection of homogeneous data with high similarity; (2) construction of sub-classifiers, in the homogeneous multi-source data, choose a suitable modelling method for the data type to reason about the task objective. In this chapter, three sub-classifiers are constructed: temporal classifier, spatial classifier and image classifier; (3) model integration, based on the inference results of multiple sub-classifiers, model integration is carried out, and the final inference model is obtained, and multi-layer neural network based on limit learning machine is used to aggregate multiple sub-classifiers in this chapter. The overall framework is shown in Fig. 2.

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Based on the feature analysis, the raw data used for fine-grained urban air quality assessment is divided into three sub-classifiers: temporal, spatial, and image. The temporal classifier is modelled using a linear regression algorithm, the spatial classifier is modelled using an optimised random forest algorithm (scalable boosted tree), and the image data is crowdsourced in this scenario and will have a cold start problem that cannot be ignored, so this section uses an incremental learning algorithm to model the image data.

Fig. 2. Multi-source heterogeneous data fusion framework

4 Experiment This experiment takes Beijing’s fine-grained PM2.5 real-time inference as an example, implements the method proposed in this chapter based on MATLAB and Weka, builds a simulation environment, implements feature value extraction using MATLAB, implements each sub-classifier and aggregator based on Weka, and evaluates the method proposed in this chapter using publicly available data. 4.1 Data Sets and Evaluation This experiment collected data from February 2016 to March 2017 in Beijing: meteorological data were collected hourly from 102 stations in Beijing published by the government; air quality records: air quality records were collected hourly from 38 air quality monitoring stations in Beijing. Each sample includes concentrations of six air pollutants and the AQI index; POI data: POI features are collected from Baidu Maps and updated at a frequency of 1 day; Traffic data: traffic data are collected from Baidu Maps15 which uses different colors (green, yellow and red) to mark traffic flow conditions. For each area, traffic flow features were calculated once per hour; Smartphone data: this experiment collected photos taken by smartphone users. Each photo was tagged with geographical location information and a time stamp. Details of the dataset are shown in Table 1. Evaluation indicators: Five evaluation indicators were chosen to compare the results of the models in this experiment: Precision, Recall, TP rate, FP rate and F-measure.

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H. Hong et al. Table 1. The final sentence of a caption must end with a period.

Data set

Number of sites

Time range

Sampling frequency

Number of instances

Meteorological data

18

2016.2–2017.3

1 hour

163664

AQI sites

38

2016.2–2017.3

1 hour

336520

POI data

Baidu map

2016.2–2017.3

1 hour

116890

Traffic data

Baidu map

2016.2–2017.3

1 hour

557637

Image data

6

2016.2–2017.3

Real time

2735

4.2 Experimental Results Based on the Beijing environmental data, was processed using a data fusion model, and the resulting data was assessed using the metrics mentioned in Section B. Two other algorithms were added for comparison: U-AIR, which assesses air quality based on a collaborative training algorithm using temporal and spatial classifiers, and MCSRF, which combines online random forest and offline forest to achieve a fine-grained assessment of air quality. The accuracy results for the environmental assessment are shown in Fig. 3 (a). Experiments demonstrate that the fusion of structured multi-source heterogeneous data can significantly improve the accuracy of the intermediate categories, with Good, Slight and Moderate in the green line showing a significant improvement in accuracy compared to the unstructured MCS-RF and U-AIR, which only considers temporal data. This conclusion is supported not only by the accuracy metric, but also by the classification results in terms of recall and false positive rate, as is shown in Fig. 3 (b) (c).

Fig. 3. (a) Accuracy (b) Recall rate (c) FP rate

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5 Conclusion To solve the problem of multi-source heterogeneous data fusion, this paper proposes a model integration-based multi-source heterogeneous data fusion method. Firstly, a knowledge extraction model combining lexical attention mechanism is proposed to classify and extract features from the data; three independent sub-classifiers are added, then the data is modelled, and finally, the final model integration is achieved by an extreme learning machine. This paper verifies that the method has a better performance by analysing and predicting data on Beijing’s air environment and by comparing it with two models, U-AIR and MCS-RF, in terms of several evaluation criteria such as accuracy, recall and false positive rate, and it can be seen that the use of knowledge extraction and sub-classifiers allows for more accurate data integration. Acknowledgment. This paper is supported by “Research and Application of Key Technologies for Multi-type Power Terminal Interconnection—Project 1: Research on Key technologies for Pan-access and intelligent Management of massive multi-source polymorphic heterogeneous terminals” (Project code 080010KK52200001; Technology project code GZHKJXM20200005).

References 1. Chiang, M., Zhang, T.: Fog and IoT: an overview of research opportunities. IEEE Internet Things J. 3(6), 854–864 (2016) 2. Yang, C., Huang, Q., Li, Z., et al.: Big Data and cloud computing: innovation opportunities and challenges. Int. J. Digital Earth 10(1), 13–53 (2017) 3. Varghese, B., Wang, N., Nikolopoulos, D.S., et al.: Feasibility of fog computing. In: Handbook of Integration of Cloud Computing, Cyber Physical Systems and Internet of Things, pp. 127– 146. Springer, Cham (2020) 4. Zheng, Y.: Methodologies for cross-domain data fusion: an overview. IEEE Trans. Big Data 1(1), 16–34 (2015) 5. Wang, P., Yang, L.T., Li, J., et al.: Data fusion in cyber-physical-social systems: state-of-the-art and perspectives. Inf. Fusion 51, 42–57 (2019) 6. Cijun, X., Aiping, L., Xuemei, L.: Knowledge fusion and evaluation system with fusionknowledge measure. In: 2009 Second International Symposium on Computational Intelligence and Design, vol. 1, pp. 127–131. IEEE (2009) 7. Chen, X., Ding, F., Wang, Y.: Knowledge fusion based on the group argumentation theory in Web 2.0 environment. Int. J. Commun. Syst. 31(16), e34 (2018)

Research on Model of Buck-Boost Converter Based on Digital Twin Yong Wan1 , Cungang Hu1(B) , Wenjie Zhu1 , Haitao Wang1 , Wenping Cao1 , Weixiang Shen2 , and Ke Zhang3 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected]

2 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, VIC 3122, Australia 3 Jiangsu Dongrun Zhilian Technology Co., Ltd., Jiangsu, China

Abstract. Digital twin could be regarded as a virtual model, presenting the features of physical entity. Through interacting with the data of the actual world, digital twin could timely adjust its parameters and accurately simulate the running characteristics of a physical entity. Mathematical model is an important part of digital twin model. Buck-Boost converter is an important converter circuit, which has been widely used in many fields due to its excellent characteristics. In this paper, Buck-Boost converter is taken as a research entity, analyzing and studying its digital twin model. Firstly, the mathematical model of Buck-boost converter is built based on its circuit topology. Secondly, a numerical solution of the mathematical model could be calculated through the fourth order Runge-Kutta algorithm. In the end, the digital twin model of Buck-Boost converter is built. Then its simulation model is built in MATLAB, which shows the model is accurate. Keywords: Buck-Boost converter · Digital twin · Runge-Kutta

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 782–790, 2023. https://doi.org/10.1007/978-981-99-4334-0_95

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1 Introduction As national economy develops, the electric power industry also makes great progress. The electronic circuit is widely applied in different fields of real life, and its importance is becoming increasingly prominent. In the power electronic circuit, the semiconductor device occupies an important position. It is one of the key devices, which plays the role of switch in the circuit. In the operation of power electronic circuit, the semiconductor device is easily damaged and is the most vulnerable component in the circuit. There are many reasons for the damage of semiconductor devices, such as high voltage, high current, and long working time [1]. In the operation fault of power electronic circuits, the most common faults are short circuit fault and leakage fault, and then open circuit fault. According to the investigation of power electronic circuit operation faults, it is indicated that many faults are attributed to the breakdown of semiconductor devices [2]. Thus, it is vital to monitor the performance degradation of the power converter. Maintain critical components before failures occur to prevent circuit failures and systemic damage [3]. Recently, digital twin technology has developed rapidly. The digital twin could be regarded as a virtual model, which presents the features of physical entity. Digital twin can adjust its own parameters in real time by interacting with the data from physical world, so as to accurately simulate the running state of the physical entity. In recent years, digital twin technology develops rapidly and is gradually applied in the field of power electronics. With the help of digital twin technology, the operation of converters can be simulated, monitored, predicted and optimized. Digital twin technology has been applied in parameter identification and health monitoring of power electronic systems due to its advantages of high cost performance, non-invasive, non-additional circuit and monitoring capacitors capabilities [4] and [5]. In recent work [1], DC converter with the simplest topology is used and the superiority in parameter identification and health monitoring is proved by experiments. Digital twin technology system from bottom to top as data protection layer, model layer, the function of digital twin layer and immersive experience, the implementation of each layer is a layer of the expansion of the model layer is the key link, it links at the bottom of the data and functional layers, the twin practical application in the middle of the data collection to digital hub [6]. In the essay, the research entity is a Buck-Boost converter, and its digital twin model is analyzed and studied. Buck-Boost converter is a common converter, which is widely used in various systems. Firstly, this paper takes the converter as the research object, briefly analyzes its operation principle, and establishes the mathematical model according to its topology. Then, to solve the mathematical model, this paper uses a common algorithm—Runge-Kutta algorithm. Finally, the Buck-Boost circuit digital twin model is built. Simulation results show the model’s accuracy.

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2 Mathematical Model of Buck-Boost Converter Figure 1 is a circuit topology, which shows the principle of Buck-Boost converter.

Vf

-

Mosfet

+

L

C R

uin

iL

iC RC

RL

io

Vo +

Fig. 1. Buck-Boost converter circuit topology.

The state of Buck-Boost converter is affected by its switching state of the Mosfet. Buck-Boost circuit works as follows: when the Mos tube is turned on, uin is supplied to the inductor L through the Mos tube to store energy. When the Mos tube is turned off, the energy is released to the load R, which is stored in the inductor L. It presents that the load voltage’s bottom is positive and its top is negative. The polarity is opposite to the supply voltage. 2.1 Mosfet On When Mosfet is on, Fig. 2 shows its circuit diagram. Rdson

C

L

R

uin

iL RL

Fig. 2. Mosfet on.

RC

io

uo +

Research on Model of Buck-Boost Converter Based on Digital Twin

According to KVL and KCL theorem, the equation is shown in Eq. (1).  uin = L didtL + (Rdson + RL )iL R uo = R+R uC C

785

(1)

uin represents the input voltage; Rdson represents the resistance when the Mosfet is on; RL represents the inductor resistance; iL represents the inductor current; Rc represents the capacitor resistance; uo represents the output voltage; uc represents the capacitor voltage. 2.2 Mosfet Off When Mosfet is on, the circuit diagram is shown in Fig. 3

-

Vf +

L

C R iL

iC RC

RL

io

Vo +

Fig. 3. Mosfet off

According to KVL and KCL theorem, the equation is shown in Eq. (2). ⎧ di RRC R L ⎪ ⎨ L dt + RL iL + R+RC iL + R+RC uC + vf = 0 uC R C dudtC = R+R iL − R+R ⎪ ⎩ u = RRC i C+ R u C o R+RC L R+RC C

(2)

vf represents the diode forward voltage. 2.3 Mathematical Model In summary, according to KVL and KCL theorem, the mathematical model is shown below.     ⎧ diL Rc R 1 1 R 1 1 ⎪ = − + R + (1 − D) − (1 − D) DR i L L dson ⎪ L Rc +R L Rc +R uc +D L uin − (1 − D) L vf ⎨ dt     duc 1 R 1 1 dt = C Rc +R iL − C Rc +R uc ⎪ ⎪ ⎩ R uo = (1 − D) RRcc+R iL + RcR+R uc

(3) When the MOSFET is on, D is 1. When the MOSFET is off, D is 0.

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3 Runge-Kutta Method to Solve the Model The differential equations, established in the previous section, could be solved in two methods. The first is the conventional method of solving differential equations. Firstly, the eigenvalues and eigenvectors of the differential equation are calculated to obtain the general solution of the differential equation. Then, according to the initial state of iL and uc , its particular solution of the differential equation is got. The calculation means is tedious and requires a lot of calculation. Another approach is to discretize the differential equation linearly. uo,n+1 =

Rc R R iL.n+1 + uc.n+1 Rc + R Rc + R

(4)

uo,n+1 represents uo at the (n + 1)th step; iL,n+1 and uc,n+1 respectively represent iL and uc at the (n + 1)th step. uo,n+1 after discretization is calculated by iL,n+1 and uc,n+1 . iL,n+1 and uc,n+1 could be derived from the values of iL and uc at the nth step. The fourth order Runge-Kutta algorithm can be used to solve differential equations. In this paper, the linear discretization of differential equations is solved by using this algorithm. To simplify the analysis process, iL equations and uc equations of the converter are shown in follows: f1 (iL , uc ) = didtL (5) c f2 (iL , uc ) = du dt With the Runge-Kutta algorithm applied, iL,n+1 and uc,n+1 could be expressed as follows: iL,n+1 = iL,n + h6 (kp1 + 2kp2 + 2kp3 + kp4 ) (6) uc,n+1 = uc,n + h6 (kq1 + 2kq2 + 2kq3 + kq4 ) h represents the step time between nth and (n + 1)th time step. kp1 − kp4 and kq1 − kq4 , as shown below: ⎧ ⎪ ⎪ kp1 = f1 (iL , uc ) ⎪ ⎪ kq1 = f2 (i ⎪ ⎪  L , uc )  ⎪ ⎪ h h ⎪ k = f ⎪ p2 1 iL + 2 kp1 , uc + 2 kq1 ⎪ ⎪   ⎪ ⎪ ⎨ kq2 = f2 iL + h kp1 , uc + h kq1 2 2   (7) h h ⎪ i = f + k , u + kq2 k ⎪ p3 1 L p2 c ⎪ 2 2 ⎪   ⎪ ⎪ h h ⎪ i = f + k , u + k k ⎪ q3 2 L p2 c q2 ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ = f (i + hk , u + hk k p4 1 L p3 c q3 ) ⎪ ⎩ kq4 = f2 (iL + hkp3 , uc + hkq3 )

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By synthesizing (4), (5), (6) and (7), uo,n+1 could be represented as: uo,n+1 = aiL,n + buc,n + c

(8)

So uo,n+1 can be represented by iL,n+1 and uc,n+1 . a, b and c are constitute of eight groups of parameters (D, L, RL , C, Rc , Rdson , vf and uin ). The digital twin model of Buck-Boost converter is shown in Fig. 4 below. The digital twin model receives the actual data such as input voltage and load of Buck-Boost converter in real world. Then the digital twin model could be used to calculate the output voltage and other state parameters. The model is updated timely through data interaction to maintain the unity of the model and the actual circuit.

Fig. 4. Digital twin model

4 Experimental Verifications To verify the accuracy of the digital twin model of Buck-Boost converter, the digital twin Buck-Boost converter is realized by s-function programming in MATLAB. The simulation model of the converter is established in MATLAB instead of the physical. Table 1 shows its key parameters. The comparison of inductor current between physical converter and digital twin converter is shown in Fig. 5. The comparison of output voltage between physical converter and digital twin converter is shown in Fig. 6. As can be seen from Figs. 5 and 6, iL and uo obtained by the digital twin model of Buck-Boost converter are basically consistent with the actual circuit. This shows that the Buck-Boost converter digital twin circuit established in the essay and the physical circuit show the same features, and the model built in this paper is correct.

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Parameter

Value

Output voltage uin

18 V

Switching frequency f

10 kHz

Road resistor R

20 

Inductor resistor RL

0.01 

Capacitor resistor Rc

0.01 

Inductor L

0.45 mH

Capacitor C

0.7 mF

Fig. 5. Inductor current (iLm is the inductor current of the physical converter; iL is the inductor current of the digital twin converter.)

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Fig. 6. Output voltage (uo,m is the output voltages of the physical converter; uo is the output voltages of the digital twin converter.)

5 Conclusion In this paper, the working features of Buck-Boost converter is studied firstly. Secondly, the core part of mathematical model in digital twin technology is completed. Then the mathematical model is simulated and verified. By comparing the inductor current waveform and the output voltage waveform of the physical converter and the digital twin converter, the accuracy of the proposed model is verified. The model has sufficient precision, which lays a foundation for further research. Acknowledgement. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation)—Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

References 1. Oldman, S.H.V.: Electrical Overstress (EOS): Devices, Circuits and Systems. John Wiley & Sons (2013) 2. Peng, Y., Zhao, S., Wang, H.: A digital twin based estimation method for health indicators of DC–DC converters. IEEE Trans. Power Electron. 36(2), 2105–2118 (2020) 3. Wen, P., Zhao, S., Chen, S., Li, Y.: A generalized remaining useful life prediction method for complex systems based on composite health indicator. Rel. Eng. Syst. Safety 205 (2021)

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4. Milton, M., De La, O.C.A., Ginn, H.L., Benigni, A.: Controller-embeddable probabilistic realtime digital twins for power electronic converter diagnostics. IEEE Trans. Power Electron. 35(9), 9850–9864 (2020) 5. Jain, P., Poon, J., Singh, J.P., Spanos, C., Sanders, S.R., Panda, S.K.: A digital twin approach for fault diagnosis in distributed photovoltaic systems. IEEE Trans. Power Electron. 35(1), 940–956 (2020) 6. Liu, D., Guo, K., Wan, B., et al.: Overview and prospect of digital twin technology. J. Instrum. 39(11), 1–10 (2018)

A Hybrid Carrier-Based DPWM Strategy with Variable Clamp Region and Controllable NP Voltage Huajian Zhou1,2,3,4 , Cungang Hu1,2,3,4(B) , Wenjie Zhu1,2,3,4 , Jixuan Zhang1,2,3,4 , and Wenping Cao1,2,3,4 1 School of Electrical Engineering and Automation, Anhui University, Anhui 230000, China

[email protected]

2 School of Internet, Anhui University, Hefei, China 3 Jiangsu Dongrun Zhilian Technology Co, Ltd., Jiangsu, China 4 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, Australia

Abstract. For T-type three-level inverter, the traditional space vector modulation (SVPWM) algorithm is relatively complex, which requires a large number of switching states in a cycle, resulting in large switching losses. Discontinuous pulse width modulation (DPWM) can simplify the algorithm and reduce switching losses, which has great advantages. DPWM control is to clamp a phase to high and low voltage or 0 within a carrier period, so that different DPWM control strategies will have different clamping areas. The size of the clamping interval is an important factor affecting harmonic content of the AC output. The peak clamping interval and zero crossing interval can be adjusted by modifying the judgment conditions of the clamping interval, but the NP voltage under the DPWM control strategy cannot be balanced. Therefore, this paper combines the hybrid carrier-based DPWM (HCBDPWM) control strategy and applies it to the DPWM control strategy with variable clamping area to achieve NP voltage balance. Keywords: T-type three-level · Variable clamping area · NP voltage · DPWM

1 Introduction T-type three-level inverter has the advantages of low switching loss and excellent AC output, which is very suitable for high voltage and high frequency applications. Compared with NPC, T-type three-level topology reduces two diodes per phase bridge arm, reduces conduction loss and has higher efficiency, so it is widely used in new energy vehicles and other fields. However, T-type three-level inverter’s number of power switches is doubled reduced with that of two-level inverter, resulting in a corresponding increase in switching loss. To solve this problem, some scholars put forward the strategy of DPWM. Compared with continuous pulse width modulation (CPWM), the switching tube of each phase of DPWM does not act in 1/3 of the fundamental wave period, which significantly reduces the switching loss, and is more suitable for high switching frequency converters © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 791–799, 2023. https://doi.org/10.1007/978-981-99-4334-0_96

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with wide band gap devices. Space-vector DPWM (SV-DPWM) includes algorithms such as judging large and small sectors, calculating vector action time, and synthesizing modulation waves, which brings huge computational burden to digital processors. For three-level inverter, there are many methods to realize DPWM. Literature [1] proposed a carrier based DPWM. Compared with the space vector based DPWM strategy, this method is not only simple to implement, but also can achieve normal operation under different modulation levels. Literature [2] proposed a unified implementation method of CB-DPWM by twice zero sequence component injection and combining sector judgment, different clamping modes can be selected in different sectors to achieve all CB-DPWM strategies. Literature [1] proposes a carrier modulation strategy of DPWM1 which can be applied to three-level inverter, but the clamping region is fixed. On this basis, literature [3] proposes to achieve clamping mode switching by injecting additional zero sequence components and adjust the midpoint potential, but does not give the carrier realization method of DPWM2.Literature[4] proposed variable clamping area CB-DPWM. On the basis of DPWM1, by changing the judgment conditions of zero crossing clamping region and the expression form of intermediate variables, zero crossing clamping area is adjusted to cut down the total THD of outcome. The control strategy HCB-DPWM is proposed in reference [5], and two contrast act on neutral point voltage clamping modes are obtained through different k values in two harmonic injections. Reference [6] optimizes the NP voltage control logic mentioned above. In this article, through optimization of HCB-DPWM regulate strategy is used to the control method of variable clamping area to balance the neutral point voltage balance under the control of variable clamping area.

2 T-type Three-Level Inverter and Its CB-DPWM Strategy 2.1 Topology for T-type Three-Level Inverter Figure 1 reveals the topology of the T-type inverter, where vdc is DC side voltage; C1 , C2 is DC side upper and lower capacitance, when the capacitor is balanced vc1 = vc2 = vdc /2; L, R is three-phase output current They are filter inductance and load resistance respectively. When the switch tube Tx1 is on and the other three switch tubes are off, the output voltage is vdc /2. When the switch tube Tx2 , Tx3 is on, the output voltage is 0; When only the switch tube Tx4 is on, the output voltage is −vdc /2; Define the output voltage corresponding to level P as vdc /2, level O as 0, and the level N as −vdc /2. Corresponding relationship between switch state and output voltage is shown in the Table 1, where ON represents the switch on, and OFF represents the switch off. To simplify the analysis, assuming vdc = 1, the three-phase voltage can be standardized as: √ ⎧ ⎨ va = (1/√3)m cos ωt (1) v = (1/√ 3)m cos(ωt − 2π /3) ⎩ b vc = (1/ 3)m cos(ωt − 4π /3) For the above formula, m is the modulation index, defined as m = vvdc1 , where v1 delegate the amplitude of the output fundamental wave of the line voltage, and m ∈ [0, 1].

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vc1

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T a1 Ta2

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an

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PNN

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PNP V18

Fig. 1. T-type three-level inverter topology and space vector diagram. Table 1. Corresponding relationship between switch state and output voltage. Output voltage

Working condition

S1

S2

S3

S4

vdc /2

P

ON

OFF

OFF

OFF

0

O

OFF

ON

ON

OFF

−vdc /2

N

OFF

OFF

OFF

ON

The expression of reference voltage vector can be obtained by converting three-phase AC voltage to two-phase static coordinate system through coordinate transformation:  2π 4π 2 van + vbn ej 3 + vcn ej 3 (2) vref = 3 After obtaining the space vector corresponding to each sector the space vector distribution is shown in Fig. 1. 2.2 CB-DPWM Strategy DPWM1 is a zero crossing clamping type DPWM. Its clamping area is mainly located near the zero crossing point and peak point, which can improve the current zero crossing distortion. Literature [1] gives the carrier implementation method of DPWM1, in which the clamping mode of DPWM1 in the first large sector is shown in Fig. 2. The zero sequence component of DPWM1 is calculated by follows: ⎧ |v max | ≥ |vmin |, voffset > −vmid −vmid ⎪ ⎪ ⎨ 1 − vmax |v max | ≥ |vmin |, voffset < −vmid (3) vz = ⎪ |v max | < |umin |, voffset > −vmid −v ⎪ ⎩ mid −1 − vmin |v max | < |vmin |, voffset < −vmid where in, vmax , vmin , vmid are respectively the maximum, minimum and intermediate values of three-phase sinusoidal modulated wave at a certain time. Intermediate variables required for judging conditions are calculated as follows:  1 − vmax |vmax | ≥ |vmin | voffset = (4) −1 − vmin |vmax | < |vmin |

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OON PPO

C=N PON

A=P OOO

POO ONN

PNN

Fig. 2. Schematic diagram of DPWM1 clamping in the first large sector.

The modulated wave of CB-DPWM1 can be obtained by injecting Eq. (3) into Eq. (1), as shown in Eq. (5), and vref _x represent the modulated wave of CB-DPWM1. vref _x = vmx + vz

(5)

Figure 3 presents the modulation wave and injected zero sequence component of CB-DPWM1. Vavdref

Vbvdref

Vcvdref

Vv_offset

Fig. 3. Modulation wave and zero sequence component of CB-DPWM1.

3 NP Voltage Control Strategy for Variable Clamp Region 3.1 DPWM Strategy with Variable Clamping Area Different clamping areas can bring lower harmonics to the output current. Through adding vth to Eq. (3) to control zero clamping range. For CB-DSVM, the traditional space vector control is used in the non-zero-crossing area, and the zero-crossing area is clamped to zero, the formula is as follows: ⎧ |v max | ≥ |vmin |, vz1 > −vmid + vth −vmid ⎪ ⎪ ⎨ 1 − vmax |v max | ≥ |vmin |, vz1 < −vmid + vth (6) uz = ⎪ |v max | < |vmin |, vz1 < −vmid − vth −v ⎪ ⎩ mid −1 − vmin |v max | < |vmin |, vz1 > −vmid − vth

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The method of changing the clamping area by translating the intermediate variable −vmid up and down is shown in Fig. 4. When vth > 0, the value of −vmid + vth will increase and −vmid − vth decrease. It is shown in the image that −vmid moving up and down vth respectively makes the zero crossing clamping area decrease to θp1 . When vth < 0, makes the zero crossing clamping area increase to θp2 . The maximum clamping area is obtained at |vr max | = |vr min |. Using coefficient kc , the clamping range can be decided by vth = kc vth max . For practical applications kc ∈ [0, 1]. 1

vr min

vr max

0.5

0

– umid

θ p1

vzn

-0.5

θp 2 θp0

-1

0

pi/3

pi/6

pi/2

2pi/3

5pi/6

pi

Angle/rad

Fig. 4. Schematic diagram of variable clamp for CB-DSVM

However, the adjustment of clamping area under this clamping strategy is limited. The adjustment range of peak clamping area and zero crossing clamping area is related and cannot be adjusted independently. 3.2 Hybrid Carrier-Based DPWM (HCB-DPWM) To realize the triangle carried-based DPWM proposed in [5], two DPWM strategies with opposite effects on the midpoint voltage can be obtained by injecting zero-sequence components into the original sine wave twice. The zero-sequence components of the two injections are as follows:  vb , vc )/2 vz1 = − max(va , vb , vc )/2 − min(v

a ,1−k k ∗ , v∗ , v∗ ∗ ∗ ∗ − max v vz2 = − 1+k az1 az1 az1 2 2 min(vaz1 , vaz1 , vaz1 ) + 4 vdc , k = 1 or − 1 (7) where 

vxz1 − 41 vdc , vxz1 ≥ 0 vxz1 + 41 vdc , vxz1 < 0

(8)

vxz1 = vx + vz1 , (x = a, b, c)

(9)

vxz = and

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In paper [14], four kinds of DPWM strategies can be expressed according to different k values selected in different large sectors. Figure 5 shows the case of space vector clamping when k = 1 or − 1.For the clamping mode when k = 1, the effect on the midpoint potential is reduced. On the contrary, when k = − 1, the midpoint potential is always increased. Therefore, the midpoint potential balance can be controlled by switching the two clamping modes. OPN

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B=P

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B=P

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A=P C=N B=P A=N OPO B=O B=P PPO OPO C=N A=O PPO PON NPO PON V 2 NON V 2 V3 NON V3 V9 V7 V9 V7 A=P A=O C=O OON B=O C=O B=O A=O OON A=N C=O C=O B=O B=O B=O C=N A=P C=N B=P B=P A=N C=O PPP B=O POO PPP A=O POO A=O C=O OPP OPP OOO V1 OOO V1 PNN NPPV16 13 V NPP VPNN 13 NOO V4 A=O ONN V16 NOO V4 B=O ONN V0 NNN C=O V0 NNN A=O C=P C=P B=O A=N B=O C=O B=O C=O A=P C=O B=N B=N B=O A=O B=O A=P C=O A=O C=O A=N POP POP OOP OOP PNO NOP PNO NOP 5 NNO VA=O NNO V5B=NA=O V6 ONO V10 V6 ONO V10 V12 V12 C=P C=P A=N A=P B=N C=P C=P B=N B=N NPO

V11

NNPV17

ONP

V11

PNP V18

(a)k=1

NNPV17

ONP

PNP V18

(b)k=-1

Fig. 5. Clamping modes of the TCB-DPWM scheme.

According to literature[6], when the midpoint potential reaches the upper limit value, k switches to 1, making the midpoint potential lower; When the midpoint potential reaches the lower limit value, k is switched to − 1, which increases the midpoint potential. However, due to hysteresis regulation, the selection of loop width will greatly affect the switching frequency of the switch state, thus causing the problem of large output current harmonics. Therefore, while changing the clamping range to reduce the output current harmonics, the application of this midpoint potential control method can reduce the low frequency harmonics of the output current while controlling the midpoint potential, and coordinate the switching loss and output current quality.

4 Simulation Verification In order to verify the research of realizing the control of the midpoint voltage while changing the clamping range, the model of T-type inverter is built in matlab and verified by simulation. The parameters are as Table 2. Figure 6 shows the output line voltage, phase voltage, phase current and harmonic analysis of the DPWM strategy under the condition vth = 0.08 and vth = 0.15.The harmonic distortion rate of output current can be reduced by appropriately reducing the switching range. As shown in the Fig. 6, when vth = 0.08, the THD of the output current is 2.55%. When vth is increased to 0.15, the THD is decreased to 1.88%. After vth is increased, the second harmonic is significantly reduced, but the third and fourth harmonic content is increased.

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Table 2. Simulation parameters. Parameter

Working condition

DC side voltage udc /V

200

Filter inductance L/mH

5

DC side capacitance C1 , C2 /F

4.7e−3

IGBT switching frequency fs /Hz

10K

(a) vth = 0.08

(b) vth = 0.15

Fig. 6. Output line voltage, phase voltage, phase current and harmonic analysis.

Figure 7 shows the output waveform of NP voltage with HCB-DPWM controlling NP voltage balance under variable clamping area. From the NP voltage waveform, it is obvious that the fluctuate of vdc is greatly majorized by mixing DPWM modulation strategy. Under the mixing DPWM modulation strategy, not only the neutral point voltage is controlled, but also the harmonic content of the output current can be reduced by changing the clamping area. As shown in Fig. 7 (c), only the NP voltage balance control method first output current harmonic content is 2.05%, and after increasing the zero crossing clamping area as Fig. 7(d), the output current harmonic content is reduced to 1.77%.

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(a) Without NP voltage balance strategy

(b) Add NP voltage balance strategy

(c) No change of clamping area

(d) Increase zero crossing clamping area

Fig. 7. NP voltage output and harmonic analysis under variable clamping area DPWM.

5 Conclusion Because DPWM only uses a small vector in a small sector, the midpoint voltage cannot be automatically balanced, so on the basis of changing the length of the clamping section, this paper proposes to apply the hybrid modulation strategy to the variable clamping area DPWM control strategy. Because the two modes of k = 1 and k = − 1 in TCBDPWM play a contrast role on neutral point voltage, that is, when the clamping mode of k = 1 reduces the NP voltage, and when the clamping mode of k = − 1 increases the NP voltage. This paper uses these two clamping modes and DPWM with variable clamping area for mixed modulation. When the NP voltage is higher than the positive limit amplitude, the clamping mode of k = 1 is used; When the NP voltage is lower than the negative limit amplitude, use the clamping mode of k = − 1. When the NP voltage is between the positive and negative limiting amplitudes, the clamping method of variable clamping area is used to control the NP voltage within the positive and negative limiting amplitudes through mixed modulation. The mixing modulation not only adjust neutral point voltage, but also adopts the variable clamping area DPWM. On the premise of neutral point voltage control with clamping range, the harmonic content can be reduced by changing the peak value and zero crossing clamping area, which has a high practical application value. Acknowledgement. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation)—Key National Industrial Technology Research and Development Cooperation Project (BZ2018014) and Natural Science Foundation of Anhui Province (2108085QE239).

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References 1. Lee, J.-S., Lee, K.-B.: Carrier-based discontinuous PWM method for Vienna rectifiers. IEEE Trans. Power Electron. 30(6), 2896–2900 (2015) 2. Jung, J.-H., Ku, H.-K., Im, W.-S., Kim, J.-M.: A carrier-based PWM control strategy for threelevel NPC inverter based on bootstrap gate drive circuit. IEEE Trans. Power Electron. 35(3), 2843–2860 (2020) 3. Lee, J.S., Lee, K.B.: Performance analysis of carrier-based discontinuous PWM method for Vienna rectifiers with neutral-point voltage balance. IEEE Trans. Power Electron. 31(6), 4075– 4084 (2016) 4. Zhu, W., Chen, C., Duan, S., et al.: A carrier-based discontinuous PWM method with varying clamped area for Vienna rectifier. IEEE Trans. Indus. Electron. 66(9), 7177–7188 (2019) 5. Li, K., Wei, M., Xie, C., Deng, F., Guerrero, J.M., Vasquez, J.C.: Triangle carrier-based DPWM for three-level NPC inverters. IEEE J. Emerg. Sel. Topics Power Electron. 6(4) (2018) 6. Ming, Y., Zhang, L., Xing, Y.: A hybrid carrier-based DPWM with controllable 7. NP voltage for three-phase Vienna rectifiers. IEEE Trans. Indus. Electron. 8(2) (2022)

A Novel Multi-robot Path Planning Algorithm Considering Dynamic Environmental Information Jiahao Zhang1 , Chengke Wu2 , Lan Cheng1 , Wei Feng2 , Yuanjun Guo2(B) , Zhile Yang2 , and Rui Yang1 1 Taiyuan University of Technology, Taiyuan, China 2 Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China

[email protected]

Abstract. Multi-robot path planning is a vital part of Simultaneous localization and mapping (SLAM) systems. In recent years, numerous studies have been conducted in the field of multi-robot path planning. This paper presents a novel method for multi-robot path planning that addresses the challenge of dynamic environments. This method joints adaptive parameters and adaptive steps strategy to the A* algorithm, which greatly improves the operational performance. This paper presents a novel multi-robot path planning method that addresses the challenge of path planning for multiple robots in dynamic environments. In addition, a multi-objective optimization algorithm is introduced and applied to the multirobot system. To address the issue of dynamic and unknown obstacle avoidance, the rolling window method and obstacle avoidance strategy are utilized. The simulation experiment demonstrates that the proposed algorithm outperforms the CPPOCA and MAPP-RL algorithms in all three metrics. Additionally, the algorithm’s practical feasibility is verified by applying it to the ROS simulation environment. Keywords: Multi-robot SLAM system · Path planning · A* algorithm · Rolling window method · Obstacle avoidance strategy

1 Introduction The Simultaneous Localization and Mapping (SLAM) [1] has been one of the most popular research topics in mobile robotics for the last two decades. Path planning plays a vital role in controlling robot actions in SLAM systems. Path planning is the basis for autonomous navigation and other advanced tasks for mobile robots. Path planning means that in various environments, the robot follows the set task requirements, identifies its position and the current environment based on the information collected by sensors, and plans a path between the starting point and the endpoint through the corresponding path planning algorithm while meeting performance indicators such as safety and collisionfree [2]. Multi-robot systems, which have greater flexibility, robustness, and ability to perform complex tasks [3], have become a hot research topic in recent years. Huang et al. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 800–806, 2023. https://doi.org/10.1007/978-981-99-4334-0_97

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[4] proposed a multi-robot coverage path planning algorithm to solve robots’ complex outdoor two-dimensional flat ground path planning problem. Japanese scholars use hierarchical hybrid probabilistic global planning roadmap to avoid local optimal solutions and achieve global optimization [5]. Russian researchers have improved path planning algorithms in various complex scenarios [6]. Dong et al. [7] combined a distributed formation control method with a robot control model to achieve obstacle avoidance between multiple robots in complex environments. Liu et al. [8] proposed a path planning method based on global path planning with local adjustment (CPP-OCA) Liu et al. [9] proposed a reinforcement learning-based multi-robot path planning method (MAPP-RL). This paper presents a multi-robot path planning algorithm that incorporates an improved A* algorithm utilizing environmental information. The algorithm is specifically designed for multi-robot systems to address the obstacle avoidance challenge posed by unknown and dynamic obstacles. To achieve dynamic obstacle avoidance, the rolling window method [10] and obstacle avoidance strategy are introduced. The rolling window method generates multiple sub-path points on the global path to accommodate possible dynamic obstacles in the environment, and local path planning is performed by introducing an obstacle avoidance strategy between adjacent sub-path points.

2 Fusion Path Planning Algorithm The proposed algorithm consists of the following main steps: Firstly, the environment’s existing obstacles are detected based on the map information obtained. Next, an improved A* algorithm, which employs an adaptive step size strategy, is designed for global path planning. Then, the rolling window method is used to generate multiple sub-path points on the global path to account for possible dynamic obstacles in the environment. Local path planning is performed by introducing an obstacle avoidance strategy between adjacent sub-path points. 2.1 Global Adaptive Improved A* Algorithm Considering Environmental Information The paper presents an enhanced A* algorithm that factors in environmental information and integrates the adaptive heuristic function and compensation strategies to boost the algorithm’s performance. Adaptive heuristic function strategies. The evaluation function of the A* algorithm is a composite of the actual cost G(n) the current node and the heuristic cost H(n). The heuristic cost G(n) in the A* algorithm plays a crucial role and significantly impacts the search performance of the algorithm. We introduce an adaptive heuristic function to adjust the cost function according to the environmental information to adapt to the environment with different complexity cases. The algorithm first analyzes the complexity of the obstacles in the environment: the starting point is (XS , YS ), the target point is (XE , YE ), and the number of obstacle grid in the surrounding environment is N , and the environmental obstacle ratio is: K=

N (|XS − XE | + 1) × (|YS − YE | + 1)

(1)

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The ratio of environmental obstacles is determined by the number of obstacles present, the starting point, and the target point of the path planning. Furthermore, this ratio varies with the distance between the starting point and the target point. To account for this, the ratio is integrated into the evaluation function, and the heuristic weight is adjusted adaptively. As a result, the algorithm automatically adapts the search space according to changes in the environment, starting point, and target point. The improved evaluation function is represented as follows: F(n) = G(n) + (1 − lnK)H (n)

(2)

As depicted in Eq. (2), when the number of obstacles in the environment is relatively low, a larger heuristic weight coefficient results in a decrease in the search space, significantly improving the search efficiency. However, when the number of obstacles in the environment is relatively high, a smaller heuristic weight coefficient causes the search space to expand, preventing the algorithm from getting trapped in a local optimum. Adaptive Step Strategy. As the initial path may contain more redundant points, the final path may not be optimal. To further optimize the planned path and reduce redundant points, we propose an adaptive step length strategy. The method is outlined below. (1) Begin at the starting point of a planned path and mark it as a collision point at time t. (2) If the connection with the subsequent path point does not intersect with an obstacle, proceed to connect it with the next path point. Otherwise, mark the preceding path point of this path as a collision point and eliminate the redundant path points between the two collision points. (3) Repeat step (2) until the target point is reached. 2.2 Local Path Planning Algorithm Based on Rolling Window Method When a robot encounters dynamic obstacles and other robots, it needs to react to them and complete obstacle avoidance. Upon detecting a dynamic obstacle, the mobile robot must respond accordingly by taking into account the surrounding environment information and its own pose. The rolling window method [10] is used as a predictive control method in various scenarios. It can continuously acquire new information in the environment as the rolling window advances and achieve optimized functionality through interactive feedback with the environment. This paper combines the adaptive A* algorithm and the rolling window method. The basic steps of the proposed local path planning algorithm are: first, map the surrounding environment information into a grid map, specify the starting point S and endpoint E of the mobile robot operation task in the map, set the detection distance R and rolling window V within the limited range of the sensor according to the map size, and complete the global path planning, then determine the window area according to the path node information and the detection of the mobile robot. After the global path planning is completed, the window area is determined according to the path node information and the detection requirements of the mobile robot, and sub-target points are generated in the local area according to certain guidelines, and the obstacle avoidance strategy is introduced for local path planning again. Repeat the above steps until the end point E is detected and the path planning is completed.

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3 Simulation Experiments In this chapter, experiments are conducted in a simulated environment and a simulation environment respectively. We will compare the analysis with established multi-robot path planning algorithms based on the following metrics: shortest path length, total time taken by the path, and overall smoothness. 3.1 Simulation Experiment I To assess the algorithm’s efficacy in a challenging environment, we conducted an experiment within a 40 × 50 occupancy grid map simulation, involving five robots. In this environment, five robots reach the target point E1 = (36.5, 7.5) E2 = (33.5, 41.5)E3 = (21.5, 1.5)E4 = (13.5, 18.5)E5 = (2.5, 37.5) from the starting point S1 = (0.5, 25.5) S2 = (1.5, 1.5)S3 = (9.5, 47.5)S4 = (22.5, 43.5)S5 = (38.5, 31.5), respectively. To simulate the realistic environment, unknown dynamic obstacles were added. In this experiment, three dynamic obstacles are set in the environment, the speed of obstacle 1 is 0.9 m/s, the speed of obstacle 2 is 1.5 m/s, the speed of obstacle 3 is 0.5 m/s, and the speed of the robots are different, the speed of the five robots are 0.8 m/s, 1.3 m/s, 2 m/s, 1.5 m/s, 0.7 m/s. After getting each robot’s After obtaining the initial path of each robot, the robots are divided into local areas according to their different rolling periods. Three algorithms were used in this experiment: CPP-OCA, MAPP-RL and the Fusion Algorithm. Figure 1 displays the results, with (a) and (b) depicting the output of the fusion algorithm, (c) depicting CPP-OCA, and (d) depicting MAPP-RL.

Fig. 1. Fusing algorithms to derive collision-free paths in a simulation environment.

Table 1. The final sentence of a caption must end with a period. Environment size

Algorithm

f1

f2

f3

40 × 50

Fusion algorithm

241.31

68.33

59.11

CPP-OCA

268

161.27

67.5

MAPP-RL

272

87.96

70

Table 1 gives the optimized objective values of the corresponding three algorithms in the simulated environment. The results indicate that the fusion algorithm outperforms the other two algorithms in complex environments. The fusion algorithm demonstrates

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adaptability in complex and dynamic environments, extending beyond obstacle avoidance among robots. It effectively navigates around unknown, dynamic obstacles, thereby enhancing the algorithm’s robustness. 3.2 Simulation Experiment II To test the algorithm in a real-world scenario, we constructed a simulation environment within the ROS framework. We utilized the Turtlebot2 robot, which was readily accessible in our lab, for modelling purposes. Two scenes were built for this experiment: an indoor scene and an outdoor scene. Figure 2 shows the robot, model and the scenes. The robot starts from different starting points and Moves at a velocity of 0.5 m/s. The robot’s path planning results are visualized in RVIZ.

Fig. 2. Turtlebot2 robot and simulation environments.

In the indoor simulation environment, robot 1 starts from (0, 1), robot 2 starts from (0, 1), robot 3 starts from (0, − 1), and sets its goal point 1 to (0.5, 0.5), (1, 0), (− 1, 0) in turn. When the robot reaches the specified goal point, Reset its target point 2 to (4, 0), (4, − 1), and (− 4,0). After that, target point 3 is set to (6, − 4), (4, − 4), and (− 5, − 5). In order to prevent random unknown obstacles in the environment, three robots carry out path planning according to the goal in turn. The experimental results in an indoor environment are shown in Fig. 3.

Fig. 3. Indoor simulation environment experiment results.

In the simulated outdoor environment, three mobile robots were allowed to move from the initial point to (5, 0), (0, 5) and (− 4, 3) respectively, denoted as target point 1. When the robot reached the specified target point, the next target point was set for it, which were (3, − 5), (3, 3), (− 3, 5) in turn, denoted as target point 2. Robot 1, Robot 2, and Robot 3 are represented by the colors red, blue, and green, respectively, to

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indicate their respective paths. The environment in which they operate contains unknown obstacles, represented by the red line in the figure. The final outcome of their movements is depicted in Fig. 4.

Fig. 4. Outdoor simulation environment experiment results.

3.3 Analysis of Experimental Results The experimental parameters of the indoor environment and the outdoor playground environment were counted separately, and each parameter is shown in Table 2. The path planning graphs generated for three robots in simulated environments demonstrate their ability to use various obstacle avoidance strategies, which allows them to effectively navigate around obstacles. This verifies the fusion algorithm’s capability for real-time obstacle avoidance while maintaining global optimality. Table 2. Optimization target values for each algorithm in the simulation environment Environment

Path search time/s

Path length/m

Robot 1

Robot 2

Robot 3

Robot 1

Robot 2

Robot 3

Indoor

60

59

70

30

29.5

35

Outdoor

49

42

55

24.5

21

27.5

4 Conclusion This paper introduces a novel global multi-robot path planning algorithm that is based on an improved A* algorithm. The primary contributions of the research are: Firstly, the addition of adaptive parameter and adaptive step size to the A* algorithm, which enhances the search performance of the original algorithm. Secondly, the combination of rolling window method and multi-objective optimization algorithm to improve the obstacle avoidance ability in dynamic environments. The proposed algorithm is compared with two other multi-robot path planning algorithms in a simulation environment, and the results demonstrate the superiority of the proposed fusion algorithm in three aspects. Finally, the effectiveness of the algorithm is verified in actual situations through a second simulation experiment.

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Acknowledgment. This work was supported by the National Natural Science Foundation China under Grants number 62073232, 52077213, 62003332 and 52208324.

References 1. Grisetti, G., et al.: A tutorial on graph-based SLAM. IEEE Intell. Transp. Syst. Mag. 2(4), 31–43 (2010) 2. Li, Q., et al.: Graph neural networks for decentralized multi-robot path planning. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE (2020) 3. Nazarahari, M., Khanmirza, E., Doostie, S.: Multi-objective multi-robot path planning in continuous environment using an enhanced genetic algorithm. Expert Syst. Appl. 115, 106– 120 (2019) 4. Huang, X., et al.: A multi-robot coverage path planning algorithm for the environment with multiple land cover types. IEEE Access 8, 198101–198117 (2020) 5. Ravankar, A.A., et al.: HPPRM: hybrid potential based probabilistic roadmap algorithm for improved dynamic path planning of mobile robots. IEEE Access 8, 221743–221766 (2020) 6. Thabit, S., Mohades, A.: Multi-robot path planning based on multi-objective particle swarm optimization. IEEE Access 7, 2138–2147 (2018) 7. Liu, C.: Safe robot navigation among moving and steady obstacles [Bookshelf]. IEEE Control Syst. Mag. 37(1), 123–125 (2017) 8. Liu, Z., et al.: Mapper: multi-agent path planning with evolutionary reinforcement learning in mixed dynamic environments. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE (2020) 9. Liu, M., et al.: Task and path planning for multi-agent pickup and delivery. In: Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS) (2019) 10. Akram, M., Habib, A., Alcantud, J.C.R.: An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers. Neural Comput. Appl. 33(4), 1329– 1342 (2021)

A Method of Constructing Admittance Matrix for Power Flow Correction in Complex AC Systems Suitable for Equivalent Simplification Maolan Peng1 , Lei Feng1 , DaChao Huang1 , Hang Liu1 , Xilin Yan1 , Fangqun Liao1 , Jialin Wang2 , Junpeng Ma2 , and Shunliang Wang2(B) 1 Extra High Voltage Power Transmission Company, China Southern Power Grid,

Guangzhou 510663, Guangdong, China 2 School of Electrical Engineering, Sichuan University, Chengdu 610065, Sichuan, China

[email protected]

Abstract. With the increasing complexity of AC system, it is difficult to obtain the admittance matrix of the whole system. From the perspective of automation, universality and precision, this paper proposes a method for constructing admittance matrix of arbitrary complex AC system. Firstly, the rated parameters of AC system are obtained by batch/automatic simulation software, and the equivalent ways of each component are classified and discussed. Secondly, this paper proposes to use frequency sweep method to judge the equivalent value of complex components by node position, and the equivalent admittance of the components is included into the matrix. Then the element is used as the minimum system admittance and the traversal algorithm is used to complete the traversal of AC system nodes. By using the ideas of power flow correction, step simplification and batch processing, the admittance matrix of the whole network and the corresponding simplified condition can be formed quickly and accurately. Finally, in order to verify the correctness of the proposed method, this paper takes IEEE9 node system as an example to verify the correctness of the admittance matrix. Keywords: Complex AC system · Admittance matrix · Power flow distribution · Equivalent reduction model

1 Introduction With the rapid economic growth and the popularity of the low-carbon concept, a large number of new energy stations have been connected to the power grid, leading to the gradual formation of regional interconnection mode in the modern power system. The integration analysis method [1] is commonly used in the calculation and analysis of interconnected ac system. However, considering the interaction between interconnected power grid systems [2], it is limited by many factors, such as the large scale of the actual system and difficult information exchange. Therefore, reserve the research core and simplify the system is gradually applied to the analysis of complex systems. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 807–813, 2023. https://doi.org/10.1007/978-981-99-4334-0_98

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At present, the equivalence simplification is divided into static equivalence [3] and dynamic equivalence [4] according to the differences in the research process. In the static equivalent, it is divided into topological method [5] and non-topological method [6]. Topology method can simplify the system external network under power frequency, such as Ward equivalent [7] and other improved static equivalent methods [8]. The admittance matrix is very important in the equivalence reduction and stability analysis of the system. In [9], by obtaining the node admittance matrix under the specific form of the system, so as to realize the analysis and judgment of the resonance mode and resonance stability of the system. In [10], simplified admittance matrix is used to realize the distribution calculation of active power-frequency. For the construction of the admittance matrix, In [11], the zero-pole matching method is used to calculate the corresponding network by using the zero-pole of the system impedance admittance function. Literature [12] used the vector fitting method to solve the high-dimensional overdetermined equations according to the transfer function formula, and obtained the equivalent admittance. The above method is tedious, the accuracy and calculation amount are opposite to each other, and it is difficult to take into account. Literature [13] solved the system node admittance matrix based on CSR, realizing the formation of admittance matrix, but it focuses on solving the distribution of system power flow, it is difficult to expand. The traditional methods are difficult to expand and require too much computation. Therefore, this paper proposes an equivalent admittance matrix construction method based on power flow data correction. Firstly, based on components, the equivalent model of components under engineering model is analyzed. The element node admittance is added to the admittance matrix as a participating element by the traversal method. It is proposed to use the power flow results of iterative solution to correct some elements, so as to ensure the correctness of the admittance matrix. For other complex elements, the simplified model is judged by the node position by frequency sweep method, and the equivalent admittance of the element is included into the system matrix. Power flow data calculation.

2 Power Flow Data Calculation Taking Newton Raphson method as an example, firstly, the admittance matrix of the system is calculated according to the system rating parameters, and the injected power of each node is calculated using the admittance matrix. The node power is: fPi = Pi − fQi = Qi −

n  j=1 n 

  Ui Uj Gij cos δij + Bij sin δij = 0;   Ui Uj Gij cos δij − Bij sin δij = 0

(1)

j=1

δij = δi − δj , G and B are the real and imaginary parts of the node admittance matrix elements Y ij . Pi and Qi represents the active power and reactive power set by node i respectively.

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According to the correction equation, the Jacobian matrix is expressed to correct each node of the system, Jacobian matrix after chunking is (2):      P HN δ (2) = Q J L U −1 U From (2), the next iteration correction can be obtained, and the original solution can be modified by this correction. After repeated iterations, the power flow errors of all nodes meet the requirements.

3 Element Equivalence Simplification 3.1 Element with Weak Correlation Between Equivalent Parameters and Power Flow Change Simplified Model of Transformer Equivalent Figure 1(a) shows the simplified circuit diagram of traditional double-winding transformer: I1 U1 GT

ZT=RT+jXT

-jBT

K:1 I2 U2

i

ZLeq

YLeqi

(a)

j YLeqj

(b)

Fig. 1. (a) Conventional double winding equivalent circuit diagram (b) Equivalent simplified model of transformer

RT is transformer copper consumption, X T is transformer iron consumption. Parallel admittance value at side i and j of transformer nodes: YLeqi =

1 − tk tk (tk − 1) , YLeqj = ZT ZT

(3)

The series impedance between nodes i and j of transformer: ZLeq =

ZT (U · tap)2 (U · tap)2 RT + j XT , ZT = tap · tk P P

(4)

t k is the transformer ratio, P is the rated capacity of the transformer, U is the primary side voltage which can be assigned according to the conversion direction, and tap is the transformer tap parameter.

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Simplified Model of Line Equivalence The equivalent parameters of the line can be calculated according to the formula Rcir , L cir , C cir : XLcir = Rcir + j · 2π f · Lcir , Bcir = 2 ·

1 j · 2π f · Ccir

(5)

X Lcir is the standard unit value of reactance, Bcir is the standard unit value of line electricity, f is the system frequency. 3.2 Element with Strong Correlation Between Equivalent Parameters and Power Flow Change Simplified Equivalent Model of Load Branch The load can be reduced to the π model. Rload is parallel branch resistor, X load is parallel branch reactance: Rload =

(U2N + U2t )2 (U2N + U2t )2 ((Q2N + Q2t ) > 0) , Xload = (P2N + P2t ) Q2N + Q2t

(6)

U 2N , P2N , Q2N is the rated parameter of the load. Q1t , P1t , U 1t is the amount of load power flow data correction. 3.3 The Admittance Calculation of Complex Combination Elements such as Converter Station The equivalent impedance of a converter station or other combined elements is often obtained by direct modeling and frequency sweeping. In the AC system, the equivalent impedance of any three-phase system is measured as shown in Fig. 2:

AC system

ugacA

ugpA

iA+ipA

ugacB

ugpB

iB+ipB

ugacC

ugpC

iA+ipC

Three phase system converter

Zac=ugpA /ipA

Fig. 2. Circuit diagram of equivalent impedance measurement

The ac impedance/admittance of inverter at ωp can be obtained the ratios by (7): Zac (ωp ) =

ugp (ωp ) 1 , Yac (ωp ) = igp (ωp ) Zac (ωp )

(7)

‘ugp ’ represents harmonic voltage disturbance, a voltage source can usually be applied to simulate harmonic disturbances: ‘igp ’ is the harmonic current of the response.

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4 Construction of Node Admittance Matrix of Complex AC System 4.1 System Node Admittance Construction Based on Power Flow Variation and Component Equivalence Model When the calculation of equivalent impedance of such components is greatly affected by the actual operating conditions, it is necessary to use power flow data to correct them. The construction flow chart of admittance matrix is shown in Fig. 3 combined with component traversal method.

No Power flow correction parameter table

The system admittance matrix is initialized

Element parameter analysis

Element subprogram

Power flow correction parameter table system admittance matrix (Global variable YBus)

Element traversal

Yes

Matrix output

Fig. 3. Flow chart of admittance matrix construction

After obtaining the power flow correction parameter table, the admittance matrix of the system is constructed using the data. Taking element nodes as objects, the calculated self-admittance and mutual admittance are added to the admittance matrix, and each cycle only adds additional components on the basis of the original admittance matrix.

5 Example Simulation and Verification Based on Admittance Matrix Simplification 5.1 IEEE9 Node System Verification In this section, AC systems are tested to verify the correctness of the above theories.The rated parameters of the components can be obtained through parameter analysis, and the admittance value of the components can be calculated by using the simplified model-level correction method described in this paper. The comparison of equivalent parameters of some components before and after power flow correction is shown in Fig. 4(a). If power flow data is not used to correct, there is a big gap between the equivalent resistance and the equivalent susceptance and the actual simulation model. After power flow correction, the equivalent result is more similar to the actual model simulation. The system node injection current verification is shown in Fig. 4(b). The injection currents of nodes 1–3 are calculated and compared with the actual simulation values. As can be seen from the figure, the calculation using the rated parameter directly can basically correspond to the actual value.

M. Peng et al. nominal parameter simulation result corrected results

550 500

450 400

equivalent reactance/Ω

1

10-3

phase angle/d egrees

equivalent resistance/Ω

600

node in jection curren t /k A

812

0.5

5 4

nominal parameter simulation result corrected results

2 0

-50

-100

0 1

2 Element number

(a)

3

1

2

Element number

3

(b)

Fig. 4. (a) Comparison of equivalent parameters before and after power flow correction of some components in IEEE9 system; (b) Node injection current verification

6 Conclusion In this paper, an admittance matrix construction method based on element equivalent model and power flow data correction is proposed to generate admittance matrix of complex AC system. The proposed method of power flow correction further increases the accuracy of establishing admittance matrix.

References 1. Wei, Y.L.: Simulation and analysis of optical storage integrated microgrid system. Shandong University of Science and Technology (2019) 2. Li, J., Ya, D., Yan, S., Lu, Y., Zhang, G.: Integrated node branch computing model service for interconnected large power grid oriented to unified computing analysis. Power Grid Technol. 41(05), 468–475 (2017) 3. Wang, C.: WARD static equivalence and case analysis based on Matlab block matrix operation. Shandong University (2010) 4. Zhang, B.Z.: Research on dynamic equivalence method and related problems of large-scale power system. South China University of Technology (2013) 5. Liu, X., Wang, L., Yan, Y.-P.: Research on improved static equivalence algorithm for power system. North China Electric Power Technol. 3, 1–5 (2010) 6. Xie, S., Hu, Z., Wu, F., et al.: Static equivalent parameter identification method for multiterminal extranet based on recursive least square method. Power Syst. Protect. Control 46(03), 26–34 (2018) 7. Hai, X., Shang-jin, Y., Xue-fen, J., Yang, W.: Power system ward equivalent method based on power flow and short circuit calculation. Power Syst. Protect. Control 46(24), 104–110 (2018) 8. Ji-keng, L., Yi-peng, Y., Tao, L., Wei-hong, Z.: Review of external system equivalence methods for electromagnetic transient simulation of power systems. Autom. Electric Power Syst. 36(11), 108–115 (2012) 9. Xu, Z., Wang, S.-J., Xing, F.-C., Xiao, H.-Q.: Research on resonance stability analysis method of power networks. Electric Power Constr. 38(11), 1–8 (2017) 10. Shen, S., Liu, R., Li, X., Song, Y., Rao, Y., Yu, B.A.: Fast frequency response analysis method based on simplified admittance matrix. High Voltage Technol. 44(10), 3284–3290 (2018)

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11. Morched, A.S., Ottevangers, J.H., Marti, L.: Multi-port frequency dependent network equivalents for the EMTP. IEEE Trans. Power Delivery 8(3), 1402–1412 (1993) 12. Bañuelos, E.S., Gustavsen, B., Gutiérrezroblesj, A., et al.: Computational efficiency improvement of the universal line model by use of rational approximations with real poles. Electric Power Syst. Res. 140, 424–434 (2016) 13. Dajun, S., Yong, S., Guangbin, Z., et al.: Fast calculation method of DC power flow in large power grid based on CSR direct column writing node admittance matrix. J. Kunming Univ. Sci. Technol. (Nat. Sci. Ed.) 45(06), 82–91 (2020)

Research on Pricing Strategy of Electricity Selling Company Based on Electricity Characteristics of Different Industry Zining Wang1 , Sheng Bi2 , Haotian Xu3 , Ciwei Gao3 , and Hao Ming3(B) 1 Trading Department, Jiangsu Huadian Energy Sales Co., Ltd., Nanjing, China

[email protected]

2 Power Market Research Center, Huadian Electric Power Research Institute Co., Ltd.,

Hangzhou, China [email protected] 3 School of Electrical Engineering, Southeast University, Nanjing, China {220225964,ciwei.gao,haoming}@seu.edu.cn

Abstract. With the opening of China’s electricity sales market, electricity selling companies have become emerging subjects in the market, and electricity sales is the core business of electricity selling companies. Electricity selling companies need to consider the characteristics of the industries, so that to customize the most appropriate electricity selling package for users. So this paper studies the pricing strategy of electricity selling companies based on the electricity consumption characteristics of subdivided industries. Firstly, this paper studies the electricity characteristics such as adjustable capacity and load transfer characteristics of each industries; secondly, studies the typical business package system of the electricity selling company, summarizes the characteristics of different packages; then analyzes the pricing influencing factors of the electricity selling company. Finally, based on the electricity consumption characteristics of the subdivided industries, the electricity price package suitable for various industries is formulated. Keywords: Electricity market · Electricity sales package · Power load

1 Introduction With the proposal of the 13th Five-Year Plan for electric power development, electricity selling companies have become emerging subjects in the market. The participation of electricity selling companies in market transactions is divided into wholesale side transactions and retail side transactions. On the wholesale side, there are various ways to purchase electricity from the market. On the retail side, electricity selling companies usually sign various forms of electricity price package with users [1]. With people’s livelihood and the rapid development of factories and enterprises, the demand for electricity has increased significantly, with obvious peak and trough periods, and the contradiction between supply and demand is gradually tense. For industrial, commercial and residential loads, the peak and trough periods of electricity consumption © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 814–824, 2023. https://doi.org/10.1007/978-981-99-4334-0_99

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are different. If the same electricity price package is adopted for various users, it will inevitably cause a waste of resources and bring greater economic pressure to the power market [2]. In order to meet the huge demand for electricity, while developing more new electricity price packages, we should also comprehensively analyze the electricity characteristics of various industries, and tailor the most appropriate packages for various industries. Appropriate electricity packages can have a direct impact on users’ electricity consumption behavior. For example, by appropriately raising the electricity price at the peak stage of electricity consumption, and appropriately lowering the electricity price at the low stage of electricity consumption, we can guide users to use the wrong peak of electricity to a certain extent, and adjust their electricity demand by themselves, so as to achieve the effect of valley cutting and peak filling [3]. In order to alleviate the contradiction between power supply and peak imbalance, we should guide the user according to their own demand and reasonably adjust the structure of electricity price, response to electricity structure optimization adjustment. It will make the power load more stable, improve the efficiency, reduce the cost of power supply, at the same time also can get the corresponding compensation as an incentive [4–6]. In terms of demand side resources and pricing, many scholars have made a lot of reports. Literature [7] considered the benefit model of power generation side and power consumption side comprehensively, confirming that adopting demand response can reduce the cost of power generation, and bring certain benefits to users. Literature [8] quantified the economic benefits, environmental benefits and reliability benefits of the system after adopting the demand response measures, which is conducive to the longterm and reliable development of the power system. Literature [9, 10] evaluated the effect of real-time demand response in New England and New York states, but the evaluation results are quite different in the electricity market, user demand and measures. Literature [11] jointly integrated the power generation side and the power consumption side into the power grid and establishes relevant linear models to quantify different response measures, and finally achieve the goal of reducing the power generation cost and environmental cost. Literature [12] built the electricity price discount model on the basis of the Pareto optimization theory, and improved the Pareto model on both the power supply side and the power supply side. Literature [13, 14] analyzed the relationship between various factors of peak and valley electricity price and established the corresponding model, and used Vensim software to verify and compare the pricing strategies and user response results. Based on the above background, this paper studies the pricing strategy of electricity selling companies based on the electricity consumption characteristics of subdivided industries. The study comprehensively considers various power characteristics such as the adjustable capacity of various segments and load transfer characteristics. At the same time, this paper studies a variety of electricity sales package business systems of electricity selling companies, and analyzes the influencing factors of the pricing of electricity selling companies, and finally develops a reasonable electricity price package for each segment industry.

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2 Research on Electricity Consumption Characteristics of Subdivided Industries In this section, Shanghai is selected as a typical case to analyze the power characteristics of industrial load, commercial load and residential load. The specific indicators of electricity characteristics include adjustable capacity, load transfer capacity and duration (h). 2.1 Evaluation of Industrial Load Power Consumption Characteristics Main characteristics of industrial electricity consumption are large demand, and the daily electricity consumption is relatively uniform, but the load of a day will vary with the different production shift system and products, and is less affected by external conditions and holidays. By analyzing the characteristics and laws of different industrial electricity consumption, tapping the potential of demand side load response, guiding large industrial users to participate in load regulation, peak load filling of power grid and promoting the consumption of clean energy [15]. In this section, some typical industry enterprises in Songjiang District are selected for investigation and investigation, to evaluate the electricity characteristics in the production activities of various industries. The field research method adopts the field investigation and inquiry to obtain the enterprise customer information, production information and load information, and the electricity characteristics are as follows (Table 1). Table 1. Electricity consumption characteristics of industrial load subdivision industry in Shanghai Load class

Adjustable capacity

Load transfer capacity

Duration /h

Metal products industry

About 5–10%

Within 5%

0–0.5

Rubber and plastic products About 10–20% industry

About 5–10%

0.5–1

Water production and supply industry

About 10–20%

About 5–10%

0–0.5

Oil, coal, and other fuel processing industries

About 5–10%

Within 5%

0–0.5

Pharmaceutical manufacturing industry

About 5–10%

About 5–10%

0–0.5

Black metal smelting and processing industry

About 15–20%

About 5–10%

0.5–1

Textile industry

About 20–30%

About 10–20%

1–2

It can be seen that some industries in industrial production have a strong load transfer capacity, mainly concentrated in the industries which have convenient shift system adjustment and process adjustment. Because the adjustable capacity and load transfer are positively correlated, the adjustable capacity of these industries is also large [16].

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2.2 Evaluation of Commercial Load Power Consumption Characteristics Although the proportion of the commercial load in the power load is less than that of the industrial load, the lighting load in the commercial load occupies the peak period of the power system. In addition, the commercial sector will increase its business hours during holidays, thus becoming one of the important factors affecting the power load in holidays [13]. We still use the field research method, visit the major shopping malls and service agencies in Shanghai, and get the electricity characteristics of various industries are as follows (Table 2). Table 2. Electricity consumption characteristics of commercial load subdivision industry in Shanghai Load class

Adjustable capacity Load transfer capacity Duration/h

Realty industry

About 10–20%

About 5–10%

0.5–1

Transportation, storage, and postal About 10–20% services

About 5–10%

0.5–1

Wholesale and retail

About 30–35%

About 10–20%

0–0.5

Leasing and business services

About 10–20%

Within 5%

0.5–1

Health and social work industry

About 5–10%

Within 5%

0–0.5

Most of the commercial load belongs to the three-level load. Air conditioning, lighting and other electrical equipment is usually open from operating in the morning to leaving work at night. In order to ensure the comfort of the shopping mall to attract the flow of people, most electrical equipment runs at full capacity for a long time. Therefore, if a part of the load is reduced in a short time and the opening time of some load is transferred, it will have little impact on the overall shopping mall. Therefore, in the commercial load, most industries have a large adjustable capacity. Therefore, it is of great significance to set up reasonable electricity price packages for various commercial industries to load power and promote the consumption of new energy. 2.3 Evaluation of Residential Load Power Consumption Characteristics Household home appliance load equipment can be divided into three types: uncontrollable home appliances, non-constant static controlled home appliances, constant static and controlled home appliances, among which constant static controllable home appliance load (such as air conditioning, water heater), with energy storage function. Controlled home appliances have the characteristics of regular electricity consumption time, so that the electricity consumption can be transferred to the low peak period of the power grid by appointment and other ways, and the transfer capacity is strong. By analyzing different electrical electricity consumption rules and the overall situation of residential electricity consumption, and setting a reasonable electricity price, the majority of residential users can participate in the regulation of the power grid (Table 3).

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Table 3. The total adjustable potential of Shanghai residential load separation equipment Load categories

Load class

Adjustable capacity

Load transfer capacity

Duration/h

Home appliance load

Air-conditioning

About 30–50%

About 10–20%

0.5–1

Water heater

About 30–50%

About 20–30%

1–2

Washing machine

About 20–30%

About 10–20%

0.5–1

Ice box

About 20–30%

About 5–10%

0–0.5

Lighting

About 5–10% About 5–10%

0–0.5

Distributed energy storage

About 30–50%

1–2

Electric vehicle

About 5–10% About 20–30%

Emerging load

About 30–50%

0.5–1

3 Basic Electricity Selling Business System of the Electricity Selling Company 3.1 Fixed-Rate-Type of Electricity Price Package Fixed-rate-type of electricity price package means that the electricity price remains unchanged within a certain contract period. Generally speaking, the contract period of this kind of package is relatively long, which is the mainstream product of selling electricity package. The advantage of such packages is that even if the energy prices rise and the power generation rate rises, the electricity price can remain unchanged during the contract period, and the risks of the energy market are borne by the electricity selling company regardless of the customer. However, it also has corresponding disadvantages. If the cost of power generation decreases, the electricity price during the contract period cannot be changed. At the same time, if you want to cancel such packages within the contract period, you generally need to pay for the corresponding consumption. Fixed rate class electricity price package mainly includes fixed unit price package and fixed total price package. “Fixed unit price package” refers to the electricity price per kilowatt-hour remaining unchanged during the contract term, while the fixed total price package means that the total price of electricity consumption per year or per month remains unchanged during the contract term. “Among them, the fixed unit price package can be divided into a single rate price package and two rate price package”. (1) Fixed unit price package: In terms of electricity price formulation, take the North American Direct Energy, a company package called Live BrighterTM 12-Fixed, as an example. The package service area is in the CenterPoint area, and the pricing formula is: P = (Cb + Ce + Cd )/Q

(1)

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P is the average electricity price, cents/kWh; Cb is basic cost, USD; Ce is electricity cost, Ce = Pe · Q; Pe is electricity rate, cents/kWh; Cd is transmission and distribution cost, Cd = Pd ·Q+cd , Pd is transmission and distribution rate, cents/kWh; cd is monthly basic transmission and distribution cost, cents; Q is monthly electricity consumption, kWh. (2) Fixed total price package: The fixed total price package is relatively simple. It stipulates that the total monthly/annual electricity price is C, and the annual/monthly electricity fee is C no matter how much the user consumes annually/month. The fixed total price package is suitable for residential and industrial and commercial users who may exceed the electricity consumption in some months, or riskaversion industrial users with poor tolerance for price fluctuations. In addition, such price packages are conducive to attract some large industrial customers with relatively stable electricity consumption at a reasonable, stable and small-risk price, and have a certain differentiation advantage in occupying the market share. 3.2 Variable Rate Type of Electricity Price Package There are many types of variable rate packages, and there are many pre-date price index packages and real-time price index packages. In the current electricity price index package, the monthly electricity price is not fixed, and it is related to the open current market unified clearing price index. The reference price is the arithmetic average of the hourly clearing price of the market unified settlement point before the electricity month called Pda,t . Suppose the index price before the set month is Pda , the linkage proportion coefficient is Kda and the monthly electricity fee C of the user with monthly electricity consumption Q is calculated as: n Pda,t (2) Pda = 1 n C = Pda × Kda × Q

(3)

3.3 Demand Response Type Electricity Price Package Demand response category electricity price packages are divided into time-sharing pricing category and real-time pricing category. Time-sharing pricing refers to the types of having different electricity prices designed in different time periods, while real-time pricing is linked to wholesale market prices, and hourly pricing is based according to market changes. Real-time pricing type of electricity sales packages are more suitable for enterprises with high risk tolerance and good budget. (1) Time-sharing pricing type of electricity price package: Take Direct Energy’s weekend free package Free Power Weekends 12-Indexed products as an example, the package service area is CenterPoint area. The Direct Energy Company pricing formula is: P = (Cb + Rd · Ce + Rd · Cd )/Q

(4)

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Rd is the ratio of electricity consumption to monthly electricity consumption during the time period from 12:00 a.m. to 5:59 p.m. on Friday of the month, which is determined by the actual electricity consumption of each user. (2) Real-time pricing of electricity price package: Take the index product launched by Griddy Energy as an example. The package service area is CenterPoint area and the pricing formula is:   (5) P = Cm + PR−T · Q + Cp + Cd /Q Cm is service fee for the membership, The company’s residential user membership service fee is $9.99/month, Membership service fee of small commercial users is divided by electricity consumption level: within 5000 kWh, the cost is US $9.99; at 5000–15,000 kWh, the cost is US $99; At 15,000–30,000 kWh, the cost is US $199; at 30,000–60,000 kWh, the cost is US $299; above 60,000 kWh, users can negotiate with the company to set the exclusive price. PR−T is for the real-time electricity market wholesale transaction cost price, Cent/kWh. ERCOT in Real-Time Market update Trading Prices per 5 min, user accounts every 15 min, including power generation costs, system operation and maintenance costs, and power supply reliability costs, The company has no markup part. To pay the handling fees, The company uses third-party payment platforms for real-time electricity market settlement for every 15 min. (3) Seasonal electricity price package: In view of the price of Guangdong power market is affected by seasonal factors such as power transmission from west to east, and adapted to the demand of users with seasonal production characteristics, according to the unit price of Psp, Psu, Pau, Pwi in spring, summer, autumn, winter and users, and the monthly electricity consumption of users is Q, and the monthly electricity fee C is calculated as 1. The settlement month is March, April and May: C = Psp × Q 2. Settlement month is June, July and August: C = Psu × Q 3. Settlement month is September, October and November: C = Pau × Q 4. The settlement month is December, January and February: C = Pwi × Q. 3.4 Volume and Price Linkage Package (1) Time-sharing pricing type of electricity price package: The ladder package of quantity and price linkage can be set as stepped increasing price or stepped decreasing price, and the electricity value standard of different steps and the corresponding price price standard are set in stages. The rule of monthly electricity charges is: C = P1 × Q1 + . . . + Pi × Qi + . . . + Pn × Qn

(6)

(2) Minimum consumption package: The minimum consumption package sets the electricity threshold Q0 and the minimum consumption amount C0, and the monthly electricity consumption Q exceeds Q0 is charged by the excess electricity price P. The rule of monthly electricity charges is:   Q < Q0 C0 , C= C0 + P × (Q − Q0 ), Q ≥ Q0

(7)

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The design of the minimum consumption limit refers to the large users whose electricity consumption is paid according to the minimum consumption amount when it is below a certain threshold value, which is suitable for large industrial users with large electricity consumption fluctuations.

4 Research on the Influencing Factors of Electricity Selling Pricing of Electricity Selling Companies 4.1 Selection of Industrial Load Electricity Sales Package As can be seen from the daily load curve of various industries in the industrial load, most industries adopt the three-shift system, and the daily load curve is basically in the zigzag wave of “two peaks and two valleys”. The “Two peaks” refers to the morning peak electricity consumption and the afternoon peak electricity consumption. The “two valleys” refers to the electricity trough during the lunch break and at night. In pharmaceutical manufacturing, for example, the maximum load is at 15:45. The 90% daily maximum load period is 9:00–11:30 and 13:45–16:00. At 18:30–23:00 p.m., the load had been decreasing, and the decline was fast, and the load had decreased slightly from 0:00 to 7:00 a.m., but the decline was slow. The peak-valley difference rate of this industry is relatively large, reaching 70.34%, and the proportion of valley electricity is much smaller than that of peak power. Peak-valley electricity price package is a kind of Time-sharing pricing type of electricity price package price package. It is suitable for users with obvious peak and valley characteristics and large elasticity of peak and valley power adjustment, but also suitable for industrial users who can flexibly adjust the large production volume in the time period. Since most of the industrial load curves analyzed above have the characteristics of “two peaks and two valleys”, and these industries have large adjustable capacity and strong load transfer capacity, and can adapt to the elasticity of electricity price adjustment in different periods, so these industries can adopt the peak-valley electricity price package. We can predict the load curve according to the previous load situation, and then price it separately according to the peak period and the valley period of the forecast curve to meet the production demand. The production characteristics of some other segments of the industrial load are not regular. The characteristics of the daily load curve of chemical raw materials and chemical products manufacturing industry can be roughly summarized as “four peaks and four valleys”, and the load curve of metal manufacturing industry is roughly “two peaks, one flat and two valleys”, while the load curve of mechanical products manufacturing industry is similar to that of metal manufacturing industry. But the load curves of these industries fluctuate greatly, and their adjustable capacity and load transfer capacity are much weaker than the other industrial loads. Unable to adapt to the electricity price elasticity brought by the peak-valley packages. Therefore, this kind of industry is suitable for the lowest electricity price package in the volume and price linkage package. When the electricity consumption is below a certain threshold, the minimum consumption amount will be paid (Table 4).

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Load class

Use of electricity sales packages

Metal products industry

Minimum price package

Rubber and plastic products industry

Peak valley electricity price package

Water production and supply industry

Peak valley electricity price package

Oil, coal, and other fuel processing industries

Peak valley electricity price package

Pharmaceutical manufacturing industry

Peak valley electricity price package

Black metal smelting and processing industry

Peak valley electricity price package

Textile industry

Peak valley electricity price package

4.2 Selection of Commercial Load Electricity Sales Package By clustering the daily load curve of the users in various industries of the commercial load, it can be found that most of the industry load becomes the “peak-type” load curve, and they all have single-peak characteristics. Take the administration and office industry as an example, the maximum daily load appears at around 13:00, with a high load at 10– 18, all reaching 90% of the maximum daily load. The load has been falling continuously at 18:30–23:00 p.m., and it has dropped more rapidly, decreasing slightly from 0:00 to 7:00 a.m., but more slowly. For this kind of industry load, we can use real-time electricity price packages. Since such industries are also heavily affected by holidays, we can learn from Griddy Energy’s packages to set reasonable electricity prices for these industries. Member service fee is set for the industry load, and the member service fee is divided according to the electricity consumption level. The specific division method can be negotiated with the company to set the exclusive price. Transaction prices are updated for every 5 min s in the realtime market, and users are settled for every 15 min s, including power generation costs, system operation and maintenance costs, and power supply reliability costs (Table 5). Table 5. Selection of electricity sales package in commercial load subdivision industry Load class

Use of electricity sales packages

Realty industry

Real-time electricity price package

Transportation, storage, and postal services

Seasonal tariff package

Wholesale and retail

Real-time electricity price package

Leasing and business services

Real-time electricity price package

Health and social work industry

Seasonal tariff package

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5 Conclusion This paper proposes a pricing strategy for selling companies considering the electricity consumption characteristics of subdivided industries, which provides new methods and new ideas for the formulation of their electricity sales strategy. This paper takes various industries in Shanghai as the scene, takes the largest profit and the least risk as the target, and matches the electricity sales package of each subdivision industry. In terms of electricity consumption characteristics of the industry, field research is used to calculate the adjustable capacity and load transfer characteristics; in the package design, a series of electricity price packages are designed and classified into five categories; in the industry electricity sales package selection, considering the wholesale market electricity price, user situation, user satisfaction and market share of electricity sales companies, combining the daily load curve and annual load curve of reasonable industry. With the gradual opening of the electricity sales side, in order to maintain the market share and enhance the user stickiness, it is necessary to provide more abundant electricity sales packages, further expand the business, and fully call the user side resources to participate in the auxiliary service market and capacity market. This article will further conduct in-depth research on the strategy of the electricity sales company.

Authors’ Background 1. This form helps us to understand your paper better, the form itself will not be published. 2. Title can be chosen from: master student, Ph.D. candidate, assistant professor, lecture, senior lecture, associate professor, full professor. Your name

Position

Research field

Zining Wang Company employee Chemical industry Sheng Bi

Engineer

Power market

Haotian Xu

Master student

Power market

Ciwei Gao

Professor

Power demand side management and demand response, power market and power regulation, energy Internet and power planning

Hao Ming

Associate researcher Power market, demand side response, big data analysis

Personal webpage

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References 1. Wang, L., Zhang, Zhang, F., Jin.:Sales business decision and risk assessment. Power Syst. Autom. 42(01), 47–54 + 143 (2018) 2. Di, W., Zhiqiang, H., Qinglan, C.: The role of demand response in the electricity market. Power Demand Side Manage. 02, 71–73 (2007) 3. Zhang, N., Lu, J., Dai, H.: Prospect of flexible resources of China’s power system under the coordinated development of source network, load and storage. China Electric Power Enterprise Manage. 16, 44–47 (2020) 4. Zeng, L.: Study on demand-side aggregate load collaborative control strategy. North China Electric Power University (Beijing) (2019) 5. Zhang, Y.: Energy internet optimization operation study. Zhejiang University (2019) 6. Wu, C.: Demand response system based on electricity consumption behavior analysis. Shandong University (2019) 7. Zhao, H., Zhu, Z., Yu, E.: Basic load calculation method and demand response performance evaluation of power market users. Power Grid Technol. 19, 72–78 (2019) 8. Ding, W., Yuan, J.: Peak-valley TOU electricity price decision model based on user price response and satisfaction. 29(20), 10–14 (2005) 9. Huang, J., Huang, X., Shao, L., et al.: Peak-valley TOU price model and simulation-(I) model establishment. Power Syst. Autom. 30(11), 18–23 (2006) 10. Huang, J., Huang, X., Shao, L., et al.: Establishment of peak-valley TOU model and simulation-(II) model based on system dynamics. Autom. Electric Power Syst. 30(12), 23–26 (2006) 11. Yunwei, S., Yang, L., Ziwei, G., Lei, Z.: The application of demand response in the power auxiliary service market. Power Syst. Autom. 41(22), 151–161 (2017) 12. Xiao, D., Wang, C., Zeng, P., et al.: Review of power system flexibility and its evaluation. Power Grid Technol. 38(6), 1569–1576 (2014) 13. Tao, S., Lingzhi, Z., Ruoying, Y.: Review of power system flexibility evaluation research. Power Syst. Protect. Control 44(5), 146–154 (2016) 14. Wang, J., Li, Y., Jinwu, B., et al.: Cost-benefit analysis of the impact of demand-side bidding on peak electricity price. China Electric Power 39(1), 31–35 (2006) 15. Huang, X., Li, J., Yang, L.: Virtual power plant multiple power supply capacity configuration based on the portfolio. Autom. Electric Power Syst. 10, 1–6 (2015) 16. Skarvelis-Kazakos, S., Papadopoulos, P., Grau, I., et al.: Carbon optimized virtual power plant with electric vehicles. In: 45th International on Universities Power Engineering Conference (UPEC), pp. 1–6. IEEE, Cardiff, Wales (2010)

Credit Risk Evaluation of Power Users in Power Sales Package Recommendation Wei Xia1(B) , Sheng Bi2 , Ciwei Gao3 , Meihui Jiang4 , and Hao Ming3 1 Marketing Department, Huadian Jiangsu Energy Co. Ltd., Nanjing, China

[email protected]

2 Power Market Research Center, Huadian Electric Power, Research Institute Co., Ltd.,

Hangzhou, China 3 School of Software, Southeast University, Nanjing, China 4 School of Electrical Engineering, Southeast University, Nanjing, China

Abstract. As China’s economic development enters a new stage, many factors such as the transformation of economic structure and changes in growth rate are highlighted. Power companies often encounter situations such as customers defaulting on their electricity bills, which prevent them from recovering their costs in time and lead to problems in the flow of funds, phenomenon that adversely affects the operation and investment development of power supply companies. Therefore, utility companies need to consider the credit history of power users and correctly assess their credit risk factors when recommending joint retail packages to them. In this paper, we firstly construct a credit risk evaluation system based on logistic regression algorithm, and secondly construct a credit evaluation index table based on the credit evaluation constituents of power users. In addition, the credit scores for consumers are calculated through operations such as splitting boxes, and finally evaluate the credit scoring effect through the mixture matrix and ROC statistics. Keywords: Credit risk evaluation · Power sales package

1 Introduction For a long time, the research on the behavior of power users has been mainly centered on electricity consumption habits, load characteristics, abnormal behavior, etc., and user analysis is conducted using the electricity consumption behavior data generated by power users. The behavior of power users includes not only power characteristics such as load size and periodic characteristics, but also the behavior of power user subjects in the credit dimension, etc. [1]. Therefore, when power companies analyze the data of electricity users, they can only evaluate the data related to the electricity dimension, but cannot measure the goodness of an electricity user in an all-round way. Besides that, since they cannot distinguish between potential users and poor users, so that they cannot provide the best power supply solution according to their own needs and the needs of users. The © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 825–836, 2023. https://doi.org/10.1007/978-981-99-4334-0_100

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evaluation of customer credit information enables power supply companies to evaluate the credit of customers before trading with them and to classify customers based on their credit risk, so as to clarify key and high-quality customers. In 1909, the Moody’s Corporation in the “Analysis of Railway Investments” reported the first credit rating of railway bond repayment at maturity. Since then, credit rating is increasingly used in a variety of financial systems, mainly as a bank for the loan enterprise customers credit rating evaluation. Nowadays, the early warning function of credit evaluation has been widely used in engineering applications, natural sciences, social sciences, etc. In 2004, the “Electricity Charge Recovery Early Warning and Handling Method” was issued to provide early warning of power risks. Power companies at all levels responded positively, adopted corresponding credit early warning mechanisms for enterprises that often experience dishonesty, and limited corporate risks by collecting deposits in advance. Ningning [2] proposes credit indicators and user payment ability based on the credit assessment scheme, constructs a user credit assessment system, and proposes risk prevention measures based on the assessment results. However, the construction of credit risk evaluation system for electricity users is still lacking and has not yet been widely popularized. With the release of the “New Electricity Reform Document No. 9”, the reform of electricity system has been further deepened. In the exploratory stage of reform, the market competition is becoming increasingly fierce, and power supply enterprises will change their existing profit model and gradually transform into a self-operating and self-financing business model. At that moment, power supply enterprises will pay more attention to the estimation and control of business risks [3]. Credit scoring models consist of two categories, traditional mathematical and statistical methods and artificial intelligence methods. In recent years, although artificial intelligence methods are increasingly used in credit scoring, they are not yet sophisticated. For instance, SUV training models take a long time and are difficult to explain. Although the predictive ability of logistic regression is not as good as that of artificial intelligence methods, it has strong interpretability and short training time for the model. Based on the immaturity of AI methods described above, logistic regression plays a key part in the progression of credit scorecards. To sum up, this paper adopts the logistic regression method to establish the credit scoring model [4]. Based on the above background, this paper studies the establishment of a credit scoring model for power user data analysis in the process of power sales package recommendation. It examines the transaction risk between power sales companies and power users. First, through the credit information of power users and their credit behavior in the process of purchasing and consuming electricity, a credit scoring index system of policy index dimension and economic index dimension is constructed. Secondly, a score card is made for the credit of power users, and each feature is classified. Through binning, users can be classified into different credit categories based on their different attributes, and the “good”, “bad” rating information of power users can be obtained. The logistic regression algorithm is used to construct a credit risk evaluation system based on the credit evaluation indicators of power users. Finally, the user credit scoring effect is comprehensively evaluated through statistics such as mixed matrix and ROC curve.

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2 Risk Evaluation Index System of Credit Scoring for Power Consumers on the Electricity Sales Side 2.1 Design Principles of Credit Evaluation System for Power Users This paper focuses on the credit evaluation of power users in the process of recommending power packages on the power sales side, and examines the problem of transaction risk between power sales companies and power users. The power users involved in this paper are mainly small and medium-sized enterprises, so the credit performance of power users in the process of purchasing and using electricity, as well as the size and business status of the enterprises themselves. Historical credit information and other aspects are considered [5]. The evaluation index construction of the evaluation model needs to meet the principles of comprehensive, operability, observability, quantifiability and flexibility. Just because a credit scoring model has been established does not mean that the model is valid. An established scorecard model can be considered valid only if three basic conditions are met. These three requirements are meaningfulness, accuracy and robustness. Commonly used methods to test these three requirements include mixed matrices, lift curves, ROC statistics, Gini statistics, KS statistics, etc. 2.2 Construction of Credit Evaluation System for Power Users Taking into account the relationship between the composition of risk factors faced by power companies on the electricity sales side and the credit score of electricity users, in the process of construction of the indicator system, the indicators of risk composition related to the credit of users are selected. Combining the principles of the construction of the evaluation index system, we constructed credit scoring indicators of the policy indicator dimension and the economic indicator dimension. Among them, the policy indicator dimension measures the credit problems of electricity customers in terms of policies, and the economic indicator dimension measures the business status and economic strength of electricity customers, which serves as a guarantee for their ability to repay electricity bills. The specific index system structure, as well as the meaning and data characteristics of each index, are shown in Table 1. 2.3 Using Logistic Regression to Create Credit Score Cards The attributes of the electricity users studied in this paper are SME users, which are similar in economic nature to SMEs that take loans from banks in the financial field, so the credit scorecard of electricity users is made by using logistic regression, a wellestablished method in the financial field. Since logistic regression returns a classification result that is not a fixed 1,0, but a probability number in the form of a decimal number, logistic regression can not only give a good or bad customer, but also provide a specific “credit score” when using logistic regression. In addition, logistic regression performs well on small data sets, which can exclude the disadvantages of small number of users and insufficient data [6].

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Module name

Indicator code

Indicator name

Policy information

env

Environmental requirements

pro

Industrial policy

10

pen

Administrative penalties

15 15

Business information

Weight (%) 5

sco

Company score

typ

Business type

5

sca

Enterprise size

5

sta

Business status

20

mor

Bank loan information

25

3 Construction of Specific Evaluation Indicators 3.1 Logistic Regression Model Top-m index: The probability of the event (y = 1) was calculated using the logistic regression model as: Pr{y = 1} =

exp(β0 + β1 x1 + · · · + βr xr ) 1 + exp(β0 + β1 x1 + · · · + βr xr )

(1)

where the constants β0 , β1 , · · · βr represent the parameters of the model and the constant β0 indicates the intercept term. In addition, the predictor variable x is written in the shape of an r + 1 dimensional vector based on the parameter β as follows: X T = [ 1 x1 · · · xr ]

(2)

β T = [ β0 β1 · · · βr ]

(3)

The form of logistic regression can be expressed as follows: Pr{y = 1} =

1 1 + exp(−β T x)

(4)

By writing the probability of the event at y = 1 as p and simplifying the symbols in the above formula, the formula can be written as: p=

1 1 + e−z

(5)

where: z = βT x

(6)

Credit Risk Evaluation of Power Users

Converting Eq. (5), we obtain:

 ln

p 1−p

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 =z

(7)

A classical method for building logistic regression models is the great likelihood estimation. The posterior probability of a single sample is: p{y|x, β} = (hβ (x))r (1 − hβ (x))1−r

(8)

The Log likelihood function is: l(β) =

m 

y(i) log(h(x(i) )) + (1−y(i) ) log(1 − h(x(i) ))

(9)

i=1

The solution is solved by gradient descent, thus iterating until convergence: (i)

βj = βj + α(y(i) − hβ (x(i) ))xj

(10)

3.2 Mixed Matrix Mixed matrix: credit scoring is actually using the historical information of existing customers to train to get a model, and then using the model to predict how a new customer will be. In short, it is to classify new customers as good or bad according to their various types of information. A good logistic regression model is one that precisely predicts those who are actually good customers as good customers, and those who are actually bad customers as bad customers. Of course, there may be cases where the model predicts the actual good customers as bad customers, and the actual bad customers as good customers. If we want to know how many predictions are correct and how many are wrong, the confusion matrix can show us this information. These results are organized into a matrix, which is shown in Table 2. Table 2. Mixed matrix True value Predicted value

P

N

P

TP

FP

N

FN

TN

True Positive: TP, that is, the actual is normal forecast also for normal customers False Positive: FP, that is, customers who are actually default forecast but are normal False Negative: FN, that is, customers who are actually normal forecast but are in default True Negative: TN, that is customers who are actually default predictions are also in default

The accuracy of the model prediction can then be derived from this matrix, and the formula is: TP + FN (11) Accuracy = TP + FN + FP + TN

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where a higher Rate value means a better model. 3.3 ROC Curve and Statistics Receiver Operating Characteristic Curve (ROC): the ROC curve is a typical method of evaluation for dichotomous models, and is used to assess the classification performance of the model. The ROC curves and statistics were obtained based on the mixing matrix above [7]. True Positive Rate: Depict the model’s ability to identify normal customers and is also referred to as sensitivity. TPR =

TP TP + FN

(12)

False Positive Rate: What is portrayed is the ability of the model to misclassify defaults as normal customers: FPR =

FP FP + TN

(13)

True Negative Rate: Also known as specificity, the horizontal axis of the ROC curve is 1-specificity(false positive class rate), and the vertical axis is sensitivity (true class rate): TNR =

TN = 1 − FPR FP + TN

(14)

4 Comprehensive Evaluation Method of Credit Model 4.1 Data Indicators From Eqs. (12) and (13), the larger the vertical coordinate is, the smaller the horizontal coordinate is, so the larger the area under the ROC curve is, the better the area under the ROC curve is called the AUC value, and the larger the AUC value is, the better it is. The closer the ROC is to the coordinate (0, 1), the better the model proves to be in identifying good and bad [8]. For the sake of judging the merits of the proposed credit scoring model, this paper measures the prediction effectiveness of the model using the accuracy, F1, KS, and AUC values based on the confusion matrix shown in Table 1. Assuming that TP denotes the number of non-defaulting enterprises discriminated as non-defaulting enterprises, FN denotes the number of non-defaulting enterprises discriminated as defaulting enterprises, FP denotes the number of defaulting enterprises discriminated as non-defaulting enterprises, and TN denotes the number of defaulting enterprises discriminated as defaulting enterprises, the model’s collated discriminant Accuracy, Recall, True FPR, Precision, FI, KS are as following: Recall = TPR =

TP TP + FN

(15)

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Precision = FI = 2 ×

TP TP + FN

Precision × Recall Precision + Recall

KS = max(TPR − FPR)

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(16) (17) (18)

4.2 Evaluation Index Weighting Determination Among them, the Accuracy shown in Eq. (11) reflects the prediction accuracy of the model as a whole, but does not reflect the classification effect of each of the positive and negative samples. Especially in unbalanced credit evaluation data with a high proportion of non-default, it may occur that all samples are predicted as non-default samples with a high Accuracy condition. In this case, the Accuracy discriminant will fail. To address this issue, studies have used other metrics to measure the performance of the model. These include Recall and Precision shown in Eqs. (11) and (16), both of which focus on the correct classification rate of non-defaulted samples. The FI value shown in Eq. (17) is the summed average of both Recall and Precision, taking values from 0 to 1. FI is a composite response to classification effectiveness [9]. Since the credit score prediction result is a probability value, the calculation of both Accuracy and FI needs to set a threshold value to determine the default sample, and the different threshold values are directly related to the classification effectiveness of the evaluation model. To solve this problem, KS value and AUC value are added in this paper to evaluate the model performance. The KS value shown in Eq. (18) fully considers the model’s ability to discriminate between non-default and default samples, and this indicator does not need to set a threshold in advance. The KS value is equal to the maximum difference between the true rate (TPR) of Eq. (11) and the false positive rate (FPR) of Eq. (11); the larger the KS value is, the better the model’s ability to discriminate [10]. 4.3 Metrics for Comparing the Performance of Credit Decision Models There are various metrics available here to compare the performance of credit decision models, such as accuracy, Gini coefficient, and area under the ROC curve (AUC). When evaluated, Accuracy does not work well in unbalanced datasets. For example, If there are 10,000 samples in the data set, 9990 of them are all positive and only 10 are negative. If all predictions were positive, the accuracy would be 99.9%. Despite the high accuracy of the predictions, this does not mean that the model works very well. The AUC value can better represent Type I error and Type II error, while other metrics (e.g., Gini coefficient) are hard to achieve. Whereas the Gini coefficient is often applied to construct decision trees to judge the goodness of a model by the entropy value of the target, although it can be used to compare the performance of multiple algorithms; the AUC value is clearly more relevant for measuring credit risk class metrics. Taking FPR and TPR as the horizontal

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and vertical coordinates respectively, the line connected on the coordinate axis can get the AUC curve, and the area enclosed by the ROC curve and the horizontal coordinate is called AUC (Area under curve). Commonly, the AUC curve is above the line y = x, therefore, the value of AUC ranges from 0.5 to 1. The larger the number is, the better the model is in discriminating small business default and non-default. In this paper, the AUC value is used as the training target when the parameters are optimized. When the results are tested, Accuracy, FI, KS, and AUC will be applied for comparison. For example, in Fig. 1. The area AUC1 of curve 1 is larger than the area AUC2 of curve 2, so curve 1 works better.

Fig. 1. Comparison of different ROC curves.

1. Case Study In this paper, we cited the classical bank lending credit indicators of small and mediumsized enterprises, plus the contents of the credit evaluation indicator table to construct the total credit evaluation indicator dataset of power user enterprises here. The meaning and data characteristics of each of these indicators are shown in Table 3. Table 3. Enterprise credit evaluation index Indicators

Meaning

SeriousDlqin2yrs

Defining good and bad credit companies

Revolve utilization unsecured lines

Ratio of available loan and credit card amount to total amount

Debt ratio

Monthly debt service divided by monthly gross income

Number real estate loans or lines

Number of mortgages and real estate loans

Environment satisfaction

Whether to meet environmental requirements

Policy satisfaction

Whether to meet the industrial policy

Administrative punishment

Is subject to administrative penalties

Ranking score

Company score

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4.4 Data Pre-processing In this paper, we use 150,000 credit data generated by simulation, and consider that there is no identical data in the display case, so we delete the identical data, likewise, remove the outlier data in connection with the actual situation, and for the missing values, use the random forest algorithm to fill the missing values. After processing, a total of 149,165 credit evaluation index data were obtained. Among all 149,165 data, users with label SeriousDlqin2yrs of 1 indicate default users and users with label SeriousDlqin2yrs of 0 indicate trustworthy users. According to the label distribution of the samples, it is found that default users account for 6.62% and trustworthy users account for 93.38%, which is in line with the normal distribution ratio, but the sample distribution of this dataset is seriously unbalanced, which will lead to the failure to learn the characteristics of default users, so the samples are up-sampled to balance, and the dataset after up-sampling has 278,584 samples;, of which label 1 accounts for 50.00% and label 0 accounts for 50.00%. 4.5 Dividing Boxes According to users’ information, we create scorecards for the credit of small and medium-sized business electricity users, assigning grades to individual characteristics and enabling scoring when a new electricity user enters. A crucial step in the production of scorecards is the dividing of boxes, which disaggregates otherwise Continuous variables, so users can be categorized into different credit categories based on different attributes. The process of discretizing continuous variables causes information loss, and information loss increases as the number of boxes becomes smaller. To scale the information content of the features and the contribution of the features to the prediction function, the banked conceptual information value (IV) is employed here: IV =

N 

(good % − bad %) × WOEi

(19)

i=1

Among them, N is the number of boxes on this feature, i represents each box, good % means the ratio of customers with label 0 in this box to all customers with label 0 in all features, and bad % is the ratio of customers with label 1 in this box to all customers with label 1 in the whole feature. WOEi expressed as:   goodv0 (20) WOEi = ln badv0 This is the weight of evidence (WOE), one metric used by the banking industry to assess the probability of default is basically the logarithm of the ratio of quality customers to non-performing customers. WOE is targeted to a box, and the larger the WOE, the more quality customers are in this box. And IV is targeted the whole features, IV stands for the amount of information of our features and the significance of the contribution of this feature to the model, which is controlled by the Table 4.

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Different attributes of power users have different scores, so we want the people in one box have the same properties, while the users in different boxes have different properties as possible. For the score card, we want all users in a box to have a similar probability of default, while the probability of default for users between boxes is very different. That is, the WOE differences are expected to be large and the bad customers ratio in each box should be different. Therefore, a chi-square test can be applied to compare the likelihood of similarity between two boxes, and if the p-value of the chi-square test among the two boxes is high, then the two boxes are similar. Therefore, these two boxes could be merged into one box. According to on this idea, we performed the following box splitting for power users. Table 4. Enterprise contribution of IV values to the prediction function IV

Contribution of features to predictive functions

< 0.03

Features have almost no useful information and are of no use to the model, such features can be ignored

0.03–0.09

Less useful information, Little use for the model

0.1–0.29

Average effective information with moderate contribution to the model

0.3–0.49

More effective information, more contribution to the model

≥ 0.5

The effective information so high that the contribution to the model is suspiciously high

The variation of the IV values of the sub-different boxes for each feature is shown in Fig. 2.

Fig. 2. Variation of value with number of boxes.

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Based on each of the above plots, the box values that should be selected for each feature are chosen, where the box numbers are chosen based on the principle that the points in the (3, 6) interval, where the turn in the curve is obvious. 4.6 Effectiveness of Credit Model Based on Logistic Regression After the assignment of each sub-box, the next step is to calculate the WOE for each sub-box. We will use the WOE superimposed data for modeling, and hope to obtain the classification results for each sub-box, i.e., the classification results for each rating item on the score card. Therefore, we replace the WOEs into the original data, and after processing the training set, we only need to map the already computed WOEs to the test set if we already have sub-boxes. After processing the training set and the test set, using logistic regression modeling, here we get a score of only 0.7758327749593185, and the learning curve in using max_iter also cannot improve the effect of the model, it looks like the model effect is not good; but considering that the most critical thing about this credit score is to capture the data of abnormal users, so the score measurement effect here is not very convincing, and what is more important to consider is the recall. We draw the ROC curve to find the value of AUC 0.85, which indicates the good effect of the model and the strong ability to capture the special values. The ROC curves as following Fig. 3.

Fig. 3. Credit scoring model ROC curve.

5 Conclusion In this paper, we propose the credit risk information measurement of power users in the power market when the power sales side recommends packages to users. Adding the credit behavior information of electricity users to the behavioral information of users provides new ideas to carve a portrait of electricity users and avoid the risk of power companies. In this paper, we adopt a mature and advanced credit evaluation model in the financial field for small and medium-sized enterprise electricity users, and combine the specific credit index dimensions of electricity users on the electricity sales side to provide

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electricity sales companies with information on the credit behavior of electricity users as a criterion to distinguish good and bad users. The article uses a logistic regression algorithm to establish a credit evaluation model that can specifically portray the user’s credit information, not only limited to distinguishing between good and bad power users, but also provide a specific credit score situation, and verify the effectiveness of the model through arithmetic data. With the further opening of the electricity sales market, the credit risk factors about electricity users will become more important. In this paper, we will continue to study the credit details of the future electricity sales side power companies for customer research and evaluation.

References 1. Qing, H.: Research on retail tariff package pricing for electricity sales companies under spot market. North China University of Electric Power (Beijing) (2021) 2. Ningning, H.: Research on electricity supply company’s electricity security risk early warning model. North China University of Electric Power (2012) 3. Yuzhe, W.: Research and software development of early warning management system for electricity bill recovery risk for large electricity users. Xihua University (2015) 4. Chen, L.: Credit scoring model based on LightGBM-BOA and its empirical study. Northwest Agriculture and Forestry University of Science and Technology (2020) 5. Sen, Y.: Research on the application of credit scoring model for small and micro enterprises base don Softmax regression. Soochow University (2017) 6. Chengxing, L.: Research on the application of logistic regression model in risky user detection of banking financial institutions. Fintech Times (2022) 7. Xingzhi, Z.: Improved SMOTE method based on XGBoost credit scoring model. Netw. Secur. Technol. Appl. 02, 37–41 (2022) 8. Hanley James, A., McNeil, B.J.: The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 144(1), 29–36 (1982) 9. Gastwirth, J.L.: The estimation of the Lorenz curve and Gini index. Rev. Econ. Stat., 306–316 (1972) 10. Kleinbaum, D.G., Klein, M.: Logistic Regression A Self-Learning Text. Springer (2010)

Operating Low Frequency Wind Power System in Variable Voltage Mode Yang Xingang1 , Xiong Xuejun1 , Du Zhaoxin1 , Zhang Yajun1 , Wang Qiming2 , and Jia Feng2(B) 1 State Grid Shanghai Electric Power Research Institute, Shanghai, China [email protected], [email protected], [email protected] 2 Shanghai University of Electric Power, Shanghai, China [email protected]

Abstract. Most of the current research on low frequency wind power systems (LFWPS) directly combines the two main technologies of low frequency AC transmission and variable speed constant frequency (VSCF) wind energy conversion system (WECS), where the low frequency transmission uses a constant voltage to transmit power. This paper proposes a variable voltage low frequency wind power system (VV-LFWPS) scheme, in which the wind farm side voltage provided by the onshore ac–ac station is dynamically varied, with the voltage decrease with decreasing wind speed and increase with increasing wind speed in general. This paper also compares the losses and the fault ride through performance of VV-LFWPS and constant voltage LFWPS (CV-LFWPS). The electromagnetic transient simulation shows the superiority of VV-LFWPS. Keywords: Offshore wind power · Low frequency transmission · Power loss · Fault ride through

1 Introduction Low frequency transmission is a new solution for distant offshore wind power system. Existing low frequency wind power system uses constant voltage to transmit electric power [1]. Since the wind power is a cube of the wind speed, and the onshore ac-ac station has flexible control capability, operating the transmission voltage at a constant and high level is not necessary, and may bring the following disadvantages [2]: (1) the wind farm point of common coupling (PCC) has been maintained at a high voltage level, the transient process under fault condition is violent, which make the fault ride through difficult; (2) when the wind speed is low, the electric power and terminal voltage of generator is low, but the relative high voltage of wind farm PCC calls for a high dc-bus voltage of back-to-back converter of wind energy conversion system, which make the switching loss very high. This paper attempts to make the transmission voltage change approximately linearly with the wind speed, or more accurately with the stator voltage of the wind generator, in order to improve the above problems. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 837–843, 2023. https://doi.org/10.1007/978-981-99-4334-0_101

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Intuitively, when transmitting the same power, lower transmission voltage means greater current and copper loss, but this does not take the effects of the capacitive charging current of the cables and the star link reactance of the modular multi-level converter (MMC) station into account [3]. This paper proposes a control method for variable voltage low frequency wind power systems, and the dynamic minimum dc-bus voltage technology [4] is used to reduce the power loss of back-to-back converter of the WECS, the above research has been verified by electromagnetic transient simulation.

2 Control Methods of Variable Voltage LFWPS 2.1 Variable Voltage Control Method of the Onshore AC–AC Station Currently, the mainstream offshore WECS adopts permanent magnetic synchronous generator (PMSG) and full power converters. The back-to-back MMCs can be used as the onshore ac-ac station of LFWPS, in which the grid side station generally adopts the double-loop control strategy [5] to control the DC voltage and the reactive power output to the grid, and the wind farm side station adopts a V/f control to provide a constant voltage for wind farm (Fig. 1). In this paper, the voltage of PCC provided by the wind farm side station U pcc is set to drop along with the stator voltage of PMSG, U g . As U g is proportionate to generator speed ωg , and ωg is proportionate to wind speed v in maximum power point tracking (MPPT) mode, so U pcc will decreases linearly with v. Since the wind power is a cube of the wind speed, the current of the generator and the transmission line will not exceed its rated value in overall wind speed region, as illustrated in Fig. 2. Both LFWPS use a transmission frequency of 20Hz. Under the MPPT control of the WECS converter, the two LFWPS have the same rotational speed and generator voltage U g at the same wind speed, and therefore, the active power Pe are also the same when the losses are ignored. The difference is that U pcc of the VV-LFWPS decreases with wind speed, although the generator phase current I g may rise slightly, but the reduced U pcc may be beneficial in reducing transient shocks caused by grid fault. In addition, for the back-to-back converter of WECS, when the voltages of the two AC ports are reduced almost simultaneously, the DC bus voltage of WECS converter can be reduced in a wide range following the wind speed when applying the dynamic minimum dc-bus voltage technology proposed in [4]. The reduced DC bus voltage is beneficial for reducing the converter electromagnetic stress, dV /dt and the switching losses [4]. The variable voltage control method is as follows: Firstly, the wind farm side converter station receives the minimum voltage demand at the current common connection point of the wind farm, then multiplies it by the ratio of step-up transformers nWT and nWF , and then a margin factor kmargin (kmargin is a number slightly greater than 1). A low-pass filter and a limiter is used to limit the change rate and range of voltage signals. The upper limit of the limiter is the nominal voltage Un , the lower limit Umin of the limiter is set to be 0.4 Un . Finally, the rated frequency fref is integrated to obtain θref , and

Operating Low Frequency Wind Power System lim U FC1

Communication networks

n WT

us1

1:n WT RSC

U

lim FC2

Direct drive

n WT

GSC WCES1

us2 GSC

WCES2

U lim

Communic ation Sender

Low frequency transmission lines

1:n WF

us3

n WT

Max

MMC1 MMC2 Wind farm side Grid side station station

Wind farm step-up transformers

1:n WT RSC

lim U FC3

DC connection link reactance

us4

Power collection systems

1:n WT RSC

GSC

us5

U FC5

U

1:n WT RSC

lim

GSC

U

n WT

f ref

kmargin

n WF

Integrator 2 Low-pass filtering

U min

WCES5

lim FCn

AC DC voltage control, reactive power control

Un

WCES4

n WT lim

Electricity network

DC

GSC WCES3

n WT

AC

1:n WT RSC

lim U FC4

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U ref

Equation (1)

Valve level control

K

usn

Communication Receiving end

1:n WT RSC

U ref =U n 1

CV-LFWPS mode: K=1 VV-LFWPS mode: K=2

GSC

WCESn

Fig. 1. General view of the system

Ig/pu

Pe/pu udc/ kV UPCC/pu fPCC/Hz Ug/ V

ωg/pu

constant speed variable speed region region (MPPT)

rated power region

1.0

CV-LFWPS VV-LFWPS

0.7 0.4 690 483 276 20 15 10 1.0 0.7 0.4 1.10 0.77 0.44 1.0 0.5 0 1.0 0.5 0

vcutin

v1

vn Wind speed

vcutout

Fig. 2. Dynamic voltage simulation results

then the above voltage reference signal Uref and θref are used to generate the reference signal for the valve level control. √ ⎧ ⎨ ua = √2U ref cos(θ ref ) (1) u = 2U ref cos(θ ref − 2π 3 ) ⎩ b √ ref ) uc = 2U cos(θ ref + 2π 3

2.2 Dynamic Minimum DC-Bus Voltage of WECS The back-to-back converter of WECS consists of two voltage source converters (VSCs), which share the same dc-bus voltage [5]. For PMSG based WECS, the RSC connects to the stator of PMSG, and the GSC connects to the point of common coupling (PCC) of wind farm [6]. The dc-bus voltage must match the current controllability requirements

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of both grid-side converter (GSC) and rotor-side converter (RSC) at the same time [7]. The dynamic minimum dc-bus voltage technique [4] has been proposed in, in which the dc-bus voltage is dynamically adjusted to obtain a highest modulation depth locating in linear modulation state for RSC and GSC. In the constant voltage low frequency wind power system, though the stator voltage of PMSG decrease with decreasing wind speed, the dc-bus voltage must remain at a high level as the PCC voltage is constant [8]. For variable voltage low frequency wind power system proposed in Sect. 2.1, the PCC voltage drops nearly simultaneously with stator voltage of PMSG, so that the dcbus voltage of back-to-back converter can be reduced with varying wind speed [4]. Since the switching loss of VSC is proportional to the dc bus voltage, it is beneficial to reduce the switching loss of back-to-back converter [9, 10]. 2.3 Simulation Results The system structure used in the simulation is shown in Fig. 1, in which the wind farm includes 90 PMSG based WECSs, each WECS is rated at 5MW. The wind speed in the simulation case stepping from 7 m/s to 6.5 m/s at 5 s and finally to 6 m/s at 25 s. The results show that both the AC bus voltage of transmission line and the DC bus voltage of the WCES can be reduced as the wind speed decreases.

AC Bus voltage of transmission line

DC Bus voltage Of WECS

Fig. 3. The feasibility and simulation results of VV-LFWPS

3 Loss Studies The system used in the simulation is shown in Figs. 1 and 3. The WCES adopts a permanent magnet synchronous generator, with wind speeds stepping from 7 m/s to 6.5 m/s at 5s and finally to 6 m/s at 25s.

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3.1 Converter Losses of WECS The converter loss includes conduction loss and switching loss, and switching loss accounts for a larger proportion for two-level voltage source converter. The voltage in VV-LFWPS may be lower than the rated voltage, and the increase of current will increase the conduction loss. For VV-LFWPS, after applying the dynamic DC bus voltage technique, the dc bus voltage of WECS converter is reduced significantly, so the switching losses that counts more can be reduced. As demonstrated in Fig. 4(a), the total losses in converter are reduced effectively. The energy loss can be calculated by integrating the minus between the active loss of CV-LFWPS and VV-LFWPS, as shown in Fig. 5(a). It shows the energy loss is reduced by 0.0963kWh in 35s. (a)power loss of WECS converter

VV-LFWPS CV-LFWPS (b)power loss of transmission line

(c)power loss of generator

Fig. 4. Comparison on power losses of CV-LFWPS and VV-LFWPS

3.2 Transmission Line Losses The loss in the transmission line is shown in Fig. 4(b), it shows the transmission line loss of VV-LFWPS is lower than that of CV-LFWPS, and Fig. 5(b) shows a 6.84kWh energy loss reduction in 35s. Theoretical analysis shows that when more segmented π-type lines are used to represent long-distance submarine cables, the losses of VV-LFWPS on the transmission line are lower than CV-LFWPS due to the influence of cables on the capacitive charging current of the ground. Besides, the connection link reactance is a necessary part of ac–ac station, the active power loss of the resistance it carries will decrease as the transmission voltage decreases. More simulation analysis shows that the loss reduction effect of variable voltage low frequency transmission is more pronounced when the length of cable are increased.

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3.3 Generator Losses Figure 4(c) can illustrate that Ig may rise slightly when the U pcc of the VV-LFWPS decrease with declining wind speed, so that the VV-LFWPS has slightly more the power loss of generator than the CV-LFWPS. Figure 5(c) shows the energy loss is increased by 0.168 kWh when compared to CV-LFWPS. In summary, the overall power losses of VV-LFWPS is lower than that of CV-LFWPS. (a)energy loss of WECS converter

(b)energy loss of transmission line

(c)energy loss of generator

Fig. 5. Difference in energy loss between CV-LFWPS and VV-LFWPS

4 Fault Transient Study In this paper, a three-phase ground fault was applied at the PCC point at 30 s for both LFWPSs, the same grounding impedance is used and the fault lasts for 625 ms, the results are shown in Fig. 6. The simulation results show that VV-LFWPS reduces the inrush current by 280A compared to CV-LFWPS, this is conducive to reducing electrical stress and reducing design redundancy.

       









Fig. 6. Comparison of CV-LFWPS and VV-LFWPS fault transient

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5 Conclusion Low frequency wind farms can operate in a variable voltage mode where the transmission voltage varies approximately linearly with the wind speed of the wind farm. Due to the capacitive charging current of cable and the connection link reactance, VV-LFWPS has a lower power loss on the transmission lines than CV-LFWPS. When applying the dynamic minimum dc bus voltage control, VV-LFWPS also has a lower switching loss on WECS converter. The VV-LFWPS can effectively reduce transient inrush currents under fault conditions, this is conducive to reducing electrical stress and reducing design redundancy. Acknowledgements. The paper was supported by the “State Grid Shanghai Electric Power Company Science and Technology Project (52094022003Q)”.

References 1. Gupta, R.A., Singh, B., Jain, B.B.: Wind energy conversion system using PMSG. In: 2015 International Conference on Recent Developments in Control, Automation and Power Engineering (RDCAPE), pp. 199–203 (2015). https://doi.org/10.1109/RDCAPE.2015.728 1395 2. Gul, W., Gao, Q., Lenwari, W.: Optimal design of a 5-MW double-stator single-rotor PMSG for offshore direct drive wind turbines. In: IEEE Transactions on Industry Applications, vol. 56, no. 1, pp. 216–225, Jan–Feb 2020. https://doi.org/10.1109/TIA.2019.2949545 3. Alizadeh, O., Yazdani, A.: A strategy for real power control in a direct-drive PMSG-based wind energy conversion system. IEEE Trans. Power Deliv. 28(3), 1297–1305 (2013). https:// doi.org/10.1109/TPWRD.2013.2258177 4. Jia, F., et al.: Bidirectional speed range extension of DFIGURE-based WECS with dynamic minimum dc-bus voltage. IET Gener. Transm. Distrib. 15, 2943–2952 (2021). https://doi.org/ 10.1049/gtd2.12231 5. Li, R., Yu, L., Xu, L., Adam, G.P.: Coordinated control of parallel DR-HVDC and MMCHVDC systems for offshore wind energy transmission. IEEE J. Emerg. Sel. Topics Power Electron. 8(3), 2572–2582 (2020). https://doi.org/10.1109/JESTPE.2019.2931197 6. Chen, L., et al.: Performance evaluation approach of superconducting fault current limiter in MMC-HVDC transmission system. IEEE Trans. Appl. Supercond. 31(8), 1–7 (2021) (Art no. 5602507). https://doi.org/10.1109/TASC.2021.3091045 7. Chinchilla, M., Arnaltes, S., Burgos, J.C.: Control of permanent-magnet generators applied to variable-speed wind-energy systems connected to the grid. IEEE Trans. Energy Convers. 21(1), 130–135 (2006). https://doi.org/10.1109/TEC.2005.853735 8. Li, S., Haskew, T.A., Swatloski, R.P., Gathings, W.: Optimal and direct-current vector control of direct-driven PMSG wind turbines. IEEE Trans. Power Electron. 27(5), 2325–2337 (2012). https://doi.org/10.1109/TPEL.2011.2174254 9. Uehara, A., et al.: A coordinated control method to smooth wind power fluctuations of a PMSG-Based WECS. IEEE Trans. Energy Convers. 26(2), 550–558 (2011). https://doi.org/ 10.1109/TEC.2011.2107912 10. Zhang, Z., Zhao, Y., Qiao, W., Qu, L.: A space-vector-modulated sensorless direct-torque control for direct-drive PMSG wind turbines. IEEE Trans. Ind. Appl. 50(4), 2331–2341 (2014). https://doi.org/10.1109/TIA.2013.2296618

Extended Kalman Filtering Power System Dynamic State Estimation Based on Time Convolution Networks Xundong Gong, Fei Hu, Li Jiang(B) , Ming Chen, Yu Zhang, Shaolei Zong, and Qiu Miu State Grid Wuxi Power Supply Company (Wuxi), Wuxi, China [email protected]

Abstract. With the proposal of “30–60” carbon peaking and carbon neutrality goals, it has become the development trend and direction of China’s power industry to construct a new power system and develop green and low-carbon energy. The current new power system real-time measurement data is multi-source and complex, which greatly challenges the existing state estimation and state prediction technology. The Kalman filter prediction step of the traditional power system dynamic state estimation assumes the system noise covariance matrix as the constant matrix, which leads to the low prediction accuracy of dynamic estimation and affects the filtering ability of dynamic state estimation model. Specific to above problems, this paper introduces artificial intelligence technology into the power system dynamic state estimation and proposes the time sequence prediction method based on time convolution network (TCN). The proposed method can accurately establish the spatial model of system state, improve the system state prediction accuracy, and provide high-quality future state values for the subsequent dynamic estimation and state evaluation. The example simulation in IEEE14 standard system shows that the estimation accuracy of proposed method performs well compared with extended Kalman filter (EKF). Keywords: Dynamic state estimation · Situation prediction · Artificial intelligence · Time convolution network · Extended Kalman filter

1 Introduction In recent years, smart grid situation awareness has gradually become a research hotspot [1, 2]. Power system state estimation is an important basis for “understanding” and “prediction” of situation awareness system, and one of the core functions of energy management system, which plays a vital role in system scheduling, economic operation and real-time control. Besides, large-scale renewable energy grid connection increases the difficulty of power balance analysis and weakens the system regulation ability. Furthermore, data loss and data anomalies among mass operating data severely affect the state estimation results and increase the potential risk of power grid operation. Therefore, accurate and real-time situation awareness technology is vital for the subsequent advanced power system analysis and application. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 844–855, 2023. https://doi.org/10.1007/978-981-99-4334-0_102

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Unlike static state estimation, dynamic state estimation can predict the running trend of system and is widely used [3]. It has the following advantages: (1) It provides prediction value while providing estimation value, which can effectively solve the insufficient short-time measurement redundancy caused by communication failure, and provide data basis for the advanced prediction function of EMS; (2) It predicts the system running state according to the power system dynamic function, and to increase the accuracy of state estimation results. Traditional dynamic state estimation mainly adopts extended Kalman filtering methods. Literature [4] introduces the STF method into the dynamic state estimation of power system, and introduces the time-varying suboptimal fading factor in the extended Kalman filter (EKF), which can adjust the prediction error covariance matrix and the corresponding gain matrix online. But, it requires the Jacobian matrix computation, which causes linearization error. To solve this problem, Julier proposed the Unscented Kalman Filtering (UKF) algorithm, and Vander Merwe extended the method and proposed the square-root UKF method [5]. However, the statistical characteristics of system noise are difficult to obtain. To improve UKF’s adaptability to system noise, Literature [6] proposes an adaptive unscented Kalman filtering (AUKF) algorithm to improve the Sage-Husa noise statistical estimator to compensate for the influence of system noise. However, the actual measurement system contains a certain proportion of bad data. Existence of bad data increases the system modeling uncertainty, making it difficult to guarantee the estimation performance. For this purpose, Literature [7] proposed a generalized unscented Kalman filtering algorithm that uses statistical linearization for accurate estimation and can effectively identify bad measurement data. Literature [8] proposes an unscented Kalman filtering algorithm based on hybrid measurement, which avoids the introduction of linearization error and Jacobian matrix computation, and improves the performance of dynamic state estimation. Literature [9] proposes an adaptive UKF estimation method which could realize accurate estimation under unknown system noise. In the above-mentioned dynamic state estimation studies, the state transfer matrix of EKF and UKF algorithms is usually set as the unit array, or constructed the state-space model by Holt’s two-parameter exponential smoothing method. These methods assume that the system noise covariance matrix remains constant and the simulation results have high accuracy. However, the state space model construction is not based on the actual power system model and only approximates the Kalman filtering state transfer process through mathematical equation. It makes the mathematical equation approximate the Kalman filtering state transfer process, limits the dynamic state estimation prediction step accuracy, and ultimately affects the filtering step estimation results [10]. Specific to difficulty in establishing the traditional dynamic state estimation prediction step state space model, this paper constructs a state space model based on time convolution network (TCN), simulates the complex state transfer relationship through the feature extraction of historical data, and estimates the power system dynamic state with EKF algorithm. The proposed method establishes the node voltage state space model based on artificial intelligence technology, considers the system noise covariance matrix, avoids the state space model error caused by the state transition matrix of constant matrix in traditional Kalman filtering method, effectively improves the accuracy of EKF prediction step, and then improves the filtering accuracy of node state.

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2 Dynamic State Estimation Model Based on EKF In this paper, the node voltage complex vector is selected as the state variable xn , and the node voltage amplitude, node injected power and branch power are measurement zm . The EKF algorithm steps are as follows [11]. (1) Prediction stage 1) Current state variable estimated value   xˆ k|k−1 = f xˆ k−1|k−1

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As can be seen, the EKF algorithm implementation is to obtain the kth state estimated value xˆ k|k from the state estimated value of k − 1. It adopts the recursion to calculate the next estimation result using the last estimation. This is not a simple recursive process and needs to use the output deviation in each estimation for feedback correction, so that the system state estimation progresses according to the expected trend, and finally achieve satisfactory identification effect.

3 TCN Model Principle The TCN model constructed in this paper takes the node voltage and error covariance matrix as input and output characteristic quantity of the network. The network input of the algorithm is the node voltage and error covariance matrix, and output is the predicted value of the voltage and error covariance matrix at the next moment. The TCN model belongs to one of the convolutional neural network models [12, 13], which is essentially a one-dimensional CNN [14] model specially modified for time-series problems with its structure shown in Fig. 1. First, TCN uses a causal convolution, i.e. the value calculation for a given node relies only on the previous value of the temporal definition. Processing the time series can effectively prevent the future information leakage caused by convolution operation with the convolution kernel. The leakage problem is

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very prominent in traditional CNN models, so TCN can have strict time constraint on the model. As shown in Fig. 1, yn at the second layer is only affected by xn−2 , xn−1 and xn of the first layer, which embodies the causal convolution. Assuming the given convolution kernel is F = (f1 , f2 , . . . , fk ) and input sequence is X = (x1 , x2 , . . . , xn ), the causal convolution at xn is defined as: (F ∗ X )(xn ) =

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where ∗ is the convolution operator. Second, traditional CNN can alleviate the long-term dependence of time-series problems merely by expanding the convolution kernel scale or stacking multiple layers. The TCN uses the expansion convolution and residual network. Expansion convolution allows the convolution kernel input to be interval sampling. When stacking multi-layer convolution layers, larger receptive fields can be obtained and the long-time dependencies in the time series can be grasped. TCN uses the expansion coefficient to determine the interval size. The d in Fig. 1 is the expansion coefficient. In addition, the residual network allows errors of the previous layer to be directly transmitted to the next layer, which can greatly alleviate the deep network’s difficulty in learning. Set X as input value of the residual module, the potential identity mapping function across layers is F(·). The result is added to the input value X , and the output value o of residual module can be expressed as: o = Activation(X + F(X ))

(7)

Finally, compared with RNN and CNN models, TCN is less difficult to train and requires the relatively small dataset. Therefore, TCN is more suitable.

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4 TCN-EKF Dynamic State Estimation Model 4.1 TCN Model Constructing In this paper, TCN model is constructed through Keras neural network with its hierarchical structure shown in Fig. 2. First, the time step is set, the input dimension is determined, and the data is normalized. The processed data is imported into the sequence input layer and two-layer residual module. Finally, the dimension is controlled through the fully connected layer and the regression output is performed. According to TCN model feature dimension and the data size of the proposed method, the TCN model is constructed as shown in Fig. 2. The number of neurons of residual module is 32 and 16 respectively. The dropout function of each layer is set as 20% according to the tuning process and empirical formula, which can accelerate the model training and effectively prevent overfitting. The maximum number of training rounds is 120, and the minimum batch size for each training iteration is 32. The voltage and covariance matrix are trained in two TCN models. First, the training set database is built. Then, the historical voltage values and covariance matrix are input. The state prediction model is constructed by using TCN one-step prediction method. The network input and output dimension is consistent with the state variable dimension. According to training model, estimation value of the previous moment is predicted in the future moment EKF calculation as a prior estimate of the current moment. 4.2 TCN-EKF Algorithm The TCN-EKF power system dynamic state estimation estimates the voltage situation of all nodes based on multi-time section partial node voltage amplitude, node injected power, and branch power measurement data. By training the node voltage data and error covariance matrix data under real load fluctuation with TCN model, the node voltage value and error covariance matrix of the next moment is predicted in EKF actual calculation with TCN model. The EKF prediction step is replaced by the data-driven mode, which avoid establishing complex models. The predicted data is calculated by measurement prediction step and filtering step. The state estimation at the next moment occurs at the end of all the node estimation at the current moment. When all moments are estimated, the data is output and the program ends. The algorithm flow chart in this paper is shown in Fig. 3. TCN network model is updated in real time according to filtering step results of the previous moment, which improves the adaptive ability of TCN training model with the load fluctuation. Only one offline training of historical data is needed to meet the real-time requirements of actual power grid operation.

5 Example Analysis Real annual load curve is selected for training. The representative load curve set could be selected for training through the typical day selection [15, 16] and other means, so that the trained model has strong adaptability and high training efficiency. Multiple time

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section flow calculation results are calculated according to load curve. Through the node admittance matrix, the entire network node voltage, node injected power and branch power are calculated and taken as the measurement value. By adding Gaussian white noise with mean value of 0 and standard deviation of 0.01, the measurement data with noise is obtained and the entire network node voltage estimated value is calculated. To obtain TCN model voltage and error covariance matrix training set data, we first calculate the node voltage and error covariance matrix data of 3000 sets of sections at the historical moment, and input it into TCN model for training. The voltage and error covariance matrix data of 100 sets of sections at the future moment is predicted. The predicted voltage and error covariance matrix are calculated with EKF filter step, and the estimated accuracy of prediction step and filter step is compared. 5.1 TCN Offline Training In this paper, the voltage value and error covariance matrix at the historical moment are used as the training set data during the offline operation. The k − 1 moment training set voltage data and error covariance matrix data is taken as TCN network model input, and the k moment data is used as model output to predict with the multi-dimensional single-step training mode. The prediction step calculation of the future moment assisted

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by filter step result of the historical moment can obtain a higher estimation accuracy than the historical moment prediction step. The hardware platform of this paper is PC-based with a processor of Intel(R) Core(TM) i5-8300H CPU @ 2.30GHz and a memory of 8.00 GB. Based on the voltage estimated value and error covariance matrix data of 3100 sets of sections, the first 3000 sets are selected as the TCN model training set, and the last 100 sets is used as the test set. Taking the node voltage amplitude model as an example, the loss function curves of training and test sets are shown in Fig. 4. As can be seen from Fig. 4, the node voltage amplitude model built in this paper has converged without overfitting or underfitting. 5.2 TCN-EKF Estimation Accuracy Analysis 5.2.1 Analysis of the Method Estimation Results of This Paper 50 time sections are selected for analysis. According to the filtering step results at k − 1 moment, TCN training model is used to predict the node voltage at k moment, so as to obtain the predicted voltage amplitude, voltage phase angle and error covariance matrix. Taking Nodes 4 and 5 as an example, the prediction step accuracy of the node voltage state variable is shown in Fig. 5. Comparing the prediction step curve with real value curve, the prediction step results can track the real value curve well, indicating that the constructed TCN prediction model has high prediction accuracy on the node voltage state quantity.

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Fig. 4. Loss function curves of training and test sets.

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After the arrival of real-time measurement data, filtering step is calculated to correct the estimated value of prediction step, so as to obtain the optimal estimated value. Comparing the node voltage amplitude value filtering step estimation results with and true values as shown in Fig. 6, it is obvious that the filtering step result can track the true value well, and the node voltage amplitude value has accurate estimation results.

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5.2.2 Estimation Accuracy Comparison with Traditional Methods Because it is difficult to accurately establish the state space model, the Holt’s mathematical model is used as the main state space model in current EKF power system dynamic state estimation studies. This state model construction often results in relatively low EKF prediction step estimation accuracy, which makes the estimation accuracy mainly depend on the filter step calculation. In this paper, the prediction step estimation accuracy of traditional EKF algorithm is further improved by TCN prediction method. By simulating measurement data with the same real load curve, method in this paper and method with Holt’s model as state space model are compared. Taking the standard system IEEE14 node as an example, the Nodes 4 and 5 prediction step and filtering step estimation results are compared with the flow true value to get the absolute error graph. The absolute error of the voltage amplitude prediction step and the absolute error of the filtering step of node 4 are shown in Fig. 7, and the absolute error of the voltage amplitude prediction step and the absolute error of the filtering step of node 5 are shown in Fig. 8. As can be seen from Figs. 7 and 8, the prediction step accuracy of the method using Holt’s model as the state space model is lower than that of the TCN time series prediction method due to the presence of system noise, so the voltage state estimation accuracy of the TCN model is higher under the EKF calculation method of the two state space models. To make the estimation results of different algorithms more intuitive, the mean absolute estimation error and maximum absolute estimation error are used indicators to

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compare the algorithm performance with the formula as: T  1   xˆ i (t) − xi (t) T t=1   = max xˆ i (t) − xi (t)

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In the formula: xˆ i (t) is the estimated value of the ith state quantity of section t; xi (t) is the true value of the ith state quantity of section t; and T is the total number of sections in test set. Table 1 lists the filter step estimation errors for nodes 4 and 5. As can be seen from Table 1, the proposed method replaces the prediction step of EKF in a datd-driven way, avoids the establishment of complex models, and therefore has better performance in estimation performance, taking the average absolute estimation error and maximum absolute estimation error of voltage amplitude of node 4 as examples, which are 18.94% and 33.56% lower than Holt’s, respectively. Through simulation results analysis, the calculation method of this paper is good in prediction step and filtering step accuracy. And the filtering step accuracy is significantly better than prediction step accuracy, which takes an active correction effect. Meanwhile, the estimation accuracy of this paper’s calculation method is better than traditional EKF algorithm.

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6 Conclusion To further develop the predictive advantage of power system dynamic state estimation and solve the problem that prediction step state space model in traditional EKF algorithm is difficult to establish, a state space model based on TCN neural network is proposed in this paper. Based on historical state quantity data features extraction, complex state-transfer relationship is simulated with a data-driven approach. Relying on the advantages of TCN network, accurate state space models are established to improve the EKF prediction performance. As shown in simulation results, filtering step accuracy of the proposed calculation method improves significantly. The proposed method can accurately predict the the power grid state before the arrival of current moment measurement, which improves the accuracy of system state estimation.

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Acknowledgements. This work was supported by headquarters management technology project of State Grid Corporation of China ‘Research on System Situation Prediction and Evaluation Technology Based on None Ideal Mass Operation Data’.

References 1. Zhou, H., Hu, R., Li, X., et al.: Design of power system operation cockpit based on situational awareness technology. Autom. Electr. Power Syst. 39(07), 130–137 (2015) 2. Wang, S., Liang, D., Ge, L.: Key technologies of situation awareness and situational guidance for smart distribution networks. Autom. Electr. Power Syst. 40(12), 2–8 (2016) 3. Yu, E.: State Estimation of Power System. Water Resources and Electric Power Press, Beijing (1985) 4. Li, H., Zhao, S.: Dynamic State estimation of power system with strong tracking filter based on WAMS/SCADA hybrid measurement. Electr. Power Autom. Equipment 32(09): 101– 105+116 (2012) 5. Wei, Z., Sun, G., Pang, B.: Application of unscented kalman filter and its square root form in power system dynamic state estimation. Proc. CSEE 31(16), 74–80 (2011) 6. Zhao, H., Tian, T.: Power system dynamic state estimation based on adaptive unscented Kalman filter. Power Grid Technol. 38(01), 188–192 (2014) 7. Zhao, J., Mili, L., Gomez-Exposito, A.: Constrained robust unscented kalman filter for generalized dynamic state estimation. IEEE Trans. Power Syst. 34(5), 3637–3646 (2019) 8. Li, D., Li, R., Sun, Y.: Dynamic state estimation of power system based on UKF under hybrid measurement. Autom. Electr. Power Syst. 34(17): 17–21+92 (2010) 9. Sun, J., Liu, M., Deng, L., et al.: State estimation of distribution network based on adaptive unscented Kalman filter. Prot. Control Power Syst. 46(11), 1–7 (2018) 10. Zhao, J., Mili, L.: Robust unscented Kalman filter for power system dynamic state estimation with unknown noise statistics. IEEE Trans. Smart Grid 10(2), 1215–1224 (2019) 11. Zhang, J.: Research on sensorless direct Torque control technology of induction motor based on Kalman filter algorithm. South China University of Technology (2016) 12. Bai, S., Kolter, J.Z., Koltun, V.: An empirical evaluatio of generic convolutional and recurrent networks for sequence modeling (2018). arXiv preprint arXiv:1803. 01271 13. Gu, M., Zhao, B., Chen, H.: Prediction method of daily electricity sales by industry based on temporal convolution network and graph attention network. Power Grid Technol. 46(04), 1287–1297 (2022) 14. Haixiang, Z., Ling, L., Li, S., et al.: Short-term global horizontal irradiance forecasting based on a hybrid CNN-LSTM model with spatiotemporal correlations. Renew. Energy 160, 26–41 (2020) 15. Peng, X., Pan, K., Zhang, D., et al.: Multi-segment short-term load forecasting based on adaptive seasonal load partitioning and important point segmentation. Power Grid Technol. 44(02), 603–613 (2020) 16. Zang Haixiang, X., Ruiqi, C.L., et al.: Residential load forecasting based on LSTM fusing self-attention mechanism with pooling. Energy 229, 120682 (2021)

A Capacitive Wireless Power Transfer System with LCLC Resonant Network Zixuan Guo, Zhaodi Li, Jinli Zhang, Siyang Liang, Fan Pu, and Weilin Li(B) Northwestern Polytechnical University, Xi’an, China [email protected], [email protected]

Abstract. Capacitive power transfer (CPT) system mainly consists of coupling mechanism, high frequency inverter and resonant network. A CPT system with unilateral LCLC tuning network is proposed in this paper, the design of the whole underwater CPT system is completed through the circuit analysis and parameter calculation of the double E Class and unilateral LCLC-S resonant network of the inverter. Using MATLAB/Simulink simulation platform to build the simulation model of CPT system, we can carry out theoretical analysis and system efficiency verification on the experimental results of the simulation model. By building the physical hardware platform, the actual operation effect and load end output voltage of the CPT system are tested, and the actual feasibility and overall performance of the hardware circuit of the CPT system can be analyzed. Keywords: Capacitive power transfer · Underwater wireless power transfer · Double E-class inverter · Resonant network

1 Introduction In recent years, the ocean has gradually become the focus of scientific research and exploration, the long-time work of marine equipment under the water makes the efficient and convenient energy supply particularly important 1. Through using the technology of underwater radio energy transmission, the unmanned underwater vehicle can continuously be charged by carrying an energy charging station in the sea survey ship, which effectively improved the efficiency and working time of the equipment. At present, there are two most mature wireless power transmission (WPT) technologies, inductive power transfer (IPT) and capacitive power transfer (CPT) 23. IPT system realizes energy transfer through the magnetic field coupling, and the way CPT realizes is different from IPT system, CPT achieves energy transfer through electric field. A high-frequency electric field can be formed between the coupling plates, and then realizes wireless power transmission through the induced current of the electric field. Because CPT system has the advantages of zero undesired eddy currents, multiple coupling mechanisms, low construction complexity and low EMI, its development prospect and overall efficiency in the field of wireless charging application are better than the well-developed IPT technology. The application of this technology in the development of marine science can improve the safety and transmission efficiency of underwater electric energy transmission, reduce the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 856–863, 2023. https://doi.org/10.1007/978-981-99-4334-0_103

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time consumption caused by fishing and launching of electric equipment 4, and be used for charging autonomous underwater vehicles (AUVs) by power supply base station in the sea, the power supply of underwater equipment by ocean buoy, the battery power supply of AUV to underwater sensor, etc. The main research focus of CPT technology is resonance compensation network and the inverter circuit 5. Aiming at the environment of shipborne energy charging base station and CPT flat coupling structure, this paper proposed a unilateral LCLCS resonant network, and adopted the double E class high frequency inverter circuit to achieve working state of the soft switching of the circuit. After using MATLAB/Simulink simulation platform to carry out simulation circuit test, a physical verification platform is built to analyze the actual circuit of the system. It is proved that the functional topology can ensure the stable non-contact energy transmission of CPT system.

2 Introduction CPT System with Unilateral LCLC-S Resonant Network 2.1 CPT System The CPT system with the unilateral LCLC-S resonant network is shown in Fig. 1. The whole system is composed of high frequency inverter, capacitor coupler and resonant network 6. In this system, we choose to use double E class high frequency inverter with soft switching characteristics and constant power output characteristics. Based on the topology of Class E inverter, two switches are alternately connected to provide power for the load, which reduces the voltage stress of the single switch. When inductance L01 , L02 , compensation capacitance and bypass capacitance of the switch tube C01 , C02 are able to meet the conditions required by the system, it can ensure that the switch is working in the soft switching status, concurrently reducing the energy loss of the Class E inverter and increasing the output powerful characteristics [7].

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(b)

Fig. 1. CPT system circuit topology. (a) Circuit structure of CPT system. (b) Equivalent circuit of the FHA.

There is a way to simplify the CPT system model, which named fundamental harmonic approximation (FHA) analysis technology. It is stemmed from AC complex research [8], and Fig. 1(b) shows the result. Where U˙ ab represents the output voltage value of Class E inverter, U˙ ab1 represents the fundamental voltage of U˙ ab , its amplitude

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Uab1m can be calculate from (1). To successfully analysis the resonance network in this system, it is necessary to research the capacitance couplers.  US 4π 2 + (π 2 − 8)2 Uab1m = (1) 4 2.2 Equivalent Analysis of Coupling Capacitor The CPT system in this paper selects the flat plate coupling mechanism with the widest application range and relatively simple structure. Flat plate coupling mechanism mostly adopts the way that two metal plates are placed in parallel and relative, and its equivalent capacity expression is as follows: C=

εr ε0 S d1

(2)

In (2), C is the equivalent capacitance of the coupling capacitor mechanism, εr is the relative dielectric constant of the filling medium between two parallel metal plates, ε0 (8.85 × 10−12 F/m) is the dielectric constant in vacuum, S is the opposite area of two parallel plates, and d1 is the spang between parallel plates. In the actual circuit, two parallel plates are connected in series, and their capacitance values are set as CS1 and CS2 respectively 9, so the equivalent capacitance value CS of the overall coupling capacitor mechanism is: CS =

1 1 CS1

+

=

1 CS2

CS1 CS2 CS1 + CS2

(3)

2.3 LCLC-S Resonant Network The CPT system illustrate in Fig. 1 can be simplified as a linear system, which is consisted of impedance and controlled source, as shown in Fig. 2. According to the requirements of the circuit, we can designed the parameters of unilateral LCLC-S resonant network in detail, which are used to realize the steady energy output of the resonant network, and content the system soft switching operating conditions in the meantime. Z in I1

Z1 L1

Z2

Z4

Z3 CS1

LS

L

I0 U ab1

C2

C1

R0 U o CS 2

N1

N

Fig. 2. Simplified asymmetric unilateral LCLC-S resonant network.

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The tuning compensation model in Fig. 2 can be divided into multi-level networks. Through analysis and calculation, the circuit impedance of each level of networks can be expressed in turn. CS1 and CS2 in the capacitive coupling mechanism are completely consistent, and their capacitance values are set to CS . The specific expression can be deduced as follows: ⎧ 1 Zin = jωL1 + jωC + Z1 ⎪ ⎪ 1 ⎪ ⎪ ⎪ Z1 = jωL + Z2 ⎨ 1 Z2 = jωC + Z3 (4) 2 ⎪ ⎪ 2 ⎪ ⎪ ⎪ Z3 = jωLS + jωCs + Z4 ⎩ Z4 = R0 By defining and taking values of the quality factor Q, capacitance ratio a and normalized frequency of the system circuit μ, the voltage gain MV of the whole system can be simplified, and the whole expression can be calculated as follows: ⎧ 1 ⎪ ⎨ Q = ω0 CS R0 +tan δ a = CCS2 (5) ⎪ ⎩ μ = ωω0 The dielectric loss angle of the dielectric PVC filled between the coupling capacitors mechanisms used in the system circuit is tanδ=0.03, the resonant frequency of the system is expressed as follows: ω0 = √

1 1 1 =√ =√ LC1 LC2 LS CS

(6)

Then the simplified expression of voltage gain MV can be deduced: |MV | = 

1  2 (μ2 − 1)2 + Q2 μ4 − (a + 2)μ2 + 1

(7)

According to (7), the circuit voltage gain is affected by the values of Q, a and μ. The value range of each parameter value can be obtained through theoretical analysis, where Q = 7.33, a = 0.04, μ = 1. This design specifies that the DC power supply voltage of the system is 5V and the AC load resistance is R0 = 10, , the circuit switching frequency is 50 kHz, then the resonant frequency of the system can be calculated according to (5): ω0 = 0.313 × 106 , the system operating frequency expression is as follows: f0 =

1 √ 2π LS CS

(8)

In order to improve the power factor of the system, the equivalent input impedance Z1 of the system is analyzed as follows: Zin =jωL1 +

R2 + jX2 = R1 + jX1 1 + jωC1 (R2 + jX2 )

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⎧ ⎪ ⎪ ⎪ ⎨ R1 =

ω2 C1 L1 R2

(1 − ωL1 X2 )2 + (ωC1 R2 )2 ⎪ ωL1 − ω2 C1 L1 X2 ⎪ ⎪ ⎩ X1 = (1 − ωL1 X2 )2 + (ωC1 R2 )2

(9)

From the above formulas, when:  Z˙ 1 = R1 + jX1 = R21 +X12  49.1◦

(10)

The equivalent input impedance Z1 meets the soft switching working conditions of the inverter circuit switch, which can validly improve the energy transmission efficiency of the system and reduce the power loss of switching.

3 Results 3.1 Simulation Results To verify the feasibility and transmission efficiency of the CPT system, the simulation circuit of the CPT system is built and tested by using MATLAB/Simulink simulation software (Table 1). Table 1. Parameter values. Parameter

Value

D

0.49

US

5V

f

50KHz

R0

10

CS1 , CS2

5.6nF

LS

3mH

C1 , C2

22nF

L

0.1mH

L1

0.14mH

Cd 1 , Cd 2

0.47uF

L01 , L02

45mH

The CPT system uses the stable DC power supply US = 5V as the power supply; In the circuit, the inverter circuit is the double E Class inverter circuit which is composed of inductors L01 and L02 , two N-channel MOSFET switches S1 and S2 , and bypass capacitors C1 and C2 , which plays a role in inverting the DC power supply US to 50 kHz AC power; C1 and C2 are the equivalent simulation capacitors of the coupling capacitor

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mechanism, and the wireless electric energy transmission is realized through the induced electric field generated by them; The resonance network composed of inductors L1 , L, LS and capacitors C1 , C2 can improve the power factor of the system and the stability of the system load voltage. According to the device parameters in Table I, the system circuit simulation model is built in MATLAB/Simulink software, and the load output voltage waveform is shown in Fig. 3. 8 Load voltage (V)

10

6

2

5 0 -5 -10 0.01

0

0.01002

0.01004

0.01006

0.01008

0.0101

0.01006

0.01008

0.0101

Time(s) 1

-2 Load current (I)

Load voltage (V)

4

-4 -6 -8 0

0.005

0.01

Time (s)

(a)

0.015

0.02

0.5 0 -0.5 -1 0.01

0.01002

0.01004

Time(s)

(b)

Fig. 3. Output simulation waveform. (a) Load voltage waveform. (b) Load voltage and current waveform after circuit stabilization.

Through the simulation waveform, it can be found that due to the large inductance value in the system circuit, it takes a certain time for the system to enter the stable state. Input voltage US = 5V, input current effective value I1 = 0.5A, output voltage effective value Vo = 5.3V, output power Pout = 2.9W, input power Pin = 3.1W and working efficiency of the overall system circuit η = Pout /Pin = 2.9W/3.1W = 91.7%. 3.2 Experiment Results The physical circuit is divided into three modules: DSP control circuit, drive circuit and power circuit. This design uses a double E-class inverter, which requires two channels of pulse width modulation (PWM) signals with 180° phase difference to control the opening and closing of the two MOSFETs in the inverter. DSP28335 development board is selected to realize the supply of 50Hz switching frequency drive signal. In order to ensure that MOS can be turned on quickly and reduce the high-frequency oscillation during turning on and off as much as possible, the driving circuit based on IR2110 driving chip is selected in the driving part of this design, and in order to improve the reliability and stability of the circuit, an optocoupler isolation circuit is added. The schematic diagram of the experimental platform is illustrated in Fig. 4. The output end of the physical circuit uses a 10  resistor as the AC load for testing. The input current waveform and output load voltage waveform of the experimental circuit are shown in Fig. 5. According to the above experimental results, the CPT system realizes the power transmission and verifies the feasibility of the topology design.

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Power circuit power supply

Drive circuit power supply

Isolated oscilloscope probe

Drive circuit

DSP control circuit

Power circuit

Fig. 4. The schematic diagram of the experimental platform.

5ms/div Ch2: Current of Power Supply

Ch2: Current of Power Supply

5us/div

20us/div Ch1: Voltage of Load

Ch2: 0.5A/div

Ch2: 100mA/div

Ch1: 5V/div

(a)

(b)

(c)

Fig. 5. Experimental waveform of physical circuit. (a) Overall waveform of input current. (b) Waveform after input current stabilization, (c) Load voltage waveform.

4 Conclusion Aiming at the application background of the capacitive coupling underwater radio energy transmission for charging the battery pack of autonomous underwater vehicles, a CPT system based on single side LCLC-S resonance network soft switching is proposed in this paper. Through the circuit analysis and parameter design of this CPT system, a simulation model can be built to verify the effectiveness of this method, and a physical hardware platform can be built to test the actual circuit. From the actual load terminal voltage waveform, it can be analyzed that this system can realize the power transmission and the compensation of resonance network, and the experimental results are in accord with the expected objectives of this design.

References 1. Hyakudome, T., et al.: Development of ASV for using multiple AUVs operation. In: OCEANS 2018 MTS/IEEE Charleston, pp. 1–4 (2018) 2. Han, J., Asada, A., Ura, T., et al.: Noncontact power supply for seafloor geodetic observing robot system. J. Mar. Sci. Technol. 12(3), 183–189 (2007) 3. Shi, J.G., De-Jun, L.I., Yang, C.J.: Design and analysis of an underwater inductive coupling power transfer system for autonomous underwater vehicle docking applications. J. Zhejiang Univ. Sci. C Comput. Electron. 15(1), 51–62 (2014) 4. Vincent, D., Huynh, P.S., Azeez, N.A., et al.: Evolution of hybrid inductive and capacitive AC links for wireless EV charging—a comparative overview. IEEE Trans. Transp. Electrification 5(4), 1060–1077

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5. Liu, C., Hu, A.P.:Steady state analysis of a capacitively coupled contactless power transfer system. In: 2009 IEEE Energy Conversion Congress and Exposition, pp. 3233–3238 (2009) 6. Chen-yang, X., Chao-wei, L., Juan, Z.: Analysis of power transfer characteristic of capacitive power transfer system and inductively coupled power transfer system. In: 2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC), pp. 1281– 1285 (2011) 7. Zhang, Z., Pang, H., Georgiadis, A., et al.: Wireless power transfer—an overview. In: IEEE Transactions on Industrial Electronics, vol. 66, no. 2, pp. 1044–1058 8. Yang, L., et al.: Analysis and design of four-plate capacitive wireless power transfer system for undersea applications. CES Trans. Electr. Mach. Syst. 5(3), 202–211 9. Kuroda, S., Imura, T.:Derivation and comparison of efficiency and power in non-resonant and resonant circuit of capacitive power transfer. In: 2020 IEEE PELS Workshop on Emerging Technologies: Wireless Power Transfer (WoW), pp. 152–157 (2020)

Cost Performance Analysis of the Typical Electrochemical Energy Storage Unit Jun Wang1 and Jianye Zhu2(B) 1 State Grid Shanghai Electric Power Company, Xuhui District, Shanghai, China 2 School of Electrical Engineering, Southeast University, Xuanwu District, Nanjing, China

[email protected]

Abstract. In power systems, electrochemical energy storage is becoming more and more significant. To reasonably assess the economics of electrochemical energy storage in power grid applications, a whole life cycle cost approach is used to meticulously consider the effects of operating temperature and charge/discharge depth on the decay of energy storage life, to measure the investment cost and power cost of two types of energy storage batteries, and to analyze the effects of temperature and charge/discharge depth on the loss cost of electrochemical energy storage batteries. The study’s findings can serve as a guide for designing and setting up energy storage systems. Keywords: Electrochemical energy storage · Life-cycle cost · Lifetime decay · Discharge depth

1 Introduction Electrochemical energy storage is widely used in power systems due to its advantages of high specific energy, good cycle performance and environmental protection [1]. The application of electrochemical energy storage in power systems can quickly respond to FM (frequency modulation) signals, reduce the load peak-to-valley difference, alleviate grid blockage, reduce network losses, delay grid upgrades, and ensure the reliability and economy of power system operation [2]. Energy storage is also one of the effective ways to solve problems caused by the high proportion of new energy penetration. Among the factors that determine the application and industrial development of electrochemical energy storage technology, the cost is one of the most important parameters [3]. Reference [4] studied the economics of energy storage systems under two application scenarios: peak shaving and valley filling, and improving the capacity of new energy consumption. In this paper, according to the current characteristics of various kinds of electrochemical energy storage costs, the investment and construction costs, annual operation and maintenance costs, and battery loss costs of various types of energy storage are measured, and the economics of various kinds of energy storage under different conditions are compared. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 864–872, 2023. https://doi.org/10.1007/978-981-99-4334-0_104

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2 Model of Electrochemical Energy Storage Cost The total number of urban residential users in China is large, ants. This paper draws on the whole life cycle cost theory to establish the total cost of electrochemical energy storage, including investment and construction costs, annual operation and maintenance costs, and battery wear and tear costs as follows: LCC = Cin + Cop + Closs

(1)

where, Cin is the investment and construction cost; Cop is the operation and maintenance cost; Closs is the battery loss cost. A. Investment and construction cost The original capex of an electrochemical energy storage includes the cost composition of the main devices such as batteries, power converters, transformers, and protection devices, which can be divided into three main parts. Its calculation formula is: = Celec + Cpcs + Ccon Cinital in

(2)

inital is the original capex cost of the electrochemical energy storage system; where, Cin Celec is the battery cost; Cpcs is the power converter cost; Ccon is the upfront construction cost. The battery cost (Celec ) depends greatly on the configured power of the energy storage system and the type of energy stored, and can therefore be expressed as [5]:   E (3) Celec = celec η × DODmax

where, celec is the battery cost of configuring unit capacity of energy storage; E is the configured capacity of energy storage system; η is the energy storage charging and discharging efficiency; DODmax is the maximum of DOD. The power converter cost (Cpcs ) is decided by the power rating of the energy storage system and can therefore be showed as: Cpcs = cpcs × P

(4)

where, cpcs is the power converter cost per unit of power; P is the rated power of the energy storage system configuration. The pre-engineering construction cost (Ccon ) can be expressed in terms of the rated power of the electrochemical energy storage system such as the cost of power transformers, protection devices, and other facilities: Ccon = ccon × P

(5)

where, ccon is the pre-engineering construction cost per unit of power. The equal annual value coefficient f (i, m) is expressed as: f (i, m) =

i(1 + i)m (1 + i)m − 1

(6)

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where, i is the baseline rate of discount; m is age limit of the energy storage system. Considering the time value of money, the investment cost of the electrochemical energy storage system is corrected and converted to the annual cost. So, Cin can be expressed as: inital × f (i, m) Cin = Cin

(7)

B. Annual operation and maintenance The operation and maintenance costs of electrochemical energy storage systems are the labor, operation and inspection, and maintenance costs to ensure that the energy storage system can be put into normal operation, as well as the replacement costs of battery fluids and wear and tear device [6], which can be expressed as:   inital × f (i, m) (8) Cop = μ1 σ1 Q + μ2 σ2 Cin Q = ncycle × DOD × E

(9)

where, μ1 , μ2 are the cost coefficients, μ1 +μ2 = 1; σ1 is the operation and maintenance cost per unit of discharged power; Q is the full life cycle charge-discharge power of the energy storage system; σ2 is the ratio coefficient of annual operation and maintenance cost to investment cost; DOD is the depth of charge-discharge. C. Battery depletion cost The inherent physical and chemical properties of batteries make electrochemical energy storage systems suffer from reduced lifetime and energy loss during charging and discharging. These problems cause battery life curtailment and energy loss, which in turn increase the total cost of electrochemical energy storage. To better analyze the battery loss cost, this paper mainly considers two influencing factors, DOD and ambient temperature, in the worst case (both thermal management system and DOD deviation controller fail). (1) Lead-Acid Battery Factors such as design, manufacturing and operating environment affect the life of leadacid batteries, of which high temperature is the most significant. Relationship between life of lead-acid battery and temperature is given in Fig. 1 by best curve fitting [7]: cycle

LLA

= aebT

(10)

Therefore, the percentage loss of capacity of lead-acid batteries affected by temperature can be expressed as:   cycle (11) Qloss,LA_T = 1 − ebT × 100% cycle

where, LLA,max is the maximum number of cycles of the lead-acid battery in an ideal temperature environment with a specific charge/discharge depth; a is the pre-exponential coefficient, taken as 3194; b is the exponential coefficient, taken as − 0.06452.

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The curve of lead acid battery life affected by DOD is displayed in Fig. 2. So the connection between life and DOD is obtained by fitting the curve in Fig. 2 [8]: cycle

LLA

= c × DOD + d

(12)

where c is the primary term coefficient, taken as -39.87, and d is the constant term coefficient, taken as 4171. Thus, the percentage capacity loss of lead-acid batteries affected by DOD can be expressed as:   cycle LLA cycle Qloss,LADOD = 1 − cycle × 100% (13) LLA,max Combining Eqs. (11) and (13), the percentage capacity loss of lead-acid batteries can be derived as cycle

cycle

Qloss,LA = Qloss,LAT × Qloss,LADOD     c × DOD + d bT = 1−e × 100 1− cycle LLA,max

(14)

Thus, the cost of battery wear and tear can be expressed as: Closs,LA = Qloss,LA × Celec,LA

(15)

(2) Lithium-ion battery After Chen et al. studied the correlation between the resistance growth of lithium battery and temperature, the relationship curve between the life of li-ion battery and temperature was obtained as displayed in Fig. 3. The best curve fitting can be used to obtain the relationship between lithium-ion battery life and temperature relationship [9]: cycle LLI ,T

=j×e

 2 − T −k l

(16)

Therefore, the percentage loss of capacity of lead-acid batteries affected by temperature can be expressed as:   2  cycle

Qloss,LIT = 1 − e cycle

−

T −k l

× 100%

(17)

where, LLI ,max is maximum number of cycles of the lithium battery in an ideal temperature environment with a specific charge/discharge depth; j is the pre-exponential coefficient, which is taken as 2164; k and l are the exponential coefficients, which are taken as 23.4 and 81.9, respectively. As displayed in Fig. 4, the number of cycles of Li-ion batteries is logarithmic concerning DOD. In other words, the cycle life of Li-ion batteries shows an exponential

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Fig. 1. Relationship curve between temperature and cycle number of lead-acid battery

Fig. 2. DOD versus cycle number curve of lead-acid battery

Fig. 3. Relationship curve between lithium battery temperature and cycle number

increase as the depth of charge and discharge decreases. Fit the curve in Fig. 4 with the following formula: cycle

ln LLI _DOD = cycle

n DOD + m n

LLI _DOD = e DOD+m

(18) (19)

where, m and n are the fitted curve coefficients, which are taken as 161.2, 17.7, respectively.

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Fig. 4. Relationship curve between DOD and cycle number of lithium battery

Thus, the percentage capacity loss of lead-acid batteries affected by DOD can be expressed as:   n e DOD+m cycle Qloss,LADOD = 1 − cycle × 100% (20) LLI ,max Combining Eqs. (17) and (20), the percentage capacity loss of lead-acid batteries can be derived as: cycle

cycle

Qloss,LI = Qloss,LAT × Qloss,LADOD  = 1−e

 2  − T −k l

1−

n

e DOD+m cycle

LLI ,max

 × 100%

(21)

Then the cost of battery wear and tear can be expressed as: cycle

Closs,LI = Qloss,LI × Celec,LI

(22)

3 Cost Performance Analysis The cost measurement of lead-acid batteries and li-ion batteries is carried out to compare the economics of these two electrochemical energy storage batteries under different temperatures and depths of charge and discharge conditions, and their specific parameters are shown in Table 1. According to the current more mature electrochemical energy storage power plant as a benchmark, energy storage installation according to 10MW/20MWh, energy storage market according to 6h, energy storage project life of 20 years. Under ideal conditions, according to the temperature of 10 °C, when the depth of charge and discharge is 60%, the cost of the electrochemical energy storage power plant is measured as displayed in Table 2 and Fig. 5. It can be seen that. Continuing with the above parameters, changing the temperature and DOD, the battery loss cost of the energy storage plant is further analyzed, and the loss cost of

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Cost data

Battery type Lead acid battery

Li-ion battery

celec (e/kWh)

264

795

cpcs (e/kW)

378

463

ccon (e/kW)

87

80

η (%)

75

95

DODmax (%)

60

80

5000

10000

ncycle (cycles)

Table 2. Costing table of electrochemical energy storage power plant Electricity cost

Battery type Lead acid battery

Li-ion battery

Investment and construction cost (e/kWh)

0.0273

0.0220

Operation and maintenance cost (e/kWh)

0.0629

0.167

Battery depletion cost (e/kWh)

0.00043

0.000398

lead-acid battery and the lithium-ion battery is shown in Figs. 6 and 7. It can be noted that whether it is a lead-acid battery or a li-ion battery, as the depth of discharge deepens, the cost of battery loss increases exponentially. Take a lithium-ion battery at 10 °C, for example, the depth of charge and discharge increases from 10% light discharge to 80% deep discharge, and the cost of battery loss increases by 4.03 times over the total cycle of the energy storage plant.

Fig. 5. Cost comparison of typical electrochemical energy storage plants

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Fig. 6. Plot of lead-acid battery loss cost versus temperature and DOD

Fig. 7. Lithium battery loss cost versus temperature and DOD

4 Conclusion On the account of the whole life cycle cost theory, the cost and the cost of a kilowatthour (kWh) of electrochemical energy storage power plants based on lead-acid batteries and lithium-ion batteries are calculated, and the study shows that the construction cost of lead-acid batteries is lower, but the cost of kWh is relatively higher. The lithium-ion battery is relatively larger due to higher battery cost and operation and maintenance cost, so the erecting of a lithium-ion energy storage power plant is relatively larger, however, its effective discharge capacity is higher under the same conditions, and if its charging and discharging benefits are considered, thus the cost of a kilowatt-hour is lower. Acknowledgements. This work is supported by Shanghai Electric Power Company Project: Research on distributed energy storage planning for distribution network efficiency improvement.

References 1. Li, C: Analysis of electrochemical energy storage technology. Electron. Compon. Inf. Technol. 6(5) (2019) 2. He, H., Zhang, N., Du, E., Ge, Y., Kang, C.: Review on modeling method for operation efficiency and lifespan decay of large-scale electrochemical energy storage on power grid side. Autom. Electr. Power Syst. Rev. 44(12), 193–207 (2020) (Art no. 1000–1026) 2.0.Tx;2-9

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3. Fu, X., Li, F., Yang, X., Yang, P.: Energy storage cost analysis based on life cycle cost. Distrib. Energy 3, 5 (2020) 4. Li, C., et al.: Multidimensional economic evaluation of energy storage participating in multiple scenarios in distribution network. Global Energy Internet 5(05), 471–479 (2022). https://doi. org/10.19705/j.cnki.issn2096-5125.2022.05.008 5. Mostafa, M.H., Aleem, S., Ali, S.G., Ali, Z.M., Abdelaziz, A.Y.: Techno-economic assessment of energy storage systems using annualized life cycle cost of storage (LCCOS) and levelized cost of energy (LCOE) metrics (in English). J. Energy Storage 29 (2020) (Art no. 101345). https://doi.org/10.1016/j.est.2020.101345 6. Xiu, X., Li, X., Wang, J., Xie, Z., Lv, X.: Generalized cost study of energy storage power station based on equivalent efficiency conversion. Electr. Power 55(4), 192–202 (2022) (Art no. 1004–9649)2.0.Tx;27. Brost, R.D.: Performance of valve-regulated lead acid batteries in EV1 extended series strings. In: Proceedings of the 1998 13th Annual Battery Conference on Applications and Advances, 13–16 Jan 1998, Long Beach, CA, USA, pp. 25–29 8. Vutetakis, D.G., Wu, H.: The effect of charge rate and depth of discharge on the cycle life of sealed lead-acid aircraft batteries. In: 35th International Power Sources Symposium, IPSS 1992, 22–25 June 1992, Cherry Hill, NJ, United states, Institute of Electrical and Electronics Engineers Inc., pp. 103–105. https://doi.org/10.1109/IPSS.1992.282019 [Online] 9. Zhou, C., Qian, K., Allan, M., Zhou, W.: Modeling of the cost of EV battery wear due to V2G application in power systems. IEEE Trans. Energy Convers. 26(4), 1041–1050 (2011). https:// doi.org/10.1109/TEC.2011.2159977

Remaining Useful Life Prediction of Multi-sensor Data Based on Spatial-Temporal Attention Network Yawei Hu1(B) , Xuanlin Li1 , Huaiwang Jin1 , Zhifu Huang1 , Jing Yu2 , and Yongbin Liu1 1 College of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected], {Z21301130,Z22301116}@stu.ahu.edu.cn, [email protected], [email protected] 2 College of Marine Engineering, Dalian Maritime University, Dalian, China [email protected]

Abstract. In recent years, the deep learning methods have been extensively applied in the field of RUL prediction. However, existing methods usually do not enable adaptively weight the importance of multi-sensor data from complex systems. In this paper, a new RUL prediction method based on spatial-temporal attention network (STAnet) is proposed for multi-sensor data. The spatial-temporal attention module in the network can adaptively weight and encode the original signal without any prior knowledge. The feature extraction module can extract the hidden features from the weighted data. The information reinforcement module can weight and decode hidden features while performing information reinforcement, filtering and complementation. Finally using a fully connected layers to map the deep degradation features into specific remaining useful life. Experiments were also conducted on a commonly used dataset, and the results demonstrate its effectiveness and superiority. Keywords: Dynamic model · Fault extraction · Roller bearing

1 Introduction The development of modern industry leads to an increase in the complexity of mechanical equipment, and the failure of components can lead to a serious accident, causing huge economic losses and even injury to people. The prediction and health management (PHM) can ensure the safe operation of equipment. As a core function module in PHM, remaining useful life (RUL) prediction is important to prevent sudden accidents and ensure the reliable operation of the system. Reliable RUL prediction provides a more accurate estimate of time to failure, which helps to implement suitable maintenance measures to prevent the serious consequences of sudden system failure [1]. The data-driven RUL prediction approach aims to establish a nonlinear correspondence between device RUL and device monitoring information [2]. Data-driven prediction methods usually include both traditional machine learning-based methods and deep © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 873–882, 2023. https://doi.org/10.1007/978-981-99-4334-0_105

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learning-based methods. A number of traditional machine learning-based methods are already applied to RUL prediction, such as support vector machines (SVM) [3], extreme learning machines (ELM) [4], etc. However, these methods usually require a certain level of a priori expertise. Deep learning as a branch of data-driven approach can obtain important features automatically from raw data. Therefore, it has been widely introduced into the RUL prediction field in recent years. Such as, convolutional neural networks (CNN), gated recurrent unit networks (GRU), Transformer and long short-term memory networks (LSTM). In generally, the importance of different features from the input raw data in deep learning networks is vary in RUL prediction. However, the different features that are automatically extracted from the data, are treated equally during the extraction process, the data are treated equal importance will affect or diminish the accuracy of the RUL prediction. Hence, it is important to introduce the attention mechanism to solve this problem. Zhao et al. combined the attention mechanism with LSTM networks for RUL prediction of an aero-engine and significantly improved the accuracy of the prediction results [5]. Wang et al. introduced the SE attention module and combined it with CNN to achieve the RUL prediction of bearings [6]. Along with the development of deep learning, it is gradually emerged Transformer [7] networks that do not rely on traditional CNN and RNN mechanisms and consist solely of attention mechanisms. Zhang et al. used a Transformer model based on dual selfattentiveness to achieve life prediction for aero-engine [8]. In addition, there are many deep learning methods that combine Transformer models with multi-headed attention, two-headed attention, self-attentiveness, etc. for RUL prediction and achieved good results. However, the Transformer networks has the disadvantages of consuming more resources due to its large size of model. This paper explores a more efficient RUL prediction method that can combine the characteristics of transformer networks using attention structures to promote the goal of real-time prediction in the industrial field. In the paper, a RUL prediction method based on spatial-temporal attention network (STAnet) is proposed for multi-sensor data of complex engineering systems. Firstly, time series signals from multiple sensors are obtained from the measurement system in engineering and input them into the STA module in the network. Secondly, the feature extraction module is used to extract features from the weighted data to obtain hidden features. After that, the extracted hidden features are input into the information reinforcement module for weighting and decoding. Finally using a fully connected layers to obtain the final RUL predictions.

2 Preliminaries and Problem Statement In the industrial field, the RUL of a device is defined as the time interval between the failure moment and the current moment, which can be expressed as: RUL = T − t(T > t)

(1)

where T denotes the failure moment of the device and t denotes the current moment.

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In the study of RUL prediction, the mapping relationship between data and the prediction results of RUL can usually be defined in the following way: Yt = f (Xt )

(2)

where Xt , t = (1, 2, . . . , T ), is the input data of the device in operation, and T is the length of the time step. f is the function of mapping, and Yt is the real-time RUL of the prediction. In the paper, STAnet is used to build the mapping function, and the relevant details are explained in the following sections. The purpose of this paper is to explore the equipment RUL prediction with multisensor data input, and to deeply exploit the potential relations between multi-sensor data, so as to achieve the improvement of model prediction accuracy under the premise of ensuring light weight. The architecture of this method is illustrated in Fig. 1. It can be divided into offline training step and online prediction step. In addition, there are several common steps in them, for example, the selection of sensor features and data pre-processing. In the offline training step, we need to build a neural network prediction model and use pre-processed data from the historical database to train the model. In the online prediction step, using the trained model and processed real-time data to make real-time RUL predictions.

Offline Steps

Online Steps

Historical Database

Real-time data Sensor feature selection

Data pre-processing

The proposed GRT model

Trained model

Model training

Real-time RUL prediction

Fig. 1. Flow chart of the proposed RUL prediction.

3 Methods 3.1 STAnet Method Architecture Combining previous studies, in order to solve the problems of existing methods, a new RUL prediction method based on STAnet is proposed. The proposed STAnet consists of three parts: spatial-temporal attention module, feature extraction module, and information reinforcement module.

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As shown in Fig. 2, the processed sensor data are first input to the spatial-temporal attention module (STAM), this module analyzes the spatial information of the data, and adaptively weights and encodes the data for the temporal relationship of the data and the different sensor channels, and inject some markers in the data sequence that can reflect the relative position. In this way, the model makes it easy to use the temporal information in the data. Next, the LSTM-based feature extraction module (FEM) can further extract features from the weighted data to learn the hidden features in the sequence data. Finally, the extracted features are input to the information reinforcement module (IRM) for weight and decode hidden features while performing information reinforcement, filtering and complementation, and input the weighted data to the fully connected layers for RUL prediction.

Fully connected layers

spatialtemporal attention module

feature extraction module

information reinforcement module

Fig. 2. Overall structure of the proposed STAnet model.

3.2 Spatial-Temporal Attention Module For complex engineering systems, the features of the monitoring data usually have different degrees of correlation with the health degradation state. Therefore, it is necessary to have a mechanism that can adaptively extract the correlation of multi-sensor data features. The raw data is pre-processed and then input into the STAM. Global averaging pooling is first performed without reducing the number of input data sensor channel dimensions (the number of columns of input data). This operation can extract the overall characteristics of each sensor channel data, reflecting its overall information. After that, in order to assign a reasonable weight to each sensor channel data, a one-dimensional convolution with a kernel size of 17 is operated. The attention weight obtained in this way is no longer only focused on the data of the current sensor channel, but is the final result after taking into account the data of several surrounding sensor channels. After convolution operation, the data is made nonlinear by the sigmoid activation function, and obtain a weight matrix associated with the input data. Then, by expanding the dimension to the same size as the input matrix, the attention weights for each sensor

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channel are obtained. After that, the weights are multiplied element by element with the input data to obtain the weighted data. The calculation is expressed in the following equation: 1 1 + e−αf

(3)

xfw = xf ⊗ Wf

(4)

Wf =

Considering that in RUL prediction, the temporal relationship of the data has an extremely important impact on the prediction accuracy. In order to mine the potential information of the data as much as possible, some markers that reflect the relative positions are injected into the data sequences [9], as a way to make the model more easily exploit the temporal information in the sequences. This paper uses different frequencies of sine and cosine functions for encoding [7]: Pt (2k) = sin(t/100002k/D mod el )

(5)

Pt (2k) = sin(t/100002k/D mod el )

(6)

where t is the time step and k is the sensor size. Thus, there is a linear relationship between Pt and Pt+l . Moreover, the vectors encoded by this method can be added element by element with the original data to obtain the data containing the location information. This makes it possible for the model easier to acquire hidden features in the temporal relationships. 3.3 Feature Extraction Module The feature extraction module (FEM) is a deep feature extraction module for sequence data consisting of two different LSTMs and lookback mechanisms. LSTM is a good variant of the traditional recurrent neural network, which not only inherits the advantage that ordinary RNNs are good at handling temporal data, but also overcomes its frequent problem of gradient disappearance or gradient explosion, and significantly improves the ability to model long-term dependencies. The basic principle of the LSTM unit is shown in Fig. 3. As shown in Fig. 4, the STAM-weighted features are input to LSTM1 (the first LSTM network) for the first feature extraction. We set the number of features in the hidden layer of the network to Hhs . The output H , hn , cn can be obtained from LSTM1. Where H is the matrix of hidden states hi spliced into each time step, H = {h1 , h2 , h3 , . . . , hn−1 }T . hn is the hidden state at the last time step and cn is the cellular state at the last time step. After that, we define LSTM2 (the second LSTM network) and set both its input feature number and hidden layer feature number to Hhs . Use hn , cn as its initialized hidden state and cell state, and hn as its sequence input. Using LSTM2 to perform deeper feature extraction on the hidden state hn of the last time step extracted by LSTM1, the output ht , ct is finally obtained. In prediction tasks, one usually uses the last time step of the hidden state for RUL prediction. But this usually leads to the omission of some important information. Due

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Fig. 3. Structure of the LSTM.

spatial-temporal attention module

LSTM1

LSTM1

h1

h2

LSTM1

LSTM1

LSTM1

hn-1

hn

h3

lookback mechanism Hlb

LSTM2 ht

information reinforcement module

Fig. 4. The structure diagram of the feature extraction.

to the nature of RUL prediction, the equipment state closer to the time of failure is more important for RUL prediction. So a lookback mechanism is considered to be introduced to process the output H of LSTM1. When lookback takes the value of 40, it means that the last 40 time steps of the hidden state are selected for subsequent processing. Due to the nature of RUL prediction, the equipment state closer to the time of failure is more important. It can be assumed that the degradation information contained in the hidden state of the backward time step is better than that of the forward time step. 3.4 Information Reinforcement Module As stated in the previous section, the deep hidden features have been extracted after processing in the feature extraction module (FEM). However, as the feature extraction deepens, the problem of information loss and certain information redundancy will inevitably arise. Therefore, it is necessary to introduce the information reinforcement module (IRM) to weight and decode the feature data again to perform information complementation while achieving adaptive screening of important information. Finally, it is input into the fully connected layers, and the deep degradation features processed by the

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IRM are mapped into a specific remaining useful life value, this value is the equipment remaining useful life value that is output by the prediction model.

4 Experiment 4.1 Data Description In this paper, we evaluate model performance using the C-MAPSS dataset. The dataset is composed of four subsets. Every subset includes a training set, a test set, and a RUL file that records the true RUL values in the test set. The sensor measurements in the training set are recorded from the start time of the run to the final failure, and in the test set only the duration until the failure occurs is recorded. The RUL file is used to assess the accuracy of the predicted RUL method compared to the predicted results. There are two failure modes in the four data sets collected, each subset has 26 columns of data, where the first column of data is the engine number, the second column of data is the number of cycles, the next three columns of data are the operating conditions, and the last 21 columns show the measurements results of the sensor. 4.2 Data Preprocessing To simplify the difficulty of model feature extraction and improve the prediction accuracy, some filtering of the input data is usually chosen. The variance of the data for each sensor was calculated in the literature [10] and it was found that the variance of the data for some sensors was very close to zero. This indicates the values of these sensor data are constant. This paper finally chooses to eliminate the data of S1, S5, S6, S10, S16, S18 and S19, and the data from the rest 14 sensors form the new data as input. The minimum-maximum normalization technique of Eq. (13) is used to map the original signal to [0, 1], i,j

i,j

xnorm =

xi,j − xmin i,j

i,j

xmax − xmin

, ∀i, j

(7)

where xi,j denotes the raw data point of the j th sensor in the i th operating condition. i,j i,j xmax and xmin are the values of the maximum and minimum of the j th sensor signal for the i th operating condition. 4.3 Performance Evaluation Metrics Two widely used performance evaluation metrics, the scoring function (Score) and root mean square error (RMSE), are used in the RUL predictions in this paper. The above two metrics can measure prediction accuracy from different perspectives, with the scoring function penalizing late predictions (that is, predicted RUL is bigger than actual labels) more severe, while RMSE focuses equally on early and late predictions. Their mathematical expressions are as follows:  1 N RMSE = (ri − ri )2 (8) i=1 N 

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⎧ N  ⎪ ri −ri ⎪ ⎪ (e− 13 − 1), when ri < r ⎪ ⎪ ⎨ 



Score =

i=1

(9)

N ⎪  ⎪ ri −ri ⎪ ⎪ (e 10 − 1), when ri ≥ r ⎪ ⎩ 



i=1

4.4 Comparisons with Other Approaches There are many RUL prediction methods that have been validated using the C-MAPSS dataset, including BLLSTM [11], KDnet [12], etc. In order to verify the superiority of the model, the performance is compared with some other publicly available advanced methods. To minimize the effect of randomness, the final results are obtained by averaging the results after several experiments. As shown in Tables 1 and 2, STAnet obtained good results on each subset compared to the other methods. Table 1. RMSE comparisons of different methods on the C-MAPSS dataset. Method

FD001

FD002

FD003

FD004

LSTM [13]

16.74

29.43

18.07

28.40

BLLSTM [11]

–

25.11 19.43

– 13.39

26.61

AGCNN [10]

12.42

21.50

DSAN [14]

13.4

22.06

15.12

21.03

HDNN [15]

13.02

15.24

12.22

18.16

KDnet [12]

13.68

14.47

12.95

15.96

Proposed

11.08

14.21

11.41

15.59

Table 2. Score comparisons of different methods on the C-MAPSS dataset. Method

FD001

FD002

FD003

FD004

LSTM [13]

388.7

10654

822.19

6370.6

BLLSTM [11]

–

4793

–

4971

AGCNN [10]

225.51

1492

227.09

3392

DSAN [14]

242

2869

497

2677

HDNN [15]

245.00

1282.42

287.72

1527.42

KDnet [12]

362.08

929.20

327.27

1303.19

Proposed

190.71

795.31

189.54

1042.31

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5 Conclusion In this paper, a deep learning method for RUL prediction of multi-sensor machines based on a spatial-temporal attention network (STAnet) is proposed. Firstly, the raw sensor data is input into the spatial-temporal attention module adaptively to weight and encode the data for different importance. Secondly, the weighted data is input to the feature extraction module, which uses its powerful ability to process temporal information to do further feature extraction on the data in order to learn the hidden features in the sequence data. After that, the extracted features are input to the information reinforcement module for weighting and decoding to achieve certain information filtering and information complementation, and the features are input to the fully connected network to complete the RUL prediction. To validate the effectiveness of our proposed method for RUL prediction, it was compared with some state-of-the-art methods. The reliability and superiority of STAnet is demonstrated experimentally in two more commonly used dataset evaluation criteria.

References 1. Cheng, Y., Hu, K., Wu, J., Zhu, H., Shao, X.: Autoencoder quasi-recurrent neural networks for remaining useful life prediction of engineering systems. IEEE/ASME Trans. Mechatron. 27(2), 1081–1092 (2022) 2. Qin, Y., Chen, D., Xiang, S., Zhu, C.: Gated dual attention unit neural networks for remaining useful life prediction of rolling bearings. IEEE Trans. Industr. Inf. 17(9), 6438–6447 (2021) 3. Chen, Z., Cao, S., Mao, Z.: Remaining useful life estimation of aircraft engines using a modified similarity and supporting vector machine (SVM) approach. Energies 11(1) (2017) 4. Javed, K., Gouriveau, R., Zerhouni, N.: A new multivariate approach for prognostics based on extreme learning machine and fuzzy clustering. IEEE Trans. Cybern. 45(12), 2626–2639 (2015) 5. Zhao, Y., Wang, Y.: Remaining useful life prediction for multi-sensor systems using a novel end-to-end deep-learning method. Measurement 182 (2021) 6. Wang, B., Lei, Y., Li, N., Yan, T.: Deep separable convolutional network for remaining useful life prediction of machinery. Mech. Syst. Signal Process. 134 (2019) 7. Vaswani, A., et al.: Attention is all you need. In: 31st Annual Conference on Neural Information Processing Systems (NIPS), Long Beach, CA, 2017, vol. 30 (Neural Information Processing Systems (Nips), LA JOLLA, 2017) 8. Zhang, Z., Song, W., Li, Q.: Dual-aspect self-attention based on transformer for remaining useful life prediction. IEEE Trans. Instrum. Meas. 71, 1–11 (2022) 9. Ren, L., Jia, Z., Wang, X., Dong, J., Wang, W.: A T2-tensor-aided multi-scale transformer for remaining useful life prediction in IIoT. IEEE Trans. Ind. Inform. 1 (2022) 10. Liu, H., Liu, Z., Jia, W., Lin, X.: Remaining useful life prediction using a novel featureattention-based end-to-end approach. IEEE Trans. Ind. Inf. 17(2), 1197–1207 (2021) 11. Huang, C.-G., Huang, H.-Z., Li, Y.-F.: A bidirectional LSTM prognostics method under multiple operational conditions. IEEE Trans. Ind. Electron. 66(11), 8792–8802 (2019) 12. Xu, Q., Chen, Z., Wu, K., Wang, C., Wu, M., Li, X.: KDnet-RUL: a knowledge distillation framework to compress deep neural networks for machine remaining useful life prediction. IEEE Trans. Ind. Electron. 69(2), 2022–2032 (2022) 13. Hsu, C.S., Jiang, J.R.:Remaining useful life estimation using long short-term memory deep learning. In: 2018 IEEE International Conference on Applied System Invention (ICASI), pp. 58–61 (2018)

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14. Xia, J., Feng, Y., Teng, D., Chen, J., Song, Z.: Distance self-attention network method for remaining useful life estimation of aeroengine with parallel computing. Reliab. Eng. Syst. Safety 225 (2022) 15. Al-Dulaimi, A., Zabihi, S., Asif, A., Mohammadi, A.: A multimodal and hybrid deep neural network model for remaining useful life estimation. Comput. Ind. 108, 186–196 (2019)

Model-Free Predictive Current Control Strategy Considering Noise Error Compensation Yao Wang1 , Tao Rui2 , Wenping Cao1(B) , Ke Zhang3 , Cungang Hu1 , and Weixiang Shen4 1 School of Electrical Engineering and Automation, Anhui University, Hefei, China

[email protected]

2 School of Internet, Anhui University, Hefei, China 3 Jiangsu Dongrun Zhilian Technology Co., Ltd, Nantong, China 4 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology,

Melbourne, VIC 3122, Australia

Abstract. Aiming at dependence about traditional model-free predictive control (MFPC) methods on the accuracy of current gradients, the essay puts forward a MFPC way using second order generalized integrator (SOGI), which improves the accuracy of current gradients from two aspects. Firstly, the current gradient look-up table is refreshed at each control moment by using the sampled current information, and the current prediction at the external time is realized by combining the updated current gradient, which reduces the influence of the traditional MFPC method update stagnation. Secondly, by analyzing the influence of measurement noise such as switching noise and environmental noise on the accuracy of the current gradient, a SOGI is designed and employed to compensate error of current gradient, enhance the reliability of current gradient, then improve output current property. Conclusively, simulation waveforms certifies efficacy of the given method in enhancing robustness of parameters and suppressing the influence of noise. Keywords: Model-free predictive control · Look-up table · Second-order generalized integrator

1 Introduction In recent years, model predictive control (MPC) has been diffusely used in many fields because of straightforward implementation and fast dynamic response [1, 2]. However, MPC depends on the parameters of the model, and incorrect parameters can result in biased prediction [3]. To decrease influence of parameters on prediction, some scholars proposed a method called model-free predictive current control (MFPCC). Literature [4] proposes recursive least squares estimation method, and literature [5] proposes hyperlocal model method. By comparing the above two methods, literature [6, 7] proposes MFPCC method based on look-up table (LUT), which has attracted much attention because of its simplicity, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 883–889, 2023. https://doi.org/10.1007/978-981-99-4334-0_106

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effectiveness and small computational burden. However, MFPCC method using LUT proposed by literature [6] only updates current gradient corresponding to voltage vector (v) used after each interrupt, which is difficult to further improve the predictive control effect. Therefore, literature [7] estimates and updates current gradients of all versus before the end of each cycle, but current gradient update stagnation still exists at this time. At the same time, because the control effect of MFPCC depends on the accuracy of the current gradient, noise error is particularly subsistent while current gradient is completely updated. When the current sampling value has errors, all the data in the LUT will have errors, which deteriorates the control performance. Based on the realization of all current gradient updates in LUT, this paper analyzes the influence of environmental noises such as switching noise and electromagnetic interference on all current gradients in LUT. The SOGI [8] is designed and employed to compensate error of current gradient to ensure the high reliability of the current gradient. Eventually, by analyzing simulation waveforms, to verify the method.

2 Basic Principles of MFPCC

Fig. 1. Topology and voltage vector of VSI

Figure 1 shows the topological structure and voltage vector diagram of the voltage source inverter (VSI), and its mathematical model in αβ axis is shown: L

d iαβ = uαβ − Riαβ − eαβ dt

(1)

where uαβ is inverter output vector of voltage, iαβ is inverter output vector of current, eαβ is vector of grid; L is inductance; R is line resistance. Formula (1) could be processed to obtain current at time (k + 1) and expressed: iαβ (x + 1) = iαβ (x) +

1 (uαβ (x) − Riαβ (x) − eαβ (x)) fs L

(2)

where 1/f s stands for controllable cycle time. To decrease influence of parameters on prediction, MFPCC strategy based on LUT was proposed in literature [6, 7], which obtained gradient of current from two control periods’ sampling values: j

j

iαβ (x) = iαβ (x + 1) − iαβ (x)

(3)

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Among them, i j αβ (k) is the current gradient corresponding used voltage V j at k th . If length of control cycles is extremely short-term, resistance R, the current iαβ and the grid voltage eαβ are approximately considered to be unchanged through the difference of the current gradients at the two moments defined in Eqs. (2) and (3), and the following can be obtained: j

iiαβ (x − 1) − iαβ (x − 2) =

1 i j (u (x − 1) − uαβ (x − 2)) fs L αβ

(4)

where i and j represent the basic voltage vectors selected during two consecutive control periods. If, instead of the i-vector, the other seven basic voltage vectors are chosen at time (k − 1), represented by l, and then compared with Eq. (4), the rest of the current gradients can be obtained after rearrangement: ⎧   ⎪ ⎨ iαl (x − 1) = iαj (x − 2) + A iαi (x − 1) − iαj (x − 2)   (5) ⎪ ⎩ iβl (x − 1) = iβj (x − 2) + B iβi (x − 1) − iβj (x − 2)  where A =

j

uαl (x−1)−uα (x−2) j uαi (x−1)−uα (x−2)

j

,B =

uβl (x−1)−uβ (x−2) j uβi (x−1)−uβ (x−2)

.

If the same basic voltage vector is selected for two consecutive control periods, that is, [A, B]T = [0, 0]T , Eq. (5) cannot continue to be calculated, which will lead to update stagnation. In such circumstances, the current gradient LUT requires for judging before each update, that is, whether it meets [A, B]T > [δ α , δ β ]T , if this condition is met, Eq. (5) is used to update the table, where δ αβ is the given threshold; If this condition is not met, all table data is updated to the next schedule. Select vector of voltage which causes the lowest value in Formula (6) and act on the next control period. ref ref (6) g = iα (x + 2) − iα (x + 2) + iβ (x + 2) − iβ (x + 2) where iref α (x + 2) and iref β (x + 2) are referential currents in the αβ coordinate system at time (k + 2).

3 Error Compensation Based on Second-Order Generalized Integrator Although the current gradient stagnation of MFPCC is improved, the precision for current gradient is still suffering by the sampling noise. Figure 2 depicts the influence of environmental noises such as switching noise and electromagnetic interference on the sampling current in the implementation of MFPCC. If there is noise in the sampled current, the current gradient value obtained according to Eq. (3) will also have a deviation, which will affect the accuracy of the remaining current gradient update.

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Fig. 2. Sampling current with noise

Fig. 3. SOGI block diagram

Assuming iα0, iβ0 are ideal values and iα, iβ are sampled values, then the relationship between ideal values and sampled values is as follows: ⎡ ⎤

 

iA iα i + λα iα0 = C3/2 ⎣ iB ⎦ = α0 (7) iβ iβ0 + λβ iβ0 iC where, [λα ,λβ ]T = C 3/2 [λA ,λB ,λC ]T , λY iY0 , Y{α,β} are sampling error caused by noise in αβ coordinates. Substitute the sampling current into Eq. (2): iαβ (x − 1) = iαβ (x) − iαφ (x − 1) 1 = (uαβ (x − 1) − RA iαβ (x − 1) − eαβ (x − 1)) fs LA

(8)

At a very high number of switching frequencies, L A , RA and eαβ are approximately considered constant during a controller cycle T s . This is illustrated in Exhibit 1, uαβ is the voltage vector corresponding to the eight output switching states of the inverter, which are eight known quantities, and different basic voltage vectors vx correspond to different current gradients ix αβ . In this case, the error of the current gradient iαβ is only related to the noise introduced by the sampled current value iαβ . In the same control period, the measurement noise has the same influence on various gradient of current. Figure 3 shows the structure diagram of SOGI. Taking current gradient i0 as the input target of SOGI, its transfer function is obtained as follows: G(s) =

kω0 s i 0 (s) = 2 i0 (s) s + kω0 s + ω02

(9)

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where k is the gain of SOGI, ω0 = 2πf 0 , and f 0 is the power grid frequency 50Hz. After transformation, the discrete equation can be obtained as follows: 

i 0 (x) = ai0 (x) + bi0 (x − 2) + ci 0 (x − 1) + d i 0 (x − 2)

where, a =

2Ts kω0 4+2Ts kω0 +Ts2 ω02

, b

=

−2Ts kω0 , 4+2Ts kω0 +Ts2 ω02

c

=

−2Ts2 ω02 +8 , 4+2Ts kω0 +Ts2 ω02

(10) d

=

−4+2Ts kω0 −Ts2 ω02 4+2Ts kω0 +Ts2 ω02

The current gradient offset error caused by measurement noise is defined as: erro(k) = i0 (k) − i 0 (k)

(11)

The error is compensated to other current gradients to enhance the precision of the current ramp in the LUT.

4 Simulation To evaluate the methodology outlined above, relevant simulations are presented. Simulation related parameters: Supply voltage on DC side 350 V, Net Power Voltage 160 V, line resistance 0.05 , filter inductance 8 mH, sampling frequency 20 kHz, The gain of the second-order generalized integrator 0.5. 4.1 Simulation Comparison of Model Parameter Mismatch The methodology introduced in the manuscript is denoted as SOGI-MFPCC. In this section, the raised approach is simulated and made comparisons with conventional MPC methodology in the case of mismatched filter inductance parameters. Figure 4(a) shows the MPC waveform and THD when filter inductor parameters are matched (8mH), Fig. 4(b) shows the MPC waveform and THD when filter inductor parameters are not matched (16 mH), and Fig. 4(c) shows the waveform and THD of the proposed method SOGI-MFPCC when inductor parameters are not matched (16mH). It is possible to notice from the Fig. 4, in case of inaccurate inductor parameters, the control effect of MPC solutions will be affected. The SOGI-MFPCC strategy does not use circuit parameters, so it does not affect its control performance in the case of mismatched inductor parameters. 4.2 Simulation Results of Prediction Effect To validate the SOGI-MFPCC in terms of current prediction effect, it is compared with the traditional MFPCC in the condition of injecting random noise to predict the current deviation. Figure 5(a) exhibits the discrepancy from predicted and reference currents in αβ coordinate axis after random noise injection in traditional MFPCC. Figure 5(b) shows the deviation between projected and referential currents under the αβ coordinate axis after random noise injection of the proposed SOGI-MFPCC. Through comparison, it is possible to get that the proposed SOGI-MFPCC strategy has less deviation in predicting current under the influence of noise, that is, the prediction effect is superior to conventional MFPCC.

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Fig. 4. Simulation comparison under inductance parameter mismatch (10A)

Fig. 5. Simulation comparison of predictive current deviation

5 Conclusion Throughout this article, a MFPCC built on SOGI is presented. Compared with MPC strategy, the presented solution has better robust parameter characteristics, simpler prediction process, faster responsiveness. Comparative to conventional MFPCC, the presented solution can obtain more accurate current gradient value under the influence of noise by error compensation through SOGI, so as to achieve better predictive control effect. Acknowledgements. This paper is supported by the Policy Guidance Plan (International Scientific and Technological Cooperation)—Key National Industrial Technology Research and Development Cooperation Project (BZ2018014).

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References 1. Andersson, A., Thiringer, T.: Assessment of an improved finite control set model predictive current controller for automotive propulsion applications. IEEE Trans. Ind. Electron. 67(1), 91–100 (2020) 2. Yan, L., Wang, F., Dou, M., Zhang, Z., Kennel, R., Rodríguez, J.: Active disturbance-rejectionbased speed control in model predictive control for induction machines. IEEE Trans. Ind. Electron. 67(4), 2574–2584 (2020) 3. Lee, K., Park, B., Kim, R., Hyun, D.: Robust predictive current controller based on a disturbance estimator in a three-phase grid-connected inverter. IEEE Trans. Power Electron. 27(1), 276–283 (2012) 4. Brosch, A., Hanke, S., Wallscheid, O., Böcker, J.: Data-driven recursive least squares estimation for model predictive current control of permanent magnet synchronous motors. IEEE Trans. Power Deliv. 36(2), 2179–2190 (2021) 5. Zhang, Y., Jiang, T., Jiao, J.: Model-free predictive current control of a DFIG using an ultralocal model for grid synchronization and power regulation. IEEE Trans. Energy Convers. 35(4), 2269–2280 (2020) 6. Lin, C., Liu, T., Yu, J., Fu, L., Hsiao, C.: Model-free predictive current control for interior permanent-magnet synchronous motor drives based on current difference detection technique. IEEE Trans. Ind. Electron. 61(2), 667–681 (2014) 7. Ma, C., Li, H., Yao, X., Zhang, Z., De Belie, F.: An improved model-free predictive current control with advanced current gradient updating mechanism IEEE Trans. Ind. Electron. 68(12), 11968–11979 (2021) 8. Ikken, N., Bouknadel, A., Haddou, A., Tariba, N.-E., El Omari, H., El Omari, H.: PLL synchronization method based on second-order generalized integrator for single phase grid connected inverters systems during grid abnormalities. In: 2019 International Conference on Wireless Technologies, Embedded and Intelligent Systems (WITS), Fez, Morocco, pp. 1–5 (2019)

An Improved Sub-pixel Corner Detection Algorithm Junhua Wu and Lusheng Ge(B) School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China [email protected]

Abstract. Aiming at the problems of low accuracy and poor stability of traditional sub-pixel corner detection algorithm, an improved sub-pixel corner detection algorithm is proposed in this paper. Firstly, the poor sub-pixel corner points are extracted, and then the cluster centered on the sub-pixel angle is constructed, the cluster angle is processed by distance weighting, and finally the least squares method is used to solve it to obtain accurate sub-pixel corner position information. Experimental results show that compared with the traditional angle algorithm, the correct extraction rate and coordinate accuracy of the improved algorithm have been greatly improved. The algorithm can provide reliable data for the research of high-precision vision systems to meet the practical application requirements. Keywords: Stereo vision research · Sub-pixel corner detection · Least square method

1 Introduction Corner point detection algorithms are widely used in vision research, image processing, target detection and other research fields [1]. It is an important pre-processing step in binocular stereo vision research, and effective improvement of the corner point detection algorithm will greatly improve the calibration accuracy and achieve the accuracy requirements in vision research [2]. This paper uses an image grayscale-based angle detection algorithm to improve it [3–5]. Firstly, the image is processed by improved bilateral filtering, and then the gray gradient method and the fitting interpolation method are combined to propose a new improved subpixel corner detection algorithm. The algorithm does not require much hardware, and the corner point information can be extracted more accurately by using a suitable corner point detection optimization formula [6, 7].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 890–896, 2023. https://doi.org/10.1007/978-981-99-4334-0_107

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2 Principle of Algorithm 2.1 Image Preprocessing When performing corner detection experiments, it is necessary to ensure the “cleanliness” of the image. In real industrial detection, noise “contamination” cannot be avoided, such as the occlusion of stains, the influence of lighting and angles during shooting, and so on. This paper first preprocesses the image “contamination” locations. The first step is to perform morphological closing operation on the noise to eliminate the obvious noise in the image; the second step uses bilateral filtering to preserve the edge information of the image and remove small noise. The output formula of bilateral filtering is:  k,l f (k, l)w(i, j, k, l)  (1) g(i, j) = k,l w(i, j, k, l) The weighting factors in Eq. 1 are as follows.   |f (i, j) − f (k, l)| (i − k)2 + (j − 1)2 w(i, j, k, l) = exp − − 2δr2 2δd2

(2)

In the above equation, (k, l) is the center of the filter template, (i, j) are the coordinates of other coefficients of the template, δd is the standard deviation of the Gaussian function in the value domain for bilateral filtering, δr is the standard deviation in the spatial domain, and f (i, j), f (k, l) denote the pixel values of points (i, j) and (k, l). The standard deviation of the filter used in this paper is 1 and the template size is 3*3 for bilateral filtering. 2.2 Extract Poor Corners Grayscale gradient method. The formula for the gray scale gradient method is: Q=

n 

(∇HiT ∇Hi )−1 ∗ (∇HiT ∇H • Pi )

(3)

i=0

where ∇HiT is the grayscale gradient vector of a point in the image, Q is the subpixel point in the image and is the unknown point, Pi is the pixel around Q in the image, and ∇Hi represents the grayscale gradient value of the point. Fitted interpolation method. The fitted interpolation method uses a two-polynomial to approximate the response function as shown in formula (4). ax2 + by2 + cxy + dx + ey + f = R(x, y)

(4)

where R(x, y) is the response function obtained by the Harris algorithm, and a, b, c, d are the coefficients of the quadratic polynomial. In the experiment, a 3*3 template is used to traverse the image, and 8 points in the field of a real corner point are taken to create 8 superdeterministic equations, and least squares is used to solve the coefficients in the

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equation. Solving for the subpixel corner locations in the Harris algorithm can only be the derivative of the quadratic polynomial for the extreme value points, and the partial derivatives are made zero. Formula (5) is obtained as follows. ⎧ δR ⎪ ⎪ = 2ax + cy + d = 0 ⎨ δx δR ⎪ (5) ⎪ = 2by + cx + e = 0 ⎩ δy

Solving the equation yields the location of the subpixel corners.

3 Improved Sub-pixel Corner Detection Algorithm Due to the high robustness of the gray gradient method, the calculation speed is fast, but the accuracy is not high. The fitting interpolation method has high accuracy but poor stability. Therefore, this paper combines the two algorithms. Using the grayscale ladder method and the fitting interpolation method, the sub-pixel-level corner position information is obtained as (xg , yg ) and (xn , yn ) respectively. The final corner position is calculated by weighting as shown on formula (6).

x = k1 xg + k2 xn (6) y = k1 yg + k2 yn where k1 and k2 denote the weighting coefficients, respectively, and the value around 0.5 was selected through several experiments for better test results. The sub-pixel corners obtained by the above formula are then screened by an improved double mask (S1 , S2 ), S1 and S2 are regarded as two classes. The size of the two masks is designed to be 3 × 3 and 9 × 9. Use the coordinates (x, y) obtained from formula (6) as the center coordinate of S1 , calculate the response value of the corner response function R of this point, and calculate the mean value of ln(|R(x, y)|) in the two classes, if the function response values are all maximal values in mask (S1 , S2 ) and the maximal value in S1 corresponds to the value of ln(|R(x, y)|) greater than the mean in class S2 . Then it is considered that the pixel point (x, y) obtained by formula (6) may be the real corner point, and the points that do not meet the above requirements are directly eliminated. This further reduces the computation of subsequent precise sub-pixel corners. The formula of the corner point response function used in the modified algorithm of this paper to determine the position of corner points is shown in formula (7). R=

λ1 λ 2 λ1 + λ2 + ε

(7)

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In the formula: ε is the coefficient factor, which is to prevent traces of the matrix from being zero, usually taking a value of 0.00001. λ1 and λ2 are the two eigenvalues of matrix N in Harris’s algorithm, and R is the corner response function. Compared with the traditional response function, the response operator used in this paper avoids the decomposition of eigenvalues, making the operator more stable and practical. After the double mask filtering process, the remaining pixel points are the points to be detected, and then take the point to be detected as the center to take all points within a certain radius as a cluster, and first perform the response function weighting process on the corner points in the cluster to respond The function R is the weight of the cluster corner, and finally the Euclidean distance between the center point and the cluster corner is weighted by the least square method to obtain the precise sub-pixel corner coordinates, as shown in formula (8): J =

n 

Pj Sj

(8)

j=1

where Sj is the square of the Euclidean distance between the centroid and the feature points (x, y) in the cluster, Pj is the weight of the corner points within the cluster, and Sj is: 



2 2 Sj = x − xj + y − yj 



(9)

Combine formula 9 and rewrite formula 8 as: J = V T PV ⎡

x − x1

(10)

⎤

⎡ P1 ⎢ y − y1 ⎥ ⎢ P ⎢ ⎥ 1 ⎢ ⎢ ⎥ ⎢ ⎢ x − x2 ⎥ P2 ⎢ ⎢ ⎥ ⎢ ⎢ y − y2 ⎥ P2 ⎢ n ⎢ ⎥  ⎢ ⎥ .. where V = ⎢ Rj and P = ⎢ ⎢ .. ⎥, Pj = Rj / . ⎢ i=1 ⎢ . ⎥ ⎢ ⎢ ⎥ ⎢ .. ⎢x − x ⎥ . ⎢ ⎢ n⎥ ⎢ ⎢ ⎥ ⎣ Pn ⎣ y − yn ⎦ 

⎤



⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦









Pn

Using the least squares method to solve: ⎧ n  ∂J ⎪ ⎪ ⎪ =2 Pj (x − xj ) = 0 ⎪ ⎪ ⎨ ∂x 



j=1

n ⎪  ⎪ ∂J ⎪ ⎪ = 2 Pj (y − yj ) = 0 ⎪ ⎩ ∂y 



j=1

(11)

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Solving formula (11) obtains: ⎧ n  ⎪ ⎪ ⎪ x= Pj xj ⎪ ⎪ ⎨ j=1 

n ⎪  ⎪ ⎪ ⎪ y = Pj yj ⎪ ⎩

(12)



j=1

In the above formula, n is the number of all pixels in the cluster with radius r, and Rj is the response function value CRF of the feature points in the cluster. Finally, the least square method is used to set J as the minimum value, and the more accurate sub-pixel corner coordinates (x, y) are obtained, which is the final corner mark obtained in this experiment. The flowchart of the improved algorithm in this paper is shown in Fig. 1. 



Fig. 1. Improved subpixel corner point detection algorithm flowchart

4 Experimental Results and Analysis 4.1 Sub-pixel Corner Point Detection Simulation In order to verify the accuracy and stability of the algorithm in this paper, this paper uses different photos to extract corner points simultaneously using Harris algorithm, traditional subpixel corner detection algorithm, and improved algorithm in this paper, and experiments are carried out on the Visual Studio 2017 platform. Figure 2 shows a comparative experiment of the three algorithms. 4.2 Sub-pixel Corner Point Detection Accuracy Simulation Table 1 shows the comparison between the traditional sub-pixel corner detection algorithm and the improved sub-pixel corner detection algorithm in this paper. The results of the detection by three algorithms are statistically and calculated as shown in Fig. 3(a). In order to objectively represent the scale invariance of the three algorithms, this paper selects multiple images with different scales through the three detection algorithms, as shown in Fig. 3(b). Analysis of Fig. 3(a) can clearly show that the recall and precision of the algorithm can be approximately 100% in images with simple gray value changes, and the accuracy of the improved algorithm in this paper is in images with complex gray changes and recall

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(a)

(b)

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(c)

Fig. 2. Comparative experiment of three algorithms

Table 1. Algorithm comparison (coordinate unit: pixel) Part of the corner

Traditional algorithm coordinate

Improved algorithm coordinate

Traditional algorithm average offset (Absolute Value)

Improved algorithm average offset (absolute value)

1

(6.254, 66.053)

(6.145, 65.891)

0.221

0.086

2

(145.669, 174.226)

(144.569, 174.023)

0.817

0.166

3

(185.669, 256.741)

(186.923, 256.569)

1.031

0.149

4

(204.015, 120.631)

(199.395, 124.015)

2.856

1.148

can exceed the accuracy of traditional subpixel algorithms by about 20%. Experimental results show that the improved algorithm not only excludes lots of pseudo-corner points, but also reduces the corner point redundancy and has a higher degree of precision. Figure 2(b) shows the corner repetition rate of Harris algorithm is close to 30%, the corner repetition rate of the traditional subpixel corner algorithm is 25%, and the corner repetition rate is only 35% and 55% when the scale parameter is 5. This indicates that the larger the scale, the worse the scale invariance of the algorithm, while the improved algorithm in this paper has more stable detection corners, better robustness and high scale invariance.

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(a)

(b)

Fig. 3 Plots of experimental results

5 Conclusion Through experimental verification, compared with the traditional corner point algorithm, the accuracy and recall rate of the improved algorithm are increased by nearly 20%, and the accuracy of the corner coordinates is increased by more than 2 times, and it has very good scale invariance, which can meet the accuracy requirements in visual research.

References 1. Luo, C., Sun, X., Sun, X., Song, J.: Improved Harris corner detection algorithm based on Canny edge detection and gray difference preprocessing. J. Phys. Conf. Ser. 1971(1) (2021) 2. Tang, H., Song, C., Qian, M. :Automatic segmentation algorithm for breast cell image based on multi-scale CNN and CSS corner detection. Int. J. Knowl. Based Intell. Eng. Syst. 24(3):195– 203 (2020) 3. An, M.S., Kang, D.S.: The distance measurement based on corner detection for rebar spacing in engineering images. J. Supercomput. 78(10), 12380–12393 (2022) 4. Hong, F., Lu, C.H., Liu, R.R.: Research on an improved adaptive learning algorithm for salient target detection in corner detection adaptive. Paper Asia 2(2), 144–146 (2019) 5. Han, S., Yu, W., Yang, H., Wan, S.:An improved corner detection algorithm based on Harris. In: 2018 Chinese Automation Congress (CAC), pp. 1575–1580 (2018). https://doi.org/10.1109/ CAC.2018.8623814 6. Zhang, H., Xiao, L., Xu, G.:A novel tracking method based on improved FAST corner detection and pyramid LK optical flow. In: 2020 Chinese Control And Decision Conference (CCDC), pp. 1871–1876 (2020). https://doi.org/10.1109/CCDC49329.2020.9164332 7. Ying, X., Zhang, Z.: Visual recognition of robot targets in complex state based on sub-pixel Harris corner. E3S Web Conf. 233 (2021)

Research on Information Interaction Technology for Mobile Energy Storage Xinzhen Feng1(B) , Chen Zhou1 , Fan Yang2 , Shaojie Zhu3 , and Xiao Qian2 1 State Grid Shanghai Energy Interconnection Research Institute Co., Ltd., NanjingJiangsu

Province 210003, China [email protected] 2 State Grid Zhejiang Electric Power Co., Ltd., Zhejiang Province, Hangzhou 310012, China 3 China Electric Power Research Institute Co., Ltd., Zhejiang Province, Hangzhou 310012, China

Abstract. The large-scale grid connected power generation of renewable energy will continue to improve. The problems of large grid fluctuations, poor power quality and poor flexibility regulation capacity caused by intermittent output are important challenges that the power system needs to deal with. Mobile energy storage technology has attracted much attention because of its strong flexibility, fast response and wide coverage. In order to implement the high reliable power supply in the Winter Olympic Games area, aiming at the demand of the mobile energy storage vehicle participating in the Winter Olympic Games support application, this paper proposes an information interaction technology for the mobile energy storage system participating in the multi scene application, which realizes the information interaction between the virtual power plant, the power supply service command system and the power supply support platform. Several application scenarios of the Winter Olympic Games are studied, and the mobile energy storage system is verified to improve the flexibility of the power grid and the ability of power supply guarantee. Keywords: Renewable energy · Mobile battery energy storage system · Multi-scenario application · Information Interaction

1 Introduction At the UN General Assembly in 2020, President Xi Jinping proposed the goals of “carbon peaking” and “carbon neutrality”. By 2030, carbon dioxide emissions will be reduced by more than 65% compared with 2005, and the proportion of non-fossil energy in primary energy consumption will reach 25%. However, the strong volatility, randomness and intermittency brought by the large-scale grid connection of new energy generation have further increased the difficulty of real-time power balance [1–4]. In order to meet the needs of different power scenarios such as peak shaving and frequency modulation and meet the new challenges of space-time constraints of power services, mobile energy storage equipment with dual characteristics of power supply and load and the advantages © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 897–904, 2023. https://doi.org/10.1007/978-981-99-4334-0_108

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of high flexibility, strong adaptability and low cost will be an important way to break through the traditional power grid planning, build a new operation mode and realize power security [5–8]. In recent years, as the cost of electrochemical energy storage technology continues to decline, more and more mobile energy storage systems are connected to the power grid for demonstration operation, and it is an inevitable trend to apply them on a large scale in the future. Mobile energy storage equipment has been applied to improve the elasticity of the power grid [9, 10] and improve the power supply capacity of the isolated island power grid in extreme weather [11, 12]. In addition, mobile energy storage vehicles can also be used to provide voltage regulation and reactive power support services and absorb abandoned wind power. Few studies have applied mobile energy storage vehicles to improve the flexibility of power grid operation. In view of the coordination and application requirements of “source-grid-load-storage” of mobile energy storage vehicles in the Beijing Winter Olympics guarantee scenario, this paper proposes an information interaction technology for mobile energy storage to participate in multi-scenario applications, which realizes the information interaction between virtual power plants, power supply service command systems and power supply guarantee platforms, and studies several typical scenarios of the Winter Olympic Games.

2 Information Interaction Logic of Energy Storage Vehicle In addition to being used as an emergency power supply in case of power grid failure, the mobile energy storage system can also be combined with the demand of the power grid and applied in the scenarios of temporary capacity increase in the distribution station area, guaranteed power supply of important loads and uninterrupted operation. The mobile energy storage system carries out information interaction with virtual power plants, power supply service command systems, and power supply guarantee command platforms, so as to realize power supply guarantee and improve flexibility. The virtual power plant sends task instructions to the energy storage vehicle. After receiving the instructions, the intelligent monitoring terminal makes logical judgment, and then feeds back to the virtual power plant whether to execute the instructions. If so, the intelligent terminal generates tasks to PCs, and then executes the corresponding tasks. At the same time, PCs sends energy storage vehicle data to the power supply guarantee command platform through the intelligent terminal in real time. The information exchange process between mobile energy storage platforms is shown in Fig. 1. 2.1 Emergency Power Protection Task In the second day after the implementation of the emergency power supply task, the power of the energy storage vehicle will remain at its best. Therefore, the specific logical steps for judging instructions are as follows. Step 1: judge the status of the energy storage vehicle. Judge each element of the C array. If the energy storage vehicle status index CC = 1, go to step 2; If CC = 0, judge to stop immediately and jump to step 4. This step continues to judge. When the state of

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Fig. 1. Interaction process between platforms of energy storage system

the energy storage vehicle does not meet the standard, the energy storage vehicle will return for maintenance.  0, ∃Ci = 0 (1) CC = 1, ∀Ci = 1 where C i are the elements of the C array. Step 2: judge the capacity of the energy storage vehicle. Calculate the number of energy storage vehicles to be dispatched H, where SES1_1 is the reserve capacity, and ES is the capacity of the energy storage vehicle.   SES 1_1 (2) H= ES where SESES1_1 round up, get h, and skip to step 4. Step 3: reject the instruction. The on-board information terminal system judges that the energy storage vehicle cannot realize the command task. Step 4: respond to instructions. The on-board information terminal system judges that the energy storage vehicle can realize the command task, feed back the response command information to the emergency power supply platform, and send the command task information to the PCS system. 2.2 Virtual Power Plant Tasks According to the real-time power supply and demand, the virtual power plant sends instructions to the energy storage vehicle. The energy storage vehicle receives the instructions and logically judges whether to implement them. When responding to the implementation, it makes a real-time response. Before receiving the new instructions, it carries out according to the original instructions. The logical judgment steps of whether the energy storage vehicle executes the virtual power plant vehicle output command are as follows: Step 1: judge the status of the energy storage vehicle. Judge each element of the C array. If the energy storage vehicle status index Cc = 1, go to step 2; If Cc = 0, judge

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to stop immediately and jump to step 4. This step continues to judge. When the state of the energy storage vehicle does not meet the standard, the energy storage vehicle will return for maintenance.  0, ∃Ci = 0 (3) CC = 1, ∀Ci = 1 where are the elements of the C array. Step 2: judge the cumulative discharge of the energy storage vehicle. Calculate whether the charging and discharging exceed the output limit of the energy storage vehicle after completing the charging and discharging task. That is, add the total charge and discharge power of this task: if = 1, skip to step 4; If = 0, skip to step 3. Step 3: reject the instruction. The on-board information terminal system judges that the energy storage vehicle cannot realize the command task, and feeds back the information of rejecting the command to the virtual power plant. Step 4: respond to instructions. Through judgment, the on-board information terminal system can realize the command task, feed back the response command information to the virtual power plant, and send the command task information to the PCS system. 2.3 Virtual Power Plant Tasks Send the environmental temperature, internal temperature, total capacity, available capacity, deployment location, climbing speed, battery unit safety status information and other visual information of the energy storage vehicle to the power supply guarantee platform for unified display.

3 Research on Collaborative Information Interaction of Energy Storage Since the execution of emergency power supply tasks has the highest priority, in addition to the execution of emergency power supply tasks, only for the energy storage vehicle when executing the virtual power plant and supply and service system commands, explore how the energy storage vehicle responds. Therefore, during the event, the energy storage vehicle only performs the task of ensuring power supply, and does not accept other scheduling instructions such as virtual power plants; in the period when there is no competition, the energy storage vehicle does not need to participate in the task of power supply and maintenance. In order to further give play to the flexible regulation attribute of the energy storage vehicle in the period of non guaranteed power supply, the mobile energy storage vehicle in the period of non guaranteed power supply participates in the virtual power plant under the command of the control center, and receives the dispatching instructions of the power supply and service department for redundant electricity. There are three main application scenarios for specific events.

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3.1 Simulation Scenario 1 When the energy storage vehicle performs the task of ensuring power supply first, there is still redundant time to participate in the scheduling of the virtual power plant. For example, when the energy storage vehicle performs the task of ensuring power supply in a venue from 9:00 to 11:00, after the execution is completed, the virtual power plant sends instructions to the energy storage vehicle after 11:00 to perform the charge and discharge task at a place near the venue. 3.2 Simulation Scenario 2 When the energy storage vehicle performs the task of ensuring power supply in the first and second time periods, there is redundant time in the middle, and it can participate in the scheduling of the virtual power plant. For example, when the energy storage vehicle performs the task of ensuring power supply in a venue from 8:00 to 10:00 and from 19:00 to 21:00 (the instructions are zl1_1, zl1_2), and the virtual power plant issues the instructions to the energy storage vehicle to perform the charge and discharge task at a place near the venue in a certain period from 11:00 to 18:00. 3.3 Simulation Scenario 3 When the energy storage vehicle performs the task of ensuring power supply after and before the task, the energy storage vehicle is in standby state. At this time, the energy storage vehicle has redundant time and can participate in the scheduling of the virtual power plant. For example, when the energy storage vehicle needs to perform the task of ensuring power supply in a venue from 19:00 to 21:00, and the virtual power plant sends an instruction to the energy storage vehicle at a time before 18:00 to perform the charge and discharge task at a place near the venue.

4 Experimental Test Carry out corresponding test experiments for the application of the developed 250 kw/500 kwh mobile energy storage vehicle in the Winter Olympic events. The system has the functions of low temperature start-up and fast grid connection switching in cold environment. The switching time is no more than 10 ms, and the harmonic content of off grid power supply is less than 3%, so as to achieve high reliability and high quality power supply for Winter Olympic Stadium equipment. In order to verify the power preservation ability of mobile energy storage system to participate in important loads, the energy storage system grid-connected to off-grid switching experiment is carried out, when the grid side fails, the energy storage system can achieve seamless switching, and the start time from the switching point is less than 10ms, which can ensure the uninterrupted power supply of important loads. The energy storage system switching from grid to grid during power preservation of important loads is shown in Fig. 2.

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In order to verify the interaction ability between the mobile energy storage system and the supply and service platform, after the power grid is restored, the mobile energy storage can realize the simultaneous control of grid connection. From the experimental results, the AC side current has no impact and no distortion of the voltage, which can achieve smooth grid connection. The simultaneous experiment of mobile energy storage vehicle connected to the grid is shown in Fig. 3.

Fig. 2. Waveform diagram of energy storage system switching from grid to grid during power preservation of important loads

Fig. 3. Simultaneous experiment of mobile energy storage vehicle

In order to verify the interaction ability between the mobile energy storage system and the supply and service platform, after the power grid is restored, the mobile energy storage can realize the simultaneous control of grid connection. From the experimental results, the AC side current has no impact and no distortion of the voltage, which can achieve smooth grid connection. In order to verify the interaction ability between the energy storage system and the virtual power plant, the grid-connected charging experiment of the energy storage system participating in the absorption of new energy was carried out, and Fig. 4 shows the charging and discharging waveform of the energy storage system.

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Fig. 4. The charging and discharging waveform of the energy storage system

5 Conclusion Aiming at the mobile energy storage vehicle participating in the emergency power maintenance support of the Winter Olympics project, this paper proposes an information interaction technology for mobile energy storage participating in multi scenario applications, which realizes the information interaction between the mobile energy storage vehicle and the virtual power plant, the power supply service command system and the power supply support platform. The conclusions are as follows: The mobile energy storage system can realize the emergency power supply guarantee of important loads and ensure the power safety of key devices in the Winter Olympic Games area. It can realize the information plug and play of mobile energy storage vehicle, and meet the needs of multi-party scheduling control. Through information interaction, the multi-function reuse of mobile energy storage vehicles is realized, the utilization efficiency of mobile energy storage vehicles is improved, and the power supply guarantee ability of important loads is improved. Acknowledgements. This work was supported by State Grid Zhejiang Electric Power Co., Ltd. Science and Technology Project, 5211DS200085.

References 1. Ling, K., Guan, Z., Wu, H., et al.: Active distribution network dispatch strategy with movable storage considering voltage control. Electr. Power Constr. 38(6):322–335 (2017) 2. Fu, X., Chen, H., Liu, G., et al.: Comprehensive evaluation method of distributed energy power quality. Proc. CSEE 34(25), 4270–4276 (2014) 3. Huang, Y., Li, G., Chen, C., Bian, Y., Qian, T., Bie, Z.: Resilient distribution networks by microgrid formation using deep reinforcement learning. IEEE Trans. Smart Grid 13(6), 4918– 4930 (2022) 4. Ding, T., Wang, Z.K., Jia, W.H., et al.: Multiperiod distribution system restoration with routing repair crews, mobile electric vehicles, and soft-open-point networked microgrids. IEEE Trans. Smart Grid 11(6), 4795–4808

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5. Li, J., Ma, H., Hui, D.: Current situation and development trend of energy storage technology integration and distributed renewable energy. Trans. China Electrotech. Soc. 31(14), 1–10+20 (2016) 6. Chen, Z., Yibin, T., Kai, B., Yu, Z.: Research on the application of energy storage system in mobile power supply system Power electronics technology 48(11), 54–56 (2014) 7. Zheng, Y., Chen, M., Li, C., et al.: Microgrid control strategy with adaptive droop coefficient adjustment. Power Syst. Autom. 7(37), 6–11 (2013) 8. Kim, J., Dvorkin, Y.: Enhancing distribution system resilience with mobile energy storage and microgrids. IEEE Trans. Smart Grid 10(5), 4996–5006 (2019) 9. Yao, S., Wang, P., Zhao, T.: Transportable energy storage for more resilient distribution systems with multiple microgrids. IEEE Trans. Smart Grid 10(3), 3331–3341 (2019) 10. Lin, J., Tang, l., Yi, Y., et al.: Research on emergency energy management method of island microgrid with mobile energy storage vehicle under extreme weather. Zhejiang Electr. Power40(01), 95–105 (2021) 11. Weng, X., Tan, Y.: Load recovery strategy of asymmetric distribution network considering the space-time support of mobile energy storage active power. Power Grid Technol. 45(4), 1463–1470 (2021) 12. Ling, K., Guan, Z., Wu, H., et al.: Active distribution network scheduling strategy with mobile energy storage considering voltage control. Power Constr. 38(6), 44–51 (2017s)

A QPSO-ELM Based Method for Load Model Parameters Identification Baojun Xu1 , Yanhe Yin1 , Junjie Yu1 , Guohao Li1 , Zhuohuan Li2 , and Duotong Yang2(B) 1 Zhongshan Power Supply Bureau of Guangdong, Power Grid Co., Ltd., Zhongshan,

Guangdong, China 2 Digital Grid Research Institute, China Southern Power Grid, Guangzhou 510663, Guangdong,

China [email protected]

Abstract. Identifying correct load model parameters is crucial for power system simulation analysis and control strategy design. To obtain real load characteristics matching up with actual operation, measurement-based methods for load model parameter identification are usually preferred. However, these methods mainly rely on iterative parameter searching process, which encounters challenges in time consumption when model complexity is high. In this paper, a parameter identification method for generalized synthetic load model (SLM) based on extreme learning machine (ELM) is proposed, aiming to improve computation efficiency. Moreover, a quantum particle swarm optimization (QPSO) algorithm is selected to train ELM model for better fitting to load response curves. Finally, the proposed QPSO-ELM based SLM parameter identification method is verified with standard test system together with parameter sensitivity analysis and simulation results prove effectiveness. Keywords: QPSO-ELM · Load model parameters · Load characteristics

1 Introduction In the current power system simulation software, prime mover, generator, etc. all have high simulation accuracy according to physical characteristics and operation mechanism, but the load model as “important user” is used due to time-varying, complexity and other factors. However, the load model, which is an “important user”, adopts the ideal overall model with typical values of parameters and only some parameters are differentiated at the provincial network level, which cannot reflect the actual load characteristics, resulting in large deviations in the model response and affecting the system simulation accuracy [1]. Therefore, the problem of parameter identification of the load model needs to be solved urgently, which is of great practical significance to improve the safe and stable operation of the power grid. In recent years, with the rapid development of intelligent algorithms, particle swarm algorithms, genetic algorithms, clonal selection algorithms and other types of optimization intelligent algorithms with both global and local search capabilities have been widely © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 905–910, 2023. https://doi.org/10.1007/978-981-99-4334-0_109

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used in the field of load model parameter identification. Literature [2] used genetic algorithm for parameter identification; Literature [3] proposed a genetic ant colony algorithm by taking advantage of the complementary advantages of fast convergence in the early stage of the algorithm and accelerated convergence in the late stage of the ant colony algorithm due to pheromone accumulation. The genetic ant colony algorithm was proposed and used for parameter identification; the literature [4] introduced the wolf algorithm into the field of load model parameter identification and used it with conventional particle swarm algorithm. The literature [5] introduced the Coyote algorithm into the field of load model parameter identification and compared it with the conventional particle swarm algorithm, and the analysis of the measured data showed its faster convergence speed. However, as the structural parameters of the load model are still changing in a complex way, the balance between local and global optimisation of the appeal algorithm is more The search for new evolutionary algorithms with faster convergence speed and higher convergence accuracy is still worthy of further research. The search for new evolutionary algorithms with faster convergence and higher convergence accuracy is still worthy of further research.

2 Load Model Structure It has been widely recognized that synthesis load model (SLM) is one of important dynamic load model that containing static model, motor model and reactive compensation model. Figure 1 shows the generalized SLM structure.

RD + jX D

ZIP

M

PV

StaƟc Load Model InducƟve Motor Model Photovoltaic Model

Fig. 1. Structure of the generalized SLM

By the parameter reduction procedure, dimensions of to-be-identified generalized SLM parameters are reduced from 24 to 7, which can improve load model parameters identification efficiency in large. The parameters of the generalized SLM to be identified are determined and list in Table 1. In this paper, the structure for machine learning based load model parameter identification is presented, which is shown in Fig. 2. It can be seen that the machine learning based parameter identification method contains two parts, i.e., offline construction and online application. In the offline training part, the first step is to collect sample data from power system simulation or actual power system historical data, which is the base for parameter identification model construction. To construct the parameter identification model, the load model responses before and after perturbations, and real load model parameters are necessary, where the former data are used as the input features and the

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latter parameters are regarded as sample labels. In this paper, the input features are set as pre-perturbation and post-perturbation loads responses in voltage and power. The observation window is set as 1s before perturbation and 1s after perturbation, and the sampling rate is set as 10Hz. Table 1. Critical Parameters of the generalized SLM Parameter name

Parameter symbols

Distributed network reactance

XD

Inductive motor active power proportion

PMP

Load ratio

KL

Stator reactance

Xs

Constant reactance load proportion

KZ

Direct current side capacitor

C

Photovoltaic output equivalent reactance

X PV

Power System Model

Actual Power System Historical Data

Perturbation

Sample Data

Machine Learning

Simulation

g ( w, x, b )

Load Model Parameter

f

x

Load Model Response

Offline Training for Load Model Parameter Identification Model

Load Model Parameter Identification Model online Application Pre-perturbation and Postperturbation Data of Loads

Voltage Information

Power Information

Load Model Parameter Identification Model

Parameter Identification Results

Pre- and Post-perturbation Power System Data Online Collection

Fig. 2. Structure of machine learning based load model parameter identification method

Once the training process of machine learning is finished, the offline construction process is finished. The load model parameter identification model then can be applied for online application. The first step of online application is collecting pre-perturbation and post-perturbation voltage and power data of loads. Then take the collected data as inputs of the load model parameter identification model. Finally, the parameter identification model output the results of expected load model parameters.

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3 Case Study In this section, the proposed QPSO-ELM based load model parameter identification method is validated with a standard system in PSASP software. The standard system is the infinite system with the generalized SLM, whose structure is shown in Fig. 1. To deal with large difference in load model parameter values, parameter outputs of QPSO-ELM is normalized by maximum and minimum normalization method. To train the ELM model, 1500 samples are generated based on the standard system by setting different load model parameters and three-phase short circuit faults with different short-circuit reactance, where 1350 samples are used for training and 150 samples are used as test samples. The ranging region of critical load model parameters is list in Table 2. Table 2. Range region of critical load model parameters Parameter X D Ranging

PMP

KL

Xs

KZ

C

X PV

[0.05, 0.15] [0, 80] [0.2, 0.8] [0.06, 0.18] [0.2, 0.6] [0, 100] [0.01, 0.06]

Table 3. Comparison of PSO and common ELM method Parameter symbols XD PMP

Set value 0.075

PSO method

Common ELM method

0.079

0.080

48.0

48.621

49.134

KL

0.5

0.465

0.445

Xs

0.09

0.085

0.094

Kz C X PV

0.35 28.0 0.03

0.367

0.355

27.251

27.089

0.028

0.028

To perform the comparison between PSO and common ELM, the PSO is configured in advance, where the maximum iterative step is set as 100 and the fitness function is the root mean square error of load responses in power and voltage. The results of identified critical load model parameters by PSO and ELM method are list respectively in Table 3. From Table 3, it indicates that the PSO method shows better performance than the common ELM method in accuracy, where mean average percentage error (MAPE) are 4.77% and 5.12% for PSO and common ELM method respectively. However, common ELM method has much higher computation efficiency than the PSO method, where common ELM method costs only 0.03s but PSO method costs 5.2 min. Hence, the common ELM method shows better adaptability to online application owing to its acceptable accuracy rate and computation time.

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After training process of ELM and QPSO-ELM, ELM and QPSO-ELM based load model parameter identification model is constructed, which is then validated with samples in testing sets. The performances of these two models on load model parameters X D , PMP and K L are shown in Fig. 3. It can be referred from the figure that the QPSO-ELM has better accuracy than common ELM. Besides these three load model parameters accuracy comparison, the remaining results on test samples in test set are list and compared in Table 4. It can be concluded that performance of the QPSO-ELM method is improved by using PSO algorithm to determine input weights and bias of hidden nodes of ELM model, instead of random determination.

(a) Relative error comparison in XD

(b) Relative error comparison in PMP

(c) Relative error comparison in KL

Fig. 3. Performance comparison between ELM and QPSO-ELM

Table 4. MAPE index comparison of common ELM and QPSO-ELM method Parameter symbols

Common ELM method (%)

QPSO-ELM method (%)

Xs

6.13

4.32

Kz

4.77

4.10

C

3.15

2.23

X PV

4.62

3.66

4 Conclusion This paper proposed a QPSO-ELM based method for generalized SLM, which considered effects of distributed photovoltaic. The structure of SLM with distributed photovoltaic is presented and analyzed by sensitivity analysis method for critical parameters determination. The QPSO-ELM takes voltage and power response of loads as input features and outputs the critical parameters of the generalized SLM. Finally, the proposed method is validated in the typical test system and performance show effectiveness.

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References 1. Dandeno, P.L., Brown, H.H., Dube, C., et al.: System load dynamics-simulation effects and determination of load constants. IEEE Trans. Power Apparatus Syst. PAS-92(2), 600–609 (1973) 2. Fliess, M., Sira-Ramírez, H.: An algebraic framework for linear identification. In: Proceedings of ESAIM, Control, Optimisation and Calculus of Variations, vol. 9, pp. 151–168 (2003) 3. Hiskens, I.A.: Nonlinear dynamic model evaluation from disturbance measurements. IEEE Trans. Power Syst. 16(4), 702–710 (2001) 4. Gensior, A., Weber, J., Rudolph, J., Guldner, H.: Algebraic parameter identification and asymptotic estimation of the load of a boost converter. IEEE Trans. Ind. Electron. 55(9), 3352–3360 (2008) 5. Mirjalili, S., Dong, J.-S.: Multi-Objective Optimization Using Artificial Intelligence Techniques. Springer, Cham, Switzerland (2019)

A Finite Time Cooperative Control Strategy for Energy Storage Systems in DC Microgrids Tianyu Shi1 , Zhiqian Zhang1 , Qi Wang1 , Cungang Hu2 , Shiming Liu1(B) , and Zhenbin Zhang1(B) 1 ShanDong University, Jinan Shandong 250001, China

{lsm,zbz}@sdu.edu.cn 2 AnHui University, Hefei Anhui 230601, China

Abstract. Maintaining the bus voltage at the rated value and distributing the output of each renewable energy according to capacity are the stable operation requirements for DC microgrids. In this paper, a cooperative control strategy based on finite-time observer is proposed. Appling a unified distributed control framework, this strategy allows the controllers for each distributed generation can achieve precise voltage control and power sharing which only exchanges voltage information with neighbor units. On this basis, to obtain higher quality of voltage observation, a finite time voltage observer is adopted, which significantly improve the convergence speed of observation values of each node. Furthermore, the strategy is insensitive to measurement noise and robust to initialization conditions. To the end, the effectiveness of the proposed method is verified by simulation. Keywords: DC microgrids · Distributed cooperative control · Finite time consensus observer

1 Introduction Microgrids combine distributed generations (DGs), energy storage systems (ESSs), protection devices and so on to form a small power gird, which can not only connect with large power gird, but also operate in island mode [1]. Nowadays, microgrids can be mainly divided into three types according to the form of electric energy: (i) AC microgrid; (ii) DC microgrid; (iii) AC–DC hybrid microgrid. Nevertheless, most of DG units and ESSs is in the form of DC output and the proportion of DC loads continues to rise. Therefore, the DC microgrids have attracted more and more attention that DC loads are increasingly applied [2]. A schematic of a common DC microgrid is shown in Fig. 1. DC microgrids have two basic operation requirements: (i) Precise bus voltage scaling; (ii) Share power in proportion to capacity. The former can maintain the stable operation of the system, and the latter can realize the output optimization of each DG. In order to achieve these goals, the existing DC microgrid control architecture can be divided into three types: (i) centralized control; (ii) decentralized control; (iii) distributed control. Among them, centralized control relies on a central controller, which has the single node invalidation and a large communication burden. And decentralized control methods only © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 911–918, 2023. https://doi.org/10.1007/978-981-99-4334-0_110

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Fig. 1. Schematic diagram of a common DC microgrid.

use local information without a central controller. For example, droop control is one of the most commonly used decentralized control methods. However, the deviation of its regulation characteristics seriously affects the control quality of the DC microgrids. Distributed control only requires critical running information of the neighbor units to realize two control objectives, which can overcome the defect of centralized control and decentralized control. Nowadays, the academia has made a lot of exploration to distributed control. Distributed control methods of DC microgrids are mostly based on the consensus algorithm. Ding et al. [3] proposed a distributed cooperative control method, which is considered one of the most effective control methods and has guiding significance for the subsequent research. In this method, voltage and power control objectives are regulated by voltage and current correction terms. Thereinto, voltage correction term is obtained by the voltage consensus algorithm and the current correction term is obtained by the comparison between the current of neighbor nodes. However, this method requires two PI controllers which will bring complex parameter tuning problem. Distributed control based on consensus algorithm has also been applied in the field of microgrid economic optimization. Li et al. [4] proposed a fully distributed control to achieve the optimal power flow control. This method uses dynamic consensus algorithm to estimate global voltage. However, the performance of consensus algorithm determines the control quality of DC microgrids. Li et al. [5] proposed a robust consensus algorithm which can restrain measurement noise and guarantee plug-and-play capacity. In addition, the consistent convergence rate is also an important evaluation index. Zaery et al. [6] proposed a distributed finite-time coordination control system. Nevertheless, this method is not

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robust to various complex operating conditions. So, the DC microgrids urgently require a robust finite time consensus algorithm to realize higher quality control. To this end, a robust finite time voltage observer based on consensus algorithm in a unified cooperative control scheme of DC microgrids is proposed in this paper. The remainder of this paper is arranged as follows. The unified cooperative control scheme of DC microgrids is introduced in Sect. 2, which can realize voltage regulation and power sharing without current information from neighbor units. And in Sect. 3, a robust finite time voltage observer is elaborated. In Sect. 4, The simulation results are provided, and the conclusion is given in Sect. 5.

2 A Unified Distributed Cooperative Control The suggested approach is made up of two key parts: a voltage controller and a bus voltage observer. The controller is detailed in length in this part, while the observer is comprehensively covered in the next subsection.

Fig. 2. The unified cooperative control scheme.

As seen in Fig. 2, Ku first amplifies the difference ue between the public bus voltage the predicted average voltage of node n. and ubus n ∗ − ubus uke = Ku (udc n )

(1)

Then, uint is delivered into Gc (s), which is the difference between uke and the voltage drop on the internal virtual resistance iio · Roi . In this part, we will create a basic compensator. Gc (s) =

1 s+β

(2)

Where the global observer parameter 0 < β  1 is kept constant to provide a significant DC gain for Gc (s). This guarantees that all poles are situated in the left half

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plane, while also displaying the frequency characteristic of Gc (s) in a manner similar to an integrator. To accomplish this purpose, the voltage reference value un∗ adjusts dynamicly, i.e.     u˙ n∗ = −αun∗ + uke − ino · Ron ≈ uke − ino · Ron (3) To understand the suggested control approach, the bus voltage observer is used to determine the average global voltage ubus n . Since its pole gets closer to zero, Gc (s) can reduce the steady-state error. As a result, the Gc (s) input is near to zero, i.e., uint ≈ 0. After removing the residuals, we obtained.  ∗  Ku udc − ubus n o in = (4) Ron It should be highlighted that ubus = ubus n m establishes all n, m ∈ V in finite time so as all agents reach an agreement. As a result, if Ku of all nodes is the same, the numerator of Eq. 4 is a constant, i.e.   ∗ = Constant (5) ino · Ron = Ku udc − ubus n Additionally, if the load current is spread according to its power rating, Ron Sm = Rom Sn

(6)

The equivalent DG has power ratings of Sn and Sm . Equation 6 is a rather simple condition to satisfy. The recommended approach also has inherent voltage restoration features. Equation 5 has undergone algebraic adjustment to produce the following equation. ∗ ubus = udc − n

ino · Ron Ku

(7)

If Ku is exceedingly big, the value of ino ·Ron /Ku is considerably minimized, according to Eq. 7. Thus far, voltage control and power sharing have been performed in tandem. A voltage closed control strategy ino ·Ron as a feedback loop is utilized instead of voltage and current double-loop control. This dramatically streamlines the controller construction and tuning technique, while reducing the requirement of communication costs by half in theory.

3 A Robust Finite Time Voltage Observer The classic voltage observer based on Eq. 8 can realize DC bus voltage accurate estimation. Nevertheless, there are three problems: (i) The differential term of the input signal exists in the Eq. 8 that is susceptible to noise level.

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(ii) Initialization condition must be observed. Otherwise, the plug-and-play capacity will be destroyed. (iii) The voltage of each node is hard to converge in finite time, which reduce system control quality.  bus u˙ n = − anm (unbus − unbus ) + u˙ n , n ∈ {1, 2, . . . , N } (8) m∈Nn

Based on the above questions, a robust finite time voltage observer is proposed. Figure 3 shows its control block diagram.  bus p˙ n = Kp sgn( (ubus n − um )) m∈Nn

ubus n

= un −



(pn − pm ) n ∈ {1, . . . , N }

(9)

m∈Nn

Compared with the Eqs. 8 and 9 mainly makes the following improvements: (i) The existence of the input differential term is eliminated. Only the input itself exists in Eq. 1. Therefore, there will be no observation error due to measurement noise. (ii) Equation 10 represents the initial conditions that the classic consensus algorithm needs to follow. When any node enters or exits the system, the left and right terms of Eq. 10 will not be equal. And Eq. 9 introduces an additional integral term, which can eliminate the need for system initialization conditions. N  n=1

ubus n (t0 ) =

N 

un (t0 )

(10)

n=1

(iii) Characteristic of nonlinear function sgn acts as if a Bang-Bang controller. The state space is divided into two regions, one corresponding to the control variable taking a positive maximum and the other corresponding to the control variable taking a negative maximum. Therefore, by such a modest mean, the convergence error bus ubus n − um will tend to zero, making each node converge in a finite time.

Fig. 3. The block diagram of Eq. 9.

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4 Simulation Validation In this section, a DC microgrid model with 4 distributed generations is built to prove the effectiveness of the proposed method under various conditions, including bus load step response, local load step response and communication failure. And all the simulations are implemented in PLECS platform. System parameters are shown in Table 1. Table 1. Simulation parameters. Parameters

Value

Parameters

Value

Bus nominal voltage vref [V]

88V

Line impedance3 R3 []L3 [μH ]

0.25 150

Power sharing ratio

1:1:1:1

Line impedance4 R4 []L4 [μH ]

0.50 80

Data exchange period Tcom [s]

0.001

Proportionality coefficient Kv

200

Line impedance1 R1 []L1 [μH ]

0.1 100

Virtual resistance Ro []

10

Line impedance2 R2 []L2 [μH ]

0.8 200

Consensus coefficient Kp

0.8

4.1 Bus Load Step Response The common bus load is initially 20. Bus load steps up to 10 at t = 0.5s and steps down to 20 at t = 1s. The control effectiveness of the suggested cooperative strategy is assessed in Fig. 4(a). As observed, the proposed method can achieve accurate voltage regulation and power sharing in the steady–state condition. And in the transient state, the proposed method can achieve fast voltage recovery and power distribution. Figure 4(b) shows the current control effect using traditional observer, which is converging from t = 0.3s to t = 0.4s. However, when the proposed robust finite time observer is applied, the convergence effect is significantly improved.

(a) the proposed observer method.

(b) the traditional observer method.

Fig. 4. The control effect of the proposed method and traditional observer.

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4.2 Local Load Step Response

Fig. 5. The control effect when local load steps up and down.

The node 4 local load steps up to 20 at t = 0.4s and steps down to 40 at t = 1.2s. As shown in Fig. 5, because node 4 directly provides instantaneous power, its output current has the largest fluctuation. However, the proposed method has nothing to do with line parameters, so unbalanced current can be quickly eliminated and the average voltage can stabilize at the rated value.

5 Conclusion In this work, based on a finite-time observer, a robust cooperative control strategy is suggested for DC microgrids. The proposed approach adopts a unified distributed cooperative control framework. On the premise of only using the voltage information of neighbor nodes, the goals of power sharing and voltage regulation are accomplished. In particular, the implementation of a finite-time voltage observer allows each distributed unit to converge to the rated value in a finite amount of time by estimating the average global bus voltage at each distributed agent. Thereby, compared with the classical voltage observer, the proposed strategy not only achieves robustness to initialization conditions, but also suppresses the observation error caused by measurement noise. In summary, under low communication bandwidth requirements, voltage regulation and accurate power allocation are realized in a finite-time, obviously increasing the control accuracy and stability of DC microgrids.

References 1. Olivares, D.E., et al.: Trends in Microgrid Control. IEEE Trans. Smart Grid 5(4), 1905–1919 (2014)

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2. Ghareeb, A.T., Mohamed, A.A., Mohammed, O.A.: DC microgrids and distribution systems: an overview. In: 2013 IEEE Power & Energy Society General Meeting, pp. 1–5 (2013) 3. Ding, L., et al.: Distributed cooperative optimal control of DC microgrids with communication delays. IEEE Trans. Ind. Inf. 14(9), 3924–3935 (2018) 4. Li, X., Dong, C., Jiang, W., Wu, X.: Distributed dynamic event-triggered power management strategy for global economic operation in high-power hybrid AC/DC microgrids. IEEE Trans. Sustain. Energy 13(3), 1830–1842 (2022) 5. Li, Y., Zhang, Z., et al.: A unified distributed cooperative control of DC microgrids using consensus protocol. IEEE Trans. Smart Grid 12(3), 1880–1892 (2021) 6. Zaery, M., Wang, P., Wang, W., Xu, D.: Distributed finite-time coordination control system for economical operation of islanded DC microgrids. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), pp. 1–6 (2019)

Wide Input and Output Voltage in Bidirectional DC-DC Converter Yibo Sun1 , Leilei Zhan2 , Xiaofeng Tao3 , Xinying Wang1 , Chaohui Cui1 , Haoran Li1(B) , Cungang Hu1 , Ke Zhang4 , and Weixiang Shen5 1 School of Electrical Engineering and Automation, Anhui University, Hefei, People’s Republic

of China [email protected] 2 Towngas Energy Investment Limited, Beijing, People’s Republic of China 3 Anhui Provincial Department of Finance, Bengbu, People’s Republic of China 4 Jiangsu Dongrun Zhilian Technology Co., Ltde, Nantong, China 5 Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Melbourne, VIC 3122, Australia

Abstract. This paper proposes an architecture for a bidirectional DC-DC converter consisting of interleaved Buck/Boost converter and LLC converter (DCX). The traditional DC-DC converter used in energy storage has problems such as unstable output voltage and large current ripple, which will seriously affect the converter efficiency. A control strategy of DC-DC converter is proposed, which can improve the stability of the converter under dynamic conditions, optimize the converter efficiency in a wide load range, and realize the regulation of the output voltage. The input voltage of 36 ~ 60 V on the low side is 100 ~ 180 V through the output bus/Boost circuit of the front 6-way interleaved parallel Buck/Boost circuit, which is fed to the DCX-LLC input, and the final high-side output voltage is adjusted between 200 and 360 V. Therefore, SiC MOSFETs can be used to apply this structure to achieve high frequency and high efficiency, because of the fast switching speed, high rated voltage, and low on-resistance. At the same time, the SR (SR) control strategy is implemented on the MOSFET on the secondary side of dcx-LLC, so as to achieve further improvement of efficiency. A 5 kW SiC bidirectional DC-DC converter was built, and the peak efficiency was 98.2% when the input voltage was 300 V, the output voltage was 150 V, and the power was 5 kW when the rated point was fully loaded. In discharge mode, the peak efficiency is 98.1% at full load with an input voltage of 150 V, an output voltage of 300 V, and a power of 5 kW. Keywords: SR · High frequency · High voltage · LLC converter · Bidirectional DC/DC converter · Efficiency optimization

1 Introduction In the field of electric vehicles, DC-DC converters are widely used in on-board systems and charging piles. Traditional fossil fuel-based vehicles, using the internal combustion engine as their power equipment, are less efficient, have weaker mechanical properties, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 919–931, 2023. https://doi.org/10.1007/978-981-99-4334-0_111

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are larger in size and emit polluting gases such as carbon monoxide and sulfur dioxide. The vehicle power system of new energy vehicles uses two-way DC-DC converters as its key equipment [1]. New energy vehicles have developed very rapidly in recent years, and the whole vehicle uses the battery as the power source to convert the energy of the battery into the kinetic energy of the motor through the two-way DC-DC converter and inverter [2]. Due to the use of electric motors instead of internal combustion engines, the whole system has further improved its work efficiency and has better dynamic performance, while the use of electric motors reduces the emission of toxic gases during driving, which is green and has broad market prospects. In battery energy storage systems, DC-DC converters are an important component for connecting high and low voltage DC buses. Battery energy storage systems require the converter to be able to switch freely and flexibly between charge and discharge modes, the converter to be able to achieve a high gain ratio, and high safety performance, but also to achieve galvanic isolation between high and low voltage DC bus. Therefore, for battery energy storage systems, high-efficiency, high-power density isolated bidirectional DCDC converters have become the focus of research. A bidirectional DC-DC converter is a device that can realize the bidirectional flow of DC energy, and its input voltage polarity is unchanged, but the direction of the input and output currents is changed, which can achieve two-quadrant operation [3, 4]. Functionally, it can be seen as consisting of two unidirectional DC-DC converters. Bidirectional DC-DC converters use a small number of components, so they have the advantages of simple structure, small size, light weight, high efficiency, and good dynamic performance. According to whether it is galvanically isolated or not, bidirectional DC-DC converters can be divided into two categories: commonly used non-isolated topologies include bidirectional Buck/Boost converters, bidirectional Cuk converters, etc., and isolated topologies include dual active bridge converters, bidirectional full-bridge LLC resonant converters, etc. [5, 6].

(a) Bidirectional Buck/Boost converter

(c) Double active bridge converter

(b) Bidirectional Cuk converter

(d) Bidirectional full-bridge LLC resonant circuit

Fig. 1. Common DC/DC converter topologies

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Among them, the bidirectional Buck/Boost converter in the non-isolated topology is the most widely studied and applied. The circuit topology is shown in Fig. 1 (a), the structure and control strategy of the converter is relatively simple, the conversion efficiency is high, but because the voltage regulation range is small, it is more used in low-power applications. Scholars at home and abroad have done a lot of research in order to improve the shortcomings of the Buck/Boost topology. For example, a staggered parallel structure is used for bidirectional Buck/Boost converters to reduce input current ripple [7]. Boost or buck control can be achieved by using forward or reverse cascading to increase the voltage range [8]. The voltage stress of the component is reduced by using a multilevel structure [9]. In summary, the Buck/Boost circuit is only suitable as a precursor to a bidirectional DC-DC converter in this chapter, similar to a regulator to meet wide input and output voltages. The bidirectional Cuk converter, shown in Fig. 1 (b), is highly symmetrical and has an inductor on both input and output sides, with current ripple on both sides are smaller. The disadvantage is that the topology is relatively complex, and the energy transfer needs to be carried out through the intermediate capacitor, and the efficiency of energy transmission is not high. Dual active bridge converters, shown in Fig. 1 (c) have a simple topology and can implement soft switching, so they are widely used in medium to high power applications. However, the range of soft switching in conventional single-phase shift control is limited by the load, and the energy stored in the auxiliary inductor at light load is not enough to support the charging and discharging of the parasitic capacitance of the switching tube, and the large circulation loss and the shutdown loss of the switching device in the absence of energy transfer one step reduces the efficiency of the converter. Dual phase shift control, triple phase shift control, etc. extend the range of soft switching [10], but it increases the difficulty of control and increases the complexity of the system. In the isolated topology, the two-way full-bridge LLC resonant converter is widely used in on-board chargers, photovoltaic power generation systems and other occasions. Its circuit topology as shown in Fig. 1 (d), simple control, can achieve zero voltage opening of the primary side switch and zero current shutdown of the secondary side switch tube in a wide input voltage and wide load range, the switch tube voltage stress is low, the electromagnetic interference is small, the deficiency is that the topology is a series resonant converter when running in reverse, the gain peak is low, and the adjustment range is limited. Therefore, considering isolation and operation at the resonant point, the bidirectional full-bridge LLC resonant converter is selected as the successor of the bidirectional DC-DC converter.

2 Wide Input and Output High Current Bidirectional DC/DC Converter Table 1 show the chapter mainly introduces the topology of a 5 kW bidirectional DC/DC converter, and first gives its technical requirements:

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Variable

Parameter

High voltage side

200 ~ 360 V

Low voltage side

36 ~ 60 V

Output current

84 ~ 140 A

Rated power

5 kW

2.1 Bidirectional DC/DC Converter Design Difficulties First of all, because the voltage of different batteries and battery packs can vary greatly. This requires a strong compatibility of DC electronic loads to accommodate different input testing needs. Secondly, as can be seen from Table 1, the input range of voltage on both the low side and the high side is very wide, the maximum voltage of 360 V on the high side is 6 times that of the low side of 60 V, and the maximum output current accompanied by the output voltage of the high side is also as high as 140 A. In addition, if high-frequency isolation is not used, the power density of the entire converter will be greatly reduced. Based on these difficulties, it is challenging to design a DC/DC converter that can achieve high efficiency, meet wide input and output, and achieve high power density at full load. Finally, conventional DC/DC converters cannot meet the requirements of high efficiency while meeting a wide input and output range, so a multi-stage conversion structure can be used to meet high-frequency isolation while meeting a wide input and output voltage range and high efficiency. 2.2 Selection of Bidirectional DC/DC Converter Topology As can be seen from the above, a multi-stage transformation structure is required to meet the technical requirements of a 5 kW bidirectional DC/DC converter, and a two-stage transformation structure is used here to meet the technical requirements. The two-stage transformation structure needs to meet the following points: (1) Adapt to a wide input and output voltage range; (2) High-frequency isolation; (3) Voltage rise and fall; (4) Load simulation function. In summary, the first stage of the transformation structure needs to adapt to a wide input and output voltage range and at the same time be able to have load simulation function and ramp voltage, and at the same time hope that there is an inductance on the input side, so that the current ripple can be reduced for the load. The second stage needs to achieve high-frequency isolation and maintain high efficiency. Combined with the points above, Fig. 2 shows the topology suitable for the 5 kW bidirectional DC/DC converter. It consists of two power stages, including a 6-way interleaved parallel Buck/Boost converter and LLC-DCX. The current stress of the conventional DC-DC converter switch tube is equal to the average of the input current on the low side, and once applied in high-power applications, it will cause the current stress of the switch tube to exceed a threshold, which will eventually burn out the switch tube. At the same time, a large on-on current will produce a very large conduction loss, which directly affects the working efficiency of

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the DC-DC converter, so in order to maintain high efficiency and not damage the switch, the interleaved parallel technology is used here. At the same time, this paper uses 6 interleaved parallel buck/Boost, the average of the single current is 23.4 A, the current stress generated by the current is within the bearing range of the circuit, and the number of interleaved parallel circuits is no longer increased to achieve the purpose of controlling costs. LLC-DCX secondary side switch can be turned off naturally at zero current, no switching loss, small output current electromagnetic interference, wide output voltage range to meet design requirements, full range of soft switching, peak efficiency is extremely high. To increase the power density of the entire converter, the switching frequencies of the six interleaved parallel Buck/Boost converters and LLC-DCX are 50 kHz and 150 kHz, respectively. Among them, the LLC-DCX operates at the resonant frequency, and this frequency under the converter is the most efficient. First of all, the excitation inductor L m never participates in resonance, and the current flowing through it is a triangular wave. LLC converter operating in this state is actually an LC series resonant converter with a resistive load. Second, the voltage of the resonant inductor L r and the resonant capacitor C r cancels each other out to zero, which is equivalent to the input voltage source directly connected to the opposite end of the resistive load. Ideally, the output voltage at this time is only related to the input voltage and transformer turns ratio, and has nothing to do with the load. At this point, because there is a dead time between the two MOSFET rotation openings, and the LLC is operating in the inductive state, the input current at this time is lagging behind the input voltage, and when the half cycle ends, the resonant current I r still exists, and this current can consume the charge stored on the parasitic capacitor, so that the voltage at the upper and lower tube nodes is reduced to zero, so that the voltage is turned on when the other switch tube is opened.

Vo

io

S3

S1 iS1

S4

iS2 S2

n:1 iLr Lr iLm * * Lm Resonant circuit

Primary-side fullbridge circuit

n:1 *

*

Q3

Q1

Q4

Q2

Q7

Q5

Q8

Q6

vin

K2

K1

Secondary-side fullbridge circuit

Fig. 2. Bidirectional DC-DC converter topology diagram

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2.3 Buck/Boost Topology Analysis The input voltage is connected to the input side of the Boost circuit, the Boost circuit part takes a single branch as an example, when the switch tube K 1 is turned on, K 2 is turned off, the current flows through the energy storage inductor, the electrical energy is stored in the inductor, and the output voltage is the same as the voltage at both ends of the capacitor; When the switch tube K 2 is turned on and K 1 is turned off, the power supply and energy storage inductor are charged to the capacitor at the same time, and the output voltage is the same as the voltage across the capacitor. Combined with the situation during the entire cycle, the output voltage is higher than the input voltage to achieve a boost effect. By controlling the drive signal of each switch tube, the opening time of the switch tube is adjusted to achieve the adjustment of the output voltage. The corresponding switch tube drive signals in the six branches are 60° in turn, realizing interleaved conduction, and the output current of the Boost circuit is the sum of the output currents of the six branches, and the average value is 6 times the average of the branch output current, and the pulsation frequency is also 6 times. However, because the pulsation amplitude of the six branch currents cancels each other out, the total output current ripple amplitude becomes very small, which reduces the output current ripple and improves the current accuracy. Therefore, the output voltage and current of the Boost circuit have less ripple and higher power quality. 2.4 LLC-DCX Topology Analysis LLC circuit when the original and secondary switch tubes open and turn off the same time, the switch tube Q1 , Q3 on, Q2 , Q4 off, or switch tube Q1 , Q3 off, Q2 , Q4 on, the primary output voltage and the primary side of the circuit input voltage is the same, the resonant circuit part of the two transformer module input side parallel output side of the series connection with the secondary side full-bridge circuit, the input voltage after the transformer conversion into the secondary side of the full bridge circuit, to obtain the final stable output voltage. The output voltage can be regulated by controlling the opening and on-time of the switching tube and the switching frequency. The LLC circuit can achieve zero voltage switching and zero current switching in the full load range, reducing the loss of the switching tube, improving the efficiency and power density of the converter.

3 Bidirectional DC-DC Converter Control Strategy 3.1 Buck/Boost Control Buck/Boost converter acts as a pre-converter in this bidirectional DC/DC converter by changing the duty cycle size to boost or step down the input voltage to obtain the desired output voltage. In the Boost state, the system controls the output voltage through the Buck/Boost converter, completes the matching of the DCX-LLC input voltage, and realizes the desired voltage output by adjusting the transformer ratio of the LLC converter; In the Buck state, the system passes the desired voltage output of the Buck/Boost converter to battery power by matching the voltages across the LLC converter. Therefore, the Buck/Boost converter needs to have good control accuracy and stability.

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If the open-loop control mode is adopted, although the structure is simple, the problem is that the anti-interference ability and control accuracy are poor, and the error cannot be eliminated. The closed-loop control mode anti-interference ability, control accuracy are strong, the system itself component requirements are not very sensitive, you can correct the deviation to achieve the stability of the system. Common closed-loop control modes are voltage control mode and current control mode. The core of the voltage control mode is to compare the sampled output voltage with the given reference voltage to obtain the duty cycle of the on-time of the control tube, and act on the switch tube to achieve a stable output of the voltage, but the disadvantage of the voltage control mode is the dynamic response speed and poor regulation accuracy. The current control mode is mainly to select the error of the voltage outer loop to set the reference value of the current inner loop, and the current sampled from the inductor at the input terminal is compared with the reference value of the current loop, so as to achieve the purpose of adjusting the duty cycle of the power device. The response speed of the current loop is faster than that of the voltage loop, so that the system can have better dynamic response and anti-interference ability. Compared with single-loop control, the dual closed-loop control greatly improves the stability and response speed of the system. Therefore, this paper adopts voltage and current dual closed-loop control as the core of the Buck/Boost converter control strategy. The double closed-loop schematic is shown in the following Fig. 3. voltage loop current loop Vref

+

Gv(s) -

Vf

Iref

+

Gi(s)

e

-

s

d(s)

Gvi(s)

Vo

-

If

G id(s)

H v(s)

Fig. 3. Schematic diagram of double closed loop control

where Gu (s) is the voltage ring correction network transfer function, Gi (s) is the current ring correction network transfer function, e−τ s is the delay caused by digital sampling, calculation, and updating of the duty cycle, Gvi (s) is the transfer function of the inductor current I L to the output voltage, Gid (s) is the transfer function of the duty cycle d to the inductor current I L , and H u (s) is the voltage sampling transfer function. In the double closed-loop control, PID is the most widely used control algorithm in practical engineering, which can not only improve the control accuracy of voltage and current, but also improve the stability and reliability of the system. Due to the high frequency characteristics of the DC/DC converter, the differential link control in the PID algorithm is too sensitive, which will lead to oscillation in the entire control system and reduce the performance of the converter. In summary, this paper should abandon differential control when selecting PID algorithm, that is, use PI algorithm as a control

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strategy. Taking the Boost mode as an example, the double closed-loop PI control block diagram of the six interleaved parallel Boost converters is shown in the following Fig. 4. + -

Current loop PI

GPWM(s)

Current loop PI

GPWM(s)

If

+ -

Gvi(s)

Gid(s)

Gvi(s)

Gid(s)

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k2 Current loop PI

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-

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Gvi(s)

-

If

+ -

k4 Current loop PI

GPWM(s)

Current loop PI

GPWM(s)

If

+

If

k5

k6 k7

Fig. 4. Interleaved parallel boost converter double closed-loop PI control block diagram

Where k 1 , k 2 , k 3 , k 4 , k 5 , k 6 are the sampling coefficients of the inductor current, and k 7 is the sampling coefficient of the output voltage. In the Buck/Boost control system, the bus voltage and inductor current are sampled simultaneously for each sampling cycle, and the sampling result is converted into a corresponding digital signal by A/D, and the digital signal is filtered and the bias amount is subtracted to obtain the final digital signal. Wherein, the high-side voltage reference value is given by the system, this given reference value is compared with the voltage value obtained by sampling to obtain an error value, the output value is compared with the PID regulator output current reference value, the current reference value is compared with the current sampling value to obtain the current error value, and the output value is output PWM register value by the PID regulator, so as to achieve the purpose of controlling the output voltage at the high voltage end and controlling the low-voltage terminal current. 3.2 LLC-DCX Control In the 5 kW bidirectional DC/DC converter designed in this paper, the key task of the LLC converter is to provide high efficiency, high power density isolation. Therefore, the SR drive strategy is a critical step in ensuring the efficiency and power density of the LLC converter. DCX-LLC operates at a fixed frequency, uses open-loop control, and applies the SR control strategy mentioned earlier to improve the operational efficiency of bidirectional DC/DC converters. The divider resistor samples the output voltage V bat , the current sampling chip samples the output current ibat , and the sampled output voltage signal and

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the output current signal are sent to the digital signal processor (DSP) for processing after the analog-to-digital converter (ADC). According to the schematic diagram, the drive signal of the original side switch tube is determined by the DSP, and because the opening time of the original side switch tube is equal to the opening time of the SR tube, the opening time of the SR tube is determined. Bring it into the SR model mentioned above, send the input signal into the DSP for processing, and obtain the required SR drive signal. Wherein, the sampling frequency of the output voltage and current is required to be consistent with the interrupt frequency in the DSP program, and the on-time of the SR is calculated at the same time after each sample. It is worth noting that the control strategy should set the boundary value of the on-time to avoid damaging the circuit by using the self-locking control method to control the SR tube. At the same time, some short circuit protection measures should also be added to deal with the occurrence of short circuits in circuit switching devices, once a fault occurs, all ePWM outputs should be lowered at this time, and all the working switch tube gate drive should be turned off, so as to protect the circuit. The detailed control flow diagram of the SR tube drive strategy proposed in this section is shown in Fig. 5. When the circuit starts working, the initial signal is the control signal of the SR tube. During the interrupt period in the figure below, the output voltage and output current sampling signals pass through the ADC input DSP to calculate the corresponding SR tube on-time. From a safety perspective, the maximum SR tube on-time value under full load conditions should be considered and set as a critical limit. Start Determine the initial on-time

Initial value

Sampling and ADC conversion Interruption cycle

PI adjustment

Calculate the exact ontime

ton 0, the following constraints should be added to the optimization model: f ≤ (1 + β)f0

(15)

To sum up, the available robust scheduling model is shown in Eq. (16). The decision solution obtained by this model is robust to the uncertainty of TOU  price. When TOU price price price fluctuates arbitrarily within the range  pt , (1 + α) , the decision solution pt can ensure that the generation cost is not higher than (1 + βc )f0 .  price price , pt Similarly, when the TOU price fluctuates randomly within (1 − α) pt , the decision solution may reduce the generation cost to (1 − β)f0 . 3.3 Algorithm Process According to the above content, the algorithm flow chart based on IGDT is shown in Fig. 2. price

a) Replace the uncertainty parameter (TOU price) with the predicted value pt , calculate the original deterministic system model (1)–(9), and obtain the objective function value f0 .

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b) According to the operation experience, the deviation factor β is given. The uncertainty system model is added to calculate (11) and (12) respectively to obtain the prediction error and the corresponding scheduling scheme. price price price price c) Calculate [(1 − α) pt , pt ], [ pt , (1 + α) pt ], end.

Start

Establish the deterministic valuation model The optimal value of the obtained objective function is set as the IGDT reference value Robust model or chance model Select the uncertainty coefficient

Select the uncertainty coefficient

Set the robustness level factor

Set the chance level factor

The model is solved with maximum uncertainty

The model is solved with minimum uncertainty To evaluate the model's ability to resist risks and maximize benefits End

Fig. 2. Flow chart of IGDT algorithm

4 The Example Analysis Select a new large-scale data center, its maximum load is 15,384 kW, equipped with lithium iron phosphate energy storage battery. The annual utilization days are 365 days and the annual utilization time is 8760 h. Energy storage battery life for 10 years, the cost of capacity is 1312 yuan/kWh, which charge and discharge efficiency are 90%. Its capacity electricity charge of the data center is 23 yuan/(kVA month). The predicted electricity price is shown in Fig. 3. The energy storage battery takes advantage of peak and valley electricity price difference, “two charge and two discharge” every day. Charge during 1:00–8:00, 13:00–14:00

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Electricity price/(Yuan ·kwh-1)

1.2

1

0.8

0.6

0.4

0.2

0 1

6

12

18

24

Time

Fig. 3. Forecast TOU price

and discharge during 11:00–12:00, 15:00–19:00. The realization of two peak and valley filling can significantly reduce the operating cost of data centers. By setting three schemes for comparison [16, 17], the specific schemes are as follows: • Solution A: No energy storage system is configured in the data center. • Solution B: Configure energy storage batteries in the data center for peak-to-valley arbitrage. • Solution C: Energy storage batteries are configured in data centers as controllable loads to participate in market demand response.

Table 1. Economic analysis of data center operation Solution

Solution A

Solution B

Solution C

Energy storage capacity/kWh

0

18,700

18,700

Storage costs/104 yuan

0

2440

2440

Capacity of transformer/kVA

20,000

40,000

24,000

The cost of electricity/104 yuan

8140

7410

–

PUE

1.28

1.30

–

Investment payback period/year

0

3.3

–

According to Scheme A and Scheme B, the optimal configuration capacity of the energy storage system of the data center is optimized. The transformer capacity of Option B is increased to 40,000 kVA, resulting in a capacity electricity bill of $11.04 million for the data center. Calculate the recovery period of investment for peak-valley arbitrage

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when energy storage batteries are configured in data centers. Table 1 shows the economic analysis of data center configuration. In addition, set the two scenarios to compare the energy cost of the data center configured with energy storage batteries. • Scenario A: Without energy storage batteries, calculate the energy consumption cost as a comparison scenario. • Scenario B: Data centers are configured with energy storage batteries to participate in peak-to-valley arbitrage and reduce energy consumption costs. Figure 4 shows the electricity charge of a data center configured with energy storage system for 24 h on a typical day. According to the predicted TOU price, the price of electricity is at the low point during the time period of 1:00–8:00. The price of electricity is at the peak during 11:00–12:00 and 15:00–19:00, and the rest of the time prices are at parity. The first round of charging will be carried out by the energy storage system at 7:00–8:00, and the first round of discharging will be carried out at 9:00–10:00. The second round of charging will be carried out by the energy storage system at 13:00– 14:00, and the second round of discharging will be carried out at 15:00–16:00. The discharge of energy storage systems in data centers reduces the load on the demand side of the power grid and greatly reduces the cost of data centers. In this operation cycle, the charging and discharging behavior of the energy storage battery plays the role of peak cutting and valley filling to reduce the power supply pressure of the grid. The PUE value in scenario B is slightly higher than that in scenario A, because the system efficiency of the energy storage battery during charging and discharging is 90%, and there is a certain loss. In addition, the recycling life of energy storage batteries is also within their life cycle. 104

Electricity prices(yuan)

2

1.5

1

0.5

0 0

2

4

6

8

10

12

14

16

18

20

22

24

Time

Fig. 4. Electricity bill of data center with 24 h energy storage system

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Solving the model according to (1)–(9), without considering the uncertainty of electricity price, the annual power consumption cost of the original value evaluation model after the energy storage system is configured is f0 = 7410 ten thousand yuan. The maximum deviation factor βc and βo are set at 5%. The corresponding pessimistic cost and optimistic cost of annual electricity consumption are fc = (1 + 5%)f0 = 7780.5 ten thousand yuan and fo = (1 − 5%)f0 = 7039.5 ten thousand yuan respectively. By calculating Eqs. (12) and (13), the maximum value of the fluctuation range of TOU price are αc = 27.61% and αo = 27.65%. It shows that the decision maker allows the flucprice price tuation range of predicted electricity price to be within [pt , (1 + 27.61%)pt ] and price price [(1 − 27.65%)pt , pt ] when making opportunistic or robust choices. The influence of uncertain parameters on the model is shown in Fig. 5. While βc and βo vary within the range of 0 ∼ 5%, the variation ranges of αc and αo obtained are shown in Fig. 6. As the generation cost increases, αc and αo show a linear increase and a linear decrease respectively. This shows that when αc is larger, the decision maker will have a more pessimistic view on the price fluctuation. The obtained energy storage configuration capacity and power consumption cost are more conservative, and the robustness of the system is higher. When αo is smaller, it means that the decision-maker’s optimism about the additional income generated by the price fluctuation is decreasing. They are more willing to expand the capacity of energy storage configuration to maximize the profit, and the annual power consumption cost of data centers increases accordingly. 1.5 Forecasting of electricity

Floating ceiling Floating floor

Floating range

1.2

0.9

0.6

0.3

0 1

6

12 Time(h)

18

24

Fig. 5. Floating range of electricity price under information gap decision theory

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Disturbance level(%)

o

27

18

9

0 0.94

0.96

0.98

1

1.02

Annual cost of electricity consumption f 0

1.04

1.06

Fig. 6. Variation curve of disturbance level with annual power consumption cost

5 Conclusion The power consumption load of large data center is about 9.75 ~ 32.5 MW. It can control the power consumption load by configuring energy storage battery, which has the potential to become the controllable load of virtual power plant. Data centers have high electricity load and power consumption, while the electricity cost accounts for 30–50% of the total operating cost. In this paper, the peak-valley TOU price and market-oriented demand response can significantly reduce the electricity cost, and the two solutions under corresponding model are obtained by IGDT theory. Taking a data center as an application example, through “two charging and two discharging” peak-valley arbitrage of energy storage batteries every day. The operation cost of the large data center is reduced by 8.96%, and the payback period of the energy storage system is 3.3 years, which has good economy. At the same time, the uncertainty is modeled to obtain the robust solution and the chance solution. In the case that the maximum gap degree is set as βc = 5% to make the system stability more conservative, the range of allowing the electricity price to deviate from the predicted value should not exceed 27.61%. In the case that the maximum gap degree is βo = 5% in order to make more profits, the range of allowing the electricity price to deviate from the predicted value shall not exceed 27.65%. Between the range of uncertain parameters and the lowest acceptable target, there is a relationship can be presented by above result.

References 1. Peng, C., Yi, Y., He, Z.: China Renewable Energy Research and Development Report 2020. General Institute of Water Resources and Hydropower Planning and Design, Beijing (2021) 2. Koomey, J.G.: Growth in Data Center Electricity Use 2005 to 2010. Analytics Press, Oakland CA (2011) 3. China IDC Circle: Data center energy saving, emission reduction and carbon reduction should focus on IT equipment, construction, infrastructure, operation and energy [EB/OL] (2022). https://xueqiu.com/4850661141/210263072

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4. Zhao, T., Zhang, H., Xu, Y., et al.: Resilience-enhanced scheduling of power system with cloud computing data centers under uncertainty. Autom. Electr. Power Syst. 45(3), 49–57 (2021) 5. Li, X.J., Ma, R., Gan, W., et al.: Optimal dispatch for battery energy storage station in distribution network considering voltage distribution improvement and peak load shifting. J. Mod. Power Syst. Clean Energy 10(1), 131–139 (2020) 6. Li, X., Guo, J.: Reliability evaluation of distributed energy system in data center. Gas Heat 36(10), 11–14 (2016) 7. Nguyen, T.A., Min, D., Choi, E., et al.: Reliability and availability evaluation for cloud data center networks using hierarchical models. IEEE Access 7, 9273–9313 (2019) 8. Sang, B., Wang, D., Yang, B., et al.: Collaborative optimization configuration of photovoltaicenergy storage based on economy in an internet data center. Power Syst. Prot. Control 48(17), 131–138 (2020) 9. Wen, Z., Liu, J.: A optimal scheduling method for hybrid wind-solar-hydro power generation system with data center in demand side. Power Syst. Technol. 53(11), 120–129 (2020) 10. Xu, X.: Research on Power Supply and Distribution System of Big Data Center and its Power Quality. Master’s Dissertation of China University of Mining and Technology, Xuzhou (2020) 11. Wang, H., Ye, Z.: Renewable energy-aware demand response for distributed data centers in smart grid. In: Green Energy and Systems Conference, pp. 1–8. IEEE, Long Beach, CA, USA (2016) 12. Tran, N.H., Dai, H.T., Ren, S., et al.: How geo-distributed data centers do demand response: a game-theoretic approach. IEEE Trans. Smart Grid 7(2), 937–947 (2016) 13. Li, J., Li, Z., Ren, K., et al.: Towards optimal electric demand management for internet data centers. IEEE Trans. Smart Grid 3(1), 183–192 (2012) 14. Xia, X.: The national development and reform commission further improves the TOU price mechanism. Mechanical and electrical business newspaper (2021) (A01) 15. Chen, K., Wu, W., Zhang, B., et al.: A robust restoration method for active distribution network based on IGDT. Proc. CSEE 34(19), 3057–3062 (2014) 16. Meng, J.: Selection of Construction Management Mode of S Bank Data Center Project. Southwest Jiaotong University, Chengdu (2019) 17. Tang, H., Cheng, Y.: Study on evaluation indicators of data center based on service capability. Telecom Power Technol. 37(10), 147–149 (2020)

Simulation Analysis of Conducted Electromagnetic Interference in Excitation Power Cabinet of Giant Hydraulic Turbine Unit Based on Time Domain Finite Integration Method Geng Zhang1 , Xiangtian Deng1(B) , Quanwen Wang1 , Qian Wang1 , and Qiannan Liu2 1 School of Automation, Wuhan University of Technology, Wuhan, China

{dengxt,qiw}@whut.edu.cn 2 Hubei Academy of Scientific and Technical Information, Wuhan, China

Abstract. With the continuous increase of the installed capacity of clean energy and the application scale of various types of high-power power electronic equipment in China, a large number of real-time data sensors are installed in these highpower power electronic equipment to monitor the status data of various equipment such as temperature and humidity in real time and online. Among them, RFID temperature online monitoring system is widely used, but in practical work, it is often in a long-term failure state due to conducted electromagnetic interference generated by high-power power electronic equipment. Therefore, in order to study the conducted electromagnetic interference generated by high-power power electronic equipment, this paper establishes a simulation model, extracts the parasitic capacitance in the conducted electromagnetic interference of high-power power electronic equipment by using the time-domain finite integration method, analyzes the influence of the parasitic capacitance on the RFID tag antenna, and compares the difference between the S11 parameter curve of RFID tag antenna before and after simulation, It is confirmed that the conducted electromagnetic interference generated by high-power power electronic equipment has a negative impact on the performance of RFID temperature online monitoring system and other sensors. Keywords: RFID · Conducted electromagnetic interference · Antenna · Parasitic capacitance · Impedance mismatch

1 Introduction At present, China has become the largest consumer of clean energy in the world, and hydropower, wind power, photovoltaic and other new energy have shown a significant growth trend. With the continuous improvement of the installed capacity of clean energy, the application scale of various types of power electronic equipment is also increasing. Therefore, the power electronic power system will gradually become a new form of power system, and the high-power power electronic equipment in operation will also cause serious electromagnetic interference to the surrounding intelligent sensing equipment and communication equipment. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 974–980, 2023. https://doi.org/10.1007/978-981-99-4334-0_116

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The electromagnetic interference of power electronic equipment has always been an important part of the electromagnetic compatibility field. Domestic and foreign scholars and experts have done a lot of research in modeling, simulation and analysis. At the same time, there are many methods to analyze and solve electromagnetic interference, such as image method, variable separation method, complex variable function method, Green’s function method, finite difference method and finite element method, etc. Paper [1] proposed a prediction method of radio wave propagation in irregular urban environment—accelerated multiple image method, and analyzed and calculated the radio wave propagation characteristics in irregular urban environment. In Ref. [2], the electromagnetic interference caused by parasitic electric line current is analyzed by Helmholtz equation combined with the principle of variable separation and superposition. In Paper [3], the author used the numerical Green’s function to reconstruct the electronic circuit source and estimate the electromagnetic interference. In Ref. [4], the author used ADIFDTD method to analyze the transient electromagnetic interference of rectangular metal shell with electromagnetic pulse aperture. Paper [5] proposed to establish the model of typical structure of electronic transformer with finite element analysis method, calculate its electromagnetic field, and propose the optimization design of electromagnetic compatibility. Paper [6] pointed out that the parasitic capacitance between the transistor and radiator of power electronic equipment is the main factor interfering with the common mode loop, and the electromagnetic interference of the converter system can be improved by controlling the parasitic capacitance impedance. It can be seen from the research status of electromagnetic interference of power electronic equipment that there is little work to analyze conducted electromagnetic interference of high-power power electronic equipment. In this paper, based on the excitation power cabinet of giant hydraulic turbine unit, an electromagnetic interference analysis method based on the time-domain finite integration method is proposed. The conducted electromagnetic interference of the power equipment in the excitation power cabinet of giant hydraulic turbine unit is simulated and the parameters are extracted. The influence of parasitic capacitance on the RFID tag antenna is analyzed. By comparing the difference between the S11 parameter curve of the RFID tag antenna before and after the simulation, it is confirmed that the conducted electromagnetic interference causes the degradation of the performance of the RFID temperature online monitoring system.

2 Analysis Method 2.1 Time Domain Finite Integration Method The numerical calculation methods of electromagnetics can be divided into time domain method and frequency domain method. The time-domain method can solve the relevant field quantities after stepping Maxwell equation by time, with reliable accuracy, faster calculation speed, and can truly reflect the essence of electromagnetic phenomena. By using time-domain method, time-domain ultra wideband response data can be obtained at one time, greatly improving calculation efficiency. In electromagnetic field simulation, mesh voltage e and plane magnetic flux b are distributed on the main mesh, while electric flux d and magnetic field intensity h are defined on the sub mesh. Then the topological matrix C is introduced as the screw operator of spatial discretization on the main mesh.

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Once the computational topological matrix is obtained, the computer can start to solve the space electromagnetic field problem. The time domain finite integration method discretizes and rewrites the integral form of Maxwell equations:  sik bk = 0 (1) 

k

qi =  k

ρdV Vi

cik ek = −

∂bi ∂t

 s dk = qi k

ik

(2) (3) (4)

Map them to the mesh space one by one to form the following mesh matrix: Sb = 0 

(5)

i + d˙ = C h

(6)

Ce = −b˙

(7)



Sd =q

(8)

By solving the mesh matrix, we can get the electromagnetic field quantity we need. 2.2 Conducted Electromagnetic Interference Principle The excitation power cabinet described in this paper uses six sets of heat pipe heatsink SCR components to form a three-phase fully controlled bridge rectifier circuit. The single self-cooling power cabinet rated output current is 2500 A. The parasitic capacitance generated by this circuit is shown in Fig. 1. In this rectifier circuit, the rectifier components are T251 type SCRs with a switching frequency of 50Hz. The characteristics of the current flowing through the SCR are that the instantaneous current change rate di/dt is very high during the on and off period and the high-frequency component of the pulse current is very large during the on period, which makes other high-frequency components in the rectifier circuit vulnerable to the influence of their parasitic capacitance [7, 8]. In order to simplify the analysis, the SCR can be regarded as a pulse generator, its anode and cathode are respectively connected with the heatsink made of aluminum profiles; While the excitation power cabinet body is grounded, the whole cabinet body can be regarded as a protective ground wire, and the parasitic capacitance (i.e., capacitance to ground) generated between the AC bus and heatsink and the cabinet body provides a flow path for common mode conduction current. This results in common mode conducted electromagnetic interference [9, 10], as shown in Fig. 2, where C0 is parasitic capacitance of AC bus to ground, C1 is parasitic capacitance of SCR anode heatsink to ground, and C2 is parasitic capacitance of SCR cathode heatsink to ground.

Simulation Analysis of Conducted Electromagnetic Interference

VT1 QF1

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C21

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Fig. 1. Parasitic capacitance circuit diagram

C0

Heatsink-2

~

Heatsink-1

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SCR C1

C2

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Fig. 2. Schematic diagram of common mode conducted electromagnetic interference

2.3 Simplification and Setting of the Model

Fig. 3. Model diagram of excitation power cabinet of the giant hydraulic turbine unit

The original model of the excitation power cabinet of the giant hydraulic turbine unit is shown in Fig. 3. The upper middle part of the metal cabinet body contains six sets of heat pipe heatsink SCR components. Since the capacitance size is only related to the positive

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area of the electrode plates, the medium between the electrodes and the electrode plate spacing, and has nothing to do with other factors, we set six sets of heat pipe heatsink SCR components into six independent parts, and the excitation power cabinet body of the giant hydraulic turbine unit is set as the grounding body and only retains the part facing the SCR components. The simplification scheme of AC bus is the same as that of heatsink. According to the actual operating conditions of the excitation power cabinet of the giant hydraulic turbine unit, the SCR components inside the power cabinet continuously output 2500 A DC current, so the output current of the SCR can be equivalent to 50 Hz, 2500 A and 1/3 duty cycle square wave current. In order to improve the simulation efficiency, 915 MHz sine wave is used for simulation analysis of the interference source signal.

3 Simulation Analysis 3.1 Parameter Extraction This section will take a conducting circuit in the SCR circuit of the excitation power cabinet of the giant hydraulic turbine unit as an example to make a simulation analysis on the parasitic capacitance of the SCR components heatsink and AC bus. The SCR component VT1 and SCR component VT2 are conduction circuit. The parasitic capacitance values obtained are respectively C11 and C12 of the heatsink of the SCR component VT1 , C21 and C22 of the heatsink of the SCR component VT2 , C1 of the AC bus L1 and C3 of the AC bus L3 . The parasitic capacitance of SCR components heatsink and AC bus is extracted through electromagnetic simulation software. The parasitic capacitance of each part is summarized as shown in Table 1. Table 1. Parasitic capacitance value of each part Capacitance

Value (pF)

C11 (VT1 anode heatsink)

3.2

C12 (VT1 cathode heatsink)

6.2

C21 (VT2 anode heatsink)

7.7

C22 (VT2 cathode heatsink)

11.5

C1 (AC bus L1 )

0.26

C3 (AC bus L3 )

0.21

3.2 Analysis of Results A RFID temperature tag antenna is taken as an example to analyze the results. The impedance of the temperature tag antenna matched with the chip near the 915 MHz frequency is 1.4789 + j199.3526 , and the approximate value is 1.5 + j200 . When there

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is electromagnetic interference with the frequency of 915 MHz, the parallel impedance value of RFID tag antenna impedance is about 9 + j500  after being affected by the parasitic capacitance C11 at the temperature measuring position. At this time, the antenna impedance value and the chip impedance value are seriously mismatched. At the same time, the curve comparison diagram of RFID tag antenna S11 parameters before and after electromagnetic interference is shown in Fig. 4.

Fig. 4. S11 parameter curve comparison chart

In Fig. 4, the curve below is the S11 parameter curve when the RFID temperature tag antenna conjugate matches. In the 860–960 MHz frequency band, S11 ≤ 10 dB, and S11 ≤ 30 dB near the 915 MHz center frequency. The curve above is the S11 parameter curve of the RFID temperature tag antenna when impedance mismatch occurs. In the 860–960 MHz frequency band, S11 ≥ 10dB, the S11 parameter curve produces serious distortion, which completely fails to meet the antenna requirements, resulting in serious degradation of the RFID temperature tag antenna performance.

4 Conclusion Aiming at the conducted electromagnetic interference problem of excitation power cabinet of giant hydraulic turbine unit, this paper simulates and analyzes the conducted electromagnetic interference of excitation power cabinet of giant hydraulic turbine unit by finite integration method in time domain, and verifies the influence of electromagnetic interference on RFID online monitoring system. Although the circuit model has shortcomings in the interference source setting and model simplification analysis method, but it also provides a reference for other intelligent sensing devices and communication devices to prevent and suppress conducted electromagnetic interference.

References 1. Zhong, S.: Analytical Calculation of Electromagnetic Radiation in Non-regular Urban Environment by Accelerated Multi-mirror Method. University of Electronic Science and Technology (2003)

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2. Choo, J., Park, J.E., Choo, H., Kim, Y.H.: Electromagnetic interference caused by parasitic electric-line current on a digital module in a closed cabinet. IEEE Access 7, 598806–598812 (2019) 3. Wang, Z.A., Xiao, Z.F., Mao, J.F., Jiang, L.J., Bagci, H., Li, P.: Source reconstruction of electronic circuits in shielding enclosures based on numerical green’s function and application in electromagnetic interference estimation. IEEE Trans. Microwave Theory Tech. 70(8), 3789–3801 (2022) 4. Chen, L., Tang, M., Mao, J.: Electromagnetic interference investigation of PCB in metallic enclosures using ADI-FDTD method. Joint 60th IEEE International Symposium on Electromagnetic Compatibility (EMC)/IEEE Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC), pp. 1274–1277. (2018) 5. Tong, Y., Wu, Y., Liu, B., Shen, J.: The optimal design of electromagnetic compatibility for electronic transformer. In: International Conference on Power System Technology (POWERCON), pp. 1037–1042. (2018) 6. Yin, W., Ming, Z., Wen, T.: Switching power supply EMC optimization design method. Electron. Lett. 56(16), 813–815 (2020) 7. Zhang, D., Ning, P., Duan Z., Zhang, J.: Analysis and prediction of electromagnetic interference in power electronic converters. In: 43rd Annual Conference of the IEEE-IndustrialElectronics-Society (IECON), pp. 7000–7005. (2017) 8. Subramanian, A., Govindarajan, U.: Analysis and mitigation of conducted EMI in current mode controlled DC–DC converters. IET Power Electron. 12(4), 667–675 (2019) 9. Xu, P., Mei, J., Qin, J.: Research on EMI control techniques of airborne power electronic equipment. In: Joint 60th IEEE International Symposium on Electromagnetic Compatibility (EMC)/IEEE Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC), pp. 837–839. (2018) 10. Peng, H., Hu, J., Jiang, C., Liu, Q., Xu, H., He, Z.: Analysis for the EMI measurement and propagation path in hybrid electric vehicle. In: IEEE Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), pp. 1087–1090. (2016)

Research on the Wind Farm Layout Optimization Considering Different Wake Effect Models Yining Gong(B) and Zhicong Wang College of Energy and Electrical Engineering Hohai University, Nanjing, China [email protected]

Abstract. Wind farm layout optimization (WFLO) problem is one of the urgent problems in the renewable energy sector. With the objective of capturing the maximum amount of wind energy and minimizing the cost per power. The velocity deficit simulations in most WFLO studies adopt the Jensen wake model due to its simplicity and effectiveness in most wind farm conditions. In this paper, three wake models including the Jensen model, Jensen-Gauss model and Abramovich (AV) model are calculated and compared with the datas from the wind tunnel experiments of Tokyo University and the Netherlands Energy Research Center. Both the vertical and horizontal comparisons combing the onshore, offshore and far-field, near-field conditions are made to ensure the comprehensive and meaningful of comparisons. Then AV wake model is chosen as the basis of the study because of its comprehensive superior performance. The genetic algorithm has good robustness and globality in contrast to traditional algorithms, which make it possible to effectively find the optimal solution of WFLO problem. Therefore, an AV wake model based method is proposed in this paper to solve the WFLO problem instead of the traditional Jensen wake model through the genetic algorithm. The calculation results show that the annual power generation is higher and the computation time is shorter when the proposed method is applied to solve the WFLO problem. Keywords: Wind farm layout optimization · Wake effect · Jensen wake model · AV wake model

1 Introduction With the world economy on a tear, human consumption of energy has also increased. Traditional fossil energy is facing the risk of increasing exhaustion while causing pollution [1, 2]. Speeding up the advancement of renewable energy power generation has become a major strategic direction and concerted action for global energy transformation and climate change. As the most valuable renewable energy, wind energy has been widely developed and utilized.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 981–992, 2023. https://doi.org/10.1007/978-981-99-4334-0_117

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In the design and planning of modern wind farms, dozens of wind turbines are arranged according to certain rules. When the spacing and arrangement are unreasonable, the wake effect will greatly affect the power generation efficiency. The wake region after the wind turbine is generated because the turbulence intensity increases, and the wind speed decreases as the airflow passes through the upstream wind turbine. Secondly, the increase of turbulence intensity affects the fatigue load and aerodynamic performance of wind turbines. Researches have shown that the efficiency loss of wind turbines working in the wake environment can reach 10–20% [3]. Therefore, it is of great academic value and economic benefit to carry out research on the calculation method of wind farm wake and then optimize the arrangement of wind turbines to maximize the efficiency of wind turbines. When studying the influence of the wake effect on wind turbines, the wake is generally divided into a near field and a far field [4]. The near field region begins behind wind turbines and extends to about 2–4 rotor diameters (D) downstream, where the shape of the rotor has a large effect on the flow of wind. In the far field, rotor geometry only reduces wind speed and increases turbulence intensity. Turbulence becomes the main influencing factor of the far field wake [5]. For the problem of optimal wind turbine placement inside an ideal square-shape wind farm Mosetti et al. started the study of wind farm layout optimization in 1994 [6]. Additionally, they also illustrated the improvements of wind farm power output after optimization. After the publication of the first wind farm layout optimization work, the focus of research has shifted to advancing the wind farm optimization methods, such as the constraint handling method [7], wind farm optimization models [8] and wind farm optimization algorithm [9]. Taking the change of Axial induction of different blade elements into account, Hamedi et al. and Ghadirian et al. studied wake profile and wind farm layout optimization by using blade element momentum (BEM) method, which is used to calculate wind turbine blade induced velocity [10, 11]. In order to study wake interaction characteristics of a single wind turbine, the wind turbine rotor actuator disk model is used to simulate the wind turbine wake by Naderi and Torabi [12] and Naderi et al. [13]. Besides, to study the aerodynamics of turbulence in the wake of a wind turbine, the full rotor modeling method was adopted by Abdulqadir et al. [14] and AbdelSalam and Ramalingam [15, 16]. The widely used PARK model is advanced by Parada et al. and in 2017, they applied it to a square-shape wind farm layout optimization [17]. In the study of wind farm layout optimization, the ideal wind conditions, which is the same as the Mosett’s work, were used to compare the optimization results of PARK model and modified model. The review of literatures shows that, due to the obstacles in figuring out WFLO problem, existing researches mostly comprise modeling methods and a few mathematical programming methods. And most WFLO studies adopt the Jensen wake model. Therefore, through the vertical and horizontal comparison of three wake models including the Jensen model, Jensen-Gauss model and AV model, AV model is chosen as the basis model of the study due to its comprehensive performance. On the other hand, the genetic algorithm has good robustness and globality in contrast to traditional algorithms, which make it possible to effectively find the optimal solution of WFLO problem. Thus

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in this paper, an AV wake model based on the genetic algorithm is introduced to solve the WFLO problem. In this paper, a basic theory of wake effect models adopted in this study are presented in Sect. 2. Section 3 gives wind speed spatial distribution of wind farms considering the multiple wake effects and Sect. 4 introduces the WFLO problem solved by the genetic algorithm based on the AV wake model. Finally, conclusions and possible future research directions are analyzed.

2 Wake Effect Modeling Firstly, the commonly used semi-empirical wake models are introduced as follows. 2.1 Jensen Wake Model The schematic diagram of the Jensen wake model is shown in Fig. 1. It is a semi-empirical wake model developed by the Jensen and Katic et al. of Danish National Laboratory [18]. It has become one of the most popular models in engineering application due to its simplicity, practicability and stability. The model is solved by Bezier’s law and the law of mass conservation. Assuming that the radius of the wake region increases linearly with distance, and the growth rate is the only free parameter of the model. Using this geometric assumption, the airflow behind the rotor is divided into a tapered wake zone and an undisturbed flow zone. At a certain distance from the fan, the wind speeds in both zones are constant. V0

Wind wheel

V0

u

Wake radius R

R

α

Fig. 1. Schematic diagram of the Jensen wake model

2.2 AV Wake Model Chen Kun et al. applied jet theory to the study of wake effect in 2003 [19]. The schematic diagram of the AV wake model is shown in Fig. 2. The model describes the wind speed distribution at all positions of the wake region. It can be used to solve the spatial distribution of the wind speed and to estimate the influence of the wake on the performance of the wind turbines. Although there are some errors between the final calculation results and the measured data at that time, the AV wake model can simulate the wake velocity distribution and its development in the whole wind turbine field.

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Wind wheel R X Vi(t) R

Fig. 2. AV wake model

3 Wind Speed Modeling of Wind Farm Considering Multiple Wake Effects 3.1 Calculation Model of Multiple Wake Effects Because the wheel of wind turbines in wind farms may be blocked by other upstream wind turbines to some extent, it is essential to think about wake effects of other wind turbines when calculating the input wind speed of this turbine. According to the momentum law of air flow, the input wind speed at a certain time can be calculated as   n   2   βk vw−ki − vi2 (1) viw = vi2 + k=1,k=i

where vw-ki is the wind speed of the wind turbine i in the wake effect of the wind turbine k, vi is the input wind speed of the wind turbine k without considering the wake effect, β k represents the ratio of shadow area of the wind turbine k at the wind turbine i to the area of wind wheel of the wind turbine i and n is the total number of the wind turbines. As shown in Eq. (1), in order to find the spatial distribution of wind speed, it is essential to calculate the windward sequence and the wake occlusion area of the wind turbine when the natural wind speed is determined. 3.2 Calculation of Occlusion Area When Wind Direction Is Determined As shown in Fig. 3, the wind wheel Arot at position (X, 0) is blocked by the shadow area A[(X )] of the upstream wind wheel. The degree of occlusion area can be divided into three types: no occlusion, full occlusion, partial occlusion. The occlusion area is the area of the wind wheel when fully occluded, and the occlusion area is 0 when there is no occlusion. The partial occlusion can be divided into two cases. In case 1, the overlapping area of wind turbine Ash1 is calculated by Eq. (2). In case 2, the overlapping area of wind turbine Ash2 is expressed by Eq. (3).   d1 d − d1 + R2 arccos − dZ (2) Ash1 = A1 + A2 = R23 arccos R3 R

Research on the Wind Farm Layout Optimization Considering

Ash2 =

R23 arccos

d 2 + R23 − R2 2dR3





d 2 + R2 − R23 + R arccos 2dR 2

A1

A1

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 − dZ

(3)

A2

A(X)

A2

Arot

A(X)

Arot Z

Z

O

O

O

O

R

d1

d2

R3 d

R

(a)

(b)

Fig. 3. Schematic diagram of the multiple wake effects. (a) Case 1: R3 < d1 < R3 + R; (b) case 2: R3-R < d2 < R3

3.3 Coordinate Transformation of Turbines if the Wind Direction Changes When the direction of the wind changes, the wind wheel is always aligned with the wind direction through its yaw control system. When calculating the influence of wake in a wind direction, it is essential to determine the wind receiving sequence of the turbines, then determine the coordinates of other wind turbines with the first wind receiving wind as a reference point, and finally calculate the influence of multiple wake effects. N y

y’

y0 WT2=(x2,y2)

y2

x0

O0

y3

α WT1=(x1,y1) O

x’

x2

x3 x

Fig. 4. Coordinate transformation of wind turbines

As exhibited in Fig. 4, the coordinates of other wind turbine (such as the second turbine) is calculated on the foundation of the first wind turbine in the wind farm. The specific steps are as follows: 1) Establish a Cartesian coordinate x0 Oy0 , and determine the coordinates of each turbine according to the relative position of the wind turbine. For example, the coordinates of the second turbine WT 2 is (x2 , y2 ).

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2) Taking the north direction as the reference direction, when the wind direction is α, the coordinate of the first wind turbine (WT 1) is calculated, and the coordinate in the Cartesian coordinate x0 Oy0 is (x1 , y1 ). 3) Establish a new coordinate system xOy with the wind turbine WT 1 as the coordinate origin and use Eq. (4) to determine the coordinate of the second turbine (xα2 , yα2 ). 4) Take point O as the center, turn the coordinate system xOy anticlockwise to coordinate system x Oy , make its horizontal axis along the wind  and use Eq. (5) to  direction,  . , yα2 determine the coordinate of the second wind turbine xα2 xα2 = x2 − x1 (4) yα2 = y2 − y1  xα2 = xα2 cos α + yα2 sin α (5)  = y cos α − x sin α yα2 α2 α2 In summary, changes in wind direction have an impact on wake effects. Therefore, in order to establish the wind speed model of a large wind farm, the arrangement of each turbine, wind speed and wind direction should be considered comprehensively.

4 Wind Farm Layout Optimization Based on the AV Model and Genetic Algorithm 4.1 Genetic Algorithm Typical wind farm optimization problems are often solved through the “climbing search method”, which is mainly based on a specified local gradient. However, one disadvantage of this algorithm is that only local optimal solution can be found. If the search space is not single connected, the global optimal solution can never be found from the same starting point. The wind farm layout problem is a typical discrete problem and cannot be solved accurately. Thus, the simple mountain climbing algorithm is difficult to apply. Dispersing a wind farm into a 10 × 10 grid, even if each grid only considers the possibility of arranging turbines or not, it means exploring 2100 possibilities, which is beyond the capabilities of most existing computers. Therefore, the genetic algorithm, which simulates the Darwinian process of biological and genetic evolution, is introduced in this study. The genetic algorithm is a highly parallel random computational model based on “survival of the fittest” adaptive optimization algorithm. The “chromosome” group, which is coded by copying, crossing, and mutating, is continuously evolved from generation to generation, and finally converges to the most suitable group, thereby obtaining the best solution of the problem. 4.2 Optimization of the Wind Farm Layout I. Research Method The numbers and locations of wind turbines are the core issues in the study of wind farm layout. This paper utilized the geographical conditions studied by Mosetti [6] and Grady

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[20] to optimize the wind farm. However, the biggest difference is that the AV wake model is adopted in this paper instead of the Jensen model in the Mosetti’s research. The adopted wind farm is in a square flat area of 2000 m × 2000 m, which is divided into a grid of size 10 × 10 and 20 × 20 squares. The possible position of each turbine is in the center of a small unit, as shown in Fig. 5. All wind turbines are identical and the parameters are shown in Table 1. The diagrams of two different wind conditions are shown in Fig. 6. Case 1 is a one-way uniform wind with wind direction of 0° and wind speed of 12 m/s; Case 2 is a variable uniform wind with wind speed of 12 m/s and wind direction changes 36 times from 0 to 10°.

Fig. 5. Wind farm discretization

Table 1. Parameters of wind turbine Parameter

Value

Parameter

Value

Rotor radius (r)

20 m

Air density ρ

1.2

Hub height (h)

60 m

Wind speed v0

12 m/s

Thrust coefficient (CT )

0.88

Enlargement of the wake (k)

0.1

Cross-section area (A)

π r2

Wind turbine efficiency (η)

0.4

II. Objective Function In general, optimized objective function is unit cost of power generation given as objective =

cost Ptotal

(6)

Mosetti et al. only consider the construction cost when summing up the total cost. The unit cost of a single wind turbine is assumed as 1. When the total number of wind

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12m/s

12m/s

Windfarm

Windfarm

Case 1

Case 2

Fig. 6. Diagrams of different wind conditions

turbines N is large enough, the maximum cost can be reduced by 1/3, and the total cost of the wind farm can be written as  2 1 0.00174N 2 (7) + e cost = N 3 3 The total power generation is the sum of the power generation of each wind turbine given as Ptotal =

N 

Pj =

j=1

n  1 J =1

2

ηρAuj3 =

n  1 J =1

2

ηρπ r 2 uj3

(8)

III. Optimized Results of Case 1 Based on the Gatbx toolbox of the University of Sheffield, the genetic algorithm was programmed. Assuming that the initial population is 1000, the maximum evolution algebra is 3000, the crossover probability Px is 0.7, the mutation probability Pm is 0.02 and the generation gap is 0.95. The wind speed is set as 12 m/s, the optimal wind farm layout is shown in Fig. 7, and the evolution curve is shown in Fig. 8. Also, it can be found from Fig. 7 that the layout mode is close to the matrix layout commonly used in engineering practice, which indicates that matrix layout is the best choice if it is planned to establish a wind farm in a region where the prevailing wind direction is constant. The evolutionary curve from Fig. 8 shows that the higher the degree of discretization of the mesh, the more the final layout will be, and the lower the unit cost of power generation. The study results in this paper under the case 1 is compared with that by Mosetti et al. [6] and Grady et al. [20] as shown in Table 2. As displayed in Table 2, compared with Mosetti’s study, the population number and evolutionary algebra are too small, resulting in the calculation results are not optimal, due to the limitations of the calculation conditions at that time. Compared with Grady’s study, the total power generation calculated based on the AV wake model is slightly smaller than the Jensen wake model, but the optimal layout is the same in the 10 × 10 discrete grid. After increasing the degree of discretization, 20 × 20 discrete grid can significantly increase the number of installed wind turbines and reduce unit power generation costs.

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Fig. 7. Optimal layout at two discrete degrees in case 1

Fig. 8. Evolution curves of two discrete degrees in case 1

Table 2. Comparisons of optimized results in case 1 Mosetti

Grady

Present study 1

Present study 2

Grid dispersion

10 × 10

10 × 10

10 × 10

20 × 20

Population

200

600

1000

1000

Evolution algebra

400

3000

3000

3000

Number of turbines

26

30

30

40

Total power (MW)

12.352

14.310

14.1069

20.4218

Efficiency (%)

91.64

92.01

90.71

98.48

Total cost

20.0064

22.0888

22.0888

27.4905

Objective

1.6197

1.5436

1.5658

1.3461

IV. Optimized Cosequences of Case 2 In case 2, the function needs to be rewritten under the same genetic conditions, and the wind direction is changed 36 times from 0 to 360°. Figures 9 and 10 show its layout and

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evolution curves respectively. It is found that the 10 × 10 grid converges faster, while the 20 × 20 grid converges slowly. For this reason, after the final layout in the 10 × 10 grid is expanded, it is calculated as an initial population of 20 × 20, which greatly saves computation time. For the same reason, it can be concluded from Fig. 9 that in the areas where the wind direction changes throughout the year, the plum blossom layout can take full advantage of wind energy. The study results in this paper under the case 2 is given in Table 3. It can be observed that the optimal layout of wind turbines calculated by Mosetti is quite small, but the generation efficiency is very high, due to that the generation efficiency is not covered in the objective function of the optimization problem. With the increase of computer operation speed, the degree of grid discretization will be increasingly higher, and the amount of wind turbines installed will grow. In the future, generation efficiency should also be included in the objective function.

Fig. 9. Optimal layout at two discrete degrees in case 1

Fig. 10. Evolution curves of two discrete degrees in case 1

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Table 3. Comparisons of optimized results in case 2 Mosetti

Grady

Present study1

Present study2

Grid dispersion

10 × 10

10 × 10

10 × 10

20 × 20

Population

200

600

1000

1000

Evolution algebra

400

3000

3000

3000

Number of turbines

19

39

42

48

Total power (MW)

9.2447

17.220

20.4887

24.1693

Efficiency (%)

93.86

85.17

93.10

97.11

Total cost

16.0460

26.9216

28.6503

32.2904

Objective

1.7371

1.5666

1.3983

1.3360

5 Conclusion In this paper, a new approach for solving WFL problem based on AV wake model and genetic algorithm is proposed. This approach maximizes total power generation and minimizes unit power cost under the multiple wake effects. In this study, the AV wake model is thought to be more suitable for the whole field wake calculation by comparing the Jensen wake model, Jensen-Gauss wake model and AV wake model with wind tunnel measured data of Tokyo University and ECN. Based on the AV wake model, considering multiple wake effects superposition, the spatial wind speed modeling of the wind farm is performed, including calculation of superimposed area, coordinate transformation, and calculation of input wind speed. Finally, the wind farm is segmented into a grid of size 10 × 10 and 20 × 20 squares, the unit generation cost is taken as the objective function and then the layout of the wind farm is optimized through using genetic algorithm. Comparing the results with the previous literatures, it is observed that the solutions of test cases based on AV wake model are better than the previous literatures and the higher degree of discretization, the better the optimal solution can be obtained. Therefore, the proposed solutions can overcome the difficulties of maximizing gross generation by limited number of turbines, and minimizing the cost of power generated by an unknown number of turbines under varying wind conditions as well. In future studies, genetic algorithm can be optimized or other algorithms can be employed due to that when the wind farm is dispersed to a higher degree the genetic algorithm converges slowly and the calculation time is long. In this study, two wind conditions are selected when wind farm layout optimization is performed. Due to the great differences of wind conditions in different regions, the calculation program applicable to any wind condition can be further compiled.

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References 1. Lamy, J.V., Azevedo, I.L.: Do tidal stream energy projects offer more value than offshore wind farms? A case study in the United Kingdom. Energy Policy 113, 28–40 (2018) 2. World Wind Energy Association: Wind Power Capacity Worldwide Reaches 597 GW, 50, 1 GW added in 2018 (2019). Available: https://wwindea.org/blog/2019/02/25/wind-power-cap acity-worldwide-reaches-600-gw-539-gw-added-in-2018/ 3. Barthelmie, R.J., Hansen, K., Frandsen, S.T., et al.: Modeling and measuring flow and wind turbine wakes in large wind farms offshore. Wind Energy 12(5), 431–444 (2009) 4. Frandsen, S.: On the Wind Speed Reduction in the Center of Large Clusters of Wind Turbines. J. Wind Eng. Ind. Aerodyn. 39(1), 251–265 (1992) 5. Crespo, A., Herna´ndez, J.: Turbulence characteristics in wind-turbine wakes. J. Wind Eng. Ind. Aerodyn. 61(1), 71–85 (1996) 6. Mosetti, G., Poloni, C., Daviacco, B.: Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm. J. Wind Eng. Ind. Aerodyn. 51, 105–116 (1994) 7. Wang, L., Tan, A.C.C., Gu, Y., Yuan, J.: A new constraint handling method for wind farm layout optimization with lands owned by different owners. Renewable Energy 83, 151–161 (2015) 8. Wang, L., Cholette, M.E., Tan, A.C.C., Gu, Y.: A computationally-efficient layout optimization method for real wind farms considering altitude variations. Energy 132, 147–159 (2017) 9. Abdelsalam, A.M., El-Shorbagy, M.A.: Optimization of wind turbines siting in a wind farm using genetic algorithm based local search. Renewable Energy 123, 748–755 (2018) 10. Hamedi, R., Javaheri, A., Dehghan, O., Torabi, F.: Energy equipment and systems a semianalytical model for velocity profile at wind turbine wake using blade element momentum. Energy Equip. Syst. 3, 13–24 (2015) 11. Ghadirian, A., Dehghan, M., Torabi, F.: Considering induction factor using BEM method in wind farm layout optimization. J. Wind Eng. Ind. Aerodyn. 129, 31–39 (2014) 12. Naderi, S., Torabi, F.: Numerical investigation of wake behind a HAWT using modified actuator disc method. Energy Convers. Manage. 148, 1346–1357 (2017) 13. Naderi, S., Parvanehmasiha, S., Torabi, F.: Modeling of horizontal axis wind turbine wakes in Horns Rev offshore wind farm using an improved actuator disc model coupled with computational fluid dynamic. Energy Convers. Manage. 171, 953–968 (2018) 14. Abdulqadir, S.A., Iacovides, H., Nasser, A.: The physical modelling and aerodynamics of turbulent flows around horizontal axis wind turbines. Energy 119, 767–799 (2017) 15. AbdelSalam, A.M., Ramalingam, V.: Wake prediction of horizontal-axis wind turbine using full-rotor modeling. J. Wind Eng. Ind. Aerodyn. 124, 7–19 (2014) 16. Wang, L., Cholette, M.E., Zhou, Y., Yuan, J., Tan, A.C.C., Gu, Y.: Effectiveness of optimized control strategy and different hub height turbines on a real wind farm optimization. Renewable Energy 126, 819–829 (2018) 17. Parada, L., Herrera, C., Flores, P., Parada, V.: Wind farm layout optimization using a Gaussianbased wake model. Renewable Energy 107, 531–541 (2017) 18. Katic, I., Højstrup, J., Jensen, N., et al.: A simple model for cluster efficiency. Proceedings 1(1), 407–410 (1987) 19. Chen, K., He, D.: Research on the mathematical model of the wind turbine wake and its influence on the performance of the wind turbines. Hydrodyn. Exp. Measur. 1(1), 84–87 (2007) 20. Grady, S.A., Hussaini, M.Y., Abdullah, M.M.: Placement of wind turbines using genetic algorithms. Renewable Energy 30, 259–270 (2005)

A Hierarchical Fast Model Predictive Control for Cascaded H-Bridge SVG Han He1 , Qianli Xing1 , Zhenbin Zhang1(B) , Zhen Li1 , Zhiqiang Guo2 , Rong Ye3 , and Zhi Li4 1 Shandong University, Jinan, China

[email protected]

2 WindSun Science and Technology Co., Ltd., Jinan, China 3 State Grid Fujian Economic Research Institute, Fuzhou, China 4 China Three Gorges Corporation, Wuhan, China

Abstract. Finite control set model predictive control (FCS-MPC) is well suited for the CHB-SVG system, which needs to optimize multi-objective simultaneously. However, the underlying system of a high voltage CHB-SVG is composed of dozens, perhaps hundreds, modules, which generally brings a heavy computation burden for the controller. In this work, we propose a three-layer fast model predictive control for CHB-SVG to reduce the computation complexity and improve the voltage balancing performance. Firstly, the proposed approach divided the voltage-balancing model predictive control into two suboptimization problems, which reduced the iteration times of the voltage-balancing control loop. Secondly, an improved capacitor voltage balancing method that allows the modules in the same phase to output complementary switching states is presented, which improves the voltage balancing performance in low reactive power output conditions. Finally, simulation results confirm the effectiveness of the proposed method in reducing the computation burden and valid restraint for the capacitor voltage imbalance. Keywords: Fast FCS-MPC · CHB-SVG · Hierarchical optimization

1 Introduction The Static-Var-Generator, a member of the sustainable energy power generation system, plays a vital role in supporting the amplitude of grid voltage, adjusting the power factor, improving the power quality, etc., which contributes to the grid-friendly sustainable energy power generation system. Further, CHB-SVG, composed of cascading H-bridge modules and widely applied, can directly connect to the high voltage grid (35 kV) with following advantages [1, 2]: (i) more output voltage level so that the output voltage and current achieving a better sinusoidal waveform; (ii) transformerless structure reduces the cost for applications above 10 MVar and eliminates the hysteresis effect which provides faster current dynamic response; © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 993–1001, 2023. https://doi.org/10.1007/978-981-99-4334-0_118

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(iii) a large number of modules makes it have the higher fault-tolerant ability. Industrial products are already available, while researchers around the world still propose various strategies to improve the performance of the CHB-SVG. Recently, FCSMPC has been widely researched and applied, due to the advantages of simple control principles, high dynamic response performance, and may contain multiple nonlinear constraints, etc. However, the FCS-MPC is a MIQP (Mixed Integer Quadratic Programming) problem, its time complexity explodes exponentially with increased elements in the control set. The CHB-SVG system comprises dozens of modules that exponentially enlarge the MPC control set, which makes FCS-MPC challenging to apply in CHB converters with short control cycles. In addition, the wide range of operating conditions poses challenge to restraining capacitor voltage imbalance. Plenty of works have been reported to solve the above issues. Some methods using adjacent vector [3], adjacent module [4] or other preselection algorithms [5] have been proposed to reduce the elements of the control set in advance to decrease the execution time. However, the above “adjacent” approaches may produce suboptimal solutions. Reference [6] proposed a sphere decoding algorithm to prune the unnecessary solution. However, the computation time depends on the initial sphere pruning radius, and a large initial radius still needs a long computation time. Hierarchical optimization approaches [7–10] has been proposed to divide FCS-MPC into multiple optimization problems: the output current/power MPC and the H-bridge cells voltage balancing (CVB)-MPC (can be solved within polynomial time). Based on the work of Zhang et al. [7], this work presents a three-layer method to reduce the computation of the FCS-MPC for CHB-SVG. The contribution of this work is proposing an approach that further divides the CVB-MPC into two optimization problems: phase voltage balancing (PVB)-MPC and module voltage balancing (MVB)MPC, which reduce the computation complexity of the CVB-MPC. Furthermore, MVBMPC allows the modules in the same phase output complementary switching state, which optimizes the CVB-MPC performance, especially when the reactive output power is low (< 0.01 p.u.). The proposed method composes of the following three layers. In the first layer, the MIQP problem of the current MPC is solved, and the optimal output voltage vector is obtained. In the second layer, the optimization problem of PVB-MPC is solved, and the output voltage level of three phases (subject to the optimal voltage vector) is obtained to balance the total DC voltage of different phases. In the third layer, the switching states of each module are obtained by solving the MVB-MPC problem, which subjects to the output voltage level of the corresponding phase and aims to balance the capacitor voltage of each module. The paper is organized as follows. Section 2 describes the system model of CHBSVG. Section 3 presents the proposed method in detail. The simulation result are presented in Sect. 4. Section 5 concludes this work and describes the future work.

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2 System Predictive Model 2.1 A Subsection Sample Figure 1 depicts the topology of the three-phase star-connected CHB-SVG system. Every phase of the CHB-SVG consists of n H-Bridge modules, and the three output states for module i of phase p can be denoted as Spi ∈ {−1, 0, 1}, where p ∈ {a, b, c} and i ∈ {1, . . . , n}. Assuming the capacitor voltage in each H-Bridge module is Vdc , then the the output output voltage levels upi = (Spi Vdc ) ∈ dc , 0, Vdc }, and  voltage levels for {−V n  n  S = V S = V each phase can be denoted as u p dc i=1 pi dc i=1 pi = Vdc Sp , where  Sp = ni=1 Spi represents the output voltage state of phase p. Assuming the capacitors and the grid side filter is three phases balancing, i.e., L = Lp , R = Rp and C = Cpi for ∀i ∈ {1, . . . , n}, ∀p ∈ {a, b, c}. Kirchhoff’s Equation in αβ coordinate can be obtained and the discrete model can be expressed as follows: iα,β (k + 1) = (1 − upi (k + 1) = upi (k) +

Ts Ts )iα,β (k) + (eα,β (k) − uα,β (k)) L L

(1)

Ts Spi ip , ∀i ∈ {1, . . . , n}, ∀p ∈ {a, b, c} C

(2)

Ts Sp ip , ∀p ∈ {a, b, c} C

(3)

up (k + 1) = up (k) +

where k and k +1 indicate the current and next control step, and Ts represents the control period. eα,β , iα,β , uα,β represent the grid voltage, output currents, and output voltage of CHB-SVG in the αβ frame, respectively.

3 Proposed FCS-MPC for CHB-SVG Predict state variables using (1) and (2) to compensate for the digital control delay effect. That is, at the k step, the optimal input switching state at the k + 1 step should be found, which optimized the control performance at the k + 2 instant. 3.1 Model Predictive Current Control The change of the output voltage vector does not obviously affect the switching effort. Therefore, minimizing the current tracking error is the only objective of the output current MPC by finding the optimal switching vector (Sα∗ , Sβ∗ ) using predictive model (1). The cost function of the current MPC is as follows:

2  2 (4) MinJ1 = iα∗ (k + 2) − iα (k + 2) + iβ∗ (k + 2) − iβ (k + 2) .       Jα

Jβ

Note that (4) has two terms, Jα and Jβ , which are decoupled and do not affect each other. Thus exhaustive search algorithm is used for α and β axis respectively, which reduce the enumeration number from 12n2 + 6n + 1 to 4n + 1, i.e., reduce the time complexity of the current MPC from polynomial time to linear time [7].

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Fig. 1. Topology of the transformerless three-phase star-connected CHB-SVG system.

Fig. 2. The flow chart of the proposed approach.

3.2 Model Predictive Phase Voltage Balancing Control Model predictive Phase  Voltage balancing (PVB) control aims to balance the total capacitor voltage Vp = ni=1 upi of phase p ∈ a, b, c by finding the optimal phase switching state (Sa∗ , Sb∗ , Sc∗ ) that makes up the optimal switching vector (Sα∗ , Sβ∗ ). The formulation of the PVB-Control is as follows: 

MinJ2 = Vp (k + 2) − Vp∗ (k + 2) + λ1 Sp (k + 1) − Sp (k) , p=a,b,c

s.t.

Sα∗

√ 3 1 ∗ = (2Sa − Sb − Sc ), Sβ = (Sb − Sc ), 3 3

(5)

where λ1 is the weighting factor. For a CHB-SVG with n modules per phase, every output voltage vector has no more than 2n + 1 candidate phase switching state combinations.

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That is, the computational complexity is linear time. Therefore, the enumeration method can be used. In addition, the adoption of l1 -norm further reduces the computation burden. The algorithm flow chart is shown in Fig. 2, where d ∈ {1, . . . , 2n+1} is the PVB control loop cycle time. 3.3 Module Voltage Balancing Control Module Voltage balancing (MVB) control aims to balance each H-bridge module’s capacitor voltage by choosing their switching state to make up the phase switching state reference (Sa∗ , Sb∗ , Sc∗ ). The formulation of the MVB-Control for each phase is: MinJp =

 n  2  2    ∗ (k + 2) + λ2 Spi (k + 1) − Spi (k) , upi (k + 2) − upi i=1

s.t. Sp∗ (k + 1) =

n 

Spi (k + 1),

(6)

i=1

where the second term is used to limit the switching effort with weighting factor λ2 . However, if the optimal switching state Sp∗ = m, Jp needs to be calculated (n−m)/2 m+k k (Cn Cn−(m+k) ) times, which makes it hard to apply in the real-time conk=0 troller. Hence, this work proposes a fast optimization approach, which consists of three steps, to solve this problem. In Step I, we transform the optimization problem of each phase into the quadratic form. Substitute (2) into (6), and for simplicity, use Spi , upi to refer to Spi (k+1), upi (k+1) respectively. Equation (6) can be rewritten as MinJp =

n

 2 Kpi Spi + Cpi Spi +Constp (k + 1),   i=1  Jpi

s.t.Sp∗ =

n 

Spi , Spi ∈ {−1, 0, 1},

(7)

i=1 ∗ ) Ts i − λ S (k)). Note that the inflow where Kpi = ( TCs ip )2 + λ22 , Cpi = 2((upi − upi 2 pi C p current ip is equal for all modules in the same phase, which makes the coefficient Kps = not affect to CVB-optimization Kpi , ∀i ∈ {1, . . . , n}, and the constant Constp (k +1) does  2 + C S ), S ∈ problem. Thus cost Function Jp is only dependent on ni=1 (Kps Spi pi pi pi {−1, 0, 1}. Therefore, Kps and Cpi have to be computed in the first step. 2 ∈ {0, 1}, J  can be calculated by: In Step II, due to Kps ≥ 0 and Spi pi

⎧ ⎨ Kps − Cpi , Spi = −1  Jpi = 0, Spi = 0 . ⎩ Kps + Cpi , Spi = 1

(8)

It can be obtained from (8) that if |Cpi | > |Kps |, ∃Spi ∈ {−1, 1} makes Jpi ≤ 0, and if |Cpi | ≤ |Kps |, ∀Spi ∈ {−1, 0, 1} makes Jpi ≥ 0. In order to find out the switching

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combination sp = {Sp1 , Sp2 , . . . , Spn } that minimizes Jp , the modules that make Jpi negative should be used as much as possible. Therefore, sorting C p = {Cp1 , . . . , Cpn }  , . . . , C  }. If S ∗ ≥ 0, the first S ∗ modules in C  with from low to high ⇒ C p = {Cp1 pn p p p1 much lower Cpi should output the positive voltage level. Conversely, if Sp∗ < 0, the last |Sp∗ | modules with much higher Cpi should output the negative voltage level. In Step III, new couples of the module with complementary switching states would be found to optimize the switching combination. Note that the above greedy algorithm  only satisfies the constraints Sp∗ = ni=1 Spi initially. There is still the possibility of optimizing the switching combination, e.g., Spk = 1 and Spj = −1 can be invested to decrease Jp without violating the constraints.     C p = {Cp1 , . . . , Cpm , . . . , Cpn }. , Cp(m+1)   

(9)

 in C  are selected to Assuming m ≥ 0, the modules corresponding to the first m Cpi p   , ∀j > k, if we need output the positive voltage level, as shown in (9). Due to Cpk < Cpj to output the positive voltage level, there has    = Kps + Cpk < Jpj = Kps + Cpj , ∀j > k. Jp(k)

And if we need to output the negative voltage level, there has    Jp(k) = Kps − Cpk > Jpj = Kps − Cpj , ∀j > k.   Therefore, a couple of modules corresponding Cp(m+1) and Cp(n) output positive and negative voltage levels, respectively, making total cost function Jp decrease the most. It     and Cp(n−1) are next to Cp(m+1) and Cp(n) is obvious that modules corresponding Cp(m+2)    in decreasing Jp and so on until Cp(m+(n−m)/2) and Cp(n−m)/2+1 have the least effect on decreasing Jp . Then check out whether the investment of the above modules decreases the total cost function Jp using     (Jp(m+k) + Jp(n+1−k) ) < 0 ⇒ Cp(m+k) − Cp(n+1−k) < −2Kps ,

(10)

where k ∈ {1, . . . , (n − m)/2}. If the module satisfies (10), that means the investment of the above modules decreases the total cost function Jp . k keeps increasing from 1 and repeats the preceding steps until not satisfying (10) or meeting constraint k > (n−m)/2. The whole FCS-MPC control algorithm flow chart is shown in Fig. 2.

4 Simulation Result The simulation parameters are presented in Table 1. Figure 3 shows the simulation waveform from 0.5 p.u. to 1.0 p.u. reactive power output. At 0.2 s, the reactive power changes from 20 to 40 MVar. As shown in the figure, the currents can be well regulated (THD = 1.738% at 0.5 p.u. and THD = 0.818% at 1.0 p.u.), and the transient time is 0.32 ms. Figure 4 shows the DC total voltage and capacitor voltage waveforms when the reactive power output is very low (0.0025 p.u. = 0.1 MVar) and λ2 = 0. The performance

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Table 1. CHB-SVG system simulation parameters. Variable

Description

Value

es

Grid voltage(RMS)

33 kV

L

Filter inductor

10 mH

R

Filter resistance

0.01 m

C

DC capacitor

8 mF

fs

Sampling frequency

10 kHz

n

Number of modules

9

Vdc

DC total voltage

33 kV

Fig. 3. Waveform of the CHB-SVG at steady and transient state (20–40 MVar).

of method [7] and the proposed approach are similar. The waveforms when λ2 = 1 are presented in Fig. 5. In this case, the method proposed in [7] fails to balance the DC voltage amount in three phases. But the proposed approach can still keep well voltage balancing performance.

Fig. 4. Waveform of the CHB-SVG at steady and transient state (20–40 MVar).

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Fig. 5. Waveform of the CHB-SVG at steady and transient state (20–40 MVar).

5 Conclusion The FCS-MPC is an interesting alternative for the CHB-SVG with simple control principles, high dynamic response performance, and may contain multiple nonlinear constraints, etc. At same time, it will also brings a heavy computational burden. This work proposes a fast FCS-MPC approach for CHB-SVG, which further divides the CVB-MPC into PVB-MPC and MVB-MPC to ease the computation complexity of the CVB-MPC. In addition, the proposed MVB-MPC allows the modules to output complementary switching states, which further optimizes the CVB-MPC performance, especially the reactive power is low. The simulation results confirm the effectiveness of the proposed method in reducing the computation burden, and valid restraint for the capacitor voltage imbalance. Acknowledgements. This work was supported in part by the National Distinguished Expert (Youth Talent) Program of China under Grant 31390089963058; in part by the General Program of National Natural Science Foundation of China under Grant 51977124; in part by the General Program of National Natural Science Foundation of China under Grant 52277192; and in part by the cooperative project of Shandong University and WindSun Science & Technology Co., Ltd under Grant 1390021068.

References 1. Zhang, Y., Yuan, X., Wu, X., Yuan, Y., Zhou, J.: Parallel implementation of model predictive control for multilevel cascaded H-bridge STATCOM with linear complexity. IEEE Trans. Ind. Electron. 67(2), 832–841 (2020) 2. Akagi, H.: Multilevel converters: fundamental circuits and systems. Proc. IEEE 105(11), 2048–2065 (2017) 3. Cortés, P., Wilson, A., Kouro, S., Rodriguez, J., Abu-Rub, H.: Model predictive control of multilevel cascaded H-bridge inverters. IEEE Trans. Ind. Electron. 57(8), 2691–2699 (2010) 4. Qi, C., Chen, X., Tu, P., Wang, P.: Cell-by-cell-based finite-control-set model predictive control for a single-phase cascaded H-bridge rectifier. IEEE Trans. Power Electron. 33(2), 1654–1665 (2018) 5. Gutierrez, B., Kwak, S.-S.: Modular multilevel converters (MMCs) controlled by model predictive control with reduced calculation burden. IEEE Trans. Power Electron. 33(11), 9176–9187 (2018)

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6. Baidya, R., Aguilera, R.P., Acuña, P., Vazquez, S., Mouton, H.T.: Multistep model predictive control for cascaded H-bridge inverters: formulation and analysis. In: IEEE Transactions on Power Electronics, vol. 33, no. 1, pp. 876–886. (2018) 7. Zhang, Y., Wu, X., Yuan, X., Wang, Y., Dai, P.: Fast model predictive control for multilevel cascaded H-bridge STATCOM With polynomial computation time. IEEE Trans. Ind. Electron. 63(8), 5231–5243 (2016) 8. Dekka, A., Wu, B., Yaramasu, V., Zargari, N.R.: Dual-stage model predictive control with improved harmonic performance for modular multilevel converter. IEEE Trans. Ind. Electron. 63(10), 6010–6019 (2016) 9. Huang, J., et al.: Priority sorting approach for modular multilevel converter based on simplified model predictive control. IEEE Trans. Ind. Electron. 65(6), 4819–4830 (2018) 10. Zhang, Y., Wu, X., Yuan, X.: A simplified branch and bound approach for model predictive control of multilevel cascaded H-bridge STATCOM. IEEE Trans. Ind. Electron. 64(10), 7634– 7644 (2017)

Speed Fluctuation Suppression Strategy of PMSM Based on Improved Linear Active Disturbance Rejection Control Yangyang Cui(B) , Zhonggang Yin, Peien Luo, and Yanping Zhang Department of Electrical Engineering, Xi’an University of Technology, Xi’an, China [email protected]

Abstract. To suppress the speed fluctuation permanent magnet synchronous motor (PMSM), an improved linear active disturbance rejection controller (ILADRC) based on feedforward differential and direct output feedback is proposed. On account of the conventional linear active disturbance rejection controller (CLADRC), the controller adds a feedforward differential signal of a given value, so that the overshoot and regulation time can be reduced when the motor is started, stopped, and loaded or unloaded; By taking the output velocity signal of the system as the direct feedback signal of the linear state error feedback (LSEF), there is no estimation error in the output of the conventional linear extended state observer (CLESO). The PMSM double closed loop drive system uses the controller to control the speed loop. Finally, the experiment verifies that ILADRC has better ability to restrain the speed fluctuation of the motor than CLADRC. Keywords: Permanent magnet synchronous motor · Speed fluctuation · Linear active disturbance rejection controller

1 Introduction High power efficiency and high power factor make PMSM suitable for rail transit, aerospace, high-end manufacturing, among other applications [1]. However, due to the influence of cogging torque, inverter dead time, shaft friction, load fluctuation and other factors, the motor often has repetitive torque pulsation during operation, thus causing periodic speed fluctuations [2, 3]. To effectively suppress torque ripple and speed fluctuation, the field of PMSM drive systems uses a wide variety of control strategies. ADRC technology combines the conventional PID controller with the state observation idea of modern control theory. It can estimate and compensate the lumped disturbance [4]. But the conventional nonlinear active disturbance rejection controller (NLADRC) has many parameters, so it is difficult to adjust it effectively; Compared with NLADRC, CLADRC has lower tracking and anti-disturbance characteristics [5]. To solve above problems, an ILADRC suitable for PMSM speed outer loop is proposed. The ILADRC leads to the feedforward differential signal of the reference value, and takes the system output value as the direct feedback signal of LSEF. Finally, the speed fluctuation suppression effect of the PMSM based on ILADRC control is verified by experiment, and is compared with that of PMSM under CLADRC control. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1002–1007, 2023. https://doi.org/10.1007/978-981-99-4334-0_119

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2 Establishment of PMSM Mathematical Model Coordinate transformation is the basis for designing PMSM drive system. The PMSM can be converted from a-b-c system to d-q system through Park transformation. The basic equation under synchronous rotation coordinate is as follows [6].  d ud = dψ dt + Rs id − ωe ψq (1) dψq uq = dt + Riq + ωe ψd  ψd = Ld id + ψf (2) ψq = Lq iq Te = J

   3  pn ψf iq + Ld − Lq id iq 2

(3)

dωr = Te − TL − Br ωr dt

(4)

where ud , uq and id , iq are the components of stator voltage and stator current on the rotating coordinate system respectively, pn is the number of poles of motor stator winding, Rs is the stator resistance, L d and L q are the inductances of motor on the rotating coordinate system, ψ d and ψ q are the component of stator flux on the rotating coordinate system, ψ f is the rotor flux linkage, ωe and ωr are electrical angular velocity and mechanical angular velocity respectively, J is the moment of inertia, Br is the damping coefficient, T e and T L are electromagnetic torque and load torque respectively.

Fig. 1. Schematic diagram of IPMSM double closed loop vector control.

As a way to achieve the established control objective, this paper uses MTPA’s double closed-loop vector control method. Since the PMSM motion equation and voltage equation are first-order differential equations, the speed loop and current loop controllers are controlled by the first-order LADRC. Figure 1 shows its control block diagram.

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3 The ILADRC Is Proposed The core of LADRC is LESO, which can estimate and compensate the lumped disturbances. However, CLADRC uses the output value of LESO as the feedback signal of LSEF. Due to the existence of observer delay and observation error, CLADRC cannot accurately estimate and compensate the lumped disturbances suffered by the system, so this paper improves CLADRC, the feedforward differential signal of reference value is introduced and the system output signal is taken as the direct feedback signal of LSEF [7]. The control algorithm is as follows. ⎧ z˙1 = z2 − β1 (z1 − x1 ) + b0 u ⎪ ⎪ ⎪ z˙ = −β (z − x ) ⎨ 2 2 1 1 = k − x + r˙ u (r ) 0 p 1 ⎪ ⎪ ⎪ ⎩ u = u0 − z2 b0

(5)

where, x 1 and x 2 are state variables, z1 and z2 are the estimated values of state variables, β 1 and β 2 are the feedback gain coefficient of LESO, b0 is the compensation factor, k p is the proportional coefficient of the controller, r is the given value, u0 is the output of LSEF, u is the output of ILADRC. By pole assignment, the observer feedback gain coefficient is assigned at the observer bandwidth, and the controller proportional coefficient is assigned at the controller bandwidth, that is.  2 s + β1 s + β2 = (s + ω0 )2 (6) s + kp = s + ωc β1 = 2ωo , β2 = ωo2 , kp = ωc Its control block diagram is shown in Fig. 2.

Fig. 2. ILADRC control structure diagram.

(7)

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According to Eq. (5), the PMSM speed loop control algorithm based on ILADRC is.   ⎧˙ ωˆ r = fˆ − β1 ωˆ r − ωr + b0 Te ⎪ ⎪ ⎪ ⎨ f˙ˆ = −β ωˆ − ω  2 ∗ r r ω ˙ r∗ = k − ω u ⎪ 0 p r r +ω ⎪ ⎪ ⎩ ˆ u = u0b−0 f

(8)

Similarly, β 1 , β 2 and k p can be configured to the corresponding bandwidth through pole configuration, as shown in (7).

4 Experimental Verification 4.1 No Load Experimental Verification To prove the correctness and effectiveness of the ILADRC, 2 kW IPMSM vector control experimental platform was built. The core processor DSP is TMS320F28335 chip of TI Company.

0

iq/A

0 1000

1000 150

iq/A

n/rpm

150 t / (1s/div)

(a)

n/rpm t / (1s/div)

(b)

Fig. 3. Speed and current waveform in acceleration stage when motor is controlled by different controllers. (a) Speed and current when motor is controlled by CLADRC. (b) Speed and current when motor is controlled by ILADRC.

Figure 3 shows the acceleration process of the motor under no-load operation. The motor starts to run from 150 rpm and then increases to the rated speed of 1000 rpm. As shown in Fig. 3. That when the motor operates with no load and adopts CLADRC control in the acceleration phase, the motor speed and q-axis feedback current have obvious fluctuations, while when using ILADRC control, the motor speed and q-axis feedback current will operate smoothly without fluctuations. 4.2 Loading Experiment Verification Figure 4 shows the waveform of 2 Nm load suddenly applied at rated speed when the motor is controlled by different controllers. As shown in figure that when ILADRC control is adopted, the motor speed and q-axis feedback current only have slight overshoot

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changes at the moment of loading; However, when the motor is controlled by CLADRC, the speed fluctuation and current fluctuation obviously appear at the moment of loading, and the regulating time is much longer than that when the motor is controlled by ILADRC. The above experiments show that the ILADRC has better speed fluctuation and torque ripple suppression ability than CLADRC, and can effectively compensate the lumped disturbance suffered by the system.

0.3

iq/A

0.3

iq/A n/rpm

n/rpm

1000

1000

t / (1s/div)

(a)

t / (1s/div)

(b)

Fig. 4. Speed and current waveform in the loading stage when the motor is controlled by different controllers. (a) Speed and current when motor is controlled by CLADRC. (b) Speed and current when motor is controlled by ILADRC.

5 Conclusion To effectively suppress the speed fluctuation and torque ripple of PMSM, this paper proposes an ILADRC based on feedforward differential and direct output feedback. The controller is applied to PMSM double closed loop vector control system. Finally, in the proposed control method, experiments are conducted to verify its correctness and effectiveness. The results show that the introduction of feedforward differential signal can reduce the overshoot and shorten the regulation time when the motor starts, stops, and loads are added or removed; By using the system output speed signal as the direct feedback signal of LSEF, the burden of LESO can be reduced, and the observation error and delay time can be reduced. Compared with CLADRC controller, this controller can compensate the lumped disturbance of the system better.

References 1. Erturk, F., Akin, B.: Spatial inductance estimation for current loop auto-tuning in IPMSM self-commissioning. IEEE Trans. Industr. Electron. 67(5), 3911–3920 (2020) 2. Yang, J., Chen, W.H., Li, S., et al.: Disturbance/uncertainty estimation and attenuation techniques in PMSM drives—a survey. IEEE Trans. Industr. Electron. 64(4), 3273–3285 (2017) 3. Mai, Z.: HF pulsating carrier voltage injection method based on improved position error signal extraction strategy for PMSM position sensorless control. IEEE Trans. Power Electron. 36(8), 9348–9360 (2021)

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4. Jingqing, H.: Active Disturbance Rejection Control Technology Control Technology for Estimating and Compensating Uncertainties, pp. 56–73. National Defense Industry Press, Beijing (2008) 5. Gao Z. Scaling and Parameterization Based Controller Tuning[C]. Proceeding of the: American Control Conference. IEEE 2003, 4989–4996 (2003) 6. Sreejith, R., Singh, B.: Sensorless predictive current control of PMSM EV drive using DSOGIFLL based sliding mode observer. IEEE Trans. Industr. Electron. 68(7), 5537–5547 (2021) 7. Wang, X.: Research on High Performance Control Strategy of Permanent Magnet Synchronous Motor. Xi’an University of Electronic Science and Technology (2019)

An Improved Distributed Wind Farm MPPT Control Based on Wake Propagation Prediction Fenglin Miao1 , Yi Fan2 , and Zhen Li1,2(B) 1 State Key Laboratory of Operation and Control of Renewable Energy and Storage Systems,

China Electric Power Research Institute, Beijing, China [email protected] 2 Shandong University, Jinan, China

Abstract. This work presents a pre-control approach based on wake propagation prediction to reduce the convergence time of the gradient-based wind farm maximum power point tracking (MPPT) distributed control method. Firstly, the proposed method modifies the control parameter before the wake affects the turbines downwind, which improve the convergence speed of the wind farm MPPT control. Secondly, a dynamic grouping method is given to build communication links between neighboring turbines, which makes the proposed method can be applied to an established wind farm. Finally, the control performance is validated by simulation results. Keywords: Wind farm MPPT · Wake interaction · Distributed control

1 Introduction 1.1 A Subsection Sample Offshore wind speeds are more stable and possess greater energy density, which is suitable for developing large-scale wind power systems and has been one of the leading development directions to cope with the future energy shortage. However, due to the more expensive manufacturing, construction, operation, and maintenance costs, the Levelized Cost of Energy (LCOE) of offshore wind power generation systems is much higher than the onshore one. How to reduce the LCOE to improve the economic benefits of the offshore wind power generation system has become a widely studied issue. Improving the wind power coefficient of the wind farm is a practical fashion to increase the electric energy production of wind power systems, which reduces the average cost per kilowatt-hour of electricity, i.e., reduces the LCOE. The conventional MPPT control technology for a single wind turbine has been widely studied. However, due to the interacting effect between wind stream conditions, the single turbine operating at the maximum power point does not indicate that the wind power coefficient of the wind farm is maximum. Centralized control structures depend on centralized processors, which are less-scalable and challenging to deal with communication failures, making them unsuitable for large-scale wind farms. Reference [1] using a hierarchical decentralized control © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1008–1014, 2023. https://doi.org/10.1007/978-981-99-4334-0_120

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structure to optimize the power generated by each agent. However, this method still needs a centralized control agent to coordinate all the distributed agents, which increases the investment in the wind farm. References [2, 3] using a distributed control algorithm base on the wake propagation model to solve the aerodynamic interaction problem. However, those methods are very complex and of less scalable ability. Gradient-base model-free control method [4] was used to solve the above problems. And some accelerated algorithms [5, 6] were reported to decrease the convergence time of the gradient-based methods. However, whatever improvements are proposed, the convergence speed of the conventional gradient-based algorithms is slow because they have to wait for the wake to propagate and affect the turbines downwind. This work uses the wake propagation model to predict the wake stream condition and modify the control parameter before the wake effect on the turbines downwind. The contribution of this work is to introduce the wake prediction model, which can reduce the convergence time of gradient-based methods. Furthermore, a communication approach base on the dynamic grouping method is given to link the neighboring turbines. This paper is organized as follows. Section 2 describes the system model of wind farm. Section 3 presents the proposed method in detail. The simulation results are presented in Sect. 4. Section 5 concludes this work.

2 System Model This section introduces the wind farm and wakes propagation models.

Fig. 1. A row of n wind turbines.

Fig. 2. The proposed approach.

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2.1 Wind Farm Model For simplicity developing the proposed approach, assuming uniform wind of constant direction and speed v∞ . Then, all turbines axis are parallel to the wind direction due to the yaw control. Considering a row of n wind turbines denoted by N = {1, 2, . . . , n}, which are arranged in a straight line, as shown in Fig. 1. In turbine aerodynamics modeling, it is typical to introduce the parameter called axial induction factor ai of turbine i ∈ N to describe the drop in wind speed, which is defined by vd = (1 − ai )v∞ , where vd represents the wind speed at the rotor. Therefore, the axial induction factor ai can indicate how much energy the turbine captures from the wind, and it can be adjusted by the tip speed rate and the blade pitch angle. The power and the thrust coefficient CPi , CTi of wind turbine i ∈ N can be calculate using CPi = 4ai (1 − ai )2 , C_{Ti} = 4a_i(1 − a_i). 2.2 Wake Predictive Model Stream movement is complex and hard to predict. The frozen turbulence hypothesis for inviscid flow [7] is applied to reduce the computation complexity of prediction, i.e., the velocities of the wake streams are then assumed to travel with the average wind speed in the longitudinal direction. In this way, the wind speed at the point p downwind will eventually be predicted by 1 d −1 v(p) = wi (d )u(p, t), wi (d ) = 1 − CTi (t0 )(1 + ) , 2 4R

(1)

where R represents the radius of the rotor, d represents the longitudinal distance between the turbine upwind and the measurement point p, and u(p, t) indicates the wind speed at point p if no turbines were present. To judge whether the turbines downwind are in the wake area of the turbines upwind, we need to compute the wake expansion according to [7]:   d = 4R2 + dR. (2) ei (d ) = 2R 1 + 4R Then, we can emulate the wake contributions of all turbines and estimate the wind speed at any point in the wind farm using vx (x, y) = ux (x, y)i∈L ai (di ),

(3)

where L is the indices set of the turbines whose wake stream affects the point p.

3 MPPT Control of a Wind Farm This section presents the scheme to implement the proposed algorithm on a wind farm with an arbitrary but known spatial arrangement of wind turbines.

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3.1 Distributed Control Structure We introduce the control structure, which consists of the dynamic grouping method of turbines and the communication between adjacent agents. In the beginning, we need to judge the direction of the incoming wind. Due to the communication graph of the wind farm is connected, the average consensus algorithm is applied to find out the wind direction. Then, N = {1, 2, . . . , n} denote the indices of turbines as defined above, let G ⊂ N be the set of turbines whose wake stream directly influences turbines downwind, and Q ⊂ N indicate the set of the rest turbines. Further, let Di denote the index of the nearest downwind turbine directly influenced by the turbine i ∈ G. Then, using the above definitions, each turbine i ∈ G only needs to communicate with the downwind turbine Di , and the FS-MPPT control update law is written as:   ∂Pi ∂PDi ai (k + 1) = ai (k) + Ksign + ∀i ∈ G, (4) ∂ai ∂ai where ∂PDi can be approximated using ∂PDi = PDi (k) − PDi (k − 1). However, the communication lines are fixed, i.e., turbine i and Di may not be directly connected by cable wires. To achieve MPP using (4), turbine i need to find the communication links with their downwind turbine Di . To this end, we introduce the graph discovery algorithm according to [8]: Each turbine in the wind farm is assigned a unique identifier ID(i), e.g., its IP address. The turbines keep communicating with their neighbor turbines to update the communication link topology between ID(i). Due to the communication graph of the wind farm is connected, we can find out at least one communication link between two arbitrary turbines. Therefore, after updating the communication graph, we can get the communication link between turbines i ∈ G and Di . The communication messages may be transmitted through other turbines. 3.2 Cooperative MPPT Control Using Wake Prediction To apply the fixed-step MPPT control update law (4), we need to measure the power generated by turbines i and Di , where i ∈ G. However, the wake stream produces by turbine i takes time to travel to the downwind turbines Di after we update the control parameter ai (k), i.e., there is a time delay Ts,d before the change of ai (k) affects the neighboring turbine downwind. Therefore, we need to wait at least Ts,d to calculate ∂PDi (k) and update the next control parameter ai (k + 1). In addition, there is another time delay Ts,t before the change of ai (k) effect on the turbine i itself, where Ts,t < Ts,d . Thus, the partial derivative ∂Pi (k) and ∂PDi (k) in the control update law can be calculated by:   Pi tk + Ts,t − Pi (tk ) ∂Pi , (5) (k) = ∂ai ai (k) − ai (k − 1)     PDi tk + Ts,d − PDi tk + Ts,t ∂PDi , (6) (k) = ∂ai ai (k) − ai (k − 1) where tk is the time instance when the control parameter ai is updated.

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Note that for a wind farm which turbines 300 m apart and wind speed 10 m/s, the wake takes at least 30 s to travel from upwind turbines to downwind turbines, which makes the convergence rate of MPPT control very slow. To reduce the convergence time of the fixed-step MPPT control, we introduce the wake predictive model (1), (2) and (3) to estimate the effect of the wake stream on downwind turbines. The MPPT control algorithm can be described as follow. Algorithm I: Let Ts denotes the control period, τ denotes the time instance, and tk denotes the update instance of control parameter ai (k), where i ∈ G at step k, then ai (k + 1) will be determined by the following steps. 1) Initialize control parameters Ts , Ts,t , Ts,d .e.g., set τ = 0. The response flag RF of turbines is set to false, which indicates whether the local turbines have completed adjusting ai (k). Then update the control parameter ai (k). 2) Measure the power Pi (tk ) produced by each turbine i ∈ G, and keep τ = τ + Ts in every control period.   3) If τ > Ts,t and RF = false, measure the power Pi tk + Ts,t produce by each turbine i ∈ F. The downwind  turbines Di send their local measurements to the upwind turbine i as PDi tk + Ts,t . Then calculate the partial derivative ∂Pi (k)/∂ai using (5), and RF is set to ture. 4) If Ts,t < τ < Ts,d , assuming the incoming wind speed is constant, the wind speed at all turbines can be estimated using the wake predictive model (1), (2) and (3). Thus the power Pi (tk + Ts,d ) produce by turbines Di can be estimated and send to the  (t + T ). Then we can calculate the partial corresponding upwind turbines i as PDi k s,d  derivative ∂PDi (k) and the control parameter ai (k + 1) using (6) and (4) respectively. After update ai (k + 1), combine with the wind speed estimated above, the power Pi (tk+1 + Ts,t ) produce by turbines i ∈ F can be estimated and the partial derivative ∂Pi (k + 1) can be calculated.   5) Repeat step (4) until all ai converge as ai (k + j). If ai (k + j) − ai (k) > 3K, ai (k) = ai (k + j). Update the control parameter ai (k). Then wait until τ > Ts,t + jTs , ∂Pi (k)/∂ai can be updated by P  (tk+j + Ts,t ) − Pi (tk + Ts,t ) ∂Pi . (k) = i ∂ai ai (k + j) − ai (k)

(7)

6) If τ > Ts,d +  jTs and RF = ture, measure the power produce by turbines  i ∈ F as send its local measurement P D Pi tk + Ts,d . The downwind turbines i  i tk + Ts,d  to the upwind turbine i as PDi tk + Ts,d . Then calculate the partial derivative ∂PDi (k)/∂ai (k) using (6), and RF is set to false. 7) Repeat step (2)–(6) until the wind farm work on maximum power point. Note that this algorithm uses the wake prediction model to estimate the wind condition at each turbine when the wake stream has not reached the downwind turbines. Thus the proposed method can improve the convergence speed of the control parameter ai . The flow chart of the above algorithm is shown in Fig. 2.

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4 MPPT Control of a Wind Farm

Table 1. Wind turbine parameters. Parameter

Value

Turbine type

NREL5MW

Rate capacity

5MW

Max CP

0.45

Rotor radius

63 m

Control period

1s

Table 2. Wind farm parameters. Parameter

Value

Wind filed size

400 m × $560 m

Number of turbines

2

Average wind speed

10 m/s

Turbulence intensity

0.001

Interval of turbines

260 m

In order to validate the effectiveness of the proposed distributed fixed-step MPPT control method, a two-turbine wind farm simulation is presented and discussed in this section. The simulation parameter is given in Tables 1 and 2. Figure 3 shows the transient simulation waveform for wind farm total output power and power coefficient of each turbine. At 1000 s, the MPPT control mode changes from turbine MPPT control to wind farm MPPT control. As shown in the figure, due to the change rate of the control parameters ai being limited, the wind farm convergences to maximum power point after updating three control laws. The transient time of the proposed method (180 s) is much shorter than the conventional FS-MPPT approach (2460 s).

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Fig. 3. A figure caption is always placed below the illustration. Short captions are centered, while long ones are justified. The macro button chooses the correct format automatically.

5 Conclusion This work presented a fast convergence wind farm MPPT approach based on wake propagation prediction. The proposed method modified the control parameter before the wake propagates to the downwind turbines, which improves the convergence speed of the wind farm MPPT method. The simulation results have validated the above contribution. Acknowledgement. This work was solely supported by the Open Fund of State Key Laboratory of Operation and Control of Renewable Energy \& Storage Systems (China Electric Power Research Institute) (NYB51202101989).

References 1. Guo, F., Wen, C., Mao, J., Chen, J., Song, Y.-D.: Hierarchical decentralized optimization architecture for economic dispatch: a new approach for large-scale power system. IEEE Trans. Industr. Inf. 14(2), 523–534 (2018) 2. Dong, Z., Li, Z., Dong, Y., Jiang, S., Ding, Z.: Fully-distributed deloading operation of DFIGbased wind farm for load sharing. IEEE Trans. Sustain. Energ. 12(1), 430–440 (2021) 3. Mohiuddin, S.M., Qi, J.: Optimal distributed control of AC microgrids with coordinated voltage regulation and reactive power sharing. IEEE Trans. Smart Grid 13(3), 1789–1800 (2022) 4. Xu, J., Zhu, S., Soh, Y.C., Xie, L.: Convergence of asynchronous distributed gradient methods over stochastic networks. IEEE Trans. Autom. Control 63(2), 434–448 (2018) 5. Qu, G., Li, N.: Harnessing smoothness to accelerate distributed optimization. IEEE Trans. Control Netw. Syst. 5(3), 1245–1260 (2018) 6. Guo, F., Li, G., Wen, C., Wang, L., Meng, Z.: An accelerated distributed gradient-based algorithm for constrained optimization with application to economic dispatch in a large-scale power system. IEEE Trans. Syst., Man, Cybern.: Syst. 51(4), 2041–2053 (2021) 7. Rathmann, O., Frandsen, S., Barthelmie, R.: BL3.199 wake modelling for intermediate and large wind farms (2007) 8. Guo, F., Wen, C., Mao, J., Song, Y.D.: Distributed economic dispatch for smart grids with random wind power. IEEE Trans. Smart Grid 7(3), 1572–1583 (2016)

Probabilistic Power Flow Computation Considering the Uncertainty of New Energy Access Yan Li, Decheng Wang(B) , Darui He, Yifei Fan, Qun Zhang, and Qingshan Wang State Grid Jiangsu Electric Power Company Economic and Technological Research Institute, Nanjing, Jiangsu Province, China [email protected]

Abstract. In light of the escalating severity of energy scarcity and environmental pollution, new energy generation is the primary development trend in the future. However, high volatility from new energy generation has the potential to disrupt the reliability of the power system. A cumulant method combined with the Gram–Charlier series is proposed to calculate probabilistic power flow resulting from the volatility of new energy. This paper establishes probabilistic models for wind power, photovoltaics, and load; subsequently, the cumulants of each component may be determined. After calculating each order cumulants of models, the cumulant of the system’s power flow response is determined through conventional power flow calculation. Then the research utilizes Gram–Charlier series expansion to fit the distribution and density function of probabilistic power flow. Case studies demonstrate that this method significantly enhances the speed and accuracy of calculations compared to the Monte Carlo approach in an IEEE 30 bus system. Keywords: New energy · Gram–Charlier expansion · Probabilistic power flow · Cumulants

1 Introduction Large-scale new energy grid connection has become an inevitable trend in the evolution of power systems due to the growing energy deficit and environmental pollution issues [1]. Nevertheless, photovoltaic and wind power are unpredictable, intermittent, and volatile, and the instantaneous large-capacity swings significantly affect the stability of the power system. Consequently, power flow computations must consider the unpredictability of new energy generation and load. Probabilistic power flow is a viable method for investigating the influence of stochastic components on the grid. It is possible to evaluate the effect of random variables on power grids with the help of probabilistic power flow. Borkowska initially suggested the notion in 1974 [2], and it can determine the probability distribution and statistical properties of power flow considering stochastic elements. The majority of probabilistic power flow computations involve simulation [3], approximation [4], and analytical methods [5]. Modernly, the Monte Carlo approach is a common technique, but it is plagued by © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1015–1024, 2023. https://doi.org/10.1007/978-981-99-4334-0_121

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numerous iterations, poor computational efficiency, and a lengthy calculation time [6]. The point estimate method is suggested by Ref. [7] as a solution to the Monte Carlo method’s low processing efficiency. Unfortunately, there are several inaccuracies in the calculation of the power flow response’s higher-order moments. The point estimate approach cannot precisely predict the probabilistic distribution of power flow response. In recent years, the cumulant approach has gained increasing prominence. Cumulant combined with Gram–Charlier series in [8] can overcome difficulties of accuracy and efficiency in probabilistic power flow estimates. Nonetheless, Ref. [8] does not consider the photovoltaic probabilistic model, the wind power probabilistic model, and the power system voltage overflow issue. To solve this issue, this paper examines the probabilistic power flow computation with massive new energy access, using a combination of cumulant and Cram-Charlier series for probabilistic tide calculation, proving the efficiency and accuracy of the method, and analyzing the probability problem of voltage overrun under different cases of new energy access.

2 Probabilistic Models of Power System Components 2.1 Wind Turbine Probabilistic Model The probabilistic model of wind turbines is composed of wind and generator models. This study assumes that the wind speed distribution follows the two-parameter Weibull distribution [9]. The two-parameter Weibull distribution is formulated as (1)      k−1 k (1) exp − vc f (v) = kc vc where k represents the shape of wind turbines, c represents the scale of wind turbines, and k > 0. They are calculated as (2) ⎧

−1.087 ⎪ ⎨k = σ μ (2) μ ⎪ ⎩c = 1  1+ k

where μ is the mean value of wind speed data, σ is the standard deviation, and  is the Gamma function. Wind turbines are asynchronous generators connected to the PQ node that absorb reactive power via the inverter and maintain a negative power factor. Therefore, the reactive power from wind turbines is formulated as (3) QWG =

PWG tan(cos ϕ)

(3)

where cos ϕ represents the power factor of wind turbines and it is a constant value. A node containing a wind turbine can be considered a PQ node.

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2.2 Photovoltaic Generator Probabilistic Model The light intensity model and the photovoltaic cell model comprise a photovoltaic generator probabilistically. It is demonstrated that the short-term distribution of light intensity is a Beta distribution, and the Beta distribution is straightforward and requires little historical data [10]. Hence it is utilized in this paper to compute probabilistic power flow. The model can be formulated as (4)

α−1

β−1 (α+β) r r (4) 1 − f (r) = (α)(β) r r max

max

where α and β represent the shape parameters of the Beta distribution, r and rmax are the actual light intensity and the maximum light intensity, respectively,  denotes the Gamma function, The photovoltaic cell’s output is affected by light intensity, temperature, and other variables. In order to simplify the model, the influence of temperature is omitted from this work. The expression for the light intensity-dependent output power of a photovoltaic cell is formulated as (5) P(r) = μ · Y · A · r

(5)

where A is the coefficient, μ is the grid-connected inverter efficiency, r is the light intensity, and Y is the photovoltaic conversion rate [11]. Inverter efficiency is recorded as μ, , and when combined with the light intensity model and photovoltaic cell model, the probabilistic density function for photovoltaic power is stated as (6)

α−1

β−1 (α+β) Pb 1 (6) 1 − PPb f (Pb ) = μ·S·Y (α)(β) P max

max

The probabilistic density function of active photovoltaic power is also Beta distribution. The control power factor is 1, and the point connected with photovoltaic power in the grid can be considered a PQ node with no reactive power in the actual grid connection process. 2.3 Load Probability Models Load size fluctuates constantly with the seasons, climate, and surroundings. Therefore, the unpredictable nature of the load must be accounted for in probabilistic trend calculations. The load approximates a normal distribution in probabilistic power flow calculation [12]. The normal distribution of active and reactive load power is formulated as (7).  2 PL − μPL 1 exp − f (PL ) = √ 2σP2L 2π σPL  2 QL − μQL 1 f (QL ) = √ exp − (7) 2σQ2 L 2π σQL where μPL and σPL are the mean and standard deviation of the active load, respectively.

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The first-order cumulant of the normal distribution is the mean μ; the second-order cumulant is the standard deviation σ , and tail the other-order cumulant is 0 [13].

3 Cumulants Method Combined with Gram–Charlier Series 3.1 Cumulant A cumulant is a quantitative feature of a random It is defined as follows: F(x)  variable.  is the distribution function, t is a real number, eitx  = 1, then the function g(x) = eitx on (−∞, +∞) concerning F(x) is productive. The real variable t corresponding to F(x) is formulated as (8)   +∞ ϕ(t) = E eitξ = ∫ eitx dF(x) −∞

(8)

Taking the natural logarithm of the eigenfunction of (9) and expanding it to the McLaughlin series, the function is formulated as (9) ln ϕ(t) = 1 +

k  γν 1

ν! (it)

ν

  + o tk

(9)

  where γν is called the ν th order Cumulant of the random variable, o t k is the remainder of the expansion. 3.2 Gram–Charlier Series Expansion It is possible to approximate the probabilistic density function and the cumulant distribution function using the Gram–Charlier series expansion after obtaining each order cumulant of the random variable. To simplify the shape of the phases, they can be stated as (10) in the stochastic production of power systems. gν =

γν σν

=

γν ν/2 γ2

(10)

where gν is called the ν th order specification cumulant and σ is the standard deviation. For any continuous random variable X , its normalized random variable is X . The probability density function and cumulative distribution function of X are f X and   F X , respectively [14]. According to the Gram–Charlier expansion, they can be approximated by the normal distribution as (11) ∞ F(x) =

ϕ(x)dx + ϕ(x) x

g

3

3!

H2 (x) +

g4 H3 (x) 4!

g6 + 10g32 g5 H4 (x) + H5 (x) + · · · 5! 6!  g3 g4 f (x) = ϕ(x) 1 + H3 (x) + H4 (x) 3! 4! +

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g6 + 10g32 g5 + H5 (x) + H6 (x) + · · · 5! 6!

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(11)

where ϕ(x) is the standard normal distribution density function and Hγ (x) is the Hermite polynomial. Figure 1 shows the probabilistic power flow algorithm based on the cumulant and Gram–Charlier series.

Fig. 1 Algorithm flow chart

4 Case Study The parameters related to the wind turbine are set to the values provided in Table 1, the PV plant consists of 400 PV panels, and the photovoltaic conversion rate is 13.5%. The proposed method is tested in a modified IEEE 30 bus system in Fig. 2. A wind turbine is wired into each of nodes 14 and 20 with parameters of 3 m/s cut-in wind speed, 15 m/s rated wind speed, and 25 m/s cut-out wind speed. Also, a photovoltaic plant is attached to node 25 [15]. Table 2 gives the 1st to 4th order cumulant of the wind power output active/reactive power.

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Node

Wind speed distribution

Power rating /MW

Cut-in wind speed (m/s)

Rated wind speed (m/s)

Cut-out wind speed (m/s)

Scale c

Shape k

14

11

4

50

3

15

25

20

7

3

20

3

15

25

Fig. 2 Modified IEEE 30 bus system

Table 2 Cumulant of voltage amplitude at some nodes and the probability of crossing the limit Node

Cumulant 1st

Voltage crossing probability 2nd

3rd

4th

3

2.9842

0.0469

0.0014

− 1.0464e−4

0

10

3.1669

− 0.0509

− 0.0022

− 1.8815e−4

0

17

6.6861

0.2285

0.00088

1.316e−4

0

22

7.6468

0.3324

0.0010

1.5645e−4

0

4.1 Speed and Accuracy of the Algorithm As a benchmark, the Monte-Carlo approach was employed to evaluate the algorithm’s operating speed and computing precision. The accuracy standard is measured by ARMS , which is defined as follows: ARMS =

 N

i=1 (CGi −MGi )

N

2

(12)

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where CGi is the value of the i th point on the probability density function with the cumulant and Gram–Charlier series method, MGi is the value of the i th point on the probability density function with the Monte-Carlo method. The number of iterations determines the Monte-Carlo method running time, and 5000 and 500 iterations are chosen; the order of cumulant is chosen to be 4–6. Table 3 Comparison of time in different approaches Method

CPU time/s

Monte-Carlo (5000 iterations)

109.624

Monte-Carlo (500 iterations)

21.9844

Cumulant and Gram–Charlier series (3rd)

0.6038

Cumulant and Gram–Charlier series (4th)

0.7075

Cumulant and Gram–Charlier series (5th)

0.7206

Cumulant and Gram–Charlier series (6th)

0.8219

Table 4 ARMS of fitting with different order steps Method

ARMS (%)

Cumulant and Gram–Charlier series (3rd)

13.529

Cumulant and Gram–Charlier series (4th)

7.892

Cumulant and Gram–Charlier series (5th)

3.384

Cumulant and Gram–Charlier series (6th)

6.523

Table 3 displays the program’s execution time utilizing various methods. In comparison with the Monte-Carlo approach, the cumulant and the Gram–Charlier method is highly efficient because it significantly decreases computing time and increases computational efficiency by two magnitudes. This method addresses the issue of the Monte Carlo method’s inefficiency. Table 4 demonstrates the fitting errors of different orders. Table 4 shows that the fitting error with fourth-order cumulant is the minimum, at only 3%. Figure 3 graphically demonstrates the efficiency and precision of the cumulant method. 4.2 Impact of New Energy Access To assess the influence of new energy access on the power system, three cases are considered: Case 1: no new energy access, where the system’s factor only includes load fluctuations; Case 2: a distributed new energy access system with one 10 MW wind turbine at each of nodes 8, 11, and 14; Case 3: a large-scale new energy access system with a 100 MW wind turbine at node 14 and a 10 MW photovoltaic plant at node 13.

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Fig. 3 The probability density function at node 18 using the Monte-Carlo and the CM&Gram– Charlier method

The probability distribution of the node voltage amplitude is obtained for each of the three cases using the proposed approach. The voltage crossing probability is computed to analyze the effect of massive new energy access on the system voltage quality.

Fig. 4 Probability distribution of voltage in three cases

Figure 4 depicts the probability density function of the voltage magnitude at the conclusion of some nodes for the three situations. Figure 5 shows the voltage amplitude of multiple nodes. In Case 1, the random voltage fluctuations are close to the usual

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Fig. 5 Node voltage for large-scale new energy access

distribution of the load, and the possibility of voltage crossing is nearly 0. In Cases 2 and 3, the unpredictability of wind power and photovoltaic power generation increases the node’s voltage volatility. It’s more likely that a voltage crossing will occur. The calculation demonstrates that there is a greater chance of voltage overrun when more new energy sources are connected to the grid, and this risk grows in proportion to the share of new energy integrated into the grid.

5 Conclusions This research examines the effect of the randomness of new energy generating output and load on the voltage quality of the power system, focusing on two new energy generation methods, wind power and photovoltaic power, and a stochastic tide algorithm using a combination of cumulant and Gram–Charlier series is proposed after establishing the probabilistic models of wind power and photovoltaic power systems. The following two conclusions are obtained by calculating and analyzing the probabilistic power flow in the modified IEEE 30 bus system as an example. (1) The algorithm utilized in this paper is highly accurate and consistent with the Monte Carlo method’s results. Nonetheless, calculating time is drastically lowered. (2) It is concluded that the large-scale connection of new energy generation to the grid will increase the probability of power system voltage overrun due to the randomness of output.

References 1. Amid, P., Crawford, C.: A cumulant-tensor-based probabilistic load flow method. IEEE Trans. Power Syst. 33(5), 5648–5656 (2018) 2. Reinders, J., Paterakis, N.G., Morren, J., Slootweg, J.G.: A linearized probabilistic load flow method to deal with uncertainties in transmission networks 2018, 1–6

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3. Wang, Z., Shen, C., Liu, F., Gao, F.: Analytical expressions for joint distributions in probabilistic load flow. IEEE Trans. Power Syst. 32(3), 2473–2474 (2017) 4. Zuluaga, C.D., Alvarez, M.A.: Bayesian probabilistic power flow analysis using Jacobian approximate Bayesian computation. IEEE Trans. Power Syst. 33(5), 5217–5225 (2018) 5. Wang, G., Xin, H., Wu, D., Ju, P., Jiang, X.: Data-driven arbitrary polynomial Chaos-based probabilistic load flow considering correlated uncertainties. IEEE Trans. Power Syst. 34(4), 3274–3276 (2019) 6. Tang, J., Ni, F., Ponci, F., Monti, A.: Dimension-adaptive sparse grid interpolation for uncertainty quantification in modern power systems: probabilistic power flow. IEEE Trans. Power Syst. 31(2), 907–919 (2016) 7. Lin, C., Bie, Z., Pan, C., Liu, S.: Fast cumulant method for probabilistic power flow considering the nonlinear relationship of wind power generation. IEEE Trans. Power Syst. 35(4), 2537– 2548 (2020) 8. B. B. Probabilistic Load Flow (1974) IEEE Trans. Power Apparatus Syst. PAS-93(3), 752–759 9. Wu, H., Zhou, Y., Dong, S., Song, Y.: Probabilistic load flow based on generalized polynomial Chaos. IEEE Trans. Power Syst. 32(1), 820–821 (2017) 10. Sun, W., Zamani, M., Zhang, H., Li, Y.: Probabilistic optimal power flow with correlated wind power uncertainty via Markov Chain Quasi-Monte-Carlo sampling. IEEE Trans. Industr. Inform. 15(11), 6058–6069 (2019) 11. Ren, Z., Wang, K., Li, W., Jin, L., Dai, Y.: Probabilistic power flow analysis of power systems incorporating tidal current generation. IEEE Trans. Sustain. Energy. 8(3), 1195–1203 (2017) 12. Liu, C., Sun, K., Wang, B., Ju, W.: Probabilistic power flow analysis using multidimensional holomorphic embedding and generalized cumulants. IEEE Trans. Power Syst. 33(6), 7132– 7142 (2018) 13. Sheng, H., Wang, X.: Probabilistic power flow calculation using non-intrusive low-rank approximation method. IEEE Trans. Power Syst. 34(4), 3014–3025 (2019) 14. Panigrahi, B.K., Sahu, S.K., Nandi, R., Nayak, S.: Probablistic load flow of a distributed generation connected power system by two point estimate method, 2017, 1–5 15. Xie, Z.Q., Ji, T.Y., Li, M.S., Wu, Q.H.: Quasi-Monte Carlo based probabilistic optimal power flow considering the correlation of wind speeds using copula function. IEEE Trans. Power Syst. 33(2), 2239–2247 (2018)

Modelling and Simulation of Demand Response in Frequency Modulation Markets Guiyuan Xue(B) , Chen Wu, Ming Zhang, Yin Wu, Chen Chen, Wenjuan Wu, and Longpeng Ma Economic Research Institute, State Grid Jiangsu Electric Power Co. Ltd., Nanjing, China [email protected], [email protected], {zhangm33, malp}@js.sgcc.com.cn

Abstract. With the increased promotion of clear energy, demand response plays a more important role in the grid. However, the mechanisms for demand response participation in the electricity market are not sufficiently developed. In this paper, considering the rules of Jiangsu province, a clearing model for demand response in the frequency modulation market is developed. By analyzing the current situation of domestic and international research on demand response, the definition and rules of frequency modulation auxiliary services are determined, as well as the way of demand response participation. In order to take the advantages of demand response and clarify the rules, a clearing model of demand response in the frequency modulation market is established. Finally, the demand response model is verified through case studies. Keywords: Demand response · Market · Modelling · Ancillary service

1 Current Status of Demand Response Research Internationally, many developed countries such as the United States, the United Kingdom and Germany have formed mature electricity markets. Their research and application of FM (frequency modulation) auxiliary services have also reached a leading level. However, during the actual operation of FM auxiliary services, there are still many unresolved problems, which are not the realization of auxiliary services themselves, but some problems related to grid coordination after the formation of the ancillary service market. Different countries have various FM auxiliary services market structures and trading mechanisms, all of which are improved and developed based on their own national conditions. China’s research on FM auxiliary services started relatively late, and there is a lack of FM service resources in the current situation. The market should consider providing a more intuitive economic signal, encouraging the power generation enterprises to provide FM auxiliary services voluntarily. Combining the international experience and domestic specificities, there is still a big space for the FM auxiliary services market research in China [1–3]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1025–1032, 2023. https://doi.org/10.1007/978-981-99-4334-0_122

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1.1 The Development of Foreign Markets • US Ancillary Services Market Founded in 1927, PJM is the largest centrally dispatched and controlled grid in North America and the largest wholesale electricity market worldwide [4]. PJM allocates FM obligations to load serving entities(LSE), instead of setting up separate FM plants, which is the key feature of frequency response services in PJM [5]. LSE can meet its FM obligations by using its own generation resources or contracting with third parties. Meanwhile, they purchase the service from the PJM standby market. PJM is responsible for providing a spinning back-up service to meet system demand for generation capacity timely in the event of a system accident. Each Regional Transmission Organization and network customer must purchase this service from PJM. • UK Ancillary Services Market The UK was one of the earlies countries in the world to introduce competition into the electricity industry. In 1990 the Electricity Pool for England and Wales was established. In the UK, the Ancillary Services Business (ASB) of the National Grid Corporation (NGC) is responsible for purchasing ancillary services in an economical way to meet the requirements of system security and dependability in the UK electricity market. The power pool pays for these ancillary services through a surcharge on customers. The scheduling of ancillary services is accordingly arranged in the same way for electricity. Various ancillary services are priced in advance, using competitive bidding. • Australian Ancillary Services Market Since September 2009, the Australian market has placed FM ancillary services into the spot market. The FM ancillary services market is a hybrid model of real-time bidding and bilateral contracts in Australian. As the Australian FM ancillary market is a real-time bidding model, the real-time market places a high requirement on FM services, while the competitiveness of the market provides cheaper electricity for customers. • Nordic Ancillary Services Market The Nordic electricity market is the world’s first regional transnational electricity market, with a single trading agency, the Nordic Power Pool, providing a trading platform for participants. The platform mainly include generators, grid owners, retailers, traders and consumers. The five main grid companies in Sweden, Norway, Denmark and Finland have set up power dispatch agencies to operate the real-time and ancillary services markets, enabling the optimal allocation of resources across borders. 1.2 The Development of Domestic Markets China has followed the international trend in recent years. Relevant research institutions, research institutes and universities have made great progress in the research of FM auxiliary service market operation mechanism and methods. In terms of operation mode, the operation mode of FM auxiliary service market is different. The power generation

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company is the main body of FM auxiliary service implementation, and the government department undertakes the work of co-ordination and guidance. At present, China’s ancillary services mainly include AGC, standby, voltage reactive support and black start. A combination of basic ancillary services and paid ancillary services is commonly used for trading. Due to the differences in the geography, grid structure and economic development, there are also differences in the trading mechanism of auxiliary services in each market.

2 Basic Framework of the FM Market 2.1 FM Auxiliary Services Fluctuations in power system frequency reflect changes in the difference between active output and load which is an important parameter to detect whether the power system can operate safely and stably. FM auxiliary services can quickly correct system frequency deviations and restore the system frequency to an acceptable range to prevent accidents from occurring. Frequency adjustment is one of the main tasks of the power system. AGC plays a vital role in the frequency stability and safe operation of the grid. AGC auxiliary services are one of the important areas of research in the power market. AGC is in dynamic regulation due to the randomness of load changes. In the case of power system deregulation, there is a need to clearly define the primary FM and AGC FM volumes and to accurately quantify the FM ancillary services of each AGC [6]. In addition, the impact of market economic factors on the dynamic response of AGC regulation is considered, and the relationship between AGC frequency regulation and regulation cost response is studied to achieve economic and optimal dispatch of AGC. Therefore, when analyzing the impact of the dynamic process of AGC regulation on the reliability of the system, it is necessary to establish an AGC regulation clearing model. 2.2 FM Clearance Rules • FM costs The cost of FM is divided into two aspects: the power plant side and the dispatch side. The costs on the power plant side include investment costs, generation efficiency loss costs, operation and maintenance costs, dispatching costs and opportunity costs [7, 8]. The cost of lost generation efficiency is the increase in fuel costs due to the reduced efficiency of the unit as a result of FM operation. In terms of O&M costs, the thermal stress on certain components of the unit is caused by the rapid regulation during the FM process, which reduces component life. In addition, the change in the direction of the unit’s response output shortens the maintenance cycle of the generating unit. The frequent switching of the FM signal can lead to a 1–2% increase in the heat consumption

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of the unit. The above costs are combined and described by simulation using quadratic functions. • Market organization The FM market is organized in the form of weekly quotations, pre-clearance before the day and intra-day calls. The specific form is as follows: power generation enterprises declare the daily FM capacity and mileage price before the day, and the market is precleared in a basic unit of 30 min. When the total FM capacity of the clearing unit meets the maximum FM demand capacity of the following day, a clearing price is obtained. The power dispatching agency will arrange for units to provide FM auxiliary services according to the actual grid operation and safety constraints, taking together with the recently market clearing results. 2.3 Demand Response Participation in FM Markets Current demand response projects such as time-of-use tariffs and interruptible loads have achieved good results in reducing load peaks and increasing load factors. However, most of these projects have long time scales, which are non-real-time and imprecise, lacking the ability to participate in power system frequency regulation. With the development of smart grids, demand-side controllable loads have the ability to influence the operation of the power system and contribute to the frequency adjustment of the power system. Specifically, demand response can participate in power system frequency regulation by changing the switching state of some power equipment or regulating the operating power of these power equipment through intelligent electrical devices [9, 10]. Unlike the traditional practice of load cutting, demand response achieves frequency regulation by controlling the power consumption behavior of some electrical equipment, such as refrigerators, washing machines and air conditioners. Most of these devices do not have high requirements for continuous power supply, and most of them have certain capacity for heat or cold storage. Cutting off their power or reducing their power consumption within a short period of time will not affect the production and life of their customers.

3 Construction of Demand Response Model in FM Market 3.1 Objective Function The demand response participation in the FM market model takes the lowest total system offer cost as the objective. Assuming that there is no network loss, the objective function of demand response units in the FM market is shown as follows.   i i vi ei + FBase (1) + Fuse − Ci max i∈I

where i is the unit in the FM market and I is its aggregation; vi is the generation energy i is the basic compensation offer of unit I; ei is the generation capacity of unit i; FBase i cost of the FM market; Fuse is the call compensation cost of the FM market; C i is the FM cost of the unit.

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The basic market compensation cost is calculated for all units in the FM market with qualified AGC functions based on FM performance, FM capacity and commissioning rate. It is calculated as follows. i i FBase = KBase × ki × Pagc

(2)

where KBase is the basic service compensation standard, which is set as 2 yuan/MW in Jiangsu; ki is the comprehensive FM performance index of unit i, which is used to measure the performance of the generating unit, including three factors of regulation i is the adjustable AGC capacity of unit rate, response time and regulation accuracy; Pagc i, which is self-declared by the unit before the day. The call compensation cost is the corresponding call cost calculated by the FM mileage, FM performance and mileage unit price for the units called in the actual operation of the market, which is calculated as follows. FCi = mi × ki × vCi

(3)

where mi is the FM mileage winning bid of unit i; vCi is the FM mileage clearance price of unit i. The cost of FM refers to the wear and maintenance costs associated with the unit’s participation in FM, including initial construction costs and operation and maintenance costs. This cost is modelled using a quadratic function, which is calculated as follows. i i )2 + t2,i Pagc C i = t1,i (Pagc

(4)

where t1,i and t2,i are function coefficients, determined by the unit’s participation in the history of frequency regulation. 3.2 Constraints The main constraints considered in this model are shown as follows.   i i Pagc,1 ≥ Rmax + εi Pagc,2

(5)

i∈I i i 0 ≤ Pagc ≤ Pagc,max

(6)

i i 0 ≤ Pagc + ei ≤ Pmax

(7)

0 ≤ mi ≤ 2

(8)

i i where Pagc,1 is the conventional unit FM capacity in unit I; Pagc,2 is the demand-side resource FM capacity in unit i; εi is the demand-side resource substitution index of unit i, representing the good substitution effect of demand-side resources for conventional AGC units under the same circumstances; Rmax is the total FM capacity required by the i i is the FM capacity limit of unit I; Pmax is the installed capacity current system; Pagc,max limit of unit i.

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4 Analysis of the Algorithm 4.1 Parameter Setting The chapter is based on the demand response model given in Chap. 3. Assume that there are three demand response units in the market providing FM services when the grid generates FM demand. Tables 1, 2 and 3 shows the market peak-valley offers, real-time offers, FM cost parameters, and basic compensation costs. Table 1. TOU price and real-time price settings Time period

TOU price/(yuan(MWh)−1 )

Real-time price/(yuan(MWh)−1 )

00:00–04:00

21.778

19.18

04:00–08:00

21.778

20.76

08:00–12:00

35.1913

38.88

12:00–16:00

31.9943

52.8

16:00–20:00

31.9943

46.29

20:00–23:00

31.9943

55.74

Table 2. FM cost parameter setting Unit

1

2

3

4

5

t1,i

0.25

0.25

0.25

0.25

0.25

t2,i

36

38

40

42

44

Table 3. Basic compensation cost of units setting Unit

1

2

3

4

5

ki

0.55

0.63

0.6

0.68

0.51

i Pagc,max / MWh

12

15

18

20

24

Basic compensation costs /yuan

13.2

18.9

21.6

27.2

10.08

4.2 Clearance Results Figures 1, 2 and 3 shows the clearing results of the demand response model based on the parameters and offer settings. The clearing results show that FM miles were cleared in all periods of the market where there was demand for FM. A cross-sectional comparison of a unit’s response

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Fig. 1. Comparison of TOU price and real-time price

Fig. 2. FM offer and unit response results

Fig. 3. FM offer and unit revenue results

between time periods shows that the higher the FM offer, the more responsive the unit is and the more FM miles are cleared. For example, the demand for FM is the same between 12:00–16:00 and 20:00–24:00. However, because of the higher real-time price between 20:00–24:00, the demand response unit puts more capacity into generation. The

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FM response between 20:00–24:00 is lower than the response between 12:00–16:00. But the overall revenue after 20:00 is higher than that in the 12:00–16:00 period.

5 Conclusion The paper designs a rule framework for demand response participation in the FM market and proposes a clearing model for demand response in the FM market, considering the rules of Jiangsu province. Under the trading mechanism of Jiangsu FM market rules, the current situation of domestic and international research on demand response are analyzed. The definition and rules of FM auxiliary services are determined. A clearing model of demand response in the FM market is established for helping the demand response resources to bid in the market. Using an FM service as the offeror and three demand response units as the scenario, the market clearing calculation is carried out and leads to the clearing results. The results show that the model is feasible and can be applied to realistic scenarios of demand response participation in the FM market. Acknowledgment. This work was supported by the technical service project of Economic Research Institute, State Grid Jiangsu Electric Power Co. LTD.

References 1. Sortomme, E., Hindi, M.M., MacPherson, S.D.J., Venkata, S.S.: Coordinated charging of plug-in hybrid electric vehicles to minimize distribution system losses. IEEE Trans. Smart Grid 2(1), 198–205 (2011) 2. Sanchez-Martin, P., Sanchez, G., Morales-Espana, G.: Direct load control decision model for aggregated EV charging points. IEEE Trans. Power Syst. 27(3), 1577–1584 (2012) 3. Yao, M., Molzahn, D.K., Mathieu, J.L.: An optimal power-flow approach to improve power system voltage stability using demand response. IEEE Trans. Control Netw. Syst. 6(3), 1015– 1025 (2019) 4. Han, H., Gao, S., Shi, Q., Cui, H., Li, F.: Security-based active demand response strategy considering uncertainties in power systems. IEEE Access 5, 16953–16962 (2017) 5. Carrion, M., Arroyo, J.M.: A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Trans. Power Syst. 21(3), 1371–1378 (2006) 6. Yang, B., et al.: On the use of energy storage technologies for regulation services in electric power systems with significant penetration of wind energy. In: 2008 5th International Conference on the European Electricity Market, Lisboa, pp. 1–6 7. Xu, B., Oudalov, A., Ulbig, A., Andersson, G., Kirschen, D.S.: Modeling of lithium-ion battery degradation for cell life assessment. IEEE Trans. Smart Grid 9(2), 1131–1140 (2018) 8. Brundage, M.P., Chang, Q., Li, Y., Arinez, J., Xiao, G.: Implementing a real-time, energyefficient control methodology to maximize manufacturing profits. IEEE Trans. Syst. Man Cybern. Syst. 46(6), 855–866 (2016) 9. Gholian, A., Mohsenian-Rad, H., Hua, Y., Qin, J.: Optimal industrial load control in smart grid: a case study for oil refineries. In: Proceeding IEEE PES Generation Meeting, Vancouver, BC, Canada, pp. 1–5 10. He, G., Chen, Q., Kang, C., Pinson, P., Xia, Q.: Optimal bidding strategy of battery storage in power markets considering performance-based regulation and battery cycle life. IEEE Trans. Smart Grid 7(5), 2359–2367 (2016)

Pitch Control Strategy for Wind Turbine Considering Operation Efficiency Biao Huang, Lawu Zhou(B) , Han Zhao, and Leyun Long School of Electrical Engineering, Changsha University of Science and Technology, Changsha, China [email protected]

Abstract. The pitch control system of wind turbine is a nonlinear, multi-coupling control system. The traditional control method has low control precision and large time delay, and does not consider the economic cost. There are some errors in the measurement of wind speed by traditional wind meter. This paper presents an economic model predictive control(EMPC) method which seeks to maximize the economic benefit of unit operation. The LIDAR was used to measure the wind in advance and preview the wind speed information. The loss of pitch bearings was considered in the objective function, and the two operating states were controlled by one objective function. The optimal control solution was obtained by using genetic algorithm to solve the objective function. The economic model predictive control method was compared with the traditional PID control method in Bladed platform. The results show that compared with the traditional PID control, the EMPC method has better maximum power tracking and constant power output capability. The output power below the rated wind speed is increased by 6.4%, and the output is smoother, showing better stability when the wind speed fluctuates. Keywords: Economic benefit · Economic model prediction · Lidar · Pitch bearing

1 Introduction When the wind speed is less than the rated wind speed of the wind turbine, the operation target of the wind turbine is the maximum power tracking to make full use of the wind energy. When the wind speed is greater than the rated wind speed, the wind turbine operation target is constant power output. Therefore, the accurate real-time measurement of wind speed is the key to the stable operation of the unit [1, 2]. In traditional wind turbine, a wind meter is installed above the engine room to measure the wind speed. There is some deviation between the measured wind speed and the actual wind speed at the wind turbine blade, and there is some time lag. Laser radar [3, 4] is a new wind measuring device, through the forward laser, using the Doppler principle, can accurately obtain the real-time wind speed in the forward area, so that the wind turbine can preview the wind speed information.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1033–1045, 2023. https://doi.org/10.1007/978-981-99-4334-0_123

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Wind turbine is a nonlinear, multi-coupling system. Traditional PID control does not establish the model of the whole control system, only rely on the control error to adjust the output, the control effect is not good, does not consider the economic benefits of the system. Aiming at the shortcomings of PID control, scholars put forward a variety of intelligent pitch control methods [5–8]. In literature [5], interference observer was used to suppress the influence of external interference on the system, and a synovial control method was proposed to improve the control effect. In literature [6], deep learning is used to estimate current wind speed and predict future wind speed, which reduces the influence of wind speed disturbance on pitch control. Fuzzy control method is adopted for pitch control. Literature [7] proposes an economic model predictive control (EMPC), which avoids frequent switching of parameters in the objective function, but the objective function only takes power as constraint, without considering other variables of the system. In literature [8], the wind speed was divided into five sections, and five MPC controllers were designed respectively, which effectively reduced the unit load, but the controller switch was too frequent. To solve the above problems, an economic model predictive control method is proposed in this paper. With power loss and bearing loss as the minimum objective function, the optimal solution of pitch control can be obtained by solving the objective function, and the lidar is used to preview the wind information in advance, so as to reduce the time delay of pitch action. A global invariant objective function is used to control the two operating states of the unit [7]. Compared with the traditional PID control, the output power is more stable.

2 Wind Turbine Modeling The captured power of the fan is: Pa =

1 ρSv3 CP (λ, β) 2

(1)

where, ρ is air density, kg/m3 ; S is the sweep area of the wind wheel, m2 ; v is wind speed, m/s; CP is wind energy utilization factor; λ is blade tip velocity ratio; β is the pitch Angle, deg. The relationship between wind energy utilization coefficient, blade tip speed ratio and pitch Angle is shown in Fig. 1.

Fig. 1. Wind energy utilization coefficient

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Fig. 2. Wind turbine operation section

When the wind speed is less than the rated wind speed, the fan maintains the optimal blade tip speed ratio, then: ωa =

λv R

(2)

where, ωa is the speed of the wind wheel, rad/s; R is the radius of the wind wheel. The output power of wind turbine is: Pg = ωg Tg

(3)

where, ωg is the speed of the generator rotor, rad/s; Tg is the electromagnetic torque, N m. The transmission system of wind turbine can be represented by the dynamic differential equation: Ja ω˙ a (t) = Ta − Kd θ − Cd θ˙

(4)

Jg Ng ω˙ g (t) = −Ng Tg + Kd θ + Cd θ˙

(5)

θ˙ = ωa − ωg /Ng

(6)

where, Ja , Jg is the moment of inertia of the wind wheel and the generator; ωa , ωg is the speed of the wind wheel and the generator rotor; Ta , Tg is the torque of the wind wheel and the generator; Kd , Cd is the stiffness coefficient and damping coefficient of the low-speed shaft; Ng is the ratio of the gearbox; θ is the torsion Angle of the drive shaft, rad. The fan will be swayed by the wind: M x¨ t = F − Ct xt − Kt xt

(7)

where, M is the mass at the top of the fan tower, xt is the displacement at the top of the tower, F is the thrust by the wind wheel, Kt and Ct is the stiffness and damping coefficient at the top of the tower.

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Establish the state-space equation for wind turbine:  x˙ = Ax + Bu y = Cx + Du

(8)

where, input variable is u = [T , β], state variable is x = [ωr , ωg , θ, xt , x˙ t ], and output variable is y = [Pg , ωr ].

3 Control Policy 3.1 Unit Operating Characteristics According to the different wind speed, the operation state of wind turbines can be divided into two conditions, as shown in Fig. 2. When the wind speed is less than the rated wind speed, the unit does not perform pitch control action, and the fan always maintains the best tip speed ratio to maximize the capture of wind energy. When the wind speed is greater than the rated wind speed, the wind wheel speed and torque have reached the rated value, and the power has reached the rated power, the unit starts to adjust the blade pitch Angle, so as to reduce the wind energy utilization coefficient. In Fig. 2, vin is the inlet wind speed, vrate is the rated wind speed, vout is the cut out wind speed, Trate is the rated torque, ωrate is the rated speed, Prate is the rated power. The operation control strategy of wind turbine should maximize the economic benefits and reduce the operation loss. The installation and maintenance cost of wind turbine is high, and the frequent maintenance and updating of wind turbine will bring economic losses. Pitch control can change the wind energy utilization factor to ensure maximum power tracking or constant power output. However, too frequent pitch control will cause fatigue loss and structural damage of pitch control transmission system, resulting in losses. The control pitch drive system of wind turbine is composed of hub, connecting bolt, pitch bearing, blade root, etc. The bearing plays the role of connecting the hub and blade root. When the blade rotates, it bears higher fatigue load than other parts. Bearing itself as a fine machining parts, the cost is relatively high. Therefore, the pitch control strategy of wind turbine should account for the loss of pitch bearings. 3.2 Bearing Life For the fatigue life prediction of bearings, this paper selects the most widely used rain flow counting method. The rain flow counting method uses the time-stress curve to divide the load in the whole time domain into several shorter load cycles, and the fatigue loss of components under multiple load cycles is equivalent to the effect of load superposition loss in the whole time domain. Load of pitch bearing was simulated on GH Bladed platform, as shown in Fig. 3. The average wind speed between the rated wind speed and the cut out wind speed was taken as the working condition of bearing load simulation because the pitch change action only occurred above the rated wind speed, and the fan worked in the low wind speed range most of the time in actual operation without changing the impeller. In

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Fig. 3. Friction torque of pitch bearing

Matlab using open source code to achieve the rain flow counting method of the program calculation. The load was graded, and the empirical S-N formula was selected to calculate the bearing life under each load. The slope from reference [9] was m = 4. The equivalent load obtained by Corten Dolan theory is used to predict the fatigue life of bearings. The bearing life expression of Corten Dolan theory is: N = k

N1

i=1 γi (σi /σ1 )

d

(9)

where, N is the bearing life; σi is the load value of the i stage; γi is the proportion of the i stage load to the total load cycle number; N1 is the bearing life under single action, σ1 is the value of the highest load level, d is the material constant, 5.8 [10]. Due to the particularity of working conditions, the rotation range of pitch bearings is usually about 90°, and their fracture failure is also concentrated in the 90° working area, so the life of pitch bearings is only calculated within the 90° range. 3.3 Economic Model Forecast The process of economic model predictive control is divided into three steps. A Prediction model Establish the forecast model of the controlled system, specify the control input and output and state variables, according to the input and state variables of the system, the future output of the system can be predicted. The model can be a state-space equation or a dynamic matrix. In the first part, the state space equation of the unit is established. B Rolling optimization There is often a difference between the actual input and the predetermined value of the controller. The model predictive control expects the actual input to approach the predetermined value smoothly, and the approach curve is the reference trajectory. The

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optimal solution of the objective function is solved and the input of the control system is obtained. And each variable in the system must meet the constraints of the constraint conditions. C Feedback correction Due to the interference of the controlled system and the nonlinearity of the system, the actual output must deviate from the ideal predicted output. The output error is fed back to the prediction model to correct the next prediction result. The control principle is shown in Fig. 4. In Fig. 4, yr is the set value of output power, u is the pitch Angle, y is the output power of the unit, ym is the output power of the forecast model, and yp is the predicted output power after correction. Given the pitch Angle u(k), the output power of the unit y(k) and the predicted output power of the prediction model ym (k + 1) can be obtained. And by the same token, from u(k + 1) you get the y(k + 1) sum ym (k + 2). The deviation between the actual output y(k + 1) at time k + 1 and the predicted output of the model ym (k + 1) at time k + 1 is regarded as the estimated value of the predicted error at time k + 1, and it is compensated into the output of the forecast model ym (k + 2) at time k + 1 as the feedback correction signal, that is, the predicted value after feedback correction is: yp (k + 2) = ym (k + 2) − yp (k + 1) + y(k)

(10)

The feedback correction at each moment is based on the actual prediction error at the last moment, which can improve the prediction accuracy in the actual operation. 3.4 Optimization of Genetic Algorithm The control law of the unit is obtained by using genetic algorithm to optimize the objective function. Genetic algorithm is suitable for solving multi-objective and nonlinear problems. Binary coding is adopted, the control objective function is used as fitness function, and the optimal solution of this generation is retained in the next generation population. The process is shown in Fig. 5. Since the selection of the predictive time domain is often an integer multiple of the control time domain, the model predictive control can obtain the control sequence of the controlled input at multiple moments in the future through a single solution based on the predictive output, while only the first control input instruction of the control sequence is used in the implementation of the control. At the next moment, according to the new state variables and inputs of the system, a new round of optimal control input is started again, and so on, to achieve online optimization.

4 Objective Functions and Constraints In the predictive control of economic model proposed in this paper, the objective function is expressed as the power loss of wind turbine and the maintenance cost loss of pitch bearing. When the wind speed is low and no pitch control operation is required, the

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Fig. 4. Economic lModel predictive control block diagram

Fig. 5. Genetic algorithm flow chart

maximum utilization of wind energy is pursued to reduce the power loss of the fan as much as possible. When the wind speed is high and the pitch needs to be changed, the control objective of the objective function is to make the output power track the rated power stably. At the same time, bearing loss is used as the suppression of the pitch control to reduce the pitch Angle oscillation. By directly writing the operation economic benefit of the unit into the objective function, the unit can always operate in a way to obtain the maximum economic benefit, which has a certain practical significance. The objective function of the system is:   3βmove J = ctPloss +cbear Dbear = ct(Pop − Pcur ) + cbear 90N

(11)

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where, Ploss is the power loss value of the unit, Pcur is the real-time power of the unit, Pop is the ideal output power of the unit, c is the electric energy price, Dbear is the bearing damage, cbear is the bearing price, relying on the data of XEMC Wind Energy Company, βmove is the propeller pitch Angle action, N is the bearing life, t is the time. In the maximum power tracking area, the ideal output power of the unit: Pop =

1 3 CP (λ, β) ρSvcur 2

(12)

where, vcur is the real-time wind speed. In the constant power operation zone, the ideal output power of the unit is rated power: Pop = Prate

(13)

The system constraint conditions are: ωg. min ≤ ωg ≤ ωg. max

(14)

−5◦ ≤ β ≤ 90◦

(15)

0 ≤ Tg ≤ Tg. max

(16)

−8 ≤ β˙ ≤ 8

(17)

0 ≤ Pcur ≤ Prate

(18)

Compared with the traditional PID control, the economic model predictive control proposed in this paper does not set the controller and parameters for the maximum power tracking area and the constant power operating area respectively, but realizes the control of the output power by solving a fixed objective function in the whole domain. At the same time, the ideal output power is directly written into the objective function, so that the controller does not need to switch different set values for different operating intervals. This strategy can avoid output fluctuation and power jump of generator during controller switching.

5 Example Analysis The control method was verified in Bladed software developed by DNV GL, and compared with the traditional PID control.2MW fan of Bladed platform was used for simulation. Simulation was carried out under three conditions of step wind, medium-low speed turbulent wind and high-speed turbulent wind. The simulation step is 0.2 s. The prediction time domain is set as 8 and the control time domain as 1. Lidar can obtain wind information in advance, but there is no lidar module in Bladed software. In order to realize the function of wind information preview, the turbulent wind

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file is extracted in Bladed, and the wind.txt file is exported. In the simulation process, the wind.txt file is read in advance so as to achieve the effect of wind information preview. In order to verify the stability of the EMPC control strategy in this paper when the rated wind speed fluctuates up and down, a step wind condition is simulated, and the wind speed jumps from 10m/s to 14m/s above the rated wind speed, as shown in Fig. 6.

Fig. 6. Step wind

Fig. 7. Step wind simulation

Step phoenix simulation results are shown in Fig. 7. When the wind speed passes the rated wind speed from bottom to top, the output power of the motor under the PID control overshoots and exceeds the rated power. However, the EMPC control basically keeps stable and accurately tracks the rated power. This indicates that the proposed EMPC control method has higher accuracy than the traditional PID control method, and has stronger output stability under the severe fluctuation of wind speed. When the wind speed is stable at 14 m/s, the pitch Angle oscillation controlled by EMPC is smaller than that controlled by PID control, indicating that the punishment of pitch Angle action in EMPC objective function plays a role. The output oscillation of the EMPC control strategy in this paper is smaller than that of the traditional PID control. A turbulent wind condition of medium and low wind speed was simulated, and the wind speed was below the rated wind speed, as shown in Fig. 8. The simulation results are shown in Fig. 9. As can be seen from Fig. 9, the motor output power under EMPC control is 6.4% higher than that under traditional PID control. This indicates that the EMPC control method proposed in this paper can adjust wind

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Fig. 8. Medium and low speed turbulent wind

Fig. 9. Simulation of medium and low speed turbulent wind

speed and generator torque according to wind speed due to the advanced wind measurement of LiDAR and the optimization of genetic algorithm, and can track the maximum tip speed ratio better than the traditional PID control method. A turbulent wind condition with high wind speed is simulated, and the wind speed is above the rated wind speed most of the time, as shown in Fig. 10.

Fig. 10. High speed turbulent wind

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The simulation results are shown in Figs. 11 and 12.

(a) power

(b) Rate of pitch Angle change

Fig. 11. High speed turbulent wind simulation

Fig. 12. Pitch angle comparison

As can be seen from Fig. 11a, the motor output power fluctuation under EMPC control is smaller than that under PID control at 0s–500s. The power output is stable near the rated power, and the output quality is improved. At 500s–600s, the wind speed fluctuates around the rated wind speed. Although the absolute fluctuation of EMPC control power is slightly larger than that of PID control, the fluctuation frequency is less and the power output is more stable. At the same time, it can be seen from the change rate of pitch Angle that the total operation range of pitch control of the leeward machine controlled by EMPC is smaller than that controlled by PID, so the pitch control loss of the unit is smaller.

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6 Conclusion In this paper, the economic model predictive control method is used to realize pitch control of wind turbine. The output power of generator and the loss of pitch bearing are written into the objective function, which not only makes the controller need not switch set values and control parameters in different wind speed intervals, but also ensures the maximum economic benefit of the unit operation. At the same time, the laser radar is introduced to measure wind speed in advance, so that the unit can obtain the wind speed change information in advance, and reduce the time delay of pitch control operation. The simulation results show that when the wind speed is below the rated wind speed, the EMPC control strategy can more accurately track the optimal tip speed ratio, and the output power is increased by 6.4% compared with the traditional PID control. When the wind speed is above the rated wind speed, the output power fluctuation of the unit under the EMPC control strategy is smaller than that under the traditional PID control, and the constant power output capacity is stronger. When the wind speed fluctuates above and below the rated wind speed, the output power of the EMPC control strategy is more stable than that of the traditional PID control. It should be pointed out that the wind from the observed place to the wind wheel still has a certain evolution due to the wind wheel obstruction and wind shear effect. The next step of this paper will focus on the establishment of wind evolution model of the near wind turbine to obtain more accurate wind speed at the wind turbine, in order to further improve the effect of pitch control.

References 1. King, K.R.: Combined feedback–feedforward control of wind turbines using state-constrained model predictive control, In: IEEE Transactions on Control Systems Technology, vol. 21, pp. 1117–1128 (2013) 2. Xiaolan, W., Jialiang, L., Chengxia, M.: Optimization control of variable-speed variablepitch wind power generation system based on power prediction. Power Syst. Prot. Control 41, 88–92 (2013) 3. Wenting, C., Bojiong, Z., Yonggang, L., Wei, L., Hang, L., Yajing, G.: Separated wind measurement individual pitch control of wind turbine based on lidar. Acta Energiae Solaris Sinica. 43, pp. 415–423 (2022).https://doi.org/10.19912/j.0254-0096.tynxb.2020-0331 4. Bing, H., Lawu, Z., Hao, C., Meng, T., Ningfeng, D.: Approach to model predictive control of large wind turbine using light detection and ranging measurements. In: Proceedings of the CSEEE, vol. 36, pp. 5062–5069+5131 (2016). https://doi.org/10.13334/j.0258-8013.pcsee. 151313 5. Wan-Jun, H., Shi-Yuan, H., Yi-Shi, J., Xin-Jing, C., Song-Qing, C., Yan-Hui, Y.: Variable pitch sliding mode control of wind turbine based on disturbance observer. In: Chinese Control and Decision Conference. Shenyang, China, pp. 5221–5225 (2018) 6. Jinghan, C., Xiangjie, L.: Economic model predictive control of variable-speed wind energy conversation systems. Control Eng. China 29, pp. 431–439. https://doi.org/10.14107/j.cnki. kzgc.20180759 7. De, T., Zhonglei, C., Ying, D.: Wind turbine load shedding control based on multi MPC algorithm. Trans. Chin. Soc. Agric. Eng. 36, 65–70 (2021) 8. Abrazeh, S., Parvaresh, A., Mohseni, S., Zeitouni, M.J., Gheisarnejad, M., Khooban, M.H.: Nonsingular terminal sliding mode control with ultra-local model and single input interval

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type-2 fuzzy logic control for pitch control of wind turbines. IEEE/CAA J. Automatica Sinica 8, 690–700 (2021). https://doi.org/10.1109/JAS.2021.1003889 9. Lipeng, M., Sheng, Y., Chunling, M.: Fatigue analysis of pitch bearing and hub connection bolt in megawatt wind turbine. J. Mech. Strength 42, 208–215 (2020). https://doi.org/10. 16579/j.issn.1001.9669.2020.01.032 10. Xiangfei, M., Ying, W., Junjie, X.: Life extension prediction of airframe based on improved corten-dolan model. Ordnance Mater. Sci. Eng. 37, 113–117 (2014). https://doi.org/10.14024/ j.cnki.1004-244x.2014.03.038

Study on Sliding Mode Method of Five-Phase Permanent Magnet Synchronous Motor Weifa Peng1(B) , Tao Lin1,2 , and Jun Liu1,2 1 School of Electrical and Automation Engineering East, China Jiaotong University Nanchang,

Nanchang 330013, China [email protected] 2 State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure ECJTU, Nanchang 330013, China

Abstract. The vector space decoupling mathematical transformation equation of five-phase permanent magnet synchronous motor in synchronous transformation method is founded based on the extended Park transform. Under the premise that the direct axis current is equal to zero, the quadrature axis current is controlled to achieve the purpose of torque control. Aiming at the weak anti-interference ability and large overshoot of five-phase motor under the classical PI control, a new sliding mode velocity control method with improved exponential power approach rate is proposed. The simulation model is established. It can be seen from the simulation results, it overcomes the inherent defect of a single exponential approach law that causes high-frequency chattering. It has different fast approaching characteristics in different approaching stages, and can control the convergence rate better. Keywords: Five-phase permanent magnet synchronous motor · Vector space decoupling · Buffeting

1 Introduction Permanent magnet synchronous motor (PMSM) has wide speed range, high efficiency and high power density, and is widely welcomed in the field of industrial control. Fivephase motor compared with ordinary three-phase motor, it can produce large electromagnetic torque at low speed and has small torque ripple, which is suitable for direct drive and high-power transmission. At the same time, because of the number of stator winding phases increases, the design and control of five phase motor is more complex than that of three phase motor. Reference [1] designed an adaptive fuzzy sliding mode controller, which has the characteristics of adaptive control and can suppress the uncertainty of parameters. Literature [2] proposed an optimal current control strategy to reduce motor torque fluctuation because the traditional control method usually uses current hysteresis control, and current hysteresis control has a series of problems such as unstable current and frequency. In reference [3], the improved sliding mode control(SMC) method is applied to the direct torque drive system, which overcomes the problem of slow response of PI control © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1046–1051, 2023. https://doi.org/10.1007/978-981-99-4334-0_124

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and improves the anti-interference performance. Reference [4] uses a combination of PI and SMC to switch control modes according to different input values, which improves control sensitivity and can suppress torque ripple. Literature [5] proposed a new exponential approach law to improve the tracking speed by overcoming the inherent chattering problem of conventional sliding mode control. This paper designs a new approximation law. The reaching law fully combines the characteristics of power term and exponential term, which can well restrain the sharp change caused by the change of small parameters of five phase motor model in conventional PI control, and weaken the defect of single exponential reaching law with highfrequency chattering. It has different fast reaching characteristics in different reaching stages, and can better control the convergence rate.

2 Ideal Module of Five-Phase PMSM Ignore the change of motor parameters, in ABCDE natural coordinate system, the matrix form of stator voltage equation is: ⎧ s ⎪ us = Rs × is + dψ ⎪ dt ⎪ ⎪ T ⎪ ⎨ us = [ uA uB uC uD uE ] T (1) is = [ iA iB iC iD iE ] ⎪ ⎪ T ⎪ ψs = [ ϕA ϕB ϕC ϕD ϕE ] ⎪ ⎪ ⎩ Rs = diag[ R R R R R ] where us is stator phase voltage matrix,is is stator phase current matrix, ψs is stator phase flux matrix, Rs is stator phase resistance matrix. In the natural coordinate system, five-phase PMSM is a multivariable, strong coupling complex system, and its solution is very difficult. Referring to the principle of coordinate transformation and amplitude invariance of three-phase motor, the generalized Park transformation matrix of five-phase motor can be derived as shown in Formula (2). ⎤ ⎡ cos θe cos(θe − α) cos(θe − 2α) cos(θe − 3α) cos(θe − 4α) ⎢ − sin θ − sin(θ − α) − sin(θ − 2α) − sin(θ − 3α) − sin(θ − 4α) ⎥ ⎥ e e e e e 2⎢ ⎥ ⎢ Tdq = ⎢ 1 cos 3α cos α cos 4α cos 2α ⎥ ⎥ 5⎢ ⎦ ⎣ 0 sin 3α sin α sin 4α sin 2α 1 2

1 2

1 2

1 2

1 2

(2) According to Eqs. (1) and (2), the stator voltage formula of five phase PMSM in dq coordinate system is derived: ⎡

⎤ ⎡ ⎤ ⎡ ud 1 id 1 Ld 0 ⎢ uq1 ⎥ ⎢ iq1 ⎥ ⎢ 0 Lq ⎢ ⎥ ⎢ ⎥ ⎢ ⎣ ud 3 ⎦ = R⎣ id 3 ⎦ + ⎣ 0 0 uq3 iq3 0 0

0 0 L1 0

⎤ ⎡ ⎤ ⎡ id 1 0 −Lq iq1 ⎢ iq1 ⎥ ⎢ Ld id 1 + φf d 0⎥ ⎥ ⎢ ⎥ + ωe ⎢ ⎣ 0 ⎦ dt ⎣ id 3 ⎦ 0 iq3 L1 0

⎤ ⎥ ⎥ ⎦

(3)

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where ud1 is the d-axis stator fundamental voltage, uq1 is the q-axis stator fundamental voltage,id1 is the d-axis stator fundamental current, iq1 is the q-axis stator fundamental current,ud3 is the d-axis third harmonic voltage of stator, uq3 is the q-axis third harmonic voltage of stator, id3 is the d-axis third harmonic current of stator,iq3 is the q-axis third harmonic current of stator, R is the stator resistance, Ld is the d-axis stator inductance, Lq is the q-axis stator inductance, ωe is electrical angular velocity of the rotor; ψf is permanent magnet flux linkage. At the same time, the calculation formula of electromagnetic torque in rotating coordinate system can be obtained as follows: Te =

5 pn [(Ld − Lq )id 1 iq1 + iq1 ϕf ] 2

(4)

where pn is the number of motor poles. When the control id is equal to zero, the torque equation can be simplified as: Te =

5 pn iq1 φf 2

(5)

The angular velocity expression of the motor is: J

dω = Te − TL − Bω dt

(6)

where ω is the mechanical angular speed of the PMSM rotor,Te is the electromagnetic torque of five-phase motor; TL is the load torque; J is the moment of inertia; B is the system friction coefficient.

3 Design a New Type Velocity Controller Define the control system state variables as: x1 = ωref − ω x2 = x˙ 1 = −ω

(7)

where ωref is the reference speed of the PMSM, generally, it is unchanged. Take the derivative of formula 7 and combine formula 4, formula 6 and formula 7 to get the following expression:

5p ϕ x˙ 1 = −ω˙ = TJL − 2Jn f iq1 (8) 5p ϕ x˙ 2 = −ω¨ = − 2Jn f ˙iq1 Let A =

5pn ϕf 2J

Eq. (8) can be changed into

x˙ 1 = x2 x˙ 2 = −A˙iq1

(9)

Study on Sliding Mode Method of Five-Phase Permanent

Therefore, the state variable matrix can be written:        0 1 x1 0 ˙ x˙ 1 = + iq1 x˙ 2 0 0 x2 −A

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(10)

The designed sliding surface function is s = cx1 + x2 , combined with Eq. 10, which can be obtained by differentiating the sliding surface: s˙ = c˙x1 + x˙ 2 = cx2 + x˙ 2 = cx2 − A˙iq1

(11)

In this paper, an improved exponential power approach rate is designed as: S

s˙ = −ε|s| |S|+a sgn(s) − qs q, ε, a > 0

(12)

In the traditional switching function, an exponential sliding mode function is added to enable the system to approach the position near the target plane quickly in a short time when starting the response, and reduce the speed when approaching the target plane to ensure the final dynamic characteristics. The system is divided into two motion stages from initial state to approaching arget plane: when |s| ≤ 1 and the system approaches target plane, this improved function can guarantee small control gain to reduce chattering; When the function |s| > 1, the fast approach characteristic of the variable power approach law greatly shortens the approach time and the adjustment time. The new design function has obvious advantages. Combining Eq. (11) and new reaching law expression (12), we can get:    S 1 cx2 + ε|s| |S|+a sgn(s) + qs dt (13) iq1 = A

4 Analysis of System Based on MATLAB Create a simulation model for the above design system. During the experiment, the target speed is set at 1000 r/min and the load of 5 N m is dragged. Figures 1, 2, 3, 4, 5 and 6 show the phase current, speed and torque waveforms in PI control mode and SMC control mode. Both control modes can reach stable state before 0.02 s, and the speed quickly increased to 1000 rpm, and the electromagnetic torque stabilized at 5 N m. The response is very fast and stable, and there is no overshoot of the speed. In addition, SMC control performance is better. SMC control has smaller phase current impulse, smaller waveform distortion, smoother torque ripple and basically no overshoot of speed. The abscissa of Figs. 1, 2, 3, 4, 5 and 6 is in seconds, the ordinate of Figs. 1 and 2 is in amperes, the ordinate of Figs. 3 and 4 is in revolutions per minute, and the ordinate of Figs. 5 and 6 is in N M.

5 Conclusion Different from the traditional approach rate, a new speed control method is proposed and verified by simulation. The experiment shows that this control method has better performance than the traditional PI control method, and is more suitable for the motor drive system with high transient performance requirements. The control system designed in this paper has smaller phase current pulse, smoother torque ripple and negligible speed overshoot. Faster torque and speed tracking.

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Fig. 1. The waveform of five-phase current under PI control

Fig. 2. The waveform of five-phase current under SMC control

Fig. 3. Rotor speed waveform of five-phase motor under PI control

Fig. 4. Rotor speed waveform of five-phase motor under SMC control

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Fig. 5. Torque waveform of five-phase motor under PI control

Fig. 6. Torque waveform of five-phase motor under SMC control

References 1. Ma, L., Xu, G.: Fault-tolerant control of microgrid inverter system based on variable theory domain fuzzy sliding mode observer. Sci. Technol. Eng. 20(31), 12827–12835 (2020) 2. Yin, H., Wang, T., Gao, C., et al.: Simulation of fault-tolerant control for five-phase permanent magnet synchronous motor. Mach. Autom. 48(6), 107–110, 149 (2019) 3. Jiarui, C., Jiangfeng, G., et al.: Sliding mode variable structure robust control of permanent magnet synchronous motor. J. Electr. Mach. Control 20(5), 84–89 (2016) 4. Fan, Y., Zhou, X., et al.: Sliding mode variable structure control of IPMSM speed governing system based on new reaching law and hybrid speed controller. J. Electr. Technol. 32(5), 9–18 (2017) 5. Zhang, X.G., Zhao, K., Sun, L., et al.: Sliding mode control of permanent magnet synchronous motor based on novel exponential reaching law. Proc. CSEE 31(15), 47–52 (2011) 6. Feng, Y., Yu, X., Han, F.: High-order terminal sliding-mode observer for parameter estimation of a permanent magnet synchronous motor. IEEE Trans. Ind. Electron. 60(10), 4272 (2013) 7. Ma, H., Li, Y.: Multi-power reaching law based discrete-time sliding-mode control. IEEE Trans. Power Electron. 28(3), 1358 (2013) 8. Tchier, F., Mobayen, S., Golestani, M.: Adaptive finite time tracking control of uncertain nonlinear n-order systems with unmatched uncertainties. IET Control Theory Appl. 10(14), 1675–1683 (2016) 9. Feng, Y., Zheng, J., Yu, X.: Hybird terminal sliding mode observer design method for a permanent magnet synchronous motor control system. IEEE Trans. Ind. Electron. 56(9), 3424 (2009) 10. Zhang, X., Sum, L., Zhao, K., et al.: Nonlinear speed control for PMSM system using slidingmode control and disturbance compensation techniques. IEEE Trans. Power Electron. 28(3), 1358 (2013)

Open-Circuit Fault Diagnosis for Wave Energy Converters with Support Vector Machine Xinqing Zhang1 , Zhen Li1(B) , Zhenbin Zhang1 , Rong Ye2 , and Zhi Li3 1 School of Electrical Engineering, Shandong University, Jinan 250061, China

[email protected]

2 State Grid Fujian Economic Research Institute, Beijing, China 3 China Three Gorges Corporation, Yichang, China

Abstract. The operational reliability of the wave energy converter (WEC) is essential for its application. Fault diagnosis is currently considered as a crucial way to improve the reliability of the WEC, which consists of a mass of semiconductor power switches. In this work, a data-driven method be proposed to diagnose singleswitch open-circuit faults, which is achieved by three-phase current waveform and support vector machine (SVM). The fault current and its corresponding output fault type are input into the support vector machine. After sufficient training, SVM model can diagnose corresponding faults with less computation. The effectiveness of the proposed method is authenticated by the simulation results. Keywords: Wave energy converter · Support vector machine · Classification · Fault diagnosis · Reliability

1 Introduction Renewable energy is now one of the hot topics in which researchers over the world are researching. As classical energy has brought serious environmental problems, renewable energy is developed to reduce the significant pollution caused by fossil fuels. Ocean wave energy is one of the feasible potential energy sources among renewable energy. Ocean wave energy, with its high power density (The average energy density is 20–50 kW/m), abundance (The global exploitable potential energy is 2 TW), and cleanness, appears to be one of the most sustainable energy sources to replace fossil fuels [1]. Over the past few decades, several devices to generate electricity from waves have been investigated [2]. Some of them have been tested and put into engineering practice [3]. In most cases, wave energy power generation system extracts energy from the heaving motion of the ocean waves, using a wave-to-wire model (W2W). The W2W model includes energy harvest system, power-take-off system and wave energy converter (WEC). In the above W2W model, the WEC can generate a substantial amount of reliable power. Researchers have proposed many different WECs for utilizing wave power for more than many years. Paper [4] proposes an offshore floating wave energy converter to protect the coastal environment and the secondary benefits of energy production. Paper [5] classified different types of WEC and analyzed their mechanical structure. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1052–1058, 2023. https://doi.org/10.1007/978-981-99-4334-0_125

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In this paper, the topology of WEC is a two-level back-to-back converter (shown in Fig. 1). Compared with other renewable energy, wave energy is a relatively immature technology. Moreover, the volume of the WEC is too large to maintain, and exist so many semiconductor power switches in the WEC. The semiconductor power switches are the most vulnerable devices in the WEC. Although switches are rugged, they suffer failures due to excess electrical, over-current, and thermal stress that is experienced in many applications. According to an industry-based, semiconductor power switch failures account for 34% of converter system failures [6]. These faults can be roughly divided into short circuit fault, open circuit fault and intermittent door misfire fault. Generally, the open-circuit circuit fault will operate for a long time and is hard to protect. As a result, it will degrade the system control performance and reliability, resulting in secondary failures. However, the diagnosis of open-circuit-circuit faults have not been covered by a normal protection system [7].

Fig. 1. The topology of WEC

The diagnosis methods of open-circuit fault can be classified into circuit model based diagnosis method and data driven diagnosis method. For the model method, the semiconductor power switches open-circuit faults will be located by monitoring the current or voltage status in the converter. The work in paper [8] used the voltage signal to detect the fault rapidly. However, this method takes a long time and requires extra sensors. Data-driven methods extract fault information in sufficient system data through data mining, artificial intelligence and other data processing technologies. The method used in this work is the SVM, which belongs to one of the data-driven methods. The operating principle of support vector machines is to build an optimal hyperplane in multidimensional feature space and maximize the distance between different categories of data samples [9]. This method has a solid theoretical basis, which has been applied in many fields, such as military, aerospace and so on [10–13]. In this paper, the open-circuit fault of WEC is studied and verified based on the support vector machine method. In this method, three-phase current is used as input fault characteristic of support vector machine. As a result, it greatly reduces the amount of computation and diagnostic time. The trained SVM model can be used to diagnose different six fault types online. The results show that the fault diagnosis accuracy of this method is 91%, which will improve system reliability.

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2 Fault Current Analysis 2.1 System Topology

Fig. 2. The topology of two-level back-to-back converter

Figure 2 shows a simplified topology of two-level back-to-back converter, which includes two working modes: rectifier and inverter. Each phase of the rectifier or inverter is composed of two power switches (Yx and Yx ) and two freewheeling diodes. x ∈ {a, b, c}, represents the phases. Y ∈ {M , G}, stands for machine or load (M) side or grid (G) side. The driving signal Sx is defined as: Sx = 1, the upper switch Yx is ON; Sx = 0, the lower switch Yx is ON. 2.2 Current Path

Fig. 3. The normal current paths

In the converter system, rectifiers and inverters work on the same principle. In this paper, the open-circuit fault of WEC is analyzed in the machine side. Figure 3 shows the normal current path of the machine side. As can be seen, there are four possible current paths may occur in the back-to-back converter depending on the direction of the current iM . In Fig. 3a, b, when the upper switch Mx open-circuit fault occurs, the current will pass the diode of lower switch Mx instead of the Mx . In Fig. 3c, d, when the lower switch Mx open-circuit fault occurs, the current will pass the diode of the upper switch Mx instead of Mx .

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For this WEC system, different current path presents diverse waveform. Under normal circumstances, the output current should present a sinusoidal symmetrical waveform. As soon as an open-circuit fault occurs on switch, the current waveform will be distorted (shown in Fig. 4). As we can see, the reliability of the three-phase current largely presents the state of the switch. To improve the reliability of the WEC, it is necessary to design an open-circuit fault diagnosis system of the switch. In conclusion, the waveform of the switch current is a vital characteristic of the WEC, since it presents whether WEC operates in a reliable state or not.

Fig. 4. Different fault locations and their respective current waveform

3 Diagnosis of WEC Based on SVM 3.1 Analysis of SVM Support vector machine (SVM) is a machine learning method used in many fields to solve prediction and classification problems. Figure 5 shows the classification model with SVM. This method has shown reliable results in different applications, from figure recognition to data categorization. Using this classification method, we consider a binary classification problem consisting of n training data. x1 , x2 . . . xi corresponds to the dataset, y(xi ) ∈ {1, −1}, corresponds to its class label. The function of the decision boundary is: y(x) = ωx + b

(1)

In this function, ω is the weight vector, and b is the threshold. For y(xi ) > 0, xi corresponds label 1; for y(xi ) < 0, xi corresponds label − 1. This is equivalent to the sign function: f (x) = sign[y(x)]

(2)

The above analysis is not limited to the binary classification problems. We can map it in higher dimensional space to solve multiple classification problems. Correspondingly, the weight vector ω is replaced by vector ωT . A function with constraints is used to solve the classification problems: 1 min ω2 ω,b 2

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  s.t. yi ωT x + b ≥ 1.

(3)

Support vector machine has multiple kernel functions which will affect the prediction and classification performance of support vector machine in regression. The commonly used kernel functions are: polynomial function, linear kernel function, and radial basis function, etc.

Fig. 5. The classification model with SVM

In this work, the radial basis kernel function is considered for SVM classification:    xi − xj    κ xi , xj = exp − (4) 2δ 2 where δ is a parameter of the kernel function, which can influence the structure of higher dimensional feature space and the performance of SVM. 3.2 Fault Diagnosis of Switch Current in WEC Let xi = {ia , ib , ic } as the input data, {ia , ib , ic } denote the three-phase current on the machine side. Let y(xi ) = {1, 2, 3, 4, 5, 6, 7} as the objective label. Labels 1–6 denote the fault occurring in Ma , Mb , Mc , Ma , Mb , Mc , and label 7 denotes the WEC is in a healthy state. The parameters used are shown in Table 1. Table 1. Parameters of the model used in PLECS Parameter

Symbol

Value

DC link voltage

Vdc

600 V

Sample frequency

fs

50 kHz

Resistance

Rg

0.1379 

Inductance

Lg

100 mH

DC-link capacitance

C

2.2 mF

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4 Simulation Results To verify the effectiveness of this work, simulations are presented as follows. First, we set the open-circuit fault location from Ma to Mc respectively, obtaining both healthy and fault current data. The data will be used to train the SVM to obtain a classification model in Matlab. The SVM model could be used to classify the fault type by inputting the three-phase current. Second, we input 726 groups of current into the SVM model, and compute the error by comparing the estimated results with the actual fault type. Finally, the classification results are shown in Fig. 6. In Fig. 6a, the blue dotted line presents the actual fault type. In Fig. 6b, the yellow dotted line shows the estimated fault type. Figure 6c shows their error.

Fig. 6. Classification of fault types. a Actual classification. b Predictive classification. c Error.

As can be seen from Fig. 6c, comparing the predictive type with the actual type, we can obtain a match rate of about 91% (663/726). SVM provides an effective method of constructing a fault classification system and estimating the open-circuit fault location of the WEC.

5 Conclusion In this paper, a data-driven open-circuit fault diagnosis method for semiconductor power switches is studied., which contributes to the reliable operation of the WEC. The effectiveness of the method proposed in this paper was verified by classifying the current fault type with the SVM method. Simulation results have shown the accuracy of the proposed method. Acknowledgement. Dr.rer.nat Zhen Li (email: [email protected]) is the corresponding author of this paper. This work is financially supported by National Natural Science Foundation of China (52007107), Natural Science Foundation of Shandong Province (ZR2020ME201), and National Natural Science Foundation of China under Grant (52277191).

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References 1. Pelc, R., Fujita, R.M.: Renewable energy from the ocean. Mar. Policy 26(6), 471–479 (2002) 2. Muetze, A., Vining, J.G.: Ocean wave energy conversion—a survey. In: Conference Record of the 2006 IEEE Industry Applications Conference Forty-First IAS Annual Meeting, vol. 3, pp. 1410–1417 (2006) 3. A. F. A. F. F. G. K. H. e. a., Clement, A., McCullen, P.: Wave energy in Europe: current status and perspectives. Renew. Sustain. Energy Rev. 6(5), 405–431 (2002) 4. Zanuttigh, B., Angelelli, E.: Experimental investigation of floating wave energy converters for coastal protection purpose. Coast. Eng. 80, 148159 (2013) 5. Hong, Y., Waters, R., Boström, M., Eriksson, J., Engström, J., Leijon, M.: Review on electrical control strategies for wave energy converting systems. Renew. Sustain. Energy Rev. 31, 329– 342 (2014) 6. Condition monitoring for device reliability in power electronic converters: a review. IEEE Trans. Power Electron. 25(11), 2734–2752 (2010) 7. Fuchs, F.: Some diagnosis methods for voltage source inverters in variable speed drives with induction machines—a survey, vol. 2, pp. 1378–1385 (2003) 8. Shu, C., Ya-Ting, C., Tian-Jian, Y., Xun, W.: A novel diagnostic technique for open-circuited faults of inverters based on output line-to-line voltage model. IEEE Trans. Industr. Electron. 63(7), 4412–4421 (2016) 9. He, Y., Du, C.Y., Li, C.B., Wu, A.G., Xin, Y.: Sensor fault diagnosis of superconducting fault current limiter with saturated iron core based on svm. IEEE Trans. Appl. Supercond. 24(5), 1–5 (2014) 10. dos Santos, C.M., Escobedo, J.F., Teramoto, E.T., da Silva, S.H.M.G.: Assessment of ann and svm models for estimating normal direct irradiation (hb). Energy Convers. Manag. 126, 826–836 (2016) 11. Zhang, Z., Guo, H.: Research on fault diagnosis of diesel engine based on psosvm (2016) 12. Shen, L., et al.: Evolving support vector machines using fruit fly optimization for medical data classification. Knowl. Based Syst. 96, 61–75 (2016) 13. Aytug, H., Sayın, S.: Exploring the trade-off between generalization and empirical errors in a one-norm svm. Eur. J. Oper. Res. 218(3), 667–675 (2012)

Design and Implementation of 4G-Based Crop Rotation Soil Information Monitoring System Shuangxi Li1 , Shumei Cai1 , Naling Bai1 , Hanlin Zhang1 , Juanqin Zhang1 , Haiyun Zhang1 , Xianqing Zheng1 , Weiguang Lv1(B) , and Shipu Xu2(B) 1 Eco-Environmental Protection Research Institute, Shanghai Academy of Agricultural

Sciences, Shanghai, China [email protected] 2 Research Institute of Information of Agricultural Science and Technology, Shanghai Academy of Agricultural Sciences, Shanghai, China [email protected]

Abstract. The 4G-based crop rotation soil information monitoring system is an Internet of Things that uses various instruments and sensors to monitor soil information. In this paper, a real-time monitoring system of crop rotation soil environment is developed by using IoT related technologies. The main content of this paper includes the system route, design and implementation. In the implementation process of the system, through the combination of various network modes, the automatic collection of soil environment information and meteorological information of farmland can be realized. Keywords: Crop rotation soil · IoT · Real-time monitoring system · Automatic collection · Environment information

1 Introduction The sustainable development of agriculture is the trend of agricultural development in the world today, and also the basic national policy of China. Sustainable agricultural development is mainly reflected in that it cannot only increase agricultural production and economic development, but also maintain ecological balance and good environment. Improving resource utilization efficiency is the core of achieving sustainable agricultural development. Traditional agricultural planting and management methods have caused a series of ecological and environmental problems, such as reducing farmland biodiversity, soil compaction, soil fertility decline, nutrient conversion and utilization decline, nitrate pollution and surface water eutrophication [1, groundwater 2]. With the development of related technologies, more intelligent systems based on the Internet of Things have been applied to agricultural production. The soil monitoring system based on information technology can monitor soil quality in real time and provide technical support for management personnel. This system mainly applies soil quality information collection to crop rotation in this field [3]. The system consists of selforganized network and low-power network nodes. The system realizes online real-time monitoring of soil quality, which is collected every five minutes [4]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1059–1064, 2023. https://doi.org/10.1007/978-981-99-4334-0_126

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2 Sensor Node Design The soil quality management system based on information technology consists of data acquisition network and control center. The system structure is shown in Fig. 1. Monitoring network has two steps: network formation and sensor data collection [5–7]. There are three types of nodes in the system: terminal, router and coordinator. The system collects soil parameters, and transmits the data to the relevant nodes through the router node relay. The final data is sent to the data storage system of the system [8].

Fig. 1. The overall architecture map.

The core processing center of the system is composed of data center and CPU. It can also store and display the received data, and draw these data into the dynamic curve analysis. The quality threshold can also be set to realize intelligent monitoring of soil quality. 2.1 Sensor Node Hardware Design According to the application scenario, the system design follows the following four points [9–11]. (1) Miniaturization. Due to the particularity of the use scenario, a large number of sensor nodes need to be deployed in the monitoring area. (2) Low cost. Because the system has many nodes and sensors, the cost of a single device will greatly affect the final cost.

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(3) Low power consumption. Because of the particularity of the environment, power consumption is a very important indicator. It can also reduce the power consumption of the system sensor itself and prolong its service life. This is very important for the stability and effective operation of the system. (4) Excellent RF. Because the wireless information signal decays exponentially with the communication distance, the long-distance communication that restricts the wide application of the system. Better RF performance can help the system’s operating ability. According to the above points, the system design diagram is shown in Fig. 2.

Fig. 2. Node map.

As shown in Fig. 2, DCP is the core module of the node. The external sensor module contains all sensors. It can realize automatic acquisition of various parameters of crops [12, 13]. JTAG interface provides test for various chips. LED module, the core module of the system, can display the working status of relevant nodes. The communication module of the system can complete the control command interaction function and transmit data. The serial module is connected with the computer through the serial port, and the acquired soil quality data is uploaded to the upper computer of the system [14]. 2.2 Sensor Node Software Design The system is developed based on IAR Embedded Workbench (IAR EW). The IDE is currently the most inclusive, inclusive and efficient code development framework. Its functions are very powerful. It supports the development of C/C++; it realizes the management of projects. The system network has three types of devices, namely, Zigbee-based router, coordinator and terminal device [15]. The router is responsible for discovery path and device

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maintenance. This equipment can collect data and complete routing work. There can only be one coordinator in this system. The terminal equipment of the system is responsible for collecting data, while the terminal node can complete data collection and feedback information. The specific formation process is shown in Fig. 3.

Fig. 3. The process.

2.3 Design of Internet Access Module This system realizes data transmission, and the embedded system on the receiving data terminal realizes the function of web server. The coordinator is connected to the server at several points, the ZigBee protocol is implemented on the coordinator, and the TCP/IP protocol is implemented on the network access module. The specific connection method is shown in Fig. 4.

Fig. 4. Internet access diagram.

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3 Intelligent Monitoring and Processing Center 3.1 Monitoring and Processing Center In this system, various technologies are integrated to collect data. The system uses topological structure to place various types of sensors in the field. The system can collect environmental data, including pH, temperature and humidity, light intensity, etc. The functional module diagram of the system is shown in Fig. 5.

Fig. 5. The software architecture processing center.

3.2 The Realization of Intelligent Monitoring and Processing Center The information collection system of crop rotation intelligent monitoring and processing center was developed.

4 Conclusions The application of Internet of Things technology in agriculture is particularly important. This paper systematically and accurately obtains the information of farmland soil environment. It providing a new development platform for China’s agricultural development, and realizing China’s agricultural modernization, information technology and intellectual development are complex themes of scale and intelligence, which still have a long way to go.

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Acknowledgment. This work is supported in part by the Domestic Cooperation program of Shanghai Science and Technology Commission (Grant No. 18295810500), and by the NAES035AE03 National Agricultural Experimental Station for Agricultural Environment, Fengxian (grant number: NAES035AE03).

References 1. Nie, P., Zhang, H., Geng, H., et al.: Current situation and development trend of agricultural Internet of Things technology. J. Zhejiang Univ. 47(2), 135−146 (2021) 2. Xiaofang, Z., Junyuan, Z.: Analysis on the development mode of agricultural IoT. J. China Acad. Electron. Inf. Technol. 9(3), 250–254 (2014) 3. Bouma, J.: Soil science contributions towards sustainable development goals and their implementation: linking soil functions with ecosystem services. J. Plant Nutr. Soil Sci. 177(2), 111–120 (2014) 4. Nagarajan, R., Mahapatra, S.: Land based information system for drought analysis. Map India 13(3), 55–58 (2012) 5. Liangyu, W., Yanhong, Z., Chen, L.: Error analysis of automatic soil moisture observation data. Meteorol. Sci. Technol. 42(5), 731–736 (2014) 6. Aubertin, G.: Nature and extent of macrospore in forest soils and their influence on subsurface water movement. For. Serve. Pap. 33(4), 138–141 (2017) 7. Awdelkreem, A.: Implementation of the optimum service granularity use hierarchical clustering. University of Khartoum, Khartoum (2014) 8. Chandrasekaran, S., Miller, J., Silver, G., et al.: Performance analysis and simulation of composite web services. Electron. Mark. 13(2), 120–132 (2013) 9. Tagarakis, A., Kateris, D., Berruto, R., et al.: Low-cost wireless sensing system for precision agriculture applications in orchards. Appl. Sci. 11(13), 5858 (2021) 10. Keswanib, M.A., Keswani P., et al.: Improving weather dependent zone specific irrigation control scheme in IoT and big data enabled self-driven precision agriculture mechanism. Enterp. Inf. Syst. 14(9), 1494–1515 (2020) 11. Huan, J., Wu, F., Cao, W., et al.: Development of water quality monitoring system of aquaculture ponds based on narrow band internet of thing. Trans. Chin. Soc. Agric. Eng. 35(8), 252–261 (2019) 12. Jianjun, L., Xiaoling, W., Yang, Y., et al.: Research on the construction of quality and safety traceability system of agricultural products based on internet of things. Northern Hortic. 44(8), 141–146 (2020) 13. Xue, F., Kumar, P.R.: The number of neighbors needed for connectivity of wireless networks. Wirel. Netw. 10, 169–181 (2004) 14. Ganesh, A., Xue, F.: On the connectivity and diameter of small-world networks. Adv. Appl. Probab. 39, 853–863 (2007) 15. Chaoying, M., Jia, W., Hongqian, C., et al.: Intelligent monitoring system based on distributed object for layer house. Trans. Chin. Soc. Agric. Mach. 48(10), 292–299 (2017)

Comparison and Analysis of Different Overvoltage Suppression Circuits for Low-Voltage Solid-State Circuit Breakers Xin Wu1(B) , Chuangchuang Tao1 , Yifei Wu1 , Wenxin Yang1 , Qiong Kang1 , Jingshuai Wang1 , and Liting Yan2 1 Xi’an Jiaotong University, 28 Xianning West Road, Xi’an, China

[email protected] 2 UHV Transformer Branch of State Grid Shanxi Electric Power Company, Taiyuan, China

Abstract. In this paper, three different overvoltage suppression circuits applied to solid state circuit breakers (SSCBs) are presented and their parameter design methods are analyzed. A simulation model of an SSCB with an overvoltage suppression circuit is built in Pspice, the turn-off voltage waveforms of these three overvoltage suppression circuits applied to a solid-state circuit breaker are given, and the influence rules of the key component parameters in the overvoltage suppression circuit are analyzed. The advantages and disadvantages of these three overvoltage suppression circuits are compared. The peak overvoltage, the voltage rise rate of the turn-off process, and the size and cost of the overvoltage suppression circuit are used as the evaluation criteria. Finally, an experimental platform is built to test the short-circuit fault turn-off waveform and an SSCB based on a parallel resistive-capacitive diode (RCD) and metal oxide varistor (MOV) overvoltage suppression circuit is designed. The rationality of the parameter design method is verified, and the designed overvoltage suppression circuit plays a good voltage buffering and overvoltage suppression effect. Keywords: Solid-state circuit breaker · Overvoltage protection · SiC MOSFET

1 Introduction Compared with AC distribution networks, DC distribution networks have many advantages, such as low line costs, good power quality, low line losses, and more economical long-distance transmission of high power, and are developing rapidly [1, 2]. In the development of DC distribution networks, fast and reliable short-circuit fault protection has been a critical issue. As a protection device, a DC circuit breaker can automatically disconnect the circuit and isolate the fault when short-circuit and overload faults occur in the DC distribution network, which has the functions of fast and reliable fault detection, fault clearance and system protection, and is the key equipment to ensure safe and reliable operation of the DC distribution network [3]. Mechanical low-voltage DC circuit breakers are slow to break, there is severe arcing during the process, noise and soot are generated during opening and closing, and their © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1065–1075, 2023. https://doi.org/10.1007/978-981-99-4334-0_127

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reliability and service life are limited [4]. Solid-state circuit breakers with power electronics as the breaking element have the advantages of fast operation, high reliability, no noise and no arcing phenomenon, which can greatly improve the reliability of the DC power system and improve the power quality of the DC power system, and are suitable for DC system fault elimination and system protection [5]. Moreover, solid-state DC circuit breakers can be used in new power generation, marine, subway and offshore DC power systems and so on, and are very promising [6]. Suppression of turn-off overvoltage is one of the challenges in the design of semiconductor power switches. For a given system voltage, the design requirements for overvoltage suppression circuits can be reduced by increasing the rated voltage of power semiconductor devices [7, 8]. However, as the breakdown voltage capability increases [9], the expected conduction loss of the device increases. Therefore, for the optimal design of solid-state power switches, the proper selection and design of overvoltage suppression circuits is critical. This paper analyzes the working principles and advantages and disadvantages of three overvoltage suppression circuits, and gives the parameter design methods of the three overvoltage suppression circuits. Then, the influence law of the key parameters of the three overvoltage suppression circuits is analyzed, and finally, the experimental platform for the verification of the proposed parameter design methods of overvoltage suppression circuits is established.

2 Different Overvoltage Suppression Circuits Three typical overvoltage suppression circuit topologies are given in Fig. 1. Figures 2, 3 and 4 gives the schematic diagrams of the operating principle of these three overvoltage suppression circuits. The following is a detailed analysis of the different operating phases of the overvoltage suppression circuit. MOV MOV MOV circuit MOV circuit

C

MOV

SiC MOSFET module

(a)

C

Snubber circuit

MOV circuit

VDC

D

R

Load VDC

SiC MOSFET module

(b)

R

Snubber circuit

Load VDC

SiC MOSFET module

Load

(c)

Fig. 1. Three overvoltage suppression circuits. a MOV; b RC+MOV; c RCD+MOV.

2.1 Solid-State Circuit Breaker with MOV Figure 1a shows the solid-state circuit breaker topology using parallelled MOV for overvoltage protection when a short-circuit fault occurs. The four phases of its operation are shown in Fig. 2.

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Stage 1: No short-circuit fault occurs in the line and the current flows through the MOSFET to power the load. Stage 2: A short-circuit fault occurs in the line and the short-circuit current rises rapidly. Stage 3: When a short-circuit fault is detected, the power electronics are controlled to shut down and the voltage across the device begins to rise rapidly. When this voltage reaches the MOV threshold voltage, the MOV is actuated and the fault current flowing through the MOSFET is commutated to the MOV branch. At this time, the solid-state circuit breaker current relationship satisfies the following equation: Iswitch + IMOV = Ibrea ker

(1)

where I switch is the current flowing through the SiC MOSFET, I MOV is the current flowing through the MOV branch, and I breaker is the current flowing through the entire solid-state circuit breaker. Based on the voltage U MOV of the MOV branch and the parasitic inductance L sMOV , the voltage of the circuit breaker can be obtained as: Uswitch = UMOV + Lst

dIMOV dt

(2)

Fig. 2. Schematic diagram of the operating principle of the SSCB with MOV.

Fig. 3. Schematic diagram of the operating principle of the SSCB with RC+MOV.

Stage 4: The current flowing through the MOSFET drops to zero, the fault current is all shifted to the MOV branch, and the energy stored in the system inductor continues dissipating through the MOV. The entire shutdown process ends when the current flowing through the MOV drops to zero. The energy dissipated by the MOV in stage 4 is: t4 WMOV = 0

  Uclamp − Usource Uclamp It4 − t dt Ldc

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Fig. 4. Schematic diagram of the operating principle of the SSCB with RCD+MOV.

  Usource 1 = + 1 Ldc It42 2 Uclamp − Usource

(3)

where U clamp is the varistor voltage of MOV; I t4 is the circuit breaker shutdown current; L dc is the total inductance consisting of the DC circuit breaker, DC line, load, and current limiting reactor, etc. 2.2 Solid-State Circuit Breaker with RC+MOV Figure 1b shows a parallel solid-state circuit breaker topology using MOV and RC snubber circuits for overvoltage protection. When a short-circuit fault occurs, the four phases of its operation are shown in Fig. 3. Stage 1: The line is in normal operation and current flows through the MOSFET to power the load. Stage 2: The line experiences a short-circuit fault and the current continues to rise rapidly. When a short-circuit fault is detected, the power electronics are controlled to shut down and the voltage across the device begins to rise rapidly. At the same time, the voltage at both ends of the device is charged to capacitor C through resistor R. Because the capacitor voltage cannot change abruptly, it limits the magnitude of dv/ dt. The fault current is gradually transferred to the snubber branch. Stage 3: The current flowing through the MOSFET drops to zero, the fault current is all transferred to the buffer branch, and the voltage across the device continues to rise until it reaches the threshold voltage of MOV. The voltage and current during the charging of the capacitor in stages 2 and 3 satisfy the following equations: ⎧ ⎨ Ibrea ker = Iswitch + IC C (4) I = C dU dt ⎩ C UDS = UC + RIC where I C is the capacitor charging current and UC is the capacitor voltage. Stage 4: The voltage across the device reaches the threshold voltage of the MOV, and the MOV is energized. The fault current begins commuting to the MOV branch, capacitor C in the RC buffer branch discharges through resistor R to MOV, and the voltage across the device begins dropping. As the energy stored in the system is continuously dissipated by

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MOV and resistor R, the current flowing through MOV gradually decreases, and when this current drops to zero, the entire opening and closing process ends and the voltage at both ends of the device returns to the normal system voltage. The following equation applies to the energy dissipation phase of MOV in stage 4: ⎧ ⎪ Ibrea ker = IMOV − IC ⎪ ⎪ ⎪ ⎪ ⎨ UMOV = UC − RIC C IC = C dU (5) dt ⎪ t4 ⎪ ⎪ ⎪ ⎪ ⎩ WMOV = UMOV IMOV dt 0

2.3 Solid-State Circuit Breaker with RCD+MOV Figure 1c shows the topology of a solid-state circuit breaker using MOV and RCD snubber circuits in parallel for overvoltage protection. When a short-circuit fault occurs, the four phases of its operation are shown in Fig. 4. The RCD+MOV circuit works similarly to RC+MOV, except that the charging and discharging process of the RCD+MOV circuit for capacitor C is done through diode D.

3 Simulation and Experimental Results for 375 V Solid-State Circuit Breakers 3.1 Comparison of Three Types of Overvoltage Suppression Circuits According to the three topologies of the overvoltage suppression circuit shown in Fig. 1, the simulation model of the semiconductor power switch is set up separately with a DC system voltage of 375 V and a peak short-circuit current of 1 kA. The drain-source voltage rating of the SiC MOSFET for simulation is 1200 V. According to the empiric formula, the voltage sensitivity of the MOV is selected according to 1.2–1.5 times the rated voltage of the system, and the MOV is selected according to 1.2 times the rated voltage of the system, that is, the voltage sensitivity of the MOV is about 450 V, 1.5 times the residual voltage of the MOV should be less than the rated voltage of the SiC MOSFET device, so the residual voltage of the selected MOV should be less than 600 V. For simulation, the 14D431K MOV model is used. The simulation parameters of the three overvoltage suppression circuits are given in Table 1, and the simulation results are shown in Fig. 5. As can be seen from the waveform comparison in Fig. 5, the MOV topology shutdown overvoltage rise rate reaches 9 kV/us, and the peak reaches 820 V. The RC+MOV topology shutdown overvoltage rise rate reached 3.2 kV/us, and the peak reached 870 V. The RCD+MOV topology shutdown overvoltage rise reaches 0.6 kV/us and peaks at 750 V. The RCD+MOV circuit has a much smaller off-over-voltage rise compared to the MOV circuit due to the capacitor’s charging process reducing the voltage change rate, which is consistent with the theoretical analysis. The RCD+MOV circuit has a smaller off-over-voltage change rate and assignment compared to the RC+MOV circuit. This is

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Topology

R

C

MOV

RCD+MOV

5

2 µF

14D431K

RC+MOV

5

2 µF

14D431K

MOV

/

/

14D431K

because the former charges the buffer capacitor through the diode and the latter charges the capacitor through the resistor R. There is a large voltage drop across the resistor R during the charging process, and the voltage drop across the resistor R is equal to the turn-off overvoltage after the voltage across the capacitor C is superimposed. The simulation results are in agreement with the theoretical analysis. Due to the effect of the resistance during capacitor charging, the total turn-off overvoltage is slightly higher.

Fig. 5. Voltage waveforms of fault current turn-off process of three SSCB topologies.

3.2 Analysis of the Influence Rule of Snubber Circuit Parameters The effect of different capacitance and resistance values on the turn-off overvoltage in the RCD+MOV circuit is given in Fig. 6a. In the RCD+MOV overvoltage suppression circuit, the value of the capacitance affects the charging rate, which in turn affects the rate of change of the turn-off transient overvoltage. From the simulation results, the shutdown overvoltage rise rate reaches 1.4 kV/us with a buffer capacitance of 0.5 uF, the shutdown overvoltage rise rate is 1.3 kV/us with a buffer capacitance of 1 uF, and the shutdown overvoltage reaches 1.2 kV/us with a buffer capacitance of 2 uF. It can be seen that the larger the capacitance of the buffer capacitor C, the smaller the rate of rising of the turn-off overvoltage. In the RC+MOV circuit, the value of the resistance affects the charging rate, which in turn affects the rate of change of the turn-off overvoltage. Also, different resistance values result in different voltage amplitudes across the resistor when charging the buffer

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capacitor, leading to different turn-off overvoltage amplitudes. The simulation results of the waveform are shown in Fig. 6b. When the resistance value of resistor R is 1 , the shutdown overvoltage voltage rise rate reaches 5.6 kV/us, and the amplitude reaches 880 V. When the resistor R is 5 , the shutdown overvoltage rise rate reaches 3.8 kV/us, and the amplitude reaches 870 V. When the resistor R is 10 , the shutdown overvoltage rise rate is only 1.4 kV/us, and the amplitude is only 820 V. It can be seen that the higher the resistance value of the resistor, the higher the rate of rising of the turn-off overvoltage and the larger the amplitude. The SSCB turn-off overvoltage is also affected by the parasitic inductance of the snubber branch and the energy dissipation branch. Figure 7 shows the simulated waveforms of the turn-off overvoltage for three different values of stray inductance of the buffer branch. The results are shown in Fig. 7. When the parasitic inductance of the MOV branch is 10 nH, the shutdown overvoltage rise rate reaches 2.7 kV/us, and the amplitude reaches 850 V. When the parasitic inductance of the MOV branch is 50nH, the shutdown overvoltage rise rate reaches 2.7 kV/us, and the amplitude reaches 790 V. When the MOV branch parasitic inductance is 10 nH, the shutdown overvoltage rise rate reaches 2.7 kV/us, and the amplitude reaches 740 V. From the results, the larger the parasitic inductance of the buffer branch, the larger the increase of the turn-off overvoltage, but the parasitic inductance of the buffer branch does not affect the maximum magnitude of the turn-off overvoltage.

Fig. 6. Impact of the snubber capacitance and resistance on the switch peak voltage: a snubber capacitance, b snubber resistance.

Fig. 7. Impact of the parasitic inductance of snubber branch and energy dissipation branch on the switch peak voltage: a snubber branch, b energy dissipation branch.

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3.3 Experimental Test To verify the feasibility of the design of the overvoltage suppression circuit parameters in this paper, the experimental platform was built according to Fig. 8 experiments. During the experiment, the SiC MOSFET drain-source voltage is measured using a differential probe, and the current flowing through the circuit breaker is measured using a Roche coil, and the experimental parameters are shown in Table 2. The experimental results are shown in Fig. 9. Table 2. Parameters of overvoltage suppression circuits Parameters

Value

Parameters

Value

Input voltage VDC

375 V

Snubber diode

IDW100E60

Capacitor bank C 0

4 mF

Snubber resistor

5

Current limiting inductor L 0

30 uH

Snubber capacitor

2 uF

SiC MOSFET

QPM3-1200-0013D

Metal-Oxide Varistor,

14D431K

The input voltage, V DC

375 V

Snubber diode

IDW100E60

The experimental results show that the SSCB with RCD+MOV overvoltage suppression circuit has a peak overvoltage of 682 V and an average voltage rise rate of 330 V/µs when breaking the 1000 A fault current. This indicates that the designed overvoltage suppression circuit has a very good protective effect. iMOSFET i0 L0

S1

iC

R C

iMOV

R1

Control Circuit

SiC MOSFET

Rogowski DCoil

i0

Oscillograph

MOV C0 S2 DC Source

Differential Probes

uswitch

Main circuit

Fig. 8. Schematic diagram of the test circuit.

The amount of energy stored in the system inductor affects the fault breaking process [10]. Using the RCD+MOV buffer circuit parameters designed in Table 2, change the system time constant for simulation. The parameters of different time constant systems are shown in Table 3. The short-circuit fault simulation of the system with different time constants shows that the fault energy required by the system through MOV is 87 J, 443 J, and 870 J, respectively, as shown in Fig. 10a. In a system of three different time constants, the

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Fig. 9. Experimental results for the RCD+MOV at 375 VDC and 1000 A turn-off current.

breaking waveform of the fault current is shown in Fig. 10b. As you can see, the larger the time constant, the more energy the system needs to dissipate, and the longer the energy dissipation. The RCD+MOV snubber circuits designed in this paper can limit the shutdown overvoltage of the system with different time constants to the target value. Table 3. Parameters of different time constant systems Time constant (ms)

Rs (m)

Ls (uH)

1

0.1

0.1

5

0.1

0.5

10

0.1

1

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a

b

Fig. 10. a Short-circuit fault energy for systems with different time constants. b Short-circuit fault breaking waveforms for systems with different time constants.

4 Conclusion Three overvoltage suppression circuits for low-voltage DC solid state power switches are compared and analyzed in this paper. Experimental and simulation analysis are used to evaluate the performance of the three overvoltage suppression circuits. The simulation and experimental results show that the RCD+MOV circuit can provide better suppression of the peak and rise rate of the solid-state circuit breaker shutdown overvoltage, where the capacitance of the buffer capacitor is the key parameter affecting its suppression effect. The influence of the stray inductance of the buffering branch and the energy dissipating branch on the voltage suppression effect in the RCD+MOV circuit is also analyzed. The results show: This overvoltage suppression circuit is more sensitive to the parasitic inductance of the MOV branch. Acknowledgments. Our research was financed by the Science and Technology Project of State Grid Corporation Research on HVDC Damping Breaking Method and Key Technology (5500202158104A-0-0-00).

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References 1. Gao, Y., Wang, Y.-w., Ma, F.-l.: Study of ultra-high-speed power switching-off of SSCB for coal mine low-voltage system. In: 2011 IEEE Power Engineering and Automation Conference, pp. 349–352 (2011) 2. Shen, Z.J., Sabui, G., Miao, Z., Shuai, Z.: Wide-bandgap solid-state circuit breakers for DC power systems: device and circuit considerations. IEEE Trans. Electron Dev. 62(2), 294–300 (2015). https://doi.org/10.1109/TED.2014.2384204 3. Zhu, F., Liu, F., Liu, W., Feng, K., Zha, X.: Performance analysis of RCD and MOV snubber circuits in low-voltage DC microgrid system. IEEE Appl. Power Electron. Conf. Exposition (APEC) 2017, 1518–1521 (2017) 4. Ren, Y., Yang, X., Zhang, F., Wang, F., Tolbert, L.M., Pei, Y.: A single gate driver based solidstate circuit breaker using series connected SiC MOSFETs. IEEE Trans. Power Electron. 34(3), 2002–2006 (2019) 5. Liu, W., Xiong, X., Yang, H., Feng, K., Liu, F.: Combined optimization of SSCB snubber and freewheeling path for surgeless and quick bus fault interruption in low-voltage DC microgrid. IEEE Energy Convers. Congr. Exposition (ECCE) 2016, 1–5 (2016) 6. Zhao, S., Kheirollahi, R., Wang, Y., Zhang, H., Lu, F.: Implementing symmetrical structure in MOV-RCD snubber-based DC solid-state circuit breakers. In: IEEE Transactions on Power Electronics, vol. 37, no. 5, pp. 6051–6061 7. Giannakis, A., Peftitsis, D.: Performance evaluation and limitations of overvoltage suppression circuits for low- and medium-voltage DC solid-state breakers. IEEE Open J. Power Electron. 2, 277–289 (2021). https://doi.org/10.1109/OJPEL.2021.3068531 8. Liao, X., Li, H., Yao, R., Huang, Z., Wang, K.: Voltage overshoot suppression for SiC MOSFET-based DC solid-state circuit breaker. IEEE Trans. Compon. Packag. Manuf. Technol. 9(4), 649–660 (2019). https://doi.org/10.1109/TCPMT.2019.2899340 9. Liu, F., Liu, W., Zha, X., Yang, H., Feng, K.: Solid-state circuit breaker snubber design for transient overvoltage suppression at bus fault interruption in low-voltage DC microgrid. IEEE Trans. Power Electron. 32(4), 3007–3021 (2017). https://doi.org/10.1109/TPEL.2016. 2574751 10. Park, D., Shin, D., Sul, S.-K., Sim, J., Kim, Y.-G.: Overvoltage suppressing snubber circuit for solid state circuit breaker considering system inductances. In: 2019 10th International Conference on Power Electronics and ECCE Asia (ICPE 2019—ECCE Asia), pp. 2647–2652 (2019). https://doi.org/10.23919/ICPE2019-ECCEAsia42246.2019.8796957

Research on Resonance Problem of DC Feed in AC System Maolan Peng1 , Lei Feng1 , Dachao Huang1 , Hang Liu1 , Xilin Yan1 , Fangqun Liao1 , Shiding Zhou2 , and Shunliang Wang2(B) 1 Maintenance and Test Center, CSG EHV Power Transmission Company, Guangzhou, China 2 School of Electrical Engineering, Sichuan University, Chengdu, China

[email protected]

Abstract. In order to analyze the resonance problem of the DC fed AC system, an oscillation risk analysis method based on s-domain node admittance array is proposed. Based on the equivalent AC network structure, this paper proposes a method to generate the s-domain node admittance matrix of the system based on the node admittance matrix of the power frequency equivalent circuit of the system, and then obtains the resonance mode of the system; Then, based on this, the sensitivity model of the oscillation risk of the AC component parameters in the system resonance mode is constructed, and the sensitivity relationship between the component parameters and the resonance mode in the oscillation frequency range is studied, which can predict the oscillation risk of the DC fed AC system; Finally, the LCC feeding three machine nine node system model is built on PSCAD/EMTDC platform and verified by simulation. The simulation results verify the correctness and effectiveness of the proposed sensitivity analysis method. Keywords: Resonance mode · S-domain node admittance array · DC fed AC system · Sensitivity analysis · Oscillation risk prediction

1 Introduction The new energy power station power supply and the DC converter station power supply are power electronic devices composed of power electronic devices, which have low inertia, fast response, and flexible control, which are very different from the mechanical inertia synchronization and excitation adjustment methods of traditional motors [1–3], and the planning and operation of a large number of high-voltage direct current transmission projects will inevitably increase the proportion of power electronic equipment in the existing power system, which will seriously affect the stability of the power system [4–7]. With access to power electronic equipment such as DC and new energy converters, the dynamic stability problem of AC-DC hybrid systems in the wide frequency band range has been widely studied and paid attention to. Literature [8–10] analyzes the oscillation problems of new energy grid-connected and HVDC transmission systems © by eigenvalue analysis method. Literature [11–15] studies the stability problem of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1076–1082, 2023. https://doi.org/10.1007/978-981-99-4334-0_128

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the inverter when it is connected to the grid based on impedance analysis. Literature [16–19] proposed the method of using the s-domain nodal admittance matrix to analyze the stability of the power system. It is very suitable for the study of harmonic resonance in distribution networks.

2 S-domain Node Admittance Matrix Method The broadband resonance analysis method of power system based on the s-domain node admittance matrix analyzes the network resonance structure of the system by constructing the s-domain node admittance matrix of the AC and DC network, and then finding the zero point of the determinant of the s-domain node admittance matrix and the eigenvector of the corresponding matrix zero eigenvalues to determine whether the system has broadband resonance problems and analyze the corresponding resonance risk [20]. 2.1 Formation of Node Admittance Matrix in S Domain This section proposes a method for generating the s-domain nodal admittance matrix of DC fed into the AC system based on the node admittance array of the equivalent circuit of the AC system under power frequency. The node admittance array is a symmetric array, the non-diagonal elements are mutual admittance, Y ij = M + jN, its value is the negative number of the admittance value of the connecting branch between the nodes, and the connecting branch between the nodes generally is a resistor series inductor, a resistance series capacitor branch, a resistor series inductor-capacitor branch, and an inductor branch. The resistor is connected in series with the inductor branch, so there is Eq. (1) to hold, where ω is the angular frequency corresponding to the system power frequency, so there is ω = 2πf 0 , and f 0 is the system power frequency. −

1 = M + jN R + jωL

(1)

From this, the s-domain expression of the resistor series inductor branch can be solved as shown in Eq. (2). Yij (s) =

1 |M 2 −N 2 |−M 2 −N 2 2M (M 2 +N 2 )

+ s ω(M N2 +N 2 )

(2)

The resistor series capacitor branch is similar to the resistor series inductor branch, where ωL can be replaced with − 1/ωC, so the s-domain expression of the resistor series capacitor branch is shown in Eq. (3). Yij (s) =

1 |M 2 −N 2 |−M 2 −N 2 2M (M 2 +N 2 )

−

Nω s(M 2 +N 2 )

(3)

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The number of resistor series inductor capacitor branches in the system is small, and the capacitor parameter C can be taken as a known quantity, so the s-domain expression can be derived from Eq. (4). Yij (s) =

1 |M 2 −N 2 |−M 2 −N 2 2M (M 2 +N 2 )

+ s( ω(M N2 +N 2 ) +

1 1 ) + sC ω2 C

(4)

The inductor branch can be obtained from Eq. (5) to obtain the s-domain expression as Yij =

Nω s

(5)

The diagonal elements of the node admittance array are self-admittance, Y ii = E + jF, and their value is the sum of all branch admittance of the connected node, so the branch admittance value connected in parallel at node i is   M ) + j(F − N) (6) Yi = (E −

2.2 Resonant Structure of S Domain Node Admittance Matrix Method The s-domain node admittance matrix of the power system is described in Formula (7) [Vf ] = [Yf ]−1 [If ]

(7)

I f , V f , and Y f are the system node injection current matrix, system node voltage matrix, and node admittance matrix at frequency f , respectively. When matrix Y f tends to be singular, serious harmonic resonance will occur, and the voltage of some nodes is very high. In order to analyze its eigenvalue, the matrix Y f can be decomposed as shown in formula (8), so formula (7) can be expressed as formula (9) [Vf ] = [Lf ][f ][Tf ]

(8)

[Tf ][Vf ] = [f ]−1 [Tf ][If ]

(9)

Y f is the eigenvalue matrix, L f and T f are the left and right eigenvector matrices respectively. U f = T f V f is the system modal voltage vector at frequency f , J f = T f I f is the system modal current vector at frequency f. The resonant mode of the power system can be obtained by the determinant zero value of the node admittance matrix in the s domain. So, we can get that the zero point of Y f is sk = −σk + jωk

(10)

where: sk is the kth zero point of matrix Y f determinant, and also represents the kth resonant mode of the system, ωK is the angular frequency. The resonant frequency of the kth resonant mode is f k = ωK /2π.

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3 Analysis of Resonance in DC Feed in AC System The definition of node participation factor matrix of power system network resonance mode is shown in Formula (11), Where, lsk is the left characteristic row vector corresponding to the zero eigenvalue of the node admittance matrix in the s-resonant mode, and rsk is the corresponding right characteristic column vector. ⎛

Psk = rsk l sk

j

⎞ rsk ,1 lsk ,1 · · · rsk ,1 lsk ,j · · · rsk ,1 lsk ,n .. .. .. ⎜ ⎟ ⎜ ⎟ . . . ⎜ ⎟ = ⎜ i ⎜ rsk ,i lsk ,1 · · · rsk ,i lsk ,j · · · rsk ,i lsk ,n ⎟ ⎟ ⎜ ⎟ .. .. .. ⎝ ⎠ . . . rsk ,n lsk ,1 · · · rsk ,n lsk ,j · · · rsk ,n lsk ,n

(11)

The elements psk,ij in the participation factor matrix reflect the influence of node j injection current on node i voltage under sk resonant mode. The sensitivity of eigenvalue to element parameters can be obtained from the partial derivative of node admittance matrix to element parameters, as shown in (11). Therefore, the node participation factor matrix can be defined as the eigenvalue λsk sensitivity matrix of sk , as shown in the following equation ∂λsk = lsk ,i ∗ rsk ,j = Psk ,ji ∂Yij

(12)

The sensitivity of eigenvalue modulus to element parameters can be divided into sensitivity to parallel element ybl = G + jQ and sensitivity to series element zcl = R + jX, whose expressions are [21] d|λk | ∂F Pr λr + Pi λi ∂|λk | = = =μ ∂G dF ∂G λ2r + λ2i d|λk | ∂F Pr λi − Pi λr ∂|λk | = = =ν ∂Q dF ∂Q λ2r + λ2i 

μ X 2 − R2 + 2vRX ∂|λk | =

2 ∂R R2 + X 2 

−2μRX + v X 2 − R2 ∂|λk | =

2 ∂X R2 + X 2

(13)

(14)

(15)

(16)

where: Pλ,ii = Pr + jPi , λsk = λr + jλi , F = |λsk |2 , In addition, it should be noted that parallel components only affect node self admittance, while series components affect self admittance and mutual admittance, The following formula is obtained ∂Y(sk ) ∂Y(sk ) ∂Yii ∂λsk = lk rk = l k rk = Pλsk ,ii ∂ybl ∂ybl ∂Yii ∂ybl

(17)

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∂λsk ∂Y(sk ) = lk rk = Pλsk ,ii − Pλsk ,ij − Pλsk ,ji + Pλsk ,jj ∂ycl ∂ycl

(18)

The sensitivity value of element parameters calculated according to Eqs. (13)–(16) only reflects the relationship between the actual network elements and the amplitude of key eigenvalues. If you need to know the relative influence of each element parameter on the resonant mode, you need to normalize it. The calculation formula is shown in Eq. (19) ∂ λsk = ∂a n

∂ λsk λs k

∂a a

∂ λsk a ∗ = λ s ∂a k

(19)

Fig. 1. a IEEE 9-bus test system; b LCC system at DC side

4 Simulation Result A sensitivity model of component parameters to oscillation risk is constructed to predict the oscillation risk. A 12 pulse LCC system on DC side is shown in Fig. 1(a), and IEEE 9-bus system is shown in Fig. 1(b). The output of the LCC inverter is connected to the B2 bus of the IEEE 9-bus system. To verify the accuracy of sensitivity modeling, this paper verifies the component parameter sensitivity of resonant mode 1,which is at 59.91 Hz. The influence area is mainly the area contained in the dotted line box in Fig. 1(b).The calculation results are shown in a column of Table 1 and compared with the simulation results. Parallel capacitors at nodes 4–9 are simulated, and the result obtained from simulation is shown in Fig. 2. From the simulation data, when 59.91 Hz harmonics are injected and the bus parallel parameters are not changed, the harmonic voltage distortion rates of nodes 4 to 9 are

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Fig. 2. a voltage of Bus 4–9 when switching parallel capacitor at Bus 4; b Harmonic voltage amplitude of Bus 4–9 when switching parallel capacitor at Bus 4; c voltage of Bus 4–9 when switching parallel capacitor at Bus 5; d Harmonic voltage amplitude of Bus 4–9 when switching parallel capacitor at Bus 5

48%, 125%, 52%, 453%, 217% and 61% respectively. The average value of the relative change multiple greater than 0.9 is used to represent the relative influence of each node on the resonant mode. The results are shown in Table 1. It can be seen from the comparison results that the adopted relative sensitivity index is related to the actual voltage distortion, which further confirms our conclusion. Table 1. Harmonic voltage distortion rate and it’s relative change value of each bus node Bus

Sensitivity

Average relative change value

Normalized sensitivity (109 )

4

0.1460

3.03

8141.2

5

0.1446

1.34

8.6428

6

0.1435

1.35

9.1818

7

0.1329

2.77

6219.8

8

0.1331

1.27

5.9088

9

0.1287

3.06

8540.8

5 Conclusion In order to analyze the resonance problem of dc fed ac system, this paper proposes a method based on s-domain node admittance matrix to analyze the oscillation risk of dc fed ac system. A method of generating system s domain node admittance matrix based on the node admittance matrix of equivalent network of DC fed AC system under power frequency is proposed. Based on this method, the system resonance mode is obtained, and the sensitivity model of system component parameters to oscillation risk is established, which provides a reference for the prediction and control of oscillation risk. Finally, a LCC fed IEEE 9-bus system is taken as an example to verify the sensitivity

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of the proposed component parameters. Simulation results show the effectiveness of the proposed method.

References 1. An, T., Bjarne, A., Norman, M.: Review of China-Europe high voltage DC power grid technology forum. Power Grid Technol. 41(08), 2407–2416 (2017) 2. Xu, Z., Xue, Y., Zhang, Z.: Key technologies and prospects of flexible DC transmission for large capacity overhead lines. Proc. CSEE 34(29), 5051–5062 (2014) 3. Tan, Z., Chen, K., Li, W.: Issues and solutions of China’s generation resource utilization based on sustainable development. J. Mod. Power Syst. Clean Energy 2, 14 (2016) 4. Ma, N., Xie, X., He, J.: A review on wide-frequency oscillation of power systems with high proportion new energy and power electronic equipment. Proc. CSEE, 20 40(15), 4720–4732 5. Jiang, Q., Wang, L., Xie, X.: Research on oscillation problem of electronic power system and its suppression measures. High Voltage Technol. 43(04), 1057–1066 (2017) 6. Wang, L., Xie, X., Jiang, Q.: Investigation of SSR in practical DFIG-based wind farms connected to a series-compensated power system. IEEE Trans. Power Syst. 30(5), 2772–2779 (2015) 7. Li, Mj., Yu, Z., Xu, T.: Research on complex oscillation caused by new energy grid connection system and its countermeasures. Power Grid Technol. 41(04), 1035–1042 (2017) 8. Xu, Z., Wang, S., Xing, F.: Qualitative analysis method of electric network resonance stability. Electr. Power Constr. 38(11), 1–8 (2017) 9. Gao, B., Liu, Y., Song, R.: Study on subsynchronous oscillation characteristics of doubly fed wind farm via LCC-HVDC. Proc. CSEE 40(11), 3477–3489 (2020) 10. Fan, L., Zhu, C., Miao, Z.: Modal analysis of a DFIG-based wind farm interfaced with a series compensated network. IEEE Trans. Energy Convers. 26(4), 1010–1020 (2011) 11. Fan, L., Miao, Z.: Nyquist-stability-criterion-based SSR explanation for type-3 wind generators. IEEE Trans. Energy Convers. 27(3), 807–809 (2012) 12. Lyu, J., Cai, X., Molinas, M.: Frequency domain stability analysis of MMC-based HVDC or wind farm integration. IEEE J. Emerg. Sel. Top. Power Electron. 4(1), 141–151 (2016) 13. Khazaei, J., Beza, M., Bongiorno, M.: Impedance analysis of modular multi-level converters connected to weak AC grids. IEEE Trans. Power Syst. 33(4), 4015–4025 (2018) 14. Liu, B., Hu, Y., Su, W.: Stability analysis of DFIG wind turbine connected to weak grid based on impedance modeling. In: 2019 IEEE Power Energy Society General Meeting, pp. 1–5. IEEE, Atlanta, GA, USA (2019) 15. Wang, X., Blaabjerg, F., Wu, W.: Modeling and analysis of harmonic stability in an AC powerelectronics-based power system. IEEE Trans. Power Electron. 29(12), 6421–6432 (2014) 16. Semlyen, A.: s-domain methodology for assessing the small signal stability of complex systems in nonsinusoidal steady state. IEEE Trans. Power Syst. 14(01), 132–137 (1999) 17. Gomes, Jr, S., Martins, N., Portela, C.: Modal analysis applied to s-domain models of AC networks. In: Power Engineering Society Winter Meeting, pp. 1305–1310. IEEE, Columbus, OH, USA (2001) 18. Xu, Z.: Three technical challenges faced by power grids with high proportion of nonsynchronous machine sources. South. Power Syst. Technol. 14(02), 1–9 (2020) 19. Liu, Y., Shuai, Z., Li, Y.: Harmonic resonance modal analysis of multi-inverter grid-connected systems. Proc. CSEE 37(14), 4156–4164 (2017) 20. Xing, F.: Research on Broadband Resonance Problems of Power System with NonSynchronous Generators, Zhejiang University (2021) 21. Yang, C.: Application of Modal Analysis on Harmonic Resonance Problem and Its Sensitivity Analysis in Power System, Wuhan University (2010)

Online Estimation of the Variable Inertia of DFIG Units Via an Improved Least Squares Method Ye He1 , Guangzeng You1 , Wei Guo2(B) , Peng Sun1 , Yixuan Chen1 , Run Huang1 , and Wuqi Zhang2 1 Power Grid Planning and Construction Research Center of Yunnan Power Grid Co., Ltd.,

Kunming, China 2 College of Electrical and Information Engineering, Hunan University, Changsha, China

[email protected]

Abstract. As more and more synchronous generator units are being replaced, the system inertia of synchronous machines is being reduced. In order to improve the inertia of the system, the renewable energy resources are required to provide inertia support to ensure the normal and stable operation of the power grid. This means that it is necessary to accurately assess the inertia of renewable energy resource. Therefore, this paper proposes an online evaluation method for the variable inertia of DFIG based on the variable forgetting factor recursive least squares (VFFRLS) method. First, due to the change of wind turbine output power with wind speed, the wind turbine is utilized to inject a disturbance via controlling the output power. Then, the inertial power and node frequency are obtained through calculation and measurement, and constructs an unknown parameter vector. Finally, an iterative solution based on VFFRLS is performed to obtain the online evaluation result of inertia and verified in 9-bus test system. Simulation results demonstrate the stability and accuracy of VFFRLS. Keywords: Renewable energy · Variable forgetting factor recursive least squares method · Online evaluation · Variable inertia

1 Introduction To achieve the goal of the carbon neutrality, an increasing number of renewable energy resources are being connected into the power grid. Therefore, the installed traditional thermal power units are reducing. These would accelerate the power grid shift towards a power system with high penetration of renewable energy resources [1, 2]. For example, in recent years, the installed capacity of photovoltaics and wind power in China has increased significantly. It is estimated that by 2035 the installed renewable energy capacity will surpass thermal power units as the largest source of electricity supply [3]. In general, the renewable energy connected to the main grid through power electronic interface. Hence, the frequency fluctuation in the grid side decoupled from the power response in converter side [4, 5]. This means, the renewable energy units under the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1083–1092, 2023. https://doi.org/10.1007/978-981-99-4334-0_129

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normal control schedule cannot provide power rescue when the grid suffered frequency disturbance, which greatly reduced the inertia of the actual power grid side. Thereby, it brings a serious challenge for the safe operation of the power system [6]. In order to improve the inertia support in the power system with high penetration of power electronic-interfaces, the virtual inertia control technology is developed by the means of adding frequency deviation signal of the grid into the power control loop, which makes converters exhibit terminal behavior that is similar to synchronous units [7, 8]. On the background of the power system with gradually decreasing synchronous inertia, the ability to accurately track the inertia providing by renewable energy resources in the power system is crucial for planners and operators of the power system. In general, the inertia of synchronous units is a constant parameter, which can be obtained by relatively mature online and offline evaluation methods. For example, the inertia of the synchronous generator can be estimated from the data obtained by the phase measurement unit (PMU) for a certain disturbance [9]. Or based on the rich historical data of system inertia and frequency fluctuations, the evaluation of synchronous inertia can be realized via machine learning [10]. However, the virtual inertia of renewable energy resource is usually affected by the weather conditions and its control topology. On the other hand, the inertia support from renewable resource exits some delay comparing with the traditional synchronous inertia. Therefore, there are many problems in accurately assessing the virtual inertia level [11, 12]. To overcome these drawbacks, in this paper, a recursive least squares method based on variable forgetting factor is proposed which can follow the so-called variable virtual inertia provided by non-synchronous units in real time. And case studies on a modified 9-bus system demonstrate the accurate of the proposed VFFRLS approach for tracking the variable inertia of the wind generators.

2 Modeling of Virtual Inertia Control for the DFIG 2.1 Virtual Inertia Control Virtual inertia control enables DFIG to exhibit a power response similar to that of a synchronous machine [13, 14]. In this way, DFIG can release or absorb kinetic energy. The released or absorbed kinetic energy can be expressed as Eq. (1). Where the basic parameters Jr can be obtained from the data on the nameplate, ω0 can be obtained from the real-time measurement data in DFIG and the value is approximately 1.0 (p.u.), ωs is the system synchronous speed. E=

1 1 2 Jr (ω2 − ω02 ) = J (ωs2 − ωs0 ) 2 2

(1)

There is a differential relationship between power and kinetic energy, so the output power expression of DFIG can be written as Eq. (2). Based on the inertia definition [15], the inertia expression of DFIG can be obtained as Eq. (3).  d ω ωn df dE = Jr ωωn = Jr ωωn (2)  Pvir = dt dt dt

Online Estimation of the Variable Inertia of DFIG Units

H=

En 1 Jr ωn2 = · Sn 2 Sn

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(3)

where Sn is the rated power of DFIG and En is the kinetic energy at the rated speed ωn . Substituting Eq. (3) into Eq. (2) and expressing it in per-unit value, we can get Eq. (4) and each parameter in formula is per unit value.  Pvir = 2Hvir

df dt

(4)

2.2 Analysis of Variable Inertia Virtual inertia control of DFIG provides power response and frequency support by tracking grid frequency changing, absorbing or releasing rotor kinetic energy. The virtual inertia response is related to the maximum kinetic energy of DFIG. Figure 1 shows the operation of DFIG in different scenes [16]. In the condition of low wind speed (5 m/s ≤ v < 6.4 m/s), the DFIG is in the start-up phase and don’t involve in frequency response. In the condition of middle wind speed (6.4 m/s ≤ v < 11 m/s), the output power runs at the highest point under Maximum Power Point Tracking (MPPT). Under the condition of high wind speed (v > 11 m/s), when the rotor speed reaches the maximum value, the rotor speed can only be reduced and can only respond to the increasing of load. When DFIG is running normally, the rotor has a minimum speed ωmin . Therefore, there is an upper limit on the maximum kinetic energy that can be released, and the rotor cannot fully release the kinetic energy it has. Similarly, when the rotor speed exceeds the cut-out wind speed, the wind turbine will automatically cut off. Therefore, the rotor also has an upper limit on the kinetic energy that can be absorbed. The rotor speed is ω, the maximum available kinetic energy is E=

1 1 Jr ω2 − Jr ωr2 min 2 2

(5)

Combined with the above analysis, the releasable kinetic energy at different wind speed levels can be expressed as ⎧ vw0 < 6.4 m/s, vw0 > 14 m/s ⎪ ⎨0 2 λopt 2 J 2 E= (6) ⎪ 2 ( R2 vw0 − ωrmin ) 6.4 m/s ≤ vw0 < 11 m/s ⎩ J 2 2 2 (ωrmax − ωrmin ) 11 m/s ≤ vw0 ≤ 14 m/s where λopt is optimum tip-speed ratio. λopt means when the DFIG is working in the MPPT area, there is an optimal tip ratio so that the DFIG can obtain the maximum kinetic energy of the rotor. λopt can be expressed as λopt =

ωr0 R v0

(7)

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Fig. 1. Operational curve of DFIG.

Refer to the derivation process of Eqs. (1)–(4), the inertial power generated by the kinetic energy of the rotor can be expressed as ⎧ ⎪ vw0 < 6.4 m/s, vw0 > 14 m/s ⎨0 J λopt ωn df (8) PI = ( R vw0 ) · dt 6.4 m/s ≤ vw0 < 11 m/s ⎪ ⎩ (J ω ω ) · df 11 m/s ≤ v ≤ 14 m/s n max w0 dt The variable virtual inertia of DFIG can be expressed as ⎧ ⎪ vw0 < 6.4 m/s, vw0 > 14 m/s ⎨0 ωn H = J λopt vw0 6.4 m/s ≤ vw0 < 11 m/s ⎪ ⎩ J ωR ω n max 11 m/s ≤ vw0 ≤ 14 m/s

(9)

3 Evaluation Method 3.1 Identification Model Considering that the operating conditions of the wind turbines in the wind farm will change with the wind speed, the mechanical power Pwm of the wind turbines can be regarded as the input disturbance of the grid and can be expressed as Eq. (10) [17]. Where kw is a constant in the aerodynamic equation of the DFIG. Pwm = kw ω3

(10)

After the virtual inertia control of the DFIG is enabled, the electromagnetic power becomes Pwe . Then, the inertial response power Pvir can be expressed as the difference between Pwm and Pwe . Pvir = Pwm − Pwe

(11)

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Combining Eq. (10) and Eq. (11), we can complete the model of the power disturbance, and then calculate the inertial power. Combined with the analysis in Sect. 2.2, the discrete expression of the variable virtual inertia identification model can be obtained as Eq. (12). Pvir (k) = 2H

f (k + 1) − f (k) Ts

(12)

where k represents the kth moment when the system is running, and Ts represents the sampling time. Expressing Eq. (12) in least squares form, we can get y(k) = ϕ T (k)θ (k). (k) is the input matrix of the system and Where y(k) = Pvir (k) and ϕ(k) = f (k+1)−f Ts θ (k) = 2H is the parameter matrix to be identified. 3.2 Least Squares Algorithm The least square method finds the optimal parameters by minimizing the square of the error Eq. (13) to realizes the identification of the system parameters [18]. With the continuous development of the theory, there are many improved least squares algorithms, such as recursive least squares, forgetting factor recursive least squares, variable forgettable factor recursive least squares and so on. With the increase of data, the recursive least squares method will appear data saturation. This will reduce the impact of newly acquired data on the identification results, and will not enable online parameter identification. After introducing the forgetting factor, the real-time influence of new data on the identification results is enhanced, and the tracking ability of the algorithm is improved. But the setting of forgetting factor depends on human experience. When the forgetting factor is set too large, the tracking ability of the algorithm decreases. If the forgetting factor is too small, the tracking performance will be improved, but the identification result will fluctuate greatly, which is not stable. After the introduction of a variable forgetting factor, the forgetting factor will be adjusted according to the real-time characteristics of the collected data to dynamically improve the tracking ability and stability of the algorithm, thus realizing the rapid identification of parameters [18]. min

N 

[y(k) − ϕ T (k)θ (k)]2

(13)

k=1

Recursive Least Squares (RLS) When the identified parameters change abruptly, the traditional recursive least squares method can track parameter by periodically resetting the covariance matrix G. By introducing Sherman-Morrison-Woodbery Formula shown as Eq. (14), recursive least squares method can be expressed as Eq. (15). (A + UV )−1 = A−1 − (A−1 U )(I + VA−1 U )−1 (VA−1 )

(14)

⎧ T ⎪ ⎨ θ (k) = θ (k − 1) + L(k)[y(k) − ϕ (k)θˆ (k − 1] G(k−1)ϕ(k) L(k) = 1+ϕ T (k)G(k−1)ϕ(k) ⎪ ⎩ G(k) = [I − L(k)ϕ T (k)]G(k − 1)

(15)

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where G(0) and θ (0) need to be defined. G(0) is the covariance matrix, usually defined as G(0) = αI , L(k) is the gain matrix and α is a large enough number. θ(0) take a positive real number that is small enough. Forgetting Factor Recursive Least Squares (FFRLS) If the identified parameters change slowly, the recursive least squares method has its limitations. As the amount of data increases, the covariance matrix G will become smaller and smaller, and the ability to correct the parameter estimation matrix θ will decrease [19]. Then, the error of real-time parameter identification will become larger and larger. To prevent the parameter hysteresis problem caused by data saturation, recursive least squares method with forgetting factor is usually used. After introducing the forgetting factor μ, the Eq. (15) can be changed to Eq. (16). The forgetting factor is μ = 0.9–1.0. ⎧ T ⎪ ⎨ θ (k) = θ (k − 1) + L(k)[y(k) − ϕ (k)θ (k − 1)] G(k−1)ϕ(k) L(k) = μ+ϕ T (k)G(k−1)ϕ(k) (16) ⎪ ⎩ G(k) = μ−1 [I − L(k)ϕ T (k)]G(k − 1) Variable Forgetting Factor Recursive Least Squares (VFFRLS) On the basis of the forgetting factor recursive least squares method, a dynamically changing forgetting factor is added to improve the tracking ability and stability of the algorithm, so as to achieve the purpose of accurate and rapid identification. The forgetting factor μ can be expressed as Eq. (17). α is a coefficient.  α μ(k) = (1 − α) + 1+ε(k) (17) ε(k) = y(k) − ϕ T (k)θ (k − 1) The method for evaluating the variable inertia of DFIG based on the variable forgetting factor recursive least square method is described as follows: Step 1: Initialize the covariance matrix G(0), and assign an initial value θ (0) to the inertia. Step 2: Introduce variable forgetting factor to improve tracking ability and stability of the algorithm. Step 3: Calculate the gain matrix L(k). Step 4: Solve the value θ (k). Update the covariance matrix G(k), and repeat steps 2 to step 4.

4 Examples and Simulations In this section, we apply the proposed algorithm for online evaluation of the maximum available inertia of a DFIG in the modified IEEE 9-bus system, in which a synchronous generator unit is replaced by a DFIG with the same capacity. The random disturbance changes with the variable wind speed, and the wind energy captured by the DFIG can be estimated by the aerodynamic model. There have been many achievements in the

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research on inertia identification of synchronous units based on the least squares method [20], which will not be repeated in this paper. All simulation were performed on a personal computer based on the Matlab/Simulink package with a core i7, 2.50 GHz CPU and 16 GB RAM. 4.1 Real-Time Data Curve

Fig. 2. Power response curve. a Measured electromagnetic power of the DFIG; b Mechanical power obtained by theoretical calculation; c Inertial power calculated from (a) and (b).

In the actual power grid, the wind speed is collected every 15 min, and the node frequency and output electromagnetic power of the wind turbine can be obtained by real-time sampling of the PMU. Take the wind speed data of one hour in a certain day as an example, assuming that the wind speed remains unchanged after sampling. The wind speed is 5 m/s between 0 and 15 min, 9 m/s between 15 and 30 min, 6.5 m/s between 30 and 45 min, and 13 m/s between 45 and 60 min. By sampling the output node of the DFIG, the change in the output power of the DFIG can be obtained as shown in Fig. 2a. According to the assumed wind speed, the theoretical mechanical power of the DFIG can be obtained from Eq. (10), as shown in Fig. 2b. The inertial power obtained from the Eq. (11) is shown in Fig. 2c. According to Figs. 2c and 3, the vector y(k) and the vector ϕ(k) can be obtained. 4.2 Real-Time Evaluation Curve The results of evaluation of the variable inertia of the DFIG by RLS, FFRLS and VFFRLS are shown in Fig. 4. The simulation results of the RLS algorithm in 900–1800 s are close

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Fig.3. Frequency response curve.

to the results of the VFFRLS algorithm, and the error is small. However, due to the shortcoming of data saturation in the RLS algorithm, the error in subsequent continuous estimation becomes larger and larger and the maximum error can reach 10%. Also, the real-time change of DFIG inertia cannot be accurately tracked.

Fig. 4. Inertia evaluation results.

Compared with the RLS algorithm, the FFRLS algorithm introduces a forgetting factor, which weakens the role of past data and enhances the algorithm’s tracking effect on inertia changes. The best forgetting factor μ is set to 0.96. However, it can be seen from Fig. 4 that the evaluation results of the FFRLS algorithm have larger oscillations and the stability is not high enough compared to VFFRLS.

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Intuitively, online inertia evaluation with VFFRLS has higher followability and accuracy. The α in the VFFRLS algorithm is 0.95. The average errors of the evaluation results using the VFFRLS algorithm in the three stages are 5%, 3.9% and 4.1%, respectively. In contrast, VFFRLS has more advantages and is more suitable for real-time estimation of DFIG inertia.

5 Conclusion In this paper, three improved methods of least squares (RLS, FFRLS and VFFRLS) are used to evaluate the variable inertia of the DFIG. The real-time inertia curve is obtained through iterative calculation based on the nodal power and frequency from measurement data. It can be seen from the evaluation result curve that the proposed VFFRLS method with real-time variable forgetting factors has better stability and following performance than FFRLS and RLS, and is more suitable for online evaluation of the variable virtual inertia of the DFIG. Acknowledgements. This research was supported by the Science and Technology Program of Yunnan Power Grid Co., Ltd (0500002022030203GH00046).

References 1. Wang, W., Li, G., Guo, J.: Large-scale renewable energy transmission by HVDC: challenges and proposals. Engineering (2022). ISSN 2095-8099 2. Xiaohuang, L.I.N., Yunfeng, W.E.N., Weifeng, Y.A.N.G.: Inertia security region: concept, characteristics, and assessment method. Proc. CSEE 41(09), 3065–3079 (2021) 3. Chen, G., Li, M., Xu, T., et al.: The practice and challenges of our country’s power grid supporting the development of renewable energy. Power Syst. Technol. 41(10), 3095–3103 (2017) 4. Lv, Z., Zhong, Q.C.: Control of modular multilevel converters as virtual synchronous machines. IEEE Power Energ. Soc. Gen. Meet. 2017, 1–5 (2017) 5. Yunfeng, W.E.N., Weifeng, Y.A.N.G., Ronghua, W.A.N.G., et al.: Review and prospect of toward 100% renewable energy power systems. Proc. CSEE 40(06), 1843–1856 (2020) 6. Tongsen, W., Xuekun, C.: Control strategy of variable droop coefficient for DFIG turbines considering speed limit. Power Syst. Prot. Control 49(09), 29–36 (2021) 7. Nguyen, H.T., Yang, G., Nielsen, A.H., et al.: Combination of synchronous condenser and synthetic inertia for frequency stability enhancement in low-inertia systems. IEEE Trans. Sustain. Energy 10(3), 997–1005 (2019) 8. Ghosh, R., Tummuru, N.R., Rajpurohit, B.S., et al.: Virtual inertia from renewable energy sources: mathematical representation and control strategy. In: 2020 IEEE International Conference on Power Electronics, Smart Grid and Renewable Energy (PESGRE2020), pp. 1–6 (2020) 9. Susuki, Y., Hamasaki, R., Ishigame, A.: Estimation of power system inertia using nonlinear Koopman modes. In: 2018 IEEE Power & Energy Society General Meeting (PESGM), pp. 1–5 (2018) 10. Cao, X., Stephen, B., Abdulhadi, I.F., et al.: Switching Markov Gaussian models for dynamic power system inertia estimation. IEEE Trans. Power Syst. 31(5), 3394–3403 (2016)

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11. Phurailatpam, C., Rather, Z.H., Bahrani, B., et al.: Estimation of non-synchronous inertia in AC microgrids. IEEE Trans. Sustain. Energ. 12(4), 1903–1914 (2021) 12. Zhang, W., Wen, Y., Chi, F., et al.: Research framework and prospect on power system inertia estimation. Proc. CSEE 41(20), 6842–6856 (2021) 13. Chamorro, H.R., et al.: Analysis of the gradual synthetic inertia control on low-inertia power systems. In: 2020 IEEE 29th International Symposium on Industrial Electronics (ISIE), pp. 816–820 (2020) 14. Kerdphol, T., Rahman, F.S., Watanabe, M., et al.: Enhanced virtual inertia control based on derivative technique to emulate simultaneous inertia and damping properties for microgrid frequency regulation. IEEE Access 7, 14422–14433 (2019) 15. Daly, P., Flynn, D., Cunniffe, N.: Inertia considerations within unit commitment and economic dispatch for systems with high non-synchronous penetrations. In: 2015 IEEE Eindhoven Power Tech. IEEE, Eindhoven, Netherlands (2015) 16. Demirkov, B., Zarkov, Z.: Study of two MPPT methods for high inertia wind turbine with direct driven PMSG. In: 2018 20th International Symposium on Electrical Apparatus and Technologies (SIELA), pp. 1–4 (2018) 17. Ndirangu, J., Nderu, J., Irungu, G.: Impact of variation of virtual inertia and virtual damping on frequency and power angle responses of virtual inertia emulation controlled converter. IEEE PES/IAS Power Africa 2022, 1–4 (2022) 18. Liu, Z., Yang, M., Xu, D.: A novel algorithm for online inertia identification via adaptive recursive least squares, IECON 2017–43rd Annual Conference of the IEEE Industrial Electronics Society, pp. 2973–2978 (2017) 19. Jayaraman, G.P., Lunzman, S.V.: Parameter estimation of an electronic load sensing pump using the recursive least squares algorithm. In: 49th IEEE Conference on Decision and Control, pp. 3445–3450 (2010) 20. Li, S., Huang, S., Li, H., et al.: Correction estimation of inertia of power plant considering the contribution of rotating load [J/OL]. Power Syst. Prot. Control 1–11 [2022-09-14]

Modeling of 12-Pulse LCC Converter Station Based on Harmonic State Space Theory Maolan Peng1 , Hang Liu1 , Lei Feng1 , Dachao Huang1 , Yuan Zhao2 , Yang Xie2 , Shunliang Wang2(B) , and Junpeng Ma2 1 Maintenance and Test Center, CSG EHV Power Transmission Company, Guangzhou, China 2 School of Electrical Engineering, Sichuan University, Chengdu, China

[email protected]

Abstract. To analyze the effect of harmonics on the stability of line commutated converter based high voltage direct (LCC-HVDC), an accurate LCC-HVDC model from commutated converter based high voltage Direct (LCC-HVDC) should be established, taking harmonic coupling into account. Based on the theory of harmonic state space (HSS), the impedance model of 12 pulsating LCC converter station is built. The impedance model takes into account not only the dynamic characteristics and frequency coupling effect of the LCC, but also the dynamic characteristics of the AC filter and the AC/DC system of the LCC converter station. The detailed modeling of the control system is also carried out. The DC harmonic impedance model is consistent with the sweep results in a wider frequency band, which greatly improves the accuracy of mathematical modeling of the LCC converter station by using HSS. Finally, the accuracy and effectiveness of the proposed LCC-HSS impedance model are verified by comparing the electromagnetic transient simulation results of PSCAD with the calculated results of HSS impedance model. Therefore, this study not only lays a foundation for stability evaluation and parameter optimization of LCC systems, but also paves the way for impedance modeling of LCC converter stations in other operating modes. Keywords: Harmonic state space · HVDC transmission · Small signal model · Harmonic impedance

1 Introduction Due to the uneven distribution of energy and load in China, in order to achieve the optimal allocation of resources, high voltage direct current (HVDC) technology has been a lot of research and rapid development. Line commutated converter (LCC) is an important part of the HVDC transmission system because of its large transmission capacity, low cost and mature technology [1, 2]. At present, scholars at home and abroad have done a lot of research on modeling and harmonic transfer characteristics of LCC-HVDC. Literature [3] used several formulas to describe the AC/DC voltage relationship on both sides of LCC converter, and established a six pulse LCC-HVDC small signal model. Literature [4] transformed © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1093–1100, 2023. https://doi.org/10.1007/978-981-99-4334-0_130

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LCC-HVDC model into dq coordinate system and established 12 pulsation LCC-HVDC model. Literature [5] divided the LCC-HVDC system at both ends into AC system, DC system, control system and converter, respectively established each system, and then connected each system as a whole by eliminating intermediate variables, establishing a small signal model of dual ended LCC-HVDC. Literature [6, 7] respectively established the small signal model of multi-infeed LCC-HVDC system and the interconnected system model of multi input and multi output. However, none of the above documents clearly explained the harmonic transmission characteristics of LCC-HVDC system. In terms of modeling method, the literature [8, 9] established the small signal model of LCC-HVDC by using the AC/DC quasi steady state relationship of LCC-HVDC, but did not consider the dynamic process of converter switching and the dynamic change of DC current. Literature [10, 11] uses the dynamic phasor method to model LCC-HVDC. The model has high accuracy and can be used to analyze the harmonic transmission mechanism. However, when considering the higher order components, the complexity of the model will increase dramatically. Literature [12] proposed the harmonic state space (HSS) method. This method makes use of the feature that time domain and frequency domain can be transformed equivalently, so that the time variable is represented by a constant, realizing the stabilization of the time-varying model of the multi harmonic converter, greatly reducing the difficulty of mathematical modeling, and facilitating harmonic analysis and calculation. At present, the application of HSS in the electrical field mostly lies in the research of voltage source converter. For example, the literature [13–16] established the small signal models of voltage source converter and modular multilevel converter based on the harmonic state space method and considering the interaction between internal harmonics, and the modeling results are very accurate. But few articles use harmonic state space method to model LCC-HVDC. In Literature [17–20], considering the harmonic coupling characteristics and based on the harmonic state space theory, a twelve pulse LCC-HVDC HSS model was established, but the influence of AC transformer and control system was not built into the state space matrix, which may lead to inaccurate model. In this paper, considering the AC filter of LCC converter station, the dynamic characteristics of AC/DC system, and the change of trigger angle under constant current control, LCC-HVDC impedance model is established based on harmonic state space theory. This model can reflect the internal dynamic characteristics and frequency coupling effects of LCC. The established AC/DC harmonic impedance model can match the sweep results in a wider frequency band, greatly improving the accuracy of mathematical modeling of LCC converter station using HSS, providing a more accurate model for LCC system stability analysis and parameter optimization, and can adapt to the impedance modeling of LCC converter station under other working models.

2 HSS Impedance Model of 12 Pulsating LCC Converter Station This paper takes the 12 pulse LCC converter station operating in the rectifier mode as an example, and its equivalent circuit structure is shown in Fig. 1. Uacj, iacj, Rdcr, Ldcr and Idcr are AC side voltage, AC side current, DC side equivalent resistance inductance and DC side current, respectively. Two converter transformers are connected at the AC

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side. One LCC converter transformer is Y- connected (the  side line voltage is 300 ahead or behind the Y side, and the  side line voltage is 300 behind the Y side in this subsection). The other LCC converter transformer is Y-Y connected. Rdcr

idcr

iac Uacj

iacj2

Y-

iacj

ud LCC1

iacY

AC filter Y-Y

Ldcr

ud

v dcr

udY LCC2

Fig. 1. Topology of 12-pulse LCC converter station.

2.1 Open Loop Time-Domain Mathematical Model of Pulsating LCC Converter Station Before establishing the mathematical model of the 12 pulse LCC converter station, the mathematical model of the 6-pulse converter circuit should be established. When the system operates stably, the voltage and current at its AC and DC sides can be expressed by switching function ⎧ ⎪ i = swj idcr ⎪ ⎨ acj  ud = swj uacj (1) j=A, B, C ⎪ ⎪ ⎩ vdcr = ud − Rdcr idcr − Ldcr didtdcr Swj is the three-phase switching function of LCC converter, which is jointly determined by the output of phase locked loop and trigger angle of LCC converter station. In this paper, LCC converter is triggered at equal intervals, and its three-phase switching function expression is ⎧ ∞  ⎪ nπ nπ 4 ⎪ s = wA ⎪ nπ sin 2 cos 6 cos[n(θ − α)] ⎪ ⎪ n=1 ⎪ ⎨ ∞  

 4 swB = sin nπ cos nπ cos n θ − 2π −α (2) nπ 2 6 3 ⎪ n=1 ⎪ ⎪ ∞ ⎪  

 ⎪ nπ nπ 2π 4 ⎪ ⎩ swC = nπ sin 2 cos 6 cos n θ + 3 − α n=1

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When the LCC operates stably and the voltage and current at the AC side are three-phase symmetrical, the three-phase model shown in Eqs. (1)–(2) can be simplified into a single-phase model as follows through positive and negative zero sequence decomposition, and the results are as follows ⎧ ⎨ iac = sw idcr  (3) u = L−1 3[sw (ω)uac (ω)]0 ⎩ d vdcr = ud − Rdcr idcr − Ldcr didtdcr In the formula, the superscript 0 represents the zero-sequence component of the variable, and L−1 represents the pull inverse transformation. 2.2 HSS Open-Loop Impedance Model of 12 Pulsating LCC Converter Station It can be seen from Fig. 1 that the 12 pulse LCC converter station is formed by cascading two six pulse LCC DC sides. For the establishment of the mathematical model of the 12 pulse LCC converter station, the mathematical modeling results of the six pulse LCC can be expanded. It can be seen from the previous derivation that the main factor causing nonlinearity in Eq. (3) is sw, and sw is actually a nonlinear function of the firing angle α. To facilitate mathematical processing, first linearize the sw in Eq. (3), we can get:

Mejn(ϕ−α) (1 + jnθ − jnα)ejnω1 t (4) sw = n∈Z,n=0

When considering the open loop state, θ = α = 0. The open loop HSS small signal mathematical model of the 12 pulse LCC converter can be obtained by writing Eq. (4) into the state space form as follows: sX lccop = (Alccop − Q)X lccop + Blccop U lccop

(5)

First, according to Eq. (6), the intermediate matrix of open-loop HSS impedance introduced into the 12 pulse LCC converter is T lcc_ op = −(Alcc − Q)−1 Blcc

(6)

According to Eqs. (6)–(7), it can be obtained that the open-loop HSS DC impedance model of the 12 pulse LCC converter is  Zdc_ LCC_ op ωp =

1 T op (46, 4) ∗ 3

(7)

2.3 HSS Closed-Loop Impedance Model of 12 Pulsating LCC Converter Station Compared with the control system of MMC converter station, LCC control system is relatively simple, usually with constant voltage control and constant current control. The constant current PI control adopted in this paper is shown in Fig. 2.

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Fig. 2. Constant-current control block diagram

Therefore, the firing angle α under constant current control can be expressed as: α(ω) = π − GPI (ω)[idcrref (ω) − idcr (ω)G1 (ω)]

(8)

Through Eq. (10), it can be obtained that the small signal model of harmonic state space for constant current control of 12 pulse LCC converter station is: α = GPI G1 idcr

(9)

In order to unify the expression and facilitate the control system to be connected to the converter, Eq. (12) is converted into the state space form: sX clcc = (Aclcc − Q)X clcc + Bclcc U clcc

(10)

Since the influence of phase-locked loop is not considered temporarily in this paper, θ = 0. In order to verify the accuracy of the established HSS small signal mathematical model of the LCC control system, the established HSS small signal mathematical model of the control system is first connected to the open-loop HSS model to form a complete LCC closed-loop HSS small signal mathematical model. Finally, the LCC closed-loop HSS model and its HSS impedance model can be obtained through this closed-loop mathematical model using the same method as in Sect. 2.2.

3 Simulation Verification 3.1 Open Loop HSS Impedance Model Verification The 12 pulse LCC-HSS open-loop impedance model is compiled with computer software, and the LCC converter model with the same parameters is built and simulated with PSCAD software. Table 1 lists the system parameters of the simulation model. The open-loop harmonic impedance of 12 pulse LCC is calculated by the established HSS open-loop impedance model, as shown in Fig. 3. The simulation value in the figure is obtained by the established PSCAD model impedance sweep. It can be seen from Fig. 4 that the calculated results of the 12 pulse LCC open-loop HSS impedance model established in this section and the swept frequency results of the PSCAD simulation model achieve high-precision coincidence in the whole measurement frequency range (1–2000 Hz), which also verifies the correctness of the 12 pulse LCC converter station open-loop HSS impedance model proposed in this section.

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Parameter

Company

Value

Effective value of AC side line voltage

kV

500

DC system equivalent inductance

mH

300

DC system equivalent resistance



1

Transformer ratio

–

500/167

Steady state value of trigger angle α

°

0.4188

Steady state value of DC current

kA

2.53465

80

Mag/dB

Mag/dB

100 50 0 -50 100

Simulation result HSS 10

1

10 3 o

0 -100 10

40

100

Phase angle/

o

Phase angle/

100

1

Simulation result HSS

20 10 2

200

-200 0 10

60

10 Frequency/Hz (a)

2

10

3

1

10 2

10 3

1

10 2 Frequency/Hz (b)

10 3

10

150 100 50 0 -50

-100 0 10

10

Fig. 3. 12-pulse LCC open-loop AC/DC harmonic impedance amplitude-frequency diagram a DC side harmonic impedance diagram; b AC side harmonic impedance diagram.

3.2 Verification of Closed Loop HSS Impedance Model Similarly, the established LCC closed-loop HSS impedance model is realized by computer code, and a simulation model with the same parameters is built in the PSCAD software. The accuracy of the LCC-HSS impedance model established in this section is verified by comparing the impedance value obtained from the frequency domain scanning of the PSCAD simulation model with the impedance value calculated by the HSS small signal mathematical model, as shown in Fig. 4. By comparing the calculation results of the HSS mathematical model with the frequency sweep results of the PSCAD simulation model, it can be seen that the calculation results of the closed-loop HSS impedance model of the 12 pulse LCC system established in this section coincide with the frequency sweep results of the PSCAD simulation model with high accuracy in the whole measurement frequency range (1–2000 Hz), which also verifies the correctness of the LCC closed-loop impedance model established in this section under constant current control and constant voltage.

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0

Mag/dB

Mag/dB

50

Simulation result HSS

-50 0

10

10

1

10

2

10

Simulation result HSS

40 20 0 10

3

200

1

10 2

10 3

1

10 2 Frequency/Hz (b)

10 3

10

200

Phase angle/

o

o

Phase angle/

60

1099

100 0

-100 -200 100

10

1

10 2 Frequency/Hz (a)

10 3

100 0 -100 -200 0 10

10

Fig. 4. Amplitude frequency diagram of LCC closed-loop AC/DC harmonic impedance under constant-current control a AC side harmonic impedance diagram; b DC side harmonic impedance diagram.

4 Conclusion In this chapter, based on the combination of harmonic state space theory and complex vector modeling method, an accurate HSS impedance model of LCC converter station is established. The conclusions are as follows: 1) The HSS impedance modeling proposed in this paper takes into account the internal dynamic characteristics and frequency coupling effect of LCC, the AC side filter of LCC converter station, the trigger delay angle under constant current control, and the dynamic characteristics of AC/DC system, greatly improving the accuracy of mathematical modeling of LCC converter station using HSS. 2) At the same time, the impedance models of AC side and DC side of 12 pulse LCC converter station are established, and the accuracy of the established HSS impedance model is verified through computer programming and PSCAD simulation. 3) The HSS impedance model established in this paper is in the form of pure state space, which provides an important model basis for system stability assessment, and the modeling method can be used for LCC system modeling in any operating mode.

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CTM-Based Collaborative Optimization of Power Distribution Network and Urban Traffic Network with Electric Vehicles Wenpei Li1 , Yan Wang2 , Guanghui Song2 , Fan Yang1 , Han Fu3 , Dongying Zhang2 , and Shiwei Xia2(B) 1 State Grid Hubei Electric Power Research Institute, No. 227 Xudong Avenue, Wuhan, China 2 North China Electric Power University, No. 2 Beinong Road, Beijing, China

[email protected] 3 State Grid Wuhan Power Supply Company, No. 1701 Jiefang Avenue, Wuhan, China

Abstract. With the increased penetration of electric vehicles, wireless charging electric vehicle (WCEV) is more popular than ever before, which results in a tight spatial-temporal coupling of Power Distribution Network (PDN) and Urban Traffic Network (UTN). Under the dynamic wireless charging mode, a large amount of charging power of WCEV would be shifted during the commuting period and possibly coincides with the original peak load of PDN and thus lead to the congestions of PDN and UTN. To solve this problem, in this paper a traffic network dynamic assignment model is firstly set up based on a cell-transmission model (CTM) with an optimal power flow model of PDN presented by a mixed integer second-order cone programming, afterward a collaborative optimization model of PDN and UTN is established to simulate the spatial-temporal distribution of WCEVs’ charging load, the congestion of PDN and UTN during a traffic jam is well alleviated by optimally determining the electricity charging price. Through the joint simulation of PDN and UTN, the congestion propagation mechanism of PDN and UTN is revealed, and the effectiveness of the proposed model is verified. Furthermore, a coordinated optimization scheme of PTN is proposed to study the impact of rational allocation of active and reactive power resources on congestion in the PTN-UTN coupling model. Keywords: Urban traffic network · Power distribution network · Wireless charging · Electric vehicle · Cell-transmission model

1 Introduction In order to achieve the efficient, green and sustainable development of energy consumption, the energy Internet, based on the traditional energy network, promotes the integration of multiple complex systems such as electricity and transportation. Technological innovation on energy types and use methods gradually form a new energy industry [1, 2]. In this context, the wireless charging electric vehicle (EV) has the advantage of realizing power transfer through nonelectrical contact, which can effectively alleviate mileage anxiety and reduce the battery volume. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1101–1109, 2023. https://doi.org/10.1007/978-981-99-4334-0_131

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On the traffic network side, the spatio-temporal changes in traffic congestion conditions and charging prices affect the distribution of electric vehicle flow, thus affecting the charging demand of charging stations in different locations; On the PTN side, changes in charging demand at different times and locations will not only affect the power flow of PTN, but also affect the charging price of the charging stations, thus affecting the driving, charging and other decisions of EV users [3, 4]. However, the current research lacks the research on short-term PTN and UTN collaborative optimization under wireless charging environment [5–8]. The key to the collaborative optimization of PTN and UTN under wireless charging is to determine the space-time distribution of electric vehicle charging load [9–12], so as to further solve the problem of PTN and UTN congestion. Since Professor Daganzo of the California University put forward the CTM [13–15], many scholars have used it as the basis to study the dynamic traffic assignment problem considering physical queuing. CTM is a dynamic network loading model, which can well describe the process of queue generation, queue propagation, queue dissipation, etc. [16–19]. At present, there are few studies on applying CTM to the collaborative optimization of PTN and UTN [20]. Based on the above considerations, this paper first establishes a PTN and UTN cooperative optimization model under wireless charging conditions, introduces CTM to model dynamic traffic, and completes the dynamic traffic assignment (DTA) flow assignment calculation and congestion analysis. Then, through a large number of simulation examples, the propagation mechanism of congestion in the PTN-UTN coupling model is deeply analyzed.

2 Framework of the Coordinated Operation of PTN and UTN The framework of PTN-UTN intelligent management system is shown in Fig. 1. Under this framework, the spatio-temporal distribution of traffic demand in each time segment of the peak period is fully exploited. Users can assist “load-peak cutting” and reduce EV charging demand in the peak period according to the operation status of the traffic network and the charging price (delaying or postponing the original travel plan in the whole dispatching period).

Fig. 1. The framework of an intelligent management system.

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When the wireless charging vehicles on the road in PTN pass the charging road, they are charged through DWC technology. This centralized dynamic charging behavior is connected to the corresponding nodes of PTN through the wireless charging station. PTN includes photovoltaic power station, reactive power compensation device, distributed power supply and other active and reactive power sources. It should be pointed out that the traffic congestion in the wireless charging section of the traffic network will be overlapped with other power load peaks in the distribution network through the wireless charging station, which may cause the node voltage to exceed the limit, that is, the distribution network congestion.

3 Proposed Coordinated Operation Model of PTN and UTN In this chapter, based on the PTN-UTN intelligent management system shown in Fig. 1, a PTN-UTN coordinated optimization operation model is established, and then a solution method is proposed. 3.1 CTM-Based UTN Model Daganzo’s CTM can simulate the traffic dynamics characteristics such as shock wave, queue formation and dissipation, and can better track the flow and number of cell vehicles in each path. Initialize the number of vehicles in each cell and the flow in the cell connector, update the number of vehicles in the cell at the current time according to the number of vehicles at the previous time, the flow into the cell and the flow out of the cell, and set the cell initialization and update process: m = 0 ∀m ∈ C, r ∈ Rw , Rw ∈ R xr,0

(1)

m,n m m xr,t = δrm · (hr,t−1 +xr,t−1 − yr,t−1 )∀m ∈ CR , n ∈ m , t = 1, . . . , T

(2)

k,m m,n m m xr,t = δrm · (xr,t−1 +yr,t−1 − yr,t−1 )∀m ∈ CO , k ∈ i−1 , n ∈ m , t = 1, . . . , T

(3)

k,m m,n m m −1 xr,t = δrk,m,n · (xr,t−1 +yr,t−1 − yr,t−1 )∀i ∈ CM ∩ CD , k ∈ m , n ∈ m , t = 1, . . . , T (4) k,m m m −1 xr,t = δrm · (xr,t−1 +yr,t−1 )∀m ∈ CS , k ∈ m , t = 1, . . . , T

(5)

Formula (1) represents cell initialization, and (2)–(5) represents the renewal process of source cell, common cell, shunt and confluent cell, confluent cell, respectively; C is the cell set; R is the path collection; Rw is the path w collection for connecting OD m indicates the number of electric vehicles belonging to the path r in the cell pairs; xr,t m,n indicates the flow from cell m to cell n in the path r at the m at the moment t; yr,t moment t; hr,t indicates the departure rate of the path r at the moment t; δrm (or δrk , δrn ) is cell marker, when the cell m (or k, n) is on the path r, δrm (or δrk , δrn ) = 1,0 on the

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contrary; CD , CM , CR , CS , CO represent the set of shunt cells, confluence cells, source cells, elimination cells and ordinary cells respectively; m is the set of successor cells −1 is the set of successor cells of Compact precell cell m. of cell m; m Suppose that the average path travel time of all travelers departing at the same time on the same path is the path travel time of the departure time in the path, and the path travel time is unique.   λor,t  s−1 −1 λr,v − λor,v dv o y w = r,t−1 o (6) ηr,t λr,t − λor,t−1 where λor,t , λsr,t are departure and arrival cumulative traffic respectively; v is the free flow w is the average travel time of all electric vehicles departing from the path r velocity; ηr,t at time t, which can be obtained by the inverse function of the cumulative flow curve. w w fr,t (ηr,t − πtw ) = 0 ∀ω ∈ W , r ∈ Rw , t ∈ T

(7)

w ηr,t − πtw ≥ 0 ∀ω ∈ W , r ∈ Rw , t ∈ T

(8)



w fr,t = qtw ∀ω ∈ W , t ∈ T

(9)

r∈Rw w where nw r,t is the travel time of the route r connecting OD pairs w at the time t; πt is the w minimum flow of all paths connecting OD pairs w at the time t; qt is the traffic demand w . The column vector of path traffic for OD pair w; nw r,tis a function of path traffic fr,t  w , ∀ω ∈ W , r ∈ Rw , t ∈ T . The minimum travel time column is expressed as f = ffr,t    w vector of each path is expressed as u = uπt , ∀ω ∈ W , t ∈ T . In order to obtain the traffic flow distribution in the region, it is necessary to solve its DUE state, that is, to satisfy the Eqs. (7)–(9). The dynamic user equilibrium condition is equivalent to the following variational inequality problem. w w (ηr,t − πtw ) = 0 ∀ω ∈ W , r ∈ Rw , t ∈ T fr,t

(10)

where f∗ is the optimal path flow distribution form; t∗n is the optimal solution;  is a set of feasible solutions. w w τr,t = θ1 βr,t + θ2 τtDWC

(11)

w is the congestion delay related rate; τ DWC is the charging price for wireless where βr,t t w is a joint charge price. charging station; τr,t The objective function of minimizing travel charges can be expressed as:  w w Min τr,t ·ηr,t r w (12) t s.t.(7) − (11)

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3.2 Second Order Cone Relaxation Based UTN Model Based on the Distflow power flow form, the mixed integer second-order cone relaxation model of distribution network is solved in this paper.  t t t t t Pi,j + PG,j − Ii,j ri,j − Pj,h − Pev,s∈j − PLd (13) ,j = 0 h t t t t + QG,j +Qpv,j + QCB,j − Ii,j ri,j − Qi,j



t t t Qj,h − Qev,s∈j − QLd ,j = 0

(14)

h t t ri,j + Qi,j xi,j ) − [(ri,j )2 + (xi,j )2 )]Ii,j Uit − Ujt = 2(Pi,j

t 2Pi,j t ≤ Ii,j + Uit 2Qi,j I − U t i,j

(15)

(16)

i

t , Q t are the active and reactive power of the branch (i, j); P t , Q t where Pi,j i,j G,j G,j are t the active and reactive power of distributed power supply of node j; Qpv,j is the reactive t is the reactive output of switching power of photovoltaic power station of the node j; QCB,j capacitor of node j; ri,j , xi,j are the resistance and reactance respectively; Ii,j is the square t , Q t are the active and reactive power of the branch (j, h); of current amplitude; Pj,h j,h t , Q t are the active and reactive power of the node j; P t t PL,j L,j ev,s∈j , PLd ,j are the active t t , QLd power of wireless charging station and conventional load of the node j; Qev,s∈j ,j are the respectively reactive power of charging station and conventional load of node j. The distributed power model can be expressed as: t ≤ PG,max PG,min ≤ PG,g

(17)

t ≤ QG,max QG,min ≤ QG,g

(18)

ramp

(19)

ramp

t−1 t − PG,g ≤ PG,g −PG,g ≤ PG,g

where PG,min , PG,max , QG,min , QG,max are respectively the maximum and minimum ramp output values of active and reactive power of DG; PG,g is the DG’s climbing limit. The active output and voltage of the photovoltaic model, and the reactive output meets the following conditions: t ≤ Qpv Qpv ≤ Qpv

(20)

where Qpv , Qpv are the upper and lower limit of photovoltaic reactive power output and can be converted to PQ type when reactive power exceeds the limit. Charging price of wireless charging station: τtDWC = τtbase + βl τtcon

(21)

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where τtbase , τtcon are the basic price and voltage congestion price; βl is the congestion electricity price coefficient. Taking the minimum total network loss as the objective function: MinF loss s.t.(13) − (20)

(22)

The PTN and UTN are coupled together through the above wireless charging stations. Specifically, the vehicle flow in UTN is linearly related to the load power of the wireless charging station nodes in PTN, realizing the interaction.

4 Example Analysis

Fig. 2. (a) Nguyen Baran&Wu 33 nodes system; (b) the celled UTN.

The modified Nguyen Baran&Wu 33 nodes system is adopted for the transportation network and distribution network, as shown in Fig. 2(a). After the transportation network is cellular, the cellular transportation network and grid coupling system are obtained as shown in Fig. 2(b), where WCS represents dynamic wireless charging station, PV represents photovoltaic power station, and CB represents a switching capacitor. All numerical simulations coded in MATLAB are solved by YALMIP and GUROBI on a 3.2 GHz Windows PC with 16 GB of RAM. 4.1 Traffic Congestion Analysis When the noon and evening rush hours come under wireless charging, the coupling between PTN and UTN is closer and the spatial-temporal distribution of electric vehicle charging load changes more acutely. This sub section selects the 12:00–13.00 fragment of noon peak for congestion analysis. In Scenario 2, a joint charge of wireless charging price and road congestion degree is set in the traffic network. In Scenario 1, no joint charge is set, and the charging price of WCS is only a fixed value. Considering that the traffic flow at the edge of the road is less affected by congestion, the traffic network nodes of diversion cells and confluence cells are analyzed. Figure 3(a) and Fig. 3(b) are the hot spots of relative traffic flow distribution corresponding to Scenarios 1 and 2, where red indicates high cell congestion.

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Fig. 3. (a) No joint charging scenario; (b) Joint charging scenario.

It can be seen from Figs. 1 and 2 that the maximum relative traffic flow density of the congestion cell 45 is reduced from 51% to 41%, and the congestion time is also greatly shortened. At the same time, the maximum relative traffic flow density of sections 34 and 37 is increased from 7% to 21% and 40% to 29%, respectively, which do not reach the congestion level. It can be seen that the overall road network congestion has been significantly alleviated. Without introducing the joint charge of wireless charging price and road congestion degree, the traffic congestion in the transportation network will affect the power flow distribution in the distribution network in the way of charging load through the wireless charging station, which may induce congestion in the corresponding nodes of the distribution network. After the joint charging of wireless charging price and road congestion degree is introduced, the node voltage congestion in the distribution network will affect the comprehensive travel cost of EV users through congestion cost, induce EV to choose travel time and travel path, make the traffic flow in the transportation network redistribute again, and the space-time distribution of traffic flow will change accordingly, thus changing the congestion situation in the transportation network. 4.2 Distribution Network Optimization Analysis Before the congestion cost is adopted, there is traffic congestion at the noon peak at node 45. The congested traffic flow brings high charging load pressure to nodes 30 and 31 of the distribution network through the wireless charging station. The node voltage is congested, and the voltage amplitude is 0.95 p.u., exceeding the lower limit. However, after the adoption of joint charging, the higher charging price makes the 45 node less attractive to EV users. Its maximum relative traffic flow density decreases from 51 to 41%, and the load pressure of distribution network nodes 30 and 31 decreases accordingly. The voltage amplitude also increases to 0.97 p.u., which is within the allowable voltage offset range as shown in Fig. 4 (a). Through the joint charging of active and reactive power compensation equipment and traffic network side, cell 37 attracts more vehicles at a lower joint charging price, which increases the maximum relative traffic flow density from 7 to 21%, and relieves the pressure of cell 45 nodes and other congestion nodes. This shows that traffic congestion occurs in EV charging sections during the peak hours of the transportation network, which leads to voltage congestion in the distribution network. However, voltage congestion can be reduced through joint charging and flexible regulation at the distribution network side.

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Fig. 4. (a) Voltage diagram of each node; (b) Energy loss.

During the afternoon peak and evening peak periods, the charging load of electric vehicles increased significantly, and then overlapped with the peak load of ordinary users in the distribution network, resulting in a drop in node voltage and power congestion. By coordinating and optimizing multiple active/reactive power sources in the active distribution network, including distributed generation, energy storage devices and reactive power compensation devices, the node congestion of the distribution network is eliminated and the loss of the distribution network is reduced. From 11:00 to 13:00, the total energy consumption of the optimized system is greatly reduced. As shown in Fig. 4 (b), especially around noon, the total energy consumption decreased by 41%.

5 Conclusion In this paper, based on the CTM-based traffic network dynamic assignment UTN model and an optimal power flow PDN model, a coordinated optimization model of PDN and UTN is established to simulate the spatial-temporal coupling of WCEVs’ charging load distribution and traffic flow during a traffic jam, and alleviates the superimposed congestions of PDN and UTN by the optimized charging price. In the future, a more comprehensive model for exploring the charging flexibility of electric vehicles from the UTN side and active/reactive power regulating capabilities from the PDN side would be further combined to eliminate UTN congestion and PDN operation economics.

References 1. Zhang, B., Kezunovic, M.: Impact on power system flexibility by electric vehicle participation in ramp market. IEEE Transactions on Smart Grid 7(3), 1285–1294 (2015) 2. Galus, M., Waraich, R., Noembrini, F.: Integrating power systems, transport systems and vehicle technology for electric mobility impact assessment and efficient control. IEEE Transactions on Smart Grid 3(2), 934–949 (2018) 3. Sortomme, E., Hindi, M., Macpherson, S.: Coordinated charging of plug-in hybrid electric vehicles to minimize distribution system losses. IEEE Transactions on Smart Grid 1(2), 198– 205 (2017) 4. Gangui, Y., Xiaodong, F., Junhui, L.: Optimization of energy storage system capacity for relaxing peak load regulation bottlenecks. IEEE Trans. Power Electron. 32(28), 27–35 (2012) 5. You, Y., Li, D., Qi, Z.: The multi-objective active power energy storage system optimize configuration. Automation of Electric Power Systems 38(18), 46–52 (2018)

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6. Ahmad, A., Alam, M., Chabaan, R.: Active-reactive optimal power flow in distribution networks with embedded generation and battery storage. IEEE Trans. Power Syst. 27(4), 2026–2035 (2020) 7. Kim, J., Dvorkin, Y.: Enhancing distribution system resilience with mobile energy storage and microgrids. IEEE Transactions on Smart Grid 10(5), 4996–5006 (2018) 8. Lv, S., Wei, Z., Sun, G.: Power and traffic nexus: From perspective of power transmission network and electrified highway network. IEEE Access 26(4), 34–51 (2020) 9. Verzijlbergh, R.A., De Vries, L.J., Lukszo, Z.: Renewable energy sources and responsive demand. Do we need congestion management in the distribution grid. IEEE Transactions on Power Electronics 35(99), 382–392 (2018) 10. Xun, W., Tong, J.: Resilience enhancement strategies for power distribution network coupled with urban transportation system. IEEE Transactions on Smart Grid 10(4), 4068–4079 (2019) 11. Vagropoulos, S., Balaskas, G., Bakirtzis, A.: An investigation of plug-in electric vehicle charging impact on power systems scheduling and energy costs. IEEE Trans. Power Syst. 32(3), 1902–1912 (2017) 12. Das, H., Rahman, M.: Bi-level optimal low-carbon economic dispatch for an industrial park with consideration of multi-energy price incentives. Appl. Energy 26(2), 262–276 (2020) 13. Cobos, G.N., Arroyo, J.M., Alguacil, N.: Robust energy and reserve scheduling considering bulk energy storage units and wind uncertainty. IEEE Trans. Power Syst. 33(5), 5206–5216 (2018) 14. Faria, R., Moura, P., Delgado, J.: Enhanced coordinated operations of electric power and transportation networks via EV charging services. IEEE Trans. Smart Grid 34(1), 311–323 (2020) 15. Yu, C., Fu, L., Song, M.: An efficient MILP approximation for the hydro-thermal unit commitment. IEEE Trans. Power Syst. 31(4), 3318–3319 (2016) 16. Johannes, K., Lance, N., Gerardo, Z.: Urban road network toughness assessment based on dynamic diversion cell transmission model. Transportation System Engineering and Information 42(4), 61–66 (2018) 17. Yan, C., Zechun, H., Xiao, D.: Review on the electric vehicles operation optimization considering the spatial flexibility of electric vehicles charging demands. Power System Technology 46(3), 981–994 (2022) 18. Zheng, H., Yue, X., Kai, L.: Demand, form and key technologies of integrated development of energy transport-information networks. Automation of Electric Power Systems 45(16), 73–86 (2021) 19. Mohamed, A., Salehi, V., Ma, T.: Cost-optimal energy management of hybrid electric vehicles using fuel cell/battery health-aware predictive control. IEEE Trans. Power Electron. 35(19), 382–392 (2022) 20. Galus, M., Waraich, R., Aoyang: Electrified transportation network distribution network operation mechanism and collaborative optimization under dynamic wireless charging. Power System Automation 34(12), 107–118 (2022)

Optimal Design of Laminated Busbar for Three Level Inverter Based on Multiple Weakening Method Shi-Zhou Xu, Min Feng(B) , Xi Yang, and Tian-Yi Pei School of Electronics and Electrical Engineering, Henan Normal University, Henan, China [email protected]

Abstract. With the rapid development of modern science and technology, all kinds of electronic and electrical equipment have been more and more widely used in industrial production and people’s life. The rapid development of these highcapacity and high-density power electronic devices provides a bright prospect for applying multilevel converters. Still, the problem of electromagnetic interference is becoming increasingly severe. In this paper, the structure design of increasing the width of the laminated busbar or reducing the thickness of the insulation layer is proposed. The parasitic impedance, parasitic capacitance and parasitic inductance of the three structures are calculated and extracted by using the multiple weakening method in ANSYS finite element software. On this basis, the magnetic field strength and the current carrying capacity are further analyzed. The results show that this method greatly reduces the parasitic inductance, weakens the magnetic field strength, and further increases the current carrying capacity of the bus. Therefore, the structure design proposed in this paper reduces the common mode interference and near-field radiation in the middle and high frequency band of the inverter system, which is of great significance to reduce the conducted electromagnetic interference and busbar temperature rise in the inverter power electronic device. Keywords: Finite Element · Parasitic Parameters · Middle and High Frequency · Conducted Electromagnetic Interference

1 Introduction With the increasing shortage of non-renewable resources, three-level inverters have huge advantages over two-level in terms of voltage stress, power capacity, and power quality. High-power switching devices have developed rapidly with their absolute benefits [1]. The three-level inverter was first proposed in 1981 and is now widely used in overvoltage prediction [2], electric vehicles [3, 4], aircraft [5], photovoltaic solar panels [6], and other occasions. However, the common mode interference of the three-level inverter still needs to be improved. Long-term over-voltage will adversely affect the system and load, reliability, and service life.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1110–1117, 2023. https://doi.org/10.1007/978-981-99-4334-0_132

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The power switching devices works in the medium and high frequency switching state, and the opening and closing actions are completed in a very short time, leading to high du/dt and di/dt. Since the over-voltage is proportional to di/dt and the distributed stray inductance, When the inductance of the bus is larger, the superposition of the peak voltage and DC circuit voltage will cause the device to be broken down, which seriously affects the safety of the system [7]. Based on this, scholars at home and abroad have proceed a lot of research to accurately model the effective parasitic parameters of laminated buses in [8]. The mutual coupling of all current paths in the model includes selfinductance and impedance, but it is still insufficient to resist the current imbalance problem of the bus. A method to optimize the switching waveform considering the bus shape is proposed, and the surge voltage, damping oscillation and switching loss are analyzed to achieve the optimized switching waveform [9]. Models transient over-voltage and improves the algorithm, and finally verifies that the over-voltage suppression measures are appropriate, which can effectively reduce electromagnetic interference [10–12].The distribution of current density and the analysis of stray inductance and capacitance are mainly introduced [13]. A new method finite element analysis (FEA) is proposed in [14, 15] to calculate and extract parasitic parameters. A time-domain reflection method (TDR) on the basis of finite element method was proposed, and used transmission line theory to extract parasitic parameters [16]. The design and advantages of laminated busbar are analyzed in [17–19]. An optimization method or model is proposed to reduce stray inductance, weaken oscillation and monitor bus temperature [20–23]. This paper uses ANSYS Q3D software to extract parasitic parameters. Based on the combination of conduction path control strategy and electromagnetic process, the multiple weakening method is used to study the parasitic parameters of the stacked bus and conducted electromagnetic interference in the three-level inverter.

2 Theoretical Analysis of Conducted Interference Paths This chapter mainly discusses the relationship between the parasitic parameters generated by the inverter during the switching process and the conducted interference path. The conducted interferences of the three-level inverter were mainly caused by the transient changes of du/dt and di/dt during switching. With the increase in power density of the three-level inverter, the parasitic parameters generated between the stacked bus, inverter, and radiator provide a coupling path for conducted electromagnetic interference. Therefore, it is essential to analyze the parasitic parameters of the laminated bus under medium and high-frequency conditions. As shown in Fig. 1, the IGBT module will be installed on the radiator to achieve heat dissipation. As a result, large distributed capacitances C1, C2, and C3 are formed between the bridge arm and the radiator, thus generating parasitic inductance, parasitic impedance, and parasitic capacitances L1, L2, R1, R2, C4 between the positive and negative buses and the radiator, thus generating parasitic capacitance C5 between the radiator and the ground. Switching action will cause potential jumps at both ends and form common-mode noise through capacitance to the ground. Therefore, the parasitic parameters of the bus, the suppression of the conducted interference in the inverter system, and the optimization of the stacked bus play a crucial role in suppressing the EMI produced by the system.

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Fig. 1. Conducted interference path.

3 Three Dimensional Modeling of Laminated Busbar This chapter mainly introduces the use of ANSYS software for three-dimensional modeling of the laminated bus to extract the accurate parasitic parameter matrix so that the product before production through simulation to verify the performance and reduce the design time and prototyping cost. The laminate busbar designed in this chapter comprises copper bars with a relative dielectric constant of 1 and a relative permeability of 0.999991. Use insulation between each layer. Insulating materials are generally polyester film (PET), mica, asbestos, epoxy glass cloth laminate (FR4), and so on. This paper, FR4 is used as insulation material, whose relative dielectric constant is 4.4 and relative permeability is 1. As the parasitic parameters of the positive busbar and the negative busbar are similar, this paper takes the positive busbar as an example to establish a three-dimensional model in ANSYS shown in Fig. 2. The yellow part represents the conductor, the gray part represents the insulator, w represents the conductor width, l represents the conductor length, h represents the conductor thickness, and d represents the insulator thickness. Since the frequency characteristics of parasitic parameters depend on the geometric dimensions of the bus, Table 1 lists three groups of data for the laminated busbar.

Fig. 2. Three-dimensional structural model.

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Table 1. Data of the structure of the laminated bus Category

l (mm)

w (mm)

h (mm)

d (mm)

Case 1

100

40

6

2

Case 2

100

60

6

2

Case 3

100

40

6

1

4 Extraction of Parasitic Parameters For the busbar, the parasitic parameters are mainly the parasitic impedance, parasitic inductance and parasitic capacitance generated between the bus and the heat sink. The skin effect occurs when the high-frequency AC current flows through the adjacent bus bar, which means that when frequency of the excitation source is high, the current flowing through the conductor tends to be distributed in a ring pattern on the outer layer of the conductor, so that the current is concentrated on the contact surface of the bus. It can be seen that the skin depth δ generated by the skin effect is  δ = 1/ π f μ0 μ1 σ where, f is the frequency of current; μ0 is the permeability of insulating medium; μ1 ,σ are the magnetic conductivity and electrical conductivity of the copper layer, respectively. Simulation results of parasitic impedance, parasitic capacitance and parasitic inductance are shown in Fig. 3.

Fig. 3. Simulation diagram of extracted parasitic parameters: (a) resistance; (b) capacitance; (c) inductance.

It can be seen from (a) that for parasitic impedance, the resistance value increases only about 0.0001ω for every 1mm reduction in insulation thickness. It can be seen from (b) that for parasitic capacitance, expanding the width of the conductor or decreasing the thickness of the insulator will significantly increase the parasitic capacitance because the two conductors form the poles of the capacitor. It can be seen (c) that for parasitic inductance, increasing conductor width or decreasing insulator thickness will reduce parasitic inductance, and increasing conductor width has a more obvious effect on reducing parasitic inductance.

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5 Magnetic Field Analysis of Conducted Interference This chapter uses finite element software to calculate and analyze the magnetic induction intensity and magnetic field intensity of the laminated bus respectively. At the moment when the power supply is turned on, the laminated bus in the conducted interference path in Fig. 1 generates a transient magnetic field due to the current. As shown in Fig. 4, (b) and (c) respectively represent increasing the width of the bus bar and decreasing the insulation layer thickness. As can be seen from the figure, the maximum magnetic induction intensity of the unoptimized laminated bus is 0.0084T. When the width of the laminated bus is increased from 40 to 60mm, the maximum magnetic induction intensity is 0.0059T. When the thickness of the insulation layer is reduced, the maximum magnetic induction intensity is 0.0084T, but the second value is reduced to 0.0078T.

Fig. 4. Simulation results of magnetic induction intensity of three structures.

As shown in Fig. 5, (b) and (c) represent increasing the width of the bus and decreasing the thickness of the insulation layer, respectively. It can be seen from the figure that the maximum magnetic field intensity of the non-optimized laminated bus is 6712 A/m. When the width of the laminated bus is increased from 40 to 60 mm, the maximum magnetic field intensity is 4708 A/m. When the thickness of the insulation layer is reduced, the maximum magnetic field intensity is 6651 A/m. The electromagnetic interference in the inverter system can be improved to some extent.

Fig. 5. The magnetic field strength of the three structures.

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6 Experiments and Tests The research on the influence of stray parameters on the switching device switching voltage of the inverter structure in Fig. 1 is of great significance to the suppression of IGBT switching voltage spikes and the engineering application of such converters. Figure 6 shows the over-voltage test platform, which is used to measure the withstand voltage value of the bus before and after optimization. Figure 7 shows the results of the measured values, it can be seen from (a) that the over-voltage of the IGBT before optimization is 510 V, and (b) that the over-voltage of the IGBT after optimization is 305 V, which means that the optimization can reduce the over-voltage by 40.2%.

Busbar

Busbar structure Laminated busbar

Signal control panel

Oscilloscope

Capacitor

Heat source generator

Fig. 6. Testing platform of laminated busbar.

Fig. 7. Testing of laminated busbar: (a) IGBT over-voltage before optimization; (b) IGBT overvoltage after optimization.

7 Conclusion This paper proposes a multiple weakening method to optimize the laminated busbar of three-level inverters. The Q3D module and Maxwell module in the ANSYS software integration platform extract parasitic parameters, simulate electromagnetic field, and carry the flow of three laminated busbars. The simulation results are compared and analyzed. The results show that the parasitic inductance is reduced by about 5.06nh~5.12nh, which is approximately 13.86%. The magnetic induction and magnetic field intensity are reduced by approximately 28.74% and 29.86%, respectively, which can reduce the

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conducted interference in the middle and high-frequency stages of the system. When the excitation is increased by 120%, the current load increases by 1.19 times. Due to the skin effect, skin effect will occur when adjacent buses pass through relatively high frequency alternating current, which means that when the excitation frequency is high, the current flowing through the conductor tends to be distributed in the outer circle of the conductor, making the current concentrated on the contact surface of the bus. According to Maxwell’s theorem, part of the magnetic fields generated by the bus can cancel each other, thus reducing the parasitic inductance and effectively suppressing the voltage spike. Finally, the experiment results show that the optimization can reduce the overvoltage by 40.2%, and has excellent thermal uniformity. In short, the magnetic induction intensity of the three bus structures and the corresponding magnetic field distribution and parasitic parameter distribution are related and confirmed. The multiple weakening method improves the reliability and security of the inverter system. Due to the limitation of experimental conditions and the influence of force majeure factors, the electromagnetic interference measurement experiment in this paper did not consider the impact of the surrounding electromagnetic environment on the laminated bus, so the test should be carried out in the shielded anechoic chamber. The experimental results obtained in this way can better ensure the accuracy and research significance of the experimental results. We hope to achieve better research in this direction in the follow-up work.

References 1. Chen, J., et al.: A review of switching oscillations of wide bandgap semiconductor devices. IEEE Trans. Power Electron. 35(12), 13182–13199 (2020) 2. Dongye, Z., et al.: Coupled inductance model of full-bridge modules in hybrid high voltage direct current circuit breakers. IEEE Trans. Industr. Electron. 67(12), 10315–10324 (2020) 3. Duan, Z., Wen, X.: A new analytical conducted EMI prediction method for SiC motor drive systems. eTransportation 3, 100047 (2020) 4. Qu, J., et al.: Conducted EMI investigation of a SiC-based multiplexing converter for EV/PHEV. IEEE Access 9, 58807–58823 (2021) 5. Cougo, B., et al.: Characterization of low-inductance SiC module with integrated capacitors for aircraft applications requiring low losses and low EMI issues. IEEE Trans. Power Electron. 36(7), 8230–8242 (2021) 6. Wang, J., et al.: Common mode noise reduction of three-level active neutral point clamped inverters with uncertain parasitic capacitance of photovoltaic panels. IEEE Trans. Power Electron. 35(7), 6974–6988 (2020) 7. Abrishamifar, A., Lourakzadegan, R., Esmaili, R., et al.: Design and construction of a bus bar for spike reduction in an industrial inverter. In: 2010 1st power electronic & drive systems & technologies conference (PEDSTC). IEEE, pp. 13–17 (2010) 8. Wang, J., et al.: Accurate modeling of the effective parasitic parameters for the laminated busbar connected with paralleled SiC MOSFETs. IEEE Trans. Circuits Syst. I Regul. Pap. 68(5), 2107–2120 (2021) 9. Mitsui, K., Wada, K.: Design of a laminated bus bar optimizing the surge voltage, damped oscillation, and switching loss. IEEE Trans. Ind. Appl. 57(3), 2737–2745 (2021) 10. Zhou, T., Yang, Q., Zhang, Y., et al.: Improved transient model of prestrikes encountered in 10 kV vacuum circuit breakers and its application to overvoltage suppression while switching on shunt reactors. IEEE Transactions on Power Delivery (2021)

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11. Han, Y., Zhang, J.: Recognition algorithm of transient overvoltage characteristic based on symmetrical components estimation. Symmetry 12(1), 114 (2020) 12. Chen, X., He, Z., Zhang, Y., et al.: Research on conducted disturbance to secondary cable caused by disconnector switching operation. Frontiers in Energy Research 898 (2022) 13. Callegaro, A.D., et al.: Bus bar design for high-power inverters. IEEE Trans. Power Electron. 33(3), 2354–2367 (2018) 14. Tang, Y., Zhu, H., Song, B., Chen, C.: EMI experimental comparsion of PWM inverts between hand and soft-switching techniques. 16 Annual VPEC seminar, pp. 247–253 (2005) 15. Zhu, H., Lai, J.-S., Hefner, A.R., Jr., Tang, Y., Chen, C.: Modeling based examination of conducted EMI emission from hard and soft-switching PWM inverters. IEEE Trans 19(3), 1383–1393 (2000) 16. Gonzalez, D., Gago, J., Balcells, J.: Analysis and simulation of conducted EMI generated by switched power converters: application to a voltage source inverter. In: IEEE proceedings of international workshop integrated power package electron. 44(2), 801–806 (2002) 17. Abrishamifar, A., Lourakzadegan, R.: Design and construction of a bus bar for spike reduction in an industrial inverter. In: 1st Power Electronic & Drive System & Technologies Conference, vol. 547186, pp. 13–17 (2010) 18. Wada, K, Yamashita, A.: Wide bandwidth and low propagation time delay current sensor applied to a laminated bus bar. Energy Conversion Congress and Exposition (ECCE) 32(18), 3083–3088 (2014) 19. Hino, A., Wada, K.: Resonance analysis for DC-side laminated bus-bar of a high speed switching circuit. Future Energy Electronics Conference (IFEEC), 2013 1st International, pp. 751–756 20. Zhang, Z., et al.: High-efficiency high-power-density CLLC resonant converter with lowstray-capacitance and well-heat-dissipated planar transformer for EV on-board charger. IEEE Trans. Power Electron. 35(10), 10831–10851 (2020) 21. Plesca, A.: Thermal analysis of busbars from a high current power supply system. Energies 12(12), 2288 (2019) 22. Liang, Z., et al.: DC-link busbar network design and evaluation method for the largecapacity power electronic converter. IEEE Journal of Emerging and Selected Topics in Power Electronics 9(4), 4137–4145 (2021) 23. Liu, B., et al.: Low-stray inductance optimized design for power circuit of SiC-MOSFETbased inverter. IEEE Access 8, 20749–20758 (2020)

Simulation and Experimental Research on Low Voltage DC Switching Fast Repulsion Mechanism Chuangchuang Tao1(B) , Jiahao Guo2 , Mingming Shi2 , Xin Wu1 , Yifei Wu1 , Yi Wu1 , and Ziteng Kang1 1 Xi’an Jiaotong University, 28 Xianning West Road, Xi’an 710000, China

[email protected] 2 Electric Power Research Institute State Grid Jiangsu Electric Power Co., Ltd., 215 Shanghai

Road, Nanjing 210024, China

Abstract. In order to meet the fastness and miniaturization of the operating mechanism of the low-voltage DC circuit breaker, an electromagnetic fast repulsion mechanism is designed to pull the mechanical switch contact by repelling the plate. The finite element method is used to analyze the action characteristics of the fast repulsion mechanism. The influence of drive circuit parameters, repulsion plate material, size and excitation coil parameters on the operating characteristics of the mechanism breaking process is obtained. The designed repulsion mechanism was optimized according to the simulation results. A prototype of the fast mechanical switch is built, and experimental tests are carried out. Comparing the experimental results with the simulation results, the viability of the proposed repulsion mechanism is verified, and the correctness of the simulation optimization method is verified. Keywords: Fast mechanical switching · Electromagnetic repulsion mechanism · Opening characteristics · Parameter optimization

1 Introduction With the rapidly developing economy and the advancement and widespread use of new energy, power electronics and new materials, the low-voltage DC distribution network has achieved rapid development with a series of excellent properties [1–3]. However, due to the “low damping” characteristics of DC systems, the high peak short-circuit current rises quickly and the fault development process is extremely fast [4, 5]. Therefore, DC system has higher requirements for the fast breaking capacity of the short-circuit fault [6, 7]. As an important device for carrying current and breaking fault currents in low-voltage DC circuit breakers, the action response time and breaking speed of the movable and static contacts of the machinery switch will have a direct impact on the circuit breaker’s performance. At present, the existing low-voltage DC circuit breaker breaking time is © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1118–1126, 2023. https://doi.org/10.1007/978-981-99-4334-0_133

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often in tens of milliseconds [8, 9]. However, some applications require faster breakoff speeds. The operation and reliability of the circuit breaker is therefore dependent on the performance of the quick-action mechanism [10, 11]. The existing low-voltage circuit breaker short-circuit fault breaking usually adopts an electromagnet to drive the operating mechanism, which is slow and cannot meet the requirements of DC switching for speed. In this paper, a fast repulsion mechanism is proposed. The proposed fast switch can achieve breaking requirements within a few milliseconds. Firstly, the principle of the proposed repulsion mechanism is analyzed. Its mathematical model and simulation model are established. The influence of the coil, repulsive disc structure parameters and drive circuit parameters on the motion characteristics of the electro-magnetic repulsion force mechanisms is simulated and analyzed. The optimization of the parameters of the fast repulsive force mechanism is carried out.

2 Design of Electromagnetic Repulsion Mechanism 2.1 Principle of Electromagnetic Repulsion Mechanism As shown in Fig. 1, The electromagnetic repulsion mechanism works as follows: The switch K is closed when an action signal is received from the system. The pre-charged capacitor discharges the coil and a current pulse flows through the coil lasting a few milliseconds. This current produces a magnetic field in the coil for a transient period of time. In the presence of a transient magnetic field, an eddy current in the opposite direction to the coil current is inducted in the repulsion disc. An electro-magnetic repulsive force is created between the coil and the repulsion disc. The electromagnetic repulsion force pushes the repulsion disc to move, and the contact is driven by the connecting mechanism to realize quick opening.

Fig. 1. Principle of electromagnetic repulsion operating mechanism.

In order to further improve the response and movement speed of the electro-magnetic repulsion mechanism, the fast repulsion structure proposed here integrates the repulsion disc and the movement contact into a single unit, as shown in Fig. 2. The connecting rod and the holding mechanism are removed, which maximizes the reduction of the mass of the movable parts and reduces the dispersion of motion. The pre-charged capacitor discharges into the coil when a fault occurs and induces eddy currents in the rejection disc. The repulsion disk is bounced off under the electromagnetic repulsion force. The moving contact connected with the repulsion disk is separated from the static contact. An arc is generated between them. After the arc is extinguished, the circuit breaker completes a disconnection.

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Fig. 2. Structure diagram of fast mechanical switch and repulsion mechanism.

2.2 Mathematics Model of the Electro-magnetic Repulsion Mechanism The electromagnetic repulsion actuating mechanism can be equivalent to the interaction between two circular coil circuits, as shown in Fig. 3. The left side of Fig. 3 is the drive circuit composed of the energy storing capacitor C and the open coil. Diode D is the continuity diode of the open coil, R1 and L1 are the resistance and self-inductance of the open coil respectively. The current that flows in the opening coil is i1 when the mechanism is operated. The right side of Fig. 3 shows the loop formed by the equivalent coil of the repulsion disk. R2 and L 2 are the internal resistance and self inductance of the equivalent coil of the repulsion disk respectively. When the mechanism acts, the current flowing through the equivalent coil of the repulsion disk is i2 . M is the cross-inductance between the open coil and the equivalence coil of the repulsive disc. u1

i1

R1 C

+

D

.. M

L1

L2

i2 u2

R2

Fig. 3. Equal circuits for electro-magnetic repulsion mechanism systems.

The fundamental circuit equations for the equivalent circuit of the electro-magnetic repulsion actuator can be obtained: t  u0 − C1 0 i1 (τ )dτ = i1 R1 + L1 didt1 + M didt2 + i2 dM dt (1) 0 = i2 R2 + L2 didt2 + M didt1 + i1 dM dt where u0 is the pre-charging voltage of capacitor C. According to the principle of energy conservation, considering coil magnetic energy, repulsive disk magnetic energy, mutual inductance magnetic energy and equivalent circuit heat loss, the analytical formula of electromagnetic repulsive force can be derived: F=

dM dW = i1 i 2 dx dx

(2)

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where dM/dx is the change rate of mutual inductance with opening distance. Without considering the effect of spring distributed mass, the motion equation of repulsion mechanism is as follows: ⎧ ⎪ FA = F − mg − f (t) − (k0 x + f0 ) ⎪ ⎪ ⎨ F = ma A (3) ⎪ v = dx dt ⎪ ⎪ 2 ⎩a = d x dt 2 m is the mass of the repulsive disc. g is the acceleration of gravity. f (t) is the friction resistance varying with the motion process. (k 0 x + f 0 ) is the load imposed by the spring. k 0 is the stiffness coefficient of the spring. f 0 is the spring preload. v is the velocity of the repulsive disc. a is the acceleration. In practical work, friction and gravity can be ignored in calculation due to the huge instantaneous electromagnetic repulsion force.

3 Modeling and Simulation of Electromagnetic Repulsion Mechanism 3.1 Simulation Model of Electromagnetic Repulsion Mechanism The movement of electromagnetic repulsion actuating mechanism is a complex process, including capacitor discharge to coil, electromagnetic induction and mechanical movement. The finite unit simulation software Simcenter MAGNET is used in this paper for solving and simulation, and the 3D simulation model built is shown in Fig. 4. (a). Because the model is an axisymmetric model, the two-dimensional analysis with motion is selected for solution.

Fig. 4. (a) Simulation of electromagnetic repulsion mechanism. (b) Drive circuit of electromagnetic repulsion mechanism.

Figure 4. (b) shows the topology of the excitation circuit, which consists of a charging circuit and a discharging circuit. S3 is the charging circuit control switch, the charging circuit resistance is set as 10 m, and S4 is the discharging circuit control switch. During transient simulation, firstly disconnect S4 and close S3 to charge the energy storage capacitor. When the capacitor voltage rises to the DC voltage source, disconnect S3. When the mechanism acts, close S4, and the capacitor discharges to the coil. The anti parallel diode D1 provides a freewheeling path for the coil when S4 is disconnected.

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3.2 Simulation Analysis The parameters of the drive circuit, including the capacitance, voltage, the thickness and mass of the repulsive disc, the number of turns and the cross-sectional area of the coil, have an impact on the motion characteristics of the repulsive disk. In this section, the maximum opening distance of the repulsion disc is chosen as an indicator to investigate the manner and effect of the above mentioned parameters on the movement of the repulsion mechanism. As the energy source of repulsion mechanism, the voltage and capacitance of energy storing capacitor directly determine the magnitude of excitation current, which affects the action effect of repulsion mechanism. When the capacitor volume is constant, the effect of increasing the capacitor charging voltage on improving the stored energy is more obvious. The simulated results of the maximum opening distance for the repulsion mechanism under variable conditions by varying the capacitance value and the precharge voltage value are shown in Fig. 5. From the figure it can be observed that when the capacitance value is fixed, the maximum opening speed increases with increasing pre-charge voltage. When the voltage is constant, the rising speed of the maximum opening distance slows down with the increase of the capacitance value.

Fig. 5. (a) The maximum open distance varies with voltage and capacitance; (b) The maximum open distance varies with voltage and capacitance.

Table 1. Comparison of copper and 6061 aluminum alloy material parameters. Material

Electrical conductivity (20 °C) (S/m)

Density(g/cm3 )

Tensile strength (MPa)

Copper

5.77 × 107

8.96

200–500

6061 Aluminum

3.87 × 107

2.71

205

The material selection of repulsive disk has a significant effect on its motion characteristics. The simulation selects copper and 6061 aluminum alloy for comparative analysis. Their parameters are shown in Table 1. Their motion characteristic curves are presented in Fig. 6(a). The results of the simulation show that a copper disc of the same volume moves faster than an aluminium disc, with a larger movement stroke and a longer total movement period.

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Fig. 6. (a) The operating characteristics; (b) Excitation current and peak repulsion value; (c) The maximum open distance; (d) The maximum opening distance and number of turns.

In general, the flatter and wider the coil shape, the more kinetic energy the excitation magnetic field energy converts to the repulsive disk, and the higher the conversion efficiency [10]. The relationship between the number of turns of the coil and the maximum excitation current, the electromagnetic repulsion and the maximum opening distance can be obtained, as shown in Fig. 6. (b)(c). The relationship between the maximum opening distance, coil turns and wire diameter is shown in Fig. 6. (d). The simulation results show that there is a quadratic relationship between the number of turns and the diameter of the wire. With the increase of the number of turns, the maximum opening distance decreases first and then increases, and then continues to decrease monotonously when it reaches a certain value. When the turns are 10, the excitation circuit current can reach a peak of 7 kA and the repulsion force can reach a peak of 5 kN. With the increase of turns, inductance and resistance, the peak excitation circuit current decreases, the current rise rate decreases and the opening distance decreases. However, with the increase of inductance, the pulse width of excitation current increases, the pulse width of repulsion force also increases, and the action time increases. As the number of laps increases further, the opening range reaches its extreme value around 36 laps. After that, the opening distance decreases monotonically. Select copper material and change the thickness of the repulsive disc for simulation. The kinematic characteristic curve of the repulsion disc appears in Fig. 7. (a). As the thickness of the repulsive disc increases, the opening distance of the repulsive disc decreases. The following simulation results are shown in Fig. 7.(b) for the variation of the peak electro-magnetic repulsive force on the repulsive disc with the thickness of the repulsive disc: when the thickness of the repulsive disc reaches 3 mm, the increase of the peak electro-magnetic repulsive force with increasing thickness slows down significantly.

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Fig. 7. (a) Effect of repulsion disc thickness on operating characteristics; (b) Effect of repulsion disk thickness on the peak value of electromagnetic repulsion.

Table 2. Optimized parameters of the fast operating mechanism. Parameters

Value

Parameters

Value

R

15 mm

N

35

h1

3 mm

U0

300 V

h2

4 mm

C

400 µF

h

0.3 mm

F0

35 N

d

1 mm

k

5 N/mm

Material

Copper

m

25 g

Based on the above simulation results, optimised parameters for the fast repulsion mechanism are shown in Table 2. In the table, R is the outer diameter of the repulsive disc and coil. h1 is the thickness of the repulsive disc, and h2 is the thickness of the coil, H is the initial clearance between the coil and the repulsive disc. d is the coil wire diameter. N is the coil turns. U0 is the capacitance pre-charging voltage. F0 is the spring pre-pressure. k is the spring elasticity coefficient. m is the mass of the repulsive disc. The repulsion plate is made of copper.

Fig. 8. Simulation results before and after optimization.

The optimised parameters were used in the simulation and the simulation results shown as Fig. 8. From the graph, it is evident that after optimisation, the peak excitation current drops from around 2500 A to around 1500 A and the current duration is shortened. The peak value of electromagnetic repulsion force has been significantly improved,

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reaching 2500 N. The opening distance of repulsion mechanism is slightly increased compared with that before optimization. On the premise of maintaining the performance of the mechanism, optimizing the design to reduce the current of the excitation circuit is conducive to the control of capacitor discharge and the design of the coil drive circuit.

4 Breaking Test of Electromagnetic Repulsion Mechanism A prototype of a fast mechanical switch, shown in Fig. 9(a), was designed on the basis of the simulations and consists of three parts: the boost module, the driver circuit and the fast mechanical switch. The prototype is tested with LC oscillation experimental circuit, and the experimental schematic diagram is shown in Fig. 9(b).

Fig. 9. (a) Prototype diagram of fast mechanical switch; (b) Experimental schematic

Fig. 10. (a) Comparison of the experimental results and simulation results of the excitation current; (b) Break voltage and drive signal.

The results of the experimental tests are shown in Fig. 10. From Fig. 10.(a) it can be seen that the peak value of the actual tested excitation current in the experiment is smaller than that in the simulation, mainly because of the stray parameters in the excitation circuit of the actual prototype, the resistance of the wire and the electrical connection. From Fig. 10.(b) it can be seen that after sending an action signal to the drive circuit, with a mechanical delay of about 5 µs, the repulsion disk begins to act, generating arcing, breaking voltage fluctuations. After another 240 µs, the fault current transfer is turned off and a shutdown is completed.

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5 Conclusion This paper proposes a fast repulsion mechanism which combines a repulsion disc with the moving contacts of a mechanical switch. The mathematical model and the finite element simulation model are established. Each part of the repulsion mechanism is simulated and optimized. Prototype of a fast mechanical switch based on simulation and optimisation results was made and tested. Test results indicated that the response delay of the proposed fast rejection mechanism was only a few microseconds. It can achieve the required opening distance in tens of microseconds and complete the fault current breaking with the fault current transfer, which verifies the feasibility of the proposed repulsion mechanism and the correctness of the simulation optimization method. It provides guidance for the subsequent optimisation of the design of such mechanisms.

References 1. Hou, Y., Shi, Z., Liu, S., et al.: Simulation study of operation mechanism in high-speed DC circuit breaker. High Voltage Apparatus 56(4), 42–47 (2020) 2. Zhang, W., Tang, Y., Zeng, N.: Multi terminal HVDC transmission technology and its application prospect. Power Grid Technology 34(9), 1–6 (2010) 3. Ma, D., Chen, W., Ye, H., Xue, C., Pan, P., Zhu, X.: An assembly high voltage DC circuit breaker based on pre-charged capacitors. In: 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC), pp. 1–4 (2018) 4. Surwade, V., Savaliya, S., Pimple, B.B.: A modified z-source dc circuit breaker for power electronic converter load application. In: 2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), pp. 1–6 (2020) 5. Sen, S., Mehraeen, S.: Improving low-voltage dc circuit breaker performance through an alternate commutating circuit. IEEE Transactions on Industry Applications 55(6), 6127–6136 (2019) 6. Rodrigues, R., Du, Y., Antoniazzi, A., Cairoli, P.: A review of solid-state circuit breakers. IEEE Transactions on Power Electronics 36(1), 364–377 (2020) 7. Rodrigues, R., Jiang, T., Du, Y., Cairoli, P., Zheng, H.: Solid state circuit breakers for shipboard distribution systems. In: 2017 IEEE Electric Ship Technologies Symposium (ESTS), pp. 406– 413(2017) 8. Sen, S., Mehraeen, S., Smedley, K.: A bipolar hybrid circuit breaker for low-voltage DC circuits. In: 2021 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 1254–1260 (2021) 9. Virdag, A., Khan, N.A., Hager, T., DeDoncker, R.W.: Performance analysis of hybrid DC circuit breaker based on counter-current injection method for low-voltage DC grids. In: 2019 IEEE Third International Conference on DC Microgrids (ICDCM), pp. 1–6 (2019) 10. Yuan, Z., Yu, X., Wei, X., et al.: Comprehensive optimization of coil-coil electromagnetic repulsive actuators. High Voltage Engineering 41(12), 4207–4212 (2015) 11. Li, X., Wu, S., Li, X., et al.: Study on dynamic characteristic of operating mechanism of high voltage circuit breaker based on co-simulation. J. Huazhong Univ. of Sci. Tech. (Natural Science Edition) 47(2), 70–75 (2019)

Research and Application of Green Power Market Operation Evaluation System in Beijing Xiaochun Cheng(B) , Hong Cheng, Qin Wang, Xingcun Wang, Chenda Zhang, and Yuxuan Zhang Capital Power Exchange Center Co., Ltd., Beijing 100031, China [email protected]

Abstract. In order to solve the problems of green power market operation evaluation, based on the SCP paradigm framework in the traditional industrial organization theory, Beijing Green Power Market Structure is discussed. Then four key factors affecting the operation of green power market, including policy orientation, market structure, market behavior, and market performance, are analyzed. The O-SCP framework for the evaluation of power market operation is proposed, and the green power market evaluation index system and green power market comprehensive evaluation model based on the O-SCP framework are built. The effectiveness of the proposed method is demonstrated based on an example. Through the evaluation of the construction results of the green power market in Beijing, the evaluation results are in line with the objective reality, and at the same time can reflect the shortcomings of the construction and operation of the green power market, which has guiding significance for market development. The final evaluation result of this example is good, indicating that Beijing’s green power market has “complete mechanism, reasonable structure, healthy and orderly performance, and good performance”. Keywords: Green electricity market · Operation evaluation · O-SCP framework · Comprehensive evaluation model

1 Introduction In order to implement the strategic deployment of the Party Central Committee and the State Council on carbon peaking and carbon neutrality, and accelerate the construction of a new power system with new energy as the main body, it is necessary to take effective measures to vigorously develop new energy. Due to the technical characteristics of the instability and volatility of new energy power generation output, the real-time balance and stable operation of the power system are more difficult, and the consumption and operating costs will increase significantly. To achieve the multiple goals of low-carbon transformation of electricity, safety and reliability, and economic affordability at the same time, it is necessary to deepen the reform of the electricity system, and make exploration and innovation in institutional mechanisms and market construction. An important goal of market mechanism © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1127–1139, 2023. https://doi.org/10.1007/978-981-99-4334-0_134

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innovation is to reduce new energy consumption. Cost. In the process of power market construction, establishing a market mechanism evaluation system to evaluate the performance of the power market after the fact is conducive to discovering the problems existing in the market mechanism and making timely revisions and adjustments. The European power market mainly focuses on four aspects: market design, market power, market supervision, and sustainable development [1–9], and the design of the evaluation index system also starts from these four aspects. Domestic scholars mainly focus on how to build a comprehensive and scientific evaluation index system when conducting electricity market evaluation research. Reference [10] constructs electricity market supervision indicators from the dimensions of market supply and demand, market structure, market strategy, supplier status and transaction results. The evaluation results can be used to provide a basis for market supervision decision-making and rule revision. Reference [11] focuses on the operation efficiency of the power market, and believes that effective market competition is a necessary adjustment to improve operation efficiency. Therefore, a market efficiency evaluation index system is constructed with the goal of effective competition, and grey relational analysis and fuzzy comprehensive evaluation are comprehensively used. Evaluate the efficiency of the electricity market. Reference [12] mainly constructs an auxiliary service market evaluation index system from four dimensions: technical assessment indicators, market condition indicators, market behavior indicators, and market risk indicators, and uses the grey relational comprehensive evaluation model based on entropy weight to carry out the evaluation. A multi-angle and all-round evaluation of the auxiliary service market. Based on the SCP paradigm theory in the theory of industrial organization, the literature [4] constructed the power market evaluation index system from five dimensions: market structure, market security, market operation, market benefit, and market risk. Reference [13] used the G-SCP paradigm to analyze the efficiency of the direct electricity trade market, and based on this, the efficiency evaluation index system of the electricity direct trade market was constructed. Reference [14] designed a market power monitoring system based on the G-SCP framework, and proposed a dynamic regulation model of market power based on the G-SCP framework and market power. Based on the SCP paradigm framework in the traditional industrial organization theory, this paper analyzes the key factors affecting the operation of the green power market, introduces policy-oriented factors, and proposes an O-SCP framework suitable for the evaluation of green power market operations. The framework’s green power market evaluation index system and green power market comprehensive evaluation model are used to evaluate the green power market construction results in Beijing.

2 Green Power Market Operation Evaluation Index System 2.1 Beijing Green Power Market Structure The system of a green power market needs to fully consider factors such as incentive policies in the region, the needs of market players, and the maturity of market players. According to the current relevant policy requirements, taking into account the demands of power users in Beijing for green power and the main sources of green power, the

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green power market in Beijing mainly includes green power market-based transactions (referred to as “green power transactions”) and new energy transactions. Green power transaction refers to the medium and long-term power transaction. New energy trading refers to the medium and long-term electricity trading in which the electricity generation of new energy companies other than green electricity trading volume is the target of the transaction. Market players can choose different types of transactions according to their own needs, and participate in transactions by means of bilateral negotiation, centralized bidding, and listing transactions. The formulation of the electricity market settlement model is also closely linked to the maturity of market entities and the types of power sources. In order to maintain the reliable and stable performance of the green power market, the Capital Trading Center has formulated the exclusive settlement rules for green power transactions to optimize the settlement process, compiled settlement examples in different scenarios, and steadily developed settlement functions; established a market with multiple business streams such as trading, marketing, and finance. Settlement structure, implement the interaction process and operation details between systems, and actively promote the online settlement of green power transactions in strict accordance with the transaction rules. 2.2 The Operating Results of the Green Power Market in Beijing in Recent Years The Capital Electricity Trading Center will introduce more clean electricity and establish a green electricity trading mechanism as key tasks. The trading center has started from the innovative development of green power trading in the Beijing Winter Olympics venues, and has been advancing year by year to improve the large-scale and normalized development of green power trading. The construction of the green power trading market in Beijing has seen fruitful results. (1) New energy trading In September 2019, the Daxing Airport green electricity transaction was organized for the first time, with a total settlement of 125 million kWh of green electricity, supporting Daxing International Airport to set an international example of green and low carbon. In June 2022, organize the 2022 Beijing company’s agency sub-center new energy transaction, and purchase 60 million kWh of clean electricity for the sub-center core office area. The completion of the transaction promoted the implementation of the green power demonstration application of the sub-center, and also marked that the Beijing sub-center officially entered the “zero carbon era”. (2) Green electricity transaction From 2019 to 2022, the Beijing Exchange and the Beijing Electric Power Exchange organized a total of 8 green power transactions for the Winter Olympics. A total of more than a dozen green power generation companies from Beijing and northern Hebei have reached transactions, generating nearly 600 million kWh of electricity. For the first time in the history of the Olympic Games, 100% green power supply has been achieved for all Winter Olympic venues and their ancillary facilities. It is worth noting that the 2022 Winter Olympics venues will innovate the transaction mode of green power

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trading, and organize green power generation enterprises in Beijing and northern Hebei to participate in the transaction through the e-trading platform to ensure that the Winter Olympics Organizing Committee has obtained a green certificate. In September 2021, the National Energy Administration successfully completed the green power transaction pilot work, and successfully organized seven major ordinary power users including Beijing Mercedes-Benz to reach a green power transaction with Shanxi New Energy Power Plant, achieving a transaction volume of 96.2 million kWh. In June 2022, organize and carry out the 2022 Beijing company’s outsourcing green electricity transaction on behalf of users, with a transaction volume of 20 million kWh. It marks that Beijing green electricity trading has entered a normalized market opening.

3 Green Power Market Operation Evaluation Index System 3.1 Analysis on the Status Quo of Green Power Market Operation Evaluation There are differences between the green power market and the traditional power market in terms of operation objectives, development forms, and market mechanisms. From the perspective of operational goals, the traditional power market focuses on the optimal distribution of resources on the premise of ensuring power supply, while the green power market focuses on promoting new energy consumption, green development of service areas and the realization of dual carbon goals; from the perspective of development form, the traditional power market has been operating smoothly for many years under the toplevel design of unified market and two-level operation, the mechanism is relatively sound, the market is mature, and the market fairness is emphasized; while the green power market is in the market cultivation period, and the whole society has no awareness of actively consuming green power. At this stage, more emphasis is placed on market efficiency. A clear way and path for new energy to participate in the market has been formed, and the new energy transaction price system that includes electric energy value, green value, and adjustment cost is not perfect. The differences in the above three aspects all require the design of a more accurate and personalized evaluation system for the green power market [15]. At present, the SCP paradigm theory in the theory of industrial organization is often used to study the evaluation of electricity market operations, that is, to analyze the interaction of market structure, market conduct and market performance. Considering that the green power market is in the market cultivation period, policies are needed to ensure the reasonable benefits and controllable costs of green power market members, policies are needed to support the optimal allocation of new energy power across provinces and regions, and policies are needed to clarify green power and carbon verification, energy dual The coordination relationship between control and control requires policies to guide the concept of green energy use in the whole society. In conclusion, Policy Orientation has become a key factor. 3.2 O-SCP Green Power Market Evaluation Index System Based on the SCP paradigm in traditional industrial organization theory, proposed index incorporates Policy Orientation into the analysis framework, and innovatively designs

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the O-SCP paradigm (see Fig. 1), namely Policy Orientation, Market Structure, Market Conduct and Market Performance, to build a green power market operation evaluation index system, the specific connotation is that policy orientation affects market structure and market behavior, market structure is the basis of market behavior, and market behavior determines market performance, and market performance feedback to policy orientation.

Policy Orientation

Market Structure

Market Performance

Market Conduct

Fig. 1. O-SCP structure.

The O-SCP green power market evaluation index system constructed in this paper includes 4 first-level indicators, 6 second-level indicators and 23 third-level indicators. (1) Policy Orientation The impact of China’s power market policies on the green power market is mainly reflected in incentive policies, including membership access conditions, transaction price restrictions, issuance of relevant green emission reduction targets, and power generation subsidies. Various policy orientations can deeply and long-term affect the development direction and evolution of the green power market, and affect the coordination of market development. Policy-oriented indicators mainly reflect market coordination and policy incentives, with market coordination and policy incentives as secondary indicators, and their corresponding three-level indicators are: policy coordination, policy appropriateness, policy stability, and complete market mechanism, and policy incentives. (2) Market Structure The market structure is the framework and basis of the electricity market, and is the overall form of performance of the electricity market. It includes the size, classification, concentration, grid structure, and types of power generation entities of market entities. Market structure indicators mainly reflect the effectiveness and stability of the market, take market effectiveness and market stability as secondary indicators, and construct their corresponding tertiary indicators: market concentration, year-on-year growth rate of transaction organizations, participation in transactions, information availability, market supply and demand ratio, price volatility index, controllability of transaction costs, and medium- and long-term contract ratios. (3) Market Conduct The various behaviors of various entities participating in the green electricity market have shaped the operation of the market. Market behavior mainly includes the main

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body participation strategy, the use of market influence, policy compliance and risk control. Market behavior indicators mainly reflect the competitiveness of the market, with market competitiveness as the second-level indicator, and its corresponding thirdlevel indicators are: market competition, market openness, transaction price deviation, and contract performance rate. (4) Market Performance Under the guidance of policy, the interaction of market structure and market behavior will produce specific market performance, and different market performance will also have a linear feedback on market behavior, which will have an effect on market structure, and even have an impact on the policy level. Market performance includes economic benefits, environmental benefits, social welfare distribution efficiency, etc. The market indicator mainly reflects the sustainability of the market, with market sustainability as the second-level indicator, and its corresponding third-level indicators are member satisfaction, cross-provincial Cross-regional transaction rate, transaction electricity growth rate, market breakthrough, market demonstration, and market brand [16].

4 Evaluation Model Based on CRITIC Weight Method 4.1 Evaluation Steps Considering that the green power market operation evaluation index system has the characteristics of multi-level, qualitative and quantitative indicators, this paper adopts the multi-level fuzzy comprehensive evaluation method to evaluate the green power policy and market mechanism for the regulation and incentive effect of power market operation, inferior. According to the characteristics of the evaluation indicators, a multi-level fuzzy comprehensive evaluation model is designed. Step 1: Build a Metric Set U = [u1 , u2 , . . . , un ]. Aiming at the influencing factors of green power market operation, this paper follows the principle of index selection, and uses the Analytic Hierarchy Process (AHP) to construct an evaluation index system. Analytic Hierarchy Process (AHP) is a way of decision making based on hierarchy of the index. The green power market operation effectiveness is taken as the evaluation object, from the four dimensions of policy orientation, market structure, market behavior, and market performance, and establishes a green power market operation evaluation index set consisting of 23 indicators, as shown in Table 1. Step 2: Build the original indicator data matrix X = [x1 , x2 , . . . , xn ]. The index value of the qualitative index is determined by the expert scoring method, the index value of the quantitative index is obtained according to the proposed method, and finally the original index data matrix is formed. Step 3: Determine the weight of each evaluation index W = [W1 , W2 , . . . , Wn ]. Considering that the quantitative index and qualitative index of the index system are equally important, in order to avoid the randomness of determining the weight of each evaluation index as much as possible, the analytic hierarchy process is adopted and the CRITIC weight method is used to determine the weight of each index.

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Table 1. Index Dimension

Indicator

Attribute

Policy guidance

Policy coordination

Qualitative

Policy appropriateness

Qualitative

Policy stability

Qualitative

Completeness of the market mechanism

Qualitative

Policy incentives

Qualitative

Market concentration

Quantitative

Year-on-year growth rate of transaction organizations

Quantitative

Market structure

Year-on-year growth rate of the number of participants in Quantitative the transaction

Market behavior

Information validity

Qualitative

Market supply and demand ratio

Quantitative

Price volatility index

Quantitative

Transaction cost controllability

Qualitative

Medium to long term contract ratio

Quantitative

Market competition

Quantitative

Market openness

Qualitative

The deviation of the transaction price of a single transaction

Quantitative

Contract performance rate Market performance Member satisfaction

Quantitative Qualitative

Cross-regional and cross-provincial transaction rate

Quantitative

Transaction power growth rate

Quantitative

Groundbreaking

Qualitative

Exemplary

Qualitative

Branding

Qualitative

Step 4: Determine the scoring criteria for each indicator and form an indicator evaluation matrix. According to the development status of the green power market in the power market system, the scoring standards for each index value of green power market operation are given. In order to facilitate the setting of evaluation standards, the maximum score of each index is set to 100 points. Combined with the original index data matrix obtained in step 2, an index evaluation matrix is formed. Single-factor evaluation set of evaluation factor i: Ai = [ai1 , ai2 , . . . , ain ]

(1)

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Then the evaluation set of m factors constitutes the index evaluation matrix: ⎤ ⎡ a11 , a12 · · · a1n .. ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ ⎢ A = ⎢ ai1 , ai2 · · · ain ⎥ ⎥ ⎥ ⎢ . . ⎦ ⎣ .

(2)

am1 , am2 · · · amn

The meaning of amn is the element of matrix A. Step 5: Determine the evaluation criteria. Since the sum of the weights is 1, the maximum score of each evaluation index is 100 points, so the maximum score of the operational effectiveness of the green power market is also 100 points. In the green power market operation evaluation process, we divide the evaluation criteria into 5 grades from excellent to poor, that is, the evaluation criteria set is: V = {v1 , v2 , v3 , v4 , v5 }

(3)

where vi is the evaluation level. Step 6: fuzzy comprehensive evaluation of indicators. In this paper, the weighted average operator is used for fuzzy operation. Single-level comprehensive evaluation: Bi = Wi oAi (i = 1, 2, · · · , n). After the single-level comprehensive assessment is completed, the Bi in the upper level is composed of Ai to complete the multi-level comprehensive evaluation. ⎤ ⎡ a11 , a12 · · · a1n .. ⎥ ⎢ ⎥ ⎢ . ⎥ ⎢ ⎥ (4) B = WA = (W1 , W2 , . . . , Wn )⎢ , a · · · a a in ⎥ = (b1 , b2 , . . . , bn ) ⎢ i1 i2 ⎥ ⎢ . .. ⎦ ⎣ am1 , am2 · · · amn Bring the obtained comprehensive score into the evaluation standard determined in step 5, and then the comprehensive evaluation level of the operation effect of the green power market can be obtained. 4.2 Weight Determination Method The subjective weight vector W s of the green power market operation evaluation index is obtained by the AHP, and the objective weight vector Wo is calculated by the CRITIC weight method, and the weight Wi of each evaluation index is determined by the comprehensive integrated weighting method based on multiplicative synthesis and normalization. (1) Determine Subjective Weight Vectors W s Taking the dimension of policy orientation as an example, according to the importance of each evaluation index in this dimension relative to the policy orientation, the comparison

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results form a 5 × 5 judgment matrix. The judgment matrix is: ⎤ ⎡ 1 z12 z13 z14 z15 ⎥ ⎢ ⎢ z21 1 z23 z24 z25 ⎥ ⎥ ⎢ H = ⎢ z31 z32 1 z34 z35 ⎥ ⎥ ⎢ ⎣ z41 z42 z43 1 z45 ⎦ z51 z52 z53 z54 1

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(5)

In the formula, zij is the importance of the indicator ui and the indicator uj . According to the hierarchical structure of green power market operation evaluation indicators, all weight judgment matrices are established, and the subjective weight vectors of each indicator are obtained after the total ranking of the hierarchy and the consistency test. (2) Determine the objective weight vector W o . ➀ Dimensionless processing of original indicator data Positive indicator (the larger the indicator value, the better): xi =

xi − xmin xmax − xmin

(6)

Inverse indicator (the smaller the indicator value, the better): xi =

xmax − xi xmax − xmin

(7)

➁ Calculate Metric Variability The index variability is expressed in the form of standard deviation, that is, the difference and fluctuation of the value within the index. In this formula, x i is the average, S i is the standard deviation.  1 n xi =

n n i=1 xi (8) 2 i=1 (xi −x i ) Si = n−1 ➂ Calculate Metric Conflict The index conflict is expressed by the correlation coefficient. Ri =

n 

(1 − rij )

(9)

i=1

➃ Calculate the amount of indicator information Ci = Si × Ri = Si

n 

(1 − rij )

(10)

i=1

➄ Calculate objective weights The objective weight of the ith indicator is: Ci WOi = n

i=1 Ci

(11)

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(3) Determine the weight of each evaluation index Wi = WSi WOi /

n 

WSi WOi

(12)

i=1

In the formula, n is the number of evaluation indicators.

5 Case Analysis Using the evaluation method of green power market operation proposed in this paper, a comprehensive analysis of the construction results of green power market in Beijing is carried out. According to the operation results of the green power market in Beijing, the evaluation index values of the three-level indicators of the green power market in Beijing are obtained. The weight judgment matrix of indicators at all levels in the green power market in Beijing is constructed, and the judgment matrix and weight vector of each indicator are obtained. The evaluation matrix formed by the three-level index evaluation vector and the corresponding index weight vector are fuzzy synthesized to obtain the evaluation vector of the second-level index and the evaluation vector of the first-level index in turn. Fuzzy synthesis of the evaluation matrix composed of the first-level index evaluation vector and the corresponding index weight vector, the evaluation vector of the comprehensive evaluation of the green power market in Beijing is obtained as:

B = 0.5837 0.2035 0.1473 0.0655 (13) The above results are analyzed and evaluated according to the determined scoring standard, because the maximum membership degree is 0.5837, and the membership degree belongs to the comment set “excellent and good”, which indicates that the evaluation result of the green power market in Beijing is “excellent and good”. Using the analysis method of maximum membership degree to evaluate the green power market, only the maximum membership degree is used, and the information brought by the comprehensive evaluation vector B cannot be fully utilized. In order to make full use of the information brought by B, assign corresponding values to the comment set vj ( j = 1,2,3,4), and comprehensively consider the evaluation parameters and evaluation results. The parameter column vector specified relative to each level is: C = (4, 3, 2, 1)T

(14)

Calculate the evaluation results of each index, and the comprehensive evaluation results of the green power market in Beijing are shown in Table 2. The corresponding rating is determined in “Step 5: Determine the evaluation criteria”. The final evaluation result of this example is good, indicating that Beijing’s green power market has “complete mechanism, reasonable structure, healthy and orderly performance, and good performance”.

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Table 2. Evaluation results Evaluation indicators

Fuzzy evaluation vector

Corresponding rating

u1

0.4872

Medium

u2

0.6854

Excellent

u3

0.5669

Good

u4

0.7022

Excellent

Comprehensive evaluation

0.6011

Good

Specifically, the policy orientation is rated as medium. Among them, the poor performance of indicators such as policy incentives and coordination indicates that in the face of ever-changing market changes and increasingly rich transaction demands, the updating and adaptation of policies needs to be improved. However, it is worth pointing out that the evaluation of the completeness of the market mechanism is excellent, that is, the completeness rate of the transaction mechanism reaches 100%, indicating that under the existing policy framework, the market mechanism is complete and can support the individualized transaction needs of various entities. The market structure was rated as excellent. The market’s effectiveness indicators and stability indicators have achieved excellent results. It shows that market information flows smoothly and transaction costs are controllable. Market behavior was rated as good. The deviation of the transaction price of a single transaction is relatively high, which reflects the low degree of competition in the green electricity market in Beijing at present, resulting in a large deviation in the understanding of green electricity prices by market players. Market performance was rated as excellent. Beijing’s green power market has a breakthrough, high brand, strong demonstration, and high sustainable development index.

6 Conclusion Based on the SCP paradigm framework in the traditional industrial organization theory, the key factors affecting the operation of the green power market are analyzed, and policyoriented factors are discussed, and an O-SCP framework suitable for the evaluation of green power market operations is proposed. The framework of the green power market evaluation index system and the green power market comprehensive evaluation model, and using the model to assess the construction results of the green power market in Beijing, the conclusions are as follows: (1) The key factors related to the operation of the green power market are summarized into four aspects: policy orientation, market structure, market behavior, and market performance; on this basis, the O-SCP green power market comprehensive evaluation index system is constructed. The constructed index system can fully reflect the whole picture of green power market operation.

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(2) The hierarchy of the index system and the characteristics of the green power market evaluation indicators are studied, and a method combining AHP and fuzzy evaluation is established. This method combines the objectivity of the membership degree of the power market indicators with the subjectivity of the expert qualitative analysis, which improves the scientificity of the evaluation process. (3) Through the assessment of the construction results of the green power market in Beijing, the evaluation results are in line with the objective reality, and at the same time is reflective of the shortcomings of the construction and performance of the green power market, which has guiding significance for market development. Acknowledgement. Science and technology project of State Grid Corporation of China: 52022322000L.

References 1. Green, R., Lorenzoni, A., Perez, Y., et al.: Benchmarking electricity liberalization in Europe (2006). http://ideas.repec.org/p/cam/camdae/0629.html 2. Wen, F., Wang, Q., Liu, M., et al.: Development of my country’s electricity market analysis and evaluation system. Journal of Electric Power Science and Technology 23(3), 47–52 (2008) 3. Liu, D., Chen, X., He, G., et al.: The principle and construction method of the power market evaluation index system. Automation of Electric Power Systems 29(23), 2–7 (2005) 4. Wang, Q., Wen, F., Liu, M., et al.: Construction of Electricity Market Evaluation Index System. Electric Power Technology and Economics 20(5), 21–26 (2008) 5. Guo, L., Wei, W., Xia, Q., et al.: Discussion on the framework of my country’s electricity market evaluation index system. Electric Power Technology and Economics 20(3), 29–34 (2008) 6. Liu, D., Wu, Y., He, G., et al.: Research on comprehensive index of electricity market. Automation of Electric Power Systems 30(3), 23–28 (2006) 7. Sadeghian, O., Oshnoei, A., Mohammadi-Ivatloo, B., et al.: Theoretical and empirical research on market power in my country’s electricity market. North China Electric Power University (Beijing) (2006) 8. Li, H.: Research on China’s power market performance evaluation index system and evaluation model. North China Electric Power University (Beijing) (2008) 9. Cao, F.: Research and empirical analysis on coordinated operation mode of electricity market system. North China Electric Power University (Beijing) (2011) 10. Liu, D., Li, R., Chen, X., et al.: Electricity market supervision indicators and market evaluation system. Automation of Electric Power Systems 28(9), 16–21 (2004) 11. Cheng, C.: Research on the evaluation index system and evaluation method of power market operation efficiency. North China Electric Power University (Beijing) North China Electric Power University (2011) 12. Zhou, X.: Evaluation system of regional electric power auxiliary service market. Shanghai Jiaotong University (2011) 13. Sadeghian, O., Oshnoei, A., Mohammadi-Ivatloo, B., et al.: A comprehensive review on electric vehicles smart charging: solutions, strategies, technologies, and challenges. Journal of Energy Storage 54, 105241 (2022) 14. Wang, X., Zheng, W., Gong, Z., et al.: Research on the dynamic regulation system of market power in the electricity market, vol. 2, pp. 164–169 (2022)

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15. Alexandru Puiu, I., Hauser, R.A.: On market clearing of day ahead auctions for European power markets: cost minimisation versus social welfare maximisation. arXiv e-prints (2022) 16. Laribi, O., Rudion, K., Nagele, H.: Combined grid-supporting and market-based operation strategy for battery storage systems. In: 2020 6th IEEE International Energy Conference (ENERGYCon). IEEE (2020)

Market Research on Electric Auxiliary Services with the Participation of Massive Distributed Power Sources Li Bo1 , Zhao Ruifeng1 , Xin Kuo2 , Lu Jiangang1 , Shi Zhan1 , and Pan Kaiyan3(B) 1 Electric Power Dispatching and Control Center of Guangdong Power Grid Co., Ltd.,

Guangzhou 510000, China [email protected], [email protected], [email protected], [email protected] 2 China Southern Power Grid Power Dispatching Control Center, Guangzhou 510663, China [email protected] 3 Dongfang Electronics Cooperation, Yantai 264010, China [email protected]

Abstract. In order to solve the problem of massive distributed power generation participating in the electric auxiliary service market, an optimization model of auxiliary service market represented by peak shaving is proposed. The frequency regulation and peak regulation characteristics of massive distributed power generation participating in auxiliary services are analyzed. An optimization model for massive distributed power generation to participate in the peak shaving auxiliary service market is established, and the model is solved based on the optimization objectives of the penetration rate and cost of renewable energy, considering various operating constraints. Finally, the effectiveness of the model proposed in this paper is demonstrated by simulation analysis. Under the conditions of the electricity spot market, the deep peak shaving unit can improve the output capacity of renewable energy by nearly 30% and play the role of renewable energy in auxiliary services such as peak shaving. Keywords: Ancillary services · Massive resources · Peak shaving characteristics · Distributed power

1 Introduction As the cost of new energy power generation continues to decline, driven by smart grid and Internet technologies, the operation of the power market has been continuously improved, and it has become an inevitable trend for a large number of distributed power sources to participate in auxiliary services such as power peaking and frequency regulation. Therefore, the market model of electric auxiliary services with massive distributed power sources is analyzed.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1140–1148, 2023. https://doi.org/10.1007/978-981-99-4334-0_135

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At present, the power auxiliary service market with distributed power supply mainly starts from the perspective of peak regulation and frequency regulation, combined with the operation characteristics of distributed power supply. Reference [1] studies the power grid peaking right transaction considering the access of distributed generation. Reference [2] analyzed the distribution network planning considering the participation of distributed electric vehicles in grid peak shaving. Reference [3] studied the optimization model of primary frequency regulation parameters of island microgrid based on the fusion of “wind-solar-storage” measurement data. Reference [4] proposed a multisource coordinated frequency control method for islanded microgrids based on reinforcement learning. Reference [5] proposed a secondary frequency regulation strategy for microgrids with multiple virtual synchronous generators. Existing studies have not conducted content analysis on the participation of massive distributed power sources in the power peaking auxiliary service market, and further research is needed on the peak-shaving performance of massive distributed power sources. This paper studies the market model for systems with massive distributed renewable energy participating in the electric auxiliary service market, establishes the corresponding model, and analyzes the basic performance of frequency regulation and peak regulation.

2 Analysis of Mass Distributed Power Participating in Auxiliary Services 2.1 Analysis of Frequency Modulation Performance of Massive Distributed Resources (1) Power frequency static characteristics of conventional generator sets The power of the load in the power system is provided by the generator set. When the active load of the system changes, the active power provided by the generator set should change accordingly to ensure that the frequency offset is within the allowable range. The relationship between the output active power and frequency of the generator set becomes the power frequency static characteristic of the generator set. The power frequency static characteristic coefficient of the generator set is as follows: kG∗ = −

PG /PGN PG∗ =− f /fN f∗

(1)

A negative sign indicates that the change in active power is opposite to the change in frequency. In the formula: fN is the rated frequency of the system; PGN is the rated active power of the generator set; PG is the variation of the prime mover power when the frequency offset is f . (2) Photovoltaic unit frequency characteristics Based on the constant power control of the photovoltaic power generation system, when the system frequency changes, the original power command is corrected by applying

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∗ , so as to change the active a correction value to obtain the final power command Pref output of the photovoltaic power station to achieve the effect of primary frequency modulation. The power correction value is directly related to the frequency change, and the relationship between the two is:

P = − kf

(2)

PGN fN

(3)

k = kG∗ (3) Wind Turbine Frequency Characteristics

At a certain wind speed, the reference value Pref of the output power of the wind turbine can be obtained by the tracking load shedding operation module, and the sum of the active power required for system frequency adjustment obtained by the frequency response module is the electromagnetic power of the doubly-fed induction fan. The frequency response module adopts virtual inertia control and droop control, and the active power increment P is: P = K

1 d f + f dt R

(4)

where f is the system frequency deviation value obtained by actual measurement; K is the inertia control coefficient; R is the droop control coefficient. (4) Energy storage frequency characteristics The additional frequency response unit of the energy storage system converts the system frequency deviation into the active power reference value of the energy storage system through droop control. When the system frequency is in the normal range, the BESS does not exchange active power with the system. When the frequency deviates, the BESS can quickly release or absorb active power to the system to provide frequency support for the system. The reference value of the active power output of the energy storage system obtained by the droop control is Pref = Kb f

(5)

2.2 Analysis of Peak Shaving Performance of Massive Distributed Resources Peak shaving is an important part of auxiliary services. Reasonably dispatching distributed power sources and participating in peak shaving auxiliary services can improve the economy of the power system. The inclusion of distributed power sources such as energy storage equipment and demand-side resources into auxiliary service resources can improve power auxiliary services, expand the main body of auxiliary services, and promote electricity spot market transactions [7–10].

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Renewable energy and distributed power sources composed of renewable energy can participate in peak regulation in the form of virtual power plants. The operating cost of the peak shaving system comes from both the virtual power plant and the traditional thermal power unit. Usually, the peak shaving model needs to consider the dual goals of the environment and the economy as a whole, with the goal of minimizing the cost, and carry out the corresponding modeling analysis. etc. to realize the specific calculation of the peak shaving model. A virtual power plant (VPP) is a virtual power plant that aggregates dispatchable or non-dispatchable distributed power sources, energy storage and controllable loads through information and communication technology. With the goal of minimizing power generation costs or maximizing benefits, plan, monitor and coordinate the power flow between various resources, realize the aggregation of various resources scattered in the grid, such as distributed power sources, energy storage and loads, and perform collaborative optimization of operation control and market transactions, realizing multienergy complementation on the power supply side, flexible interaction on the load side, and providing auxiliary services such as peak regulation, frequency regulation, and reserve to the power grid.

3 Mass Resources Participate in the Market Model of Peak Shaving Auxiliary Services 3.1 Objectives In the context of the electricity spot market, renewable energy is quoted and traded under the constraints of physical entities while maintaining a real-time balance. In addition, the penetration rate of renewable energy in modern power networks continues to increase, and the difficulty of unit combination is also increasing. The main consideration is that the uncertainty and volatility of renewable energy will bring certain challenges to the arrangement of network units. At present, the economic dispatch of units and the combination of units are mainly controlled by the minimum cost. Considering that the connection of renewable energy to the grid will bring certain economic and environmental benefits, it is necessary to take into account the penetration of renewable energy in the objective function. Finally, the economic dispatch objective function of peak-shaving units in the spot market is formed as Eq. (6). F = min

S  s=1

  ρs CT ,S + CPR + CDG,S

(6)

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Among them, s is the number of scenarios; CTs is the operating cost of thermal power units in scenario s; CPR is the operating cost of peak-shaving units; CDGs is the reduction cost of renewable energy units in scenario s. 1. Thermal power unit operating cost The operating cost of thermal power unit includes marginal cost and unit start and stop cost, as is shown in Eq. (7). CT ,s =

T      2 ai + bi PS,i,t + ci PS,i,t + γi,t Ci+ + ηi,t Ci−

(7)

t=1 i∈G

Among them, G is the unit set; T is the scheduling period; ai , bi , ci are the cost coefficients expressed in the form of quadratic functions; t is the secondary system variable of unit operation; C i + is the start-up cost of the unit; C i − is the shutdown cost of the unit. 2. Peak shaving cost Since the price function of formula (1) is a non-decreasing function, its cost can be further expressed as Eq. (8): K         CPR ≥ π Mik MS,i,t + π Mik − π Mik+1 Mik

(8)

k=1

  Among them, Mik is the variable in the kth segment; π Mik is the corresponding price. 3. Renewable energy cost reduction Considering the environmental benefits of renewable energy, renewable energy generation output should not be curtailed, and if it occurs, a penalty function should be considered. Its objective function is as follows: CDG,S = cDG

T  

C Ps,j,t − Ps,j,t

 (9)

t=1 j∈D

Among them, cDG is cost reduction; Ps,j,t is the output of renewable energy; and Ps,j,t C is the maximum possible unit output. 3.2 Constraints Ui   t=1

Di     1 − xi,t xi,0 + xi,t 1 − xi,0 = 0

(10)

t=0

    Ui = min T , max Tion − HiU xi,t

(11)

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    off Di = min T , max Ti − HiD 1 − xi,t

(12)

 i∈G

Ps,i,t +

 j∈D



Ps,j,t +

Ps,l,t −

l∈in



Ps,l,t = Dt

(13)

l∈out

C 0 ≤ Ps,j,t ≤ Ps,j,t

(14)

0 ≤ Ms,i,t ≤ Ms,i,t,max

(15)

−Pl max ≤ Ps,l,t ≤ Pl max

(16)

  Pi,min − Ms,i,t xi,t ≤ Ps,i,t ≤ Pi,max xi,t

(17)

Ps,l,t =

+ − − θs,l,t θs,l,t

(18)

Xl up

−Rdn i − Pi,t,max γi,t ≤ Pi,h,t − Pi,h,t−1 ≤ Ri + Pi,t,max ηi,t

(19)

γi,t + ηi,t ≤ 1

(20)

xi,t − xi,t−1 = γi,t − ηi,t

(21)

Among them, Ui and Di are the start and stop time of the unit; xi,t is the start and stop state of the unit; xi ,0 is the unit state at the initial moment; Ti on and Ti off are the rated start and stop time of the unit; Hi U and Hi D are the total continuous time of start and stop; θs,l,t + and θs,l,t − are the phase angles at the beginning and end of the transmission line l; Ps,l,t are the power flow of the line l in the scenario s; Ri dn and Ri up are the maximum downhill and uphill values; Xl is the line impedance; Dt is the load during the t period.

4 Solution Since binary variables (Pi,min – M s,i,t )x i,t are added to the model in this paper, the problem in this paper is nonlinear mixed integer programming, which is difficult to solve. However, since the binary variable is a continuous variable, the term can be linearized by the big M method, and the following is obtained as Eq. (22)–(24): i,t ≤ Ps,i,t ≤ Pi max xi,t         −M 1 − xi,t + Pi,min − Ms,i,t ≤ i,t ≤ Pi,min − Ms,i,t + M 1 − xi,t −Mxi,t ≤ i,t ≤ Mxi,t

(22) (23) (24)

Among them, M is a large number; when xi , t is 1, the following formula is established; when xi , t is 0, the above formula is established.

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5 Numerical Results 5.1 System Introduction In this paper, the IEEE30 node system is selected for simulation analysis, as is shown in Fig. 1, and the simulation environment is MATLAB2014b. The system scheduling period is 24 h, and this paper considers that the uncertainty of the predicted output of renewable energy is a normal distribution. The node positions of the thermal power unit and the peak-shaving unit are shown in Fig. 2, and the corresponding unit parameters are shown in the following Table1. Table 1. Units parameters. Unit

Pmax

Pmin

Pmin

M

RU

1

200

120

40

8

65

2

85

45

15

6

10

13

36

15

6

2

5

Fig. 1. IEEE 30 bus feeder system.

5.2 Analysis Since there are many output scenarios of distributed power and renewable energy, unit 1 is analyzed, and the result is shown in Fig. 3. It can be seen that after the participation and optimization of deep peaking units, the output of renewable energy units has been effectively improved. This is because thermal power units can reduce their output through fuel. Although this will increase the cost of power generation, the output of renewable energy will increase, bring greater benefits. It can be seen that under the conditions of the electricity spot market, the deep peak shaving unit can improve the output capacity of renewable energy by 30% and play the role of renewable energy in auxiliary services such as peak shaving.

Power(MW)

Market Research on Electric Auxiliary Services with the Participation ×103 8 7 6 5 4 3 2 1 0 0

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Renewable Resources Power Output(MW)

Fig. 2. Load demand and original RES output. ×103 2

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Fig. 3. RES output.

6 Conclusion The market model for systems with massive distributed renewable energy participating in the electric auxiliary service market is studied, and the corresponding model is analyzed, and the basic performance of frequency regulation and peak regulation is established. Through simulation analysis, it is shown that the ancillary service market model with massive distributed renewable energy participation proposed in this paper can effectively solve the basic model of such resources participating in peak regulation, give full play to the role of renewable energy in auxiliary services such as peak regulation, and improve renewable energy. The output capacity of renewable resources further increases the stability of the system. 30% of increase of renewable energy output capacity can be seen from the simulation. The model proposed in this paper can effectively solve the problems raised, has strong robustness and applicability, and can promote the further improvement of the proposed mechanism. Acknowledgements. The Key Science and Technology Project of China Southern Power Grid Co., Ltd. 【036000KK52210047】.

References 1. Jin, Y., Wang, Z., Jiang, C.: Research on power grid peaking rights trading considering distributed power access. Electrical Appliances and Energy Efficiency Management Technology 02, 48–52 (2016)

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2. Yang, H., Huang, Y., Liu, B., Yi, D., Wang, B.: Distribution network planning considering the participation of distributed electric vehicles in power grid peak regulation. Journal of Electric Power Science and Technology 27(01), 48–53 (2012) 3. Chen, K., Shang, L., Luo, J., Yao, Y.: Optimization model of primary frequency regulation parameters of island microgrid based on “wind-light-storage” measurement data fusion. Renewable Energy 40(03), 383–388 (2022) 4. Yao, J., Hu, S., Wang, G., Shen, Y., Jiang, L., Feng, Y., Gong, C., Zhang, Z., Liu, W.: Multisource coordinated frequency control method for island microgrid based on reinforcement learning. Electric Power Construction 41(09), 69–75 (2020) 5. Tu, C., Yang, Y., Lan, Z., Xiao, F., Li, Y.: Secondary frequency regulation strategy of microgrid with multiple virtual synchronous generators. Journal of Electrotechnical Technology 33(10), 2186–2195 (2018) 6. Li, C., Wang, C., Yin, F., et al.: Optimal power flow calculation of distribution network with power flow router. Power System Protection and Control 47(6), 1–8 (2019) 7. Dib, M., Nejmi, A., Ramzi, M.: New auxiliary services system in a transmission substation in the presence of a renewable energy source PV. Materials Today: Proceedings (2020) 8. Fattaheian-Dehkordi, S., Abbaspour, A., Lehtonen, M.: Electric vehicles and electric storage systems participation in provision of flexible ramp service (2021) 9. Naidu, K.B., Rajani, B., Ramesh, A., et al.: An efficient energy management of hybrid renewable energy sources based smart-grid system using an IEPC technique (2021) 10. Agostini, M., Bertolini, M., Coppo. M., et al.: The participation of small-scale variable distributed renewable energy sources to the balancing services market. Energy Economics 97(2):105208 (2021)

Safety Constrained Economic Scheduling Model with Mass Distributed Generation Participation Jiangang Lu1(B) , Li Bo1 , Wenjie Zheng1 , Xin Kuo2 , Haixiang Gao1 , and Pan Kaiyan3 1 Electric Power Dispatching and Control Center of Guangdong Power Grid Co., Ltd.,

Guangzhou 510000, China [email protected] 2 China Southern Power Grid Power Dispatching Control Center, Guangzhou 510663, China 3 Dongfang Electronics Cooperation, Yantai 264010, China

Abstract. In order to solve the economic dispatch of massive distributed power generation participation, this paper proposes a system security-constrained economic dispatch model with mass distributed power generation participation, and analyzes the safety-constrained economic scheduling relationship of massive distributed power generation participation. An optimal scheduling model aiming at cost minimization is established, considering the uncertainty of distributed power generation, and proposes to solve the problem by using improved particle swarm method. Finally, the simulation model is used to verify the effectiveness of the content proposed in this paper. A comparison between the classical particle swarm optimization and improved particle swarm optimization is made illustrating the effectiveness of the proposed method. At the same time, the numerical analyses carried out in this paper, demonstrate that the model proposed can effectively solve the problem of the economic dispatch with massive distributed power system, not only reducing the dispatch cost in the day I had market, but also taking the uncertainty output of the wind and the solar system into consideration. Keywords: Distributed Power · Massive Resources · Security Constraints · Economic Dispatch

1 Introduction As the cost of new energy power generation continues to decline, driven by smart grid and Internet technologies, the operation of power systems including large-scale distributed power sources has been continuously improved, and it has become an inevitable trend for a large number of distributed power sources to participate in power system scheduling. Therefore, the security-constrained economic dispatch model with massive distributed power sources is proposed. At present, the security-constrained economic dispatch of power system with a large number of distributed power sources mainly focuses on the model objective function and the solution algorithm. Reference [1] proposes an economic optimal dispatch strategy for active distribution networks considering light-load uncertainty and spinning reserve constraints. Reference [2] proposes an economical scheduling strategy for distributed power © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1149–1158, 2023. https://doi.org/10.1007/978-981-99-4334-0_136

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generation based on the cooperative consensus algorithm of super nodes. Reference [3] studied the economic dispatch of the integrated energy system in the park considering the uncertainty of distributed power and demand response. Reference [4] analyzed the microgrid adaptive pricing strategy and economic scheduling method based on blockchain technology. Reference [5] studied the low-carbon economic dispatch of electricity-gasheat integrated energy system considering the dynamic characteristics of tube storage. All the above mentioned reference don’t touch the massive distributed power system, which is equipped with much larger volume of distributed energy and resources. The massive distributed system has a different operation requirement compared to the original one, so it needs further study. In view of the deficiencies of the above literatures, a system security-constrained economic dispatch model involving the participation of massive distributed power sources is proposed, and the safety-constrained economic dispatch relationship with the participation of massive distributed power sources is analyzed. An optimal scheduling model aiming at cost minimization is established, considering the uncertainty of distributed power generation, and proposes to solve the problem by using improved particle swarm method. Finally, the simulation model is used to verify the effectiveness of the content proposed in this paper.

2 Massive Distributed Power System 2.1 Massive Distributed Resources Mass distributed power system is to aggregate dispatchable or non-dispatchable distributed power, energy storage and controllable load rapidly. With the goal of minimizing power generation costs or maximizing benefits, plan, monitor and coordinate the power flow between various resources, realize the aggregation of various resources scattered in the grid, such as distributed power sources, energy storage and loads, and perform collaborative optimization of operation control and market transactions, realizing multi-energy complementation to the power grid. The entry of such massive resources into the power grid requires a unified management system, and the unified deployment of a large number of data resources requires resource fusion and information coordination. System features include: (1) Resource redistribution. Aggregated resources mainly include power generators such as photovoltaics and wind power, gas-to-electricity/heat equipment such as micro-gas turbines and boilers, rechargeable and dischargeable energy storage equipment such as EVs, heat storage tanks and batteries, and flexible demand response resources, etc. (2) Two-way communication. There are more types and quantities of equipment in the system, covering a wide range of areas, complex operating status of the system, and widely deployed data collection and monitoring resources, which can realize multi-dimensional communication of massive resources, which is conducive to the participation of massive resources in electricity market transactions.

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The principle of massive distributed power system is shown in Fig. 1.

Power grid

VPP energy management system

Trade

Dispatch

VPP EV

PV

Load

E2G

ESS

Microdiesel

Boiler etc.

Fig. 1. Schematic diagram of massive distributed power system.

It is known that in the context of the development of the power system, the massive resources connected to the power grid are widely distributed in the transmission and distribution networks, including large-scale centralized wind power generation, large-scale centralized photovoltaic power generation, large-scale energy storage and other resources in the transmission system; including distributed new energy generation, energy storage devices, intelligent control devices, low-voltage microgrid loads, mobile power generation vehicles, residential loads, mobile energy storage, charging piles and other new energy equipment Wait. The above massive resources are closely related to the medium-voltage DC network, the low-voltage distribution network, and the low-voltage microgrid, and finally realize the massive data resources featuring big data, Internet of Things, and control centers. 2.2 Participation in Economic Dispatch of Massive Resources With the renewable energy, the network has the opportunity to control its own unit operating costs; on the other hand, by implementing demand response projects, distribution system operators can control the participation of responsive loads and optimize unit output. In this case, real-time control and continuous optimization of the unit is required. Distributed power sources and loads can respond according to price or incentive policies. The illustration of the responsive system in shown in Fig. 2.

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Annual

Ancilliary Service

TOU

Mensual

RTP

Day-ahead

demand bid

PTP

Intra-day

emergency response

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Vbat

(23)

   V − Rˆi − V   V − V      bat bat dc  bat dc  ˆibat ) K > (i −   ≈   e bat    L L

(24)

By substituting (21)–(24) into (11), it has ˆibat (k) − ˆibat (k − 1) 0 Flag0 = 0 otherwise  1 ˆibat > 0 Flag1 = 0 otherwise

(25)

(26) (27)

4 Simulation Validation Figure 2 shows the simulation results for the open-circuit fault in S0. The observed current can track the actual value. The fault detection and location flags are all zero. As the open-circuit fault occurs, the observed battery current rises above 0, and the absolute value of the battery current error exceeds the threshold. In addition, both the flags Flag and Flag0 are changed. Hence, the simulation results show the open-switch fault can be detected and located.

L. Xiang et al. ibat iˆbat

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1 0.5 0

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Fig. 2. Actual and observed valves (left) and the flags of fault detection and fault location (right).

Figure 3 shows the simulation results for open-circuit fault in charge tube S1 . It can be seen that, as the fault occurs, ibat decreases to 0, the observed valve decreases below 0, and the absolute value of the error exceeds the set threshold. Moreover, both the flags Flag and Flag1 are equal to 1. So, the simulation results show that, by the fault flags, the open-switch fault can be detected and located.

0 -20 2.5

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Fig. 3. Actual and observed valves (left) and the flags of fault detection and fault location (right).

5 Conclusions This paper proposes a sliding mode observer-based open-circuit fault diagnosis method for BDDC. The design of synovial observer is based on the global mathematical model of bidirectional DC/DC converter. In this method, the open-circuit fault is detected by the absolute value of the battery current error. The fault location is obtained by the observed current. A BDDC system is built for simulation verification. The results show that the proposed fault diagnosis method can obtain the open-circuit fault detection and location.

References 1. Jamshidpour, E., Poure, P., Gholipour, E., Saadate, S.: Single-switch DC-DC converter with fault-tolerant capability under open- and short-circuit switch failures. IEEE Trans. Power Electron. 30(5), 2703–2712 (2015) 2. Jamshidpour, E., Poure, P., Saadate, S.: Photovoltaic systems reliability improvement by realtime FPGA-based switch failure diagnosis and fault-tolerant DC-DC converter. IEEE Trans. Ind. Electron. 62(11), 7247–7255 (2015) 3. Shahbazi, M., Jamshidpour, E., Poure, P., Saadate, S., Zolghadri, M.R.: Open- and short-circuit switch fault diagnosis for nonisolated DC-DC converters using field programmable gate array. IEEE Trans. Ind. Electron. 60(9), 4136–4146 (2013) 4. Farjah, E., Givi, H., Ghanbari, T.: Application of an efficient Rogowski coil sensor for switch fault diagnosis and capacitor ESR monitoring in nonisolated single-switch DC-DC converters. IEEE Trans. Power Electron. 32(2), 1442–1456 (2017)

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5. Cho, H.K., Kwak, S.S., Lee, S.H.: Fault diagnosis algorithm based on switching function for boost converters. Int. J. Electron. 102(7), 1229–1243 (2015) 6. Pei, X., Nie, S., Chen, Y., Kang, Y.: Open-circuit fault diagnosis and fault-tolerant strategies for full-bridge DC-DC converters. IEEE Trans. Power Electron. 27(5), 2550–2565 (2012) 7. Wang, H., Pei, X., Wu, Y., Xiang, Y., Kang, Y.: Switch fault diagnosis method for series-parallel forward DC-DC converter system. IEEE Trans. Ind. Electron. 66(6), 4684–4695 (2019) 8. Chen, Y., Pei, X., Nie, S., Kang, Y.: Monitoring and diagnosis for the DC-DC converter using the magnetic near field waveform. IEEE Trans. Ind. Electron. 58(5), 1634–1647 (2011)

A SiC MOSFET Current Balancing Technique Based on the Gate Driver with a Multi-channel Output Stage Zekun Li1 , Bing Ji1(B) , and Wenping Cao2 1 University of Leicester, Leicester LE1 7RH, UK

[email protected] 2 Anhui University, Hefei 230039, China

Abstract. The improvement of the current handling capacity necessitates the parallel connection of power semiconductors in multichip power modules (MPMs). Derating is a common engineering practice by constraining chips in a narrower operating envelope to address the uneven current sharing and non-homogeneous thermal conditions among paralleled chips. This paper investigates the uneven current sharing issue for paralleled devices and how this can be mitigated using a gate drive with a multi-channel output stage. In particular, the conventional gate drivers incorporating an output stage with a single-buffer layer (SBL) is evaluated and compared to that with a multi-buffer layer (MBL), it is found that the driver structure proposed in this paper can reduce the uneven current sharing in parallel devices by constraining the ground loop current. Keywords: SiC MOSFET · Current balancing · Parallel · Gate driver

1 Introduction With the advances of new semiconductor materials, wide bandgap (WBG) power devices such as silicon carbide (SiC) MOSFETs have proved their market attraction to replace silicon devices in road transport electrification. SiC MOSFETs provide superior performance with respect to Si IGBTs including low switching losses, high switching frequency, and high-temperature capability, but they are more expensive. Chips of small die sizes are preferred for economic reasons and are normally used by device manufacturers in a parallel configuration. To minimize the cost at a given semiconductor fab yield, multichip power modules (MPM) incorporating multiple chips in the parallel connection are commonly used to increase the current capability and the overall thermal performance in high-power applications [1]. The uneven current distribution and inhomogeneous temperature among parallel devices are major concerns to constrain the overall current capacity and thus the safe operating area (SOA) of MPMs [2]. To tackle such issues, a conservative design philosophy is conventionally applied where the device is de-rated (electrically and thermally) by the device manufacturers and system integrators based on their best engineering estimate © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1246–1253, 2023. https://doi.org/10.1007/978-981-99-4334-0_148

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and experience so that the intended field robustness and reliability can be guaranteed. However, derating is not without cost and, further, there are concerns about its potential to compromise reliability and performance. Advanced gate drivers with optimized structural and functional approaches can significantly improve the control and protection of SiC MOSFETs, while their output stages are in the close vicinity of power semiconductors and can directly shape the switching trajectories by controlling the turn-on and turn-on transitions. From the gate driver controllability viewpoint, gate drives can be categorized as conventional (fixed) gate drivers and active gate drivers. From the structural viewpoint concerning the output channel for SiC MOSFETs connected in parallel, the output stages can be categorized as three different types as shown in Fig. 1, namely the Single-Buffer Layer (SBL), the Multi-Buffer Layer (MBL) and its isolated version, i.e., iMBL.

Fig. 1. Schematic diagram of (a) SBL, (b) MBL, and (c) iMBL output stage topologies for the gate driver.

Compared to conventional SBL-based gate drivers, both multiple buffer options enable a smaller gate loop design by positioning the output stage and its filter capacitors closer to the gate input of associated MOSFETs. Thus, a low inductive, more balanced and less-oscillating gate loop can be achieved to accommodate the fast-switching performance provided by SiC MOSFETs. In addition, asynchronous chip-level control can be achieved with individual output stages for any parallel MOSFETs, which offers a new avenue for precise control of MPMs. For example, design choices such as the gate resistor values, the driver supply voltage values, and active gate control strategies can be independently implemented at the chip level for parallel devices. This paper investigates the benefits of using the iMBL output stage in comparison with the benchmarking SBL-based gate drivers. It proceeds with an analytical analysis of the switching transitions in the next section, followed by simulation results in Sect. 3. Section 4 shows the experimental result and finally, a conclusion of the paper is given in Sect. 5.

2 Dynamic Current Sharing Model To analyze the dynamic current imbalance issue among parallel devices, the dynamic performance of SiC MOSFETs during turn-on transients is studied [7] using a halfbridge circuit under an inductive load and its circuit diagram is shown in Fig. 2 (a) [3–5]. The effective inductances in both the gate loop and the power loop are derived

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to simplify our analysis, as shown in Fig. 2(b). The top MOSFET of the converter leg is replaced by a junction barrier diode, which is parallel connected to a load inductance for the double-pulse test.

LDC_T DT

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S

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LS_i S

S (a)

(b)

Fig. 2. A half-bridge circuit under an inductive load with (a) detailed parasitic inductances and (b) simplified inductances.

The equivalent circuit models of a dual-parallel MOSFET configuration with gate a SBL-based gate driver and an iMBL-based gate driver are comparatively analysed as shown in Fig. 3. The typical values of circuit parameters and parasitic are given in Table 1. With the iMBL-based gate driver, a symmetrical gate loop design with reduced parasitic inductances can be achieved resulting in equal Kelvin source inductances and equal common source inductances [6]. Besides the uneven parasitic inductances of the power-source in the Kelvin connection, other parasitic inductances have little effect on the dynamic current distribution. However, this conclusion is not fully applicable to the iMBL structure. Therefore, in conjunction with practical applications, this chapter develops analytical models for both SBL and iMBL topologies, considering the possible uneven external parasitic parameters in the circuit topology, as well as the possible internal dynamic current sharing mechanism in case of inconsistent turn-on timings in the multi-buffer. 2.1 SBL Connection According to Fig. 3(a), during the turn-on transient,   i1 = gm vgs1 − Vth  i2 = gm vgs2 − Vth

(1)

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Fig. 3. Equivalent circuit models for dual-parallel MOSFETs with their gate drivers using (a) a SBL-based and (b) an iMBL-based output stage. Table 1. Parameters of the equivalent circuit. Symbol

Parameters

Value

VDC

DC bus voltage

600 V

CDC

Bus bar capacitor

2000 µF

Cj

Diode junction capacitor

1.04 nF

Lp

Power loop inductance

237 nH

Lload

Load inductance

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VG_1,2

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− 5/15 V

LS_1,2

Power source inductance

15 nH

Lks_1,2

Kelvin source inductance

20 nH

LCS_1,2

Common source inductance

Unknow

RG_1,2

Effective gate resistance

10 

By using KVL in the two gate loops, where,     dig1 dig1 diloop di1 + + + Lks1 − VG vgs1 = ig1 Rg1 + Lcs1 dt   dt dt   dt dig2 dig2 diloop di2 + + − Lks2 − VG vgs2 = ig2 Rg2 + Lcs2 dt dt dt dt At the same time, taking the initial current commutation time as the initial time, vgs1 =

1 Ciss

t iG1 dt + vgs1 (0) 0

(2)

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vgs2

1 = Ciss

t iG2 dt + vgs2 (0)

(3)

0

The KVL equation for the ground loop circuit is given by, (Lks1 + Lks2 )

diloop dt

+ Lks1

dig1 dt

− Lks2

dig2 dt

= Ls1 didts1 − Ls2 didts2

(4)

where, is1 = i1 − iloop , is2 = i2 + iloop . 2.2 iMBL Connection Compared to SBL, iMBL eliminates the additional effect of ground loop current on the gate loop, the gate loop KVL equation changes to     dig1 dig1 di1 vgs1 = ig1 Rg1 + Lcs1 + + Lks1 − VG dt   dt   dt (5) dig2 dig2 di2 + + Lks2 − VG vgs2 = ig2 Rg2 + Lcs2 dt dt dt Since there is no loop current Iloop , the gate voltages Vgs of the parallel devices are identical when the drive voltage VG and the gate loop parasitic parameters are identical, thus effectively suppressing the uneven current sharing of the devices.

3 Simulation Results The common source inductances, LCS1 and LCS2, can normally produce the di/dt kick-back voltage during the turn-on transitions and their inductance values are largely influenced by the circuit design interfacing both power source and Kelvin source. Due to the dedicated multi-channel output stage, Kelvin source inductances and common source inductances for both parallel switches are minimized while any mismatch is neglected due to their symmetrical gate loop design. Therefore, the simulation focuses on the impact of mismatched power source inductances, that is LS1 of 10 nH for Q1 and LS2 of 25 nH for Q2, on the dynamic current imbalance during the turn-on transients. To justify the design of the simulated circuit parameters, Fig. 4 first verifies the double-pulse results of the SBL circuit when all the parasitic parameters are perfectly symmetrical, showing that the drain-source currents and gate voltages of the two paths coincide almost exactly. Figure 5 shows the circuit operation in the two topologies when the power source inductance differs by 15 nH. (b) shows a significant unevenness in the current in the SBL case. To exclude oscillation, a smoother section of the turn-on transient was selected for analysis. At 19.03 µs, when the uneven current in Ids reaches 7.7 A, while due to the ground loop current, the A current of 749 mA is generated on the Kelvin Source and the voltage induced by this current on the Lks leads to a difference of 744 mV in the gate voltage, which in turn increases the difference in the drain source current. In contrast, the

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Fig. 4. DPT results under symmetrical circuit topology. ILks Vgs1-Vgs2

Iloop Vgs1-Vgs2

Vgs1,V gs2

Vgs1,V gs2

Ids1-Ids2

Ids1-Ids2

Ids1,Ids2

Ids1,Ids2

(a)

(b)

Fig. 5. A fragment of turn-on transient from 19 µs to 19.045 µs for (a) iMBL and (b) SBL structure both when Ls = 15 nH.

iMBL shows a better current distribution result in the same case. At the same sampling point, the gate loop of the iMBL is not affected by the ground loop due to the isolation of the gate loops, as shown in the waveform diagram at the top of Fig. 5(a). As there is no loop current in this structure, the current flowing through Lks can only be measured by testing one of the branches during turn-on, and at this point it is only 214 mA and gradually decays. So that the gate voltages of the two devices do not produce a large difference, Id unevenness in the iMBL case is only affected by the inductance unevenness of the power loop and does not superimpose the gate voltage and the final unbalance of the two branches is only 3.09 A. The simulation demonstrates that the iMBL has a better ability to suppress current unevenness in the case of Ls unevenness.

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4 Experiment Verification As shown in Fig. 6, the test bench for this experiment was modified from Cree’s CRDHB12NJ1 parallel device test bench, which had an SBL structure, by changing the gate interface to allow simultaneous testing of the iMBL. By testing both gates loop topologies, it is found in Fig. 7 that when there is an unevenness of 15 nH in Ls, there is a greater oscillation and unevenness in the turn-on phase of the two of the path currents under the SBL structure compared to the iMBL, corresponding to the simulation results and theoretical derivation. The suppression of current unevenness by the iMBL in the presence of Ls unevenness is again demonstrated.

Fig. 6. Paralleled devices double pulse test rig.

SBL

iMBL

17.00

17.50

(a)

17.50

17.00

(b)

Fig. 7. Parallel test results for (a) iMBL and (b) SBL when Ls = 15 nH.

5 Conclusion The article analyses the current unevenness in parallel devices during turn-on transients affected by ground loop current, which is formed mainly because the unevenness of power source inductance leads to the formation of a current path between the kelvin

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sources of the parallel devices, and the voltage drop induced by this current on Lks affects the gate voltage, thus increasing the current unevenness. To solve this problem, this paper proposes an iMBL structured gate topology that isolates the parallel gate loops from each other and avoids the generation of ground loop currents. Through simulations and experiments, it is demonstrated that the method effectively suppresses the branch current unevenness caused by Ls asymmetry and provides an effective reference for subsequent circuit design and the design of power modules.

References 1. Zeng, Z., Zhang, X., Zhang, Z.: Imbalance current analysis and its suppression methodology for parallel SiC MOSFETs with aid of a differential mode choke. IEEE Trans. Ind. Electron. 67(2), 1508–1519 (2020) 2. Zhao, C., Wang, L., Zhang, F.: Effect of asymmetric layout and unequal junction temperature on current sharing of paralleled SiC MOSFETs with Kelvin-source connection. IEEE Trans. Power Electron. 35(7), 7392–7404 (2020) 3. Zeng, Z., Zhang, X., Li, X.: Layout-dominated dynamic current imbalance in multichip power module: mechanism modeling and comparative evaluation. IEEE Trans. Power Electron. 34(11), 11199–11214 (2019) 4. Zhang, B., Wang, S.: Parasitic inductance modeling and reduction for wire-bonded half-bridge SiC multichip power modules. IEEE Trans. Power Electron. 36(5), 5892–5903 (2021) 5. Lv, J., Chen, C., Liu, B., Yan, Y., Kang, Y.: A dynamic current balancing method for paralleled SiC MOSFETs using monolithic Si-RC snubber based on a dynamic current sharing model. IEEE Trans. Power Electron. 37(11), 13368–13384 (2022) 6. Funaki, Y., Wada, K.: Gate drive circuit configuration for current balancing of SiC MOSFETs connected in parallel. In: IEEE International Future Energy Electronics Conference (IFEEC), pp. 1–5. (2021)

The Parametric Array Speaker: A Review Shangming Mei, Hui Xu(B) , Yihua Hu, Mohammed Alkahtani, and Yangang Wang School of Physics, Engineering and Technology, University of York, York, UK [email protected]

Abstract. The parametric array speaker uses the directivity characteristic of ultrasonic waves to spread sound in beamform within a specific range. The basic principle of parametric array speakers is to modulate the audible acoustic signal onto the ultrasonic carrier signal and transmit it into the air by the ultrasonic transducer. However, there are problems with the sound quality of small-size parametric loudspeakers. Due to the influence of finite amplitude sound theory, the audible sound demodulated by parametric loudspeakers has poor sound pressure in the middle and low-frequency bands. As the frequency of the demodulated sound increases, the sound pressure of the demodulated sound increases monotonically. This paper summarizes the basic principle, modulation, and design method of the parametric speaker and the ultrasonic transducer. It puts forward the improvement of its amplifier module, which plans to apply the GaN power device to the output stage of the parametric speaker power amplifier. Keywords: Parametric speaker · GaN device · Power amplifier · Modulation method · Ultrasonic transducer

1 Introduction The Directional Sound System is a device that allows sound waves to pass only in one direction by using the nonlinear characteristics of the air to self-demodulate and modulate the ultrasonic signal [1]. It is possible to produce devices that use beamforming to directly control audio directionality, which can be used to reduce ambient noise and provide isolated audio experiences in many applications, such as public address systems, home theaters, airplanes, and buses [2]. The sound characteristic of parametric speakers has been shown in Fig. 1. Application for parametric speaker: One of the advantages of using parametric speaker is creating a personal space in public space. For example, a study has shown that using parametric speakers in nursing homes to play the music can help reduce dementia behavior in the elderly [4]. Some Studies have also demonstrated the feasibility of using a parametric speaker and face-tracking traffic warning system at street intersections [5, 6]. Moreover, the application scenario of the parametric speaker is broad. One study has shown the feasibility of parametric speaker application in radio acoustic sounding © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1254–1271, 2023. https://doi.org/10.1007/978-981-99-4334-0_149

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Fig. 1. The sound propagation characteristic of parametric speaker [3]

systems (RASS) [7]. Some studies also offer the possibility of the parametric speaker in active noise reduction-related technologies [8, 9]. A directional loudspeaker works in a completely different way to a conventional loudspeaker. The most significant difference is that they do not use a single, moving electromagnetic coil and diaphragm to produce the normal, audible waves of sound that we hear. Instead, they use an array of electrical devices called piezoelectric transducers or polyvinylidene fluoride (PVDF) film [10]. According to Huygens’ principle, it is difficult for ultrasonic waves to have diffraction phenomena. Most ultrasonic waves travel in a straight line, which means that ultrasonic waves are very directional [3]. According to the theory of analog communication, the method of transmitting a sound signal over a long distance by a carrier sine wave of high frequency is described. The ultrasonic sound waves act as a carrier for audible sound frequency and if frequency and amplitude is high enough (20–100 kHz) [11, 12], air itself becomes a non-linear medium which act as a demodulator, and audible frequency is delivered to the receiver. Which means if modulated frequency from Directional sound system hits someone or receiver the demodulation of frequency occurs that is ultrasonic sound waves and audible input signal separates and input signal or audible frequency is delivered to receiver [13, 14]. The most prevalent forms of carrier modulation are AM (amplitude modulation) and FM (frequency modulation). And the demodulating process in air. Parametric speakers usually have high directivity, high THD, beamforming ability to produce a steerable array. But the performance is poor low-frequency output, and low audible output. The ultrasound with different frequencies demodulates to several new frequencies in the air, only a very small part of the sound which has suitable frequency can be used. These require that the ultrasonic speaker usually need a significant amount of energy to generate the original frequency ultrasound. The high THD is caused by the same reason. The primary purpose of this paper is to review the parametric speaker and provide a parametric speaker design scheme based on FPGA.

2 Topologies for Parametric Speaker The concept for the parametric array sound generating system is shown in Fig. 2. It is made up of three parts: the emitting transducer, the power amplifier, and the signal processing unit. The modulator processes audio signals by stacking the original signal with the carrier. Power amplifiers are indispensable components for amplifying audio signals to an acceptable level. They should have wide bandwidth and enough linear output

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characteristics. Finally, the transducer array also affects the output of the parametric speaker. This section will discuss these parts.

Fig. 2. Architecture of directional sound system [15]

A. Modulation Method of Parametric Speaker/Digital process Ultrasonic wave is the carrier of audible sound frequency. When the frequency and amplitude are high enough (high sound pressure level), air, as a demodulator, becomes a nonlinear medium. Carriers interact with other spectral components of the ultrasonic beam to generate new spectral features along the ultrasonic beam. This means that if the modulated frequency of the directional sound system travel in the air, the frequency will demodulate; Therefore, the ultrasonic wave source generates a beam of ultrasonic waves that acts as a virtual array of sound sources [16]. The demodulation process has been shown in Fig. 3.

Fig. 3. Output PAA of directional sound system [3]

The loudspeaker is fed with two ultrasonic signals with frequencies f1 and f2 , that are very close to each other, as shown in Fig. 4. A small portion of the acoustic energy will be transformed into new spectral components in the signal, such as 2f1 , 2f2 and f1 + f2 , and high order harmonics, etc. The high-frequency components will be substantially attenuated in air and diminish quickly as the distance from the speaker increases. Due to the comparatively poor absorption of this term in air, the differential frequency f1 − f2 is created. Additionally, the acute directivity of this low-frequency sound is the result of acoustic nonlinearity, and it inherits the spatial properties of the fundamental waves [17].

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Fig. 4. Nonlinear interaction process in air [1]

1) Double sideband amplitude modulation (DSB) Double sideband amplitude modulation (DSBAM) is a mature carrier modulation method. It was used in parametric speaker system in 1983 [18]. The modulation envelope for the parametric speaker system is: Ay(n) = [1 + mx(n)] ∗ Acos(2π fc t)

(1)

where: m modulation index x message signal fc carrier frequency (Hz). According to the experiments in [19], THD will increase as the value of m increases; with the maximum m of 1, THD will increase by 80%. In order to increase the high voltage level demodulated signal, a high value of M is needed. Therefore, if DSBAM is used, a trade-off between high THD and low demodulation is required, which is disadvantageous for the design of a parametric speaker, so DSBAM would not be the preferred choice (Fig. 5).

Fig. 5. DSB with carrier generation block diagram

2) Modified amplitude The Modified Amplitude Modulation (MAM) method, a class of hybrid AM and SRAM methods based on orthogonal AM, is proposed in [20, 21]. The block diagram of the MAM method is shown in Fig. 6. A compromise between audio loudness and sound quality must be struck when choosing a modulation technique and modulation index. A large modulation index will

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Fig. 6. Block diagram of the MAM method

produce audible sound that is louder but has greater distortion [22]. One option to obtain a demodulated signal that is distortion-free is to use the square rooting method [23], although this method necessitates the use of wide bandwidth transducers. 3) Single-Sideband Adopting the single-sideband with carrier (SSB-WC) system as seen in Fig. 7 is an alternate strategy to eliminate distortion. The SSB utilizes electrical power and bandwidth more effectively than AM.   p1 (t) = m g(t) cos(ωc t) ± g(t) ˆ sin(ωc t) + sin(ωc t) (2) where m is the modulating index, g(t) is the input signal and g(t) ˆ is the Hilbert transform of the input signal. In Fig. 6, the positive (+) and negative (−) symbols refer to the LSB and USB modulation, respectively. The Hilbert block is a Hilbert transform with a transfer function H(ω) = −jsgn(ω), where sgn(ω) is defined as sgn(ω) = 1 for ω > 0, sgn(ω) = 0 for ω = 0 and sgn(ω) = −1 for ω < 0. For a normalized signal g(t) = cos(ω − t), the function of Hilbert transform is to perform a delay phase shift of π/2 so that g(t) ˆ = sin(ω − t). The output of the single sideband modulator, ϕ SSB(t), can therefore be written as follows:   ϕSSB (t) = 0.5 m cos(ωc t) ± 0.5 m sin ω_ t   = 0.5 m cos (ωc ∓ ω− )t (3) where ωc is the carrier angular frequency. The modulated output signal is:    ϕLSB−WC (t) = 0.5 cos(ωc t) + mcos (ωc − ω− )t

(4)

And the modulated output signal for USB-WC is:    ϕUSB−WC (t) = 0.5 cos(ωc t) + mcos (ωc + ω− )t

(5)

4) Acoustic Beamforming Capability Acoustic beamforming is a form of spatial filtering in which signal processing techniques can control the propagation of directional sound waves. This requires a set of sensors

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Fig. 7. Single sideband modulation with carrier (SSBWC).

and a delay value added to a single sensor. It is similar to phased array technology [24, 25]. The parametric speaker can implement an acoustic beam due to the design of multiple transducers. A parametric transducer array design with beamforming capability is shown in Fig. 8. By adding drivers and amplifiers to each transducer element, different delay values can be added between the transducer elements. This is actually a huge challenge for the amplifier module because it multiplies the number of amplifier circuits that need to be designed, and the size and cost of the module also multiplies [26].

Fig. 8. Parametric loudspeaker array with beamforming capability utilising digital processing.

B. Power amplifier for parametric speaker Parametric speaker system is capable of supporting a wide variety of amplifier topologies, much like other audio systems. Figure 9 displays a comparison of the efficiency of several audio power amplifier types. According to various operating circumstances, traditional analogue power amplifiers can be divided into Class A, Class B, Class AB and other types of amplifiers. Due of their great fidelity, these amplifiers can produce sounds with outstanding quality. However, analog amplifiers have a very poor power conversion efficiency. Digital amplifiers are a recent development that address this issue. The fundamental benefit of switching type amplifiers Class D over linear power amplifiers (Class A) and non-linear amplifiers (Class AB, Class B, and Class C) is their potential 100% power efficiency [19, 27, 28]. At their highest modulation index, well-designed

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Class D amplifiers generally have a power efficiency of well over 90% [29]. Class D is now the best option for commercial audio amplification and is increasingly replacing linear analogue amplifiers [30, 31].

Fig. 9. Efficiency comparison of each amplifier [32]

1) Analog amplifier in parametric speaker: Class A amplifiers are widely used in parametric speakers. It is in the signal input cycle is the on-state (including positive and negative cycles), so even if there is no signal input, the power amplifier is continued in the power consumption; for this reason, Class A amplifier has the best linearity and low distortion degree. But the power efficiency of a Class A amplifier is usually 15–30%. Articles [15, 33] suggest a new power amp and power source to overcome these disadvantages. The linear power amplifier is a Class B push-pull amplifier with a lower DC operating point than Class A, thus ensuring high efficiency and wide bandwidth. Since the DC operating point of Class B amplifier is lower than that of a Class A power amplifier, the signal distortion of the Class B power amplifier is relatively large, and the DC current consumption is small [34, 35]. In order to improve the linearity of the power amplifier, [36] propose a pre-linearized Class B power amplifier to improve linear performance. The power amplifiers’ linearity characteristics are enhanced by decreasing voltage gain variances [37]. The Class C amplifier is other kind of non-linear power amplifiers, could substitute the linear power amplifier (Class A) in the parametric system. However, Class C power amplifiers produce less output power, reducing system sensitivity. To overcome this problem, in [38], a new diode expander structure is proposed for power amplifiers in order to reduce the effect of sinusoidal pulses on the power supply. The proposed structure can increase the input

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pulse amplitude of the central transistor in a power amplifier and thus increase the output voltage of such an amplifier. 2) Digital amplifier in parametric speaker: Class D amplifiers have a unique topology which has a lower power consumption than the linear amplifiers previously discussed. The topology of a Class D amplifier is shown in Fig. 10, where analogue audio signals are sampled and pulse width modulated signals are generated. The signals produced by the output stage are filtered by the filter circuit or the loudspeaker itself and converted into sound signals. Class D amps are classified into four common models based on several different modulation schemes [39–41].

Fig. 10. The topology and wave form for Class D amplifier

The Class D topology has much better efficiency than other Class amplifiers. While the Class D Amplifier does not necessarily have the best distortion rate or signal-to-noise ratio, its high energy efficiency means it fits a wide range of end devices, especially highpower or mobile power sources [42, 43]. There is another advantage of Class D power amplifiers. Digitally modulated signal can be converted directly to pulse by the pulse modulation module, so using the DAC module is no longer necessary [26]. 3) Output stage of Amplifier The output stage is the fundamental component of the power amplifier. Figure 11 shows an essential Complementary Metal Oxide Semiconductor (CMOS) linear switch output stage. In traditional transistor amps, the output stage contains a continuous instantaneous output transistor. Even in the most efficient linear range, the power consumption is still significant. In many applications, this diversity gives Class D a huge advantage. Because of material property limitations, improving the overall performance of existing silicon-based devices through improvements in device structure and fabrication methods is challenging [44, 45]. This calls for new high performance power devices that offer better conversion efficiency, with smaller leads and lower switching losses for variable frequencies. Wide bandgap (WBG) semiconductors based on silicon carbide (SiC) or gallium nitride (GaN) have recently been developed, enabling Class-D amplifiers with exceptional distortion and bandwidth performance [46, 47]. GaN devices reportedly function at greater voltages and lower leakage currents than Si devices [48]. GaN devices have substantially lower on-resistance and conduction losses than Si devices because their vacuum saturation rate is 2.8 times higher. The intersection in common GaN devices’ capacitance allows for switching frequencies of up to Mhz. Table 1 displays the parameter comparison between the GaN device and the Si device. The device’s performance

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Fig. 11. CMOS linear switch output stage

is enhanced by the wider bandgap and the damaged electric field’s insulating properties, which lower conduction resistance. The resultant high carrier mobility and rapid electron saturation rate allow the device to operate at high speeds [49, 50]. GaN devices can result in class D amplifiers with a greater power and reduced THD, according to experiments reported in [51]. The impact of a 60 V GaN device and a Si device class D audio amplifier is compared in [52], and it is concluded that the GaN power device has a significantly greater power density than the Si device [53]. GaN FET is more affordable, faster, and thermally efficient than conventional Si MOSFET. Reference [54] demonstrate a compact Class-D resonant amplifier with eight phases and a frequency of 5 MHz for a targeted ultrasound cancer therapy application. As a GaN-based Class D amplifier device, it shows the advantages of GaN in the ultrasonic field. Table 1. Comparison of characteristic parameters for various semiconductor materials Characteristic parameters

Unit

Si

SiC

GaN

Energy gap

eV

1.1

3.26

3.49

Electron mobility

cm2 /Vs

1500

700

2000

Saturated electron velocity

107 cm/s

1

2

2.8

Electric breakdown field

MV/cm

0.4

2

3.3

Thermal conductivity

W/cm*K

1.5

4.5

> 1.5

Relative permittivity

Er

11.8

10

9

C. Configuration of the transducer array. 1) Design of transducer The sound pressure level of self-demodulated audio is proportional to its angular frequency [55]. In order to eliminate the tendency to respond by this frequency, The sound pressure level (SPL) of the piezoelectric transducer must have a single broad resonant peak or more than two resonant peaks. Many studies have also made efforts to the miniaturization of transducers to make parametric loudspeakers that can be installed on various devices.

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Reference [56] created a circular loudspeaker, specifically by installing double connected diaphragm and two radial cones on the piezoelectric transducer to ensure the high sound pressure level and using a waveguide composed of acoustic crystals to realize the narrow directivity of ultrasonic waves. Piezoelectric micro-machined ultrasonic transducers (PMUTs) are compact and efficient units for use with parametric array sources [57]. Due to the influence of the size of the radiation structure on the radiation impedance, the thin plate PMUT is used to achieve higher electro-acoustic efficiency. For example, in [58], they have implemented a highly oriented air-coupled parameterized loudspeaker using single chip microcomputer-based CMOS compatible with dual crystal AlN PMUTs. Reports show a 200% increase in output performance at a beamwidth of fewer than 5°, and 246 PMUT units are integrated into a 13 mm by 13 mm chip. In order to expand the bandwidth of the transducer array with two sets of loudspeakers resonating at different frequencies, out-of-phase driving (OPD) was utilized [59]. The above techniques describe the implementation of a tiny PA loudspeaker with reasonably low power requirements and high fidelity using the PMUT array, which makes the parametric speaker available for many portable devices such as laptops and mobile phones. 2) Configuration of the transducer The right setup of the cluster relies upon the application and the mounting space accessible for each situation. Different array morphologies produce distinct responses in audio frequency and directivities because the generation length depends on the array’s morphology. The transducer’s density determines the acoustic wave’s directivity with the same signal input. Directivity and power efficiency typically decreases with increasing density [33]. Olszewski and Linhard compared parametric speaker configurations and suggested a ring configuration that could reduce the parametric speaker’s low-frequency beamwidth. The front view of the ring configuration is shown in Fig. 12 (a). Furthermore, providing phase deviations between the nodes of the ultrasound transducer as shown in Fig. 12 (b) leads to additional effects of sound, such as creating an accurate source of noise immunity, reducing the overall noise level, or providing 3D sound reproduction. When a horn was attached to the parametric speaker, as depicted in Fig. 12 (c), it not only altered the array configuration but also increase its directivity. Array aperture, which is roughly equal to array length, is a key to understanding directivity. The range f_min to f_max of maximum directivity for an ordinary array is empirically bounded: given ultrasonic speed c ≈ 340 m/s in free air at sea level [60]. c 1 2 aperture

≤ fmin ≤ fmax ≤

c 2spacing

(6)

The aperture should be at least twice the largest wavelength to be collimated. Speaker spacing should be no more than half the smallest wavelength. The effective aperture of an ultrasonic array is far greater than the actual array length; excellent horizontal focus can be obtained from an ultrasonic array only tens of centimetres long. The main properties of speaker array directionality can be summarized as the following. (1) A larger aperture (loudspeaker array length) is required for low frequency directivity.

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Fig. 12. Various array configurations of the PAL [6].

(2) The higher the frequency of directivity requires a single speaker spacing is more diminutive. (3) The focus is weakened (the beamwidth is increased), and the frequency is decreased.

3 Implementation of the Parametric Speaker The implementation is divided into simulation, hardware design, software design, test and verification. The idea of the experiment design has shown as follow: The investigation will design a parametric speaker for data collection and analysis. It should analyze the influence of frequency variation on sound fidelity, directivity, and fidelity, and specific numerical collection and calculation will be carried out in this experiment. A design of a parametric speaker array without beamforming capability utilizing digital processing will be created in the experiment. The method of the ADC and amplifier of the parametric speaker is simplified in this experiment but not considering the Beamform capability. A. Simulation To characterize the overall system before building the device, extensive simulation using MATLAB will be used to validate the system design. This will include time and frequency domain analysis of the different modulation techniques being used in the Audio amplifier, as well as the modulation techniques that defines how modulated ultrasonic signals are able to demodulate in air. VHDL code can be used for FPGA simulation, and Vivado can be used for accurate simulation calculation, which directly corresponds to the prototype implementation. The simulation results are loaded into MATLAB for further analysis. For simulation design, the individual double-sided PWM will be output in CSV format to drive the transducer group using Vivado for VHDL module simulation. These signals are then loaded into MATLAB for further processing to complete the simulation. Further processing includes applying a piezoelectric transducer simulation filter, transducer signal summation, and a nonlinear demodulation model that simulates the demodulation of ultrasonic signals in the air (Fig. 13).

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Fig. 13. Simulation block diagram

B. Hardware design for a parametric speaker based on FPGA The hardware design requirements include an field-programmable gate arrays (FPGA) development board, where the modulation requirements will be implemented, a Class D audio amplifier, which is based on the GaN device power stage, and the power supply for the FPGA board and Class D Power Amplifier. In addition, a control group based on the Si power device and SiC power device will be built to compare and test the influence of the power device. In order to reduce design complexity and hardware costs, a programmable oscillator will be implemented on the FPGA as an input to the system [61]. This negates the need for any kind of external signal generation and Analog-to-Digital (ADC) conversion. The PWM conversion will all be implemented using VHDL for the FPGA development board. The PCB design will be completed using “Altium Design”, and manufactured by an online manufacturer or work shop. FPGAs are an attractive option for performance, power consumption and configurability, although there are many alternatives for implementing this experiment. This is because the entire parametric loudspeaker system needs to include several signal processing tasks, including the generation of the ultrasonic carrier and the control signal for the Class D digital amplifier. The digital processing required to implement a parametric loudspeaker system involves ultrasonic frequency oscillators and ultrasonic frequency modulation. A high sampling frequency (at least twice the carrier frequency) is required to perform both processing tasks. The FPGA has the programmable nature of logic units. These can be interconnected to execute signal processing algorithms in a sequential or parallel manner. Sequential processing is used to perform calculations in typical digital signal processor chips. Figure 14 shows the FPGA chip and the audio analog-to-digital, and digital-toanalog converters. Low pass filters on the interface board provide signal conditioning, and voltage regulators provide a clean and stable DC power supply throughout the board [62]. C. Test and verification The main objective of audio characterisation measurement is to evaluate a device’s performance in the audible range, which spans 20 Hz–20 kHz. The larger spectrum is the industry norm and enables more precise device comparisons, despite the fact that

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Fig. 14. Connection between FPGA board and interface board.

most individuals cannot hear frequencies below 50 Hz or over 15 kHz. The main tests include: level test, THD + N, Frequency Response, and Directivity/Off Axis response: 1) Level test: In this test, it may be necessary to test output level, power, and gain. Generally, test the maximum distortion (1%) under the premise of the level. During the tests, the product output termination under test load (product based on the actual need to pick up the corresponding load). Next, measure the burden on both ends of the signal, and adjust the product volume under test to the maximum. Adjust the signal amplitude, and check the signal distortion size on instruments in real-time; when the distortion is 1%, the signal is not the biggest distortion signal in the subsequent tests. Generally, the input level under this particular distortion is used as the excitation signal source [63]. Generally, the test signal frequency is 1 kHz. This kind of test speed is high precision, and the automatic test is easier to realize [64]. 2) THD + N: Total harmonic distortion is the sum of all harmonics measured in the bandwidth of the DUT [65]. The function of THD + N is shown as follow:

   2 + V 2 + · · · + V 2 + Noise Vh1 h2 hn (7) THD + N = VIN  the level of harmonics of the input frequency, and Vh12 to 2Vhn refer to 2 is the total energy of the harmonics, Noise is the energy of Vh1 + Vh2 + · · · + Vhn the total energy of the noise at the output. VIN is the energy of the input signal [66]. Generally speaking, the SNR shouldn’t be less than 70dB [67]. 3) Frequency Response: Frequency response is the range of frequencies that the sound system can reproduce within the permissible amplitude range and the amount of signal variation within this range [68].

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Numerous techniques may be used to test the full-range frequency response, but the most common is to sweep a sine wave from the lowest to the highest frequency in the range and graph the results. 4) Directivity/Off Axis response: Directivity of speaker refers to how a speaker’s frequency response alters at offaxis angles. A speaker classified as parametric has a switching axis amplitude that is fundamentally distinct. A microphone is positioned at the appropriate distance in order to assess the speaker’s response at a particular location in space. The microphone should be placed far away from the speaker. The impulse response is then recorded on the microphone in response to a stimulus signal, such as a sine wave flowing across the speaker at various frequencies [69]. A complete audio product test should include other parts, such as EMC, Crosstalk, and Phase Response. Due to the single-channel of Parametric speaker, Crosstalk will not be considered, and Phase Response and EMC will be considered in future tests.

4 Future Work After finishing this experiment, the future work should solve the following questions or discover the clue. 1. How we should further de-noise the parametric speaker needs to be considered from the whole system. It is difficult to determine which part will produce the most noise. It is also important to determine the noise sources and resolve them in future work. 2. Influence of carrier frequency on sound quality, few papers have discussed the influence of carrier frequency changes on sound quality. An experiment to explore the changes in sound quality under different carrier frequencies is significant. 3. The influence of the Doppler effect on sound propagation, a phenomenon in which the sound frequency is distorted when the target is moving, is a potential risk affecting the “parametric speaker.”

5 Conclusion This paper reviewed the literature on parametric speakers, which mainly includes the basic principle of modulation methods, power amplifiers, and ultrasonic transducer arrays. At the same time, it also consists of the design scheme of each component of the Parametric speaker and the comparison between these schemes. This provides a theoretical basis for future experiments. In this paper’s amplifier output stage section, the GaN device and the adaptability of GaN devices to power amplifiers. In a single high-frequency amplifier system, high fidelity and power efficiency are often a challenge. GaN devices offer a new way to realise this ideal. A number of studies have demonstrated the advantages of GaN devices in class D amplifiers, including the high efficiency and the lower THD + N compared to the amplifier based on Si devices. This also allows for implementing the high-quality

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parametric speaker because GaN devices have more advantages in the high-Frequency band. In addition, this paper also describes the experiment and several kinds of tests, an FPGA-based system used to test the benefit of GaN devices on parametric speakers. The parameterized loudspeaker based on FPGA has the characteristics of a short design cycle, simple modification, and high reliability. Compared with the parametric speaker based on Single-Chip Microcomputer, the proposed method can be compatible with higher frequency and more complex audio signals.

References 1. Olszewski, D., Linhard, K.: 3g-3 optimum array configuration for parametric ultrasound loudspeakers using standard emitters. In: IEEE Ultrasonics Symposium (2006) 2. Tanaka, N., Tanaka, M.: Active noise control using a steerable para metric array loudspeaker. J. Acoust. Soc. Am. 127(6), 3526–3537 (2010) 3. John, K.M.: Heavy Hypersonic Dual Acoustic System (2021) 4. Yuko, N., Hoshiyama, M., Konagaya, Y.: Use of parametric speaker for older people with dementia in a residential care setting: a preliminary study of two cases. Hong Kong J. Occup. Ther. 31(1), 30–35 (2018) 5. Burka, A., Qin, A., Lee, D.D.: An application of parametric speaker technology to bus-pedestrian collision warning. In: 17th International IEEE Conference on Intelligent Transportation Systems (ITSC) (2014) 6. Kashiwase, S., Kondo, K.: Towards a parametric speaker system with human head tracking beam control. In: IEEE 3rd Global Conference on Consumer Electronics (GCCE), pp. 22–23 (2014) 7. Adachi, A., Hashiguchi, H.: Application of parametric speakers to radio acoustic sounding system. Atmos. Meas. Tech. 12(10), 5699–5715 (2019) 8. Komatsuzaki, T., Iwata, Y.: Active noise control using high-directional parametric loudspeaker. J. Environ. Eng. 6(1), 140–149 (2011) 9. Furuhashi, H., Mori, Y., Suzuki, S.: Active noise control of a plane sound wave by a parametric speaker. In: INTER-NOISE and NOISE-CON Congress and Conference Proceedings, Vol. 260, No. 1, pp. 227–233. Institute of Noise Control Engineering (2019) 10. Yang, J., Gan, W.S., Tan, K.S., Er, M.H.: Acoustic beamforming of a parametric speaker comprising ultrasonic transducers. Sens. Actuators, A 125(1), 11–99 (2015) 11. Keele Jr., D.B.: Vertical sound-field simulations (2011). Available: convexoptimization.com/TOOLS/CBT36VerticalSoundFieldSimulations.pdf 12. Ji, P., Gan, W.S., Tan, E.L., Yang, J.: Performance analysis on recursive single-sideband amplitude modulation for parametric loudspeakers. In: IEEE International Conference on Multimedia and Expo, pp. 748–753. (2010) 13. Kashid, R.R.: Directional Sound System. B.E. Department of Mechanical Engineering, MGM’s CET Kamothe, India 14. Ballad, E.M., Vezirov, S.Y., Pfleiderer, K., Solodov, I.Y., Busse, G.: Nonlinear modulation technique for NDE with air-coupled ultrasound. Ultrasonics 42(1–9), 1031–1036 (2004) 15. Kim, J., Choi, S., Kim, I., Moon, W.: Design of compact and high-efficiency power supply and power amplifier for parametric array transducer. In: IEEE 2nd International Future Energy (2015) 16. Nuttall, A.H., Benjamin, A.C.: Approximations to directivity for linear, planar, and volumetric apertures and arrays. NUWC-NPT Technical Report 10,798, Naval Undersea Warfare Center, Newport, Rhode Island. (1997)

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17. Directional Audio System—ACOUSPADE—Technical Specification. Ultrasonic Audio Technologies (10 June 2019). Available: https://ultrasonic-audio.com/acouspade-technicalspecification/ 18. Lathi, B.P.: Modern Digital and Analog Communication Systems, 3rd edn. Oxford University Press (1998) 19. Hamza, K.H., Nirmal, D.: A review of GaN HEMT broadband power amplifiers. AEU-Int. J. Electron. Commun. 116, 153040 (2020) 20. Yoneyama, M., Fujimoto, J., Kawamo, Y., Sasabe, S.: The audio spotlight: an application of nonlinear interaction of sound waves to a new type of loudspeaker design. J. Acoust. Soc. Am. 73(5), 1532–1536 (1983) 21. Tan, E., Gan, W., Ji, P., Yang, J.: Distortion analysis and reduction for the parametric array. In: 124th Convention of the Audio Engineering Society, Amsterdam. (2008) 22. Tan, E., Ji, P., Gan, W.: On preprocessing techniques for bandlimited parametric loudspeakers. Appl. Acoust. 71(5), 486–492 (2010) 23. Kamakura, T., Yoneyama, M., Ikegaya, K.: Development of parametric loudspeaker for practical use. In: 10th International Symposium on Nonlinear Acoustics, p. 147. (1984) 24. Arnela, M., Guasch, O., Sánchez-Martín, P., Camps, J., Alsina-Pagès, R.M., Martínez-Suquía, C.: Construction of an omnidirectional parametric loudspeaker consisting in a spherical distribution of ultrasound transducers. Sensors 18(12), 4317 (2018) 25. Van Veen, B.D., Buckley, K.M.: Beamforming: a versatile approach to spatial filtering. IEEE ASSP Mag. 5(2), 4–24 (1988) 26. Chen, C., Joe, Yao, K., Hudson, R.E.: Source localization and beamforming. IEEE Signal Process. Mag. 19(2), 30–39 (2002) 27. Gaalaas, E.: Class D audio amplifiers: what, why, and how. Analog Dialogue 40, 1–7 (2006) 28. Wang, Y., Li, X., Xu, L., Xu, L.: Ssb modulation of the ultrasonic carrier for a parametric loudspeaker. In: International Conference on Electronic Computer Technology (2009) 29. Breed, G., Director, E.: An overview of common techniques for power amplifier linearization. IEEE Microwave and Wireless Components, Letter 18 (2008) 30. TPA2037D1—3.2W Mono Class-D Audio Power Amplifier With 6-dB GAIN and Auto ShortCircuit Recovery. Texas Instrument (2010) 31. Kwon, S., Kim, I., Yi, S., Kang, S., Lee, S., Hwang, T., Moon, B., Choi, Y., Sung, H., Koh, J.: A 0.028% THD+ N, 91% power-efficiency, 3-level PWM Class-D amplifier with a true differential front-end. In: IEEE International Solid-State Circuits Conference. pp. 96–98. (2012) 32. Jiang, X.: Fundamentals of audio Class D amplifier design: a review of schemes and architectures. IEEE Solid-State Circuits Mag. 9(3), 14–25 (2017) 33. Kim, J., Choi, S., Song, S., Kim, I., Moon, W.: Design of high-efficiency power amplifier system for high-directional speaker. In: IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia), pp. 1093–1097. (2016) 34. Kazimierczuk, M.K.: RF Power Amplifier. Wiley, Hoboken, NJ, USA (2014) 35. Razavi, B.: RF Microelectronics; Prentice Hall: Upper Saddel River. NJ, USA (2011) 36. Choi, H.: Prelinearized Class-B power amplifier for piezoelectric transducers and portable ultrasound systems. Sensors 19(2), 287 (2019) 37. Katz, A.: Linearization: reducing distortion in power amplifiers. IEEE Microw. 2, 37–49 (2001) 38. Choi, H.: Development of a class-c power amplifier with diode expander architecture for point-of-care ultrasound systems. Micromachines 10(10), 697 (2019) 39. Gan, W., Yang, J., Kamakura, T.: A review of parametric acoustic array in air. Appl. Acoustics 73(12), 1211–1219 (2012)

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40. Velasco-Quesada, G., Roman-Lumbreras, M., Perez-Delgado, R., Conesa-Roca, A.: Class H power amplifier for power saving in fluxgate current transducers. IEEE Sens. J. 16(8), 2322–2330 (2016) 41. Piessens, T., Steyaert, M.: Highly efficient xDSL line drivers in 0.35-μm CMOS using a self-oscillating power amplifier. IEEE J. Solid-State Circuits 38, 22–29 (2003) 42. Colli-Menchi, A.I., Sánchez-Sinencio, E.: A high-efficiency self-oscillating class-D amplifier for piezoelectric speakers. IEEE Trans. Power Electron. 30(9), 5125–5135 (2014) 43. Yang, L., Xu, L., Yang, T., Zhang, B.: Class D power amplifier for audio beam system. In: IEEE International Conference on Mechatronics and Automation, pp. 3469–3474. (2007) 44. Baliga, B.J.: Trends in power semiconductor devices. IEEE Trans. Electron Devices 43(10), 1717–1731 (1996) 45. Yang, F., Xu, C., Akin, B.: Experimental evaluation and analysis of switching transient’s effect on dynamic on-resistance in GaN HEMTs. IEEE Trans. Power Electron. 34(10), 10121–10135 (2019) 46. ElectronicDesign.70: GaN FET technology solving audible challenges for high-performance audio amplifiers (2021). Available: www.electronicdesign.com 47. Blomley, P.: New approach to Class B amplifier design. Wireless World 57–61 (1971) 48. Mauerer, M., Tüysüz, A., Kolar, J.W.: Distortion analysis of low-THD/high-bandwidth GaN/SiC class-D amplifier power stages. In: IEEE Energy Conversion Congress and Exposition (ECCE), pp. 2563–2571. (2015) 49. Microsemi, P.P.G.: Gallium nitride (GaN) versus silicon carbide (SiC) in the high frequency (RF) and power switching applications. Digi-key 82, 2014 (2014) 50. Ueda, T.: Recent advances and future prospects on GaN-based power devices. In: International Power Electronics Conference (IPEC-Hiroshima 2014—ECCE ASIA), pp. 2075–2078. (2014) 51. Mauerer, M., Kolar, J.W.: Distortion minimization for ultra-low THD class-D power amplifiers. CPSS Trans. Power Electron. Appl. 3(4), 324–338 (2018) 52. Sangid, J., Long, G., Mitchell, P., Blalock, B.J., Costinett, D.J., Tolbert, L.M.: Comparison of 60 V GaN and Si devices for Class D audio applications. In: IEEE 6th Workshop on Wide Bandgap Power Devices and Applications (WiPDA), pp. 73–76 (2018) 53. Sangid, J.M.: GaN Versus Si for Class D Audio Applications (2018) 54. Gu, L., Stedman, Q., Rasmussen, M., Pai, C.N., Brenner, K., Ma, B., Ergun, A.S., KhuriYakub, B., Davila, J.R.: Multiphase GaN class-D resonant amplifier for high-intensity focused ultrasound. In: 20th Workshop on Control and Modeling for Power Electronics (COMPEL), pp. 1–6 (2019) 55. Kuroda, J.: Study to fabricate high-quality and portable parametric speakers. In: Proceedings of Meetings on Acoustics 172ASA, vol. 29, No. 1, p. 030009 (2016) 56. Kuroda, J., Oikawa, Y.: Parametric speaker consisting of small number of transducers with sonic crystal waveguide. Acoust. Soc. Am., Acoust. Sci. Technol. 41(6), 865–876 (2020) 57. Je, Y., Lee, H.S., Moon, W.K.: The impact of micromachined ultrasonic radiators on the efficiency of transducers in air. Ultrasonics 53(6), 1124–1134 (2013) 58. Shao, Z., Pala, S., Liang, Y., Peng, Y., Lin, L.: A single chip directional loudspeaker based on PMUTS. In: IEEE 34th International Conference on Micro Electro Mechanical Systems (MEMS) (2021) 59. Je, Y., Lee, H., Been, K., Moon, W.: A micromachined efficient parametric array loudspeaker with a wide radiation frequency band. J. Acoust. Soc. Am. 137(4), 1732–1743 (2015) 60. Shi, C., Kajikawa, Y., Gan, W.S.: An overview of directivity control methods of the parametric array loudspeaker. APSIPA Trans. Signal Inf. Process. (2014) 61. Yu, S.H., Hsieh, Y.F., Lai, P.Y., Chen, Y.L., Yang, C.P., Lin, K.: FPGA-based resonantfrequency-tracking power amplifier for ultrasonic transducer. In: International Conference on Applied Electronics (AE), pp. 285–288. (2015)

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Realization of PT Controlled Buck Converter Using Switchable Memristor Based Pulse Generator Jingjing Yu1,2(B) and Xiaotong Zhou2 1 Corigine (Nanjing) Semiconductor Technology Co. Ltd., Nanjing, China

[email protected] 2 School of Electrical Engineering, China University of Mining and Technology, Xuzhou, China

Abstract. Traditional pulse train (PT) controlled Buck converters requiring two signal generators to obtain two pulse trains with different duty cycles. In this paper, a binary memristor (MR)-based pulse train generator is designed and applied to regulate the output voltage of PT controlled Buck converter. In order to suppress the low-frequency voltage oscillations with high amplitude generating in this MR based PT-controlled Buck converter operated in continuous conduction mode (CCM), an inductor current feedback based PT (ICF-PT) control method is designed and utilized together with the proposed MR-based pulse generator. The advantage of this converter is that only one pulse train generator is used to regulate the output voltage. Simulation results show that the ICF-PT controlled Buck converter with the MR-based pulse generator can achieve fast transient response and minimum low-frequency voltage oscillations. Keywords: Buck converter · Memristor · Pulse train

1 Introduction Memristor (MR) is considered the fourth fundamental circuit element in addition to resistor, capacitor and inductor. MR has been used for designing signal generators [1], neuromorphic computation [2, 3], neuronal synapse [4, 5], data memory [6, 7] and logic circuits [8]. MR-based signal generators have attracted great research attention due to its unique characteristics. In [9], a simple mathematical model is proposed to describe a locally active MR, which is then used for building a second-order and a thirdorder chaotic signal generator. By using an active MR, a nonlinear Duffing oscillator is proposed in [10], wherein the memristance is controlled by changing the cubic function between flux and charge, and the chaotic dynamics of this MR-based Duffing oscillator is numerically studied. In [11], two generalized flux-controlled MRs are applied to construct a four-dimensional hyperchaotic oscillator. This new hyperchaotic oscillator can produce complex dynamics including the coexisting chaos phenomenon. These studies have shown that MRs can be utilized to realize oscillators with rich dynamic behaviors. However, research on applying MR-based signal generators to control power converters is still lacking in the literature. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1272–1280, 2023. https://doi.org/10.1007/978-981-99-4334-0_150

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Pulse Train (PT) control can adjust the output voltage of DC-DC converters by combining two groups of PTs with same frequency and different duty cycles. The main advantages of PT control are fast response speed and simple control structure. In this study, a MR-based pulse train generator with switchable duty cycle is designed and applied to construct the PT controller for Buck converters. The hysteresis between the output voltage and the inductance current of Buck converter is reduced by limiting the inductance current, hence diminishing the low-frequency oscillations. Simulation and experimental studies have been conducted in this work to verify the effectiveness of the proposed MR-based pulse generator for suppressing low-frequency oscillations in PT-controlled Buck converters.

2 MR Based Pulse Train Generator As shown in Fig. 1(a), a pulse train generator is designed by using an MR M1, two voltage divider resistors Ros1 and Ros2 , and an energy storage capacitor C os . Operational amplifier together with Ros1 and Ros2 are used for configuring a hysteretic comparator, and M1 and C os are utilized to constitute an RC delay circuit. The output voltage vout of the operational amplifier is either + U Z or − U Z due to output saturation. The threshold voltage U T of the voltage comparator can be expressed by ±UT = ±

Ros1 UZ . Ros1 + Ros2

(1)

If vin is greater than + U T , the output state of op amp is reversed and the output voltage will drop to its lower saturation voltage. When the input voltage is less than − U T , the output state of the op amp is reversed again and the output voltage changes from − U Z to + U Z . The binary MR has two memristance values. When the voltage applied to both ends of the memristor is positive, the memristance is Ron ; when the voltage applied to both ends of the memristor is negative, the memristance is Roff . Taking advantage of this property, in the circuit shown in Fig. 1(b), the memristance is reversed simultaneously with the signal generator output voltage. The memristance of the charging circuit is different from that of the discharge circuit, so a rectangular wave with an unfixed duty cycle can be obtained. When vout is equal to + U Z , the memristance is reduced to Ron . When vout is equal to − U Z , the memristance is increased to Roff , the charging time T 1 and discharging time T 2 of C os can be obtain, respectively, by the following equations, ⎧   ⎨ T1 = Ron Cos ln 1 + 2Ros1 Ros2   . (2) ⎩ T2 = Roff Cos ln 1 + 2Ros1 Ros2

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The period and duty cycle of the emitted rectangular wave can be obtained by   2Ros1 , (3) T = (Ron + Roff )Cos ln 1 + Ros2 D=

T1 Ron . = T Ron + Roff

(4)

Therefore, by setting proper memristance values, the rectangular pulse train with different frequencies and duty cycles can be obtained.

Fig. 1. Binary memristor based signal generator (a) Circuit schematic (b) operating voltage.

Fig. 2. A MR-based signal generator with switchable binary duty cycles.

The pulse train signal generator with switchable binary duty cycles can also be designed based on MR, as shown in Fig. 2. Term vx is only decided by flux ϕ AB across the MR. When the voltage applied to the MR terminal is positive, the memristance is Ron ; when the voltage applied to the MR is negative, the memristance is Roff . As shown in Fig. 3(a), when switch S 12 is connected to the open terminal of M1, C os is charged and then discharged via M1. When C os is charged, the memristance is Ron1 and the charging time is T 1 . When C os is discharged, the memristance is Roff1 and the discharging time is T 2 . When switch S 12 is connected to the open terminal of M2, C os is charged through M2 with memristance Ron2 and the charging time is T 3 . During the discharging operation,

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the memristance is Roff2 and the discharge time is T 4 . The charging and discharging time can be derived by ⎧  ⎧    ⎨ T1 = Ron1 Cos ln 1 + 2Ros1 ⎨ T3 = Ron2 Cos ln 1 + 2Ros1 Ros2  Ros2    , . (5) ⎩ T2 = Roff1 Cos ln 1 + 2Ros1 ⎩ T4 = Roff2 Cos ln 1 + 2Ros1 Ros2 Ros2 The operation waveform of this signal generator with variable duty cycles is shown in Fig. 3, where the values of duty cycles are dependent on the circuit configurations. To realize different output frequencies and duty cycles, two MRs and one switch is used in the pulse generator in Fig. 2. Compared with the pulse generator constructed by MR shown in Fig. 1(a), introducing switches can achieve controllable frequency and duty cycle.

Fig. 3. Output waveform of MR-based signal generator with switchable duty cycle.

3 ICF-PT-Controlled Buck Converter According to the operation principle of the pulse train generator with a switchable duty cycle shown in Fig. 2, a PT-controlled Buck converter based on the proposed pulse generator is designed, as shown in Fig. 4. The pulse generator designed in this study can satisfy two functions, namely, pulse generation and pulse selection, which further reduces the complexity of the control circuit.

Fig. 4. ICF-PT control Buck converter with MR.

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The inductor current iL is sampled and compared with reference current I o . At the start of each switching cycle, vo and iL are simultaneously sampled and compared with reference voltage V ref and output current I o , respectively. The comparison results are computed by an AND gate and then delivered to the D terminal of D trigger. When vo < V ref and iL < I o , the output of the AND gate is high, and the output of the Q-terminal of D trigger is also high. Inside the signal generator, switch S 12 is connected to M1 to produce a pulse with a high duty cycle PH for controlling the power converter. When vo > V ref or iL > I o , a low signal is generated by the AND gate, and then the output of the Q-terminal of D trigger is also low. Switch S 12 is connected to M2 to generate low power pulse PL . The output duty cycle of the AND gate can be expressed by DH , vo ≤ Vref and iL ≤ Io D= . (6) DL , vo > Vref or iL > Io By introducing the MR-based ICF-PT control to the power converter, iL is sampled as feedback and hence the lag between vo and iL can be reduced.

Fig. 5. Operation states of the ICF-PT-controlled Buck converter in CCM.

The ICF-PT-controlled Buck converter in the CCM can be divided into four operation states according to the initial values of iL and vo of each switching cycle, by reference current I o , current iLup and current iLdown , as shown in Fig. 5. Six operation states of Buck converter controlled by ICF-PT in CCM are listed in Table 1. According to Fig. 5, in region III, vo is increased regardless of the selected pulse signals. When the traditional PT control method is applied, PH is selected and iL is increased, and vo may be increased or decreased according to different initial values of iL and vo . With the proposed ICF-PT control method, inside region III, iL > I o leads to the selection of PL and iL is dropped. When iL ≤ I o , the controller selects PH to increase iL , so that vo keeps increasing until vo > V ref , and thus the output voltage of the converter can be adaptively regulated. At this stage, iL fluctuates around the output current I o , without oscillating ripples.

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Table 1. Operation states of Buck converter controlled by ICF-PT in CCM Six states

Relationship between iL and I o , vo and V ref

Pulse selection

iL

vo

I

iL ≤ iLdown , vo ≤ V ref

PH

+

−

II

iLdown < iL ≤ iLup , vo ≤ V ref iL > iLup , vo ≤ V ref

PH

+

−

PL , if iL ≥ I o

−

+

III

PH , if iL ≤ I o

+

PL

−

+

V

iL > iLup , vo > V ref iLdown < iL ≤ iLup , vo > V ref

PL

−

−

VI

iL ≤ iLdown , vo > V ref

PL

−

−

IV

4 Simulation Verification The simulation parameters of the ICF-PT controlled Buck converter are configured as follows: DC input voltage V in = 24 V, C = 500 µF, load Ro = 5 , switching frequency f = 40 kHz, high duty cycle DH = 0.4, and low duty cycle DL = 0.2, respectively. The reference voltage is configured as V ref = 8 V. When the converter is operated in DCM, inductance L is set to 60 µH; For operations in the CCM, inductance L is set to 500 µH, to comparatively observe the low-frequency oscillations. The output voltage and control signal of the PT-controlled Buck converter in CCM and DCM are shown in Fig. 6.

Fig. 6. Output voltage and control signal of the PT-controlled Buck converter.

It can be seen that, in DCM, the output voltage of the PT-controlled Buck converter can be stabilized to the reference voltage with small ripples. The peak-to-peak value of voltage ripples is 0.24 V, and the sequence of pulse train is 1PH -1PL -1PH -3PL 1PH -3PL . The ICF-PT-controlled Buck converter using the MR-based pulse generator is simulated to verify the oscillation suppression performance. The output voltage and inductor current of the Buck converter under the traditional PT and ICF-PT control are

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shown in Fig. 7. The upper and lower boundaries of the inductor current are obtained as iLup = 1.584 A and iLdown = 1.464 A, respectively. From Fig. 7(a), the output voltage vo of PT-controlled Buck converter shows lowfrequency oscillations, which varies within the interval of [7.57, 8.22] V, and the peakto-peak value of output voltage vo is about 0.65 V. The inductor current also exhibits low-frequency oscillations within the range of [0.107, 3.086] A, and the peak-to-peak current value is greater than 2.979 A. It can be seen that the inductor current can be continuously increased or decreased, by passing through the current region between iLup and iLdown .

Fig. 7. Comparison simulation results between the traditional PT control and the proposed ICF-PT control for Buck converter.

The output voltage vo and inductor current iL of the ICF-PT-controlled Buck converter is shown in Fig. 7(b). It can be observed that there are no low-frequency oscillations of vo and iL . The output voltage vo can be stabilized within much smaller voltage range of [7.97, 8.26] V. The peak-to-peak value of voltage oscillation ripple is now only 0.05 V, and the inductor current iL can also be stabilized to the output average current of 1.6 A with small fluctuations. Hence, the output voltage vo can be considered as a constant. With the same steady-state simulation parameters, the transient characteristics of the ICF-PT-controlled Buck converter with input voltage and load variations are analyzed by Multisim, as shown in Fig. 8. The output voltage and transient inductor current when the load resistance is changed from 5 to 10  at t = 5 ms are shown in Fig. 8(a). The output voltage and transient inductor current of the Buck converter controlled by ICF-PT in CCM as the input voltage varies from 24 to 27 V at time t = 5 ms are shown in Fig. 8(b). When the input voltage changes, the output voltage of the Buck converter controlled by ICF-PT can be rapidly stabilized to the reference voltage without overshoots, and the dynamic response time is approximately only 0.04 ms. However, the peak-to-peak value of the output voltage ripple is slightly increased, from 0.05 to 0.08 V after input voltage variation. When the load is changed, voltage overshoot can be detected. The transient time is about 0.87 ms, the peak-to-peak value of the output voltage in the transient stage is 0.15 V, and the load current decreases from 1.6 to 0.8 A within about 0.2 ms.

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Fig. 8. Transient waveforms of the ICF-PT-controlled Buck converter.

These simulation results have shown that in the ICF-PT-controlled Buck converter using MR-based pulse generator, the ripples of iL can be effectively controlled within a small range, and the phase difference between vo and iL is reduced. Also, low-frequency oscillations of vo can be suppressed, and the advantages of PT control such as fast response have been retained.

5 Conclusions A pulse train generator with controllable duty cycle and frequency of the output rectangular signals is designed in this paper. This MR-based pulse train generator is innovatively applied to a to ICF-PT-controlled Buck converter, to replace the traditional pulse train generator. Only one MR-based pulse generator is required in the control structure. Introducing this MR-based pulse train generator can simplify the ICF-PT control structure and diminish the low-frequency oscillations. The simulation results have validated the proposed control approach, which can provide valuable references for future explorations of binary MR circuits.

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References 1. Chen, M., Sun, M., Bao, H., Hu, Y., Bao, B.: Flux–charge analysis of two-memristor-based Chua’s circuit: dimensionality decreasing model for detecting extreme multistability. IEEE Trans. Industr. Electron. 67(3), 2197–2206 (2019) 2. Sung, C., Sun, M., Yoo, I.K.: Perspective: a review on memristive hardware for neuromorphic computation. J. Appl. Phys. 124(15), 151903 (2018) 3. Yang, J.J., Strukov, D.B., Stewart, D.R.: Memristive devices for computing. Nat. Nanotechnol. 8(1), 13–24 (2013) 4. Bao, H., Hu, A., Liu, W., Bao, B.: Hidden bursting firings and bifurcation mechanisms in Memristive neuron model with threshold electromagnetic induction. IEEE Trans. Neural Netw. Learn. Syst. 31(2), 502–511 (2019) 5. Li, K., Bao, H., Li, H., Ma, J., Hua, Z., Bao, B.: Memristive Rulkov neuron model with magnetic induction effects. IEEE Trans. Industr. Inf. 18(3), 1726–1736 (2021) 6. Vontobel, P.O., Robinett, W., Kuekes, P.J., Stewart, D.R., Straznicky, J., Williams, R.S.: Writing to and reading from a nano-scale crossbar memory based on memristors. Nanotechnology 20(42), 425204 (2009) 7. Jo, K.H., Jung, C.M., Min, K.S., Kang, S.M.: Self-adaptive write circuit for low-power and variation-tolerant memristors. IEEE Trans. Nanotechnol. 9(6), 675–678 (2010) 8. Kim, K.M., Williams, R.S.: A family of Stateful Memristor gates for complete cascading logic. IEEE Trans. Circuits Syst. I Regul. Pap. 66(11), 4348–4355 (2019) 9. Liang, Y., Wang, G., Chen, G., et al.: S-type locally active Memristor-based periodic and chaotic oscillators. IEEE Trans. Circuits Syst. I Regul. Pap. 67(12), 5139–5152 (2020) 10. Sabarathinam, S., Thamilmaran, K.: Effect of variable memristor emulator in a Duffing nonlinear oscillator. AIP Conf. Proc. 1832(1), 060007 (2017) 11. Jiang, Y., Li, C., Zhang, C., Zhao, Y., Zang, H.: A Double-Memristor hyperchaotic oscillator with complete amplitude control. IEEE Trans. Circuits Syst. I Regul. Pap. 68(12), 4935–4944 (2021)

A High-Robust Control Scheme for the Dual-Active-Bridge-Based Energy Storage Unit Shiqing Ji(B) Shenzhen Baoan Renda Electrical Appliance Industrial Co. Ltd., Shenzhen, China [email protected]

Abstract. When the renewable energy such as photovoltaics and wind turbine system is developing, the power system with these renewable energies and multiple energy storage systems are become as a promising one for establishing a low-voltage dc (LVDC) bus and supplying power to users such as the electric automobile and the living area. To manage the power flowing and stabilize the dcbus voltage, the master-slave control strategy is recommended, where one energy storage system is used to achieve the LVDC bus voltage and others inject current to the dc bus. Notably, the energy storage systems should be selected as master mode in turn, and the corresponding operating process is presented. In addition, each energy storage system contains several dual-active-bridge (DAB) dc-dc modules for boosting the power capacity, and when the energy storage system is acted as master mode, a novel voltage droop control (NVDC) scheme is proposed for adjusting the transferred power sharing performance and maintaining the dc bus voltage, which should increase the reliability and the extendibility of the DAB modules based on independent controller cells. Moreover, excellent dynamic results should also be provided when the resistor load, the output power of other power storage units and the transferred power of the renewable energy area are changed. In this article, the simulation model is employed to illustrate the behavior of the whole converter, and a small-scale experimental equipment is used to see the results of the presented NVDC scheme. Keywords: Power sharing · Energy storage system · Dual-active-bridge · Fast-dynamic response

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1281–1291, 2023. https://doi.org/10.1007/978-981-99-4334-0_151

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1 Introduction The use of renewable energy units has obviously increased over past years, such as photovoltaics (PV) and wind energy [1]. However, the generated powers of these renewable energy systems are too unstable to the load consumer because of the variational environment conditions such as sunshine and wind speed [2, 3]. To deal with this issue, the energy storage unit becomes the most promising one for addressing the difference between the new energy source and the load user [4, 5]. Usually, the voltage and the power capacity of the energy storage unit such as battery are limited, and multiple batteries are required to form a high-voltage dc-link terminal with high power capacity for the dc microgrid as seen in Fig. 1 [6], where the isolated bidirectional dual-active-bridge (DAB) dc-dc system is selected. Usually, the output power of PV unit is always changed for achieving the max output power performance and is changed based on the environmental condition such as the sun. To make sure the high operation and power quality of the dc system, a stable dclink voltage should be obtained for the electric automobile and the living place, and the changed output power should be compensated. So, the energy storage unit is usually established in the dc system to compensate the power change between the new energy system and the load condition.

Fig. 1. The energy storage system for MVDC with multiple batteries.

Then, the usual system of the dc microgrid should be illustrated in Fig. 1, where the energy storage system is distributed in the grid, and the energy storage system is always based on battery units [6–10]. To the distributed energy storage system, there are usually two important purposes including achieving the dc-link voltage and realizing the power changing performance of the battery system, and there are two main concepts including master-slave control scheme and droop-based control strategy to satisfy these

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two requirements [11, 12]. Now, with the isolated, bidirectional, and symmetric characteristics, the DAB dc-dc converter becomes a good converter for the dc power system [12], which should be used for different power requirements. Therefore, based on DAB structure, a DAB-based energy storage system is presented as seen in Fig. 2. By adding a compensated terminal, the dc-bus voltage should be adjustable for dealing with the change among the renewable energy system and the load user. Then, the main output power of batteries is directly used to the load side, which should boost use of the batteries’ energy importantly. So, compared to the traditional one as seen in Fig. 1, batteries should directly provide or absorb the power to or from the load consumer without dc-dc conversion, which should help to reduce the power loss of the energy storage unit.

Fig. 2. The DAB-based energy converter system with multiple batteries.

Fig. 3. The general diagram of the traditional control concept.

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Therefore, the general picture of the master-slave control method should be seen in Fig. 3. The master-slave technique has been employed in the multiple converters system with parallel or series connections [13–18], where one module is always operated to offer a constant dc bus voltage, and other modules are acted as the current source or the power source. In [15, 16], the measured output current of the master module is acquired as the desired output current of the slave modules for the power balancing control. Moreover, a decoupled master-slave current balancing control method is used to reduce the influence on the voltage regulation by the variation of the current balancing controller [17]. When these energy storage systems are located at different places, communication equipment is usually required [15, 18]. So, to improve the fast dynamic condition of this DAB-based energy system, a highrobust control method is presented for achieving the total dc-bus voltage when the load users including the new power source and the power user are changed. The high-robust control method is seen for this DAB power system in Sect. 2. Besides, the simulation model and the experiment are used to see the useful results of the converter system and the proposed method in Sect. 3. Finally, the conclusion is summarized in Sect. 4.

2 The Proposed High-Robust Control Scheme In this one, the proposed high-robust use method is seen for maintaining the output voltage of the DAB power system as seen in Fig. 2, and this is employed to deal with the modification of the load consumer including load user and the constant-current load (CCL). Moreover, the state of charge (SOC) balance among batteries should also be realized. For the DAB structure in Fig. 3, the simple-phase-shift (SPS) method is seen to achieve the transferred power and current of DAB module [12], which should realize the bidirectional power transmission easily. Then, the pictures of the SPS method for forward and back power transmission should be seen in Fig. 4. As seen in Fig. 4(a), when the output current of the renewable energy source is bigger than that of the load requirement, the power of the compensated port should be transferred to the battery. As seen in picture Fig. 4(b), when the transferred power of the renewable energy source is smaller than that of the load use, the used battery should transfer power to the compensated port for supporting the all dc-bus voltage. Based on the most popular SPS modulation concept, the corresponding modulation method for this DAB dc-dc power system should be seen in Fig. 4. The gate signals of the three full-bridge circuits are seen in S a1 , S b1 , and S c1 waveforms, where these signals are square waveforms. Dac and Dbc are the used phase-shift ratios. The used currents through these three windings are ia , ib and ic .

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Fig. 4. The SPS method of the dual-active-bridge converter for forward and back power conditions.

According to Fig. 4, and combining the principle of SPS method [9] the transferred powers Pac and Pbc among these three ports should be calculated as, ⎧  nac UA UC Dac (1−Dac )Ts ⎪ (Pac ≥ 0) ⎪ 2La ⎪ P = ⎪ ac nac UA UC Dac (1−Dac )Ts ⎨ (Pac < 0) − 2La  (1) nbc UB UC Dbc (1−Dbc )Ts ⎪ (Pbc ≥ 0) ⎪ 2Lb ⎪ P = ⎪ ⎩ bc − nbc UB UC Dbc (1−Dbc )Ts (P < 0) 2Lb

bc

where T s is the switch’s period, nac and nbc are the transformer turns, and L a and L b are the ac inductances. Compared with the original three-port DAB power converter, the used powers of the presented DAB converter should be easily obtained. Then, according to (1), this DAB-based dc-dc power converter should be tried as two different single DAB power converters. Therefore, the calculated transferred power in (1) should be suitable for both the steady’s condition and the transient process [10]. It means this dual input DAB dc-dc power converter should response to the disturbance at switching period level, so this converter has the potential ultrafast dynamic performance.

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For a certain load, the total required transferred power Pc at Port C should be used as, ∗ PC = Uv ioc = Uv

UC∗ ioc UC

(2)

where U v is the output voltage from the outer PI controller, which should be used for the model difference caused by some uncertain factors such as the power loss. Moreover, U * C is the desired terminal voltage of Port C, and ioc is the load current. Then, the controlled transferred power Pac from Port A to Port C and the controlled transferred power Pbc from Port B to Port C should be calculated as,  Pac = kac Pc (kac + kbc = 1) (3) Pbc = kbc Pc where k ac and k bc are the corresponding power sharing coefficients. According to (1), phase-shift ratios Dac and Dbc should be used for realizing the powers as, ⎧  ⎨ 1 − 1 − 8Lα IT α (IT α ≥ 0) 2 nα UBα Tsα  Dα = (4) ⎩ 1 − 1 + 8nα Lα IT α (IT α < 0) 2 UBα Tsα To get the change of load resistor, the used current i* MD of each element for achieving the electricity consumer should be got as, ∗ = iMD

∗ UMD U ∗ iMD = MD Req UMD

(5)

Fig. 5. Control system of the DAB-based converter system for energy storage system.

As seen in Fig. 5, the proposed high-robust technology scheme should be realized. The output voltage of each battery U Bα , the total dc-link voltage U MD and the load current iMD are measured. Based on the load current iMD , the total dc-link voltage U MD and the required output current i* MD should be calculated according to (5). Besides, combining the used all dc-link voltage U * MD and the measured total dc-link voltage U MD , the used current iMD should be got through the integral system. Then, getting the obtained required output one i* MD , the total transferred power of batteries I T through

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the DAB units should be obtained. Moreover, based on the current sharing coefficient k α , the required transferred power I Tα for all DAB units should be got as, IT α = kα IT

(6)

In addition, based on the required used current I Tα for all DAB units, the used phaseshift ratio Dα should be calculated as (4). Furthermore, when the SOCs of batteries are not balanced, the SOC balance should be obtained for changing the power sharing coefficient k α for each battery, where battery with higher SOC shares more transferred current. Then, the SOC balance should be gradually obtained.

3 Verification In this Section, a DAB-based power converter system with two batteries (U B1 , U B2 ) and one compensated port (U C ) is built to see the useful results of the presented power system and the presented high-robust technique scheme, where the CCL is changed between 0A and 10A, the resistor load is modified from 20 and 50 . The main converter parameters of the DAB-based power converter system should be seen in Table 1. Table 1. Circuit parameters of the dab-based energy storage system. Parameters

Value

R

20–50 

CCL

0–10 A

U Bα (nominal voltage)

48 V

Rated capacity

50 Ah

Battery response Time

30 s

U*o

120 V

According to Fig. 6, it’s clear that the transmission powers of each DAB power system should be allocated discretionarily with the proposed method, and the output voltage should keep the same under the modification of input side value and load user. Figure 7 shows the simulation parts when the resistor conditions including the load user and the CCL are modified. As seen in Fig. 7(a), when the CCL is changed from 0A to 10 A and the resistor load is change between 20 and 50 , the required transferred powers of the DABs are adjusted quickly for different load conditions as seen in Fig. 7(b). Then, as seen in Fig. 7(c) and Fig. 7(d), the output voltage of the compensated port should be kept stable during the change of load conditions, and the whole dc-bus voltage should maintain at its required value. So, fast dynamic results should be seen.

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Fig. 6. Simulation results under input voltage changes.

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Fig. 7. Simulation results when the load conditions are changed.

4 Conclusion In this paper, a DAB-based power converter is presented for multiple batteries, which should boost the utilization of the energy. Besides, the power loss should be reduced since the main power is used to the load consumer without power conversion. Moreover, a

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high-robust technique one is proposed for this DAB-based power system. Furthermore, the simulation part and the experiment part are used to seen the good results of the presented DAB-based power system and the presented high-robust technique method.

References 1. Liserre, M., Sauter, T., Hung, J.Y.: Future energy systems: integrating renewable energy sources into the smart power grid through industrial electronics. IEEE Ind. Electron. Mag. 4(1), 18–37 (2010) 2. Carrasco, J.M., et al.: Power-electronic systems for the grid integration of renewable energy sources: a survey. IEEE Trans. Industr. Electron. 53(4), 1002–1016 (2006) 3. Blaabjerg, F., Teodorescu, R., Liserre, M., Timbus, A.V.: Overview of control and grid synchronization for distributed power generation systems. IEEE Trans. Industr. Electron. 53(5), 1398–1409 (2006) 4. Xu, L., Chen, D.: Control and operation of a DC microgrid with variable generation and energy storage. IEEE Trans. Power Deliv. 26(4), 2513–2522 (2011) 5. Xiao, J., Wang, P., Setyawan, L.: Hierarchical control of hybrid energy storage system in DC microgrids. IEEE Trans. Industr. Electron. 62(8), 4915–4924 (2015) 6. Hou, N., Li, Y.W.: A tunable power sharing control scheme for the output-series DAB DC–DC system with independent or common input terminals. IEEE Trans. Power Electron. 34(10), 9386–9391 (2019) 7. Gao, L., Dougal, R.A., Liu, S., Iotova, A.P.: Parallel-connected solar PV system to address partial and rapidly fluctuating shadow conditions. IEEE Trans. Industr. Electron. 56(5), 1548– 1556 (2009) 8. Badawy, M.O., Bose, S.M., Sozer, Y.: A novel differential power processing architecture for a partially shaded PV string using distributed control. In: IEEE Trans. Ind. Appl. 57(2), 1725–1735 (2021) 9. Sun, K., Qiu, Z., Wu, H., Xing, Y.: Evaluation on high-efficiency thermoelectric generation systems based on differential power processing. IEEE Trans. Industr. Electron. 65(1), 699–708 (2018) 10. Chu, G., Wen, H., Hu, Y., Jiang, L., Yang, Y., Wang, Y.: Low-complexity power balancing point-based optimization for photovoltaic differential power processing. IEEE Trans. Power Electron. 35(10), 10306–10322 (2020) 11. Olalla, C., Clement, D., Rodriguez, M., Maksimovic, D.: Architectures and control of submodule integrated DC–DC converters for photovoltaic applications. IEEE Trans. Power Electron. 28(6), 2980–2997 (2013) 12. De Doncker, R.W.A.A., Divan, D.M., Kheraluwala, M.H.: A three-phase soft-switched highpower-density DC/DC converter for high-power applications. In: IEEE Trans. Ind. Appl. 27(1), 63–73 (1991) 13. Li, Y., He, L., Liu, F., Li, C., Cao, Y., Shahidehpour, M.: Flexible voltage control strategy considering distributed energy storages for DC distribution network. IEEE Trans. Smart Grid 10(1), 163–172 (2019) 14. De Din, E., Siddique, H.A.B., Cupelli, M., Monti, A., De Doncker, R.W.: Voltage control of parallel-connected dual-active bridge converters for shipboard applications. IEEE J. Emerg. Sel. Topics Power Electron. 6(2), 664–673 (2018) 15. Delghavi, M.B., Yazdani, A.: Sliding-mode control of AC voltages and currents of dispatchable distributed energy resources in master-slave-organized inverter-based microgrids. IEEE Trans. Smart Grid 10(1), 980–991 (2019)

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16. Liu, Z., Liu, J., Hou, X., Dou, Q., Xue, D., Liu, T.: Output impedance modeling and stability prediction of three-phase paralleled inverters with master-slave sharing scheme based on terminal characteristics of individual inverters. IEEE Trans. Power Electron. 31(7), 5306–5320 (2016) 17. Roh, Y., Moon, Y., Park, J., Jeong, M., Yoo, C.: A multiphase synchronous buck converter with a fully integrated current balancing scheme. IEEE Trans. Power Electron. 30(9), 5159–5169 (2015) 18. Chen, H., Lu, C., Rout, U.S.: Decoupled master-slave current balancing control for three-phase interleaved boost converters. IEEE Trans. Power Electron. 33(5), 3683–3687 (2018)

Optimized Design of High Torque Density Permanent Magnet Synchronous Motor with Halbach Magnet Jiye Sun1,3 , Chenwei Yang2,3 , Xiaoyan Huang1,3(B) , Yi Wang2,3 , Zhaokai Li1,3 , and Huifan Yang1,3 1 Zhejiang University, Hangzhou, China

{22160109,xiaoyanhuang}@zju.edu.cn

2 Laboratory of Aerospace Servo Actuation and Transmission, Beijing, China 3 Beijing Institute of Precision Mechatronics and Controls, Beijing, China

Abstract. Permanent magnet synchronous motor (PMSM) is widely used because of its simple structure, reliable operation, small size and high operating efficiency. In this paper, the structural optimization design of permanent magnet synchronous motor is analyzed, and the maximum torque is optimized while minimizing the moment of inertia, motor mass and cogging torque during the design by selecting the motor size. Under general conditions, the performance of the motor is greatly influenced permanent magnets, so this paper focuses on analyzing the influence of the shape and magnetization of the permanent magnet on the motor. Halbach magnets were the main design factors of high torque permanent magnet synchronous motors which arranged and combined permanent magnet blocks with different magnetization directions according to certain rules to obtain a more ideal unilateral magnetic field distribution, and the influence of magnetization angle and magnet size was studied. Finally, finite element simulation is proposed and verified by finite element simulation. Keywords: Permanent magnet synchronous motor · Halbach magnetization · Differential evolution algorithm · High torque density

1 Introduction Nowadays, permanent magnet synchronous motor (PMSM) has been widely used in the applications required high efficiency and high power density such as house appliance, transportation [1] due to its inherent merits. In the electric transportation applications, high torque density is of great importance due to the limited installation space. The fraction slot concentrated winding (FSCW) motor received massive intension in the safety critical applications such as electrical transportation vehicles. The different performance of the PMSM was determined by different rotor magnetic circuit structures. The Halbach magnetization for surface mount PMSM has the advantages in terms high torque and low harmonics and therefore received massive attention nowadays. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1292–1299, 2023. https://doi.org/10.1007/978-981-99-4334-0_152

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Y. Park studied the outer rotor permanent magnet brushless DC motor with Halbach magnet array and Response Surface Method (RSM) was used to reduce motor weight [2]. A. Halbach magnet array with a novel segmentation technology was used by Erich Schmidt to achieve the target of very high performance and low mass [3]. Several kinds of PM materials and PM shapes were compared by X. Wang to optimize two-segment Halbach magnet array [4]. Halbach array and particle swarm optimization were used to reduce the cost and size of permanent magnet synchronous generator [5]. The relationship between the Halbach magnet array and the air-gap field distribution was studied by Liu et al. [6]. A topology of Dual Rotor Halbach BLDC motor was proposed by B.V. Ravi Kumar to increase the torque density [7]. This paper focus on the design of the high torque FSCW PMSM motor. The Halbach magnets are adopted to increase the airgap flux density and further increase the torque density of the motor. The influence of the magnetization angle on the torque is studied, and finally the optimal design of the motor is proposed.

2 Influence of Halbach Magnet Design Rotor structure design is the core of motor design, reasonable design of rotor structure can not only effectively improve the performance of motor torque density, efficiency, etc., but also improve material utilization and reduce production costs. Under general conditions, the performance of the motor is greatly influenced by the size of parameters and installation position of permanent magnets, so this paper focuses on analyzing the influence of the shape and magnetization of the permanent magnet on the motor [8, 9]. 2.1 Permanent Magnet Thickness The magnetic flux provided per unit area of the permanent magnet is related to its thickness, that is, the thickness of the excitation direction, and the total magnetic flux provided is related to the area of the permanent magnet, that is, the product of the width of the permanent magnet and the length of the core. In this optimization design, keeping other parameters constant, the thickness of the permanent magnet hm varied between 1–8 mm, the torque can be seen increase with the thickness as shown in Fig. 1. However, when the motor start to saturate, increase the thickness will no be helpful. 2.2 Permanent Magnet Magnetization Angle Halbach magnetization is adopted in this paper, the Halbach block coefficient of the motor defined in this optimization refers to the proportion of the main pole (as shown in Fig. 2) in the entire permanent magnet, and the magnetizing angle refers to the difference between the charging angle of the auxiliary pole and the main pole, as shown in Fig. 3. The torque variation of the motor under different magnetizing angle when the Halbach block coefficient of the motor are set to 0.4, 0.5, 0.6, 0.7 and 0.8 respectively are compared. Further more, the torque variation of the motor under the corresponding block coefficients when the magnetization angle is set to 10°, 20°, 30° and 45° respectively are compared in Fig. 5.

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Fig. 1. Effect of permanent magnet thickness on torque.

Fig. 2. Halbach magnet.

Fig. 3. Halbach magnetizing angle.

It can be seen from Fig. 4 that under different block coefficients, the torque shows a trend of first increasing and then decreasing with the magnetization angle from − 45° to 45°. The larger the block coefficient, the larger the magnetization angle was required to achieve the maximum value. From Fig. 5, it can be concluded that the torque first increases and then decreases with the magnetization angle from 10° to 45°, where 10°, 20° and 30° all increase with the block coefficient from 0.2 to 0.8 and tend to stabilize after the growth rate slows down, fluctuating at 30° and decreasing at 45°. Due to the different effects on torque under each magnetizing angle and each block coefficient, under this optimization condition, the maximum value can be taken between

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Fig. 4. The effect of magnetizing angle on torque corresponding to different block coefficients

Fig. 5. The effect of the block coefficient corresponding to different magnetization angles on the torque.

0.4–0.7 and the magnetizing angle is taken at about 30°. However, since the two parameters affect each other, it is of great significance to optimize the two parameters at the same time.

3 The Optimized Design of FSCW PMSM 3.1 Multi-objective Differential Evolution Algorithm Many variables are presented in the motor optimization process, these optimization variables are mutually restricted and influenced by each other. The multi-objective differential evolution algorithm is selected to optimize the near-slot pole with fractional slot concentrated winding motor using Halbach permanent magnet array. The differential evolution algorithm is employed for the multi-objective design. Strategies for differential variation, cross-variation, and selection are used in the multi-objective differential evolution algorithm to constantly look for the optimal solution.

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The size of each optimization variable can be arbitrarily changed by MATLAB software due to the completion of the parametric modeling process, and Ansys Maxwell software can be controlled to calculate the performance indicators of the motor under the corresponding parameters. Eight parameters are optimized for design: the radius of the permanent magnet Rr, the Halbach block coefficient of the motor polar_arc_factor, the air gap length airgap, the wide angle of the stator groove bsa, the opening angle of the stator groove bso, the bottom radius of the stator groove Rsb, the angle between the auxiliary pole and the tangential direction th_PM_assist, and permanent magnet thickness hm as shown in Fig. 6. The maximum torque and efficiency should be obtained while minimizing the moment of inertia and cogging torque during the design (Fig. 7).

Fig. 6. Schematic diagram of each parameter.

Fig. 7. Multi-objective optimization Pareto frontier.

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3.2 Analysis of Optimization Results The differential evolution algorithm is used to optimize the design of motors with arbitrary values, the initial motor parameters are random selected. The design goals are shown in Table 1. The optimized motor parameters are shown in the following Table 2. The torque before and after optimization is shown in Fig. 8. Table 1. The design requirement of the motor. Parameters

Constraint

Rated speed

3800 r/min

Peak torque

7Nm

Outer diameter

75 mm

Current density

≤ 20 A/mm2

Table 2. The optimized motor parameters. Parameter

Value

Permanent magnet inner diameter/mm

41.6

Permanent magnet block factor Airgap/mm Angle inside the slot/deg Notch length/mm

0.47 0.48 23.8 4.13

Stator slot deep radius/mm

22.5

Magnetization angle/deg

29.4

Permanent magnet thickness/mm

7.31

Among them, Fig. 8a is the torque curve before optimization, the average torque is 2.66 N m, Fig. 8b is the optimized torque curve, the average torque is 7.18 N m, it can be clearly seen that the optimized motor torque has been greatly improved and the optimization is effective. The magnetic density in the case of no load and full load is shown in Fig. 9. The electromagnetic torque of the motor at different input currents is shown in Fig. 10.

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Fig. 8. The torque before (a) and after (b) optimization and the corresponding motor schematic diagram.

Fig. 9. No-load magnetic flux density (a) and full-load magnetic flux density (b).

Fig. 10. The electromagnetic torque of the motor at different input currents.

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4 Conclusion In this paper, firstly impact of the magnet dimension and the magnetization angle on the output torque are evaluated. Then, the differential evolution algorithm optimization combined with Ansys Maxwell is implemented for the multi-objective design. The FEM results are provided to verify the optimized design.

References 1. Łukaniszyn, M., Młot, A.: Torque characteristics of a BLDC motor with multipolar excitation. COMPEL Int. J. Computat. Math. Electr. Electron. Eng. 28(1), 178–187 (2009) 2. Park, Y., Kim, H., Jang, H., Ham, S.-H., Lee, J., Jung, D.-H.: Efficiency improvement of permanent magnet BLDC with Halbach magnet array for drone. In: IEEE Transactions on Applied Superconductivity, vol. 30, no. 4, pp. 1–5, Art no. 5201405 (2020). https://doi.org/10. 1109/TASC.2020.2971672 3. Schmidt, E., Lechner, C.: Design and assembling of a permanent magnet synchronous machine with a Halbach magnet array for the application in an electric driven race car. In: 2015 Australasian Universities Power Engineering Conference (AUPEC), Wollongong, NSW, Australia, pp. 1–6.https://doi.org/10.1109/AUPEC.2015.7324808 4. Wang, X., Wu, L., Zhou, S., Hu, C., Zhao, M.: Optimization design of in-wheel motor based on Halbach (Ce,Nd)FeB Magnet. In: 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, pp. 1–4 (2019). https://doi.org/10.1109/ICEMS.2019. 8921463 5. Alshibani, S.: Application of particle swarm optimization in the design of Halbach permanent magnet synchronous generators for megawatt level wind turbines. In: 2018 7th International Conference on Renewable Energy Research and Applications (ICRERA), Paris, France, pp. 865–868 (2018). https://doi.org/10.1109/ICRERA.2018.8566736 6. Liu, K., Yin, M., Hua, W., Ma, Z., Lin, M., Kong, Y.: Design and analysis of Halbach ironless flywheel BLDC motor/generators. In: IEEE Transactions on Magnetics, vol. 54, no. 11, pp. 1–5, Art no. 8109305 (2018). https://doi.org/10.1109/TMAG.2018.2833958 7. Kumar, B.V.R., Kumar, K.S.: Design of a new dual rotor radial flux BLDC motor with Halbach array magnets for an electric vehicle. In: 2016 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Trivandrum, India, 2016, pp. 1–5. https:// doi.org/10.1109/PEDES.2016.7914552 8. Liu, Y., Liu, X., Sun, C.: Comparative study of electromagnetic performance of multi-tooth switching flux permanent magnet memory machine. IEEE Student Conf. Electr. Mach. Syst. 2018, 1–5 (2018) 9. Zhu, Z.Q., Howe, D.J.I.P.P.B.: Halbach permanent magnet machines and applications: a review. 148(4), 299–308 (2001)

Author Index

A Ai, Zishuo 260 Alkahtani, Mohammed Ao, Bo 249

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B Bai, Cong 939 Bai, Jingtao 404, 418 Bai, Naling 1059 Bi, Sheng 814, 825 Bin, Wang 1195 Bo, Li 1140, 1149, 1159 C Cai, Shumei 1059 Cao, Wenping 380, 523, 699, 782, 791, 883, 1246 Chang, Mengting 675, 681 Chen, Chen 1025 Chen, Hechong 603 Chen, Huanlin 491 Chen, Manlu 1168 Chen, Meiru 511 Chen, Ming 844 Chen, Ping 748 Chen, Weihai 423 Chen, Weihua 491 Chen, Wenjie 423 Chen, Xiang 186 Chen, Xianglin 498 Chen, Xiaodong 532 Chen, Xiaonan 323 Chen, Xinghui 51 Chen, Yixuan 1083 Cheng, Guojian 9 Cheng, Hong 1127 Cheng, Lan 800 Cheng, Xiaochun 1127 Cheng, Yong 129 Chu, Qiu 392 Chun, Zhang 138

Cui, Chaohui 594, 919 Cui, Han 73 Cui, Qi 89 Cui, Yangyang 1002 D Deng, Tianbai 279 Deng, Xiangtian 974 Deng, Xueyuan 313 Deng, Yaping 565 Deng, Yi 439 Deng, Yifan 457 Ding, Liang 447 Dong, Kejun 39 Dong, Run 665 Dong, Shuo 195 Dong, Wenchao 305, 404, 418 Dong, Xinsheng 323 Dong, Yu 305 Dong, Zhao 1 Duan, Naixin 82 Duan, Zhaoyu 387 F Fan, Jinli 565 Fan, Ming 404, 418 Fan, Yi 1008 Fan, Yifei 1015 Fan, Yongwei 553 Fan, Zhiyuan 207 Fang, Fang 123 Fang, Wang 1195 Fang, Yingying 186 Fei, Haoyang 19 Feng, Fang 220 Feng, Jia 837 Feng, Lei 807, 1076, 1093 Feng, Min 169, 1110 Feng, Wei 491, 800 Feng, Xinzhen 517, 897 Feng, Xue-Yan 609

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 C. Hu and W. Cao (Eds.): CoEEPE 2022, LNEE 1060, pp. 1301–1307, 2023. https://doi.org/10.1007/978-981-99-4334-0

1302

Fu, Han 1101 Fu, Jiekai 932, 1224 Fu, Tao 430 Fu, Xiao 202, 269 G Gao, Ciwei 814, 825 Gao, Diju 255 Gao, Haixiang 1149 Gao, Min 89, 101 Gao, Pengcheng 161 Gao, Wenpeng 305 Gao, Xinmai 333 Gao, Yixuan 939 Ge, Erqian 154 Ge, Lusheng 111, 117, 890 Ge, Quanwu 1 Gong, Xundong 844 Gong, Yining 981 Gu, Lingyun 305 Guan, Chunsheng 571 Guo, Fei 392 Guo, Jiahao 1118 Guo, Su 212 Guo, Tianshi 387, 511 Guo, Wei 1083 Guo, Yuanjun 491, 800 Guo, Zhiqiang 993 Guo, Zixuan 856 H Han, Bin 356 Han, Chunyi 491 Han, Qimeng 681 Han, Song 279 Han, Weitao 333 Han, Xiangrong 356 Han, Xiaonan 409 Haoyu, Li 138 He, Boran 681 He, Darui 1015 He, Han 993 He, Long 479 He, Xin 129 He, Ye 1083 Heldwein, Marcelo Lobo 479 Holtz, Joachim 439 Hong, Huijun 761, 768, 775 Hong, Ruofei 582

Author Index

Hou, Jilei 239 Hu, Aiqun 178 Hu, Cungang 380, 523, 594, 699, 717, 782, 791, 883, 911, 919 Hu, Fei 844 Hu, Guowei 532 Hu, Tiebin 1168 Hu, Wanyue 154 Hu, Xiaonan 1178 Hu, Xin 178 Hu, Xu 195 Hu, Yawei 873 Hu, Yihua 1254 Huang, Biao 1033 Huang, Dachao 1076, 1093 Huang, DaChao 807 Huang, Rong 186 Huang, Run 1083 Huang, Tao 409 Huang, Tianxiang 932, 1224 Huang, WeiMing 748 Huang, Xiaoyan 1292 Huang, Zhifu 873 Huaying, Zhang 654 Hui, Luo 1232, 1239 Huo, Chao 82 J Ji, Bing 1246 Ji, Shiqing 1281 Jia, Kai 239 Jia, Qingquan 675 Jia, Weina 582, 588 Jia, Yicheng 675, 681 Jian, Chu 1232, 1239 Jian, Zhang 1159 Jiang, Huafeng 498 Jiang, Li 844 Jiang, Meihui 825 Jiang, Ming 239 Jiang, Tao 129 Jiang, Wei 447, 457 Jiang, Yu 178 Jiang, Yurou 932, 1224 Jiangang, Lu 1140, 1159 Jiao, Xize 323 Jiao, Yadong 89 Jiao, Zhenhua 288 Jie, Wei 1232, 1239 Jie, Yewei 404, 418

Author Index

Jin, Huaiwang 873 Jing, Jiangping 542 Jinhua, Huang 1159 Ju, Lvfeng 333 K Kai, Ma 1195 Kaiyan, Pan 1140, 1149, 1159 Kang, Qiong 1065 Kang, Ziteng 1118 Ke, Dongliang 466 Ke, Zhehan 466 Kennel, Ralpha 479 Kong, Deren 374 Kun, Xie 1195 Kuo, Xin 1140, 1149 L Lang, Jiahong 148 Lei, Jiaxing 517 Lei, Yanxiao 333 Li, Biao 1189 Li, Bingkun 387, 511 Li, Chenglin 932, 1224 Li, Chunyan 392 Li, Dacheng 212, 220 Li, Fei 154 Li, Guang 430 Li, Guohao 905 Li, Haiwei 82 Li, Hanzhi 1178 Li, Haoran 594, 919 Li, Haoxiang 932, 1224 Li, Haoyu 161 Li, Hong 339, 348 Li, Jingyu 1178 Li, Junpeng 129 Li, Kai 339 Li, Kezhou 932, 1224 Li, Peng 230, 457 Li, Pengcheng 1178 Li, Qiang 207 Li, Qing ye 63 Li, Qingye 364 Li, Shaochong 603 Li, Shengnan 129 Li, Shuangxi 1059 Li, Weilin 665, 856 Li, Wenpei 1101

1303

Li, Xu 220 Li, Xuanlin 873 Li, Xuliang 82 Li, Xv 212 Li, Yan 1015 Li, Yu 582, 588 Li, Zekun 1246 Li, Zhaodi 856 Li, Zhaokai 1292 Li, Zhen 993, 1008, 1052 Li, Zhen-Bi 609 Li, Zhenguo 675, 681 Li, Zhi 993, 1052 Li, Zhuohuan 905 Liang, Chao 710 Liang, Dazhuang 582, 588 Liang, Lin 19 Liang, Siyang 665, 856 Liang, Xueqing 761 Liang, Zhengbo 504 Liao, Fangqun 807, 1076 Liao, Ye 186 Lin, Tao 1046, 1204 Lingchen, Wu 138 Liu, Chuanhao 517 Liu, Fu wen 63 Liu, Hang 807, 1076, 1093 Liu, Jiawei 398 Liu, Jun 1046, 1204 Liu, Junlei 32 Liu, Minxin 1209 Liu, Peng 687 Liu, Qiannan 974 Liu, ShangHai 687 Liu, Shaojie 1219 Liu, Shiming 911 Liu, Tong 939 Liu, Xiaoge 339, 348 Liu, Xinmiao 32 Liu, Yangfan 1209 Liu, Yayun 1209 Liu, Yiqi 387, 511 Liu, Yongbin 873 Long, Leyun 1033 Long, Weili 186 Lou, Yuanyuan 32 Lu, Bingbing 1219 Lu, Geye 730 Lu, Hui 761, 768, 775 Lu, Jiangang 1149

1304

Lu, Mingjin 148 Lu, Xun 32 Lu, Youfei 761, 768 Luo, Jiaohong 409 Luo, Peien 1002 Luo, Sujuan 313 Luo, Wei 51, 202 Luo, Youkun 313 Luo, Yuan 946 Lv, Weiguang 1059 Lv, Zhenhua 207 M Ma, Guangchen 398 Ma, Junpeng 807, 1093 Ma, Longpeng 1025 Ma, Xinyu 699, 717 Ma, Zhenqi 404, 418 Mei, Shangming 1254 Meng, Tao 392 Meng, Xian 129 Miao, Fenglin 1008 Min, Gao 654 Ming, Hao 814, 825 Mingxing, Zhu 654 Miu, Qiu 844 N Ni, Shilin 620, 629 Niu, Wenjuan 356 Niu, Yanzhao 504 P Pan, Hong 220 Pan, Jinchang 339, 348 Pan, Tianhong 123 Pang, Yong 57, 230, 756 Pei, Tian-Yi 169, 1110 Pei, Yu 710 Peng, Chao 504 Peng, Hui 186 Peng, Kun 404, 418 Peng, Maolan 807, 1076, 1093 Peng, Weifa 1046, 1204 Pengcheng, Gao 138 Pu, Fan 856 Q Qi, Cui 654

Author Index

Qi, Xin 439 Qian, Xiao 897 Qiao, Jianqiang 430 Qiming, Wang 837 Qing, Wang 654 Qiu, Siqi 946, 962 Qiu, Wei 148 R Rao, Lei 603 Ren, Bixing 207 Ren, Jiashi 439 Ren, Jinbiao 1168 Ren, Shuaihui 775 Ren, Yazhao 323 Rong, Xiuting 82 Ru, Wei 447 Rui, Tao 380, 523, 699, 883 Ruifeng, Zhao 1140 S Sa, Pengcheng 447, 457 Shan, Ren 1195 Shang, Shuo 710 Shangguan, Xu 348 Shaojian, Li 1232, 1239 She, Haibo 1209 Shen, Hao 154 Shen, Lang 288 Shen, Mengyuan 638, 647 Shen, Weixiang 380, 523, 594, 699, 717, 782, 883, 919 Shen, Zhangliang 542 Sheng, Cong 1189 Sheng, Yin 962 Shi, Gang 1219 Shi, Guangnan 457 Shi, Mingming 1118 Shi, Shuo 603 Shi, Tianyu 911 Shi, Wenhui 404, 418 Shuang, Wu 138 Si, Yu 260 Song, Fei 111 Song, Guanghui 1101 Song, Guotao 553 Song, Heng 323 Song, Jiajun 761, 768, 775 Song, Tianze 212, 553

Author Index

Song, Xueguan 57, 63, 230, 364, 430, 756 Sui, Bengang 404, 418 Sun, Fanxin 1189 Sun, Gang 430 Sun, Jiye 1292 Sun, Linlin 323 Sun, Mingzhe 511 Sun, Peng 1083 Sun, Qihang 675 Sun, Wei 57, 230, 756 Sun, Xiantao 423 Sun, Xiaolei 380 Sun, Xinjie 542 Sun, Yibo 594, 919 Sun, Yichao 207 Sun, Yonghao 594 Sun, Yudong 398 Suo, Zhixin 761, 768, 775 T Tang, Xin 594 Tao, Chuangchuang 1065, 1118 Tao, Jun 123, 279, 571 Tao, Xiaofeng 594, 919 Tao, Xiyang 409 Tao, Yuan 946, 962 Tian, Bing 1209 Tian, Dengji 148 Tian, Yun 212, 220 Tong, Xin 603 Tong, Zejun 161 W Wan, Yong 782 Wang, Chenggen 207 Wang, Da 1168 Wang, Decheng 1015 Wang, Fengxiang 466, 479 Wang, Haitao 782 Wang, Houying 620, 629 Wang, Huilai 32 Wang, Jialin 807 Wang, Jianjun 447 Wang, Jianzhong 288 Wang, Jiayan 761, 768, 775 Wang, Jingshuai 1065 Wang, Jun 864 Wang, Kuang 111, 117 Wang, Lei 404, 418

1305

Wang, Qi 911 Wang, Qian 565, 974 Wang, Qiao 32 Wang, Qin 1127 Wang, Qing 279 Wang, Qingfeng 288 Wang, Qingshan 1015 Wang, Quanwen 974 Wang, Qunjing 571 Wang, Shuai 498 Wang, Shunliang 807, 1076, 1093 Wang, Shuo 63 Wang, Suhang 57 Wang, Tengda 404, 418 Wang, Weidong 1178 Wang, Xiaocan 498 Wang, Xiaoming 710 Wang, Xiaoyang 82 Wang, Xingcun 1127 Wang, Xinying 594, 919 Wang, Xiuqin 571 Wang, Yan 1101 Wang, Yang 1, 39 Wang, Yangang 1254 Wang, Yao 883 Wang, Yi 260, 1292 Wang, Yifan 603 Wang, Yitang 57, 756 Wang, Yixuan 775 Wang, Yu 148, 392 Wang, Yuying 249 Wang, Zhensheng 123 Wang, Zhicong 981 Wang, Zining 814 Wei, Yao 466 Wenjie, Zheng 1159 Wu, Chen 532, 1025 Wu, Chengke 800 Wu, Di 212, 220 Wu, Junhua 890 Wu, Shuang 161 Wu, Wenjuan 1025 Wu, Xian 571 Wu, Xin 1065, 1118 Wu, Yan 305 Wu, Yi 1118 Wu, Yifei 1065, 1118 Wu, Yin 532, 1025 X

1306

Xia, Kun 51, 195, 202, 269 Xia, Shiwei 1101 Xia, Wei 825 Xiang, Li 1232, 1239 Xiao, Xiong 313 Xiao, Yiyang 517 Xie, Fang 620, 629, 638, 647 Xie, JiaJun 748 Xie, Jin-Yang 609 Xie, Yang 1093 Xie, Yi-Chen 609 Xie, Zhen 297 Xin, Huang 1195 Xing, Qianli 993 Xingang, Yang 837 Xiong, Hanwu 504 Xiong, Zeliang 498 Xu, Baojun 905 Xu, Deming 439 Xu, Han 582 Xu, Haotian 814 Xu, Hui 1254 Xu, Ji 946, 962 Xu, Qiming 565 Xu, Shipu 1059 Xu, Shi-Zhou 169, 1110 Xu, Wei 9 Xu, Wenyuan 946, 962 Xu, Zibo 447 Xu, Zunbin 710 Xue, Guiyuan 532, 1025 Xue, Jianzhi 582, 588 Xue, Weining 249 Xue, Zhiying 398 Xuejun, Xiong 837 Y Yadong, Jiao 654 Yajun, Zhang 837 Yan, Liting 1065 Yan, Qin 932, 1224 Yan, Xilin 807, 1076 Yan, Yaoliang 404, 418 Yang, Chenwei 1292 Yang, Duotong 905 Yang, Fan 374, 897, 1101 Yang, Hong 82 Yang, Huifan 1292 Yang, Nan 260 Yang, Rui 800

Author Index

Yang, Siyi 665 Yang, WeiWei 687 Yang, Wenxin 1065 Yang, Xi 169, 1110 Yang, Yinming 423 Yang, Yunhu 582, 588 Yang, Zhi 588 Yang, Zhibo 101 Yang, Zhichang 339, 348 Yang, Zhile 491, 800 Yao, Daojin 710 Ye, Rong 993, 1052 Yin, Laicheng 387, 511 Yin, Yanhe 905 Yin, Zhonggang 939, 1002 Ying, Zhou 333 Yong, Huang 1232, 1239 You, Guangzeng 1083 Yu, Jing 873 Yu, Jingjing 1272 Yu, Junjie 905 Yu, Wang 1232, 1239 Yu, Yue 398 Yuan, Fang 9 Yuan, Qingqing 195, 202 Yuan, Tao 279 Yuan, Tian 504 Yuan, Xiaolin 239 Yuan, Ying 313 Yue, Haifeng 430 Z Zejun, Tong 138 Zeng, Jianxin 1168 Zhai, Pengfei 1209 Zhan, Leilei 594, 919 Zhan, Shi 1140 Zhang, Ao 364 Zhang, Chenda 1127 Zhang, Chun 161 Zhang, Chunhua 9 Zhang, Congfa 1189 Zhang, Dan 255 Zhang, Dongying 1101 Zhang, Geng 974 Zhang, Haiyun 1059 Zhang, Hanlin 1059 Zhang, Hong 404, 418 Zhang, Huaying 89, 101, 123, 279, 571 Zhang, Jiahao 800

Author Index

Zhang, Jianing 439 Zhang, Jianwen 1219 Zhang, Jin 504 Zhang, Jinli 856 Zhang, Jinqiang 638, 647 Zhang, Jixuan 791 Zhang, Juanqin 1059 Zhang, Ke 380, 523, 594, 699, 717, 782, 883, 919 Zhang, Liudong 542 Zhang, Liusheng 297 Zhang, Liyan 699, 717 Zhang, Lizong 457 Zhang, Maosong 571 Zhang, Ming 1025 Zhang, Pinjia 730 Zhang, Quanzhu 249 Zhang, Qun 1015 Zhang, Shuai 57, 230 Zhang, Tianci 430 Zhang, Wenhan 962 Zhang, Wenyu 638, 647 Zhang, Wu 1189 Zhang, Wuqi 1083 Zhang, Xinqing 1052 Zhang, Yan 932, 1224 Zhang, Yanfeng 63 Zhang, Yanhui 491 Zhang, Yanping 1002 Zhang, Yongchang 129 Zhang, YongGao 687 Zhang, Yu 768, 775, 844 Zhang, Yuxuan 1127 Zhang, Zhenbin 911, 993, 1052 Zhang, Zhiqian 911 Zhang, Ziyang 19 Zhang, Zuchao 239 Zhao, Chuanrong 374 Zhao, Han 1033 Zhao, Juan 82 Zhao, Longqing 297 Zhao, Yingying 1219 Zhao, Yuan 1093

1307

Zhaoxin, Du 837 Zheng, Dayong 730 Zheng, Junyuan 387 Zheng, Kun 212 Zheng, Mingzhou 404, 418 Zheng, Qinggui 498 Zheng, Shicheng 148 Zheng, Wenjie 1149 Zheng, Xianqing 1059 Zheng, Xiaonan 220 Zheng, Yuankun 398 Zhi, Yali 423 Zhong, Chenming 195 Zhou, Chen 897 Zhou, Feiyan 305 Zhou, Hang 73 Zhou, Huajian 791 Zhou, Jianqiao 1219 Zhou, Kai 117 Zhou, Lawu 1033 Zhou, Shiding 1076 Zhou, Weihao 364 Zhou, Xiaotong 1272 Zhou, Xinyi 409 Zhou, Zexi 339, 348 Zhou, Zhongzheng 51 Zhu, Hongqin 73 Zhu, Hongzhen 374 Zhu, Jianye 864, 946 Zhu, Jingsong 356 Zhu, Kexin 202 Zhu, Mingxing 89, 101 Zhu, Qianlong 279 Zhu, Shaojie 897 Zhu, Wenjie 717, 782, 791 Zhu, Yuhang 523 Zijun, Zhang 1232, 1239 Zong, Chaoyong 364 Zong, Shaolei 844 Zou, Shirong 761, 768 Zou, Xiaoming 207 Zuo, Guizhong 239 Zuo, Kunkun 479