Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering: Power Electronics, Energy Storage and ... Notes in Electrical Engineering, 899) 9811919216, 9789811919213

Table of contents :
Contents
Power Electronic Components and Devices
Study on the Influence of Parasitic Parameters on the Switching Characteristics and High Frequency Oscillation of SiC MOSFET
1 Introduction
2 Switching Transient Process Analysis
2.1 Turn-On Process
2.2 Turn-Off Process
3 Simulation
3.1 Power Circuit Oscillation Simulation Considering Parasitic Parameters
3.2 Drive Circuit Oscillation Simulation Considering Parasitic Parameters
4 Conclusion
References
A DSRD-Based Trigger Circuit for RBDT
1 Introduction
2 Theory of Operation
3 Experimental Setup
4 Experimental Results
4.1 Influence of the Trigger Process on the Characteristics of RBDT
4.2 Influence of the Voltage of the Main Circuit
5 Analysis and Discussion
6 Conclusion
References
Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical Coupling Method
1 Introduction
2 Modeling
2.1 Press Pack IGBT Characteristics
2.2 FE Model Development
3 Result and Discussion
3.1 Press-Pack Simulation Varying Power Density
3.2 Press-Pack Simulation Varying Clamping Force
3.3 Press-Pack Simulation with One Chip Failed
3.4 Press-Pack Simulation with Two Chips Failed
4 Conclusion
References
Investigating the Dynamic Performance of Power Semiconductors in Parallel Connection
1 Introduction
2 Dynamic Modeling of SiC MOSFETs in Parallel
2.1 Turn-On Switching Analysis
2.2 Modeling the I-V and C-V Characteristics of SiC MOSFET
3 Model Implementation
4 Limitation of Analytical Model
5 Conclusion
References
Turn-On Switching Analysis of SiC/Si Hybrid Switch
1 Introduction
2 Modelling of HyS Turn-On Switching Transient
3 Model Implementation
4 Conclusion
References
Plastic Strain Analysis of IGBT Solder Layer
1 Introduction
2 Finite-Element Analysis
3 Analysis IGBT Module Structure Parameters by Orthogonal Analysis
4 Effect of Different Material Solder Layers on the Plastic Strain of the IGBT Module
5 Conclusion
References
Design of a New Drive Circuit for Gallium Nitride
1 Introduction
2 Two-Stage Drive Circuit
2.1 Ideal Drive Circuit
2.2 Actual Drive Circuit
2.3 Two-Stage Drive Circuit
3 Experimental Simulation
4 Conclusion
References
Review of SiC MOSFET Failure Analysis Under Extreme Conditions: High Temperature, High Frequency and Irradiation
1 Introduction
2 Failure Analysis Under High Temperature
2.1 Generation of Extreme High Temperature Condition
2.2 Catastrophic Failures Mechanism
2.3 Characterizations
2.4 Withstand Capability
3 Failure Analysis Under High Frequency
3.1 Potential Failure Analysis of Power Circuit
3.2 Potential Failure Analysis of Control Circuit
4 Failure Analysis Under Irradiation
4.1 Total Ionization Dose
4.2 Single Event Burnout
4.3 Single Event Gate Rupture
5 Improving Reliability Under Extreme Conditions
6 Conclusion
References
Power Converter Topologies and Control
Non-singular Terminal Sliding Mode Control Algorithm for DC/DC Boost Converter System Based on a Finite-Time Convergent Observer
1 Introduction
2 Mathematical Modeling and Traditional NTSMC Method
2.1 Mathematical Modeling
2.2 Traditional NTSMC Method
3 Novel Sliding-Mode Controller Design
3.1 Design of Finite-Time Convergent Observer
3.2 Controller Design
4 The Analysis of System Stability
4.1 The Analysis of Finite-Time Convergent Observer Stability
4.2 The Analysis of NTSM Controller Stability
5 Simulation Results
6 Conclusions
References
A Wide-Range Input Multi-phase Interleaved DC/DC Converter Suitable for Fuel Cells
1 Introduction
2 Operating Principle of the Proposed Converter
2.1 Basic Operating Principle
2.2 Steady State Analysis
3 Control of the Proposed Converter
3.1 Small Signal Model
3.2 Average Current Control Model
4 Simulation Verification
5 Conclusion
References
FHSS-4FSK Based Power and Signal Synchronous Transmission for Cascaded DC/DC Converters
1 Introduction
2 The Modulation for Cascaded Buck Converters
3 Demodulation Strategy Based on FHSS-4FSK
4 Modeling and Response Characteristics Analysis
5 Experiment Verification
6 Conclusion
References
Power & Signal Synchronous Transmission Strategy for Three-Phase Voltage Source Inverter
1 Introduction
2 Proposed Power and Signal Synchronous Transmission
2.1 System Structure
2.2 System Modeling and Analysis
2.3 Analysis of the Closed-Loop Stability
3 Experimental Results
4 Conclusions
References
Improved Seven-Level Floating Capacitor Control Strategy
1 Introduction
2 7L-TANPC Inverter Topology
2.1 Basic Working Principle
2.2 Modulation Strategy
3 Control Strategy
3.1 Traditional Floating Capacitor Voltage Balance Control
3.2 Improved Voltage Control of Floating Capacitor
4 Simulation
5 Conclusion
References
Predictive Control Method for Secondary Ripple Suppression of Two-Stage Single-Phase Inverter
1 Introduction
2 Analysis of the Second Harmonic Generation Mechanism
3 PI Model Predictive Control with Notch Filter
4 Simulation Results
5 Conclusion
References
Research on Second Harmonic Ripple Suppression of Two Stage DC-AC Inverter
1 Introduction
2 Generation Mechanism of Secondary Ripple Current
3 Secondary Ripple Current Suppression and Dynamic Performance Improvement
3.1 The Basic Method is Put Forward
3.2 Selection of Virtual Impedance
3.3 Load Current Feedforward Control with Band Stop Filter
3.4 Second Harmonic Current Control of Series Virtual Resistance
4 Comparison of Control Methods
5 Simulation Results
6 Conclusion
References
Discrete Fuzzy Control Algorithm for Single-Phase-Shift Control of Isolated Full-Bridge DC-DC Converter
1 Introduction
2 Principle of Isolated Full-Bridge DC-DC Converter
3 Discrete Fuzzy Single-Phase-Shift Control Strategy
3.1 Discrete Domain Fuzzy Controller Design
3.2 Single-Phase-Shift Control System Based on Discrete Fuzzy Controller
4 Simulation Verification
5 Conclusion
References
Fault Diagnosis of Three-Level Inverters Based on Ensemble Empirical Mode Decomposition and Deep Neural Network
1 Introduction
2 Fault Type Analysis
3 Fault Diagnosis Method Based on EEMD-DNN
3.1 Ensemble Empirical Mode Decomposition
3.2 Deep Neural Network
4 Simulation and Analysis
4.1 Simulation and Result
4.2 Contrastive Analysis
5 Conclusion
References
A Direct Power Control of Single-Phase PWM Rectifiers Without Gird Voltage Sensor
1 Introduction
2 Direct Power Control Without Gird Voltage Sensor
2.1 System Description
2.2 Instantaneous Power Estimator
2.3 System Parameter Initialization
2.4 Inductance and Resistance Compensation
3 Experimental Results
4 Conclusion
References
Research on Current Ripple Characteristics of Interleaved Vienna Rectifier
1 Introduction
2 Analysis of Current Ripple Characteristics
2.1 Topology of the Interleaved Vienna Rectifier
2.2 Control Strategy of the Interleaved Vienna Rectifier
2.3 Current Ripple Characteristics
3 Simulation and Experimental Results
4 Conclusion
References
Endogenous Multimode Operation of Non-inverting Buck Boost Converter for Wide Range Voltage Regulation
1 Introduction
2 Multimode Operation
2.1 Steady-State Voltage Conversion Ratio of NIBB
2.2 Definition of Equivalent Duty Ratio deq
3 LPV System Model
4 Control Design
5 Experimental Verifications
6 Conclusion
References
New and Renewable Energy
Coordinated Control Strategy to Enhance FRT Capacity for Offshore Wind Farms Connected MMC-HVDC
1 Introduction
2 System Outline and Steady State Control of MMC-HVDC Connected Wind Farms
2.1 System Topology
2.2 Steady State Control
3 Coordinated FRT Control Strategy
3.1 FRT Control Strategy of the WFMMC
3.2 FRT Control Strategy of the GSVSC
3.3 Coordinated FRT Control Strategy with DC Chopper
4 Simulation Verification and Analysis
4.1 Asymmetric Fault Occurs in the Receiving Power Grid
4.2 Symmetrical Failure of the Receiving Power Grid
5 Conclusion
References
Frequency Regulation Method for HVDC System with Wind Farm
1 Introduction
2 System Configuration
2.1 DFIG
2.2 HVDC
3 Frequency Coordinated Regulation Method
3.1 HWFRS Power Allocation Strategy
3.2 WT Allocation Strategy in WF
3.3 Active SFD Restrain Strategy
4 Case Study
4.1 Introduction to the Simulation System
4.2 Simulation Results
5 Conclusions
References
An Adaptive Control in a LV Distribution Network Integrating Distributed PV Systems by Considering Electricity Substitution
1 Introduction
2 Control Framework
3 Distribution Network Adaptive Control Model
3.1 Day-Ahead Optimization
3.2 Control Within Days
4 Control the Process and Solve the Method
4.1 Control the Process
4.2 Solution Methods
5 Analysis
5.1 Background
5.2 Power Substitution
5.3 Optimization
5.4 Daily Control Scheme
6 Conclusions
References
A Two-Layer Scheme for Operating Renewable Based-Micro-Grid by Considering Economics and Grid Stability
1 Introduction
2 Two-Layer Optimization Model
2.1 System Structure
2.2 Two-Layer Optimization
3 Economic Optimization
3.1 Objective Function
3.2 Binding Conditions
4 Stability Optimization
4.1 Objective Function
4.2 Binding Conditions
5 Solution Method
5.1 Greedy-Genetic Algorithm for Solving Upper-Level Optimization Problems
5.2 Genetic Algorithm for Solving Lower Level Optimization Problems
6 Example Analysis
6.1 Example Overview
6.2 Example Results
7 Conclusion
References
Evaluation of Power Grid Flexibility Based on PV Output Characteristics
1 Introduction
2 Grid Flexibility Theory
2.1 Definition of Grid Flexibility
2.2 Analysis of PV Output Characteristics
3 Construction of Flexibility Indicators
3.1 Flexibility Static Evaluation Indicator
3.2 Flexibility Dynamic Evaluation Indicator
4 Examples
5 Conclusion
References
Super-Twisting Sliding-Mode Based Photovoltaic Grid-Connected Inverter Control
1 Introduction
2 LCL Three-Phase Photovoltaic Grid-Connected Inverter Model Design
2.1 Topological Structure of Three-Phase LCL Inverter
2.2 Mathematical Model of Inverter Based on LCL Filter
3 Sliding Mode Controller Design
3.1 Voltage Controller Design
3.2 Current Controller Design
4 Simulations
5 Conclusion
References
Supplementary Novel Damping Control of MMC-STATCOM to Mitigate SSCI
1 Introduction
2 System Configuration
3 SSCI Mitigation Strategy of MMC-STATCOM
4 Performance Verification with Time-Domain Simulation
5 Conclusion
References
Smart Grids, Power Flow and Load Control
The Simulation of Injected Pulse Signal into Grounding Electrode Lines of HVDC Transmission System for Fault Location Based on PSCAD
1 Introduction
2 Propagation Process of Injected Pulse Signal
3 Principle of Fault Location Method Based on Injected Pulse Signal
3.1 Fault Detection
3.2 Fault Location
3.3 Final Result
4 The Selection of Pulse Signal
4.1 Pulse Type
4.2 Pulse Width
5 Simulation
5.1 Modeling
5.2 Fault Location Simulation
6 Conclusion
References
Research on Evaluation System of AC/DC Hybrid Distribution Network with Common High Frequency Bus Multi Port EER
1 Introduction
2 Common High Frequency AC Bus Topology
2.1 Mathematical Model of MMAB
2.2 Main Working Mode
3 Effectiveness Impact Factors
3.1 Selection Principle of Evaluation Index
3.2 Energy Effectiveness Impact Factors
4 Effectiveness Impact Factors
4.1 Index Analysis
4.2 Comprehensive Evaluation Model
4.3 Example Analysis
5 Conclusion
References
Multi-time Scale Optimal Dispatch for AC/DC Distribution Networks Based on Cluster Partition
1 Introduction
2 Clustering Based Cluster Partition Method
2.1 Improved Electrical Distance
2.2 Spectral Clustering Algorithm and Application
3 Multi-time Scale Optimal Dispatch Model for AC/DC Distribution Networks Based on Cluster Partition
3.1 Long-Time Scale Optimization Model
3.2 Short-Time Scale Optimization Model
4 Case Study
4.1 Optimization Result Discussion
4.2 Cluster Partition Algorithm Analysis
5 Conclusion
References
Distribution Network Reconfiguration Based on BAS-IGA Algorithm
1 Introduction
2 Mathematical Model of Distribution Network Reconfiguration
3 Improved Genetic Algorithm
3.1 Genetic Operator
3.2 Adaptive Cross-Variance Probability
4 Research on BAS-IGA Based Network Reconstruction Method
4.1 Principle of the Beetle Antennae Search Algorithm
4.2 BAS-IGA Algorithm Flow Chart
5 Simulation Verification
6 Conclusion
References
Load Forecasting Based on Improved Long Short-Term Memory Artificial Neural Network
1 Introduction
2 Long Short-Term Memory Artificial Neural Network
3 Load Forecasting Model Based on Improved LSTM Algorithm
3.1 Grey System Correlation Theory
3.2 Load Forecasting Model Combining Grey System Correlation Degree and LSTM
3.3 Evaluation Method
4 Case Analysis
4.1 Correlation Analysis
4.2 Forecast Result
4.3 Forecast Effect Comparison
5 Conclusions
References
Multi-objective Coordinated Partition Governance of Distribution Network with DG and SVG
1 Introduction
2 Working Principle of DG Multi-ojective Power Quality
3 Multi-objective Optimization Configuration Strategy for Coordinating DG and SVG
3.1 Planning Model
3.2 Distribution Network Partition
4 Multi-objective Model of Distribution Network
4.1 Load Sensitivity Index in Various Region
4.2 Mathematical Model of Multi-objective Optimal Operation
5 Simulation and Analysis
5.1 Research on Park Distribution Network Planning
5.2 Partitioning Study
5.3 Study on Optimal Operation Under Typical Conditions
6 Conclusion
References
Comprehensive Evaluation for Distribution Network Reliability Considering the Difference of User’s Requirements
1 Introduction
2 Difference in Load Characteristics and Evaluation Index System
2.1 Power Supply Reliability and Difference in Load Characteristics
2.2 Evaluation Index System Considering User’s Requirements
3 Weight Determination and Comprehensive Evaluation
3.1 Determination of Subjective Weight
3.2 Determination of Objective Weight
3.3 Determination of Comprehensive Weight
3.4 Comprehensive Evaluation Based on Fuzzy Matter-Element Model
4 Conclusion
References
Research on LC Ratio of Metro Traction Drive System Applied in Oscillation Analysis
1 Introduction
2 Stability Analysis Based on Simplified Second-Order System
3 The Stability Analysis Considering the Dynamics of the Motor and Its Current Controller
3.1 Dynamics of the Motor and Its Current Controller
3.2 System Transfer Function
4 Simulation Verification and Analysis
4.1 The Stability Analysis Result Based on Simplified Second-Order System
4.2 The Stability Analysis Considering the Dynamics of the Motor
4.3 Stability Verification of the Metro Traction Drive System
5 Conclusion
References
A Feature Analysis and Clustering Method Based on User Electricity Data
1 Introduction
2 Data Prepocessing and Characteristics Analysis
2.1 Cleaning Data
2.2 Select Typical Data
2.3 Feature Extraction
3 Elaborate Behavior Analysis
3.1 Single Temperature Effect Response Coefficient
3.2 Single Temperature Effect Response Coefficient
3.3 Double Effect Response Coefficient
4 Case Study Results
4.1 Load Morphology Clustering
4.2 User Response Clustering
4.3 Verify the Results
5 Conclusion
References
Identification of Weak Links in Active Distribution Network Based on Vulnerability Assessment
1 Introduction
2 Index of Vulnerability Assessment Based on Complex Network Theory
2.1 Node Degree and Line Degree
2.2 Node Injection Power
2.3 Node Betweenness
2.4 Line Betweenness
3 Line Power Supply Weakness
3.1 Calculation of Power Supply Capacity
3.2 Line Power Supply Weakness Index
4 Case Study Results
5 Conclusion
References
A Method for Calculating Flicker of Fluctuating Loads by Instantaneous Power
1 Introduction
2 Key Issues and Models of Flicker Responsibility Allocation
3 Multi-Fluctuation Load Flicker Responsibility Allocation Algorithm
3.1 Signal Preprocessing
3.2 Flash Calculation and Responsibility Allocation Algorithm
4 Project Case Analysis
4.1 Algorithm Verification
4.2 Practical Application
5 Conclusion
References
An Optimization Method for Compensation Network Parameters in Double-Sided LCC Wireless Power Transfer System
1 Introduction
2 Modeling and Calculation of Double-Sided LCC Compensated WPT System
2.1 Equivalent Circuit Model
2.2 Influence of Transmission Coil Misalignment on Efficiency
2.3 Compensation Network Selection for Maximum Efficiency
3 Standard PSO Combined with Simulation Topology Model in Simulink
3.1 Weight Coefficient and Optimization Objective
3.2 Optimization Algorithm
3.3 Optimization Results and Analysis
4 Conclusion
References
Enterprise-Level Model Construction of Distribution Network Topology Based on Graph Database
1 Introduction
2 Topology Model of Distribution Networks
2.1 Topology Structure of Distribution Networks in Professional Work Perspective
2.2 Topology Structure of Distribution Networks in Professional Work Perspective
3 Application Analysis of Topology Database in Distribution Networks
3.1 Application Analysis of Power Grid Topology Based on Relational Database
3.2 Application Analysis of Power Grid Topology Based on Graph Database
4 a Graph Database-Based Topology Model Design of Distribution Networks
4.1 Definition of the Graph Data Model
4.2 Design of Topology Model
5 Automatic Diagram Generation of Distribution Networks Topology Model
5.1 Data Parsing and Conversion of the CIM/XML and the CIM/E
5.2 Algorithm Model of FR Force-Directed
5.3 The Process of Automatic Diagram Generation
6 Conclusion
References
Research on Application of Innovative Linear Active Disturbance Rejection Control in Three-Phase Four-Wire System DSTATCOM
1 Introduction
2 Establishment of Mathematical Model of Three-Phase Four-Wire DTSTACOM System
3 Traditional LADRC and Innovative LADRC Design
3.1 Traditional LADRC Design
3.2 Innovative LADRC Design
4 Performance Analysis of the Innovative LADRC
4.1 Disturbance Immunity Analysis of the Innovative LADRC
4.2 Stability Analysis of the Innovative LADRC
5 Simulation Experiment Analysis
6 Conclusion and Prospect
References
How Did the COVID-19 Crisis Affect the Efficiency of European Intraday Electricity Markets?
1 Introduction
2 Methodology and Data
2.1 Graphical and Statistical Analysis
2.2 Data
3 Results
3.1 Results of the Overall Investigation
3.2 German Electricity Prices
3.3 French Electricity Prices
3.4 Norwegian Electricity Prices
4 Discussion
4.1 Critical Appraisal
4.2 Research Limitations
5 Conclusion and Outlook
References
State Estimation of Intelligent Distribution Network Based on Data Fusion
1 Introduction
2 Multi Source Data Fusing
2.1 Fusion Based on Data Components
2.2 Fusion Based on Data Precision
2.3 Fusion Based on Data Refresh
3 State Estimation of Intelligent Distribution Network
3.1 Weighted Least Square State Estimation
3.2 Weight Determination Based on Data Fusion
4 Case Study Results
5 Conclusion
References
Preliminary Research on the Voltage Level of Low Voltage Direct Current System
1 Introduction
2 Configuration Principles and Constraint Condition
2.1 Configuration Principles of the Voltage Level
2.2 Constraint Condition of the Voltage Level
3 Evaluation Indicators and Evaluation Methods
3.1 Evaluation Indicators
3.2 Evaluation Methods
4 The Voltage Level of Different Application Scenarios
4.1 DC Building
4.2 ICT DC Power Supply System
4.3 Smart Park
5 Conclusion
References
Stability Analysis of DC Microgrid with Multi-converter Parallel Operation Based on Impedance Model
1 Introduction
2 System Structure of DC Microgrid
3 Small Signal Modeling of DC Microgrid
3.1 Model of DC Bus Voltage Control Unit
3.2 Model of Load
4 Analysis of System Stability
4.1 The Influence of DC Bus Capacitance on System Stability
4.2 The Influence of Converter Control Parameters on System Stability
4.3 The Influence of Load Power on System Stability
4.4 The Influence of the Parameter Matching of the DC BVC Units on System Stability
5 Conclusion
References
SCD File Visualization and Test Boundary Definition Method for Smart Substation
1 Introduction
2 SCD File Overview
3 SCD Profile Visualization
3.1 Improvement of SCD File Visualization
4 SCD File Comparison and Test Boundary Definition
4.1 SCD File Comparison Process
4.2 Test Boundary Definition
5 Conclusion
References
Power Load Forecasting Based on Sine-SSA-BP Neural Network
1 Introduction
2 Predictive Model
2.1 The Improved Sparrow Search Algorithm
2.2 Optimize BP Neural Network
3 Simulation Analysis
4 Conclusion
References
Energy Internet-Oriented Distribution Network Long-Term Load Forecasting Method Based on Prophet-BiLSTM-CRITIC Mode
1 Introduction
2 Power Load Forecasting Model
2.1 Prophet Forecasting Model
2.2 Bi-Directional Long-Short Term Memory (BiLSTM)
3 Hybrid Forecasting Model
4 Conclusion
References
Modular Capacitor-Based Full Bridge Interline DC Power Flow Controller: Topology Analysis and Performance Study
1 Introduction
2 Modular C-Based Full-Bridge IDCPFC
2.1 Structure and Working Principle
2.2 Control Strategy
2.3 Characteristics Analysis
2.4 Comparisons Between Two Topologies of Modular C-Based IDCPFC
3 Simulation Validation
3.1 Simulation Verification
4 Conclusions
References
Real-Time Electricity Price Optimization Strategy in Power Market Based on Markov Decision Chain
1 Introduction
2 Real-Time Electricity Price Optimization Based on Markov Decision Chain
2.1 Markov Decision Chain Modeling
2.2 Real-Time Electricity Price Model Based on Markov Decision Chain
3 Particle Swarm Optimization Algorithm
4 Example Simulation
5 Conclusion
References
Distribution Grid Topology Estimation Using 1D-CNN
1 Introduction
2 Principles of One-Dimensional Convolutional Neural Network
2.1 The Structure of 1D-CNN
2.2 Convolutional Layer
2.3 Pooling Layer
2.4 Fully Connected Layer
3 Topology Estimation Method of Distribution Grid Using Convolutional Neural Network
3.1 The Original Input Data Set of CNN Model
3.2 Original Data Processing
3.3 Sample Label Processing
3.4 CNN Model Structure
3.5 Topology Estimation Process
4 Case Studies
4.1 Case Description
4.2 Data Set Construction
4.3 Topology Estimation Evaluation Index
4.4 Simulation Result
5 Conclusion
References
Energy Storage
Development and Optimization of Aquaponics Greenhouse Thermal-Water Environment Monitoring System Based on LabVIEW
1 Introduction
2 Material and Methods
2.1 Experimental environment
2.2 Main Hardware Equipment
2.3 Software System Design
2.4 Greenhouse Thermal Environment Model
2.5 PID Control Principle
2.6 Fuzzy Control Principle
3 Results
3.1 Monitoring Experiment of Aquaponics System
3.2 Temperature Early Warning and Optimization
4 Discussion
5 Conclusion and Future
References
Identifying the Feasibility of Implementing of Heat Pump for Heating a Factory Aquaponics Greenhouse in Beijing
1 Introduction
2 Methods and Materials
3 Preliminary Thermal Analysis for Greenhouse Aquaponics
3.1 Air Heating Load
3.2 Heating Load for Water in Aquaponics
3.3 Primary Energy Consumption
4 Results and Discussion
4.1 Air Heating Load of Aquaponics Greenhouse
4.2 Water Heating Load of Aquaponics Greenhouse
4.3 Primary Energy Consumption and Carbon Emission
4.4 Operating Costs
4.5 Summary and Conclusions
References
Management and Control of Hybrid Energy Storage System in Ship Integrated Power System
1 Introduction
2 Ship Integrated Power System with DC Bus
3 Energy Management and Control Strategy of Hybrid Energy Storage System
3.1 Energy Management Strategy of Hybrid Energy Storage Unit
3.2 Bi-directional DC/DC Converter Control Strategy
4 Control Strategy of Rectifier Generator
5 Results and Analysis
6 Conclusion
References
Research on Control Strategy of PV-Energy Storage System Connected to Low Voltage Distribution Network
1 Introduction
2 PV Energy Storage Structure Connected to Low Voltage Distribution Network
3 Voltage Over-Limit Principle Proposed System
3.1 Principle of Voltage Over-Limit of PV-Energy Storage System Connected to Low-Voltage Distribution Network
3.2 Principles of PV-Energy Storage System to Manage Voltage Over-Limit
4 Control Strategy of PV-Energy Storage System
4.1 Control Strategy of PV-Energy Storage System
4.2 Battery Charge and Discharge Control
4.3 Control Stragegy of Grid-Connected Inverter
4.4 Voltage Control Strategy of VSI
5 Simulation
6 Conclusion
References
In the Electricity Market Environment for the Industrial Park Electrical Energy with Energy Optimization Strategy
1 Introduction
2 Optimal Modeling of Park Power Consumption in the Power Market
2.1 Park Hybrid for Power System Optimization Object Modeling
2.2 Optimize the Objective Function
2.3 Model Constraints
3 Improved Differential Evolution Algorithm
3.1 Improved Differential Evolution Algorithm
4 Optimize the Calculation Process
5 Calculation Example Analysis
6 Conclusion
References
Stackelberg Game Optimal Scheduling of User-Side Energy Storage Considering Source-Load Uncertainty
1 Introduction
2 Stochastic Optimal Scheduling Model for Distributed Energy Storage
3 Source Load Uncertainty Modeling
3.1 User Side Model
3.2 Distribution Network Model
3.3 Construction of Stackelberg Game Model
4 Case Analysis
4.1 Basic Data
4.2 Internal Prices
4.3 Optimization of the User Side Energy Storage System
4.4 Net Load Analysis
5 Conclusions
References
Harmonic Analysis, Monitoring and Digital Twins
Dynamic Harmonic Analysis of Electric Energy Routers with Common High Frequency Bus Under Multi-Source-Load Interaction
1 Introduction
2 The Development Status of Power Routers and System Structure of Topologies
2.1 Development Status
2.2 System Structure
3 Topological Structure of Electric Energy Router with Common High-Frequency Bus
4 Coordination of Dual-Loop Decoupling Control Strategy and Dual-Phase Shift Power Flow Control Strategy
4.1 Surrounding Control Method
4.2 Central Control Method
4.3 Hybrid Control Model
5 Dynamic Harmonic Analysis of Composite Ports Under Different Control Strategies
5.1 Simulation Results for Four Ports
5.2 Suppression of Harmonics Under Dual-Loop Decoupling Control Strategy
5.3 The Impact of Different Ports and Loads on System Harmonics
6 Conclusion
References
Research on Digital Twin Model of Three-Phase Inverter
1 Introduction
2 Mathematical Model of Three-Phase Inverter
3 Mathematical Model Analysis Method of Three-Phase Inverter
4 Realization of Digital Control
5 Simulation Verification
6 Conclusion
References
An Online Condition Monitoring Method of Single-Phase PWM Rectifier Based on Digital Twin
1 Introduction
2 Digital Twin System and Control Scheme
2.1 System Description
2.2 Direct Power Control
3 Proposed Parameter Identification Method
4 Simulation
4.1 Parameter Identification
4.2 Repeatability Test
5 Conclusion
References
Parameter Identification Method Based on Digital Twin of Boost Converter
1 Introduction
2 Mathematical Analysis Model of Boost Converter
3 Parameter Identification of Boost Converter
4 Simulation Verification
5 Conclusion
References
Transmission Line Tower Fault Identification Based on Image Processing Technology
1 Introduction
2 Image Preprocessing
2.1 Image Grayscale
2.2 Edge Detection Based on Canny Algorithm
3 Feature Extraction
3.1 Gradient Calculation
3.2 Gradient Histogram Statistics
4 Support Vector Machine(SVM) and Convolutional Neural Network (CNN)
5 Conclusion
References
Uniformly Observability of the Semi-discrete Schrödinger Equation
1 Introduction
2 Exponential Stability and Observability Inequality of the Schrödinger Equation
3 Decay Property of the Semi-discrete Scheme and Its Observability Inequality
4 Summary
References

Citation preview

Lecture Notes in Electrical Engineering 899

Cungang Hu · Wenping Cao · Pinjia Zhang · Zhenbin Zhang · Xi Tang   Editors

Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering Power Electronics, Energy Storage and System Control in Energy and Electrical Power Systems

Lecture Notes in Electrical Engineering Volume 899

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, 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, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany 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, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Yong Li, 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 Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Luca Oneto, Department of Informatics, Bioengineering., Robotics, University of Genova, Genova, Genova, Italy Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Walter Zamboni, DIEM - Università degli studi di Salerno, Fisciano, Salerno, Italy Junjie James Zhang, Charlotte, NC, USA

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Cungang Hu · Wenping Cao · Pinjia Zhang · Zhenbin Zhang · Xi Tang Editors

Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering Power Electronics, Energy Storage and System Control in Energy and Electrical Power Systems

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

Pinjia Zhang Department of Electrical Engineering Tsinghua University Beijing, China

Zhenbin Zhang School of Electrical Engineering Shandong University Jinan, Shandong, China

Xi Tang School of Electrical Engineering and Automation Anhui University Hefei, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-19-1921-3 ISBN 978-981-19-1922-0 (eBook) https://doi.org/10.1007/978-981-19-1922-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 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

Power Electronic Components and Devices Study on the Influence of Parasitic Parameters on the Switching Characteristics and High Frequency Oscillation of SiC MOSFET . . . . . . Gongde Xu, Yuanyuan Sun, Zhenguang Liang, Zhen Liu, Lisheng Li, and Yang Liu A DSRD-Based Trigger Circuit for RBDT . . . . . . . . . . . . . . . . . . . . . . . . . . . Xinyuan Huang and Lin Liang Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical Coupling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bowen Gu, Haimeng Wu, Volker Pickert, Bing Ji, Siyang Dai, and Zhiqiang Wang Investigating the Dynamic Performance of Power Semiconductors in Parallel Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jixuan Wei, Jiajun Yu, Kun Tan, Hongfei Chen, Haimeng Wu, Paul Lefley, and Bing Ji

3

11

23

35

Turn-On Switching Analysis of SiC/Si Hybrid Switch . . . . . . . . . . . . . . . . . Jixuan Wei, Zekun Li, Kun Tan, Chen Li, and Bing Ji

47

Plastic Strain Analysis of IGBT Solder Layer . . . . . . . . . . . . . . . . . . . . . . . . Zhengyi Ren, Yao Zhao, Zheng Liu, Zhiqiang Wang, and Ninghui Wang

57

Design of a New Drive Circuit for Gallium Nitride . . . . . . . . . . . . . . . . . . . . Wei Liu, Cungang Hu, Wenjie Zhu, Zhishang Yan, and Xinyu Ma

69

Review of SiC MOSFET Failure Analysis Under Extreme Conditions: High Temperature, High Frequency and Irradiation . . . . . . . Ziyang Zhang, Lin Liang, and Hai Shang

81

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Contents

Power Converter Topologies and Control Non-singular Terminal Sliding Mode Control Algorithm for DC/DC Boost Converter System Based on a Finite-Time Convergent Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Mengmeng Qi, Ying Shu, Chao Wan, Jiahong Lang, and Shicheng Zheng A Wide-Range Input Multi-phase Interleaved DC/DC Converter Suitable for Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Li Wei and Wen Yan FHSS-4FSK Based Power and Signal Synchronous Transmission for Cascaded DC/DC Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Yang Leng, Ziren Wei, Tailai Wang, and Dongsheng Yu Power & Signal Synchronous Transmission Strategy for Three-Phase Voltage Source Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Haiyang Liu, Yang Leng, and Dongsheng Yu Improved Seven-Level Floating Capacitor Control Strategy . . . . . . . . . . . 155 Donghui Liu, Changbao Zheng, and Cungang Hu Predictive Control Method for Secondary Ripple Suppression of Two-Stage Single-Phase Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Liyan Zhang, Cungang Hu, Wenjie Zhu, and Jialiang Jiao Research on Second Harmonic Ripple Suppression of Two Stage DC-AC Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Jialiang Jiao, Cungang Hu, Wenjie Zhu, and Liyan Zhang Discrete Fuzzy Control Algorithm for Single-Phase-Shift Control of Isolated Full-Bridge DC-DC Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Junyu Gan, Wenping Cao, Wenjie Zhu, Cungang Hu, and Xi Chen Fault Diagnosis of Three-Level Inverters Based on Ensemble Empirical Mode Decomposition and Deep Neural Network . . . . . . . . . . . . 207 Hongzhe Li, Jinsong Kang, and Weimin Li A Direct Power Control of Single-Phase PWM Rectifiers Without Gird Voltage Sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Wenwen Huang, Cungang Hu, Bi Liu, Wenjie Zhu, and Tao Rui Research on Current Ripple Characteristics of Interleaved Vienna Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Changan Li, Hongyang Zhang, Mingxia Xu, and Zhiqiang Wang Endogenous Multimode Operation of Non-inverting Buck Boost Converter for Wide Range Voltage Regulation . . . . . . . . . . . . . . . . . . . . . . . 239 Jianjun Ma, Miao Zhu, Chunyang Pan, and Xu Cai

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New and Renewable Energy Coordinated Control Strategy to Enhance FRT Capacity for Offshore Wind Farms Connected MMC-HVDC . . . . . . . . . . . . . . . . . . . 255 Wenqiang Wu, Ke Jia, Laiyun Hou, Jin Sun, and Bohan Liu Frequency Regulation Method for HVDC System with Wind Farm . . . . 263 Yuhong Wang, Jie Zhu, Qi Zeng, and Zongsheng Zheng An Adaptive Control in a LV Distribution Network Integrating Distributed PV Systems by Considering Electricity Substitution . . . . . . . 277 Yongxiang Cai, Anqian Yang, Xiangping Chen, Xiankui Wen, Yu Fu, Xiaobing Xiao, Yue Li, and Lianchao Zhang A Two-Layer Scheme for Operating Renewable Based-Micro-Grid by Considering Economics and Grid Stability . . . . . . . . . . . . . . . . . . . . . . . . 297 Jinbiao Li, Changqing Dang, Daoyin Long, Lianchao Zhang, Jing Zhang, Qinmu Wu, Min Liu, Yuhong Cai, and Xiangping Chen Evaluation of Power Grid Flexibility Based on PV Output Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Chaofan Wang, Jie Lou, Xiaohan Shi, Yuanyuan Sun, and Kejun Li Super-Twisting Sliding-Mode Based Photovoltaic Grid-Connected Inverter Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 Minghao Zhou, Haofan Yu, Xingguo Wu, Hongyu Su, Siwei Cheng, and Yunhao Xu Supplementary Novel Damping Control of MMC-STATCOM to Mitigate SSCI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Yiqi Liu, Junyuan Zheng, Mingfei Ban, and Zhenjie Li Smart Grids, Power Flow and Load Control The Simulation of Injected Pulse Signal into Grounding Electrode Lines of HVDC Transmission System for Fault Location Based on PSCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Yining Zhang, Yueyang Wang, and Kun Liu Research on Evaluation System of AC/DC Hybrid Distribution Network with Common High Frequency Bus Multi Port EER . . . . . . . . . 355 Yang Liu, Lisheng Li, Mingyang Li, Yong Li, Hejin Liu, Min Huang, Guoqiang Su, and Feng Wang Multi-time Scale Optimal Dispatch for AC/DC Distribution Networks Based on Cluster Partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 Lisheng Li, Yang Liu, Mingyang Li, Hejin Liu, Yong Li, Min Huang, Guoqiang Su, and Feng Wang

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Distribution Network Reconfiguration Based on BAS-IGA Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Yang Liu, Lisheng Li, Yong Li, Min Huang, Mingyang Li, Hejin Liu, Feng Wang, and Guoqiang Su Load Forecasting Based on Improved Long Short-Term Memory Artificial Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 Qinglin Zhao, Lianchao Zhang, Yuhong Cai, and Xiangping Chen Multi-objective Coordinated Partition Governance of Distribution Network with DG and SVG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Hua-Ying Zhang, Ming-Gang Song, Wei-Zhou Zhang, Xian Wu, and Jun Tao Comprehensive Evaluation for Distribution Network Reliability Considering the Difference of User’s Requirements . . . . . . . . . . . . . . . . . . . 423 Yongchun Yu, Shu Mao, Youmin Li, Xiankai Chen, Xiaolan Sun, Qiang Yu, and Linfeng Wang Research on LC Ratio of Metro Traction Drive System Applied in Oscillation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Jing Gu, Jinsong Kang, and Wanlu Guo A Feature Analysis and Clustering Method Based on User Electricity Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 Qiao Yu, Yan Wen, Hailei Meng, Xiaoyue Li, Zilong Liang, Xiaoyan Yang, and Zhaoyuan Liu Identification of Weak Links in Active Distribution Network Based on Vulnerability Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 Yongchun Yu, Shu Mao, Hailei Meng, Chenyu Zhao, Xiankai Chen, and Chaoqun Zhou A Method for Calculating Flicker of Fluctuating Loads by Instantaneous Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 Ming-Xing Zhu, Yi-Heng Zhang, and Bin Xu An Optimization Method for Compensation Network Parameters in Double-Sided LCC Wireless Power Transfer System . . . . . . . . . . . . . . . . 471 Shengqi Zhao, Zhaokai Li, Xiaoyan Huang, Dongdong Jiang, and Chenxi Zhou Enterprise-Level Model Construction of Distribution Network Topology Based on Graph Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 Pengxi Liu, Jiacheng Liang, Jiakai Xiao, Dongliang Hu, Gongjie Shi, and Mingyao Ma Research on Application of Innovative Linear Active Disturbance Rejection Control in Three-Phase Four-Wire System DSTATCOM . . . . . 495 Youjie Ma, Xinyu Jiang, and Xuesong Zhou

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How Did the COVID-19 Crisis Affect the Efficiency of European Intraday Electricity Markets? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 Daria Gottwald, Jan Niklas Buescher, and Florian Momm State Estimation of Intelligent Distribution Network Based on Data Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 Daoyu Li, Yuanyuan Sun, Lintao Yuan, Chao Wang, Peng An, and Yanqing Pang Preliminary Research on the Voltage Level of Low Voltage Direct Current System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541 Longwei Xu, Yuanyuan Sun, Yahui Li, Anbin Zhang, and Fan Wang Stability Analysis of DC Microgrid with Multi-converter Parallel Operation Based on Impedance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 Anbin Zhang, Yuanyuan Sun, Qingshen Xu, Longwei Xu, Tao Yu, and Yanqing Pang SCD File Visualization and Test Boundary Definition Method for Smart Substation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Xiaodong Zhao, Guoping Chen, Feng Li, Leilei Fu, Bo Xu, and Zhenxing Qi Power Load Forecasting Based on Sine-SSA-BP Neural Network . . . . . . 565 Dingjiang Zou and Tianyu Liu Energy Internet-Oriented Distribution Network Long-Term Load Forecasting Method Based on Prophet-BiLSTM-CRITIC Mode . . . . . . . 573 Wenying Li, Qinghong Guo, Ming Wen, Yun Zhang, Xin Pan, and Shuzhi Yang Modular Capacitor-Based Full Bridge Interline DC Power Flow Controller: Topology Analysis and Performance Study . . . . . . . . . . . . . . . . 583 Jing Yi, Miao Zhu, Xu Zhong, Hongyi Zhang, Siqi Liu, and Xu Cai Real-Time Electricity Price Optimization Strategy in Power Market Based on Markov Decision Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 Xiaoxuan Guo, Shuai Han, Leping Sun, and Wanlu Wu Distribution Grid Topology Estimation Using 1D-CNN . . . . . . . . . . . . . . . . 607 Li Tong, Haiwei Liang, and Xudong Zou Energy Storage Development and Optimization of Aquaponics Greenhouse Thermal-Water Environment Monitoring System Based on LabVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621 Shihao Wu, Jinqi Yang, Quanwu Ge, Zhixin Ke, and Yang Wang

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Identifying the Feasibility of Implementing of Heat Pump for Heating a Factory Aquaponics Greenhouse in Beijing . . . . . . . . . . . . . . 637 Quanwu Ge, Zhixin Ke, Shihao Wu, and Yang Wang Management and Control of Hybrid Energy Storage System in Ship Integrated Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 Chuan Xiang, Yuhan Li, Qi Cheng, and Wenhua Xu Research on Control Strategy of PV-Energy Storage System Connected to Low Voltage Distribution Network . . . . . . . . . . . . . . . . . . . . . 659 Wenqi Hao, Jiazhu Xu, Guoqing Tong, Weiming Zhang, Yuxing Liu, and Nihan Tong In the Electricity Market Environment for the Industrial Park Electrical Energy with Energy Optimization Strategy . . . . . . . . . . . . . . . . . 675 Xiaoxuan Guo, Shuai Han, Leping Sun, and Wanlu Wu Stackelberg Game Optimal Scheduling of User-Side Energy Storage Considering Source-Load Uncertainty . . . . . . . . . . . . . . . . . . . . . . . 687 Kui Luo, Zhidong Guo, Tao Rui, and Cungang Hu Harmonic Analysis, Monitoring and Digital Twins Dynamic Harmonic Analysis of Electric Energy Routers with Common High Frequency Bus Under Multi-Source-Load Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 Zhen Liu, Yuanyuan Sun, Gongde Xu, Lisheng Li, Yang Liu, and Yanqing Pang Research on Digital Twin Model of Three-Phase Inverter . . . . . . . . . . . . . . 713 Haitao Wang, Cungang Hu, Wenjie Zhu, Weiye Yang, and Xiangyu Zheng An Online Condition Monitoring Method of Single-Phase PWM Rectifier Based on Digital Twin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723 Weiye Yang, Cungang Hu, Bi Liu, Haoran Li, and Haitao Wang Parameter Identification Method Based on Digital Twin of Boost Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735 Xiangyu Zheng, Cungang Hu, Wenjie Zhu, Haitao Wang, and Weiye Yang Transmission Line Tower Fault Identification Based on Image Processing Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 Wencheng Sun, Lingyun Wu, Jiaxin Yuan, Nuochun Liu, Liwen Peng, and Xianfeng Zheng Uniformly Observability of the Semi-discrete Schrödinger Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 Kunyi Yang, Lei Chen, and Jietao Zou

Power Electronic Components and Devices

Study on the Influence of Parasitic Parameters on the Switching Characteristics and High Frequency Oscillation of SiC MOSFET Gongde Xu , Yuanyuan Sun , Zhenguang Liang, Zhen Liu, Lisheng Li, and Yang Liu Abstract Compared with silicon-based switching devices, silicon carbide (SiC) MOSFET has higher temperature and pressure resistance levels, switching speeds and lower switching losses, it has huge application prospects in electric vehicles and power conversion controllers. However, because of extremely high switching speed, under the effect of parasitic parameters, the problem of voltage and current spike oscillations is more prominent, which will adversely affect the efficient and safe operation of devices and power electronic devices. This paper will study the influence of parasitic parameters on the switching oscillation of SiC MOSFET. Based on the analysis of the mechanism of voltage and current spikes in the switching process of SiC MOSFET, a double pulse test circuit is used to simulate the influence of parasitic parameters on the switching oscillation. Keywords Silicon carbide MOSFET · Parasitic parameters · Oscillation

G. Xu · Y. Sun (B) · Z. Liang · Z. Liu Shandong University, Jinan 250001, China e-mail: [email protected] Z. Liang e-mail: [email protected] Z. Liu e-mail: [email protected] L. Li · Y. Liu State Grid Shandong Electric Power Company, Jinan 250001, China e-mail: [email protected] Y. Liu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_1

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1 Introduction Wide-gap semiconductor materials with higher breakdown electric field and thermal conductivity can work at high voltages, high temperatures and higher switching frequencies. They have received extensive attention from the industry and are recognized as the most promising new generation semiconductor materials [1]. The dielectric breakdown field strength that is one order of magnitude higher than that of silicon devices enables SiC to withstand higher voltage levels; higher electron saturation drift speeds enable higher switching speeds; higher breakdown voltage and current density make SiC have more superior power density characteristics, SiC has smaller conduction loss and turn-off loss, higher thermal conductivity, and can withstand higher temperatures [2–5]. However, the unique fast switching characteristics of SiC MOSFET make the system have voltage and current oscillation problems during the switching process. The oscillation problem will not only cause the system power loss, but also threaten the reliability of the system. Therefore, this problem has been widely discussed by industry experts and scholars at the application level. The turn-on and turn-off time of the switching process of silicon carbide MOSFET is only tens of nanoseconds, which is very sensitive to parasitic parameters. This causes parasitic parameters to form a resonant circuit at extremely high dv/dt and di/dt, resulting in voltage and current oscillations, which may damage the device itself, increase power loss, and introduce a large amount of electromagnetic interference noise; higher voltage fluctuations will affect the switch action, cause the switch to malfunction, making the switch fail to work normally. Therefore, applying SiC MOSFETs to power electronics applications faces severe challenges [6–8]. There have been literature studies on the switching oscillation problem of SiC MOSFETs. The research on this problem is mainly from two aspects: package parasitic parameters and loop parasitic parameters. There are some studies analyzing the influence of device parasitic parameters on switching oscillation and overshoot during switching period [9–11]. Lemmon et al. [12] gives a physical model of SiC MOSFET, but this model cannot be used to analyze the switching process of SiC MOSFET. In 2015, Kainan Chen of Tsinghua University and others studied the influence of the nonlinear characteristics of the drain-source parasitic capacitance on the switching characteristics [13]. This article focuses on the analysis of the first type of oscillation problem. Firstly, this paper analyzes the mechanism of voltage and current oscillation during switching of SiC MOSFET, and through theoretical analysis and simulation verification, the influence of SiC MOSFET parasitic parameters on the voltage and current oscillation during switching is analyzed, finally, the simulation analysis of the oscillation problem of the dual active bridge circuit considering the parasitic parameters of the SiC MOSFET is carried out.

Study on the Influence of Parasitic Parameters on the Switching …

5

2 Switching Transient Process Analysis Generally, a double-pulse test circuit is used to analyze the switching dynamic characteristics of power switching devices. The double-pulse test circuit considering parasitic parameters is shown in Fig. 1. The double-pulse test circuit mainly includes a power circuit and a drive circuit. V s is the DC bus voltage, S 1 is the SiC MOSFET to be tested, D1 is the freewheel diode, L d is the load inductance, C d is the stabilized capacitor, and V g1 is the drive circuit voltage. The parasitic parameters mainly include load equivalent parallel capacitance C f , drain parasitic inductance L d , source parasitic inductance Ls, gate drive resistance Rg , gate-source capacitance C gs , gate-drain capacitance C gd and drain-source capacitance C ds . The oscillation of the switch is caused by the resonant circuit formed by the parasitic parameters of the switching device and the loop. The damping is caused by the equivalent series resistance of the snubber capacitor, the on-resistance of the MOSFET, and the high-frequency resistance of the DC bus, but the equivalent resistance is very small, the suppression effect on resonance is not obvious.

2.1 Turn-On Process When the driving circuit voltage U gs rises to the threshold voltage U th , the SiC MOSFET begins to turn on, and the drain current id begins to rise. At this stage, the MOSFET works in the saturation region, and the relationship between the drain current and the gate-source voltage satisfies: i d = gm (u gs − Uth )

(1)

where, gm is transconductance of SiC MOSFET. The peak current during the turn-on process occurs when the switch is turned on and the drain current rises. The freewheel diode bears the bus voltage, the MOSFET Fig. 1 Double-pulse test circuit

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channel is not fully opened, and the device works in the saturation region. The MOSFET charges the junction capacitance and parasitic capacitance of the diode and the load inductance, the charging current flows through the MOSFET, and a relatively large overcurrent occurs during the turn-on phase. Δ i d = C F

du ds du F − Coss dt dt

(2)

where, uF is the diode terminal voltage, C oss is the output capacitance. After the turn-on current reaches the peak value, the interaction of the loop parasitic inductance and parasitic capacitance makes the current gradually decrease to the stable value in the form of two-stage damped oscillation. The voltage equation of the loop is as follows: (L s + L d )C f

d 2 VC f d VC f + VCds + VC f + Rd C f + Rd I L = Vdc 2 dt dt

(3)

The oscillation frequency and damping are: ωn1 = ζ1 = √

1 Cf (L s + L d )

(4)

Rds Rd (L s + L d )C f

(5)

2.2 Turn-Off Process During the turn-off process, a large di/dt is generated when the drain current drops rapidly, and a large voltage drop is generated on the line inductance and switch parasitic inductance. This voltage drop is added to the drain-source voltage of the MSOFET, then a voltage spike will appear. The oscillating circuit formed by the equivalent parasitic capacitance of the diode, the load inductance and its equivalent capacitance causes the voltage to oscillate. Oscillation frequency and damping coefficient is shown as follow: 1 ω2 = / ) ( (L d + L s ) C f + Cd / C f + Cds ζ2 = 4(L s + L d )

(6)

(7)

Study on the Influence of Parasitic Parameters on the Switching …

7

3 Simulation 3.1 Power Circuit Oscillation Simulation Considering Parasitic Parameters Based on the above simulation platform, the effects of drain equivalent inductance, drain-source capacitance, gate-drain capacitance, and driving resistance on the MOSFET switching oscillation are discussed separately. Equivalent drain inductance Ld . Changing the value of the equivalent drain inductance L d , the simulation results obtained are shown in Fig. 2. It can be seen from the simulation results that the larger the drain inductance, the higher the turn-off voltage oscillation amplitude and the larger the oscillation frequency. The rise time of the turn-on current becomes longer. Equivalent parallel capacitance C f . The drain-source capacitance has an effect on the voltage oscillation and current oscillation of the complementary switch. In the double pulse test circuit, C f is equivalently replaced, change the value of C f to simulate, the result is shown in Fig. 3. The capacitance has a significant effect

Fig. 2 Voltage oscillation and overshooting due to drain inductance L d

Fig. 3 Current waveform due to C f

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Fig. 4 Voltage waveform due to gate resistance Rg

on current oscillation. The larger the capacitance value, the larger the oscillation amplitude and frequency. Because of the reverse recovery process of the anti-parallel diode of the complementary conduction switch, a larger du/dt will produce a current spike on the capacitance during the turn-off period, which is consistent with the previous theoretical analysis. Gate drive resistance Rg . The gate drive resistance has a significant effect on the voltage and current oscillation. The larger the resistance value, the smaller the voltage oscillation, and the longer it takes to reach a steady state, as is shown in Fig. 4. Increasing the gate resistance Rg can slow down the switching speed of the SiC MOSFET and reduce the device voltage and current spikes, but it will increase additional losses. Therefore, it is necessary to make a trade-off between voltage and current spikes and switching loss when designing the drive circuit.

3.2 Drive Circuit Oscillation Simulation Considering Parasitic Parameters Under the simple driving circuit, the influence of driving resistance, gate-source capacitance and source parasitic inductance on the driving circuit is mainly considered. Gate drive resistance Rg . The gate drive resistance has significant influence on the drive voltage. The larger the gate resistance, the smaller the drive voltage fluctuation, and the time it takes to reach a stable voltage value is longer, as is shown in Fig. 5.

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Fig. 5 Voltage oscillation due to gate resistance Rg

4 Conclusion This paper studies the oscillation problem of SiC MOSFET switching process considering parasitic parameters. Based on the LTspice simulation platform, a dualpulse test circuit is established to simulate and analyze various parasitic parameters. Finally, a dual active bridge simulation circuit is established to analyze the parasitic parameters of switching on high-frequency transformers. Influence of square wave oscillation. Get the following conclusions: (1)

(2)

The parameters that have a greater impact on switching oscillation include drain equivalent inductance L d, drive resistance Rg , load inductance and diode equivalent parallel capacitance C f . To a certain extent, the suppression of oscillation can be achieved by reducing or increasing parasitic parameters, but while suppressing spikes, the switching speed decrease and additional losses increase. Therefore, it is necessary to make a trade-off between overshoot and switching loss and speed when designing the drive circuit.

Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

References 1. Buttay C, Planson D, Allard B et al (2011) State of the art of high temperature power electronics. Mater Sci Eng, B 176(4):283–288 2. Hamada K, Nagao M, Ajioka M et al (2015) SiC-emerging power device technology for next-generation electrically powered environmentally friendly vehicles. IEEE Trans Electron Devices 62(2):278–285

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3. Han D, Noppakunkajorn J, Sarlioglu B (2014) Comprehensive efficiency, weight, and volume comparison of SiC-and Si-based bidirectional DC-DC converters for hybrid electric vehicles. IEEE Trans Veh Technol 63(7):3001–3010 4. Williamson S, Rathore AK, Musavi F (2015) Industrial electronics for electric transportation: Current state-of-the-art and future challenges. IEEE Trans Industr Electron 62(5):3021–3032 5. Qian Z, Zhang J, Sheng K (2014) Status and development of power semiconductor devices and its applications. Proceedings of the CSEE 34(29):5149–5161 6. Fujita H (2013) A resonant gate-drive circuit with optically-isolated control signal and power supply for fast-switching and high-voltage power semiconductor devices. IEEE Trans Power Electron 28(11):5423–5454 7. Yi P, Murthy PKS, Wei L (2016) Performance evaluation of SiC MOSFETs with long power cable and induction motor. In: IEEE Energy Conversion Congress and Exposition (ECCE), 1–7 8. Bödeker C, Kaminski N (2015) Investigation of an overvoltage protection for fast switching silicon carbide transistors. IET Power Electronics 8(12):2336–2342 9. Safari S, Castellazzi A, Wheeler P (2013) Experimental study of parasitic inductance influence on SiC MOSFET switching performance in matrix converter. In: European Conference on Power Electronics and Applications (EPE),Lille, France, 1–9 10. Chen H, Divan D (2015) High speed switching issues of high power rated silicon-carbide devices and the mitigation methods. In: IEEE Energy Conversion Congress and Exposition (ECCE), Montreal, QC, 2254–2260 11. Wang Z, Zhang J, Wu X, et al (2014) Analysis of stray inductance’s influence on SiC MOSFET switching performance. In: IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, 2838–2843 12. Lemmon A, Banerjee S, Matocha K, et al (2016) Analysis of packaging impedance on performance of SiC MOSFETs. In: International Exhibition & Conference for Power Electronics. Nuremberg, Germany: PCIM Europe, 1–8 13. Chen K, Zhao Z, Yuan L, et al (2015) The impact of nonlinear junction capacitance on switching transient and its modeling for SiC MOSFE. IEEE Trans Electron Devices 62(2):333–338

A DSRD-Based Trigger Circuit for RBDT Xinyuan Huang and Lin Liang

Abstract In the pulse power circuit based on RBDT (reverse blocking diode thyristor), a trigger circuit capable of generating pulses with a high voltage rise rate is required to trigger the RBDT. In this paper, the DSRD (drift step recovery diode)-based pulse power circuit is used as the trigger circuit of RBDT, and an experimental circuit is built to test three types of RBDTs with different blocking voltages. The DSRD as the semiconductor switch in the trigger circuit can be easily connected in series without complicated control methods, which can improve the reliability of the trigger circuit. Under different circuit conditions, the characteristics of the three types of RBDTs, including the peak value of the pulse current and the rise rate of the pulse current, are studied. In the experiment, the maximum current rise rate of 6.1 kA/µs is acquired, which is the highest value for RBDT until now, with the peak current of 1.25 kA. The voltage rise rate of the trigger pulse is 58 kV/µs, provided by DSRD. Experiments show that the RBDT can be switched on with the trigger switch DSRD. Keywords RBDT (reverse blocking diode thyristor) · DSRD (drift step recovery diode) · Pulse power circuit · Device characterization

1 Introduction RBDT is a solid-state switch that can be used to generate short, high rate-of-rise current pulses. The switch is originally designed for the applications of radar modulator and laser pulser [1–4]. According to existing reports, the blocking voltage of RBDT can reach 1200 V, the peak current flowing through RBDT can reach 5000 A, and the current rise rate that RBDT can withstand during the turn-on process is above 2 kA/µs. X. Huang · L. Liang (B) Key Laboratory of Power Electronics and Energy Management, Ministry of Education of China, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_2

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In order to switch the RBDT from the blocking state to the conducting state, a voltage pulse with a voltage rise rate higher than several kV/µs needs to be generated by the trigger circuit to trigger the RBDT. In [4], two trigger methods are introduced, including network energy trigger and driven trigger. The network energy trigger approach is to trigger the RBDT through the energy stored in the capacitor of the pulse forming network. The driven trigger approach is to provide a trigger voltage pulse for RBDT through an external trigger source. The driven trigger method does not rely on the energy storage of the pulse forming network, so the energy storage of the pulse forming network can be changed without affecting the triggering of the RBDT. However, there is no information on how to design an external trigger source in the paper. In general, to reduce the requirement of the supply voltage of the trigger circuit and obtain the pulse with the largest voltage rise rate, the all-solid-state Marx generator with IGBT or MOSFET as the switching device can be used as the trigger circuit, which has higher requirements for the continuity of multiple switching devices. DSRD is a two-terminal high-power semiconductor opening switch, which can be used to generate a voltage pulse with a voltage rise rate up to several kV/ns [5–7]. Compared with IGBT and MOSFET, DSRD is easier to connect in series to obtain pulse with a high voltage rise rate [8]. A circuit topology using a DSRD-based pulse power circuit as the trigger circuit of RBDT, which helps to improve the reliability of the pulse power circuit, is proposed in this paper. The test circuit is built according to the proposed circuit topology and used for the study of the operating characteristics of RBDT. The operating characteristics of the three types of RBDTs with different blocking voltages under different circuit conditions are tested separately. In the experiment, the influence of the trigger current on the peak value and the rise rate of the pulse current during the conduction of the RBDT are studied.

2 Theory of Operation As shown in Fig. 1, RBDT is a two-terminal device and has a pnpn four-layer structure. RBDT has the ability to block bidirectional voltage. When a fast-rising forward voltage pulse is applied to the RBDT that blocks the forward voltage, the voltage across the device rises rapidly until it is slightly higher than the blocking voltage of the device. Then the device quickly switches on. During the rapid rise of the voltage across the device, a displacement current appears inside the device. This current will be shunted by the emitter shorts at the cathode, and a lateral voltage drop is formed in the P base area at the cathode, which makes the J1 junction in the center area of the N emitter forward bias. It results in effective injection of multiple discrete points at the emitter, which in turn causes the device to enter the conduction state. During the operation of DSRD, a forward current flows through the device, and pumps electron–hole plasma inside the device. Then a reverse current flows through the device, extracting the plasma stored inside the device. When the plasma inside

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Fig. 1 Schematic diagram of RBDT structure

the device is completely extracted, the reverse current is cut off and transferred to the load, generating a high voltage pulse. The duration of the forward current and reverse current flowing through the device is only a few hundred nanoseconds, which is much shorter than the nonequilibrium carrier lifetime of the n-base and p-base inside the device. When several identical DSRDs are connected in series, the amount of plasma introduced by the forward current in different devices is the same, which can ensure the consistency of the turn-off process of DSRDs. Therefore, DSRD is suitable for generating high-voltage pulses by connecting multiple devices in series without complicated control methods.

3 Experimental Setup The circuit diagram of the pulse power circuit based on DSRD as the trigger circuit of RBDT is shown in Fig. 2. The working principle of the circuit is as follows: First, the capacitors C1 and C0 are charged to the power supply voltages U1 and U2 , respectively. Then, when the switch tube Q is triggered to turn on, C1 discharges through the loop C1 -Q-w1 -L1 . At the same time, after the discharge current passes

Fig. 2 Circuit diagram of the pulse power circuit

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through the saturable transformer Tr, it flows through the DSRD in the forward direction in the loop w2 -DSRD-C2 and charges the capacitor C2 . When the magnetic core of the saturable transformer Tr is saturated, C2 discharges through the circuit C2 -w2 -DSRD, and the reverse current flows through DSRD. When the DSRD cuts off the reverse current, the reverse current is transferred to the RBDT in the loop w2 C2 -D1 -RBDT, and a trigger voltage pulse with high dv/dt is generated on the RBDT. When the RBDT is switched to the conduction state, the capacitor C0 is discharged through the loop C0 -D2 -RBDT-RL loop, and a pulse of high current peak is generated on the load RL . The parameters of the components in the pulse power circuit are shown in Table 1. Three types of RBDT-RBDT1 , RBDT2 and RBDT3 with different structural parameters are tested in the experiment, and their respective blocking voltages are shown in Table 2. The diameter of the three types of RBDT is 24 mm. The test circuit in the experiment is shown in Fig. 3. The DSRD and RBDT in the circuit are prepared by our laboratory. The DSRD stack is composed of six identical DSRDs in series. In the experiment, the trigger circuit power supply voltage U1 and the main circuit power supply voltage U2 are changed to test the characteristics of the RBDT with three different blocking voltages. When testing different types of RBDT, U1 is changed in steps of 50 V between 150 V and 600 V, and U2 should be less than the blocking voltage of the tested RBDT. For example, U2 is at 200–400 V for RBDT1 , U2 is 200-500 V for RBDT2 , U2 is 200–700 V for RBDT3 , and U2 is changed in 100 V steps. During the operation of the pulse power circuit, the voltage waveforms on C2 and RBDT, as well as the current waveforms flowing through RBDT are measured. Before the saturable transformer core is saturated, the higher the voltage on C2 is charged, the greater the reverse current cut off by DSRD, and the greater the trigger Table 1 Parameters of the components in the pulse power circuit

Table 2 Three types of RBDT tested in the experiment

Components

Parameters

U1

150–600 V

U2

200–700 V

Rs1 , Rs2

10 kΩ

C1

100 nF

L1

300 nH

C2

8.8 nF

C0

400 nF

RL

0Ω

Type

Blocking voltage

RBDT1

500 V

RBDT2

600 V

RBDT3

800 V

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Fig. 3 Photograph of the test circuit in the experiment

current transferred to the RBDT. However, since the DSRD-based trigger circuit is not affected by the pulse current generating circuit, the magnitude of the voltage on C2 in the trigger circuit is only related to U1 . The waveforms during the operation of the circuit are shown in Fig. 4, which shows that the pulse power circuit based on DSRD can be used to trigger the RBDT to generate a high-peak current pulse. In Fig. 4, UC2 is the voltage on C2 , URBDT is the voltage on RBDT, and IRBDT is the current flowing through RBDT.

Fig. 4 Waveforms during the operation of the circuit

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4 Experimental Results 4.1 Influence of the Trigger Process on the Characteristics of RBDT Through the experimental test, it can be inferred that the voltage on C2 is only related to U1 of the trigger circuit. As shown in Fig. 5, with the increase of U1 , the maximum voltage on C2 gradually increases, which indicates that the trigger current transferred to RBDT also increases. Therefore, the magnitude of the trigger current transferred to the RBDT can be changed by changing the voltage U1 to study the influence on the characteristics of RBDT. When U2 is 400 V, the relationship between the peak value of the pulse current flowing through different types of RBDT and U1 is shown in Fig. 6. For RBDT1 and RBDT3 , with the increase of U1 , the pulse current peak value shows an overall increasing trend. However, the peak value of the pulse current of RBDT3 is more affected by U1 than RBDT1 . Therefore, the voltage U1 should be as high as possible when RBDT1 and RBDT3 are used to generate high peak current pulses. For RBDT2 , when U1 is between 250 and 450 V, as U1 increases, the pulse peak current gradually increases. However, when U1 exceeds 450 V, as U1 increases, the pulse current peak value drops rapidly, which is completely different from RBDT1 and RBDT2 . Therefore, when RBDT2 is used to generate current pulses, it is necessary to select a suitable U1 to ensure that the circuit obtains the highest pulse current peak value. The calculation method of the current rise rate dI/dt is shown in Eq. 1. The rise time t0.2–0.9 represents the time when the current pulse rises from 20 to 90% of the peak current. ) ( dI/dt = 0.9Ipeak − 0.2Ipeak /t0.2−0.9 Fig. 5 Relationship between the maximum voltage on C2 and U1

(1)

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Fig. 6 Relationship between the peak value of the pulse current flowing through different types of RBDT and U1

When U2 is 400 V, the relationship between the dI/dt of different types of RBDT and U1 is shown in Fig. 7. The dI/dt of RBDT1 is between 2.5 kA/µs and 3 kA/µs, which is almost unaffected by U1 . When U1 exceeds 450 V, the peak value of the pulse current flowing through RBDT2 decreases. The dI/dt decreases after U1 exceeds 450 V, but it is still higher than 2 kA/µs. The peak value of the pulse current of RBDT3 increases with the increase of U1 , so dI/dt increases with the increase of U1 . But when U1 is greater than 550 V, the rise time of the pulse current increases, which leads to a decrease in dI/dt. When U2 is 700 V, the relationship between the dI/dt of RBDT3 and U1 is shown in Fig. 8. The maximum current rise rate of 6.1 kA/µs is acquired, which is the highest value for RBDT until now, with the peak current of 1.25 kA. The voltage rise rate of the trigger pulse is 58 kV/µs. Fig. 7 Relationship between the dI/dt of different types of RBDT and U1

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Fig. 8 Relationship between the dI/dt of RBDT3 and U1

4.2 Influence of the Voltage of the Main Circuit When U1 is 600 V, the relationship between the peak value of the pulse current flowing through different types of RBDT and U2 of the pulse current generating circuit is shown in Fig. 9. As U2 increases, the pulse current flowing through the RBDT also increases. When RBDT3 is tested and the voltage U2 is 700 V, the pulse power circuit obtains the maximum pulse current peak value of 1.3 kA. Under the same condition of U1 and U2 , the peak values of the pulse current flowing through RBDT1 and RBDT3 are almost equal. However, the peak value of the pulse current of RBDT2 is lower than that of RBDT1 and RBDT3 . It indicates that the loss of RBDT2 during the switching process is greater than that of RBDT1 and RBDT3 , which leads to the reduction of the peak value of the pulse current. Fig. 9 Relationship between the peak value of the pulse current flowing through different types of RBDT and U2

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5 Analysis and Discussion Using the pulse circuit topology proposed in this article to test different types of RBDT devices, the following results can be obtained: (1) The pulse current peak value of RBDT1 and RBDT3 increases with the increase of U1 , while the pulse current peak value of RBDT2 decreases when the trigger voltage exceeds the optimal value; (2) The dI/dt of RBDT1 is hardly affected by U1 , the dI/dt of RBDT2 decreases when U1 exceeds the optimal value, and the dI/dt of RBDT3 increases with the increase of U1 , but when U1 exceeds the optimal value, dI/dt no longer increases or even decreases. For RBDT1 , RBDT2 and RBDT3 , when U1 increases from 250 to 450 V, the peak current flowing through the RBDT increases. The greater U1 , the greater the peak voltage on the capacitor C2 , and the greater the trigger current transferred to the RBDT. Therefore, the increase of the trigger current increases the number of discrete regions where RBDT is initially turned on, thereby reducing the on-state loss of RBDT and increasing the peak current flowing through the RBDT and dI/dt. For RBDT2 , when U1 gradually decreases from 600 to 250 V, the switching process of RBDT2 changes. As shown in Fig. 10, it is the voltage on the RBDT2 and the current through the RBDT2 during the turn-on process of RBDT2 at different U1 , and U2 is 400 V. As U1 decreases, the time interval between the moment when

Fig. 10 Voltage on the RBDT2 and current through the RBDT2 at different U1 . a 600 V. b 450 V. c 300 V

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the current flowing through the RBDT2 starts to increase and the moment when the RBDT2 is triggered gradually increases. The time interval helps increase the initial conduction area of the RBDT, thereby reducing the on-state loss of the RBDT and increasing the peak current flowing through the RBDT. Therefore, a suitable U1 needs to be selected to optimize the operating characteristics of RBDT2 . When RBDT2 is used in the circuit of this paper, U1 should be between 400 and 500 V.

6 Conclusion In this paper, a DSRD-based pulse power circuit is proposed to trigger RBDT. A test circuit is bulit using the DSRD and RBDT developed in our laboratory. It is proved to be feasible to use a DSRD-based pulse power circuit as the trigger circuit of RBDT. The trigger circuit based on DSRD is conducive to improving the reliability and reducing the size of pulsed power circuits based on RBDT. Three types of RBDTs with different blocking voltages are tested. When U2 is 700 V, the maximum dI/dt of RBDT3 is 6.1 kA/µs, which is the highest value for RBDT until now, with the peak current of 1.25 kA. And the voltage rise rate of the trigger pulse provided by DSRD is 58 kV/µs. When U2 remains unchanged, the operating characteristics of different types of RBDT are affected differently by U1 . Therefore, for different types of RBDT, it is necessary to select the appropriate trigger voltage to optimize the characteristics of RBDT during its operation. Acknowledgements This work was supported by the National Natural Science Foundation of China (51877092).

References 1. Chu CK, Johnson JE, Brewstei JB (1977) 1200 V and 5000 A peak reverse blocking diode Thyristor. Jpn J Appl Phys 16(S1):537–540 2. Brewster JB, Sherbondy GF (2005) Complete characterization studies provide verification of RBDT(RSR) reliability. IEEE Trans Electron Devices 26(10):1462–1468 3. Gardenghi RA, Hooper EH, Zimmermann FS (2015) A new high power RSR solid state switch. In: Power Electronics Specialists Conference. IEEE, Culver City, CA, USA 4. Gardenghi RA (1975) A super power RSR. In: Electron Devices Meeting, 1975 International. IEEE, Washington, DC, USA 5. Grekhov IV, Efanov VM, Kardo-Sysoev AF et al (1985) Power drift step recovery diodes (DSRD). Solid State Electron 28(6):597–599 6. Min BD, Pavlov E, Kim JH, et al (2006) A new high speed pulse generators for automotive gas treatment application. In: IEEE Power Electronics Specialists Conference. IEEE, Jeju, Korea (South)

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7. Korotkov SV, Smorodinov VV, Yu VA et al (2019) Semiconductor generator of high voltage nanosecond pulses for plasma technologies. IOP Conference Series: Materials Science and Engineering 643:012081 8. Grekhova IV, Mesyatsb GA (2005) Nanosecond semiconductor diodes for pulsed power switching. Physics–uspekhi 48(7):735–744

Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical Coupling Method Bowen Gu, Haimeng Wu, Volker Pickert, Bing Ji, Siyang Dai, and Zhiqiang Wang

Abstract Press-pack Insulated Gate Bipolar Transistors (PP IGBT) are becoming increasingly used in HVDC and FACT applications. Due to its unique packaging, its reliability issues have also attracted increasing attention in the engineering field. More comprehensive investigation into the thermal, electrical and mechanical factors should be conducted to reveal the operation condition and status of the devices. The objective of this work is to study the relationship among the deformation of the collector groove and the thermal stress of the chip as well as the contact pressure by simulating the PP IGBT under normal and abnormal conditions. A sophisticated 3D finite element (FE) model of a PP IGBT has been developed which includes the coupling with thermal–mechanical effect. Also, the influence of different pressure and thermal stress on deformation is discussed thoroughly that can provide insight of how to monitor the status of a PP IGBT from the perspective of deformation. Keywords Press-pack IGBT · Thermal–mechanical · Deformation · 3D FE model · Reliability

B. Gu (B) · V. Pickert School of Engineering, Newcastle University, Newcastle upon Tyne, UK e-mail: [email protected] H. Wu Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle upon Tyne, UK B. Ji School of Engineering, University of Leicester, Leicester, UK S. Dai · Z. Wang Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_3

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1 Introduction IGBTs have been a popular high-power solution in recent years, and they are also well suited to high-reliability applications, like for example in high-voltage direct current (HVDC) applications [1, 2]. Compared with traditional packaged IGBTs, press-pack (PP) IGBTs are outstanding in terms of capacity and reliability, which has also become the ideal choice for high power traction drive and wind generation [3, 4]. However, the structure of a PP IGBT is much more complicated compared to the classical solder-based packaged module and produces therefore other potential issues for the system reliable operation. The two potential failure modes are: the gate-oxide damage and the micro eroding between the die and molybdenum plate [5]. In particular, the uneven pressure and internal thermal stress distribution can cause a catastrophic failure that results in system shutdown [6]. At present, two bondless structures of press pack technologies are commercially available on the market. One is the spring-type crimping technology from ABB which can balance the pressure unevenness to a certain extent [7], but the short-circuit failure mode (SCFM) can only be maintained for a short time. More research focused on the other type of press pack technology. The other type of structure is the hardcrimping technology which is mostly applied in HVDC and wind power applications. Manufacturers are Toshiba and Westcode [8] to name a few. The majority of the published research on PP IGBT devices is mainly focused on analyzing the changes of physical parameters of the devices using simulation analysis. For example [9] investigates the operation under a thermal cycle using finite element modelling (FEM) but did not consider the impact of the clamping fixtures. To study the performance of PP IGBT with clamping fixture, a 3D FEM simulation is conducted to investigate the clamping conditions of the static thermal scatter of the chips [10]. Also, an investigation has been carried out to reveal the relationship between the clamping force and the electrical contact resistance and thermal contact resistance [11]. The results show that the pressure distribution is significantly affected by the clamping force. In [12] a CFD simulation of PP IGBT is conducted using a unique coolant channel design to reduce temperature spread [12]. Another research work proposed the influence of the pressure between the molybdenum plate and silicon chip stating that low and high pressure can cause severe damage [13] concluding that the clamping force is an important parameter which affects the PP IGBT reliability. In [14] a comparison of different sensors has been investigated to measure defamation of the PP IGBT. The plasma-extraction transit-time (PETT) method has been proposed in [15] to detect the temperature of the chip inside the PP IGBT. In this paper, the finite element (FE) method is applied to determine the thermal stress and deformation strain in press-pack IGBT. A real size-based model is established with the physical condition including the thermal and mechanical parameters. The simulation results are analyzed and discussed in detail according to different operating conditions. The findings reveal a relationship between the deformation of the collector lid groove, the chip’s thermal distribution, and the clamping force. The heat difference on the chip is caused by the uneven pressure distribution, which

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ultimately affects the pressure dispersed on the lid. The lid gradually deforms as a result of this. The goal of this research is to show how different clamping forces and different types of thermal distribution affect the deformation of the groove, which can further demonstrate how to determine the device’s condition by sensing deformation.

2 Modeling 2.1 Press Pack IGBT Characteristics In this research, a 4500 V-800A multi-chip press pack IGBT is used as a case study. The cross-section view of the module schematic is shown in Fig. 1, where the structure can be determined as 6 layers, the collector and emitter pole which are made of copper, upper and lower molybdenum plates with the silicon chip in the middle and a thin silver layer underneath the lower molybdenum plates. The function of soft silver foil is to ensure the uniformity of pressure distribution and electrical contact to the maximum extent. The collector and emitter copper lid have a positioning hole in the center to connect with the heatsink to prevent the relative position of the heatsink and the module from being misaligned. The gate distribution board is connected to the IGBT chip via a spring-loaded pin and the entire structure is laid in a sealed capsule. Clamping force is applied to achieve the thermal and electrical contact within the PP IGBTs, the flatness of all the components is crucial since the high requirement of the even contact pressure distribution.

Fig. 1 Cross-section schematic of press-pack IGBT

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2.2 FE Model Development In order to reduce the computational burden as much as possible while ensuring the accuracy of the simulation, the model considers the relationship between the deformation of the collector groove and the internal chip thermal stress as well as the mechanical stress of the fixture. The internal sub-module plastic frame and gate distribution board and the gate pin of the PPI are removed, because for the analysis of deformation, it is an acceptable approximation to model only the chip, the Mo plate, and the copper electrode in contact with the longitudinal rigid surface, thereby further reducing the calculation workload significantly. Figure 2 shows the 3D model that remove the components mentioned above with the multi-zone meshing which balance the results and computation speed at the same time. In the simulation, all elements of PPI are stacked layers of materials with uniform, isotropic and elastoplastic mechanical response, and have isotropic flow rules. In the simulation process, the physical properties of the material are the key parameters for establishing the model. A summary of the material properties of all components of the model is presented in Table 1. The FE model is simulated with the static thermal and structure platform. The calculation of the two processes all assumes the friction model which affected most by the surface roughness and the different material combination, and the friction coefficient 0.5 is used for all calculations. To analyze the relationship between deformation and the static strain of thermal and mechanical, the thermal generated by the power consumption of the internal chip and the pressure exerted by the external fixture are used as two key variables

Fig. 2 3D FE model of PPI with multi-zone mesh

Table 1 Mechanical properties used in the FE model Material

Young’s module (GPa)

Possion’s ratio

Material density (kg/m3 )

Coefficient of thermal conductivity [W/(m*K)]

Coefficient of thermal expansion α (1/°C)

Silicon

162

0.23

2330

148

4.8E-6

Molybdenum

320

0.28

10,220

130

4.9E-06

Copper

129

0.34

8933

385

1.71E-05

Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical …

27

to produce deformation. In this work, the constraints of the simulation are listed as follows. The device is assumed to operate in a normally on state, and the average current injected into the chip is used as the source of thermal strain. At the same time, a convective heat transfer coefficient is set between the outside of the device and the heat sink and the outer edge of the heat sink is maintained at room temperature. In addition, the pressure applied by the external clamping fixture is set on the top of the collector heatsink and kept uniform while setting a fixed support on the bottom of the emitter heatsink.

3 Result and Discussion 3.1 Press-Pack Simulation Varying Power Density In the simulation, the relationship between the deformation of the collector groove and the internal thermal stress and external pressure is mainly selected and analyzed. Figure 3 shows the basic simulation procedure in modeling and thermal, mechanical analysis. The 3D geometry model is developed in Inventor with the detailed dimension, then the model is transferred to Ansys platform. The heatsink block is built in the Designer of the Ansys, after that, the static thermal software is used for the thermal analysis, all the thermal material property are set in this step. The final step is the deformation analysis by using the static structure, the mechanical property and multizone mesh are used for finding the deformation results. Setting different boundary conditions on the influence of heat stress and pressure on deformation is investigated under the assumption that the module structure and material properties are consistent. First, according to the characteristics of the steady-state operation of the module, when the module is working at the rated current, the on-state loss is distributed to the 14 IGBT chips and 7 diodes, in this work the uniform load applied to the IGBT chip is 600pw/ um3 and to the diode chip 200 pw/ um3 (1/3 of rated current). With a rated force of 30KN applied on the top heatsink, Figs. 4 and 5 present the deformation distribution and the thermal distribution of the chip layout based on different power dissipation. From the simulation result of Fig. 4, it can be seen that the highest chip temperature is 80 °C when the module reaches to the thermal steady state, and the temperature of the outer ring for the IGBT chips is higher than the

Fig. 3 Simulation flowchart: modeling, thermal analysis and mechanical analysis

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Fig. 4 a Temperature distribution across chip surface and b deformation against lid groove at 80 °C

Fig. 5 a Temperature distribution across chip surface and b deformation against lid groove at 149 °C

internal ring for the IGBT chips. The deformation on the groove is more consistent along the direction perpendicular to the tangent plane because the internal pressure and thermal stress are more uniform. This represents the reflection of the deformation of the device under the rated current and pressure in a healthy state. In order to study the relationship between deformation and thermal stress in a healthy and evenly distributed state, the simulation has been conducted by keeping the external clamping force constant and changing the power consumption of the chip. Figure 6 shows the relationship between the temperature and deformation caused by the variation of the power consumption. It is evident that as the power consumption increases, the chip temperature rises accordingly, as a result, the deformation of the groove is increased linearly with a constant gradient overall. Since the deformation is mainly caused by the accumulation of heat and the external clamping force. (1) reflects the process of calculating the temperature from the accumulation of power consumption, where ρ stands the density, k, Cp and Q are the thermal conductivity, the specific heat capacity, and the heat flux, respectively. T is the temperature function

Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical …

29

Fig. 6 Relationship between the temperature and deformation

containing the position x and time t. (2) shows the process of deformation caused by thermal stress where ε is strain, which is the function of the temperature T. Equation (3) express the basic total deformation composition. C pρ

∂ T (x, t) − k∆T (x, t) = Q ∂t ε = α∆T

UUtotal =

∕ Ux2 + U y2 + Uz2

(1) (2) (3)

3.2 Press-Pack Simulation Varying Clamping Force To further investigate the relationship between the deformation and the clamping force, a varying clamping force has been applied to the developed PP IGBT model. Figure 7 shows how the deformation changes as the clamping force are increased. This is accomplished by maintaining a consistent power dissipation. When the clamping force is increased from 5 to 40 KN, it is obvious that the overall deformation of the groove, which is represented by the blue curve, reduces, but this is not substantial. The red line which shows the deformation of the lid along the X axis, is practically stable with a small rise. When compared to the results of altering the power density in the chip, it is evident that when all other parameters are normal, power dissipation has a bigger impact on deformation than pressure. However, this is based on the assumption that everything

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Fig. 7 Relationship between the clamping force and deformation

is in perfect contact, so that heat can be transferred effectively even if the pressure is insufficient. In reality if the pressure is too low or too high, the uneven pressure on each chip will result in an uneven current and the chip will fail. The chip’s contact thermal resistance and electrical resistance change over time, causing some chips to overheat and short-circuit. Therefore, it is necessary to analyze the relationship between deformation and internal thermal stress and external pressure in this extreme case by establishing a model of overheating of a certain chip.

3.3 Press-Pack Simulation with One Chip Failed In this section, a 3D model containing a failed chip is established to undertake the analysis. From Figs. 4 and 5, it was shown that the chip with the highest temperature is concentrated in the upper left part in a healthy state of normal operation, so this chip is selected as an overheated chip for modeling. The findings of the deformation distribution and the thermal distribution of the chip arrangement are shown in Fig. 8. This result is based on applying the higher power dissipation on this specific chip while keeping the power dissipation on the rest IGBT chips uniform as well as applying the diodes with uniform load. The figure clearly shows the position of the overheated chip. Besides, it can be seen that the deformation of the groove at the position of the overheated chip exceeds other parts, which indicates that the position and size of the deformation can be used to determine the status of the module when there is a fault on the chip. To further explore the influence of the overheated chip on the deformation, the result of Fig. 9 is obtained by adjusting the power loss. When the power loss continues to rise, not only the deformation of the groove closest to the overheated chip, but also the deformation of adjacent components, increases

Deformation Analysis of Press-Pack IGBT Using Thermal Mechanical …

31

Fig. 8 a Temperature distribution across chip surface with one overheated chip and b deformation against lid groove at 97 °C

Fig. 9 Relationship between the temperature and deformation

significantly. The temperature of the remaining chips rises due to the thermal coupling of the internal chip, which causes the temperature of the collector lid to rise as well. Comparing the previous results where an even power dissipation on the chips with varying power density and clamping force was applied. It can be seen that the previous simulation with the increase of power loss and the increase of the applied clamping force, the deformation of the groove part also increases, but because the two variables are uniformly distributed, and the layout of the internal IGBT and diodes are centrally symmetrical and asymmetrical, so the resulting deformation is more evenly distributed on the entire groove. However, when a chip is overheated or even short-circuited, the deformation will increase with the increase of power loss. Also, it can be clearly seen that the deformation of the groove near the hot spot

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Fig. 10 a Temperature distribution across chip surface with two overheated chips and b deformation against lid groove at 112 °C

is significantly larger than the other parts of the groove. From this point, it can be determined that the chip in this area is not working properly and may cause the final failure of the module.

3.4 Press-Pack Simulation with Two Chips Failed Although the simulation result of an overheated chip shows the difference in the deformation at the groove, it is necessary to study the situation when there are multiple chips overheated. In order to simulate the extreme situation where there are two failed chips another simulation was conducted. Figure 10 shows the results of deformation distribution and thermal distribution. It can be seen that the deformation near the grooves of the two overheated chips is significantly larger than the other parts, similar to the previous conclusion. Compared with the previous result where only one chip was overheated, under the condition of the same total power dissipation, the dominant level of deformation is reduced but the difference between the minimum deformation point and the maximum deformation point is still obvious. Thus, the groove deformation can be used as indicator for overheating chips.

4 Conclusion This paper studies the relationship between the deformation of the collector lid groove and the internal chip thermal stress and external clamping force through 3D physical modeling of a press pack IGBT. It is concluded that the thermal stress has a much

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33

greater influence on the deformation than the clamping force. In addition, a model with an overheated chip has been established, and the relationship between deformation and internal thermal stress in this case was studied to prove the difference of deformation under the distinct condition. Also, a model with two overheated chips located diagonally is studied and derived similar findings. It can be concluded that deformation of the lid groove can be used to determine the status of the device.

References 1. Vrana TK, Energi S (2016) Review of HVDC component ratings: XLPE cables and VSC converters. In: 2016 IEEE International Energy Conference (ENERGYCON) Leuven 2016, 1–6 2. Bordignon P, Zhang H, Shi W, Serbia N, Coffetti A (2016) HV submodule technology based on press pack IGBT for largest scale VSC-HVDC application. In: 12th IET International Conference on AC and DC Power Transmission (ACDC 2016), Beijing, pp 1–6 3. IEEE T&D committee 2000—CIGRE WG-B4 04 2003 4. Wakeman F, Pitman J, Steinhoff S (2016) Long term short-circuit stability in Press-pack IGBTs. In: 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, pp 1–10 5. Tinschert L, Rygg Årdal A, Poller T, Bohlländer M, Hernes M, Lutz J (2015) Possible failure modes in Press-Pack IGBTs. Microelectron Reliab 55(6):903–911 6. Dai S, Song X, Li G, Ji B, Pickert V (2019) Electromagnetic analysis of press pack IEGT with transient skin and proximity effects In: International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management (PCIM-Asia), Shanghai, China, 26–28 June 7. Recommendations regarding mechanical clamping of Press Pack High Power Semiconductors, ABB 8. Oh H, Han B, McCluskey P et al (2015) Physics-of-failure, condition monitoring, and prognostics of insulated gate bipolar transistor modules: A review. IEEE Trans Power Electron 30(5):2413–2426 9. Darveaux R, Turlik I, Hwang LT, Reisman A, IEEE Trans Comp Hybr Manuf Tech 12(4):663– 672 10. Dai S, Wang Z, Wu H, Song X, Li G, Pickert V (2021) Thermal and mechanical analyses of clamping area on the performance of press-pack IGBT in series-connection stack application. IEEE Trans Comp Packaging Manufacturing Technology 11(2):200–211 11. Poller T, Lutz J, D’Arco S, Hernes M (2013) Determination of the thermal and electrical contact resistance in press-pack IGBTs. In: 2013 15th European Conference on Power Electronics and Applications (EPE), Lille, 2013, pp 1–9 12. Chen H, Cao W, Bordignon P, et al (2015) Design and testing of the World’s first single-level press-pack IGBT based submodule for MMC VSC HVDC applications. In: Energy Conversion Congress and Exposition (ECCE), 2015 IEEE. IEEE, 2015:3359–3366 13. Deng E, Zhao Z, Lin Z, Han R, Huang Y (2018) Influence of temperature on the pressure distribution within press pack IGBTs. IEEE Trans Power Electron 33(7):6048–6059 14. Gu B, Wu H, Pickert V, Dai, Wang Z, Li G, Ding S, Ji B (2020). Condition monitoring of press-pack IGBT devices using Deformation Detection Approach 15. Gu M, et al (2019) Condition monitoring of high voltage IGBT devices based on controllable RF oscillations. In: 31st International Symposium on Power Semiconductor Devices and ICs (ISPSD). Shanghai, China 2019:355–363

Investigating the Dynamic Performance of Power Semiconductors in Parallel Connection Jixuan Wei, Jiajun Yu, Kun Tan, Hongfei Chen, Haimeng Wu, Paul Lefley, and Bing Ji

Abstract The parallel connection of power semiconductors is generally used for higher current levels. However, due to the design variations in both power devices and associated electrical circuits (such as parasitic inductances, parasitic capacitance), devices in parallel may result in unmatched current, voltage and power losses, degrading their overall switching performance and reliability as a whole. In this paper, the in-circuit switching behavior of power devices in the parallel configuration and their impacting factors are investigated using an analytical electrical model, which allows the current sharing and voltage balance behavior can be analyzed easily by changing parasitic parameters. The analytical model was verified by LTspice and shows an excellent match. Simulation results shows that the uneven common source inductance, gate resistance and gate capacitance has the greatest influence on current sharing. Keywords Parallel connection · SiC MOSFET · Analytical model

1 Introduction Modeling the power semiconductor devices assists researchers and field application engineers to understand and predict their electrical and thermal characteristics at various operating conditions. Simulation tools with dedicated models are widely used to facilitate the design and control analysis of power converters with lower cost and shorter time-to-market. This paper leverages an analytical model for the switching behavior analysis of SiC MOSFETs in parallel, with a focus on mathematical implementation using the J. Wei · K. Tan · H. Chen · P. Lefley · B. Ji (B) University of Leicester, Leicester, UK e-mail: [email protected] J. Yu Hunan University, Changsha, China H. Wu Northumbria University, Newcastle, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_4

35

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MATLAB. Critical device parameters are extracted from the manufacture datasheet and incorporated into the analytical model. The proposed model demonstrates good alignment in switching behaviors of the parallel MOSFETs comparing with that simulated in the LTspice. The impact of circuit and devices parameter drifts on the switching performance is investigated by varying model parameters, which provides guidance to application of the parallel connected SiC MOSFETs in power converters.

2 Dynamic Modeling of SiC MOSFETs in Parallel 2.1 Turn-On Switching Analysis The turn-on transition process of a single SiC MOSFET under the hard-switching applications is divided into four stages by convention, namely the turn-on delay stage (S1), the current rising stage (S2), the voltage falling stage (S3), and the final gate-source capacitor charging stage (S4) [1–5]. Accordingly, when paralleling two SiC MOSFET chips (T1 and T2), as shown in Fig. 1, together with corresponding equivalent circuits at each stage (i.e. S1–S5) to account for the unbalanced current sharing between both two devices. The circuit- and packaging-related parasitic inductances including the common source inductances L Sn and the power loop inductances L P + L Dn are considered (where n = 1 or 2), whereas the gate-loop inductances are Vdc

Cd

vGS (t)

Vth2 Vth1

Vdc

t

vDS (t)

Cd

Iload

Lp Rs

Ld1

Ld1 id1

Ld2

iD(t)

vds2

Cds1

Cgd1

Rg1

Rg2

Cgs1

ig1 vgs1

ig2 vgs2

iD2

S4

Cds2

vd

Cd

Iload

Ld1 id1

Ls1

S3

Cgd1

vgd1 Rg1

Cgs1

ig1 vgs1

ig2 vgs2

Cds1

Ls2

S1

Cgd1

vgd1 Rg1

vgd2 Rg2

Cgs1

ig1 vgs1

ig2 vgs2 Vgin

Cd

Iload

ich1

Cgd2 Cds2

vds2

vds1

Cgs2 Ls2

id2

Cgd1

vgd1 Rg1

vgd2 Rg2

Cgs1

ig1 vgs1

ig2 vgs2

Cds1

Ls1

S4

Ls2

Iload Rs

Rs

ich2

vds2

Lp

Ld1 id1

Ld2

Cds2

S2

Lp id2

Cgd2

Cgs2

Vgin

Ls1

Ld2

Vdc

Cd

Lp Rs

Cds1

vds1

vgd2 Rg2

Vdc

Vdc

vds1

vds2

Cgs2

Vgin

Ls1

t

S5

Cgd2

Switching waveform of SiC MOSFET in parallel

ich1

id2

ich1

iD1

S1 S2 S3

Iload

Lp Rs

Vgin

Ld1 id1

Ld2

id2

Cgd2 Cds2

vds2

vds2

Cds1

Cgd1

Rg1

Rg2

Rds1

ig1 vgs1

ig2 vgs2

Cgs1

Cgs2 Ls2

Ld2

ich2

ich1

ich2

Vgin

Ls1

Cgd2 Rds2 Cds2

vds2

Cgs2 Ls2

S5

Fig. 1 Turn-on switching waveforms and equivalent circuits for switching transient stages of SiC MOSFETs connected in parallel

Investigating the Dynamic Performance of Power Semiconductors …

37

neglected due to their comparably less impact on the switching performance [1]. The reverse current of the SiC Schottky barrier diode (SBD) is neglected (with zero reverse recovery time). CD represents the sum of the SBD junction capacitance and the parasitic inductance across the load. (1)

S1: Turn-on delay for both MOSFETs

Initially, both MOSFETs are at off-state and in the cut-off region, while the load current flows through the SBD. The gate current i g starts to charge the input capacitance (equal to C gs + C gd ) of T1 and T2, leading to the rising of vgs . The gate-source capacitance C gs absorbs majority gate current due to its significantly larger capacitance value compared to the Miller capacitance C gd at a high drain-source voltage (close to the dc-link voltage Vdc ). Consider the variation of C gs and Vgs(th) , S1 finishes when vgs1 takes the lead to reach the gate threshold voltage Vgs(th)1 . Thus, the state variables of T1 and T2 including vge1 , i g1 , vgs2 and i g2 are identified as the state variables and their corresponding state equation can be derived from the equations below.

(2)

· · i g1 = C gs1 vgs1 + C gd1 vgd1

(1)

· i g1 Rg1 = Vgin − vgs1 − L s1 i gl

(2)

vgs1 = vgd1 + vds1

(3)

· · i g2 = C gs2 vgs2 + C gd2 vgd2

(4)

· i g2 Rg2 = Vgin − vgs2 − L s2 i g2

(5)

vgs2 = vgd2 + vds2

(6)

S2: T1 current rise and T2 turn-on delay

At the beginning of S2, T1 starts conducting and load current gradually commutates from SBD to T1 as vgs1 increases from Vgs(th)1 . The voltage across T1 and T2 starts to decrease, and the impact of the kick-back voltages induced by the common source inductance L s and those induced by the power loop inductances are described in Eqs. (7–10), · · i g1 Rg1 = Vgin − vgs1 − L s1 i gl − L s1 i d1

(7)

· · i g2 Rg2 = Vgin − vgs2 − L s2 i g2 − L s2 i d2

(8)

38

J. Wei et al. · · · vds1 = Vdc − L pd1s1 i d1 − L p i d2 − L s1 i g1 − Rs (i d + i d2 )

(9)

· · · − L p i d1 − L s2 i g2 − Rs (i d1 + i d2 ) vds2 = Vdc − L pd1s1 i d2

(10)

The discharge current of output capacitance flow into the channel due to the voltage decrease, and the drain current of T1 can be expressed by channel current and output capacitance current: · i d1 = i ch1 + Coss1 vds1

(11)

Since the voltage of T2 does not reach the threshold voltage, the drain current of T2 can be expressed by output capacitance current, as shown in Eq. (12). S3 finished when vgs2 reach to the threshold voltage: · i d2 = Coss2 vds2

(12)

vgs1 , vgs2 , i g1 , i g2 , vds1 , vds2 , i d1 and i d2 are identified as the state variables and their corresponding state equation can be derived from Eqs. (1), (3), (4), (6), (7–12). (3)

S3: T1 and T2 current rise

During S3, the gate voltage of T2 reaches to threshold voltage and T2 starts to conduct current. S3 finished when all the load current commutated from upper diode to T1 and T2. The drain current of T2 can be expressed by · i d2 = i ch2 + Coss2 vds2

(13)

vgs1 , vgs2 , i g1 , i g2 , vds1 , vds2 , i d1 and i d2 are identified as the state variables and their corresponding state equation can be derived from Eqs. (1), (3), (4), (6), (7–11), (13). (4)

S4: Voltage fall

During S4, the drain current reaches the load current, and the current starts to charge the capacitance of upper diode, which makes the voltage across diode increase and the voltage across T1 and T2 decrease. The channel current consists of load current, output capacitance current and diode capacitance current during this period. S4 finished when vds reach to the on-state voltage. The voltage across T1, T2 and Cd can be expressed by · · · vds1 = Vdc − L pd1s1 i d1 − L p i d2 − L s1 i g1 − Rs (i d + i d2 ) − vd

(14)

· · · vds2 = Vdc − L pd1s1 i d2 − L p i d1 − L s2 i d1 − Rs (i d1 + i d2 ) − vd

(15)

vd· =

1 (i d1 + i d2 − Iload ) Cd

(16)

Investigating the Dynamic Performance of Power Semiconductors …

39

vgs1 , vgs2 , i g1 , i g2 , vds1 , vds2 , i d1 , i d2 and vd are identified as the state variables and their corresponding state equation can be derived from Eqs. (1), (3), (4), (6), (7), (8), (11, 13–16). (5)

S5: Ringing

During S5, SiC MOSFET enters the ohmic region, the power loop parasitic inductance and resistance, device capacitance form an RLC resonant circuit. The whole turn-on transient will be finished when gate voltage rises to vgin . The drain current of T1 and T2 can be expressed by i d1 =

vds1 · + Coss1 vds1 Rds1

(17)

i d2 =

vds2 · + Coss2 vds2 Rds2

(18)

vgs1 , vgs2 , i g1 , i g2 , vds1 , vds2 , i d1 , i d2 and vd are identified as the state variables and their corresponding state equation can be derived from Eqs. (1), (3), (4), (6), (7), (8), (14–18). Similarly, the turn-off transition process is a reverse order of the turn-on transition.

2.2 Modeling the I-V and C-V Characteristics of SiC MOSFET When the gate voltage reaches the threshold voltage, the MOS channel is open and allows the drain current to commutate from the SBD gradually. The nonliner functional dependance of the channel current i ch on vgs can be simplified and represented by the Gaussian function. i ch = a ∗ e

) ( v −b 2 − gsc

(19)

Both SBD junction capacitance and the MOSFET capacitances are non-linear, and they are approximated using the following exponential function. c = a ∗ eb∗v + b ∗ ed∗v

(20)

Curve fitting ensures a good alignment as shown in Fig. 2, when compared to the datasheet of C2M0160120D and C4D10120D, which are the SiC MOSFETs and SBD, respectively. The voltage-dependent inter-electrode capacitance values are updated every 500 ps when the drain voltage is less than 200 V, considering a trade-off between simulating time and accuracy. Other circuit parasitic elements, initial value of device parameters and operating condition are summarized in Table 1.

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Fig. 2 Curve fitting of a transfer characteristics of device, b the parasitic capacitance of MOSFET, c junction capacitance of the freewheeling diode Table 1 Parasitic elements and operating conditions with its value

Part

Parameter

Symbol

Value

SiC MOSFET

Gate-Source Capacitance

C gs

521 pF

Gate-Drain Capacitance

C gd

4 pF

Drain-Source Capacitance

Cds

43 pF

SiC Diode

Circuit

Operating condition

Drain Inductance

Ld

6 nH

Common-Source Inductance

Ls

9 nH

Internal Gate Resistance

Rg_int

6.5 Ω

Total Capacitance

Cd

25 pF

Anode Inductance L a

6.5 nH

Cathode Inductance

Lk

6.5 nH

Power Loop Inductance

Lp

50 nH

Power Loop Resistance

Rs

0.5 Ω

External Gate Resistance

Rg_ext

10 Ω

DC Voltage

Vdc

600 V

Load Current

Iload

30 A

Supplied Gate Voltage

Vgin

18 V

Investigating the Dynamic Performance of Power Semiconductors …

41

3 Model Implementation The ordinary differential equations in the state equations for consecutive switching stages are solved by using MATLAB’s ode45 solver. Initial values for each stage are given or calculated using the previous stage. The analytical model was compared with LTspice using the manufacture device models, with package parasitic element considered in both modeling methods. Firstly, the turn-on switching transient behaviors for identical parallel branches (i.e. equal parasitic elements and device parameters) are compared under different operating conditions. Results for different Vdc (600 V and 400 V) and Iload (30A and 20A) are shown in Fig. 3. The vds , i d and pon waveforms pertinent to both branches coincide, which also demonstrate an acceptable match with LTspice results. The switching losses decrease in line with the DC voltage and load current. The load current has a greater impact on the turn-on overlap energy loss because it affects both the peak power and overlapping period. Secondly, the impact of parasitic parameters on oscillations during ringing period is analyzed. The SBD junction capacitance Cd is increased by 100 pF and the turnon transient is shown in Fig. 4a. The SDB diode is reverse blocked until the end of S3, and therefore the corresponding switching waveforms of both MOSFETs remain unchanged. During S4, the load current starts to charge the SBD capacitance as shown

Fig. 3 Turn-on switching transient with different Vdc and Id

Fig. 4 Turn-on switching transient with different Cd and Rg

42

J. Wei et al.

in Eq. (16). When there is a larger value of the SBD capacitance, the voltage decay is extended, and its slope becomes smaller. Therefore, the turn-on loss is increased from 0.114 mJ to 0.141 mJ. During S5, a higher SDB capacitance results in smaller ringing frequency. Thirdly, the impact of different gate resistance values on current and voltage imbalance is analyzed. The external gate resistor of T2 is changed from 10 Ω to 3.5 Ω, with a fixed internal gate resistance. Figure 4b shows nonequal Rg causes uneven current sharing, since a larger Rg can slow down the dynamic switching process as well as the gate voltage rise to reach the threshold voltage. The unbalanced peak current and turn-on energy loss are 2.5A and 0.024 mJ respectively. Finally, the impact of uneven device parasitic parameters is investigated. The common source inductance L d (9 nH to 12 nH) and drain inductance L d (6 nH to 36 nH) of T2 are changed, respectively. The simulation results are shown in Fig. 5. The unbalanced common source inductance has greater impact on current sharing due to the impact of di/dt on common source inductance, which in turn gives negative feedback on the gate loop during current rise period, as shown in Eqs. (7) and (8). The peak current and turn-on loss differences between both switches are 3.5A and 0.027 mJ, respectively. An auxiliary Kelvin source connector can help largely reduce the common source inductance and promote the dynamic current balance [6]. The drain inductance mismatch has comparatively less influence on current imbalance compared with that of the common source inductance. The influence of parasitic parameters on switching transient of SiC MOSFET in parallel are summarized in Table 2, the internal and external parameters of T2 changed while T1 remain unchanged. As can be seen from the table, the peak current and switching energy increase with the increase of parasitic capacitance of upper diode. Besides, the gate resistor, gate capacitance and common source inductance have great influence on current sharing, the smaller their value, the greater the switching loss and peak current. Since the SiC device has a smaller input and Miller capacitance, the discharge current of the device output capacitor cannot be ignored during the voltage drop stage and the channel current consists of load current, the charging current of upper SBD capacitance as well as discharge current of device output capacitance. The output capacitance discharge current is not included in the drain current, and the analytical

Fig. 5 Turn-on switching transient with different L d and L s

17.16

18.41

2 ∗ Cd (Vds )

0.1323

0.1039

0.1149

0.5 ∗ Cd (Vds ) 16.34

I peak (A) E on (mJ)

Cd (Vds )

Cd (Vds ) (pF)

2*Rg_ext

Rg_ext

0.5*Rg_ext 3.74

0

2.16 0.0393

0

0.0198 Ls + 6 6.25

0 3.53

Ls Ls + 3

0.0511

0.0264

0

2*C gs

C gs

0.5*C gs

5.03

0

2.81

0.0534

0

0.0273

Rg_ext2 (Ω) ΔI peak (A) ΔE on (mJ) L s2 (nH) ΔI peak (A) ΔE on (mJ) C gs2 (pF) ΔI peak (A) ΔE on (mJ)

Table 2 Influence of parasitic parameters on switching transient of SiC MOSFET in parallel

Investigating the Dynamic Performance of Power Semiconductors … 43

44

J. Wei et al.

Fig. 6 a Turn-on switching transient with channel current, b Experimental setup, c Comparison of measured and analytical model

model can predict the full channel current by using Eq. (11) and (13). The results shown in Fig. 6a, as can be seen from the picture, the channel current is larger than the drain current during voltage fall period and leading to larger turn-on switching loss. The CRD-5FF0912P SiC MOSFET evaluation board is used to verify the model for single device, as shown in Fig. 6b. The device under test is C3M0065090J with 7L D2PAK package, which is similar with TO-247–3 package except for much smaller common-source inductance. The experimental result and analytical model result under 30A 300 V is shown in Fig. 6c, and analytical model shows good match with experiment.

4 Limitation of Analytical Model Although the analytical model demonstrates considerable accuracy with good simulation speed and simplicity for the transient behavior analysis, it is worth pointing out that the accuracy of model can be further improved. (1)

(2)

(3)

While the Gaussian and exponential function are used for curve fitting in this paper, other functions bearing more physical meaning [7, 8] such as the modified BSIM variants can be used at the price of computational complexity. In Eqs. (17) and (18), the on-state resistance is equivalent to a fixed value during ringing stage, but the gate voltage rises simultaneously, which means that the on-resistance gradually becomes smaller, therefore, the 3D modeling of output characteristics can improve the accuracy. The datasheet only gives the transfer characteristic under a specific voltage (e.g. 20 V), but during the current rise period, the device is kept at a high voltage. Besides, the C gd during the turn-on period is also different from the data sheet. Therefore, the transfer characteristic under large voltage and Q gd needs to be measured [9].

Investigating the Dynamic Performance of Power Semiconductors …

45

5 Conclusion An analytical model of parallel connection of SiC MOSFET was introduced and verified by LTspice. The impact of different parasitic parameters on switching transient can be analyzed by this model. Simulation results shows that the parasitic capacitance of upper switch have impact on current oscillation and slow down the voltage drop. Besides, the gate resistor, gate capacitance and common source inductance variation has significant impact on current sharing between parallel devices.

References 1. Ahmed M, Todd R, Forsyth A (2017) Predicting SiC MOSFET behavior under hard-switching, soft-switching, and false turn-on conditions. IEEE Trans Industr Electron 64(11):9001–9011 2. Ren Y, Xu M, Zhou J, Lee F (2006) Analytical loss model of power MOSFET. IEEE Trans Power Electron 21(2):310–319 3. Yuan D, Zhang Y, Wang X, Gao J (2021) A Detailed analytical model of SiC MOSFETs for bridge-leg configuration by considering staged critical parameters. IEEE Access 9:24823–24847 4. Roy S, Basu K (2019) Analytical estimation of turn on switching loss of SiC MOSFET and Schottky diode pair from datasheet parameters. IEEE Trans Power Electron 34(9):9118–9130 5. Wang J, Chung H, Li R (2013) Characterization and experimental assessment of the effects of parasitic elements on the MOSFET switching performance. IEEE Trans Power Electron 28(1):573–590 6. Li H, Munk-Nielsen S, Wang X, Maheshwari R, Beczkowski S, Uhrenfeldt C, Franke W (2016) Influences of device and circuit mismatches on paralleling silicon carbide MOSFETs. IEEE Trans Power Electronics 31(1):621–634 7. Xiang F (2012) Characterization and modeling of SiC power MOSFETs. Ph.D. dissertation, Grad. Progr Elect Comput Sci, Ohio State Univ, Columbus, OH, USA 8. Arribas P, Krishnamurthy M, Shenai K (2014) A simple and accurate circuit simulation model for high-voltage SiC power MOSFETs. ECS Trans 64(7):99–110 9. Dong Z, Wu X, Xu H, Ren N, Sheng K (2020) Accurate analytical switching-on loss model of SiC MOSFET considering dynamic transfer characteristic and Qgd. IEEE Trans Power Electron 35(11):12264–12273

Turn-On Switching Analysis of SiC/Si Hybrid Switch Jixuan Wei, Zekun Li, Kun Tan, Chen Li, and Bing Ji

Abstract SiC/Si hybrid switch (HyS) has been proven to be a cost-effective switch by later turn-off of SiC MOSFET, the tail current of IGBT can be eliminated and therefore, achieve a turn-off zero voltage switching. During turn-on transient, different turn-on delay time will impact the switching losses and device stress. Normally, zero turn-on delay time is used. In this case, the total switching losses of the HyS may not be minimal, In addition, in order to achieve cost-effectiveness, the current ratio of the HyS will keeps low (1:4 or 1:5), zero turn-on delay time may cause excessive stress on the SiC MOSFET. In this paper, an analytical model of HyS was proposed, the turn-on switching loss of HyS can be analysed by changing turn-on delay time. The analytical model was verified by LTspice. Simulation result shows that a small negative turn-on delay time with small IGBT gate resistor can achieve minimum switching loss while reduce the stress of SiC MOSFET. Keywords Si IGBT · SiC MOSFET · Hybrid switch · Analytical model

1 Introduction In recent years, the emergence of third-generation semiconductors based on silicon carbide (SiC) materials have greatly improve the performance of power devices. Compared with the silicon (Si) power device, the SiC power device has low losses and can operating at higher junction temperature and higher frequency. However, the current capacity of single-chip SiC MOSFET is much lower than Si IGBT due to the limitation of wafer growth and chip processing capabilities of SiC. Another factor that limits the current capacity is the cost, increasing the die size is the main method to improve the current capacity. At present, SiC substrates are generally defective, and increasing the die size forcibly will result in a drop in yield and soaring prices. In J. Wei · Z. Li · K. Tan · B. Ji (B) University of Leicester, Leicester, UK e-mail: [email protected] C. Li Cardiff University, Cardiff, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_5

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high current applications, Si IGBT + SiC MOSFET hybrid switch (HyS) is a good choice, HyS combines the advantage of low switching loss of SiC MOSFET and the large current capability of Si IGBT, which is suitable for high current, high switching frequency, and high-power density applications. Deshpande and Luo, Wang et al., Li et al. [1–3] has proved that the HyS with low current ratio is a cost-effective switch by changing turn-on, turn-off delay time. A power loss model of HyS was proposed in [4] and indicates that a small turn-on delay time can achieve a minimum loss due to the higher di/dt. But most paper are focus on the experiments, there is a lack of analytical analysis of the HyS. In this paper, an analytical model of HyS during turn-on transient was proposed, analytical modelling is a good approach to predicting and understand the switching behaviour [5].

2 Modelling of HyS Turn-On Switching Transient A typical half-bridge circuit topology is shown in Fig. 1, which incorporates an upper switch, a lower switch and a DC voltage source (to represent the DC link capacitor). Each switch consists of a SiC MOSFET, a SiC Schottky barrier diode (SBD) and a Si IGBT in the parallel connection, where the SBD is required due to the comparatively small current capacity of SiC MOSFET which is purposely designed [6]. For simplicity, assume only the SBD in the upper switch communicates currents when the lower switch is actively controlled during on/off switching transitions. The SiC MOSFET and Si IGBT of lower switch is controlled by two gate drivers, respectively, whereas the upper switch is turned off with zero gate voltage. To consider the turn-on transitions, the performance of the HyS is studied in comparison to that from two identical MOSFETs in the parallel connection. Due to the difference in attributes and model parameters between SiC MOSFETs and Si IGBTs, HyS are considered from the perspectives of semiconductor devices and associated gate control. Depending on the variations of the gate control delay between both devices, the turn-on transient of the HyS can be divided into 11 sub-intervals, namely Q1 turn-on delay while Q2 off, Q1 current rise while Q2 off, Q1 voltage fall while Q2 off, Q1 ringing while Q2 off, Q1 and Q2 turn-on delay, Q1 and Q2 current rise, Q1 and Q2 voltage fall, Q1 and Q2 ringing, Q1 current rise while Q2 turn-on delay, Q1 voltage fall while Q2 turn-on delay, Q1 ringing while Q2 turn-on delay. Q1 and Q2 can arbitrarily represent SiC MOSFET or Si IGBT, and the entire turn-on switching transient are permutations and combinations of case 1–11 according to turn-on delay time. The equivalent circuit of these 11 cases is shown in Fig. 1. The following equations are based on IGBT turn-on first. If SiC MOSFET turn-on first, the state equation is the same except parameters need to be changed accordingly. Case 1. Q1 turn-on delay while Q2 off During turn-on delay time, the gate current charge up the input capacitance, leading to a rise of gate voltage, the gate current rise initially and then drops due to the

Turn-On Switching Analysis of SiC/Si Hybrid Switch

49

VDC

VDC

LCS VGIN1 vD IL

vGS

iGM

LCS VGIN1

E

RGI

CDS

CGD

vCE CCE

CG

CJ

IL

iGM

vD

vGS

RGM

C

LD iD

RP

LP

vGE

VGIN2 iGI vDS

CGS

RGM

CJ

LCE CG

LC iC

Case 5

vD

vGS

iGM

VGIN2

vGE

CCE CGC iCH_Q2 LC iC

iGI

vD

vCE RGI

vGS

iGM

RGM

CJ

IL

C CGC iCH_Q2 CE

LD iD

RP

LCS VGIN1

CGE

LC iC

LP

vGS

iGM

RDS

vGE

vCE RGI

CDS

CGE CGC

LD iD

RCE

CCE

LC iC

Case 8 LCE vGE

VGIN2 iGI vDS

CGS

RGM

CCE CGC iCH_Q2

LD iD

RP

LCS VGIN1

CGE vCE

RGI

CDS

CGD LP

CGD

LCE VGIN2 iGI vDS

VDC LCS

VG IN1 vD

CGS

RP

Case 7 VDC

CJ

vCE RGI

LD iD

LCE

CGS

vDS CDS CGD iCH_ Q1

RGM

CJ

LP

IL

iCH_Q1 CDS

CGE

Case 6

LCS

IL

vGE

VGIN2 iGI vDS

VDC

VDC

VGIN1

CGD

RP

LP

LCE

CGS

CJ

IL

vD

vGS

iGM

RGM

LP

RP

Case 9

vGE

CGE vCE

RGI

CDS

CGD

LC iC

LCE VGIN2 iGI vDS

CGS

LD iD

CCE CGC iCH_Q2 LC iC

Case 10 Q1

Q2

SBD

Q1

Q2

SBD

SW1

VDC LCS VGIN1 vD IL

iGM

vGS

RGM

CJ

LP

RP

CGS

CGD

RDS

LCE VGIN2 iGI vDS

vGE

vCE RGI

CDS

LD iD

CGE CGC

RCE

VS

CCE

SW2

LC iC

Case 11

half-bridge topology

Fig. 1 The half-bridge topology and its related equivalent circuits during the turn-on transition

increase of gate voltage. There is no current flow into IGBT until the gate voltage reach to the threshold voltage. From Eqs. (1–3), the state equation of iGI and vGE in case 1 can be obtained. '

'

iGI = CGE vGE + CGC vGC

(1) '

iGI RGI = VGIN 1 − vGE − LCE iGI

(2)

vGE = vGC + vCE

(3)

Case 2. Q1 current rise while Q2 off During current rise period, the gate current continues to charge up the input capacitance as same as turn-on delay time. As the gate voltage has exceeded the threshold voltage, the load current starts to commutate from upper diode to IGBT and, as a result, voltage starts fall due to the parasitic inductance. From Eqs. (1, 3–8), the state equation of iGI , vGE , vCE , iC , vDS and iD in case 2 can be obtained.

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J. Wei et al. '

'

iGI RGI = VGIN 1 − vGE − LCE iGI − LCE iC '

'

'

vCE = VDC − (LP + LC + LCE )iC − LP iD − LCE iGI − Rs (iD + iC ) '

'

vDS = VDC − (LP + LC + LCE )iD − LP iC − Rs (iD + iC ) '

iC = iCH _Q1 + COSSI vCE

(4) (5) (6) (7)

'

iD = COSSM vDS

(8)

Case 3. Q1 voltage fall while Q2 off Voltage fall period starts when the entire load current has commutated from upper diode to IGBT. The current flow into IGBT continue to rise because the current start to charge up the capacitance of upper diode. From Eqs. (1, 3, 4, 7–11), the state equation of iGI , vGE , vCE , iC , vDS , iD and vD in case 3 can be obtained. '

'

'

vCE = VDC − (LP + LC + LCE )iC − LP iD − LCE iGI − Rs (iD + iC ) − vD '

'

vDS = VDC − (LP + LC + LCE )iD − LP iC − Rs (iD + iC ) − vD '

vD =

1 (id + ic − IL ) CD

(9) (10) (11)

Case 4. Q1 ringing while Q2 off The IGBT enters saturation region during this stage, the relationship between collector current and collector-emitter voltage can be obtained from the output characteristics. From Eqs. (1, 3, 4, 8–11, 12), the state equation of iGI , vGE , vCE , iC , vDS , iD and vD in case 4 can be obtained. '

iC = iRI + COSSI vCE

(12)

The switching transient of SiC MOSFET is the same as IGBT, therefore, the equation of SiC MOSFET can be rewritten according to the equation of IGBT, as shown below. Case 5. Q1 and Q2 turn-on delay From Eqs. (1–3) and (13–15), the state equation of iGI , vGE , iGM vGS in case 5 can be obtained. '

'

iGM = CGS vGS + CGD vGD

(13)

Turn-On Switching Analysis of SiC/Si Hybrid Switch

51 '

iGM RGM = VGIN 2 − vGS − LCS iGM

(14)

vGS = vGD + vDS

(15)

Case 6. Q1 and Q2 current rise. From Eqs. (1, 3, 4, 5, 7, 13, 15–18), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC and iD in case 6 can be obtained. '

'

iGM RGM = VGIN 2 − vGS − LCS iGM − LCS iD '

'

'

vDS = VDC − (LP + LD + LCS )iD − LP iC − LCS iGM − Rs (iD + iC ) '

iD = iCH _Q2 + COSSM vDS

(16) (17) (18)

Case 7. Q1 and Q2 voltage fall From Eqs. (1, 3, 4, 7, 9, 11, 13, 15, 16, 18, 19), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC , iD and vD in case 7 can be obtained. '

'

'

vDS = VDC − (LP + LD + LCS )iD − LP iC − LCS iGM − Rs (iD + iC ) − vD

(19)

Case 8. Q1 and Q2 ringing From Eqs. (1, 3, 4, 9, 11, 12, 13, 15, 16, 19, 20), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC , iD and vD in case 8 can be obtained. '

iD = iRM + COSSM vDS

(20)

Case 9. Q1 current rise while Q2 turn-on delay From Eqs. (1, 3, 4, 5, 7, 8, 13, 15–17), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC and iD in case 9 can be obtained. Case 10. Q1 voltage fall while Q2 turn-on delay From Eqs. (1, 3, 4, 7–9, 11, 13, 15, 16, 19), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC , iD and vD in case 10 can be obtained. Case 11. Q1 ringing while Q2 turn-on delay. From Eqs. (1, 3, 4, 8–9, 11–13, 15, 16, 19), the state equation of iGI , vGE , iGM vGS , vCE , vDS , iC , iD and vD in case 11 can be obtained. Our devices under test include C2M0160120D, IHW40T120 and upper diode C4D10120A. Given that only nonlinearity of the miller capacitance of both devices

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Fig. 2 Curve fitting of a transfer, b output characteristics and c miller and diode junction capacitance

are considered together with nonlinear junction capacitance of upper diode, which vary with the voltages across them. Their curve-fitting results expressed with polynomical function and power function are shown in Fig. 2. As can be seen from the figure, the modelled value shows a good match with datasheet value.

3 Model Implementation State equations arising from the circuit are derived to conduct the time-domain simulation and the terminal voltage and currents are plotted by MATLAB. The entire turn-on switching transient is the combination of each case depending the turn-on delay time. Due to the current and voltage continuity during switching transitions, the current switching interval provide initial conditions of subsequent internal. The attributes of device and circuit and initial operating conditions are shown in Table 1. The switching transient of HyS under 0 turn-on delay time is shown in Fig. 3a. Due to the larger gate supply voltage and smaller time constant (partly resulted from smaller gate capacitance) in the gate loop, the gate voltage of the SiC MOSFET reaches its gate threshold before the IGBT. Thus, the MOSFET starts to conduct current while the IGBT is in the turn-on delay stage. Once the IGBT reaches its gate threshold voltage, both devices conduct current simultaneously, leading to an increased di/dt, and thereby reduced the switching losses. Once the entered load current is commutated from the upper diode to the lower HyS, the voltage across the HyS begins to drop. IGBT needs an extra current to achieve a same dv/dt with SiC MOSFET due to its much larger output capacitance, and this extra current is provided by discharging of IGBT gate capacitance. It is important to note that the load current cannot exceed the maximum pulse current of the SiC MOSFET due to the entire load currents will commutate from IGBT to SiC MOSFET during voltage fall stage. When the HyS enters ringing stage, the gate voltage of IGBT starts to rise again, causing the on-resistance to drop and most of the load current flows back to the IGBT.

Turn-On Switching Analysis of SiC/Si Hybrid Switch Table 1 Parasitic elements and operating conditions

53

Part

Parameter

Value

SiC MOSFET

Cgs

521 pF

Cgd

4 pF

Cds

43 pF

Ld

6 nH

Ls

9 nH

Rg_int

6.5 Ω

Si IGBT

Cge Cgc Cce Lc Le Rg_int

2390 pF 110 pF 20 pF 6 nH 9 nH 6Ω

SiC diode

Cd

25 pF

La

6.5 nH

Lk

6.5 nH

Lp

50 nH

Rs

0.5 Ω

Rg_ext_IGBT Rg_ext_MOS

10 Ω 10 Ω

Vdc

600 V

Iload

40 A

Vgin_IGBT Vgin_MOS

15 V 18 V

Circuit

Operating condition

Fig. 3 Turn-on switching transient of HyS with 0 and 40 ns turn-on delay time

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Fig. 4 Switching losses of HyS with different turn-on delay time

Different turn-on delay time affect the time when the currents of the two devices rise at the same time, which in turn affects total turn-on losses. The switching transient of HyS with 40 ns turn-on delay time is shown in Fig. 3b, as the absolute value of turnon delay time increase, the time for the currents of two devices to rise simultaneously is reduced while total switching losses increase, as shown in Fig. 4a. As the turn-on delay time increases, although the total loss increases, but the SiC MOSFET loss decreases. This is very important, especially in the case of HyS with small current ratio. The optimum turn-on delay time is around 50 ns, it greatly reduces the stress of SiC MOSFET while keeps the total losses low. When the turn-on delay time is large enough, the switching loss of the hybrid device is equal to the hard switching of single IGBT or SiC MOSFET. Since the maximum current of the HyS depends on the SiC MOSFET under the optimal turn-on delay time, and the HyS can suppress the current oscillation [7], therefore, the gate resistance of the IGBT can be further reduced. The switching loss of HyS with IGBT gate resistance of 4 Ω is shown in Fig. 4b and the comparison is shown in Fig. 4c, the total switching loss of the HyS decreases with the decrease of the IGBT gate resistor, this is because the di/dt increase as the gate resistance decreases. Besides, the stress of SiC MOSFET further reduced.

4 Conclusion An analytical model of HyS was proposed and shown a good match with LTspice. Different turn-on delay time and IGBT gate resistor was compared, a small turn-on delay time with small IGBT gate resistor not only reduce the total switching losses, but also reduce the stress of the SiC MOSFET.

References 1. Deshpande A, Luo F (2019) Practical design considerations for a Si IGBT + SiC MOSFET hybrid switch: Parasitic interconnect influences, cost, and current ratio optimization. IEEE Trans Power Electron 34(1):724–737

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2. Wang J, Li Z, Jiang X, Zeng C, Shen Z (2019) Gate control optimization of Si/SiC hybrid switch for junction temperature balance and power loss reduction. IEEE Trans Power Electron 34(2):1744–1754 3. Li Z et al (2020) Active gate delay time control of Si/SiC hybrid switch for junction temperature balance over a wide power range. IEEE Trans Power Electron 35(5):5354–5365 4. Li Z, Wang J, Ji B, Shen Z (2020) Power loss model and device sizing optimization of Si/SiC hybrid switches. IEEE Trans Power Electron 35(8):8512–8523 5. Ahmed M, Todd R, Forsyth A (2017) Predicting SiC MOSFET behavior under hard-switching, soft-switching, and false turn-on conditions. IEEE Trans Industr Electron 64(11):9001–9011 6. Rahimo M, Papadopoulos C (2015) The cross switch “XS” silicon and silicon carbide hybrid concept. In: PCIM Europe, Nuremberg 7. Kicin S, et al (2019) Characterization of 1.7kV SiC MOSFET/Si IGBT cross-switch hybrid on the LinPak platform. In: PCIM Europe

Plastic Strain Analysis of IGBT Solder Layer Zhengyi Ren, Yao Zhao, Zheng Liu, Zhiqiang Wang, and Ninghui Wang

Abstract In order to investigate the plastic strain changes of power device packaging in thermal cycling test, a 3D finite element model based on IGBT (Insulate Gate Bipolar Transistor) module was established by using SCDM, then conducted the thermal-structural coupling analysis of IGBT module with ANSYS software, compared the plastic strain distribution at the different thickness of different components by orthogonal analysis method, and compared the plastic strain of IGBT module under solder layer of different materials. The results show that the equivalent plastic strain of the IGBT module decreases with the substrate thickness and the DBC layer thickness. With the increase of substrate solder layer thickness, the equivalent plastic strain has an overall upward trend, decreasing first, then increasing, and then decreasing again, but remaining higher than the initial value. Besides, the thickness of the substrate solder layer has the most critical influence on the plastic strain of the module, while the thickness of the DBC copper layer has the least influence on it. Furthermore, using Nano silver as the solder layer can reduce the plastic strain of the IGBT module, which is 19.14% lower than the initial parameters. Keywords Thermal cycling · Solder layer · Plastic strain

1 Introduction The IGBT (Insulated Gate Bipolar Transistor) module has high blocking voltage, fast switching speed and high power density, and has been widely used in the high voltage high power field [1]. A large number of actual operation fault statistics and test data show that the IGBT module is prone to thermal–mechanical stress related package failure under the action of alternating stress due to the mismatch of the coefficient of thermal expansion (CTE) of each physical layer, and the bond wire and solder layer are the weakest links of packaging [2, 3]. Generally, when the solder layer fails to a certain extent, the bond wire will fail [4]. Therefore, the solder layer Z. Ren · Y. Zhao · Z. Liu (B) · Z. Wang · N. Wang School of Electrical Engineering, Dalian University of Technology, Liaoning 116024, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_6

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is one of the weakest links in the device packaging structure, so it is necessary to study the thermal stability of the device on the solder layer defects. At present, domestic and foreign scholars have studied the fatigue failure mechanism of the module solder layer, but mainly from the perspective of surface detection or external current parameters, lacking the deep discussion of the failure of the solder layer from the physical mechanism. Moreover, since the package of the IGBT module is a laminated structure, which is composed of 7 layers of material, including two solder layers, chip solder layer and substrate solder layer, therefore, most studies ignore the impact of the upper and lower layer of solder layer on the failure of the solder layer. To further clarify the mentioned problem, this paper established a finite element model under IGBT thermal cycle test based on Anand viscoplastic model. Using ANSYS finite element analysis software, the plastic strain distribution characteristics under the thermal cycle are analyzed to find the fragile layer. Then, according to the laminated structure of IGBT module, the influence of different thicknesses of DBC copper layer, substrate solder layer and substrate on the plastic strain of IGBT module is analyzed. Finally, the plastic strain of the solder layer with different materials is compared.

2 Finite-Element Analysis The IGBT module is of complex structure, from top to bottom, the layers are chip, chip solder layer, DBC, substrate solder layer and substrate, the structure is shown in Fig. 1. This paper uses a 1200 V/600A dual IGBT module, FF600R12ME4_B11. Each IGBT module contains three IGBT chips and three diodes, as shown in Fig. 2. Because the IGBT module is symmetric structure, half of the model can be studied during analysis; this method can save computing time and computer resources. Since the heat conduction of the aluminum bonding wire is very small relative to the whole Albondingwire

Siliconchip Uppercopperlayer DBC

Ceramiclayer Lowercopperlayer Coppersubstrate

Fig. 1 Structure diagram

Uppersolderlayer

Lowersolderlayer

Plastic Strain Analysis of IGBT Solder Layer

59

Fig. 2 IGBT module FF600R12ME4_B11

module, the bonding wire was ignored in the model. At the same time, due to the small thermal conductivity of the packaging material and filled silicon gel, the heat is mainly dispersed through the substrate, so this paper ignored the silica gel and the packaging above and considered that the module is in an adiabatic condition [5]. The finite element model of IGBT module is composed of copper substrate, chip, solder layer and DBC. The structure with concentrated stress distribution such as solder layer was refined, such as solder layer, the finite element mesh model is shown in Fig. 3.

Fig. 3 Finite element mesh model of IGBT module

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In the simulation analysis, the boundary conditions and parameters of the IGBT finite element model were set as follows: the ambient temperature is 25 °C, the crosssection of the IGBT module is set as frictionless constraint, and the cross section’s bottom edge is set as frictionless set as a fixed constraint. The finite element analysis was performed using a typical thermal cycle in the JESD22-A104D, as shown in Fig. 4. The maximum temperature is 125°C; the minimum temperature is −40 °C, maintains 15 min, and the rising and falling rate is 10°C/min; four cycles can ensure the accuracy of the test [6]. The initial temperature was set to 25°C, which can ensure the consistency between finite element simulation and experiment. The material parameters of the IGBT module are shown in Table 1. In particular, since the low melting point of the solder layer, the service temperature of electronic devices will generally reach more than half of the melting point temperature. The viscoplastic mechanical behavior will become the main form of the solder layer

Fig. 4 Thermal cycle load

Table 1 Material properties Layer material

ρ kg/m3

E MPa

ν

CTE 10–6 /K

K W/m·K

C J/kg·K

Silion chip

2328

113,000

0.28

3

90

700

Solder SAC305

7400

47,000

0.4

20

40

234

DBC copper

8933

120,000

0.38

17.7

400

385

Ceramic Al2 O3

3960

370,000

0.22

9.16

35

850

DBC copper

8933

120,000

0.38

17.7

400

385

Solder SAC305

7400

47,000

0.4

20

40

234

Copper substrate

8933

120,000

0.38

17.7

400

385

Plastic Strain Analysis of IGBT Solder Layer

61

deformation, and therefore the elastic mechanical parameters can not accurately describe the mechanical response process of the solder layer. Document [7] shows that the Anand constitutive model can effectively describe the viscoplastic properties of solder joints and can be effectively used to simulate the reliability of welding points in electronic packaging. Therefore, the Anand model is used to describe the inelastic properties of the solder layer. In the Anand model, strain hardening and softening behavior are described by a flow rule and three corresponding evolution rules. The Anand unified viscoplastic equation can be expressed as [8].    m1 ξσ e−Q / RT ε p = A sinh s

(1)

where εP is inelastic strain rate, A is constant, ξ is stress multiplication coefficient, σ is stress, S is deformation resistance, R is gas constant, m is strain rate sensitivity, Q is activation energy and T is the absolute temperature. And the rate of the deformation resistance equation is.   B • • ε s = h 0 (|B|)α |B| p B =1− 

∧

s∗ = s

(2)

s s∗

1 • −Q / RT se Ap

(3) n (4)

where s∗ is the saturation value of s, s is the coefficient of the deformation resistance saturation value, and n is the strain rate sensitivity. According to the equation, material parameters need to be defined in the Anand model was shown in Table 2. Because plastic work only exists in the viscoplastic elements. Therefore, only the solder layer has plastic strain, and the other layer structure only has elastic deformation, at the end of the thermal cycle, the deformation of this part is basically restored without strain accumulation, which has little influence on IGBT module life. But the solder layer has viscoplastic characteristics and the viscoplastic deformation is heat-activated and unrecoverable. With the increase of thermal cycles, the inelastic strain of the solder layer keeps accumulating. When the inelastic strain accumulates 

Table 2 Parameters of solder layer material SAC305 in the Anand model [9] Parameter (Unit)

So (Pa)

Q/R (K)

A (1/s)

ξ

m

h0 (Pa)

s (Pa)

n

a

SAC305

4.59 × 107

7460

5.87 × 106

2

0.0972

9.35 × 109

5.83 × 107

0.015

1.5

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to a certain extent, it will lead to the initiation and growth of the cracks in the solder layer, and after the cracks extend to a certain extent, it will lead to fatigue failure [10]. As shown in Fig. 5, the maximum plastic strain is located near the edge of the substrate solder layer and the chip solder layer has less plastic strain compared to the substrate solder layer. With the increase of thermal cycles, the plastic strain value also increases gradually (as shown in Fig. 6), so the substrate solder layer is most prone to fatigue damage in the thermal cycle aging test. Therefore, during the temperature circulation, the failure is easy to occur at the edge of the substrate solder layer, and with the increase of the number of cycles, it slowly extends to the interior of the solder layer, which is consistent with the experimental results in reference [11].

Fig. 5 Plastic strain distribution of IGBT module during thermal cycling

Fig. 6 Plastic strain of substrate solder layer changes over time during thermal cycling

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In order to study the influence of various structural factors on the solder layer connection of the IGBT module substrate, this paper changed the thickness of a single connection component in the component, and studied the impact of the layer component thickness on the substrate equivalent plastic strain by lateral comparison and research. The simulation experiment results are shown in Fig. 7. It can be seen from Fig. 7 that the maximum plastic strain decreases as the substrate thickness increases. The reason is with the thickness of the substrate, the rigidity and deformation resistance increase. The maximum plastic strain also decreases with the increase of the thickness of the DBC copper layer. With the increase of the thickness of solder, the maximum plastic strain first decreases, then increases and then decreases again. Considering that the thickness of the solder layer is too thick, it will increase the difficulty of the welding process, and it is easy to produce voids or even cracks, so it is particularly important to choose the appropriate thickness of the solder layer.

3 Analysis IGBT Module Structure Parameters by Orthogonal Analysis In the previous section, the influence analysis of the structural parameters of each layer on the IGBT module plastic strain was completed, and the plastic strain changes with the structural thickness of each layer was obtained. However, through the above results, we can not get the order of the influence of the thickness of each layer on the plastic strain. In order to analyze the influence of each layer on the plastic strain of IGBT module more accurately, the orthogonal analysis method was used to analyze the structural parameters, obtained the influence of the thickness of the substrate, DBC copper and solder on the plastic strain. This provides a refer for the optimal design of the IGBT module. A, B and C were used to represent the substrate thickness, substrate solder layer thickness and DBC copper layer thickness, respectively, and four average values (Level 1, 2, 3 and 4) were selected for these 3 factors, as shown in Table 3. The L16 (43 ) orthogonal table lists 16 different combinations of orthogonal tests. According to the simulation results, the equivalent plastic strain of IGBT module after four temperature cycles is selected to obtain the range of each factor level, thus obtaining each factor level’s effect on the result. Table 4 Orthogonal test table designed for the simulation experiment. Ki in Table 4 is the sum of the results obtained by each factor at the i-th level, ki is the average corresponding to each level and the range is the difference between the maximum value and the minimum value of ki , which represents the effect on the experimental results when the factor level changes. According to the last line of Table 4, the range of the substrate solder layer thickness is the largest, followed by the range of substrate thickness, and the range of DBC copper layer thickness is the smallest. This shows that the thickness of the substrate solder layer has the

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Fig. 7 The influence of layer component thickness on the maximum plastic strain a Substrate; b Substrate solder layer; c DBC copper layer

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Table 3 Parameter level of solder layer connection structure of substrate Parameter

Level 1

Level 2

Level 3

Level 4

A/mm

2.8

3.3

3.8

4.3

B/mm

0.15

0.2

0.25

0.3

C/mm

0.25

0.3

0.35

0.4

Table 4 Orthogonal design of IGBT module structural factors Test number

A

B

C

Equivalent plastic strain

1

1

1

1

0.011474

2

1

2

2

0.013549

3

1

3

3

0.028451

4

1

4

4

0.02591

5

2

1

2

0.0074286

6

2

2

1

0.011833

7

2

3

4

0.022937

8

2

4

3

0.017419

9

3

1

3

0.0075241

10

3

2

4

0.0095982

11

3

3

1

0.021078

12

3

4

2

0.016616

13

4

4

4

0.0070096

14

4

2

3

0.0087507

15

4

3

2

0.021538

16

4

4

1

0.019472

K1

0.079384

0.0334363

0.063857

K2

0.0596176

0.0437309

0.0591316

K3

0.0548163

0.094004

0.0621448

K4

0.0567703

0.079417

0.0654548

k1

0.019846

0.008359075

0.01595675

k2

0.0149044

0.01093275

0.0147829

k3

0.013704075

0.023501

0.0155362

k4

0.014192575

0.01985425

0.0163637

Range

6.141925 × 10–3

1.5141925 × 10–2

1.5808 × 10–3

greatest influence on the plastic strain, and the DBC copper layer thickness has the least influence on the plastic strain.

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4 Effect of Different Material Solder Layers on the Plastic Strain of the IGBT Module In the development history of solder layer, traditional high lead materials such as Sn–Pb materials were once widely used in high-power power supply, aviation, electric vehicles and other fields because of their high stability even in a hot and electric temperature environment. Later, the use of Sn–Pb materials was limited by many countries because of a large amount of lead gas in the manufacturing process, absorbed by the human body, which hinders the normal synthesis of protein, endangers physical health, and increases the probability of chronic diseases. Subsequently, Sn-Ag and Sn–Ag–Cu were used as the most suitable alternatives and soon gained general use [12]. With the development of SiC hybrid module, the module has higher and higher requirements for the solder layer. As a new generation of packaging material, nanosilver welding paste has low-temperature sintering, and high-temperature service characteristics. The interconnecting layer structure formed after sintering has unique high-temperature resistance and high thermal conductivity [13]. This paper analyzes the IGBT module under the three solders of Sn3.5Ag, SAC305, nanosilver. The parameters of the three materials are shown in Table 5, and the Anand model parameters are shown in Table 6. The obtained equivalent plastic strain cloud map of IGBT module is shown in Fig. 8. It can be seen from Fig. 8 that when nano silver is used as the solder layer material, the plastic strain of the IGBT module is the smallest and the maximum equivalent plastic strain is only 0.0094669, which is 58.45% lower than Sn3.5Ag and 19.14% lower than SAC305. Therefore, using nano silver solder as the welding layer material Table 5 Material parameters of solder layer Material

ρ kg/m3

E MPa

ν

CTE 10–6 /K

k W/m·K

C J/kg·K

Sn3.5Ag

7300

54,050

0.4

21.85

54

230

SAC305

7400

40,000

0.3

23

32.7

150

Nano silver

8580

9000

0.37

19

240

234

Table 6 Anand model parameters Material

So (Pa)

Q/R (K)

A (1/s)

ξ

m

h0 (Pa)

S (Pa)

n

a

Sn3.5Ag

3.036 × 107

8765

52,690

6

0.182

7.206 × 109

7.6944 × 107

0.018

1.2321

SAC305

45.9 × 106

7460

5.87 × 106

2

0.0972

9.35 × 109

5.83 × 107

0.015

1.5

Nano silver

3.93 × 106

5706.3

9.81

12

0.6572

1.46 × 1010

1.017 × 108

0.0036

1.0

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Fig. 8 Equivalent plastic strain of different solder layers a Sn3.5Ag; b Nano Silve

of the module can reduce the plastic strain of IGBT module in the thermal cycle and help to improve the IGBT module’s reliability.

5 Conclusion In this paper, the FEM method is used to simulate the plastic strain changes of the IGBT module during the thermal cycle. Using the control variable method and orthogonal analysis to explore the influence of each component thickness and material on the maximum plastic strain combined with the Anand model of the solder layer, the following conclusions are obtained:

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(3)

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Increasing the thickness of the substrate can effectively reduce the plastic strain generated in the thermal cycle of the IGBT module; The thickness of the substrate solder layer has the greatest influence on the maximum plastic strain, followed by the thickness of substrate, and the thickness of DBC copper layer has the least influence on the plastic strain. Through the above analysis, the plastic strain occurring in the 13th test number was minimal, decreasing by about 40% compared to the original 0.011708, which referred to the IGBT module’s design. Compared with other materials, the plastic strain of IGBT module is the smallest when nano silver is used as solder layer material, which has guiding significance to the design of IGBT module package structure.

References 1. Tan L, She C, Liu P et al (2020) Research progress on failure mechanism of solder layer of IGBT module. Eeectronic Components Mat 39(12):15–21 2. Liu Y, Zhang Y, Bao J, et al (2021) Reliability analysis of IGBT hybrid module based on finite element simulation. Chinese J Electron Devices 44(1):7–13 3. Wang X, Zhang B, Wu H (2019) A review of fatigue mechanism of power devices based on physics-of-failure. Trans China Electrotechnical Society 34(04):85–95 4. Lai W, Chen M, Ran L et al (2015) Analysis of IGBT failure mechanism based on ageing experiments. Proceedings of the CSEE 35(20):5293–5300 5. Chen M, Chen Y, Gao B et al (2018) Lifetime evaluation of IGBT module considering fatigue accumulation of solder layers. Proceedings of the CSEE 38(20):6053–6061 6. Müller-Fiedler R, Knoblauch V (2003) Reliability aspects of microsensors and micromechatronic actuators for automotive applications. Microelectronics Reliability 43(7):1085–1097 7. Tseng HK, Wu ML (2013) Electro-thermal-mechanical modeling of wire bonding failures in IGBT. In: International Microsystems, Packaging, Assembly & Circuits Technology Conference. IEEE 8. Lall P, Zhang D, Yadav V, et al (2016) High strain rate constitutive behavior of SAC105 and SAC305 leadfree solder during operation at high temperature. Microelectronics Reliability 62:4–17 9. Zhang L, Han J et al (2014) Anand model and FEM analysis of SnAgCuZn lead-free solder joints in wafer level chip scale packaging devices. Microelectron Reliab 54(1):281–286 10. Chen M, Gao B, Yang F et al (2015) Healthy evaluation on IGBT solder based on electrothermal-mechanical analysis. Trans China Electrotechnical Society 30(020):252–260 11. Ji B, Song X, Sciberras E et al (2014) Multiobjective design optimization of IGBT power modules considering power cycling and thermal cycling. IEEE Trans Power Electron 30(5):2493–2504 12. Tian H (2017) The development of low Ag Sn-Ag-Cu solder is discussed. New Tech & New Products of China 000(017):52–53 13. Long H, Li H, Wang X et al (2020) Study on the long term reliability of nanosilver Sintered Press Pack. Proceedings of the CSEE 40(18):5779–5787

Design of a New Drive Circuit for Gallium Nitride Wei Liu, Cungang Hu, Wenjie Zhu, Zhishang Yan, and Xinyu Ma

Abstract The third generation of wide-band gap semiconductor GaN transistor has low conduction impedance, low parasitic parameters and faster switching speed, which has unique advantages in high-speed and high power density applications. It is expected to replace the traditional SI MOSFET and become the implementation scheme of future high-performance power supply system. However, GaN devices have their own unique physical characteristics, such as maximum gate voltage limitation, low threshold voltage, and reverse conduction voltage. Therefore, the gate drive circuit needs to be designed according to device characteristics. This article mainly analyzes the main problems in the high-speed switching process of GaN HEMTs, and analyzes several common GaN drive circuits, and proposes one on this basis. A fast turn-off GaN HEMT device drive circuit, and finally the feasibility of the designed circuit is verified by simulation. Keywords Gallium Nitride · High electron mobility field effect transistor · Drive circuit · Switching converter1

1 Introduction In recent years, Si-based GaN transistors have become a research hotspot for widebandgap semiconductor power devices, and are expected to become high-efficiency, high-performance, and low-cost power system solutions in the future. Compared with Si MOSFET, GaN device has lower on-resistance and gate charge under the same voltage resistance, fast switching speed and high power density, and can be well suited W. Liu · C. Hu (B) · W. Zhu · Z. Yan · X. Ma School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_7

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to the application of megahertz high current switching power supply. However, there are some factors that need special attention when driving GaN HEMT devices, such as low threshold voltage, low upper limit of gate source voltage, reversible conduction and sensitivity to parasitic inductance [1]. GaN Systems products require drive voltages ranging from −10 V to +7 V. The maximum voltage must not exceed +7 V or the gate will be broken down. The driving voltage of the driver chip of SI MOSFET is in the range of 4.5~18 V, so the traditional driver chip has been unable to meet the requirements of GaN devices, which greatly affects the application of GaN devices in various power topologies. Literature [2] for gallium nitride drive circuit under high frequency harmonic drive circuit, can be GaN HEMT devices provide a stable voltage, at the same time to realize energy feedback, reduce loss, but it USES a resonant inductance value to class nH in actual application are cloth plate, the parasitic inductance and other stray parameters of the device, the influence of the design more difficult. And this driving mode only reduces the loss significantly at UHF. Literature [3] provides an independent drive circuit, which separates the on–off circuit from the off-off circuit of the gallium nitride device. This drive mode changes the on–off time by adjusting the resistance value of the charging and discharging circuit resistors. This is one of the most commonly used driving methods, but its disadvantage is that the rising time is long, which will greatly affect the switching speed of GaN device, the driving ability is weak, the gate can not obtain the expected driving voltage, and the ring is large during the turn-off, which is easy to cause the misleading communication of GaN HEMT device. Literature [4] proposes a diode clamping type drive circuit, in order to prevent the shut off when the reverse current charging influence on grid voltage, use against a resistor in parallel diode as GaN HEMT shut off when the discharge channel, this way can make the grid voltage clamp in the pressure drop of the diode conduction values, which in turn can lead to GaN HEMT misleading. The two-stage drive circuit proposed in this paper ensures that the device can be turned on quickly, and at the same time greatly reduces the overshoot during the turn on and the ringing during the turn off. The feasibility of the two-stage drive circuit is verified by simulation.

2 Two-Stage Drive Circuit In view of the shortcomings of the driving circuit proposed in literature [2–4], this paper firstly analyzes the ideal driving model and then the actual circuit model, and then proposes a two-stage driving circuit.

2.1 Ideal Drive Circuit Figure 1 is the ideal driving circuit model.RDRIVE is the driving resistor, R1 and R2 are pull-up and pull-down resistors respectively, In order to speed up the turn-off speed,

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D

Fig. 1 Ideal driver circuit

RDRIVE R1

R2 Cgs

Vd

a diode D is used, Vd is the driving voltage. Figures 2 and 3 show the opening and closing process of the ideal driving model. Combined with the above figure, Kirchhoff’s voltage law can be obtained: Vgs = Vd − (R1 + RDRIVE ) · ig

(1)

among them:

ig = Cgs

dVgs (t) dt

(2)

The turn-on and turn-off time of the switch tube is the charge and discharge time of the gate-source capacitor: Fig. 2 Turn-on circuit

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Fig. 3 Turn off the circuit

Vgs_on (t) = Vd · (1 − e−τ1 t )

(3)

Vgs_off (t) = (Vd − VF )e−τ2 t + VF

(4)

τ1 = (R1 +RDRIVE )·Cgs ,τ2 = R2 ·Cgs is time constant, According to Eq. (3), The closer Vgs is to Vd , the slower the rising speed. From Eq. (4), when the GaN HEMT device is turned off, the voltage drop on the diode will cause the gate voltage to be clamped at the on-state voltage VF of the diode(VF = 0.7). It is close to the threshold voltage (VTH _GaN = 1.1V ) of GaN device and easy to mislead [5]. Therefore, attention should be paid to these problems when designing. The charge and discharge waveform is shown in Fig. 4a, b.

2.2 Actual Drive Circuit The normal operation of the drive of the switching device is the basis for the normal operation of the power converter. The gate-source of the GaN HEMT is more fragile than the Si MOSFET, so the design of the drive circuit is particularly important. During the layout process, there will be parasitic inductance in the circuit and the package of the device, which will affect the quality of the driving voltage [5]. The circuit model of the gate-source loop after adding parasitic inductance is shown in Fig. 5

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(a) Charging waveform

(b) Discharge waveform Fig. 4 Charge and discharge waveforms of an ideal drive circuit Fig. 5 The actual gatesource loop

VL

ig

RDRIVE Vd

Lr V gs

Cgs

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According to Kirchhoff’s voltage law: Vd = Vgs + RDRIVE Cgs

dVgs dVgs + Lr Cgs dt dt

(5)

Laplace transform (5) to get: (

) Lr Cgs s2 + RDRIVE Cgs s + 1 Vgs (s) = Vd (s)

(6)

Transfer Function: G(s) =

Vgs (s) 1 = = 2 Lr Cgs s + RDRIVE Cgs s + 1 Vd (s) s2 +

1 Lr Cgs RDRIVE s Lr

+

1 Lr Cgs

(7)

Combine (7) with a typical second-order system: G(s) =

ω2 s2 + 2ζ ωn s + ωn

(8)

By comparison, you can get: 1 ωn = √ Lr Cgs / RDRIVE Cgs ζ = 2 Lr

(9)

(10)

The actual circuit is usually under-damped. From Eq. (7), we can see that in the under-damped state(0 < ζ < 1), Both ends of capacitor Cgs will oscillate, as shown in Fig. 6

2.3 Two-Stage Drive Circuit Parallel capacitors are connected to the gate-source to reduce the gate-source voltage oscillation, but at the same time it becomes a challenge to make the gate-source voltage reach the desired value. In order to solve this problem, this paper proposes a two-stage drive circuit, as shown in Fig. 7. Q1 and Q2 are N MOSFET and P MOSFET respectively, Z1 is the comparator (V − > Vref ,Z1 output high impedance state, V − < Vref , Z1 output low level), Vref takes 1 V, VCC2 takes 6 V, B1 is N-type triode. Turn-on stage: Q1 turns on, Q2 turns off,V − < Vref , and the comparator outputs a high-impedance state, the triode is turned on, the current is charged by Q1 − R4 − Cgs

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(a) Charging waveform

(b) Discharge waveform Fig. 6 Charging and discharging waveforms of the actual drive circuit

and Q1 − B1 − R5 − Cgs to C1 and Cgs ,Vgs rapid rise. When Vgs > 5.3 V, the triode turns off, the current continues to charge C1 and Cgs through Q1 − R4 − Cgs , until GaN HEMT is fully opened. Turn-off stage:Q2 turns on, Q1 turns off,V − < Vref , the comparator outputs low level, VCC2 is pulled to the ground, the triode turns off, the current flows through Vgs − D1 − R3 − Q2 and discharges rapidly, until the GaN HEMT turns off. Parallel capacitor C1 in the gate-source electrode reduces the oscillation of the gate-source voltage and at the same time reduces the driving capability of the circuit, so that Vgs cannot reach the predetermined value. Therefore, two-stage charging is used. In the first stage, a large current is used to quickly increase Vgs to near the desired voltage, and then the transistor is clamped by its own voltage to reduce the current, and continue charging with a small current to make Vgs reach the desired voltage.

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Fig. 7 Two-stage drive circuit model

Through the two-stage drive, it not only ensures the turn-on speed of the device, but also avoids excessive overshoot.

3 Experimental Simulation In order to verify the reliability of the two-stage drive circuit, a flyback circuit based on gallium nitride devices was designed and compared with the drive circuit in literature [2, 3]. Table 1 shows the simulation circuit parameters. Figure 8 is a simulation circuit model. As shown in Figs. 9 and 10, respectively, are resonant drive circuit and independent drive circuit, and the gate source drive voltage waveform obtained in the flyback circuit. It can be seen from Fig. 9 that the drive voltage of the resonant drive circuit has a long rise time, and the maximum drive voltage is only 5.5 V, which is far from the given 6 V; Fig. 10 The drive voltage of the independent drive circuit is at the off position Obviously, the oscillation of the maximum turn-off voltage can reach 2 V, while the threshold of GaN HENT is only 1.1 V, which can easily cause the GaN HEMT device to be turned on by mistake. The voltage waveform of the two-stage drive circuit is shown in Fig. 11. Table 1 Simulation circuit parameters Primary side inductance (uh)

Secondary inductance (uh)

Cgs (pf)

Cgd (pf)

Cds (pf)

Switching frequency (Hz)

Driving voltage (V)

240

30

70

0.4

40

50,000

6

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Ls 2

Ls1

VIN

Cin

n*1 n2 *

Lm1

Cout

RL

Vout

GaN

Cgd

Cgs

Cds

Fig. 8 Simulation circuit model

Fig. 9 Waveform of resonant drive circuit gate source voltage

As shown in Fig. 11, the two-stage drive circuit uses a large current in the first half to quickly increase the drive voltage to near the desired voltage of 6 V, and then uses a small current to avoid oscillations at the turn-on moment, and at the same time, the voltage oscillations at turn-off are gated. The capacitor connected in parallel with the source is suppressed within a controllable range.

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Fig. 10 Independent drive circuit voltage and current waveforms

Fig. 11 Two-stage drive voltage waveform

4 Conclusion This paper proposes a two-stage drive circuit scheme. Under the condition that other parameters remain unchanged and only the drive circuit is changed, compared with the traditional drive circuit in the flyback topology, the resulting drive waveform is more generated than the traditional drive circuit. The waveform is better, which makes the turn-on speed of the device faster and higher stability. The feasibility of this drive scheme is verified.

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References 1. Xin M, Xuan Z, Qi Z, Hai H, Analysis and design of active clamp flyback converter based on GaN 2. Qinglin Z, Shaowei C, Jing Y, Deyu W (2019) Low-voltage GaN device resonant drive technology and its reverse conduction characteristics. Trans Chinese Society Electrical Eng 34(S1):133–140 3. Gamand F, Li MD, Gaquiere C (2012) A 10-MHz GaN HEMT DC/DC boost converter for power amplifier applications. IEEE Trans Circuits Syst II Express Briefs 59(11):776–779. https://doi. org/10.1109/TCSII.2012.2228397 4. Huang X, Feng J, Du W, et al (2016) Design consideration of MHz active clamp flyback converter with Ga N devices for low power adapter application. In: 2016 IEEE Applied Power Electronics Conference and Exposition (APEC). IEEE, 2334–2341 5. Meiting C (2015) Research on the characteristics and applications of GaN devices. Beijing Jiaotong University

Review of SiC MOSFET Failure Analysis Under Extreme Conditions: High Temperature, High Frequency and Irradiation Ziyang Zhang, Lin Liang, and Hai Shang

Abstract With the inherent advantages of material, SiC MOSFET is promising in many applications. There is much research on failure analysis of SiC MOSFET under extreme conditions. A comprehensive review is critical to provide reference for weak locations of chip in device design or application stage. Under three types of extreme conditions of high temperature, high frequency and irradiation, the failure mechanism and mode, characterization, withstand capability and factors affecting reliability are reviewed in detail. The analysis of failure mechanism can provide a basis for chip designers to improve chip performance for specific operating conditions, and provide device users with advice on circuit design. A clear safe working area allows practitioners to maximize the performance of the device. The methods to improve reliability of SiC MOSFET are proposed at the end of the paper. Keywords Extreme conditions · SiC MOSFET · Reliability

1 Introduction With the development of applications of electrified transportation, new energy power system, specific power supply and etc., power electronic equipments are required to be of high efficiency, high power density and high reliability. As a kind of wide bandgap semiconductor materials, silicon carbide (SiC) has the advantages of high thermal conductivity, high melting point, high electron drift velocity and wide bandgap. Thus it can be widely used in high temperature, high frequency and irradiation applications, such as aerospace, geothermal, exploration wells, nuclear energy and electric vehicles [1], as shown in Fig. 1. In harsh environments, power semiconductor devices are subjected to complex electrical, thermal, and mechanical stresses, which influence their long term reliable operation. In the application of Z. Zhang · L. Liang (B) · H. Shang State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_8

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Z. Zhang et al.

Electric High Temperature Vehicles High Frenquency Rail Transportation High Temperature High Frenquency

Aerospace

SiC Devices

High Temperature Irradiation Nuclear Power

Vessel

hybrid/electric vehicle, deep well exploration and geothermal, the junction temperature of SiC MOSFET can be extremely high, which is easy to cause chip thermal runaway, packaging material degradation and etc. [2, 3]. In high power density converters, the switching frequency of SiC MOSFET is very high, which induces common mode current, transient noise, voltage and current overshoot problems in the power circuit and control circuit [4, 5]. The devices suffer from higher electrical stress due to these issues, reducing reliability of devices [6, 7]. In the fields of space power system and nuclear power station and etc., SiC MOSFET can be irradiated by heavy ions, neutrons, protons and high-energy electrons, which may cause characteristic degradation or catastrophic failure [8–11]. The reliability problems of SiC MOSFET are widely concerned in the applications of harsh working environments requiring low failure rate and high maintenance cost. The mode and mechanism of degradation and failure of SiC MOSFET are summarized under extreme conditions of high temperature, high frequency and irradiation. Ways to improve reliability under extreme conditions are proposed.

2 Failure Analysis Under High Temperature At present, the maximum junction temperature of commercial Si-based chip is 175 °C, while the theoretical limit temperature of SiC chip is 600 °C. Si-based devices are unable to work in some extreme applications such as oil and gas well drilling generators, aero-engine controllers, aircraft wireless sensors and sustainable energy geothermal meters, while SiC-based devices are expected to work in these environments owing to their high limiting temperature and high thermal conductivity, as shown in Fig. 2 [12]. In order to ensure the reliable operation of SiC MOSFET under Fig. 2 Extreme high temperature environments

Limit temperature of Si devices

ºC

ºC

Extreme High Temperature

ºC

ºC

ºC

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83

extreme high temperature conditions, it is necessary to analyze the failure mechanism and characteristic degradation of device.

2.1 Generation of Extreme High Temperature Condition In order to analyze and verify the failure mechanism of SiC MOSFET under extreme high temperature conditions, many domestic and foreign scientific research institutions have carried out a lot of research. Extremely high junction temperature can be achieved through external environment heating [13–16] or device self-heating effect, such as short circuit, avalanche and surge conditions [2, 17–28]. The advantages of external environment heating are that the real-time temperature, temperature rise rate and peak value can be controlled artificially. They are helpful to study the failure mechanism of the device at specific temperature and temperature rise rate. But it is difficult to create an external high-temperature environment by reason of high costs. On the contrary, high junction temperature is easy to achieve by chip power dissipation. But it is difficult to monitor the junction temperature in real time. It is necessary to establish numerical simulation model in the TCAD simulation software in order to extract the lattice temperature and analyze the failure mechanism. The test schematic diagram of three working conditions using the self-heating effect is shown in Fig. 3. In this paper, the extreme high temperature conditions are mainly focused on the self-heating effect of devices. Under short circuit condition, the device under test (DUT) is subjected to bus voltage. The junction temperature rises sharply due to huge power dissipation under short circuit current. Different from the short-circuit condition, the voltage of DUT under avalanche condition is higher than the bus voltage. The instantaneous power dissipation at the moment of avalanche and the temperature rise rate are greater than that under short-circuit condition. Short circuit and avalanche conditions can even make the crystal lattice transient temperature above 1200 K. These two conditions are both aimed at the reliability of SiC MOSFET operating in the first quadrant, while surge condition is mainly aimed at the reliability of SiC MOSFET body diode. Under surge condition, the gate voltage of DUT should close channel so as to allow drain current just to flow through the body diode. Because the waveform of surge current is usually 10 ms sinusoidal half wave, the temperature rise rate is small. The influence of three conditions on the device is shown in Fig. 4.

2.2 Catastrophic Failures Mechanism Under extreme high temperature conditions caused by self-heating effect, chip level failure is main failure form. According to the failure device profile and drain current waveform, the failure modes of SiC MOSFET can be divided into thermal runaway

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DUT Vdc

DUT

C

Vdc

C

CVR

CVR

(a) Short circuit condition

(b) Avalanche condition auxiliary device Vdc DUT

CVR

(c) Surge condition Fig. 3 Extreme high temperature test schematic diagram

Vds/V

short circuit avalanche condition surge current condition

rise rate of lattice ºC

maximum lattice temperature/K

Ids/A

withstand time/μs

Fig. 4 Comparison of influence of SiC MOSFET under three types of extreme high temperature conditions

and gate source short circuit. In the case of thermal runaway, melting pits are formed on the surface of failure device. The drain current is out of control. In the case of gate source short circuit, there are no apparent damages and defects on the surface of failure device.

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Lattice Temperature

Fig. 5 Lattice temperature and failure mode after thermal runaway

Al Melt Point

Failure Time

Thermal Runaway After thermal runaway failure occurs, there are melting points on the source pad of chip. The internal lattice temperature can far exceed the melting point of Al, as shown in Fig. 5. In addition, the resistance among the drain, source and gate terminals is smaller [28]. At present, there have been a lot of literatures on the failure of SiC MOSFET due to thermal runaway under extreme high temperature conditions. Whether the cause of thermal runaway is parasitic BJT conduction remains to be discussed. Firstly, the short circuit condition of three kinds of 1200 V SiC MOSFET is compared experimentally. It is concluded that the leakage current of SiC MOSFET increases rapidly when the lattice temperature exceeds 700°C. Large leakage current causes parasitic bipolar junction transistor (BJT) to turn on, which makes the leakage current of the device uncontrolled, leading to thermal runaway. Then, the short-circuit condition is simulated based on TCAD. When the bus voltage is 800 V, the parasitic BJT turns on under the short-circuit condition, resulting in thermal runaway [25]. However, the P-Base/Drift region of SiC MOSFET has high doping concentration and low resistivity. The built-in potential of SiC P–N junction is about 3 V. Under these two factors, BJT is difficult to turn on under avalanche conditions. The reason for thermal runaway is that high energy dissipation makes the local junction temperature too high [19, 21]. Therefore, whether the thermal runaway is completely attributed to parasitic BJT conduction needs further comparatively study. Thermal runaway failure also depends on the SiC MOSFET gate structure and case temperature. By comparing the failure mode of planar and trench SiC MOSFET under short circuit conditions, it is found that the failure mode of planar SiC MOSFET must be thermal runaway. But the double trench SiC MOSFET behaves as thermal runaway failure only when the case temperature is high. The failure mode of asymmetric trench SiC MOSFET is always thermal runaway, independent of case temperature [22, 28].

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D

G

fault

G

S

S

Fig. 6 Gate-source short circuit failure

Gate-Source Short Circuit The second failure mode of SiC MOSFET under extreme high temperature is gatesource short circuit. After the encapsulation material is removed, there is no apparent difference between the failed chip and the healthy chip. The reason of gate source short circuit is that the chip temperature exceeds the melting point of source metal Al (660°C), causing Al to melt. Meanwhile, the internal stress of gate oxide increases under electric-thermal–mechanical stress, causing oxide to crack. The melted Al diffuses and fills the cracks, resulting in gate source short circuit, as shown in Fig. 6. After short circuit failure, the cell of the device is analyzed using Focused-Ion Beam (FIB) technique, which shows that the gate oxide cracks and metallic luster appeared at the cracks, as shown in Fig. 6. Then, the elements at the cracks of the gate oxide are detected using EDX technique. The Al element is found at the crack [20, 25]. During the short circuit, a lot of hot holes are generated in the drift region and injected into the gate oxide, forming continuous hole current and leading to the breakdown of the gate oxide [22]. Through the simulation analysis of the failure mechanism of different gate structures, high power dissipation is generated under the surge current stress, resulting in lattice temperature exceeding Al melting point. The failure mode of device is gate-source short circuit [24, 27]. As for avalanche condition, there is no research to explain the failure mode as gate-source short circuit.

2.3 Characterizations Even if the device does not suffer catastrophic failure under extreme high temperature conditions, its electrical characteristics can degrade. Throughout the life of the power semiconductor, the external electrical characteristics of device have great influence on the reliable operation of power electronic system. No matter how the junction temperature of the power semiconductor is increased, the electrical characteristics changes with temperature are the same. This section mainly summarizes the degradation of electrical characteristics of SiC MOSFET under extreme high temperature in the existing literature, so as to provide reference for the application of extreme high temperature.

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Through high temperature experiment, dynamic and static electrical parameters of SiC MOSFET are tested, as shown in Fig. 7. In terms of static electrical parameters, on resistance and threshold voltage are mainly affected. On resistance Rds(on) is mainly

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Specific Ron (m Ω·cm2)

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Junction Capacitance (pF)

100

Tj (K)

12 9 6 3

0 100

200

300

Tj (K)

(f)

Fig. 7 Variation of electrical characteristics with junction temperature a On-state resistance [29] b Threshold voltage [15] c Junction capacitance [16] d Switching energy [30] e Reverse recovery waveform [16] f Body diode voltage drop [16]

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composed of channel resistance Rch and drift region resistance Rd , both of which are affected by electron mobility. As temperature increases, electron mobility decreases and on resistance increases [29], as shown in Fig. 7a. The relationship between threshold voltage and temperature is not constant. Under extreme high temperature, the curve of threshold voltage changing with junction temperature slows down, as shown in Fig. 7b [2, 15]. Below 200°C, the threshold voltage changes with temperature at a rate of −9 mV/K, but when the temperature exceeds 200°C, the threshold voltage changes with temperature at a rate of −2 mV/K. When the temperature increases, the junction capacitance increases and the switching speed of the device decreases, as shown in Fig. 7c [16]. The switching energy of SiC MOSFET changes little at high temperature, as shown in Fig. 7d. So the influence of switching energy can be ignored [30]. When the temperature increases, the body diode voltage drop of SiC MOSFET decreases. But because its initial value is much greater than that of SiC SBD, the power dissipation generated by the diode at high temperature is still high, as shown in Fig. 7f. As shown in Fig. 7e, the reverse recovery performance of the body diode is mainly affected by the lifetime of minority carriers. As the junction temperature increases, the reverse recovery performance of the body diode becomes more severe and the drop rate of voltage increases. Therefore, using SiC SBD as freewheel diode in high temperature bidirectional power conversion circuit can significantly reduce the power dissipation [16].

2.4 Withstand Capability Under extreme high temperature conditions such as short circuit, avalanche and surge, the factors affecting device reliability include bus voltage, inductance, short circuit time, avalanche time, surge current, etc. However, the key parameter causing device failure is the energy that the device is finally subjected to. It even determines the failure mode of the device. To analysis the withstand capability of SiC MOSFET, it is essential to aware how much energy the device bears. The safe working area of the device is characterized by the withstand energy. The higher the temperature, the lower the maximum avalanche energy that the device can withstand. It is essential to study the maximum withstand avalanche capability that the device can withstand under different case temperature to determine area of safe operation at different ambient temperature [21]. Avalanche energy is an important factor in the failure which determines the final temperature of the device. The failure mode is also affected by the peak avalanche power. Because the higher the peak avalanche power is, the faster the junction temperature rises [22]. Therefore, avalanche withstand capability under different peak power needs to be studied, as shown in Fig. 8 [19]. The higher the case temperature is, the lower the peak power and avalanche withstand capability of the device are. It shows an approximately linear relationship.

Review of SiC MOSFET Failure Analysis … Fig. 8 Relationship between withstand avalanche energy and peak power

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Avalanche Energy (J/cm 2)

Peak Avalanche Current Density (A/cm 2)

However, this characteristic is also related to the device structure. The asymmetric trench and planar SiC MOSFET show linear relationship, as shown in Fig. 9, while the double-trench structure shows a trend of first increasing and then decreasing [19, 28, 31]. Compared with the high voltage and low current stress under avalanche, the devices under short circuit are subjected to low voltage and high current stress. The failure mode of short circuit also depends on energy and peak power. As shown in Fig. 10, the relationship between energy and peak power under short-circuit condition is the same as that under avalanche condition. The short-circuit energy basically remains unchanged when the temperature rises to a certain degree, as shown in Fig. 11 [18, 23].

5.5

600 280

320

360

400

440

5.0 480

Temperature (K)

Fig. 9 Comparison of temperature-dependent peak avalanche current density and avalanche energy [21]

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Fig. 10 Relationship between withstand short circuit energy and peak power

E sc/J

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15

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Ppeak/kW

Fig. 11 Withstand short circuit energy at different case temperatures

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At present, there is no research on the surge reliability of SiC MOSFET at different case temperatures. The surge experiment at room temperature can also increase the chip temperature, even as high as 1000 K [27]. It can be seen from Table 1 that the withstand surge energy of body diode is related to the device structure [24]. SiC JMOS and SiC DMOS refer to monolithic schottky barrier diode integrated SiC MOSFET and Planar MOSFET respectively. Surge Capability is equal to I max /I rated . SiC JMOS can withstand the lowest surge energy density, and its withstand surge capability is weak. Asymmetric trench gate structure can withstand the highest surge energy density. In Table 1, AT and DT refer to Asymmetric Trench and Double Trench respectively. Although the device types in Table 1 are only single-tube, the conclusions are the same for the high- power modules composed of these chips.

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Device type

Surge capability

Surge energy density/(J/mm2 )

SiC AT-MOS 13A

4.23

3.41

SiC DT-MOS 17A

3.53

1.75

SiC JMOS 25A

3.4

0.427

SiC DMOS 25A

7.6

0.885

Because the failure under extreme high temperature condition originates from the chip, not from the packaging material.

3 Failure Analysis Under High Frequency With the development of high power density converter, the switching frequency of power semiconductor is required to be higher and higher. High frequency conditions can be understood as high switching speed and multiple switching in a short time. Under the condition of high frequency, the parasitic parameters of the packaging structure have a great impact on the reliable operation of SiC MOSFET, as shown in Fig. 12. These problems exist in every high-speed switching process of SiC MOSFET. At a certain switching frequency, when the SiC MOSFET must switch as fast as possible, these problems become prominent. Parasitic parameters of the power circuit can trigger overshoot and oscillation of the drain voltage and current, which challenges the blocking voltage of device. Parasitic parameters of the control circuit can cause gate voltage oscillation, gate structure damage, and driver chip triggering mistakenly. The crosstalk and radiated EMI problems are caused by the parasitic parameters of power loop and control loop. Condition: Extremely Fast Switching Parasitic Parameters of Control Loop

Gate Drive IC False Triggering Gate Voltage Overshootand Oscillation

Parasitic Parameters of Power Loop

Crosstalk Radiated EMI Issues

Drain Voltage Overshoot Drain Voltage and Current Oscillation

Fig. 12 Reliability problems caused by parasitic parameters under high frequency

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3.1 Potential Failure Analysis of Power Circuit In the application circuit of SiC MOSFET, parasitic parameters such as inductance, capacitance and resistance are inevitably introduced in both power loop and control loop. These parasitic parameters can affect the reliability of the device during the fast switching process. To analyze the effects of different parasitic parameters, the switching equivalent circuit of SiC MOSFET with parasitic parameters is first established, as shown in Fig. 13. The oscillations of drain voltage and current during the turn-on process are mainly caused by the energy exchange among the drain parasitic inductor L d , loop parasitic inductor L loop and diode parasitic capacitance C J . The oscillations of drain voltage and current during the turn-off have nothing to do with the diode junction capacitance. The reason of oscillation is mainly the energy exchange among the drain parasitic inductor L d , the loop parasitic inductor L loop and the output capacitor C oss of the device. The output capacitance still varies with the turn-off voltage [32, 33]. The reason of overshoot of the drain current during the turn-on is the charge of the diode junction capacitor C J . The overshoot amplitude is determined by the drive circuit resistor R, gate-source capacitance C gs and diode junction capacitor C J [6, 33]. Multiple overshoots of the current in a short time can cause reliability problems. High dI d /dt on L s and L d can cause overshoot of drain voltage [34]. Drain overvoltage is the main factor affecting device selection. High margin of blocking voltage brings high cost while low margin may reduce reliability. Therefore, attention should be paid to the influence of parasitic parameters of drain overvoltage [35]. High dV d /dt can generate displacement current between the N-drift region and the P-source region inside the device. When the displacement current makes the parasitic Lloop Lload

+Vdc Cf Ld Cgd Rg

Lg Cds

Singal Gate Drive IC

Cgs Ls

Fig. 13 SiC MOSFET switch equivalent circuit model with parasitic parameters

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BJT turn on, thermal runaway failure occurs [36]. In addition, when the loads are reactive load, the output capacitor C oss also causes the oscillation and overshoot of the load current. The charge and discharge of the output capacitor during the switching transient process can also cause the difference between the channel current and the drain current, resulting in the inaccuracy of the traditional switching loss model [7, 37–39]. Parasitic parameters don’t only affect the device itself, but also increase the probability of coupling failure due to near-field radiation in high integration circuits. Literature [40] has measured the near field radiation of the SiC MOSFET module in the Buck converter. It is found that the current loop antenna composed of the drain and source electrode of power semiconductor module can produce 30–100 MHz near field radiation.

3.2 Potential Failure Analysis of Control Circuit The main problems affecting the reliability of the control circuit are cross talk, oscillation and overshoot of gate voltage, and drive IC error trigger. The crosstalk problem is caused by the miller capacitor C gd coupling the control side and the power side together. When the power side voltage fluctuates, the Miller current can affect the gate voltage, and even lead to direct conduction between the upper and lower bridge [41, 42]. The gate overvoltage is mainly determined by the gate circuit resistance Rg and parasitic inductor L g . Smaller Rg and larger L g lead to greater overvoltage and greater stress on the gate oxide. Repeated stress accumulation under high frequency may reduce the device lifetime [43]. The oscillation of gate voltage is mainly determined by gate parasitic resistance Rg , gate parasitic inductor L g , common source parasitic inductor L s and gate parasitic capacitance C gs . With a greater Rg , the attenuation rate of gate voltage oscillation increases and the switching speed of the device decreases. The C gs determines the amplitude of the oscillation of the gate voltage, while L s determines the attenuation rate of the second-order oscillation of the gate circuit. Increasing L s can reduce the oscillation of the gate voltage, but it still reduces the stability of the gate circuit [41]. When multiple chips are connected in parallel, the gate-source capacitance C gs and parasitic inductor L g of multiple drive loops in the module can also be coupled to each other, which results in gate voltage oscillation. The common mode noise introduced by the gate circuit oscillation can also cause the false trigger of the gate drive IC [42]. Unlike EMI problem caused by parasitic parameters of the power loop, radiation interference of 150-500 MHz can be generated by a dipole antenna composed of the gate-source control loop and the gatesource connection terminal [40, 44]. Therefore, in order to turn on SiC MOSFET as quickly as possible and reduce the oscillation and overshoot of voltage and current, C gd , L g , L d and L s should be reduced as far as possible and C gs should be increased. Since Rg is easy to change, the hierarchical driving mode can be adopted [45]. In summary, the impact of parasitic parameters on reliability is shown in Table 2. The

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Table 2 Effect of parasitic parameters on reliability Parasitic parameters

Problems

Correlation

Seriousness

Rg

Oscillation of gate voltage; Oscillation amplitude of drain voltage and current

Negative

★

C gs

Oscillation of gate voltage

Negative

★★

C gd

Crosstalk

Positive

★★★★

C ds

Oscillation of load current; Oscillation of gate voltage

Positive

★★

Cf

Frequency of gate voltage oscillation

Negative

★

L bus

Frequency of gate voltage oscillation

Negative

★

Ls

Overshoot of drain voltage

Positive

★★★★

Ld

Overshoot of drain voltage; Oscillation of drain voltage and current

Positive

★★★

Lg

Oscillation of gate voltage

Positive

★★

seriousness is mainly determined by the impact of the problems on the lifetime of the SiC MOSFET. For instance, the crosstalk causes the device to fail quickly, while the gate voltage oscillation may not cause the device to fail in a short time.

4 Failure Analysis Under Irradiation Due to the wide bandgap of SiC material, the theoretical irradiation resistance of SiC power semiconductor is stronger than that of Si power semiconductor. The failure effect of SiC MOSFET in space environment can be divided into total ionization dose effect (TID), single event burnout effect (SEB) and single event gate rupture effect (SEGR), as shown in Fig. 14. Single event burnout and single event gate rupture failure are mainly caused by heavy ions and neutrons. Total ionizing dose failure is mainly caused by high energy electrons, protons and γ rays.

4.1 Total Ionization Dose Catastrophic Failure Mechanism When the SiC MOSFET is irradiated by electron, proton or γ ray, the regions of damage are mainly gate oxide and semiconductor region. A mass of electron–hole pairs are produced inside the gate oxide. Under the action of electric field, since the drift velocity of electrons is faster than that of holes, electrons can be swept out of the gate oxide quickly, while holes can be captured by traps.

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Fig. 14 Failure analysis under irradiation

Reliability of SiC MOSFET Under Irradiation Conditions Irradiation: Electron, γ ray, Proton Gate Oxide Degradation

TID

As a result, a large number of holes exist in the gate oxide. At the same time, the interfacial density of SiC/SiO2 also increases. As for the semiconductor region, irradiated N-type doped semiconductor is embedded in the acceptor center, resulting in the degradation of carrier lifetime and mobility [11, 46–48]. Characterizations The damage of total ionizing dose effect on SiC MOSFET mainly depends on the irradiation particle energy and irradiation dose. The high energy particle has long penetration distance and causes serious damage to the device. The characteristics of device can degrade at the small irradiation dose. When the energy of irradiated particles is smaller, the higher dose is needed to produce the same degradation of device characteristics. Literature [11, 46] respectively studied the degradation of threshold voltage under the irradiation of 0.9 meV and 4.5 meV electrons. The results show that when the degradation effect is the same, irradiation dose of 0.9 meV is two orders of magnitude more than that of 4.5 meV. According to the analysis of failure mechanism in 4.1.1, the on-resistance and threshold voltage degrade by ionization damage. The degradation situation is shown in Fig. 15. Irradiated particles with different energies only affect the change rate of electrical characteristics, but the overall change trend can not change. The threshold voltage decreases due to the increase of the hole concentration inside the oxide. Then it goes back to initial value due to the negative charge embedded in the electron trap at the SiC/SiO2 interface. The on-resistance decreases slightly and then increases. Initially, the channel resistance decreases slightly owing to the smaller threshold voltage. With smaller carrier concentration, mobility, and effective cross-sectional area of JFET region, on-resistance then increases due to greater resistance of drift region and JFET region [47].

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Fig. 15 Degradation of threshold voltage V th and on resistance Rdson

Vth/V

Rdson /Ω

Datasheet Limit

0

0

0 TID(kGy)

Effect Factors In addition to the electron energy and irradiation dose mentioned in 4.1.2, the drain leakage current in the initial status of the device also affects the degradation results. If the initial drain leakage current is larger, the threshold voltage drift will be higher under the same irradiation conditions [11]. Gate oxide thickness and manufacturing technology can also affect the anti-irradiation performance [46].

4.2 Single Event Burnout Different from the effect of total ionizing dose, the single event burnout failure mainly results from heavy ions with energy about 250 meV, such as Br, I, Fe, Ni, Kr, impinging on SiC MOSFET, as shown in Fig. 16. Catastrophic Failure Mechanism Under heavy ion irradiation environment, the failure mechanism of Si MOSFET may be that the transient current generated by high-energy ions hitting the device causes the parasitic BJT turning on [8]. The single event burnout failure mechanism of SiC MOSFET is still discussed. When the SiC MOSFET is exposed to heavy ion irradiation, it can undergo three regions: charge collection region, leakage current increase region and single event burnout region, as shown in Fig. 17. The drain voltage at the failure point generally does not exceed half of the rated voltage of the device [49]. Some researchers believe that when heavy ions collide with devices, Si and C can occur recoil, and the recoil energy can generate a mass of electron–hole pairs in the collision path. With high drain-source voltage, the electrons can move towards the drain electrode and the holes can move towards the source electrode. As a result, the drain leakage current forms. When the PN junction formed

Review of SiC MOSFET Failure Analysis … Fig. 16 Single event burnout failure

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-Vgs Gate

Gate

Source

N

N P

Direction of Electron Movement

Direction of Hole Movement

N-

N+ Drain

Failure

Region 3 Drain Leakage Current

Fig. 17 Three damage regions under heavy ion irradiation [54]

+Vds

Region 2

Region 1

Drain Bias Voltage

by the channel/base and source/emitter is forward bias, the current flowing through the source region is amplified. The accumulation of joule heat increases the lattice temperature near the drain electrode. At the same time, the electric field inside the device can be redistributed. The peak value of the electric field intensity can move from the N+ source region/P base region to the N- drift region/N+ substrate, which accelerates collision ionization and forms positive feedback with BJT. It causes the lattice temperature to exceed 1500°C and thermal runaway [8, 49–53]. However, some researchers found that SiC MOSFET and SiC diode have the same single event burnout threshold voltage. They think that the failure mechanism of both SiC MOSFET and SiC diode is the same. However, there is no parasitic BJT inside the SiC diode. Therefore, there is second one failure mechanism for single event burnout failure. It is local thermal failure due to avalanche induced by current. When

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Fig. 18 Comparison of single event burnout failure results before and after eliminating parasitic BJT [56]

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10-11

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heavy ions collide with SiC MOSFET, a large current is formed in a short term. This current can increase the electron concentration near the N−/N+ interface. Then the electric field in the diffusion region of the N+ source region is broken down. As a result, huge power dissipation is generated inside the device and SEB failure occurs [55, 56]. In order to illustrate that parasitic BJT conduction is not a key factor for single event burnout failure, the N+ source region is removed in the simulation, which eliminates parasitic BJT inside of the device. But the lattice temperature and failure current have no significant change when the single event burnout failure occurs, as shown in Fig. 18. Characterizations When the device is irradiated by heavy ions, the single event burnout failure can not occur under low drain bias, but its electrical characteristics degrades, as shown in region 1 and 2 in Fig. 17. This section mainly summarizes the degradation of the electrical characteristics of the device when the drain bias voltage is lower than the single event burnout threshold. The mode of device characteristic degradation is that the leakage current of drain and gate increases and the blocking ability decreases [9, 57, 58]. When V ds < 1/3V ds,rate , small damage points are formed inside the gate, and the number increases with the increase of irradiation dose. These small damage points are equivalent to small conductive paths, making the current flow between drain and gate. When 1/3V ds,rate < V ds < 1/2V ds,rate , the structure of drain electrode is damaged. The leakage path is mainly formed by the drain and source electrode. These conductive paths are formed due to collision between two adjacent particles and device. The first particle hits the device, causing damage. Then the second particle activates the damage point, causing the resistance path to be formed at the damage point.

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Effect Factors In the single event burnout failure, the key factors that affect the SEB failure include the incident position of the particles, the linear energy transfer (LET) of the device under test, and the drain voltage bias. For planar SiC MOSFET, its JFET region is the most sensitive to single event burnout failure. When heavy ions impact to JFET region, a large number of holes are more likely to inject to the source horizontally, which is easy to make the base-emitter forward bias and parasitic BJT turn-on [8, 59]. However, when heavy ions incident in other regions, more energy is needed to make the deposited charge diffuse to the sensitive region to trigger parasitic BJT [49]. When the LET of heavy ions is low, SEB is sensitive to both LET and V ds . As the energy of incident particles exceeds a certain value (LET > 20 meV/cm2 /mg), the drain bias voltage of SEB failure no longer decreases. When the drain bias voltage is the failure threshold voltage, the single event burnout failure occurs, as shown in Region 3 in Fig. 17. As the drain bias voltage of the SiC MOSFET continues to increase, the failure in time (one FIT equals one failure per billion hours) rate of SEB failures increases exponentially with the drain bias voltage [60].

4.3 Single Event Gate Rupture The single event gate rupture and single event burnout failure are caused by the same irradiated particles. They are both produced by the irradiation of heavy ions and neutrons, but the impact positions of two failure are different. The single event gate rupture failure is caused by heavy ions impinging the gate oxide region, as shown in Fig. 19. Catastrophic Failure Mechanism In the failure mode of single event burnout, the leakage current of the drain electrode is large [61]. However, the single event gate rupture failure occurs, because the electric field strength in gate oxide exceeds the breakdown electric field limit. The equation of critical breakdown field strength is shown in Eq. (1) [62]. E cr =

E0 1 + L E T /B

(1)

The increase of electric field intensity in gate oxide mainly comes from two aspects [10, 52]. First, heavy ions passing through the device produce a mass of electron– hole pairs along particles trajectory. When the heavy ions pass through the epitaxial layer of the device, the concentration of the electron–hole pairs can be greater than the doping concentration of the epitaxial layer. Therefore, the electric field along the path of the particle trajectory is suppressed. Under the condition of constant voltage, the electric field in the gate oxide increases, as shown in Fig. 20. With the increase

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Heavy Ion -Vgs Source

Source

Gate N P

N P

Direction of Electron Movement

Direction of Hole Movement

N-

N+

Drain

+Vds

Electric Field/(V/cm)

Electric Field/(V/cm)

Electric Field/(V/cm)

Fig. 19 Single event gate rupture failure

oxide Epitaxy

oxide Epitaxy

oxide Epitaxy

Substrate Ecr Heavy Ion

Longitudinal Length of the Device Substrate Ecr

Heavy Ion

Longitudinal Length of the Device Substrate Ecr

Longitudinal Length of the Device

Fig. 20 Variation of electric field along the trajectory of particle

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of the incident distance of heavy ions, the electric field in the gate oxide gradually increases. As a result, the electric field strength is the greatest when the heavy ions penetrate the device. Second, a mass of electron–hole pairs are generated in the gate oxide after heavy ions impact the device. The electrons are swept out axially and the holes are captured by the traps in the oxide, which further increases the electric field in the gate oxide. Characterizations When the internal electric field does not cause oxide breakdown, the device can not suffer from single event gate rupture failure. But its electrical characteristics can degrade. For example, the gate leakage current increases [57, 63]. The gate leakage current increases mainly owing to the potential damage of the gate structure. Literature [57] compares the variation of the gate leakage current and the gate voltage of SiC MOSFET before and after irradiation. The results show that the larger gate leakage current appears when the irradiated device is lower than the initial gate breakdown voltage. Effect Factors The factors that affect the single event gate rupture failure mainly include the impact position and angle of heavy ions, the thickness and quality of the gate oxide and the voltage of drain and gate bias during irradiation. It is difficult for holes to flow out from the source electrode when heavy ions vertically impact the middle position of gate oxide. In this case, the electric field intensity inside gate oxide is the highest [61, 64, 65]. When the incident angle of heavy ion is gradually parallel to the gate oxide, the resistance to single event gate rupture failure is gradually enhanced. With the incident angle exceeding 60°, the single event gate rupture failure basically does not occur [65]. The influence of particle LET value on the single event gate rupture failure is the same as that of the single event burnout failure [61]. For the device under test, the thicker the gate oxide is, the smaller the electric field strength is under the same voltage, and the stronger the resistance to single event gate rupture failure is [66]. The separation speed of electron–hole pairs and the duration of the transient electric field strength in the oxide are both affected by the drain bias voltage during irradiation [67].

5 Improving Reliability Under Extreme Conditions Although the intrinsic temperature of SiC material is high, the melting point of most packaging materials is far lower than that of SiC. The problem of reliability under extreme high temperature conditions can be improved from the following three aspects. First, packaging materials with higher melting point can be used so that they do not diffuse into the gate oxide crack and cause gate-source short circuit. Secondly, the long-term reliability at high temperature can be improved by enhancing the ability to withstand mechanical stress [68]. Third, in order to reduce the risk

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of thermal runway, these measures can be adopted, such as increasing the doping concentration, carrier mobility, active region area and drift region thickness [18]. The key factor limiting the high frequency operation of SiC MOSFET is the influence of parasitic parameters. In order to make the SiC MOSFET switch as fast as possible, the following measures can be taken. The package structure and gate drive layout are optimized to reduce parasitic parameters of the drive loop. In addition, the driver chip and power chip are integrated [7, 34, 45]. The RC buffer is added to suppress the oscillations of drain voltage and current during the switching process [32]. In order to eliminate the effects of crosstalk, voltage overshoot and reverse recovery and increase the switching speed limit, the parasitic capacitance of the chip needs to be optimized and the ratio of C gs to C gd needs to be increased [5, 69]. Modeling EMI noise and designing filter can reduce common mode noise and radiation interference at low cost [44, 70–72]. In general, irradiation damage is mainly caused by the external environment, so the easiest way to block radiation particles is to add anti-radiation materials. It allows the irradiated particles to deposit maximum energy in the shielding layer, so that the energy of particles entering the device is reduced [66]. From the perspective of device structure, the high doping buffer layer can be added to reduce the peak electric field intensity inside the device, reduce the collision ionization at the N-drift region /N+ substrate junction, increase the difficulty of parasitic BJT conduction, and enhance the ability of anti-single event effect [8, 50, 56, 61]. In addition, the irradiation damage to devices mainly comes from the generation and separation of a mass of electron–hole pairs. The anti-irradiation performance can be improved by enhancing the recombination ability of electron and hole or by making hole current flow out in other ways [17, 24]. Finally, redundant systems can be used to improve the reliability of the system in severe reliability applications.

6 Conclusion In applications based on SiC MOSFET, there is a problem of excessive margin, which makes the device performance unable to be fully utilized. When the device operates under extreme conditions, the reliability of the device is prominent. The failure analysis of SiC MOSFET under extreme temperature, extreme switching speed, and strong radiation is focused on. Failure reasons of SiC MOSFET can be divided into internal causes (defect, overheating, breakdown) and external causes (harsh environment). The study of high temperature, high frequency and irradiation conditions can provide basis for the failure mechanism and moment of SiC MOSFET in practical application. The reliability problems of SiC MOSFET under extreme conditions are systematically described. The existing researches are summarized from three aspects of failure mechanism, characteristic degradation and external influence factors. The main conclusions are as follows.

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The failures caused by high temperature and high frequency conditions are attributed to internal factors. The reason of failure under high temperature condition is the increase of lattice temperature owing to the self-heating of the device. The failure modes are mainly thermal runaway and gate-source short circuit. At the same time, the degradation of the electrical parameters under high temperature condition, such as threshold voltage, on-resistance, and junction capacitance, is summarized. Under high frequency condition, high dv/dt and di/dt can cause overshoot and oscillation of voltage and current, which can reduce reliability. The failures caused by irradiation are attributed to external factors. The reason of failure is thermal failure or electric field breakdown caused by the impact of irradiated particles. Acknowledgements This work was supported by JCJQ Program (2020-JCJQ-ZD-105) and the Natural Science Foundation of Hubei Province (2020CFB806).

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Power Converter Topologies and Control

Non-singular Terminal Sliding Mode Control Algorithm for DC/DC Boost Converter System Based on a Finite-Time Convergent Observer Mengmeng Qi, Ying Shu, Chao Wan, Jiahong Lang, and Shicheng Zheng

Abstract This brief proposes a control strategy to regulate the DC/DC Boost converter system affected by line and load uncertainties. The objective of regulating the output voltage in the presence of uncertainties in input voltage and load is met by proposing a non-singular terminal sliding mode control (NTSMC) method combined with a finite-time convergent observer (FCO). The stability of the controller in tracking the reference voltage and regulation of the output voltage is analyzed. Extensive simulations comparison results are implemented to verify the effectiveness of the proposed control method. Keywords Non-singular terminal sliding-mode control (NTSMC) · Finite-time convergent observer (FCO) · The DC/DC Boost converter system · Circuit parameter uncertainties and disturbances

1 Introduction DC/DC converter systems have been universally used as main output voltage supplies in modern industry such as DC microgrids, uninterruptible power supplies, electric vehicles systems, wind energy systems etc. Among them, the DC 24 V power supply system is a commonly used power supply system for industrial systems. It is generally used as the main power supply or backup power supply for the control system, and plays a very important role in the control system [1–3]. As a matter of fact, the DC/DC converters with switching operation are essentially variable-structure systems, the design of high-quality DC/DC converters control algorithms has become research hotspot [4]. In [5], the voltage jumps produced by multiple switching devices and parasitic parameters existing in the electrical components have been considered in the prediction model for the electro-magnetic interference in a DC/DC converter. Besides, the disturbance of input voltage and load resistance variation, e.g., the voltage of photovoltaic power systems is closely related to the intensity of sunlight, M. Qi · Y. Shu · C. Wan · J. Lang · S. Zheng (B) Anhui University of Technology, Ma’anshan, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_9

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which could affect the actual value of the input voltage in DC/DC converters [6]. As a consequence, it is significant for the DC/DC converter systems to exhibit superior control performance such as lower overshoot, strong disturbance rejection ability, faster transient response and guaranteed stability. For the DC/DC converter systems, many typical control algorithms were employed to strengthen the system performance, synergetic control method [7], fuzzy logic control method [8], predictive control method [9], sliding-mode control method [10–16] etc. As a commonly used nonlinear method, sliding-mode control (SMC) has been verified to be a more suitable option than other control methods for its variablestructure characteristics [10]. In [11], a new terminal sliding model controller based on energy storage function is designed for Boost converter. However, the change of circuit parameters is not considered in this paper. In [12], an adaptive terminal sliding mode control (TSMC) strategy was used to enhance the anti-disturbance capability for the Buck system. Later In [13], a non-singular terminal sliding-mode control (NTSMC) approach based on literature [12] was used for controlling the Buck converter to avoid the singularity. In [14], by using a new sliding discrete-time approximation strategy, a nonlinear digital controller was presented to improve the output voltage tracking capability for the Boost converter. In order to achieve the disturbance compensation for the Buck converter, a sliding mode controller with extended state observer was designed in [15]. By using the linear active disturbance rejection control theory, the unknown circuit parameters problem of the Boost converters could be solved by the proposed cascade control strategy [16]. In this brief, a finite-time convergent observer (FCO)-based NTSMC algorithm is proposed to handle the problem of parameter uncertainties for the DC/DC Boost converter. Besides, the entire controller design procedures could be divided into three parts. Firstly, based on the Boost circuit schematic, a state-space averaged model for the whole algorithm design could be obtained. Next, for the parameter uncertainties, the estimation values of unknown load resistance and input voltage could be obtained with the finite-time convergent observer theory. Then, considering the nonminimum phase characteristic of DC/DC Boost converter, an energy storage function method is adopted to design the non-singular terminal sliding mode (NTSM) surface. Moreover, the constant switching frequency achieved by pulse width modulation (PWM) also avoid the disadvantages of traditional hysteresis modulation. As a result, the proposed (FCO)-based NTSM controller is developed. The advantages of the proposed scheme are: (1) direct output voltage control (2) assured constant switching frequency without any additional hardware (3) robustness against line, load uncertainties and can track the reference voltage.

Non-Singular Terminal Sliding Mode Control Algorithm for DC/DC … Fig. 1 The circuit schematic of Boost converter

iL

111

L D

Vin

Sw

V0 C

R

2 Mathematical Modeling and Traditional NTSMC Method 2.1 Mathematical Modeling Figure 1 shows a Boost circuit schematic, where L represents the inductor, C represents the capacitor, R represents the load resistance, D represents a freewheeling diode, S w represents a controlled power switch, and V in , iL , V o represent input voltage, inductor current and average output voltage, respectively. For the DC/DC Boost converter, the state-space averaged model is given by ⎧

L i˙L = Vin − (1 − μ)Vo C V˙o = (1 − μ)i L − θ Vo

(1)

where, θ = 1/R, and μ is the control input, that is, the duty cycle of the switch S w , which satisfies μ ∈ [0, 1].

2.2 Traditional NTSMC Method In this section, the energy storage function model will be employed to handle the nonminimum phase problem existing in the Boost converter system. The energy storage function is designed as ϕ1 =

1 2 1 Li + C V 2 2 L 2 o

(2)

where, ϕ1 is the total system energy, coming from energy storage elements in Boost converter, i.e., inductor L and capacitor C. Then, for energy storage system (2), its first derivative and second-order derivative can be expressed as ⎧ 2 ⎨ ϕ˙1 = Vin i L − Vo θ 2 2 2 ⎩ ϕ¨1 = −(1 − μ)( 2Vo i L θ + Vin Vo ) + 2Vo θ + Vin C L C L

(3)

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For the above system (3), when the system is in steady state, that is to say, ϕ˙1 = ϕ¨1 , the corresponding expressions of reference inductor current iLref and reference output voltage V ref can be given by ⎧ ⎪ ⎨i ⎪ ⎩

Lr e f

Vr e f

=

Vr2e f

Vin = Vr e f

θ

(4)

Substituting (4) into system (2), then the corresponding reference value of total system energy ϕ1r e f in steady state could be written as 4

ϕ1r e f =

1 1 Vr e f 1 1 2 Li Lr e f + C Vr2e f = L 2 θ 2 + C Vr2e f 2 2 Vin 2 2

(5)

Defining an energy error e1 = ϕ1r e f − ϕ1

(6)

Then its derivative can be calculated as e˙1 = Vo2 θ − Vin i L

(7)

Let e2 = e˙1 , then its derivative can be got as ( e˙2 = (1 − μ)

2Vo i L θ Vin Vo + C L

)

( −

V2 2Vo2 θ 2 + in C L

) (8)

By combing (7) and (8), the dynamic model of energy error is given by ⎧ 2 ⎪ ⎨ e˙1 = Vo θ − Vin i L ( ) ( 2 2 ) Vin2 Vin Vo 2Vo i L θ 2Vo θ ⎪ + + e ˙ = − μ) − (1 ⎩ 2 C L C L

(9)

Then, the nominal NTSM surface function for DC/DC Boost converter could be designed as S = e1 +

1 p/q e β 2

where, β > 0, and p, q (p > q) are positive odd integers. Based on energy error system (9), then its derivative could be expressed as

(10)

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) p −1 1 p( 2 Vo θ − Vin i L q S˙ = Vo2 θ − Vin i L + βq ) ( 2 2 )⎤ ⎡( V2 Vin Vo 2Vo θ 2Vo i L θ + + in (1 − μ) − C L C L

(11)

In addition, aiming to eliminate the chattering and improve the reaching speed for NTSM controller, an exponential reaching law is proposed as S˙ = −εsgn(S) − ηS

(12)

where, a relatively small value of ε can be selected to weaken the high-frequency jitter of the system. At the same time, a relatively large value of η can be selected to increase the dynamic quality of the sliding mode. Theorem 1 The control law of the traditional NTSMC of DC/DC Boost converter is designed as LC u =1− Vo (Vin C + 2Li L θ ) ⎡ 2 2 ⎤ p V2 2Vo θ q + in − β (Vo2 θ − Vin i L )2− q − εsgn(S) − ηS C L p

(13)

3 Novel Sliding-Mode Controller Design 3.1 Design of Finite-Time Convergent Observer In this section, we use the finite-time convergent observer to obtain the estimated values of the unknown load and input voltage in the Boost circuit [17]. Theorem 2 Based on the above state-space averaged model, the FCO dynamics could be designed as ⎧ · |α1 ( )| iL θ ⎪ | | ⎪ ⎪ V = − μ) − V + k V sign V − V − V V (1 | | o 1 o o o o o o ⎪ ⎪ C C ⎪ ⎪ ⎪ · |α2 ( )| ⎪ ⎪ V V ⎪ ⎨ i L = −(1 − μ) o − in + k2 sign i L − i L ||i L − i L || L L · |α3 ( )| ⎪ ⎪ | | ⎪ ⎪ θ = −k V sign V − V − V | |V 3 o o o o o ⎪ ⎪ ⎪ ⎪ ⎪ |α4 ( )| ⎪ ⎪ · | | ⎩ Vin = k4 sign i L − i L |i L − i L | Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

Δ

(14)

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where, Vˆo , iˆL , θˆ , Vˆin are the estimate values of Vo , i L , θ, Vin , respectively; ˙ˆ V˙ˆ are the differentials of Vˆ , iˆ , θˆ , Vˆ , respectively. Based on [16, V˙ˆo , i˙ˆL , θ, in o L in Th.3.1], it can be seen that there are suitable gains k 1 , k 2 , k 3 , k 4 to make the system converge in a finite time, where k 1 , k 2 , k 3 , k 4 are appropriate positive gains;α1 > 0.5, α2 < 1, α3 = 2α1 − 1, α4 = 2α2 − 1.

3.2 Controller Design In this section, a novel FCO-based NTSM controller is designed for solving the unknown circuit parameter uncertainties problem of DC/DC Boost converter. A novel first-order NTSM manifold for system (9) with parameter uncertainties is designed as S1 = eˆ1 +

1 p/ q eˆ β 2

(15)

where, β > 0, and p, q (p > q) are positive odd integers, eˆ1 , eˆ2 are the estimate values of energy error e1 and its derivative e2 , respectively. The specific expressions of eˆ1 , eˆ2 could be expressed as ⎧ ( 2 )2 ( ) ˆ ⎪ ⎪ 1 1 2 1 2 2 ⎨ eˆ = 1 Vr e f θ + C Vr e f − Li + C V 1 2 2 L 2 o 2 Vˆin ⎪ ⎪ ⎩ eˆ2 = Vo2 θˆ − Vˆin i L

(16)

Similarly, the exponential reaching law shown in Eq. (12) is adopted. Take the derivative of S 1 and combine it with Eqs. (12 and 16). The proposed FCO-based NTSMC law is designed as u1 = 1 −

LC ∧

Vo (Vˆin C + 2Li L θ ) ⎤ ⎡ 2 ˆ2 p Vˆin2 q 2 2Vo θ 2− + − β (Vo θˆ − Vˆin i L ) q − ε1 sgn(S1 ) − η1 S1 C L p

(17)

where, ε1 , η1 > 0, then the accurate tracking of the given output reference voltage for the system could be achieved in a limited time. The control block diagram of the designed algorithm is shown in Fig. 2, in which the output voltage and inductor current could be measured with the help of sensors, and the proposed FCO will estimate the values for unknown load resistance and input voltage, then by combing the estimated values and NTSMC technology, the design of novel controller is implemented.

Non-Singular Terminal Sliding Mode Control Algorithm for DC/DC …

Vref

NTSMC

PWM

DC/DC Boost Converter

115

Vo iL

FCO Vin Fig. 2 Control block diagram of the designed algorithm

4 The Analysis of System Stability 4.1 The Analysis of Finite-Time Convergent Observer Stability Define estimation errors ω1 = Vo − Vˆo , ω2 = θ − θˆ , ω3 = i L − iˆL , ω4 = Vin − Vˆin

(18)

For the system of (18), by taking the time derivative of ω1 , ω2 , ω3 , ω4 , we obtain |α1 | ⎧ Vo | | ⎪ ω˙ 1 = − ω2 − k1 Vo sign(Vo − Vˆo )|Vo − Vˆo | ⎪ ⎪ ⎪ C ⎪ |α3 | ⎪ ⎪ ⎪ ⎨ ω˙ 2 = k3 Vo sign(Vo − Vˆo )||Vo − Vˆo || |α2 | ω4 ⎪ | | ⎪ ω˙ 3 = − k2 sign(i L − iˆL )|i L − iˆL | ⎪ ⎪ ⎪ L ⎪ | | ⎪ ⎪ ⎩ ω˙ = −k sign(i − iˆ )| − iˆ |α4 4 4 L L |i L L|

(19)

Defining the following Lyapunov function V =

1 2 1 2 1 2 1 Cω12 + ω2 + Lω3 + ω 2k3 2 2k4 4 2

(20)

Then its derivative could be expressed as V˙ = −k1 Vo Cω1 sign(ω1 )|ω1 |α1 − k2 Lω3 sign(ω3 )|ω3 |α3 = −k1 Vo C|ω1 |α1 +1 − k2 L|ω3 |α3 +1 ≤ 0

(21)

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where, ωsign(ω)|ω|α = |ω|α+1 . Therefore, it can be concluded from Lasalle’s invariant principle [18] that the whole error system (18) would reach steady state within a finite time if the observer gains (k 1 , k 2 , k 3 , k 4 ) are selected appropriately.

4.2 The Analysis of NTSM Controller Stability Substituting the control law into model (11), then the model (11) can be rewritten as p 1 p 2 (Vo θ − Vin i L ) q −1 [ − εsgn(S) − ηS] S˙ = βq

(22)

When e2 /= 0,then p 1 p 2 (V θ − Vin i L ) q −1 > 0 βq o

(23)

Defining a bounded function V 1 as V1 =

1 2 S 2

(24)

Then its derivative can be written as p 1 p 2 V˙1 = S S˙ = (Vo θ − Vin i L ) q −1 [ − εSsgn(S) − ηS 2 ] ≤ 0 βq

(25)

Therefore, it could be concluded that system (9) under the control law (13) will reach a steady state within a finite time. / Since lim V˙in = 0, lim R˙ = 0, θ = 1 R, therefore, t→∞

t→∞

θˆ ≡ θ, Vˆin ≡ Vin

(26)

Then using (24) and (26), we obtain the following equations eˆ1 ≡ e1 , eˆ2 ≡ e2

(27)

Therefore, it can be concluded that under the designed NTSM manifold (15) and proposed control law (17), the states of error system (9) would reach a steady state within a finite time.

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5 Simulation Results In this section, some simulations are provided to illustrate the features of the proposed FCO-based NTSM controllers for regulating the output voltage of the DC/DC Boost converter. The values of parameters used in the Boost converter are given in Table 1. In order to have a control performance comparison, traditional SMC control algorithm is employed here to be compared with the proposed FCO-based NTSMC scheme. Based on the MATLAB/Simulink, the parameters of the NTSMC + FCO controller are: β = 1000, ε = 200000, qp = 53 , η = 20000, α1 = 0.7, α2 = 0.6, α3 = 0.4, α4 = 0.2, k1 = 8000, k2 = 900, k3 = 100, k4 = 1000. The sliding mode surface function is designed as ∫ S = l1 I L + l2 Vo +

(Vo − Vr e f )dt

(28)

The sliding mode control law is designed as u=

1 (1 − sign(S)) 2

(29)

The parameters in SMC controller (28) are selected as l1 = 0.0025, l 2 = 0.0025. Figure 3 shows the simulated responses of output voltage when V ref drops from 24 to 20 V at 0.1 s. It is evident that the novel NTSMC + FCO control system has a better reference tracking ability. Figure 4 shows the simulated responses of output voltage when R rises from 45 Ω to 60 Ω and drops from 60 Ω to 45 Ω at 0.1 s. It is obvious that the novel NTSMC + FCO control system has a quicker respond speed and smaller voltage deviation. Therefore, compared with the traditional SMC control system, it is clear that the simulation results confirm the novel NTSMC + FCO control system is more superior in voltage regulation and anti-disturbance performance. Table 1 Values of parameters used in the Boost converter

Description

Parameter

Nominal value

Input voltage

Vin

12 V

Reference output voltage

Vr e f

24 V

Inductance

L

0.1 mH

Capacitance

C

2 mF

Load resistance

R

45 Ω

Switching frequency

f

20 kHz

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Fig. 3 Output voltage simulation waveform when V ref drops from 24 to 20 V

Fig. 4 Output voltage simulation waveforms during load variations a 45–60 Ω b 60–45 Ω

6 Conclusions The parameter uncertainties problem of the DC/DC Boost converter system has been studied in this paper. By utilizing the disturbance estimation technique based on FCO, a novel NTSM controller has been developed. The simulation results show that the output voltage not only has good dynamic and steady state performance, but also has strong robustness. Acknowledgements This research was supported by The University Synergy Innovation Program of Anhui Province (GXXT-2019-019).

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References 1. Park HH, Cho G-H (2014) A DC–DC converter for a fully integrated PID compensator with a single capacitor. IEEE Trans Circuits Syst II, Exp Briefs 61(8):629–633, Aug 2. Freitas A, Tofoli FL, J´unior EMS, et al (2015) High-voltage gain dc–dc Boost converter with coupled inductors for photovoltaic systems. IET Power Electron 8(10):1885–1892 3. Trevino BAM, Aroudi AE, Vidal-Idiarte E, et al (2018) Sliding-mode Control of a boost converter under constant power loading conditions. IET Power Electronics 12(3) 4. Wang Q, An Z, Zheng Y et al (2013) Parameter extraction of conducted electromagnetic interference prediction model and optimisation design for a DC– DC converter system. IET Power Electron. 6(7):1449–1461 5. He J, Li YW, Munir MS (2012) A flexible harmonic control approach through voltagecontrolled DG-grid interfacing converters. IEEE Trans Ind Electron 59(1):444–455 6. Zerroug N, Harmas MN, Benaggoune S, et al (2018) DSP-based implementation of fast terminal synergetic 1 control for a DC–DC Buck converter. J Franklin Institute 355(5):2329–2343 7. Cetin E, Omer D, Huseyin S (2009) Adaptive fuzzy logic controller for DC–DC converters. Expert Syst Appl 36(2):1540–1548 8. Zhou G, Xu J, Jin Y (2011) Improved digital peak current predictive control for switching DC–DC converters. IET Power Electron. 4(2):227–234 9. Tan SC, Lai YM, Tse CK (2011) Sliding mode control of switching power converters. Techniques and Implementation. CRC Press, Boca Raton, FL, USA 10. Wang Y, Cao Y, Liu T, et al (2016) Terminal sliding mode control of Boost converter using an energy storage function model. IECON 2016–42 Annual Conference of the IEEE Industrial Electronics Society. IEEE 11. Komurcugil H (2012) Adaptive terminal sliding-mode control strategy for DC-DC buck converters. ISA Trans 51(6):673–681 12. Komurcugil H (2013) Nonsingular terminal sliding mode control of DC–DC buck converters. Control Eng Pract 21:321–332 13. Vidal Idiarte E, Marcos-Pastor A, Garcia G, et al (2015) Discrete-time sliding mode-based digital pulse width modulation control of a Boost converter. IET Power Electron 8(5):708–714 14. Wang JX, Li SH, Yang J et al (2015) Extended state observer-based sliding mode control for PWM-based DC–DC buck power converter systems with mismatched disturbances. IET Control Theory Appl 9(4):579–586 15. Li H, Liu XX, Lu JW (2019) Research on linear active disturbance rejection control in DC/DC boost converter. Electronics 8(11):1249 16. Du H, Qian C, Yang S, Li S (2013) Recursive design of finite-time convergent observers for a class of time-varying nonlinear system. Automatica 49(2):601–609 17. Khalil HK (1996) Nonlinear systems, 2nd edn. Prentice-Hall, Upper Saddle River, NJ, USA

A Wide-Range Input Multi-phase Interleaved DC/DC Converter Suitable for Fuel Cells Li Wei

and Wen Yan

Abstract Fuel cells have attracted much attention due to their high power generation efficiency, low environmental pollution, and high reliability. However, the output voltage of the fuel cells varies greatly, which cannot meet the fast response requirements of load transients, therefore, a DC/DC converter is required to maintain the stability of the output voltage. This paper proposes a wide-voltage range multi-phase interleaved DC/DC converter topology suitable for fuel cells. The converter can be adjusted into the Buck mode, Boost mode and Extended-Duty-Ratio (EDR) mode. And this topology has the characteristics of wide range input, high gain and low ripple. In addition, by adopting the current control method, current sharing and fast dynamic response are well realized. The operating principle and the control algorithm of the topology are discussed in this paper, and the validity of the analysis is verified by simulation. Keywords Fuel cells · DC/DC converter · Wide-voltage · High voltage gain · Low current ripple

1 Introduction As a widely concerned green energy, with the advantages of high converter efficiency, high reliability, and low pollution, fuel cells have broad application prospects in the fields of high-reliability backup energy, distributed power generation devices, and automotive power energy [1]. However, the fuel cells’ output voltage varies widely, which cannot meet the fast response requirements of load transients [2, 3]. Therefore, they need to be used in conjunction with a DC/DC converter to ensure the stability of the output voltage [4]. A DC/DC converter with step-down/step-up, high gain, and low ripple can not only convert a wide fuel cell voltage into a desired value, but also has the advantages of high power density, high efficiency, and high reliability for fuel cell vehicle applications [5]. L. Wei (B) · W. Yan Tongji University, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_10

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The output voltage of fuel cells varies greatly. When the high-voltage direct current bus voltage is in the output range of the fuel cells, a converter that can step-down and step-up is required [6, 7]. At present, the research on DC/DC of fuel cell vehicles is mainly focused on Buck and Boost circuits [4, 8], but it is obvious that the two topologies cannot meet the needs of a wide range of step-down/step-up. Several existing classic non-isolated step-down /step-up converters, such as Sepic, Cuk, Buck-Boost and Zeta converters, are not suitable for the application of high-power, wide-range like fuel cells [9]. The input current of the Buck-Boost is non-continuous, which will greatly reduces the efficiency and service life of fuel cells. Circuits such as sepic, cuk, and zeta use too many components, which are not conducive to high power output and module integration [10]. Although the isolated converter can easily achieve a wide range of step-down/step-up converter, the existence of the transformer will increase the volume of the converter and reduce the converter efficiency [11, 12]. With the increasing of DC bus voltage, high-gain boost converter has become one of the research directions of fuel cell DC/DC [13]. Although the isolation converter can flexibly select the turns ratio to achieve high gain, it has the disadvantages of higher switching voltage stress, current spikes and lower efficiency [14–16]. Nonisolated converters can achieve high gain through switched capacitors [17], voltage multiplier units (VMC) [18], three-state switches [19], coupled inductors [20] or their combination [21], etc., and have higher efficiency, smaller size and lower cost. The extended duty period (EDR) converter has been mentioned in many researches as a buck converter in the past. In some studies in recent years, EDR has been used in bidirectional and step-up converter [22, 13]. The EDR converter inherits the advantages of switched capacitor and interleaved inductance technology. While providing wide gain, it can also effectively reduce the voltage stress and conduction loss of the switch, and reduce the current ripple. However, the EDR topology can only achieve maximum gain and current balance in a specific duty period region, which also limits the application of EDR topology in a wide range of input. Another problem of fuel cell DC/DC is that the converter or load will generate high-frequency ripple components in the fuel cell current, which will reduce the durability of the membrane and reduce the output power of the fuel cell stack [23]. For most non-interleaved converters, increasing the switching frequency of power devices can help reduce current ripple, but the higher the switching frequency, the greater the switching loss. The interleaved parallel technology can not only greatly reduce the current ripple, increase the power density, but also reduce the power loss of the converter, and has high reliability and high flexibility [24]. In general, a topology of wide range input voltage and low current ripple is required in the application of fuel cells. Dual active bridge converter has been studied a lot in recent years, and it has the characteristics of wide voltage range and easy realization of soft switching. Although it can reduce the current ripple through multi-phase parallel or snubber, the complexity of the circuit and control will be increased [25]. In [26], an interleaved step-up/step-down converter was proposed, which has the characteristics of low ripple and high efficiency but with greater redundancy. In [27], a Current Fed Buck Flyback-Forward is proposed, which has a large input voltage

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range, small current ripple, soft switching, and low switching loss, but the efficiency needs to be improved. Based on the EDR boost converter, this paper proposes a wide range stepdown/step-up multi-phase interleaved topology Buck-Boost-EDR suitable for fuel cell vehicles. This topology not only retains the advantages of high gain and low ripple of EDR, but also achieves step-down/step-up, which greatly meets the output requirements of fuel cells, and by adopting the current control mode, the current sharing control and fast dynamic response are realized. The paper is arranged as follows: The operating principle of Buck-Boost-EDR converter is analyzed in detail firstly, then the small signal model is built and the control algorithm is designed. The validity of the analysis is verified by simulation in Sect. 4. Finally, conclusion is present at the end of the paper.

2 Operating Principle of the Proposed Converter 2.1 Basic Operating Principle The Buck-Boost-EDR topology (Fig. 1) is composed of n-phase four-switch bidirectional converters connected in parallel through switched capacitors, and has three operating modes: Buck (Fig. 2), Boost (Fig. 3), and EDR (Fig. 4). The gain change and current sharing control of EDR boost converter in different working areas are studied in detail in [13], when the duty period is between (N-1)/N and 1, the gain can reach N/(1-D), and current sharing can be realized, where N is Fig. 1 Two-phase interleaved Buck-Boost-EDR converter

Iin

S1

D3

D1

` L1 S3

D4

D2

L2 S4

Vin S2

D5

S5 C1 C2

Vout

D3

Fig. 2 The Boost mode of Buck-Boost-EDR converter

Iin Vin

L1 S3 L2 S4

C2 D4

Vout

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Fig. 3 The Buck mode of Buck-Boost-EDR converter

Iin

S1 D1

L1

Vin S2

L2

C2

Vout

D2

D5

Fig. 4 The EDR mode of Buck-Boost-EDR converter

Iin Vin

L1 S3 L2 S4

D3

C1 C2

Vout

the number of phases in parallel. While in other duty ratios, the gain is smaller and the currents of each channel are not balanced, which may causes a certain phase to be overloaded. Therefore, the Buck-Boost-EDR topology proposed in this paper abandons the non-inherent current sharing zone of the EDR topology. When the circuit needs a higher gain, it can be switched to the EDR mode. When the circuit needs a lower gain, it can be switched to the Boost mode. Thus, while retaining the characteristics of the highest EDR gain ratio and inheriting current sharing, it also expands the application range. Take two-phase Buck-Boost-EDR as an example. When Vin > Vout , S3 and S4 are turned off, S5 and S6 are turned on, the converter enters Buck mode. When Vout /4 < Vin < Vout , S1 , S2 , S5 are turned on, S3, S5 are turned off, the converter enters Boost mode. When Vin < Vout /4, S1 and S2 are turned on, and S3 , S4 , S5 are turned off, the converter enters EDR mode. According to the principle of volt-second balance, the relationship between output voltage and input voltage can be derived:

Vout

⎧ ⎪ ⎨ DVin Buck mode 1 Vin ] Boost mode = 1−D ⎪ ⎩ n V EDR mode 1−D in

(1)

where Vout is the output voltage, Vin is the input voltage, D is the switching duty period, and n is the number of parallel phases. It can be seen that this topology can cover a wide range of voltage (voltage gain range D ~ n/(1–D)). Moreover, because of the multi-phase parallel connection, the current ripple can be effectively reduced and the service life of the fuel cell can be increased.

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2.2 Steady State Analysis Assuming that the devices used are all ideal devices, and ignoring the wire loss in the circuit, the steady-state model of the circuit is derived, and the state equations are listed for the switching states in the three modes. For buck and boost circuits, since the two circuits are completely the same, the switch states can be combined. In buck mode, list the state equations of the switch on and off: ⎧ dI ⎨ L i dti = Vin − VC2 2 ∑ dV V ⎩ C2 dtC2 = Ii − RC2

(2)

i=1

⎧ ⎨

L i ddtIi = −VC2 2 ∑ dV ⎩ C2 dtC2 = Ii − i=1

VC2 R

(3)

In buck mode, list the state equations of the switch on and off: ⎧

L i ddtIi = Vin dV V C2 dtC2 = − RC2

⎧ dI ⎨ L i dti = Vin − VC2 2 ∑ dV V ⎩ Ci dtC2 = Ii − RC2

(4)

(5)

i=1

In EDR mode, since the topology in this paper only uses the inherent current sharing zone((N−1)/N ≤ D ≤ 1) of EDR, the switching states can be divided into three types: When S3 , S4 are turned on: ⎧ dI ⎪ ⎨ L 1 dt1 = Vin L 2 ddtI2 = Vin (6) ⎪ ⎩ C d VC2 = − VC2 2 dt R When S3 is turned on, S4 is turned off: ⎧ ⎪ L 1 ddtI1 = Vin ⎪ ⎪ ⎨ L d I2 = V + V − V in C1 C2 2 dt d VC1 ⎪ C = −I 1 dt 2 ⎪ ⎪ dV V ⎩ C2 dtC2 = I2 − RC2 When S3 is turned off, S4 is turned on:

(7)

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⎧ d I1 ⎪ ⎪ L 1 dt = Vin − VC1 ⎪ ⎨ L 2 ddtI2 = Vin dV ⎪ C1 dtC1 = I1 ⎪ ⎪ V dV ⎩ C2 dtC2 = − RC2

(8)

Based on period average method, state space average equation is written as follows: x˙ = Ai x + Bi uii = 1, 2, 3

(9)

A1 , A2 , A3 , B1 , B2 , and B3 respectively correspond to the coefficient matrix of the state vector x and the control variable u in Buck, Boost, and EDR modes. The definitions of Ai and Bi are as shown in (10). According to the steady-state model, the steady-state voltage and current waveforms are drawn as shown in Fig. 5. The waveforms of S1 , S2 , S3 , S4 , and S5 are PWM signals of five switches. In buck mode, when t = t0 ~ t3 , S1 is turned on, the input of the first phase powers the inductor and output. When t = t2 ~ t5 , S2 is turned on, the input of the second phase powers the inductor and output, and the two phases are interleaved for half a period. Fig. 5 Steady-state waveform of Buck-Boost-EDR converter

vout iin vC1 iS5 iS4 iS3 iL2 iL1 iS2 iS1 S5 S4 S3 S2 S1 t1 t3 t5 t0 t2 t4 Buck mode

t6

t7

t9 t11 t8 t10 Boost mode

t13 t15 t17 t12 t14 t16 EDR mode

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The energy transfer process of boost is the same as buck. In EDR mode, when t = t13 ~ t14 , S3 is turned on, S4 is turned off, the second phase input powers the inductor and switched capacitor C1 . When t = t14 ~ t15 and t16 ~ t17 , S3 , S4 are turned on, both inputs powers the inductor, the output is powered by capacitors C2 and C1 . When t = t15 ~ t16 , S3 is turned off, S4 is turned on, The first phase input powers the inductor and output, and the second phase powers the output through the switched capacitor C1 . It can be seen that in the Buck, Boost, and EDR modes, the input current ripple has been significantly improved, and as the number of interleaved phases increases, the current ripple will be further reduced. In the EDR mode, due to the effect of the switched capacitor C1 , the output voltage can be increased, the gain ratio reaches n/1-D. ⎤ ⎡ ⎡ ′ ⎤ 0 0 0 −1 0 0 0 LD1 L1 ⎢ 0 0 0 −1 ⎥ ⎢ 0 0 0 −D′ ⎥ ⎥ ⎢ ⎢ L L2 ⎥ 2 A1 = ⎢ ⎥ ⎥ A2 = ⎢ ⎣ 0 0 0 0 ⎦ ⎣ 0 0 0 0 ⎦ ′ ′ D D 1 1 0 C−1 0 C−1 C2 C2 C2 C2 2R 2R ⎧ ⎤′ ⎡ (10) ⎤ ⎡ −D ′ ⎪ x = I1 I2 VC1 VC2 0 0 L1 0 ⎪ ⎪ ⎪ ⎡ ⎤′ ⎢ 0 0 D′ −D′ ⎥⎨ D D ⎥ ⎢ A3 = ⎢ D′ −D′ L 2 L 2 ⎥ B1 = L 1 L 2 0 0 ⎪ ⎣ C1 C1 0 0 ⎦⎪ ⎡ ⎤′ ⎪ ′ ⎪ ⎩ B2 = B3 = 1 1 0 0 0 CD2 0 C−1 L1 L2 2R

3 Control of the Proposed Converter 3.1 Small Signal Model Based on the steady-state model of (9), adding small AC signals and performing Laplace transform on the state equation, the transfer function from duty to current in three modes can be obtained as (11–13), where n is 1 or 2. For buck mode, iSn refers to the period average current of S1 and S2 . For Boost mode and EDR mode, iLn refers to the period average current of L1 and L2 . ⎧ ⎞ V in 1 s + ˆi Sn (s) RC 2 Ln G i dn_Buck (s) = = 2 1 2 ˆd n (s) s + RC s + Ln C2 2 ⎧ ⎞ V in 1 s + RC Ln iˆ L n (s) 2 G i dn_Boost (s) = = 2 s2 + 1 s + 2(1− D) dˆ n (s) RC 2

Ln C2

(11)

(12)

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⎧ ⎞ V in 1 s + RC Ln iˆ L n (s) 2 G i dn_E D R (s) = = (1− D)2 1 s + s2 + RC dˆ n (s) 2L n C 2 2

(13)

3.2 Average Current Control Model For traditional DC/DC converters, people tend to adjust the duty by detecting the output voltage. However, the output current of the fuel cell varies greatly, and the impact on the output power is very significant. The voltage control method cannot follow this characteristic of the fuel cell. Therefore, for fuel cell DC/DC, the input current of the DC/DC converter can be used as the control variable to adjust the output power of the fuel cell, and it has a faster dynamic response. The topology proposed in this paper adopts the average current control method. The control block diagram is shown in Fig. 6. The control variable is the duty of the switches, given the input current reference value Iin_ref, the current adjustment target of each phase is Iin_ref/2. GCnx is the current controller function, Gidnx is the transfer function of the proposed converter, where n refers to the phase number of the converter, and x refers to the three modes of the converter. H is the feedback transfer function, Fig. 6 The control algorithm of Buck-Boost-EDR converter

Start Vin >Vout

>Vout/4 Buck mode

Boost mode

Current Control Switch Duty

System Stable End

EDR maode

A Wide-Range Input Multi-phase Interleaved DC/DC Converter … D3

i1 Iin_ref

1/2

GC1x

i1

Iin

d1 GC2x

d2

S1

Vin

129 iout

D5

R

Vout

L1 D1 S3

S5 C1 C2

L2 S2

D4

D2 S4

Gidnx

H1 H2

Fig. 7 The control block diagram of Buck-Boost-EDR converter

G Cnx (s) = k pnx + k i nx

1 s

(14)

where kp and ki used in this paper for Buck, Boost, EDR mode are 0.01, 0.05 respectively. By detecting the two phases’current, and comparing them with the reference current of each phase, the phase current is adjusted to keep close to the reference value. The control algorithm of the topology proposed in this paper is shown in Fig. 7. The fuel cell output is connected to the DC/DC input. By detecting the output voltage of the fuel cell, Buck-Boost-EDR circuit enters different modes. When Vin > Vout, the circuit enters Buck mode. When Vout /4 < Vin < Vout , the circuit enters Boost mode, when Vin < Vout/4, the circuit enters EDR mode, and then continuously adjusts the switches’ duty through current control to make the phase current reach a predetermined value.

4 Simulation Verification Based on the Buck-Boost-EDR topology proposed in this article, simulation and verification are carried out in this section. The simulation module and control logic are built in matlab. The simulation parameters are shown in Table 1. The input voltage is 4-80 V, the output voltage is 40 V, and the gain range is 10–1/2. Table 1 The simulation configuration

Configuration

Value

Configuration

Value

Input voltage

4–80 V

C1

100 uF

Input current

20–40A

C2

220 uF

Output voltage

40 V

L1 /RL1

10 uH/8 mΩ

Frequency

100 kHz

L2 /RL2

8 uH/10 mΩ

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The input voltage Vin is controlled to jump from 4 to 20 V at 0.2 s, and from 20 to 80 V at 0.4 s. The input current reference value Iin_ref is synchronously controlled to jump from 40 to 20A at 0.4 s. And to verify the current-sharing control of the controler, The inductance L and the equivalent resistance RL of the two phases are set to different values.The overall waveforms of the simulation is shown in Fig. 8. It can be seen that the designed converter can quickly enter the corresponding mode according to the input voltag. The steady-state waveforms of the simulation is shown in Figs. 9, 10, 11. It can be seen that no matter in the buck mode, boost mode or EDR mode, the two-phase currents are kept balanced, the total input current Iin can follow Iin_ref well, and the Iin ripple is significantly improved, which is about 1/2 of the ripple of each phase’s current, and the frequency of Iin has also doubled. In Buck mode, due to the discontinuity of the switching current, the branch input current is discontinuous and fluctuates greatly, but from the simulation waveform of this topology, it can be seen that the total input current waveform in Buck mode is continuous, and the ripple is reduced by about 1/3. The low-ripple input current is conducive to choosing a smaller inductor, reducing the volume of the DC/DC converter and reducing the cost, and as the number of Buck- Boost-EDR parallel phases increases, the input current ripple will be further improved.

Fig. 8 The overall waveforms of the simulation

Fig. 9 The steady-state waveforms of Buck mode

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131

Fig. 10 The steady-state waveforms of Boost mode

Fig. 11 The steady-state waveforms of EDR mode

The dynamic waveforms of the simulation is shown in Fig. 12. It can be seen that when the input voltage jumps from 4 to 20 V, the switching of DC/DC is very fast. The converter from EDR mode to Boost mode is completed within 1 ms, and the current is reached stable. When the input voltage jumps from 20 to 80 V, the DC/DC also completes the switching from Boost mode to EDR mode in about 1.5 ms. It can be seen that the control model proposed in this paper has good dynamic response and stable characteristics.

5 Conclusion Based on the EDR topology, this paper proposes a wide-voltage range interleaved DC/DC converter topology suitable for fuel cells. While fully retaining the EDR’s high gain, inheriting current sharing, and low ripple characteristics, it also expands the input voltage range. The topology proposed in this paper is composed of two fourswitch circuits connected in parallel through a switched capacitor, and can enter three working modes of Buck, Boost and EDR according to the output and input voltage transformation ratio, which increases the reliability of the converter. By adopting

Fig. 12 The dynamic waveforms of the simulation: a EDR mode to Boost mode. b Boost mode to Buck mode

132 L. Wei and W. Yan

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the current control method, the current sharing control and fast dynamic response are realized. Future work includes experimental verification of large voltages and currents and road testing. Acknowledgements The presented study was supported by the National Key R&D Program of China (2018YFB1503100) and the National Natural Science Foundation of China (E51777141).

References 1. Sharaf OZ, Orhan MF (2014) An overview of fuel cell technology: Fundamentals and applications. Renew Sustain Energy Rev 32:810–853 2. Wang C, Hashem Nehrir M, Shaw S (2005) Dynamic models and model validation for PEM fuel cells using electrical circuits. IEEE Power Eng Soc Gen Meet 3(2):2115 3. Forrai A, Funato H, Yanagita Y, Kato Y (2005) Fuel-cell parameter estimation and diagnostics. IEEE Trans Energy Convers 20(3):668–675 4. Ali MS, Kamarudin SK, Masdar MS, Mohamed A (2014) An overview of power electronics applications in fuel cell systems: DC and AC converters. Sci World J 5. Guilbert D, Member IS, Gaillard A, Member I, Diaye AN (2013) Energy efficiency and fault tolerance comparison of DC/DC converters Topologies for Fuel Cell Electric Vehicles 6. Kuo J-K, Wang C-F (2011) An integrated simulation model for PEM fuel cell power systems with a buck DC–DC converter. Int J Hydrogen Energy 36(18):11846–11855 7. Seyezhai R, Mathur BL (2012) Design and implementation of interleaved boost converter for fuel cell systems. Int J Hydrogen Energy 37(4):3897–3903 8. Valdez-Resendiz JE, Sanchez VM, Rosas-Caro JC, Mayo-Maldonado JC, Sierra JM, Barbosa R (2017) Continuous input-current buck-boost DC-DC converter for PEM fuel cell applications. Int J Hydrogen Energy 42(51):30389–30399 9. Haibo Q, Yicheng Z, Yongtao Y, Li W (2006) “Analysis of buck-boost converters for fuel cell electric vehicles”, 2006 IEEE Int. Conf Veh Electron Safety, ICVES, pp 109–113 10. Saha SS (2011) Efficient soft-switched boost converter for fuel cell applications. Int J Hydrogen Energy 36(2):1710–1719 11. Somaiah B, Agarwal V, Choudhury SR, Duttagupta SP, Govindan K (2011) Analysis and comparative study of pulsating current of fuel cells by inverter load with different power converter topologies. Int J Hydrogen Energy 36(22):15018–15028 12. Depernet D, Narjiss A, Gustin F, Hissel D, Péra M-C (2016) Integration of electrochemical impedance spectroscopy functionality in proton exchange membrane fuel cell power converter. Int J Hydrogen Energy 41(11):5378–5388 13. Roy J, Ayyanar R (2017) Sensor-less current sharing over wide operating range for extendedduty-ratio boost converter. IEEE Trans Power Electron 32(11):8763–8777 14. Watson R, Lee FC, Hua GC (1996) Utilization of an active-clamp circuit to achieve soft switching in flyback converters. IEEE Trans Power Electron 11(1):162–169 15. Lee JJ, Kwon JM, Kim EH, Kwon BH (2008) Dual series-resonant active-clamp converter. IEEE Trans Ind Electron 55(2):699–710 16. LaBella T, Lai JS (2014) A hybrid resonant converter utilizing a bidirectional GaN AC switch for high-efficiency PV applications. IEEE Trans Ind Appl 50(5):3468–3475 17. Cheung CK, Tan SC, Tse CK, Ioinovici A (2013) On energy efficiency of switched-capacitor converters. IEEE Trans Power Electron 28(2):862–876 18. Zhang N, Sutanto D, Muttaqi KM, Zhang B, Qiu D (2015) High-voltage-gain quadratic boost converter with voltage multiplier. IET Power Electron 8(12):2511–2519

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19. Barreto LHSC, Praa PP, Oliveira DS, Silva RNAL (2014) High-voltage gain boost converter based on three-state commutation cell for battery charging using PV panels in a single converter stage. IEEE Trans Power Electron 29(1):150–158 20. Gules R, dos Santos WM, dos Reis FA, Romaneli EFR, Badin AA (2014) A modified SEPIC converter with high static gain for renewable applications. IEEE Trans Power Electron 29(11):5860–5871 21. Hu X, Gong C (2014) A high voltage gain DC-DC converter integrating coupled-inductor and diode-capacitor techniques. IEEE Trans Power Electron 29(2):789–800 22. Shenoy PS, et al (2015) Automatic current sharing mechanism in the series capacitor buck converter. Proc 2015 IEEE Energy Convers Congr Expo, pp 2003–2009 23. Gerard M (2011) Ripple current effects on PEMFC aging test by experimental and transactions of the ASME 8(021004) 1–5 24. Wang H, Gaillard A, Hissel D (2019) A review of DC/DC converter-based electrochemical impedance spectroscopy for fuel cell electric vehicles. Renew Energy 141:124–138 25. Babokany AS, Jabbari M, Shahgholian G, Mahdavian M (2012) A review of bidirectional dual active bridge converter. In: 2012 9th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, pp 1–4 26. Gao DW, Jin ZH, Liu JX, Ouyang MG (2016) An interleaved step-up/step-down converter for fuel cell vehicle applications. Int J Hydrogen Energy 41(47):22422–22432 27. Chelghoum R, Sousa LD, Bendani L, Sadarnac D (2016) Wide voltage input range insulated current fed buck flyback-forward for HV/LV power converter in electric/hybrid vehicle. PCIM Europe 2016. International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, pp 1–7

FHSS-4FSK Based Power and Signal Synchronous Transmission for Cascaded DC/DC Converters Yang Leng , Ziren Wei, Tailai Wang, and Dongsheng Yu

Abstract DC/DC converter is an important part of the DC distributed power generation system (DPGS). To improve the operation efficiency and flexibility of DPGS with multi-converters-based power supply network, and ensure a safe and reliable communication, for the cascaded Buck converters, a frequency hopping spread spectrum (FHSS) signal transmission strategy is studied in this paper. Based on the frequency-shift keying (FSK) modulation principle, a multi-frequency carrier signal is superimposed on the reference voltage to obtain the FHSS-4FSK signal modulation and demodulation scheme. Through the transfer function and Bode diagram, the stability of the cascaded Buck converters is analyzed under the control loop parameters. Also, the signal response characteristics of the system are determined. Simulation and experiment verify the feasibility of the FHSS-4FSK power and signal synchronous transmission strategy (PSST). Keywords DPGS · PSST · FHSS-4FSK · Cascaded buck converters

1 Introduction Since renewable energies are geographically dispersed with intermittent and random characteristics, power generation and conversion require high performance of power quality. To effectively harvest and utilize renewable power, distributed power generation system (DPGS) is established to decrease power transmission loss and boost the effectiveness of renewable sources [1]. However, power converters inside DPGS without communication can neither improve the coordination capability of distributed power generation devices nor

Y. Leng · T. Wang · D. Yu (B) China University of Mining and Technology, University Road, Xuzhou 221116, China e-mail: [email protected] Z. Wei State Grid Jiaozuo Power Supply Company, Tanan Road, Jiaozuo 454150, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_11

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optimize the conversion of renewable energies [2]. Therefore, it is of great significance to integrate communication among power converters and other equipment for DPGS to realize renewable energy sharing and talkative power [3]. Power line communication (PLC), which connects multiple electronic devices including power converters, has bright good application prosperity as it can exempt extra communication lines, decrease the establishment cost, and realize power and signal synchronous transmission (PSST), and hence increase the reliability and flexibility of the DPGS [4]. With regards to PSST strategy, in [5], a hybrid modulation based on frequency division multiplexing technology is proposed, which can modulate digital code on gate signals for power converters to realize the switched ripples communication and demodulate transmitted signal via discrete Fourier transform (DFT). The PSST methods can simplify communication system structure and hence decrease hardware costs. However, due to the high-frequency noises [6], the small switching ripple can be easily disturbed. In addition, there is a frequency-selected fading on the power line, which can lead to the unavoidable attenuation of carrier ripple and bit error rate. To strengthen the resistance to signal interference, spread spectrum communication (SSC) method has been proposed. SSC method modulates signals via spreading code to obtain a wide frequency spectrum, which can hence achieve high electromagnetic capacity (EMC) ability [7]. And this method can be categorized into direct sequence spread spectrum (DSSS), frequency hopping spread spectrum (FHSS), and chirp modulation spread spectrum (CMSS). A novel FHSS-4FSK based PSST strategy for cascaded Buck converters is investigated in this paper, and the FHSS-FSK strategy implemented on the cascaded Buck converters is discussed. By using the autocorrelation of the spreading code, transmitted signals can be demodulated. The proposed PSST strategy can increase the reliability and coordination capacity of the DPGS.

2 The Modulation for Cascaded Buck Converters With regards to the FHSS communication system, the carrier frequency hops in a band range as the value of spreading code changes. With a low power spectrum density, the carrier wave can improve transmission security and strengthen the robustness against multipath interference. The diagram of the cascaded Buck converters is shown in Fig. 1, where the data stream is marked with a blue dotted line, and the arrow shows the data flow direction. The carrier is generated by a frequency synthesizer. Then the selected carrier waves are compared with the reference voltage V ref 1 and the feedback part H v1 vo1 for modulation. The hopping code generator at the receiver side duplicates that of the transmitter online via synchronization. Because the signal is demodulated by multiplication with the synchronous hopping codes, the spreading code should possess a strong autocorrelation characteristic. The FHSS-4FSK strategy is chosen to make carriers hop among frequencies 1, 2, 3 and 4 kHz. Waveforms

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Fig. 1 Schematic of the cascaded buck converters

during modulation are drawn in Fig. 2, where T b is the time interval of a baseband signal, T s is the period of carrier waves, equals to a quarter of T b . vdata is the baseband signal code, vss the spreading code, and vFHSS the carrier wave. v1k , v2k , v3k and v4k Fig. 2 Waveforms during modulation

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represent the trigger signal of carrier waves with frequencies of 1 kHz, 2 kHz, 3 kHz and 4 kHz, respectively. To minimize the hopping bits of spreading code when the carrier frequency changes, the hopping sequence has schemed to [1 3 4 2] kHz when transmitting digit ‘1’, which matches the spreading sequence [0 0 1 0 1 1 0 1]. The spreading code for transmitting digit ‘0’ should maintain a negative correlation with that for transmitting digit ‘1’. So the digit ‘0’ matches [1 1 0 1 0 0 1 0], and the carrier hops in the order of [4 2 1 3] kHz.

3 Demodulation Strategy Based on FHSS-4FSK Based on FHSS-4FSK method, multiple procedures are executed for demodulation, including band-pass filtering, envelope detection, low-pass filtering and threshold comparison. The voltage ripple is filtered by band-pass filters. Each carrier wave undergoes envelope detection and low-pass filtering to obtain envelop signals. Then, envelop signals are transferred to the digital processor to attain the spreading code. A schematic of the demodulation scheme is shown in Fig. 3. The system complexity is high since a rigid synchronization between transmitter and receiver sides is required. To simplify the demodulation circuit, spreading code with strong autocorrelation is used. The FHSS-4FSK strategy uses carrier wave hopping in the order of [1 2 3 4] kHz, which represents a 2-bit digital code, so the demodulated code should be moved 2bits forward in each period of the carrier wave for autocorrelation calculation, while digit ‘1’ is represented by number ‘1’, and digit ‘0’ is changed by the number ‘ − 1’. The result is shown in Fig. 4, where invalid points appear. The value at invalid points for positive autocorrelation coefficient is Threshold Comparison Bandpass

vband1 Envolope

ven1

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vband2 Envolope ven2

Lowpass

vlow1 Constant Spreading Sequence

Detection

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vband3 Envolope ven3

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Save the Result in a Register 1 0 0 1 0 1 0 0

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0 0 1 0 1 1 0 1

vband4 Envolope ven4

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fCF4

Fig. 3 Schematic of the demodulation scheme

vlow4

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Output

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(b) Negative

Fig. 4 The autocorrelation curves

− 1, while for negative autocorrelation coefficient equals 1, all of which damages the autocorrelation of spreading codes. For a better autocorrelation, when the autocorrelation coefficient is − 1, the result of the last two digits will be detected; if the value is − 1, the autocorrelation coefficient is set to 0; otherwise, the demodulation result will be retained. Similarly, when the calculation result is 1 and the detected result equals − 1, the calculation result will be set to 0. The modified autocorrelation coefficient is expressed in Fig. 5. The real-time received code vssc should multiply the modified spreading sequence vspc [−1 − 1 1 − 1 1 1 − 1 1] by bits to calculate the correlation coefficients. When it equals 1, the output is 1; when it equals -1, the output is 0. As shown in Fig. 6, through calculating the autocorrelation coefficients, the signals can be demodulated by only one data bit delay. Rx(j)

Rx(j) -8 -7 -6 -5 -4 -3 -2 -1

1

1 2 3 4 5 6 7 8 0

-8 -7 -6 -5 -4 -3 -2 -1

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(a) Positive Fig. 5 The modified autocorrelation curves

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4 Modeling and Response Characteristics Analysis As the cascaded converters may step into instability and generate unexpected oscillation, the cascaded Buck converters should be stable when communicating. The parameters of converter 1 are as follows: input voltage V i = 24 V, capacitor C = 220 uF, reference voltage V ref = 12 V, carrier wave amplitude V m = 1 V, inductance L = 300 uH, switching frequency f s = 100 kHz, proportional coefficients of voltage controller k p = 20, voltage sampling factor H v = 1, Load resistance R = 4 Ω, while the parameters of converter 2 are as follows: V i = 12 V, C = 100 uF, V ref = 5 V, integral coefficients of voltage controller k i is from 10 to 100, V m = 1 V, L = 200 uH, f s = 100 kHz, k p is from 0.1 to 1, voltage sampling factor H v = 1, R = 1Ω. The small-signal block diagram of the cascaded Buck converters is shown in Fig. 7, and the open-loop transfer function of the system can be written as vi(s)

vref1(s)

ve(s)

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vc(s)

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Fig. 7 Small signal block diagram of the system

Zo1(s)

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Frequency (Hz)

(a) The Bode diagram of the open-loop

(b) The Bode diagram of the closed-loop

Fig. 8 Bode diagram of the cascaded buck converters

Tol (s) =

T (s) 1 + Z o1 (s)/Z R (s)

(1)

where T (s) = Gc1 (s)Gm1 (s)Gvd1 (s)H v1 (s), Z R = Z ic2 //R1 . Z ic2 is the closed input resistance of the load Buck converter while Z o1 is the output resistance of Buck converter 1. The closed-loop transfer function of the system can be rewritten as Tc1 (s) =

G c1 (s)G m1 (s)G vd1 (s) 1 + Z o1 (s)/Z R (s)

(2)

Bode curves of the open-loop and closed-loop transfer functions can be drawn in Fig. 8. Crossing frequency ωc is large and the phase margin Pm is small. When the signal is loaded, the system can respond rapidly with stability regardless of the overshoot. The amplitude Gm of the system is infinite, which indicates stability. When the carrier waves are superimposed on the input, the response amplitude of the output side is approximately 0 dB, indicating that the amplitude of the output signal almost equals that of the input signal, and the output signal doesn’t attenuate as the carrier frequency increases. Hence, it is unnecessary to compensate for the high-frequency transmission signal. The output voltage of low-pass filter vlow is compared with the threshold voltage V Ti . When vlow surpasses the threshold voltage V Ti with a rising value, the signal demodulation is activated. The received code is stored in the lower two bits of the array and calculated with the synchronous spreading code, and the result is stored in the lowest bit of the 8-bit register. When the stored result is 1 or −1, it will be compared with the result in the sixth bit of the register; if the eighth bit is 1 and the sixth bit is −1, the eighth position will be reset to 0; if the eighth position is −1 and the sixth position is 0, then the 8th position will also be reset to 0.

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5 Experiment Verification The analog filter circuit and envelope detection circuit are built to extract the carrier signal while the demodulation is carried in a digital processor. The period T b of the baseband signal is set to 40 ms, so the time interval of each carrier wave is 10 ms. In Fig. 9, the carrier frequency hops in terms of the spreading code [0 0 1 0 1 1 0 1] when vdata reaches a high level. When vdata is low, the sequence of spreading code is [1 1 0 0 0 1 0]. The waveform of vo1 going through band-pass filters is depicted in Fig. 10. Since the amplitude of voltage ripples is quite small, to facilitate the demodulation, each amplitude of ripples can be effectively amplified by setting the band-pass amplification factor Akb to 24. The waveform sampled after envelope detection is demonstrated in Fig. 11. The signal waves of signals are shown in Fig. 12.

vdata:[5V/div]

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vo1:[50mV/div]

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4k Time:[20ms/div]

Fig. 10 Waveforms of the band-pass filter output

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ven1:[200mV/div]

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Fig. 11 Waveforms of the envelope output

vdata:[2V/div]

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vdemo:[2V/div]

Demodulated signal

Time:[200ms/div] Fig. 12 Waveforms of the transmitted and demodulated signals

The demodulated data is [1 1 0 1 0] with a 40 ms delay. Results show that the FHSS-4FSK method realizes the PSST in the cascaded Buck converters.

6 Conclusion This paper aims to realize PSST for the cascaded Buck converters. An FHSS-4FSK method is adopted by superimposing the carrier waves on the reference voltage. To improve the autocorrelation of spreading code, a modified coding method is designed, which avoids invalid point of autocorrelation coefficient curves. Both the simulation

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and experiment results confirm that the data can be correctly demodulated inside a wide parameter range. This work could benefit the coordination of power converters connected in the DPGS. Acknowledgements This work was supported in part by National Natural Science Foundation of China under Grant No. 51977208.

References 1. Gou X, Chen Q, Sun Y (2021) Holistic analysis and optimization of distributed energy system considering different transport characteristics of multi-energy and component efficiency variation. Energy 228:120586 2. Zhuang YZ, Liu F, Huang YH (2021) A multiport modular DC-DC converter with low-loss series LC power balancing unit for MVDC interface of distributed photovoltaics. IEEE Trans Power Electron 36(7):7736–7749 3. He XN, Wang RC, Wu JD (2020) Nature of power electronics and integration of power conversion with communication for talkative power. Nat Commun 11(1):2479 4. Miller D, Mirzaeva G, Townsend CD (2021) The use of power line communication in standalone microgrids. IEEE Trans Ind Appl 57(3):3029–3037 5. Choi HJ, Jung JH (2017) Enhanced power line communication strategy for DC microgrids using switching frequency modulation of power converters. IEEE Trans Power Electron 32(6):4140– 4144 6. Nieman KF, Lin J, Nassar M (2013) Cyclic spectral analysis of power line noise in the 3–200 kHz band. In: 2013 17th IEEE international symposium on power line communication and its applications (ISPLC),pp 315–320 7. Mathur P, Raman S (2020) Electromagnetic interference (EMI): measurement and reduction techniques. J Electron Mater 49(5):2975–2998

Power & Signal Synchronous Transmission Strategy for Three-Phase Voltage Source Inverter Haiyang Liu, Yang Leng, and Dongsheng Yu

Abstract In this paper, a power and signal composite modulation and synchronous transmission strategy for a three-phase voltage source inverter (VSI) system is proposed, which can transmit signals without requirement of additional communication line. By modulating the baseband data with 2FSK, two signal modulation strategies are presented. To analyze the stability of the VSI after injecting the signal, the small-signal model of the three-phase VSI is discussed. The experimental platform is then built and the feasibility of a DC-AC converter-based PSST system is verified. Keywords Three-phase VSI · Power and signal composite modulation · Small-signal model

1 Introduction Ripples of output voltage or current can be injected to power line and controlled in terms of frequency, phase or amplitude as a carrier of information for communication, which is generally called as power and signal synchronous transmission (PSST). PPST can be applied to device protection, data updating, online monitoring, fault diagnosis and so on. With regards to distributed power systems, microgrid and electric vehicles, the requirement of information interaction among different system nodes and devices makes PSST method promising. Several PSST methods have been proposed and widely applied in various areas. Most conventional methods focus on injecting the modulated signals into power line through coupling circuit [1]. Power over Ethernet (PoE) is also a method of PSST, which multiplexes twisted-pair wires for transmitting signals and supplying power to IP terminals [2]. The PSST methods implemented by power switches inside power converters have been recently proposed. In [3], PSST was implemented in a multi-load Buck converter, where the signals were transmitted from Buck converter to the selected load H. Liu · Y. Leng · D. Yu (B) China University of Mining and Technology, University Road, Xuzhou 221116, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_12

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side. In [4], bidirectional signal transmission between two DC/DC converters was completed using time-division multiplexing. In [5], direct sequence spread spectrum is adopted to transmitting signal in Buck converter, which can greatly improve the signal bandwidth and communication confidentiality. However, very few researches focus on applying PPST to DC/AC converters [6]. In [6], PSST method is designed and tested in a cascaded inverter, where additional signal H-bridge is required and hence overall cost is increased. In this paper, PSST method is designed and applied to a three-phase SPWM VSI.

2 Proposed Power and Signal Synchronous Transmission 2.1 System Structure The system structure of a PSST based three-phase SPWM VSI is shown in Figs. 1 and 2. 2FSK is one of the most commonly used digital signal modulation methods. According to two inputs of PWM modulator, namely power reference and a triangle carrier, two compound strategies for VSI based PSST system using 2FSK can be obtained, which are called power reference-based method and power carrier-based method. With regards to power reference-based PSST method, by turning S1 to section A in Fig. 2, the baseband data will be modulated and superimposed on the power

ua udc

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reference wave. For power carrier-based PSST method, turning S1 to section B in Fig. 2, the switching frequency changes between f 1 and f 2 to carry baseband signal.

2.2 System Modeling and Analysis The typical three-phase VSI topology is shown in Fig. 1. Since only one switch of each phase conducts at any moment, the switching function is defined as si (i = a, b, c). when si = 1(0), the upper switch turns on (off) while the lower one turns off (on). Defining vectors as below, ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ sa uA ia ⎣ ib ⎦ s = ⎣ sb ⎦ uC = ⎣ u B ⎦ i l = u ic sc ⎡ C⎤ ⎡ ⎤⎡ ⎤ ua 2 −1 −1 sa uinv = ⎣ u b ⎦ = u3dc ⎣ −1 2 −1 ⎦ ⎣ sb ⎦ = u3dc Qs −1 −1 2 sc uc According to KVL and KCL, the system equations of the three-phase VSI can be listed by ⎛

di l dt duc dt

= =

u dc Qs− L1 uC 3L 1 1 i − RC uC C l

(1)

The switching period operator is introduced to average all variables in (1), and then transformed to the synchronous frame through Park-Clark transformation. (2)

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id L Idc

ddUdc

Ddid ddId Dqiq dqIq

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ωL/Udc

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(b)

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Gv

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Fig. 3 a Three-phase VSI small-signal model diagram; b Decoupling scheme of three-phase VSI dq small-signal model

is derived by introducing small perturbation method by. ⎡ˆ ⎤ ⎡ 0 ω − L1 0 id ⎢ ⎢ ⎥ ˆ −ω 0 0 − L1 d ⎢ iq ⎥ =⎢ 1 1 dt ⎣ ⎣ ⎦ 0 − RC ω uˆ d C 1 1 0 C ω − RC uˆ d

⎤⎡ˆ ⎤ id ⎥ ⎢ iq ˆ ⎥ ⎥⎢ ⎥+ ⎦ ⎣ uˆ d ⎦ uˆ d

Udc L

⎡ˆ ⎤ dd ⎢ dˆ q ⎥ ⎢ ⎥ ⎣0⎦ 0

(2)

The diagrams of three-phase VSI model under synchronous frame are shown in Fig. 3. As shown in Fig. 3b, voltage PI compensation and bipolar SPWM modulation method are adopted for the VSI system. The transfer function of system output voltage ud (s) to control signal d(s) can be obtained, G vd (s) =

Udc LCs 2 + LR s

(3)

2.3 Analysis of the Closed-Loop Stability The power reference-based method is equivalent to introducing a fixed disturbance to original system. There are two points that this “perturbation” can be injected, which is shown in Fig. 3b. The open-loop transfer function obtained from Fig. 3b with perturbation A can be shown by ( G 0 (s) = k p +

ki s

(

Udc 1 α 2Vtri LCs 2 +L/R s

(4)

V tri is triangular carrier amplitude, k p and k i are the proportional and integral coefficient respectively, the voltage feedback coefficient α = 1 and the switching frequency f s = 15 kHz. Substituting the system parameters into (4), the Bode Plots of G0 (s) can be drawn in MATLAB, which is shown in Fig. 4.

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Magnitude(dB)

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-180 104 Frequency(Hz)

Fig. 4 Open-loop bode plot for voltage feedback control

As it can be seen from Fig. 4, the low-frequency band attenuates by −20 dB/dec, and the gain at 50 Hz is about 40 dB. In the high-frequency band, the frequency characteristic plot crosses the 0 dB line with −40 dB/dec at frequency 2.4 kHz, which can effectively attenuate the harmonics and interference in the high-frequency band. The phase margin is about 31 degrees, and hence the system can be operated with good stability. Using the dynamic error coefficient method to analyzing the system stability after the injecting sinusoidal signal carrier. Defining Φ d (s) as the transfer function for system with signal carrier, we have Φd (s) =

LCs 3 +

Udc 2Vtri (k p s + ki ) αk p Udc L 2 αk p Udc R s + 2Vtri s+ 2Vtri

(5)

Substituting parameters into (5), the Bode plots for Φ d (s) is shown in Fig. 5, from which we can see the frequency characteristic is approximately a straight line in the low-frequency band with a small spike around 2.35 kHz and then attenuates by − 40 dB/dec. The crossing frequency is about 3.3 kHz with a phase margin of 45°. This result reveals that the signal carrier frequency is closely related to the error transfer Phase(deg)

Magnitude(dB) 20 0

-45

-20

-40 -60 -80

0

-90 Amplitude-frequency characteristics Phase-frequency characteristics

101

-135 102

103

Fig. 5 Closed-loop bode plot for VSI system to signal carrier

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function. The bandwidth of the power loop is about 2.4 kHz, and the signal carrier frequency should choose from the area with a stable gain of Φ d (s) below 2.4 kHz. Therefore, 2 and 1 kHz are selected as the carriers of baseband signal.

3 Experimental Results The proposed PSST strategy by injecting signals to power reference wave is experimentally verified. For testing, DC voltage source is 390 V, rated power is 750 W, rated load R is 50 Ω, rated phase voltage is 110 V, filter capacitor is 2.2 uF, filter inductor is 5 mH, k p = 0.015 and k i = 1. Signal carrier frequencies are configured to 1 and 2 kHz for presenting data 0 data 1, respectively. Signal carrier amplitude is 1 V. The amplitude of output voltage before signal injection is 155 V with about 0.8% THD, as shown in Fig. 6. When the load changes from 100 to 50 Ω, the output voltage shows fast dynamic response which can be recovered within 2 ms. By introducing power reference-based PSST method, the obtained voltage waveform is shown in Fig. 7, of which the voltage ripples represent the modulated signal. It can be seen that those ripples have negligible impact on system power quality. The THD of the output voltage is only about 1 ~ 2%. Transmitting binary data “11,001,001” with amplitude of 1 V. When the transmission rate increase from 0.02 bit/s to 0.01 bit/s, as shown in Figs. 8 and 9, the sampled ripples are attenuated with decreased amplitude, which would increase the signal demodulation complexity. Hence, the increment of transmission rate could lead to high error codes. The suggested bit rate is below 100 bps. Meanwhile, when the transmission rate is maintaining at 0.02 bit/s and the frequency of the signal carrier is increased, as shown in Figs. 8 and 10, the signal carrier is greatly attenuated due to the function of signal filters.

V(50V/grid) Load change

ua ub uc

t(10ms/grid) Fig. 6 The voltage of VSI with load changed before signal injection

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V(50V/grid)

ua ub uc

Signal ripple

t(10ms/grid) Fig.7 The voltage of VSI with load change after signal injection

V(2V/grid) 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1

2kHz 0.02s/bit 1kHz 0.02s/bit

t(40ms/grid) Fig. 8 1 and 2 kHz signal carrier filted from load with 0.02 s/bit

V(1V/grid)

2kHz 0.01s/bit 1kHz 0.01s/bit

t(20ms/grid) Fig. 9 1 and 2 kHz signal carrier filted from load with 0.01 s/bit

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V(200mV/grid) 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1

4kHz 0.02s/bit 3kHz 0.02s/bit

t(40ms/grid) Fig. 10 3 and 4 kHz signal carrier filted from load with 0.02 s/bit

2V/grid

Signal demodulated Signal transmitted

1 1 0 0 1 0 0 1 500mV/grid

t(40ms/grid) Fig. 11 The transmitted baseband signal and its corresponding demodulated wave

The sampled voltage ripples passing through the envelope detection circuit and low pass filter, is then compare with the preset threshold voltage to demodulate the baseband data. The demodulated signals shown in Fig. 11 reveals that the power reference based PSST strategy can realize signal transmission without affecting the output power quality of VSI. In comparison with the transmitted signal, a phase delay can be found, which is generally caused by sampling and filtering process.

4 Conclusions PSST strategies for DC/AC VSI system is newly designed for transmitting signals on the powerline without requirement of extra signal transmission channel and signal injection devices. The proposed PSST strategies can be implemented on VSI with

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no degrading on system stability and dynamic response, and hence can be attempted to be used in VSI based power conversion systems. Acknowledgements This work was supported in part by National Natural Science Foundation of China under Grant No. 51977208.

References 1. Lampe L, Tonello AM (2016) Power line communications: principles, standards and applications from multimedia to smart grid, 2nd, Wiley 2. Mao C, Chen Z (2019) An enhanced POE-based method with identified transmission errors for serial robotic kinematic calibration. In: 2019 IEEE 15th international conference on automation science and engineering, pp 1568–1573, Canada, BC, Vancouver 3. Stefanutti W, Mattavelli P (2006) Communication on power lines using frequency and duty-cycle modulation in digitally controlled dc-dc converters. In: IECON 2006—32nd annual conference on IEEE industrial electronics, pp 2144–2149. France, Paris 4. Wu J, Li C, He X (2010) A novel power line communication technique based on power electronics circuit topology. In: 2010 twenty-fifth annual IEEE applied power electronics conference and exposition (APEC), pp 681–685. USA, CA, Palm Springs 5. Wang R, Lin Z (2017) Direct sequence spread spectrum-based PWM strategy for harmonic reduction and communication. IEEE Trans Power Electron 32(6):4455–4465 6. Zhang Y, Chen G, Hu Y, Gong C, Wang Y (2020) Cascaded multilevel inverter based power and signal multiplex transmission for electric vehicles. CES Trans Electr Mach Syst 4(2):123–129

Improved Seven-Level Floating Capacitor Control Strategy Donghui Liu, Changbao Zheng, and Cungang Hu

Abstract This article introduces a new type of hybrid seven-level inverter topology, and analyzes its working principle and topological advantages. On the basis of fewer topological switching devices, in order to continue to reduce the complexity of the system, a new control strategy that selects the switching state according to the current level state, floating capacitor voltage and load current is proposed, which can be used without affecting reliability. The system reduces two levitation capacitor voltage sensors, reduces cost, and reduces volume. Finally, simulations and experiments verify the superiority of the topology and the effectiveness of the capacitor voltage control strategy. Keywords Seven-level inverter · Voltage balance control · Stacked carrier

1 Introduction Multi-level inverters have become the best choice for medium and high voltage transmission applications due to their low output voltage harmonic content and high withstand voltage levels [1]. With the development of technology in recent years, multilevel inverters have also been widely used in low-voltage and low-power converters. The output harmonic performance, efficiency and circuit complexity of low-power converters are of concern to many scholars. Hotspots [2, 3]. Increasing the number of inverter output levels can effectively reduce the harmonic content of the inverter output. Literature [4] proposed a new seven-level topology to solve the voltage equalization problem of the devices, but the topology is complicated D. Liu · C. Zheng · C. Hu (B) School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Zheng · C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_13

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and costly. Higher Literature [5] proposed a new topology 7L-TANPC topology in order to further reduce the number of switching devices in the seven-level circuit, improve system reliability, increase the efficiency of the inverter and reduce losses. In order to further simplify the system complexity, this paper proposes a new floating capacitor voltage modulation strategy, which can reduce the use of two floating capacitor voltage sensors in the inverter without affecting the system reliability, and further reduce the inverter volume.

2 7L-TANPC Inverter Topology 2.1 Basic Working Principle The seven-level converter topology used in this article is shown in Fig. 1. Compared with other seven-level topologies, this topology has fewer switching devices and is more suitable for low-voltage applications. The circuit is mainly composed of 7 switching devices and 2 floating capacitors. In this inverter, the DC bus voltage is 6E. The voltage across the two capacitors C1 and C2 is adjusted to half of the DC bus voltage, which is 3E. During normal operation, the average voltage of the two FCs: C x 3 and C x 4 must be maintained at E, where x represents the serial numbers A, B, and C of the three-phase bridge arms. It can generate seven voltages from − 3E to 3E. The voltage stress on S x 1, S x 2, S x 3 and S x 4 is 3E, while the voltage stress on S x 5, S x 6 and Sx7 is E. The 7-level topology circuit proposed in this article has a total of 12 switch states, some of which have an impact on the charging and discharging of the floating capacitor as the current direction is different, as shown in Table 1. In Table 1, “1” represents the switch is on, “0” represents the switch is off; Vo is the inverter output voltage.

Fig. 1 7L-TANPC inverter topology

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Table 1 TANPC_9L inverter switch status table Sx1 − Sx7

Switching states

VCx3

VCx4

VO

IO > 0

IO < 0

IO > 0

IO < 0

1,000,100

P3

–

–

–

–

3E

1,000,010

P2P

↑a

–

↓b

–

2E

0,010,100

P2N

↓

↓

↑

↑

2E

1,000,001

P1P

↑

↑

↓

↓

E

0,010,010

P1N

–

↓

–

↑

E

0,100,100

OP

–

–

–

–

0

0,010,001

ON

–

–

–

–

0

0,100,010

N1N

↑

–

↓

–

−E

0,001,100

N1P

↓

↓

↑

↑

−E

0,100,001

N2N

↑

↑

↓

↓

− 2E

0,001,010

N2P

–

↓

–

↑

− 2E

0,001,001

N3

–

–

–

–

− 3E

Note (1): a: ‘↑’ means the capacitor is charged; b: ‘↓’ means the capacitor is discharged

2.2 Modulation Strategy In this paper, the stacked carrier modulation method is used to control the output of the converter. By comparing the sinusoidal reference signal and the 6-triangular carrier, the corresponding switching state can be generated and a 7-level voltage is output, as shown in Fig. 2.

9

Fig. 2 Implementation of SPWM for the proposed 7-level inverter

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When outputting 2E, E, 0, − E and − 2E levels, there are two corresponding switch states respectively. These redundant switch states provide more degrees of freedom for the inverter’s floating capacitor voltage balance control. For example, when the circuit outputs the P2 level, you can choose to use the P2P switch state or the P2N switch state. These two switch states have different effects on the voltage of the floating capacitor (Fig. 3).

C3

3E Sx6

3E

C2

Sx3

E

0

3E

C2

Sx7

C1

3E

C3

Sx2

Sx6

0

Zx

3E

C2

Sx3

E

0

3E

C2

0 3E

C2

E

0

Sx3

C2

C1

E

3E

C3

Sx2

Sx7

0

Zx 3E

C2

Sx3 Sx4

E

Sx6

C2

Sx3

Fig. 3 7L-TANPC inverter switch state path

(k) UOx = - 2E

Sx5 C3 Sx7

C2

0

E

C3

Sx2

Sx7 Zx

3E

Sx6

C1

Sx6

Sx5

Sx1 3E

0

C4

E

(i) UOx = - E

C4

0

Sx7

Zx

C3

Sx4

UOx =0

Sx4

Sx7

E

(f)

E

Sx3

Sx5

E

C4

Sx2

3E

Zx 3E

C4

UOx =-2E (j)

0

0

UOx = - E

Sx2

E

Sx1

Sx6

C1

0

3E

Sx3

C1

3E

C4

Sx1

Sx6

Sx4

Sx7

(h) Sx5

C2

Sx5

E

Sx5 C3

E

Zx

C3

Sx4

(g) UOx =0 Sx1

Sx7

C1

(e) UOx =E

E

0

C4

Sx2

3E

Zx

Sx6

0

C4

Sx2

3E

C4

Sx4

E

Sx1 3E

Sx7

C1

0

Sx7 Zx

Sx3

E

Sx1

3E

C3

Sx2

C2

Sx3

(c) UOx =2E

Sx6

Sx3 Sx4

Sx5 E

Sx6

Sx4

C3

Sx2

Sx7

Sx1 C1

3E

Sx5

E

(d) UOx= E

3E

Sx2

Sx7

C1

C3

Zx

C4

Zx

C4

Sx4

E

Sx1

Sx5 E

Sx3

0

E

(b) UOx =2E

0

3E

Sx6

Sx4

(a) UOx =3E Sx1

C3

Zx

C4

Sx4

E Sx2

Sx5

C1

0

0

Zx

C1

3E

0

E Sx2

Sx1

Sx5

0

C1

0

3E

Sx1

0

Sx5

Sx1

C2

Sx3 Sx4

E

C4

UOx =-3E (l)

Sx6

0

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3 Control Strategy 3.1 Traditional Floating Capacitor Voltage Balance Control The basic condition for the operation of the 7-level converter proposed in this paper is that the voltage of the floating capacitor can be stabilized to E. Therefore, the control of the floating capacitor voltage is the core problem that needs to be solved in the design of the converter controller. Because the seven-level space vector pwm is more complicated, this article adopts the control strategy of reverse stacked carrier modulation. As shown in Fig. 1, the floating capacitor of the topology proposed in this article is composed of two capacitors C × 3 and C × 4 in series, and the terminal voltages of the two capacitors are both E. As mentioned earlier, the redundant switch states P2P, P2N, P1P, P1N, N1P, N1N, N2P, and N2N can affect C × 3 and C × 4 at the same time. Therefore, when controlling the voltage of the floating capacitor, it is necessary to control the voltage of C3 and C4. To determine the priority adjustment capacitor, the traditional floating capacitor control strategy is divided into four situations for analysis: (1)

(2)

(3)

(4)

When VC3 > VrefC3, VC4 > VrefC4, both C3 and C4 need to be discharged, when the output current Ix > 0, select P2N or N1P to discharge the capacitor, when Ix ≤ 0, select P1P or N2N to discharge the capacitor. When VC3 ≤ VrefC3, VC4 > VrefC4, C3 needs to be charged and C4 needs to be discharged. When ΔVC3 > ΔVC4, C3 gets the priority adjustment right. At this time, when Ix > 0, choose P2P and N1N to charge C3, when Ix ≤ 0, choose P2N and N1P to charge C3; when ΔVC3 ≤ ΔVC4, C4 obtains the priority adjustment right. At this time, when Ix > 0, select P1N and N2P to discharge C4, when Ix ≤ 0, select P1P and N2N to discharge C4. When VC3 > VrefC3, VC4 ≤ VrefC4, C3 needs to be discharged and C4 needs to be charged. When ΔVC3 > ΔVC4, C3 gets the priority adjustment right. At this time, when Ix > 0, choose P2N and N1P to discharge C3, when Ix ≤ 0, choose P2P and N1N to discharge C3; when ΔVC3 ≤ ΔVC4, C4 obtains the priority adjustment right. At this time, when Ix > 0, select P1P or N2N to charge the capacitor, when Ix ≤ 0, select P2N or N1P to charge the capacitor. When VC3 ≤ VrefC3, VC4 ≤ VrefC4, both C3 and C4 need to be charged. When the output current Ix > 0, select P1P or N2N to charge the capacitor, when Ix ≤ 0, select P2N or N1P to charge the capacitor.

3.2 Improved Voltage Control of Floating Capacitor According to the characteristics of the triangular carrier, the maximum or minimum value of the special point carrier can be selected for sampling calculation. Divide the modulation wave into six different stages. Since the output phase voltage has the

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participation of the levitation capacitor only in the case of level, it is only necessary to analyze the level of each modulation wave corresponding to different stages. The selected carrier sampling point will vary with different stages. For the VC × 3 floating capacitor voltage, the following formula can be used to estimate. When the switch state is P2P, use VFCS_c = Vdc1 − Vo to estimate the maximum and minimum values. When the switch state is P2N, the maximum and minimum values are estimated with VFCS_c = VFCS_c − (VFCS_c + VFCX_c − Vo)/2. When the switch state is P1P, the maximum and minimum values are estimated with VFCS_c = VFCS_c + (Vdc1 − Vo − VFCS_c − VFCX_c)/2. When the switch state is N1N, the maximum and minimum values are estimated with VFCS_c = −Vo. When the switch state is N1P, the maximum and minimum values are estimated with VFCS_c = VFCS_c − (VFCS_c + VFCX_c − Vdc2 − Vo)/2. When the switch state is N 2 N, the maximum and minimum values are estimated with VFCS_c = VFCS_c-(VFCS_c + VFCX_c + Vo)/2. In the same way, the floating capacitor voltage of VCx4 can also be estimated with the following formula. When the switch state is P1N, the maximum and minimum values are estimated with VFCX_c = Vo. When the switch state is P2N, the maximum and minimum values are estimated with VFCX_c = VFCX_c − (VFCS_c + VFCX_c − Vo)/2. When the switch state is P1P, the maximum and minimum values are estimated with VFCX_c = VFCX_c + (Vdc1 − Vo − VFCS_c − VFCX_c)/2. When the switch state is N2P, the maximum and minimum values are estimated with VFCX_c = Vdc2 + Vo. When the switch state is N1P, the maximum and minimum values are estimated with VFCX_c = VFCX_c − (VFCS_c + VFCX_c − Vdc2 − Vo)/2. When the switch state is N2N, the maximum and minimum values are estimated with VFCX_c = VFCX_c − (VFCS_c + VFCX_c + Vo)/2. The above calculation is carried out by the estimated voltage value of the floating capacitor later. It is found that the simulation result is not much different from the normal carrier modulation, but it can save two floating capacitor voltage sensors, reduce the complexity of the system, reduce the cost and further increase the power density.

4 Simulation In order to verify the performance of the proposed TANPC_7L and the capacitor voltage balance control method, a simulation model of the three-phase inverter was built in the MATLAB/Simulink simulation software. The simulated DC bus voltage is 300 V, the DC bus capacitances C1 and C2 are 20,000 uF, the floating capacitances C

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× 3 and C × 4 are 0.0035 F, the fundamental frequency is 50 Hz, the load impedance Z = 10 Ω, L = 3 mH. Figure 4a and b respectively show the line voltage and floating capacitor voltage waveforms under the traditional control strategy, and Fig. 4c and d show the waveforms under the improved control strategy. After that, the unfiltered line voltages of the two control strategies are analyzed by FFT, as shown in Fig. 5a and b. From the summary of the figure, it can be seen that the harmonic content of the two waveforms is close to the same, and the harmonic

(a) Traditional control strategy line voltage waveform

(b) Traditional control strategy Floating capacitor voltage waveform

(c) Improved control strategy line voltage waveform Fig. 4 Simulation waveforms

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(d) Improved control strategy Floating capacitor voltage waveform Fig. 4 (continued)

Traditional control strategy line voltage FFT analysis diagram

Improved control strategy line voltage FFT analysis diagram Fig. 5 FFT waveforms

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content of the improved control strategy is only 0.65% more, but it reduces the use of two floating capacitor voltage sensors.

5 Conclusion This paper proposes a new type of voltage balance control strategy for the floating capacitor of the seven-level inverter. This control strategy can reduce the number of voltage sensors in the seven-level circuit without affecting the reliability, reduce the cost, and further reduce the size of the inverter. The volume and increase the power density are finally verified by simulation. It provides a solution from the control strategy for the further optimization of TANPC_7L topology.

References 1. Rodriguez J, Bernet S, Bin W et al (2007) Multilevel voltage source converter for industrial medium voltage drives[J]. IEEE Trans Industr Electron 54(7):2930–2945 2. Kouro S, Malinowski M, Gopakumar K et al (2010) Recent advances and industrial applications of multilevel converters[J]. IEEE Trans Industr Electron 57(8):2553–2580 3. Tan G, Deng Q, Liu Z (2013) An optimized svpwm strategy for five-level active NPC (5L-ANPC) converter[J]. IEEE Trans Power Electron 29(1):386–395 4. Ghias AMYM, Pou J, Acuna P et al (2017) Elimination of low-frequency ripples and regulation of neutral-point voltage in stacked multicell converters[J]. IEEE Trans Power Electron 32(1):164– 175 5. Cungang H, Hao D, Yunlei Z, Jie L (2020) Hybrid active neutral point clamped seven-level inverter and its control strategy[J]. J Electr Mach Control 24(04):40–49

Predictive Control Method for Secondary Ripple Suppression of Two-Stage Single-Phase Inverter Liyan Zhang, Cungang Hu, Wenjie Zhu, and Jialiang Jiao

Abstract The output power of the two-stage single-phase inverter has a pulsation that is twice the basic frequency of the output voltage, so a double-frequency pulsation will be superimposed on the DC bus voltage and DC current. The cause of the secondary ripple and the mechanism of propagation was analyzed in this article. Try to suppress the current ripple on the DC side from the perspective of model predictive control, and try to add a notch filter to improve the ripple suppression performance. Finally, the effectiveness of the control method is verified by simulation. Keywords Two-stage single-phase inverter · Secondary ripple · Model predictive control

1 Introduction Two-stage single-phase inverters are widely used in photovoltaic grid-connected and off-grid power generation. The front-stage DC-DC conversion circuit is used for voltage matching, and the latter-stage single-phase inverter is used to generate AC power, which can directly supply power to the load or be connected to the grid. However, the output power of the two-stage single-phase inverter has a pulsation that is twice the fundamental frequency of the output voltage. Without considering the power loss, this power pulsation will superimpose the second harmonic component in the DC bus voltage and current. This harmonic component will not only affect the stability of inverter operation, but also make the output superimpose higher harmonics. It will also cause irreversible damage to the electrodes and electrolyte, L. Zhang · J. Jiao School of Electrical Engineering and Automation, Anhui University, Hefei, China C. Hu (B) · W. Zhu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China e-mail: [email protected] Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_14

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greatly reducing the service life of the bus capacitance and the battery. It will also affect the soft switching characteristics of the switching device, making the soft switching control of the device more difficult. Traditional control methods can be divided into the following categories. Virtual impedance method: By increasing the virtual impedance of the previous circuit, the second harmonic current of the previous circuit is greatly reduced, but this method will increase the current stress of the capacitor and affect the dynamic response characteristics of the circuit [1, 2]. AC side power decoupling method: additional circuits are added to the AC side to compensate for pulsating power [2]. DC bus parallel device method: divided into active suppression and passive suppression. Compensate for the second harmonic by connecting an additional circuit in parallel with the DC bus, such as an LC resonant circuit and a bidirectional DC-DC conversion circuit. Although this method is effective, it will add additional components, increase the control difficulty and equipment volume, and is not conducive to the improvement of system power density [3]. Model predictive control is a kind of non-linear control, and its essence is a control method to obtain the optimal amount. Through sampling the current state, the open-loop control of the control variable that minimizes the objective function is solved. Therefore, model predictive control has the characteristics of convenient modeling and good dynamic characteristics. This paper analyzes the mechanism of the secondary ripple generation and propagation of the two-stage single-phase inverter, and applies the model predictive control to it, and adds a notch filter to improve the ripple suppression performance. Finally, the effectiveness is verified by simulation.

2 Analysis of the Second Harmonic Generation Mechanism The structure of the two-stage single-phase inverter is shown in Fig. 1. The front stage of the circuit is a Boost DC-DC conversion circuit, and the latter stage is a single-phase inverter. In order to control the variables, the subsequent single-phase inverter adopts single-phase dq decoupling control uniformly. Since there is only one

Fig. 1 Two-stage single-phase inverter

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Fig. 2 Two-stage single-phase inverter control

AC quantity, the coordinate transformation cannot be performed directly. Therefore, a virtual variable perpendicular to the output voltage is generated by a second-order generalized integrator, and through coordinate transformation, the AC voltage in static coordinate system is transformed into DC voltage in dq rotating coordinate system. Then the dq component can be controlled without error through the PI regulator to reach the set value. The control block diagram is shown in Fig. 2. If the control is effective, the load voltage and load current are both the fundamental wave of 50 Hz. Assuming that the load is a resistive and inductive load, the output voltage and load current of the inverter are respectively: u o = Uo sin(ωt)

(1)

i o = Io sin(ωt − ϕ)

(2)

Among them, U o and I o are the amplitudes of the load voltage and current respectively. The instantaneous output power available from the output voltage and load current is: pac = u o i o =

1 1 Uo Io cos ϕ − Uo Io cos(2ωt − ϕ) 2 2

(3)

From the formula (3), the instantaneous output power is composed of DC power and a double frequency pulsating power. Without considering the power loss, the DC input power is equal to the AC output power. If the DC voltage and current are both standard DC, then the power it provides will be a constant value, and the pulsating power will be nowhere to be provided, so the DC input must be superimposed with a double-frequency pulsating power. It is assumed that the pulsating frequency can be completely absorbed by the DC bus capacitance, the bus capacitor voltage is V dc , the ripple voltage is V s :

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Vdc C

1 dvs = Uo Io cos(2ωt − ϕ) 2 dt

(4)

Integrate both sides of the formula (4), the capacitor voltage pulsation is: vs =

Vo Io sin(2ωt − ϕ) 4ωC Vdc

(5)

Assuming that the inductor can completely absorb the power ripple, then: IL L

di s 1 = Uo Io cos(2ωt − ϕ) 2 dt

(6)

Integrate the above formula as well, and the pulsation of the inductor current is: is =

Vo Io sin(2ωt − ϕ) 4ωL I L

(7)

It can be seen from the above formula that the frequency of the ripple is twice the fundamental frequency. When the capacitance value of the capacitor or the inductance value is infinite, the pulsation can be completely eliminated. But in reality, consider the volume of capacitance and inductance, the capacitance value and the inductance value cannot be infinite, so the secondary ripple exists in both the DC bus voltage and the DC current.

3 PI Model Predictive Control with Notch Filter In the two-stage single-phase inverter, the Boost circuit works in a continuous current state. In this state, the circuit has two working modes. Figure 3 shows that when the switch is turned on, the power supply and the inductance form a branch separately,

Fig. 3 Equivalent circuit when switch S1 on

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Fig. 4 Equivalent circuit when switch S1 off

and the inductance stores energy. The diode is cut off in order to prevent energy backflow. The capacitor discharges to supply power to the load. As shown in Fig. 4, the voltage induced by the inductor when the switch is off is the same polarity as the power supply. So the power supply and the inductor jointly transfer energy to the subsequent stage to achieve voltage pumping, and charge the capacitor while supplying power to the load. The output voltage of the Boost circuit is the same polarity as the input voltage. The discrete state equation of Boost DC-DC conversion circuit is [4]: 

 T    (dk −1)·T  1 i (kT ) i (k+1)T L + L Uin = (1−dk )·T T 1 − RC u (kT ) 0 u (k+1)T C  i (k+1)T = i (kT ) + (dk −1)·T · u(kT ) + TL · Uin L T · u (kT ) u (k+1)T = (1−dCk )·T · i (kT ) + 1 − RC

(8)

(9)

In the formula (9), i(kT) and u(kT) are the sampling values of the inductor current and output voltage at the current moment, and i(k+1) T and u(k+1)T are based on the inductor current, output voltage, input voltage, period, duty cycle, capacitance value, and inductance value to predict the inductance circuit and output voltage value at the next moment. After having the above discrete state equation, we must also establish an objective function. The objective function needs to reflect the error between the predicted value and the set value, so that the objective function is minimized and the optimal control variable is selected to control the Boost DC-DC converter circuit. In the two-stage single-phase inverter, our goal is to suppress the second harmonic on the DC side, so the objective function can be set as:   y = i (k+1) − ir e f 

(10)

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Since the absolute value and the square have the same characteristics, the formula (9) can be equivalent to: 2  y = i (k+1)T − ir e f

(11)

Substitute the state equation of the Boost DC-DC conversion circuit into formula (11):  2 T (dk − 1) · T y = i (kT ) + · u (kT ) + · Uin − ir e f L L

(12)

When the objective function is the smallest, it is the optimal duty cycle we are looking for. The above equation finds the first derivative and the second derivative of d k : 

 2T 2 · u 2(kT ) 2T · u (kT ) T · Uin  · (dk − 1) + · i (kT ) − ir e f + (13) y = L L L2 y  =

2T 2 · u 2(kT ) L2

(14)

The second derivative is a square term, so the second derivative must be nonnegative, so the first derivative is a monotonic increasing function, and it can be approximated as i(kT) = iref in the steady state. When d k = 1: y =

2T · u (kT ) T · Uin · L L

(15)

It is easy to know that the formula (15) is always greater than 0. When d k = 0: y = −

2T 2 · u 2(kT ) L2

+

2T 2 · u (kT ) · Uin L2

(16)

Because this circuit is a Boost circuit, the output must be greater than the input, so the above formula is less than zero. Therefore, the duty cycle must have a solution within (0, 1) to minimize the objective function. Set y’ = 0 to obtain the duty cycle that minimizes the objective function: dk =



T · Uin L · ir e f − i (kT ) − +1 T · u (kT ) L

(17)

The above formula is the optimal solution under this objective function. It is not enough to have the optimal duty ratio of the above formula. In a singlestage Boost circuit, the quantity to be controlled is the output voltage or the inductor current, which corresponds to the duty ratio one-to-one. In a two-stage single-phase

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inverter, both the DC bus voltage and the inductor current need to be controlled. It is obviously impossible to control the bus voltage and the inductor current at the same time with a duty cycle, so it is necessary to introduce PI controller into the loop. The outer loop is the bus voltage loop, the inner loop is the inductor current predictive control, and the output of the PI controller is used as the reference for the inductor current model predictive control. From the foregoing analysis, it can be seen that only when the DC bus capacitance tends to infinity, the pulsating voltage on the DC bus capacitance can be completely eliminated. Therefore, the feedback at the previous stage is a pulsating amount superimposed by the second harmonic, which leads to the current reference value is also a pulsating quantity. This pulsating reference value will affect the model predictive control, so this double frequency component must be filtered out. Only in this way can the DC reference value be obtained. Therefore, a notch filter whose characteristic frequency is consistent with the harmonics can be added to the output of PI controller. The transfer function of the notch filter is as follows: G notch (s) =

s 2 + ωn2 s 2 + ωQn s + ωn2

(18)

where Q is the quality factor and ωn is characteristic angular frequency. When the value of the quality factor Q is larger, the filter effect of the notch filter on the characteristic frequency harmonics is better, but its frequency adaptability will also deteriorate accordingly, that is, the less harmonics can be filtered. In addition, the notch filter will introduce a large negative phase shift in the frequency band below the characteristic frequency, but because it is connected in series in the feedforward branch, it will not affect the stability of the system. The overall PI model predictive control block diagram with the notch filter is shows in Fig. 5:

Fig. 5 Model predictive control block diagram

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Table 1 Two-stage inverter parameter table U in

U bus

V out(RMS)

C bus

L1

C

Switching frequency

30 V

50 V

21.21 V

10000e-6F

0.1 mH

120 uF

10 kHz

Table 2 Control parameter table

Kp

Ki

Qnotch

2

50

0.707

4 Simulation Results In order to verify its correctness, a two-level inverter simulation was carried out in Matlab/Simulink. The simulation parameters are shown in the Tables 1 and 2. Inverter output voltage is shown in Fig. 6. It can slao be seen from Figs. 7 and 8 that both the DC bus voltage and the inductor current have double-frequency pulsation, which is consistent with the theoretical analysis. Before adding the notch, the pulsation of the inductor current on the DC side reached 1.85A, accounting for 13.7% of the DC, which is much higher than the specified 10%. The DC current at this time will not only affect the battery life, but also increase the difficulty of soft switching. After adding the notch, the pulsation of the inductor current on the DC side is reduced to 0.6A, which accounts for 4% of the DC. Load jump experiment, at 0.6 s, the impedance jumps from Z = 1 + j0.628 to Z = 0.5 + j0.314, the DC side inductor current waveform, output voltage waveform and DC bus voltage are respectively shown in Figs. 9, 10 and 11. DC side inductor current can quickly stabilize at the new value, and the overshoot is small, and the DC bus voltage can be restored to the reference value after the drop. Due to the drop of the DC bus voltage, the output voltage will also produce small fluctuations, but it can also be tracked to the reference value again in a short time.

5 Conclusion From the above theoretical analysis and simulation, it can be seen that the PI model predictive control alone has a small suppression effect on the secondary ripple. The addition of a notch filter can greatly reduce the DC side inductor current ripple, but there is no suppression effect on voltage ripple in the DC bus. And thanks to the fast dynamic response of the model predictive control, during the load jump experiment, the overshoot of the DC side inductor current is small, and the response time is relatively fast. The DC bus voltage can also quickly recover to the set value after a short drop. It can be seen that this strategy has a good effect on secondary ripple suppression and dynamic characteristics.

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Fig. 6 Inverter output voltage (a is after adding the notch filter, b is before adding the notch filter)

The work is supported by the National Natural Science Foundation of China (51777001), Educational Commission of Anhui Province (KJ2020A0031).

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Fig. 7 DC-DC inductor current waveform (a is after adding the notch filter, b is before adding the notch filter)

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Fig. 8 DC bus voltage waveform (a is after adding the notch filter, b is before adding the notch filter)

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Fig. 9 Load jump DC side inductor current

Fig. 10 Load jump output voltage waveform

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Fig. 11 DC bus voltage waveform during load jump

References 1. Li Z, Xinbo R, Xiaoyong R (2015) Control method of front-end DC converter in two-level inverter[J]. Proc Chin Soc Electr Eng 35(03):660–670 2. Bin L, Jianjun H, Mei S, Yao S, Hui W, Qingsong T (2013) Two-stage single-phase inverter input ripple current dual feedback suppression[J]. Trans Chinese Soc Electr Eng 28(08):187–193 + 217 3. Zhang L, Ruan X, Ren X (2018) One-cycle control for electrolytic capacitor-less second harmonic current compensator. IEEE Trans Power Electron 33(2):1724–1739. https://doi.org/ 10.1109/TPEL.2017.2682420 4. Kai K (2019) Research and implementation of two-phase interleaved parallel BOOST converter based on PI-model predictive control method[D]. Beijing University of Technology, 2019.

Research on Second Harmonic Ripple Suppression of Two Stage DC-AC Inverter Jialiang Jiao, Cungang Hu, Wenjie Zhu, and Liyan Zhang

Abstract Reducing the secondary ripple and improving the dynamic performance are the basic control goals of the front-end DC-DC converter in the two-level inverter. From the perspective of impedance, this paper makes the closed-loop output impedance of the front-end DC converter present high impedance at twice the output voltage frequency, and low impedance at the non-double output voltage frequency. The virtual impedance is connected in series in the front-end converter and the virtual impedance is connected in parallel at the bus capacitor to suppress the secondary ripple component value on the DC side. Taking the BUCK-type pre-converter as an example, according to the control block diagram that realizes the virtual series impedance and the virtual parallel impedance, two common secondary ripple current suppression methods are obtained. Build a two-stage inverter simulation model with a BUCK type as the front stage in the Matlab/Simulink platform, and analyze the theory and simulation results to improve the secondary ripple current suppression effect of different control methods and the improvement of the dynamic performance of the system compared. Keywords Two-level inverter · BUCK-type pre-converter · Second harmonic current · Virtual impedance

J. Jiao · C. Hu (B) · W. Zhu · L. Zhang School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_15

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1 Introduction Two-level inverters are frequently used in photovoltaic power generation systems in which the input and output voltages differ greatly from each other [1]. Among them, the front-stage DC-DC converter is used to achieve electrical matching and electrical isolation, and the latter-stage inverter converts direct current into alternating current. For a single-phase inverter, its instantaneous output power pulsates at twice the output voltage frequency, so that there is a secondary ripple current in its input current. The secondary ripple current will not only increase the current stress of the switch tube, but also increase the conduction loss of the switch tube and the loss of magnetic components [2]. In the photovoltaic power generation system, the secondary ripple current will cause the photovoltaic cell to oscillate at the maximum power point, which will affect the realization of maximum power tracking and reduce the system efficiency [3]. Therefore, it is still very necessary to suppress the second harmonic current in the front-stage DC-DC converter. There are three commonly used methods for suppressing the second harmonic current of the front-end DC-DC converter: (1) Increasing the middle bus capacitance, its function is to reduce the impedance at twice the output voltage frequency, so that the second harmonic current can flow through the middle bus capacitance as much as possible, but the middle bus capacitance is generally required to be too large. It is not conducive to the selection of the device [4]. (2) Parallel a bidirectional inverter on the intermediate bus capacitor, and provide the pulsating power required by the single-phase inverter through the bidirectional inverter, which can effectively reduce the secondary ripple current in the front-stage DC-DC converter. But it will increase the complexity of the system and reduce the stability [5]. (3) Adopt an appropriate control strategy to increase the closed-loop output impedance of the front-stage DCDC converter at twice the output voltage frequency, which is much larger than the capacitive reactance of the intermediate bus capacitor, so that the second harmonic of the back-stage inverter. The current mainly flows from the bus voltage. From the perspective of impedance, this paper makes present high impedance at twice the output voltage frequency, and low impedance at the non-double output voltage frequency [6]. The virtual impedance is connected in series in the front-end converter and the virtual impedance is connected in parallel at the bus capacitor to suppress the secondary ripple component value on the DC side. Taking the BUCKtype pre-converter as an example, according to the control block diagram that realizes the virtual series impedance and the virtual parallel impedance, two common secondary ripple current suppression methods are obtained. Finally, through theoretical analysis and simulation comparison, the influence of the two control methods on the steady-state and dynamic characteristics of the system is analyzed.

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2 Generation Mechanism of Secondary Ripple Current Take a two-stage inverter whose front stage is a BUCK converter as an example. Figure 1 is a block diagram. Among them, Lf is the output filter inductance of the previous DC-DC converter; Cf is the output filter capacitor of the previous converter, which is generally called the middle bus capacitor. The schematic diagram of inverter assumes that the voltage waveform is an ideal sine wave uo : u o = Uo sin(ωt)

(1)

Among them, uo and ω are the output voltage amplitude and angular frequency of the inverter respectively. Zload is linear load, Io is output current of inverter: i o = Io sin(ωo t − ϕ)

(2)

Io is the output current amplitude of the inverter; ϕ is the load impedance angle. The instantaneous output power: Po = u o i o =

1 1 Uo Io cos ϕ − Uo Io cos(2ωo t − ϕ) 2 2

(3)

It is assumed that the conversion efficiency of single-phase inverter is 100%. Then the input power Pin and output power Po of the later stage inverter are equal. i inv =

Uo I o Uo I o cos ϕ − cos(2ωo t − ϕ) 2UC f 2UC f

(4)

According to Eq. (4), the input current iinv is composed of a DC component and a second harmonic component. It can be seen from Fig. 1 that the second harmonic component can only be provided by the former DC-DC inverter and the Cf .

Fig. 1 Schematic diagram of two-stage single-phase inverter

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3 Secondary Ripple Current Suppression and Dynamic Performance Improvement 3.1 The Basic Method is Put Forward According to Thevenin’s theorem from Fig. 1, the front-end DC converter can be equivalent to the open circuit voltage Uoc and the output impedance Zori (s). If the highfrequency harmonic components in the input current of the inverter are neglected, the subsequent inverter can be equivalent to the parallel DC current source Idc and the second harmonic current source I2nd [7]. The schematic diagram of the equivalent two-stage single-phase inverter in Fig. 1 is shown in Fig. 2. In Fig. 2, Zo (s) is the front-stage closed-loop output impedance. Because the second harmonic component can only be provided by the DC converter and the bus capacitor. It is necessary to increase the impedance amplitude of Zo (s) at 2fo (twice the voltage output frequency), and to ensure that the system has better dynamic (The smaller the impedance in the DC-DC inverter, the better the dynamic performance), it is necessary to minimize the impedance amplitude of Zo (s) at non-2fo . If the impedance amplitude of Zo (s) can be increased at 2fo , and the impedance amplitude can be reduced at non-2fo , the requirements can be met simultaneously [8]. Therefore, it is proposed to connect the virtual impedance ZS (S) in series at Zori (s), and then connect the virtual impedance ZP (s)/GN (s) in parallel. In order to maximize the impedance amplitude of Zo (s) at 2fo , the virtual impedance is connected in parallel. The open circuit characteristics should be present at 2fo . The schematic diagram of introducing series virtual impedance and parallel virtual impedance is shown in Fig. 3. Figure 4 is a simplified circuit schematic diagram of a two-stage single-phase inverter, where Lf is the filter inductance; rd is the equivalent series resistance. Based on Figs. 4 and 5a is a control block diagram for realizing virtual series impedance and virtual parallel impedance. Among them, KPWM is the gain of the pulse width modulation modulator; Hv is the sampling coefficient of the bus voltage; The block diagram after transformation is shown in Fig. 5b. Fig. 2 The equivalent schematic diagram of a two-stage single-phase inverter

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Fig. 3 Introducing virtual series impedance and virtual parallel impedance in the inverter

Fig. 4 Two-stage single-phase inverter with Buck-type DC converter as the front stage

Fig. 5 Control block diagram of virtual series impedance and virtual parallel impedance

The proposed series resistance is to increase the closed-loop output impedance of the front-stage DC converter. At the same time, for the consideration of dynamic characteristics, the selected impedance is preferably high impedance at 2f0 and low impedance at non-2f0 . Among them, the inductor current feedforward is to increase the speed and accuracy of the system. The load current feedforward can effectively improve the dynamic characteristics of the converter when the load jumps. In fact, reducing the amplitude of the output impedance of the inductor branch is contradictory to suppressing the secondary ripple current.

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3.2 Selection of Virtual Impedance (1)

If the virtual impedance ZS (s) is a fixed value, the impedance amplitude of Zo (s) at non 2fo should be reduced as much as possible in order to achieve high impedance of Zo (s) at 2fo . Then the parallel virtual impedance should be in the form of ZP (s)/GN (s). G N (s) =

(2)

s ( 2π ·2 )2 + 1 f0 s ( 2π ·2 )2 + f0

s Q·2π ·2 f 0

+1

(5)

If the virtual impedance ZS (s) has the form of riGBPF (s), the expression is as follows: G B P F (s) =

s Q·2π ·2 f 0 s ( 2π ·2 )2 + Q·2πs ·2 f0 f0

+1

(6)

In this case, the virtual impedance ZP (s)/GN (s) can be selected not to be paralleled. (3)

If the series virtual impedance Zs (s) has the form of riGBPF (s), and the parallel virtual impedance has the form of ZP (s)/GN (s).

This article selects the series virtual impedance Zs (s) = riGBPF (s), the parallel virtual impedance ZP (s)/GN (s) (taking into account the secondary ripple current suppression and the improvement of dynamic characteristics) and only the series virtual impedance Zs (s) = ri (only pay attention to the suppression of secondary ripple current) two control methods.

3.3 Load Current Feedforward Control with Band Stop Filter In order to effectively improve the dynamic characteristics of the converter when the load jumps, the load current feedforward method can be sampled to reduce the amplitude of the front-stage converter closed-loop output impedance, as shown in the following Fig. 8 on the Z01 (s) amplitude-frequency characteristic curve. Using virtual impedance Zs (s) = riGBPF (s), and adding parallel virtual impedance ZP (s)/GN (s), the following relationship can be obtained from Eqs. (5) and (6): G N (s) = 1 − G B P F (s)

(7)

Incorporate formula (7) into Fig. 5b, and adjust the lead-out point from capacitor voltage to capacitor current, and then get the control block diagram 6 through a series of equivalent transformations.

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(a) Equivalent transformation 1

(b) Equivalent transformation 2

(c) Equivalent transformation 3

(d) Equivalent transformation 4

Fig. 6 Load current feedforward control with band stop filter

If the added virtual impedance is: Z p (s) s L f + rd + ri G B P F (s) = G N (s) sC f ri G N (s)

(8)

Then you can get the control block diagram of Fig. 6c, and then combine the inductor current feedback and the capacitor current feedback with the same feedback item, and finally get the control block diagram of Fig. 6d. Since the value of GN (s) at 2fo is close to zero, it can be obtained from Eq. (8): ⎧ ⎪ ⎪ ⎨ ∞,

Z p (s) = G N (s) ⎪ ⎪ ⎩

s L f +rd , sC f ri

s = 2π (2 f o ) (9) s /= 2π (s f o )

The parallel virtual impedance presents an open circuit at 2f0 , high impedance near 2f0 , and lower impedance amplitude at other frequency points. It can be deduced that the closed-loop output impedance of the front-stage DC converter is: Z 01 (s) =

s L f + rd + ri (1 − G N (s)) 1 + sC f ri G N (s) +

Uin Hv G v (s) Um

(10)

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Fig. 7 Second harmonic current control of series virtual resistance

3.4 Second Harmonic Current Control of Series Virtual Resistance The control method adopts the series virtual impedance Zs (s) = ri, and does not add the parallel virtual impedance. The impedance amplitude of Zo (s) in the whole frequency band is very large. This method can suppress the second harmonic current but will make the dynamic performance of the system worse. The control block diagram is shown in Fig. 7. The closed-loop output impedance of the front-stage DC converter is: Z 02 (s) =

s L f + rd + ri 1+

Uin Hv G v (s) Um

(11)

4 Comparison of Control Methods Through the previous two control methods, we can see that their essential ideas are still the same. Due to the different methods of the two control strategies and the selected virtual impedance, the front-stage DC converter will be different, resulting in different effects on suppressing the second harmonic current and improving the system dynamic performance. In this paper, the aforementioned load current feedforward control with band stop filter (called “method one”) and secondary ripple current control with series virtual resistors (called “method two”) will be mentioned. The above two front-stage DC converters are respectively Eqs. (10) and (11). Combined with Fig. 8, the following conclusions can be drawn:

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Fig. 8 Amplitude-frequency characteristic curve of Z01 (s), Z02 (s), Z03 (s) when GN (s) is the same

(1)

(2)

(3)

(4)

(5)

If the voltage regulator Gv (s) and the virtual impedance ri are the same. By comparing their closed-loop output impedance, Z01 (s) has a higher amplitude at 2f0 . If the voltage regulator Gv (s) is the same, but the virtual impedance ri is different. Method 1: In order to ensure that voltage of the front-end DC converter can reach the rated value under the condition of the lowest input voltage and full load, the virtual resistance ri has an upper limit. Without considering the dynamic stability, ri can take a very large value in the second method. For example, when ri=500Ω, the closed-loop impedance Z03 (s) is shown in Fig. 8, so that the front-end DC converter is closed-loop at 2f0 The output impedance is larger, so as to achieve a better suppression of the secondary ripple current effect. In terms of dynamic characteristics, the amplitude of Z01 (s) is high at 2f0 , the amplitude of non-2f0 is low, and the amplitude of Z02 (s) is high at both 2f0 and non-2f0 . Because the smaller the impedance amplitude in the DC-DC converter, the better the dynamic performance of the system. At non-2f0 , the amplitude of Z01 (s) is lower than the amplitude of Z02 (s), so the dynamic characteristics of method two are not as good as those of method 2 One. The voltage stress of the bus capacitor. In the steady state, because the bus capacitance is generally large, the fluctuation of the bus voltage is actually not large. At this time, the difference in the voltage stress of the bus capacitance between the two control methods is not obvious. When it is dynamic, the dynamic characteristics of method one is better than that of method two, so the bus voltage of method two is more prone to large fluctuations, and the voltage stress of the bus capacitor of method two is greater. The current stress of the filter inductor. In the steady state, since the amplitude of Z01 (s) is higher than the amplitude of Z02 (s) at 2f0 , the first method has a better effect of suppressing the second harmonic, so the first method has a smaller

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current stress on the filter inductor. In the dynamic state, since the amplitude of Z02 (s) is higher than the amplitude of Z01 (s) at a position other than 2f0 , the dynamic characteristics of method one are better than those of method two. In method two, the secondary ripple current of the inductor fluctuates more. The current stress on the inductor is also greater.

5 Simulation Results In order to verify the correctness of the above theoretical analysis, two sets of comparative simulation experiments were carried out. Table 1 shows the main parameters of the simulation. Table 2 shows the parameters of the voltage regulator Gv (s) and virtual resistance ri of the two methods in the two sets of comparative experiments. In the first group, when the voltage regulator and the virtual impedance are the same, compare the steady-state simulation waveforms of the two methods; in the second group, when the voltage regulator and the virtual impedance are both the same, compare the dynamic performance of the system under the two methods (the load is Switch between full load and half load). Table 1 Main parameters of simulation

Table 2 The parameters of GV (s) and ri in the experiment were compared

Parameter

Numerical value

Parameter

Numerical value

Input DC voltage Uin /V

100

Bus capacitance Cf /uF

10,000

Output AC voltage Uo /V

28

Switching frequency fs /KHZ

10

Output voltage frequency f0 /HZ

50

Carrier amplitude Um /V

1

Intermediate bus voltage UCf /V

70

Voltage sampling factor Hv

1

Filter inductance Lf /uH

1000

Damping resistance rd /Ω

1

Method 1

Method 2

GV (s)

15 + 3/s

15 + 3/s

ri/Ω

250

250

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Bus voltage

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Inductor current (a) Method 1

Bus voltage

Inductor current (b) Method 2

Fig. 9 Steady state simulation waveform

Figure 9 shows the steady-state simulation waveforms of the inverters of the two methods in the first group of comparison methods. The bus voltage and inductor current are given in detail. It can be seen from Fig. 9 that when the voltage regulators GN (s) and ri are the same, the bus voltage fluctuation amplitude in method one is 1.5 V, while the bus voltage fluctuation amplitude in method two is 1.7 V. The frequency is 100 Hz, the fluctuation range of method one is smaller than that of method two, and the bus voltage of method one is more stable than that of method two. And the fluctuation amplitude of the inductor current in the first method is 2.2 A, and the fluctuation amplitude of the inductor current in the second method is 3.2 A, and the frequency is 100 Hz. The fluctuation range of the first method is significantly smaller than that of the second method, which suppresses the secondary ripple current better result. Therefore, in the steady state, the method two increases the current stress of a pair of front-stage DC-DC converter switch tubes more than the method. Figure 10 shows the dynamic simulation waveforms of the inverters of the two methods in the second group of comparison methods. The bus voltage and inductor current are given in detail. It can be seen from Fig. 10 that when the voltage regulators GN (s) and ri are the same, the voltage of the method two drops around 0.5 V, and the method one has almost no obvious voltage drops. The recovery time can hardly be observed in the first method, and the recovery time in the second method is even longer (about 20 ms). Both of the bus voltage fluctuations are not obvious. When the load jump is stable, the inductor current fluctuation amplitude of method 1 is 1.3 A, while the inductor

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Bus voltage

Inductor current (a) Method 1

Bus voltage

Inductor current (b) Method 2

Fig. 10 Dynamic simulation waveform

current fluctuation amplitude of method 2 is 2.3 A, and the frequency is 100 Hz. The fluctuation range of inductor current of method 1 is smaller, so the second method is suppressed. In terms of sub-ripple current, method one is also significantly better than method two. The voltage stress on the bus capacitor and the current stress on the inductor current increase less.

6 Conclusion From the point of view of impedance, in order to balance the secondary ripple current suppression, this paper adopts the method of virtual impedance. The output impedance of the front-end DC converter is connected in series with the virtual impedance, and the virtual impedance is connected in parallel with the intermediate bus capacitor, so that the closed-loop output impedance of the front-end DC converter presents a high impedance where is at twice the output voltage frequency, but at a non-double output voltage Low impedance at frequency. Then take the BUCK circuit in the previous stage as an example to reveal the internal relationship between them. Finally, compare two different secondary ripple current suppression methods. Through theoretical analysis and actual simulation, it can be known that when the voltage regulator GN (s) and the virtual resistance ri are the same, regardless of the steady-state characteristic or the dynamic characteristic, the load current feedforward

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control method with band stop filter suppresses the secondary ripple current. The suppression effect is better than the secondary ripple current control method of series virtual resistance. In addition, the load current feedforward control with band stop filter has better dynamic characteristics, and increases the voltage stress of the bus capacitor and the current stress of the inductor current less.

References 1. Li Z, Xinbo R, Xiaoyong R (2015) Control method of front stage DC converter in two stage inverter [J]. Chinese J Electr Eng 35(03):660–670 2. Guoping Z, Xinbo R, Xuehua W, Zhibing Y (2013) Suppression of secondary ripple current and improvement of dynamic characteristics of two-stage single-phase inverter [J]. Chinese J Electr Eng 33 (12): 72–80 + 188. 3. Di Z (2020) Research on control method of two stage inverter [D]. China University of mining and technology 4. Kai K (2019) Research and implementation of two phase interleaved boost converter based on PI model predictive control [D]. Beijing University of technology 5. Jianhua W, Xuqian L, Fanghua Z, Chunying G (2012) Two-stage single-phase inverter input current low-frequency ripple analysis and suppression[J]. Proc Chinese Soc Electr Eng 32(06):10–16 6. Kai R, Qiangang G, Xifeng Z (2014) Two-stage single-phase photovoltaic grid-connected inverter bus voltage control strategy[J]. J Electr Power Syst Autom 26(10):74–77 7. Xu J, Bingying D, Mengchun Z, Ling Q, Shaojun X, Xuxu H (2019) Two-stage single-phase photovoltaic inverter input voltage double frequency ripple suppression [J]. Renewable Energy 37(05):683–687 8. Xia S, Xinjin W, Hui P, Ji Q (2017) Research on single-phase two-stage photovoltaic gridconnected inverter based on disturbance tracking method[J]. Navigation and Control 16(03):56– 60

Discrete Fuzzy Control Algorithm for Single-Phase-Shift Control of Isolated Full-Bridge DC-DC Converter Junyu Gan, Wenping Cao, Wenjie Zhu, Cungang Hu, and Xi Chen

Abstract Full-bridge isolated DC-DC converters have gradually become research hotspots and have been widely used due to their high power density, bidirectional energy transfer, and easy realization of soft switching. Single-phase-shift control, as a basic control strategy of this topology, has instructive significance for other phase-shift control strategies. First, this paper analyzes the single-phase-shift control principle of the isolated full-bridge DC-DC converter; then, proposes and analyzes a discrete fuzzy control algorithm for single-phase-shift control of isolated full-bridge DC-DC converter; finally, the proposed control algorithm is simulated and verified. The simulation results show that, compared with the traditional single-phase-shift control, the proposed control strategy has better dynamic performance. Keywords Discrete fuzzy control algorithm · Isolated full-bridge DC-DC converters · Single-phase-shift control

1 Introduction Isolated full-bridge DC-DC converters have a very important position in many fields such as electric vehicles and smart grid [1–4]. For this topology, common control methods include frequency conversion control, duty cycle control, and phase-shift control. Among them, phase shift control is the most important control method. According to different phase -shift angles, phase-shift control is divided J. Gan School of Electrical Engineering and Automation, Anhui University, Hefei, China W. Cao (B) · W. Zhu · C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China e-mail: [email protected] Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China X. Chen Hubei Normal University, Huangshi, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_16

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into single-phase-shift control, extended-phase-shift control, and triple-phase-shift control. Single-phase-shift control is the most basic phase-shift control method, which has guiding significance for all phase-shift control methods that appear later. In order to improve the dynamic performance of the system, literature [5] established the state space average model and small-signal model of the isolated fullbridge DC-DC converter, and proposed a double closed-loop control method of voltage outer loop and current inner loop. Literature [6] proposed a model-based optimal phase-shift control method. Literature [7] studied the generalized state space average model of isolated full-bridge DC-DC converters, and derived a more accurate output-to-control transfer function. Literature [8] established a linear harmonic model of the isolated full-bridge DC-DC converter, and proposed a load current feedforward compensation control method. Literature [9] proposes an adaptive control method to improve the dynamic response performance of the converter, but it uses more circuit parameters. Literature [10] proposed a virtual direct power control method for isolated full-bridge DC-DC converters, combining power control with feedforward control to improve the dynamic response of the converter. However, the above methods have disadvantages such as relying on system parameters, inaccurate models, and complicated calculations. The single-phase-shift isolated full-bridge DC-DC converter system has nonlinearity, and it is difficult to establish an accurate mathematical model, so the traditional PI controller is not the most suitable controller. Fuzzy control, which does not require precise mathematical models and has good robustness, is very suitable for the control of nonlinear systems. This paper proposes a discrete fuzzy single-phase-shift control of isolated fullbridge DC-DC converter. In view of different output voltage errors and error rate of change, the discrete fuzzy controller will output the corresponding control value through a look-up table. It is verified by simulation that the above method can ensure that the system has better rapidity.

2 Principle of Isolated Full-Bridge DC-DC Converter The topology of the full-bridge isolated DC-DC converter is shown in Fig. 1. Uin is the input voltage, L is the series inductance, and T is the high-frequency transformer which transformation ratio is n:1. There is a full-bridge circuit on both sides of the transformer, which contains 8 switching tubes in total. In single-phase-shift control, the H-bridge outputs on both sides are two-level voltages with a duty ratio of 50%, and the output can be adjusted by adjusting the phase-shift angle. Figure 2 shows the switching tube drive signal under single-phase-shift control, as well as the voltage between some important points and the inductor current waveform. At any moment, the inductor voltage is U L = U ab −nU cd . When the primary current flows through S1 , S4 or D1 , D4 , the voltage is U ab = U in and U ab = −U in when the primary current flows through S2 , S3 or D2 , D3 . When the secondary side current flows through S5 , S8 or D5 , D8 , the voltage is U cd = U out and U cd = −U out when the secondary current flows through S6 , S7 or D6 , D7 .

Discrete Fuzzy Control Algorithm for Single-Phase-Shift …

S1

S3 D1

+ a Uin

S5

+ UL

C1

Uab

-

iL

D3 n:1

S2

D7

+

c Ucd

R

C2

Uout

d

T

S6

S4 D2

S7 D5

L

b -

195

D4

S8

-

D6

D8

Fig. 1 Full-bridge isolated DC-DC converter topology

Fig. 2 Full-bridge isolated DC-DC converter operating waveform

DThs

Ths

S1S4 S2S3 S5S8 S6S7 Uab

Ucd

UL

iL t0

t2

t7

t4

t1

t3 t5

t

t6

Now analyze the current state (t1 -t7 ) in a cycle: (1)

t1 − t2 : The primary current flows through S1 , S4 and the secondary current flows through S6 , S7 , the inductor current at this stage: i L (t) = i L (t1 ) + (Uin + nUout )/L × (t − t1 )

(2)

(1)

t2 − t3 : S6 , S7 switch off, the primary side current flows through S1 , S4 and the secondary side current flows through D5 , D8 , the inductor current at this stage:

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i L (t) = i L (t2 ) + (Uin − nUout )/L × (t − t2 ) (3)

t3 − t4 : S1 , S4 switch off, the primary side current flows through D2 , D3 and the secondary side current flows through D5 , D8 , the inductor current at this stage: i L (t) = i L (t3 ) + (−Uin − nUout )/L × (t − t3 )

(4)

(4)

t5 − t6 : S5 , S8 switch off, the primary side current flows through S2 , S3 and the secondary side current flows through D6 , D7 , the inductor current at this stage: i L (t) = i L (t5 ) + (−Uin + nUout )/L × (t − t5 )

(6)

(3)

t4 − t5 : the primary side current flows through S2 , S3 and the secondary side current flows through S5 , S8 , the inductor current at this stage: i L (t) = i L (t4 ) + (−Uin − nUout )/L × (t − t4 )

(5)

(2)

(5)

t6 -t7 : S2 , S3 switch off, the primary side current flows through D1 , D4 and the secondary side current flows through D6 , D7 , the inductor current at this stage: i L (t) = i L (t6 ) + (Uin + nUout )/L × (t − t6 )

(6)

Assuming t0 = 0, then t2 = DThs , t3 = Ths , t5 = (1 + D)Ths , t6 = 2Ths . When the circuit is stable, according to the symmetry of the inductor current: i L (t0 ) = −i L (t3 ), i L (t2 ) = −i L (t5 ), combined with Eqs. (1) – (6), current expression is obtained: ⎧ i L (t0 ) = nUout /4L f · (1 − 2D − k) ⎪ ⎪ ⎪ ⎨ i (t ) = nU /4L f · (1 + 2Dk − k) L 2 out (7) ⎪ i L (t3 ) = −nUout /4L f · (1 − 2D − k) ⎪ ⎪ ⎩ i L (t5 ) = −nUout /4L f · (1 + 2Dk − k) where k = U in /U out . Therefore, the average value of the input current is: 1 I = Ths

∫ Ths i L (t)dt = 0

The converter transmission power is:

nUout D(1 − D) 2fL

(8)

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197

P = Uin I = nUin Uout /2 f L × D(1 − D)

(9)

Take the reference value of transmission power as PN = nU in U out /8f L, then the standardized transmission power is: u out = P/PN = 4D(1 − D)

(10)

Regardless of the transmission loss, considering the resistive load R: 2 P = Uout /R

(11)

Using Eqs. (9) and (11), the output voltage can be expressed as follows: u out = nUin R/2 f L × D(1 − D)

(12)

Take the reference value of voltage as U N = nU in R/8f L, then the standardized output voltage is: u out = u/u N = 4D(1 − D)

(13)

The power transmission characteristic curve drawn by Eq. 10 is shown in Fig. 3. From Eq. 13, it can be seen that the output voltage characteristic curve is consistent with the power transmission characteristic curve. When the input voltage and load remain unchanged, output voltage first increases and then decreases with the increase of D, and the maximum value is taken when D = 0.5. Generally, the control range of D is within [0, 0.5]. Due to the non-linearity of the system, the traditional PI controller will inevitably limit the performance of the Fig. 3 The power transmission characteristic curve

p

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

D

0.6

0.7

0.8

0.9

1

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system. Compared with traditional PI controllers, fuzzy controllers are more suitable for nonlinear systems.

3 Discrete Fuzzy Single-Phase-Shift Control Strategy 3.1 Discrete Domain Fuzzy Controller Design After the converter output voltage error and the error rate of change are scaled and quantified, they are converted to a basic domain, which is shown in formula 16. In this domain, a membership table of each variable and fuzzy control rules are used to generate a control table, the corresponding output control value can be directly obtained by looking up the table from the output voltage error and error rate of change. The selection of membership function and the formulation of fuzzy rules will affect the performance of the system. The block diagram of the fuzzy control system in the discrete domain is shown in Fig. 4. The domains of output voltage error E, error rate of change D and fuzzy controller output control quantity C are: { } E, D, C ∈ −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6

(14)

The membership of the output voltage error E is shown in Table 1. The membership of the rate of change of the output voltage error and the output control quantity are shown in Table 2. In the table, "NB" to "PB" represent different magnitude of a value, such as "NB" for "Negative Big", and "PB" for "Positive Big". The fuzzy control rules are shown in Table 3. The fuzzy set of E has a total of 8 elements, and the fuzzy set of D has a total of 7 elements. Therefore, Table 3 contains a total of 56 rules. For any quantized E, D, through these 56 rules, a unique control quantity is generated. When the quantized error value is 6 and the quantized error rate is 6, for the first rule in Table 3: If E is NB and D is NB, Then C is NB. According to Tables 1 and 2: ⎡ ⎤ E N B = 1 0.8 0.7 0.4 0.1 0 · · · 0 1×13

k1

Quantify

error

Control Table d dt

k2

(15)

k3

Quantify

Fig. 4 The block diagram of the fuzzy control system in the discrete domain

output

Discrete Fuzzy Control Algorithm for Single-Phase-Shift …

199

Table 1 The membership table of error E NB

−6

−5

−4

−3

−2

−1

0

1

2

3

4

5

6

1.0

0.8

0.7

0.4

0.1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

NM

0.2

0.7

1.0

0.7

0.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

NS

0.0

0.1

0.3

0.7

1.0

0.7

0.2

0.0

0.0

0.0

0.0

0.0

0.0

NZ

0.0

0.0

0.0

0.0

0.1

0.6

1.0

0.0

0.0

0.0

0.0

0.0

0.0

PZ

0.0

0.0

0.0

0.0

0.0

0.0

1.0

0.6

0.1

0.0

0.0

0.0

0.0

PS

0.0

0.0

0.0

0.0

0.0

0.0

0.2

0.7

1.0

0.7

0.3

0.1

0.0

PM

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.2

0.7

1.0

0.7

0.3

PB

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.4

0.7

0.8

1.0

Table 2 The membership table of the error rate of change D and the control quantity C −6

−5

−4

−3

−2

−1

0

1

2

3

4

5

6

NB

1.0

0.7

0.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

NM

0.3

0.7

1.0

0.7

0.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

NS

0.0

0.0

0.3

0.7

1.0

0.7

0.3

0.0

0.0

0.0

0.0

0.0

0.0

ZE

0.0

0.0

0.0

0.0

0.3

0.7

1.0

0.7

0.3

0.0

0.0

0.0

0.0

PS

0.0

0.0

0.0

0.0

0.0

0.0

0.3

0.7

1.0

0.7

0.3

0.0

0.0

PM

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.3

0.7

1.0

0.7

0.3

PB

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.3

0.7

1.0

Table 3 Fuzzy control rule table NB

NM

NS

ZE

PS

PM

PB

NB

NB

NB

NB

NB

NM

ZE

ZE

NM

NB

NB

NB

NB

NM

ZE

ZE

NS

NM

NM

NM

NM

ZE

PS

PS

NZ

NM

NM

NS

ZE

PS

PM

PM

PZ

NM

NM

NS

ZE

PS

PM

PM

PS

NS

NS

ZE

PM

PM

PM

PM

PM

ZE

ZE

PM

PB

PB

PB

PB

PB

ZE

ZE

PM

PB

PB

PB

PB

⎡ ⎤ D N B = 1 0.7 0.3 0 · · · 0 1×13

(16)

⎡ ⎤ C N B = 1 0.7 0.3 0 · · · 0 1×13

(17)

The implied operation adopts the intersection method, and the composite operation “◦” adopts the maximum-minimum method.

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⎛

R1E = E N B → C N B

R1D = D N B → C N B

⎞ 1 ⎛ ⎞ ⎜ 0.8 ⎟ ⎜ ⎟ 1 0.7 0.3 ⎜ 0.7 ⎟ ⎜ 0.8 0.7 0.3 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎜ 0.4 ⎟ ⎡ ⎤ ⎜ ⎜ 0.7 0.7 0.3 0 ⎟ ⎜ ⎟ = ⎜ 0.1 ⎟ ∧ 1 0.7 0.3 0 · · · 0 = ⎜ ⎟ ⎜ 0.4 0.4 0.3 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎝ 0.1 0.1 0.1 ⎠ ⎜ ⎟ ⎜ .. ⎟ 0 0 13×13 ⎝ . ⎠ 0 (18) ⎡ ⎤ ' C1E = E ' ◦ R1E = 1 0 · · · 0 1×13 ◦ (19) ⎡ ⎤ R1E = 1 0.7 0.3 0 · · · 0 1×13 ⎛ ⎞ ⎛ ⎞ 1 1 0.7 0.3 ⎜ 0.7 ⎟ ⎜ 0.7 0.7 0.3 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎜ 0.3 ⎟ ⎡ ⎤ ⎜ 0 0.3 0.3 0.3 ⎜ ⎟ ⎟ ∧ 1 0.7 0.3 0 · · · 0 = ⎜ =⎜ ⎟ ⎜ 0 ⎟ ⎜ ⎟ 0 0 0 ⎜ ⎟ ⎜ ⎟ ⎜ .. ⎟ ⎝ ⎠ 0 0 0 ⎝ . ⎠ 0 0 13×13 0 (20) ⎡

'

C1D = D ' ◦ R1D = 1 0 · · · 0

⎤ 1×13

⎡

◦ R1D = 1 0.7 0.3 0 · · · 0

⎤

⎡ ⎤ ' ' ' C1 = C1E ∩ C1D = 1 0.7 0.3 0 · · · 0 1×13 '

'

1×13

(21) (22)

'

According to the same method to find C2 , C3 , …, C56 , finally find: 56 ⎡ ⎤ ' C ' = U Ci = 1 0.7 0.3 0 · · · 0 1×13 i=1

(23)

The weighted average method is used to clarify the calculated output fuzzy sets, and we get: c=

1 × (−6) + 0.7 × (−5) + 0.3 × (−4) = −5.35 1 + 0.7 + 0.3

(24)

Follow the same method to obtain other elements in the Table, and finally generate the control Table.

Discrete Fuzzy Control Algorithm for Single-Phase-Shift …

Uin+ -

A

Fuzzy Controller

D

Pulse Generator

201 DC/DC Uout Converter

Fig. 5 Control block diagram of single-phase-shift control system based on discrete fuzzy controller

3.2 Single-Phase-Shift Control System Based on Discrete Fuzzy Controller The input of the discrete fuzzy controller is the error of the output voltage. After calculating the error rate of change, the fuzzy controller will scale and quantify the error and error rate of change, and then obtain the output of the fuzzy controller by looking up the table. The control block diagram of the single-phase-shift control system based on the discrete fuzzy controller is shown in Fig. 5. In Fig. 5, the structure of the fuzzy controller is shown in Fig. 4. Among them, k1 , k2 , and k3 are the coefficients of scale transformation of the output voltage error, the voltage error change rate, and the output control quantity. All of them affect system performance. When the voltage error is large, it should be at the two extreme positions (6 or − 6) after scale change and quantification. When the voltage error enters a relatively small range, it will enter the middle value (−5 ~ 5) after scale change and quantification. If the system are expected to be faster and have a smaller steady-state error, the system should enter the intermediate value when the error is small, so k1 should be set larger. However, the increase of k1 may cause the system to overshoot, and the output voltage ripple may increase. A larger k2 leads to smaller overshoot and worse rapidity. The ratio of k1 to k2 determines the weight of voltage error and error rate of change. A larger k3 means better system dynamic performance, but too large k3 may cause overshoot. The values of the three coefficients are not unique. There may be several sets of different values for a system that can make it have good response performance. Quantification is to replace the quantity with the number in the domain (−6, − 5, …, 4, 5, 6) with the smallest absolute value of the difference with the quantity. The fuzzy controller looks up the table to get the value in the range of [−5.35, 5.35], multiplies it by k3 to get the value in the range of [−0.5, 0.5]. So calculate k3 according to the following formula: k3 =

0.5 = 0.094 5.35

(25)

A larger reference voltage requires a larger k1 to correct the steady-state error, a smaller reference voltage requires a smaller k1 to reduce the voltage ripple, so take: k1 = 0.0012Ur e f

(26)

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After determining the values of k1 and k3 , it is verified by simulation that it has good performance when k2 = 0.0002, take k2 = 0.0002. After limiting the amplitude, the D in the range of [0, 0.5] is transmitted as the phase shift amount to the pulse generation module.

4 Simulation Verification The simulation parameters are shown in Table 4. Set the initial voltage of the output side capacitor to 350 V, the initial voltage reference value is 400 V, jump to 565 V in 0.03 s, and the simulation time is 0.06 s. The output voltage waveform of the traditional PI regulator is shown in Fig. 6 with a setting time 0.04 s. Using the discrete fuzzy controller, the output voltage waveform is shown in Fig. 7 with a setting time 0.01 s and the overshoot is very Table 4 Simulation parameter table

650

Value

Rated output power

10 kW

Transformer ratio

1: 1

Switching frequency

10 kHz

L

200 uH

Input voltage

400 V

Half load

400 V, 32 Ω

Full load

565 V, 32 Ω

Kp

0.005

Ki

2

Output Voltage

600

Output Voltage/V

Parameter

Reference Voltage

550 500 450

t=0.04s

400 350 0

0.01

0.02

0.03

0.04

0.05

0.06

Time/s

Fig. 6 Output voltage waveform of traditional PI regulator

0.07

0.08

0.09

0.1

Discrete Fuzzy Control Algorithm for Single-Phase-Shift …

650

Output Voltage/V

600

Reference Voltage

550

203

Output Voltage

500 450 400

t=0.01s

350 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Time/s

Fig. 7 Discrete fuzzy controller output voltage waveform

small. The voltages of the transformer primary side and secondary side are shown in Figs. 8 and 9. It can be seen from Fig. 6 that in the process of switching from half load to full load, traditional PI control will cause overshoot, which takes about 0.04 s to stabilize. It can be seen from Fig. 7 that discrete fuzzy control will not cause overshoot, and it takes about 0.01 s to stabilize. It can be seen from Figs. 8 and 9 that under the discrete fuzzy control, the voltages of the primary and secondary sides of the transformer both rise from 400 to 565 V within 0.01 s. Compared with the traditional PI control, the discrete fuzzy controller completely eliminates the output voltage overshoot and has better dynamic performance.

Fig. 8 Voltage of transformer primary side

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Fig. 9 Voltage of transformer secondary side

5 Conclusion Aiming at the shortcomings of traditional PI controllers, this paper proposes a discrete fuzzy control algorithm for single-phase-shift control of isolated full-bridge DC-DC converter. Compared with the traditional PI control, the proposed method has no output overshoot with better dynamic performance, and has a positive effect on the improvement of the phase-shift-control performance of the isolated full-bridge DC-DC converter. Acknowledgements The work is supported by the National Natural Science Foundation of China (51777001), Natural Science Foundation of Anhui Province (2108085QE239) and the Hubei Education Department Science and Technology Research Program for Guiding Project (B2020132).

References 1. Xue L, Shen Z, Boroyevich D, Mattavelli P, Diaz D (2015) Dual active bridge-based battery charger for plug-in hybrid electric vehicle with charging current containing low frequency ripple. IEEE Trans Power Electron 30(12):7299–7307 2. Zhao B, Song Q, Liu W, Sun Y (2014) Overview of dual-active-bridge isolated bidirectional DC–DC converter for high-frequency-link power-conversion system. IEEE Trans Power Electron 29(8):4091–4106 3. Xuewei P, Rathore AK (2014) Novel bidirectional snubberless naturally commutated softswitching current-fed full-bridge isolated DC/DC converter for fuel cell vehicles. IEEE Trans Industr Electron 61(5):2307–2315 4. Zhao B, Song Q, Liu W, Xiao Y (2013) Next-generation multi-functional modular intelligent UPS system for smart grid. IEEE Trans Industr Electron 60(9):3602–3618 5. Demetriades GD, Nee H (2008) Dynamic modeling of the dual-active Bridge topology for high-power applications. IEEE Power Electron Spec Conf 2008:457–464

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6. Bai H, Mi C, Wang C, Gargies S (2008) The dynamic model and hybrid phase-shift control of a dual-active-bridge converter. In: 2008 34th annual conference of IEEE industrial electronics, pp 2840–2845 7. Qin H, Kimball JW (2012) Generalized average modeling of dual active bridge DC–DC converter. IEEE Trans Power Electron 27(4):2078–2084 8. Segaran D, Holmes DG, McGrath BP (2013) Enhanced load step response for a bidirectional DC–DC converter. IEEE Trans Power Electron 28(1):371–379 9. Segaran D, McGrath BP, Holmes DG (2010) Adaptive dynamic control of a bi-directional DC-DC converter. In: 2010 IEEE energy conversion congress and exposition, pp 1442-1449 10. Song W, Hou N, Wu M (2018) Virtual direct power control scheme of dual active bridge DC–DC converters for fast dynamic response. IEEE Trans Power Electron 33(2):1750–1759

Fault Diagnosis of Three-Level Inverters Based on Ensemble Empirical Mode Decomposition and Deep Neural Network Hongzhe Li, Jinsong Kang, and Weimin Li

Abstract The three-level inverter has the advantages of large output capacity, high output voltage and small current harmonic content, etc. It has been widely used in the field of frequency conversion and speed regulation of high-voltage and high-power AC motor. Aiming at the problem of fault diagnosis of three-level inverter, a fault diagnosis method based on Ensemble Empirical Mode Decomposition (E-EMD) and neural network algorithm is proposed in this paper. Firstly, the output signals are processed by ensemble empirical mode decomposition, and the fault signals are decomposed into different intrinsic mode components. Then the energy values of the decomposed modal components are extracted as the fault feature vectors. Finally, the deep neural network is constructed to classify and identify the faults. Through MATLAB/Simulink simulation experiments verify that the proposed method has higher fault identification accuracy and better robustness to noise compared with the traditional method. Keywords Three-level inverter · Ensemble empirical mode decomposition · Deep neural network · Fault diagnosis

1 Introduction With the rapid development of power electronic technology, power electronic devices have a wide application prospect in AC/DC power transmission, new energy power conversion, frequency conversion motor control and harmonic control of distribution network. Compared with the traditional two-level inverter, the Neutral Point Clamped (NPC) three-level inverter is more widely used due to its advantages such as high H. Li College of Electronic and Information Engineering, Tongji University, Shanghai, China J. Kang (B) Institute of Rail Transit, Tongji University, Shanghai, China e-mail: [email protected] W. Li Shandong Institute of Advanced Technology, Chinese Academy of Sciences, Jinan, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_17

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output voltage quality, low switching stress and small electromagnetic interference [1]. The NPC three-level inverter, which is including three bridge arms A, B and C. With the increase of the number of power devices, the probability of failure also increases. According to statistical analysis, inverter faults are mainly divided into short circuit faults and open circuit faults of power devices. In practical application, when the power device has a short circuit fault, the sharp increase of current will cause the protection fuse to break, so that the short circuit fault will eventually be transformed into an open circuit fault. Therefore, in the research of inverter fault diagnosis, the open-circuit fault diagnosis of power devices is the main direction. [2]. For the fault diagnosis of NPC three-level inverter, there are two problems that need to be solved urgently: (1) fault feature extraction, that is, using information analysis and processing methods to extract effective information of different types of faults; (2) fault identification, that is, locating faults according to the extracted fault features. For problem 1, literature [3] adopt Fourier transform method to extract signal frequency domain characteristics as features. Although the method is simple, this method has the problem of loss of signal time-domain features. In literature [4], wavelet transform and wavelet packet decomposition were introduced into fault diagnosis, which effectively improved the accuracy. However, the adaptive decomposition of signals was not realized depending on the selection of wavelet basis function, and the robustness was not strong. Literature [5] used empirical mode decomposition to do fault diagnosis, but the modal aliasing is not solved. For problem 2, literature [6] adopts support vector machine (SVM) classifier to achieve fault classification, but the selection of kernel function is still a problem that has not been solved perfectly. With the development of deep learning, neural network has been widely used in classification problems due to its advantages of simple structure, strong learning ability, nonlinear approximation ability and high classification accuracy [7]. To sum up, in order to make feature extraction simple and effective, this paper uses ensemble empirical mode decomposition to process the output voltage, extracts the energy values of the decomposed modal components with different connotations as the fault feature vectors, and then uses neural network to classify the fault types. This method has the characteristics of fast speed, strong robustness and signal selfadaptation. Then, the control variable method is used to compare this method with Fourier decomposition, wavelet packet decomposition, decision tree classification and support vector machine classification respectively, and the results show that this method has the highest success rate.

2 Fault Type Analysis Open circuit faults of three-level inverter are mainly divided into single tube open circuit and multi tube open circuit. Among them, the probability of two or more tube open circuit is very small and will not be considered in this paper. And then,

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the situation that two IGBTs in the same bridge arm are closed at the same time is the same as the single tube open circuit state, so there is no need to waste research energy. According to the symmetry of the circuit, the fault features of each phase are the same, so only A-phase faults need to be analyzed. Figure 1 shows a simplified diagram of a single bridge arm of a three-level inverter. To sum up, the fault types diagnosed in this paper include: single tube fault: Sa1 − Sa4, VDa1, VDa2 circuit break; Double tube fault: Sa1 and Sa3, Sa1 and Sa4, Sa2 and Sa3 open circuit, a total of ten types of faults. At any moment, the faults that may occur in phase A are shown in Table 1, and for each fault, a code is made which is necessary for classifier to analyzing. Fig. 1 Simplified topology of a single bridge arm of a three-level inverter

Table 1 Fault type and code Fault number

Fault type

Fault code

Fault number

Fault type

Fault code

0

Fault-free

0000

5

VDa1

0101

1

Sa1

0001

6

VDa2

0110

2

Sa2

0010

7

Sa1 + Sa3

0111

3

Sa3

0011

8

Sa1 + Sa4

1000

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Sa4

0100

9

Sa2 + Sa3

1001

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3 Fault Diagnosis Method Based on EEMD-DNN 3.1 Ensemble Empirical Mode Decomposition Traditional EMD is a signal analysis method proposed by Dr. Huang E from NASA [8]. It decomposes the signal according to the time scale characteristics of the data itself without any basis function. In theory, EMD method can be applied to any type of signal decomposition, so it has obvious advantages in processing non-stationary and nonlinear data. Therefore, EMD method has been applied quickly and effectively in different engineering fields once it was proposed, but the most prominent problem is modal aliasing. This is why the EEMD was proposed [9]. The process of EEMD decomposition is as follows: Let the input signal be a time series x(t), Firstly, the maximum point x(tm ) and minimum point x(tn ) of x(t) are calculated respectively, and the maximum envelope H(t) and L(t) are obtained according to formula (1) and (2); H (t) =

L(t) =

N  x(tm )(t − t1 ) . . . (t − tm−1 )(t − tm+1 ) . . . (t − t N +1 ) (tm − t1 ) . . . (tm − tm−1 )(t − tm+1 ) . . . (tm − t N +1 ) m=1

(1)

N  x(tn )(t − t1 ) . . . (t − tn−1 )(t − tn+1 ) . . . (t − t N +1 ) (tn − t1 ) . . . (tn − tn−1 )(tn − tn+1 ) . . . (tn − t N +1 ) n=1

(2)

Then calculate the envelope mean H (t) + L(t) 2

(3)

C1 (t) = x(t) − m(t)

(4)

m(t) = Let

Then C1 (t) is the first modal component. The above process is repeated, namely, the decomposition of C1 (t) continues until the two adjacent factorizations Ck−1 (t) and Ck (t) satisfy the stop formula (5). sd ≥

T   Ck−1 (t) − Ck (t)|2 t=0

2 Ck−1 (t)

(5)

sd is between 0.2 and 0.3. From above, we get a vector [C1 (t), …, Ci (t), …, Cn (t)], which is the result of traditional EMD. To solve the problem of modal aliasing, the Random white noise is added to the analyzed signal, and traditional EMD method is used to decompose the signal with white noise into various eigenmode functions.

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Repeated this step over and over again, but each time a different white noise sequence is added. A final set of intrinsic mode functions (IMF) is obtained by integrating the IMF obtained on average each time. Figure 2 shows the flow chart of EEMD, and Fig. 3 shows the result of it. From Fig. 3, for each IMF Ci (t), its energy index is extracted as the feature vector according to formula (6), and E = [E 1 , …E i , … E n ] is taken as the input of the neural network.  Ei =

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Fig. 3 Result of EEMD

3.2 Deep Neural Network Back Propagation (BP) neural network was proposed by scientists led by Rumelhart and McClelland in 1986. It is a multi-layer feedforward neural network trained according to the error back propagation algorithm, and it is the most widely used neural network. BP neural network has arbitrary complex pattern classification ability and excellent multi-dimensional function mapping ability. Structurally speaking, BP network has input layer, hidden layer and output layer. Assume that the number of nodes in the input layer is d, the number of nodes in the hidden layer is q, and the number of nodes in the output layer is l. The weight of the input layer to the hidden layer are vi h , the weight of the hidden layer to the output layer are wh j , the bias of the input layer to the hidden layer are bh , and the bias is hidden in the input. The learning rate is η, and the incentive function is g(x). Defines the error E as a formula (7): E=

l 1  (Y j − O j )2 2l J =1

(7)

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E is also called error of mean square (MSE), from where, Y j is the expected output and O j is the actual output. Our goal is to minimize the error function, it means min(E), so that, the gradient descent is used. The updated formula of weight is ωi j = ωi j + ηH j (1 − H j )xi

m 

ω jk ek

(8)

k=1

In this paper, the input vector is the energy of IMFs, and it will be covered in more detail in the next section.

4 Simulation and Analysis 4.1 Simulation and Result The original data collection is extracted through the established Simulink simulation model. The sampling interval time is 1 × 10−6 s and the sampling duration is 0.05 s, then the data of each group is 50,000. In order to improve the accuracy of the experiment, 300 groups of data were obtained under different output voltages and loads for each fault condition. A total of 10 × (300 × 50,000) of original data were extracted for 10 fault conditions. Then, each (1 × 50,000) data sequence was decomposed by ensemble empirical mode. The proportion of white noise was 10%, the number of decompositions were 20 times, and the number of IMF generated by each sub-decomposition was set as 6. After the decomposition is completed, the energy value of each IMF is extracted according to formula (6), and the (10 × 300) eigenvectors whose shape are (6 × 1) are obtained. Figure 4a−b shows the energy of each IMF1 and IMF3. 10 6

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Fig. 5 Loss of model

If the fault classification is conducted directly at this time, the problem of gradient disappeared [10] may be caused. Therefore, it is essential to normalize the data. The normalization formula is as follows: x∗ =

(x − μ) σ

(9)

μ is the mean of the data and σ is the variance of the data. Finally, 2800 sets of data extracted from 10 kinds of fault conditions were taken as the input of BP neural network, and the corresponding fault codes were also sent into the neural network to train it. The neural network adopts three-layer, the number of nodes in input layer is 6, the number of nodes in hidden layer is 50, and the output layer nodes is 100. The maximum number of iterations in the training process is set to 200, learning rate is 0.03, and the error value to be achieved by network setting is 0.01. Finally, the data of 200 groups of 10 failure conditions and the corresponding fault codes are tested in the neural network as test input and expected output input respectively. Based on the randomness of neural network test training, repeated test training was conducted and the test results were obtained as shown in Figs. 5, 6 and 7.

4.2 Contrastive Analysis In order to illustrate the advantages of the fault diagnosis method proposed in this paper, the control variable method is adopted to combine different feature extraction methods and classification methods into a complete fault diagnosis algorithm, which is tested in the computing environment of this paper (Linux 18.04, Python 3.8,4 × GEFORCE RTX 3090). The comparison results with this algorithm are shown in the following Table 2. Experimental results show that the proposed algorithm has obvious advantages in feature extraction and fault classification.

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Fig. 6 Accuracy of model

Fig. 7 The confusion matrix Table 2 Comparison of control variables Feature extraction/classifier/accuracy

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5 Conclusion Based on the intelligent detection algorithm, the fault diagnosis of the Neutral Point Clamped (NPC) three-level inverter is researched, and the original fault number is determined by ensemble empirical mode decomposition. The data is decomposed and the energy spectrum is obtained to form the fault characteristics, then the fault features are taken as the input of BP neural network, and the preset fault codes are taken as the output of the neural network, and then it is trained to classify and detect faults. The method is verified by simulation experiment, and the control variable method is used to compared with other algorithms. The results show that our method is best. It’s not just that our algorithm has a high accuracy rate, and it is also simple and easy to implement, which can well meet the needs of inverter fault diagnosis.

References 1. Hochgraf C, Lasseter R, Divan D, et al (1994) Comparison of multilevel inverters for static Var compensation[C]. In: IEEE conference on industrial applications, 921–928. 2. Uni S, Zolghadri MR, Khodabandeh M et al (2017) Improvement of post fault performance of a cascaded H-bridge multilevel inverter[J]. IEEE Trans Ind Electron 64(4):2779–2788 3. Chen D, Ye Y (2013) Open circuit fault diagnosis method of three-level inverter device based on multi-neural network [J]. Trans China Electrotechnical Soc 28(06):120–126 4. Liu HM (2021) Digital piano audio signal feature recognition method based on wavelet packet transform [J]. Automa Instrum 05:21–24 5. Desavale RG, Jadhav PM, Dharwadkar NV (2021) Dynamic response analysis of gearbox to improve fault detection using empirical mode decomposition and artificial neural network techniques[J]. ASME J Risk Uncertainty Part B 6. Kr K, Kv AR, Pillai A (2019) An improved feature selection and classification of gene expression profile using SVM. In: 2019 2nd international conference on intelligent computing, instrumentation and control technologies (ICICICT), pp 1033–1037 https://doi.org/10.1109/ICICIC T46008.2019.8993358. 7. Liu Y, Wang J, Shen Y (2020) Research on verification of sensor fault diagnosis based on BP neural network. In: 2020 11th international conference on prognostics and system health management (PHM-2020 Jinan), pp 456–460 8. Huang NE, Shen Z, Long SR et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proc Math Phys Eng Sci 1971(454):903–995 9. Wu Z, Huang N (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method [J]. Adv Adapt Data Anal (1) 10. Kolarik M, Burget R, Riha K (2020) Comparing normalization methods for limited batch size segmentation neural networks. In: 2020 43rd international conference on telecommunications and signal processing (TSP), pp 677–680 https://doi.org/10.1109/TSP49548.2020.9163397

A Direct Power Control of Single-Phase PWM Rectifiers Without Gird Voltage Sensor Wenwen Huang, Cungang Hu, Bi Liu, Wenjie Zhu, and Tao Rui

Abstract This paper presents a simple direct power control scheme for single-phase pulse width modulated (PWM) rectifiers without a dedicated gird voltage sensor. In order to realize gird voltage sensorless control, the system active and reactive powers are divided into two components, respectively, which can be estimated by the input powers of the rectifier, and powers of the equivalent inductance and resistance of ac-side inductor, instead of the gird voltage and line current. Then a system parameter initialization method is given to solve the startup problem of control system. Simultaneously, an on-line inductance estimation method is presented to tackle the parameter sensitivity of the proposed scheme. Finally, the proposed scheme is verified by experimental tests, the experimental results have verified the correctness and validity of the proposed scheme. Keywords Single-phase PWM rectifiers · Power estimation · Gird voltage sensorless control · System parameter initialization · Inductance estimation

1 Introduction Single-phase pulse width modulation (PWM) rectifiers have been widely used in the fields of new energy power generation, uninterrupted power supply and railway locomotive traction due to their high grid-side power factor, low current harmonics, and bidirectional energy flow [1, 2]. At present, there are many mature control methods for single-phase PWM rectifiers. These control methods can be roughly divided into current-tracking control and power-tracking control. W. Huang · C. Hu · B. Liu (B) · W. Zhu · T. Rui School of Electrical Engineering and Automation, Anhui University, Hefei, China e-mail: [email protected] C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_18

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Power-tracking control has the advantages of simple control and good output performance, and it is widely used in a variety of topologies. Direct power control takes the grid-side active and reactive power as the control object, and indirectly realizes the decoupling control of the active and reactive components of the gridside current. It is an ideal choice for PWM rectifier control. In recent years, the development of deadbeat predictive DPC [3] and model predictive DPC [4] schemes has further improved the performance of the control system. Irrespective of the control schemes mentioned above, the gird voltage information is essential for most of them. The grid voltage is generally measured by a dedicated gird voltage sensor, and a phase locked loop (PLL) is adopted to extract the gird voltage information, including amplitude, angle and frequency. However, in situation where the gird is physically far from the rectifier, installing the gird voltage sensor needs additional circuitry and wire, which will increase the complexity of circuit design and overall cost [5]. Thus, in order to eliminate the gird voltage sensor, various grid voltage sensorless control strategies have been proposed. Malinowski et al. [6] presents a DPC scheme based on virtual flux orientation, called VF-DPC, to replace the grid voltage sensor by a virtual flux estimator. It can gain good steady state and dynamic performance, but the virtual flux estimation involves an integration operation, which will result in a dc drift problem. Substituting the integrator with a low pass filter (LPF) to tackle the dc drift problem, but phase lag and attenuation occurs through the LPF. In this paper, the design principle and implementation method of a simple DPC scheme without grid voltage sensor for single-phase PWM rectifier is presented. The main contribution of the proposed scheme is that the system active and reactive powers are divided into two components, which can be estimated by the input powers of the rectifier, and powers of the equivalent inductance and resistance of ac-side inductor. Then, to solve the startup problem of control system, the system parameter initialization is designed. In order to tackle the AC-side parameters sensitivity of the proposed scheme, an on-line inductance estimation method is presented. Experimental results are provided to show the effective performance of the proposed scheme.

2 Direct Power Control Without Gird Voltage Sensor 2.1 System Description Figure 1 shows the topology of a single-phase two-level PWM rectifier, where us and is are the grid voltage and line current, respectively. L s and Rs represent the equivalent the inductance and resistance of ac-side inductor, respectively. uab is the modulated voltage of the rectifier. iL and udc are the load current and DC-link voltage, respectively. C d and RL are symbols for the equivalent capacitance and resistance

A Direct Power Control of Single-Phase PWM Rectifiers … Fig. 1 The topology of a single-phase, two-level PWM rectifier

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Ls us

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in the DC-link. S1 , S2 , S3 , and S4 represent four IGBT modules with anti-parallel diodes. The grid voltage us , line current is , and modulated voltage uab of the adopted rectifier in d-q rotary reference frame are defined as u s = Usm sin(ωt + θu ) = u d sin ωt + u q cos ωt

(1)

i s = Ism sin(ωt + θi ) = i d sin ωt + i q cos ωt

(2)

u ab = Uabm sin(ωt + θab ) = u abd sin ωt + u abq cos ωt

(3)

where ω represents angular frequency of the grid voltage us , U sm , I sm , U abm are the peak value of the fundamental components in us , is , uab , respectively, θ u , θ i , θ ab are the phase angles of us , is , uab ; ud, id , uabd represent the d-axis components of us , is , uab ; uq, iq , uabq represent the q-axis components of us , is , uab . The d-axis and q-axis components of us , is , uab can be expressed as ⎧ ⎪ ⎨ u d = Usm cos θu , u q = Usm sin θu i d = Ism cos θi , i q = Ism sin θi ⎪ ⎩ u abd = Uabm cos θab , u abq = Usm sin θab

(4)

Generally, the grid voltage us is orientated to d-axis in d-q frame, where ud = U sm , uq = 0. From Fig. 1, the power mathematical model in d-q frame of single-phase PWM rectifier can be written as [7] ⎧ 2ωL s Q 2L s dP 2Rs P ⎪ ⎪ + Usm − − ⎨ u abd = − Usm Usm Usm dt (5) dQ 2R Q P 2ωL 2L ⎪ s s s ⎪ ⎩ u abq = + − Usm Usm Usm dt

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where P, Q are the instantaneous active and reactive powers of the adopted system. In conventional PI-based DPC scheme, the modulated voltages uabd , uabq are realized by two inner-loop PI-based power controllers. The inner-loop control mathematical model of the PI-based DPC system can be written as ⎧ K i_ P ⎪ )(Pref − P) ⎨ u abd = −(K p_ P + s K i_ Q ⎪ ⎩ u = (K )(Q ref − Q) abq p_ Q + s

(6)

where K p_P , K i_P and K p_Q , K i_Q represent the proportional and integral parameters of active and reactive power PI controllers, respectively. Pref and Qref are the active and reactive reference powers.

2.2 Instantaneous Power Estimator The instantaneous active power P and reactive power Q of the adopted rectifier can be shown as follows. ⎧ 1 ⎪ ⎨ P = u d id 2 (7) ⎪ ⎩ Q = −1u i d q 2 But the powers P and Q can not be estimated by (7) under grid voltage sensorless condition. The equivalent circuit of single-phase PWM rectifier is shown in Fig. 2. From Fig. 2, the active power P consist of input active power Pin of the rectifier and active power PR of resistance Rs , while reactive power Q consist of input reactive power Qin of the rectifier and reactive power QL of inductance L s . P and Q can be expressed as

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Fig. 2 The equivalent circuit of single-phase PWM rectifier

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(8)

On the basis of single-phase power theory, the input powers of the adopted rectifier can be written as ⎧ ) 1( ⎪ ⎨ Pin = u abd i d + u abq i q 2 (9) ⎪ ⎩ Q = 1 (u i − u i ) abq d abd q in 2 The active power PR and reactive power QL can be expressed as ⎧ 1 2 ⎪ ⎨ PR = Rs Ism 2 ⎪ ⎩ Q = 1 ωL I 2 L s sm 2

(10)

Thus, the powers P and Q can be estimated by (8)–(10). The trig functions of grid voltage angle can be deduced as ⎧

sin(ωt + θu ) = sin(ωt + θi − ϕ) = sin(ωt + θi ) cos ϕ − cos(ωt + θi ) sin ϕ cos(ωt + θu ) = cos(ωt + θi − ϕ) = cos(ωt + θi ) cos ϕ + sin(ωt + θi ) sin ϕ (11)

where ⎧ iα iβ ⎪ ⎪ ⎨ sin(ωt + θi )= I , cos(ωt + θi ) = I sm sm P Q ⎪ ⎪ , cos ϕ = √ ⎩ sin ϕ = √ 2 P 2 + Q2 P + Q2

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where ϕ represents the angle between us and is , iα and iβ are the α-axis and β-axis components of is in the two-phase stationary coordinate system. The second-order generalized integral (SOGI) method [8] is adopted to estimate the β-axis component of is . Figure 3 shows the block diagram of the proposed DPC scheme.

2.3 System Parameter Initialization In practical application, the rectifier startup process needs to operate in the uncontrolled and PWM rectifier stages, sequentially. While in the uncontrolled rectifier stage, the modulated voltages uabd , uabq are invalid, calculation of the active and

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And the setup values of the trig functions of grid voltage angle are defined as ⎧

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(14)

where ω0 is the nominal angular frequency.

2.4 Inductance and Resistance Compensation From (8)–(10), it can be obtained that the proposed scheme are sensitive to system parameters. Generally, Rs is very small, its influence on the active power P can be ignored. According to (8) and (10), if the inductance adopted in the proposed method is not equal to its actual value L s , steady-state errors will occur in the estimated powers and gird voltage angle. Thus, it needs to estimate the actual value of the grid-side inductance. Ignoring the influence of Rs , (5) can be written as dQ 1 = Usm u abq + ω P dt 2L s

(15)

Assuming that the switching period T s is much smaller than the fundamental period of the grid voltage, the differential expression of reactive power with respect to time t can be obtained as

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dQ Q(k + 1) − Q(k) = dt Ts

(16)

where Q(k + 1), Q(k) represent the reactive powers at the (k + 1)th and kth switching interval. The goal of power control is that Q(k + 1) = Qref (k). Then, on the basis of (15) and (16), the actual inductance L s can be estimated as L s (k) =

Usm (k)u abq (k)Ts 2[Q ref (k) − Q(k) − ω P(k)]

(17)

When the control system starts up, the initial value of the inductance should be set as the value L m marked on the inductor nameplate, that is L s (0) = L m . Due to the power ripples, a low-pass filter is adopted in practical application to keep the estimated inductance value smooth. Then the filtered value of L s (k) is limited by a saturator, whose upper-limit is 2.5L m and lower-limit is 0.1L m , avoiding extreme conditions.

3 Experimental Results The proposed scheme has been tested in a scale-down single-phase PWM rectifier experimental prototype. Parameters of the adopted converter are set as follows: the grid voltage U s = 65 V, the reference of dc-link voltage U dc * = 120 V, ac-side inductor L m = 4.76mH, DC-link load RL = 20Ω, switching frequency f s = 5 kHz. Figure 4 shows steady-state experimental waveforms of the grid voltage us , line current is and DC-link voltage udc and FFT analysis results of the line currents in the proposed DPC scheme. From Fig. 4, the waveform quality of the line current in the proposed DPC scheme is good and the total harmonic distortion (THD) of the line current is 3.32%.

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Figure 5 shows the comparison results of the estimated grid voltage angle of the proposed scheme and SOGI-PLL method. From Fig. 5, it can be seen that the estimated grid voltage angle and frequency of the proposed method are the same as these of SOGI-PLL method. Figure 6 shows the experimental waveforms of active and reactive powers when the control system starts up. From Fig. 6, it can be noticed that the proposed algorithm can achieve a smooth start-up of the control system. Figure 7 shows the experimental waveforms of the inductance parameter estimation scheme, where us and us_est represent the actual and estimated grid voltages. From Fig. 7, when the initial value of inductance is set as 0.2L m , the phase of estimated grid voltage lags the actual grid voltage by 12.6 ° and the harmonic content of line current increases. When the inductance parameter estimation scheme operates, the estimated inductance can quickly track to its actual value, and the estimated grid

Fig. 5 Comparison of the estimated grid voltage angle of the proposed scheme and SOGI-PLL method. (f s , f s_PLL : 25 Hz/div, Time: 5 ms/div)

Fig. 6 Experimental waveforms of the grid voltage, line current, active and reactive powers when the system starts up. (us : 40 V/div, is : 20A/div, P: 360 W/div, Q: 360Var/div, Time: 20 ms/div)

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Fig. 7 Experimental waveforms of the proposed inductance parameter estimation scheme. (us , us_est : 40 V/div, is : 20A/div, L m : 5mH/div, Time: 10 ms/div)

voltage can accurately track its actual value in a very short time, then the harmonic content of line current decreases.

4 Conclusion This paper presents a simple direct power control of single-phase PWM rectifiers without grid voltage sensor. The instantaneous powers are estimated by the line current and modulated voltage. In order to achieve a smooth startup of the control scheme, a system parameter initialization method is presented. Simultaneously, an on-line inductance parameter estimation scheme is presented to solve the problem of parameter sensitivity of the proposed method. The performance of the proposed DPC scheme is evaluated on a single-phase PWM rectifier experiment platform. The proposed scheme can achieve good control performance without grid voltage sensor. Acknowledgements The work is supported by the National Natural Science Foundation of China (51777001), Educational Commission of Anhui Province (KJ2020A0031).

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References 1. Gou B, Ge X, Wang S, Feng X, Kuo JB, Habetler TG (2016) An open-switch fault diagnosis method for single-phase PWM rectifier using a model-based approach in high-speed railway electrical traction drive system. IEEE Trans Power Electron 31(5):3816–3826 2. Liu B, Song W, Ma J et al (2018) Dynamic performance improvement of single-phase PWM converters with power hysteresis control scheme. IEEE Trans Power Electron 11(12):1894–1902 3. Liu B, Chen T, Song W (2018) The essential relationship between deadbeat predictive control and continuous-control-set model predictive control for PWM converters. In: 2018 international power electronics conference, pp 1872–1876 4. Song W, Deng Z, Wang S, Feng X (2016) A simple model predictive power control strategy for single-phase PWM converters with modulation function optimization. IEEE Trans Power Electron 31(7):5279–5289 5. Mukherjee S, Chowdhury VR, Shamsi P et al (2018) Grid voltage estimation and current control of a single-phase grid-connected converter without grid voltage sensor. IEEE Trans Power Electron 33(5):4407–4418 6. Malinowski M, Jasinski M, Kazmierkowski MP (2004) Simple direct power control of threephase PWM rectifier using space-vector modulation(DPC-SVM). IEEE Trans Ind Electron 51(2):447–454 7. Ma J, Song W, Jiao S, Zhao J, Feng X (2016) Power calculation for direct power control of singlephase three-level rectifiers without phase-locked loop. IEEE Trans Ind Electron 36(5):2871– 2882 8. Kulkarni A, John V (2013) A novel design method for SOGI-PLL for minimum settling time and low unit vector distortion. In: 2013 proceedings IEEE industrial electronics society conference, pp 274–279

Research on Current Ripple Characteristics of Interleaved Vienna Rectifier Changan Li, Hongyang Zhang, Mingxia Xu, and Zhiqiang Wang

Abstract Vienna rectifier is one of the popular topologies used for active power factor correction. Compared with the classical Vienna rectifier, the interleaved Vienna topology provides superior performance with high efficiency, low input current ripple and low total harmonic distortion. However, the input current ripple characteristics of the interleaved Vienna are not fully analyzed. In this paper, a 10 kW three-phase three-level interleaved Vienna rectifier is presented. The classical and interleaved Vienna rectifier are compared via numerical analysis by adopting space vector pulse width modulation (SVPWM) control strategy. The simulation data shows the total harmonic distortion rate of the input current reduced by 2.79% applying interleaved Vienna rectifier. The peak value of the input current ripple of interleaved Vienna rectifier also becomes smaller. Finally, a prototype of the interleaved Vienna rectifier is constructed. The experimental results show that the input current ripple amplitude is decreased effectively, and the overall performance of the rectifier is further improved by combining the interleaved topology and SVPWM together. Keywords Interleaved vienna rectifier · Space vector pulse width modulation · Current ripple characteristics

1 Introduction It is well known that the smoothing capacitor in the diode rectifier circuits might cause high input current ripple, significant harmonic distortion and low power factor, which reduces the converting efficiency and the power quality of the grid [1, 2]. Active power factor correction (PFC) circuit is commonly used to reduce the harmonic distortion and increase the power factor, such as Boost PFC, PWM rectifier, Vienna rectifier and so on [3–7]. The Vienna rectifier has been widely used because of its high efficiency, C. Li · M. Xu · Z. Wang (B) School of Electrical of Engineering, Dalian University of Technology, Liaoning 116024, China e-mail: [email protected] H. Zhang SINOPEC Dalian Research Institute of Petroleum and Petrochemicals, Liaoning 116045, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_19

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high power density, and high reliability [8, 9]. However, with the increasing input power, the Vienna rectifier’s relatively high input current ripple still is a weak point, which should be further improved [10]. For this, researchers proposed some improved control strategies. A modified discontinuous pulse width modulation (MDPWM) method is suggested [11] by modifying the zero sequence component to reduce the current ripple. The hybrid discontinuous pulse width modulation (HDPWM) strategy based on SVPWM and DPWM is studied to weaken current ripple amplitude [12, 13]. Besides, the predictive control of the Vienna rectifier is applied to select the optimal switching state sequences and ensure the minimum input current ripple proposed [14]. From the converter topology aspect, the interleaved mode is also an effective method to reduce the input current ripple. For example, Qiong designed a three-phase interleaved Vienna rectifier with an efficiency of over 99% that can well reduce current ripple [15]. A pair of parallel Vienna rectifiers through the coupling transformer is proposed in [16], which could reduce the volume of the magnetic components and input current ripple. Although the interleaved Vienna rectifier can improve the input current quality, the current ripple characteristics have not been fully analyzed. Therefore, this paper mainly discusses the influence of the interleaved Vienna rectifier on the input current ripple characteristics. Firstly, the current ripple characteristics of the two-channel interleaved bridge arms are presented and analyzed. Then, the current ripple amplitude and total harmonic distortion (THD) between the classical and interleaved Vienna rectifier are compared through SIMULINK. Finally, an experiment platform verifies the accuracy of theoretical analysis.

2 Analysis of Current Ripple Characteristics In this section, the topology and operation principle of the two-channel interleaved Vienna rectifier are introduced. In addition, the characteristics of input currents with SVPWM are presented by simulation and experiment results.

2.1 Topology of the Interleaved Vienna Rectifier The classical three-phase three-level Vienna rectifier topology was first proposed by Austrian scholar Kolar [17]. The circuit topology is shown in Fig. 1. The main circuit consists of three boost inductors L a ~ L c , six Schottky diodes D1 ~ D6 , three power switch tubes S a1 ~ S c1 , two output capacitors C p and C n , RL is the DC load. Each phase bridge arm composes a pair of power switch tubes connected in reverse series, which reduces the number of switch tubes and avoids the phenomenon of straight through the upper and lower tubes of the same bridge arm. But the topology still has high input current ripple.

Research on Current Ripple Characteristics … D1

n

D2

ea

La

ia A

eb

Lb

ib

ec

Lc

ic

229 D3

ip S a1

B

S b1

io

o

RL

S c1 C

D4

Cp

D5

D6

Cn in

Fig. 1 Topology of classical Vienna rectifier

ea

Lsa ia

Lma Lma

n

eb

Lsb ib

Lmb Lmb

ec

Lsc ic

Lmc Lmc

D1 D2 D3 D4 D5 D6 Sa1 ia1 A1 Sa2 ia 2 A2 Sb1 ib1 B1 Sb2 ib 2 B2 Sc1 ic1 C1 S c2 ic 2 C2 D7 D8 D9 D10 D11 D12

ip Cp

Udc1

io

o

Cn

RL Udc

Udc2

in

Fig. 2 Topology of interleaved Vienna rectifier

This paper analyzes the input current ripple characteristics of the interleaved topology, as shown in Fig. 2. Compared with the classical topology, three coupled inductors L ma ~ L mc , six Schottky diodes D7 ~ D12 and three groups of power switch tubes S a2 ~ S c2 are added. The power bridge arms of each phase are in a staggered parallel.

2.2 Control Strategy of the Interleaved Vienna Rectifier In this paper, the SVPWM with iq = 0 is used to prove the improvement effect of interleaved Vienna rectifier, as shown in Fig. 3. It composes a three-phase digital phaselocked loop, SVPWM generator, dq-axis current decoupling, voltage and current PI double closed loop. With the interleaved Vienna rectifier, the phase voltage can be clamped to threelevel states p( + Udc/2), n(−Udc/2) or o(0) by controlling the turn-on and turn-off of the common source MOSFETs. Since the phase voltage is limited by the polarity of the input current ia , ib and ic , the interleaved Vienna rectifier adopts 25 spaces voltage vectors, as shown in Fig. 4. It contains 6 small positive vectors V s1 + (poo) ~

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Fig. 3 Control strategy of interleaved Vienna rectifier

Fig. 4 Vector diagram of interleaved Vienna rectifier

V s6 + (pop), 6 small negative vectors V s1 − (onn) ~ V s6 − (ono), 6 medium vectors V M1 (pon) ~ V M6 (pno), 6 big vectors V L1 − (pnn) ~ V L6 − (pnp) and 1 zero vector V o (ppp). In order to ensure that the MOSFETs switching action is optimal in each SVPWM cycle, a 7-segment wave is employed. Taking the big sector I as an example, the switching state sequence of SVPWM at sector I is shown in Fig. 5. In Fig. 5a, if the reference voltage V ref falls in sub-sector 1, and ib < 0, the switching state sequence

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Fig. 5 Switching state sequences of SVPWM at sector I a sub-sector 1, b sub-sector 2, c sub-sector 3, d sub-sector 4, e sub-sector 5, f sub-sector 6

selects onn → oon → ooo → poo → poo → ooo → oon → onn, otherwise, selects oon → ooo → poo → ppo → ppo → poo → ooo → oon. The switching state sequence of sub-sector 2 ~ 6 is shown in Fig. 5b ~ 5f. Besides, the balance of the output midpoint voltage is adjusted by calculating the action time of the positive and negative small vectors. Moreover, the interleaved Vienna rectifier bridge arms are paralleled, such as A1 O and A1 O, so it needs two SVPWM waves. One is SVPWM with a phase of 0 °, and another is the former shifted by 180 °.

2.3 Current Ripple Characteristics In order to analyze the current ripple characteristics clearly, then the phase-A equivalent circuit of the interleaved Vienna rectifier is illustrated in Fig. 6, where va1o and va2o represent the terminal voltage of A1 and A2 , ea represents the utility grid voltage, von stands for the voltage difference between middle point and neutral point, L sa and L ma represents the boost inductance and coupled inductance of phase-A, respectively. Based on Fig. 6, the inductor voltage of the interleaved Vienna rectifier can be calculated and derived as follows. Fig. 6 Phase-A equivalent circuit of interleaved Vienna

ea n

L sa

ia

L ma

ia 1 A1

va1o

ia 2 A 2

va2o

o

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L sa

di a 1 = ea − (va1o + va2o ) − von 2 dt

(1)

Furthermore, as depicted in Fig. 2, where von is expressed in. 1 von = − (vao + vbo + vco ) 3

(2)

where von of the interleaved Vienna rectifier can be derived in. von = −

1  1  vi1o − vi2o 6 i=a,b,c 6 i=a,b,c

(3)

Substituting (1) into (3) yields     di a 1 1  1  1 = vi1o + vi2o ea − va1o + ea − va2o + L sa 2 3 i=a,b,c 3 i=a,b,c dt 2

(4)

According to (1)–(4), the phase-A inductor voltage of the interleaved Vienna rectifier can be calculated by L sa

  di a di a1s di a2s 1 = + L sa L sa 2 dt dt dt

(5)

where ia1s and ia2s respectively represent the input current of the independent bridge arm A1 and A2 through the inductor L sa . It shows that the total input current ia has nothing to do with the coupled inductor L m , but is related to the input current of the two single-arm. In the sub-sector 1 of the big sector I, when the current ib < 0, the current ripple characteristics of the input current of A1 channel is shown in Fig. 7. The ia1s represents instantaneous current, I a1s represents average current. The current ripple changes periodically when the switching state sequence is onn → oon → ooo → poo → poo → ppp → oon → onn. Fig. 7 A1 channel input current ripple characteristics

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Fig. 8 A2 channel input current ripple characteristics

Fig. 9 Current ripple of interleaved Vienna in sector I-1

The A2 channel input current ripple characteristics, as shown in Fig. 8. The phase of the SVPWM wave has a 180 ° phase shift. From Fig. 8, it can be seen that ia2s get the peak point c when the switching state is oon. Then, the inductor voltage at c point is ea -Udc/6 from Eq. (4). Thus, the maximum current ripple of the A1 channel can be calculated by Δi a1sm

  t0 t0 Udc = Uc = ea − 2 f s L sa 6 2 f s L sa

(6)

According to (5), the input current ripple of the two-channel interleaved Vienna rectifier is derived by averaging ia1s and ia2s , as shown in Fig. 9. Here, ia is the instantaneous input current of the interleaved rectifier. Based on Fig. 9, the inductor voltage at the point e is ea -Udc/3. It can be clearly seen that the interleaved Vienna topology has a smaller current ripple amplitude.

3 Simulation and Experimental Results The simulation models of the classical and interleaved Vienna rectifier are established in the SIMULINK, and the parameters of the simulation models are shown in Table 1. Figure 10 shows the voltage and current simulation waveform of the classical and interleaved Vienna rectifier, and the ia , ib and ic represent three-phase input current, U a , U b and U c represent three-phase input voltage. From Fig. 10a and b, it can be seen that the input current waveform of the interleaved Vienna rectifier is smoother than that of the classical Vienna rectifier. By

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Table 1 Parameters of the simulation models

Symbol

Parameter

Value

V line

Input voltage

380 V/50 Hz

V0

Output voltage

800 V

fs

Switching frequency

40 kHz

Ls

Filter inductance

686 µH

Lm

Coupled inductance

7.1 mH

Fig. 10 Voltage and current waveform a classical Vienna b interleaved Vienna

partially amplifying the input current waveform, the ripple content is more obvious, which proves that the interleaved Vienna topology can effectively improve the input current ripple. Figure 11a shows the input current harmonic spectrum of the classical Vienna rectifier topology, and its total harmonic distortion rate is 5.45%. However, as shown in Fig. 11b, the total harmonic distortion rate of the input current in the interleaved

(a)

(b)

Fig. 11 Total harmonics distortion a classical Vienna b interleaved Vienna

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Vienna rectifier is 2.66%, reduced by 2.79% compared to the former. Thus, the interleaved Vienna topology can improve the current ripple and reduce the THD value of the current. In order to verify the correctness of the theoretical analysis, a 10 kW interleaved Vienna rectifier experimental setup is designed in Fig. 12. It consists of I–VII parts and measure tools, and the I part is EMI filter circuit, II and VII parts are boost and coupling inductors respectively, III part is capacitor bank of output storage, IV part is control and power supply part of the whole system, V and VI parts are MOSFETs power and rectifier diodes circuits, the measuring instrument adopts tex wave device and current clamp. The experiments are conducted to verify the performance of the proposed interleaved Vienna rectifier topology. Figure 13a and b are the experimental results, which represent the current ripple of phase-A with the classical and interleaved Vienna rectifier, respectively.

Ⅶ

Ⅵ

Ⅴ

Ⅳ Ⅰ

Ⅱ Ⅲ Fig. 12 The interleaved Vienna rectifier experimental setup

C u r r e n t ri p p l e/ A

22 21 20 19 18 17 16

Udc1 20V/div

Udc2 20V/div Ua 20V/div ia 10A/div

Udc2 20V/div Ua 20V/div ia 10A/div

Current Ripple /A 0

2

4

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8

Time/s Time/ms

(a)

10

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C C uu rrrr ee n n tt rr ii pp ppll ee // A A

5ms/div

Udc1 20V/div

Current Ripple /A 0

2

4

6

8

Time /s Time/ms

10

12

(b)

Fig. 13 Experimental results of current ripple a classical Vienna b interleaved Vienna

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From Fig. 13, it can be found that the input current ripple amplitude of classical Vienna rectifier is about 4 A, while the current ripple amplitude of the interleaved Vienna rectifier is 2 A. Therefore, the advantages of the interleaved Vienna topology in reducing current ripple have been proved strongly.

4 Conclusion This manuscript mainly analyzes input current ripple characteristics of the interleaved Vienna rectifier, the numerical simulation and experimental comparison are made between the interleaved Vienna and classical Vienna under SVPWM control strategy. The interleaved Vienna rectifier can reduce the input current ripple effectively. So, the size of the boost inductor and EMI magnetic components are reduced, further improve efficiency and power density. Compared with the classical Vienna rectifier, experimental results also can be clearly seen that the current ripple amplitude of interleaved Vienna rectifier is reduced. And the total harmonic distortion rate of the interleaved Vienna rectifier is 2.66%, reduced by 2.79%, however the robustness of the interleaved vienna rectifier system has not been verified.

References 1. Liu B, Ben H, Bai Y (2016) Analysis and suppression of current harmonics in grid side of PWM rectifiers during light load[J]. Trans China Electrotechnical Soc 31(S1):162–168 2. Jiang W, Wang Y, Wang J (2016) Maximizing instantaneous active power capability for PWM rectifier under unbalanced grid voltage dips considering the limitation of phase current[J]. IEEE Trans Industr Electron 63(10):5998–6009 3. Hu Q, Qu B, Lu Z (2006) A novel method for current control used in PFC converter[J]. Proc CSEE 26(3):64–68 4. Lee PW, Lee YS, Cheng DKW (2000) Steady-state analysis of an interleaved boost converter with coupled inductors[J]. IEEE Trans Indus Electron 47(4):787–795 5. Xiao H, Xie S (2010) An interleaving double-switch buck-boost converter for PV gridconnected inverter[J]. Proc CSEE 30(21):7–12 6. Giral R, Martinez-Salamero L (2000) Sliding-mode control of interleaved boost converters[J]. IEEE Trans Circuits Syst I: Fundam Theory Appl 47(9):1330–1339 7. Yang P, Xu J, Zheng D (2013) Quadratic boost power factor correction converters with small input inductor current ripple[J]. Proc CSEE 33(12):32–38 8. Kolar JW, Friedli T (2013) The essence of three-phase pfc rectifier systems—part I[J]. IEEE Trans Power Electron 28(1):176–198 9. Friedli T, Hartmann M, Kolar JW (2014) The essence of three-phase PFC rectifier systems—part II[J]. IEEE Trans Power Electron 29(2):543–560 10. Wang T, Chen C, Liu T (2020) Current ripple analysis of three-phase Vienna rectifier considering inductance variation of powder core inductor[J]. IEEE Trans Power Electron 35(5):4568–4578 11. Huang H, Wang C, Wang H (2020) Modified DPWM strategy for Vienna rectifier considering current harmonic distortions reduction and neutral point voltage balance[J]. Electr Mach Control 24(4):23–31

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12. Lee J, Lee K (2015) Carrier-based discontinuous PWM method for Vienna rectifiers[J]. IEEE Trans Power Electron 30(6):2896–2900 13. Zhu W, Chen C, Duan S (2019) Carrier-based discontinuous PWM method with varying clamped area for Vienna rectifier[J]. IEEE Trans Industr Electron 66(9):7177–7188 14. Lee J, Lee K (2016) Predictive control of Vienna rectifiers for PMSG systems[J]. IEEE Trans Industr Electron 64(4):2580–2591 15. Wang Q, Zhang X, Burgos R (2018) Design and implementation of a two-channel interleaved Vienna-type rectifier with > 99% efficiency[J]. IEEE Trans Power Electron 33(1):226–239 16. Di M, Yang W, Wei C (2016) Three-phase interleaved parallel vienna rectifier based on coupling transformer[C]. In: International conference on power engineering & energy, environment 17. Kolar JW, Drofenik U, Zach FC (1999) VIENNA rectifier II-a novel single-stage high-frequency isolated three-phase PWM rectifier system[J]. IEEE Trans Industr Electron 46(4):674–691

Endogenous Multimode Operation of Non-inverting Buck Boost Converter for Wide Range Voltage Regulation Jianjun Ma, Miao Zhu, Chunyang Pan, and Xu Cai

Abstract Non-inverting Buck Boost converter (NIBB) operates with both voltagestep and step-down capability due to the combination of buck, boost and transition working modes. In endogenous multimode operation of NIBB, the real-time working mode selection requires high performance control strategy applicable for the multiple working modes. In this paper, with consideration of NIBB properties at all three working modes, a linear parameter varying (LPV) system model has been first established, and a digital control design method has been proposed to attain both robust stability and fast dynamic response. Different from traditional small-signal model, the LPV system offers new insights on multimode operation of NIBB, and the influences of equivalent duty ratio definition have been first revealed. To verify the analysis, the proposed control design method is applied three equivalent duty ratio definitions. The experimental comparisons show good agreement with the analysis results. Keywords Non-inverting buck boost converter · Wide working range · Voltage regulation

1 Introduction Increasing applications are required of DC–DC converters with wide range voltage regulation capability. For RF power amplifier, the supply voltage would depending on load condition and varies in wide range for efficient power management [1, 2]. In photovoltaic generation system, the regulated voltage of module integrated converter (MIC) would vary with irradiation and temperature to harvest the maximum power from PV panel [3]. For all the working cases, it is desirable of the interfacing circuit to maintain high steady-state efficiency while have fast dynamic response at the same time. J. Ma · M. Zhu (B) · C. Pan · X. Cai School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_20

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Fig. 1 Non-inverting buck-boost converter for wide-range voltage regulation

Conventional single-mode converter is often constrained by the trade-off between wide output voltage range and conversion efficiency [4]. As the alternative, multimode DC-DC converter has received an increasing research interest, such as the LLC, NIBB, etc. By flexibly configuring the converter in different working modes, it can attain wide operation capability the traditional single-mode converter incapable of, as shown in Fig. 1. However, multimode converter also exhibits complex dynamic property varying with the working mode. How to carry out control design considering the multiple working modes poses new challenges to existing converter modeling and control theory. Small-signal modeling method has been widely applied for the conventional single-mode converter [5]. For the operation of multimode converter, the major challenge is to select the steady-state point and the corresponding linearized model that can represent the converter dynamics. Besides, with the variation of converter working condition, additional mode selection logic is required to determine the real-time converter working mode [6, 7]. The mode selection logic can be classified into two fundamental types: exogenous mode selection and endogenous mode selection. In exogenous mode selection, the converter working mode is directly decided by the external input voltage vg with the reference output voltage vo . As the alternative, endogenous mode selection relies on the inner generated control output for mode selection [8–11]. An equivalent duty ratio can be defined across the three working modes. By comparing the generated equivalent duty ratio with the corresponding value range of each mode, NIBB working mode can be autonomously determined. Since the control output covers three working modes, endogenous mode selection requires control strategy applicable for all these three working modes. In this paper, NIBB dynamics in multimode operation is analyzed with LPV system method [12], and a linear digital control synthesis method is proposed. Rest of the paper is organized as follows: In Sect. 2, the multimode operation of NIBB converter is reviewed. In Sect. 3, the dynamics of NIBB is modeled as a LPV system. In Sect. 4, the control of NIBB is designed with LMI method. The performances of NIBB are comparatively evaluated through experimental results in Sect. 5.

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2 Multimode Operation The equivalent circuit of NIBB is shown in Fig. 2. The converter load is represented by a resistor R in parallel with a current source is . The total load current is given by iload .

2.1 Steady-State Voltage Conversion Ratio of NIBB The dynamic model of NIBB can be developed by linearize and discretize the average converter model with the preset steady-state point. For given steady-state output voltage V o and inductor current I L , the discrete-time small-signal model of NIBB is given by (1), where the upper-case format denotes the dc value, and the lowercase format with a hat (~) denotes the perturbation. The sampling and control period are the same of T s . ⎛

D2 Ts D1 Ts Vin Ts ˜ Vo Ts ˜ i˜L (k + 1) = i˜L (k) ( − TLs )v˜ o (k) + DL2 Ts v˜ in (k) + I L TLs d1 (k) +Ts L d4 (k) v˜ o (k + 1) = 1 − RC v˜ o (k) + C i˜L (k) − C d˜4 (k) − C i˜s (k)

(1)

where vin is the input source voltage, vo is the output load voltage, iL is the inductor load current. d 1 and d 4 are the duty ratio of switch S 1 and S 4 respectively. d4 (t) = 1 − d2 (t)

(2)

In steady-state, the voltage conversion ratio V o /V in is developed by (3) where D1 , D2 denote the duty cycle of S 1 , S 2 respectively. K=

D1 Vo = D2 Vin

(3)

The voltage conversion ratio K can be graphically illustrated as in Fig. 3. Here D1 is given as the vertical axis and D2 given as the lateral axis. The conversion ratio is the slope of line connecting “O” and the working point (D1 , D2 ). The working modes can also be graphically illustrated. In “Buck mode”, D2 = 1 always holds and Fig. 2 Equivalent circuit diagram of NIBB converter

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Fig. 3 Illustration of operation regions of NIBB working modes

the working region is B1 B2 . In “Boost mode”, D1 = 1 always holds and the working region is A1 A2 . Considering the switch dead time and control delay, the duty ratio D1 , D2 have the maximum value Dmax . The maximum duty ratio limit will results in discontinuous voltage conversion between 1/Dmax (OA1 ) and K = Dmax (OB1 ). To solve the challenge, NIBB has to operate within the area σ for continuous voltage conversion. Any line in the area σ connecting C m C n with E m E n can be adopted as the Transition mode, as shown in Fig. 3. For example, in Boost-clamping mode a = –1/Dmax 2 , b = 0. a ∗ D1 + b ∗ D2 + 1 = 0

(4)

In summary, steady-state duty ratios (D1 , D4 ) and the corresponding voltage conversion ratio K are given in the following.

2.2 Definition of Equivalent Duty Ratio deq According to Table 1, with the defined Transition mode in (4), a one-to-one mapping relation is developed between steady-state voltage conversion ratio K and the duty ratio combinations (D1 , D4 ). Under each mode, the two control variables d 1 and d 4 are interdependent. Therefore, it is possible to define an equivalent duty ratio d eq to eliminate the redundant variable. For ease of implementation, a piecewise linear relation of d eq with practical switch duty ratio combinations (d 1 , d 4 ) is here considered. In Buck mode and Boost mode, d eq can be defined as a shift of the practical duty ratios (d 1 in Buck mode, d 4 in Boost mode).

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Table 1 Relation of voltage conversion ratio k with switch duty cycles (D1 , D4 ) Range of voltage conversion ratio ⎤ ⎡ Vmin Vo , Dmax

Mode Buck mode

⎡

Transition mode Boost mode

⎛

⎡

Dmax ,

1 Dmax

Vmax 1 Dmax , Vo

Buckmode : Boostmode :

⎤

D1

D4

D1 = K

D4 = 0

D1 =

⎤

−K a∗K +b

D1 = 1

D4 = 1 +

1 a∗K +b

D4 = 1–1/K

) ⎡ d1 = deq + C1 , d4 = 0, deq ∈ ⎡D Bu_ min , D Bu_ max ) d1 = 1, d4 = deq + C2 , deq ∈ D Bo_ min , D Bo_ max

(5)

Without loss of generality, the shift value C 1 in Buck mode is taken as 0. DBu_min , DBu_max are in the same minimum/maximum values of practical power switch Dmin , Dmax . In Boost mode, the maximum and minimum equivalent duty ratios DBo_min , DBo_max are given by (6). ⎛

D Bo_ min + C2 =Dmin D Bo_ max + C2 =Dmax

(6)

As for Transition mode, a general linear relationship of d eq with practical duty ratios d 1 , d 4 is given by (7). ) ⎡ Transitionmode : d1 = k1 deq + C3 , d4 = k2 deq + C4 , deq ∈ D Bu_ max , D Bo_ min (7) The maximum and minimum values of d 1 , d 4 in Transition mode are in accordance with Table 1. As a result, the maximum and minimum values of d eq can be determined as DBu_max and DBo_min in (8). ⎛

max k1 D Bu_ max + C3 = − a DDmax +b , 1 k2 D Bu_ max + C4 = 1 + a Dmax +b

⎛

1/Dmax k1 D Bo_ min + C3 = − a/D max +b 1/Dmax k2 D Bo_ min + C4 = 1 + a/D max +b

(8)

Since the duty ratios (d 1 , d 4 ) in Transition mode also follow the defined Transition mode in (4), by substituting (7) into (4), the interdependent relations of k 1 , k 2 and C 3 , C 4 are given in (9, 10). k1 a = (k2 /= 0, b /= 0) b k2

(9)

a ∗ C3 + b ∗ C4 + 1 = 0

(10)

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Fig. 4 Interdependent relationship of NIBB “equivalent duty ratio d eq ”, “switch duty ratio d 1 , d 4 ” and “voltage conversion ratio K”

According to (9), when k 2 /= 0, k 1 /k 2 value is solely determined by the selected Transition mode. By combining (4–10), for the selected Transition mode, there is still one freedom variable left. The only undetermined parameter k 1 or k 2 is equivalent duty ratio gain, and it serves as another freedom variable for equivalent duty ratio definition. In summary, the equivalent duty ratio is determined by the selected “Transition mode” and “equivalent duty ratio variables k 1 or k 2 ”. With Transition mode given by (4) and the defined equivalent duty ratio parameters k 1 or k 2 , the related duty ratio values in (5) and (7) can be uniquely determined. A graphic illustration of equivalent duty ratio d eq definition is shown in Fig. 4. In the K ~ d eq plane, d eq is attained by shifting the K ~ d 1 curve in Transition mode and shifting the K ~ d 4 curve in Boost mode. The equivalent duty ratio d eq serves as an intermediate variable to connect voltage conversion ratio K with practical switch duty ratios d 1 , d 4 . For the other Transition modes and k 1 or k 2 values, similar d eq definition also applies.

3 LPV System Model Based on the equivalent duty ratio, the general NIBB model for all three working modes is represented as (11). Assuming the input voltage vG is well-regulated, the disturbance term w(t) comes from load variation and is represented by the current source iload . It should be noted that more uncertainties such as L, C parameter deviations and line voltage deviation can be included in the converter model, at the expense of more conservative synthesis results. ˙˜ = A(λ)x(t) ˜ x(t) ˜ + Bdeq (λ)d˜eq (t) + Bw w(t)

(11)

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System state-space matrixes A(λ), Bdeq (λ), Bw (λ) in (15) vary with particular operation mode and the working condition. The corresponding matrixes are given in (12). ⎡ A(λ) =

1 C

⎡ ⎤ ⎤ ⎤ ⎡ Vg 0 0 − L1 ∗ ψ ∗ ζ1 L , Bw = , Bdeq (λ) = − C1 ∗ ψ − C1 ∗ R1 −Vg ∗ R1 ∗ ζ2

(12)

where the equivalent load R is an independent variable determined by the external load condition. ψ, ζ1 and ζ2 are variables relating to working mode as well as voltage conversion ratio. Their values and varying ranges are discussed in the following. In Buck mode: The varying state-space matrixes A(λ) and Bdeq (λ) in Buck mode are given by A1 and Bdeq1 . ⎡ A1 =

0 1 C

− L1 − C1 ∗

⎤ 1 R

, Bdeq1 =

⎡ Vg ⎤ L

(13)

0

Comparing (13) with (12), the varying parameter ψ in A1 is constantly 1. For Bdeq1 , ζ1 is constantly 1 and ζ2 is constantly 0. ψ = 1, ζ1 = 1, ζ2 = 0

(14)

In Transition mode: The varying state-space matrixes A(λ) and Bdeq (λ) in Transition mode are given by A2 and Bdeq2 . ⎡ A2 =

1 C

⎡ ⎤ ⎤ Vg ∗ + k ∗ k (k ) 0 − L1 ∗ D2 1 2 , Bdeq2 = L Vg 1 ∗ D2 − C1 ∗ R1 − C ∗ R ∗ Dk2 ∗ k2

(15)

Comparing (15) with (12), ψ in A2 is given by (16). ψ = D2

(16)

The variation range of ψ in (16) involves with particular Transition mode. The variation range of ψ is determined as (17). ⎤ ⎡ ⎤ −1 −1 −1 , , or ψ∈ a/Dmax + b a Dmax + b a Dmax + b a/Dmax + b ⎡

−1

(17)

For ζ1 and ζ2 in Beq (λ), they can be rewritten as (18). ⎛⎛ ζ1 =

k1 k2

⎞ + k ∗ k2 , (k2 /= 0) k1 , (k2 = 0)

, ζ2 =

k ∗ k2 D2

(18)

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In comparison, the variation ranges of ζ1 and ζ2 are more complex terms. They depend on both Transition mode and equivalent duty ratio definition (the term k 1 , k 2 ). In Boost mode: The varying state-space matrixes A(λ) and Bdeq (λ) in Transition mode are given by A3 and Bdeq3 . ⎡ A3 =

1 C

⎡ ⎤ Vg ∗ D12 0 − L1 ∗ D2 L , Bdeq3 = Vg 1 1 − C ∗ R1 ∗ ∗ D2 − C ∗ R

⎤ 1 D22

(19)

ψ, ζ1 and ζ2 in Boost mode are given by ψ = D2 , ζ1 =

1 1 , ζ2 = 2 D2 D2

(20)

As a result, NIBB in three working modes can be developed as a linear parameter varying (LPV) system with R, ψ, ζ1 and ζ2 as the varying parameters. With the Transition mode selected as Boost-clamping mode, the corresponding (ζ1 , ζ2 ) value can be rewritten as (21). ζ 1 = k 1 , ζ2 = 0

(21)

For different definition of equivalent duty ratio, a comparison of the polytopic covering is illustrated in Fig. 5. • When k 1 = 1, the operation region of Transition mode D1 overlaps with Buck mode region A and the polytopic covering is ABC. Fig. 5 Polytopic coverings of (ζ 1 , ζ 2 ) with different equivalent duty ratio definition with boost-clamping transition mode

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• When k 1 = 0.5, the operation region of Transition mode is D2 and the corresponding polytopic covering is ACD2 . • When k 1 = 2, the operation region of Transition mode is D3 and the corresponding polytopic covering is ABCD3 . In comparison, the minimum polytopic covering is attained when k 1 = 1. Any deviation of k 1 value from 1 will results in larger polytopic covering.

4 Control Design With the selected Boost-clamping transition mode and the equivalent duty ratio d eq , the control is designed in this section. With the control aim of output voltage, an additional variable e(t) is introduced as (22). To eliminate the steady-state voltage deviation, the integration of voltage deviation is also defined as vint (t) in (23). e(t) = vo (t) − vr e f (t) ∫ vint (t) =

(22)

⎡ ⎤ vo (t) − vr e f (t) dt

(23)

For control implementation, the converter model is discretized with ZOH (sampling time of T s ). The augmented state array ρ(k) is given as (24). With the given reference voltage vref (t), the converter disturbance array is represented as w(k). Due to the presence of control delay (one switching cycle), an intermediate control variable is introduced as u(k). The corresponding discretized converter model is given as (25)–(26). ⎤ ⎡ ⎤ x(k) ˜ i˜load (k) ⎦ ⎣ ˜ = = v˜ int (k) , w(k) ρ(k) ˜ v˜ ref (k) d˜eq (k) ⎡ ⎡ ⎤ ⎤ ⎡ ⎤ 0 0 0 ATs + I 0 B deq Ts T ⎢ s ⎢0⎥ ⎥ ⎤ ⎡ ⎢ ⎥ u(k)+ ⎢ − C 0 ⎥ ⎦ ρ(k) 1 0 ρ(k ˜ + 1) = ⎣ 0 Ts ˜ ⎣ 0 Ts ⎦ w(k) ⎣0⎦ ˜ 0 0 0 0 1 0 0          Ad ⎡

Bu

⎡ ⎤ y˜ (k) = 0 1 0 0 ∗ ρ(k) ˜

(24)

(25)

Bw

(26)

It should be noted that the digital implementation does not alter the varying parameters and the corresponding varying range. For close-loop control, the linear controller is adopted due to easy implementation and the similar structure with PI control. The developed equivalent duty ratio is given

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in (27). Implementation of the linear controller is shown in Fig. 6. ⎤ ⎡ ˜ u(k) ˜ = K ∗ ρ(k) ˜ = ki p kv p kvi kd ∗ ρ(k)

(27)

Both control stability and recovery time of the close-loop control can be coordinately optimized with the following Theorem. Theorem: For given real positive scalars d and r, defining the circle within the unit circle as shown in Fig. 7. If there exist symmetric positive definite matrices wi and matrices G, Z for the given positive μ, such that for i = 1 ~ n and j = 1 ~ n ⎡ ⎢ ⎢ ⎣ (Ad−i

G T +G − wi 0 −1 − d I )r G + Bu r −1 Z Ci G

∗ μI Bw 0

∗ ∗ wj 0

⎤ ∗ ∗ ⎥ ⎥>0 ∗ ⎦ μI

Fig. 6 Digital control diagram for endogenous multimode operation of NIBB

Fig. 7 Close-loop eigenvalue region for LPV system

(28)

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holds, then the state feedback gain K = G −1 Z

(29)

ensures 1. The system eigenvalues all locate inside the (r, d) circle shown in Fig. 7. 2. The H∞ norm of close-loop system has a prescribed value of μ.

5 Experimental Verifications In verification of the developed converter control, a NIBB converter prototype is built. The circuit specifications follow Table 2. The control and sampling rate are the same as switching frequency f sw = 20 kHz. The dynamic performance of NIBB are first compared in Buck mode under load variation. The output voltage vo is regulated constantly at 20 V. As shown in Fig. 8a– c, the output voltage and inductor current are compared with R steps from Rmax = 30 Ω to Rmin = 10 Ω. In comparison, Boost-clamping mode with equivalent duty Table 2 Specifications of NIBB converter

Parameter

Value

Nominal value

R

[10,30] Ω

20 Ω

C

570 μF

−

L

0.58 mH

−

Dmax

0.8

−

Switching frequency fs

20 kHz

−

Vg

48 V

−

Vo

Buck: [20,25.6] Transition: [25.6,40] Boost: [40,48]

Buck: 23 V Transition: 33 V Boost: 44 V

Fig. 8 Evaluation of NIBB responses under Buck mode, a transition mode: boost-clamping mode, k 1 = 1, k 2 = 0, b transition mode: boost-clamping mode, k 1 = 0.5, k 2 = 0, c transition mode: boost-clamping mode, k 1 = 2, k 2 = 0

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Fig. 9 Evaluation of NIBB responses under Boost mode, a transition mode: boost-clamping mode, k 1 = 1, k 2 = 0, b transition mode: boost-clamping mode, k 1 = 0.5, k 2 = 0, c transition mode: Boost-clamping mode, k 1 = 2, k 2 = 0

ratio gain k 1 = 1 has the lowest voltage drop and recovery time, in accordance with the analysis result. The dynamic performance of NIBB are also compared in Boost mode with the output voltage vo regulated at 48 V. As is shown in Fig. 9a–c, the output voltage and inductor current are compared with R steps from Rmax = 30 Ω to Rmin = 10 Ω. In comparison, Boost-clamping mode with equivalent duty ratio gain k 1 = 1 has the lowest voltage drop and recovery time, in accordance with the analysis result.

6 Conclusion NIBB exhibits different dynamic properties during multimode operation and poses new challenge to converter modeling and control method. To ensure robust stability and fast load response of through multiple working modes, NIBB converter is analyzed with LPV system method and a linear digital control is designed based on LMI method. Based on the polytopic covering, robust stability and dynamic indexes (including recovery time and damping ratio) of NIBB control are simultaneously guaranteed through LMI method. The designed control gains has been tested for robust voltage regulation and compared with small-signal PI control. Boostclamping transition mode together with equivalent duty ratio gain k2 = 1 can attains the minimum recovery time under load disturbance, in verification of the analysis results. Acknowledgements This work is sponsored by the National Natural Science Foundation of China under Grant 52007118, and is also sponsored by Soft Science Research Program of Shanghai City (20692110500).

References 1. Chen CW, Chen KH, Chen YM (2014) Modeling and controller design of an autonomous PV module for DMPPT PV systems. IEEE Trans Power Electron 29(9):4723–4732

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2. Kasper M, Bortis D, Kolar JW (2014) Classification and comparative evaluation of PV panelintegrated DC–DC converter concepts. IEEE Trans Power Electron 29(5):2511–2526 3. Rodriguez M, Stahl G, Corradini L, Maksimovic D (2013) Smart DC power management system based on software-configurable power modules. IEEE Trans Power Electron 28(4):1571–1586 4. Anun M, Ordonez M, Zurbriggen IG, Oggier GG (2015) Circular switching surface technique: high-performance constant power load stabilization for electric vehicle systems. IEEE Trans Power Electron 30(8):4560–4572 5. Ma J, Zhu M, Li X, Cai X (2018) Bumpless transfer of non-inverting buck boost converter among multiple working modes. In: 2018 IEEE applied power electronics conference and exposition (APEC), San Antonio, TX, pp 1909-1914 6. Ma J, Zhu M, He G, Cai X (2017) Breaking performance limit of asynchronous control for non-inverting buck boost converter. In: IECON 2017—43rd annual conference of the IEEE industrial electronics society, Beijing, pp 928–933 7. Ren X, Ruan X, Qian H, Li M, Chen Q (2009) Three-mode dual-frequency two-edge modulation scheme for four-switch buck-boost converter. IEEE Trans Power Electron 24(2):499–509 8. Lee Y, Khaligh A, Chakraborty A, Emadi A (2009) Digital combination of buck and boost converters to control a positive buck-boost converter and improve the output transients. IEEE Trans Power Electron 24(5):1267–1279 9. Jones DC, Erickson RW (2013) A nonlinear state machine for dead zone avoidance and mitigation in a synchronous noninverting buck-boost converter. IEEE Trans Power Electron 28(1):467–480 10. Aharon I, Kuperman A, Shmilovitz D (2015) Analysis of dual-carrier modulator for bidirectional noninverting buck-boost converter. IEEE Trans Power Electron 30(2):840–848 11. Restrepo C, Konjedic T, Calvente J, Giral R (2015) Hysteretic transition method for avoiding the dead-zone effect and subharmonics in a noninverting buck-boost converter. IEEE Trans Power Electron 30(6):3418–3430 12. Ma J, Zhu M, Li Y, Cai X (2021) Dynamic analysis of multimode buck-boost converter: an LPV system model point of view. IEEE Trans Power Electron 36(7):8539–8551

New and Renewable Energy

Coordinated Control Strategy to Enhance FRT Capacity for Offshore Wind Farms Connected MMC-HVDC Wenqiang Wu, Ke Jia, Laiyun Hou, Jin Sun, and Bohan Liu

Abstract VSC-HVDC technology is the first choice for large-scale offshore wind power grid connection in the deep ocean. Offshore wind farms connected MMCHVDC system should have fault ride-through (FRT) capability when the grid side fails. Currently, DC Chopper is commonly used to achieve FRT, but the capacity of DC Chopper is usually the rated capacity of the wind farms, and the switching time is long, resulting in high project cost. To address the problem of large design capacity and long switching time of the existing DC Chopper, this paper proposes a non-communication coordinated control method between DC Chopper and wind farm side converter and wind farms. When a fault on the grid side causes the DC voltage to exceed the action threshold of the DC Chopper, the DC Chopper is used to initially absorb the unbalanced power. If the DC voltage continues to rise to exceed the action threshold of the voltage drop method, the wind farm side converter reduces the input power by reducing the amplitude of the AC bus voltage of the wind farms and cooperating with the wind farms to reduce the active power. The proposed method not only reduces the rated capacity and switching time of DC Chopper, but also limits the DC voltage to the allowable value more quickly, and the system can achieve safe and reliable FRT. Keywords Offshore wind farm · DC chopper · Coordinated control

1 Introduction Offshore wind power is developing rapidly worldwide. As of 2020, the total installed capacity of offshore wind power in Europe has reached 19.5–28 GW, and that of China has reached 5 GW [1]. However, during AC power grid faults, the grid-connected inverter must greatly reduce the active power output due to the nature of the fault W. Wu · K. Jia (B) · L. Hou · J. Sun North China Electric Power University, Beijing, China e-mail: [email protected] B. Liu State Grid AC Project Construction Co. Ltd., Beijing, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_21

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and the requirement of reactive power support, and the unbalanced power at both ends of the modular multilevel converter-HVDC (MMC-HVDC) system will cause overvoltage [2]. Therefore, it is urgent to study a reliable FRT control method for MMC-HVDC connected offshore wind farms. DC Chopper is commonly used in engineering to realize AC side FRT. Refs. [3, 4] proposed the installation of DC Chopper in the onshore converter station. When the onshore power grid fails, the DC Chopper is used to absorb the excess power according to the DC bus overvoltage. Refs. [5, 6] summarized the topology of the existing DC Chopper, analyzed the shortcomings of the existing topology, and proposed a new type of DC Chopper topology on this basis, but the problem of the large design capacity of the DC Chopper is still not solved. Ref. [7] proposed a coordinated control strategy for DC Chopper and wind farm, but the reliable power reduction of wind farm is based on communication equipment. Large delays will cause wind farm to not be able to reduce power in time, and the FRT effect will be poor. To solve the problem of large rated capacity and long switching time of DC Chopper in engineering, this paper proposes a coordinated control strategy of DC Chopper and wind farm side converter and wind farm. When the onshore power grid fails and the DC voltage exceeds the action threshold of the DC Chopper, the DC Chopper is triggered, and is put into the circuit to initially absorb the unbalanced power. If the DC voltage continues to rise to exceed the action threshold of the voltage drop method, the wind farm side converter reduces the input power by reducing the AC bus voltage amplitude and cooperating with the wind turbine grid-side converter to reduce the reference value of the d-axis component of the current inner loop. The proposed method can greatly reduce the design capacity and switching time of the DC Chopper, and ensure that the DC voltage is within the allowable value range and the wind turbine is not off-grid, and the reliable FRT of the system can be realized.

2 System Outline and Steady State Control of MMC-HVDC Connected Wind Farms 2.1 System Topology The topological structure of MMC-HVDC connected offshore wind farms is constructed with a total offshore wind farm capacity of 1000 MW, as shown in Fig. 1. Offshore wind farms are composed of PMSG and step-up transformer (690 V/35 kV). After the voltage is transformed to medium voltage, it is connected to the offshore booster station (35 kV/220 kV). Both converter stations use an MMC and the wind turbine back-to-back converter uses a two-level voltage-source converter (VSC). Throughout the remainder of this paper, the offshore converter station is referred to as the wind farm side-converter (WFMMC), and the onshore converter station is referred to as the grid-side converter (GSMMC).

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MMC-HVDC 0.69V/35kV 35kV/220kV

SM SM

SM SM

370kV/220kV

DC Cable SM SM

SM SM

WTVSC GSVSC

WFMMC

±320kV

Fault

Main Grid

GSMMC

Fig. 1 System structure diagram of MMC-HVDC connected offshore wind farms

2.2 Steady State Control To ensure that the DC voltage of the MMC-HVDC is stable and the reactive power output is zero, a voltage and current double closed-loop vector control strategy based on grid voltage orientation is usually adopted for the GSMMC. When the d-axis is oriented at the grid voltage, a complete decoupling of the d, q-axis for the currents is achieved by using a proportional-integral (PI) controller. In steady-state operation, the WFMMC keeps the AC bus voltage and frequency of the wind farms stable, absorbs the active power of the wind farms, and often adopts V-F control. The outer loop of the GSVSC has a constant DC voltage and constant reactive power to ensure that the DC voltage is stable and the reactive power output is zero during steady-state operation.

3 Coordinated FRT Control Strategy 3.1 FRT Control Strategy of the WFMMC When the AC side fails and the DC voltage exceeds the DC Chopper action threshold (1.05 pu), the DC Chopper is triggered and absorbs a portion of the power, but the DC voltage will still rise in a short time. When the DC voltage exceeds 1.075 pu, WFMMC starts the voltage drop method to reduce the input power of the wind farm. Reducing the input power by reducing the reference value of the AC bus voltage of the wind farm can be expressed as: 

UWFref = UWFref − KFRT (Udc − Udcthr ) KFRT =

UWFref − UWF min Udc max − Udcthr

(1) (2)

where U WFref and U Wfref ’ are the reference value and correction value of the AC bus voltage of the wind farm respectively; U dc and U dcthr are the measured value of the DC voltage and the DC voltage threshold of the voltage drop method respectively;

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K FRT is the FRT coefficient; U dcmax and U WFmin are the maximum allowable DC voltage and the maximum voltage drop depth of the AC bus of the wind farm.

3.2 FRT Control Strategy of the GSVSC GSVSC adopts a vector control strategy in steady state, the outer loop determines the DC voltage and reactive power, and the active power output can be changed by changing the reference value of the current inner loop d-axis current. Considering that the AC voltage is allowed to fluctuate by ±5% during steady state operation of the system, the d-axis current reference value of the GSVSC current inner loop during steady state and fault period can be expressed as:  idref

 =

idref , UWF ≥ 0.95 pu UWF idref , UWF < 0.95 pu

(3)

where idref , idref  are the reference value and correction value of the d-axis current respectively; V dcref , V dc are the reference value of the wind turbine DC voltage and the measured value of the wind turbine DC voltage respectively.

3.3 Coordinated FRT Control Strategy with DC Chopper By setting the action thresholds of the DC Chopper and the voltage drop method to be different, the two can achieve FRT through cooperation, and the capacity of the DC Chopper can be reduced. Through coordination and cooperation, the value and switching time of the DC Chopper are shown in Eq. (4) and Eq. (5): 

2 kUdcref = PGS(1.05) − PGS(1.075)

(4)

ton PGS(1.05) − PGS(1.075) = T PWF max

(5)

Rchopper 

D =



where PGS (1.05) and PGS (1.075) are the output power of GSMMC when the DC voltage reaches 1.05 pu and 1.075 pu, respectively.

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4 Simulation Verification and Analysis 4.1 Asymmetric Fault Occurs in the Receiving Power Grid Figure 2 is a waveform diagram of various electrical quantities during the FRT process when phase A to ground short-circuit occurs at the GSMMC outlet at t = 0 s. The duration of the fault is set to 625 ms required for the grid connection of the wind farm. As shown in Fig. 2a, when phase A to ground fault occurs in the receiving power grid, the voltage drop is about 50%. As shown in Fig. 2b, c, an asymmetric fault on the grid side will cause the output power and DC voltage to fluctuate with double frequency components. When the DC voltage exceeds 1.05 pu (about 80 ms), the DC Chopper is used to absorb unbalanced power, but the rated capacity of the DC Chopper is small, the resistance of the DC Chopper is large, and the absorbed energy is limited, and the DC voltage will continue to rise. When the DC voltage exceeds 1.075 pu, WFMMC starts the voltage drop method to reduce the input power. After the wind farm detects that the AC bus voltage is lower than 0.95 pu, the wind farm actively corrects the current reference value of the inner loop d-axis current to further

Grid side voltage/kV

Phase B

Phase C

100 0 -100 -200

Fault occurrence

0

0.2

0.4

1000

The power of MMC-HVDC /MW

Phase A

200

Fault occurrence

0

0.2

0.4

0.6

t/s

(b) 600

Power absorbed by DC Chopper/MW

1.05 1.1

DC voltage/p.u.

400

t/s

(a)

1.05 1 0.95 Proposed method

0.9 0.85

Output power

600

200

0.6

Input power

800

DC Chopper alone

0

0.2

0.4

(c)

0.6

t/s

Fig. 2 FRT process of phase A to ground short-circuit

Proposed method

400

DC Chopper alone

200

0

0

0.2

0.4

(d)

0.6

t/s

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reduce the output power of the wind farm. During a fault, changing the control strategy can achieve a rapid power reduction. After the DC voltage is lower than 1.05 pu, the DC Chopper is cut off. As shown in Fig. 2d, the switching time of DC Chopper of the proposed method is about 100 ms, which is much shorter than the switching time of using DC Chopper alone for FRT.

4.2 Symmetrical Failure of the Receiving Power Grid Figure 3 shows a waveform diagram of various electrical quantities during the FRT process when a three-phase grounding short-circuit fault occurs at the GSMMC outlet at t = 0 s. The failure duration is 625 ms. As shown in Fig. 3a, a three-phase short circuit on the grid side causes a voltage drop of about 70%, and the active power output by GSMMC is very small. As shown in Fig. 3b, c, when the DC voltage exceeds 1.05 pu, the DC Chopper is triggered and initially absorbs unbalanced power. If the DC voltage continues to rise to 1.075 pu, the WFMMC controller starts the voltage drop method. To reduce the AC bus voltage of the wind farm, GSVSC disconnects the voltage outer loop and reduces the input

Grid side voltage/kV

The power of MMC-HVDC /MW

1000

200

Phase A Phase B Phase C

100 0 -100 -200

Fault occurrence

0

0.2

0.4

(a)

0.6

600 400 200 0

Fault occurrence

0

0.2

0.4

(b)

0.6

t/s

Power absorbed by DC Chopper/MW

1000

1.1

DC voltage/p.u.

Input power Output power

t/s

1.15

1.05 1 0.95

Proposed method DC Chopper alone

0.9 0.85

800

0

0.2

0.4

(c)

0.6

t/s

Fig. 3 FRT process of three-phase short-circuit

800

Proposed method DC Chopper alone

600 400 200 0

0

0.2

0.4

(d)

0.6

t/s

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power by modifying the reference value of the d-axis component of the current inner loop. The decrease of the input power will cause the DC voltage to drop. When the DC voltage is less than 1.05 pu, the DC Chopper is cut off from the circuit. The proposed method of coordination and cooperation can still achieve a rapid reduction in DC voltage even when the receiving end power grid has a serious failure. As shown in Fig. 3d, the switching time of the DC Chopper is about 100 ms, while the DC Chopper needs to be inputed 625 ms when the DC Chopper is used alone for FRT. The proposed method can greatly shorten the input time of the DC Chopper.

5 Conclusion Aiming at the large capacity and long switching time of DC Chopper, this paper proposes a coordinated FRT control method. Through the coordination of DC Chopper and voltage drop of WFMMC and active power reduction of wind farm, the rated capacity and switching time of DC Chopper have been greatly reduced. To prevent the wind farm from going offline during the FRT period, the voltage reduction depth of WFMMC is limited. To maintain the power balance, a control strategy for active power reduction of the wind farm without communication is proposed. The proposed method can quickly limit the DC voltage within the allowable value range, which is more conducive to the reliable FRT of the system.

References 1. Bidadfar A, Saborío-Romano O, Cutululis NA, Sørensen PE (2021) Control of offshore wind turbines connected to diode-rectifier-based HVDC systems[J]. IEEE Trans Sustain Energy 12(1):514–523 2. Moawwad A, El Moursi MS, Xiao W. A novel transient control strategy for VSC-HVDC connecting offshore wind power plant [J]. IEEE Trans Sustain 3. Moawwad A, El Moursi MS, Xiao W (2016) Advanced fault ride-through management scheme for VSC-HVDC connecting offshore wind farms [J]. IEEE Trans Power Syst 31(6):4923–4934 4. Rauf AM, Khadkikar V, El Moursi MS (2019) A new fault ride-through (FRT) topology for induction generator based wind energy conversion systems [J]. IEEE Trans Power Delivery 34(3):1129–1137 5. Nanou S, Papathanassiou S (2015) Evaluation of a communication-based fault ride-through scheme for offshore wind farms connected through high voltage DC links based on voltage source converter [J]. IET Renew Power Gener 9(8):882–891 6. Pannell G, Zahawi B, Atkinson DJ, Missailidis P (2013) Evaluation of the performance of a DC-link brake chopper as a DFIG low-voltage fault-ride-through device [J]. IEEE Trans Energy Convers 28(3):535–542 7. Li W, Tang G, Kang Y (2014) Improving low voltage ride through capability of wind farm gridconnected via dynamic chopper controlled breaking resistor based MMC-HVDC transmission system [J]. Power Syst Technol 38(5):1127–1135

Frequency Regulation Method for HVDC System with Wind Farm Yuhong Wang, Jie Zhu, Qi Zeng, and Zongsheng Zheng

Abstract Under the background of high wind power permeability, the frequency regulation capability of high voltage direct current (HVDC) sending system tends to deteriorate. For this reason, this paper regards the wind farm (WF) and HVDC as a combined frequency regulation system, and proposes a strategy to cooperate with HVDC and WF to participate in frequency regulation based on fuzzy logic control. First of all, at the system level, in order to realize the dynamic cooperation of the WF and the HVDC to participate in frequency regulation, two fuzzy logic controllers (FLCs) are designed to determine the total power support of the combined system and the coefficient of the WF participating in the frequency regulation according to the frequency deviation of the system and the operation state of the WF, respectively. Secondly, at the WF level, considering the rotating kinetic energy and capacity of wind turbines (WTs), a power allocation strategy is proposed to maximize the utilization of frequency regulation capacity of the multiple WTs in WF. Finally, based on the fast power regulation of HVDC, an active secondary frequency drop (SFD) restrain strategy is proposed to avoid the possible SFD caused by speed recovery of WFs. The simulation results show that the proposed strategy can making full use of the frequency regulation ability of the WF and HVDC, and effectively improve the frequency characteristics of the HVDC sending system. Keywords HVDC · Frequency response · Fuzzy logic control

1 Introduction In order to deal with the energy crisis and carbon emissions, wind power generation technology has developed rapidly, and the proportion of wind power in the power system has increased year by year in the past decades [1, 2]. However, large-scale wind energy resources are often far away from the load center. The conventional HVDC transmission based on line commutation converter (LCC-HVDC) has become Y. Wang · J. Zhu · Q. Zeng (B) · Z. Zheng Sichuan University, Chengdu, Sichuan Province, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_22

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the first choice for long-distance transmission of large-scale onshore wind power because of its large-capacity transmission capacity and lower loss [3]. After a large scale WF connected to the power grid through the HVDC system, due to the complete decoupling between the control of the following WTs and the system frequency, the frequency stability of the transmission system is faced with great challenges [4]. On the other hand, both WTs and HVDC systems can provide frequency support for the power grid under appropriate control modes. A series of papers have studied the use of WFs and HVDC systems to participate in frequency regulation []. For the WF, the literature [4, 5] studies the frequency feedback control such as additional virtual inertia control and droop control, and uses the rotor kinetic energy of the WT to participate in the frequency regulation of the system. Based on the operation mode of overspeed load reduction and variable propeller load reduction, the standby wind energy is used to participate in the frequency regulation of the system [6]. For HVDC transmission system, using down frequency control to participate in frequency regulation is a simple and easy method to be widely used, but because the frequency changes slowly, this method can not give full play to the fast regulation ability of HVDC active power. The frequency differential droop link is added on the basis of frequency droop control in reference [7]. Because the differential index of frequency can respond to the change of frequency more sensitively, the frequency response ability of HVDC system is faster. However, the above literature only focuses on the frequency regulation of HVDC system and WF alone. In order to coordinate the participation of WF and HVDC in frequency regulation, a nonlinear mathematical prediction model of cooperative frequency regulation of HVDC and WF is established in reference [8]. Based on the method of situation perception, the coordination of WF and HVDC system to participate in frequency regulation is realized, but the effect of frequency regulation is affected by the accuracy of the prediction model. In reference [9], wind power plants work in load shedding mode, and variable pitch control is used with HVDC system to participate in frequency regulation. Reference [10, 11] analyze that WFs based on MPPT use rotor kinetic energy and HVDC system to achieve frequency response. It is worth pointing out that the randomness and volatility of wind speed can not ensure that WTs have long-lasting and reliable inertia response capacity, and it is easy to cause secondary fluctuations of system frequency. Although the control strategies proposed in the above research have improved the frequency regulation ability of the HVDC transmission system with wind power to a certain extent. However, all the control strategies, HVDC and WFs can not achieve dynamic cooperation. In addition, the coordination method in the above literature only starts from the level of the WF and does not consider how to distribute reasonably among the units in the WF after the WF receives the power instruction. Based on the above background, this paper proposes a strategy to cooperate with HVDC system and WF to participate in frequency regulation based on fuzzy logic control. First of all, at the system level, according to the frequency deviation of the system and the operation state of the WF, two fuzzy logic controllers are used to calculate the total amount of frequency regulation of the WF and HVDC system and

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the coefficient of the WF participating in the frequency regulation, respectively. In order to realize the dynamic cooperation of the frequency response of the WF and the HVDC system. Secondly, at the WF level, the frequency regulation allocation strategy of WT is proposed according to the rotating kinetic energy and adjustable capacity of WT, which maximizes the utilization of WT frequency regulation capacity. Finally, using the fast power regulation ability of HVDC, an active secondary frequency drop suppression strategy is proposed to effectively alleviate the possible SFD caused by WF speed recovery.

2 System Configuration The model of wind power share system asynchronously connected by HVDC is shown in Fig. 1. Among them, the HVDC transmission system is composed of rectifier station, inverter station and HVDC line. The AC power grid at the sending end includes a traditional generator set, a load and a WF. The receiving-end AC power network is an equivalent AC system, which is asynchronously connected with the sending-end AC power grid through HVDC transmission. As the doubly-fed inductive generator (DFIG) is widely used, this paper only takes DFIG of VSCW as an example for follow-up analysis.

2.1 DFIG DFIG converts part of the kinetic energy in the air into mechanical energy through the WT. According to the aerodynamics, the mechanical power input by the WT can be expressed as follows [12]: Pm =

1 ρπ R2 vw3 Cp (λ, β) 2

(1)

where ρ is the air density, R is the radius of the WT blade, vw is the wind speed, and Cp is the wind energy utilization ratio, which is the function of the blade tip speed ratio λ and the pitch angle β. In order to maximize the use of wind energy, most fans Sending end AC grid

Reactor

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~

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Rectifier

Inverter

Load

Fig. 1 One-line diagram of HVDC transmission system with WF

~

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currently adopt the MPPT operation mode, in which the output mechanical power of the WT can be expressed as follows [13]: PMPPT =

1 ρπR2 vw3 Cp,max = kopt wr3 2

(2)

where k opt is a constant only related to fan parameters, and wr is fan rotor speed. During the normal operation of the fan, the rotor of the fan contains sufficient rotational kinetic energy, which can be expressed as follows [14]: EK =

1 JWT wr2 2

(3)

where J WT is the inertia of DFIG rotor. In order to make full use of this part of the kinetic energy stored in the WT to participate in the power grid frequency regulation, the power loop (supplementary power loop, SPL) control is usually added under the conventional control mode of the WT (Fig. 2). When the power imbalance occurs in the system, SPL makes the WT release kinetic energy actively by controlling the power grid frequency-power feedback control, which responds to the change of system frequency and restrains the change rate of system frequency. It is generally believed that the maximum additional power of WT is set as 0.1 pu [15], that is, when the frequency drop event occurs, the maximum short-term additional power of WT is 10% of the rated power, which will greatly improve the frequency characteristics of high wind power permeability power grid. However, there are three problems in using WT inertia response to participate in power grid frequency regulation: first, the kinetic energy stored in WTs is limited, so WTs can not provide extra power output for a long time like thermal turbines. Secondly, the operating state of WT is affected by the change of wind speed, which makes the WT can not maintain a stable frequency regulation ability at all times. Third, in the process of releasing the rotor kinetic energy of the WT to participate

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in the frequency response of the system, the rotor speed of the generator will be reduced. When the WT ends the frequency response, it is necessary to absorb the electromagnetic power from the power grid to restore the rotor speed to the initial value, which will inevitably lead to the secondary frequency drop in the recovery of the system frequency.

2.2 HVDC In general, the HVDC converter station takes the HVDC transmission power as the direct control target, and its control characteristics do not change with the voltage and frequency fluctuation of the AC power grid, so as to realize the asynchronous interconnection of the AC systems on both sides. When the HVDC system is required to participate in the frequency control of the AC system, the basic principle is to add an additional frequency-power control loop to the rectifier side controller as shown in Fig. 3 [9].

3 Frequency Coordinated Regulation Method Large-scale wind power access reduces the moment of inertia of AC power grid based on asynchronous interconnection of flexible HVDC transmission, and the frequency problem is important. Based on this, this paper regards HVDC system and WF as a joint frequency modulation system: HVDC-WF frequency regulation system (HWFRS), proposes a strategy for flexible HVDC transmission and WF to participate in frequency control. The cooperative frequency control strategy consists of three sub-strategies: (1) HWFRS power allocation strategy, (2) turbine power allocation strategy in WF, and (3) frequency secondary drop suppression strategy.

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3.1 HWFRS Power Allocation Strategy The HWFRS power allocation strategy is based on the following two fuzzy logic controllers. Among them, the first fuzzy logic controller (FLC1) is used to determine the total active power increment of the HWFRS participating in the frequency response of the system, and the second fuzzy logic controller (FLC2) is used to determine the participation coefficient of the WF, that is, the active power output of the WF in the frequency response. The controller structure of FLC1 is shown in Fig. 4a. The corresponding relationship between input and output and the membership function curve are shown in Fig. 4b–d, which contains seven fuzzy subsets. The fuzzy language of input variable Δf and ΔPf_total are ML (large), L (large), M (middle), S (small), MS (small) and VS (very small) are VL (very large), ML (large), L (large), M (middle), S (small), MS (small) and VS (very small), while the fuzzy language variables of input variable df/dt are NL (negative high), NM (negative middle), NS (negative low), Z (zero), PS (positive low), PM (middle), PL (positive high). FLC1 adjusts the total active power output of HWFRS participating in the frequency regulation of the system in real time according to the current frequency characteristics of the system, and dynamically simulates the inertia response characteristics of synchronous generators. Based on this, this paper establishes a table of fuzzy logic rules as shown in Table 1. The controller structure of FLC2 is shown in Fig. 5a. The corresponding fuzzy language variable definition can be referred to FLC1.

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Table 1 The rules of FLC1 Δf

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In order to fully tap the frequency modulation potential of WFs and avoid overdependence on WFs, this paper establishes a table of fuzzy logic rules shown in Table 2. Table 2 The rules of FLC2 αw

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Through the cooperation of fuzzy logic controller FLC1 and FLC2, the active power output ΔPf_WF of HWFRS stroke farm can be determined as shown in formula (4). ΔPf _WF = ∂w ΔPf _total

(4)

After obtaining the active power output of the WF, the active power output ΔPf_HVDC of the HVDC system in HWFRS is as follows: ΔPf _DC = (1 − ∂w )ΔPf _total

(5)

The dynamic distribution of the output of the HWFRS stroke electric field and the frequency response of the HVDC system can be realized by Eq. (4) and Eq. (5).

3.2 WT Allocation Strategy in WF The kinetic energy utilization μKE and capacity utilization μP-WT of WT rotor are defined as follows: μKE =

EKt − EK min w2 − wr2 min = 2r EK0 − EK min wr0 − wr2 min

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In the formula: E Kt , E K0 , E Kmin are the rotor kinetic energy of WT under the condition of current speed value wr , rated speed value wr0 and speed lower limit value wr min , respectively, PWT_t , PWT_min are the output power of WT under current speed value and speed lower limit value respectively, and PWT_0 is the rated power of WT. In this paper, the distribution of power in the WTs is carried out according to formula (8): ΔPf _WT ,i =

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(8)

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In the formula, ΔPf_WT, i is the frequency modulation power value assigned to the WT in the WF, and N is the number of WTs in the wind power site.

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3.3 Active SFD Restrain Strategy The active suppression control of secondary frequency drop in HVDC system is proposed in this paper, as shown in Fig. 6, where ΔPinit and α are the preset power initial values and attenuation coefficients. When the WT ends the inertia response and enters the speed recovery phase, the secondary frequency drop suppression control should be started. At this point, the HVDC system will be superimposed with an additional power instruction with an initial value of ΔPrec_WT and attenuated with the function e-α t, as shown in Eq. (9). ΔPrec_DC = ΔPinit e−αt

(9)

If the change process of the power instruction ΔPrec_HVDC can be close to that of the WT in the process of speed recovery, the secondary drop of the system frequency can be restrained to a large extent.

4 Case Study 4.1 Introduction to the Simulation System To verify the effectiveness of the HVDC-WF cooperative frequency control strategy proposed in this paper, and build the simulation system shown in Fig. 1 on the Matlab/Simulink platform. The equivalent system AC grid1 has a capacity of 2000 MW. The traditional generator in the AC grid2 consists of nine synchronous generators with rated power of 150 MW, and the governors of all generators are IEEE Type 2 structure. The WF contains 150 DFIG, with rated power of 5 MW and the maximum capacity can be 750 MW. The load is flexibly adjusted according to the active power output of the generator and WF to ensure that the system frequency is maintained at the rated value at the initial time. The detailed parameters of HVDC

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system and DFIG are taken from reference [10], and the detailed parameters of synchronous generator are taken from literature [16].

4.2 Simulation Results This section simulates the proposed HVDC-WF cooperative frequency control strategy, fan integrated inertia and droop control strategy [5] and no additional control under the frequency drop event, and verifies the effectiveness and superiority of the HVDC-WF cooperative frequency control strategy by comparing the simulation results of the three control methods. In order to simplify the simulation process, the WF is divided into three regions: R1, R2 and R3. The stroke electricity permeability α w of AC grid2 is set to 50%. At this time, only 5 synchronous generators in AC grid2 are connected to the grid, and the total capacity is 750 MW. All the WTs in the WF are connected to the grid to generate electricity, and the total capacity is 750 MW. The number of units in the three regions of WFs R1, R2 and R3 is 50, and the corresponding wind speeds are 13 m/s, 12 m/s and 11 m/s, respectively. The simulation conditions are uniformly set when the simulation time is 5 s, the load suddenly increases 200 MW, and the simulation results are shown from Figs. 7, 8, 9 and 10, and the system frequency data under different frequency control modes are shown in Table 3. From Fig. 7a, Fig. 9a shows that all the units in the WF operate in MPPT mode without control, which can not respond to the change of system frequency. In AC grid2, only synchronous generators participate in frequency regulation, and the lowest point of system frequency is 49.59 Hz. When the WT adopts integrated control to Table 3 Simulation results Methods

f nadir1

t nadir1

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/

/

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1.05

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participate in the frequency regulation of the system, the lowest frequency of the system is raised to 49.77 Hz, which is higher than that without control. However, when the WT ends the frequency response, the output power of the WF decreases significantly as shown in Fig. 9b, which leads to a significant secondary drop in the system frequency, and the system frequency falls again from 49.84 Hz to 49.71 Hz. When adopting the coordination strategy proposed in this paper, under the condition of high wind speed and high wind power permeability, the HWFRS stroke farm undertakes more power regulation, and its maximum output after disturbance is higher than that of the DC system, so that the frequency modulation capacity of the WF is fully released. When the WF withdraws from the frequency response, the DC system rapidly increases the DC power under the control of SFD suppression, which makes up for the power gap caused by WT speed recovery, thus effectively suppressing SFD. Under the coordinated control strategy in this paper, the lowest point of the system frequency is only 49.83 Hz. Figures 8, 9 and 10 shows the power and speed changes of WTs in each region of the WF. Because the regional R1-R3 is in the operating condition of high wind speed, the initial operating speed of the stroke generator set in the three regions is relatively high, and the rotational kinetic energy stored by the fan rotor is very abundant. Among them, the initial speed of WTs in R1 and R2 is 1.2 pu. But due to the larger

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wind speed in R1, the WT output in this area is closer to the upper limit. Figure 8a shows that because the integrated control strategy does not take into account the operating status of WTs, the output power of WTs in area R1 under this strategy is limited because it reaches the upper limit. However, the units in the regional R2-R3 do not fully participate in the frequency modulation, and the speed change is small as shown in Figs. 9b and 10b. Under the cooperative frequency control strategy, the WTs in each region of the WF coordinate and participate in the frequency regulation according to the frequency modulation capacity., as shown in Figs. 9a and 10a. It can be seen that the coordinated control strategy proposed in this paper can fully release the frequency modulation potential of the WF, effectively reduce the frequency offset of the system, and alleviate SFD. At the same time, the unit allocation strategy can effectively avoid the limitation of power output of high wind speed units and realize the maximum utilization of kinetic energy of fan rotor.

5 Conclusions In this paper, a coordinated control strategy based on fuzzy logic control for combining HVDC and WF to participate in HVDC sending system’s frequency regulation is proposed. Through the simulation, the conclusions are obtained as follow: (1)

From the system level, based on the frequency cooperative control method proposed in this paper, the WF can dynamically cooperate with the HVDC system to participate in the frequency regulation according to its own running state. Under the operating condition of high wind speed and high wind power permeability, the WF undertakes the main frequency regulation task to fully release the frequency regulation potential of the WF; under the operating condition of low wind speed and low wind power permeability, HVDC undertakes the main frequency regulation task to avoid excessive participation of WTs in frequency regulation.

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From the WF level, based on the frequency modulation power allocation strategy proposed in this paper, when the WF participates in frequency regulation under various operating conditions, the WF power can be allocated reasonably and orderly.

References 1. Kosmatopoulos EB (2016) Occupancy-based demand response and thermal comfort optimization in microgrids with renewable energy sources and energy storage. Appl Energy 163:93–104 2. Mendoza-Vizcaino J, Sumper A, Galceran-Arellano S (2017) PV, wind and storage integration on small islands for the fulfilment of the 50–50 renewable electricity generation target. Sustainability 9(6):905 3. Brenna M, Foiadelli F, Longo M, Zaninelli D (2017) Improvement of wind energy production through HVDC systems. Energies 10:157 4. Zhang Z-S, Sun Y-Z, Lin J, Li G-J (2012) Coordinated frequency regulation by doubly fed induction generator-based wind power plants. IET Renew Power Gener 6(1):38–47 5. Arani MFM, Mohamed ARI (2015) Analysis and impacts of implementing droop control in DFIG-based WTs on microgrid/weak-grid stability. IEEE Trans Power Syst 30(1):385–396 6. Vidyanandan KV, Nilanjan S (2013) Primary frequency regulation by de-loaded WTs using variable droop. IEEE Trans Power Syst 28(2):837–846 7. Huang J, Preece R (14–16 Feb 2017) HVDC-based fast frequency support for low inertia power systems. In: Proceedings of the 13th IET international conference on AC and HVDC power transmission (ACHVDC 2017). Manchester, UK, pp 1–6 8. Ai Q, Liu T, Yin Y, Tao Y (2020) Frequency coordinated control strategy of HVDC sending system with wind power based on situation awareness. IET Gen Trans Dis 14(16):3179–3186 9. Miao Z, Fan L, Obsorn D (2010) Windfarms with HVDC delivery in inertia response and primary frequency control. IEEE Trans Energy Convers 25(4):1171–1178 10. Sun K, Xiao H, You S, Li H, Pan J, Li K-J, Liu Y (2020) Frequency secure control strategy for power grid with large-scale WFs through HVDC links. Int J Electr Power Energy Syst 117:105706 11. Zhang M, Yuan X, Hu J (2015) Wind power transmission through LCC-HVDC with WT inertial and primary frequency supports. IEEE Power Energy Society General Meeting Denver. CO, USA 12. Xia Y, Ahmed KH, Williams BW (2012) WT power coefficient analysis of a new maximum power point tracking technique. IEEE Trans Ind Electron 60(3):1122–1132 13. Heier S (2014) Grid integration of wind energy: onshore and offshore conversion systems. Wiley, pp 50–65 14. Attya AB, Dominguez-Garcia JL, Anaya-Lara O (2018) A review on frequency support provision by wind power plants: current and future challenges. Renew Sustain Energy Rev 81(2):2071–2087 15. Gautam D, Goel L, Ayyanar R (2011) Control strategy to mitigate the impact of reduced inertia due to doubly fed induction generators on large power systems. IEEE Trans Power Syst 26(1):214–224 16. Kundur P (1994) Power system stability and control. McGraw-Hill, NewYork

An Adaptive Control in a LV Distribution Network Integrating Distributed PV Systems by Considering Electricity Substitution Yongxiang Cai, Anqian Yang, Xiangping Chen, Xiankui Wen, Yu Fu, Xiaobing Xiao, Yue Li, and Lianchao Zhang Abstract Distributed photovoltaic and electric energy substitution are two crucial technologies for building a clean energy system where electricity contributes a great support for responding to national strategic goals of “rural revitalization”, “carbon peak” and “carbon neutrality”. However, PV generation features with volatility and randomness while electricity substitution further brings about higher peaks so as to affect the reliability of power supply. There is an urgent need for developing adaptive control strategies for distributed photovoltaic grid-connected, especially in low-voltage distribution networks. This paper firstly studies the topology of a low voltage distribution network with specific parameters. Afterwards, by taking into account the operational costs of the power grid and the safety issue of the equipment, a two-stage control architecture of “concentration-in-place” is proposed. Furthermore, the imbalance of three phase power systems, network losses, transformer losses are considered to form a multi-objectives optimization problem which is solved by tuning voltage, power output from PV system, energy storage and demand side response schemes. By integrating actual parameters in the model, the effectiveness of the proposed methods are validated, where the data is from the local networks in Bijie region in Guizhou province. The results show that the network loss and three-phase imbalance can be effectively relieved. In addition, the voltage fluctuation and overstay caused by photovoltaic and load fluctuations can be mitigated accordingly. Keywords Low-voltage distribution network · Distributed photostatic · Power substitution · Adaptive control · Two-stage control

Y. Cai · X. Wen (B) · Y. Fu · X. Xiao · Y. Li Power Science Research Institute, Guizhou Power Grid Co., Ltd., Guiyang, Guizhou 550002, P. R. China e-mail: [email protected] A. Yang · X. Chen School of Electrical Engineering, Guizhou University, Guiyang, Guizhou 550025, P. R. China L. Zhang POWERCHINA Guizhou Engineering Co., Ltd, Guiyang, Guizhou 550027, P. R. China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_23

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1 Introduction The Proposal of the Central Committee of the Communist Party of China on the Formulation of the 14th Five-Year Plan for National Economic and Social Development and the Vision For 2035 (the “Recommendations”) put forward: “Priority should be given to the development of agricultural and rural areas and the overall promotion of rural revitalization”. One of the important foundations of rural revitalization is electric power construction. However, the network frame in rural areas is weak and the quality of power supply is prominent. The characteristics of low voltage, three-phase imbalance and high network loss are obvious, and the problem of heavy load and overload of power distribution transformer during peak load is very prominent, which affects the production and consumption of electricity by residents. In addition, the Recommendations refer to “the development of a programme of action for the peak of carbon emissions by 2030”. “Carbon Peak” and “Carbon Neutrality” have become the strategic objectives of China’s energy industry development in the future [1]. Taking Guizhou as an example, the clean and efficient power industry represented by “roof photostatic” and “electricity substitution” has become one of the top ten industrial industries in Guizhou Province, and will also be an important support for the strategy of “village revitalization” during the 14th Five-Year Plan period. Considering the rapid growth trend of “roof photostatic” and “power substitution” poses a serious challenge to the current distribution network. The addition of electricity replacement at the lotus end will make the electricity consumption increase suddenly, increase the operating burden of the distribution and change, affect the reliability of power supply, and the incorporation of the source into distributed photostatic will lead to more serious problems such as reverse current and voltage overshoot, while its own volatility and randomness will affect the stability of the power grid and the quality of electricity produced and used by farmers. The superposition of the source-load end will lead to the load of “peak-on-peak”, aggravate the severity of the problem, easily lead to the distribution of burn-out, reduce the safety and economy of power grid operation, it is difficult to effectively support the “village revitalization” and “carbon peak, carbon neutral” two strategic objectives. In recent years, the research on the coordination and control strategy of low voltage distribution network has attracted much attention. Based on the energy storage to achieve the trend of distribution network peak filling, but the required energy storage capacity is very large, high capital investment, but also cannot be widely used in the distribution network [2, 3]. Energy storage and photovoltaic inverter reactive collaborative control technology while ensuring voltage quality [4, 5], further reduce the low voltage distribution network for energy storage capacity demand, improve the economics of control, but it is difficult to solve the load peak and valley difference in the background of the distribution transformer overload and burn loss risk. In the context of power substitution, it has been studied that the use of regulatorconditioning and tuning technology is more effective to prevent the burning of power distribution transformers, improve the economics of transformer operation, but also to a certain extent to improve network losses, reduce the risk of voltage over-limits

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[6–9], but for large-scale distributed photovoltaic grid-connected three-phase imbalance, high volatility and randomness issues have not been fully considered [10–13]. In the practical experience of Guizhou power grid, it is also found that if the pressure conditioning technology does not consider to cooperate with the three-phase imbalance management, it will cause a lot of single-phase overload problems or the non-essential action of the tuning switch. In view of the existing problems in the current research, this paper studies the adaptive control of the low voltage distribution network for distributed photovoltaic grid and power substitution, first of all, on the scale of the day, comprehensive consideration of network loss, three-phase imbalance, transformer overload and voltage overshoot and other key issues. A collaborative optimization control strategy is proposed to consider the tuning regulator transformer, energy storage, photovoltaic inverter and demand side response, and secondly, on the short-term control scale of day, a short-term response strategy of tuning switch and photovoltaic inverter is proposed. To prevent the overload of the weight of the distribution due to photovoltaic uncertainty and to suppress the voltage disturbance of the system, and improve the power supply quality of the distribution network.

2 Control Framework This article proposes a—control architecture called Central—In Place. The central control and time scale of the optimization stage are one hour, and the in-place control and time scale of the daytime control stage are five minutes. Because load fluctuation, high network loss and three-phase imbalance are global problems, all nodes need to run control overall planning. It is more appropriate to use centralized control with strong computing power to achieve global optimization control. Recently, the optimization stage, each node is directly connected with the central controller, before the control upload of the state information of the node, after control to accept the reference optimization results. Given the high computing and communication requirements of centralized control and the long time required, centralized control alone is not sufficient to respond to photovoltaic and load fluctuations in a timely manner. In-place control with simple measurement computing power and rapid response is required. During the day-today control phase, each node relies on measurement values for rule-based correction control, enabling each node to respond quickly to power fluctuations. The main purpose of designing the two-phase control framework for—control as shown in Fig. 1 is to calculate optimal current calculation optimization constraint variables based on hourly historical data (load and photovoltaic failure) and network loss, three-phase imbalance, and transformer loss as the target functions. In the innerday control phase, the optimization results of the recent optimization are not fully adapted to the random fluctuations of the minutes of photovoltaics and loads, and rule-based correction control (photovoltaic reactive, tolerant taps) must be set to achieve rapid response to photovoltaic and load fluctuations and to suppress voltage

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Power

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• • • •

Reactive power of PVs Terminals of transformers Real-time power ……

Rule-base operation

Fig. 1 Two-stage control framework of day-ahead optimization and intra-day control

overstaying of each node. Through the optimization of the day and the control phase in the hour optimization, minute level correction, to get better optimization control effect. The advantage of designing a two-stage control framework is that it takes into account the economics of the power grid and the security of the distribution. To ensure the economy and stability of power grid operation in the optimization phase. Ensure the safe operation of the distribution transformer during the daytime control phase. The proposed controls provide rapid response during the inner-day control phase. Significant fluctuations in photostatic are usually between a few seconds and 10 min, and load fluctuations are difficult to achieve high-accuracy predictions. According to the results of the recently optimized hourly optimization, it is too late to respond and adjust to the photovoltaic and load fluctuations, the network is likely to experience voltage overstays, voltage fluctuations, and counterweight overload. The proposed control can respond quickly to photovoltaic and load power fluctuations, suppress the voltage overstay of the network and reduce voltage fluctuations, in addition, the mating connection can also be adjusted to make the mating changes without heavy overload phenomenon, to ensure the safe operation of the matching.

3 Distribution Network Adaptive Control Model Based on the optimal trend of three-phase four-wire system, the distribution network establishes an optimized control model, with the goal of network loss, transformer loss, three-phase imbalance and voltage overstay, and optimizes the power distribution network to regulate voltage switches, photovoltaic inverters, reactive and energy storage.

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3.1 Day-Ahead Optimization The target functions of the recent control layer mentioned in this article includes as follows: (1)

Objective function ′

′

′

min F = F1 + F2 + F3 =

F2 F3 F1 + + s1 s2 s3

(1)

F = Ploss.tot

(2)

F1 = Ploss.net

(3)

F2 = Pcu + PFe

(4)

F3 =

Σ

VUFi , ϕ ∈ ϕ

(5)

i∈K ′

∗ Ploss.net = [Iline ⊗ Iline ] R

(6)

Iline,t = MUinj,t

(7)

Uinj,t = Yij−1 Iinj,t

(8)

Ploss.net = [(MYij−1 Iinj )∗ ⊗ MYij−1 Iinj ]T R

(9)



Mi→j = Yij Mj→i = −Yij

(10)

In the form: the value of the target function; for the scale factor; For the total loss of the tuning regulator transformer; For network loss; Copper loss (line loss) for toleration of regulator change within one day; For one day to adjust the iron loss (empty load loss); set to fixed value; Three-phase imbalance for nodes; Represents a collection of nodes in the distribution network; Represents a collection of three phases.

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Where represents the transpose of the matrix; is the line current,; represents the corresponding elements of the two matrices multiplied; /b116 > Phase resistance; A mapping matrix of node voltage and branch current, e.g. represents the association of branch current to node voltage between slave nodes; is the node /b131 > a conductive matrix between and; for the voltage of each node during the period; Inject current into each node during the time period. 2 PCu = Iline R

VUFi =

(11)

Uneg,i Ua,i + α 2 Ub,i + αUc,i = Upos,i Ua,i + αUb,i + α 2 Uc,i

(12)

where and are the nodes with negative and positive voltages; /b117 > , phase voltage; (2)

Constraints

The constraints of the control layer mentioned are in order to operate safely and steadily in the distribution network, and the constraints such as current, voltage, regulator tap, toning critical load, neutral line voltage and power need to be met. ⎧ Re(Ui ) = (Re(Yij )−1 )Re(Iinj ) ⎪ ⎪ ⎨ −(Im(Yij )−1 )Im(Iinj ) Im(Ui ) = (Im(Yij )−1 )Re(Iinj ) ⎪ ⎪ ⎩ +(Re(Yij )−1 )Im(Iinj )

(13)

Iij = Yij (Ui − Uj )

(14)

Yij = Gij + jBij

(15)

/ |Iij | = |Yij ||Vij | = (Gij2 + Bij2 ) / (Re(Ui ) − Re(Uj ))2 + (Im(Ui ) − Im(Uj ))2 ⎡

Gia,ja ⎢ Gib,ja Gij = ⎢ ⎣ Gic,ja Gin,ja ⎡ Bia,ja ⎢ Bib,ja Bij = ⎢ ⎣ Bic,ja Bin,ja

Gia,jb Gib,jb Gic,jb Gin,jb

Gia,ic Gib,ic Gic,jc Gin,jc

Bia,jb Bib,jb Bic,jb Bin,jb

Bia,ic Bib,ic Bic,jc Bin,jc

⎤ Gia,jn Gib,jn ⎥ ⎥ Gic,jn ⎦ Gin,jn ⎤ Bia,jn Bib,jn ⎥ ⎥ Bic,jn ⎦ Bin,jn

(16)

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The safe and stable operation of the distribution network needs to be met the balance of active and reactive power at the time-injection and outflow nodes, i.e.: where and are expressed as matrix real and imaginary parts; and are phase conduction and induction between nodes and. (1)

The node voltage constraint

In order to ensure the safe operation of the distribution network, the node voltage should be stable within the safe range [14], that is: min max Uϕ,i ≤ Uϕ,i,t ≤ Uϕ,i

(17)

where and the lower and upper limits of the voltage amplitude of the phase node, respectively. (2)

Neutral line voltage constraint

To ensure the stable operation of the line, the voltage amplitude at the moment needs to be less than the maximum allowable value of the neutral line voltage, i.e.: ⎥ ⎥ ⎥Uneu,i,t ⎥ ≤ Uneu

(18)

where is the voltage amplitude of the moment on the neutral line of the node; The maximum allowable value for the neutral line voltage. (3)

Regulator tap constraints

The range of regulator with load-regulated pressure adjustment is limited, and its decomposition head gear cannot exceed the voltage-regulating range, i.e.: min max Tvol ≤ Tvol,t ≤ Tvol

(19)

Type: for the split joint gear of the moment–time regulator transformer; and for the lower and upper limits of the on-load regulator transformer split joint gear. (4)

Adjust critical load constraints

Considering the accuracy of the on-board tuning control strategy, the tuning critical load needs to be within the safe tuning range of i.e.: min max Prate.cap ≤ Preal.cap,t ≤ Prate.cap

(20)

Preal.cap < δPrate.cap

(21)

 Prate.cap =

100, If Tcap,t = 0 300, If Tcap,t = 1

(22)

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In the formula: for the time period to adjust the actual capacity of the regulator transformer; and for the lower and upper limits of the capacity of the tuning regulator; Set the scale factor; Adjust the split joint gear for the time period. (5)

Energy storage constraints

Considering the distributed photovoltaic grid-connected, there is a need for a power storage device for charge and discharge coordination, assuming that the energy storage is injected into the grid with positive power, i.e.: ESS,dis ESS,cha ESS = α1 Pϕ,i + α2 Pϕ,i Pϕ,i

(23)

α1 + α2 =1

(24)

t t Δt Σ dis εin Δt Σ cha Pϕ,i,t − P cap cap EESS t ′ =1 εout EESS t ′ =1 ϕ,i,t

(25)

ESS ESS SOCϕ,i,t = SOCϕ,i ,t0 − n

where for energy storage capacity; and for energy storage charge and discharge efficiency; for energy storage devices to the grid to inject total active power; b20 > / Phase nodes The initial charge state of energy storage; and the active power is absorbed/injected into the grid for energy storage. There is an upper and lower limit on the SOC of the moment energy storage unit:  ∀t

ESS,rated ESS,cha < Pϕ,i,t The maximum reactive power of the photovoltaic inverter. (7)

Demand-side constraints

The demand-side response model is consistent with energy storage constraints. The amount of electricity used is equal to the amount of charge, and the movement of the electricity segment is the demand side response [15]. Don’t go into more detail here.

3.2 Control Within Days The target of the inner-day control layer mentioned in this article is the gear of the reactive and tolerant disassoilation connector of the photovoltaic inverter. (1)

Reactive power in PV systems

Photovoltaic reactive control uses the literature’s variable slope sagging control model. Qcor = Qref + mi (Uno_cor − Uref )

mi =

2

/( )2 ( )2 SPV .rate − P PV .rate Uupper − Ulower

(33)

(34)

Type: for the day-to-day control phase of the modified photovoltaic reactive; for the uncorrected voltage; and for reactive and voltage optimization; For the sagging slope, rated capacity for photovoltaic inverters; Rated for photovoltaic inverters; and the maximum/small value for voltage scale values, generally 1.07 and 0.93. According to the formula (33) and (34) the reactive control of the photovoltaic inverter is obtained, the control results of reactive control are obtained, and the new voltage amplitude change is measured.

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Split joints in capacity regulating system

In order to ensure that the mating does not overload, the tuning dispensing connector must be modified in real time. And taking into account the infrequent action factors of the tuning switch, set: if the interval between two gear movements is less than 30 min do not act. Σ Tcap,t = 5, IfTcap,t + Tcap,t+6 = 2 (35) t∈I

where a collection of time for to. For example, the 25 min load is high, the tuning switch gear is in 1st gear, because the load fluctuates faster, the 26th min is offset by more photovoltaic force to offset some of the load, the load is lower, the switch gear action to 0th gear, and after 20 min, the switch moves again to 1st gear due to the increase in load. In this case, the set tuning switch does not move and remains in 1st gear from 25 min until the gear action after the next interval of 30 min. According to the optimization results obtained by the optimization layer, the voltage change caused by photovoltaic fluctuations and load mutations is measured. As shown in Fig. 2.

4 Control the Process and Solve the Method Figure 2 is the distribution network day control—day control two-tier control flowchart. Before performing the optimization control, the distribution network parameters, load data and the net photovoltaic power need to be uploaded. After obtaining the distribution network information, the control layer has carried out the calculation of three-phase trend and optimal trend, and has been optimized to control the reference to the success. The reference values are then released to each control variable.

4.1 Control the Process The specific steps of the control process are as follows: S1: Upload distribution network parameters, load data and photovoltaic net power and so on; S2: Get photovoltaic, load data; S3: Formula (1) ~ (12) as the target function, formula (13) ~ (32) as a constraint, the optimal trend calculation of continuous variables; S4: To carry out the optimization control of discrete variables, such as tuning the gear of the voltage-regulating dispenser; S5: Output optimization variable results to each node;

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Start Parameters, PV power and load data

Load forecasting based on ARMA model Unbalance < threshold

Yes

No Optimal power flow calculation under the objective function（1）～（9）and contraints（10）～（38） Optimal control after discretization

Sending optimal value to each node （P_PV、P_LOAD、Q_PV、Q_LOAD、V）

Short-term regulation

t=0 Real-time data measuring （Q_PV*、Q_LOAD*、 V*）

Reactive power regulation

Q* = Qref + M i * (V * − Vref )

Voltage/capacity regulation for the first transformer

Data updating（V**）

t=t+1 t=12

No

Yes End

Fig. 2 Flow chart of day-ahead and intra-day control

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S6: Measure real-time data; S7: Photovoltaic reactive adjustment according to the formula; S8: According to the formula for the tuning of the connector gear real-time correction; S9: Measure new data; S10: For each correction,. /b13 > When you restart measuring real-time data. Adaptive control strategies for variables.

4.2 Solution Methods Through the embossed model, the non-convex nonlinear problem is converted into a simpler second-order cone planning problem. Since the ratio of positive to negative voltage is not a convex function, the pair(12)needs to be converted to: In formula (16), the root number is removed after squared on both sides of the equation to further convex the formula. The resulting formula (16) can therefore be converted to: ⎥ ⎥ ⎥Iij (t)⎥2 ≤ I 2 ij

(36)

The convexity of discrete variables differs from continuous variables, such as the 0–1 discrete variable switch for the tuning regulator, which requires binary expansion and large-M methods to maintain the convexity of the discrete variables [16, 17]. Finally, the convexity of the entire optimal trend calculation is guaranteed, and the optimal solution is obtained by solving using the CPLEX algorithm. VUFi =

Uneg,i Ua,i + α 2 Ub,i + αUc,i ≈ Upos,i Uϕ

(37)

5 Analysis 5.1 Background This paper uses the actual model of a low-voltage distribution network in Bijie, Guizhou Province, to simulate the three-phase, four-wire network. Figure 3 is the network structure, and Fig. 4 represents the photovoltaic and load graph (Appendix A1). At the same time, after optimizing the control parameters through the established optimization model, the unnecessary reactive flow in the network can be avoided, thus reducing the network loss and ensuring the economy of the network operation. Rated at 380 V, line self-impedance and inter distorization parameters (Appendix A2).

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PV array Phase b 2

1

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21

6

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14

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Energy storage system Phase d

Phase c 3

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4

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8

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Fig. 3 21-node low-voltage distribution network

1

PV power and equvalent load Original load PV power

0.9 0.8 0.7

PU

0.6 0.5 0.4 0.3 0.2 0.1 0 0:00

6:00

12:00

18:00

24:00

Time

Fig. 4 PV and load unit value curves

Distributed photovoltaic and energy storage access nodes (Appendix A3), singlephase photovoltaics are rated at 5 kW and photovoltaic inverters have a capacity of 1.1 times the active capacity of photovoltaics. A single energy storage unit is rated at 20 kWh with a maximum charge and discharge power of 4 kW per phase. This article uses a 315 kVA common transformer and a 100 (315) kVA tuning regulator transformer. To compare the effect of the—control strategy proposed in this article, control strategy is used to compare results. (1)

(2)

CS-1:Use the control methods proposed in the literature. The network frame structure model is consistent with this paper. The model simulation of threephase four-wire system is carried out with network loss and three-phase unbalance as the target function. However, there is no tuning control technology, transformer overload on the economics of grid operation and intraday control strategy. CS-2:That is, the two-stage control strategy of—control proposed in this paper. The control framework is shown in Fig. 3.

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(a) Transformer output power without PV and alternative electricity

(c) Voltage variation at node 16 without PV and alternative electricity

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(b) Transformer output power with PV and alternative electricity

(d) Voltage variation at node 16 with PV and alternative electricity

Fig. 5 Comparison chart of the outlet performance of a three-phase transformer

5.2 Power Substitution In the actual operation of the power grid, the transformer operating power exceeds 80%of the rated power, and the transformer is determined to be overloaded. Figure 6a–d represent a graph of the voltage amplitude of 16 for the power and end nodes before and after the replacement of photovoltaics, electrical energy substitution. As can be seen from Fig. 5, in the scene of no photovoltaic and power replacement, the transformer already has a long-term overload problem, which seriously affects the service life of the transformer and the safe operation of the power grid; In the photovoltaic, electrical energy replacement scene, due to photovoltaic grid-connected lead to reverse currents, transformer reverse overload and overload problems coexist, increasing the burden of distribution and transformation operation. Therefore, there is an urgent need for a low-voltage distribution network adaptive control strategy for distributed photovoltaics and power substitution.

5.3 Optimization This section mainly compares whether the three control methods in 4.1 can consider network loss, three-phase imbalance, transformer overload and voltage overstay in

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Fig. 6 Voltage variation for node 16 under control strategy 1

the context of power substitution and distributed photovoltaic grid, so as to ensure the economic operation of the power grid, the safe operation of the distribution transformer and the reliability of power supply. Figure 5d is a voltage graph of 16 nodes without control, which is most prone to overvoltage and undervoltage because it is the last point of the network structure. In the noon period, the photovoltaic output power is significantly higher than the load power, there is a serious overvoltage problem in the network, in the evening period, there is no photovoltaic output, the load power reaches the peak of electricity consumption, so that the network has the problem of undervoltage. The three-phase imbalance is much higher than the 2%required by the grid. It is not economical and safe to operate the power grid, so control policies must be adopted to optimize control. Optimization control based on CS-1 gives a voltage graph of 16 nodes as shown in Fig. 6. There was no voltage oversizing problem, and the three-phase imbalance was much lower than 2%, but the heavy overload and loss of the distribution transformer was not considered. Using CS-1 makes it difficult to balance mismatch with load and optimal economic benefits. Using the previous optimization control strategy proposed by CS-2, the problems of network loss, transformer loss, three-phase imbalance and voltage overshoot are considered, and the PV inverter is the control variable with no function, energy storage, and regulated voltage switch, and Figs. 7, 8 and 9 are used to get the optimization results according to the load curve. After the control, the grid loss and three-phase imbalance of the three control schemes are shown in Table 1. As can be seen from Table 1, CS-2 not only reduces system loss by 32.1% compared to CS-1, but also has a smaller three-phase imbalance. Explain that CS-2 guarantees good economic benefits while ensuring safe operation of the matching.

292 Fig. 7 Voltage variation for node 16 under control strategy 2

Fig. 8 Optimal day-ahead operation with switch control

Fig. 9 Short-term regulation with intra-day schedule

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Control schemes System losses Three-phase imbalance (%) CS-1

187.61 kWh

0.33

CS-2

125.89 kWh

0.27

Fig. 10 Voltage variation for node 16 after regulation

5.4 Daily Control Scheme This section describes the intraday control strategy proposed by CS-2 to adjust switches, photovoltaic inactivity as control variables to prevent overweight and system voltage disturbances. Figure 9 is a real-time correction diagram of the tuning of the split joint gear. Recently optimize the consideration of operating economy, day control consider equipment safety. The intraday control tuning switch action threshold is higher than the previous optimization threshold, taking into account the non-essential action rules for tuning. Therefore, the daytime control phase switch does not necessarily move when the switch action is optimized. As can be seen from Figs. 10 and 11, voltage overshoots and fluctuations can be suppressed and power distribution transformers can be prevented from overloading and burning accidents through photovoltaic reactive control and tuning of the dispenser gear correction. As can be seen from Figs. 12 and 13, the a-phase voltage of node 16(the very end) is more close to the a-phase voltage curve optimized for the day. And set the adjustment split joint action rules, reduce unnecessary switching action. Therefore, the in-day control strategy proposed in this paper, while ensuring that the matching does not overload, suppresses voltage fluctuations, reduces network operating losses, and extends the service life of the toned dispenser, as shown in Table 2 (the voltage deviation ratio is the percentage difference between the voltage before and after the correction and the previous optimized voltage). Udev =

Σ ⎥ ⎥ ⎥Uref − Ucor ⎥ × 100%

(38)

294 Fig. 11 10 Voltage variation for node 16 before regulation

Fig. 12 Voltage variation of phase a at node 16 under CS-2 (over 24 h)

Fig. 13 Voltage variation of phase a at node 16 under CS-2 (from 11:00 to 13:00)

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295

CS-2 control scheme

Udev (%)

Before

16.53

59.45

126.21 kW

5.32

33.38

125.99 kW

After

Uflu

Σ ⎥⎥ Ut − Ut+1 ⎥⎥ ⎥ ⎥ × 100% = ⎥ ⎥ Un

Uflu (%)

System losses

(39)

In: for voltage deviation rate; for correction of voltage amplitude before and after control; for voltage volatility; For the voltage amplitude of the moment; Represents a voltage amplitude of 1.0.

6 Conclusions This paper has proposed a two-stage control strategy by combing day-ahead and in-day control schemes. The main contributions of the study include three aspects as follows: (1)

(2)

(3)

In the optimization stage, under the scenario of power substitution and distributed photovoltaic grid-connected, taking into account the key issues such as network loss, three-phase imbalance, voltage overstaying limit, transformer overload, a collaborative optimization control strategy is proposed to consider the corresponding co-optimization control strategy of tuning regulator transformer, energy storage, photovoltaic inverter and demand side, and proves that the control strategy proposed in this paper is more comprehensive, more effective and reliable. During the day-to-day control phase, the short-term correction strategy of tuning switch and photovoltaic inverter is adopted to deal with the problem of weight overload and voltage rapid disturbance caused by photovoltaic uncertainty and load fluctuation in time. The voltage fluctuates rapidly while ensuring that the match does not burn. With the goal of reducing loss, three-phase imbalance and ensuring the safe operation of the matching, two-stage optimization control method is proposed. The proposed scheme loses 32.1% less power than the CS-1 control scheme. Because the tuning regulator technology does not adapt to all the application scenarios, so in view of the weak network frame, long power supply radius, small wire diameter of the power supply scene, consider combining low voltage AC DC technology and tuning voltage control technology, to solve the end user low voltage, load fluctuations and high network loss problems.

Acknowledgements The project supported by Technology Project of Southern Power Grid Corporation of China (Research, development and demonstration of key technologies and equipment of power supply quality improvement and energy saving for agricultural power grid load fluctuation), and NSFC project under the grant No. 51867007.

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References 1. The full text of the 14th five-year plan outline (EB/OL) December 10th. https://www.wzktys. com/fanwen/140963/ 2. Hu D, Li G, Liu Y et al (2020) Take into account the distribution network random—robust hybrid optimization scheduling of optical storage fast charge integrated stations. Grid Technol 1–15 3. Liu D, Zhao N, Li P et al (2020) Model based on “Shared energy storage—demand-side resources” to jointly track the renewable energy generation curve grid technology. pp 1–12 4. Cai Y, Tang W, Zhang B (2019) A two-stage volt-var control in LV distribution networks with high proportion of residential PVs. Power Syst Technol 43(4):1271–1279 5. Cai Y, Zhang L, Tang W (2017) A voltage control strategy for LV distribution network with high proportion residential PVs considering reactive power adequacy of PV inverters. Power Syst Technol 41(9):2799–2808 6. Wang J, Sheng W, Fang H (2014) Design of a self-adaptive distribution transformer. Autom Electr Power Syst 38(18):86–92 7. Wang J, Sheng W (2009) Simulation Analysis of Capacity Regulating Transformer. Transformer 46(7):19–23 8. Su Y (2019) Optimization configuration and operation research of on-load capacity and voltage regulating distribution transformers after electric energy substitution. Postgraduate thesis, Chongqing University, P R China 9. Tang W, Li T, Zhang W (2020) Coordinated control of photovoltaic and energy storage system in low-voltage distribution networks based on three-phase four-wire optimal power flow. Autom Electr Power Syst 44(12):31–42 10. Yao Z, Wang Z (2020) Two-level collaborative optimal allocation method of integrated energy system considering wind and solar uncertainty. Power Syst Technol, 44(12):4521–4529 11. Su X, Chen S, Mi Y (2019) Sequential and optimal placement of distributed battery energy storage systems within unbalanced distribution networks hosting high renewable penetrations. Power Syst Technol 43(10):3698–3707 12. Yang J, Tang W, Liu Q (2020) Three phase unbalanced optimization method considering distributed photovoltaic. Chinese J Power Sources 44(10):1522–1524 13. Watson JD, Watson NR, Lestas I (2018) Optimized dispatch of energy storage systems in unbalanced distribution networks [J]. IEEE Trans Sustain Energy 9(2):639–650 14. Jianjun L, Jinlei H, Xiaoping L et al (2015) Constrol strategy study and discussion of on-load capacity regulating transformer [J]. 337–340 15. Gill S, Kockar I, Ault GW (2014) Dynamic optimal power flow for active distribution networks [J]. IEEE Trans Power Syst 29(1):121–131 16. Liu Y, Wu WC, Zhang B (2014) A mixed integer second-order cone programming based active and reactive power coordinated multi-period optimization for active distribution network. Proceedings of the CSEE. 34(16):2575–2583 17. Liu Y, Wu WC, Zhang B (2014) Reactive power optimization for three-phase distribution networks with distributed generators based on mixed integer secondorder cone programming. Automa Electr Power Syst 38(15):58–64

A Two-Layer Scheme for Operating Renewable Based-Micro-Grid by Considering Economics and Grid Stability Jinbiao Li, Changqing Dang, Daoyin Long, Lianchao Zhang, Jing Zhang, Qinmu Wu, Min Liu, Yuhong Cai, and Xiangping Chen Abstract Micro-grid can effectively integrates variable renewable energy sources so as to enhance the possibilities of distributed power generation. Besides, it is an essential need to increase the flexibility of power supply. The operation optimization of micro-grid can ensure an efficient, safe and high quality operation for power grids. In this paper, we propose a two-layer optimization scheme by setting up a model considering operating costs and interactive power from the grid and associated power systems where economy and system stability are taken into account. Firstly, the structure of the system with operational objectives is built up. Afterwards, the model is combined the demand-side response for minimizing the operating cost following the outcomes of the upper-layer optimization where the purpose of the first-layer optimization is to minimize the interaction power between micro-grid and main grid. Afterwards, the objective function of the upper layer is solved by a greedygenetic-based algorithm. In the study, the lower layer optimization is transformed into unconstrained optimization by using the disciplinary function which is solved by a genetic algorithm to find the optimal solution. Finally, the effectiveness of the proposed model is verified by the data from practical cases. The results have shown that the operating profits and energy consumption rate in the micro-grid are both effectively improved. Keywords Micro-grid · Two-layer optimization · Operating costs · Interactive power · Demand side response

J. Li · C. Dang · J. Zhang · Q. Wu · M. Liu · Y. Cai · X. Chen (B) School of Electrical Engineering, Guizhou University, Guiyang, Guizhou 550025, China e-mail: [email protected] D. Long · L. Zhang POWERCHINA Guizhou Engineering Co., Ltd, Guiyang, Guizhou 550027, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_24

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1 Introduction Along with the shortage of fossil energy reserves and the aggravation of environmental pollution, it has become a global consensus to develop and utilize new energy sources on a large scale [1]. As an effective way to increase the proportion of new energy utilization and solve the problem of distributed power generation, micro-grid has been regarded as an indispensable part of the grid development plan. Due to the intermittent nature of distributed generation equipment, micro-grids produce fluctuations in exchange power when switching between off-grid and on-grid modes, which in turn affects the operation status and power quality of the grid [2–4]. The optimization of micro-grid operation can achieve efficient, safe and highquality operation of the system, effectively suppressing network fluctuations and improving grid efficiency. The optimization targets are generally based on system economy, environmental protection, and stability, and single or multiple objectives are selected and combined with corresponding algorithms to achieve optimization, thus providing a reference for the actual operation of the system [5, 6]. Several general optimization objectives are summarized in Fig. 1. In the system optimization process, constraints such as power balance, network losses, and equipment capacity need to be considered at the same time [7]. Economy has always been the primary selection objective of operation optimization, and literature [8] proposed a calculation model of annualized net benefit of micro-grid with maximization of net benefit as the optimization objective, taking

Optimization of microgrid system

Environmental performance index

Economic index

Operating cost

User revenue

Equipment input cost

Carbon penalty charges

Fig. 1 A flow chart for optimization process

Hazardous gas emission

Stability index

Interactive power

Capacity factor

Active loss

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299

into account the cost of power investment, operation and maintenance as well as the benefits of energy saving, emission reduction and loss reduction, and finally obtained the most economical power allocation scheme; literature [9] took the lowest cost of micro-grid operation under severe scenarios as the optimization objective. The original problem is decomposed into a mixed integer linear programming problem using column constraint generation algorithm and strong pairwise theory for alternate solutions. The literature [10] combines the transferable load model in demand-side response to improve the overall economic efficiency of the micro-grid by maximizing the time-series match between the actual load demand and the target load profile. In terms of stability optimization, literature [11] analyzed the causes of voltage and frequency deviations of micro-grid inverters when using sag control, and established a two-layer optimization scheme based on sag coefficients and stability boundaries to ensure the quality of voltage at the output; literature [12], on the other hand, conducted a study on energy system optimization of micro-grids, and proposed an optimization scheme of robust model predictive control based on the uncertainty of renewable energy output In [12], a robust model predictive control optimization scheme is proposed based on the uncertainty of renewable energy output, which achieves a reasonable system power allocation and effectively reduces the negative impact of system uncertainty in energy management. The above mentioned papers all adopt single-objective optimization design, which has only unique solutions in the solution set and has some limitations when facing multi-decision variables problems. In order to solve the multi-objective optimization problem in micro-grid operation optimization, literature [13] used model predictive control for optimization with the objectives of minimizing voltage deviation at common point and minimizing operation cost, and combined two kinds of control, rolling optimization and real-time feedback correction, to find the optimal solution, and finally completed the multitime scale operation optimization; The literature [14] proposes a two-tier optimal dispatching model that takes into account interactive power and bilateral bidding, with minimization of interactive power fluctuation as the upper-level objective and minimization of comprehensive cost as the lower-level objective, and adopts a bilateral bidding strategy to coordinate the power allocation among multiple micro-grids to achieve the economic and stability objectives, but the optimization objectives need to be re-selected when different interests are involved. With the improvement of market environment, users are also more involved in the pricing mechanism. Demand-side response can use the price mechanism or incentive mechanism to guide users to change their electricity consumption habits to achieve peak and valley reduction and improve system stability [15, 16]. It can also reduce the investment cost of micro-grid, improve the motivation of customers to use electricity, and further enhance the economy of the system. In this paper, we use demand-side response as a basic tool to introduce time-of-use tariff and load shifting to relieve the pressure of electricity consumption during peak periods, and construct a micro-grid operation model to solve an operation strategy that reduces the operating cost and increases the local energy utilization of the micro-grid using an optimization algorithm.

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Based on the above considerations, the micro-grid operation model is constructed by introducing demand-side response, and the operating cost of micro-grid is solved by load shifting and time-of-use tariff mechanism. At the same time, the interactive power is chosen as the target in terms of stability, and the energy storage system is used to maximize the local energy consumption, thus reducing the frequency of grid fluctuations. The optimization objective of this paper is economy and stability, and a two-layer optimization is chosen to find the optimal solution.

2 Two-Layer Optimization Model Aiming at the economy and stability of micro-grid operation, a two-layer optimization model is designed and established in this paper. The economic optimization is embodied in the minimization of the operating cost of the micro-grid, while the stability optimization is embodied in the minimization of the interactive power between the micro-grid and the main grid.

2.1 System Structure The system is mainly composed of three modules: wind power generation system, energy distribution system and energy storage system. In this system, the wind energy is converted into electric energy by the wind generator, and the electric energy is consumed by feeding into the power grid, absorbing the local load, and producing hydrogen and oxygen gas by electrolysis of water. In the energy storage system, after hydrogen and oxygen are produced by electrolytic cell with the help of electric energy, the two gases are stored in tank by compressor. When the energy storage system is needed to supply power, the gas flow can be controlled through a controlled pump, and after the hydrogen and oxygen fuel cell discharges, the power mechanism will convert it into stable electric energy for supply [17–19]. The system structure diagram is shown in Fig. 2.

2.2 Two-Layer Optimization Bracken J and McGill J.T first proposed the mathematical model of two-level optimization, and solved the optimization problem of multiple decision variables by using hierarchical setting [20, 21]. The specific method is as follows: the decision variables are given by upper optimization, and the parameters of lower layer are taken as parameters, and the optimal solution is obtained by combining the objective function and constraint conditions and fed back to the upper layer. The upper

A Two-Layer Scheme for Operating Renewable Based-Micro-Grid … Wind turbine system

Power distribution system

AC/DC

301

Energy storage system

DC/DC

+

Wind Generator

-

Water electrolyzer

Grid AC/AC

Air Compressor

Gasholder:H2

Controlled pump H2

Air Compressor

Gasholder:O2

Controlled pump O2

Hydrogen

Load

Oxygen

G

AC/AC

Power machine

Water

Excess Oxygen Electrolyte hydrogen-oxygen fuel cell

Fig. 2 Grid-connected system integrating wind-electrolysis-fuel cells

optimization is based on this to obtain the global optimal solution. Its mathematical model can be expressed as: 

J1 = min F(x, y1 , y2 , . . . ym ) x



s.t. G(x) ≤ 0 J2 = min f (x, y1 , y2 , . . . ym ) y

s.t.g(x, y1 , y2 , . . . ym ) ≤ 0

(1)

(2)

Wherein, J1 is the objective function of upper optimization; x is the decision vector of upper optimization; G(x) is the upper constraint; J2 is the objective function of the lower layer optimization. y is the optimized decision vector of the lower layer; g(x, y1 , y2 , . . . ym ) is the lower constraint. Based on the economy and stability of the system operation, a two-layer optimization model is established. The operation cost is minimized as the upper model and the cost is calculated by combining the demand side response. The interaction power between the micro-grid and the main grid is minimized as the lower layer model, and the adverse state in the operation power flow is avoided by setting the penalty function, so as to improve the accuracy of the optimization results.

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3 Economic Optimization The economy of micro-grid is the guarantee of stable operation of the system. With the improvement of power pricing mechanisms such as time-of-use electricity price and real-time electricity price, the influence of users in marketization operation is also increasing, and demand side response has become an indispensable link in economic optimization [22–25]. Figure 3 shows the revenue settlement process based on demand side response.

3.1 Objective Function In this paper, the operation cost of microgrid is minimized as the objective function, which can be specifically described as:   f 1 = min C(i_ j ) + Cbuy − Rwind (1)

(3)

Demand side model

The demand-side model is embodied in the process that users participate in the load transfer according to their own needs and micro-grid subsidies. The key to the optimization of demand side response is to ensure the interests of users in the process of load transfer, and then mobilize the enthusiasm of users to participate in the load transfer. The corresponding model is as follows: C(i_ j ) = a∗Pi_ j ∗Ti_ j + b Prediction

Market information adjustment

Output devices

Based on the price

Output power forecast

Historical Data

Power network dispatch center Short-term forecasting Historical Ultra short Data term forecast

Load

Perform load transfer

Based on the incentive

Fig. 3 Settlement process of revenue

Settlement proceeds

Microgrid

TOU RTP CPP Power network dispatch center DLC IL DSB EDR

(4)

Power purchase costs Power network dispatch center load transfer

Electricity price information

User

Online income

Grid User subsidies

User

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where, Pi_ j is the load transfer amount from time i to time j; Ti_ j is the time interval from time i to time j; a is the variable cost coefficient; b is the fixed cost coefficient. (2)

Power side model

The power side model mainly shows the income and expenditure relationship between the micro-grid and the power grid. When the micro-grid is unable to supply the local load, it will purchase electricity from the grid, And then there’s a cost Cbuy . When the micro-grid completes the local load supply, the remaining electricity can be sold to the grid, thus generating revenue Rwind . The modeling process is as follows: Cbuy = C h ×



Ph + Cu ×

t∈Th



Pu + Cl ×

t∈Tu



Pl

(5)

t∈Tl

Wherein, C h , Cu and Cl represent the electricity purchase cost at peak time, normal time and valley time respectively; Ph , Pu and Pl represent the electricity purchase at peak time, normal time and valley time respectively; and Th , Tu and Tl represent the time periods of peak time, normal time and valley time respectively. The income from electricity sales, Rwind , is the income from Internet access, which can be expressed as: Rwind = (Rwh + Rwb ) × ×





Pwh + (Rwu + Rwb )

t∈Th

Pwu + (Rwl + Rwb ) ×

t∈Tu



Pl

(6)

t∈Tl

Where Rwb is the feed-in subsidy revenue of wind power from new energy farms, Rwh , Rwu , and Rwl are the feed-in revenue at peak, usual and valley hours, respectively, Pwh , Pwu , and Pwl are the feed-in power at peak, usual and valley hours, respectively, while Th , Tu , and Tl represent the time periods at peak, usual and valley hours.

3.2 Binding Conditions According to the actual setup of the model, there are power constraints and load constraints on the system: 0 ≤ P(k)wind ≤



P(k)wind

(7)

P(k)load

(8)

T

0 ≤ P(k)load ≤

 T

Where P(k)wind and P(k)load represent the turbine power and local load at moment k respectively.

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When load transfer is carried out, loads in the same response period can only be transferred. Therefore, there is a transfer period constraint. tin ∈ T, tout ∈ T

(9)

Where tin and tout denote the moment of transfer in and the moment of transfer out respectively; T is the load response period, which is generally 24 h. After the load completes the transfer, its total load is the same as before the transfer, and there is a limit to the amount of load transfer participation. It is expressed as: 

Pa f ter =



T

Pbe f or e

(10)

T

ΔP ≤ Ptotal × θ

(11)

Where Pbe f or e and Pa f ter denote the amount of load at each moment before and after the transfer respectively; T is the load response period; ΔP denotes the amount of load transfer participation; Ptotal is the total amount of load; θ is the percentage of load allowed to be transferred and the value is given by the micro-grid.

4 Stability Optimization The stability of micro-grid operation is mainly reflected in active losses, interactive power and equipment utilization. In order to calm down the fluctuation of the grid, it is necessary to minimize the interaction between micro-grid and main grid, so that the energy can be consumed locally. At the same time, energy storage system can be introduced as a load to improve the energy dissipation capacity and as a distributed power supply when the power supply is insufficient [26–30].

4.1 Objective Function The optimization model aims at minimizing the interactive power of the micro-grid with the main grid.  24   f 2 = min Pgrid (k) k=1

Where, Pgrid (k) is the corresponding interaction power at moment k.

(12)

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4.2 Binding Conditions Safety requirements exist for the system’s energy storage equipment. Using the equivalent state of charge (ESOC) as a standard parameter, the ESOC value for the entire energy storage system should be between 0.2 and 0.9. ⎧ ⎨ 0.2 < E S OC O (k) < 0.9 0.2 < E S OC H (k) < 0.9 ⎩ 0.2 < E S OC S (k) < 0.9

(13)

Where E S OC O (k), E S OC H (k) and E S OC S (k) denote the equivalent charge states of the oxygen storage tank, hydrogen storage tank and the whole energy storage system at moment k. Power conservation needs to be satisfied during the operation of the system, and the power generated by the wind turbine is the sum of grid interaction, load dissipation and system energy storage. It can be expressed as: Pwind (k) = Pgrid (k) + Pload (k) + Psoc (k)

(14)

Among them, Pgrid (k) is the wind energy at moment k;Pgrid (k), Pload (k) and Psoc (k) denote the energy of interaction with the main grid, load dissipation and energy storage system, respectively. After considering the size of wind turbine output, the size of local load value and the corresponding energy storage state, the power flow states of the system are divided into nine types, which correspond to different operation states. Several of these states will affect the reliability and economy of system operation, and such operating states can be minimized or avoided in the optimization search process by setting the response disciplinary function. The specific parameter settings are shown in Table 1. The power exponent of the disciplinary function corresponds to the strength of the constraints in the process of finding the optimal system, and a high exponent is required to avoid finding the optimal solution in this item. The specific analysis of each state is as follows. State 1: The new energy of the system is more, and the gas storage of the energy storage device is more, the load is supplied by the energy storage device as a priority, followed by the new energy supply, and the excess new energy will go online. State 2: The system has more new energy and the gas storage capacity of the energy storage device is moderate, the load is also supplied by the energy storage device first, then by the new energy, and the excess energy will be put on the grid. State 3: The system has more new energy and the gas storage capacity of the storage device is smaller. The load is supplied by the new energy, and the storage device needs to be charged at the same time, and the remaining part will be put on the grid. Since the new energy in this state can supply both new energy and energy storage device, the index is smaller.

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Table 1 System power flow status table Status

New energy and load comparison

Energy storage system state

Disciplinary function

1

Pwind > Pload

Larger E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))4

2

E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))4

3

Lesser E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))2

Larger E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))4

5

E S OC S

Pgrid (k) = 0

6

Lesser E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))2

Larger E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))2

8

E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))2

9

Lesser E S OC S

Pgrid (k) = (Pwind (k) − Pload (k) − Psoc (k))4

4

7

Pwind = Pload

Pwind < Pload

State 4: The storage capacity of the system is larger, and the load is supplied by the storage device, after the new energy is supplied to the load, some of the balance will be put on the grid. State 5: The system is self-sufficient and reaches the most ideal operation state, no need to set the disciplinary function. State 6: The system has less storage capacity of energy storage devices, and after all the new energy is supplied to the load, electricity will be purchased from the grid to supply the energy storage devices. State 7: The new energy of the system is less, and the gas storage of the energy storage system is more. The energy storage device and the new energy will supply the load successively, and then the power will be purchased from the main grid. State 8: The new energy of the system is less, and the gas storage of the energy storage system is moderate, then the energy storage device and the large grid supply the load, and finally the power is purchased from the main grid. State 9: The system has less new energy and the gas storage capacity of the energy storage device is also less, so the power needs to be purchased from the main grid to meet the load and charge the energy storage device.

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5 Solution Method 5.1 Greedy-Genetic Algorithm for Solving Upper-Level Optimization Problems In order to find the optimal solution of the upper objective function, this paper uses genetic algorithm (GA) as the optimization search algorithm and combines greedy algorithm to group the population according to whether load shifting occurs or not, after which the adaptation degree for performing load shifting is sequentially obtained and thus the overall adaptation degree is calculated in order to solve for the optimal load power data and microgrid operation cost [31]. The flow of the optimization algorithm is as follows. (a) (b) (c)

Importing load data and normalizing them. Encoding the normalized load data and generating the initial population according to the constraints. The adaptation degree is calculated and the value of the adaptation degree is obtained by the greedy algorithm. The specific steps are: (1)

(2) (3) (4) (5) (6) (7) (d)

Calculate the difference vector Q between the local load and the generated population, the elements in Q include positive, negative and zero values. A positive value means that there is a load transfer from that moment, a negative value means that there is a load transfer from that moment, and a zero value means that there is no load transfer at that moment. Grouping the elements in the vector Q with positive elements as one group and non-positive elements as another group. Divide the original problem into n sub-problems according to the number of positive elements n. Solve each sub-problem in turn and calculate the subsidy cost required when load shifting occurs for each user separately. Integrate all sub-problems to obtain the total subsidy cost of the microgrid to the user. Calculate the cost of power purchase and feed-in subsidies for the microgrid according to Eqs. (5) and (6). Substitute into the upper objective function and solve for the value of the fitness of this population, which is the operating cost of the micro-grid.

Judge whether the end condition is satisfied. If it is satisfied, the population and fitness function are output at this time; if not, the selection, crossover and variation operations are performed again to get a new population and return to step c. The corresponding algorithm flow chart is shown in Fig. 4.

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J. Li et al. Genetic algorithm section

Greedy algorithm section

Calculate the difference vector Q between the local load and the generated population

Begin

Import data

Calculate fitness

Pretreatment

Coding

Divide the vector Q into two groups: positive and non-positive elements

Divide multiple subproblems according to the number of positive elements

Calculate fitness

Met stopping Criterion?

Y

Solve each subproblem in turn Output result

N Selection

End

Integrate the subproblems to get the load transfer cost

Crossover

Mutation

Calculate the income of new energy power station

Calculate total cost

Fig. 4 Flow chart of the upper layer optimization

5.2 Genetic Algorithm for Solving Lower Level Optimization Problems The optimal solution of the lower level objective function is found by the genetic algorithm (GA). The constrained objective function by the disciplinary function is transformed into an unconstrained objective function, which is then solved by using the superiority of the genetic algorithm in global search [32, 33]. The algorithm flow is as follows. (a)

(b)

(c)

Population initialization and encoding. Generating the initial values of the equivalent charge state of the energy storage system at each moment and encoding them according to the actual operation of the system. Adaptation degree calculation. Judging the operation state the system is in according to the information at each moment, and calculating the interaction power between the micro-grid and the main grid at each moment according to the disciplinary functions in different operation states, so as to obtain the target function value. Determine whether the end condition is satisfied. If it is satisfied, the population under the current adaptation is decoded, and then the equivalent charge state

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Genetic algorithm section

Begin

Population initialization

Penalty function

Coding

Mutation

Status 1 Calculate fitness

Crossover

Calculate fitness Status 2

Selection Met stopping Criterion?

Y

... Status 9

Output result

End

Fig. 5 A flow chart of the lower level optimization

of the energy storage system and the interaction power between the microgrid and the main grid at each moment are obtained; conversely, the current population is selected, crossed and mutated again to obtain a new population, and return to step b. The corresponding algorithm flow chart is shown in Fig. 5.

6 Example Analysis 6.1 Example Overview In this paper, two cases are selected for optimization simulation. Case 1 is based on the measured data of a micro-grid in a northern region of China; Case 2 is based on

310 Table 2 Relevant parameters of algorithm 1

Table 3 Relevant parameters of algorithm 2

J. Li et al. Parameter name

Parameter values

Peak price (7:00–11:00)

1.0407 yuan/kW·h

Valley price (0:00–6:00)

0.2561 yuan/kW·h

Usual price (Other time)

0.6022 yuan/kW·h

Peak time online subsidies

0.81 yuan/kW·h

Valley time online subsidies

0.17 yuan/kW·h

Usual time online subsidies

0.42 yuan/kW·h

Online subsidy income

0.15 yuan/kW·h

Variable cost coefficient-a

0.3

Fixed cost factor-b

0.1

Parameter name

Parameter values

Peak price (7:00–11:00)

1.2678 yuan/kW·h

Valley price (0:00–6:00)

0.3536 yuan/kW·h

Usual price (Other time)

0.7607 yuan/kW·h

Peak time online subsidies

0.92 yuan/kW·h

Valley time online subsidies

0.20 yuan/kW·h

Usual time online subsidies

0.53 yuan/kW·h

Online subsidy income

0.15 yuan/kW·h

Variable cost factor-a

0.3

Fixed cost factor-b

0.1

the measured data of a micro-grid in a European region. The energy storage system of both cases uses fuel cell energy storage. Two days are taken from the two cases for simulation analysis, numbered as day A, day B and day C, day D respectively. The parameters related to Case 1 and Case 2 are shown in Tables 2 and 3 respectively.

6.2 Example Results The load transfer results of the calculation cases 1 and 2 are obtained by MATLAB simulation. Figures 6, 7, 8 and 9 correspond to the power comparison before and after load shifting on Case A, Case B, Case C and Case D respectively.

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Fig. 6 Power comparison before and after load shifting in Case A

Fig. 7 Power comparison before and after load shifting in Case B

It can be seen from the graph that after load shifting, the load curve has decreased in the peak period and increased in the low period, which has achieved the purpose of peak shaving and valley filling. The following quantitative analysis of the economic optimization effect is done for the specific data of load shifting in each day. Firstly, the following two indicators are determined: the grid operation revenue and the peak-to-valley ratio of load, which are calculated as follows.

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Fig. 8 Power comparison before and after load shifting in Case C

Fig. 9 Power comparison before and after load shifting in Case D

Rgrid = Rwind − C(i_ j ) − Cbuy μ=

Pmax − Pmin × 100% Pmax

(15) (16)

Where, Pmax , Pmin represent the daily maximum load and daily minimum load respectively.

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Table 4 Microgrid operating economy indicators The date of the example

Terms

Before load transfer

After load transfer

A

Revenue from micro-grid operation (yuan)

102,253.73

103,165.20

Peak valley ratio/%

15.18

12.43

B

Revenue from micro-grid operation (yuan)

−132,363.62

−131,619.15

Peak valley ratio/%

14.74

11.87

Revenue from micro-grid operation (yuan)

−204,805.84

−195,059.26

Peak valley ratio/%

20.57

16.65

Revenue from micro-grid operation (yuan)

−263,532.87

−207,240.74

Peak valley ratio/%

22.82

15.59

C

D

The values of the micro-grid operation indexes for the four arithmetic days are obtained by calculation as shown in the following table. The values of the micro-grid operation indexes for the four arithmetic days are obtained by calculation as shown in Table 4. After load shifting, the operation quality of the micro-grid is improved in all cases. The profit of the micro-grid increased by about 911.47 on Case A, and the peak-to-valley ratio of the micro-grid decreased from 15.18% to 12.43% after load shifting; on Case B, the micro-grid was in loss because the new energy power was less on that day, and the loss was reduced from 132,363.62 to 131,619.15 after load shifting, and the peak-to-valley ratio decreased by 2.87% on that day. In Case C and Case D days, the magnitude of load shifting is greater, and the resulting changes in the indicators of micro-grid operation are more obvious. Through load shifting, the loss of micro-grid in Case C day decreases by 9,746.59, while the loss in Case D day decreases by 56,292.12, which improves the economy of micro-grid operation, and the peak-to-valley ratio also decreases by 3.92% and 7.23%, respectively, and also ensures the stability of micro-grid operation. In terms of system stability optimization, the power flow of the system is analyzed by genetic optimization algorithm, and the optimized energy storage system output data and the interaction data with the micro-grid and main grid are obtained. the MATLAB simulation results are shown in the following figure, Fig. 10 shows the optimized effect of microgrid operation for Case A, Fig. 11 shows the corresponding optimized effect for Case B, Fig. 12 shows the corresponding optimized effect for Case C and Fig. 13 shows the corresponding optimized effect for Case D. As can be seen from the figure, after the participation of the energy storage system in the micro-grid optimization, the change of ESOC value is larger, while the interactive power between the micro-grid and the main grid is reduced. The online time of the micro-grid is significantly reduced, and the optimization goal of minimizing the interaction power initially meets the expectation.

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Fig. 10 Microgrid operation optimization effect diagram in Case A

Fig. 11 Microgrid operation optimization effect diagram in Case B

The following is a quantitative analysis of the stability optimization effect for the goal of maximizing the local consumption of new energy. Firstly, the following index is introduced: the consumption rate of new energy. 24 k=1 Pgrid (k) × 100% τ = 1 − 24 k=1 |Pwind (k)|

(17)

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Fig. 12 Microgrid operation optimization effect diagram in Case C

Fig. 13 Micro-grid operation optimization effect diagram in Case D

Where Pgrid (k) and Pwind (k) represent the interaction power and new energy power between the micro-grid and the main grid at moment k, respectively. From this, the new energy consumption rates for the four calculation days can be calculated as shown in Table 5. As can be seen from the table, after stability optimization, the consumption rate of new energy on days A, B, C and D increased by 24.82%, 27.25%, 26.54% and

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Table 5 Microgrid operational stability indicators The date of the example

The absorption rate before optimization/%

Optimized absorption rate/%

Δτ /%

A

69.47

94.29

24.82

B

28.48

55.73

27.25

C

48.59

75.13

26.54

D

57.18

78.42

21.24

21.24%, respectively, which maximized the local consumption of new energy and thus improved the stability of micro-grid operation.

7 Conclusion This paper proposes a two-layer optimization of micro-grid operation based on the application of demand response and energy storage system, which can effectively improve the operating economics of micro-grid and reduce disturbances to the main grid where renewable intake can be ensured. The two-layer optimization model is simulated with different cases to verify the feasibility and effectiveness of the proposed scheme. For the sake of the optimization of the economy and stability of the grid, the algorithm optimization strategy can be adjusted according to the actual situation to regulate the system weights to ensure the economics or stability to accommodate the actual engineering needs. Acknowledgements This research is supported by National Natural Science Foundation of China (NSFC 51867007, 51867006, 51867005).

References 1. Yinbiao S, Zhigang Z, Jianbo G, Zhengling Z (2017) Analysis of key factors of new energy consumption and research on solution measures [J]. Chin J Electr Eng 37(01):1–9 2. Shiles J et al (2017) Microgrid protection: an overview of protection strategies in North American microgrid projects. In: 2017 IEEE power and energy society general meeting. pp 1–5 3. Garg VK, Sharma S (2018) Overview on microgrid system. In: 2018 Fifth international conference on parallel, distributed and grid computing (PDGC). pp 694–699 4. Yang Xinfa S, Jian LZ, Haitao L, Rui L (2014) Review of microgrid technology[J]. Chin J Electr Eng 34(01):57–70 5. Shen C (2014) Research on microgrid optimal dispatching model and method [D]. Guangdong University of Technology 6. Bui V, Husain A, Kim H (2018) Diffusion strategy-based distributed optimization for operation of multi-microgrid system. TENCON 2018–2018 IEEE region 10 conference. pp 1578–1583

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Evaluation of Power Grid Flexibility Based on PV Output Characteristics Chaofan Wang, Jie Lou, Xiaohan Shi, Yuanyuan Sun, and Kejun Li

Abstract With the continuous increase in the proportion of renewable energy sources such as photovoltaics connected to the grid, the establishment of a grid flexibility assessment model based on photovoltaic output characteristics is very important for the development of renewable energy grids. This paper first puts forward the concept of grid flexibility centered on the peak regulation capability of the system; through AP clustering algorithm, the photovoltaic output curve under typical sunshine conditions is obtained, and the mechanism of the influence of photovoltaic power access on the peak regulation capability of the system is analyzed; The static flexibility measurement indicators are proposed from the perspective of power grid flexibility requirements and resources, and the two output curves are decomposed on a 15-min time scale using morphological algorithms, and dynamic flexibility measurement indicators are proposed from the perspective of the relationship between flexible supply and demand; Finally, the analytic hierarchy process and the flexibility scale weighting method are used to determine the flexibility index weights, and the calculation examples verify that the index system proposed in this paper can effectively reflect the system flexibility of the evaluation object. Keywords Flexibility evaluation · PV output characteristics · Flexible supply–demand relationship · Analytic hierarchy process

1 Introduction With the increasingly prominent social and environmental problems today, the development of low-carbon and clean renewable energy has been promoted. Among them, photovoltaics, as one of the fastest-growing renewable energy sources, has the characteristics of volatility and randomness in output. In the process of large-scale replacement of traditional power supply systems by photovoltaic power sources, it also brings huge challenges to the power system’s peak shaving and stable operation C. Wang · J. Lou (B) · X. Shi · Y. Sun · K. Li School of Electrical Engineering, Shandong University, Jinan, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_25

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capabilities [1]. In this context, the assessment of the flexibility of the power system has become a hot research content on a global scale.

2 Grid Flexibility Theory 2.1 Definition of Grid Flexibility In a broad sense, flexibility refers to the ability of the system to respond to internal and external uncertain factors, that is, the ability to maintain the safe and stable operation of the system [2, 3]. Combining with the status quo of large-scale integration of renewable energy sources such as photovoltaics, this article defines grid flexibility as: the power system optimizes and allocates various flexible resources to respond to the volatility and randomness of renewable energy output. That is, the ability of system flexibility resources to meet flexibility requirements [4]. Compared with traditional flexible resources (such as hydropower, thermal power), photovoltaics, as a renewable energy, hardly participate in the power adjustment of the grid after they are connected to the grid. Therefore, the flexible resources of the system mainly include: coal-fired units, gas-fired units, Adjustable hydropower unit, energy storage and demand side response, etc. Since the flexibility of renewable energy such as photovoltaics is weak, and the output of PV is volatile and random, the flexibility requirements of the system can be represented by photovoltaic and load peak shaving requirements.

2.2 Analysis of PV Output Characteristics Based on the daily output data of photovoltaic units in a provincial power grid, the AP clustering algorithm is used to adaptively cluster and filter the output data with a step length of 15 min, and the output curve of photovoltaic units under typical sunny conditions is selected. Since most of the photovoltaic power output changes are passively determined by light and weather, and almost do not actively participate in power adjustment, it can be regarded as the reverse load of the system. The net load output of the system is defined as the load output minus the photovoltaic output. Therefore, the peak shaving demand of the system under the access of renewable energy will be determined by the net load output curve. It can be seen from the Fig. 1 that during the peak period of photovoltaic unit output, the peak regulation demand for net load output has changed from upward adjustment to downward adjustment. This section only selects the net load curve under typical sunny conditions for demonstration and analysis. The changes in the

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Fig. 1 Net load output curve under typical sunny conditions

photovoltaic and net load output curves under different weather conditions will not be repeated.

3 Construction of Flexibility Indicators After photovoltaic and other renewable energy sources are connected to the grid, traditional flexible resources (such as hydropower and thermal power) are replaced by renewable energy, which greatly reduces the capacity of conventional flexible resources. The traditional power balance method has been unable to achieve net load coverage. Network [5], the system may have insufficient flexibility in certain periods or working conditions, which requires comprehensive consideration of flexibility resources, flexibility requirements, and flexibility supply–demand relations. Carry out a quantitative assessment.

3.1 Flexibility Static Evaluation Indicator From the perspective of flexibility requirements The peak regulation ability of the system is an important indicator to measure the level of flexibility. Based on the above research on the net load output characteristics,

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this section proposes benchmarking evaluation indicators that measure the flexibility requirements of the system by peak regulation demand. (1)

Net peak regulation demand PD =

PDmax − PDmin PN

(1)

The net peak regulation demand of the system can be expressed by the intraday peak-valley difference of the net load, where PDmax and PDmin represent the maximum and minimum output of the net load in a certain day, and PN is the reference value. (2)

Variation of peak regulation demand RV =

PD − PO PN

(2)

The variation of peak regulation demand of the system can be represented by the difference between the peak-valley difference of the net load and the original load, where PO and PD are the peak-valley difference between the original load and the net load in a certain day. From the perspective of flexibility resources The flexible supply capacity of the generator set can reflect the flexibility level of the system to a certain extent. In order to evaluate the flexible supply capacity of the generator set under a unified standard, the benchmarked unit parameters are introduced as a static assessment of the system’s flexibility requirements. (1)

Flexibility adjustment range of the unit K

k=1 (Pkmax

RA =

− Pkmin )

PN

(3)

The flexibility adjustment range of the system can be expressed by the operating range of all units under the base capacity, where k is a certain type of unit, Pkmax is the maximum capacity of this type of unit, and Pkmin is the minimum stable power generation of this type of unit, PN is the reference value. (2)

Maximum climb rate of the unit K RC =

k=1

RN

Rk

(4)

This indicator represents the total climb rate of all units under the reference capacity, where Rk is the maximum climb rate of the k-th type of unit.

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(3)

323

Minimum continuous uptime of the unit K TD =

k=1

K

Tk · Pk

k=1

(5)

Pk

This indicator represents the average of the minimum continuous uptime of all units, where Tk is the minimum continuous uptime of the k-th type of unit, and Pk is the installed capacity of the k-th type of unit.

3.2 Flexibility Dynamic Evaluation Indicator When photovoltaic energy is connected to the system, the real-time correspondence between the flexibility supply on the power generation side and the flexibility demand on the load side is included in the scope of the system flexibility assessment, and the total output curve and net load output curve of the generator set are decomposed on a 15 min time scale, and through the comparative analysis of N output segments on both sides between the source and load, the dynamic evaluation indicators of system flexibility are obtained. (1)

The probability of lack of flexibility Plack =

n N

(6)

This indicator represents the probability that the system flexibility demand is greater than the flexibility supply, where n is the number of insufficiently flexible output segments, and N is the total number of output segments. (2)

The mean of flexibility margin N E margin =

− Pi ) N · PN

i=1 (Fi

(7)

This indicator represents the overall flexibility of the system, where Fi is the output of the generator set in the i-th output section, and Pi is the net load output of the system in the i-th output section. (3)

The mean of lack of flexibility n  Elack =

j=1

P jlack − F jlack n × PN

 (8)

This indicator reflects the severity of the system flexibility gap by counting the flexibility gap of the output segment with flexibility margin less than zero, where

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P jlack is the system net load output in the j-th segment with insufficient flexibility output, F jlack is the output of the generator set in the j-th segment with insufficient flexibility.

4 Examples This section analyzes its system flexibility based on the actual data of conventional units in a provincial power grid. The total installed capacity of the system units is 82230 MW, of which the coal-fired turbine assembly capacity participating in the dispatch is 31282 MW; the gas turbine assembly capacity is 18400 MW; the adjustable hydroelectric generator assembly capacity is 12536 MW, and the photovoltaic installed capacity is 20012 MW, accounting for 24.3% of the total installed capacity The maximum load is about 70,000 MW, and the peak-to-valley difference of the maximum load is 11200 MW. Bring the unit parameters into the indicator to calculate, the value of each indicator can be seen from Table 1. The weight analysis method is used to calculate the weights of static indicators [6], score the importance of each static indicator with reference to the degree of flexibility influence and the numerical relationship of the indicators, and construct a judgment matrix A: ⎡

1 ⎢ 3.33 ⎢ ⎢ A=⎢ 2 ⎢ ⎣ 5 2.5

0.3 1 0.61 1.51 0.75

0.5 1.67 1 2.5 1.25

0.2 0.67 0.4 1 0.5

⎤ 0.4 1.33 ⎥ ⎥ ⎥ 0.8 ⎥ ⎥ 2 ⎦ 1

 Rule-level weight vector: w = 0.0722 0.2409 0.1449 0.3615 0.1805 . Largest characteristic root: λ = 5.0054. Consistency index: CI = 0.0013. Concordance ratio: CR = 0.0012 < 0.1 The consistency of the matrix is acceptable. The weight of the static evaluation indicators for flexibility can be seen from Table 2. The flexible scale weighting method is used to calculate the weights of dynamic indicators [7], and bring the corresponding data of the flexibility resource and net load output curve decomposed on the 15 min time scale into the formula for calculation, Table 1 The values of various indicators Indicators

PD

RV

RA

RC

TD

Plack

E margin

Elack

Value

12.6

1.4

3.5

1.39

2.36

0.0428

0.578

0.0299

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Table 2 Weight of flexibility static evaluation indicators Indicators

PD

RV

RA

RC

TD

Weights

0.0722

0.2409

0.1449

0.3615

0.1805

Table 3 Weight of flexibility dynamic evaluation indicators

Indicators

Plack

E margin

Elack

Weights

4.0431

4.0431

4.0431

and the weight of the dynamic evaluation indicators of flexibility can be seen from Table 3. Then the data is brought into the flexibility evaluation model for quantitative calculation, and the comprehensive evaluation result of the flexibility of the system is obtained: F = 5.28513847, and the evaluation result is qualified.

5 Conclusion Aiming at the problem of grid flexibility, this paper proposes a comprehensive evaluation method for grid flexibility based on photovoltaic output characteristics. Constructed a system’s flexibility assessment model, and set calculation examples based on actual data from a provincial power grid Validate and analyze the constructed flexibility evaluation model. The results of the calculation example show that the flexibility adjustment ability of the grid is basically qualified. While verifying the validity of the model, it also shows that it is difficult to rely solely on the flexibility adjustment ability of the traditional generator set when photovoltaic and other renewable energy sources are connected. To meet the development and reliable operation of a high proportion of renewable energy grids, further research on access to energy storage systems and their configuration is needed in the future. Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

References 1. Zongxiang L, Li H, Qiao Y (2016) Flexibility planning and challenges of power system with high proportion of renewable energy. Autom Electr Power Syst 40(13):147–158 2. Chandler H (2011) Harnessing variable renewables: a guide to the balancing challenge 3. Li D, Wang J, Zhang J (2021) Analysis of energy storage output characteristics based on photovoltaic volatility. Power Syst Clean Energy 37(02):99–107

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4. North American Electric Reliability Corporation (2009) Special report: accommodating high levels of variable generation. American, North American Electric Reliability Corporation 5. International Energy Agency (2011) Harnessing variable renewables. Paris, International Energy Agency, pp 41–67 6. Huang Z (2020) Research on the optimization of 110 kV substation comprehensive automation transformation scheme based on analytic hierarchy process. Jilin University, Changchun 7. Zhan X (2020) Multi-scale power supply flexibility assessment and energy storage configuration research for high-proportion renewable energy grids. South China University of Technology, Guangzhou

Super-Twisting Sliding-Mode Based Photovoltaic Grid-Connected Inverter Control Minghao Zhou, Haofan Yu, Xingguo Wu, Hongyu Su, Siwei Cheng, and Yunhao Xu

Abstract This paper proposes a super-twisting sliding-mode control method for the three-phase photovoltaic grid-connected system to control the tracking of the subsequent grid-connected current. Three sliding-mode controllers are designed to generate continuous control signals and regulate the control loop in the grid-side inverters. Owing to the super-twisting sliding manifold and the super-twisting control law, the large steady-state error and slow convergence speed of the AC volume caused by the PI control are improved, so the overall robustness of the system is enhanced, as well as the response speed and accuracy of grid-connected current tracking. Simulations validate the proposed method. Keywords Photovoltaic power generation system · Sliding mode control · Super-twisting algorithm

1 Introduction Due to the renewable and environmentally friendly characteristics, distributed generation technology is widely used in micro grids [1]. Among them, photovoltaic power generation has a great prospect due to its low requirements for terrain. It can be foreseen that photovoltaic power generation will be applied as a mainstream new energy power generation method. However, the output voltages and currents is always nonlinear due to external uncertainties, thus lead to random and discontinuity [2]. Also, when large micro-grids are connected to the grid, there will be fluctuations in voltage and frequency, which will lead to unstable operation. The grid connection of inverters is an important part of the power generation, and many control strategies are used in the operation [3]. In [4], PI control cannot M. Zhou (B) · H. Yu · X. Wu · H. Su · S. Cheng School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin, Heilongjiang 150001, China e-mail: [email protected] Y. Xu Combined Charging System, Sinexcel, Shenzhen 518055, Guangdong, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_26

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guarantee the signal integrity of the output. Fuzzy control method [5] has good output quality, but the response is slowed down, making it difficult to track the rapid changes of the micro grid. Sliding mode control (SMC) is a nonlinear control method [6], and it is widely utilized due to its high robustness and simplicity of implementation [7], but it has chattering problems. The super-twisting sliding-mode (STSM) [8] control can completely eliminate chattering through the integrator, enhance the stability of the system. This paper adopts super-twisting sliding mode (STSM) control method for the voltage control loop and the current control loop to enhance the robustness and tracking speed of the photovoltaic grid-connected system. The simulations validate the effect of the control method.

2 LCL Three-Phase Photovoltaic Grid-Connected Inverter Model Design 2.1 Topological Structure of Three-Phase LCL Inverter The grid-connected inverter structure is voltage type, which has a large capacitor in parallel on DC side. LCL filter has a better suppression of high-frequency harmonics. The inverter topology and control block diagram are shown in Fig. 1.

2.2 Mathematical Model of Inverter Based on LCL Filter The inverter can approximately be considered to work under ideal conditions. The mathematical model of inverter based on LCL filter can be expressed as: L D PV

C1

Cdc

V1

V3

V5

L1

L2

i2a

i1a

Udc

i2b

i1b V4

V6

i2c

i1c V2 C

Fig. 1 Three-phase grid-connected inverter topology

ua ub uc

Super-Twisting Sliding-Mode Based Photovoltaic Grid-Connected …

⎧ R1 i 1k u ck uk di 1k ⎪ ⎪ =− − + ⎪ ⎪ L1 L1 L1 dt ⎪ ⎪ ⎨ u gk di 2k u ck R2 i 2k ; k = (a,b,c) = − + ⎪ dt L L L 2 2 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ du dc = i 1k − i 2k C C dt

329

(1)

Through coordinate transformation, we have: ⎧ di R d ⎪ = − i d + ωi q + ⎨ L dt ⎪ ⎩ di q = − R i − ωi + q d L dt

1 1 u d − u gd L L 1 1 u q − u gq L L

(2)

where id and iq stand for the d axis and q axis value of the output current of the gridside converter, ω the angular velocity of coordinate system, L the total inductance of the LCL filter, L = L1 + L2 , R the total parasitic resistance of L1 and L2 , R = R1 + R2 , ug the grid voltage, ud = udc S d , uq = udc S q , udc the DC bus voltage.

3 Sliding Mode Controller Design 3.1 Voltage Controller Design The voltage outer loop adopts the super-twisting sliding mode control, which makes the DC bus voltage stabilize more quickly, so that the voltage on the input side of the inverter reaches a stable state within a limited time. In a three-phase inverter system, according to the instantaneous power theory, the active power and reactive power can be derived as follows: ⎧ 3 ⎪ ⎨ Pg = (u gd i gd + u gq i gq ) 2 (3) ⎪ ⎩ Q = 3 (u i − u i ) gd gq gq gd g 2 where the symbol Pg represents active power, and the symbol Qg reactive power. The requirement is unity power factor grid connection, then from Eq. (3), we can get: ⎧ 3 ⎪ ⎪ ⎨ i inv u dc = u gd i gd 2   3u gd i gd du 1 ⎪ dc ⎪ = i pv − ⎩ Cdc 2u dc dt

(4)

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where iinv the current input to the inverter, Cdc the inverter input capacitance, and ipv the current flowing to the DC capacitance. The DC bus voltage tracking error is: e = u dc − u ∗dc

(5)

where u ∗dc is the reference of DC voltage. Through further simplification, the derivative of the above equation is: e˙ = −

3u gd 1 i pv + i gd 2Cdc u dc Cdc

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Combining (6) with the super-twisting, the control law could be: i d∗

2u dc i pv + a1 |s|0.5 sgn(s) + b1 = 3u gd

 sgn(s)dt

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Theorem 1 When the parameters a1 and b1 are both greater than zero, according to the Lyapunov stability criterion, the system can converge to the sliding mode surface and remain stable within a certain period of time. Proof Consider a Lyapunov function V = 0.5s2 . According to the Lyapunov stability criterion, when V˙ is less than zero, the system state can converge to the sliding mode surface and maintain stability within a certain period of time.    0.5 ˙ V = s · s˙ = −s a1 |s| sgn(s) + b1 sgn(s)dt < 0 The detailed proof process has been given in [9]. If the parameters a1 and b1 are greater than 0, the system can reach the sliding surface in a limited time and maintain on it and then converge to zero.

3.2 Current Controller Design In the paper, the current inner loop selects super-twisting sliding-mode control: ⎧ di R d ⎪ = − i d + ωi q + ⎨ L dt di R ⎪ q ⎩ = − i q − ωi d + L dt

1 u dc Sd − L 1 u dc Sq − L

1 u gd L 1 u gq L

(8)

where L is the sum of the inverter side inductance and the grid side inductance, and R is the sum of the parasitic resistance. The two sliding mode surface functions are defined as follows:

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s1 = i d∗ − i d = 0

(9)

s2 = i q∗ − i q = 0 Based on the equivalent control design, ud and uq can be expressed by: u = u eq + u ap

(10)

Derivation of both sides of Eq. (10) at the same time can be obtained:

u˙ (d)eq = Ri d − ωLi q + u gd

(11)

u˙ (q)eq = Ri q + ωLi d + u gq Combining (8), (9) and (10), the inner loop control law is:  ⎧ ⎪ 0.5 ⎪ u = Ri − ωLi + u + a |s | sgn(s ) + b sgn(s1 )dt d q gd 2 1 1 2 ⎨ d  ⎪ ⎪ ⎩ u q = Ri q + ωLi d + u gq + a3 |s2 |0.5 sgn(s2 ) + b3 sgn(s2 )dt

(12)

Theorem 2 If the parameters a2 , b2 , a3 and b3 are all greater than zero, according to the Lyapunov stability criterion, the system can converge to the sliding mode surface within a certain period of time and remain stable. Proof The proof process is similar to that in voltage-loop proof.

4 Simulations The parameters of mathematical model of the photovoltaic inverter system are shown in Table 1. The simulation results are shown in Figs. 2, 3 and 4. The voltage waveform on the DC bus side is shown in Fig. 2. It can be seen that the system reaches the sliding Table 1 Main simulation parameters of the system

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mode surface after about 0.04 s. The tracking error is only 0.3 V, and the effect is good. In Fig. 3, the grid-connected voltage- and current-wave form of the system have the same phase and no significant distortion. From Fig. 4 the Total Harmonic Distortion (THD) is 2.09%, which meets the grid-connected requirements.

5 Conclusion In this paper, a super-twisting sliding-mode control method is proposed for the three-phase photovoltaic grid-connected system. The super-twisting sliding-mode controllers are designed for the inner and outer loops. Simulation results show that

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Fig. 4 FFT analysis of grid-connected current

the grid-connection effect of the inverter is good and meets the technical requirements of grid-connection.

References 1. Fei J (2017) Adaptive fuzzy sliding control of single-phase PV grid-connected inverter. PLoS ONE 12(8):e0182916 2. Pati AK (2017) Adaptive super-twisting sliding mode control for a three-phase single-stage grid-connected differential boost inverter based photovoltaic system. ISA Trans 69:296–306 3. Chang E-C (2020) High-performance pure sine wave inverter with robust intelligent sliding mode maximum power point tracking for photovoltaic applications. Micromachines 11(6) 4. Cortajarena JA (2019) Sliding mode control of an active power filter with photovoltaic maximum power tracking. Int J Electr Power Energy Syst 110:747–758 5. Panda A (2016) A single phase photovoltaic inverter control for grid connected system. S¯adhan¯a 41(1):15–30 6. Venkatesan M (2020) Research on FPGA controlled three phase PV inverter using multi carrier PWM control schemes. Microprocess Microsyst 76 7. Villanueva I (2020) LCL filter for photovoltaic grid-connected inverter: a reliability study. Int J Photoenergy 2020 8. Gurrola-Corral C (2020) Optimal LCL-filter design method for grid-connected renewable energy sources. Int J Electr Power Energy Syst 120 9. Levant A (1993) Sliding order and sliding accuracy in sliding mode control. Int J Control 58(6):1247–1263

Supplementary Novel Damping Control of MMC-STATCOM to Mitigate SSCI Yiqi Liu, Junyuan Zheng, Mingfei Ban, and Zhenjie Li

Abstract Series compensation is usually adopted to improve the power transmission capacity of the DFIG-based wind farm. However, its interaction would cause a new type of sub-synchronous oscillation (SSO), namely sub-synchronous control interaction (SSCI). This paper proposes a supplementary control strategy for STATCOM based on Modular Multilevel Converter (MMC-STATCOM) to mitigate SSCI. MMC-STATCOM has high voltage level, large dynamic compensation capacity, and high output waveform quality. A novel supplementary damping controller, including filter and gain is designed for MMC-STATCOM, which can mitigate SSCI rapidly. A time-domain simulation model of the DFIG-based wind farm was built on MATLAB/SIMULINK to verify the effectiveness of the supplementary damping control strategy of MMC-STATCOM to mitigate SSCI. Keywords Series compensation · Sub-synchronous control interaction · Damping controller · MMC-STATCOM

1 Introduction Under the target of carbon neutrality and carbon peak, the renewable energy represented by wind power and photovoltaic develops rapidly and applies widely [1]. Vigorously developing renewable energy such as wind power and photovoltaics is the only way to achieve the goal of dual-carbon and build a new power system with new energy. In China, due to the limitation of natural endowment, more than 60% of wind power is located in the north and west of China. However, the main load center of China lies in the east and south of China, so that it is necessary to improve the large-scale wind power transmission capacity. Series compensation is usually adopted to improve the power transmission capacity of the doubly-fed induction generator (DFIG), which is widely used in engineering because of its high reliability and low cost. However, its interaction Y. Liu · J. Zheng (B) · M. Ban · Z. Li Northeast Forestry University, Harbin 150040, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_27

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with nearby DFIGs can cause a new type of sub-synchronous oscillation, namely sub-synchronous control interaction [1–3]. As early as October 2009, the ERCOT wind farm in Texas, the United States, had an SSCI of about 20 Hz, which caused a large number of wind turbine crowbar circuits to be damaged [4]. Since 2013, China’s Hebei Guyuan wind power system has occurred 3–10 Hz sub-synchronous oscillation, which once caused thousands of wind turbines to be abnormally disconnected from the grid [5]. Nowadays, many efforts have been made to research the suppression of SSCI. The strategies for mitigating SSCI are mainly divided into both generation and network sides. The generation strategy is to adjust or modify the traditional wind generator controller to suppress SSCI, such as changing the rotor side controller parameters or supplementary damping controller (SDC) in the rotor side or stator side [6]. The other requires an SSCI suppression device. Existing research shows that Flexible AC Transmission System (FACTS) devices additional suppression strategy is utilized for SSCI mitigation [7–9], including static var compensator (SVC), static synchronous compensator (STATCOM), static synchronous series compensator (SSSC), and unified power flow controller (UPFC). This paper proposes a supplementary control strategy for STATCOM based on Modular Multilevel Converter (MMC-STATCOM) to suppress SSCI. MMCSTATCOM has high voltage level, large dynamic compensation capacity, and high output waveform quality. The novel SDC is designed for MMC-STATCOM to mitigate SSCI, which is improved on the basis of the conventional SDC. Finally, a time-domain simulation model of the DFIG-based wind farm was built on MATLAB/SIMULINK to verify the effectiveness of the additional sub-synchronous current control strategy of MMC-STATCOM to mitigate SSCI.

2 System Configuration Figure 1 presents DFIG-based wind farm connects to the grid via series compensation, including both generation and network side. The above system consists of several parts: DFIG-based wind farm, two-wingdings transformer, AC transmission lines, MMC-STATCOM, and AC grid. It is adopted with connecting DFIG-based

T1

Line

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Fig. 1 Structure of DFIG-based wind farm grid-connected system

AC Grid

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+ Up

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inc

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wind farm composed of 66 DFIGs with rated power of 1.5 MW and rated frequency of 60 Hz to the AC grid through a fixed series compensated transmission system comprising an MMC-STATCOM. There are differences between STATCOM and MMC-STATCOM. Figure 2 shows the topology of the MMC-STATCOM. MMC is divided into three phases, and each phase has two arms; each arm is composed of n half-bridge sub-module. By controlling the on-off of two IGBTs, T1 and T2 , the sub-module outputs two levels of zero and capacitor voltage uc .

3 SSCI Mitigation Strategy of MMC-STATCOM In [10], when the system damping is negative, the system lacks positive damping after being disturbed, resulting in unstable oscillation. Conference [11] pointed out that when the SSR occurs: the controlled current output sub-synchronous current, which phase and gain are close to the sub-synchronous voltage of the system. MMC-STATCOM is an electronic device with voltage source converter as the core component, and the function of MMC-STATCOM is to regulate the PCC voltage and provide reactive power to the system. By adding a damping control strategy, MMC-STATCOM plays a role in mitigating SSCI.

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ZDFIG1

ZGRID(fsub) Zsys

ZDFIG(fsub) ZCL ZT

ZNL

ZDFIGn

SSDC

MMC-STATCOM

Fig. 3 Principle of MMC-STATCOM mitigating SSCI

In Fig. 3, Z DFIG (f sub ) represents DFIG-based wind farm impedance at the subsynchronous frequency. Z GRID (f sub ) consists of series compensation impedance Z CL and system impedance Z sys . The impedance model of DFIG is shown in Formula (1). The impedance models of wind farm lines (Z NL ), series-compensated lines (ZCL), transformers (ZT), and system (Zsys) are shown in Eqs. (2)–(5). 

ZDFIG

 (Kp + rr )s + sLr //(sLm ) + Rs + sLs = s − jωr

(1)

ZNL = RNL + sLNL

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ZCL = 1/(sC) + RCL + sLCL

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ZT = RT + sLT

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Zsys = Rsys + sLsys

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When MMC-STATCOM is connected, ZΣ is shown in Eq. (6), through the function of GSDC, the system’s resistance at the sub-synchronous frequency is changed to mitigate SSCI. ZΣ =

ZW + ZN 1 + Hi + Hu Zw

(6)

In order to achieve the above functions, the supplementary control strategy for MMC-STATCOM is to extract the sub-synchronous current from the line. The subsynchronous current passes through a specific filter link and gain to generate the subsynchronous voltage reference single to mitigate SSCI. The control strategy proposed in this paper omits the phase-shifts, so that MMC-STATCOM supplementary novel damping strategy can mitigate SSCI in various complex conditions.

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4 Performance Verification with Time-Domain Simulation The time-domain simulation has been performed in MATLAB/ SIMULINK to verify the effectiveness of the supplementary damping control strategy. At the beginning of the simulation, 66 DFIGs usually operate, the wind speed is 11 m/s, and the SSCI phenomenon arises at 0.5 s. With the variation of line series compensation and wind speed put into operation, the active power also varies, which is shown in Fig. 4. The simulation results show that MMC-STATCOM supplementary damping controller efficiently captured the oscillation and generated compensation current to dampen the oscillation, as shown in Fig. 4. These results ensure the performance of the MMC-STATCOM supplementary damping controller in damping oscillation at different operation conditions. 250

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5 Conclusion This paper proposed a novel strategy for MMA-STATCOM to mitigate SSCI. By extracting and gaining the sub-synchronous signal of the grid-side electrical quantity, the modulation signal of mitigating SSCI has been obtained. The effectiveness of the SSCI mitigation strategy has been demonstrated by time-domain simulation. Simulation results indicate that the novel can mitigate SSCI rapidly and does not require phase-shifts with the variation of compensated level.

References 1. Chowdhury MA, Mahmud MA, Shen W, Pota HR (2017) Nonlinear controller design for series-compensated DFIG-based wind farms to mitigate subsynchronous control interaction. IEEE Trans Energy Convers 32:707–719 2. Ding et al (2018) Mitigation of sub-synchronous control interaction of a power system with DFIG-based wind farm under multi-operating points. In: IET generation, transmission distribution 3. Zhu XY, Sun HS, Wen JY (2014) Subsynchronous interaction and its mitigation in DFIG-based wind farm and turbine-generator bundled systems. Adv Mater Res 860–863:319–323 4. Adams J, Carter C, Huang SH (2012) ERCOT experience with subsynchronous control interaction and proposed remediation. In: Transmission & distribution conference & exposition. IEEE, New York 5. Wang L et al (2015) Investigation of SSR in practical DFIG-based wind farms connected to a series-compensated power system. IEEE Trans Power Syst 30(5):2772–2779 6. Chernet S et al (2017) Mitigation of SSCI in DFIG based wind farms through modification of rotor-side converter controller. In: Future energy electronics conference & ECCE Asia. IEEE, New York 7. Xie X, Yang T, Jiang Q et al (2008) Mechanism study on the mitigation of SSR with SVC. Dianli Xitong Zidonghua/Automat Electr Power Syst 32(24):1–5 8. Hosseini SMH, Samadzadeh H, Olamaei J et al (2013) SSR mitigation with SSSC thanks to fuzzy control. Turk J Electr Eng Comput Sci 21(10):2294–2306 9. El-Moursi MS, Bak-Jensen B, Abdel-Rahman MH (2010) Novel STATCOM controller for mitigating SSR and damping power system oscillations in a series compensated wind park. IEEE Trans Power Electron 25(2):429–441 10. Yinghong H, Chun D, Xiaorong X et al (2016) Additional damping control of DFIG series compensated transmission system. Power System Technol 40(4):1169–1173 11. Liang W, Xie X, Jiang Q et al (2015) Centralized solution for subsynchronous control interaction of doubly fed induction generators using voltage-sourced converter. Generat Transmiss Distrib IET 9(16):2751–2759

Smart Grids, Power Flow and Load Control

The Simulation of Injected Pulse Signal into Grounding Electrode Lines of HVDC Transmission System for Fault Location Based on PSCAD Yining Zhang, Yueyang Wang, and Kun Liu

Abstract The traditional fault location methods for grounding electrode lines of HVDC transmission system lack high accuracy, a fault location method based on injected pulse signal which enjoys high precision and strong adaptability is proposed, this paper applies PSCAD to simulate the injected pulse signal into grounding electrode lines of HVDC transmission system, where the width and polarity of the pulse signal can be varied. The simulation model of injected pulse signal generator and HVDC transmission system with grounding electrode lines are shown, where the generator periodically injects a pulse signal into the neutral bus bar of the grounding electrode line, and the fault location can be detected according to the time interval of the signals. When the fault of grounding electrode line is detected, the fault location will be calculated by changing the pulse width and the polarity to reduce the fault location error. The simulation results verify the effectiveness and accuracy of the fault location method based on injected pulse signal. Keywords HVDC transmission · Grounding electrode lines · Injected pulse signal · Fault location · PSCAD

1 Introduction HVDC transmission has been developed rapidly in China due to its unique advantages. And the bipolar operation mode of HVDC transmission system has been widely used. The grounding system of this mode is mainly composed of the grounding electrodes, grounding electrode lines and diversion system [1], the main function of grounding electrode lines in the system is to provide a path for DC current. The fault in the grounding electrode lines will affect the safe and reliable operation of the HVDC transmission system [2, 3].

Y. Zhang (B) · Y. Wang · K. Liu M&T Center, CSG EHV Power Transmission Company, Guangzhou 510633, Guangdong Province, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_28

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The fault location methods for grounding electrode lines of HVDC transmission system can be divided into three main categories: impedance method, traveling wave method and wave recording data analysis method. Impedance method needs an additional power generator to inject an AC signal with certain frequency into the grounding electrode lines in the converter station, then measuring the ratio (impedance) of voltage and current phasor at the head end of the grounding electrode line in real-time to obtain the location of the fault. The basic idea of this method comes from the impedance ranging method for AC transmission lines. But the ranging accuracy could be affected by factors such as line parameters, fault type and transition resistance. Traveling wave method, obtains the fault location by detecting the propagation time of transient traveling wave on grounding electrode line [4–7], which can be divided into three types: A-type single-ended traveling wave method, C-type single-ended traveling wave method (injected pulse signal method) and D-type double-ended traveling wave method. Traveling wave method is first used for fault detection of AC lines (Including overhead line and cable) [8–10], its main feature contains high precision and strong adaptability. Wave recording data analysis method use the fault data of the grounding electrode line recorded by the regular recorder in the converter station to construct the fault location function, and then calculate the fault distance [11, 12]. In this paper, we use injected pulse signal method for fault location of grounding electrode lines in HVDC transmission system. Its main characteristic is the variability of width and polarity of the pulse signal.

2 Propagation Process of Injected Pulse Signal As shown in Fig. 1, the pulse signal is injected into the neutral bus bar of the HVDC transmission system, and the pulse signal will propagate along the grounding electrode line to the grounding electrode. If a fault occurs on the grounding electrode line, it will form an impedance mismatch at point F and the injected pulse will be Fig. 1 Propagation diagram of injected pulse signal into a grounding electrode line

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reflected and transmitted at that point. The reflected wave propagates to the neutral line M and the reflection will occur again when it reaches it. The transmitted wave propagates to the grounding electrode N, and the reflection occurs as well when the pulse reaches the point N. If there is no fault on the grounding electrode line, the injected pulse will reflect when it reaches the grounding electrode N.

3 Principle of Fault Location Method Based on Injected Pulse Signal The fault location method based on injected pulse signal is a single-ended ranging method, it periodically injects a pulse signal from the neutral bus bar of the HVDC grounding electrode line, and detects the fault distance according to the time interval of the signal round trip between the launch-end to the fault point.

3.1 Fault Detection The pulse signal generator is installed on the point M of the neutral bus bar in the HVDC transmission system. In the normal operation of the grounding electrode line, the generator injects a unipolar pulse signal with pulse width t1 periodically to the grounding electrode line with set time, as shown in Fig. 2. The pulse signal is a forward traveling wave signal, while the signal reflected from the grounding electrode N is a reverse traveling wave signal. Set tM1 as launch time of the injected pulse signal, tM2 as the time when it reaches the measurement point M, Δt as the time interval, where Δt = tM2 − tM1 . And the distance between the transmitting terminal and the reflection point can be expressed as: l=

M

1 v1 Δ t 2

t1 t

(1)

N

d

Fig. 2 Propagation diagram of injected unipolar pulse signal when the grounding electrode line is in normal operation

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Fig. 3 Propagation diagram of injected unipolar pulse signal when the grounding electrode line is in fault state

M

t1

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t

dx

In this formula: v1 represents the propagation velocity of injected pulse signal on the grounding electrode line. In the normal operation of the grounding electrode line, the measurement point always receives the pulse reflection signal with the same time interval. The length of the grounding electrode line can be obtained by the formula (1). When the time interval of the pulse reflection signal received by the measurement point is different from the normal state, it indicates that the reflection wave is not from the grounding electrode line, but from some other position (fault point) on the line, as shown in Fig. 3. The fault can be detected by the change of signal returning time interval in the measurement point.

3.2 Fault Location When the fault on grounding electrode line is detected, the distance between the measurement point and the fault point will be obtained according to the Formula (1). The result could be considered as a preliminary result. Further, the fault distance will be detected by changing the pulse width ( 21 t1 and 41 t1 ) and the polarity (bipolar), as shown in Fig. 4.

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3.3 Final Result Adopting the above methods, 4 results were obtained. But it is feasible to generate more pulse width to detect the location according to the actual situation, theoretically, the results shall be the same each time. In practical application, the result of detection may be incorrect considering the interference and other factors. Therefore the accuracy of fault location can be improved by selecting several valid data (within preset range) and calculate their average value as the final result.

4 The Selection of Pulse Signal When operating fault location of HVDC grounding electrode line by using injected pulse signal method, it is necessary to select suitable transmitting pulse signal, mainly including pulse type and pulse width in order to improve the reliability and accuracy.

4.1 Pulse Type A pulse signal is a rectangular signal that returns to its initial state rapidly after a sudden change of amplitude in a short time. Due to its fast-rise-fast-return characteristic, the waveform is less likely to be distorted, and the wave head of reflection wave is easy to be detected. This paper chooses unipolar and bipolar rectangular pulse as an example to conduct analysis, thus lays the foundation of the fault location method for grounding electrode line in HVDC transmission system based on injected pulse signal.

4.2 Pulse Width When selecting injected pulse signals, considering only reducing the measurement blind area, smaller pulse width is better, but it brings more high-frequency component, larger transmission loss in HVDC grounding electrode line, shorter measurable line length, and lower reliability of signal recognition. Therefore considering both reducing the measuring blind area and improving the reliability, the initial width of the pulse signal is selected as 2n microseconds (n is positive integer), and can be binary reduced to achieve the best ranging result.

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5 Simulation 5.1 Modeling In this paper, the simulation model of HVDC transmission system under the bipolar operation mode is established by the electromagnetic transient analysis software PSCAD, as shown in Fig. 5. AC1, AC2 are 500 kV AC power supply, T1 and T2 are transformers, HB1 and HB2 are converter bridges, D is HVDC transmission lines, C and H constitute harmonic filters. X1, X2 are two parallel overhead lines (with the same length), representing the grounding electrode line, the head ends were parallel connected and connect to DC system neutral point with grounding capacitor. The tail end is parallel connected and connect to the ground resistor R and earthed. Set fault point F on the grounding electrode line X1, the pulse signal for fault detection is generated by a controllable pulse power source and injected into the head end (measurement point) of the grounding electrode line. Subsequent paragraphs, however, are indented. The relevant parameters are set as follows: (1) (2) (3) (4) (5) (6)

length of HVDC transmission line: 400 km length of grounding electrode line: 100 km ground capacitance of grounding electrode line at the head end: 9.54 nF grounding resistance of grounding electrode line at the tail end: 0.3 Ω amplitude of pulse power supply: 48 V simulation calculating step length: 1 µs

According to the simulation calculation, the propagation velocity of traveling wave in HVDC grounding electrode line is v = 298 km/ms. D

Fig. 5 Simulation model of HVDC grounding system

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5.2 Fault Location Simulation 5.2.1

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Under the normal operation of the grounding electrode line, the unipolar pulse signal with width t1 = 64 µs is injected periodically from the line measurement end, and the typical transient waveform of the injection pulse signal is recorded as shown in Fig. 6. By analyzing the waveform data of Fig. 6 and calculating the time interval between the pulse signal launched moment and the reflected wave received moment, the time interval is Δt = 670 µs. The corresponding distance will be: l = 21 × 298 × 0.67 = 99.83 km. When the grounding electrode line is in normal operation, the distance calculated by injected pulse signal method corresponds to the full length of the grounding electrode line.

5.2.2

Near Distance Fault

Setting the fault point 20 km away from measurement end on the grounding electrode line, with the type of non-metallic grounding fault, and the transition resistance is 1 Ω. Inject a unipolar pulse signal with width t1 = 64 µs at the measurement point. The transient waveform generated by the injected pulse signal is shown in Fig. 7.

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Fig. 7 Transient waveform generated by injected unipolar pulse signal when a fault occurred on the grounding electrode line, 20 km away from the measurement point (under normal pulse width 64 µs)

By analyzing the waveform data of Fig. 7, the time interval between the pulse signal launched moment and the reflected wave received moment is Δt = 133 µs. Comparing to the normal state, the time interval between the pulse signal launched moment and the reflected wave arrived moment has significantly changed, indicating that there could be fault on the line. The result of the initial fault location is: l1 = 1 × 298 × 0.133 = 19.82 km. 2 Figure 8 shows the transient waveform generated by the injected pulse signal at the measurement point when the pulse width is 32 µs and 16 µs, The fault distance calculated is l2 = 19.67 and l3 = 19.82 km respectively. Figure 9 shows when injecting bipolar pulse signal (with width of 32 µs), measurement point recorded the produced transient waveform and the fault distance obtained is l4 = 19.82 km. 60

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Fig. 8 Transient waveform generated by injected unipolar pulse signal when a fault occurred on the grounding electrode line, 20 km away from the measurement point (under different pulse width) a Pulse width is 32 µs b Pulse width is 16 µs

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The results of the four above fault location are close, so we take the average value as the final ranging result: l = 41 (l1 + l2 + l3 + l4 ) = 19.78 km. 5.2.3

Remote Distance Fault

Setting the fault point 70 km away from measurement point on the grounding electrode line, with the type of non-metallic grounding fault, and the transition resistance is 1 Ω. Inject a unipolar pulse signal with width t1 = 64 µs at the measurement point. The transient waveform generated by the injected pulse signal is shown in Fig. 10. By analyzing the wave data of Fig. 10, the time interval between the pulse signal launched moment and the reflected wave received moment is Δt = 469 µs. Comparing to the normal state, the time interval between the pulse signal launched moment and the reflected wave received moment has significantly changed, indicating that there could be fault on the line. The result of the initial fault location is: l1 = 21 × 298 × 0.469 = 69.88 km. Figure 11 shows the transient waveform generated by the injected pulse signal recorded at the measurement point, when the pulse width is 32 µs and 16 µs, The fault distance obtained is l2 = 69.73 km and l3 = 70.03 km respectively. Figure 12 shows the case when injecting bipolar pulse signal (with width = 32 µs), measurement point recorded the produced transient waveform and the fault distance obtained is l4 = 70.03 km.

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The results of the above four fault location are close, and we take the average value as the final ranging result: l = 41 (l1 + l2 + l3 + l4 ) = 69.92 km.

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Results Statistics

Table 1 gives the final ranging results obtained by injected pulse signal method when the non-metallic ground fault occurs in six different locations on the DC grounding electrode line. It can be seen that the ranging error of injected pulse signal method can be limited within 1.10%. Table 1 gives the final ranging results obtained by injected pulse signal method when the non-metallic ground fault occurs in six different locations on the DC grounding electrode line. It can be seen that the ranging error of injected pulse signal method can be limited within 1.10%. Table 1 Results statistics

Actual fault distance (km)

Ranging result (km)

Range error (%)

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0.57

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6 Conclusion In this paper, the simulation model based on PSCAD is established to verify a fault location method adopting injected pulse signal for grounding electrode line of HVDC transmission system. The fault location is based on detecting the time interval between the pulse signal launched moment and the reflected wave received moment at the measurement point. Furthermore, the fault location accuracy can be improved by changing the pulse width and the pulse polarity. When HVDC transmission system operating in bipolar operation mode, the traveling wave signal generated by the fault is rather weak to be detected reliably. While the injected pulse signals method can not only improve the detection sensitivity, but also detect the fault points with different pulse width and polarity, which improves the reliability and accuracy of fault location.

References 1. Ma J, Dawalibi FP, Ruan W (2005) Design considerations of HVDC grounding electrodes. In: Transmission and distribution conference & exhibition. IEEE, New York 2. Alwazah I, Nasyrov RR, Shaban F (2020) The importance of grounding in HVDC power transmission systems. In: 2020 International ural conference on electrical power engineering (UralCon), pp 131–135 3. Ge Y (1996) The principle and technology of new type of relay protection and fault location. Xi’an Jiao Tong University Press, Xi’an 4. Sawai S, Gore RN, Naidu O (2020) Novel traveling wave phase component-based fault location of transmission lines. In: 2020 IEEE international conference on power electronics, drives and energy systems (PEDES), pp 1–5 5. Andanapalli K, Varma BRK (2013) Travelling wave based fault location for teed circuits using unsynchronised measurements. In: 2013 International conference on power, energy and control (ICPEC), pp 227–232 6. Wang C, Jiang Y, Wang J et al (2014) The HVDC electrode line fault simulation on PSCAD/EMTDC. China Power 47(2):69–72 7. Zhang Y, Wang C, Chen P (2015) Analysis of propagation characteristics of transient traveling waves in HVDC grounding electrode line faults. China Electr Power 48(3):88–93 8. Chen P (2003) Modern traveling wave fault location for transmission line and its application. Xi’an Jiao Tong University, Xi’an 9. Cai X, Yang Y, Tian Y et al (2007) Study on fault location of distribution network for pulse transmission principle. Relay 35(2):1–6 10. Xu M, Bai C, Qin Y et al (2007) Method of power cable fault automatic location based on low voltage pulse. Relay 35(7):37–40 11. Shu H, Tian H, Zhang Y (2015) Research on short-circuit fault identification and fault location algorithm for HVDC electrode line. Power Grid Technol 39(12):84–91 12. Zhang Y, Shu H, Tian H (2015) Research on fault location algorithm for HVDC electrode line high impedance fault. Power Syst Protect Control 43(24):1–7

Research on Evaluation System of AC/DC Hybrid Distribution Network with Common High Frequency Bus Multi Port EER Yang Liu, Lisheng Li, Mingyang Li, Yong Li, Hejin Liu, Min Huang, Guoqiang Su, and Feng Wang Abstract A comprehensive evaluation method for energy effectiveness of AC/DC hybrid distribution network is proposed in this paper. This paper first analyzes the topology and main working mode of AC/DC hybrid distribution system with HFBEER, then analyzes the new factors affecting the effectiveness of AC/DC hybrid distribution system, and deduces the quantitative models of various factors. Then, from four aspects of medium voltage AC distribution network, EER and distribution transformer, low voltage DC distribution network and low voltage AC distribution network, the energy effectiveness evaluation index system of AC/DC hybrid distribution network with HFB-EER is constructed. Finally, taking a distribution network as an example, the effectiveness evaluation is carried out, and the results show that the improved evaluation index system can effectively evaluate the energy effectiveness. Keywords Electric energy router · Effectiveness · High frequency AC bus

1 Introduction With the access of a large number of distributed renewable energy, energy storage equipment, electric vehicles and other new loads in the power grid, the source end and load end of the distribution system present a strong uncertainty [1]. Due to the limitation of open-loop operation conditions, the traditional AC distribution system can not track and respond to the changes of distributed energy output and load quickly, and can not adjust the power flow continuously and accurately, which makes the system voltage deviation become an increasingly prominent problem in the operation and management of distribution network [2]. The introduction of DC distribution Y. Liu (B) · L. Li · H. Liu · M. Huang · G. Su · F. Wang State Grid Shandong Electric Power Research Institute, Jinan 250003, China e-mail: [email protected] M. Li School of Electrical Engineering, University of Manchester, Manchester M13 9PL, UK Y. Li State Grid Shandong Electric Power Company, Jinan 250001, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_29

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technology and the construction of AC/DC hybrid distribution system based on power electronic converter is an important means to deal with this challenge. AC/DC hybrid distribution system can give full play to the fast response characteristics of power electronic devices, and greatly reduce the power conversion link, which can realize the fast, flexible, continuous and accurate power and voltage regulation of distribution network under the condition of strong uncertainty of source and load [3]. On the other hand, with the development of power electronics, power semiconductor devices and magnetic materials, electric energy router (EER) has become a hot issue in industry and academia [4]. EER is a highly integrated, universal, open and compatible device. As the core equipment of AC/DC hybrid distribution system, it undertakes the functions of power conversion, coordination and control, and plays a key role in improving the flexibility, stability and reliability of AC/DC hybrid distribution system [5]. At the same time, because the EER has the function of energy routing, it can effectively control and allocate the energy flow in the AC/DC distribution network, so it can realize the rapid matching of the power demand of each line, realize the rapid adjustment of the power flow direction of each line, which is conducive to adjusting the power flow distribution in the system, thus reducing the network loss and improving the economy of the distribution network operation. Therefore, it is of great significance to carry out the effectiveness analysis and Improvement Research of AC/DC hybrid distribution system with common high frequency AC bus and multiport electric energy router (HFB-EER). At present, the effectiveness evaluation of AC distribution network is relatively mature, but the research on the effectiveness evaluation of AC/DC hybrid system is still lacking. Literature [6] established the technical and economic evaluation index system of AC/DC distribution network, but did not consider the impact of AC/DC hybrid distribution network structure and equipment on energy effectiveness; literature [7] established a more systematic energy effectiveness evaluation system of AC/DC distribution network, but did not consider the impact of power electronic equipment access; literature [8] conducted energy effectiveness evaluation for distribution network with power electronic transformer. The purpose of this paper is to analyze the effectiveness of AC/DC hybrid distribution system with HFB-EER. The calculation method of effectiveness analysis of AC/DC hybrid distribution system with HFB-EER is studied, and the general effectiveness evaluation model and evaluation index system are proposed, which lays the foundation for analyzing the operation effectiveness of AC/DC hybrid distribution system with HFB-EER.

2 Common High Frequency AC Bus Topology Figure 1 shows a simplified form of the proposed common high frequency AC bus electric energy router. The converter consists of four modules and four output ports. Module units 1, 2 and 4 are connected to the high frequency AC bus through high

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Fig. 1 High frequency AC bus electric energy router

frequency transformers (HFT), and module unit 3 is connected to the high frequency AC bus through high frequency inductor. Based on the idea of modular design, the structure of modular multi active bridge (MMAB) is proposed in reference [9]. The topology takes “H-bridge unit and highfrequency transformer” as a power module, and each module is connected to the high-frequency AC bus through HFT; the modules are combined on the DC side to meet the requirements of different power and voltage levels.

2.1 Mathematical Model of MMAB Because any two sub modules in MMAB can form DAB structure, which is the same as the single phase shift (SPS) control mode of DAB, the bidirectional regulation of power flow can be realized by changing the phase shift angle between H-bridges between ports. Therefore, the H-bridge of each MMAB sub module can be replaced by a high-frequency square wave, and the “Y” shape equivalent model of MMAB is shown in Fig. 2.

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Fig. 2 Equivalent model of MMAB

2.2 Main Working Mode The converter composed of multi module units in parallel has two states: uncontrolled rectifier mode and fully controlled mode. All modules in the converter actively participate in the commutation, and the turn-on and turn off of each switch is controlled by the driving signal of the controller. This mode is called fully controlled mode. The switching devices of some modules are in controllable state, and the driving pulse locking of the remaining modules is called uncontrolled rectification mode: (1)

(2)

(3)

The starting process of multi module in converter: In multi module converter, the control system of sub module is often powered from their DC bus. Before the DC bus voltage is established, the control circuit and driving circuit do not work and the switch tube is not controlled. Similar to the pre charging process of traditional DAB, the remaining modules are charged by a port module through high frequency AC bus, and the whole process is locked by the switching tube of charging unit. Port active standby or shut down: In normal operation, for multi port converter, when some ports do not need to work or are in standby mode, the corresponding module switch of the port is locked. The converter is in fault operation: For multi port converter, when one port fails, the other normal ports keep working. At this time, the system is in uncontrolled rectifier mode.

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3 Effectiveness Impact Factors The evaluation index system is composed of a series of evaluation indexes reflecting a certain characteristic of the evaluated object. The comprehensive effectiveness index system of distribution network is composed of a series of indexes reflecting the effectiveness characteristics of distribution network. It is a bridge between the influencing factors and the effectiveness level of distribution network. The key to accurately reflect the effectiveness level of distribution network is to select the correct effectiveness index, build an objective, reasonable and comprehensive effectiveness index system, and then select the correct effectiveness evaluation algorithm [10].

3.1 Selection Principle of Evaluation Index In order to build an objective, reasonable and comprehensive effectiveness index system, we can select the indexes of the comprehensive evaluation system of distribution network effectiveness according to the following four basic principles: (1) (2)

(3)

(4)

Systematic principle: The selected effectiveness evaluation index must be able to reflect the effectiveness of all aspects of the distribution network. Scientific principle: Each evaluation index should be independent of each other, but organically combined. Each index can independently reflect the nature of a certain aspect of distribution network effectiveness, and the correlation between indexes should be minimized to ensure the independence of indexes. The principle of objectivity: In order to objectively reflect the effectiveness of the distribution network, we should improve the evaluation method and select the objective, real, scientific and effective comprehensive evaluation index. Practical principle: The selection of evaluation index should also consider the feasibility and practicability. It should be easy to collect relevant information and easy for staff to use. The effectiveness situation reflected by the comprehensive evaluation index should be real and easy to analyze, and the index content should be clear and reasonable.

3.2 Energy Effectiveness Impact Factors The establishment of effectiveness evaluation system and evaluation model of AC/DC hybrid distribution network with common high frequency AC bus electric energy router is the basis of effectiveness analysis and improvement of the system. However, there are still some problems in the existing research, such as the influence of electric energy router is not considered, and the selection of effectiveness index is not reasonable [11]. Therefore, this paper analyzes the effectiveness of AC/DC hybrid distribution system with common high frequency AC bus and multi port electric energy router, and

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constructs a more comprehensive, effective and practical AC/DC distribution system effectiveness evaluation index system. Some of the main performance indicators are as follows: (1)

Access Capacity of Distributed Generation

When the distributed generation is connected to the distribution network, the distribution network will be transformed from a single power supply system to a multi power supply system [12], so the flow direction and distribution of power flow in the system will change. When the system power flow changes, the network loss of each line will also change, which will affect the operation effectiveness of the system. Figure 3 shows the topology before and after the distributed generation is connected to the distribution network. Before the distributed generation is connected, the network loss of the system is: 

PL ΔP = 3 U

2 RG + 3PL

(1)

If the capacity ratio of distributed generation is λ, it can be expressed as: λ=

PDG × 100% PL

(2)

After the distributed generation is connected, the current I DG at the network side of the distribution network and the current I DG at the branch where the distributed generation is located can be expressed as: Fig. 3 Topology before and after distributed generation connected to distribution network

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⎧  P 1−λ P − PDG ⎪  ⎪ ⎨ IG = G = L = PL U U U ⎪ λP L ⎪ I = ⎩ DG U

(3)

After the distributed generation is connected, the line loss of distribution network is as follows: 



ΔP = 3RG (1 − λ)

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2

 + 3PL + 3R DG λ

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2 (4)

Combined with (3) and (4), the change of distribution network loss before and after the connection of distributed power supply is as follows: 



ΔP − ΔP = 3

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(5)

RG , f (λ) has a Let f (λ) = 2λRG − λ2 RG − λ2 R DG , when λ = λm = RG +R DG maximum. Therefore, when PDG < λm PL , the network loss of distribution network becomes smaller with the increase of DG access capacity; when PDG = λm PL , the network loss of distribution network is the smallest; when PDG > λm PL , the network loss of distribution network increases with the increase of DG access capacity; when DG access capacity is λm PL , the performance of distribution network is the best. However, due to the continuous change of the access capacity and load of distributed generation, it is still necessary to adjust the access capacity of distributed generation reasonably in order to improve the effectiveness of the system.

(2)

Effectiveness of Electric Energy Router

The effectiveness of electric energy router is also one of the key indicators to judge its performance. When the electric energy router is connected to the power grid, improving the conversion effectiveness of the electric energy router can reduce the cost of power generation, increase the effective part of the system power transmission, and even become the driving force of the industry technology development. Because in the AC/DC hybrid distribution system with high frequency AC bus and multiport electric energy router, the electric energy router is the transmission and transfer center of system energy. The higher the effectiveness of the electric energy router, the greater the effective transmission of power, and the better the operation effectiveness of the system. Therefore, the improvement of electric energy router effectiveness will be directly transformed into the growth of economic benefits. The effectiveness definition of the electric energy router is shown in (6).

E out × 100% ηp =

E in

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where, η p is the effectiveness of the electric energy router; E out is the total output power of all ports within the specified detection time (T), for a certain port: E out = T

E in is the total input power of all ports within the specified detection 0 Pout dt; T time (T), for a certain port: E out = 0 Pout dt.

4 Effectiveness Impact Factors The evaluation index system is composed of a series of evaluation indexes reflecting a certain characteristic of the evaluated object. The comprehensive effectiveness index system of distribution network is composed of a series of indexes reflecting the effectiveness characteristics of distribution network. It is a bridge between the influencing factors and the effectiveness level of distribution network. The key to accurately reflect the effectiveness level of distribution network is to select the correct effectiveness index, build an objective, reasonable and comprehensive effectiveness index system, and then select the correct effectiveness evaluation algorithm.

4.1 Index Analysis (1)

Index System Construction

According to the idea of analytic hierarchy process, the index layer of distribution network index system is divided into: O = {energy effectiveness level of distribution network}, A = {medium voltage distribution network, distribution transformer and electric energy router, low voltage DC distribution network, low voltage AC distribution network}, B = {power quality, economy, reliability, new energy, security, electric energy router control ability}, and p layer containing each single index. Refer to the relevant national standards and related literature [9] to establish the energy effectiveness index system of AC/DC hybrid distribution network, as shown in Fig. 4.

Fig. 4 A and B layer index system of hybrid distribution network

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For the indicators in layer A, the effectiveness of medium voltage DC distribution network, low voltage DC distribution network and low voltage AC distribution network is analyzed from five aspects of power quality, economy, reliability, new energy and security; the effectiveness of electric energy router and distribution transformer is analyzed from the aspects of economy and control ability of electric energy router, some indicators are as shown in the Fig. 4. The p layer contains each single index. According to the single index of p layer and its influence on the energy effectiveness level of distribution network, it is divided into positive index and negative index. In other words, if a single indicator is positively correlated with the level of energy effectiveness, it is a positive indicator, such as the proportion of distributed generation and the charging and discharging effectiveness of energy storage. The second is the reverse index, such as current harmonic distortion, three-phase imbalance, etc. Some p-layer indexes are shown in the Fig. 5. (2)

Index System Description

Medium voltage DC distribution network, distribution transformer and electric energy router, low voltage DC distribution network and low voltage AC distribution network can reflect the energy effectiveness level of distribution network from a macro perspective, so they are regarded as four parts of A-level index [13]. At the same time, because the energy effectiveness of the distribution network is closely related to the static equipment parameters and their corresponding operating conditions, the indicators of layer B are the corresponding power quality, economy, reliability, security, new energy and electric energy router control ability. The main innovation of the index system is the introduction of power electronic transformer related index, energy effectiveness index and distributed generation index. Considering the rapid development trend of electric energy router in the future, in this index system, the cost of EER, the effectiveness of EER and other related indicators are included in the evaluation index system. Therefore, in the four parts of layer a, the energy effectiveness index of ordinary distribution transformer is not simply considered, but the index of electric energy router is included together, as shown in Fig. 1, which improves the integrity of the evaluation index of AC/DC hybrid distribution network, and has reference significance for the energy effectiveness evaluation of AC/DC hybrid distribution network with EER in the future. Fig. 5 Some p-layer indexes

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4.2 Comprehensive Evaluation Model At present, most of the evaluation models use AHP to calculate the weight of the evaluation index. Although the method is relatively simple, if there are many evaluation indexes, the calculation amount of the judgment matrix will multiply, and the consistency test of the judgment matrix needs to be carried out. When the test fails, the judgment matrix needs to be adjusted. The calculation complexity is high and the steps are cumbersome. In view of the characteristics of many evaluation indexes in AC/DC hybrid distribution network, this paper proposes an improved grey correlation method to determine the index weight from the subjective and objective point of view to ensure the rationality of the index weight. (1)

Determination of Index Weight

Grey correlation analysis is a technology to analyze the correlation degree of various factors in the system, which can be used to determine the weight of the evaluation index by calculating the correlation degree of the value judged by the experience of the expert group. The greater the degree of correlation, the more important the index is in the whole index system, and the greater the weight is. However, the traditional grey correlation analysis method is easily affected by the value ρ of resolution coefficient in the calculation process, which makes the weight value of calculation subjective uncertainty, and brings inconvenience to the decisionmaking work. In order to overcome this defect, this paper uses the improved grey correlation analysis method to solve the index weight [14]. The specific calculation method and steps are as follows: (1)

Determine the evaluation index and initial weight value. M experts are set to make empirical judgment on the weights of N evaluation indexes at the same time, and the empirical judgment data sequence of each index weight is obtained. The matrix form is shown in (7) and (8). A = [A1 , A2 , · · · An ]T

(7)

⎞ a11 . . . a1m ⎟ ⎜ A = ⎝ ... . . . ... ⎠ an1 · · · anm

(8)

⎛

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Determine the reference sequence A0 , that is, select a maximum weight value from the empirical judgment matrix A as the “common” reference weight value, and each expert’s reference weight value is given this value, see Eq. (9). A0 = (a01 , a02 , · · · , a0m )

(3)

(9)

Calculate the distance between each index sequence A1 , A2 , …, An and the reference data column A0 , as shown in Eq. (10).

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0.3207

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0.2657

A3

0.2003

A4

0.2133

D0i =

m 

(a0k − aik )2

(10)

k=1

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Calculate the weight of each index and normalize the index. ωi = 1/(1 + D0i ) ωi = ωi /(

n 

ωi )

(11)

(12)

i=1

Through the pure numerical calculation method, on the basis of making full use of the subjective information of expert experience judgment value, the objectivity of the calculation process is ensured, so that the weight obtained reflects the subjective and objective degree at the same time. The weights of some indicators are shown in Table 1. (2)

Index Scoring Method

Firstly, the micro evaluation indexes are divided into three categories: benefit index, cost index and specific index. Among them, benefit index means that the score increases with the increase of index value; cost index means that the score increases with the decrease of index value; and specific index means that the score is the highest when a value or sub interval in the middle is selected. Then, according to the different types of indicators and ideal values of indicators, a reasonable scoring standard is established, that is, the corresponding relationship between the value of indicators and the score of indicators.

4.3 Example Analysis Based on the operation data of a regional distribution network, this paper evaluates the energy effectiveness of AC/DC hybrid distribution network with simulation to verify the practicability of the evaluation system. In Table 2, the values and scores of the micro evaluation indexes under the economy of electric energy router and distribution transformer are counted. By multiplying the corresponding weights and scores of each index, the score of development

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Table 2 Some basic indexes of evaluation objects Index B

Index p

Score

Weight

Total score

Economy

EER efficiency

91

0.5703

90.4485

EER cost

90

0.1267

Power density of EER

88

0.0600

Electrical isolation of EER

90

0.0248

Reactive power compensation capability of EER

87

87

Efficiency of distribution transformer

90

90

Load rate of distribution transformer

93

93

Table 3 Total score of AC/DC hybrid distribution network Total score

Index score of layer A

88.7018

A1

A2

A3

A4

88.2098

90.3580

88.7809

87.3043

Table 4 Effectiveness grading standard Comprehensive score

≥90

[80,90)

[70,80)

[60,70)

D3 > D2 > D5 > D4

(2)

The degree of importance between adjacent indicators is: 1.6, 1.2, 1.4, 1.2. The judgment matrix R1 is constructed as follows: ⎛

⎞ 1 1.920 1.600 3.226 2.688 ⎜ 0.520 1 0.833 1.680 1.400 ⎟ ⎜ ⎟ ⎜ ⎟ R1 = ⎜ 0.625 1 1 2.016 1.680 ⎟ ⎜ ⎟ ⎝ 0.310 0.595 0.496 1 0.833 ⎠ 0.372 0.714 0.595 1.200 1

(3)

The largest eigenvalue of this matrix λmax = 4.9642. At this time, the corresponding feature vector that is normalized is ζ 1 . ζ 1 = (0.3560, 0.1856, 0.2153, 0.1105, 0.1326). Then we check the consistency of matrix, C R < 0.1, so the matrix meets the consistency requirement. In the same way, the subjective weights of three equivalent indicators that consider power quality can be obtained. ζ 2 = (0.3684, 0.3684, 0.2632). According to expert opinions, the weight ratio of the two types of indicators is 7:3, so the final subjective weight is: ζ = (0.2492, 0.13, 0.151, 0.077, 0.093, 0.1104, 0.1104, 0.0789).

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3.2 Determination of Objective Weight The entropy method is a typical objective weighting method, which determines the index weight according to the amount of information contained in each evaluation index in the original data [6]. This method can effectively use the value of the data. The basic steps are as follows: Standardization of indicators: the standardized data matrix B can be obtained: ⎡ ⎤ 0.859 0.144 0.382 0.002 0.450 0.996 0.129 0.662 (4) B = ⎣ 0.996 0.002 0.002 0.224 0.002 0.002 0.002 0.996 ⎦ 0.002 0.996 0.996 0.996 0.996 0.223 0.996 0.002 Calculate the entropy weight of each evaluation index according to [6, 7], and the results are as follows: v = (0.0901, 0.1591, 0.1120, 0.1374, 0.1056, 0.1376, 0.1641, 0.0940).

3.3 Determination of Comprehensive Weight A single assignment method is easily affected by the weighting method and leads to deviations. AHP relies too much on expert opinions and entropy method often leads to equalization of indicator weights [7]. In this paper, the multiplicative weighting method is used to determine the overall weight. The subjective weight is w = (w1 , w2 , …, wn ), and the objective weight is v = (v1 , v2 , … vn ). On this basis, the comprehensive weight can be calculated as: ω=

wi vi (i = 1, 2, · · · n) n wjvj

(5)

j=1

3.4 Comprehensive Evaluation Based on Fuzzy Matter-Element Model The compound Fuzzy Matter-element is used in this paper to evaluate the reliability of power supply. According to reference [5, 8], the specific evaluation process is as follows. Difference Square Compound Fuzzy Matter-element can be calculated:

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⎡

4 × 10−6 ⎢ 1 × 10−6 RΔ = ⎢ ⎣ 0 5 × 10−7

0 0 0 0 0.81 0.445 0.25 0.36 0.83 0.563 0.44 0.56 0.84 0.544 0.07 0.61

⎤ 0 0.0074 1.6 × 10−3 0.25 0.2948 4 × 10−4 ⎥ ⎥ ⎦ 0.39 0.4835 0 −4 0.72 0 1.66 × 10

(6)

Calculation of Approach Degree: The closeness degree reflects the closeness of the evaluated index value to the standard index value [8]. This paper uses the Euclid approach degree as the evaluation standard, and its calculation formula is: ⎡ ⎥ ⎥ m ωi j Δi j ρ Hi = 1 − ⎥

(7)

j=1

where ωij is the weight value corresponding to each evaluation index. ρH i represents the closeness between the sample i and the evaluation standard. The classification standard for the evaluation levels (excellent, qualified, and poor) of the three regions are shown in Table 4. Therefore, each evaluation sample can be ranked and graded according to the value of ρH i . According to the weight values of S i in Table 3 and evaluation levels standard in Table 4, the ρH i of three power supply regions are calculated. The results are shown in Table 5. Table 3 Comprehensive weight value of 8 indicators in each region Region

D1

D2

D3

D4

D5

D6

D7

D8

S1

0.1883

0.1735

0.1418

0.0887

0.0824

0.1201

0.1431

0.0622

S2

0.2013

0.1956

0.1249

0.0986

0.1055

0.1009

0.1221

0.0511

S3

0.2365

0.2022

0.1655

0.1122

0.1219

0.0587

0.0828

0.0202

Table 4 Classification of evaluation levels in each region Index

D1

D2

D3

D4

Regions

S1

S2

S3

S1

S2

S3

S1

S2

S3

S1

S2

S3

Excellent

99.99

99.95

99.90

0.87

4.38

8.76

1

2

2

5

7

10

Qualified

99.90

99.90

99.80

8.76

8.76

13.10

3

4

5

10

12

15

Poor

99.80

99.70

99.60

10.00

10.00

15.00

4

6

7

15

17

20

Index

D5

D6

D7

D8

Regions

S1

S2

S3

S1

S2

S3

S1

S2

S3

S1

S2

S3

Excellent

20

30

40

3

3

5

5

7

8

99

98

97

Qualified

50

60

70

6

10

15

10

12

15

97

96

95

Poor

80

90

100

8

12

18

15

17

22

95

94

95

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Table 5 Euclid approach degree of the three regions Regions

Excellent

Qualified

Poor

ρH i

S1

0.9659

0.4276

0.3473

0.3944

S2

0.6654

0.4444

0.3745

0.7587

S3

0.9901

0.5990

0.4945

0.3854

The evaluation results can be seen from Table 5: (1) The ρH 1 of S 1 is between 0.3473–0.4276, and its evaluation grade is qualified; (2) The ρH 2 of S 2 is higher than 0.6654, and its evaluation grade is poor; (3) The ρH 3 of S 3 is less than 0.4945, and its grade is poor.

4 Conclusion Due to the difference of user demand, the traditional reliability evaluation of distribution network has limitations. The difference in user needs has been considered in the process of determining the weight of the evaluation system indicators in this paper. And the requirements of power supply reliability and power quality are considered comprehensively. A new power supply reliability evaluation index system has been established. Comprehensive evaluation from both the network side and the user side through 8 evaluation indicators. AHP and entropy weight method are used to determine the index weight. The comprehensive weighting method that combines subjective and objective not only can determine the power supply requirements of different levels of load based on expert suggestions, but also can fully mine the information of the original data. The weight difference of the evaluation index of different levels of load has been guaranteed. Finally, the calculation example verifies the effectiveness of the proposed index and evaluation method, which can more accurately reflect the power supply region where the power supply level and user demand are more contradictory. Therefore, the work in this paper provides more accurate reference information for the optimization of the power supply reliability scheme. Funding: State Grid Shandong Electric Power Company Science and Technology Project Funding “Research on Key Technologies of Highly Reliable Power Supply in Guzhenkou Innovation Demonstration Zone” (5206002000T2).

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References 1. Jianguo L, Lin C, Lei L, Mei H (2020) Analysis of the characteristics of the differentiated electricity consumption behavior based on the subdivision of the customer group. Power Syst Clean Energy 36(10):68–72 2. Hui Q (2021) Analysis on power supply reliability of power distribution network. Electric Technol Econ 01:27–30 3. Danling C (2019) Reliability ealuation and analysis of distribution network based on electric energy data. South China University of Technology 4. Sallam AA, Desouky M, Desouky H (1990) Evaluation of optimal-reliability indices for electrical distribution systems. IEEE Trans Reliab 39(3):259–264 5. Liyuan L (2018) Research on power supply reliability evaluation of distribution system considering user experience and power quality. South China University of Technology 6. Bihan Z, Zhongdong Y, Haisen Z (2016) Power quality comprehensive evaluation for low-voltage DC power distribution system. Electric Power Constr 37(05):125–131 7. Milanovic JV, Abdelrahman S, Liao HL (2018) Compound index for power quality evaluation and benchmarking. IET Gener Transm Distrib 12(19):4269–4275 8. Gang L, Wei G, Xiaodong Y (2009) Application of gray theory in power quality comprehensive evaluation. Smart Grid 29(11):62–65+70

Research on LC Ratio of Metro Traction Drive System Applied in Oscillation Analysis Jing Gu, Jinsong Kang, and Wanlu Guo

Abstract Metro is a kind of green transportation with low energy consumption and large capacity, which has the characteristics of high speed, high efficiency and low pollution. In the metro traction drive system, due to the negative impedance introduced by the traction motor and the limited selection of filter parameters, it is likely to cause continuous oscillation of the DC bus voltage and current, resulting in system instability. In order to provide a theoretical basis for the suppression of oscillation, the stability analysis of the simplified second-order system is carried out by the Routh criterion in this paper. In addition, the small signal equivalent model of the system considering the motor control module is established and the Nyquist stability criterion is used to analyze the system stability. The simulation results show that the stability analysis method based on simplified second-order system is more intuitive, and the accuracy is not reduced when the errors of the two methods and the actual simulation results are 2.6% and 5.9% respectively. It has a good significance for the parameter selection of filter link in the traction drive system. Keywords Metro traction drive system · LC resonance · Small signal model

J. Gu College of Electronic and Information Engineering, Tongji University, Shanghai, China J. Kang (B) Institute of Rail Transit, Tongji University, Shanghai, China e-mail: [email protected] J. Gu · J. Kang · W. Guo The State Key Laboratory of Heavy Duty AC Drive Electric Locomotive Systems Integration, Zhuzhou, China W. Guo CRRC Zhuzhou Electric Locomotive Co, Ltd, Zhuzhou, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_35

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1 Introduction With the acceleration of the global urbanization process, the urban rail transit represented by the metro has responsibility for alleviating the increasingly serious urban traffic congestion problem. The traction drive system is the core part of the metro. At present, international equipment manufacturers such as Siemens and Bombardier have regarded the permanent magnet synchronous motor (PMSM) traction drive system as their research direction because of its significant advantages such as high power density, high efficiency, high power factor, low noise, and light weight. However, the DC bus oscillation of the traction system is one of the main problems encountered in the actual operation of the metro. Due to the negative impedance introduced by the traction motor, it is likely to cause continuous oscillation of the DC bus voltage and current. It will also cause traction motor torque ripple as well as the overvoltage and overcurrent fault protection. Therefore, system stability analysis is particularly important. The steps of system stability analysis mainly include modeling and analysis. There are two modeling methods. One is the ideal constant power load (CPL) model, in which the traction converter and the traction motor are equivalent to a controllable current source [1, 2]. The other is the traction drive system frequency domain model, which is obtained by linearizing the motor and its control module [3–5]. In the ideal CPL model, there are two methods for system stability analysis: one is to solve the system damping coefficient [6], and the other is the characteristic root locus of the coefficient matrix of the small signal equivalent state space equation. However, the above-mentioned literatures only discuss the influence of LC parameters on system stability but do not provide suggestions for selecting LC parameters. Two methods for judging the stability of the system are discussed in this paper. The first method is to simplify the system to a second-order system and judge the stability of the system by the Routh criterion. According to the principle of impedance ratio criterion, the second method derives the small signal model of the motor working in MTPA mode, and uses the Nyquist criterion for stability analysis. The PMSM traction drive system includes a DC traction network for power supply, a filter circuit composed of a filter inductor and a support capacitor, a traction converter and 4 traction motors, which is shown in Fig. 1.

2 Stability Analysis Based on Simplified Second-Order System The mathematical model of the system mainly consists of the DC bus filter circuit, the traction converter and the traction motor. Regarding the motor as a constant power load, assuming that there is no power loss in the traction converter, the converter and the motor can be equivalent to a

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433 Traction Motor

DC Traction Network

Traction Converter

Lf

M1

DC

Cf

M2 AC

M3

M4

Fig. 1 Schematic of traction drive system

controlled current source. The simplified equivalent circuit of the system is shown in Fig. 2. According to the state equation of the DC bus of the system, the characteristic equation is established s2 + (

R f PL Rf PL 1 − )s + (1 − 2 ) = 0 2 LfCf Lf C f u c0 u c0

(1)

where R f is the internal resistance of the inductor, L f is the filter inductance, PL is the power of the converter-motor system, C f is the support capacitance, and u c0 is the mean value of DC voltage. Based on the Routh criterion of the second-order system, the condition to stabilize the system is as follows

Rf

iL

Lf

Udc

ic

Cf

PL Udc

Uc

Yout Fig. 2 The simplified equivalent circuit of the metro traction drive system

Yin

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R f · u 2c0 Lf < Cf PL

(2)

From the first formula (2), the L f /C f needs to satisfy the inequality to make the system stable. It also reveals that as the capacitance increases and the inductance decreases, the traction drive system tends to be more stable.

3 The Stability Analysis Considering the Dynamics of the Motor and Its Current Controller 3.1 Dynamics of the Motor and Its Current Controller In the steady state, the voltage equation of PMSM can be expressed as 

u d = Rs i d − ωe L q i q u q = Rs i q + ωe (L d i d + ψ f )

(3)

where u d ,u q are d-q axis stator voltages, Rs is the stator resistance, i d ,i q are d-q axis stator currents, ωe is the rotor electrical angular velocity, L d ,L q are d-q axis stator inductances, ψ f is the permanent flux linkage. The electromagnetic torque equation of the PMSM is Te =

3 · pn [ψ f · i q + (L d − L q ) · i d · i q ] 2

(4)

where pn is the number of pole pairs of the PMSM. The kinetic equation of the PMSM is J

dωr = Te − Tl dt

(5)

where J is the moment of inertia, ωr is the mechanical angular velocity, Tl is the torque load. Maximum Torque per Ampere (MTPA) control is adopted in this paper. The current regulator adopts the PI regular, which can be described as ⎧ K id ∗ ⎪ )(i d − i d ) − pn ωr L q i q ⎨ u ∗d = (K pd + s ⎪ ⎩ u ∗ = (K + K iq )(i ∗ − i ) + p ω (L i + ψ ) pq q n r d d f q q s

(6)

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where K pd , K id are the proportional coefficient and integral coefficient under d-axis, K pq , K iq are the proportional coefficient and integral coefficient under q-axis, i d∗ , i q∗ are the reference values of the given current under d-q axis, u ∗d , u q∗ are the reference values of the given voltage under d-q axis.

3.2 System Transfer Function The open-loop transfer function of the system is G(s) = Yin /Yout , where Yin is the input admittance and Yout is the output admittance, which is shown in Fig. 2. When the system is in steady state operation, the small signal equivalent model of the system is established, and the system disturbance ΔTL = 0, Δi q∗ = 0, Δi d∗ = 0, and the input admittance is Yin =

Δi c Δu c

3i q0 1 ∗{ · {u q0 (Rs + s L q ) ∗ 2J s/[u c0 (Rs + s L q + G q (s) u c0 2 ψ f u q0 3 pn2 ψ f i q0 u d0 (L d − L q ) + ] + i d0 u q0 u c0 (Rs + s L q + G q (s) u c0 (Rs + s L d + G d (s) + =

u c0 (Rs +s L q +G q (s)

i q0 u d0 i d0 u q0 3 p 2 i d0 L d + n [(L d − L q ) ∗ ( + ) u c0 (Rs + s L d + G d (s) u c0 (Rs + s L q + G q (s) 2J s ψ f u q0 L d u d0 (u d0 − i d0 (Rs + s L d) ]− } + u c0 (Rs + s L q + G q (s) i q0 L q u c0 (Rs + s L d + G d (s) u q0 (u d0 − i d0 (Rs + s L d )) u d0 (Rs + s L d ) 3i d0 { + + 2 u c0 (Rs + s L d + G d (s) i q0 u c0 (Rs + s L q + G q (s)) − +

3 pn2 i q0 L q i q0 u d0 i d0 u q0 [(L d − L q ) ∗ ( + ) u c0 (Rs + s L d + G d (s) u c0 (Rs + s L q + G q (s) 2J s

2 3u q0 3u 2d0 ψ f u q0 ]} + + − i c0 } 2u c0 (Rs + s L d + G d (s) 2u c0 (Rs + s L q + G q (s) u c0 (Rs + s L d + G q (s) (7)

The output admittance is Yout =

L f C f s2 + R f C f s + 1 L fs + Rf

(8)

436 Table 1 Parameters of metro traction drive system

J. Gu et al. Parameters

Symbols

Value

Units

DC bus voltage

Udc

1500

V

Rated power

P

300

kW

Rated speed

we

2600

rpm

Stator resistance

Rs

0.5

Ω

d-axis inductance

Ld

10

mH

q-axis inductance

Lq

20

mH

Number of motor pole pairs

pn

2

–

Motor flux

ψf

0.9

Wb

Filter inductance

Lf

4

mH

Support capacitor

Cf

5

mF

Inductance internal resistance

Rf

0.04

Ω

4 Simulation Verification and Analysis 4.1 The Stability Analysis Result Based on Simplified Second-Order System The parameters of the metro traction drive system are shown in the Table 1. Substitute the parameters into, we can get the stability analysis result of the simplified second-order system is L f /C f < 0.9701. It reveals that the condition for the system stability is that the L f /C f is less than 0.9701.

4.2 The Stability Analysis Considering the Dynamics of the Motor The result of the Nyquist criterion stability analysis of the system is shown in Fig. 3. In the figure, each point represents the stability of the system under the set of system parameters, among which, black represents instability and red represents stability. Select critically stable and unstable points in the figure for fitting. The slopes of their first-order function fitting are all 1.055.

4.3 Stability Verification of the Metro Traction Drive System This section will verify the ratio through simulation. The operating condition of the system is constant load acceleration. The given load torque is 400 N m, and the given speed reference is 2000 rpm.

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Fig. 3 System stable and unstable point diagram obtained from the transfer function

It can be seen from Fig. 4b that when the system resonates, the voltage of the support capacitor oscillates. The fast Fourier transform analysis shows that the oscillation frequency is 25 Hz which √ is shown in Fig. 5. At the same time, the LC resonance frequency is also 1/(2π L f C f ) = 25 Hz. It can be considered that the instability of the system is caused by the LC resonance. Sorting out the simulation results of the system under multiple sets of parameters, it can be seen that the slopes of the first-order function fitting are all 0.9959. Combining the above model analysis and simulation results, the comparison result shown in the Fig. 6 below can be obtained. Line L f = 0.9959 ∗ C f represents the analysis result of the simulation data.

Fig. 4 Simulation waveform of metro traction drive system

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Fig. 5 FFT analysis of capacitor voltage

Fig. 6 Comparison of the three sets of results

J. Gu et al.

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Line L f = 0.9701 ∗ C f represents the analysis result of the simplified secondorder system. The error between it and the simulation result is only 2.6%. Therefore, it is considered effective. Line L f = 1.055 ∗ C f represents the analysis result of the Nyquist stability criterion. The error between it and the simulation result is 5.9%, which can be considered as in line with reality.

5 Conclusion The relationship between the stability of the metro traction drive system and the parameter configuration of the filter link is studied in this paper. Based on the Routh criterion of the simplified second-order system and the Nyquist stability criterion of the open-loop transfer function of the small signal model, the results are as follows: when other parameters are determined, the system stability depends on the filter link. There is such a proportional function, when the operating point is below the function, the system is stable, and vice versa. The two adopted stability judgment methods are verified by simulation. The simulation results show that the stability analysis method based on simplified second-order system is more intuitive, and the accuracy is not reduced when the errors of the two methods and the actual simulation results are 2.6% and 5.9% respectively. It has a good significance for the parameter selection of filter link in the traction drive system.

References 1. Sun DN, Liu ZG, Lin WL, Diao LJ (2011) Research on DC-link oscillation suppression strategy in metro traction converter. J China Railway Soc 33(8):52–57 2. Zhao LT, Diao LJ, Dong K, Liu ZG (2013) Stabilization control for metro traction converter— motor system. Trans China Electrotech Soc 28(6):102–107 3. Fang XC (2016) Permanent magnet synchronous traction motor control and inverter DC-link oscillation suppression for urban rail train. Doctor Degree Thesis. Beijing Jiaotong University, pp 75–95 4. He WL (2020) Based on active damping oscillation suppression strategy to solve the DC voltage of traction converter oscillation problem. Master Degree Thesis. South China Univer-sity of Technology, pp 26–55 5. Liutanakul P, Awan AB, Pierfederici S, Babak NM, Farid MT (2010) Linear stabilization of a DC bus supplying a constant power load: a general design approach. IEEE Trans Power Electron 25(2):478–488 6. Zhang Y, Wang HM, Ge XL (2018) DC-link stabilization method for metro traction convertermotor system based on feedforward voltage compensation. Proc CSEE 38(09):2728–2735+2842

A Feature Analysis and Clustering Method Based on User Electricity Data Qiao Yu, Yan Wen, Hailei Meng, Xiaoyue Li, Zilong Liang, Xiaoyan Yang, and Zhaoyuan Liu

Abstract The development of smart grids has been facilitated by advances in power electronics technology. Huge amounts of data are collected and some problems have arisen. In order to solve the problem of the rapid increase of electricity data collection and the difficulty of power distribution calculation and control, a user classification method based on the user’s response to each change has been proposed. This paper deals with the data and extracts the user behavior characteristics. Aiming at the shape of load curve or the characteristics of daily load, this paper further classifies users according to their response to changes on the basis of the previous methods of user classification. The ultimate goal is to implement user tags to make data processing faster. This paper takes a real electricity consumption data as the data source. Large amounts of data are processed and users are classified through simulation calculations. This classification method has been proved to be effective. Keywords User behavior analysis · Clustering analysis · User classification

1 Introduction Smart grid is the development direction of the future power system, and it is also one of the most important application fields of big data. The progress of electricity information acquisition system has brought about a large amount of power distribution data, and the behavior analysis and classification of power users has become a part of the construction of smart grid [1]. Meanwhile, clustering analysis method plays a dominant role in load analysis. Reasonable power consumption strategies should be developed from the change rule of load curve and electricity consumption, which can help the power grid to understand users’ personalized and differentiated service Q. Yu (B) · X. Li · Z. Liang · X. Yang · Z. Liu Qingdao Power Supply Company, State Grid Shandong Electric Power Company, Qingdao 266002, China e-mail: [email protected]; [email protected] Y. Wen · H. Meng State Grid Shandong Electric Power Company, Jinan 250001, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_36

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demands. It is of great significance to improve the reliability of power supply and to make load scheduling plan and operation control. At present, there have been many researches on user classification. An appliance signature identification solution for appliance signature is proposed in [2]. The feature optimization and clustering number optimization methods are proposed in [3, 4]. This method only targeted at the existing common features. At present, the existing research mainly classifies users according to the shape or characteristics of the loadday curve. Increasingly diverse user types and user needs are not being met. Now, a more detailed user classification method is needed. In this paper, the effects of holidays and temperature are taken into account. Based on the existing classification, a method of subdividing users according to their responses to different factors is proposed.

2 Data Prepocessing and Characteristics Analysis 2.1 Cleaning Data Smoothing the outliers in the data. Complete missing data and carry out horizontal and vertical processing. The load data obtained within 2 h before and after are taken as the benchmark data, and the missing values are smoothing by means of average value. Standardization is the scaling of data to make it fall into a small specific interval. The data unit limit is removed, and it is transformed into a dimensionless pure value. There is no general rule to follow in the selection of data standardization methods.

2.2 Select Typical Data The typical load curve can be used to analyze the characteristics of regional load power consumption and simplify the calculation. This paper attempts to use Pearson Correlation Coefficient to select typical data. Pearson’s correlation coefficient measures a linear correlation [5]. Correlation coefficient r is: n

(xi − x)(yi − y) 2 n 2 i=1 (x i − x) i=1 (yi − y)

r = / n

i=1

(1)

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443

2.3 Feature Extraction Due to the limitation of calculation and information acquisition, users’ electricity load is usually taken as the data source to extract features to represent the characteristics of users’ electricity behavior. The classification standard of power users is determined by the characteristic quantity. Before clustering the data, it is necessary to select the appropriate characteristic vector. Common features of user classification include daily average load, daily load rate, peak power consumption rate, valley power coefficient, etc. [6]. Each feature has a certain relationship with the electricity consumption behavior, but the clustering results will be affect by too many features. Sometimes it is important that functionality be optimized and weights calculated.

3 Elaborate Behavior Analysis When carrying out load forecasting, other influencing factors need to be taken into account in the analysis of user behavior. The calculation time is relatively long when large amount of user data are being calculated. In this paper, the influence of external factors is also taken as a classification standard. By calculating the influence, the users can be further finely divided. And the users who will change greatly due to the change of external factors can be accurately found. This can improve the quality of power supply service and facilitate load forecasting.

3.1 Single Temperature Effect Response Coefficient Due to travel changes of users during holidays, the load of residential users will usually increase to a certain extent, and the peak power consumption rate will easily be affected by it. But there are also some users may be due to the nature of work or other reasons, holidays have a small impact on their load changes. In this paper, the influence is calculated by weighting the ratio of average daily load to peak power consumption rate on typical days of weekdays and holidays: μday = α1 ·

βday Pday + α2 · −1 βnor Pnor

(2)

where α1 and α2 are the weights, and α1 +α2 = 1, Pday and βday are the average daily load and peak hour power consumption rate at typical normal temperature and holidays respectively; Pnor and βnor are the average daily load and peak hour power consumption rate at typical normal temperature and non-holidays respectively.

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3.2 Single Temperature Effect Response Coefficient When the temperature is too high or too low, the user will usually turn on the air conditioner or other refrigeration and heating equipment. The grain electric coefficient is going to be affected by turning on the electric appliance for a long time. However, different users have different tolerance to temperature changes. In this paper, the ratio of the daily average load and grain current coefficient obtained on weekdays and typical days with high temperature is weighted to calculate the reaction size: μtem = α3 ·

γtem Ptem + α4 · −1 Pnor γnor

(3)

3.3 Double Effect Response Coefficient User behavior can be influenced by both holidays and temperatures. There is not necessarily a positive correlation between the two factors for specific categories of users. In this paper, the ratio of the average daily load, peak power consumption rate and valley power coefficient of the obtained normal and high temperature holidays is weighted to calculate the reaction size: μdt = α5 ·

Pdt βdt γdt + α6 · + α7 · −1 βnor γnor Pnor

(4)

4 Case Study Results The data used in this paper came from UMASS Smart Dataset of MIT, ‘The Apartment Dataset contains data for 114 single-family Apartments for The period 2014–2016’. The standardized method is selected with range normalization.

4.1 Load Morphology Clustering In order to reduce the influence of some users’ special load curve shape on user response clustering, the user load shape clustering is first carried out. The clustering results of the first type of user load patterns are shown in Fig. 1, including 31 users in total.

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Fig. 1 The first type of load form user clustering results

From the first type of load shape diagram, it can be seen that the load curve shape of this type of user is relatively close, and if there is a characteristic change, it can be clearly expressed from the curve, which is suitable for further classification analysis.

4.2 User Response Clustering The typical day of normal temperature non-holiday on April 2, normal temperature holiday on 5, high temperature non-holiday on 14, and high temperature holiday on 12 are selected to calculate the response coefficients of users of the first type of load. Take α1 =α3 = 0.6, α2 =α4 =α5 =α6 = 0.4, α7 = 0.2. K-means algorithm is used for clustering. The results of the clustering are shown in Fig. 2: It can be seen that strong responses to high temperature are shown by the second type of users, but not to holidays. This type of users may work at home or without holidays such as power or supermarket industry. Obviously responses to holidays are shown by the fourth type of users load but they are less responsive to holidays when the temperature is high. This type of users may prefer to go out on high-temperature holidays. Strong response to holidays and certain response sto high temperature are shown by the fifth type of users, and there is a certain positive correlation between the

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Fig. 2 Clustering results of users’ response coefficients

two factors. Therefore, attention should be paid to such users during high temperature holidays.

4.3 Verify the Results In addition, some dates separately are selected for verification. The range for each category is set. When the results of the second experiment did not exceed the verification range, the user’s category is considered unchanged. Set up the range where the response is not obvious is 0 ≤ α < 0.12. The range where the response to a certain degree is 0.08 ≤ α < 0.22. The range where the response is strong is α ≥ 0.18. The change results of each group are obtained by calculation (Fig. 3). The results show that most of the loads are in the original category. It proves that this classification method is effective. According to the experimental results, when predicting the load state or planning the power supply, the loads that are most likely to have great changes and those that do not have great changes can be find through the data of the corresponding factors.

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Fig. 3 Changes in various categories

This user classification method can be used as a reference for load forecasting and power supply planning and simplified calculation.

5 Conclusion In this paper, based on the previous methods of user classification for the shape of load curve or the characteristics of daily load, the user’s response to the change is further classified. The simulation is carried out to verify. The effectiveness of the analysis of users’ power consumption behavior is improved by above work and some information support for the relevant operation scheduling and load forecasting are provided. However, this paper only carries out simulation verification on the influence of high temperature and holidays. In addition, there are many other factors that can participate in user classification, and further study is needed in their correlation. Meanwhile, the calculation method of user response size needs to be improved. Acknowledgements Funding: State Grid Shandong Electric Power Company Science and Technology Project Funding “Research on Key Technologies of Highly Reliable Power Supply in Guzhenkou Innovation Demonstration Zone” (5206002000T2).

References 1. Shen Y, Lu Y, Chen R (2016) Power user behavior analysis and application status based on big data technology. Electr Autom 50–52 2. Chui KT, Tsang KF, Chung SH, Yeung LF (2013) Appliance signature identification solution using K-means clustering. In: IECON 2013—39th annual conference of the IEEE industrial electronics society, pp 8420–8425 3. Lu J, Zhu Y, Peng W, Sun Y (2017) Feature selection strategy for electricity consumption behavior analysis in smart grid. Autom Electric Power Syst 58–63+83 4. Gong G, Chen Z, Lu J, Wang C, Qi B, Cui G (2018) Clustering optimization strategy for electricity consumption behavior analysis in smart grid. Autom Electric Power Syst 58–63

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5. Wu J, Ting L, Ren J (2020) Parameter automatic optimization for feature selection fusion algorithm. Comp Syst Appl 145–151 6. Chen Z (2019) Intelligent analysis method of demand side user state under energy interconnection. North China Electric Electron Eng

Identification of Weak Links in Active Distribution Network Based on Vulnerability Assessment Yongchun Yu, Shu Mao, Hailei Meng, Chenyu Zhao, Xiankai Chen, and Chaoqun Zhou

Abstract With the large amount of distributed energy and intermittent load access, the operation risk of distribution system is increasing day by day. In order to improve the reliability of power supply in distribution network, weak link identification must be indispensable. Aiming at this problem, this paper proposes a weak link identification method for active distribution network (ADN) based on vulnerability assessment. Firstly, considering the correlation of distributed generators’ output, some index of vulnerability assessment based on complex network theory is proposed. Then, considering the N−1+1 of the line, combined with the repeated power flow calculation method, the line power supply weakness index is proposed. Finally, an example is given to demonstrate the effectiveness of the proposed method. The results show that the proposed method based on vulnerability assessment is effective. The weak links in the distribution network can be quickly identified by this method. The identification results can assist the scheduler to make decision. Keywords Active distribution network · Vulnerability assessment · Weak links

1 Introduction With the large amount of distributed energy and intermittent load access, the operation risk of distribution system is increasing day by day [1]. There are weak links in the active distribution network that are affected by the correlation of distributed generator output. Accurate identification of weak links can provide scientific guidance for the Y. Yu (B) · S. Mao Power Reliability Management and Project Quality Supervision Center, National Energy Administration, Beijing 100031, China e-mail: [email protected]; [email protected] H. Meng · C. Zhao State Grid Shandong Electric Power Company, Jinan 250001, China X. Chen · C. Zhou Qingdao Power Supply Company, State Grid Shandong Electric Power Company, Qingdao 266002, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_37

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control of electric power devices [2, 3]. Vulnerability assessment is a key method to identify weak links, which focuses on the topological vulnerability of the grid structure [4]. When these nodes or lines are affected by external influences or system interference, they will cause successive failures of line components and cause largescale power outages, which can be identified as the weak link. In References [5] and [6], it calculates voltage risk indicators and their rate of change indicators based on fuzzy reasoning, a vulnerability index reflecting the voltage level is established. From the above review, it can be seen that data-based distributed generator output correlation is rarely considered in vulnerability assessment. Therefore, it is necessary to reorganize the vulnerability indicator evaluation process from the perspective of weak link identification, and use nodes and lines as the evaluation object, focusing on the location of each indicator. A method for identifying the weak links in ADN based on vulnerability assessment is proposed in this paper.

2 Index of Vulnerability Assessment Based on Complex Network Theory The traditional characteristic quantity of complex network is no longer suitable for active distribution network. It requires certain improvements to traditional indicators such as degree and betweenness in this paper.

2.1 Node Degree and Line Degree The traditional definition of node degree and line degree cannot reflect the difference between nodes with the same degree, so certain improvements are needed: ⎧ ⎨ DN i = ⎩D = u

Di  2 D j=V ad

Zu √ D

Dj (1)

D N i1 D N i2

where: Di is the number of nodes connected to node i; V ad is the set of all nodes connected to node i. The degree of the node defined in the formula takes into account the sum of the degrees of all nodes connected to it.

2.2 Node Injection Power The injected power of the node can reflect the importance of the node in transmitting and allocating power. This paper considers the multiple scenarios of the correlation

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of distributed power output, and proposes that the node injected power is: N Pi

N 1  = λs Pis Sb s=1

(2)

where Pis is the injected power of node i in the correlation scenario s. λ is the probability of the occurrence of the correlation scene.

2.3 Node Betweenness This paper considers the output correlation of distributed power sources, and further improves the indicator based on multiple scenarios of output correlation. BN i =

N  s=1

As (i ) =

λs

Uis s A (i) Ub



Iisj (i )

(3) (4)

j∈Vad

where: Uis is the voltage of node i under scenario s.

2.4 Line Betweenness This paper proposes the line betweenness considering distributed generator output correlation scenarios. The expression is: B Li =

N  s=1

λs

Pisj Pi j max

Iisj (i )

(5)

On the one hand, the expression reflects the transmission capacity of the line in the network topology, and on the other hand, the ratio to Pij max reflects the power transmission capacity of the line under the current operating state of the distribution network.

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3 Line Power Supply Weakness In order to better reflect the weakness of the components in the power supply capacity of the distribution network. Based on the evaluation and calculation of power supply capacity, this paper proposes the line power supply weakness index.

3.1 Calculation of Power Supply Capacity In this paper, the power supply capacity calculation method based on repeated power flow is adopted to calculate the power supply capacity. The constraints include node voltage constraints, line and transformer capacity constraints, as is shown in (6). ⎧ 0.95 ≤ V j∗ ≤ 1.05 ⎪ ⎪ ⎪ ⎪ ⎨ i∗ ≤ 1 j ⎪ S ⎪ T ≤ Smax ⎪ ⎪ ⎩ S DG ≤ S DG max

(6)

where V j is the standard unit value of the voltage at node j, which is different from the standard for voltage deviation of 10 kV and below.

3.2 Line Power Supply Weakness Index This paper considers the N−1+1 of the line, combined with the repeated power flow calculation method considering the distributed power, and takes the load increase multiple K after the line N−1+1 as the line power supply weakness. Since there may be multiple options for closing the switch after the distribution network N−1+1, this paper also considers it as a part of the weak power supply of the line. Defining the weakness of line power supply is as follows HL i = K i n i

(7)

where K i is the maximum value of the load increase multiple in all closed tie switch schemes after N−1+1 is applied to line i; ni is the number of power supplies that can be closed tie switch to power loss load when line i is opened.

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4 Case Study Results In this paper, a typical IEEE 33-bus distributed system is used for simulation. The IEEE33-bus distribution network topology is shown in Fig. 1. Table 1 shows the distributed generator output correlation scenario. The method in Sect. 2 of this paper is used to calculate the component structure weakness evaluation index considering the output correlation. The simulation results show that when a certain index of the node is at the maximum, the other indexes are not at the maximum, or even very small. It can be seen that an indicator can only reflect some aspects, and it is necessary to comprehensively consider the various indicators of the node to determine whether it is a weak link. Calculating the power supply weakness of the line needs to consider the evaluation result of the maximum power supply capacity after N−1+1. In this paper, the N−1+1 simulation of the line is based on repeated power flow calculations. The network structure of the power distribution system changes after the failure of different lines and the transfer of supply through the lines. The vulnerability assessment results of the line can be obtained in Table 2. In the betweenness index, the corresponding index value of the line is relatively small, which is related to the generally small current value in the line. In the degree index, the line degree gives new characteristics to the traditional defined degree 19

20

21

22 PV1

1

2

3

4

5

6

26 23

24

8

7

27

25

9 10

28 29

11 12

30 31

32

13 14

15 16

17

18

33

PV2

Fig. 1 IEEE 33-bus distribution network topology

Table 1 Distributed generator output correlation scenario

Scenario

PV1 output/(kW)

PV2 output/(kW)

Probability

S1

333.2

359.8

0.076

S2

423.9

425.3

0.173

S3

568.7

552.1

0.199

S4

688.8

682.8

0.239

S5

810.3

828.5

0.223

S6

1000.5

992.1

0.089

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Table 2 Results of line vulnerability assessment Line

D Li

HL i

B Li

Line

D Li

HL i

B Li

1–2

0.065

0

0.904

17–18

0.275

1.709

0.054

2–3

0.919

3.141

0.614

2–19

0.260

3.383

0.030

3–4

0.508

5.285

0.335

19–20

1.546

3.140

0.021

4–5

0.366

5.385

0.331

20–21

0.368

3.438

0.019

5–6

1.247

5.432

0.288

21–22

0.349

1.732

0.011

6–7

0.713

3.797

0.029

3–23

0.678

1.523

0.037

7–8

0.570

3.699

0.051

23–24

0.748

1.543

0.050

8–9

0.867

1.807

0.055

24–25

0.337

1.629

0.025

9–10

0.911

5.385

0.057

6–26

0.261

3.711

0.224

10–11

0.146

5.350

0.047

26–27

0.237

3.551

0.061

11–12

0.281

5.320

0.046

27–28

1.001

3.586

0.020

12–13

1.329

3.492

0.061

28–29

0.753

3.621

0.025

13–14

0.638

3.492

0.072

29–30

0.403

1.416

0.063

14–15

0.565

3.543

0.067

30–31

0.975

1.611

0.021

15–16

0.658

1.795

0.063

31–32

0.288

1.693

0.016

16–17

1.295

1.686

0.019

32–33

0.184

1.773

0.004

after the introduction of impedance parameters. This is also where the pure network topology characteristics are distinguished. Next, the analytic hierarchy process is used to determine the weight of each index, and the comprehensive vulnerability assessment results of each node and line are further obtained. The relative size is determined by sorting, and the top 20% is regarded as the weak link. The weak link identification results are shown in Table 3. It can be seen that the indicators proposed in this paper can well identify the weak links in the ADN. Bus 16 and 26 are the obvious weak links as distributed photovoltaic grid-connected points, and bus 2 is the weakest link. As far as lines are concerned, line 1–2 is the weakest link, and the weakness of other lines is not much different. Table 3 Results of weak line identification

Bus

Comprehensive index

Line

Comprehensive index

2

1.0083

1–2

0.8084

1

0.7801

16–17

0.5839

3

0.7544

30–31

0.5512

26

0.6551

23–24

0.5360

16

0.6233

3–23

0.5262

4

0.5083

8–9

0.5230

5

0.4945

29–30

0.5082

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5 Conclusion The results show that compared with the traditional indicators, the improved indicators in this paper can combine the characteristics of the network topology with the power flow considering the correlation of distributed power output, reflect the structural weakness of each node and line, and accurately identify the weak nodes and lines. The method can provide accurate advice for subsequent grid structure optimization and transformation, and provide certain reference for operation and maintenance personnel to further ensure the safe and reliable operation of the medium and low voltage distribution network after the high penetration rate of distributed power is connected. Acknowledgements Funding: State Grid Shandong Electric Power Company Science and Technology Project Funding “Research on Key Technologies of Highly Reliable Power Supply in Guzhenkou Innovation Demonstration Zone” (5206002000T2).

References 1. You Y, Liu D, Zhong Q (2015) Research on optimal schedule strategy for active distribution network. Autom Electric Power Syst 38(9):177–183 2. Xu L, Chen D (2011) Control and operation of a DC microgrid with variable generation and energy storage. IEEE Trans Power Deliv 26(4):2513–2522 3. Liu H, Mao C, Lu J et al (2010) Energy storage system of electronic power transformer and its optimal control. Trans China Electrotech Soc 25(3):54–60 4. Ding M, Han P (2008) Vulnerability assessment to small-world power grid based on weighted topological model. Proc CSEE 28(10):20–25 5. Chen W, Jiang Q, Cao Y (2005) Voltage vulnerability assessment based on risk theory and fuzzy reasoning. Proc CSEE 25(24):20–25 6. Hua W, James DM, Vittal V (2000) Risk based voltage security assessment. IEEE Trans Power Syst 15(4):1247–1254

A Method for Calculating Flicker of Fluctuating Loads by Instantaneous Power Ming-Xing Zhu, Yi-Heng Zhang, and Bin Xu

Abstract In order to solve the problem that the existing voltage flicker researches cannot accurately and reasonably allocate the voltage flicker responsibility among the fluctuating loads, a method based on instantaneous power to allocate the flicker responsibility of multi fluctuation load is proposed. First, we measure the instantaneous power of the fluctuating loads and perform the backward difference operation to obtain the power fluctuation sequence, and calculate the voltage fluctuation sequence in combination with the system parameters. Then we use the Fourier transform to obtain the fluctuation value of different frequency components and be equivalent to 8.8 Hz. Finally, according to the corresponding relationship between 8.8 Hz sine wave voltage fluctuation and flicker, the voltage flicker value is calculated. Simulation results show that this method can still accurately measure the flicker contribution rate of each fluctuating loads and the improvement rate of the compensation device when there exist multiple fluctuating loads, and realize the accurate allocation of the flicker responsibility of multiple undulating loads. Keyword Multiple fluctuating loads · Voltage flicker · Instantaneous power fluctuation · Compensation device · Responsibility allocation

1 Introduction In recent years, with more and more high-power fluctuating loads put into the distribution network, voltage flicker is more frequent [1, 2], resulting in the problem of safe and stable operation of the power grid [3], which has been highly concerned by M.-X. Zhu · Y.-H. Zhang (B) College of Electrical Engineering and Automation, Anhui University, Hefei, China e-mail: [email protected] M.-X. Zhu e-mail: [email protected] B. Xu Research Institute of State Grid Anhui Electric Power Co., Ltd, Hefei, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_38

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both power supply and demand [4]. Accurate measurement and responsibility allocation of voltage flicker are of great significance for coordinating the contradiction between power supply and demand and ensuring the safe and stable operation of distribution network [5].1 The existing research on voltage flicker mainly focuses on voltage flicker detection, such as optimizing voltage envelope extraction and envelope parameter algorithm or using line impedance model to locate flicker source. At present, the mainstream voltage envelope extraction method is the square detection method recommended by IEC [6]. However, when this method is applied to multi-frequency or low-frequency flicker signals, the error is large [7], and there are shortcomings such as digitalization and difficulty in spectrum analysis [8, 9]. In view of the above problems, Reference [10] proposed a voltage flicker detection method based on improved HHT. Four-point interpolation subdivision algorithm and HHT algorithm were used to extract flicker parameters, but there were problems such as unable to isolate harmonics and large amount of calculation. In reference [11–14], the extraction factor and error factor of Teager energy operator are further calculated, and the voltage flicker envelope is extracted. The spectral analysis of the extracted flicker envelope signal is carried out by using the improved Rife-Vincent window, Nuttall window and six cosine window, and the accurate and fast calculation of voltage flicker parameters is realized. However, the calculation accuracy is affected by the selection of window functions, and the window interpolation method still has certain fence effect and spectrum leakage. Therefore, the superposition interpolation of the spectrum processed by the rotation factor is carried out in reference [8], which suppresses the spectrum leakage and eliminates the fence effect. Reference [15] proposed a dynamic voltage flicker measurement method based on the Taylor-Fourier filter (TFF), which realized the time-frequency feature extraction of flicker components. However, the voltage flicker measurement method based on the envelope extraction has a large amount of calculation, which is difficult to put into practical engineering application. For the problem of flicker source location, Reference [5] introduced in detail the location method based on the principles of fluctuation power flow, current-voltage relationship and flicker fluctuation intensity, and pointed out the key of flicker source location. References [12] and [16] locate the flicker source according to the direction of flicker power flow and evaluate the flicker pollution. Reference [17] proposed a flicker detection and source localization method based on S transform, modeled according to the principle of flicker source localization, and located the flicker source through the upstream and downstream related parameters. Reference [18] integrated the four kinds of flicker source localization methods mentioned in Reference [5], such as voltage-current correlation, and combined with the LSVM algorithm for modeling, which had higher accuracy than the single criterion localization method. Although the above researches have achieved satisfactory results in voltage flicker measurement and voltage flicker traceability, they do not involve the quantitative

1

State Grid Anhui Electric Power Co., Ltd. Science and Technology Project (521,205,190,025).

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calculation of flicker value of each fluctuating load, and do not consider the influence of interharmonics and compensation devices on voltage flicker calculation, which makes it difficult to assign subsequent flicker responsibility. In Reference [19], aiming at the problem that the traditional flicker research cannot directly allocate the responsibility for flicker pollution, the flicker interference source was modeled, and the responsibility of each object was graded and evaluated according to the two parameters of system voltage and load impedance. Although this method can effectively analyze whether the main responsibility side is the load side or the system side, it is only qualitative for responsibility allocation, and does not involve the quantitative calculation of the flicker responsibility of each fluctuating load. In order to realize the accurate calculation of voltage flicker value of multivolatility load and the reasonable assessment of flicker responsibility when setting dynamic compensation device, this paper proposes a method of assessment of flicker responsibility of multi-volatility load based on instantaneous power. Firstly, the instantaneous power of fluctuating load is measured directly, and the power fluctuation sequence is obtained by backward difference operation, and the voltage fluctuation sequence is calculated by combining the system parameters. Then, the voltage fluctuation values of different frequency components are obtained by Fourier transform, and all components are equivalent to 8.8 Hz. Finally, according to the relationship between the voltage fluctuation value of 8.8 Hz sine wave and flicker, the voltage flicker value is calculated. The method in this paper can quantitatively obtain the flicker contribution value of each fluctuation load, accurately assign the flicker responsibility, and evaluate the flicker control effect of the compensation device.

2 Key Issues and Models of Flicker Responsibility Allocation The bus voltage flicker of distribution network is usually caused by multiple fluctuation loads and compensation devices. As shown in Fig. 1, the typical grid-connected model of multi-fluctuation load is shown, where HV represents the bus of the previous voltage level, LV represents the bus of the current voltage level, L1–Ln corresponds to the 1st–nth fluctuation load, and B represents the compensation device. Define

~

Fig. 1 Grid connected model of typical multi fluctuation load

HV S

L1

L2

...

LV Ln

B compensation installation

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U LV as LV bus voltage. X Li (i = 1,2, …, n) defines the contribution of the first fluctuating load to LV flicker. X B is defined as the contribution of compensation device B to LV flicker. X S is defined as the contribution of HV load to LV flicker. According to Fig. 1, the corresponding relationship between voltage envelope and flicker parameters can be obtained as follows: Pst = f (ULV )

(1)

ULV = g(X Li , X B , X S , t), i = 1, 2, . . . , n

(2)

It is not difficult to see from the above equation that if the voltage flicker parameter extraction method based on voltage envelope is used to measure the voltage flicker, the voltage flicker value after the comprehensive influence of multiple factors such as the compensation device on the bus at the corresponding level can only be obtained, and it is impossible to quantitatively calculate the actual flicker responsibility of each fluctuation load under the bus at the corresponding level. Therefore, it is necessary to establish an accurate and reasonable flicker liability allocation model from the fluctuation load itself. In practical engineering applications, the common voltage flicker pollution sources such as arc furnace and refining furnace should be put into use after the compensation device is put into operation in principle. Therefore, the concepts proposed below are proposed on the premise that the compensation device has been put into operation. In Fig. 1, assuming that the voltage on the LV is regulated by the compensation device, the voltage flicker caused by the fluctuation power of the first fluctuating load injected into the system at the short-circuit capacity of the system is defined as the flicker emission level of the fluctuating load, denoted as Pst, i, i = 1, 2, …, n, then there are: Pst,i = h( pi , qi , t), i = 1, 2, . . . , n

(3)

Among them, pi and qi are the instantaneous power sequences of the first fluctuating load. The contribution rate of the ith fluctuation load to the total flicker emission level is defined as Eq. (4): λi =

Pst,i × 100% Pst Σ

(4)

where PstΣ is the voltage flicker value caused by the sum of the fluctuation power of all the fluctuation loads compensated by the compensation device. By comparing the contribution rate λi of each fluctuation load to the flicker, the responsibilities of each fluctuation load can be determined.

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The improvement rate of the compensation device reflects the change of the voltage flicker value caused by the fluctuation power of the injection system relative to the total fluctuation power of the whole fluctuation load after the compensation device is compensated, defined as formula (5): c=

PstΣ − Pst,c × 100% PstΣ

(5)

Among them, Pst, c is the voltage flicker value caused by the fluctuation power injected into the system after the compensation device compensates all the fluctuation loads. By calculating and analyzing the value and trend of the improvement rate c of the compensation device, we can judge whether the compensation device is effective and whether the parameter setting of the compensation device is reasonable.

3 Multi-Fluctuation Load Flicker Responsibility Allocation Algorithm 3.1 Signal Preprocessing Considering that the influence of harmonics above 100 Hz on voltage flicker is small, and negative sequence harmonics such as second harmonic may produce new fluctuations. In order to reduce the computational complexity and ensure the accuracy of the algorithm, the sampling signal is preprocessed. The three-phase voltage and current after sampling are recorded as u’ abc (mT S ) and ’ i abc (mT S ), where m = 1, 2, …, N, the number of sampling points of a week wave is N = 256, and the sampling interval T S = (20/N) ms. The u’ abc (mT S ) and i’ abc(mT S ) are filtered to pass through the 6th-order Butterworth low-pass filter with a cutoff frequency of 95 Hz to reduce the influence of (inter) harmonics on the calculation results, and uabc (mT S ) and iabc (mT S ) are obtained. The 6-order Butterworth low-pass filter can be expressed as: 7 Σ l=1

al y( j + 1 − l) =

7 Σ

bk x( j + 1 − k)

(6)

k=1

The difference equation coefficients al and bk are shown in Table 1. In order to meet the requirements of rapidity in engineering applications, this algorithm calculates every eight sampling points, let n = 8 m, that is, the calculated point voltage and current are denoted as uabc (nTS ) and iabc (nTS ).

462 Table 1 The coefficients of the filter difference equation

M.-X. Zhu et al. al

bk

a1

1

b1

1.4700e−10

a2

−5.8198

b2

8.8201e−10

a3

14.1153

b3

2.2050e−09

a4

−18.2620

b4

2.9400e−08

a5

13.2925

b5

2.2050e−08

a6

−5.1611

b6

8.8201e−10

a7

0.8351

b7

1.4700e−10

3.2 Flash Calculation and Responsibility Allocation Algorithm It can be seen from the above analysis that the traditional voltage flicker calculation method based on voltage envelope or impedance model cannot quantitatively calculate the voltage flicker value caused by each fluctuation load alone. This paper studies from the perspective of fluctuation load itself, and proposes to use the instantaneous power of fluctuation load to calculate its voltage fluctuation sequence, and then calculate the flicker emission level of each fluctuation load according to the relationship between voltage fluctuation and flicker. Since the voltage fluctuation of the higher-level bus has little effect on the higherlevel bus compared with the voltage fluctuation generated by the higher-level bus, the background flicker from the higher-level bus can be ignored in this algorithm. The calculation block diagram of voltage fluctuation sequence shown in uabc (nT S ) and iabc (nT S ) input Fig. 2 after preprocessing. In Fig. 2, ‘⊗’ are defined as point multiplications of two matrices. p(nT s ) and q(nT s ) are the instantaneous values of active and reactive power of fluctuating load, respectively.Δp(nT S ) and Δq(nT S )are the results of difference operations for p(nT s ) and q(nT s ). d(nT S ) is voltage fluctuation sequence. When calculating Pst, i, Pst Σ and Pst,c , the meanings of the parameters in the graph are slightly different, as shown in Table 2. The transfer functions G1 , G2 , G3 and GS are as follows: Such partitioning issues can be solved using clustering methods. Hierarchical clustering analysis is a more commonly used clustering analysis algorithm. It can be detailed as follows: first, treats all nodes as a single class, then compares the merge

Fig. 2 Block diagram of voltage fluctuation sequence calculation

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Table 2 The coefficients of the filter difference equation Type of calculation

uabc (nT S ) meaning

iabc (nT S ) meaning

p(nT S )/q(nT S ) meaning

Pst ,i

busbar voltage

Fluctuation i load feeder current

Fluctuating power of the ith fluctuating load

PstΣ

busbar voltage

Feeder current of each fluctuating load

Sum of fluctuating power of each fluctuating load

Pst,c

busbar voltage

Injection system current

Fluctuating power of injection system

distance of each step, finally, combines the two classes with the minimum merge distance into one class until the final number of clusters meets the requirements. The most important step in the process of clustering is to define the distance between two classes. The partition process in this paper is realized by using the condensed hierarchical clustering method based on Ward distance, which ensures the minimum sum of squares of deviations of the same type in each merging. The calculation formula is shown in Eqs. 9 and 10. The calculation steps are as follows: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

⎡ ⎤ ⎤ 1 0 −1 u a (n)i a (n)+ G 1 = ⎣ −1 1 0 ⎦ ⇒ p(n) = ⎣ u b (n)i b (n)+ ⎦ u c (n)i c (n) 0 −1 1 ⎧ ⎫ ⎡ ⎤ 100 ⎨ [(u a (n) − u b (n))i c (n)]+⎬ G 2 = ⎣ 0 1 0 ⎦ ⇒ q(n) = √13 [(u b (n) − u c (n))i a (n)]+ ⎩ ⎭ [(u c (n) − u a (n))i b (n)] 001 ⎡ ⎤ −1 0 0 . . . 0 ⎢ 1 −1 0 . . . 0 ⎥ ⎢ ⎥ ⎢ ⎥  ⎢ 0 1 −1 . . . 0 ⎥ ⎢ ⎥ ⇒ Δp(nTS ) = p(nTS ) − p[(n − 1)TS ] ⎪ = G ⎪ 3 . . . . . ⎢ . . . . . ⎥ ⎪ Δq(nTS ) = q(nTS ) − q[(n − 1)TS ] ⎪ ⎢ . . . . . ⎥ ⎪ ⎪ ⎢ ⎥ ⎪ ⎪ ⎣ 0 0 0 ... 1 ⎦ ⎪ ⎪ ⎪ ⎪ ⎪ 0⎧ 0 0 . .⎡. −1⎤ ⎪ ⎪ ⎪ ⎪ 1 RS ⎪ ⎪ ⎪ ⎪ Gs = 2 ⎪ ⎪ ⎪ ⎪ XS ⎨ ⎪ U ⎪ N/ ⎪ 2 S )X S ⎪ ⇒ d(nTS ) = Δp(nTS )R SU+Δq(nT X S = U ⎪ 2 S d N ⎪ N ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ / ⎩ ⎩ RS = X s p ⎡

(7)

In Eq. (7), U N is the voltage level of the system; S d is the operating short-circuit capacity of the system, and the size of the required S d should be determined according to the specific application scenarios; p is the resistance inductance ratio. In high voltage system, the value of p is generally 7~10. Then input the calculated voltage fluctuation sequence d(n) into the voltage flicker calculation block diagram shown in Fig. 3

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Fig. 3 Block diagram of voltage flicker value calculation

In Fig. 3, D(h) is the voltage fluctuation value of each frequency component obtained after DFT of d(n); K(f ) is the apparent sensitivity coefficient of each frequency component; d equ,8.8 is the voltage fluctuation equivalent to 8.8 Hz; C is a constant, C = 2.856, and the derivation process is shown in Eq. (10 and 11); The calculation method of K(f ) and d equ,8.8 is as follows: K( f ) =

8.8 Hz voltage fluctuation d(% ) when s= 1 f Hz voltage fluctuation d(% ) when s= 1 dequ,8.8

(8)

N Σ 1 =( K 2 (h f 1 )D 2 (h)) 2

(9)

h=1

The formula given in 4.10.1 of IEC 61,000-4-15 is shown in Eq. (10): 1

Pst = (0.0314P0.1 + 0.0525P1 + 0.0657P3 + 0.28P10 + 0.08P50 ) 2

(10)

where: P0.1 , P1 , P3 , P10 and P50 are the unit values of perception for the time of instantaneous flicker visual sensitivity exceeding 0.1, 1, 3, 10 and 50%. For periodic sine wave voltage fluctuation, we can consider P0.1 = P1 = P3 = P10 = P50 = S(t), Therefore, it can be deduced that: √ Pst = 0.714 S(t) = 4 × 0.714ds,8.8 = 2.856ds,8.8 (11) According to the input of the corresponding parameters in Table 2, the final Pst is Pst,i , PstΣ or Pst ,c . The calculated Pst,i , PstΣ and Pst ,c are substituted into the formula (4) and formula (5) to obtain the flicker contribution rate of each fluctuation load in each period and the governance of the compensation device.

4 Project Case Analysis 4.1 Algorithm Verification In practical engineering applications, it is difficult to calculate the voltage flicker responsibility of each fluctuating load or quantitatively evaluate the flicker control effect of the compensation device. Using this algorithm to analyze the measured data

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can obtain the real and specific flicker contribution rate of each fluctuating load and the improvement rate of the compensation device. A 150 t AC electric arc furnace in an enterprise has a 33 kV bus. The main loads under the bus are EAF furnace, LF furnace and SVC device. The algorithm in this paper is used to analyze the relevant data of the AC arc furnace of the enterprise. According to the bus three-phase voltage and current data, the instantaneous fluctuation power of the injection system is calculated, as shown in Fig. 4. Then the voltage fluctuation sequence is calculated according to the calculated instantaneous power, and the trend is consistent with the fluctuation reactive power of the injection system, as shown in Fig. 5. In order to facilitate the comparison between the calculated value of flicker and the measured value, the same calculation interval as the measured value is used to 150

Active power of injection system

90

90

60

60

30

30

0 -30

0 0

500

1000

1500

2000

t(s) Fig. 4 Fluctuating power injection system

Fig. 5 Voltage fluctuation sequence

2500

3000

-30 3500

q(MVar)

Reactive power of injection system 120

120

p(MW)

150

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obtain the calculated value of voltage flicker caused by the fluctuation power of the injected system after SVC treatment, as shown in Fig. 6. The error between the calculated value and the measured value is within ±5%, which meets the accuracy requirements of engineering application. The correctness of the proposed algorithm is verified, as shown in Fig. 7.

Fig. 6 Voltage flicker curve compensated by SVC

20 15 10 5 0 -5 -10 -15 -20

500

1000

1500

2000

t(s) Fig. 7 Voltage flicker calculated value error curve

2500

3000

3500

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7 flicker curve of EAF

6

flicker curve of LF

Pst

5

4 3 2 1

0

500

1000

1500

2000

2500

3000

3500

t(s) Fig. 8 Voltage flicker caused by each fluctuating load

4.2 Practical Application According to the bus three-phase voltage and the fluctuation load feeder current, the flicker emission level curves of EAF furnace and LF furnace are obtained, as shown in Fig. 8. According to the calculated flicker emission level of each fluctuation load, the flicker contribution rate of each fluctuation load at different times can be obtained. The time data of each fluctuation load in working state are analyzed, and the flicker contribution rate of each fluctuation load is obtained as shown in Table 2.According to the statistical analysis, the average contribution rate of flicker of EAF furnace is 84.83%, and that of LF furnace is 15.17%. It can be seen that the flicker responsibility in this period should be mainly borne by EAF (Table 3). Finally, the voltage flicker caused by the fluctuating power injected into the system after the compensation device treatment is compared with the voltage flicker caused by the total fluctuating power of each fluctuating load, and the improvement rate of the compensation device is calculated. The data of each fluctuating load in the working state period are selected for analysis, as shown in Fig. 9. Table 3 Flicker contribution rate caused by each fluctuating load

Calculation point number

Contribution rate of EAF flicker (%)

Contribution rate of LF flicker (%)

1

86.80

13.20

2

87.77

12.23

3

81.55

18.45

4

82.16

17.84

5

85.86

14.14

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Fig. 9 Compensation effect curve of compensation device

From the improvement rate curve of the compensation device, it can be seen whether the compensation device is effective and the parameter setting is reasonable. The improvement rate of SVC in this case is about 50–60%, which has a certain improvement effect on voltage flicker.

5 Conclusion In view of the problem that the existing research on voltage flicker does not involve the quantitative calculation of the flicker responsibility of each load under the condition of multiple fluctuation loads, this paper proposes a method for determining the flicker responsibility of multiple fluctuation loads based on the instantaneous power. Through the simulation experiment and the analysis of the measured case, the following conclusions are drawn: (1)

(2)

(3) (4)

This algorithm considers the influence of inter-harmonics near the fundamental wave and negative-sequence harmonics on voltage flicker calculation, and adopts signal preprocessing methods such as 6—order Butterworth low-pass filter and equal-interval sampling, which takes into account the calculation amount and accuracy of the algorithm. This algorithm realizes the quantitative calculation of the flicker emission level of each fluctuating load in the case of multiple fluctuating loads, and verifies the correctness of the algorithm by comparing the calculated value with the measured value. This paper defines the flicker contribution rate of each fluctuation load, which provides a basis for accurate and reasonable allocation of flicker responsibility. This paper defines the improvement rate of compensation device, which can intuitively evaluate the flicker control effect of compensation device and analyze whether the compensation device is reasonable.

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References 1. Liang Y, Ma X, Zhao F et al (2019) A high accuracy detection method of voltage flicker signal based on time-frequency transform. In: 2019 9th international conference on power and energy systems (ICPES) 2. Xiangning XIAO (2010) Power quality analysis and control. China Electric Power Press, Beijing 3. Li F, Gao Y, Cao Y et al (2016) Improved teager energy operator and improved chirp-Z transform for parameter estimation of voltage flicker. IEEE Trans Power Deliv 31(1):245–253 4. Shao Z, Wu D, Lin Y, Evaluating the flicker interference of fluctuating load. Power Syst Protect Contr 5. Ganyun LV, Qiyu WU, Chenyuan WU et al (2019) Review on methods for voltage fluctuation and flicker source location. Proc CSU-EPSA 31(06):7–14 6. International Electrotechnical Commission (IEC) (2010) Standard 61000—4—15 Electromagnetic Compatibility (EMC)-part 4: testing and measurement techniquessection 15: flickermeter-functional and design specifications 7. An H, Li Z, Yue N et al (2020) Envelope tracking of voltage flicker caused by wind power integration based on sparse recovery algorithm. Autom Electr Power Syst 44; 677(07):221–229 8. Li L, Ma M, Chao S et al (2016) The voltage flicker detection algorithm based on rotation factor transforming interpolation. Trans China Electrotech Soc (22) 9. Wang X, Meng KQ, Zhang Z et al (2017) Voltage flicker measurement of wind turbines using Kaiser window correction based on FFT and HHT. J Electron Measur Instrum 31(005):802–808 10. Ni L, Xiao L, Lv G, et al (2017) Voltage flicker parameters detection based on modified HHT. Electr Measur Instrum 54(018):72–78 11. Gao Y, Li F, Chen J et al (2014) Voltage flicker measurement using the Teager-Kaiser energy operator based on Rife-Vincent window spectral correction. Trans China Electrotech Soc 29(6):248–256 12. Gao Y, Chen J, Li L et al (2016) Trace of flicker sources based on fluctuating load power analysis. J Hunan Univ (Nat Sci) 043(008):92–100 13. Wu C, Gao Y, Zhang Y, et al (2019) Flicker parameter detection based on improved energy operator and K-RV mutual convolution window. Chinese J Sci Instrum 040(004):69–76 14. Gu T, Gao Y, Wu C et al (2019) Voltage flicker envelope parameter detection based on improved energy operator and six-term cosine window spectrum correction. Power Syst Prot Control 47(23):44–51 15. Kuang H, Wen H (2020) Voltage flicker measurement based on Taylor-Fourier transform. Trans China Electrotech Soc 35(22):4798–4806 16. Ni L, Xiao L, Li X et al (2018) Flicker source tracing based on HHT and flicker power flow direction method. Power Syst Clean Energy 34(1):26–31 17. Lv G, Wu Y, Shi X et al (2018) Flicker detection and source location method based on Stransform. Power Capacitor React Power Compensation 39(05):87–93 18. Wu Q, Lv G, Wu C et al (2019) Intelligent location of flicker source based on multiple criterions. Proc CSU–EPSA 31(12):95–100 19. Shao Z, Wu D, Zhang Y (2013) Distributing contribution of voltage flicker at PCC. Adv Technol Electr Eng Energy 32(02):63–67

An Optimization Method for Compensation Network Parameters in Double-Sided LCC Wireless Power Transfer System Shengqi Zhao, Zhaokai Li , Xiaoyan Huang , Dongdong Jiang, and Chenxi Zhou Abstract In the wireless power transfer system of electric vehicles, the output power and transmission efficiency decrease due to the variation of coupling coefficient resulting from coil misalignment. This paper presents an optimization design method of resonant compensation network of double-sided Inductor-Capacitor-Capacitor (LCC) topology for high transmission efficiency. Based on the analysis for the high efficiency, the particle swarm optimization (PSO) algorithm is performed using the MATLAB/Simulink to optimize the parameters of the compensation network. Under different coupling coefficients, the transmission efficiency of the initial and optimized system is compared and analyzed to validate the proposed optimization method. Keywords Wireless power transfer · Double-sided LCC topology · Compensation network parameters

1 Introduction Wireless power transfer (WPT) technology is used in the household application, medical electronics and electric vehicles benefitting from its advantages of safety, reliability, flexibility and convenience [1–3]. In WPT system, the common topologies of resonant compensation network include series (S), parallel (P), LCL, and LCC topology [4–7]. Different topologies and compensation network parameters will affect the transmission efficiency. Besides, when an electric vehicle stops, the transmission coils might be misaligned, which will affect the coupling coefficient between transmission coils and therefore decrease the output power and transmission efficiency. Compared with the traditional SS compensation topology, the doublesided LCC topology is less susceptible to coil misalignment [8]. A parametric design method is proposed to optimize efficiency by adjusting the ratios of primary and secondary compensation inductances in [9].

S. Zhao · Z. Li (B) · X. Huang · D. Jiang · C. Zhou Zhejiang University, Hangzhou 310027, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_39

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In this paper, the selection of capacitance and inductance parameters in the doublesided LCC circuit topology is analyzed to establish the relationship between the transmission efficiency and coil misalignment. These parameters are optimized using PSO algorithm to achieve the maximum weighted average efficiency.

2 Modeling and Calculation of Double-Sided LCC Compensated WPT System 2.1 Equivalent Circuit Model The circuit structure of double-sided LCC topology in the WPT system is shown in Fig. 1. Uin is the input high frequency AC power supply. L 1 , C1 , C p ,L 2 , C2 , and Cs are the inductance and capacitance compensation network of primary and secondary sides. L p and L s are the self-inductances of primary and secondary coils, respectively. M is the mutual inductance. r1 and r2 are the resistances of transmission coils. Req is the equivalent load in the circuit. According to [10], when high transmission efficiency is achieved in the doublesided LCC circuit topology, both the primary and the secondary side compensation networks should be completely resonant. In this way, each component parameter in the compensation network can be expressed by L 1 and L 2 as C1 =

1 ω2 L

(1) 1

1 ω2 L 2

(2)

Cp =

1 ( ) ω2 L p − L 1

(3)

Cs =

1 ω2 (L s − L 1 )

(4)

C2 =

Fig. 1 Circuit structure of double-sided LCC topology in the WPT system

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where ω is the resonant frequency of the system. In Fig. 1, the impedance parameters of the circuit can be obtained, in which the secondary impedance Z s , the reflection impedance Z r and the input impedance Z in are respectively shown as Z s = r2 + Zr = Z in =

ω2 L 22 Req

(5)

ω2 M 2 Zs

(6)

ω2 L 21 r1 + Z r

(7)

Input current Iin , primary side current I p , secondary side current Is and output current Iout are respectively shown as Uin Z in

(8)

Uin j ωL 1

(9)

Uin Z r ω2 M L 1

(10)

Iin = Ip = Is = Iout =

− j ωL 2 MUin ( ) L 1 Req r2 + ω2 L 22

(11)

For the simplified circuit in Fig. 1, input power Pin , output power Pout and transmission efficiency η can be obtained as Pin = Uin Iin

(12)

2 Pout = Iout Req

(13)

η=

Pout Pin

(14)

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2.2 Influence of Transmission Coil Misalignment on Efficiency In the WPT system, coil misalignment will make a difference on transmission efficiency. Considering the loose coupling structure between the primary and secondary coils with the large air gap, the coupling coefficient is small. Therefore, it is easily affected by coil misalignment. The equation between coupling coefficient k and mutual inductance M is M L p Ls

(15)

ω4 L 22 M 2 Req )( ) Req r2 + ω2 L 22 r1r2 Req + ω2 L 22 r1 + ω2 M 2 Req

(16)

k=√ Using (1)–(13), Eq. (14) is rewritten as η= (

It can be observed that the relationship between efficiency and mutual inductance is determined if the circuit components and operating frequency are fixed in the system. The simulation model of transmission coils is established in JMAG, as shown in Fig. 2. The parameters are shown in Table 1. The resonant frequency is set as 85 kHz and the vertical distance between two coils is set as 120 mm. The coupling coefficient varies at different offset distances as shown in Fig. 3. With the increase of the offset distance, the coupling coefficient decreases significantly. From (15) and (16), mutual inductance is proportional to the coupling coefficient. Therefore, it can be concluded that the efficiency will decrease with the increase of the offset distance.

Fig. 2 Coupling coils simulation model in JMAG

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Table 1 Parameters of transmission coils Values

Parameters Primary side coil

Secondary side coil

Number of turns

20

Inner radius

80 mm

Outer radius

300 mm

Self-inductance

102 µH

Number of turns

20

Inner radius

80 mm

Outer radius

300 mm

Self-inductance

102 µH

Vertical distance

120 mm

Resonant frequency

85 kHz

Fig. 3 The variation of coupling coefficient with offset distance

2.3 Compensation Network Selection for Maximum Efficiency According to (16), when the compensation networks are completely resonant using the parameters of Table 1, the curve of transmission efficiency is varied with L 2 , as shown in Fig. 4. It can be observed that when L 2 is set to 28.4 µH, the maximum transmission efficiency η is 0.9165. From (13), the output power Pout is affected by the compensation inductances L 1 and L 2 . When L 2 is constant, the curve of output power varying with the L 1 is shown in Fig. 5. When Pout meets the rated output power of 2.6 kW, the corresponding L 1 is equal to 18.2 µH. According to (1)–(4), the parameters of

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Fig. 4 The transmission efficiency varies with the compensation inductance L 2

Fig. 5 The output power Pout varies with the inductance L 1 in the case of constant L 2

other components in the compensation network can be obtained to achieve complete resonance.

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Fig. 6 The fitness evolution curve with 50 iterations

3 Standard PSO Combined with Simulation Topology Model in Simulink 3.1 Weight Coefficient and Optimization Objective Since coil misalignment of electric vehicles has a great influence on the coupling coefficient and the transmission efficiency. In order to maximize efficiency, it is necessary to consider the probability of different coupling coefficients as the(weight ) coefficient. The misalignment probability model obeys normal distribution N 0, σ 2 . According to SAE-J2954™ standard, the offset range of the coil misalignment is set at ±75 mm. Due to the characteristic of normal distribution, 99.8% of values lie within the range of ±3σ , thus σ is set to 25 mm. Depending on the probability, the offset distance is divided into three portions for weighting. In order to maximize the average efficiency, the optimization objective can be expressed as ) ( ηm = max pk1 ηk1 + pk2 ηk2 + pk3 ηk3

(17)

where ηm is maximum weighted average efficiency. k1 , k2 and k3 are the corresponding coupling coefficients when the offset distances are σ , 2σ and 3σ . It can be observed from Fig. 3, k1 = 0.202, k2 = 0.179, k3 = 0.144.ηk1 , ηk2 and ηk3 are the corresponding transmission efficiency. pk1 , pk2 and pk3 are respectively the probabilities that offset distances lie in [−σ, σ ], [−2σ, −σ )∪(σ, 2σ ], [−3σ, −2σ )∪(2σ, 3σ ], and pk1 + pk2 + pk3 = 1. Proportionally pk1 = 0.683, pk2 = 0.273, pk3 = 0.044.

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Table 2 Comparison between the initial design and the optimized result Parameters

Initial design

Optimized result

C1

192.6 nF

191.5 nF

C2

123.4 nF

129.0 nF

Cp

41.8 nF

40.7 nF

Cs

47.6 nF

45.7 nF

ηm

0.9035

0.9087

3.2 Optimization Algorithm The optimization objective is to design parameters (C1 , C2 , Cs and C p ) of compensation networks. PSO is used to optimize the parameters with maximum inertia weight Wmax = 0.8, minimum inertia weight Wmin = 0.4, learning factors c1 = 1.5 and c2 = 1.5. The compensation network for the maximum efficiency and rated output power is used as the initial design in algorithm.

3.3 Optimization Results and Analysis The double-sided LCC circuit model is analyzed in MATLAB/Simulink. The transmission efficiency is changed with the compensation network parameters using PSO. The optimization results are shown in Table 2. Under different coupling coefficients, the transmission efficiency curves of initial design and optimized result are shown in Fig. 7. It can be observed that when the coupling coefficient is large, the efficiency with the optimized compensation network is approximately equal to the initial design, but the overall average efficiency is higher.

4 Conclusion In this paper, the circuit model of double-sided LCC topology in WPT system is established. The output power and transmission efficiency are calculated with compensation networks of primary and secondary sides completely resonant. The simulation model of transmission coils in JMAG is used to obtain the values of self-inductance and mutual inductance. The parameters of components in the compensation network are selected at rated output power for achieving maximum transmission efficiency. Considering the possibility of coil misalignment, PSO algorithm is used to optimize the compensation network parameters with simulation model in MATLAB/Simulink to reach maximum weighted average efficiency. The results are analyzed to validate the effect of optimization. Future work will be conducted on the maximum efficiency of whole WPT system.

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Fig. 7 The transmission efficiency with the compensation networks of initial design and optimized result vary with coupling coefficient

Acknowledgements This paper was supported by Zhejiang Key R&D Program (2019C01044).

References 1. Chinthavali M, Wang ZJ (2016) Sensitivity analysis of a wireless power transfer (WPT) system for electric vehicle application 2. Fujita T, Yasuda T, Akagi H (2016) A wireless power transfer system with a double-current rectifier for EVs 3. Kang SH, Choi JH, Harackiewicz FJ, Jung CW (2016) Magnetic resonant three-coil WPT system between off/in-body for remote energy harvest. IEEE Microw Wirel Co 26(9):741–743 4. Zhang Y, Chen K, He F, Zhao Z, Lu T, Yuan L (2016) Closed-form oriented modeling and analysis of wireless power transfer system with constant-voltage source and load. IEEE T Power Electr 31(5):3472–3481 5. Madawala UK, Thrimawithana DJ (2011) Current sourced bi-directional inductive power transfer system. IET Power Electronic 4(4):471–480 6. Liu C, Ge SK, Guo Y, Li H, Cai GW (2016) Double-LCL resonant compensation network for electric vehicles wireless power transfer: experimental study and analysis. IET Power Electr 9(11):2262–2270 7. Yao Y, Wang Y, Liu X, Lin F, Xu D (2018) A novel parameter tuning method for a double-sided LCL compensated WPT system with better comprehensive performance. IEEE T Power Electr 33(10):8525–8536 8. Li W, Zhao H, Deng J, Li S, Mi CC (2016) Comparison study on SS and double-sided LCC compensation topologies for EV/PHEV wireless chargers. IEEE T Veh Technol 65(6):4429– 4439

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9. Chen Y, Zhang H, Shin C, Jo C, Park S, Kim D (2020) An efficiency optimization-based asymmetric tuning method of double-sided LCC compensated WPT system for electric vehicles. IEEE T Power Electr 35(11):11475–11487 10. Li S, Li W, Deng J, Nguyen TD, Mi CC (2015) A double-sided LCC compensation network and its tuning method for wireless power transfer. IEEE T Veh Technol 64(6):2261–2273

Enterprise-Level Model Construction of Distribution Network Topology Based on Graph Database Pengxi Liu, Jiacheng Liang, Jiakai Xiao, Dongliang Hu, Gongjie Shi, and Mingyao Ma

Abstract With the rapid development of the electric power industry in China, the structure and operation of power grids become more and more complicated. And this is followed by a surge of power data. To cognize and analyze the state of grids more comprehensively and efficiently which supports a precise decision of power supply, transmission and utilization, ‘Digital Twins’ has become a critical technology. And the topology is the most basic and important part of the ‘Digital Twins’ power grids. In distribution networks, through the distribution automation system and the GIS system, State Grid Corporation of China (SGCC) has realized the dispatching operation management and the power equipment management based on topologies. At the same time, by using Data Switching Technology, the equipment ledgers of two systems can be connected. However, it is unable to construct a shared enterpriselevel topology given ‘a whole diagram of power grids’ because of those differences of topology models in two distribution power systems. And there are still some problems such as repeated maintenance of topology data and poor maintenance. In addition, because both systems apply relational databases to store and compute data of grid topology, the efficiency of distribution network topology analysis is quite P. Liu · J. Liang · M. Ma (B) Hefei University of Technology, Hefei, China e-mail: [email protected] P. Liu e-mail: [email protected] J. Liang e-mail: [email protected] J. Xiao Anhui Electric Power Company, State Grid Corporation of China, Hefei, China e-mail: [email protected] D. Hu Beijing Guowang Xintong Accenture Information Technology Co., Ltd, Beijing, China e-mail: [email protected] G. Shi Beijing SGITG-Accenture Information Technology Co., Ltd, Beijing, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_40

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low. Therefore, the application effect of distribution network topology in outage analysis and load flow calculation is not satisfactory. Considering the problem of difficulties and high cost in modification of underlying system model, this paper studies the topology model of distribution automation system and GIS system, and then constructs an enterprise-level topology model for distribution network based on graph databases. This lays a solid foundation for realizing a shared enterprise-level digital topology of distribution networks and efficient topology analysis. Keywords Graph database · Topology model design · Automatic diagram generation

1 Introduction In recent years, with the rapid development of power grids construction, the power system has become larger in scale. Electricity companies at all levels accumulate huge amounts of data on power equipment and operation management of the system [1–3]. Therefore, it is an important consideration for us to store and apply these data better and to deeply excavate their value. The graph database is one of the non-relational databases which widely used in the parallel processing of massive data recently [4]. It is helpful to realize parallel traversal more effectively, reveal the power network topology more intuitively, and promote kinds of professional work for power grids [5, 6]. In this paper, an enterprise-level model construction method of power distribution network topology based on graph databases is proposed. First, the topology structure and topology model of distribution networks are separately described in Sect. 2 from the perspective of professional work and data. Then, in Sect. 3, relational databases and graph databases applied in distribution network topology are compared with their advantages and disadvantages in terms of data storage, data computing, topological relation revealing. Also, the necessity of using graph databases to build a topology model is clarified. Section 4 gives a graph database-based enterprise-level design method for a topology model from three aspects: type, attribute and topological diagram. The process of CIM/XML and CIM-E data conversion and resolution, optimized FR force-directed algorithm, as well as the generation of topology model, will be elaborated in Sect. 5. Finally, Sect. 6 concludes the paper.

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2 Topology Model of Distribution Networks 2.1 Topology Structure of Distribution Networks in Professional Work Perspective Distribution networks are important sections that connect the customers and the power supplier. It receives electrical energy from transmission networks or regional power plants, then distributes it to different users on the spot or level by level according to voltage [7, 8]. Power equipment in the distribution network includes bus-bar switches, overhead power lines, cables, distribution line towers, distribution transformers, isolating switches, lightning arresters, reactive power compensators, etc. [9]. A typical physical model of the distribution network is shown in Fig. 1. In this physical model, the topology of the distribution network refers to the layout of stations and equipment in the network, as well as the connection mode of power lines connecting them. The topology structure of distribution networks is mainly divided into two parts: connection relationships and topological relationships. Connection relationships refer to electrical connection relations among power equipment, which ignore switch positions and their on–off status. But topological relationships include all switch positions and can reflect the running state of the power grids [10].

Fig. 1 A typical physical model of the distribution network

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2.2 Topology Structure of Distribution Networks in Professional Work Perspective To describe the data structure of power grids and realize the information sharing and data exchange among different systems, the national standard IEC61970 puts forward the Common information model (CIM) and the CIM/XML information exchange format of power systems [11]. And State Grid Corporation of China proposes the CIM/E information exchange format based on CIM [12]. The distribution automation system describes the topology model of distribution networks through CIM/E information exchange format, but the power grid GIS system does that through CIM/XML information exchange format. Figure 2. shows how CIM/XML and CIM/E describe the topology of distribution networks. In CIM/XML information exchange format, there are three topological relation elements, including Equipment, Terminal, and Connectivity Node which form a relationship that exists between primary key and foreign key. Accordingly, it is able to build the multiple-node connectivity in the form of ‘Equipment—Terminal— Connectivity Node—Equipment’, and construct the distribution network topology [13]. In the CIM/E information exchange format, the main topological relation elements are ‘Equipment’ and ‘Connectivity Node’. There is an association between the primary key and foreign key between these two elements. And according to this association, it can build a multiple-elements connection relationship and then construct the topology of distribution networks.

Fig. 2 Topology of distribution networks in the CIM/XML and CIM/E information exchange formats

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3 Application Analysis of Topology Database in Distribution Networks 3.1 Application Analysis of Power Grid Topology Based on Relational Database Generally, relational database stores data via tables, and all power equipment’s data is stored in one or several tables. When each kind of power equipment has to create its table for data storage, there need to be a dozen of tables according to different types, and the equipment connectivity among tables needs to be constructed by using ‘join’ statements in the form of primary key and foreign key. For example, if there is a graph when the query depth is set to 4, that means it has to join 4 times from the start node. Now we assume that the data volume of one certain type of equipment is 10000, then it has to compute 100004 times. However, there may be only a few dozen required records in the results. So, the computation amount grows exponentially with the size of data sets. If all data of power equipment is stored in one table and graph nodes are represented by self-connection mode, the data sets will become dauntingly huge and the query performance will get worse, although this approach could help solve the problem of how to establish connections.

3.2 Application Analysis of Power Grid Topology Based on Graph Database Graph databases contain two basic data types: Nodes and Relationships. They both have properties in the form of key/value. Nodes are connected by Relationships, and then a relational network structure is built. In addition, Relationships are saved in a doubly-linked list that users can find ‘from-to Node’ conveniently. For instance, by the storage model above, if 1st property and 1st ID are saved in the ‘Node A’, it is easy to traverse the topology diagram which takes the ‘Node A’ as a starting point. Thus, graph databases have high query speed and show relationships more intuitively that are very useful for highly interconnected data [14]. Therefore, compared to traditional relational databases, graph databases have great advantages in topology storage and computation of distribution networks. Graph databases can clearly show the relationships among data nodes and edges that realize the visualization for highly interconnected data. Also, they can quickly query complicated topologies and effectively cope with massive, complex, interconnected and variable data.

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4 a Graph Database-Based Topology Model Design of Distribution Networks 4.1 Definition of the Graph Data Model As required by professional work and application scenarios, the design of the graph database’s data model should define the corresponding type of nodes, edges and attributes [15]. (1)

Type definition:

(2)

Every node and every edge in the graph database has a corresponding type. Nodes represent entities and edges represent relationships among entities which include connection relation, dependency relation, and so on. At the same time, every node must have one or more edges associated with it. Attribute definition:

(3)

The attribute is a binary array—‘(Attribute Dame, Value Domain)’, and ‘Value Domain’ is a set of all attribute values (nodes and edges). Of all the attributes of node (or edge), there must be the only primary key. Topology definition: Topology represents the associated set of all nodes and edges, and it is a graph of data model without directions.

From the above definitions, we can see that in a graph data model, if the node types are different, they have different sets of attributes, and if there are several edges between two different nodes, the types of edges must be not the same.

4.2 Design of Topology Model In the course of topology model design, the power grid topology could be regarded as a graph structure composed of nodes and edges. Power equipment like busbars, load nodes, voltage regulators, switches, parallel capacitors, etc. can be modeled as nodes. And the relationships among power equipment can be modeled as edges. Establishing the mathematical model of the graph according to the CIM model standard. The distribution network is defined as a graph network G(V, E), where V is the set of nodes and E is the set of edges. And it can be described as Formula (1). G = {V (g), E(g)}

(1)

where, V (g) = {v1, v2, v3, v4, v5, · · ·}; E(g) = {e1, e2, e3, e4, e5, · · ·}. Combined with the CIM model, the definitions of V (g) and E(g) is as follows:

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Fig. 3 The graph structure constructing process of distribution networks

V (g) are examples of the subclass of class ‘Equipment’ (switches, breakers, transformers, feeder lines, line sections, etc.) and class ‘Connectivity Node’; E(g) should be divided into two types. One is ‘Terminal’ which defines the connection relationship. Another is the affiliation that ‘Equipment’ and ‘Equipment Container’ contain. The abstracting process of the entire model construction is shown in Figs. 3 and 4. reveals an example of outputs according to the above modeling method.

5 Automatic Diagram Generation of Distribution Networks Topology Model By abstracting the relationships among nodes and edges of distribution networks in the graph database, we can regard the node of the topology diagram as a small ball and regard the edge linked to the ball as a spring. Firstly, parsing and converting the CIM/XML and CIM/E data files. Then, the FR force-directed algorithm is used in the iterative calculation for tensile force and repulsive force of every node. Finally, when node stress is balanced, it can set a series of esthetic parameters and complete the layout.

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Connect

Power Transformer

Breaker

Distribution Transformer

AC Line Segment

AD Break Switch

Fuse

Fig. 4 A topology database expression example of distribution networks

5.1 Data Parsing and Conversion of the CIM/XML and the CIM/E Data parsing and conversion of the CIM/E. After getting XML files from the power grid GIS system, we can select power equipment like stations, breakers, busbars, current transformers and potential transformers with ‘Connectivity Nodes’, and make the nodes of the topology model in the graph database. In this way, the dataset of every node could form an independent file. Selecting ‘Terminals’ which can represent connection relationship and form edges of ‘Connect’ type. Then, select the affiliation of equipment and equipment container and form edges of the ‘belong’ type. Every data set of edges could also build an independent file. At last, searching the relationships among nodes and edges and constructing an entire topology database model of distribution network. The process of data parsing and conversion is shown in Fig. 5.

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Fig. 5 Parsing and converting CIM/XML files into graph database files

Data parsing and conversion of the CIM/E. After getting CIM/E files from the distribution automation system, how we should deal with the affiliation of equipment and equipment containers is the same as CIM/XML files. But there is no direct ‘Terminal’ and ‘Connectivity Node’ in CIM/E files, so it requires a special processing method of the data [16]. The specific processing mode is as follows: (1)

(2)

Selecting the start and the end node-numbers from equipment and equipment attributes and generating ‘Terminal’ which can serve as the ‘Connect’ type edge of topology model. If the start and the end node-numbers are interconnected, the system would randomly generate a ‘Connectivity Node’ with an associated code, which can be regarded as the node of the topology model. The process of data parsing and conversion is shown in Fig. 6.

5.2 Algorithm Model of FR Force-Directed Combined with Coulomb’s law, the tensile force acting on the node can be expressed as Formula (2).

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Fig. 6 Parsing and converting CIM/E files into graph database files

Fa (v) =

Σ

(| pu − pv |)

(u,v)∈E

=

p u − pv | p u − pv |

Σ | pu − pv |2 pu − pv | p u − pv | K (u,v)∈E

(2)

And the repulsive force acting on the node can be expressed as Formula (3). Fr (v) =

Σ

fr (| pu − pv |)

u∈v,u/=v

=

Σ u∈v,u/=v

p u − pv | p u − pv |

K2 p u − pv | p u − p v | | p u − pv |

(3)

In order to accelerate the speed of force balancing on the node and boot the layout efficiency, we introduce the concept of temperature t. So, the actual displacement of the node can be represented as Formula (4). Δpv = min{ pv , t}

pv | pv |

(4)

By using the temperature variable t, it is able to control the magnitude of node displacement when the automatic layout is in each iteration [17]. When the overall force acting on the node is equal to 0, the temperature reaches a peak. And the magnitude of node displacement increases as the temperature increases, vice versa.

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Fig. 7 The flow chart of automatic diagram generation

5.3 The Process of Automatic Diagram Generation Combined with the parsing and converting process and the FR force-directed algorithm above, we get the flow chart of automatic diagram generation which shows in Fig. 7. The process consists of three steps: STEP 1: Parsing and converting CIM/XML files and CIM/E files into storage nodes and edges which are based on graph databases. STEP 2: Using the FR force-directed algorithm to automatically generate the topology diagram. And setting layout parameters, filling from north to south and from west to east; Following the horizontal and vertical principle when connecting and reducing the crossover and crowding between lines. STEP 3: Proceeding the iterative update until the layout is finished. The effect of automatic layout is shown in Fig. 8

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Company A Box-type Substation A1 Transformer B1 Transformer B2

Line #1

10kV Switch

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Branch Switch

Transformer B3 Transformer B4 Section Switch B1

Box-type Substation B2 Box-type Substation B3

Company C

Section Switch A2 Transformer A2

Box-type Substation B1

Section Switch B2 Transformer B5 Transformer B6 Transformer B7

Section Switch C1

Section Switch C2

Company D

Fig. 8 The effect of automatic layout

6 Conclusion As smart power grids and informatization have vastly developed, graph database becomes more and more popular in power professional work and plays the role of booster in power grids’ data management and application. By analyzing traditional relational databases and graph databases, this paper proposes an enterprise-level topology model design method of distribution networks based on graph databases. This method achieves the unity and fusing between the underlying graph and model. Then, based on it, the automatic diagram generation of distribution network topology is realized by using of optimized FR force-directed algorithm. In order to make power grids more intelligent, in the future, we will carry out research about graph database-based multigraph model validation, dynamic topology update, the automatic layout of thematic maps on the basis of this paper. Acknowledgements This work was sponsored by the Aeronautical Science Foundation of China (2019440P4001).

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References 1. Gao Y (2009) Research and implementation of topology automatic layout algorithm in network management system. Northeastern University 2. Zhao Y, Zhong Z, Wu Y et al (2015) A hierarchical layout algorithm based on graph matching. Comp Modernization 08:107–111 3. Zhou A, Qiu H, Gao K et al (2018) Research on graph database based power grid topology analysis technology. Electr Power Inf Commun Technol 16(08):23–27 4. Ravikumar G, Khaparde SA (2017) A common information model oriented graph database framework for power systems. IEEE Trans Power Syst 32(4):2560–2569. https://doi.org/10. 1109/TPWRS.2016.2631242 5. Huang H, Dai J, Wang Y et al (2019) Graph database based construction and network topology of CIM/E for power grid. Autom Electr Power Syst 43(22):122–129 6. Tan J, Zhang G, Liu G et al (2019) Graph computing based power distribution system modeling and analysis. Distrib Utilization 36(11):28–34+54 7. Mi W, Xin Y, Jiang G et al (2013) Comparative analysis of grid model exchange standard CIM/E and CIM/XML. Power Syst Technol 37(04):936–941 8. Lu C, Zhang W (2005) CIM topology analysis for electric power networks. Zhejiang Electr Power 04:5–8 9. Cui L, Wang Z, Wu Y (2018) Analysis of power grid model based on CIM/E. Comp Syst Appl 27(01):168–173 10. Hu W, Zhang W, He X (2009) Analysis and conversion of power network model based on CIM expression. Microcomp Appl 25(05):53–56+6 11. Zhou Z et al (2018) CIM/E oriented graph database model architecture and parallel network topology processing. IEEE Power Energy Soc Gen Meet (PESGM) 2018:1–5. https://doi.org/ 10.1109/PESGM.2018.8586367 12. Zhu X, Liang G, Lu J et al (2016) Research on physical model design of power grid based on IEC 61970. Electric Eng 12:16–18 13. Yan H, Han W, Yu W et al (2014) Automatic generation of single-line diagram for distribution network based on CIM. East China Electric Power 42(12):2502–2505 14. Dong Z, Duan X, Li Q et al (2009) Universal graphic platform of electric power system and the production of static topology. Power Syst Prot Control 37(18):89–92 15. Deng Q, Su K, Zhao L (2009) Topology analysis and modeling for distribution network based on complicated equipment. Eng J Wuhan Univ 42(04):491–495 16. Chen L, Han B, Zhao J et al (2017) Automatic graphing based verification techniques for model topology of distribution network and its implementation. Autom Electr Power Syst 41(02):160–164 17. Nitin (2012) On untangled meshes via Fruchterman Reingold force directed graph embedding. In: UK Sim 14th international conference on computer modelling and simulation, 2012, pp 39–45. doi: https://doi.org/10.1109/UKSim.2012.15

Research on Application of Innovative Linear Active Disturbance Rejection Control in Three-Phase Four-Wire System DSTATCOM Youjie Ma, Xinyu Jiang, and Xuesong Zhou

Abstract In order to improve the compensation accuracy and speed of the static synchronous compensator (DSTATCOM) for the unbalanced load, a novel linear active disturbance rejection controller is proposed in this paper. The controller is applied to the current tracking control of DSTATCOM, and its mathematical model is derived. The performance of the new linear active disturbance rejection controller is analyzed by frequency domain analysis to prove its correctness. Finally, the operation performance of DSTATCOM under the action of the new controller is verified by MATLAB/Simulink simulation platform, and compared with the traditional ADRC controller. The results show that the capacitive split DSTATCOM controller has better compensation performance and is more practical. Keywords DSTATCM · Linear active disturbance rejection control · Three phase four wire system · Unbalanced load

1 Introduction In recent years, with the rapid development of society, users have higher and higher requirements for power quality, and the access of a large number of nonlinear devices in the distribution network seriously affects the reactive power content in the network, and then affects the normal and safe operation of the electrical equipment in the system [1]. As an advanced and ideal reactive power compensation device, stationary synchronous compensator of distribution network (DSTATCOM) can efficiently compensate nearby reactive power, so it is widely used to improve power quality [2]. Because its key control technology is not mature enough, it has not been widely used, so the control method of three-phase four-wire system DSTATCOM has become the main problem studied in this paper. At present, scholars at home and abroad have proposed many control strategies applied to DSTATCOM system. These control strategies are mainly divided into three Y. Ma · X. Jiang (B) · X. Zhou Tianjin Key Laboratory of Control Theory and Application for Complex Systems, School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin 300384, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_41

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categories: traditional proportional integration (PI) control [3]; Intelligent Control Technology Based on Neural Network and Fuzzy Control [4]; Control method based on traditional modern control theory [5]. However, the traditional PI control is easily affected by system parameter changes or external uncertain disturbances. For the nonlinear, time-varying and strong coupling characteristics of DSTATCOM system, the control effect is more difficult to meet the requirements. The convergence time of intelligent control algorithm is slow and it is difficult to meet the real-time requirements of control. Modern control theory is too dependent on accurate mathematical model for analysis, so it is difficult to establish accurate mathematical model of DSTATCOM system, modern control theory is difficult to achieve satisfactory control effect in practice. Chinese scholar Han Jingqing proposed Active Disturbance Rejection Control (ADRC) technology [6], which does not rely on the precise mathematical model of the controlled object, and uses its extended state observer (ESO) to estimate and compensate the total disturbance of the system. However, the wide application of ADRC has been hindered by the numerous parameters it has been adjusted. Therefore, Professor Gao Zhiqiang linearizes and parameterizes ADRC in literature [7] and Linear Active Disturbance Rejection Controller (LADRC) technique is proposed. In reference [8], LADRC is applied to the three-phase three-wire system DSTATCOM, but the observation ability of total disturbance was low. In this paper, a new type of LADRC is proposed and applied to the three phase four wire system DSTATCOM current tracking control. Firstly, the mathematical model of the physical system is established. Secondly, the design of the innovative LADRC is carried out. Then, the disturbance immunity and stability of the new controller are analyzed and proved. Finally, the MATLAB/Simulink simulation platform is used to verify that the three-phase four-wire DSTATCOM under the new LADRC control has a faster and more accurate reactive power compensation capability than the traditional LADRC control.

2 Establishment of Mathematical Model of Three-Phase Four-Wire DTSTACOM System At present, the main circuit topology of three-phase four-wire DSTATCOM is widely used, such as three-phase combined DSTATCOM, capacitive split three-phase fourwire DSTATCOM, three-phase four-wire four-bridge arm DSTATCOM [9]. In view of the cost of the device and the dual consideration of unbalanced load compensation capacity, In this paper, the capacitance split three-phase four-wire DSTATCOM topology is selected and its reactive power and unbalance load compensation ability is discussed. Its topology is shown in Fig. 1. In the figure below, u sa , u sb and u sc represents the three-phase AC voltage source of the power grid; R concentrates on the inverter loss and the resistance connecting the reactor loss and the loss on a part of the power grid lines; L represents the

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Fig. 1 Capacitor split-phase four-wire DSTATCOM system structure diagram

inductance connected to the reactor; u ca , u cb and u cc refer to the three-phase voltage output on the AC side of DSTATCOM; i a , i b and i c are the three-phase compensation current output by the device to the power grid, that is, the three-phase current output by the AC side of the inverter, and i n is the compensation current of the midline. Cdc1 and Cdc2 are the capacitors of the upper and lower bridge arms on the DC side respectively, representing the splitting capacitor voltages Udc1 and… The total capacitance voltages on the DC side are Udc and 0.5Udc = Udc1 = Udc2 ; T1 , T2 … T6 is six IGBTs. Before the mathematical model of STATCOM is established, the power electronic switching device is assumed to be an ideal component. According to the equivalent circuit diagram shown in Fig. 1 and Kirchhoff’s voltage law and current law, the mathematical model of the main circuit of capacitive split three-phase four-wire DSTATCOM in the abc coordinate system can be obtained: ⎧ ⎪ L didta = u ca − u sa − Ri a ⎪ ⎪ ⎪ di ⎪ ⎨ L dtb = u cb − u sb − Ri b di c L dt = u cc − u sc − Ri c ⎪ dUdc1 ⎪ ⎪ C ⎪ dc1 dt = Sa i a + Sb i b + Sc i c ⎪ ⎩ C dUdc2 = (S − 1)i + (S − 1)i + (S − 1)i dc2 dt a a b b c c

(1)

In the above equation, SK (K = a, b, c) is the device switching function. When SK = 1, the switch of the upper axle arm is on and the switch of the lower axle arm is off. When SK = 0, the opposite state will be observed. By coordinate transformation of Eq. (1), the mathematical model in the dq0 coordinate system can be obtained:         d id u cd − u sd id iq = −R + ωL L u cq − u sq iq −i d dt i q

(2)

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Cdc1 dUdtdc1 = 23 (Sd i d + Sq i q + 3S0 i 0 ) Cdc2 dUdtdc2 = 23 (Sd i d + Sq i q + 3S0 i 0 ) − 3i 0

(3)

In the above formula, Sd , Sq and S0 are components of the device switching function on dq0 axis;i d , i q and i 0 are the output current of STATCOM AC side on dq0 axis respectively. u sd and u sd are components of three-phase voltage of the power grid on the dq axis; u cd and u cq represent the output current of the AC side of the inverter on the dq axis; ω is the fundamental wave frequency of the system. It can be clearly seen from Eq. (2) that the current components of d-axis and q-axis still have a coupling relationship after coordinate transformation. It can be obtained from Eq. (3) that the current difference between the DC side splitting capacitance is 3i 0 . The voltage equalization of the two capacitors on the DC side is related to the zero-sequence current. When the three-phase load is symmetric, i a +i b +i c = 0, i n = 0 at the moment. And when the disturbance in the process of power grid operation, the asymmetric threephase load, at this time, i a + i b + i c = 0, and will produce larger and zero sequence current through the central circulation, and large Central Line current will affect the voltage stability, lead to voltage asymmetry, midpoint voltage offset, influenced the stability of the equipment operation [10], so the follow-up analysis of unbalanced load reactive power compensation.

3 Traditional LADRC and Innovative LADRC Design From the above analysis, it can be known that the capacitive split DSTATCOM is susceptible to adverse factors in the operation process, and the performance of the current loop in DSTATCOM double closed-loop control directly affects the accuracy of the device’s reactive power compensation. Therefore, this paper selects the LADRC with strong disturbance immunity to be applied to the current loop to achieve accurate tracking of the instruction current.

3.1 Traditional LADRC Design The LADRC consists of three components, Linear Tracking Differential (LTD), Linear State Error Feedback (LSEF), Linear Extended State Observer (LESO), as shown in Fig. 2. Among them, LTD extracts differential signals and arranges the transition process to avoid the contradiction between rapidity and overshoot [11]. In reality, it is generally not used to design LADRC. LSEF combines interference estimation to generate control signals. LESO, as the core of LADRC, is used to estimate and compensate the total disturbance in real time.

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Fig. 2 Traditional LADRC structure block diagram

In Fig. 2: v represents the system reference input; b0 is the control gain; u is the control quantity; z 1 , z 2 are two state variables representing the output and total disturbance of LESO observation system; y is the system output. Since the mathematical model established by the controlled object is a first-order differential equation, a first-order LADRC controller is designed. According to literature [12], the differential equation of the system discussed in this paper can be written into the following general form: y˙ = −a0 y + ω + bu

(4)

where ω is the unknown external disturbance, a0 is the system parameter, b is the input control gain and part of it is known (b0 is the known part). Equation (5) can be further simplified to obtain: y˙ = f + b0 u

(5)

In the above equation, f = −a0 y +ω+(b−b0 )u is the total disturbance including internal disturbance and external disturbance. x1 = y and x2 = f are selected as state variables, then Eq. (5) is transformed into the form of continuous extended state space:

   ⎧    ⎪ x1 01 b0 0 u ⎨ x˙1 = + x˙2 x2 0 1 f˙ 00 ⎪ ⎩ y = x1 The corresponding second-order LESO is established:

(6)

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⎧ ⎨ e = z1 − y z˙ = z 2 − β1 e + b0 u ⎩ 1 z˙ 2 = −β2 e

(7)

In Eq. (7), z 1 tracks y and z 2 tracks f . β1 and β2 are the gain coefficients of the observer. Design disturbance compensation link formation control quantity:  u = (u 0 − z 2 ) b0

(8)

If the estimation error of z 2 to f is not taken into account, Eq. (5) can be simplified as: y˙ = f + b0 u = ( f − z 2 ) + u 0 ≈ u 0

(9)

The design control rate is: u 0 = kp (v − z 1 )

(10)

kp is the proportional control gain coefficient of the controller. According to the pole assignment method in reference [13], pole assignment is carried out for the traditional LADRC observer and controller as follows:  2 s + β1 s + β2 = (s + ω0 )2 (11) s + kp = (s + ωc ) So we get β1 = 2ω0 , β2 = ω02 and kp = ωc . ω0 is the bandwidth of the observer; ωc is the controller bandwidth.

3.2 Innovative LADRC Design In the traditional LESO design, it can be concluded that the tracking of z 1 to x1 and the tracking of z 2 to x2 are achieved through the adjustment of deviation e. However, in the actual operation process, after z 1 is quickly tracked to x1 , e is already very small at the moment, and it is difficult to adjust z 2 by e. Therefore, it is necessary to select a new deviation between z 2 and x2 for adjustment. The traditional second-order LESO model can be obtained as follows:  z 1 = e + x1 (12) z 2 = z˙ 1 + β1 e − b0 u Substituting Eq. (5) into Eq. (12), we can obtain:

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z 1 = x1 + e z 2 = x2 + e˙ + β1 e

501

(13)

So the deviation between z 2 and x2 has become e+β ˙ 1 e. However, the core of LESO is the dynamic estimation and compensation of the total disturbance. Therefore, the total disturbance differential signal is introduced on the basis of the new deviation to improve the observation ability of the total disturbance dynamic. The result is the innovative LESO ⎧ e = z1 − y ⎪ ⎪ ⎨ z˙ 1 = z 2 − β1 e + b0 u ⎪ z˙ = z 3 − β2 (e˙ + β1 e) ⎪ ⎩ 2 z˙ 3 = −β3 (e˙ + β1 e)

(14)

In the above formula, z 3 tracks the differential signal of f , and β3 is the new coefficient of observer gain. Re-pole assignment of the new LESO is carried out, and the pole assignment of the controller remains unchanged, so that β1 = ω0 , β2 = 2ω0 , β3 = ω02 , and kp = ωc are finally obtained. Thus, we can get the overall structural block diagram of innovative LADRC as shown in Fig. 3. Taking A-phase current as an example, the current tracking control of the innovative LADRC is analyzed. According to Eq. (1), it can be obtained: y˙a = −

Rya + u sa 1 + u ca L L

(15)

ya represents the output A-phase current of DTSTCOM system. Construct the state space equation: Fig. 3 Block diagram of innovative LADRC structure

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⎧ x˙1a = x2a + b0a u a ⎪ ⎪ ⎨ x˙2a = x3a ⎪ x˙ = f¨a ⎪ ⎩ 3a ya = x1a

(16)

  In this formula, b0a = 1 L and f a = −(Rya + u sa ) L. Then the DSTATCOM current tracking control model based on innovative LADRC: ⎧ ⎪ z˙ 1a = z 2a − β1 (z 1a − ya ) + b0a u a ⎪ ⎪ ⎪ ⎪ z ⎪ ⎨ ˙ 2a = z 3a − β2 [(˙z 1a − y˙a ) + β1 (z 1a − ya )] z˙ 3a = −β3 [(˙z 1a − y˙a ) + β1 (z 1a − ya )] ⎪ u 0a = kp (i a - ref − z 1a )ya ⎪ ⎪ ⎪ u − z 2a ⎪ ⎪ ⎩ u a = 0a b0a

(17)

4 Performance Analysis of the Innovative LADRC Since disturbance immunity and stability are important factors to evaluate the quality of a closed loop control system. Therefore, the two performances of the innovative LADRC are analyzed next.

4.1 Disturbance Immunity Analysis of the Innovative LADRC According to the above LADRC design can be obtained:  u = (ωc (v − z 1 ) − z 2 ) b0

(18)

You plug the parameter into (14), and you take the Laplace transform of it ⎧ ⎪ ⎪ Z 1 (s) = ⎨

Z 2 (s) = ⎪ ⎪ ⎩ Z (s) = 3

3ω0 s 2 +3ω02 s+ω03 b0 s 2 Y (s) + (s+ω 3 U (s) (s+ω0 )3 0) 2 2 2b0 ω0 s+b0 ω02 2ω0 s +ω0 s Y (s) − (s+ω0 )2 U (s) (s+ω0 )2 b0 ω02 s ω02 s 2 Y (s) − (s+ω 2 U (s) (s+ω0 )2 0)

(19)

The Laplace transform of Eq. (18) is carried out and (19) is substituted into the following equation U (s) =

G 1 (s) [ωc V (s) − H (s)Y (s)] b0

(20)

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2ω s 3 +3(ω2 +ω ω )s 2 +(ω3 +3ω2 ω )s+ω3 ω

(s+ω0 ) 0 0 c 0 0 0 c 0 c where, G 1 (s) = s 3 +(ω . At this 2 , H (s) = (s+ω0 )3 0 +ωc )s time, the simplified structure diagram of the control system can be obtained. Combined with Fig. 4, the output response of the system can be obtained as 3

y=

s 3 + (ω0 + ωc )s 2 ωc v+ f s + ωc (s + ω0 )3 (s + ωc )

(21)

As can be seen from the above equation, the system output consists of tracking term and disturbance term. However, the disturbance term is mainly affected by ω0 and ωc , so the disturbance immunity characteristics of the control system are discussed by the values of ω0 and ωc . Specific frequency domain characteristic curves are shown in Figs. 5 and 6. It can be seen from the Bode diagram that the increase of ω0 and ωc

Fig. 4 The innovative LADRC simplified structure block diagram

Fig. 5 Frequency domain characteristic curve of perturbation transfer function (ω0 = 60)

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Fig. 6 Frequency domain characteristic curve of perturbation transfer function (ωc = 60)

makes the disturbance gain decrease and the disturbance immunity performance of the system become better. Similarly, the transfer function of the traditional LADRC closed-loop system can be obtained, and the comparison of the amplitude phase characteristic curves of the two perturbation terms is shown in the figure below. Figure 7 shows that the disturbance gain of the new type of LADRC is smaller and the disturbance immunity is slightly better than that of the traditional one.

4.2 Stability Analysis of the Innovative LADRC When the influence of external disturbance and model parameter  uncertainty is not taken into account,f = (b − b0 )u. So at this time y = bu s. Meanwhile, it is assumed that p = b b0 , and p >1 can be known according to the system parameters of DSTATCOM, so G(s) = pb0 s can be obtained. Then it can be substituted into the closed-loop transfer function of the system y=

ωc (s + ω0 )3 v a4 s 4 + a3 s 3 + a2 s 2 + a1 s + a0

(22)

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Fig. 7 Amplitude phase characteristic curves of traditional LADRC and innovative LADRC perturbation terms

In the above formula, a0 = ω03 ωc; a1 = ω02 (3ωc + ω0 ); a2 = 3ω0 (ωc + ω0 ); a3 = 2ω0 + (ωc + ω0 ) p; a4 = 1 p. Since both controller bandwidth ωc and observer bandwidth ω0 are positive. So we can infer ai > 0(i = 0, 1, 2, 3, 4). According to the Lynard-Chiapart stability criterion, on the premise that all the coefficients of the characteristic equation are positive, if all the odd-order Hervitz determinant are regular system stable, that is a1 a0 0 Δ3 = a3 a2 a1 = a1 a2 a3 − a0 a32 − a12 a4 > 0 0 a a 4 3

(23)

From the above analysis can be further obtained Ap 2 + Bp − C > 0

(24)

Among them, A = 2ω0 (3ω02 +10ω0 ωc +9ωc2 ) > 0; B = 2ω03 +5ω02 ωc +8ω0 ωc2 + > 0; C = ωc (ω0 + ωc )2 > 0. The above inequality is established by selecting certain parameters, so the control system is stable. 9ωc3

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5 Simulation Experiment Analysis In order to verify the correctness and effectiveness of the new LADRC strategy proposed in this paper, the Matlab/Simulink simulation software platform is used to build the three-phase four-wire DSTATCOM simulation model of capacitor marchtype, as shown in Fig. 1. The operation performance of DSTATCOM under the two control modes is compared and analyzed by using the traditional and new LADRC respectively. Relevant parameter design is shown in Table 1. In order to better compare the performance of the two LADRC, the parameters of both are set as ω0 = 10,000(rad/s), ωc = 5000(rad/s), and b0 = 1000. Figure 8 shows the comparison diagram of midline current under the action of two kinds of LADRC. Table 1 DSTATCOM system parameters

Parameter

Value

Unit

Effective value of grid line voltage

380

V

System frequency

50

Hz

DC side capacitance voltage

700

V

DC side split capacitance up and down

3300

µF

Filter output inductance

3

mH

Fig. 8 The midline current is used for both traditional and innovative LADRC

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The capacitive split DSTATCOM is put into operation at t = 0.05(s). As can be seen from the figure, when DSTATCOM is not put in, there is a large current on the midline. However, after t > 0.05(s), the midline current decreases under both control modes, indicating that LADRC technology can be well applied in DSTATCOM’s compensation of unbalanced load. However, the midline current under the action of the new LADRC will reach a smaller value, indicating that the DSTSTCOM under the control of the new LADRC has better compensation accuracy and the tracking performance of the new LADRC is better than that of the traditional LADRC. Figure 9 shows the voltage and current simulation waveform of A-phase power grid under two control modes. t = 0(s) DTATCOM is incorporated into the grid. It can be seen that DSTATCOM cannot play a good role when it is just incorporated into the power network, and the current phase of the power network still lags behind the voltage phase of the power network. After A period of time, the A-phase current is compensated to the same phase as the voltage under the two types of LADRC operation, indicating that LADRC can enable DSTATCOM to perform good reactive power compensation for inductive load. However, it is obvious that under the action of traditional LADRC, it takes 0.085 s transition time to compensate the current and voltage in the same phase, while under the action of innovative LADRC, it only takes 0.075 s to complete this goal. Obviously, the new LADRC has less transition time and faster compensation speed. The following figure shows the waveform of the total

0.075s 0.085s

Fig. 9 Using the traditional LADRC and improved LADRC voltage and current waveform on the lower side of the network

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Fig. 10 DSTATCOM DC voltage stabilization waveform

voltage change on the DC side of the capacitive split DSTATCOM under the action of two kinds of LADRC. As can be seen from the Fig. 10, DSTATCOM DC side voltage can be stabilized at 700 V under the action of both types of LADRC, while the new type of LADRC requires a short time to reach stability. DSTATCOM is incorporated into the power grid. Under the new LADRC system, the total voltage fluctuation of the DC bus is small and the overshot is small. This shows that the dynamic characteristics of the new LADRC are better than that of the traditional LADRC.

6 Conclusion and Prospect The reactive power compensation effect of three-phase and four-wire DSTATCOM system for unbalanced load is an important factor to determine the power quality of the power grid, and the control performance directly determines the operation ability of DSTATCOM device. Therefore, this paper adopts an improved LADRC to control the current tracking ring to improve the reactive power compensation ability of the three-phase four-wire DSTATCOM to the unbalanced load. On the basis of LESO, the total perturbation differential signal is introduced to improve the tracking accuracy of total perturbation. The disturbance immunity and stability of the new LADRC are proved in the frequency domain. Finally, through simulation comparison and analysis, the new type of LADRC capacitance split DSTATCOM compensation

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accuracy is better, the compensation speed is faster, but also has a certain antiinterference ability, has a good engineering application value. In addition, this paper does not involve much in the parameter adjustment of LADRC. I hope to do further related research in the following work.

References 1. Lv L (2007) The research of three-phase four-wire distribution static synchronous compensator control method. Xi’an University of Technology 2. Zhou JF, Gu YQ, Wei SQ (2007) The comprehensive analysis and comparison of SVC and STATCOM. Electr Power Autom Equip 27(12):57–60 3. Tavana MR, Khooban MH, Niknam T (2017) Adaptive PI controller to voltage regulation in power systems: STATCOM as a case study. ISA Trans 66:325–334. https://doi.org/10.1016/j. isatra.2016.09.027 4. Karami A, Galougahi KM (2019) Improvement in power system transient stability by using STATCOM and neural networks. Electr Eng 101(1):19–33. https://doi.org/10.1007/s00202019-00753-5 5. Rao YS, Pathak MK (2020) Model predictive control for three-level cascaded H-bridge DSTATCOM. IETE J Res 66(1):65–76. https://doi.org/10.1080/03772063.2018.1476189 6. Han JQ (1998) Active disturbance rejection controller and its applications. Control Decis 13(11):19–23 7. Gao ZQ (2003) Scaling and bandwidth-parameterization based controller-tuning. In: Proceedings of the 2003 American control conference. IEEE, Denver, USA, pp 4989–4996 8. Ma YJ, Zhou XS, Sun XT (2020) Research on D-STATCOM double closed-loop control method based on improved first-order linear active disturbance rejection technology. Energies 13(15):11–17 9. Zhou C, Zheng YH, Wang X, Li LX, Zhou LD, Zhang Y (2014) Control strategy based on dual-loop controller for split-capacitor-type three-phase-four-wire. Electr Power Autom Equip 34(08):114–121 10. Yang YL, Wang FQ (2004) Additional loss and voltage deviation caused by unbalanced operation of distribution transformer and countermeasures. Power Syst Technol 28(8):73–76 11. Li J, Qi XH, Wan H et al (2017) Active disturbance rejection control: theoretical results summary and future researches. Control Theor Appl 34(3):1–15 12. Zhou XS, Tian CW, Ma YJ, Zhao J (2012) Double closed-loop linear auto disturbance rejection control of SHAPF. Power Electron 46(03):1–3 13. Yuan D, Ma XJ, Zeng QH, Qiu XB (2013) Research on frequency-band characteristics and parameters configuration of linear active disturbance rejection control for second-order systems. Control Theory Appl 30(12):1630–1640

How Did the COVID-19 Crisis Affect the Efficiency of European Intraday Electricity Markets? Daria Gottwald, Jan Niklas Buescher, and Florian Momm

Abstract Our goal is to examine the efficiency of different intraday electricity markets and if any of their price prediction models is more accurate than others. The focus is on the German intraday market for electricity. We want to find out whether the COVID-19 crisis has an influence on the price development. This paper includes a comprehensive review between Germany, France and Norway (NOR1) day-ahead and intraday electricity market prices. These markets represent different energy mixes which would allow us to analyse the impact of the energy mix on the efficiencies of these markets. To draw conclusions about extreme market conditions (i) we reviewed the market data linked to COVID-19. We expected a higher volatility in the lockdowns than before and therefore decrease in efficiency of the prediction models. With our analysis, (ii) we want to draw conclusions as to whether a mix based mainly on renewable energies such as that in Norway implies lower volatilities even in times of crisis. This would answer the question (iii) whether a market with an energy mix like Norway is more efficient in highly volatile phases. For the analysis we use data visualization and statistical models as well as sample and out-of-sample data. Keywords Energy efficiency · Energy mix · Energy markets · COVID-19 · Out-of-sample data

D. Gottwald (B) FOM University of Applied Sciences, isf Institute for Strategic Finance, Leimkugelstraße 6, 45141 Essen, Germany e-mail: [email protected] J. N. Buescher RWTH Aachen, Automatisierungstechnik, Templergraben 55, 52062 Aachen, Germany e-mail: [email protected] F. Momm Hochschule Ruhr West, Energie- und Wasserökonomik, Duisburger Str. 100, 45479 Mülheim, Ruhr, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_42

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1 Introduction While digitalisation and climate change continue, renewable electricity generation such as wind power and solar power will be further expanded [1–3]. At the same time SARS-CoV-2 (COVID-19) has a major impact on the entire global economy. Changes are particularly noticeable in the energy sector, as both supply and demand are affected. These effects were particularly noticeable with regard to WTI and BRENT oil prices, which in some cases fell into negative values in April 2020 [4]. Since the focus of this paper will be Europe, here are a few examples of European energy prices: The BRENT oil price dropped by 59% compared to its last peak on the 17th of February. Also, gas prices dropped to a minimum since 1995 at the same time [5]. Since the COVID-19 crisis had a major impact on other commodities such as oil and gas, the question now arises as to what the situation was on the whole-sale electricity markets. Unlike the other commodities, electricity cannot be stored to the same extent, which is why there are special features with regard to price forecasts [6]. Similar to what has already been done with other commodities, one aim of this paper is to divide the period 01.01.2020–01.02.2021 into different phases and to highlight the impacts of the lockdowns. The paper by Ali and Kahn [7], serves as a model for this procedure. They looked at the agricultural commodity prices for various products in India and examined the influences on prices in the individual phases of the local lockdowns. They had found that the weighted average of prices fell during the lockdown [7]. Some papers focus on the links between the financial and commodity markets. One example is the paper of Elsayed et al. [8]. They investigate co-movements between the energy market and the financial markets. Furthermore, time patterns of volatility spillovers [8]. The paper by Adekoya and Oliyide [9] highlights the link between financial and commodity markets. In addition, it refers to the main price drivers. These linkages are mainly captured through the analysis of price movements and volatilities [9]. Our paper aims to analyse price and volatility movements as well. Among all financial assets spot electricity prices belong to the most volatile asset classes. One of the reasons for the high volatility is the non-storable nature of volatility. In their study L. Han et al. point out the risks for the market participants caused by volatilities and extreme price outcomes. For their analysis, they also looked at the different market regions in Australia individually and then compared them with each other. We take a similar strategic approach in this paper, as we examine and compare various European markets on the basis of their volatilities and prices [10]. In our paper we want to find out whether there is a link between the type of energy generation and the price or volatility movement in an extreme economic situation. In doing so, we will follow the approach of Halbrügge et al. [4] and their comprehensive analysis of the German electricity market as well as Fezzi and Fanghella [11], who analysed the Italian Electricity market [4, 11]. In order to use (i) out-of-sample data to improve forecasting accuracy in a similar way to traditional asset management, we have examined two types of prices in extreme situations for this paper [12]. We used intraday prices as well as day-ahead prices. One of our goals is to find out whether the forecasting

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methods have been improved by using this data. The periods March to May 2020 and December to February 2020/21 are crucial. In addition, countries in Europe reacted with different measures to the pandemic. Taking both into consideration, the COVID-19 measures and also the (ii) different energy mixes it leads to the question if it had an impact on the prices [11, 13, 14]. In other words, did the energy mix influence the prices during high volatility periods caused by lockdowns? To investigate the question, we looked at the energy markets in Germany, France and Norway (NO1). Our overall research problem is whether (iii) the forecasting accuracy in the German intraday market has improved in the second lockdown. In order to clarify this question, the paper is structured as follows: we first present common methods with regard to volatility and explained our calculation method with regard to confidence intervals. After that, we looked at the data we used. Our results are structured as follows: A general introduction to our approach, followed by a structured analysis looking first at intraday and then at day-ahead prices. In the case of Germany and France, we have also analysed the volumes. This is followed by a discussion, conclusion and outlook. To present our results, we refer to (i) extreme market conditions, (ii) the energy mix and (iii) energy efficiency.

2 Methodology and Data 2.1 Graphical and Statistical Analysis 2.1.1

Price Analysis

The methods used in this paper are mainly graphical analyses in order to draw conclusion. Following an order that starts with some kind of general overview via graphs that include all price data for German intraday and day-ahead electricity products. Afterwards we divided the data into the observed regions (Germany, France and Oslo–Norway) and added the 30-day volatility and also confidence intervals to the analysis. In addition, the electricity generation was also taken into consideration. Thereby, we pointed out different energy sources (renewables and fossil fuels). The following statistical values are determined: Mean, median, standard deviation and the 95% confidence interval. In order to calculate volatility, the following formula is used in literature for spot prices observed from historical data. To obtain the volatility estimates, price returns are used in this example [15]. ( )2  σ 2 dt = E dS/S where: S σ

Spot Price. Spot Price Volatility.

(1)

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variance.

For the 30- and 90-day volatility we made use of Bloomberg data and did not calculated the values ourselves. In order to calculate the 95% confidence interval which will be used in the visualisations α is set to 0.05 using the standard normal approximation [16]. βk = [bk − 1.96se(bk ), bk + 1.96se(bk )]

(2)

This type of analysis is carried out in order to draw connections between the lockdown periods, the price development and the energy production. The focus is on the German market. The data for France and Norway (NO1) serves as support, as both countries/regions have different energy mixes. z=

x − E(x) V ar (x)

(3)

In order to perform the standardisation according to the z-transformation, formula 3 was applied. The standardisation was carried out for the energy mixes and partly for German electricity prices [16].

2.1.2

Volume Analysis

To prove that the price developments during the lockdown periods had the COVID19 pandemic crisis as the main driver, a volume analysis is included for Germany. For France, the volume data are used to support hypotheses. For NO1, this analysis is not performed as no data are available in Bloomberg. Similar to prices, the following statistical quantities are determined for German and French intraday and day-ahead volumes: Mean, Median and Standard Deviation. For the German intraday and dayahead volumes, an additional graph was created that also includes the 95% confidence interval. However, this type of analysis only serves to support the statements, whereby the focus is on the German spot market for electricity.

2.2 Data 2.2.1

Electricity Prices

For the price analysis Bloomberg data for the German, French and Norway (NO1) day-ahead and intraday prices have been used. As stated before, the 30-day-volatility and 90-day-volatility was retrieved from Bloomberg. The confidence intervals are based on own calculations in Python. In the case of the German and French electricity prices, Epex Spot prices were used. In the case of the Norwegian price data, prices

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Table 1 General statistics across all price categories in MWh/EUR Statistics

German intraday

German day-ahead

France intraday

France day-ahead

NO1 intraday

NO1 day-ahead

Count

6356

6532

5367

6532

6532

6248

Mean

38.23

34.67

37.49

36.16

14.17

12.72

Std.

35.93

17.02

18.54

16.97

17.65

14.82

Median

35.00

33.58

36.50

35.40

8.84

8.08

Min

− 150.00

− 83.94

− 25.20

− 8.65

− 1.73

0.02

Max

1000.00

189.25

328.20

189.25

205.68

152.25

from Nord Pool were used. All calculations are based on hourly data and their mean values. The prices for Germany, France and NO1 prices were provided in euros. The analysis is based on the daily closing prices of the traded hours. In addition to the prices, the 30- and 90-day volatility were also subtracted for the same data set. Table 1 gives an overview of all relevant statistical data regarding the prices used. More than 5000 data points were used in each case.

2.2.2

Electricity Volumes

For the volume analysis the daily closing volume of the individual hours was used for further analysis. The same data set was also used regarding German and French volumes (Table 2). The entire record refers to five business days in a week and does not include weekends and national bank holidays. If there was no data for a specific product in the record due to a bank holiday or if the product was not traded on that day due to low liquidity, the record will have a blank field. Table 2 General statistics across German and French volumes in MWh/EUR Statistics

German intraday

German day-ahead

France intraday

France day-ahead

Count

5689

6816

6392

6486

Mean

5689.82

24,379.26

169.43

14,082.17

Std.

2844.92

4,164.75

288.43

2814.81

Median

5805.00

23,881.50

40.00

13,963.10

Min

0.00

14,441.00

0.00

6892.00

Max

61,234.00

43,600.00

2917.00

25,013.00

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Electricity Generation

The electricity generation data was gathered from the ENTSO-E Transparency Platform. The observation period starts at the 01.01.2020 and ends at the 31.12.2020. To get a quick overview on the main electricity sources we have plotted the main electricity generation sources per country. Figures 1, 2 and 3 show the standardised values on the left side and the non-standardised values in MWh on the right side each [17].

3 Results 3.1 Results of the Overall Investigation We performed a graphical analysis to draw conclusions about the energy price and volatility situation during and between the two lockdowns in the three countries

Fig. 1 German electricity generation

Fig. 2 French electricity generation

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Fig. 3 Norway (Oslo) electricity generation

under consideration. We looked at intraday prices and day-ahead prices. The data is divided into a country/region-based analysis and also into two different lockdown periods. In addition, the 30-day volatility and the confidence intervals are considered as well. The following data is not standardised. The focus of the analysis will also be on the influence and crisis-proofing of renewable energies. Therefore, the electricity price development in France and in the NO1 region in Oslo, Norway, will also be considered. For all three countries/regions, the following periods were considered: Price und volatility level in January 2020 as pre-COVID-19 phase compared to the price level in January 2021. The respective first and second lockdown period. The periods differ due to national regulations. In addition, the summer months are considered because the scope of the measures was small in all three countries.

3.2 German Electricity Prices In this part of the analysis the German market is considered first. The following graphs follow the same structure. On the left there is always an analysis of the price level. The right sight displays the volatility development. The last two graphs include the mean as well as a 95% confidence level. A wide confidence level indicates more dispersion and thus an uncertainty around the actual mean value. Germany had two lockdown periods during the observation period. The first lockdown period started in March 2020 and ended in May 2020. The second lockdown period started as a so-called soft lockdown in November and was then tightened in December. At the time of the data withdrawal in February 2021, the second lockdown in Germany had not yet ended [18]. In terms of energy mix, Germany drew most of its energy from onshore wind power when it comes to the mean value analysis. Following the same mean value approach lignite came in second place. It is striking with regard to the energy mix that none of the electricity generation sources make up the majority, i.e. have a share of over 50% [17] (Fig. 1).

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Fig. 4 German intraday electricity prices

3.2.1

German Intraday Prices

Figure 6 shows that there was a clear increase in volatility April 2020. The confidence level also shows greater volatility between April and May. In the second lockdown, on the other hand, volatility does not increase as much again. The reasons for the volatility increase in April 2020 could be many and varied. On the one hand, it could be related to the drop in oil prices, as there are correlations, or to weather data. This is particularly evident regarding the 30-day volatility, where a rise is visible after approx. fourteen days. However, this paper considers only the analysis of price, volatility, and production data. Correlations with other commodities are omitted [4, 11]. Before April 2020, both prices and volatilities were at a stable level. After showing high outliers April 2020, the price level recovers again, so that in May it is back at the level before April. The sample regarding the second lockdown starts at the first of November 2020 and ends at the first of February 2020. It gives us an indication about the similarities of the first lockdown. In contrast to the first lockdown, the price level remains at a higher level. Volatility, on the other hand, is lower. It had recovered in May 2020, after the first lockdown, and remains at a constantly low level. Except for the numerous outliers that can be clearly highlighted in the price range based on the confidence levels, the price movement shows an upward trend. For example, the price in January 2020 at 37.81 EUR is below the price in January 2021 at 54.51 EUR. The lowest price in the data set here is − 150.00 EUR and the highest price is 1000.00 EUR (Fig. 4).

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Fig. 5 German day-ahead electricity prices

Fig. 6 German average traded volumes per day in Intraday markets

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German Day-Ahead Prices

Figure 5 shows that the impact on volatility was greater on the day-ahead market than on the intraday market. Volatility also shows the highest level during the first lockdown and decreases towards the end of the lockdown. The prices show a clear drop in April 2020, which is the exact opposite development to the intraday market. After the first lockdown, the price level recovers. In April 2020, the average price under consideration drops significantly into negative territory. As Valitov [19] has shown, negative prices have been possible in the day-ahead market in Germany since 2008. The reason for this is the high feed-in of RES, for example in times of low demand [18]. The lowest price in the data set is − 83.94 EUR, whereas the highest price is 189.25 EUR which is also an indicator for high outliers. High outliers are also characterized by higher confidence intervals in the price graph. In the beginning of December, the price level increased and showed high swings. During the bank holidays around Christmas the price level decreased again before it moves up in January. Also, the 30-day volatility moves down during the bank holidays before it increased around the 15th of November. In January, the volatility increases again and by the end of January there is a drop in volatility. The price level in December 2021 is also higher than the price level in December 2020. Compared to the intraday area, the confidence level in the day-ahead area is constantly wider (Table 3). The average price was 38.23 EUR for intraday and 34.67 EUR for day-ahead prices. The standard deviation was 35.93 for intraday and 17.02 for day-ahead. • Compared with France and NO1, Germany has the most diverse energy mix, but is also heavily dependent on the fluctuating energy production from onshore wind, which accounts for the largest share even before lignite. • The wide confidence levels could be explained by the strongly fluctuating electricity production via offshore wind. • Day-ahead and intraday prices diverge sharply in the first half of the year but have converged significantly in the second half of the year. Table 3 General statistics about german prices and volatilities Observation period

Germany intraday (mean price; mean vola)

Germany intraday (std. price; std. vola)

Germany day-ahead (mean price; mean vola)

Germany day-ahead (std. price; std. vola)

January 2020

37.81; 1045.02

21.40; 308.11

33.91; 1138.85

13.54; 1066.01

January 2021

54.51; 1110.88

26.48; 404.37

54.72; 1110.18

17.34; 944.49

First lockdown

24.01; 1692.26

39.88; 531.82

21.60; 1842.29

13.03; 984.57

Second lockdown

48.71; 1023.19

33.32; 399.93

48.31; 1226.78

17.71; 1047.86

Summer months

38.10; 1146.86

39.42; 336.66

32.99; 1214.32

14.15; 916.56

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• The first lockdown shows a fundamentally lower price level than the second. At the same time, the first lockdown is the period with the highest volatility. • The price level in January 2021 is significantly higher than the price level in January 2020. 3.2.3

German Traded Volumes

Figure 6 compares the volumes traded on the German intraday and day-ahead (Fig. 7) markets. The light blue shadow represents the 95% confidence level. When looking at the day-ahead volumes this figure does not indicate any abnormalities during the COVID-19 pandemic crisis. Rather, this figure indicates seasonal fluctuations. In the intraday area, however, the situation is different. The confidence levels show large outliers, especially in the summer months. Higher traded volumes on the intraday market is linked to a higher level of flexibility. • In January 2020, higher volumes were traded than in January 2021 • In the first lockdown, the standard deviation in the day-ahead area was higher than in later periods, and more average daily volume was traded in the day-ahead market. It does not decrease again until late summer • On the day-ahead market, it is noticeable that the confidence level is always quite constant and that the volumes increase in the summer months

Fig. 7 German average traded volumes per day in Day-Ahead markets

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• In the second lockdown, more was traded in the intraday area/less was traded in the day-ahead area (compared to the first lockdown period).

3.3 French Electricity Prices The graphical analysis follows the same pattern for France. The same parameters are superimposed, and day-ahead and intraday prices are also compared. As each country in Europe has its own lockdown rules, the lockdown periods in France differ from those in Germany. In France, the first lockdown period was from March to June/July. This extends the observation period compared to Germany. The second lockdown began in mid-October and was relaxed again in mid-December. Until the end of our observation period on 1 February, a curfew remained in place from 6 p.m. to 6 a.m. CET [20]. France obtains most of its electricity from nuclear energy sources. The calculations based on the average values showed that almost 70% of the electricity produced over the year came from nuclear sources. Hydropower and onshore wind power take second and third place in France. The mean values of both accounted for less than 10% of the energy mix on an annual average [17] (Fig. 3).

3.3.1

French Intraday Prices

In direct comparison with the German intraday electricity prices, it is noticeable that the price level of the French intraday prices fluctuates even more. However, the general price level falls between March and May 2020 and rises again from June. Volatility initially fell sharply in February 2020, but jumped again in March, coinciding with the first COVID-19 measures. Volatility in June is lower than in

Fig. 8 French intraday electricity prices

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Fig. 9 French day-ahead electricity prices

the previous month. The confidence interval of volatility from March to June also indicates a higher dispersion and thus also greater uncertainty with regard to forecasts. As volatility decreases and prices rise in June, the confidence level also decreases. At the time of the announcement of the second national lockdown, prices and volatility rise simultaneously. Also, the confidence level of volatility shows greater excesses. At the end of the second lockdown, there is a clear drop in prices and a jump in volatility. However, the situation recovers quickly thereafter. Compared to prices in January 2020, prices in January 2021 are at a higher level. In contrast, intraday volatility is at a lower level. The highest price in the data set is 328.20 EUR and the lowest is -25.20 EUR. This indicates outliers, which are also evident in the price range via the confidence level (Fig. 8).

3.3.2

French Day-Ahead Prices

The price development in the day-ahead area hardly differs from the intraday area. Only the confidence intervals are somewhat larger in the intraday area. This becomes visible via the outliers. In the day-ahead area, the lowest price is − 8.65 EUR and the highest 189.25 EUR. Like the intraday area, the prices are lower in summer than in winter. A particularly low price level during the first lockdown should be noted. Compared to the price level in January 2020, the price level in January 2021 is also higher. Differences to the intraday prices are visible when it comes to volatility. Volatility is characterized by two peaks during the two lockdowns. First, there was a clear increase in April 2020 and another in June 2020. In the period in between, volatility fell once again. At the same time, the confidence level also decreases during this period. The development of volatility and confidence intervals during the second lockdown shows similarities to the development in the intraday area (Fig. 9).

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Table 4 General statistics about French prices and volatilities in EUR Observation period

France intraday (mean price; mean vola)

France intraday (std. price; std. vola)

France day-ahead (mean price; mean vola)

France day-ahead (std. price; std. vola)

January 2020

38.31; 1221.29

12.21; 717.49

37.55; 546.84

10.73; 321.90

January 2021

62.37; 601.00

18.39; 309.41

61.24; 644.05

17.17; 647.56

First lockdown

22.00; 1397.17

9.78; 476.57

21.30; 1161.13

9.32; 795.95

Second lockdown

47.09; 843.06

16.76; 405.42

46.26; 824.63

15.41; 651.17

Summer months

41.45; 527.49

16.33; 242.01

40.76; 567.71

12.34; 490.50

The average price per day was 37.49 EUR; 36.16 EUR and the standard deviation for the entire period was 18.54; 16.97. • In France, less nuclear power is produced in the summer months and a little more use is made of renewable energy sources such as solar. No link between generation and price level visible • Table 4 shows that there are no major fluctuations between day-ahead and intraday. Thus, it can be said for the forecast accuracy that it is higher in France. • In the first lockdown, prices fell sharply and showed a high volatility. In the second lockdown, prices rose sharply and volatility was low. • Day-ahead and intraday prices were always close to each other in the mean and median. However, they also show strong outliers. 3.3.3

French Traded Volumes

The following is a brief supporting analysis of the volumes. The average volume traded per day was 169.43; 14,082.17 MWh and the standard deviation for the entire period was 288.43; 2,814.81. • During the first lockdown, less than normal trading took place on the intraday market. • During the second lockdown, the most trading took place on the intraday market. The standard deviation is also above average. • During the summer months, less than average was traded via the day-ahead market. • In January 2021, more than the average was traded on the day-ahead market and more compared to the previous year. • The standard deviation of the day-ahead volumes is quite constant.

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3.4 Norwegian Electricity Prices The graphical analysis follows the same pattern for Norway. It only considers the Oslo region (NO1). The Norwegian government declared a national lockdown in midMarch 2020. At the end of April, the first relaxations were decided, and relaxations were introduced until mid-June [21]. Norway introduced new national restrictions by end of October 2020. These restrictions were still in place once the observation period ended [22]. In terms of energy production, Norway produces electricity mainly from hydropower. This energy source is divided into hydro water reservoir and hydro run-of-river and poundage. Together, these two energy sources account for almost 100% on an annual average. Wind onshore or fossil gas account for less than 5% of Norway’s energy production [17] (Fig. 3).

3.4.1

NO1 Intraday Prices

The price development in the intraday area shows a bearish trend including several outliers until April. In the beginning of June, the price level is relatively stable at EUR 9.00. During the second lockdown period the prices show volatile movements. The trend is a rising price. Compared to the price level in January 2020, the price level in January 2021 is higher. However, the curve shows a high price level in winter and a low price level in summer. The confidence level of the prices does not show any conspicuous features and is evenly distributed over the year. The lowest price in the data set here is − 1.73 EUR and the highest price is 205.68 EUR. The 30day volatility also increased during the first lockdown period. Thus, it started being around 350 in the first lockdown and end up at a level of 770 during the second

Fig. 10 NO1 intraday prices

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Fig. 11 NO1 day-ahead electricity prices

lockdown. The confidence level of the 30-day volatility increased between March and July and decreases again in September. The second lockdown also shows a widened confidence level (Fig. 10).

3.4.2

NO1 Day-Ahead Prices

The price development in the day-ahead area also shows a bearish trend until April. Like in the intraday area the prices reached their lowest point June. From June the day remain at nearly the same level. During the summer months the price level remains at a low level and shows some peaks in September and November. From December the prices level it increases again. Compared to January 2020 the price level is higher in January 2021. With regard to the confidence level of the prices, there are no conspicuous features in the day-ahead area. This indicates that the uncertainty regarding prices is less great. In the day-ahead area, the curve also shows a low price level in summer and a high price level in winter. In terms of this shape, there is a similarity to the intraday prices. The lowest price in the data set here is 0.02 EUR and the highest price is 152.25 EUR. In the end of March, volatility starts increasing and reaches first peak in the mid of April where it remains relatively stable. The volatility shows more peaks between May and October. In November it starts to rise and ends up at a higher level compared to January 2020. Between November and March also the confidence level widens until it narrows again in January (Fig. 11). The average price of the daily traded volume was 14.17 EUR for intraday and 12.72 EUR for day-ahead prices. The standard deviation was 17.65 for intraday and 14.82 for day-ahead (Table 5).

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Table 5 General statistics about NO1 prices and volatilities in EUR Statistics

NO1 intraday (mean price; mean vola)

NO1 intraday (std. NO1 day-ahead price; std. vola) (mean price; mean vola)

NO1 day-ahead (std. price; std. vola)

January 2020

25.34; 160.33

4.19; 100.58

23.68; 97.94

4.06; 29.08

January 2021

59.16; 575.52

28.79; 124.94

52.41; 539.61

19.25; 162.48

First Lockdown

8.96; 354.71

4.86; 178.76

7.79; 193.10

2.05; 76.19

Second Lockdown

28.86; 773.76

28.10; 332.86

26.10; 688.65

22.98; 365.61

Summer Months

5.47; 620.98

5.20; 299.48

4.71; 419.00

4.65; 272.55

• During the first lockdown, the price in the day-ahead as well as in the intraday area fell sharply. This trend was reinforced in the summer months. In the summer months, less electricity was produced by waste and wind power. • In the second lockdown, the price level and the level of volatility increased. At the beginning of the second lockdown, the production of hydropower by water reservoirs also collapsed. • The price level in January 2021 is significantly higher than the price level in January 2020. The same applies to volatility. • Intraday and day-ahead prices both have low confidence level shears and have a similar shape (low prices in summer and high prices in winter) • There are no strong outliers, as is the case with German and French prices. Intraday prices show more outliers than Day-Ahead prices. • Hydropower as the largest generation source can be stored and is more independent of the weather. • Both curves show very similar price and volatility developments. The results confirm the statement that the 2nd lockdown had a stronger impact on the energy markets in the NO1 region.

4 Discussion 4.1 Critical Appraisal The following section discusses elements of the paper based on the current state of research. Since a further step in the analysis of the data would be prediction methods, we will now briefly discuss back testing, which is commonly used in practice. We can refer to the study by Han et al. [11]. They pointed out that spot electricity prices are among the financial products with the highest price deviations and the greatest volatility. They attribute this to the non-storable nature of electricity [11]. Due to the

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many uncertainties caused by the high volatilities and the price outliers, increasingly complex technologies are being used on the energy markets to predict prices [11, 23]. This is necessary because errors arise, for example, through back testing. This is the case because back testing cannot detect so-called black swans [24, 25]. An example of a so-called black swan event was the negative oil prices in April 2020 [5, 25]. Machine learning (ML) can get around this problem. For example, multivariate analyses using ML can be used to find important indicators that point to a crisis [24]. Different energy markets would support the research here. Therefore, we recommend ML techniques for further analysis of the data. Another challenge regarding the forecasting accuracy of German electricity is the rapidly changing energy mix. The higher volatilities caused by this also require further complex models and automated trading techniques. In addition, there is a growing need for more comprehensive analyses of alternative data types, such as weather [4, 6, 26]. This alternative data type is an additional element of the analysis compared to the financial markets. Adekoya and Oliyide [9] and Elsayed et al. [8] have highlighted the links between financial markets and other commodities during the COVD-19 crisis. This comparison is not made in this paper, as the focus is on pure price and volatility movements, supported in some cases by volume data [8, 9]. Ali and Kahn [7] analysed the markets according to the lockdown periods [7]. The same procedure was used in this paper. However, weaknesses of the method have become apparent, since in a comprehensive comparison of countries the lockdown periods differ due to national regulations [18, 20, 22]. This leads to a more difficult comparability of the data. However, we have deliberately decided to extend the analysis to include different countries and, in contrast to Halbrügge et al. [4] and Fezzi and Fanghella [11] to carry out a country comparison [4, 11]. Furthermore, this analysis should draw attention to the growing importance of the intraday electricity markets during the expansion of renewable energies [27, 28]. In this way, links to the energy mixes of the countries and the response to COVID-19 can be established.

4.2 Research Limitations In order to obtain even more valid results, factors such as weather, seasonal fluctuations and correlations with other commodities and, if applicable, public holidays would also have to be considered. Furthermore, the data quality of the Norwegian data is limited as there is no volume data available. For further analyses, it would therefore be helpful to draw on other Nordic markets and more regions in Norway with a high share of renewable energies as well. Sweden or Denmark, for example, could be considered [13]. This paper does not consider different price systems. For instance, in Europe and Australia a zonal price system is common whereas e.g. the U.S. use a nodal price system. In case of a wider selection of countries these differences need to be considered [29]. An additional factor that could be considered is the COVID-19 case numbers or, in the meantime, the vaccination rate for the countries studied.

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5 Conclusion and Outlook This paper finds that COVID-19 had an impact on the energy markets in Germany, France, and Norway (NO1). The German electricity market is facing changes. Due to the increase in energy production from renewable energies, more and more energy is being traded on the intraday market [30]. This trend is confirmed by our analysis of the volume. Our overall objective was to find out whether (iii) forecasting methods in intraday electricity markets in Germany have improved. To find out, we compared day-ahead prices and intraday prices. We did this because the day-ahead price is the market clearing price [28, 29, 31]. In the comparison, we found that prices in France and Norway were consistently close. (ii) The power generation in France, which consists mainly of nuclear electricity, gives a hint here. We conclude that France shows close intraday and day-ahead prices. This may be due to the constant use of nuclear power. We had expected that (ii, iii) Norway would also be highly efficient. Based on our analysis we can also conclude the intraday and day-ahead prices are closely together. Norway seems to be an exception here. Based on our data NO1 data we can conclude they have low prices and hardly any outliers which is particularly evident in the first lockdown period when comparing to the developments to the German and France day-ahead and intraday markets. Regarding the day-ahead data, the 30-day volatilities were consistently lower than in Germany and France. These findings provide an indication of the link to the increased use of hydropower and hydro reservoirs in Norway (NO1) [17]. In Germany, prices were initially far apart during the first lockdown period. During the second lockdown period, there was a convergence of prices in the mean and median. This convergence is (i) an indication, but not proof, that the use of the out-of-sample data of the first lockdown may have improved the forecast accuracy. In addition, (iii) the constantly changing energy mix in Germany may have played a role. The results for the German market could be used as pioneering data for other countries that want to undertake such an energy transition [29]. Other results are as follows: • All products considered show a higher price in January 2021 compared to the previous year. • In the case of German electricity, however, a lower daily average volume was traded in January 2021 compared to the previous year. The volume in France remains constant in the intraday area and is increased in the day-ahead area. • All prices considered fell in the first lockdown, whereas volatilities rose sharply in some cases. • In contrast to France and Germany, the electricity prices for NO1 show fewer outliers, which could be explained by the generation from water reservoirs and hydropower. • All prices increased in the second lockdown. Unlike the other products, the volatility of NO1 increased particularly strongly in the second lockdown. This suggests that NO1 was hit harder by the second lockdown than by the first.

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In the general price and volatility analysis, it was also noticed that the weather factor is omitted in the case of nuclear electricity and electricity from hydropower, which could lead to a higher forecast accuracy and thus obviously also to greater crisis security. Furthermore, the aim of our research is to provide statistical evidence for the relationship between energy production and price and volatility movements. We want to do this because this paper only makes assumptions based on the results of the graphical analysis. To produce more valid results, we plan to expand the dataset and consider further crisis periods. Generalisable indicators from the time series used are employed to filter out crisis situations. This should be possible even though there are different energy mixes and lockdown periods. The research goal is to develop methods that can predict the crisis or key indicators such as the volatility.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.

Marshman D, Brear M, Jeppesen M, Ring B (2020) Energy Econ 89:1–15 Detemple J, Kitapbayev Y (2020) Energy Econ 89:1–14 Härtel P, Korpås M (2021) Energy Econ 93:1–13 Halbrügge S, Schott P, Weibelzahl M, Buhl HU, Fridgen G, Schöpf M (2021) Appl Energy 285:1–3 Ghiani E, Galici M, Mureddu M, Pilo F (2020) Energies 13:13 Duso T, Szücs F, Böckers V (2020) Energy Econ 92:1–15 Ali J, Kahn W (2020) Publ Affairs 20:4 Elsayed A, Nasreen S, Tiwari AK (2020) Energy Econ 90:1–16 Adekoya OB, Oliyide JA (2021) Resour Policy 40 Fezzi C, Fanghella V (2020) Environ Resour Econ 76:885–900 Han L, Kordzakhia N, Trück S (2020) Energy Econ 90:1–26 Snow D (2019) Machine learning in asset management. SSRN Electron J Rintamäki T, Siddiqui AS, Salo A (2017) Energy Econ 62:270–282 Cramton P (2017) Oxf Rev Econ Policy 33:4 Pilipovi´c D (1998) Energy risk. McGraw-Hill, New York Verbeek M (2017) Modern econometrics. Wiley Custom, Croydon ENTSO-E (2021) Actual generation per production type. https://transparency.entsoe.eu/genera tion/r2/actualGenerationPerProductionType/show. Last accessed 2021/6/5 Robert Koch Institute (2021) https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronav irus/nCoV_node.html. Last accessed 2021/6/5 Valitov N, Maier A (2020) Energy Econ 89:1–10 Government (2021) https://www.gouvernement.fr/en/coronavirus-covid-19. Last accessed 2021/6/5 Ursin G, Skjesol I, Tritterc J (2020) Health Policy Technol 9:4 Government.no (2021) https://www.regjeringen.no/en/topics/koronavirus-covid-19/id2692 388/. Last accessed 2021/6/5 Wang B, Wang J (2020) Energy Econ 90:1–14 López de Prado MM (2020) Machine learning for asset managers. Cambridge University Press, Cambridge Selmi R, Bouoiyour J, Hammoudeh S (2020) hal-02570614, pp 1–8 Agnello L, Castro V, Hammoudeh S, Sousa RM (2020) Energy Econ 90:1–11 A. Kramer, R. Kiesel, Energy Economics, (to be published, 2021) Glas S, Kiesel R, Kolkmann S, Kremer M, Graf von Luckner N, Ostmeier L, Urban K, Weber C (2020) J Math Ind 10:3

How Did the COVID-19 Crisis Affect the Efficiency … 29. Grimm V, Rückel B, Sölch C, Zöttl G (2021) Energy Econ 93:1–21 30. Kiesel R, Paraschiv F (2017) Energy Econ 64:77–90 31. Martin de Lagarde C, Lantz F (2018) Energy Policy 117:263–277

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State Estimation of Intelligent Distribution Network Based on Data Fusion Daoyu Li, Yuanyuan Sun, Lintao Yuan, Chao Wang, Peng An, and Yanqing Pang

Abstract Higher information processing needs have been brought about by the development of smart grids. In order to solve the problem that there are many types of existing intelligent measurement terminals and modeling standards are not unified. In this paper, the data of various intelligent measuring terminals are preprocessed. The multi-source measurement data is washed and the wrong data is eliminated. Then a data fusion method considering the data characteristics of different intelligent terminals is proposed. A specific distribution network state estimation process based on data fusion results is proposed. Finally, the state estimation of smart distribution network based on data fusion can improve the accuracy of state estimation, which is proved by experiments. The simulation results show that the regional distribution network state changes can be effectively tracked by the intelligent distribution network state estimation method based on data fusion. The estimation error is reduced. The system state can be accurately grasped by the operator of regional distribution network in real time. Situational awareness at the basic level is achieved. Subsequent advanced applications such as status assessment and vulnerability identification can be supported by data. Keywords Data fusion · Smart distribution network · State estimation

D. Li · Y. Sun (B) · L. Yuan School of Electrical Engineering, Shandong University, Jinan 250061, China e-mail: [email protected]; [email protected] C. Wang Qingdao Power Supply Company, State Grid Shandong Electric Power Company, Qingdao 266002, China P. An State Grid Shandong Electric Power Company, Jinan 250001, China Y. Pang Shandong Taikai Robot Co., Ltd., Taian 271000, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_43

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1 Introduction With the development of smart power grid, more and more measuring terminals are arranged in distribution network. And the modeling standard that each system follows is not uniform. Multi-source data fusion technology is a theory and method for multilevel, multi-faceted and multi-level processing of data from multiple data sources to generate new and meaningful information. State estimation is a method to estimate the internal state of a dynamic system according to the available measurement data. State estimation plays an important role in understanding and controlling a system [1]. It is necessary to study multi-source information fusion technology for distribution network state estimation based on mixed measurement. In terms of state estimation of smart distribution network, Paper [2] proposed a new state evaluation method combining with normal cloud distribution. Paper [3] studied the safety assessment method of hydroturbine generator set. Paper [4] proposed a comprehensive evaluation method of smart distribution network operation state based on situational awareness. Paper [5] used fishbone diagram analysis method to build a hierarchical model of distribution network operation status evaluation. However, the above evaluation method of distribution network operation state is not comprehensive enough to analyze data fusion. In order to make better use of intelligent measurement terminal data, a distribution network state estimation method based on multi-source data fusion is proposed.

2 Multi Source Data Fusing 2.1 Fusion Based on Data Components The state estimation technology of distribution network is the key technology to obtain the real-time running state of distribution network. As shown in Table 1, for Table 1 Comparison of PMU, SCADA and AMI data PMU

SCADA

AMI

Data component

Voltage phasor, current phasor

Node voltage amplitude, branch current amplitude, node injection power, branch power

User information, node voltage amplitude, branch current amplitude, node injection power, branch power

Data accuracy

Grade 0.05

Grade 2

Grade 0.5

Time mark

Have

Not

Have

Time delay

Little

Large

Huge

Refresh rate

10 ms

2s

15 min

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distribution network state estimation, different types, precision, and time scales of data can be provided by Pressure Measuring Unit (PMU), supervisory control and data acquisition (SCADA) and advanced metering infrastructure (AMI). Equivalent transformation method is usually used to fuse multivariate measurement data [6].

2.2 Fusion Based on Data Precision In the distribution network, the accuracy of three sets of data are different. The accuracy of state estimation can be increased by reasonably distributing the weight of each measurement. εi = δdi + δmi

(1)

where ε is defined as the overall error of the measured data; δd is defined as the error caused by time synchronization; δm is defined as the measurement error of the measuring device. It can be measured experimentally.

2.3 Fusion Based on Data Refresh AMI and PMU measurements have time scales, while SCADA measurements have no time scales. The correlation between PMU measurement and SCADA measurement was maximized by using correlation theory. The moment when PMU measurement has the highest correlation is defined as the system reference moment. Add a timer to SCADA data. Three kinds of measurement data synchronization can be achieved.

3 State Estimation of Intelligent Distribution Network 3.1 Weighted Least Square State Estimation In power system state estimation, the mathematical model of state estimation is established, as shown in Eq. (2). z = h(x) + e

(2)

where z stands for quantity measurement, x stands for the quantity of states, e stands for measurement noise.

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The essence of the weighted least square method is to solve the following mathematical problems: min J (x) = (z − h(x))T W (z − h(x))

(3)

∂ J (x) = −2H T (x)W [z − h(x)] = 0 ∂x

(4)

where h is defined as a measurement equation. W is defined as the measurement weight.

3.2 Weight Determination Based on Data Fusion Considering data refresh time, recursive dynamic state estimation based on time scale is adopted [7]. When SCADA measurement is updated, PMU real-time measurement is used to replace the corresponding part. Pseudo measurements corresponding to AMI are retained. The SCADA pseudo-measurement is corrected according to the actual SCADA measurement. This method improves the utilization of data, but at the same time, it leads to changes in data accuracy and requires a new method to determine the weight. This paper proposes a method to determine the measurement weight according to the data fusion to increase the accuracy of state estimation. The specific method is shown in the following formula. Time delay td does not equal 0. 1 αP =  2 tdP δmP + K P (e T P − 1) ⎧ 1 ⎪ α S1 =  ⎪ ⎪ ⎪ tS 2 ⎪ ⎨ δmS + K S TdS 1 ⎪ ⎪ ⎪ α S2 =  2 ⎪ ⎪ tS ⎩ δmS + K S Tr S 1 αA =  δmA + K A ln(1 +

2 tdA ) A T

(5)

(6)

(7)

where α P , α S and α A represent the weights of PMU, SCADA, and AMI respectively. T stands for measuring period. Considering that AMI measurement update cycle is the longest. Therefore, the tdP

AMI measurement weight in this paper adopts e T P − 1 as a variable. And the lowest

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weight. PMU data is the most accurate. Shortest measurement period. In this paper, tA THE PMU measurement weight adopts ln(1 + TdA ) as a variable, which should be given the maximum weight. SCADA does not have a time scale. α S1 is used as the weight after the time scale is obtained through the correlation theory, otherwise α S2 is used. trS is a function that follows a normal distribution.

4 Case Study Results As shown in Fig. 1, an 8-node regional distribution network is taken as an example to verify the distribution network state estimation algorithm based on data fusion. The event moment is set to the 50 s of the simulation timeline. To verify the accuracy of the state estimation. Only the PMU is configured in the 10 kV substation. In this configuration, the error of each node and the state estimation results of voltage amplitude and voltage phase Angle change of 10 kV substation, A3 node and B3 node are shown in Figs. 2 and 3 respectively. The results show that the improved method can identify system changes effectively. The calculated error results are shown in Table 2. Simulation results show that improved state estimation method reduces measurement error. It can achieve better state estimation effect.

Fig. 1 8-node regional distribution network

(a) using traditional method

(b) using improved method

(c) nodal error comparison

Fig. 2 Comparison of estimation results of voltage amplitude variation

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(a) using traditional method

(b) using improved method (c) nodal error comparison

Fig. 3 Comparison of estimation results of phase angle change

Table 2 Error result statistics Node Average voltage Average voltage Average phase angle Average phase angle amplitude error amplitude error error (traditional error (improved (traditional method) (improved method) method) method) 1

0.026

0.015

0.058

0.039

2

0.035

0.013

0.056

0.024

3

0.036

0.020

0.061

0.037

4

0.039

0.016

0.059

0.038

5

0.022

0.013

0.062

0.036

6

0.015

0.008

0.062

0.022

7

0.015

0.018

0.049

0.009

8

0.027

0.012

0.047

0.035

5 Conclusion In this paper, the state estimation model of distribution network and the equivalent model of multivariate measurement are studied. Measurement based on intelligent measurement terminal of distribution network. A weighted least squares method for weight determination based on data fusion is proposed. Finally, a simulation example is given to verify the results. The simulation results show that the state changes of regional distribution network can be tracked effectively by the proposed state estimation method based on data fusion. The estimation error is reduced and the operator of regional distribution network can master the system status accurately in real time. Subsequent requirements such as status assessment and vulnerability identification are supported by data. Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

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References 1. Wu Z, Yu X, Dong X et al (2018) Real-time situational awareness and evaluation of distribution network based on state estimation. Proc CSU-EPSA 30(3) 2. Feng J, Wang Z (2011) State evaluation of overhead transmission line based on normal cloud model. Mechan Electr Inf 24:66–67 3. Li HH, Chen DY, Arzaghi E et al (2018) Safety assessment of hydro-generating units using experiments and grey-entropy correlation analysis. Energy 165:222–234 4. Tao Y, Diao S, Zhu Y, An P, Cheng K (2020) Operation state evaluation of smart distribution systems based on the situation awareness. Shandong Electr Power 47(02):13–19 5. Xing X, He T, Zhuo W, Zheng X, Sun C (2019) Construction of hierarchical model and evaluation method for distribution network operation status evaluation. Smart Power 47(04):81–86 6. Li Q, Zhou J, Yu E et al (2005) Linear state estimation of power system based on phasor measurement. Autom Electr Power Syst 29(18) 7. Yu Q, Peng B, An S, Zhou C, Tian Z, Yang S, Zhu X, Zheng J (2020) A multi-time scale recursive dynamic state estimation method and system for distribution network. Shandong, CN109586289B, 2020-12-29

Preliminary Research on the Voltage Level of Low Voltage Direct Current System Longwei Xu, Yuanyuan Sun, Yahui Li, Anbin Zhang, and Fan Wang

Abstract Low voltage direct current (LVDC) system has advantages on high efficiency and low-carbon growth. The voltage level is a key issue in the planning and operation of LVDC system. However, the discussion of the voltage level is still inconclusive. To present the research results of LVDC voltage level, in this paper, the recommendatory values and relevant standards of LVDC voltage level are summarized. After that, the configuration principles and constraint condition of the voltage level are introduced. On this basis, the evaluation indicators and methods are described. The voltage level of different application scenarios such as DC buildings is analyzed. Finally, the development trend of LVDC voltage level is discussed. Keywords LVDC · DC voltage level · Relevant standards · Application scenarios

1 Introduction LVDC system can take full advantages of efficient power utilization and improving system operational flexibility, reliability and power qualities. Meanwhile, DC power supply has high transmission power and low loss. The selection of the voltage level is one of the most critical problems which impede the development of LVDC system. The use of standard DC voltage level can avoid disorder and reduce the demand for DC/DC converters. Moreover, the complexity and cost of DC grid also are reduced. It improves the reliability and security of power grid. The general rules and recommendatory values of LVDC voltage level are given in the existing relevant standards. LVDC had been divided into two bands in IEC 60038 and IEC 61140. From 120 to 1500 V DC is defined as LVDC band and voltage less than 120 V is extra LVDC (ELVDC) band which is more suitable for supplying electronic loads. According to GB/T 35727-2017 “Guideline for standard voltages of medium and low voltage DC distribution system”, the optimal values of the voltage level of LVDC system were identified as 1500(± 750) V, 750(± 375) V, 220(± L. Xu · Y. Sun (B) · Y. Li · A. Zhang · F. Wang School of Electrical Engineering, Shandong University, Jinan 250061, China e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_44

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110) V. T/CEC 107-2016 “DC distribution voltage” gave nominal voltage values of DC distribution system which is ± 1500, ± 750, ± 380, ± 110, and ± 600 V is alternative value. Relevant scholars had done theoretical research on LVDC voltage level. Reference [1] introduced the development status of LVDC system and proposed the sequence of recommendatory values (1.5 kV/750 V/380 V/110 V/48 V) for low voltage. Reference [2] gave recommendatory voltage values for future DC distribution networks as ± 0.4/0.75/1.5 kV. Reference [3] suggested that technical research, equipment development and demonstration projects should first be carried out for distribution network of 400 and 750 V DC. Then they should be popularized and applied.

2 Configuration Principles and Constraint Condition 2.1 Configuration Principles of the Voltage Level 2.1.1

Two for Three

According to the domestic and foreign research of the voltage level, the ratio of adjacent voltage level is too large, higher requirements are put forward for the manufacture and operation of power electronic equipment. The number of output lines increases. If it is so small, power supply scope overlaps. The number of power changes increase and investment and operating costs increase, etc. Therefore, the ratio of adjacent voltage level should be close to “3” and not less than “2”.

2.1.2

Geometric Mean

Economic voltage value and standard voltage value are similar to geometric mean value in mathematics: Uj =

√ Ui Ui+1

(1)

where U j , U i , Ui+1 is a set of adjacent voltage values in the voltage level sequence. To minimize costs, the ideal situation is that every voltage value in the sequence is economic. The relationship of “geometric mean” is satisfied between them.

2.1.3

Multiple Method

The modular power electronics device can be connected in series and parallel. So, its capacity and voltage can be increased. According to the multiple method, a set of

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preliminary sequence values can be obtained [2]. Taking ± 375 V as the base value, we can get 375 × 2n = 375, 750, 1500...(n = 0, 1, 2 . . .).

2.2 Constraint Condition of the Voltage Level 2.2.1

Load Demand

The proportion of DC load in the total grid load is gradually increasing. In order to remove the AC–DC convert and improve the operation efficiency, the adaptability of load should be considered in the selection of the voltage level [4].

2.2.2

Power Supply Capacity

Transmitting the same power, the higher the voltage is, the lower the line loss is. At the same time, the thinner the wire can be. So, the capacity of power supply increases. Taking the bipolar system as an example, the loads distance is expressed as: λ= P×L=

2 ΔU × Udc RL

(2)

where ΔU is voltage difference between the head end and the end, Udc is standard voltage of DC bus, R L is the unit DC resistance of the wire [4]. On the basis of meeting the power demand of various loads, the needs of future power grid should be considered.

2.2.3

Technology of Electrical Equipment

The operation of system must meet the limitations of voltage, short-circuit current, insulation and electromagnetic compatibility.

2.2.4

Human Safety

Areas with frequent human activities have higher requirements for electrical safety. According to GB 16,895.21-2011 “Low-Voltage Electrical Installations”, it can be known that in a normal dry environment DC voltage values which do not exceed 60 V are considered to be directly touched. The current effect is shown in Fig. 1. According to the current effect and the resistance of the human body, the touch voltage of the human body is less than 75 V (25 mA). The voltage of 75 V can

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Fig. 1 Time/current zones of effects DC current on persons for a longitudinal upward current path

be touched for a long time and is relatively safe. If it is relaxed to the domain of ventricular fibrillation, the corresponding voltage value is 190 V.

3 Evaluation Indicators and Evaluation Methods Evaluation indicators need to be scientific, consistent, systematic, independent, practical and adaptable [4].

3.1 Evaluation Indicators 3.1.1

Economy

The indicator of economy evaluation is mostly divided into investment economy and operation economy. Investment economy includes construction investment, equipment investment and operation and maintenance costs. Operation economy mainly includes network loss (including line loss and converter loss), equipment utilization and supply radius.

3.1.2

Adaptability

The indicator of adaptability evaluation is mainly divided into the adaptability of load development, the adaptability of distributed power access, the adaptability of

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research and development (R&D) and manufacture technology, and the adaptability of social development.

3.1.3

Reliability

The indicator of reliability evaluation is divided into the reliability of the DC converter station and the reliability of the DC distribution line. The reliability of the DC converter station includes the failure rate of the high-voltage bus of the converter station, the maintenance rate of the converter and the duration of the converter failure. The reliability of the DC distribution line includes the failure rate of the distribution line, the time for the line to complete the load transfer and the failure rate of breaker of the line. It can be ensured according to the fault data and operation data of the converter station and line.

3.2 Evaluation Methods Reference [5] used the Delphi weighting method to ensure the weights of each evaluation indicators and the fuzzy comprehensive evaluation method was used to obtain the optimal 380 V scheme. Reference [4] used hierarchical analysis to evaluate the weights of indicators and used the Vague language and the method of data analysis to process the indicator data. The scheme of DC distribution voltage level was evaluated comprehensively through TOPSIS multi-objective decision-making. It focused on its adaptability and simplifying the voltage level, selecting ± 300 V as the low voltage level of DC distribution. Reference [6] used the triangular fuzzy number to improve the analytic hierarchy process to improve the credibility of the evaluation, and the multi-level sequence of ± 750, ± 200, 48 V was selected as low voltage. The evaluation indicators and evaluation methods of LVDC voltage level proposed above still lack practical tests. It is necessary to continuously test whether the evaluation indicators are appropriate based on the actual development of the LVDC network. More comparisons should be made for the various evaluation methods.

4 The Voltage Level of Different Application Scenarios 4.1 DC Building DC building is a building with a high proportion of photovoltaic access and flexible DC equipment, where a LVDC distribution system is used and energy storage equipment and charging piles are installed. And it has the ability to interact with the urban grid. DC building eliminates the AC–DC conversion between DC equipment

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and the distribution network. At the same time, it relaxes the restrictions on voltage and frequency. Reference [7] proposed a method to specify the upper voltage limit for the safety of human electric shock, and the lower limit of ultra-low voltage for the distance of supply. 60 V was used as the voltage level in the building of DC power supply, and the voltage level of LVDC distribution system should be selected between 280 and 300 V. Reference [8] proposed the voltage level of DC building from the aspects of economy, safety and compatibility. The voltage level of ± 10 kV, ± 375 and 220 V DC was recommended to be adopted. Reference [9] combined with the nominal voltage values recommended in the standard, the voltage level can be selected as 375, 400 V, and the voltage can be selected as 48 V for short-distance power supply with higher requirement of safety. Reference [10] proposed that 380 V DC can supply power to kitchen loads and high-power household appliances, while low-power equipment, such as LED lighting, can be powered by 48 V DC. From the comprehensive domestic and international progress, 375 V DC and 48 V ELVDC are the two voltage levels most commonly used at present.

4.2 ICT DC Power Supply System 48 V DC is the basic voltage of power supply in the communications industry. 5G technology has high efficiency of data transmission and high-power consumption, many of which use constant voltage 57 V to supply power. Some pull far Active Antenna Unit (AAU) are hundreds of meters away from the base station, so the voltage was raised to 280 or 400 V DC. Data center develops HVDC power supply, adopting two formats of 240 and 336 V. In order to improve the efficiency, the mode of direct supply is also widely used in the industry. The normal voltage range of the power supply interface is specified as 260–400 V DC by ITU-T L.1200.

4.3 Smart Park Operation informationization, digital intelligence, service platform and community mobility are realized in smart park. 400 V DC is used in Baolong Industrial City for DC distribution demonstration project. Reference [11] gave the recommendatory value of the LVDC voltage level sequence of the smart park, which is ± 48/110/220/310/380 V DC that conform to the configuration principle of “geometric mean”.

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5 Conclusion The study of LVDC voltage level needs to be continuously deepened and perfected. The determination of LVDC voltage level should adhere to the principles of simplifying the voltage level. Considering different factors such as topology, cable economy, load distance, equipment characteristic, insulation, control strategies, protection requirements, etc. Making comprehensive evaluation and analysis of economy, reliability and power supply capacity to form differentiated industry or scenario standards and unified international standard sequence. Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

References 1. Sheng W, Li R, Li Y et al (2016) A preliminary study on voltage level sequence and typical network architecture of direct current distribution network. Proc CSEE 36(13):3391–3403. (in Chinese) 2. Duan J, Wei Z, Zhou Y, Yang Q (2018) Research on voltage level sequence of future DC distribution network. Proc CSEE 38(12):3538–3545+13. (in Chinese) 3. Wang F, Wang L, Zhang X, Wang J, Li S (2021) Voltage level study for DC distribution grid based on comprehensive evaluation. In: 2021 IEEE international conference on power electronics, computer applications (ICPECA). Guangzhou, pp 492–496 4. Li S (2017) DC distribution network voltage class series. Zhejiang University. (in Chinese) 5. Liu L, Jiang Z, Liu Z (2014) Research on the voltage class of DC distribution power system. Distrib Utilization (7): 20–23. (in Chinese). 6. Xiao Y (2020) Triangular fuzzy number improved analytic hierarchy process to evaluate the voltage level of DC distribution network. Shanxi University. (in Chinese) 7. Chen H, He G, Shi J et al (2017) Research on DC voltage level of hybrid AC/DC building power supply system. Proc CSEE 37(20):5840–5851. (in Chinese) 8. Yu L (2019) Study on application of building direct current (DC) distribution system. Zhengzhou University. (in Chinese). 9. Wang X (2020) Research on DC power supply technology of residential building. Beijing Jiaotong University. (in Chinese) 10. Boroyevich D, Brasov R, Cvetkovic I et al (2010) Future electronic power distribution systems: a contemplative view. In: 12th international conference on optimization of electrical and electronic equipment (OPTIM). Brasov, pp 1369–1380 11. Wang J, Jia L, Jiang Q (2020) Economic study on voltage grade sequence of low voltage DC distribution network. Electr Drive:1–7. (in Chinese)

Stability Analysis of DC Microgrid with Multi-converter Parallel Operation Based on Impedance Model Anbin Zhang, Yuanyuan Sun, Qingshen Xu, Longwei Xu, Tao Yu, and Yanqing Pang

Abstract In the DC microgrid, in order to solve the DC bus voltage fluctuations caused by the randomness of distributed energy, multiple groups of DC bus voltage control units (DC BVC) are connected to the system through converters. The mechanism of the influence of the parameters of the converter on the stability of the DC microgrid system is still unclear. In this regard, this paper establishes the small signal model of DC BVC and load, and analyzes the output impedance characteristics of the source-side converter. Secondly, considering the influence of the interaction of multiple converters on the stability of the system, the equivalent impedance model of the DC microgrid is established. And according to the impedance matching principle, the influence characteristics of system parameters, converter control parameters and load power on system stability under different setting schemes are analyzed. Finally, the influence of the matching of multi-converter control parameters on system stability is analyzed. Keywords DC microgrid · Small signal model · Converter parameters · System stability

1 Introduction DC microgrid has the advantages of high system reliability, few conversion links, low loss, etc., and there are no frequency and phase problems. As an effective way A. Zhang · Y. Sun (B) · Q. Xu · L. Xu Shandong University, Jinan 250061, China e-mail: [email protected] A. Zhang e-mail: [email protected] T. Yu Jinan Urban Planning and Designing Institute, Jinan 250101, China Y. Pang Shandong Taikai Robot Co., Ltd., Taian 271000, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_45

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of distributed energy generation and consumption, DC microgrid has a wide range of application scenarios [1, 2]. The DC bus voltage is the only indicator to measure the stability of the DC microgrid [3]. Various DC bus voltage control devices are connected to the system through converters, and are based on centralized or distributed control strategies to maintain the DC bus voltage stability [4]. However, the parallel operation of multiple converters, the mutual coupling between converters, and the negative impedance characteristics of constant power loads have led to serious deterioration of the stability of the DC microgrid system [5, 6]. Domestic scholars have done a lot of research on the stability of DC microgrid. Among them, the small signal stability analysis is the most extensive, through the establishment of a small signal model of the system. Using Middlebrook, GMPM (Gain Margin and Phase Margin), Opposing Argument, ESACC (energy source analysis consortium criterion) and other impedance criteria to analyze the stability of the DC microgrid [6]. Reference [5] pointed out that the low damping LC link formed by the equivalent impedance of the line in the system and the stabilized voltage capacitor of the converter would cause the system to oscillate at high frequencies; Reference [6] established a DC microgrid impedance model with virtual inertia control. According to the principle of impedance matching, the influence of system parameters on stability is analyzed. The above conclusions mostly focus on the influence of a single converter parameter on the stability of the system, and do not consider the parameter matching problem when multiple converters are operated in parallel. Aiming at the system stability problem caused by the parallel operation of multiple converters in the DC microgrid, this paper first establishes an equivalent model of the DC microgrid. Then the equivalent output impedance of the DC BVR and the equivalent input impedance of the load are deduced. Finally, with the help of Bode diagram, the influence of the parameters of the multi-converter on the stability of the system is analyzed.

2 System Structure of DC Microgrid This paper mainly focuses on the research of DC microgrid with radial network structure. The schematic diagram of the structure is shown in Fig. 1. The system consists of distributed power sources, energy storage, AC and DC loads and power electronic converters. (1) In order to make full use distributed energy, Photovoltaic unit generally work in Maximum Power Point Tracking (MPPT), so they are equivalent to constant power supply (CPS); (2) AC and DC loads are divided into constant impedance loads and constant power loads (CPL), and they can be equivalent to the form of current source parallel impedance; (3) DC BVC is composed of a constant DC voltage source and a bidirectional Buck-Boost DC/DC converter to maintain the DC bus voltage stability and Power balance. These units are based on droop control, and the voltage and current PI control is used to track the change of bus voltage. The AC/DC converter

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DC Bus AC DC

DC AC

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AC Grid

DC DC Distributed Power

ZS1 US1

DC Load DC DC

DC Load ·······

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DC AC

ZSi AC Load

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Uin-cps

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PCPS ZCPS

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Loads

PCPL ZCPL

Fig. 1 Typical structure of DC microgrid

adopts power control, so the decoupling operation of the AC and DC system can be realized. Therefore, the AC grid unit can be equivalent to a special type of constant power load with negative output power.

3 Small Signal Modeling of DC Microgrid 3.1 Model of DC Bus Voltage Control Unit The DC BVC unit i is composed of an energy storage system U si and a bidirectional DC/DC converter. The system structure is shown in Fig. 1. Among them, U si and iLi are the battery power supply voltage and output current, respectively, Rsi and L si are the filter impedance, Rline and L line is the line impedance, Z si is the output impedance of the DC BVCi , C i is the DC side capacitance, U oi and ioi are the output voltage and output current, respectively, and U dc is the DC bus voltage. The DC BVR adopts voltage and current droop control mode. The control system is shown in Fig. 2. If i = 1, the state equation of the DC bus voltage control unit and the converter duty cycle expression can be derived from Fig. 2 as

Udc-ref Uoi

UdcN ioi

Udc-ref = UdcN - ioRdroo p Gu_i

Gu_i

Di

iLi Rsi

PWM

iLi

Fig. 2 DC bus voltage control unit structure diagram

Usi

Lsi S1

S2

ioi Uoi

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⎧ dU o1 ⎪ = (1 − d1 )i L1 − i o1 C1 ⎪ ⎪ ⎪ dt ⎪ ⎨ di L1 + (1 − d1 )Uo1 Us1 = Rs1 i L1 + L s1 ⎪ dt ⎪ ⎪ ⎪ ⎪ di o1 ⎩U = R + Udc o1 line1 i o1 + L line1 dt

(1)

Linearize (1) at the stable point to get the following small signal model ⎧ ⎪ ⎨ sC1 ΔUo1 = (1 − d1 )Δi L1 − Δd1 i L1 − Δi o1 ΔUs1 = Rs1 Δi L1 + s L s1 Δi L1 + (1 − d1 )ΔUo1 − Δd1 Uo1 ⎪ ⎩ ΔUo1 = Rline1 Δi o1 + s L line1 Δi o1 + ΔUdc

(2)

According to the small signal model of the DC bus voltage control unit established in (1), (2) and Fig. 2, the output impedance of the converter can be obtained as shown in (3). Z s1 = −

ΔUdc G io1 (s)G us1 (s) − G uo1 (s)G is1 (s) = Z line1 − G p1 (s)G us1 (s) − G q1 (s)G is1 (s) Δi o1

(3)

3.2 Model of Load The loads studied in this paper are constant power loads. According to [7], the small signal input impedance of the constant power load can be obtained as ZC P L =

U2 Δu dc = − dc Pconst Δi dcL

(4)

where Δudc is the disturbance of the DC voltage and ΔidcL the input current of the DC side of the load converter, U dc is the steady-state value of the DC voltage, Pconst is the steady-state value of the load power. According to (3), (4) and Fig. 1, the output and input impedance (Z out and Z in ) of system can be obtained, as shown in (5). ⎧ ⎪ ⎨ Z out = Z s1 Z s2 Z s3 Z in = Z C P L Z C P S ⎪  ⎩ Tm (s) = Z out Z in

(5)

The criterion of the impedance matching principle is that the system is stable when the Nyquist curve of the loop gain T m = Z out /Z in does not enclose the point (− 1, j0) on the s-plane.

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Fig. 3 Bode diagram of Z out and Nyquist diagram of T m (s) under different DC capacity conditions

4 Analysis of System Stability According to the DC microgrid model in Fig. 1, the influence of the change of the multi-converter parameters on the system stability is analyzed based on the impedance ratio criterion.

4.1 The Influence of DC Bus Capacitance on System Stability The droop coefficients Rdi of the three DC BVC units are all set to 0.01, and the DC bus capacitance C i is increased from 2000 to 4000 µF, the Bode diagram of output impedance Z out of DC BVC and the Nyquist curve of the system loop gain T m (s) is shown in Fig. 3. As the DC capacity increases, the resonant peak value of Z out decreases, and the resonant frequency also decreases. The Nyquist curve does not enclose the point (− 1, j0) and shifts to the right, the system resonant frequency gradually decreases, and the phase margin increases, which indicates that the stability of the DC microgrid system gradually increases.

4.2 The Influence of Converter Control Parameters on System Stability The K pi and K ii of the current controller in the converter control loop are changed to study the influence of the control parameters on the stability of the system. K ii = 50, K pi takes 0.3, 0.32, and 0.34 in sequence; then, K pi = 0.3, K ii takes 50, 40, and 35 in sequence. From the Nyquist diagram of T m (s) drawn in Fig. 4, the stability of the system increases with the increase of K pi . The stability of the system decreases with the increase of K ii .

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Fig. 4 Bode diagram of Z out under different control parameters of DC BVC (K pi , K ii )

4.3 The Influence of Load Power on System Stability Keeping the parameters of the three source converters the same and unchanged, the load power PCPL gradually increases from 10 kW, taking 10, 15, and 25 kW in turn. From the Nyquist diagram of T m (s) drawn in Fig. 5, when the load power is 10 and 15 kW, the Nyquist curve does not enclose the point (− 1, j0), so the system is stable. When the load power is 25 kW, the system becomes unstable. With the load power continues to increase, the Nyquist curve moves to the left. So the stability of the system decreases.

Fig. 5 Nyquist diagram of T m (s) under different power of load

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Fig. 6 Bode diagram and Nyquist diagram of T m (s) under different parameter settings

4.4 The Influence of the Parameter Matching of the DC BVC Units on System Stability Two converters are operated in parallel. The system parameters of each converter remain the same, but the control parameters are set differently (C 1 = C 2 = 2000 µF, Rd1 = Rd2 = 0.01, PCPL = 2 kW; K ii_A = K ii_B = 50, K pi_A = 0.3, K pi_B = 0.34). The Bode and Nyquist diagram are shown in Fig. 6 under two working conditions (with the same parameters and different parameters). When the parameters are the same, the equivalent impedance of the system has a larger impedance peak. On the contrary, the peak decreases and the Nyquist curve moves to the right, the stability of the system is enhanced.

5 Conclusion This paper derives the output and input impedance of the system by constructing a small-signal model of a DC microgrid with multiple converters operating in parallel. (1)

(2)

When using a detailed model analysis of the DC microgrid converter, the lowdamping LC link composed of line impedance and DC stabilized capacitor in the system interacts with the output impedance of the DC BVC unit, which causes the system to generate high-frequency oscillations and reduce system stability. The DC bus voltage stabilizing capacitor increases the inertia of the system, and the increase of the capacitance value will increase the stability margin of the system; the control parameters of the converter will also have a significant impact on the stability of the system. But the constant power load will reduce the system stability, and as the load power increases, the system stability decreases.

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(3)

For multi-converter parallel operation conditions, the equivalent impedance has a larger impedance peak in the resonance band and the system stability is poor when all converter parameters are consistent. If the parameters are different, the system equivalent impedance is better suppressed in the resonance band. Therefore, the parameter difference between multiple converters is conducive to the improvement of system stability.

Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

References 1. Li X,Guo L, Wang C (2016) Key technologies of DC microgrids: an overview. Proc CSEE 36(1):2–17 2. Wan Q, Xia C, Guan L, Wu C (2019) Review on stability of isolated microgrid with highly penetrated distributed generations. Power Syst Technol 43(02):598–612 3. Zhu X, Li Z (2021) Stability analysis of multi converter DC microgrid. Power Syst Technol 45(04):1400–1410 4. Anand S, Fernandes BG, Guerrero JM (2013) Distributed control to ensure proportional load sharing and improve voltage regulation in low-voltage DC microgrids. IEEE Trans Power Electron 28(4SI):1900–1913 5. Guo L, Feng Y, Li X et al (2016)Stability analysis and research of active damping method for DC microgrids. Proc CSEE 35(4):927–936 6. Zheng K, Du W, Wang H (2021) DC microgrid stability affected by aggregated constant power loads based on impedance method. Power Syst Technol 45(01):134–148 7. Zhu X, Meng F (2020) Stability analysis of DC microgrid with virtual inertia control. Power Syst Technol 44(01):208–218

SCD File Visualization and Test Boundary Definition Method for Smart Substation Xiaodong Zhao, Guoping Chen, Feng Li, Leilei Fu, Bo Xu, and Zhenxing Qi

Abstract When building and expanding the smart substation, it is difficult to describe the upgrade details completely and define the upgrade device. The visualization system of configuration description file of smart substation and the method of defining test boundary are studied. Firstly, the problem of incomplete information in traditional SCD file visualization is improved. The substation configuration description (SCD) files with configuration information were extracted, and the comparison files were formed. Then SCD files comparison was done through three levels of sequential comparison. Finally, in order to ensure no power outage or less power outage in the process of smart substation reconstruction and expansion, the test boundary problem is defined. In the process of substation operation and maintenance, the number of primary equipment can be reduced, the work efficiency can be improved, and the construction period can be shortened. It is of great significance to improve the certainty of smart substation reconstruction and expansion project and the safety of on-site operation. Keywords Smart substation · SCD file · Visualization · Version comparison · Test boundary

1 Introduction In the smart substation based on IEC 61850 communication specification, the architecture of three layers and two networks is adopted, and a large number of secondary loop cables are replaced by process layer networks [1–3]. In the process layer, merging unit and intelligent terminal are used to realize information digitization, which lays the foundation for information sharing based on network platform. The X. Zhao · X. Zhao · G. Chen · G. Chen · F. Li · L. Fu · B. Xu Suzhou Power Supply Company of Anhui Electric Power Company of State Grid, Suzhou 234000, China Z. Qi (B) School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_46

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hard terminal of secondary loop is transformed into virtual terminal based on sample value (SV) and general object oriented substation events (GOOSE) [4, 5]. Virtual terminal mapping table is usually used to reflect the connection relationship of secondary loop. The SCD file is the configuration file of the whole station system [6, 7]. All IED instance configuration and communication parameters, communication configuration between IEDs and primary system structure of substation are described by SCD file. The research on IEC 61850 mainly focuses on communication performance and relay protection reliability, modeling technology, secondary system design and multivendor equipment engineering integration software application under IEC 61850 system [8, 9]. With the rapid development of smart substation construction, the focus of SCD file management has gradually extended from supporting unified modeling and substation system construction to supporting equipment operation and maintenance and effective control of secondary loop. At present, the management mode of SCD file is mainly offline decentralized management. The change of SCD file on site is lack of tracking and recording. The change of SCD file mainly depends on manual management, so it is difficult to guarantee the correctness and uniqueness of the file. In the smart substation system, the system configuration tool is provided to realize the syntax verification of structured control language (SCL), support the import of IED capability description (ICD) configuration file, the generation of SCD file and the export of configured IED description (CID) file [10, 11]. But before the actual installation, the device configuration also needs to supplement the extracted CID file information. The human–computer interaction function of manufacturer tools is quite different, and the visualization degree of configuration process is not high. At the same time, most of the device configuration needs manual intervention and correction. After the device configuration changes, the verification of related functions mainly depends on the re testing of all related devices. Smart substation SCD file management depends on the manufacturer, upgrade details cannot be completely described. In addition, in the process of reconstruction and expansion, it is difficult to define the devices that need to be upgraded. Therefore, this paper studies SCD visualization and test boundary definition methods. By improving the visualization of traditional SCD files, the visualization degree of SCD files is further improved. The different points of different versions of SCD files are obtained by comparing SCD files. Finally, the test boundary in the process of reconstruction and expansion is defined to ensure the safety of operation and maintenance and improve the efficiency of substation operation and maintenance.

2 SCD File Overview The primary system architecture of substation, IED configuration information, signal contact information between IEDs, location and address of communication access point are described by SCD file. SCD file is composed of five parts, which are

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header, substation description, IED description, communication system description and data type templates. The header contains the version, name and regulation of SCD file. Substation describes the functional structure, primary equipment and primary topology of substation. IED describes the configuration and function of IED. Communication describes the communication information of secondary equipment. Data type templates describes data type template information.

3 SCD Profile Visualization Firstly, The SCL class read in is parsed by SCD parsing module, and the complete IEC 61850 model architecture is obtained. Secondly, IED types are classified and IED devices are hierarchically processed. Finally, IED single device level is visualized and displayed in graphical form.

3.1 Improvement of SCD File Visualization The optical fiber link of smart substation is divided into point-to-point direct connection loop and networking optical fiber link loop. For the point-to-point direct connection loop, indirect discrimination method can be used to realize the monitoring and diagnosis of optical fiber link. For the networking optical fiber link loop, SV, GOOSE and MMS information can be combined to realize the monitoring and diagnosis of optical fiber link. Based on SCD file definition and optical link diagnosis discrimination, optical physical link display and diagnosis can be realized. At the same time, the virtual loop visualization is used to realize the visualization of the optical fiber loop indirectly. The virtual terminal information is bound with the starting port information of the secondary equipment to associate the virtual loop information with the optical fiber loop information. Finally, the visualization of the optical fiber loop is realized. The visualized optical fiber loop is shown in Fig. 1.

4 SCD File Comparison and Test Boundary Definition In the process of smart substation expansion, there will be a large number of different versions of SCD files, which is not conducive to the work of maintenance personnel. Aiming at different versions of SCD files in the process of smart substation reconstruction and expansion, the differences are quickly located through the comparison of virtual secondary loop and other aspects. And the differences are visually displayed through graphics. The test boundary of smart substation reconstruction and expansion is defined, which is conducive to enhance the project certainty and the safety of on-site operation.

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Fig. 1 Visualized fiber loop

4.1 SCD File Comparison Process The SCD file comparison process is shown in Fig. 2, and the specific steps are as follows: (1)

The first level of comparison: all the information related to the virtual loop is found, and the XML file and the unique CRC check code are generated. Then the virtual loop configuration information of the changed device is determined by comparing the CRC check codes of all IEDs.

Fig. 2 SCD file comparison process

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Fig. 3 The comparison results of virtual loop and logical link

(2)

(3)

The second level of comparison: for the changed IED, the link information is compared to further determine the different links. The link relationship between IED and external device is visualized. The third level of comparison: the change of communication information is obtained through the comparison of data parameters before and after the change of link information. The changes of link increase and decrease are obtained by comparing the links before and after the virtual loop changes. The changed IED link parameters and virtual loops are shown.

According to the above steps of SCD file comparison, the comparison results of virtual loop and link in SCD file are shown in Fig. 3. The “+” symbol indicates the added link, the “×” symbol indicates the reduced link, the “!” symbol represents the link where the data changes.

4.2 Test Boundary Definition In addition to SCD file comparison visualization, it is also necessary to define the test boundary in the reconstruction and expansion. No power outage, less power outage or shorter power outage time are assured for operating equipment. The efficiency of operation and maintenance, reconstruction and expansion field test has been improved. As shown in Fig. 4, the cyclic redundancy check (CRC) [12] verification diagram of virtual return path of associated IED. The reconstruction area is divided into extended IED domain, associated IED domain and extended IED domain. Two sections are formed, which are between the IED domain and the associated IED domain, and between the associated IED domain and the affected IED domain. The affected area of reconstruction and expansion is determined by judging the change of sub-CRC of section virtual loop. Taking the extension of a line Bay as an example, the associated IED is bus protection. The virtual loop of bus protection and every IED equipment affected by bus protection, and the sub-CRC is formed. If the sub-CRC check code remains unchanged, the secondary virtual loop between the reconstructed and expanded associated IED and the affected IED equipment remains unchanged. According to the above-mentioned sub-CRC verification rules, the interval devices with virtual loop changes are automatically identified. The list of test equipment is

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Fig. 4 The CRC verification diagram of virtual return path of associated IED

given in the reconstructed SCD configuration file. And the list of test equipment is obtained, including the test boundary for reconstruction, expansion and maintenance. It provides the basis for online and offline test of system equipment.

5 Conclusion With the development of smart substation, the visualization degree of traditional SCD configuration file is low and some key information is missing. A highly visualized SCD configuration file visualization system is proposed, which solves the problem of key information display missing of traditional SCD configuration file visualization tools. Aiming at the problems of unclear test boundary in reconstruction and maintenance, a method of test boundary definition is proposed. It not only provides convenience for the operation and maintenance personnel, but also guarantees the safe and stable operation of smart substation. At present, the system has been applied to the debugging and defect elimination of intelligent substation. It can be seen that the use of the system greatly simplifies the field work process and improves the work efficiency.

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References 1. Zhao J, Qian K, Yao J, Wang S, Yang Z (2015) A network scheme for process bus in smart substations without using external synchronization. Int J Electr Power Energy Syst 64:579–587 2. Li H, Wang L (2011) Research on technologies in smart substation. Energy Proc 12:113–119 3. Ali NH, Ali B, Basir O (2016) Protection of smart substation based on WLAN complies with IEC 61850 using traveling wave analysis. Electr Power Syst Res 140:20–26 4. Feizimirkhani R, Bratcu AI, Bésanger Y (2018) Time-series modelling of IEC 61850 GOOSE communication traffic between IEDs in smart grids—a parametric analysis. IFAC PapersOnLine 51–28:444–449 5. Asim M, Suhail A, Alic H (2020) IEC 61850 based substation automation system: a survey. Int J Electr Power Energy Syst 120:1–12 6. Hun B, Kim L (2017) Harmonizing IEC 61850 and CIM for connectivity of substation automation. Comput Stand Interf 50:199–208 7. Xiong H, Wan Y, Gui X (2015) Design and implementation of visual management and analytical decision system for smart substation SCD files. Electr Power Autom Equip 35(5):166–171 8. Hu D, Wo J (2010) Intelligent substation virtual loop system based on IEC 61850. Power Syst Autom 34(17):78–82 9. Sidhu T, Yin Y (2007) Modelling and simulation for performance evaluation of IEC 61850 based substation communication system. IEEE Trans Power Delivery 22(3):1482–1489 10. Wang J, Wang Z (2021) Research and implementation of virtual circuit test tool for smart substations. Proc Comput Sci 183:197–204 11. Cavalieria S, Regalbutob A (2016) Integration of IEC 61850 SCL and OPC UA to improve interoperability in smart grid environment. Comput Stand Interf 47:77–99 12. Mekkanena M, Antilab E, Virrankoski R (2014) Using OPNET to model and evaluate the MU performance based on IEC 61850-9-2LE. Proc Comput Sci 36:72–79

Power Load Forecasting Based on Sine-SSA-BP Neural Network Dingjiang Zou and Tianyu Liu

Abstract Aiming at the problems of low accuracy, and instability of short-term power load forecasting, a short-term power load forecasting method based on sine chaotic map improved sparrow search algorithm combined with BP neural network is proposed. The sine chaotic map is used to initialize the sparrow population so that the population is evenly distributed in the space, and the sparrow individuals with the highest fitness ranking are selected as the initial population to optimize the initial weights and thresholds of the standard BP neural network. Through simulation experiments, the Sine-SSA-BP prediction results are compared with the results of the standard BP neural network prediction load, which verifies the accuracy and effectiveness of the prediction method. It shows that this method can reduce the prediction error, has good stability and strong global search ability, and is feasible in practical application. Keywords Sine chaotic map · Sparrow search algorithm · BP neural network · Short-term power load forecasting

1 Introduction Short-term power load forecasting plays an indispensable role in the economic, safe and reliable operation of the power system. Short-term power load forecasting mainly refers to forecasting and estimating the power load in a few hours, a day or a few days in the future. The purpose is to arrange the power generation plan for each power plant. It is the most critical type of power system load forecasting [1]. However, many prediction models have not yet reached a high level of accuracy and stability. Through the active research of load forecasting in various countries, the theoretical research of load forecasting has been developed rapidly, and at the same time, many methods of load forecasting have appeared [2, 3]. In the literature [4, 5], an improved prediction model of BP neural network is proposed, and the results show that this D. Zou · T. Liu (B) Shanghai Dianji University, Pudong, Shanghai 201306, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_47

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method improves the prediction accuracy. In literature [6], a short-term power load forecasting method based on the combination of empirical mode decomposition and long-term short-term memory network is proposed, and the results show that this method can improve the forecasting accuracy. In literature [7], a short-term load forecasting method based on particle swarm optimization PSO and least squares support vector machine is proposed. The results show that this method can effectively improve the training speed and prediction accuracy. In literature [8], a prediction method combining improved fruit fly algorithm and generalized regression neural network is proposed. The results show that this method reduces the prediction error and improves the stability of the algorithm. These studies provide a theoretical basis for solving short-term forecasting methods of power systems. On the basis of the above background, this paper proposes a short-term load forecasting method combining the improved sparrow search algorithm and BP neural network. The model uses load data and weather information as input factors, optimizes the weights and thresholds of the BP neural network through an improved algorithm, and verifies the accuracy of this prediction method through simulation.

2 Predictive Model The sparrow search algorithm is a newer intelligent optimization algorithm, proposed in 2020, mainly inspired by the foraging behavior and anti-predation behavior of sparrows. There are two different types of sparrows in the sparrow population: discoverers and joiners, and a reconnaissance and early warning mechanism has been added [9]. The discoverer is mainly responsible for finding food and providing foraging areas and directions, and the joiner will follow the discoverer for food. When the population is aware of the danger of a predator, it will immediately engage in antipredation behavior. This algorithm has the advantages of strong optimization ability, fast convergence speed, and fewer parameters.

2.1 The Improved Sparrow Search Algorithm Chaos mapping is used to generate a chaotic sequence, which is a random sequence generated by a simple deterministic system. The general chaotic sequence has the main characteristics of nonlinearity, sensitive dependence on the initial value, ergodicity, randomness, universality, score maintenance, and so on [10]. In the field of optimization, chaotic mapping can be used to replace pseudo-random number generators to generate chaotic numbers between 0 and 1. This paper chooses the chaos of the Sine chaotic map instead of random initialization, which can make the sparrow population more evenly distributed in the search space and avoid falling into the local optimum. The Sine chaotic map is a unimodal map, and the chaotic sequence is as follows:

Power Load Forecasting Based on Sine-SSA-BP Neural Network

xk+1 =

a sin(π xk ) 4

567

(1)

In the formula, its value range is [− 1, 1], where the value range of a is (0, 4], and the value range of the initial value x 0 is (0, 1). The sparrow population matrix can be expressed as follows: ⎡

x12 · · · x22 · · · .. . ··· xn1 xn2 · · ·

x11 ⎢ x1 ⎢ 2 x =⎢ . ⎣ ..

⎤ x1d x2d ⎥ ⎥ .. ⎥ . ⎦

(2)

xnd

Among them, d represents the dimension of the variable, and n represents the number of sparrows. Therefore, the fitness value of the sparrow can be expressed as follows: ⎡  ⎤ f ( x11 x12 · · · x1d ) ⎥  ⎢ ⎢ f ( x21 x22 · · · x2d ) ⎥ Fx = ⎢ (3) ⎥ ⎣ ⎦  1 ·2· · f ( xn xn · · · xnd ) Among them, f represents the fitness value of sparrows. The implementation steps of the improved algorithm are as follows: 1.

2. 3. 4.

Use the Sine chaotic map to initialize the sparrow population position, fitness, and N, n, PD, SD, ST parameters (N represents the maximum number of iterations, n represents the population size, PD represents the number of discoverers, SD represents the number of sparrows that have sensed danger, ST Represents a safety value). Start loop, iteration < N. Sort the population to obtain the current optimal sparrow individual position and optimal fitness value. Foraging. The discoverer with a better fitness value will give priority to obtaining food in the search process, and guide all joiners to the direction of the food source. The location update description of the discoverer is as follows:

X t,t+1 j

=

−i X t,t+1 j · exp( α·N ), R2 < ST t+1 X t, j + Q · L , R2 ≥ ST

(4)

In the formula, t is the current iteration number, j = 1, 2, 3, …, d, Q is a random number that obeys a normal distribution, L is a unit row vector, and α(α ∈ [0, 1]) is a random number, R2 (R2 ∈ [0, 1]) is the sparrow warning value, ST (ST ∈ [0.5, 1]) is the sparrow safety value. When R2 < ST, it indicates that there is no danger of predators around, and the discoverer can search extensively; if R2

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≥ ST, it indicates that sparrows in the population have found the predator and issued an alarm. At this time, all sparrows must go to safety quickly Foraging in the area. Update the location of the joiner, and update as follows:

X t,t+1 j

6.

7. 8.

=

X wor st −X t

t, j Q · exp( ) , i < n/2 i2  t+1 t+1 X P +  X t, j − X P  · A+ · L , i ≥ n/2

(5)

Among them, X worst is the current worst position globally, X P is the best position occupied by the current discoverer, and A+ is a row vector containing only two elements 1 and − 1 randomly. When i < n/2, it indicates that the i-th joiner with a lower fitness value has not found food and needs to fly to other places to find food. Anti-predation behavior. The number of sparrows that are aware of danger accounts for 10–20% of the total. The positions of these sparrows are randomly generated, and their positions are constantly updated, which can be expressed as:   ⎧   t t t ⎪ + β · − X X X ⎨ best t, j best  , i f f i > f g    t+1  t  t (6) X t, j = X t, j −X wor st  ⎪ ⎩ X t,t j + K · ( fi − fw )+ε , i f f i = f g Among them, X best is the current global optimal position; β is a random number that controls the step size and obeys the standard normal distribution; K (K ∈ [0, 1]) is a random number; f i is the individual fitness value; f g and f w respectively represent the global best fitness value and the global worst fitness value; ε is a constant close to 0. When f i < f g , sparrows are at the edge of the population and are easily attacked by predators. When f i = f g , Sparrows in the middle of the population are also threatened. At this time, they need to be close to other sparrows to reduce the risk of being caught. Update the historical optimal fitness. Steps 3–7 are executed, the loop ends when the maximum number of iterations is reached, and the optimal individual position and fitness are output.

2.2 Optimize BP Neural Network As shown in Fig. 1, the BP neural network is composed of an input layer, a hidden layer, and an output layer. It is currently one of the most widely used neural network models. Its learning rule is to use the gradient descent method to continuously adjust the weights and thresholds of the network through backpropagation. However, the BP neural network is very sensitive to weights and thresholds. If the parameters are wrong, it is easy to cause the network to fall into a local optimum. Therefore, the

Power Load Forecasting Based on Sine-SSA-BP Neural Network Fig. 1 BP neural network structure

Input Layer

569

Hidden Layer

Output Layer

improved sparrow algorithm is used to optimize the initial weights and thresholds of the BP neural network, jumping out of the local optimum, and making the network more stable. Sine-SSA optimized BP neural network prediction steps are as follows: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Set the parameters of the improved sparrow search algorithm; Enter the data and normalize it; Determine the topology of the BP neural network; Initialize the weights and thresholds of the BP network; Calculate the population fitness value and update the optimal individual position; Foraging and anti-predation behaviors, update individual sparrow positions; Determine whether the end conditions are met. if not satisfied, continue to step 5; Output the optimal weight and threshold parameters; The BP neural network uses the optimal parameters for training and simulation prediction and then ends the process. The forecast flow chart is shown in Fig. 2.

Begin Input data and normalize it Determine the topology of the BP neural network

Initialize the weight and threshold of BP

Output optimal weight and threshold parameters

Calculate the population fitness value and update the optimal individual position

Foraging and antipredation,updating individual sparrow positions

NO

Obtain optimal parameters for training and prediction

YES Whether the end condition is met

Fig. 2 Sine-SSA optimized BP neural network flow chart

End

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3 Simulation Analysis To more intuitively evaluate the effectiveness of the Sine-SSA-BP model, this paper uses the public electricity data set in Australia for instance verification and selects the load of 0–24 o’clock on each day from 2006-2-13 to 2006-3-13 in the data set The data is used as a training sample to predict the 24-h load on March 14, 2006, and compare it with the BP prediction result. Using a multiple-input single-output model, variables such as historical load, weather information, and day type are selected as an input, and the predicted load value of a certain day and hour is used as output. The sparrow population size n is 30, and the maximum evolutionary generation number N is 50 times. The relative error absolute value |RE| is selected as the predictive evaluation index. The specific evaluation results are shown in Table 1 and Fig. 3. Table 1 Comparison of predicted and actual values on March 14 (Tuesday) BP

Model Time

Actual value/MW

Predictive value /MW

Sine-SSA-BP |RE|/%

Predictive value/MW

|RE|/%

01: 00

7664.9

7461.3

2.66

7512.5

1.99

02: 00

6961.5

6745.1

3.11

6778.8

2.62

03: 00

6626.9

6459.2

2.53

6441.3

2.80

04: 00

6669.5

6556.7

1.69

6566.5

1.54

05: 00

7183.1

7253.2

0.98

7274.5

1.27

06: 00

8533.7

8224.4

3.62

8294.3

2.81

07: 00

9408.4

9244.4

1.74

9240.6

1.78

08: 00

9866.4

9623.9

2.46

9853.6

0.13

09: 00

10,238.9

9881.0

3.50

10,139.0

0.98

10: 00

10,340.9

9966.0

3.63

10,212.0

1.25

11: 00

10,362.5

10,083.0

2.70

10,320.0

0.41

12: 00

10,345.7

10,095.0

2.42

10,251.0

0.92

13: 00

10,326.6

10,076.0

2.43

10,255.0

0.69

14: 00

10,331.9

10,208.0

1.20

10,356.0

0.23

15: 00

10,376.5

10,154.0

2.14

10,385.0

0.08

16: 00

10,412.0

9998.0

3.98

10,279.0

1.28

17: 00

10,196.8

10,030.0

1.64

10,262.0

0.64

18: 00

9831.1

9737.9

0.95

9982.7

1.54

19: 00

9693.9

9476.5

2.24

9666.9

0.28

20: 00

9397.7

9055.9

3.64

9225.4

1.83

21: 00

8770.8

8750.7

0.23

8993.0

2.53

22: 00

8559.9

8210.4

4.08

8425.3

1.57

23: 00

8317.8

7865.1

5.44

8129.7

2.26

24: 00

7869.9

7542.6

4.16

7842.3

0.35

Power Load Forecasting Based on Sine-SSA-BP Neural Network

(a).

571

(b).

Fig. 3 a Sine-SSA iterative convergence. b Comparison of the two models’ forecast curves and actual daily load curves

It can be seen from Fig. 3 that the sparrow population obtains the optimal solution in the 20th generation. Compared with the BP prediction curve, the Sine-SSA-BP prediction curve fits the true value curve better, and has less fluctuation, which proves that the Sine-SSA-BP prediction model can effectively jump out of the local optimum caused by gradient descent, and enhances The ability to search globally. In order to clearly express the forecast error, Table 1 shows the load forecast data of the two models and the relative error of each time period. It can be seen from Table 1 that 9 of the absolute values of the relative errors predicted by the BP model exceed 3%, and their average relative errors are 2.63%; while the absolute values of the relative errors predicted by the Sine-SSA-BP model are all less than 3%, Its average relative error is 1.32%, which improves accuracy by about 1.68%, and meets the forecast error requirements of the power industry. Through further analysis, the prediction error of Sine-SSA-BP is as low as 0.08%, and the prediction error of BP is as low as 0.23%, indicating that the Sine-SSA-BP prediction model not only improves the stability but also reduces the prediction error. In practical applications It is feasible.

4 Conclusion Short-term power load forecasting has important practical value for the economic operation of power dispatching. In order to reduce the error of power load forecasting, this paper proposes the Sine chaotic mapping improved sparrow search algorithm to optimize the initial weights and thresholds of the BP neural network. Through the Sine chaotic mapping, the initial sparrow population can be evenly distributed to avoid falling into the local maximum in the optimization process. The optimal solution enables the BP neural network to obtain the best initial weight and threshold. Using the original BP neural network model to compare with the Sine-SSA-BP network, the improved prediction model has a greater improvement in prediction accuracy and stability, which provides a feasible reference for future short-term load forecasting.

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References 1. Park K, Yoon S, Hwang E (2019) Hybrid load forecasting for mixed-use complex based on the characteristic load decomposition by pilot signals. IEEE Access 7:12297–12306 2. Quilumba FL, Lee W-J, Huang H et al (2015) Using smart meter data to improve the accuracy of intraday load forecasting considering customer behavior similarities. IEEE Trans Smart Grid 6(2):911–918 3. Browell J, Fasiolo M (2021) Probabilistic forecasting of regional net-load with conditional extremes and gridded NWP. IEEE Trans Smart Grid 12(6):5011–5019 4. Kejie W, Rui Z (2019) Research on short-term power load forecasting method based on improved BP neural network. Electr Measur Instrument 56(24):115–121 5. Liu G, Huang J, Liu X (2005) Short-term load forecasting based on improved BP neural network. Electrotech Appl 24(12):110–113 6. Yu W, Dajun M, Wanli H, Bin L (2020) Short-term load forecasting based on EMD and long short-term memory neural network. J Eng Thermal Energy Power 35(04):203–209 7. Yan L, Xinxia P, Sida Z (2021) Research on short-term power load forecasting method based on improved LS-SVM. Electr Measur Instrument 58(05):176–181 8. Zhu X (2020) Research on short-term power load forecasting method based on IFOA-GRNN. Power Syst Protect Control 48(09):121–127 9. Yang L, Li Z, Wang D et al (2021) Software defects prediction based on hybrid particle swarm optimization and sparrow search algorithm. IEEE Access 9:60865–60879 10. Xin Z (2019) Research on optimization performance comparison of different one-dimensional maps. Appl Res Comput 29(3):913–915

Energy Internet-Oriented Distribution Network Long-Term Load Forecasting Method Based on Prophet-BiLSTM-CRITIC Mode Wenying Li, Qinghong Guo, Ming Wen, Yun Zhang, Xin Pan, and Shuzhi Yang Abstract Power load forecasting plays a pivotal role in improving the safety and stability of the distribution networks. First, the Prophet and Bi-directional Long shortterm memory (BiLSTM) models were established respectively. Then, the CRITIC weight method was used to linearly combine the two models. Finally, the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) were defined evaluation indicators. Through comparing with Prophet, BiLSTM, ARIMMA forecasting model of one distribution network, the prediction accuracy of the Prophet-BiLSTM-CRITIC model proposed in this paper was significantly higher than the other single models. Keywords Distribution network · Prophet · BiLSTM · CRITIC

1 Introduction Prediction algorithms are widely used in finance, transportation, and are extended to power systems [1–3]. The accurate prediction algorithm can not only ensure the safe and stable operation of the power grid, but also plan the construction of the power grid reasonably and improve the economy. The single prediction model usually only contains part of the information of the prediction object. By combining the single models through certain rules, more factors can be considered to improve the prediction accuracy [4]. At present, the commonly used combination forecasting methods were divided into two categories: linear combination and non-linear combination forecasting. The paper [5] pointed Science-Technology Innovation Platform and Talents Program of Hunan Province, China, under Grant 2019TP1053. W. Li (B) · M. Wen · X. Pan State Grid Hunan Electric Power Company Ltd. Economic and Technical Research Institute, Changsha, China e-mail: [email protected] Hunan Key Laboratory of Energy Internet Supply-Demand and Operation, Changsha, China Q. Guo · Y. Zhang · S. Yang State Grid Hunan Electric Power Company Limited, Changsha, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_48

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out that the effect of the linear combination method in the medium and long-term load forecasting model is better than the non-linear one. In view of the large amount of data and strong timing of long-term power load forecasting, this paper used the objective weight method CRITIC to linearly combine the Prophet forecasting algorithm and the BiLSTM forecasting algorithm. On the one hand, it solved the problem of the disappearance of the gradient caused by the huge amount of long-term power load forecasting data. On the other hand, considering holiday factors, the accuracy of power load forecasting was improved. The rest of this paper was organized as follows. Section 2 explained the principles of Prophet prediction algorithm and BiLSTM prediction algorithm. Section 2 presented the Prophet-BiLSTM-CRITIC prediction model. Section 3 used power load of one distribution networks as a case to simulate and verified the hybrid forecasting model by comparing with three kinds of single model: Prophet, BiLSTM, ARIMA. The results show that the method proposed in this paper can improve the prediction accuracy. Section 4 summarized the paper.

2 Power Load Forecasting Model 2.1 Prophet Forecasting Model Prophet, proposed by Sean J. Taylor of Facebook in 2017, is an additive model, which generates time series forecasts by fitting curves to different components and accumulating them [6]. The algorithm is mainly composed of four parts: trend item, period item, holiday factor item, and random item. The basic form of the model is: y(t) = g(t) + s(t) + h(t) + ε(t)

(1)

Among them, g(t) is the trend item, s(t) is the period item, h(t) is the holiday item, ε(t) is the error, and y(t) is the output forecast value. The trend item g(t) adopts logistic regression function, and selects sigmoid function g(t) = C/(1 + ex p( − k(t − b))). C is the model capacity, k is the growth rate, and b is the offset. In the actual environment, C, k, and b of the trend item may all change over time.  Making: a j (t) =

1 , t ≥ Sj 0 , other

(2)

Then, the growth rate on the timestamp t j was rewritten as k + α T δ. According to the continuous condition of the line segment, the b was determined by the end point of the line segment and changed to b + α(t)T γ . And the γ j is:

Energy Internet-Oriented Distribution Network …

γ j = (S j − b −



γl ) · (1 − (k +

l> j

 l< j

δl )/(k +

575



δl )), δl ∼ Laplace(0, τ ) (3)

l≥ j

The trend term model obtained by comprehensive formulas (1)–(3): g(t) = C(t)/(1 + exp(−(k + α(t)T ) · (t − (m + α(t)T γ ))

(4)

Among them, α(t), δ(t) and γ (t) are column vectors. Seasonal term Use Fourier series to approximate periodicity, as follows: s(t) =

N 

(an cos(2π nt/ p) + bn sin(2π nt/ p))

(5)

n=1

Among them, P is the period of the time series, 2n is the number of cycles used in the model, and N is the number of divisions of the time series. The holiday factor item h(t) is set under the assumption that the influence of the holiday is independent, as follows: h(t) = [1{t∈D1 } , 1{t∈D2 } , ..., 1{t∈DL } ] · (κ1 , κ2 ..., κ L ) , κ j ∼ N or mal(0, υ 2 )

(6)

where, κi is the influence range of holidays, and it is related to υ. If υ is larger, the influence of holidays on the model is greater. DL is a period of holidays. The random term ε(t) satisfies a normal distribution, which represents fluctuations not predicted by the model [7]. Initialize the Prophet model, and set the parameter Changepoint = 0.9 after debugging. It shows that the growth trend has a more appropriate effect on the change which means the results will not cause over-fitting or under-fitting. By default, the initial training period is set to three times the horizon, and there is a cutoff for every half of the horizon. The prediction interval is from January 2020 to December 2020, and besides the time granularity is “days”. After that, set the Chinese major holidays in the formula h(t), as shown in Table 1. In order to predict the load change in a period of time in the future. First, the original data is divided into training set and test set in proportion of 3:1, and then the training data set is input to the Prophet model for training. Trends are composed of different components, such as general trends, years, seasons, months, weeks, etc. We need to extract these components from the trends to see the trends of different components. It can be seen from Fig. 1 that the yearly trend in the region has three obvious peaks. Respectively shows at the beginning of February, August as well as the end of December, and reached the maximum peak from the end of January to early February. The valley was obviously reached in May and October, and the lowest was in May. From the weekly trend, the load value from Thursday to Sunday is significantly higher than other times. Figure 2 shows the results of individual analysis of each part. After the analysis of the prophet model, the load data of a certain area from 2018 to 2020 generates three results: trend, yearly trend, and weekly trend.

576 Table 1 The major holidays and corresponding dates in China

W. Li et al. Holidays

Dates

New year’s day

‘2018-01-01’, ‘2019-01-01’, ‘2020-01-01’, ‘2021-01-01’

Spring festival

‘2018-02-15’, ‘2019-02-04’, ‘2020-01-24’, ‘2021-02-11’

Lantern festival

‘2018-03-02’, ‘2019-02-19’, ‘2020-01-03’, ‘2021-02-26’

Ching Ming festival

‘2018-04-05’, ‘2019-04-05’, ‘2020-04-04’, ‘2021-04-03’

Mid-autumn festival

‘2018-09-22’, ‘2019-09-13’, ‘2020-10-01’, ‘2021-09-19’

National day

‘2018-10-01’, ‘2019-10-01’, ‘2020-10-01’, ‘2021-10-01’

Labor day

‘2018-04-29’, ‘2019-05-01’, ‘2020-05-01’, ‘2021-05-01’

Dragon boat festival

‘2018-06-18’, ‘2019-06-07’, ‘2020-06-25’, ‘2021-06-12’

Valentine’s day

‘2018-02-14’, ‘2019-02-14’, ‘2020-02-14’, ‘2021-02-14’

The Prophet model measures the fitting effect according to the root mean square error. While the goal is to minimize the root mean square error. In addition, Prophet has a cross-validation function. The specific method is to select some cut-off points in the historical data. For these cut-off points, only the data before these points are used to fit the model, and then compare the true value and the predicted value. Figure 2 uses the Prophet model to analyze and predict the last year’s load data according to the historical data. Among them, horizon represents the number of predicted days after each cutoff, initial represents the initial time, and period represents how often to set a cutoff. In Fig. 2a set horizon = 180 days, initial = 720 days, and period = 365 days. Through the visualization index, check the visualization about the average absolute error (MAPE) index as shown in Fig. 2b. It can be seen that the forecast error for the next six months is maintained at about 0.2. Figure 2c shows the final fitting effect and prediction results of the model from historical data. The red dot denotes the actual value, the dark blue denotes the predicted value, as well as the light blue shaded area indicates the uncertainty area. The data interval without a yellow dot represents the forecast interval of the future trend of the load. The load change trend in this interval has a great correlation with the historical data change trend, which proves that the periodicity of the time series data is relatively significant.

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Fig. 1 Analysis of each component

2.2 Bi-Directional Long-Short Term Memory (BiLSTM) BiLSTM is composed of forward LSTM and backward LSTM [8]. LSTM uses gating to control the flow of information, including input gates, forget gates and output gates. Gating can be regarded as a fully connected layer, which is realized by the Sigmoid function and the dot multiplication operation. The general form of gating is [9]: g(x) = σ (Wx + b)

(7)

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W. Li et al.

Horizon

(a) The cross_validation of prophet

(b) Prediction of Prophet (MAPE)

(c) Forecast Fig. 2 Predictive analysis results of prophet

where, σ is the Sigmoid activation function, W x represents the weight matrix of the network, b represents the bias matrix of the network. The input gate it is used to determine how much information of the network’s input x t is stored in the unit state C t at the current moment. The calculation formula is: i t = σ ([Wxi · xt + Whi · h t−1 ] + bi )

(8)

where, ht −1 is hidden state for the last moment, x t is the input item at the current moment, W fh and W fk are the weight matrix of ht −1 and x t respectively. Forgetting gate f t uses to decide how much information of the unit state C t needs to be retained in the unit state C t −1 at the time t−1. Its calculation formula is: f t = σ ([Wx f · h t−1 + Wh f · xt ] + b f )

(9)

t = tanh(Wxc · xt + Whc · h t−1 + bC ) C

(10)

t Ct = f t  Ct−1 + i t  C

(11)

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Fig. 3 BiLSTM overall framework

where, tanh(x) is the activation function which select the hyperbolic tangent function, W xC and W hC are the weight matrix of the memory gate ht −1 and x t respectively. Output gate ot controls the influence of the memory unit C t on the current output value ht . In other word, some parts of the memory unit will be output at the time step. The calculation formula is: ot = σ (Wxo · xt + Who · h t−1 + bo )

(12)

h t = ot  tanh(Ct )

(13)

where, W xo and W ho are the weight matrix of ht −1 and x t respectively. Suppose the input data is x = {x 1 , x 2, … x t-n }, and the output data is y = {y1 , y2 , …, yt−n }. BiLSTM can improve the long-term dependence of learning and improve the accuracy of the model by training LSTM in two directions [10]. In the first round, LSTM{ is applied to the forward direction of the input sequence, and the } → → → → o 2 , ..., − o t+1 . In the second round, the LSTM’s output is ← o = − o 1, − o− = output − } {← − ← − ← − − → ← − o 1 , o 2 , ..., o t+1 . Finally, the o and the o are combined through the weight matrix [11]. Its structure is shown in Fig. 3.

3 Hybrid Forecasting Model The CRITIC weighting method was used to determine the weight coefficients of the Prophet model and the BiLSTM model in paper, respectively. The CRITIC weighting method is a method of comprehensively measuring objective weights through the contrast intensity and reentrancy of indicators, which step as follows: Step 1

Calculate two types of evaluation indicators, as fallow [12]:

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Positive indicators: xi j_nor mal = (xi j − min(x j ))/(max(x j ) − min(x j )) (14) Negative indicators: xi j_nor mal = (max(x j ) − xi j )/(max(x j ) − min(x j )) (15) Step 2

Calculate the correlation coefficient, which is used to measure the degree of correlation between various indicators, and its calculation formula is [13]: ri j = [

N 

⎡ | N N |   (x hi − x i )2 (x h j − x j )2 ] , i = j (x hi − x i )(x h j − x j )]/[|

h=1

h=1

h=1

(16)

Step 3

where, x hi and x hj are the value of the evaluation index i and j for the candidate plan h, x i with x j are the mean value of the evaluation index i and j of the standardized evaluation matrix. The amount of information C j contained in the index j is: Cj = δj

n 

(1 − ri j )

(17)

i=1

Step 4

Which, δ j is the standard deviation of the standardized column vector of the evaluation matrix. The objective weight W j contained in the index j is: Wj = Cj/

m 

Cj

(18)

j=1

The Prophet model and the BiLSTM model are used separately to predict the power load, and the weight coefficients of the two models are determined by the CRITIC weighting method to construct a combined model [14]: yfinal = WP · yP + WB · yB

(19)

where, W is the weight coefficients, y is the prediction results, yfinal is the prediction result of the combined model, The subscripts P and B represent Prophet and BiLSTM. In order to verify the application performance of the Hybrid forecasting model, this article uses the Prophet model, the BiLSTM model, and the ARIMA model to conduct a comparative experiment. After the predictive values of the two models were obtained, the weights of the Prophet and BiLSTM models were calculated to be: W B = 0.46 and W P = 0.54. Then, the evaluation results of each model are listed in Table 2. It shows that the

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Table 2 Performance comparison of different models Models

RMSE

MAE

Prophet

5.501

4.405

BiLSTM

5.710

3.462

ARIMA

36.263

17.956

2.625

1.743

Prophet-BiLSTM (W B = 0.46, W P = 0.54)

prediction performance of the Prophet is equivalent to BiLSTM single-term models respectively, and they both significantly better than the ARIMA model. The Hybrid forecasting model further optimizes the prediction accuracy on the basis of their single-term model, namely the prediction effect is the best.

4 Conclusion Analyzing the characteristics and laws of mid- and long-term load historical data to improve model prediction accuracy. It is of great significance to power grid planning. This paper proposed a Prophet-BiLSTM combined model based on Prophet and LSTM. Moreover, combined CRITIC to obtain the best weights which gave full play to the advantages of the two models. The experimental results showed the feasibility and superiority of this model. However, the two models did not consider the influence of various factors such as temperature and weather on the load data. In the future, we can further explore the role of various influence factors in load time series data forecasting, and improve the accuracy of medium and long-term load forecasting.

References 1. Yenido˘gan I, Çayir A, Kozan O et al (2018) Bitcoin forecasting using ARIMA and PROPHET. In: 2018 3rd international conference on computer science and engineering (UBMK). IEEE, Sarajevo, Bosnia and Herzegovina, pp 621–624 2. Shuvo MAR, Zubair M, Purnota AT et al (2021) Traffic forecasting using time-series analysis. In: 2021 6th international conference on inventive computation technologies (ICICT). IEEE, Coimbatore, India, pp 269–274 3. Parizad A, Hatziadoniu CJ (2021) Using prophet algorithm for pattern recognition and short term forecasting of load demand based on seasonality and exogenous features. In: 2020 52nd North American power symposium (NAPS). IEEE, Tempe, AZ, USA, pp 1–6 4. Holden K, Peel DA (2010) An empirical investigation of combinations of economic forecasts. J Forecast 5(4) 5. Liwen L, Dabin Z (2019) A review of construction and application of combination forecast model. Statist Decis 35(01):18–23 6. Taylor SJ, Letham B (2018) Forecasting at scale. Am Statist 72(1):37–45 7. Chang T, Guo Z, Xu L (2019) Scale prediction of AQI based on prophet-random forest optimization model. Environ Pollut Control 41(7):758–761+766

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8. Graves A, Schmidhuber J (2005) Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Netw 18(5–6):602–610 9. Li Y, Yuxi W, Junli W et al (2018) Research on recurrent neural network. J Comput Appl 38(z2):1–6, 26, 1–6+26 10. Siami-Namini S, Tavakoli N, Namin AS (2019) The performance of LSTM and BiLSTM in forecasting time series. In: 2019 IEEE international conference on big data (big data).IEEE, Los Angeles, CA, USA, pp 3285–3292 11. Kiruthiga D, Manikandan V (2021) Time series load forecasting using multitask deep neural network. In: 2021 IEEE second international conference on control, measurement 12. Zhang H, Lu M, Luo X et al (2019) Evaluation of black-start schemes based on prospect theory and improved TOPSIS method. In: 2019 IEEE international conference on energy internet (ICEI). IEEE, Nanjing, China, pp 339–344 13. Wenjie F, Xiangning X, Shun T (2018) A multi-index evaluation method of voltage sag based on the comprehensive weight. In: 2018 China international conference on electricity distribution (CICED). IEEE, Tianjin, China, pp 613–617 14. Li YJ, Yang Y, Zhu K et al (2021) Clothing sale forecasting by a composite GRU-prophet model with an attention mechanism. Trans Ind Inform

Modular Capacitor-Based Full Bridge Interline DC Power Flow Controller: Topology Analysis and Performance Study Jing Yi, Miao Zhu, Xu Zhong, Hongyi Zhang, Siqi Liu, and Xu Cai

Abstract DC power flow controller is a research hotspot to increase control freedom degrees of power flow and improve rationality of power flow distribution in meshed HVDC grid. Based on previous analysis and research on C-based full-bridge interline DC power flow controller, a modular n-line C-based full-bridge interline DC power flow controller is proposed to give a systematic explanation of this type controller framework. The topology can realize active control of (n − 1) lines at most. A modular 3-line C-based full-bridge interline DC power flow controller is taken as an example to detail operation principle, control strategy, characteristics analysis. Simulation results verify the topology is capable of controlling two lines actively. By comparison, similarities and differences between C-based full-bridge and half-bridge interline DC power flow controller are summarized. Keywords Dc power flow · Power flow controller · Modular interline dc power flow controller · Multiple control freedom degrees

1 Introduction Interline direct current power flow controller (IDCPFC), as an efficient approach to adjusting power flow and transforming energy between two lines, occupies an important station in DCPFC research [1–5]. C-based full-bridge IDCPFC as an alternative for IDCPFC has gain wide concern [2]. A general theory of multi-IDCPFC is detailed in [6]. Topologies of 2-line and 3-line C-based full-bridge IDCPFC have been proposed before. But neither the maximum power flow regulation capability of this series topology nor any systematical modular solutions are proposed [7]. Simplified topology can realize active control on two lines but it is uncapable to be applied to occasions when power flows are negative [8, 9]. A novel modular construction theory for the most popular C-based full-bridge multi-line DC power flow controller is proposed systematically. Through the novel J. Yi · M. Zhu (B) · X. Zhong · H. Zhang · S. Liu · X. Cai School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_49

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modular design of the topology, the process of regulating trends can be shown in a more structured way. And the number of controlled lines can be adjusted by increasing or decreasing the number of modules according to the demand, which means the topology is scalable. Generally, a controller consisted with n modules can regulate n lines at most. Furthermore, comparisons between C-based full-bridge and halfbridge [10] are made. The maximum power flow control ability is clarified by taking C-based full-bridge 3-line IDCPFC as an example additionally. Simulation results validate that the proposed modular IDCPFC is capable of regulating power flow according to any demands.

2 Modular C-Based Full-Bridge IDCPFC 2.1 Structure and Working Principle Modular n-line C-based full-bridge IDCPFC consists of one energy buffer and n external link units connected into n dc lines. The energy flow path between energy buffer and external link units is formed by Bus a, Bus b and Bus0. Every external link unit shares the same structure of a full-bridge topology composed of 4 IGBTSs and 4 anti-parallel diodes. Energy buffer is a capacitor withstanding a voltage of UC. Definitions and reference directions of electrical quantities are shown in Fig. 1.

Fig. 1 Topology of modular C-based full-bridge IDCPFC

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Fig. 2 Operation principle of 3-line C-based full-bridge IDCPFC when I 1 , I 2 and I 3 are in positive direction a sub-state1, b sub-state2, c sub-state3

In a regulation period, each external link is put into operation one after another, thus in a period there exist n sub-states. The topology can control n lines and (n − 1) of them are active control at most. For details, an operation principle instance of 3-line C-based full-bridge modular IDCPFC, as shown in Fig. 2, can be referred to. There are 8 different combinations of flow directions, and each of them can be regulated to 7 different targets including all currents unchanged, thus it is supposed to be 56 different working cases in total. The modular construction theory for the most popular C-based full-bridge multi-line DC power flow controller simplifies topology designs and gives a summary to the working principle of a series of similar DCPFC topologies. When QC1 , QC2 and QC3 or QB1 , QB2 and QB3 are all on during the positive flow or QA1 , QA2 and QA3 or QD1 , QD2 and QD3 are all on during the negative flow, the energy buffer is bypassed, the topology working on the initial state. A selected working case below is exemplified to illustrate the regulation process. In this case, currents of Line1, Line2 and Line3 are all positive, and the control target is to decrease the power flow of Line1 and Line2 and increase Line3. There are 3 sub-states divided in a period. Sub-state1: QB2 and QB3 are turned on. The power flow path of Line1 is into node p1 → DA1 → Capacitor → DD1 → out of node c1 ; Line2 is into node p2 → QB2 → DD2 → out of node c2 ; Line3 is into node p3 → QB3 → DD3 → out of node p3 . Capacitor works as a negative voltage source in Line1, thus voltage of node p1 is U 0 + U C and p2 and P3 are all U 0 . Power flow of Line1 decreases consequently. Sub-state2: QB1 and QB3 are turned on. The power flow path of Line1 is into node p1 → QB1 → DD1 → out of node c1 ; Line2 is into node p2 →

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DA2 → Capacitor → DD2 → out of node c2 ; Line3 is into node p3 → QB3 → DD3 → out of node c3 . Capacitor works as a negative voltage source in Line2, thus voltage of node p2 is U 0 + U C and p1 and p3 are all U 0 . Power flow of Line2 decreases consequently. Sub-state3: QC1 , QC2 , QB3 and QC3 are turned on. The power flow path of Line1 is into node p1 → DA1 → QC1 → out of node c1 ; Line2 is into node p2 → DA2 → QC2 → out of node c2 ; Line3 is into node p3 → QB3 → Capacitor → QC3 → out of node c3 . Capacitor works as a positive voltage source in Line1, thus voltage of node p3 is U 0 –U C and p1 and p2 are all U 0 . Power flow of Line3 increases consequently. After a while, QC1 , QC2 and QC3 are turned off, QB2 turned on. Then a new operation period will start. In the final analysis, the capacitor is utilized to transform power to Line3 from Line1 and Line2, to increase I 3 and decrease I 1 and I 2.

2.2 Control Strategy The control strategy of the modular 3-line C-based full-bridge IDCPFC can be seen in Fig. 3. The reference values of I 1ref and I 2ref are sent to be compared to their actual values. Then by logic operation on signals from the differences with PID regulation and the saw-tooth carrier, PWM waves are produced including three complementary pulse signals PWM1, PWM2 and PWM3.

Fig. 3 Diagram of control strategy

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2.3 Characteristics Analysis Take the working case mentioned before as an example to analyze the operation characteristics. Assume the duty cycle of sub-state1 is D1 , sub-state2 is D2 and substate3 is D3 . In an operation period, D1 + D2 + D3 = 1. Based on voltage of capacitor U C changes constantly, (1) can be achieved. I 1 D1 + I 2 D2 − I 3 D3 = 0

(1)

Equivalent voltage in series between node p1 and c1 U c1 is: ⎡

Uc1

⎤ D1 Ts (Uc + U0 − U0 ) + D2 Ts (U0 − U0 ) = /Ts +D3 Ts (U0 − U0 ) = D1 U c > 0

(2)

T s equals an operation period. Equivalent voltage in series between node p2 and c2 U c2 is: ⎡

Uc2

⎤ D1 Ts (U0 − U0 ) + D2 Ts (Uc + U0 − U0 ) = /Ts +D3 Ts (U0 − U0 ) = D2 U c > 0

(3)

Equivalent voltage in series between node p3 and c3 U c3 is: ⎤ D1 Ts (U0 − U0 ) + D2 Ts (U0 − U0 ) /Ts = +D3 Ts (U0 − Uc − U0 ) ⎡

Uc3

= −D3 Uc < 0

(4)

Based on the equations above, it can be concluded that the equivalent voltages in series in Line1, Line2 and Line3 are negative, negative and positive respectively, corresponding to working principle analysis in Sect. 2.1. Then the equations about equivalent voltages and power flow of each line can be derived: I1 UC1 + I2 UC2 + I3 UC3 = 0

(5)

According to (5), it can be concluded that if there exists no extra loss, power can be 100% transformed with IDCPFC. Combined with equations above, circumstances under n-line IDCPFC can be derived: n Σ i=1

Ii Di = 0, Uci = Di Uc ,

n Σ i=1

Ii Uci = 0

(6)

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2.4 Comparisons Between Two Topologies of Modular C-Based IDCPFC If the basic unit of the topology is deduced, modular C-based full-bridge IDCPFC can be changed into C-based half-bridge IDCPFC, as shown in Fig. 4. The two topologies share similar structures and control capabilities. While in different flow control demands, both have advantages and disadvantages. Considering extra mechanical switched equipped, half-bridge IDCPFC may require overheating protection additionally. The two topologies share similar structure and working principle. Comparisons between the two topologies are shown in Table.1. Fig. 4 Topology of n-line C-based half-bridge IDCPFC

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Table 1 Comparisons between full-bridge IDCPFC and half-bridge IDCPFC Full-bridge IDCPFC Structure Control capability

Device cost

Half-bridge IDCPFC

Similarities Both are composed of a capacitor as an energy buffer, ecternal link units and buses Both can realize all regulation targets of power flows of all directions and impossible to increase/decrease all the power flows synchronously in a period Differences 4n IGBTs

(2n + 4) IGBTs

If n ≥ 2, full-bridge topology is less economical than half-bridge Utilization ratio of IGBTs

At most (4n − 2) of 4n2 IGBTs involved in a period

At most (3n − 2) of n(2n + 4) IGBTS

If n < 5, vacancy rate of half-bridge is higher. And vice versa Overheating protection

No extra mechanical Needs n extra mechanical switches, lower possibility switches, higher of overheating failure possibility of overheating failure

3 Simulation Validation 3.1 Simulation Verification To validate the proposed 3-line C-based full-bridge IDCPFC, a 4-terminal monopole meshed HVDC grid is built in MATLAB/Simulink environment as shown in Fig. 5. In this grid, VSC1, VSC2 and VSC3 inject constant power into the system, at 300 MW, 120 MW and 200 MW respectively. VSC4 works as a constant voltage, U 4 = 200 kV. The controller is installed on Bus4. Equivalent resistances R12 , R24 , R34 , R12 and R23 are 2 Ω, 1.5 Ω, 2 Ω, 1 Ω and 1 Ω respectively. Capacitor is set as 50 mF and switching frequency is 2 kHz. When IDCPFC is uninstalled or bypassed, the initial condition is I 14 = 1.056 kA, I 24 = 1.123 kA, I 34 = 0.8917 kA, I 12 = 0.4282 kA, I 23 = − 0.09945 kA, U 1 = 202.11 kV, U 2 = 201.68 kV, U 3 = 201.78 kV. • Mode 1—Power Flow Reversal In this simulation, I 14 is regulated to − 0.2 kA and I 24 is 1.8 kA. In Fig. 6a changes of power flows can be seen. I 14 decreases at first, then increases in the negative direction. I 24 is positive in this case and goes through a process of reduction after an initial increase, then stablizes at 1.8 kA. I 34 keeps rising positively. Equivalent voltages in series of three lines are all positive, and U C reaches around 9 kV, as shown in Fig. 6b. This simulation tesifies that this topolgy is capable of coping with power flow reversal and regulating two lines actively. • Mode 2—Power Flow jumps

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Fig. 5 4-terminal monopole meshed HVDC grid

Fig. 6 Simulation results a currents of I 14 , I 24 and I 34 , b voltages of equivalent voltages in series and U C

In this simulation, at t = 0 ~ 1 s, IDCPFC is bypassed. At t = 1 s, IDCPFC is put into operation to regulate power flow of Line14 and Line24, I 14 and I 24 to 1.2 kA and 1.3 kA respectively. The simulation results are shown in Fig. 7. At t = 2 s, power injected from VSC3 jumps from 200 to 240 MW and reference values of I 14 and I 24 are unchanged. In Fig. 7a changes of power flows can be seen. I 14 reaches the stable value of 1.2 kA after a small fluctuation at t = 1 s and t = 2 s. I 24 becomes stable around 1.3 kA after going through a similar process. While I 34 drops to 0.57 kA at first and at t = 2 s, it rises to 0.77 kA due to increased injection from VSC3. Equivalent voltages in series of three lines are shown in Fig. 7b. U C3 is positive while U C1 and U C2 are negative, which is consistent with the changing trends of power flow. In addition, the sum of absolute values of U C1 U C2 and U C3 equals to U C approximately, which corresponds to theoretical calculation.

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Fig. 7 Simulation results a currents of I 14 , I 24 and I 34 , b voltages of equivalent voltages in series and U C

This simulation tesifies that this topolgy is capable of maintaining power flow unchanged when power injection of VSC jumps. • Mode 3—Power Flow Reduces In this simulation, at t = 0 ~ 1 s, IDCPFC is bypassed. At t = 1 s, IDCPFC is put into operation to regulate power flow of Line14 and Line24, I 14 and I 24 to 0.9 kA and 0.8 kA respectively. The simulation results are shown in Fig. 8. At t = 2 s, power injected from VSC1 reduces from 300 to 240 MW and reference values of I14 and I24 are unchanged. In Fig. 8a changes of power flows can be seen. I14 reaches the stable value of 0.9 kA after a small fluctuation at t = 1 s and t = 2 s. I24 becomes stable around 0.8 kA after going through a similar process. While I34 increases to 1.37 kA at first and at 2 s, it drops to 1.07 kA due to power injection reduction of VSC1. Equivalent voltages in series of three lines are shown in Fig. 8b. U C3 is negative while U C1 and U C2 are positive, which is consistent with the changing trends of power flow. In addition, the sum of absolute values of U C1 U C2 and U C3 equals to U C approximately, which corresponds to theorectical calculation. This simulation tesifies that this topolgy is capable of maintaining power flow unchanged when power injection reduction occurs.

Fig. 8 Simulation results a currents of I 14 , I 24 and I 34 , b voltages of equivalent voltages in series and U C

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4 Conclusions A modular n-line C-based full-bridge IDCPFC, which can control (n − 1) lines actively and satisfy power flow regulation demands of various directions, is proposed in this paper to build a systematical structure theory and working principle design. A specific 3-line C-based full-bridge IDCPFC is taken as an example to analyze, including working principle, control strategy, characteristic analysis and simulation in a 4-terminal monopole meshed HVDC grid. The results of simulations verify the proposed IDCPFC can actively control of two lines. • The proposed C-based full- bridge IDCPFC explains the flow of electrical power in a structured and modular way by introducing parts of energy buffer, external links and dc buses, which simplifies topology designs and gives a summary to the working principle of a series of similar DCPFC topologies. • The novel modular design allows the process of regulating trends to be shown in a more structured way. And the number of controlled lines can be adjusted by changing the number of modules flexibly according to the regulation demand. And the largest power flow regulation capability is explained additionally. • By comparing 3-line full-bridge IDCPFC and half-bridge IDCPFC, both sides have their own advantages and disadvantages. But the proposed IDCPFC needs no extra mechanical switches, which means less possibility of overheating failure. • The modular C-based 3-line full-bridge IDCPFC realizes power flow reversal, regulation demands on occasions of power injection jumps and reduces by controlling two lines actively. The simulation results correspond to theoretical calculation. Acknowledgements This work was sponsored by Science and Technology Project of State Grid Corporation, China (No.: 52094021000M).

References 1. Barker CD, Whitehouse RS (2012) A current flow controller for use in HVDC grids. In: 10th IET international conference AC and DC power transmission, Dec 2012, pp 1–5 2. Zhong X, Zhu M, Huang R, Cai X (2017) Combination strategy of DC power flow controller for multi-terminal HVDC system. In: 6th IET international conference on renewable power generation, Oct 2017, pp 1–7 3. Zhong X, Zhu M, Chi Y, Du X, Liu S, Cai X (2018) Combined DC power flow controller for DC grid. Int Power Electron Conf 2018:1491–1497 4. Liu S, Zhu M, Zhong X, Cai X (2019) A triple interline DC power flow controller with dualfreedom control function. IEEE Conf Ind Electron Appl 2019:1903–1908 5. Zhong X, Zhu M, Chi Y, Liu S, Cai X (2020) Composite DC power flow controller. IEEE Trans Power Electron 35(4):3530–3542 6. Chen W et al (2016) A novel interline DC power-flow controller (IDCPFC) for meshed HVDC grids. IEEE Trans Power Deliv 31(4):1719–1727

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7. Diab HY, Marei MI, Tennakoon SB (2016) Operation and control of an insulated gate bipolar transistor-based current controlling device for power flow applications in multi-terminal highvoltage direct current grids. IET Power Electron 9(2):305–315 8. Balasubramaniam S, Ugalde-Loo CE, Liang J, Joseph T, King R, Adamczyk A (2018) Experimental validation of dual H-bridge current flow controllers for meshed HVDC grids. IEEE Trans Power Del 33(1):381–392 9. Sau-Bassols J, Ferrer-San-Jose R, Prieto-Araujo E et al (2020) Multiport interline current flow controller for meshed HVDC grids. IEEE Trans Ind Electron 67(7):5467–5478 10. Yi J, Zhu M, Zhong X, Wang H, Cai X (2020) An improved triple interline DC power flow controller for bidirectional power control. In: 2020 IEEE region 10 conference (TENCON), pp 1301–1306

Real-Time Electricity Price Optimization Strategy in Power Market Based on Markov Decision Chain Xiaoxuan Guo, Shuai Han, Leping Sun, and Wanlu Wu

Abstract The article uses the Markov chain decision-making process to affect this two-way effect and the transferability of the user’s power consumption state is described to form the power consumption characteristics of the users in the industrial park; the correlation between the user’s power consumption and the power supply of the power supplier is considered, and the mathematical model is established with the goal of maximizing social welfare. The model established by the Kofu Chain is solved to obtain the strategic advantage of real-time electricity prices. Keywords Markov chain · Real time electricity price · Particle swarm optimization · Smart grid

1 Introduction In recent years, some scholars at home and abroad have conducted a lot of research on real-time electricity prices, including on-grid electricity prices, transmission pricing, and ancillary service pricing [1]. Solving the real-time electricity price pricing problem mainly revolves around the social welfare maximization model aiming at the minimum power supply cost of the power supplier and the maximum user’s total utility [2]. From the perspective of the whole society, the social welfare maximization model can fully mobilize the enthusiasm of users to participate in power operation [3]. On the basis of the real-time electricity price model proposed by many scholars, some extended forms have been obtained considering different situations. The quadratic utility function in the original optimization model is replaced with a logarithmic utility function, and the dual-gradient algorithm is used to solve the problem. Literature [4] introduces the price strategy to maximize the interests of power selling companies and users under the background of new energy power generation. Literature [5] established a two-level stochastic model of real-time demand response under

X. Guo (B) · S. Han · L. Sun · W. Wu Electric Power Research Institute, Guangxi Power Grid Corporation, Nanning 530023, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_50

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the framework of Markov decision process (MDP) to ensure the interests of energy suppliers and suppliers. Most of the above-mentioned studies have not fully demonstrated the before and after relevance of electricity consumption by users and power supply providers. The Markov decision process can use the state transition probability to describe the relevance of the two stages before and after, effectively describing the multi-stage user power state process [6]. In view of this, this article describes the two-way impact and the transferability of the user’s power consumption state through the Markov chain decision process, highlighting the power consumption characteristics of the users in the industrial park; considers the correlation between the user’s power consumption and the power supply of the power supplier. A mathematical model is established for the goal of maximizing social welfare, and finally the particle swarm algorithm is used to solve the model established by the Markov chain to obtain the strategic advantage of real-time electricity prices.

2 Real-Time Electricity Price Optimization Based on Markov Decision Chain 2.1 Markov Decision Chain Modeling Markov decision chain process according to the observed state at each moment, one of the available action sets is selected to make a decision. The next state of the system is random, and the state transition probability has markov property. Decision-makers make new decisions based on the newly observed state, and so on. That is, markov chain is a random system, which must satisfy two conditions: The system at any time can be described by one of the finite possible states; The system has no aftereffect, that is, once the state of a certain stage is determined, the evolution of the subsequent process will no longer be affected by the previous states and decisions. In fact, when the electricity price is too high, the industrial park users’ willingness to use electricity decreases and their psychological expectation is lower, so they have a higher probability of choosing to use less electricity. Otherwise, the opposite is true. On the other hand, price making will according to the total load of all industrial park users the power to make real-time pricing to make the supply side and demand side of the sum of the utility value maximum. Real-time electricity price process is a dynamic discrete process, so 24 h a day can be taken as a stage set, so that a finite stage Markov decision process can be obtained, and the finite stage real-time electricity price model can be established, which is expressed by markov decision chain process as follows: {T , St , Rt , pt (St+1 |St , Rt+1 ), Ft (St , Rt )} T is the decision period. That is, the decision-making time of the day:

(1)

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T = {1, 2, 3, 4...N }, N < ∞

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(2)

St is the possible power consumption status of industrial park users in time period t. In this paper, it refers to the power load of industrial park users, namely, electricity consumption: St = [0, s], s < ∞

(3)

Rt is the action set available to the electricity price provider in time period t. In this paper, the price pricing decision in time period t is: Rt = [0, r ], 0 ≤ Rt ≤ r

(4)

pt (S t+1 |S t , Rt+1 ) is the transition probability. That is, the probability of electricity consumption S t+1 in the period t + 1 is determined by the electricity price Rt+1 in the period t + 1 and the electricity consumption in the period t. Make each time the use of electricity independent of each other, which means the power consumption status in the previous period does not affect the power consumption in this period. Therefore, the influencing factors are only attributable to the electricity price in this period. Its probability distribution is: ⎧ ⎤ ⎡ P1 ... P1r ⎪ ⎪ ⎪ ⎪ ⎦ P = (St+1 |St , Rt+1 ) = ⎣ ⎪ ... ⎪ ⎨ t PS1 ... Psr ⎪ S ⎪

⎪ ⎪ ⎪ ⎪ Pi j = 1 ⎩

(5)

i=1

The matrix size is S rows and R columns. Pij represents the probability that the electricity load of industrial park users is i when the electricity price is j.

2.2 Real-Time Electricity Price Model Based on Markov Decision Chain In order to maximize social welfare, F t (S t , Rt ) is defined as the total social compensation value, that is, the total compensation value of all industrial park users and power suppliers within the period t. The total compensation value is the electricity utility of users in the industrial park minus the cost of generating electricity.

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⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩

Ft (St , Rt ) =

Q

 U ωq , St − Ct (L), t ∈ T q=1

(6)

S = S1 + S2 + ... + St

U(ωq , S t ) is the utility function of electricity consumption of industrial park users. Q is the number of industrial park users, q ∈ [1, Q], q is an integer; S t is the power load of users in the industrial park at time period t. S is the user load at all times involved in the Markov decision process. In function U(ωq , S t ), ωq represents the power purchase intention of users in the industrial park, and the utility function satisfies: ⎧  ⎪ ⎨ ∂U ωq , St > 0 ∂ωq (7) ⎪ ⎩  U ωq , 0 = 0 C t (L) is the cost of power generation and the cost function of electricity load. Its form is as follows: C L (t) = at L 2 + bt L + ct

(8)

at > 0, bt ≥ 0, ct ≥ 0, L is the total power load in the decision period of S, that is, the sum of the power load of all users in the industrial park in the same period. When T ≥ 0, the nth-order expected total utility function under the strategic price Rt is: VN (S, R) =

N

E qS [Ft (St , Rt )] + E qS [Ft (S N )]

(9)

t=1

V N (S, R) is the total utility value in the statistical period. q indicates the user of industrial park q. E qS [Ft (St , Rt )] represents the expected compensation value of electricity consumption of user q in industrial park at time period t. F t (S N ) is the termination reward of the process, which is generally zero. In economics, the utility function satisfies: 



Ut ωq , St =

ωq ln St + d, St > 0 0, St = 0

ωq is the parameter of the power-buying hospital, and d is a constant.

(10)

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Through the above analysis, the real-time electricity price optimization model of maximizing the sum of the demand side and supply side utilities represented by the industrial park users and power suppliers can be obtained. The objective function is as follows: max VN (S, R) =

N

E qS [Ft (St , Rt )]

t=1

⎧ Q

q ⎪ ⎪ ⎪ St = L t ⎪ ⎨ q=1 s.t. q q q ⎪ ⎪ min St ≤ St ≤ max St , t ∈ T , q ∈ Q ⎪ ⎪ ⎩ min L t ≤ L t ≤ max L t , t ∈ T

(11)

q

L t is the power load of all industrial park users in time period t, St is the power load of industrial park users q in time period t, minL t and maxL t are the minimum and q q maximum loads in time period t respectively. min St and max St are the minimum load and maximum load of industrial park user q at time period t. q is the total number of industrial park users.

3 Particle Swarm Optimization Algorithm This paper uses particle swarm optimization algorithm to solve the optimization problem. Particle swarm optimization (PSO) is a kind of heuristic algorithm. By transferring the position of particles with low fitness to particles with high fitness, the global optimum is found, where fitness refers to the value of the objective function. The particle position transfer formula is: Rk+1 = Rk + Vk

(12)

k is the number of iterations, Rk+1 is the power price of generation k + 1, Rk is the power price of generation k, and V k is the particle transfer rate. Vk+1 = C1 Vk + C2 (Rbest − Rk )

(13)

The above equation is the update formula of particle transfer speed. Rbest is the optimal fitness price of electricity in the iteration process, Rk is the price of electricity in the iteration, and C i is the weight coefficient, which can be obtained through the random function. In order to obtain the discrete requirement, all results in the speed update are rounded by rounding method and stopped when the fitness difference

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Fig. 1 Flow chart of PSO

between the two adjacent generations is less than the acceptable error. The algorithm steps are shown in Fig. 1.

4 Example Simulation The decision cycle is 24 h a day, T = {1, 2, 3..., 24}.The possible hourly electrical load of industrial park users is St = {1, 2, 3, . . . , 10},the unit is kW · h. There are five strategies for price decision-making, Rt = {1, 2, 3, 4, 5}, the unit is RMB. The number of industrial park users in the system is Q = 5. The probability transfer matrix of power load of industrial park users is Pq , q is the industrial park user variable. The selection probability of electricity consumption behavior of each industrial park user at each price is randomly evaluated, values are normally distributed. The average value is the psychological expectation of industrial park users at each electricity

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price, the variance is 1. The occurrence frequency of all rounded values is divided by the total number of all random numbers as the probability for industrial park users to select the electricity consumption under the price. Pi j =

[ri + ξ ] , i ∈ [1, s] s

(14)

r i is normally distributed, ζis the psychological expected value of electricity in industrial park users,[r i + ζ] is an integer value, The following results are available: ⎛

⎛ ⎞ ⎞ 0 0 0 0 0.05 0 0 0 0 0.1 ⎜ 0 0 0 0.05 0.05 ⎟ ⎜ 0 0 0.05 0.05 0.1 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0 0 0 0.05 0.4 ⎟ ⎜ 0 0 0.05 0.05 0.3 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0 0 0.05 0.3 0.2 ⎟ ⎜ 0.05 0.05 0.1 0.2 0.2 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0 0 0.1 0.2 0.1 ⎟ ⎜ 0.05 0.1 0.15 0.3 0.2 ⎟ P1 = ⎜ ⎟P2 = ⎜ ⎟ ⎜ 0 0.1 0.3 0.2 0.1 ⎟ ⎜ 0.1 0.2 0.4 0.15 0.05 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0.1 0.4 0.3 0.1 0.05 ⎟ ⎜ 0.1 0.2 0.1 0.15 0.05 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0.4 0.2 0.1 0.05 0.05 ⎟ ⎜ 0.4 0.2 0.1 0.05 0 ⎟ ⎜ ⎜ ⎟ ⎟ ⎝ 0.3 0.2 0.1 0.05 0 ⎠ ⎝ 0.3 0.1 0.05 0 0 ⎠ 0.2 0.1 0.05 0 0 0.1 0.05 0 0 0 ⎛ ⎛ ⎞ ⎞ 0 0 0 0 0.05 0 0 0 0 0.05 ⎜ 0 0 ⎜ 0 0 0 0.1 0.15 ⎟ 0 0.05 0.15 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0 0 ⎜ 0 0 0.1 0.05 0.3 ⎟ ⎟ 0 0.2 0.4 ⎜ ⎜ ⎟ ⎟ ⎜ 0 0 0.05 0.15 0.15 ⎟ ⎜ 0 0 0.1 0.2 0.2 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0.1 0.05 0.2 0.3 0.1 ⎟ ⎜ 0 0 0.1 0.2 0.2 ⎟ P3 = ⎜ ⎟P4 = ⎜ ⎟ ⎜ 0.1 0.05 0.3 0.1 0.1 ⎟ ⎜ 0.1 0.1 0.4 0.15 0.05 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0.1 0.4 0.2 0.1 0.05 ⎟ ⎜ 0.1 0.3 0.1 0.15 0.05 ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ 0.3 0.2 0.1 0.05 0 ⎟ ⎜ 0.3 0.3 0.1 0.05 0 ⎟ ⎜ ⎜ ⎟ ⎟ ⎝ 0.3 0.2 0.1 0 ⎝ 0.3 0.1 0.05 0 0 ⎠ 0 ⎠ 0.2 0.1 0.05 0 0 0.1 0.05 0 0 0 ⎛ ⎞ 0 0 0 0 0.05 ⎜ 0 0 0.05 0.05 0.1 ⎟ ⎜ ⎟ ⎜ 0 0 0.05 0.05 0.3 ⎟ ⎜ ⎟ ⎜ 0.05 0.05 0.2 0.4 0.2 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 0.05 0.1 0.15 0.3 0.2 ⎟ P5 = ⎜ ⎟ ⎜ 0.1 0.2 0.1 0.15 0.05 ⎟ ⎜ ⎟ ⎜ 0.1 0.2 0.1 0.15 0.05 ⎟ ⎜ ⎟ ⎜ 0.3 0.1 0.1 0.05 0 ⎟ ⎜ ⎟ ⎝ 0.05 0.05 0.05 0 0 ⎠ 0.05 0

0

0

0

602 Table 1 User load demand in industrial parks

X. Guo et al. Time (h)

Load demand (kW ∗ 100)

Time (h)

Load demand (kW ∗ 100)

1–5

basets = rand[1, 6]

14–18

basets = rand[9, 15]

6–10

basets = rand[5, 15]

19–22

basets = rand[1, 7]

11–13

basets = rand[6, 11]

23–24

basets = rand[1, 5]

The electricity purchase desire ωq is a uniform random distribution within [0,4], at = 0.01, bt = 0, ct = 0. The basic power load of users in industrial parks is different at each moment. Table 1 shows the basic load of users in the industrial park at each time period, the lowest power load. Figure 2 shows the total electricity load in each time period. It can be seen that in the total electricity load, except for the very small load in individual periods, other periods are relatively stable and fluctuate, and there is no peak power consumption. Figure 3 shows the optimal segmented electricity price for each period of 24 h. It can be seen that the electricity price mainly fluctuates between 1.5 and 3.2 RMB, and the average electricity price is 2.3 RMB, which is in a reasonable change zone and there is no extreme price. Aiming at the effect of the optimal electricity price, numerical simulations are carried out on the electricity load and electricity utility under the fixed electricity price. The fixed electricity price adopts 0.5 RMB, 1.5 RMB, 2 RMB, and 3 RMB respectively for 24-h simulation to obtain different time periods. The impact of different electricity prices on demand side electricity consumption at different times is shown in Fig. 4. At the same time, the comparison results of the sum of social

Fig. 2 Fluctuation diagram of total power load

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Fig. 3 Real-time electricity price fluctuation graph

Fig. 4 Load demand fluctuation graph

welfare on the supply side and the demand side caused by different electricity price environments are presented in Fig. 5. Fig. 5 Comparison of social welfare under different electricity prices

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Fig. 6 Real-time electricity price improves user electricity cost

Figure 5 shows the changes in the demand side load at each time period at different electricity prices. It can be seen that the electricity consumption of the real-time electricity price is at an intermediate level, and fluctuates between the highest electricity price and the lowest electricity price. The positive impact is conducive to the realization of peak power consumption, peak shaving and valley filling. Figure 6 shows the social welfare value of each period under the fixed electricity price and the real-time electricity price. It can be seen that the total utility of electricity consumption in each period under the real-time electricity price is much higher than the other five fixed electricity prices. This also shows that the real-time electricity price can be obtained from the other side. Optimizing electricity prices can help maximize social welfare, and can help maximize the relevant benefits of the industrial park users and power suppliers. For e-commerce sellers, through real-time electricity prices and the 24-h load distribution of typical industrial parks, real-time electricity prices can improve load power costs and maximize benefits. (Assuming that the electricity purchase cost of the retailer is a fixed value). We analyze and compare user electricity costs with real-time electricity prices and RMB 2 electricity prices. According to experimental data, in 83.3% of cases, real-time electricity prices can significantly reduce users’ electricity costs compared to RMB 2 electricity prices.

5 Conclusion Based on the correlation between user power consumption and power supply, this paper describes the change trend of real-time electricity price in a day by using

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Markov decision chain process, and establishes a real-time electricity price optimization model to maximize the sum of utility on the demand side and supply side with the goal of maximizing social welfare. Finally, it is solved by particle swarm optimization algorithm. This paper studies the real-time electricity price system in the smart grid environment, and can draw the following conclusions: • The limited-stage real-time electricity price model established by the Markov decision chain process can effectively respond to the electricity consumption behavior of each industrial park user, and can achieve the goal of maximizing the total utility of the demand side and the supply side with the optimal real-time electricity price. • Using particle swarm algorithm to solve the electricity price optimization model in this paper, it is concluded that real-time electricity price can guide users to use electricity reasonably and to use electricity at staggered peaks. • From the perspective of e-commerce sellers, compare the electricity price of RMB 2 with real-time electricity prices. Real-time electricity prices can effectively reduce users’ electricity costs and maximize the benefits of e-commerce sellers. To sum up, the real-time pricing mechanism proposed in this article can ensure that users in industrial parks use peak-to-peak electricity and avoid peak periods, while ensuring the greatest benefit of power supply and maximize welfare.

References 1. Jianping H, Haoyong C, Zhenjia L, Jiayu Z (2021) Summary of research and practice of TOU price under the background of demand side response. Power Syst Protection Control 49(09):178– 187 2. Bo YB, Liang S, Lidong C (2021) Coordinated and optimal dispatching of distribution network system with combined cooling, heating and power generation microgrid considering TOU price. Power Autom Equip 41(04):15–23 3. Dai Y, Sun X, Qi Y, Leng M (2021) A real-time, personalized consumption-based pricing scheme for the consumptions of traditional and renewable energies. Renew Energy 180 4. Zhang N, Yang NC, Liu JH (2021) Optimal time-of-use electricity price for a microgrid system considering profit of power company and demand users. Energies 14(19) 5. Sandeep C, Parul M, Rohit B (2021) Bi-level approach for load serving entity’s sale price determination under spot price uncertainty and renewable availability. Technol Econ Smart Grids Sustain Energy 6(1) 6. Chang HS (2014) Value set iteration for Markov decision processes. Automatica 50(7):1940– 1943

Distribution Grid Topology Estimation Using 1D-CNN Li Tong, Haiwei Liang, and Xudong Zou

Abstract In order to improve the safety level and economy of distribution grid, a flexible and reconfigurable grid topology is the basic feature of future smart distribution grid. Many advanced functions of intelligent distribution grid, such as state estimation, power flow calculation and voltage control, require a correct grid topology as a prerequisite. Therefore, it is of great significance to find an accurate topology estimation method for distribution grid. This paper proposes a topology estimation method based on the one-dimensional convolutional neural network (1D-CNN). The proposed method firstly obtains the required voltage amplitude and phase angle data of distribution grid through simulation. The data should be standardized after the first step. Then the processed data is used to train the 1D-CNN model. Finally, the trained 1D-CNN model can be used for topology estimation. Compared to the existing methods, the proposed method does not need much historical data of each node in the distribution grid, and the calculation speed can support the online topology estimation. Meanwhile, this method is suitable for radial and weak loop grid structures. The effectiveness and superiority of the proposed method are validated by IEEE 33-node distribution grid. Keywords Distribution grid · Topology estimation · One-dimensional convolutional neural network

1 Introduction With the rapid development of the smart grid, more and more smart sensor devices have been deployed in the distribution grid. Smart meters and micro synchrophasor measurement units (µPMU) composed the advanced metering infrastructure (AMI), L. Tong State Grid Zhejiang Electric Power Research Institute, Hangzhou 310000, P.R. China H. Liang (B) · X. Zou State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430070, P.R. China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_51

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which can provide many important data of distribution grid such as the load profiles, facilitating bi-directional flow and real time voltage amplitude and phase information. These high-quality data from the AMI provide the possibility for the realization of many advanced applications of distribution grid like state estimation demand response and voltage control which can enhance the efficiency and stability of the distribution grid [1]. Many researches about those advanced applications have been pursued, and in most of these cases, it is assumed that grid topology information is available. Therefore, an accurate grid topology is the prerequisite for most applications in the distribution grid [2]. In the past, the topology estimation methods mainly focus on the transmission grid. The main purpose of topology estimation of transmission grid is to find errors in the records of Geographical Information System (GIS). Because the transmission system is equipped with a large number of redundant measurements, its topology estimation technology is relatively mature. The topology information of transmission grid can be obtained by the topology processor and state estimation. However, because of the reconfiguration, repairs, and load balancing, the distribution grid topology can change frequently, which brings great challenge to the topology estimation of distribution grid. For example, some changes because of the routine reconfiguration, such a topology change can be once 4 weeks for medium-voltage grids [3]. But other changes due to the outages are unknown, which makes the topology change more frequently [4]. Many previous assumptions on topology estimation method that are suitable for transmission grid become invalid due to the frequent topology reconfiguration [5, 6]. With the wide deployment of AMI, more useful operation data of distribution grid could be available, which provides a new opportunity to overcome the above difficulties. A sparse Markov random field is used as the tool for the reconstruction of the grid topology through the grid nodal voltage magnitudes [7, 8]. A graphical model is presented to describe the probabilistic relationship among different voltage measurements which can deal with tree and partially meshed distribution grids, the connection relationship between the nodes in grid can be obtained by analysing probability distribution of the nodal voltage [9]. Smart meter energy measurements are used to infer the topology by using Principal Component Analysis (PCA) and theoretic interpretation [10]. These topology estimation methods use mathematical statistics to analyze the connection relationship between nodes. Most of these methods only are applicable to radial distribution grid. But many urban distribution grids with high load densities have a meshed structure and operate as a weak meshed grid in some scenarios. Some research use optimization based approach to infer grid topology from time series of power measurements. Mixed Integer Programming (MIP) has been proposed to solve the estimation problem, but this method is computationally intensive to solve without relaxing the constraints [11]. In [12], authors transform the topology estimation to a optimization problem, then an expectation–maximization algorithm is used to recover different distribution topology. The nodal connectivity and grid topology estimation problems are formulated as a linear regression with a least ab solute shrinkage regularization on grouped variables (group lasso) in [13]. In order to ensure accurate estimation effect, all above methods need lots of historical

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data, so the efficiency of these methods may be low, and if the grid topology changed during the sampling period, the algorithm performance cannot be guaranteed. Artificial intelligence technology represented by neural network has been developing rapidly in recent years, which is widely used in many fields [14]. Because the actual number of distribution grid topology is limited, topology estimation of the grid can be transformed into a classification problem. Meanwhile, the power flow variable in the distribution grid such as voltage amplitude and phase angle which can get from smart meters and µPMUs hides a wealth of information. It is possible to realize topology estimation of distribution grid by using neural network to excavate hidden information among power flow variables. In this paper, we propose a topology estimation method based on one-dimensional convolutional neural network. Firstly, we obtain the voltage amplitude and phase angle information of each node in the distribution grid under all potential topological structures through simulation. Secondly, we standardized the obtained data. Then the data is used to train the 1D-CNN model. Finally, the grid topology can be estimated by the trained model. The proposed method does not need a large amount of historical data, and is suitable for the actual situation of frequent changes of distribution grid topology, which can achieve the online topology estimation. Besides, this method also has a good effect for the meshed distribution grid. The remainder of this paper is organized as follows. Section 2 gives the overview of the 1D-CNN model. Section 3 describes data processing method and topology estimation method of distribution grid using the proposed model. In Sect. 4, the proposed method is tested via simulation on the IEEE-33 node case, in order to verify its effectiveness and superiority.

2 Principles of One-Dimensional Convolutional Neural Network 2.1 The Structure of 1D-CNN Convolutional Neural Network (CNN) [15] is a deep learning method based on convolutional computation, which can learn the features of input data end-to-end and solve classification problems. 1D-CNN is a kind of convolutional neural network, which is composed of an convolution layer, a pooling layer and a fully connected layer, the composition of 1D-CNN is shown in Fig. 1. Convolutional layer can obtain a set of optimal convolutional kernels satisfying the minimum loss function through training, and use the convolutional kernels to realize automatic feature extraction. Pooling layer can extract the most important features from the convolution layer and carry out dimensionality reduction. Fully connection layer is the module that plays a classification role in the whole CNN model. In this paper, we use softmax as the activation function in the last fully connection layer to solve the multi-target classification problem.

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Fig. 1 The composition of 1D-CNN

Input Layer

Fully Convolutional Pooling Output Connected Layer Layer Layer Layer

2.2 Convolutional Layer Different from the common 2D-CNN, the convolution kernel of 1D-CNN only moves in one direction to extract the features of the input data. The convolution process is as follows: oic = f (X ⊗ ωic + b)  f (x) = max(0, x) =

x, x > 0 0, x ≤ 0

(1)

(2)

where X ∈ Rs×d is the input data; ⊗ stands for one-dimensional convolution; ωic is a weight matrix, i ∈ [1, n c ]; n c is the number of convolution kernels; b is the bias; oci represents the ith feature map generated by the convolution kernel ωic . f (x) is the activation function. We use the common ReLU function in the convolution layer to nonlinear the data after the convolution operation.

2.3 Pooling Layer The pooling operation is used to capture the most useful information of the output data characteristics of the convolutional layer, and it also has a certain degree of prevention in over–fitting. Pooling operations usually have two forms: max-pooling and average-pooling. We use max-pooling in this paper, the expression is as follows: oip = max(

Σ i∈n c

oic ) + b

(3)

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2.4 Fully Connected Layer The fully connection layer is usually at the end of CNN, which is connected with all the nodes in the upper layer to integrate the features extracted from the previous layer. It is composed of multiple hidden layers and can complete the corresponding tasks through different kinds of activation functions. The output of CNN model can be expressed as the following formula: y˜ = f s (o p ωfc + b)

(4)

ez i f s (Z) = Σ z j j e

(5)

where ωfc is a weight matrix of the fully connection layer; y˜ is the output vector of the whole CNN model. Due to the topology estimation can be transformed to a multi-target classification, we choose softmax as the activation function in the last fully connection layer to solve the problem. The expression is shown in formula (5). The results of multiple classifications can be presented in the form of probability through softmax. In order to further prevent the occurrence of overfitting phenomenon, we use Dropout [16] strategy in the fully connection layer which can make the model more generalizable by letting a neuron stop working with a certain probability during the forward propagation.

3 Topology Estimation Method of Distribution Grid Using Convolutional Neural Network 3.1 The Original Input Data Set of CNN Model As input to the model, initial features have an important impact on the performance of the whole model. Therefore, we should select variables to build the original input data set carefully. The power flow equation of the distribution network can be expressed as: Σ V j (G i j cos δi j + Bi j sin δi j ) = 0 (6) Pi − Vi j∈i

Q i − Vi

Σ

V j (G i j cos δi j − Bi j sin δi j ) = 0

(7)

j∈i

δi j = δi − δ j

(8)

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where Pi ,Q i are the active power and reactive power of node i respectively. Vi , δi are the voltage amplitude and phase angle of node i. δi j is the phase angle difference between node i and j. The current distribution grid topology can be determined by solving the power flow equation. From Sect. 1 we can see that the nodal voltage amplitude and phase angle can be obtained from AMI. Considering the actual operation characteristics and measurement configuration of distribution grid, the nodal voltage amplitude V and phase angle δ are chosen to compose the original input data set of the proposed model.

3.2 Original Data Processing For a distribution grid with N nodes, the input data set can be built as a vector: { } X = X 1, X 2, . . . , X j , . . . X M

(9)

{ } j j j j j j j j X j = V1 , V2 , . . . , Vi , . . . , VN ; δ1 , δ2 , . . . , δi , . . . δ N

(10)

j

j

where M is the sample size of the data set, Vi and δi represent the voltage amplitude and phase angle of node i at the same time in the jth sample. However, dimensions of voltage amplitude and phase angle are inconsistent, which may cause a negative effect on the algorithm performance [17]. To avoid this adverse effect, the voltage amplitude and phase angle of the input data set need to be normalized respectively. Z-score standardization is a common method of data processing, which can convert data of different magnitude into uniform Z-score value for comparison. The formula of Z-score can be expressed as: j

j

zi =

xi − μi σi M Σ

μi =

j=1

(11)

j

xi

M

⎡ | M | Σ j (xi − μi ) σi = | N1

(12)

(13)

j=1

j

where xi is the original value of the ith feature in the jth sample. μi is the mean j j value of the ith feature. σi is the standard deviation. z i is the z-score of xi whose dimensional effect has been eliminated.

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3.3 Sample Label Processing Topology estimation is a multi-label classification problem. Topologies can be seen as labels. One sample can only correspond to one label. But there’re several potential topological structures for a distribution grid. So the one-hot-code (OHC) method is introduced to encode the topology structure with N-state into N-bit status register. For example, if there is a grid which has 3 potential topology structures, the labels can be numbered 0–2 for each topology structure. With the OHC method, the numerical label 0–3 are encoded to 001, 010, 100, which can improve computational efficiency significantly [8].

3.4 CNN Model Structure In this paper, we build a topology estimation model with 2 convolution layers to extract topological features hidden in the power flow data of grid as is shown in Fig. 2. Where 1D-Conv means 1D-Convolution Layer; Max-pooling is the Pooling Layer; FC is the Fully Connected Layer. N represents the number of the potential topology structures. Flatten is the flatten layer whose role is to transform multidimensional inputs into one-dimensional. 1D-Conv/64/ReLu means the number of the convolution kernel in current 1D-Convolution Layer is 64 and the activation function in this layer is ReLu. FC/128/ReLu means the current Fully Connected Layer has 128 neurons and its activation function is ReLu. In this model, the feature extraction is completed by the first four layers, then the extracted features are sent to the fully connected layers to determine which the topology could be. The final classification result is given by the last full connection layer through softmax. Input data

Fig. 2 The structure of 1D-CNN for topology estimation

1D-Conv/64/ReLu Feature extraction

Max-pooling 1D-Conv/64/ReLu Flatten FC/256/ReLU

Topology classification

FC/128/ReLU FC/N/Softmax

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Fig. 3 The flow chart of proposed topology estimation process

Offline training

Choose voltage amplitude and phase Angle to form the original data set

Build the 1D-CNN model

Use the origina data sets to train the model

Online estimating

Input real-time data to estimate the current distribution grid topology

3.5 Topology Estimation Process The proposed topology estimation method consists of two parts: offline training and online assessment. At first we can get the corresponding power flow data through simulation of distribution grids with different topologies and form the original input data set like shown in Sect. 3.1. Label corresponding to each sample should be encoded by the OHC method. After completing the construction of the original data set, these data is used to train the CNN model offline. The optimization of the model parameters is carried out by the Adam algorithm. When the CNN model is trained, we can input real-time data into the model and evaluate the current topology of the distribution grid online. The flow chart of the proposed topology estimation process is as follow:

4 Case Studies 4.1 Case Description In order to verify the effectiveness of the proposed topology estimation method, we use IEEE 33-node distribution system as test example. Its initial topology is shown in Fig. 4. The dotted line in Fig. 4. represents there’s a tie switch in the corresponding line. The number of tie switch in the IEEE 33-node system is 5, so there’re 32 possible topologies for this distribution grid system including radial and meshed structure. The numerical nodal injections are generated using Monte Carlo method. And the power flow data is executed by MATPOWER. The frameworks used for deep learning is TensorFlow2.0.

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21

22

Fig. 4 Initial topology of IEEE 33-node distribution grid

4.2 Data Set Construction Based on the initial topology in Fig. 4., we choose all 32 topologies as the topological structures need to be estimated and set the topology label to 0–31. 2000 samples are generated through simulation for each topology, the total number of samples is 64,000. Each sample is composed of voltage amplitude and phase angle of each node, so the dimension of one sample is 66. We randomly select 70% of the samples as the training set and the rest is the test set.

4.3 Topology Estimation Evaluation Index We use accuracy to judge the effectiveness of the proposed model. Accuracy represents the correct classification proportion of the constructed CNN model and can evaluate the overall performance of the CNN model. The accuracy can be expressed as follow: Acc =

T n

(14)

where T is the number of samples that are correctly classified, n is the total number of samples.

4.4 Simulation Result In order to visually demonstrate the accuracy and convergence speed of the proposed model, Fig. 5 respectively shows the change of accuracy and loss function values of training set and test set with the increase of iteration times. Figure 5 shows that with the increase of iteration times, the loss function values of training set and test set decrease rapidly. After 30 rounds of training, the loss function

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Fig. 5 The change of accuracy and loss function values

accuracy

1 0.98 0.96 0.94 0.92 0.9 0.88 0.86 0.84 0.82

test_accuracy train_accuracy 0

10

20

30

40

50

iteration (a) The change of accuracy 0.6

loss function value

test_loss train_loss

0.5 0.4 0.3 0.2 0.1 0

0

10

20

30

iteration

40

50

(b) The change of loss function values

of CNN model has leveled off and is no longer decreasing, which means the model has converged now. And the accuracy of the test set is more than 0.99 after training, which demonstrates the validity of the proposed model in topology estimation of distribution grid. The computation time of each estimation process is less than 1 s for a trained model, so the proposed method can achieve the online topology estimation. In order to verify the superiority of proposed model, it is compared with several other commonly used machine learning algorithms such as random forest (RF), support vector machine (SVM), KNeighbors Classifier (KNN). The best performance comparison of the four learning methods is shown in Table 1. It can be seen from Table 1. that the proposed method has the highest accuracy of test set under the same conditions among four methods. The superiority of the proposed method is verified again. Table 1 The performance comparison of the four learning methods

Method

Test_accuracy

1D-CNN

0.9956

RF

0.9678

SVM

0.9693

KNN

0.8225

Distribution Grid Topology Estimation Using 1D-CNN

617

5 Conclusion A correct topology information of distribution grid is the prerequisite for many advanced functions. In this paper, we propose a topology estimation method based on the 1D-CNN. The proposed method does not need much historical data of each node in the distribution grid, and the calculation speed can support the online topology estimation. Meanwhile, this method is suitable for radial and meshed grid topology structures. The effectiveness and superiority of the proposed method are validated by IEEE 33-node distribution grid. Acknowledgements This project is supported by Science and Technology Project of State Grid Zhejiang Electric Power Company (5211DS190037).

References 1. Wang Y, Chen Q, Hong T, Kang C (2019) Review of smart meter data analytics: applications, methodologies, and challenges. IEEE Trans Smart Grid 10(3):3125–3148 2. Fan J, Borlase S (2009) The evolution of distribution. IEEE Power Energy Mag. 7(2):63–68 3. Fajardo OF, Vargas A (2008) Reconfiguration of MV distribution networks with multicost and multipoint alternative supply, Part II: reconfiguration plan. IEEE Trans Power Syst 23(3):1401– 1407 4. Abur A, Exposito AG (2004) Power system state estimation: theory and implementation. CRC Press, Boca Raton, FL, USA 5. Huang J, Gupta V, Huang Y-F (2012) Electric grid state estimators for distribution systems with microgrids. In: Proceedings of IEEE 46th annual conference on information science systems, pp 1–6 6. Lugtu R, Hackett D, Liu K, Might D (1980) Power system state estimation: Detection of topological errors. IEEE Trans Power Appl Syst PAS-99(6):2406–2412 7. Bolognani S, Bof N, Michelotti D, Muraro R, Schenato L (2013) Identification of power distribution network topology via voltage correlation analysis. In: 52nd IEEE conference on decision and control, pp 1659–1664 8. Zhao J, Li L, Xu Z et al (2020) Full-scale distribution system topology identification using Markov random field. IEEE Trans Smart Grid PP(99):1–1 9. Weng Y, Liao Y, Rajagopal R (2017) Distributed energy resources topology identification via graphical modeling. IEEE Trans Power Syst 32(4):2682–2694 10. Pappu SJ, Bhatt N, Pasumarthy R, Rajeswaran A (2018) Identifying topology of low voltage distribution networks based on smart meter data. IEEE Trans Smart Grid 9(5):5113–5122 11. Arya V, Jayram TS, Pal S, Kalyanaraman S(2013) Inferring connectivity model from meter measurements in distribution networks. In: Proceedings of 4th international conference future energy systems, Berkeley, CA, USA, pp 173–182 12. Yu J, Weng Y, Rajagopal R (2019) PaToPaEM: a data-driven parameter and topology joint estimation framework for time-varying system in distribution grids. IEEE Trans Power Syst 34(3):1682–1692 13. Liao Y, Weng Y, Liu G, Rajagopal R (2019) Urban MV and LV distribution grid topology estimation via group lasso. IEEE Trans Power Syst 34(1):12–27 14. Schmidhuber J (2015) Deep learning in neural networks: an overview. Neural Netw 61:85–117 15. Oord AVD, Dieleman S, Zen H et al (2016) WaveNet: a generative model for raw audio [EB/OL]. [2016-09-11].http://adsabs.harvard.edu/abs/2016arxiv160903499v

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16. Srivastava N, Hinton G, Krizhevsky A et al (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15(1):1929–1958 17. Larose DT, Larose CD (2014) Discovering knowledge in data: an introduction to data mining. John Wiley & Sons Inc., Hoboken, USA

Energy Storage

Development and Optimization of Aquaponics Greenhouse Thermal-Water Environment Monitoring System Based on LabVIEW Shihao Wu, Jinqi Yang, Quanwu Ge, Zhixin Ke, and Yang Wang

Abstract The development of aquaponics technology, as a kind of intensive production mode, which combines hydroponics and aquaculture, is a great significance for energy consumption reduction and sustainable development of resources. However, due to the construction difficulty, high maintenance and cleaning threshold factors, it is still a lot of room for energy saving and optimization. Therefore, this study introduces a monitoring and early warning system for thermal environment and water environment in the aquaponics greenhouse. The system used virtual instrumentation technology to monitor greenhouse thermal and water environment in the real-time, and process exceptional environmental alarm. It can greatly reduce the aquaponics system operating and maintenance costs for the protection of the environment, reduce energy costs, improve the efficiency of agricultural production. Through the comparison of diverse control methods, the fuzzy PID control system for thermal environment has high stability and quick response speed, and the adjustment time is 209.5 s, the static error is zero. It could thus help reduce energy consumption of heating and cooling equipment. Keywords Energy · Greenhouse · Fuzzy PID control · Virtual instrumentation · LabVIEW · Aquaponics

1 Introduction The sustainable production of food, demand of land and resources are the common concerns of the society and the agricultural industry [1, 2]. Through long-term S. Wu · J. Yang · Q. Ge · Z. Ke · Y. Wang (B) College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China e-mail: [email protected] National Innovation Center for Digital Fishery, China Agricultural University, Beijing 100083, China Beijing Engineering and Technology Research Center for Internet of Things in Agriculture, China Agricultural University, Beijing 100083, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_52

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research and practice in agriculture, which consumes 70% of the world’s available fresh water [3]. In some areas, freshwater resources are among the lowest in the world and are dominated by non-renewable groundwater resources. According to the FAO, agricultural production consumes 67% of the world’s usable fresh water, and 90% in the Middle East and North Africa [4]. In terms of production in China, the population is growing, but the arable land is decreasing by 3000 km2 every year. The Rural Development Report jointly issued by the Rural Development Institute, Chinese Academy of Social Sciences and the China Social Sciences Press estimates that during the 14th Five-Year Plan period, China may be short of grain by 130 m tons [5]. It will be the future trend of agriculture to use modern information technology to increase agricultural yield, promote energy efficiency, develop a co-cultivation system and save landless resources. The application of aquaponics technology can improve the utilization efficiency of natural resources and reduce energy consumption, it is friendly to the environment and sustainable development. In 2010, a report by the European Research Service identified aquaculture as one of the “10 life-changing technologies” that promise to transform the way we produce food to meet the needs of a growing population [6]. For the above reasons, the development of aquaponics technology has great significance for resource conservation, reduce energy consumption, environmental protection and the development of new agricultural production mode. In recent years, with the development of Internet technology, many researches discussed agriculture from various perspectives such as picking robot [7, 8], new cultivation technology and equipped breeding [9, 10]. Shi et al. [11] applied virtual instrumentation technology in the field of intelligent breeding. Shan et al. [12] utilized virtual instrumentation technology in the field of greenhouse. But few scholars have studied the cocultivation system of circulating water in greenhouse by using virtual instrumentation technology [13]. The objectives of this study were to (1) develop an aquaponics thermal-water environment monitoring and early warning system based on LabVIEW, (2) optimize the thermal-water environment of aquaponics system, (3) explore the approaches of energy saving and cleaner production for aquaponics greenhouse in the future.

2 Material and Methods 2.1 Experimental environment Based on the national digital fishery innovation center—aquaponics demonstration base for experimental center (Fig. 1), the base is located in Tongzhou district, Beijing and has been established on May 31, 2020. Compared with traditional agriculture, Tongzhou aquaponic system can recycle more than 90% of the water. To a certain extent, low energy consumption agricultural production is realized, land saving and environment friendly, which has exploration

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Fig. 1 Schematic diagram a, c, d of studied aquaponics system and picture (b) of inside

significance for the development of modern green agriculture. The schematic diagram of aquaponics system is illustrated in Fig. 2.

2.2 Main Hardware Equipment The normal operation of the fish-vegetable symbiosis system requires the support of some modern equipment. The main hardware devices were deployed on site are listed in Table 1. Besides, the representative equipment and devices in aquaponics greenhouse are illustrated in Fig. 3. Through these sensing devices, the information of the aquaponics greenhouse can be obtained to accurately control the operation status of the aquaponics greenhouse in real time. At the same time, the working equipment should be reasonably adjusted and optimized according to the environmental conditions, so as to reduce the energy consumption of aerator, light filling equipment, heating and cooling equipment due to useless functions.

2.3 Software System Design LabVIEW is developed by NI Corporation in the United States, which has a profound impact on the traditional instrument field and formed a new concept of “software is hardware instrument” in the modern sense [14]. LabVIEW technology was applied in Tongzhou factory aquaponics base to realize the design and development of monitoring system for thermal-water environment of aquaponics greenhouse. The main functions of this system are divided into the following modules:

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Fig. 2 Schematic diagram of aquaponics system in Tongzhou, Beijing

Table 1 Main equipment in aquaponics greenhouse of Tongzhou, Beijing

2.3.1

Serial number

Name

Type

1

Coarse filter equipment

YL-WJ-60

2

Vertical flow separator

YL-ZW-60

3

Pump

STP-50,STP-75

4

Culture pond

–

5

Integrated biochemical treatment unit

YL-SH-14

6

Oxygen cone

YL-YZ-60

7

Liquid oxygen storage tank

DPL450-175-1.4

8

Air flotation machine

YL-1500

9

Micro nano aerator

TL-HP50-A

Login Function

In this system, MySQL database and LabVIEW are used for joint debugging. And the administrator can assigns the user account and password (Fig. 4). Therefore, only

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Fig. 3 Representative equipment and devices in aquaponics greenhouse: a Pump, b Carbon dioxide sensor, c Light sensor

Fig. 4 Aquaponics monitoring system

internal personnel can have the login authority, and other unauthorized personnel can‘t view the working status of the aquaponics greenhouse, which has a protective effect on the greenhouse environment, and ensures that the greenhouse environment will not be malicious damage or information leakage.

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System Warning Principle

At present, the water temperature control in Tongzhou aquaponics base uses relatively simple traditional manual methods. As a result, heating and cooling equipment will run for a long time or be started and stopped frequently, resulting in a large amount of unnecessary energy consumption. On the other hand, the traditional control method, such as on/off control, could cause the greenhouse environment to fluctuate obviously, which isn’t conducive to the growth of vegetables and fish. In this study, a monitoring and early warning system based on virtual instruments was developed for the factory aquaponics base in Tongzhou, and the thermal-water environment of the aquaponics system was optimized. In this way, a more energysaving and efficient operation mode of the aquaponics system will be determined. Tongzhou factory aquaponics base is mainly raising with sturgeon, goldfish and trout, and mainly planting with celery and lettuce. After investigation and experiments, taking the goldfish aquaculture area as an example, the upper limit of temperature was set at 25 °C and the lower limit was set at 10 °C [15]. Water temperature as an example to design the warning function as illustrated in Fig. 5.

2.4 Greenhouse Thermal Environment Model According to the conservation of energy theorem, the change amount of stored energy in the greenhouse is equal to the difference between the inflow energy and outflow energy in the greenhouse in unit time, namely, the formula is as follows: C

d(Ti ) = Q − B S(Ti − T0 ). dt

(1)

where C is the specific heat capacity of the greenhouse in kJ/K; Ti is the controlled temperature of greenhouse in K; T0 is the ambient temperature near the greenhouse in K; B is the heat transfer coefficient in the greenhouse in kJ/sm2 K; Q is the heat generated by the heating device in unit time in kJ/s; S is the heat transfer area of the greenhouse in m2 . The mathematical model of the thermal environment of the greenhouse is C

d(Ti ) + B S(Ti ) = Q + B S(T0 ) dt

(2)

When the thermal environment of the greenhouse reaches a steady state, it can be considered that the temperature of the greenhouse will not change, and then: ⎧ ⎨

d(Ti ) dt 

= 0; T = T , Q = Q  ; ⎩ i Q = B S T  − T0

(3)

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Fig. 5 Schematic diagram of early warning for aquaponics monitoring system

When the thermal environment of the greenhouse is not stable, we believe that the temperature in the greenhouse is changing, that is, the unit time change of temperature is not zero.  Ti = T  + ΔT ; . (4) Q = Q  + ΔQ Substituting the above equation into it, C

d(T ) + B SΔT = ΔQ dt

(5)

Let BCS = T , B1S = K , then the transfer function of the greenhouse thermal environment model can be deduced as,

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G(s) =

ΔT K = ΔQ Ts + 1

(6)

where K is the scale coefficient of the greenhouse, and T is the time constant. Since the thermal environment of the greenhouse is characterized by inertia and large time delay, a time delay link needs to be added, that is, the final transfer function is, G(s) =

K e−τ s ΔT = Ts + 1 ΔQ

(7)

where K is the gain coefficient; T is the time constant; τ is the lag time constant. In this study, K = 0.92, T = 144, τ =30 are selected [16].

2.5 PID Control Principle PID control is the deviation ratio P, deviation integral I, deviation differential D control abbreviation. The mathematical principle of PID controller is as follows [17]: t

u(t) = K P e(t) + K I ∫ e(τ )d x + K D 0

de(t) dt

(8)

where e(t) is the deviation between the set value of the system and the measured value of the system, e(t) = r(t) − y(t), as the input of the PID controller.

2.6 Fuzzy Control Principle Fuzzy control is based on fuzzy set theory, according to the deviation, the deviation rate of control on-line automatic adjusting proportion coefficient, integral and differential coefficient of fuzzy controller. Compared with traditional control methods, fuzzy control has some advantages. The application of fuzzy control can make the system have higher flexibility, stronger adaptability and robustness, so as to obtain good control effect [18]. The basic domain of error could be set as [−xe , xe ], the basic domain of error change is [−Xec , Xec ], and the basic analects of control quantity is [−yu , yu ]. The domain of fuzzy subset obtained by error variables is {−n, −n + 1,…, 0, …, n − 1, n}. The domain of fuzzy subset obtained by variable error is {−m, −m + 1, …, 0, …, m − 1, m}. The domain of fuzzy subset obtained by the control quantity is {−l, −l + 1…, 0, …, l−1, l}.

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Fig. 6 Fuzzy controller structure

The quantization factor is generally expressed by K, and the quantization factor of error Ke and the quantization factor of error change Kec are respectively determined by the following two formulas: ke =

n xe

(9)

kec =

m xe

(10)

The scaling factor of output control quantity is determined by the following formula: ku =

yu l

(11)

The fuzzy controller structure used in this paper is two-dimensional, while the conventional two-dimensional fuzzy controller structure is indicated in Fig. 6.

3 Results 3.1 Monitoring Experiment of Aquaponics System After field investigation, thermal-water environment monitoring system was developed respectively in the aquaculture area (including goldfish, trout and sturgeon farming areas) and hydroponics area (celery and lettuce) in Tongzhou. Taking the goldfish monitoring experiment as an example, the monitoring result is as demonstrated in Fig. 7.

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Fig. 7 Monitoring interface of water environment in Goldfish area

3.2 Temperature Early Warning and Optimization In the monitoring process of Tongzhou factory aquaponics greenhouse, it was found that the actual thermal environment of the base did not completely meet the healthy growth conditions of greenhouse crops and fish. In order to optimize aquaponics system, reduce equipment energy consumption and improve the efficiency of production, the greenhouse thermal-water environment of aquaponics is controlled to keep a suitable condition for fish and vegetable crop growth. Four control modes for circulating water temperature of aquaculture in aquaponics greenhouse have been designed and compared, including threshold control, PID control, fuzzy control and fuzzy PID control with circulating water temperature as control variable, and simulation experiments have been carried out. A.

Experimental study on thermal-water environment warning and threshold control

Traditional manual control mainly depends on the long-term work experience of agricultural workers, which has high labor cost, low technical content, low benefit, and other drawbacks. Combined with the warning principle mentioned above, this study carried out a threshold controller design on thermal environment of aquaponics system through the virtual instrument technology (Fig. 8). B.

PID control

PID control is currently a relatively mature control strategy in the industry. Compared with the threshold control strategy, PID control is better to improve the stability of aquaponics greenhouse thermal-water environment, and avoid the damage of equipment due to frequent actions and other factors. PID control model in Matlab/Simulink has been established to investigate aquaculture water temperature performance. After

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Fig. 8 Early warning and threshold control for water temperature in aquaculture of aquaponics

repeated parameter adjustment experiments, the control effect is obviously better when the selected parameters Kp = 4, Ki = 0.02 and Kd = 0. Assuming the setting temperature T = 25 °C, the simulation results are illustrated in Fig. 9. The curve of controlled water temperature using PID control is obtained and water temperature finally will maintain stable after around 800 s. It can be illustrated that the performance indicators are as follows: rise time TP = 76.08 s, overshoot about 19.2%, adjustment time TS = 220.4 s, steady state error ESS = 0. After system optimization for many times, the PID controller responds quickly and has good stability. C.

Fuzzy control

The traditional PID control is difficult to adjust online and has some shortcomings, the emergence of fuzzy control just make up for this defect, in recent years, many

Fig. 9 PID simulation result for water temperature in aquaculture of aquaponics

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Fig. 10 Simulation results for water temperature in aquaculture of aquaponics using fuzzy control

scholars have widely used fuzzy control to control the furnace temperature [19], but few scholars have applied fuzzy control to study aquaponics thermal environment. The following requirements for the greenhouse thermal environment system were put forward: the target of control is 25 °C, the range of temperature control error is (−25, 25), the rate of change of error is (−5, 5), τ = 30 s, is the control period of controlled object is one representative parameter of thermal environment—water temperature in aquaculture. The fuzzy subsets of control error and error change rate are not less than 7. Assume that the set-point water temperature T is 25 °C, and the experimental results are indicated in Fig. 10. It could be seen that the performance indicators are: rise time TP = 73.5 s, overshoot is around 10.8%, steady state error is about 0.8%. Compared with PID control, the rise time of fuzzy control is decreased by approximately 3 s, and the overshoot is reduced by around 9%. D.

Fuzzy PID control

Greenhouse thermal environment system is a nonlinear system with large inertia [20, 21]. For such a system, it is difficult to establish a more accurate mathematical model, but the fuzzy control has some limitations. In order to further optimize the control performance, according to the principle of fuzzy PID control [22], this work tried to utilize a fuzzy PID to control the aquaponics thermal-water environment. The simulation results of water temperature are demonstrated in Fig. 11. Observed from Fig. 11, the response curve in the oscilloscope was measured, and the dynamic performance indexes were obtained as follows: rise time TP is 76.4 s, overshoot was about 19.6%, adjustment time TS = 209.5 s, steady state error ESS = 0%. Compared with the fuzzy control, the adjustment time of the fuzzy PID control could decrease approximately 66 s, which illustrates its control performance is obviously better.

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Fig.11 Simulation result for water temperature in aquaculture of aquaponics using fuzzy PID control

4 Discussion The thermal-water environment monitoring and early warning system based on LabVIEW for Tongzhou factory aquaponics base has been designed and developed in this study. Based on different production modes of aquaponics, the proposed monitoring system could adjust and optimize the working state of equipment, through realtime monitoring factors e.g. temperature, dissolved oxygen etc., water temperature early warning, control and other measures. In order to save energy and improve dynamic performance of system, this paper proposes the use of PID and fuzzy control method to numerically adjust the aquaponics greenhouse thermal environment. The proposed control methods including PID, fuzzy and PID fuzzy control can effectively maintain temperature stable within a certain range, in this way to avoid the system actuator, such as fan, air conditioning and other frequent switch start-stop, finally save energy. At the same time, it provides a good and stable growth environment for plants and fish, which highlights the characteristics and advantages of low energy consumption and sustainable development of the aquaponics greenhouse system. At present, this method has been carried out by simulation, and it still needs further verification and improvement in practice in the future. Table 2 evaluates the experimental results of several control methods based on the control experiment of the thermal environment in aquaponics greenhouse. Observed from Table 2, traditional PID control method indicates good advantages in accuracy and stability, but the response speed is slightly insufficient. Using fuzzy control, the system can respond quickly and adjust, but the performance in stability and robustness is not satisfactory. The performance of fuzzy PID control mode is best among them, the adjustment time is shortened around 10 s compared with PID control, and the characteristics of high accuracy and small steady-state error of PID

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Table 2 Performance comparisons of different control methods Rise time (s)

Overshoot

Settling time (s)

Static error (%)

PID control

76.08

19.2%

220.4

0

Fuzzy control

73.5

10.8%

276

0.8

Fuzzy PID control

76.4

19.6%

209.5

0

control are retained. In the future, after the actual test in the base, the fuzzy rules will be adjusted according to the actual effect. On the other hand, this program is highly extensible, and there is still a lot of room for development in the future, such as the development and design of functions such as disease and insect control based on vision, fish growth monitoring, dead fish screening and so on.

5 Conclusion and Future This research aims to design and develop an aquaponics greenhouse thermal-water environment monitoring and warning system using LabVIEW virtual instrument technology in Tongzhou factory aquaponics base. After optimizing the system design, the proposed platform could provide the remote online monitoring, which could avoid the cultivation mode of employees’ long-time on-site work, and could reduce energy consumption through the digital information service. The early warning system can adjust the equipment according to environmental factor thresholds of the proposed monitoring system to ensure suitable environmental requirement for fish and vegetable growth. In the process of practical monitoring, it is found that real environmental conditions on site is not completely suitable for fish and vegetable growth. The thermal environment model is thus established, and threshold, PID, fuzzy and fuzzy-PID control method have been investigated, respectively. The comprehensive comparison of simulation results in MATLAB/Simulink demonstrate that the fuzzy-PID control strategy has most significant advantages among them. The water temperature in aquaculture could be stabilized at 25 °C only after 209.5 s using fuzzy PID control in the aquaponics greenhouse, and its static error is zero. According to the concept and development direction of unmanned farm, intelligent algorithm will be used in combination with neural network model to further optimize the control effect of thermal-water environment in aquaponics greenhouse. In addition, with the help of cloud computing and big data technology, the greenhouse environment data with system operation and management experience may be put on the cloud in the future, and each farm can realize data interconnection and learn from each other, so that it provides the reference for energy saving optimization and intelligent management for administrators and farmers.

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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. Guo Y, Zhao H, Zhang S, Wang Y, Chow D (2020) Modeling and optimization of environment in agricultural greenhouses for improving cleaner and sustainable crop production. J Cleaner Prod 124843 2. Lagerberg C, Brown MT (1999) Improving agricultural sustainability: the case of Swedish greenhouse tomatoes. J Clean Prod 7:421–434 3. Fox JA, Adriaanse P, Stacey NT (2019) Greenhouse energy management: the thermal interaction of greenhouses with the ground. J Clean Prod 235:288–296 4. Frenken K (2005) Irrigation in Africa in figures: AQUASTAT survey, 2005. Food & Agriculture Org 5. Shi y (2020) People take food as safety— thinking about the problem of food security in our country. Huabei Natural Resour, pp 133–134 6. Van Woensel L, Archer G, Panades-Estruch L, Vrscaj D (2015) Ten technologies which could change our lives: potential impacts and policy implications. Depth analysis 7. Yang D, Kong J, Su X (2019) Design and research of ginkgo leaves retractable picker. Appl Eng 3 8. Zhang L, Tang S, Li P, Cui S, Guo H, Wang F (2018) Structure design of a semi-automatic pineapple picking machine. IOP Conf Ser Mater Sci Eng 452 9. Bing H, Yongshun L, Ying H, Jilian L (2019) High-yield cultivation techniques of Huangyuan carrot. In: High-yield cultivation techniques of Huangyuan carrot. Santiago, Chile, p 4 10. Singh G, Singh G (2017) Constraints in adoption of recommended button mushroom cultivation techniques. Agric Update 12 11. Shi C, Wang Q, He X, Zhang X, Li D (2020) An automatic method of fish length estimation using underwater stereo system based on LabVIEW. Comput Electron Agric 173:105419 12. Shan X, Guo R, Fei J (2020) Design of distributed agricultural greenhouse based on LabVIEW. Agric Eng 10:46–49 13. Nagayo AM, Mendoza C, Vega E, Al Izki RK, Jamisola RS (2017) An automated solar-powered aquaponics system towards agricultural sustainability in the Sultanate of Oman. Presented at the (2017) 14. Zhang Y, Zhou M (2006) Discussion on the construction method and characteristics of virtual instrument. DA ZHONG KE JI. 74–75 15. Chen T, Wong MKH, Chan BCB, Wong AOL (2019) Mechanisms for temperature modulation of feeding in goldfish and implications on seasonal changes in feeding behavior and food intake. Front Endocrinol 10:133 16. Yong L (1992) Design of single—parameter mold—paste controller. Appl Electron Tech, pp 7–11 17. Mahmood QA, Nawaf AT, Esmael MN, Abdulateef LT, Dahham OS (2018) PID temperature control of demineralized water tank. IOP Conf Ser Mater Sci Eng 454

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18. Guan ZQ, Luo XM, Song LP (2015) Fuzzy self-tuning PID temperature control modeling and simulation system. Appl Mech Mater 3744 19. Huang Q, Yang J (2017) The design of Incinerator control system based on fuzzy self-tuning PID. J Mach Des 20. Trabelsi A, Lafont F, Kamoun M, Enea G (2007) Fuzzy identification of a greenhouse. Appl Soft Comput 7:1092–1101 21. Li K, Wang X (2013) Fuzzy PID control for greenhouse temperature. Ind Control Appl 32:14–17 22. Xie G, Zheng K, Jia Y (2018) Design of fuzzy PID temperature control system. In: MATEC web of conferences, vol 228

Identifying the Feasibility of Implementing of Heat Pump for Heating a Factory Aquaponics Greenhouse in Beijing Quanwu Ge, Zhixin Ke, Shihao Wu, and Yang Wang

Abstract The heating system for the aquaponics greenhouse is crucial to realize economical and efficient hydroponics and aquaculture in cold climate zone. This paper investigated the technical feasibility and economics of a heat pump heating system in the aquaponics greenhouse and compared it with the original heating system. A mathematical model of technical and economic analysis under different heating modes was established. Using the mathematical model, different heating systems were contrasted with their primary energy consumption, pollution emissions, and winter operating cost. The results show that in a heating cycle in winter, the experimental air source heat pump (ASHP) and ground source heat pump (GSHP) save 8,959 CNY and 13,881 CNY, respectively, compared with coal-fired boilers, and reduce CO2 emissions by 53.0% and 62.2%. Heat pump heating systems have relatively high energy efficiency, relatively low dioxide pollution emissions, and economical way. Keywords Aquaponics greenhouse · Heating system · Heat pump · Operation cost · Carbon emissions

1 Introduction Aquaponics is a combination of aquaculture and hydroponics. Its core is to use the wastewater from aquaculture to grow plants [1]. It is a sustainable agricultural model, which hydroponics reduces dependence on the land, recycles water to reduce waste, and uses fish manure to decrease energy use [1]. The factory aquaponics greenhouse Q. Ge · Z. Ke · S. Wu · Y. Wang (B) College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China e-mail: [email protected] National Innovation Center for Digital Fishery, China Agricultural University, Beijing 100083, China Beijing Engineering and Technology Research Center for Internet of Things in Agriculture, China Agricultural University, Beijing 100083, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_53

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is a commercial agriculture mode, which reduces the energy consumption of fish and crops through large-scale breeding. While a factory aquaponics greenhouse needs to heat both the greenhouse’s indoor air and the water in the aquaponics system, a traditional agricultural greenhouse only needs to heat the greenhouse’s indoor air, especially in winter [2]. An agricultural greenhouse is one of the most energy-consuming sectors in agriculture, and its energy consumption is mainly related to the heating of the greenhouse [3]. According to statistics, in northwestern China, heating energy consumption accounts for about 20–40% of the total operating cost of agricultural greenhouses [4]. Nowadays, traditional energy sources used for heating greenhouses are fossil fuels such as liquefied petroleum gas, diesel, and natural gas. It means that conventional greenhouse pollution emissions are relatively high. In addition, the operation of a greenhouse consumes a lot of fossil fuel energy, and the price of fossil fuel is relatively expensive. Some commercial growers believe that greenhouse heating costs are now a significant production cost [5]. Love et al. [6] surveyed large commercial aquaponics farmers. This survey found that commercial aquaponics systems, often located in greenhouses, are engineered to maximize fish and plant production. Greenhouse climate control requires high investment and management costs. However, energy-saving is necessary to ensure farmers’ income and alleviate global warming [7]. Currently, many researchers are interested in using renewable energy for greenhouse heating [8]. Moreover, heat pump systems have become a suitable choice to reduce greenhouse heating energy use and costs [9]. Heat pumps are a promising technology that is widely used in industry, agriculture, and homes to regulate indoor air temperature and provide hot water. It is based on the principle of the Carnot cycle, using renewable energy sources, such as solar energy, ambient air energy, geothermal energy, or waste heat from industry, and generating low-pollution heating energy [10]. Compared to the traditional heating method, heat pump heating systems can be energy-efficient, cost-effective, and safe [2]. Yang et al. [7] used a surplus air heat pump system for a glasshouse with a 100 m2 floor area in Hwasung, Korea. The results show that energy conservations were determined to be a maximum of daily 76.3% and monthly 25.7%. Luo et al. [11] implemented a case study focusing on a greenhouse in Zhongxiang city of Hubei province, China. This case comparison of coal-fired boiler-based and groundwaterheat-pump-based heating and cooling solution. The results display that the coefficient of performance (COP) of the GWHP system averages at 4.1 for cooling and 3.3 for heating. The study recommends a groundwater heat pump system to replace traditional boilers in regions with similar climatic conditions. Nem´s et al. [12] analysed the heating system of a greenhouse in Poland, comparing it with ASHP and GSHP heating systems, and concluded that the payback period of the investment of air source heat pumps is only 5.5 years. Under Polish climatic conditions, the ASHP heating system should be selected. This study focuses on the feasibility of heating system retrofitting for a factory aquaponics greenhouse in Tongzhou District, Beijing. The current heating method used in the greenhouse is traditional boiler heating. This paper presents the calculation of the design load of the aquaponics greenhouse to determine the heating demand

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in the coldest months of winter. And analyse the winter economic performance and carbon emission analysis of Beijing, a typical cold climate area in China, using the new heating system of ASHP and GSHP to replace the traditional boiler room.

2 Methods and Materials The object of this study is a portion of a large agricultural greenhouse located in Tongzhou District, Beijing, China (latitude 39° 91′ N, longitude 116° 66′ E), with an area of 1152 m2 (length 40 m, width 28.8 m), and its geometric configuration is demonstrated in Fig. 1. The sill wall around the greenhouse is a brick wall with a height of 1 m and a thickness of 0.37 m, and the foundation has no insulation layer. The greenhouse covering material is 4 + 9A + 4 mm thick insulating glass, and the roof is an 8 mm thick polycarbonate (PC) sheet. The schematic diagram of the studied aquaponics system is depicted in Fig. 2. An individual system covers an area Greenhouse roof

9.6m Greenhouse sill wall

Greenhouse gutter

9.6m

9.6m

Greenhouse roof

6.8m

Greenhouse gutter

6.8m

6.0m

6.0m

1.0m

1.0m 9.6m Greenhouse sill wall

±0.0m

(a) North wall

9.6m

9.6m

±0.0m

(b)South wall

6.8m

6.8m

6.0m

6.0m

1.0m

1.0m

4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m ±0.0m

4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m 4.0m ±0.0m

(c) East wall

(d) West wall

Fig. 1 Geometry of aquaponics greenhouse

Fig. 2 Schematic diagram a, c, d of studied aquaponics system and picture (b) of inside

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of 62 m2 (length 12.4 m, width 5 m). The aquaponics system is composed of five parts, including two fish ponds, four hydroponic zones (three layers with an opening rate of about 10%), a filtration nitrification tank, two reflux tanks, and pipes. The breeding object is Acipenser schrencki, a rare fish with high economic value, and the cultivated vegetables include celery and lettuce according to the season. Vegetables grown in the hydroponic area in aquaponics require an air temperature of 15–20 °C during the growing season [13]. In addition, fish flourishing in the fishpond area in aquaponics require a water temperature of 21–22 °C during the growing season [14, 15]. However, due to the problem of maintaining the air and water temperature set-points, the most vital period is the winter coldest months from the beginning of December to the end of February. In summary, the design temperature of the indoor air in the greenhouse is 16 °C, and the design water temperature of the aquaponics system is 22 °C. The experimental data were collected from December 1, 2020, to December 27, 2020. It is worth noting that the data in this study are after heating because Beijing has started heating after October 15. Figure 3 displays the outdoor air temperature varied between −11.5 and 7.3 °C, the indoor air temperature varied between 9.0 and 22 °C, and the water temperature changed between 11 and 15.3 °C. Under current conditions, neither the air temperature of the greenhouse nor the water temperature of the aquaponics system can meet the suitable needs of the aquaculture and vegetables. Therefore, it is quite essential to provide additional heating.

Fig. 3 Actual measured outside, inside and water temperature in the greenhouse from December 1, 2020 to December 27, 2020 (T o is the outdoor air temperature in °C; T i is the indoor air temperature in °C; T w is the water temperature in °C; T i,r is the indoor air reference temperature in °C; T w,r is the water reference temperature in °C)

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3 Preliminary Thermal Analysis for Greenhouse Aquaponics 3.1 Air Heating Load The heating load of the greenhouse was considered to be composed of two components: envelope structure and ventilation. The simplified heating load calculation model for greenhouse heating is [16, 17]: Qg = Q1 + Q2

(1)

where Qg is heating system heat supply in the greenhouse in W; Q1 is the heat transfer and heat loss of envelope structure (roof, ground, exterior wall, door, window and other envelope structure) in W; Q2 is the heat loss of indoor and outdoor air exchange in the greenhouse in W. The heat transfer and heat loss of envelope structure can be calculated as formula: Q 1 = Q en + Q g

(2)

where Qen is the heat transfer and heat loss of greenhouse envelope structure above ground in W; Qg is the heat loss from ground heat transfer in greenhouse in W. Equations for heat loss Qen and Qg are as: Q en = Uen Aen (Ti − To )

(3)

Q g = Ug Ag (Ti − To )

(4)

where U en is the heat transfer coefficient of envelope structure above ground in W/m2 °C; U g is the heat transfer coefficient of envelope structure above ground in W/m2 °C. Aen and Ag are the area of envelope structure above ground and ground (Table 1), respectively. These coefficients are all in m2 . T i and T o are the indoor set temperature and outdoor temperature in °C. Table 1 Area and heat transfer coefficients of various parts in the aquaponics greenhouse

Item Glass wall Roof

Area [m2 ] 699.9 1288.0

Sill wall

134.8

Ground

1152.0

U-values [W/(m2 °C)] 3.1 [18] 3.3 [17, 19] 1.52 [16] Zone 1 0.24 [17] Zone 2 0.12 Zone 3 0.06

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Heat loss of indoor and outdoor air exchange in the greenhouse can be calculated as: Q 2 = 0.5kwind V N (Ti − To )

(5)

where kwind is the wind speed impact factor, k wind = 1; V is the greenhouse volume in m 3 ; N is ventilation rate in h −1 , N = 1.

3.2 Heating Load for Water in Aquaponics The total energy balance of the constant temperature aquaponics system is described as the equation [20, 21] (Eq. 6). Q a = −Q sw + Q Lw + Q Vw + Q wall + Q r + Q sky

(6)

where Qa is the heat supplied to the water in W, Qsw is the solar radiation absorbed by the water in W; QLw is the latent heat loss from the evaporation of the water in W, QVw is the sensible heat transfer between the water surface in W; Qwall is the heat transfer and heat loss of aquaponics wall in W; Qr is the heat exchange of make-up water in W. The solar radiation absorbed by the water is calculated as: Q sw = (1 − ρsw )Aw I

(7)

Aw = Aw,f + Aw,h + Aw,f + Aw,n

(8)

where Aw is the total water surface area in m2 ; Aw,f is the fishpond water surface area in m2 ; Aw,h is the hydroponic area water surface area in m2 ; Aw,r is the return water tank water surface area in m2 ; Aw,n is the filter nitrification tank water surface area in m2 ; τc is transmissivity of a single layer of cover to solar radiation; ρ sw is the reflectivity of water surface; I is the average radiation during heating time in W/m2 °C. The calculation parameters used by the aquaponics system are demonstrated in Table 2. The sensible heat transfer between the water: Q Vw = h Vw Aw (Tw −Ti )

(9)

where the convective coefficient between the water surface and the inside air h Vw = 1.86 · |Tw −Ti |0.33 in W/m2 °C; T w is the water temperature in °C. The latent heat loss from the evaporation of the water:

Identifying the Feasibility of Implementing of Heat Pump … Table 2 Caulated parameters of the proposed aquaponics system

Item

Value

643 Item

Value

τc [19]

0.79

HR [16]

75.0%

ρ sw [20]

0.1

C a [16]

1.01 kJ/kg °C

εw [20]

0.97

ρw

997.7 kg/m3

Cw

4.18 kJ/kg °C

W/m2

I

100

Vw

45.3 m3

Note The thermophysical property of water is a value of 22 °C, and the thermophysical property of air is a value of 16 °C. I is the average solar radiation during heating, V w is the total water volume of the aquaponics system

Q Lw = h Lw Aw (ew∗ − ei )

(10)

where the convective coefficient for latent heat between the water surface and the inside air was defined h Lw = ν · Le1/3 · h V w /Ca in W/m2 °C; Le is the Lewis number representing the ratio of thermal diffusivity to mass diffusivity, Le = 0.89; v is the latent heat of water vaporization in W/m2 °C; C a is the specific heat capacity of air in J/kg °C; e* w is the saturated water vapor concentration of water temperature in kg/m3 ; the water vapor concentration of the inside air was defined ei = HR · e* (T ) in kg/m3 ; HR is average humidity of the aquaponics greenhouse during heating time in %. The relationship between saturated water vapor concentration and air temperature is e* (T ) = 0.000832 · T + 0.00247. Q wall = Awall Uwall (Tw − Tw,out )

(11)

where, Awall is the wall area of the part of aquaponics system in m2 ; U wall is the heat transfer coefficient of the part of aquaponics system in W/m2 °C; T w,out is the temperature outside the wall, air or soil in °C. The heat exchange of replenishment water is: Q r = Cw ρw G(Tw − Tgw )/t

(12)

where C w is the constant pressure specific heat capacity of water in J/kg ·°C; ρ w is the densityof water in kg/m3 ; the daily water supply was defined G = ρ w · V b in kg; t is the heating time in s; T gw is the supply water temperature, assuming T gw = 15 °C; V b is the daily water supplement in aquaponics system in L. The maximum design value of daily water exchange is 5%. Assuming the sky is a black body, the net thermal radiation between the water surface and the sky is:   4  Q sky = σ · εw · τc (Tw + 273.16)4 − Tsky + 273.16

(13)

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Table 3 Characteristic parameters of the proposed aquaponics system

Item

Design parameters

Fish pond

R: 0.7 m, H: 1.2 m, δ: 0.005 m, λ: 0.25 W/m °C

Filter nitrification tank

L: 1 m, W: 1.6 m, H: 1.2 m, δ: 0.2 m, λ: 1.28 W/m °C

Return water tank

L: 1 m, W: 1 m, H: 1.2 m, δ: 0.2 m, λ: 1.28 W/m°C

Hydroponics planting area

L: 8 m, W: 0.2 m, H: 0.14 m, δ: 0.004 mm, λ: 0.15 °C

Pipe

R: 0.025 m, L: 60 m

Note Hydroponics planting area design parameters are one-level parameters. R is the raidus in m; L is the length in m; W is the width in m; H is the height in m; δ is the thickness of wall in m; λ is the thermal conductivity in W/m °C

where σ is the Stefan–Boltzmann constant; εw is the emissivity of the water surface. The sky temperature was defined T sky = 0.0552 ·(T o + 273.16)1.5 − 273.16 in °C. The heat transfer coefficient U depends on the thickness of the material, the conductivity coefficient of the material from which the partition was constructed (Table 3), and heat transfer coefficients, and is described using Eq. (14):  U=

δ 1 1 + + λ h out h in

 (14)

where hin is the coefficient of heat transfer from the inside material in W/m2 °C; hout is the coefficient of heat transfer from the outside material in W/m2 °C; the coefficient of heat transfer of air, water, and soil are 5, 1000, and 0.47 W/m2 °C respectively; δ is the thickness of material in m; λ is the heat transfer coefficients of material in W/m °C.

3.3 Primary Energy Consumption The primary energy consumption of different heating methods is calculated as follows [22]: The primary energy consumption of large coal-fired boiler heating method can be calculated as formula: Q = Q t /(ηhnet1 · ηhnet2 · ηcb ) + (Whnet1 /ηe . + Whnet2 /ηenet ./ηe )

(15)

The primary energy consumption of low temperature air source heat pump heating method can be calculated as formula:

Identifying the Feasibility of Implementing of Heat Pump …

Q = Q t /(C O Ph )

645

(16)

where, Q is the primary energy consumption per unit area in the heating season in kgce/m2 ; Qt is the heating load per unit area in the heating season in kgce/m2 ; ηe is the national average power generation efficiency, 35%; ηenet is the grid transmission efficiency, 92%; ηhnet1 is the thermal efficiency of primary network, 95%; ηhnet2 is the thermal efficiency of secondary network, 90%; ηcb is the heating efficiency of coal-fired boiler, 75%; Whnet1 is the power consumption per unit area of primary network in kgce/m2 ; Whnet2 is the power consumption per unit area of secondary network in kgce/m2 ; COPh is the heating coefficient of performance of heat pump in total heating season.

4 Results and Discussion In order to facilitate the analysis of the heating load of the proposed factory aquaponics greenhouse, the following assumptions are provided: (a) (b) (c)

The respiration heat of crops, soil, water, etc. and the heat consumption of crop physiological and biochemical conversion and exchange are ignored [23]. The heat transfer process through the envelope of the greenhouse building is continuous [22]. There will be ten identical aquaponics systems in the proposed factory agricultural greenhouse.

4.1 Air Heating Load of Aquaponics Greenhouse The air heating loads under different outdoor air temperatures of the aquaponics greenhouse, as shown in Fig. 4. The corresponding heating hours under different outdoor air temperatures of the aquaponics greenhouse, as exhibited in Fig. 5. According to assumption (b), he heating consumption in a heating season can be obtained by calculating the heating hours under different heating loads.

4.2 Water Heating Load of Aquaponics Greenhouse The individual aquaponics system total water design heating load of different indoor air temperatures as indicated in Fig. 6. The total design heating load of the factory aquaponics greenhouse, as shown in Table 4. According to the market investigation, based on the heating load of the proposed aquaponics greenhouse, the average COP of the ASHP used in this article is

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Fig. 4 Air heating load under different outdoor temperatures

Fig. 5 Heating hours under different outdoor air temperature

Fig. 6 Individual aquaponics system total water design heating load of different indoor air temperature

Identifying the Feasibility of Implementing of Heat Pump … Table 4 Calculated heating load of the proposed aquaponics greenhouse

647

Item

Value

Indoor design heating temperature [°C]

16

Aquaponics design water temperature [°C]

22

Calculated outdoor temperature of heating[17] [°C]

−12

Air design heating load [kW]

295.9

Water design heating load [kW]

39.1

Total design heating load [kW]

335.0

3.3, whose type is ZGR-320IIAD (use two) [24], and the average COP of the GSHP is 4.1, whose type is PSRHH 1302-Y (use one) [25].

4.3 Primary Energy Consumption and Carbon Emission Wu et al. [26] investigate and statistic the operating hours of heat pump units showed that the heating in winter in Beijing has an average of 10 h of work per day. Annual full load operation 30%, 66.6% load 40%, and 33.3% load 30%. Combined with the heating load (Q) per unit area of the greenhouse at the average outdoor temperature (-1.7 °C) during the heating period, the total energy consumption in winter can be obtained. For analysis of pollution emission of different heating modes, each kilowatt-hour of electricity saving 1 kg of standard coal would reduce the number of pollutant emissions including 2.493 kg of carbon dioxide [22]. Figure 7 displays the primary energy consumption and carbon emissions under different heating methods at the average outdoor air temperature (−1.7 °C) in heating time. The results can be sorted from low to high as follows: GSHP, ASHP, coal-fired boiler. Compared with traditional heating methods, the heat pump heating system

Fig. 7 Primary energy consumption and carbon emissions under different heating methods

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Fig. 8 Operating cost under different heating methods at the average outdoor air temperature (−1.7 °C) in heating time

is an energy-efficient heating method, ASHP’s primary energy consumption and carbon emissions accounted for 47.0% of boiler heating systems, while GSHP only accounted for 37.8%.

4.4 Operating Costs According to the National Bureau of Statistics of China, the price of 5,000 kcal of coal is 690 CNY/ton [27], electricity price was calculated at 0.62 CNY/kWh. Under the average outdoor temperature (−1.7 °C) in winter, the estimated operating costs under different heating methods in heating time as exhibited in Fig. 8. The results are sorted from low to high as follows: GSHP, ASHP, coal-fired boiler. Compared with traditional boiler heating methods, ASHP operating cost is 73.8% of the boiler, and GSHP operating cost is only 59.4% of the boiler. ASHP winter operation can save 8,959 CNY, and GSHP winter operation can save 13,881 CNY.

4.5 Summary and Conclusions Based on the prediction and calculation of energy consumption in a proposed aquaponics greenhouse, this paper analyses the economic benefits of three types of heating systems and draws the following conclusions: 1.

Compared ASHP and GSHP with the coal-fired boiler heating system, in the coldest three months of winter, the energy-saving rate and emission reduction rate can reach 53.0% and 62.2%, which will reduce the use of primary energy by 17.5 tons and 20.5 tons of standard coal, respectively.

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Compared ASHP and GSHP with the coal-fired boiler heating system, in the coldest three months of winter, the operating cost rate can attain 26.2% and 40.6%, which save 8,959 CNY and 13,881 CNY, respectively.

In conclusion, a heat pump heating system is a competitive method. Compared with the traditional boiler, using the heat pump heating system to heat the aquaponics greenhouse in winter is better than the inefficient boiler in terms of economy and environmental protection. In winter, the COP of GSHP is higher than that of ASHP, which has better benefits. However, heat pump systems can also be used as greenhouse cooling systems in summer. Designing a more suitable heat pump system for a greenhouse needs to be evaluated on the year-round scale. Future work will focus on the application of heat pump systems in factory aquaponics greenhouses, including cooling and heating, analysis of the coupling relationship between the greenhouse microclimate and the aquaponics system, and optimization methods for greenhouse environmental control. 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. Yanes AR, Martinez P, Ahmad R (2020) Towards automated aquaponics: a review on monitoring, IoT, and smart systems. J Clean Prod 263:121571 2. Chen P, Zhu G, Kim H-J, Brown PB, Huang J-Y (2020) Comparative life cycle assessment of aquaponics and hydroponics in the Midwestern United States. J Clean Prod 275:122888 3. D’Arpa S, Colangelo G, Starace G, Petrosillo I, Bruno DE, Uricchio V, Zurlini G (2016) Heating requirements in greenhouse farming in southern Italy: evaluation of ground-source heat pump utilization compared to traditional heating systems. Energy Effic 9:1065–1085 4. Sun X, Zhou Z, Zhao K, Bi S, Guo K (2015). Experiment on heating effect in greenhouse by solar combined with air-source heat pump. Trans Chin Soc Agric Eng 31(22):215–221 5. Jeon J, Lee D, Paek Y, Kim H (2015) Study on heating performance of hybrid heat pump system using geothermal source and solar heat for protected horticulture. J Korean Sol Energy Soc 35:49–56 6. Love DC, Fry JP, Li X, Hill ES, Genello L, Semmens K, Thompson RE (2015) Commercial aquaponics production and profitability: findings from an international survey. Aquaculture 435:67–74 7. Yang S-H, Rhee JY (2013) Utilization and performance evaluation of a surplus air heat pump system for greenhouse cooling and heating. Appl Energy 105:244–251 8. Zou D, Ma X, Liu X, Zheng P, Cai B, Huang J, Guo J, Liu M (2017) Experimental research of an air-source heat pump water heater using water-PCM for heat storage. Appl Energy 206:784–792

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9. Voinea S, Dinu S, Ladaru B (2019) Building and monitoring the aquaponics experimental lab for students. In: Vlada M, Albeanu G, Istrate O, Adascalitei A (eds) Proceedings of the 14th international conference on virtual learning, Icvl 2019. Bucharest University Press, Bucharest, pp 519–523 10. Ji J, Fu H, He H, Pei G (2010) Performance analysis of an air-source heat pump using an immersed water condenser. Front Energy Power Eng China 4:234–245 11. Luo J, Xue W, Shao H (2020) Thermo-economic comparison of coal-fired boiler-based and groundwater-heat-pump based heating and cooling solution—a case study on a greenhouse in Hubei, China. Energy Build 223:110214 ´ 12. Nem´s A, Nem´s M, Swider K (2018) Analysis of the possibilities of using a heat pump for greenhouse heating in polish climatic conditions—a case study. Sustainability 10:3483 13. Yan Y, Lei B, Wang L, Bie Z (2010) Effects of different day and night temperature on the growth and quality of hydroponic lettuce. J Chang Veg, pp 39–42 14. Li D, Zhuang P, Yan A, Zhang L (2005) Optimum temperatures for growth and feeding of juvenile Amur sturgeon Acipenser schrenckii. J Fish Sci China, pp 294–299 15. Song C, Zhuang P, Zhang L, Zhang T (2014) J Fish Sci China Mar Fish 36:239–246 16. Fu J, Zhou C, Wang L (2020) Methods for calculation of heating load in gutter-connected glasshouse. Trans Chin Soc Agric Eng 36:235–242 17. Design regulation on greenhouse heating system: JB/T10297–2014[S] (2014) 18. Technical specification for design and fabricating of plastic doors and windows: JGJ 362– 2016[S] (2016) 19. Fitz-Rodríguez E, Kubota C, Giacomelli GA, Tignor ME, Wilson SB, McMahon M (2010) Dynamic modeling and simulation of greenhouse environments under several scenarios: a web-based application. Comput Electron Agric 70:105–116 20. Li S, Willits DH, Browdy CL, Timmons MB, Losordo TM (2009) Thermal modeling of greenhouse aquaculture raceway systems. Aquac Eng 41:1–13 21. Zhang N, Yang YB, Zhang DG (2018) Study on calculation method of heat load of tropical fish pond in Dalian. Build Energy Environ 22. Zhang Q, Zhang L, Nie J, Li Y (2017) Techno-economic analysis of air source heat pump applied for space heating in northern China. Appl Energy 207:533–542 23. Jianlu F, Changji Z, Liu W (2020) Methods for calculation of heating load in gutter-connected glasshouse. Trans Chin Soc Agric Eng 36:235–242 24. OUTES. Available online: http://www.outes.com/: ZGR-320IIAD 25. CLIMAVENETA. Available online: http://www.climaveneta.com.cn/: PSRHH 1302-Y 26. Wu Y, Di Y, Jiang H (2016) Study of energy-saving on a greenhouse heating system in a Beijing’s agricultural sightseeing garden. Refrig Air Cond 30:696–699+711 27. National Bureau of Statistics of China. Available online: http://www.stats.gov.cn/: Energy production in May 2021.

Management and Control of Hybrid Energy Storage System in Ship Integrated Power System Chuan Xiang, Yuhan Li, Qi Cheng, and Wenhua Xu

Abstract For the ship integrated power system (SIPS) with DC bus, the DC bus voltage fluctuates greatly with the load change causing by the switch of the ship navigation conditions. In this study, a hybrid energy storage system (HESS) was adopted to suppress the fluctuation of DC bus voltage, and an energy management strategy of HESS considering generator load rate (SVA) and state of charge (SOC) of the energy storage unit was proposed. The HESS can switch flexibly between the constant voltage mode and the charging mode according to SOC and SVA. The HESS supplies power to maintain the stability of DC bus voltage when the load exceeds the rated power of the rectifier generator under some extreme conditions, Keywords Ship integrated power system · DC bus voltage · Hybrid energy storage system · Energy management and control strategy

1 Introduction Ship Integrated Power System (SIPS) integrates power generation, power supply and propulsion power into one system to dispatch and manage the power generation, power distribution, electric propulsion and power consumption of other equipment [1–4]. SIPS with DC bus is one of the main development directions of Marine power system [5–7]. However, the fluctuation of load power navigation, the overload operation of the rectifier generator will reduce the DC bus voltage greatly and endanger the reliable and stable operation of SIPS seriously [8, 9]. Therefore, it is very important to study the method and strategy to stabilize the DC bus voltage of SIPS. HESS can be used to suppress voltage fluctuation of DC bus. Reference [10] proposed an active disturbance rejection controller of HESS, this strategy makes the speed of dynamic response faster and reduces the voltage fluctuation of DC bus. Reference [11] used the fuzzy PI control strategy to manage the charge and discharge of the energy storage unit accurately, suppress the voltage fluctuation of the DC bus. C. Xiang (B) · Y. Li · Q. Cheng · W. Xu Dalian Maritime University, Dalian 116026, Liaoning, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_54

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Reference [12] proposed a method to control the charging and discharging process through dual-active bridge phase shift for the HESS. However, these strategies all require the generator to charge the energy storage unit when the power is low. The high SVA of generator should be taken into account when designing the HESS. In order to solve the above problems, a control and management strategy of HESS considering the SVA of generator and the SOC of energy storage unit is proposed in this paper. The HESS can flexibly adjust the working state according to these two indexes and maintain the voltage stability of DC bus. In addition, when the SVA of the generator is greater than 100%, the output of the HESS can be controlled to provide auxiliary electric energy for the system, so as to improve the reliability and stability of SIPS.

2 Ship Integrated Power System with DC Bus A typical SIPS of DC bus architecture consists of a generator, a HESS, a propulsion motor, and a ship’s daily AC load and power converter, etc. The three-phase synchronous generator is selected in this paper, which can be combined with AC/DC to be a rectifying generator. The HESS is composed of lithium battery and super capacitor. The energy storage unit is connected to the DC bus by a bidirectional DC/DC converter. The load part is mainly composed of the propulsion load and the daily AC load. The propulsion motor is three-phase permanent magnet synchronous motor. Daily AC load is composed of lighting, ventilator, air conditioning, etc., the required threephase AC power is supplied by DC/AC inverter.

3 Energy Management and Control Strategy of Hybrid Energy Storage System 3.1 Energy Management Strategy of Hybrid Energy Storage Unit Due to the frequent changes of ship load, it is necessary to monitor the remaining energy of the energy storage unit in real time. (1)

Charging and Discharging Strategy of Energy Storage Unit In this paper, it is set that the HESS enters the charging state when both the SVA of rectifier generator is lower than 80%, the SOC of energy storage device is less than the upper limit SOChigh of the normal working area. When the SOC of the energy storage device is greater than SOChigh or the load rate of the rectifier generator is higher than 80%, the HESS switches from the charging

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Fig. 1 Schematic diagram of energy management strategy of HESS

(2)

state to the constant voltage mode, and the generator does not take the initiative to charge the energy storage device. Overcharge and Over-discharge Protection Strategy of Energy Storage Unit

When the energy storage device is in the no-charging area, it is forbidden to charge the energy storage device; When HESS is in the forbidden discharge area, the energy storage unit is forbidden to discharge. The energy management strategy of the HESS is shown in Fig. 1, where SOC refers to the state of charge of lithium battery or super capacitor in general.

3.2 Bi-directional DC/DC Converter Control Strategy The HESS is connected to the DC bus by a bidirectional DC/DC converter, which is used to control the charging and discharging of HESS to compensate the load

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Fig.2 The topology of the buck/boost converter

fluctuation and maintain the voltage stability of the DC bus. Its topological structure is shown in Fig. 2. . (1)

Control Strategy of Bidirectional DC/DC Converter In Constant Voltage Mode

The deviation between the DC bus voltage reference value U dc-ref and the actual DC voltage value U dc is output as the current reference value. I ref of the energy storage device after PI control and adjustment. The difference between the current reference value and the actual measured current value I bat/SC is made. After PI regulation and amplitude limiting, the PWM pulse switch signal is modulated and generated. Realize the charging and discharging state switch of the HESS (Fig. 3). (2)

Control Strategy of Bidirectional DC/DC Converter in Charging Mode

The set charging current I ref of the energy storage device is different from the actual measured current value I bat/SC of the energy storage device. After PI adjustment and amplitude limiting, the difference value is generated through the modulation of the modulated wave to generate the PWM pulse switch signal, so as to realize the charging and discharging state switching of HESS (Fig. 4).

Fig. 3 Dual closed-loop control block diagram of bi-directional DC/DC converter

Fig. 4 Current single-loop control block diagram of bi-directional DC/DC converter

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Fig. 5 Rectifier double closed loop control principle block diagram

4 Control Strategy of Rectifier Generator The rectifier adopts voltage/current double closed-loop control strategy, in which the outer loop is DC output voltage feedback loop and the inner loop is AC current feedback loop. The rectifier double-loop control principle block diagram can be obtained, as shown in Fig. 5.

5 Results and Analysis In this paper, the SIPS simulation model was built in the Matlab/Simulink environment. Simulation conditions are as follows: the rated power of the rectifier generator is 300 kW; propulsion motor full load 200 kW; the capacity of lithium battery is 800Ah, rated voltage is 600 V, the initial SOC is set to 50%; The capacity of the super capacitor is 500F, the rated voltage is 600 V, and the initial voltage is 300 V; The DC bus voltage rating is 720 V. Pushing load power, daily load power and corresponding the SVA of rectifier generator under various working conditions are shown in Table 1. The actual operating conditions of ships are very complex. Select five sailing conditions to analyze the dynamic response characteristics of the system in this paper. It can be seen from the analysis of Figs. 6, 7 and 8 that: (1)

At t = 1 s, the total load power increases to 200 kW. The DC bus voltage drops to 645 V, with a decline of 11%, and the transient duration is 0.3 s. When the HESS is added, the DC bus voltage drops to 700 V and starts to adjust, the

656 Table 1 Main power parameters of the system under different operating conditions

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Propulsion load power (kW)

Daily load power (kw)

SVA (%)

Condition1

50

50

33

Condition2

50

100

50

Condition3

100

100

66

Condition4

150

100

83

Condition5

200

130

>100

Fig. 6 Dynamic response curve of DC bus voltage before and after the energy storage system was added

Fig. 7 SOC waveform of HESS

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Fig. 8 Active power output of HESS and rectifier generator

(2)

(3)

(4)

decline drops to 2.7%, and the transient duration decreases to 0.2 s. The SVA of rectifier generator was 66%. The SOC of the HESS all decreases briefly and then becomes an increasing trend. When t = 2 s, the total load power is reduced to 150 kW. The DC bus voltage rises to 762 V instantaneously and then starts to adjust, increasing by 5%, and the transient duration is 0.3 s. When the HESS is added, the DC bus voltage rises to 733 V and starts to adjust, the increase decreases to 2%, and the transient duration decreases to 0.2 s. In this stage, the SVA of rectifying generator is 50% and it enters the low-load operation state again. The SOC curves of the HESS are all on the rise, but the slope becomes temporarily larger at 2 s. The energy storage unit enters the charging mode after it participates in subduing the DC bus voltage. When t = 3 s, the total load power increases to 250 kW. The DC bus voltage drops to 640 V and then starts to adjust, with a decline of 11.1% and a transient duration of 0.3 s. When the HESS is added, the DC bus voltage drops to 700 V and starts to adjust, the decline drops to 2.5%, and the transient duration decreases to 0.2 s. In this stage, the SVA of the rectifier generator is 83% and it enters the state of high load. The SOC curves all turn to an upward trend after a short decrease. The energy storage unit enters the constant voltage mode after participating in suppressing the voltage fluctuation of the DC bus. When t = 4 s, the total load power increases to 330 kW, greater than the rated power of the rectifier generator. In fact, the rectifier generator has overload protection, as shown in simulation condition 5. When there is an energy storage unit, the DC bus drops to 700 V. The DC bus voltage oscillates between 710 and 725 V. The maximum output power of the rectifier generator is 300 kW, and the excess load power is provided by the lithium battery. The SOC curve of the lithium battery continues to decrease.

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6 Conclusion This paper main research conclusions are as follows: (1)

(2)

The energy management and control strategy of the HESS proposed in this paper can effectively reduce the voltage fluctuation of the DC bus and the transient duration. The voltage fluctuation range of DC bus is reduced from 11% above the national standard to 3% within the safe range, which ensures the system. safe and stable. When switching working conditions, the HESS switches between the charging mode and the constant voltage standby mode according to the SVA of generator and the HESS SOC to maintain the voltage stability of DC bus. In particular, when the load power is greater than the rated power of the generator, The HESS can output auxiliary electric energy to make up the power shortage, which satisfied the requirements of DC bus voltage fluctuation standard.

References 1. Lan H, He B, Cheng P (2019) Fuzzy PI control strategy of marine electric propulsion system based on hybrid energy storage. Ship Eng 1(41):58–62 2. Chen C, Wang XH, Xiao JM (2014) Application of energy storage unit in marine electric propulsion system. Navig China J 37(04):25–29 3. Tang DG, Yan XP, Yuan YP (2016) Power management technology in ship’s integrated power system. Chin J Ship Res 11(1):72–79 4. Andrea C, Andrea V (2019) Open challenges in future electric ship design: high-frequency disturbance propagation in integrated power and energy systems on ships. IEEE Electrification Mag 7(4):98–110 5. Phuc H, Arijit B (2019) Integrated generator-rectifier for electric ship DC power system. In: 2019 IEEE electric ship technologies symposium, pp 592–598 6. Yang XG, Sun P (2018) Storage device for ship electric propulsion system. Navig China 41(02),9–14+62 7. Zhu W (2014) Brief discussion on integrated electric propulsion system and related technologies of warship. Marine Electric 34(12):14–18 8. Sun R (2020) Energy management of ground energy storage system of urban rail transit. Trans China Electrotech Soc 2020(01):41–43+46 9. Mao YZ, Yu MH (2018) The application of hybrid energy storage technology in the ship power grid. Ship Sci Technol 40(13):96–100+105 10. Wang TT, Sun SM (2020) Research on microgrid control strategy based on hybrid energy storage. Modern Electron Tech 43(21):119–121+126 11. Guo Y, Yu SZ, Li H, Guo JC (2019) Research on application of hybrid energy storage management strategy based on fuzzy logic for ship medium-voltage DC power system. Ship Sci Technol 17(03):172–181 12. Huang Y (2017) Research on hybrid energy storage systems for shipboard power systems. Mech Electr Equip 34(01):34–37+43

Research on Control Strategy of PV-Energy Storage System Connected to Low Voltage Distribution Network Wenqi Hao, Jiazhu Xu, Guoqing Tong, Weiming Zhang, Yuxing Liu, and Nihan Tong

Abstract In order to improve the utilization coefficient and reliability of photovoltaic (PV) power generation system and reduce the abandonment of light, the PV power generation system needs to be equipped with a certain capacity of energy storage device, to form a PV-energy storage system. This paper studies the overall coordination control strategy of the PV-energy storage system, of which is connected to the low-voltage distribution network. On the one hand, the energy storage device coordinates the balance between photovoltaic output and load power, and provides stable active power support for low-voltage distribution network. On the other hand, through the reasonable control strategy of the grid-connected inverter, the gridconnected point voltage control of the low-voltage distribution network can be realized, and the voltage quality of the distribution network of the optical storage system can be improved. Finally, the effectiveness of the proposed optical-storage-inverse coordination control strategy is verified by simulation. Keywords PV-energy storage system · Distribution power system · Coordinated control · Local voltage control

1 Introduction With the policy and economic support in China for developing sustainable energy power generation systems, nowadays, photovoltaic (PV) power generation stations have a rapidly and large growth. Among them, low-power PV power generation stations, such as PV power generations on the building roof obtained increasing attention for low cost, convenient construction and local consumption. Moreover, they can be directly connected to the low-voltage distribution network, to form an intelligent distribution network system. The intelligent distribution network system W. Hao Railway Mechanical and Electrical College, Hengyang 421002, China J. Xu (B) · G. Tong · W. Zhang · Y. Liu · N. Tong Hunan University, Changsha 410082, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_55

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can reduce the grid loss, and decrease the peak-valley difference of the power grid, and improve the economy of the power supply [1–3]. The low-voltage distribution network, as the end of generation-transmissiondistribution (GTD) power system, directly determines the power consumption level of grid users. With the rapid development of China’s economy and the improvement of residents’ living standards, the requirements for power supply quality have gradually increased. However, the low-voltage distribution network is often obsessed with seasonality, dispersion, and long-distance of load from the power source. Therefore, it is always operating with large peak-to-valley differences and unbalance of three-phase loads, its voltage quality problem is also the most prominent. At present, the low-voltage distribution network needs to absorb the electric energy of photovoltaic, wind power, and other distributed energy power generation systems, which easily leads to the voltage over-limit of the low-voltage distribution network. All of the above will affect the normal operation of power supply equipment and users’ electrical appliances, shortening their service life, and cause greater losses to users and power companies. Therefore, reasonable power compensation is required for the low-voltage distribution network. Although, the reactive power compensation is mainly concentrated in the high and medium voltage distribution network, while the low voltage distribution network has less line compensation and lacks voltage regulation measures. When the load changes greatly, it is difficult to ensure the voltage level of the grid user [4–6]. Thus, it is very important to carry out research on voltage management measures for photovoltaic systems connected to low-voltage distribution networks, which can greatly improve the power consumption level of grid users. To improve the efficiency and reliability of the PV power generation system, energy storage devices are added to the PV power generation system to form a PVenergy storage system. It can reduce abandoned light and coordinate the energy between PV power generation and output power of grid-connected inverters. This paper focuses on the control strategy of the PV-energy storage system and the gridconnected inverter. The output of the PV power generation system and energy storage are matched to provide stable active power support for the low-voltage distribution network; through the reasonable voltage control of the grid-connected inverter, the voltage of the low-voltage distribution network can be compensated. Therefore, this paper uses the cooperation of PV power generation system and energy storage device to reasonably allocate and track the active and reactive components of the required compensation power to realize the stable and controllable output power of the PVenergy storage system and the purpose of voltage control at the grid connection point. The effective use of solar energy can be ensured by the MPPT control and energy storage system [7]. Moreover, compared with traditional voltage regulation methods, the method proposed by this paper owns the advantages of active and reactive power controllable and a wider range of voltage regulation. Which can reduce the active power output and capacity of the grid-side transformer, and slow down its noise, vibration, and heat, and decrease and grid loss working in an overload state during the peak load period. Therefore, it has good engineering application value.

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2 PV Energy Storage Structure Connected to Low Voltage Distribution Network Figure 1 shows the schematic diagram of a typical PV-energy storage system connected to a low-voltage distribution network. Among them, the output power of PV is greatly affected by light and temperature, in order to effectively use solar power, the PV power generation systems are controlled with DC/DC converters, and the energy storage units are added to the PV power generation system to form a PV-energy storage system, which can smooth the PV active power output, make the PV power generation system work in the maximum power point tracking (MPPT) mode. There are a variety of topologies for PV-energy storage systems. One is that the PV power generation system and energy storage system are connected to the distribution network separately. The other is that the PV power generation system and energy storage are both connected to the DC bus to form a DC micro-grid system and then use the same grid-connected inverter. The former has the advantage of flexible control, while the latter can reduce a grid-connected inverter. Therefore, the latter topology is adopted in this paper for economic. The low-voltage distribution network is composed of power sources and loads. When the power generated by the PV power generation system is injected into the low-voltage distribution system, it can cause grid safety issues such as the over-limit voltage at the point of common coupling (PCC). However, the grid-connected voltage source inverter system itself has a certain reactive power adjustment ability, and through reasonable control, it can effectively solve the problem of grid-connected voltage over-limit. This paper is mainly to study the coordinated control strategy of the PV-energy storage system, and realize the power quality management of the low-voltage distribution network through the grid-connected voltage control strategy.

PV 1

DC/DC

PV n

DC/DC

0.4 kV

Power source

PCC VSI

Battery

DC/DC

PV-energy storage system

Load

Low-voltage Distribution network

Fig. 1 Typical PV-energy storage system connected to low voltage power system

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3 Voltage Over-Limit Principle Proposed System 3.1 Principle of Voltage Over-Limit of PV-Energy Storage System Connected to Low-Voltage Distribution Network Figure 2 shows the equivalent circuit of the PV-energy storage system connected to the low-voltage distribution network. Which U G and U S denotes to the voltage of power source and PCC, respectively. Z G and RG is the reactance and resistance components on the power supply side, respectively. PS and PL represent the active power of VSI and load, respectively. QS and QL represent the reactive power of VSI and load, respectively. According to the characteristics of low-voltage distribution network, when the influence of line distributed capacitance is ignored, the voltage drop between the power source and load can be obtained as: U˙ S − U˙ G = ΔU + δU (PS − PL )X G − (Q S − Q L )RG (PS − PL )RG + (Q S − Q L )X G +j = US US (1) In (1), the voltage drop of the low-voltage distribution network depends on the longitudinal component and the horizontal component. However, the voltage phase difference between the source and load of the distribution network line is close. Therefore, the voltage loss caused by the horizontal component can be ignored, and the voltage drop is mainly caused by the longitudinal component. The Eq. 1 can be approximated as: (PS − PL )RG + (Q S − Q L )X G U˙ S − U˙ G = ΔU = US

(2)

The low-voltage distribution network is different from the high-voltage transmission network. This is due to the impedance ratio (RG /X G ) of the low-voltage distribution network is usually higher, and the resistance component (RG ) cannot be directly ignored. Therefore, in Eq. 2, the (PS − PL )RG (the product of line active power and resistance component) will significantly affect the voltage change. That is PG、 Q G

Fig. 2 Equivalent circuit of PV-energy storage system connected to low voltage distribution power system

ZG+jXG UG

P S、 Q S

P L、 Q L US

ZL+jXL

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to say, in addition to relying on reactive power compensation to increase the voltage of PCC. The influence of active power and line resistance component RG parameters should also be fully considered. Traditional high-voltage distribution network always equip with voltage and reactive power regulation devices, such as SVG, TCR and so on. In this paper, the local voltage control strategy of the grid-connected inverter will be adopted to realize the voltage regulation at the PCC of the low-voltage distribution network, and compare with SVG, TCR and other reactive power voltage regulation methods, it has the advantage of a wider range of voltage regulation [8].

3.2 Principles of PV-Energy Storage System to Manage Voltage Over-Limit The power generated by the PV power system is depended on the light intensity, temperature and other conditions. To obtain the best power generation performance, the PV power generation system usually works in MPPT control mode. At this time, In order to ensure the active output power of the PV power generation system, the active power of VSI injected to PCC is equal to the PV generated power. However, if the active power injected into the PCC is larger than the load, the voltage of PCC will increase, it is the same that the PV power generation is less than the load, and the voltage of PCC will decreases. Therefore, when the PV power generation system is directly connected to the low-voltage distribution network, and the power control of the PV power generation system injection into the PCC is unreasonable, it will cause the problem of voltage over-limit. According to the IEEE 1547 standard, the maximum critical voltage of the distribution network voltage is 1.1 p.u, and the minimum critical voltage is 0.88 p.u. If the voltage exceeds the threshold voltage range, some measures should be taken to adjust the voltage of PCC to a reasonable voltage range. As shown in Fig. 2, The PV-energy storage system is equivalent to connecting a constant power current source here. When the load changes significantly, the power difference between the grid and the load can be provided by the PV-energy storage system. The VSI system also outputs a certain amount of reactive power to improve the power factor of the grid and compensate the reactive power of the PCC. The unique advantage of the PV-energy storage system is that as a power supply of the PV generate power and VSI output power can be adjusted by energy storage system, it can be used to solve the problem of voltage over-limit by coordinating the active power balance of the PV power generation system and the load. Reduce the abandoned light when the voltage exceeds the upper limit, increase the active output when the PV power generation is insufficient. Therefore, fully utilized both the active and reactive power control ability of the VSI.

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4 Control Strategy of PV-Energy Storage System Figure 3 shows the diagram of DC microgrid system composed of the PV and energy storage system. The DC/DC adopts a two-stage non-isolated converter, and the frontstage PV converter adopts a Boost circuit to connect the PV with DC bus. The energy storage device is connected to the DC bus through a bidirectional DC/DC converter to realize the flexible flow of energy. The latter stage converter of DC/AC adopts a threephase full-bridge inverter circuit, which connects the DC bus and the low-voltage distribution network through a filter circuit. As aforementioned that both active and reactive output power regulation can effectively stabilize the voltage of the distribution network. When there is a voltage over-limit at the PCC of the low-voltage distribution network, the VSI system needs to provide reactive and active power support to control the voltage of the distribution network. At the same time, the output power of the PV-energy storage system needs to be changed in real time. In order to reduce the grid loss, so as to achieve the greatest economic benefits. The active output power of PV-energy storage system should be as large as possible [9]. Power source PG+QG

PCC PL+QL

PV

MPPT

PS+QS

Upv, Ipv DC/DC Battery Ubat Ibat

VSI

DC/DC voltage control

Charge and discharge control SOC estimate

Fig. 3 The control strategy of PV-energy storage system

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4.1 Control Strategy of PV-Energy Storage System In order to improve the operating efficiency of the PV power generation system, the DC voltage level of PV side is generally lower than the output voltage of DC bus, so its power control is mainly realized through the control of a Boost converter. Boost has three working modes: MPPT, constant voltage and idle mode. When the light is sufficient and the active power can be absorbed by the load or the energy storage, the Boost converter works in MPPT mode; however, if the generated power of the PV system cannot be absorbed immediately, the Boost converter works in the constant voltage control mode, when the at night or insufficient light, the Boost converter works in the idle mode. Figure 4 shows the control strategy of the PV converter system. The output voltage and output current signals of the PV cell are collected. And the PV converter is controlled with PI controller, which is designed with voltage outer-loop and current inner-loop. In MPPT mode, out-loop of voltage is used to control the voltage of PV (U pv ), the reference voltage of the U pv is calculated by maximum power point tracking (MPPT) methodes. In constant voltage mode, out-loop of voltage is used to control the voltage of DC bus (U dc ), the reference voltage of the U pv can be calculated by PI control of difference of set U dc and measured U dc , The inner-loop current PI controller is adopted for improving the response speed. Finally, to obtain the duty-ratio and PWM control signal. The constant voltage control mode can keep the solar energy utilization rate above 92%, while maintaining the stability of the system, it is more suitable for small PV power generation systems. DC bus

PV Upv, Ipv

Udc DC/DC

Upv, Ipv

MPPT

Udc_ref

+ − Upv + − Udc

Fig. 4 The control strategy of PV converter

PI

MPPT

Ip_ref +

idle PI

Constant voltage

d − Ip

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4.2 Battery Charge and Discharge Control Since the common used bidirectional DC/DC converters are divided into two categories according to their characteristics and structures, which is non-isolated and isolated structure. Isolated converters can achieve electrical isolation between the two stages of the converter through an isolation transformer, and they are suitable for high-power transmission circuits. But, this structure is relatively complicated and not easy to control. The non-isolated converter has no electrical isolation part. However, its structure is relatively simple, small, and easy to control. For that the low-voltage distribution network and does not require electrical isolation, so a typical non-isolated Buck/Boost bidirectional converter is applied in this paper. Since the energy storage system (battery)’s role is to balance the power generated by the PV and the output of VSI, so it needs to work in both charging and discharging state. Figure 5 shows the charging and discharging control strategy of energy storage system. To prolong the life of battery, the state of charge (SOC) of battery should be fully concerned, Generally speaking, the battery will not be damaged, if it is used within a reasonable SOC range, and To suppress the voltage fluctuations of the DC bus, at this time, the Battery is controlled with constant voltage control mode, the charging and discharging power of the energy storage is controlled by a bidirectional DC/DC converter. When the SOC is lower than the lower limit, it can only work in the current-limiting charging mode, and when the SOC is higher than the upper limit, it can only work in the current-limiting discharge mode. Fig. 5 The charging and discharging control of energy storage system

S1 Ib Battery

Pb_ref

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Ibref

S1

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PI

S2

S1 S2

> Ib -1 Current limit discharging mode Udc_ref

PI Udc

PI Ib

Constant voltage control mode

S1 > -1

S2

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Ubat =

ton

667

ton ton Udc = Udc = αUdc + to f f T

(3)

When the battery is discharged, turn off, the duty cycle of the control can be obtained: Udc =

ton + to f f T 1 Ubat = Ubat = Ubat to f f β to f f

(4)

4.3 Control Stragegy of Grid-Connected Inverter Figure 6 shows the power compensation diagram of the VSI. According to the previous analysis, the control strategy of the grid-connected inverter of the PV-energy storage system determined the overall performance of the PV-energy storage system. To effective solve the problem of voltage over-limit in the PCC of low-voltage distribution network, it is necessary to reasonably control the active and reactive power output by the VSI. The grid-connected inverters connected to the low-voltage distribution network generally adopt the PQ control method. According to the instantaneous reactive power theory, the formula for calculating active power and reactive power output by the inverter can be expressed as ⎧ ) 3( ⎪ ⎨ PS = Usd Isd + Usq Isq 2 ⎪ ⎩ Q = 3 (U I − U I ) S sq sd sd sq 2

iG PG+QG

iL iS

PS+QS

UG

US

PV

Fig. 6 The power compensation diagram of VSI

(5)

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Udc_ref

PI Udc Qref

usd

isd_ref

STATCOM mode 2/3Usd+

PI

isd

ωLs

isq

ωLs

isq_ref

us,abc

M W P V S

abc dq

PI usq

Fig. 7 The control strategy of grid connected inverter

When the active power output of the PV system is insufficient, the VSI can also be used as a STATCOM device for reactive power compensation and power quality management. Figure 7 shows the overall power control strategy of the grid-connected VSI. It is necessary to detect the voltage, current, and power of the load of a low-voltage distribution network. And then judge the active and reactive power of the PV-energy storage system to meet the power compensation requirements. When at night, the PV system is work in idle mode, and power of the energy storage system is also insufficient. Therefore the VSI can switches to the STATCOM mode. At this time, the reference current of the VSI can be obtained by outer-loop voltage PI controller, and the reactive power is given by the compensated power detected by the system. Finally, the given value of the current of the VSI is calculated through the given value of active and reactive power, and then, the terminal voltage is obtained through the d–q current decoupling control. Finally, the PWM modulation signal is generated by the space vector modulation method.

4.4 Voltage Control Strategy of VSI If ordinary PQ control is used, it may cause the voltage of PCC exceeding the limit. Therefore, it is necessary to set a reasonable voltage control strategy for the gridconnected VSI, so as to get the reasonable value of active and reactive power of VSI to control the voltage of PCC. When the voltage of PCC is lower than 0.88pu, the active output of the VSI should increase. When the voltage of PCC is higher than the rated value of 1.1pu, the active output power of the VSI should decrease, if the power generated by PV system is more than the output power of VSI, these exceed active power can be storage to the battery. At this time, the PV power generation system can still work in MPPT mode, which can reduce the waste of photovoltaic energy. Set the apparent power of the grid-connected VSI to SS , which can be obtained as

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669 2 Pref = S S2 − Qref

Us,up

PI Qmax=SS

Us

Us,down

Pref

2 Qmax = S S2 − PPV

Qref

PI

Fig. 8 Voltage control strategy of grid connected VSI

SS =

/

Q 2S + PS2

(6)

where QS is the reactive power generated by the grid-connected inverter, and PS is the active power generated by the grid-connected inverter. Figure 8 shows the voltage control strategy of the grid-connected inverter. When the voltage exceeds the upper limit, the difference between the given maximum voltage and the current voltage is controlled by PI regulator to get the required inductive reactive power. But the inductive reactive power cannot exceed the apparent power of the grid-connected VSI (S S ). When the voltage exceeds the lower limit, the active power compensation also can increasing the voltage of PCC. Therefore, the active power Pref at this time can be set as / the generated power of PV (PPV ). Therefore,

the given reactive power is limited by SS2 + PP2 V . After the given reactive power is determined, the given active power can be calculated by Eq. 6. The overall control strategy of the PV-energy storage and its grid-connected system is more flexible than the traditional PV system due to the addition of the energy storage system. In this paper, the PV arrays can always work in the MPPT mode when the energy storage system is not fully charged. But when the energy storage is full (SOC greater than 80%), it needs to run at reduced power mode (constant voltage mode). At night, the photovoltaic array will work in an idle state. The battery carries out reasonable charge and discharge control according to its SOC state. In order to effectively extend the service life of the battery, when SOC of the energy storage system is greater than 20%, it provide a certain amount of active power support for the grid-connected inverter. If the energy storage is insufficient, the grid-connected inverter will work in STATCOM mode, which fully uses the reactive power regulation capability of the grid-connected inverter.

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5 Simulation In this section, a simulation model of PV-energy storage system connected to the low-voltage (380 V) distribution network is established using the simulation software MATLAB/Simulink. Which is used for verified the control strategy proposed by this paper. The detail simulation parameters are shown in Table 1, and the voltage of the DC link is set to 700 V. On the basis of theoretical analysis, this paper proposes a control strategy based on the PV-energy storage systems connected to the low-voltage distribution networks, builds a equivalent system model, and the coordinal control of PV-energy storage system and the voltage control method is verified through simulation, and the simulation results are analyzed, and the conclusions are obtained. (1)

Simulation of the PV power generation system

Figure 9 shows the simulated waveform of PV arrays under condition of changes in light intensity and temperature. As the light and temperature change, the output power of PV array the photovoltaic converter is still working in the MPPT mode. This verifies the effectiveness of the MPPT control mode. (2)

DC voltage control simulation of PV-energy storage system

To simulate and verify the DC voltage control strategy of the DC microgrid composed of a PV-energy storage system. As shown in Fig. 10, the light intensity and temperature of the photovoltaic cell are respectively set to 1000 W/m2 and 25 °C. At this time, the PV array is working in the MPPT mode, and the input power is 24.8 kW. Table 1 The simulation parameters

System

Parameters

Values

PV system

Open circuit voltage/V

64.2

Short-circuit current/A

5.96

Voltage of max power point/V

54.7

current of max power point /A

5.58

Seris connected components

8

Parral connected components

8

Grid voltage/V

380

Parral connected components

8

Grid voltage/V

380

Grid frequency/Hz

50

Grid side impedence/Ω

0.02

Filter reactor/mH

2.4

VSI

Battery

Capacitor of DC bus/mF

4

Rated voltage/V

360

Rated capacity/Ah

50

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Power(W)

Tempretur e(°C)

Solar (W/m2)

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Time(s) Fig. 9 The simulated waveform of PV arrays

Figure 11 shows the active power of the grid-connected inverter is set to 30 kW, 20 kW, and 10 kW in 1 s, 2 s, and 3 s, respectively, and the reactive power is set to 0 kW, 10 kW, and 20 kW in 1 s, 2 s, and 3 s, respectively. Therefore, the compensation power of VSI is unbalanced with the power generated by the PV system. However, according to the control of the energy storage system, the simulation result of DC bus voltage in Fig. 12 shows that the DC voltage can maintain the set value (700 V) stability.

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Fig. 10 The simulated waveform of photovoltaic array

Time (s)

Power(W)

(a) Simulation waveform of active power of VSI

Time (s)

(b) Simulation waveform of reactive power of VSI Fig. 11 The simulated waveform of VSI

(3)

Simulation of the voltage control of VSI

Figures 13 and 14 show the voltage and current waveforms at the PCC of the lowvoltage distribution network using traditional power control strategies and voltage control strategies, respectively. In Fig. 13, the output power of the grid-connected inverter is 30 kW. The active power of the load is set to 0.5 kW, 30 kW, and 50 kW in 0–1 s, 1–2 s, and 2–3 s, respectively. It can be seen that when the output power of VSI is larger than the load, the voltage of PCC will be increased to over-limit. When the

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Time (s)

Fig. 12 The simulated waveform of DC voltage

1.1pu

Votage(V)

0.88pu

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Fig. 13 The waveform of power grid based with traditional control strategy 0.88pu

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1.1pu

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Fig. 14 The waveform of power grid based with local voltage control strategy proposed in this paper

output power of VSI is lesser than the load, the voltage of PCC will be also decreased to over-limit. However, if the voltage control strategy of VSI is adopted, as shown in Fig. 14, the active output of the VSI will decrease in 1 s, and increase the reactive output in 2 s, so that the voltage of PCC can maintain within the normal range (0.88– 1.1 pu). Therefore, the effectiveness of the grid-connected voltage control strategy is verified.

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6 Conclusion On the basis of theoretical analysis, this paper proposes a control strategy based on the PV-energy storage system connected to the low-voltage distribution networks, builds a equivalent system simulation model. After that, the control strategy of PV-energy storage system and voltage control method of VSI is verified, and the following conclusions are obtained: (1)

(2)

(3)

The hybrid system composed of PV power generation and energy storage device can effectively balance the power between PV and output power of VSI; The voltage at the PCC of VSI may change greatly, if the grid-connected inverter output power and the load are not balanced, and the voltage at PCC may be over-limit. The voltage control strategy proposed in this paper can effectively prevent the voltage over-limit and has a good voltage stabilization function; The PV-energy storage systems can effectively improve the power quality of the low-voltage distribution network and reduce the corresponding investment of reactive power compensation.

References 1. Iziomon MG, Mayer H (2002) Assessment of some global solar radiation parameterizations. J Atmos Solar-Terrestrial Phys 64(15) 2. Shu YS, Ma LL, Peng C (2013) Study on project of photovoltaic power plant connecting to the grid. Appl Mech Mater 2617(380) 3. Kotra S, Mishra MK (2015) Energy management of hybrid microgrid with hybrid energy storage system. In: 2015 International conference on renewable energy research and applications (ICRERA), pp 856–860 4. Liu B, Zhuo F, Zhu Y, Yi H (2015) System operation and energy management of a renewable energy-based dc micro-grid for high penetration depth application. IEEE Trans Smart Grid 6(3):1147–1155 5. Mishra MK, Karthikeyan K (2007) Design and analysis of voltage source inverter for active compensators to compensate unbalanced and non-linear loads. In: 2007 International power engineering conference (IPEC 2007), pp 649–654 6. Remache S, Remache SEI, Barra k (2019) Algeria power management of grid connected PV system with integrated energy storage. In: 2019 1st International conference on sustainable renewable energy systems and applications (ICSRESA), Tebessa, Algeria, pp 1–6 7. Shi S, Zhang Y, Fang C, Wang Y, Ni A, Fu Z (2019) Energy management mode of the photovoltaic power station with energy storage based on the photovoltaic power prediction. In: 2019 6th International conference on systems and informatics (ICSAI), Shanghai, China, pp 319–324 8. Ming W, Meng N (2011) The design of a new system of PV-energy storage grid-connected generation. In: 2011 International conference on electrical and control engineering, Yichang, China, pp 5061–5064 9. Palomino E, Stevens J, Wiles J (1996) A control system for improved battery utilization in a PV-powered peak-shaving system. In: Conference record of the twenty fifth IEEE photovoltaic specialists conference, Washington, DC, USA, pp 1525–1528

In the Electricity Market Environment for the Industrial Park Electrical Energy with Energy Optimization Strategy Xiaoxuan Guo, Shuai Han, Leping Sun, and Wanlu Wu

Abstract In March 2021, National People’s Congress and Chinese People’s Political Consultative Conference of China proposed “carbon neutral”, “carbon peak” target, due to the abundant resources of coal, thermal power is the main power generation in China. In order to achieve the “carbon peak” and “carbon neutral” goals as scheduled, as the demand side of electricity consumption, vigorously develop new energy sources, and the development and utilization of clean energy has become the focus of current research and practice. In order to maximize the use of solar and wind energy, the article optimizes their quantity. When the large power purchase, in order to further reduce purchase cost, demand-side user should consider the different tariff periods under reasonable deployment load, and wind and solar energy storage system to achieve cost optimal. Articles of the park load energy, wind machines, light-volt energy storage hybrid power supply system is modeled analysis, Using differential evolution algorithm, to calculate the wind machine light volt number generating means. By Matlab simulation analysis platform, the optimal fans, solar and battery quantity, and reduce the amount of electricity after the load dispatching costs. Keywords Load allocation · Optimal energy storage · Differential evolution algorithm · Optimal cost

1 Introduction The optimization model of the power grid, wind power, photovoltaic, and battery hybrid power supply system is of great significance to improve the utilization efficiency of renewable energy, promote the consumption of renewable energy, and achieve the goal of reducing carbon emissions [1–3]. The academic research of Wang Hao and others is focused on how to better and more economically use energy

X. Guo (B) · S. Han · L. Sun · W. Wu Electric Power Research Institute, Guangxi Power Grid Corporation, Nanning 530023, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_56

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storage to realize energy transfer across time under multiple energy forms, coordinate the source-load imbalance in the network, smooth the output of new energy, and restrain its power fluctuation. But there is no further optimization of integrated energy allocation [4]. This article based on typical daily load curve industrial park, wind and solar energy output data of the monitoring and analysis, power grid, wind power, photovoltaic, battery hybrid power supply joint optimization model. Discussed the relationship between the battery cost and the cost of purchasing electricity from the large grid, and perfected the aspects that were not discussed in the literature [5]. Through Matlab simulation, a feasible equipment distribution plan and load dispatching plan were put forward to optimize the park’s electricity bill.

2 Optimal Modeling of Park Power Consumption in the Power Market 2.1 Park Hybrid for Power System Optimization Object Modeling This article focuses on the expenditure of electricity bills in industrial parks. In the context of “carbon neutrality” and “carbon peaking”, the park should try its best to reduce the use of electricity generated by traditional coal. Use as much electricity as possible from the photovoltaic and wind turbine equipment in the park. Reduce the use of traditional energy, let clean energy gradually replace traditional energy, and make due contributions to the early realization of “carbon neutrality” and “carbon peaking”. Therefore, this model puts the electricity generated by photovoltaics and wind turbines in the first echelon of use, when photovoltaic energy, the load is greater than the energy delivered by the fan is required, the excess electrical energy stored in batteries. During periods of insufficient sunlight and wind, the electric energy stored in the battery needs to be released, and if it is insufficient, it is necessary to purchase electricity from the large grid to ensure the stable operation of the load. Through optimization, the most economical power plan can be obtained on the premise of meeting the power requirements of the park. Figure 1 shows wind and solar energy hybrid power supply system configuration diagram, the main apparatus including wind power systems, photovoltaic systems, batteries, power and load controllers. Wind power generation system A large amount of experimental data shows that the instantaneous power generation of a wind turbine is related to wind speed, and the specific relationship is as follows [6, 7]:

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Distributed controller

Wind power

Transfer able load

Solar power Load controller

Battery

Transfer able load

Inverter

Load

Load

Power grid

Load

Fig. 1 Structure diagram of hybrid power supply system of wind and solar power grid

⎧ ⎪ ⎨ 0, v ≤ vi , v ≥ v0 i , vi ≤ v ≤ ve Pw = pe vv−v e −vi ⎪ ⎩ p ,v ≤ v ≤ v e e 0

(1)

In the formula, v is the hub height of the wind speed of the blower wheel; vi is cut wind machine Winds; v0 is cut out the fan wind speed; ve is rated wind speed; pe is rated output power. Photovoltaic power generation system The output power of the photovoltaic power generation device can be expressed by the following formula [8]: pg (t) = N g ηg PST C

Ir (t) + β(T A + 0.02Hθ − Tt ) I ST C

(2)

In the formula, pg (t), and Ir (t) are shown as t the electric power and light intensity output period, N g shows the number of photovoltaic power generation system photovoltaic panel, ηg showing the power generation efficiency of the system. I ST C , PST C respectively expressed as the light intensity and rated power under standard test conditions. β is the inclination angle of the photovoltaic solar panel, T A is the ambient temperature, Hθ is the total solar radiation on the solar panel, and Tt is the standard temperature, which is 25 ◦ C.

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Power storage device The photovoltaic power and wind power generation are combined and calculated below. Pt (t) = Pw (t) + Pg (t)

(3)

In the formula, Pt (t) is the power supply of the wind-solar hybrid system at time t. In this system, the energy of the battery changes dynamically. When the total output power of photovoltaic and wind power is greater than the load power, the battery is in a charged state; when the total output power of photovoltaic and wind power is less than the load power, the battery is in discharging Status. The battery charge at time t is expressed as [9]:  Pb (t) =

Pb (t − 1) − (Pt (t) − Pηdinv(t) )ηb Pb (t − 1) − ( Pηdinv(t) − Pt (t))

(4)

ηinv and ηb respectively efficiency of the inverter and the charging efficiency of the battery; Pd (t) as t load required time; for the battery at t time the stored energy, Pb (t) − Pb,min (t) for the battery at t energy available time, Pb,min (t) for the SB minimum predetermined Energy storage.

2.2 Optimize the Objective Function The objective function minF is to meet the park under the premise of performance indicators, the electrical charges and wind photovoltaic power generation system, battery system operation and maintenance costs to a minimum [9]. min F = min(Cw + C g + Cb + Cd )

(5)

In the formula, F is the total cost of the system; Cw ,C g ,Cb , and Cd are the costs of wind power generation system, photovoltaic power generation system, storage battery system, and power purchase from the large power grid. Cw =

wi Pi

⎤ r0 (1 + r0 )n + u(P ) i (1 + r0 )n − 1

g j Pj

r0 (1 + r0 )n + u(P j ) (1 + r0 )n − 1

w ⎡ Σ i=1

Cg =

g ⎡ Σ j=1

(6)

⎤ (7)

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Cb =

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⎤

b ⎡ Σ

bk Pk

k=1

N (t) =

r0 (1 + r0 )n + u(Pk ) (1 + r0 )n − 1

Pd (t) − Pt (t) − Pb (t) ηinv

Cd = Pt ∗ N (t) ∗ Δt

(8)

(9) (10)

In the formula, w, g, b are the number of wind power generation systems, photovoltaic power generation systems, and batteries; wi , g j , and bk are the units of the i, j, and k-th wind power generation systems, photovoltaic power generation systems, and batteries, respectively Cost;Pi ,P j ,Pk are respectively the i, j, and k-th wind power generation system, photovoltaic power generation system, and battery capacity; u(Pi ), u(P j ), u(Pk ) are corresponding in maintenance and operating costs; n is provided apparatus depreciation period; r0 is the discount rate. Pt is t tariff period, Nt is t time interacting with the power grid, Δt is the time interval. The transferable load model is expressed as follows: ⎧ N2 N1 h max Σ Σ−1 Σ ⎪ ⎪ Nin (t)P1,n + Nin (t − h)P(h+1),n ⎨ Q in (t) = n=1

h=1 n=1

N2 N1 h max Σ Σ−1 Σ ⎪ ⎪ ⎩ Q out (t) = Nout (t)P1,n + Nout (t − h)P(h+1),n n=1

(11)

h=1 n=1

h max ≥ 2 In the formula, Q in (t), Q out (t) are the load in and out of time period t, Nin (t), Nout (t) is the number of turning in and out units in time period t; N1 is the total number of transferable load types; N2 is the total number of transferable loads whose power supply duration is greater than a dispatching period; P1,n is the n-type transferable load 1 h and power; P(h+1),n Is the power of class N transferable load in the period h + 1 within its continuous power supply time; Nin (t − h), Nout (t − h) is the number of class n load units transferred and transferred out in h + 1 period; h max is the maximum number of continuous power supply hours, h max ≥ 2. The use time of non-transferable loads is determined, and the power consumption is set by the park itself. The electricity consumption model is as follows: 

Pct = xct Pcrated E c = Pcrated dc

(12)

In the formula, c ∈ C represents non-transferable loads, including production equipment and air conditioners that need to work 24 h a day. Pct represents the power of load c at time t; xct represents the status of load c at time t; Pcrated represents the rated power of load c; E c represents the total power consumption of load c; dc represents the length of working time of load c.

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2.3 Model Constraints Constraints on the operating characteristics of batteries [9] 

Pb,min < Pb,soc < Pb,max Pb < Pb,cap,max

(13)

In the formula, Pb is the change in battery power per hour; Pb,cap,max is the maximum amount of energy specified in the battery per hour; Pb,min is the minimum required power of the battery; Pb,max is the battery’s maximum power. Wind power, photovoltaic, and battery quantity constraints. ⎧ ⎨ 0 ≤ Nw ≤ Nw,max 0 ≤ N g ≤ N g,max ⎩ 0 ≤ Nb ≤ Nb,max

(14)

In the formula, Nw,max , N g,max , Nb,max means of wind power, solar, battery, respectively, by a number that satisfies the required park load demand. Constraints on the inclination of photovoltaic solar panels. 0◦ < β < 90◦

(15)

Interaction power constraints with large power grids: Ntmin ≤ N (t) ≤ Ntmax

(16)

Ntmin and Ntmax are the minimum and maximum values of the power grid and load interaction, respectively. Observing the above constraints, we can see that all constraints satisfy the following form: x j,min ≤ xi, j ≤ x j,max

(17)

In this form, in the process of using the differential evolution algorithm, when the generated particles do not meet the constraint conditions, the following formula can be used for processing [9]  xi, j =

x j,max xi, j > x j,max x j,min xi, j < x j,min

(18)

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3 Improved Differential Evolution Algorithm 3.1 Improved Differential Evolution Algorithm Algorithm extension model The DE/current-to-best/2/bin strategy is used to generate the difference vector, which is characterized by maintaining the diversity of the population while emphasizing the convergence speed of the algorithm. t t t t t Z i,t+1 j = X i, j + Fac(X best, j − X i, j ) + Fac(X r 1, j − X r 2, j )

(19)

t t X best, j is the optimal individual in the population. X i, j is the i-th individual in the population of generation t.

Algorithm extension model Variability factor Fac larger facilitate efficient, rapid global search and optimization for the initial optimization; by the post-optimization stage, a large variation factor against local algorithm searches search. Herein variability factor from 0.8 to 0.5 decreases linearly. Fact = Fac1 − (Fac1 − 0.5)

t Np

(20)

In the formula, Fact is the variation factor of the t generation; Fac1 = 0.8.In the initial optimization, a small hybrid factor can improve the local search; and optimization at a later stage, the larger hybrid factor can prevent local optimization algorithm, thus Dynamic herein hybrid factor 0.3 to 0.6 linearly increasing, formula (14), in which c1R = 0.3. ctR = c1R + (0.6 − c1R )

t Np

(21)

In the formula, N P is the population size. By comparison, it is concluded that the original difference algorithm needs 50 iterations to obtain the optimization result, while the improved difference algorithm only needs 30 iterations to obtain the optimization result. The following examples will prove this point.

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Set optimization dimension, population number, maximum number of iterations, and initial population.

N

the number of iterations is reached ?

Calculate the optimal individual in the population Y According to the variation operation of Equations (21) and (25) According to the crossover operation of Equations (22) and (23)

Output solar panel inclination, number of solar panels, number of fans, and total cost

Select operation End

Fig. 2 Improved differential algorithm main program flow chart

4 Optimize the Calculation Process The implementation steps of the improved difference algorithm to optimize the hybrid power dispatching in the park are as follows (Fig. 2):

5 Calculation Example Analysis This paper analyzes a grid-connected wind and solar power supply park in Nanning, Guangxi (22.5° north latitude).During the four seasons of the year, the sunshine amount of a typical day in each season is selected to approximate the sunshine data of the quarter. The research of Yang [9] showed that the inclination angle design of photovoltaic solar panels is different from the local latitude. Based on this, in order to improve the optimization speed, the following simulation will limit the solar panel inclination range to 10°–30°, and further explore the impact of other factors on the total cost. The evolutionary differential algorithm is used to optimize the number of photovoltaics and the number of wind turbines. At this time, no storage battery is added, and the stable operation of the system is maintained by the large power grid. The optimization process is shown in the Fig. 3. According to the optimization results, the number of photovoltaics is selected at 2800, and the number of wind turbines is selected at 12. At this time of the year for the total amount of PV 13.53 million kWh, the total amount of fan power is 62.85 million kWh, the purchase of electricity from large power 35.48 million kWh. In the periods when the output of wind and wind is relatively weak, in order to maintain the stability of the system, it is mainly dependent on the electric energy input of the large power grid to the park. After calculation, it is found that the total energy provided by wind, light, and power grid is 111.86 million kWh, while the total demand for load is only 52.73 million kWh. In order to make good use of this part of the discarded energy

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Fig. 3 Number PV optimization process

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3000

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2000 0

5

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and further reduce the purchase of electricity from the large grid, it is necessary to introduce a battery energy storage structure into the system. From Fig. 4 can be clearly seen, with the increase in the number of batteries, the battery cost (including the cost of discounts) increases linearly. The cost of purchasing electricity from the grid decreases as the number of batteries increases. Because when there is no battery storage system, when the wind and solar hybrid power supply system is insufficient, the shortage of electricity is supplied by the grid, and the electricity bill is relatively high. 7000

Electricity free Battery cost Sum

Cost / Ten thousand Yuan

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0

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Fig. 4 Relationship purchase cost and battery

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When the battery is added, the excess power during the day can be stored by the battery, and then released by the battery at night. However, the excess power generated by wind and wind power generation during the day is not stable. When the park load is basically stable, the weather will affect the total amount of wind and wind power generation. At night, the electricity stored in the battery during the day is not enough to make up for the power supply gap of the hybrid power supply system, and electricity needs to be purchased from the large power grid. Therefore, the reduction in the cost of purchasing electricity from the grid is getting smaller and smaller, and finally tends to be flat. At this time, increasing the number of batteries will not reduce the cost of electricity purchase, but will increase the cost of batteries. According to the simulation results, the number of batteries set to 60, the battery capacity was 840,00 kWh, best value for money. When the number of devices reaches the optimal level, some optimizations can be performed on the power user side. It is possible to transfer some of the transferable loads to the time period when the electricity price is lower as much as possible, and perform appropriate peak shaving and valley filling. Consider that electricity prices are lower at night and higher during the day. On the basis of the original load, the use of some transferable loads (such as disinfection cabinet, equipment needing charging in the park, whose maximum transferable power is 1800 kW) is dispatching from daytime to after 0:00, at which time the electricity price is 0.43 Yuan/kWh. Some equipment that does not need to run 24 h a day is scheduled for off-peak hours as much as possible. Avoid the peak load is too high, the lack of photovoltaic power supply resulting in high electricity purchase costs. The generation of the adjusted load the simulation model calculations, the experimental data obtained in Fig. 5, by adjusting the load, electricity compared to decrease Power charge after dispatch Power charge before dispatch Cost of batteries and accumulators after dispatch Cost of batteries and accumulators before dispatch

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preload scheduling. Some will be moved to the load transfer nighttime scheduling schemes may have effect to reduce electricity bills.

6 Conclusion (1)

(2)

(3)

After optimization, the optimal inclination design of photovoltaic solar panels is 20° (local latitude 22.5°), the number of photovoltaic panels is 2800, and the total photovoltaic power generation in a year is 13.53 million kWh. The number of fans is 12, and the total power generated by fans is 62.85 million kWh. Through the analysis of the relationship between the power purchase cost and the number of batteries, it can be seen that the total cost of both decreases first and then increases with the number of batteries, and the economic cost is optimal when the number of parallel batteries is 60. In the user demand side management, by transferring the transferable load to use at night, also achieve the purpose of reducing electricity consumption. After calculation, when using 60 groups of batteries, the electricity charge after dispatch is about 700,000 yuan less than that before dispatch in a year.

References 1. Zhang MZ, Huang YC, Wang M (2019) Optimization of wind power configuration in distribution network based on scenario clustering and power flow entropy. In: Proceedings of 2019 international conference on power, energy, environment and material science (PEEMS 2019), pp 587–591 2. Wang C, Chen S (2019) Optimization strategy of constant power peak cutting and valley filling for battery energy storage system based on variable smoothing time constant. In: Proceedings of 2019 3rd scientific conference on mechatronics engineering and computer science (SCMC 2019). Francis Academic Press, pp 388–393 3. Merei G, Leuthold M, Sauer DU (2013) Optimization of an off-grid hybrid PV–Wind–Diesel system with different battery technologies using genetic algorithm. Solar Energy 97:11–12 4. Wang H, Zhang S, Li W, Tang Y, Gao Z (2020) Survey of energy storage used in power system application. Electr Eng 3:21–24+27 5. Wei H, Ting H, Huan Z, Guannan W, Yiping C (2014) Dynamic economic optimal dispatch of microgrid based on improved differential evolution algorithm. Autom Electric Power Syst 38(09):211–217 6. Yu W, Liu S, Chen Q, Zhang C (2017) Multi-objective optimal dispatching method for photovoltaic microgrid considering demand-side management. Acta Energiae Solaris Sinica 38(11):2972–2981 7. Jiangzhou C, Zengcheng R (2021) Optimal dispatch of microgrid segmented hybrid strategy considering power quality coefficient. Renew Energy Resour 39(02):215–221 8. Yang Q, Zhang J, Liu Z, Xia S, Li W (2009). Multi-objective optimization of hybrid PV/wind power supply system. Autom Electric Power Syst 33(17):86–90 9. Meng X (2011) Power system reactive power optimization including wind farms based on improved differential evolution algorithm. Hebei Agricultural University, MA thesis

Stackelberg Game Optimal Scheduling of User-Side Energy Storage Considering Source-Load Uncertainty Kui Luo, Zhidong Guo, Tao Rui, and Cungang Hu

Abstract Aiming at the distributed energy storage optimal scheduling problem considering source load uncertainty, a user side energy storage stochastic optimal scheduling strategy considering master–slave game is proposed in this paper. This method comprehensively considers the uncertainty of photovoltaic (PV) power generation and user side load, and constructs a Stackelberg game model with distribution network operators as leaders and user side as followers. By solving the internal optimal electricity price, the electric energy interaction between the user side and distribution network operator (DNO) is stimulated. While improving the operation economy of both sides of the game, promote the consumption of renewable energy at the distribution network side. At the same time, the optimal scheduling plan of user side energy storage is obtained. The example results show that the optimization method proposed in this paper can effectively adapt to PV power consumption and improve the operation economy and stability of distribution network operators and users. Keywords Distribution side system · Source-load uncertainty · Stochastic optimization · Stackelberg game

1 Introduction The large-scale application of renewable energy is of great significance to alleviate the shortage of fossil energy and accelerate the realization of carbon peak and carbon K. Luo State Key Laboratory of Operation and Control of Renewable Energy & Storage Systems, China Electric Power Research Institute, Beijing 100000, China Z. Guo · C. Hu (B) School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] T. Rui · C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei 230601, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_57

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neutralization [1]. The uncertainty of renewable energy output has a certain impact on the safe and stable operation of power system. Due to its easy integration and flexible interaction, distributed energy storage can better solve the adverse impact of randomness and fluctuation of renewable energy output on the normal operation of power grid [2, 3]. Among them, the user side distributed energy storage plays a more direct and efficient role in adapting to renewable energy consumption. The distributed energy storage equipment on the user side can improve the power supply reliability of the system, help to implement the time of use price response mechanism and expand the response capability on the demand side [1, 3]. Under the background of opening the power market, more and more energy storage systems will be connected to the power system in the form of decentralized investment. A large number of distributed energy storage will be connected to the power grid disorderly as random disturbance power supply, which will interfere with the safe and stable operation of the system side. For the user side, the lack of effective energy storage scheduling strategy will lead to the loss of users’ own economic benefits. In order to further optimize the charging and discharging behavior of end-user energy storage devices in user side microgrid, an optimization model of TOU price in user side microgrid is proposed [4]. Reference [5] presents a method to facilitate users’ decision-making in demand response participation by using several resources especially energy storage systems. In the power market transaction, the distribution network operator, as a power selling company, ensures its own interests in the power market by formulating reasonable purchase and sale price, and guides the market entities to participate in the power transaction reasonably. This transaction process can be described by a Stackelberg-game model. The Stackelberg-game game theory has been applied in the study of power market considering the user side [6, 7]. Based on the above analysis, this paper establishes a distribution network and user side energy management system with multi market players and distributed PV power generation, and proposes a stochastic optimal scheduling strategy of user side energy storage based on master–slave game to optimize the above model. In view of the uncertainty of PV power generation and load forecasting error, this method uses Latin hypercube sampling theory to transform the certainty of chance constrained model, and establishes a master–slave game trading framework with DNO (distribution network operator) as the leader and user side as the follower. In this framework, DNO formulates the time-of-use transaction price within the model, and the user side responds to the price. In this paper, differential evolution algorithm is used to solve the master–slave game model, which maximizes the interests of both sides of the game and promotes the local consumption of renewable energy in the distribution network. Finally, an example is given to verify the effectiveness of the proposed method.

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2 Stochastic Optimal Scheduling Model for Distributed Energy Storage The system structure of distribution side studied in this paper is shown in Fig. 1. The main body of the market is composed of DNO with ownership of renewable energy PV power generation system and users with energy storage. The Stackelberg game is used to optimize the transaction behavior between distribution network and users. DNO, as the leader of the game model, not only considers the uncertainty of the system’s internal load, but also establishes a reasonable internal time-of-use transaction price. When the PV power generation is sufficient, it encourages users to store as much excess electricity as possible by reducing the electricity selling price of the distribution network; When the PV power generation is insufficient, we can encourage users to sell as much electricity as possible by increasing the power purchase price of the distribution network, so as to reduce the electricity transaction between the distribution network and the large power grid, reduce their own operating costs, and realize the local consumption of PV. As the follower of the game, users adjust their electricity consumption behavior according to the transaction price of the distribution network in order to improve their own benefits, while considering their own load uncertainty.

Energy Information

Transformer

User1

Fig. 1 System structure diagram

User2

DNO

User3

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3 Source Load Uncertainty Modeling Generally, the PV power prediction error can be expressed as a normal distribution with mean value of 0 and variance of σ P2 V . In the following, the PV prediction error is taken as the uncertainty variable of distribution network side for stochastic optimization. Where σ P2 V obeys N (0, σ P2 V ) and the probability distribution function is: 

ΔP P V

1



φ(ΔP P V ) = √ 2π σ P V



e

P

2

Δ − 2σ P V PV



dΔP P V

(1)

−∞ 

Similarly, the load forecasting error Δ P l oad obeysN(0, σl2oad ), the probability distribution function is: 1





φ(ΔP load ) = √ 2π σload





Δ P load

e

−

P

2

Δ load 2σload

−∞



dΔP load

(2)

Actual output of PV power generation P P V is 

PP V = PP V + ΔP P V

(3)

where P P V is the predicted value of PV power generation. The actual value of the load P load is 

 Pload = Pload + ΔP load

(4)

 where P load is the load forecast value.

3.1 User Side Model Objective function The objective function of user side is the lowest operation cost, which is composed of transaction cost between user and distribution network side and operation cost of energy storage on user side. The mathematical expression is: min

Cui

=

24  t=1

t [Psyt E sy, i

−

t t Pby E by, i]

+c

24  t=1

t [|E ess, i |]

(5)

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where t is the time; T is the time period which is 24, C iu is the operating cost of user i during one period; P tby , P tsy are the buying price and selling price of DNO, respectively, E tsy,i , E tby,i are the net load of buying electricity and selling electricity of DNO, respectively; c represent the operating cost coefficient of energy storage device; E tess,i is charging and discharging capacity of user i. Constraint condition The constraints in user side model mainly include power balance constraints and energy storage constraints: (1)

power balance constraints t t t Pr{E Lt ,i + E ess,i + E sy,i + ΔE Lt ,i ≤ E by,i }≥α

(6)

t,max t t E by,i r g,i ≥ E by,i ≥0

(7)

t,max t t E sy,i rs,i ≥ E sy,i ≥0

(8)

t t r g,i + rs,i ≤1

(9)

where E tL .i is the load forecast value of user i; ΔE tL ,i is the load forecasting error of user i; E tsy.i , E tby.i are the net load of buying electricity and selling electricity of user i, respectively. Boolean variable r tg,i , r ts,i is used to indicate the power purchase and sale status of user i; r tg,i = 1, r ts,i = 0 means that user i purchases electric energy from the distribution network side; r tg,i = 0, r ts,i = 1 means that user I sells electric energy. (2)

energy storage constraints t t t E ess,i = E ch,i ηch,i − E dis,i ηdis,i

(10)

max t min E ess,i ≥ E ess,i ≥ E ess,i

(11)

t−1 t t E soc,i = E soc,i + E ess,i Δt

(12)

1 E soc,i

=

24 

t E ess,i

(13)

t=1 max t min E soc,i ≥ E soc,i ≥ E soc,i

(14)

where E tch,i , E tdis,i is the charging and discharging power of the user i side energy storage, respectively; ηch,i , ηdis,i is the charging efficiency and discharging efficiency

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of energy storage for the user i side, respectively; Δt is one hour which means the min time interval for charging and discharging of the stored energy; E max ess,i , E ess,i are the maximum and minimum value of charging and discharging power, respectively; min E tsoc,i is the capacity value of energy storage equipment of user i; E max soc,i , E soc,i are the upper and lower limits of users’ energy storage capacity. In this paper, the power balance method is combined with the deterministic transformation method of chance constrained programming based on Latin hypercube sampling in Ref. [8] to carry out deterministic transformation. The formula is transformed into: t t t E Lt ,i + E ess,i + E sy,i + ΔE Lt ,i − E by,i

− ΔE Lt ,i (ceil(N sample × α)) ≤ 0 Δ E Lt ,i − sor t ([E Lt ,i (1), E Lt ,i (2), . . . , E Lt ,i (sa)])

(15)

where N sample is the number of Latin hypercube sampling points; ceil(∗) is an upward rounding function, that is, to find the smallest integer greater than or equal to ∗;sor t(∗) is an ascending permutation function, that is, phasor ∗ is arranged from small to large.

3.2 Distribution Network Model Considering the power flow loss, the operation cost of DNO include the transaction cost between DNO and users and the transaction cost with large power grid. The mathematical expression is as follows: C D N O = C D N + Cu + Cus + C P A R CDN =

T N  

t t t t (Pgs ∗ E bd,i − Pgb ∗ E sd,i )

(16)

(17)

i=1 t=1

Cu =

N  T 

t t t (Pby ∗ E by,i − Psyt ∗ E sy,i )

(18)

i=1 t=1

Cus =

N  T 

t t (−Pgb ∗ E sys,i )

(19)

i=1 t=1 t C P A R = 24θ max{Pnet }/

T 

t (Pnet )

(20)

t=1 t t E sys,i = Ploadgd,i

(21)

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where C D N O is the operating cost of DNO within 24 h; C D N is the transaction cost of DNO and distribution network; C u is the transaction cost between DNO and users; C us is the transaction cost between DNO and fixed load users; C P A R 9 is the extra network cost due to peak load pressure; P tgs , P tgb are the transaction price between distribution network and power grid, respectively; P tnet is the net load of distribution t network; E tsys,i is the electricity purchased from DNO by fixed load users; P loadgd,i is the load of fixed load user i. In the distribution side model, the uncertainty of PV power generation should also be considered, which is the same as the calculation method in the user side model. Combined with the Latin hypercube sampling principle, the power and load forecasting data of PV power generation are processed in the power flow calculation. The power flow model is shown in the following formula: Pit − i it j (Ri j + j X i j ) = P jt

(22)

Q it − i it j (Ri j + j X i j ) = Q tj

(23)

v tj = vit − 2(Ri j Pitj + X i j Q it j ) + (Ri2j + X i2j )i it j

(24)

where Ri j , X i j are the resistance and inductance of ij branch respectively; i it j is the current of the branch ij at time t; P tj , Q tj are the active power and reactive power of j node at time t respectively; P it , Q it are the active power and reactive power of i node at time t respectively; v it , v tj is the voltage of node i, j at time t respectively.

3.3 Construction of Stackelberg Game Model In the stackelberg game model proposed in this paper, DNO, as the leader in the stackelberg game, receives the PV forecasting data and load forecasting data, and formulates the transaction price with the user side. According to the received price signal, based on the uncertainty of load forecasting error, the user side determines the scheduling scheme of energy storage and the interactive power between each user and DNO, and feeds back the relevant information to DNO. Based on the information obtained, DNO can get the lowest operating cost by considering the uncertainty of PV generation prediction error on distribution network side and the uncertainty of load forecasting error in fixed load users, so as to complete a round of game calculation. By comparing with the results of the previous round, we can judge whether to enter the next round of game operation until the comprehensive operation cost cannot be reduced, that is, to reach the equilibrium point of the game. The mathematical expression can be described as follows: G = {{I ∪ D N O}, {Pby }, {Psy }, {E ess }, {Cui }{C D N O }}

(25)

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where I ∪ D N O represents the two sides of the game are users and DNO; { P by } is the set of internal power purchase price for DNO in one day; { P sy } is the set of internal electricity selling prices for DNO in one day; {E ess } it is the collection of charging or discharging power of the energy storage system on the user side; {Cui } is the user’s own operation cost set; {C D N O } is the operation cost collection of distribution network operators. It can be seen from the above formula, { P by }, { P sy }, {E ess } is the solution set of the stackelberg game. When both {C iu } and {C D N O } reach the minimum value. There is an optimal solution set of G which can be described as follows: ∗

∗

∗

∗

∗

∗

t t t t t t t Cu,i (Pby , Psyt , Eess,i ) ≤ Cu,i (Pby , Psyt , E ess,i , Eess,−i ) t t ∈ Eess,i ∀i ∈ I, ∀E ess,i ∗

∗

(26)

∗

∗

t t t t C Dt N O (Pby , Psyt , Eess,i ) ≤ C Dt N O (Pby , Psyt , E ess,i ) t ∈ Ptby , ∀Psyt ∈ Ptsy ∀Pby ∗

∗

∗

(27) ∗

∗

∗

t t t t t t Eess,−i = {E ess,1 , E ess,2 , · · · E ess,i−1 , E ess,i+1 , · · · E ess,I } ∗

(28)

∗

where P tby , P tsy represents the equilibrium solution which are the buying and selling t is the equilibrium solution of optimal energy storage strategy set price of DNO; Eess,i t∗ for each user; Eess,−i is the equilibrium solution of optimal energy storage strategy set for all users except the i-th user; Ptby , Ptsy are the set of all pricing strategies. Based on the above modeling, the differential evolution algorithm is used to solve the model.

4 Case Analysis 4.1 Basic Data In the MATLAB 2018b platform, the Gurobi solver is called to verify the effectiveness of the optimization scheduling strategy in the improved IEEE33 system as shown in the Fig. 2. The energy storage capacity of user side is 200 kW for user 1, 300 kW for user 2 and 300 kW for user 3 respectively. The maximum charging and discharging power are 50 kW, 50 kW and 75 kW respectively, the initial state of charge (SOC) is 0.2, the maximum value of SOC is 0.9. The charging and discharging efficiencies of the energy storage devices are all 95%. The cost coefficient of energy storage depreciation is 0.02 Ұ:(kW:h)−1 . The distribution of PV prediction error follows the normal distribution with expectation value of 0 and variance value of 0.0009, the distribution of load forecasting error follows the normal distribution with expectation

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19 20 21 22

1

2

3 4

5

6 7

8

9 10 11 12 13 14 15 16 17 18

23 24 25

26 27 28 29 30 31 32 33

Fig. 2 Improved IEEE 33-bus distribution system

Table 1 Time-of-use tariff Hour/h

Selling price/Ұ:(kW:h)-1

Purchasing/Ұ:(kW:h)−1

Peak

09:00–12:00,17:00–22:00

1.2412

0.3573

Flat

08:00–09:00,12:00–17:00,22:00–23:00

0.7793

0.3573

Valley

23:00–08:00

0.4880

0.3573

value of 0 and variance value of 0.0016. Penalty parameter θ is 300.The grid price can be expressed as time-of-use price as shown in Table 1 PV and load data are shown in (Fig. 3).

4.2 Internal Prices According to the given basic data, the TOU price of DNO optimized by stackelberg game is shown in Fig. 4. It can be seen from the result that during the time slots 0:00–8:00, due to the lack of light or low light intensity, during this period, the PV power generation is low and cannot meet the load demand on the user side, so DNO sets a lower electricity selling price to promote users to purchase electricity from DNO. During the time 9:00–15:00, the PV power reaches the peak value and exceeds the load power demand of the user side, DNO reduces the electricity selling price during this period, which enables users to purchase more electricity from DNO, thus promoting the PV consumption. In the time slots 16:00–22:00, since the gradual decrease of light intensity until there is no light, DNO cannot satisfy the electricity demand of users, so DNO sets a higher electricity purchase price to promote users to sell electricity to DNO.

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Fig. 3 Basic data in hour: a PV energy output for 2 generations, b load demands for 3 users, c fix load for 3users

pcb DNO buying pcs DNO selling pgb Grid buying pgs Grid selling

1.4

Price/CNY·kW h-1

1.2

1

0.8

0.6

0.4

0.2 6

10

14

18

22

2

5

Time (h)

Fig. 4 Comparison of internal prices and grid prices

Through the above analysis, it can be seen that DNO can promote the power transaction between the user side and the distribution network side by adjusting the electricity price during the peak period and night period of PV.

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4.3 Optimization of the User Side Energy Storage System Figure 5 shows the dispatching results of the energy storage station in user side. In the time slots 6:00–9:00 in order to satisfy the power demand of the load under the condition of low PV power in this period, the energy storage on the user side is under balanced charging. At the time of 10:00, the highest selling price of DNO during the period of 10:00–15:00, the energy storage devices on the user side all choose to discharge, so as to meet the demand of load power on the user side at this time, and at the same time, ensure that the user side can absorb more PV power during the subsequent peak period of PV power generation. The three user side energy storage devices are charged to the upper limit of energy storage capacity before the arrival of power consumption peak. During the period of 16:00–22:00; the energy storage devices all choose balanced discharge to ensure the normal power consumption of users in the evening peak period and make the energy storage devices meet the time coupling characteristics. Through the above analysis, it can be seen that the proposed method can make the energy storage device reasonably charge in the case of PV generation surplus or low electricity price and discharge in the case of PV energy deficit or high electricity price, which can effectively promote the PV consumption, meet the user’s power demand, and reduce the user side power cost to a certain extent.

Fig. 5 Optimal scheduling of energy storage system

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Fig. 6 Comparison of net energy of distribution network

Original net load Optimized net load

300

Energy(kW h)

200 100 0 -100 -200 -300 6

10

14

18

22

2

5

Time(h)

4.4 Net Load Analysis In order to further elaborate the promotion effect of the adopted scheme on photovoltaic power consumption, the net load power curve of distribution network in each time period of a day is shown in Fig. 6. The figure shows the net load power comparison curve of the distribution network before and after the optimization. It can be seen from Fig. 6 that the optimized internal transaction price between the distribution network side and the user side makes the energy interaction between the distribution network side and the large power grid significantly reduce during the period of high photovoltaic power. Thus, the local consumption of photovoltaic power is effectively improved. As shown in the Fig. 7, before the game optimization, the internal electricity price of the system is the electricity price of the power grid, and the users do not sell electricity to the distribution network. After the game optimization, DNO sets a higher electricity purchase price during time slots 19:00 to 23:00, so users choose to sell electricity to DNO in this period, which can guarantee their own electricity demand and reduce their own operating costs. As shown in Table 2, the PV consumption rate is 68.14% before the game optimization and 79.77% after the game optimization. The results show that the proposed method can effectively improve the utilization rate of distributed photovoltaic in distribution network. As shown in Table 3, it is the operating cost of each market subject before and after the optimization of the master–slave game (In the table, a positive value of the cost data indicates the actual operating cost of the entity, and a negative value of the cost data indicates the operating income of the entity.). According to the data in the table, the operation cost of DNO is reduced by 4.93% after the game optimization, while the operation cost of users 1, 2 and 3 is reduced by 7.59%, 2.90% and 4.77% respectively after the game optimization. Based on the above simulation results, the optimal scheduling strategy proposed in this paper can obtain the optimal scheduling strategy of user side energy storage,

0

20

40

60

80

6

14

Time (h)

18

22

2

User1 User2 User3

(a) Before the game optimization

10

Fig. 7 Comparison of energy trading in energy market

Energy (kWh)

100

5

-40

-20

0

20

40

60

80

100

6

14

18

Time (h)

22

2

(b)After the game optimization

10

User1 User2 User3

5

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Energy (kWh)

700 Table 2 Comparison of PAR and PV utilization ratio

Table 3 Operating costs of various market entities Comparison of PAR and PV utilization ratio

K. Luo et al. Optimization method

PV absorption rate (%)

Peak-to-average ratio

Before game optimization

68.14

3.26

After game optimization

79.45

2.98

Before game optimization/CNY

After game optimization/CNY

DNO

−3246.30

−3406.27

User1

813.18

751.46

User 2

523.60

508.40

User 3

414.36

394.60

improve the photovoltaic consumption level of the system and the economic benefits of each market entity.

5 Conclusions In this paper, an optimal scheduling strategy of user side energy storage considering the uncertainty of new energy generation is proposed. In the system model, DNO, as the leader, sets the internal transaction price with the lowest operation cost as the goal, and the user, as the follower, responds to the internal price for energy storage scheduling. In this study, differential evolution algorithm is used to calculate the equilibrium solution of the Stackelberg game model. Finally, the experimental results show that the proposed scheduling strategy can reduce the operation cost of each market entity, improve the photovoltaic power consumption rate of the distribution side, and improve the stability of the system operation. Acknowledgements Supported by Open Fund of State Key Laboratory of Operation and Control of Renewable Energy & Storage Systems (China Electric Power Research Institute) (No. NYB51202001734).

References 1. Chen Q, Fang X, Guo H et al (2021) Participation mechanism of energy storage in electricity market: status quo and prospect. Autom Electric Power Syst 45(16):14–28 2. Xu X, Chen Q, Yan Z et al (2021) Overview of power system uncertainty and its solutions under energy transition. Autom Electric Power Syst 45(16):2–13

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3. Song T, LI T, Han X et al, Coordinated operation strategy of energy storage system participating in multiple application scenarios. Autom Electric Power Syst, pp 1–11 4. Granado PCD, Pang Z, Wallace SW (2016) Synergy of smart grids and hybrid distributed generation on the value of energy storage. Appl Energy 170:478–488 5. Mohseni S, Brent AC, Kelly S et al (2021) Strategic design optimisation of multi-energy-storagetechnology micro-grids considering a two-stage game-theoretic market for demand response aggregation. Appl Energy 287:116563 6. Liu N, Zhou L, Wang C et al (2020) Heat-electricity coupled peak load shifting for multi-energy industrial parks: a Stackelberg game approach. IEEE Trans Sustain Energy 11(3):1858–1869 7. Wei W, Liu F, Mei S (2017) Energy pricing and dispatch for smart grid retailers under demand response and market price uncertainty. IEEE Trans Smart Grid 6(3):1364–1374 8. Li Z, Study on stochastic optimal dispatch of energy power systems with high proportion of scenery. North China Electric Power University (Beijing) 9 Fan S , Ai Q , Piao L . Bargaining-based cooperative energy trading for distribution company and demand response[J]. Applied Energy, 2018, 226(SEP.15):469–482

Harmonic Analysis, Monitoring and Digital Twins

Dynamic Harmonic Analysis of Electric Energy Routers with Common High Frequency Bus Under Multi-Source-Load Interaction Zhen Liu , Yuanyuan Sun , Gongde Xu , Lisheng Li, Yang Liu, and Yanqing Pang Abstract With developing renewable energy and accelerating the transformation of energy to the clean and low-carbon direction having gradually become the theme of energy development around the world, traditional power systems cannot cope with many challenges such as unstable output and harmonic injection caused by the high proportion of new energy and high proportion of power electronic equipment. The electric energy router with common high-frequency bus based on power electronic devices can not only provide flexible and diverse interfaces for multi-sourceload interaction scenarios, but also realize the function of actively controlling and managing the multi-directional flow of energy. The main task of this paper is to perform dynamic harmonic analysis for different working conditions and control strategies of the established electric energy router model under the interaction of multiple sources and loads. Firstly, the article introduces the current development status of electric energy routers with its various types of topological structures and gives the working principle and control strategy of the multi-port electric energy router with common high-frequency bus. Then it analyzes the coupling relationship of energy flow between different ports. Finally, the article designs different multisource-load interaction scenarios to study its impact on system harmonic injection. Z. Liu · Y. Sun (B) · G. Xu Shandong University, Jinan 250001, China e-mail: [email protected] Z. Liu e-mail: [email protected] G. Xu e-mail: [email protected] L. Li · Y. Liu State Grid Shandong Electric Power Company, Jinan 250001, China e-mail: [email protected] Y. Liu e-mail: [email protected] Y. Pang Taikai Group Robot Co., Ltd, Tai’an City, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_58

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In the follow-up simulation verification, the results verify that the dual-loop decoupling control strategy can suppress the harmonics injected by the router into the power system, and the dual-phase-shift control strategy can achieve flexible control of the direction of power flow inside the router. This article establishes a dynamic harmonic analysis model of the electric energy router with common high-frequency bus for the purpose to lay the foundation for the harmonic analysis of the multi-source-load interaction system. Keywords Renewable energy · Multi-source-load interaction · Common high-frequency bus power router · Control strategy · Harmonic dynamic analysis

1 Introduction As the power system develops towards the direction of intelligence and cleanliness, fragmented distributed energy will have a wider range of application scenarios, which will bring about profound changes to the supply and demand structure of the existing energy system [1]. The traditional power system with a top-down tree-like structure cannot cope with the output characteristics of distributed energy such as the dispersion and time-varying nature, and it cannot flexibly control the transmission of reactive power [2]. The electric energy router with common high-frequency bus based on power electronic devices can not only control the direction of the energy flow of the distribution network but also solve the problem of harmonic injection caused by the increasing penetration of renewable energy [3, 4]. This paper constructs the electric energy router model with a common high-frequency bus in the multi-source-load interaction scenario which realizes the active control of the energy flow direction through the dual phase-shifting power flow control strategy under the premise of ensuring the maximum absorption capacity of renewable energy. At the same time, the dual-loop decoupling control strategy is proposed to suppress the impact of harmonics on the system when the electric energy router is connected to the system [5], and realize the comprehensive improvement of economy, safety, reliability, and multiple benefits.

2 The Development Status of Power Routers and System Structure of Topologies 2.1 Development Status The rapid development of power electronic device technology has laid the foundation for the derivation and development of power routers [6]. The architecture of power routers is also gradually changing toward multi-port, integrated modularization [7]. Intelligent measurement technology based on sensor networks and data analysis

Dynamic Harmonic Analysis of Electric Energy Routers …

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support technologies can efficiently and reliably collect important data streams in routers [8, 9].

2.2 System Structure The basic structure of the electric energy router is shown in Fig. 1: The energy topology of the electric energy router consists of three parts: the information processing layer, the energy management system and the power electronic device, which effectively controls the energy exchange between the power supply side and the load side [10].

3 Topological Structure of Electric Energy Router with Common High-Frequency Bus The distributed energy and energy storage system can be connected to the electric energy router by changing the form of the DC port of the multi-port modular electric energy router with common high-frequency bus. The simulation topology is shown in Fig. 2: The simulation model applying this structural topology includes the renewable energy system, diversity load and energy storage system, that means it can simulate the interactive scene of multiple source loads.

Sensor Power side Energy storage system

Power router Information processing Information Processing System

Energy Management System

Distributed Power

Load side Controllable load DC load

Wind power Power Systems

Sensor

Inverter

High frequency transforme r

Fig. 1 The basic architecture of the power router

Rectifier

AC load

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HVDC system

Electrical isolation

uabc L1

Low voltage DC system

High frequency transformer

+

+ Udc1 First load

Udc -

Low voltage DC bus

Common high frequency bus

+

Low voltage AC system L2

+ Udc2

Udc3 -

Series or parallel modulariza tion

L3

-

Second load

Fig. 2 The simulation topology

4 Coordination of Dual-Loop Decoupling Control Strategy and Dual-Phase Shift Power Flow Control Strategy This paper proposes the following three control schemes based on how to suppress the negative impact of large-scale distributed power access routers and actively control the energy flow of the router system by coordinating the control strategies of different devices.

4.1 Surrounding Control Method The surrounding control method means that it implements the control strategy for actively controlling the power flow to the power electronic converters at all the outer loop ports of the router system while carries out open-loop control strategy to the power electronic converters at the high-frequency transformer.

4.2 Central Control Method The central control method means that it implements the control strategy for actively controlling the power flow to the power electronic converters at the high-frequency transformer while carries out open-loop control strategy to the power electronic converters at all the outer loop ports of the router system.

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Fig. 3 Central control methode

4.3 Hybrid Control Model Combining the advantages of surround control and central control, this paper proposes hybrid control model as follows: Dual-loop decoupling control strategy In order to match the filter device and the high-side rectifier switch, the dual-loop decoupling control strategy is proposed to eliminate the harmonic component injected into the grid by introducing the LC filter device which is shown in Fig. 3: Dual phase shift power flow control strategy The dual phase shift control strategy can precisely control the phase shift angle between different ports to change the power value of the exchange between different ports.

5 Dynamic Harmonic Analysis of Composite Ports Under Different Control Strategies Performing harmonic simulation analysis under different working conditions.

5.1 Simulation Results for Four Ports The three-phase current on the grid side is shown in Fig. 4.

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Fig. 4 Three-phase current

5.2 Suppression of Harmonics Under Dual-Loop Decoupling Control Strategy The comparison of harmonics under different control strategies is shown in Figs. 5 and 6.

Fig. 5 The harmonic analysis of single-phase current

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Fig. 6 Harmonics under the control of common control strategies

Fig.7 The harmonic analysis with three ports

5.3 The Impact of Different Ports and Loads on System Harmonics The harmonic analysis of the input current of the electric energy router with multiports is shown in Fig. 7.

6 Conclusion 1.

The low-order harmonics of the DC port are generated by the high-frequency transformer rectifier, and the change of the DC load has no effect on the

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harmonics of the current injected into the grid and the harmonics of the output voltage of the DC port. The dual-loop decoupling control strategy can realize the stable operation of the router after it is connected to the filter system, while reducing the current harmonic content and The harmonic content injected into the grid by the router system. The article concludes that when the number of ports increases, the router can better suppress inter-harmonics and reduce the total harmonic content. This article establishes a dynamic harmonic analysis model of an electric energy router with a common high-frequency bus, in order to realize the electric energy router in a multi-source dynamic scenario in the future. Lay the foundation for the harmonic analysis of the system.

Acknowledgements Funding: This work is supported by National Natural Science Foundation of China (No. 51977123), Key R&D Program of Shandong Province (No. 2019GGX103008), Young Scholar Program of Shandong University (No. 2016WLJH07).

References 1. Ibrahim KM, Jhanjhi NZ, Humayun M, Sivanesan SK, Masud M, Hossaine S (2021) Hybrid smart grid with sustainable energy efficient resources for smart cities. Sustain Energy Technol Assess 46(5):101211 2. Zhuo Z, Zhang N, Xie X, Li H, Kang C (2021) Key technologies and development challenges of high-proportion renewable energy power systems. Autom Electric Power Syst 45(9):171–191 3. Hou L, Yang X, Sha Y, Fan Z, Lu P (2021) Study on the key technology of new multi-port power router. Inf Technol 1(1):48–52 4. Zhao X, Zhang C, Chai X, Guo X, Wang L (2021) Flexible operation and power flow control strategy of regional power router with series-parallel architecture. J Electro tech Technol 36(7):1480–491 5. Velenturf Anne PM, Purnell P, Jensen PD (2021) Reducing material criticality through circular business models: challenges in renewable energy. One Earth 4(3):350–352 6. Wang X, Liu J, Xiang J, Mao T (2016) Research on electric energy router based on power electronic transformer. Autom Instrum (11):4–8 7. Yi S, Yuan L, Li K, Shen Y, Zhao Z (2019) High-efficiency simulation modeling method for regional power routers. J Tsinghua University (Natural Science Edition) 59(10):796–806 8. He Z, Xiang Y, Liao K, Yang J (2021) Demands, forms and key technologies for the integration of energy-transportation-information networks, Autom Electr Power Syst 45(16):1–14 9. Liu Y, Wang Q, Zeng Q, Ye Y, Liu C, Xu L (2021) Key technologies and prospects of 5G network energy consumption management and control under the background of energy Internet. Commun Power Technol 45(12):174–183 10. Duan Q, Le J, Lu Z, Wan P, Ma C (2017) Power quality control of distribution network using power router. Electr Instrum 54(14):57–63

Research on Digital Twin Model of Three-Phase Inverter Haitao Wang, Cungang Hu, Wenjie Zhu, Weiye Yang, and Xiangyu Zheng

Abstract In this paper, the digital twin model of three-phase inverter is studied and analyzed. Firstly, the mathematical model of the three-phase inverter is established. Secondly, the mathematical model is solved by the fourth order Runge–Kutta method, and then the closed-loop controller is discretized. Finally, the digital twin model of the three-phase inverter is established. The correctness of the digital twin model is verified by simulation. Keywords Digital twin · Three-phase Inverter · Fourth order Runge–Kutta

1 Introduction The key components of the inverters may cause loss and degradation during long-term operation. This requires regular inspection and maintenance of these components to avoid component failures that may lead to system breakdown and economic loss. Therefore, to enable the equipment to operate normally and reliably, it is necessary to predict the degradation process of the key components of the inverter to replace vulnerable parts before failure. Digital twin technology constructs a virtual model for the physical object in a digital way to simulate its behavior in the real environment. The virtual “digital twin” of power electronic converter can be constructed by digital twin technology to evaluate and optimize the health state of the converter, to improve the reliability and life cycle of power electronic converter.

H. Wang · C. Hu (B) · W. Zhu · W. Yang · X. Zheng School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Hu · W. Zhu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_59

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In [1, 2], the digital twin technology is used to sample and compare the output signals of the digital twin circuit and the physical circuit in real time to diagnose the fault of the power converters. The content of digital twin is mainly divided into two parts: digital representation of physical system and data processing algorithm [3]. The digital representation is the mathematical representation of the three-phase inverter model, and the data processing algorithm is the method of analyzing and processing the three-phase inverter model. In this paper, firstly, the mathematical model of the three-phase inverter is obtained according to the topology of the three-phase inverter, the mathematical model is analyzed by numerical solution, the controller is discretized. Finally, the digital twin model of the three-phase inverter is established. The subsequent research is carried out on this basis.

2 Mathematical Model of Three-Phase Inverter The topology of the main circuit of the three-phase inverter is as follows (Fig. 1): Without considering the switching dead zone, the switching signals of the upper and lower circuits are complementary, and the expression of the three-phase switch signals Di is as follows:  Di =

1 0

(i = a, b, c)

(1)

where Di = 0 indicates that the switch tube of the upper bridge arm in the i-phase circuit is on and the switch tube of the lower bridge arm is off, Di = 1 is the opposite. The voltages V aN’ , V bN’ , V cN’ between the midpoint of each bridge arm of the three-phase inverter and the midpoint N’ of the parallel capacitor are:

Fig. 1 Main circuit topology of three phase voltage source inverter

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⎤ ⎡ ⎤⎡ D ⎤ Va N ′ a 100 ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ′ ⎣ VbN ⎦ = 0 1 0 ⎣ Db ⎦Vdc 001 VcN ′ Dc

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⎡

(2)

where V dc is DC voltage. The three-phase branch voltages Via, V ib , V ic are shown below: ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎡ D ⎤ Va N ′ VN N ′ Via a 2/3 −1/3 −1/3 ⎢ ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎣ Vib ⎦ = ⎣ VbN ′ ⎦ − ⎣ VN N ′ ⎦ = ⎣ −1/3 2/3 −1/3 ⎦⎣ Db ⎦Vdc −1/3 −1/3 2/3 Vic VcN ′ VN N ′ Dc ⎡

(3)

The voltage V NN’ between the load midpoint N and the bus parallel capacitor midpoint N’ is: VN N ′ = (Va N ′ + VbN ′ + VcN ′ )/3

(4)

According to the KVL theorem, the three-phase branch voltages are as follows: ⎧ di La ⎪ + i La ra + i La R La + i oa Rloada Via = L a ⎪ ⎪ ⎪ dt ⎪ ⎨ di Lb Vib = L b + i Lb rb + i Lb R Lb + i ob Rloadb ⎪ dt ⎪ ⎪ ⎪ ⎪ ⎩ V = L di Lc + i r + i R + i R Lc c Lc Lc oc loadc ic c dt

(5)

where L i , C i , RLi , Rci (i = a, b, c) are the three-phase inductance values, capacitance values, inductance parasitic resistance values and capacitance parasitic resistance values respectively, iLa , iLb , iLc are the three-phase inductor currents, vca , vcb , vcc are the three-phase capacitor voltages, ioa , iob , ioc are the three-phase output currents respectively, and r a , r b , r c are the internal resistances of the switch tubes in the three phase branches. According to the KCL theorem, the current equations for the filter capacitors of each phase branch: ⎧ dvca ⎪ + i oa i La = Ca ⎪ ⎪ ⎪ dt ⎪ ⎨ dvcb + i ob i Lb = Cb ⎪ dt ⎪ ⎪ ⎪ ⎪ ⎩ i = C dvcc + i Lc c oc dt

(6)

From (5) and (6), the three-phase inductor current differential equations can be expressed as:

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⎧ 1 Rloada Rca Rloada di La ⎪ ⎪ = ((−( + R La + ra ) · i La − vca ) + Via ) ⎪ ⎪ La Rloada + Rca Rloada + Rca dt ⎪ ⎪ ⎨ di 1 Rloadb Rcb Rloadb Lb = ((−( + R Lb + rb ) · i Lb − vcb ) + Vib ) ⎪ L dt R + R R b loadb cb loadb + Rcb ⎪ ⎪ ⎪ ⎪ di 1 Rloadc Rcc Rloadc ⎪ ⎩ Lc = ((−( + R Lc + rc ) · i Lc − vcc ) + Vic ) Lc dt Rloadc + Rcc Rloadc + Rcc (7) From (5) and (6), the differential equations of the three-phase capacitor voltages are expressed as: ⎧ dv Rloada i La − vca ca ⎪ = ⎪ ⎪ ⎪ Ca (Rloada + Rca ) dt ⎪ ⎪ ⎨ dv Rloadb i Lb − vcb cb = ⎪ dt C b (Rloadb + Rcb ) ⎪ ⎪ ⎪ ⎪ dv R loadc i Lc − vcc ⎪ ⎩ cc = dt Cc (Rloadc + Rcc )

(8)

3 Mathematical Model Analysis Method of Three-Phase Inverter There are two ways to solve the above-mentioned differential equations. The first method is to first construct the general solution of the differential equations, and then obtain the special solution according to the initial values of the three phase inductor currents and the three phase capacitor voltages [4]. The main disadvantage of this method is the relatively large amount of calculation. The other method is the numerical solution method. For the first-order ordinary differential equation y′ = f (x, y), the numerical solution is to discretize the solution y(x) into n nodes, improve the accuracy, and establish a recursive formula for the numerical solution, the distance between two nodes is called the calculation step time h. The three-phase output voltages and currents of the inverter can be discretized as follows: ⎧ Rca Rloada ⎪ ⎪ + vca,n+1 voa,n+1 = i La,n+1 ⎪ ⎪ R + R R ca + Rloada ca loada ⎪ ⎪ ⎨ Rloadb Rcb + vcb,n+1 vob,n+1 = i Lb,n+1 ⎪ Rcb + Rloadb Rcb + Rloadb ⎪ ⎪ ⎪ ⎪ Rloadc Rcc ⎪ ⎩ voc,n+1 = i Lc,n+1 + vcc,n+1 Rcc + Rloadc Rcc + Rloadc

(9)

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⎧ ⎪ i oa,n+1 = ⎪ ⎪ ⎪ ⎪ ⎨ i ob,n+1 = ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ i oc,n+1 =

voa,n+1 Rloada vob,n+1 Rloadb voc,n+1 Rloadc

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(10)

voi,n ,iLi,n and vci ,n are the values of output voltages, inductive currents and capacitive voltages in the nth time step, which are known. voi,n+1 , iLi,n+1 , vci ,n+1 are the values of output voltages, inductive currents and capacitive voltages in the nth time step, which are unknown. Among them, iLi,n+1 and vci ,n+1 can be derived from the values of the inductor currents and capacitor voltages at the current nth time step. Therefore, voi,n+1 can be obtained by iLi,n+1 and vci ,n+1 . The fourth order Runge–Kutta method is a typical numerical method for solving differential equations. Using fourth order Runge–Kutta method to linearize the above differential equations can reduce the error of the three-phase inverter model to a small amount [5]. The three-phase inductor current equations and capacitor voltage equations of the inverter are expressed as follows:

f 1 (i Li , vci ) = f 2 (i Li , vci ) =

di Li dt dvci dt

(11)

Using the fourth-order Runge–Kutta method, the inductor currents and capacitor voltages iLi,n+1 , vci,n+1 can be expressed as: ⎧ h ⎪ ⎨ i Li,n+1 = i Li,n + (k xi1 + 2k xi2 + 2k xi3 + k xi4 ) 6 h ⎪ ⎩v ci,n+1 = vci,n + (k yi1 + 2k yi2 + 2k yi3 + k yi4 ) 6

(12)

where k xi1 -k xi4 and k yi1 -k yi4 are the slopes of Runge–Kutta algorithm, as follows: ⎧ k xi1 ⎪ ⎪ ⎪ ⎪ ⎪ k yi1 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ k xi2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ k yi2 ⎪ ⎪ ⎪ k xi3 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ k yi3 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ k xi4 ⎪ ⎪ ⎪ ⎩ k yi4

= f 1 (xi,n , yi,n ) = f 2 (xi,n , yi,n ) h h = f 1 (xi,n + k xi1 , yi,n + k yi1 ) 2 2 h h = f 2 (xi,n + k xi1 , yi,n + k yi1 ) 2 2 h h = f 1 (xi,n + k xi2 , yi,n + k yi2 ) 2 2 h h = f 2 (xi,n + k xi2 , yi,n + k yi2 ) 2 2 = f 1 (xi,n + hk xi3 , yi,n + hk yi3 ) = f 2 (xi,n + hk xi3 , yi,n + hk yi3 )

(13)

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Equation (13) can be expressed as: ⎧ voi,n+1 = ki1 i Li,n + ki2 vci,n + ki3 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ i oi,n+1 = voi,n+1 /Rloadi ki1 = f 3 (L i , Ci , R Li , Rci , ri ) ⎪ ⎪ ⎪ ki2 = f 4 (L i , Ci , R Li , Rci , ri ) ⎪ ⎪ ⎪ ⎩ ki3 = f 5 (L i , Ci , R Li , Rci , ri )

(14)

where the coefficients k i1 , k i2 and k i3 are composed of seven groups of parameters (L i , C i , RLi , Rci , r i , Di and V dc ), which have complex combinations. Therefore, using the three-phase inductor currents and capacitor voltages of the nth step, the threephase output voltages, and output currents of the (n + 1)th step can be calculated. (i = a, b, c).

4 Realization of Digital Control Then, the PI controller should be digitally represented. The detailed flow of the controller is shown as in Fig. 2. Three-phase output current is transformed by Clark transform: 

⎡ ⎤    i oa,n 1 1 i oα,n 2 1− −√2 ⎢ ⎥ √2 = ⎣ i ob,n ⎦ 3 0 23 − 23 i oβ,n i oc,n

(15)

where ioα , ioβ are the α-axis and β-axis components of the three-phase output current. The Park transformation matrix is as follows:

Fig. 2 System block diagram (N is the sampling number of the DC voltage of the physical threephase inverter, n is the number of iteration steps of the digital twin three-phase inverter)

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i od,n i oq,n





cos(ωt) sin(ωt) = − sin(ωt) cos(ωt)

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i oα,n



i oβ,n

ωt = (ωt + 2π f · h)

(16) (17)

where iod and ioq are the d-axis and q-axis components of the three-phase output current, and f is the fundamental wave frequency. The mathematical expression of the PI controller is as follows: ⎧ i ed = ir e f − i od ⎪ ⎪ ⎪ ⎪ ⎪ i eq = 0 − i oq ⎪ ⎪ ⎨  i = k i ed dt + k p i ed md i ⎪ ⎪ ⎪  ⎪ ⎪ ⎪ ⎪ ⎩ i mq = ki i eq dt + k p i eq

(18)

where iref is the reference of the d-axis current, ied and ieq are the error between the d-axis and q-axis output currents and their reference values respectively, imd , imq are PI output d-axis and q-axis signals, k p and k i are PI controllers parameters. The closed-loop controller can be discretized as follows: ⎧ i ed,n = i ed,n+1 ⎪ ⎪ ⎪ ⎪ ⎪ i eq,n = i eq,n+1 ⎪ ⎪ ⎪ ⎪ ⎪ i md,n = i md,n+1 ⎪ ⎪ ⎪ ⎨i =i mq,n

mq,n+1

⎪ i ed,n+1 = ir e f − i od,n+1 ⎪ ⎪ ⎪ ⎪ ⎪ i eq,n+1 = 0 − i oq,n+1 ⎪ ⎪ ⎪ ⎪i ⎪ md,n+1 = i md,n + ki hi ed,n+1 + k p (i ed,n+1 − i ed,n ) ⎪ ⎪ ⎩ i mq,n+1 = i mq,n + ki hi eq,n+1 + k p (i eq,n+1 − i eq,n )

(19)

The PI output signals imd , imq are then reversed by Park: 

    i mα,n+1 cos(ωt) − sin(ωt) i md,n+1 =K sin(ωt) cos(ωt) i mβ,n+1 i mq,n+1

(20)

where K is the proportional coefficient. Then imα,n+1 , imβ ,n+1 can get pulse signals through PWM, which act on the power tubes of the three-phase inverter.

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Value

DC voltage V dc

700 V

Swithing frequence f s

10 kHz

step length h

5 µs

Three phase load Rloada / Rloadb / Rloadc

1.3Ω

Three phase inductances L a /L b /L c

1mH

Parasitic resistance of three phase inductances RLa /RLb /RLc

0.2Ω

Three phase capacitances C a /C b /C c

1µF

Parasitic resistances of three phase capacitors Rca /Rcb /Rcc

0.2Ω

Internal resistances of power tube r a /r b /r c

0.1Ω

5 Simulation Verification To verify the accuracy of the digital twin model of the three-phase inverter, the program is written in the s-function in MATLAB/Simulink to represent the digital twin three-phase inverter, and the simulation model was built in MATLAB /Simulink to replace the physical three-phase inverter. The parameters of the three-phase inverter are as follows (Table 1). The comparison of the three-phase output voltages of the physical circuit and the digital twin circuit is shown below (Fig. 3): The three-phase output voltages of the three-phase inverter physical circuit and the three-phase inverter digital twin circuit are almost overlapped, which indicates that the three-phase inverter digital twin circuit established in this paper has the same characteristics as the physical circuit.

6 Conclusion In this paper, the mathematical model of three-phase inverter is firstly analyzed, then the mathematical model is solved by the fourth order Runge–Kutta method, and the closed-loop controller is discretized. A digital twin model of three-phase inverter is established. Through the comparison of the output voltage waveforms of the physical three-phase inverter and the digital twin three-phase inverter, the threephase inverter digital twin model established in this paper is enough accurate, which lays the foundation for the following research. The work is supported by the National Natural Science Foundation of China (51777001), Educational Commission of Anhui Province (KJ2020A0031).

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Fig. 3 Comparison of three phase output voltages between physical circuit and digital twin circuit of three phase inverter (voa , vob , voc are the three-phase output voltages of digital twin three-phase inverter, voma , vomb , vomc are the three-phase output voltages of physical three-phase inverter)

References 1. Milton M, De La O CA, Ginn HL, Benigni A (2020) Controller-embeddable probabilistic realtime digital twins for power electronic converter diagnostics. IEEE Trans Power Electron, pp 1–1 2. Jain P, Poon J, Singh JP, Spanos C, Sanders SR, Panda SK (2020) A digital twin approach for fault diagnosis in distributed photovoltaic systems. IEEE Trans Power Electron 35(1):940–956 3. Peng Y, Zhao S, Wang H (2021) A digital twin based estimation method for health indicators of DC–DC converters. IEEE Trans Power Electron 36(2):2105–2118 4. Li BX, Low KS (2016) Low sampling rate online parameters monitoring of dc-dc converters for predictive-maintenance using biogeography-based optimization. IEEE Trans Power Electron 31(4):2870–2879 5. Zhang F, Mao C (2020) Pressure optimal control model of high-pressure tubing based on fourth-order Runge-Kutta method. In: 2020 IEEE international conference on mechatronics and automation (ICMA), pp 88–93

An Online Condition Monitoring Method of Single-Phase PWM Rectifier Based on Digital Twin Weiye Yang, Cungang Hu, Bi Liu, Haoran Li, and Haitao Wang

Abstract To monitor the inductance, resistance, dc-link capacitance and load status of single-phase two-level PWM rectifier, a digital twin based online status monitoring method is presented in this paper. By analyzing the external characteristics of the circuit through voltage and current sensors, the proposed method can real-time monitor the operating state of the rectifier without interfering the normal operating of the circuit. Firstly, the mathematical model of the adopted rectifier is built, including the main circuit model and control scheme, discretize them with Runge–kutta. Then, the particle swarm optimization (PSO) algorithm is applied to updates the parameters of the digital model in real time by comparing the data measured by the sensor with the data of the digital model, which can optimize the established digital model, so that the digital model can accurately reflect the real-time status of physical system. Finally, the proposed method is verified in Matlab/Simulink, the simulation results verify the correctness and validity of the proposed method. Keywords Single-phase PWM rectifier · Digital twin · PSO intelligent algorithm · Parameter identification · Condition monitoring

1 Introduction With the rapid development of wind power generation and high-speed rail power supply system, single-phase PWM rectifiers are widely used [1], power supply reliability is important for those applications. However, the failure of the PWM rectifier

W. Yang · C. Hu (B) · B. Liu · H. Li · H. Wang School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Hu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_60

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occurs frequently. In some specific applications, fault is not allowed or should be eliminated in time. Generally, the fault mechanisms of the rectifier can be divided into two categories: (1) abrupt failure due to excessive stress, (2) wearing and aging due to long-term operation. This article only focuses on the second type of failure. The degradation process of the circuit element can be reflected by the change of its characteristic parameter, such as the inductance value of the inductor. Therefore, it is very important to monitor the operation state of rectifier on-line. Literature [2] and [3] monitors the status of power semiconductor by using its on-state resistance/voltage. The capacitance of the capacitor is used as an indicator of the health of the capacitor in [4]. Although these methods can effectively monitor the degradation of capacitor, additional circuit will intrude into the main circuit and increase system cost. To tackle these drawbacks, a model-based parameter identification method is presented in [5], where the generalized gradient descent algorithm is used to estimate the inductance. Biogeography-based optimization method is used to identify the parameters in Buck circuit [6]. But the main challenge of these methods is that it needs to obtain the practical modulation signal in real time. This paper proposes a condition monitoring method based on digital twin for single-phase PWM rectifiers. Firstly, the digital model of the main circuit is developed, which includes main circuit and control strategy. The digital model is a virtual copy corresponding to the physical rectifier. Then, the digital model can continuously update itself by using the particle swarm optimization (PSO) algorithm. Thus, the output characteristics of physical entities and digital twins are almost the same. Compared with the traditional state monitoring method, the proposed method does not affect its corresponding physical prototype. Finally, simulation results verify the correctness and validity of the proposed method.

2 Digital Twin System and Control Scheme 2.1 System Description Figure 1 is the topology of a single-phase two-level PWM rectifier, where us , is , uab represent the AC voltage, input current and modulation voltage of the rectifier, respectively. L s and Rs are the equivalent inductance and resistance, udc and ic are the DC voltage and capacitor current, respectively. Si (Di )(i = 1 ~ 4) represent IGBT switch modules with parallel freewheeling diodes. There are four working modes when PWM rectifier adopts unipolar modulation strategy, as shown in Table 1. The internal resistance of IGBT and anti-parallel diode are ignored. The current path diagram of these four modes is shown in Fig. 2. According to Fig. 2, the PWM mathematical model is as follows:

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Fig. 1 Topological structure diagram of single-phase two-level PWM rectifier

Table 1 Working mode under unipolar PWM modulation Switch mode

1

2

3

4

Conduction device

S1 (D1 ) S4 (D4 )

S2 (D2 ) S3 (D3 )

S1 (D1 ) D3 (S3 )

S2 (D2 ) D4 (S4 )

The value of uab (t)

udc

−udc

0

0

Fig. 2 Current path diagram under different switching modes

⎡

di s dt du dc dt

⎡

⎤ =

B) − LRss − (SAL−S s SA −SB − RL1·C C

⎤⎡

⎤ ⎡ ⎤ u is + s u dc 0

where switching function S A and S B are defined as:

(1)

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 SA =

1 S1 turns on, S2 turns off

0 S1 turns off, S2 turns on  1 S3 turns on, S4 turns off SB = 0 S3 turns off, S4 turns on

(2)

(3)

In this paper, Runge–Kutta algorithm is adopted to solve Eq. (1). The basic equations of Runge–Kutta is as follows: h (k1 + 2k2 + 2k3 + k4 ) 6 f (xn , yn ) h h f (xn + , yn + k1 ) 2 2 h h f (xn + , yn + k2 ) 2 2 f (xn + h, yn + hk3 )

yn+1 = yn + k1 = k2 = k3 = k4 =

(4)

where h is the calculation step time of Runge–Kutta, k 1 -k 4 are the average rate of change of variables between n and n + 1, and f represents the Eq. (1). In this paper, is and udc correspond to yn+1 in the formula, f corresponds to the two differential equations in Eq. (1), Based on (4), Eq. (1) can be linearized, replacing yn+1 with is and udc , is,n+1 ,udc,n+1 can be obtained as follows: h (ka1 + 2ka2 + 2ka3 + ka4 ) 6 h = u dc,n + (kb1 + 2kb2 + 2kb3 + kb4 ) 6

i s,n+1 = i s,n + u dc,n+1

(5)

2.2 Direct Power Control Direct power control [1] is adopted in this paper to control the inductive current and dc voltage, as shown in Fig. 3. The differential equation of P, Q is expressed by Eq. (6). Similarly, with Runge–Kutta method, Pn+1 and Qn+1 can be expressed by Eq. (7). The direct power control method needs the information of active and reactive currents id , iq , therefore the second-order generalised integral (SOGI) method is utilized to construct orthogonal virtual current components to decouple the inductive current [1].

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Fig. 3 Block diagram of direct power control

⎡ dP ⎤ ⎢ dt ⎥ ⎣ ⎦= dQ dt

⎡

− LRss −ω ω − LRss

⎤⎡

⎤ ⎡ ⎤ P Usm Usm − u abd + 2L s u abq Q

h (kc1 + 2kc2 + 2kc3 + kc4 ) 6 h = Q n + (kd1 + 2kd2 + 2kd3 + kd4 ) 6

(6)

Pn+1 = Pn + Q n+1

(7)

In Fig. 3, outer-loop and inner-loop PI controllers need to be discretized. Taking the discretization of outer-loop voltage PI controller as example, the formula can be deduced as: ve,n = ve,n+1 vm,n = vm,n+1 ve,n+1 = Vref − vab,n+1

(8)

vm,n+1 = vm,n + K p (ve,n+1 − ve,n ) + K I hve,n+1 where V ref is the reference voltage, V e is the error, V m is the modulation signal, K p and K i are proportional coefficient and integral coefficient respectively. h is the above-mentioned Runge–Kutta step time. The discretization of active and reactive power PI controllers are similar to this.

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3 Proposed Parameter Identification Method Section 2 introduces the PWM digital twin model, including the main circuit and control circuit. The input parameters of digital twin are obtained by intelligent algorithm. It can be seen that Eq. (1) is a highly nonlinear function with four variables. PSO algorithm is applied to search parameters due to its superior performance [7]. PSO is a heuristic algorithm, which evaluates the quality of the solution through fitness and guides the particles to find the global optimal solution. On this basis, PSO algorithm can be used to obtain the parameters of the rectifier prototype. According to the principle of PSO algorithm, the first step is to build a fitness function based on the application object. A fitness function is as follows:

N f obj =

j=1

[(i s, j − i sm, j )2 + (u dc, j − u dcm, j )2 ] N

(9)

where is,j and udc,j represent the inductive current and dc voltage of the digital twin system, ism,j and udcm,j represent the inductive current and dc voltage of the physical prototype, and N is the number of data points collected in one calculation. The process of the proposed monitoring method based on digital twin is shown in Fig. 4,

Fig. 4 Block diagram of the proposed condition monitoring method

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which consists of three parts: the physical entity of the adopted rectifier, the digital model system, and the PSO intelligent algorithm. Par is the parameter set including L s , Rs , C, RL , that is, the input parameters of the digital twin. Firstly, Par, is, udc , and the switch status S A , S B are initialized at the beginning time step. Then, is , udc , P, Q at next step can be obtained by (5) and (7), and parameter updated by (10) and (11). Finally, SA and SB are updated through the developed control circuit model and sent back into PWM rectifier model. Since h of Runge-kutta algorithm is inconsistent with the sampling period t s , the number of output points of the digital twin is reduced to N by N=hn/t s . The fitness value f obj corresponding to each particle can be calculated by (9). Disturbance is added to prevent PSO algorithm from falling into local optimum. Thus the optimal f obj can be obtained. If f obj is smaller than the preset threshold, it can be considered that the searched parameters are consistent with the actual rectifier parameters, that is, the purpose of parameter identification is achieved; if f obj is bigger than the preset threshold, the parameter set Par is updated by the following formula (10) and (11). Vi, j,d = ωi−1 Vi−1, j,d + ci−1,1 r1,i−1, j (ParG,d − Pari−1, j,d ) + ci−1,2 r2,i−1, j (ParL,i−1, j,d − Pari−1, j,d )

(10)

Pari, j,d = Pari−1, j,d + Vi, j,d

(11)

where i is the number of iterations, j is the number of particles, d is the dimension of the particle, V i,j,d are the d-dimensional velocity of the jth particle of the ith generation, Pari,j,d are the jth particle of the ith generation in the d-dimensional position, ωi-1 is the inertia weight of the i-1 generation, ci-1,1 and ci-1,2 are the two learning factors of the i-1 generation, where ci-1,1 reflects the social role of the population, ci-1,2 reflects the individual role of the particle, ω, c1 , c2 change adaptively according to the state of the particle swarm, r 1, i-1, j and r 2, i-1, j are random values between two (0, 1). Par G,d is the dth dimension of the global extremum, Pari-1,j,d is the dth dimension of the jth particle of the i-1th generation, Par L,i-1,j,d are the dth dimension of the local extremum of the jth particle of the i-1 generation.

4 Simulation To verify the proposed method, a simulation model of a single-phase PWM rectifier is built, which includes the main circuit and control system. The simulation parameters are listed in Table 2.

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Table 2 Simulation system parameters

Electrical parameters

Value

Effective value of inductive voltage U s

65 V

DC side voltage given value U dc_ref

120 V

Rated load of DC side RL

20Ω

Inductance L s

4.76mH

Resistance Rs

0.1Ω

Capacitance C

1.65mF

Switching frequency f sw

5 kHz

4.1 Parameter Identification Figure 5a shows the convergence process of f obj . The preset threshold in the simulation is 0.05. From Fig. 5a, it can be seen that f obj drops below the threshold after about 50 s. f obj is smaller than the threshold value, which means that the output

(a) Optimization process of fobj

(c) Rs

Fig. 5 Process of parameter convergence

(b) Ls and C

(d) RL

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(b) The inductive current

Fig. 6 The waveforms of digital twin system and its physical counterpart

waveforms of the physical prototype and digital model are almost identical. Therefore, the parameters obtained by PSO algorithm can be regarded as the parameters of the actual circuit, and the digital twin system accurately reflects the condition of the physical prototype. The parameter identification process are shown in Fig. 5. The L s and C identification process is shown in Fig. 5b, while Rs and RL identification process is shown in Fig. 5c, d respectively. The convergence value of each parameter is marked in the corresponding figure. It can be seen that the error between actual physical circuit parameters and convergence values is very small and can be ignored. The comparison waveforms of the output dc voltage and inductive current of the actual entity and digital twin are shown in Fig. 6a, b respectively, and the difference between simulation model and digital twin can be ignored. Therefore, the digital twin system can completely simulate the physical entity. The above simulation results verify the correctness of the proposed method.

4.2 Repeatability Test The PSO algorithm is a stochastic optimization algorithm. In order to verify the effectiveness of the proposed method and prevent randomness from affecting the simulation results, multiple simulation tests are performed and the simulation results are recorded. The simulation results are shown in Fig. 7. It can be seen from Fig. 7 that the parameters can be accurately identified in multiple simulations with very small errors, and the proposed method is not affected by the randomness of the algorithm.

5 Conclusion This paper presents a parameter identification method of single-phase PWM rectifier based on digital twin. The digital model of PWM rectifier is built, and PSO algorithm

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(a) Ls

(c) Rs

(b) C

(d) RL

Fig.7 Comparison of the estimated parameters and actual values

is applied to update the parameters of digital model by processing the data of simulation model and digital model. Simulation results show that the proposed method is able to identify the parameters of PWM rectifier online without additional circuits, so the state of the physical prototype can be monitored in real time. Repeated test results prove that the randomness of the PSO algorithm has no effect on the proposed method. The work is supported by the National Natural Science Foundation of China (51777001), Educational Commission of Anhui Province (KJ2020A0031).

References 1. Liu B, Song W, Chen J, Feng X (2020) Model predictive power control for grid-connected ac– dc converters with trajectory optimisation of the modulated voltage vector. IET Power Electron 13(10):2060–2068 2. Dusmez S, Akin B (2015) An accelerated thermal aging platform to monitor fault precursor on-state resistance. In: 2015 IEEE international electric machines drives conference (IEMDC), pp 1352–1358

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3. Choi U, Jørgensen S, Blaabjerg F (2016) Advanced accelerated power cycling test for reliability investigation of power device modules. IEEE Trans Power Electron 31(12):8371–8386 4. Vogelsberger MA, Wiesinger T, Ertl H (2011) Life-cycle monitoring and voltage-managing unit for dc-link electrolytic capacitors in PWM converters. IEEE Trans Power Electron 26(2):493– 503 5. Poon J, Jain P, Spanos C, Panda SK, Sanders SR (2017) Fault prognosis for power electronics systems using adaptive parameter identification. IEEE Trans Ind Appl 53(3):2862–2870 6. Li BX, Low KS (2016) Low sampling rate online parameters monitoring of dc-dc converters for predictive-maintenance using biogeography-based optimization. IEEE Trans Power Electron 31(4):2870–2879 7. Peng Y, Zhao S, Wang H (2021) A digital twin based estimation method for health indicators of DC–DC converters. IEEE Trans Power Electron 36(2):2105–2118

Parameter Identification Method Based on Digital Twin of Boost Converter Xiangyu Zheng, Cungang Hu, Wenjie Zhu, Haitao Wang, and Weiye Yang

Abstract In order to identify the key parameters in power electronic converters, this paper proposes a boost converter parameter identification method based on digital twins. Compared with traditional parameter identification, this method is more economical, efficient and reliable. This method not only does not require additional hardware circuits and calibration requirements, but also can identify key parameters such as inductance and capacitance at the same time. In this paper, the mathematical analysis model of the boost converter is established, and the digital twin model is obtained by the Runge–Kutta method. Using the particle swarm optimization (PSO) algorithm, by comparing the output signals of the digital twin model and the mathematical analytical model, key parameters such as inductance and capacitance in the converter can be identified. In the Matlab/Simulink environment, a digital twin model and simulation were built. The simulation results demonstrate the effectiveness of the boost converter parameter identification method based on the digital twin. Keywords Boost converter · Digital twin · Parameter identification · PSO algorithm

1 Introduction After long-term operation of the DC-DC converter, due to functional and environmental pressures, failures are often caused. Therefore, the identification of key parameters such as the inductance and capacitance of the DC-DC converter is of great significance in order to replace vulnerable parts before failure. X. Zheng · C. Hu (B) · W. Zhu · H. Wang · W. Yang School of Electrical Engineering and Automation, Anhui University, Hefei 230601, China e-mail: [email protected] C. Hu · W. Zhu Engineering Research Center of Power Quality, Ministry of Education, Anhui University, Hefei, China Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_61

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The traditional parameter identification method based on the model, although it can effectively identify the parameters, but when the number of unknown parameters is more than the number of known equations, it will cause transmission errors, and even no feasible solution [1]. Using the generalized gradient descent algorithm, although parameters such as the inductance and capacitance of the boost converter can be calculated, additional signals need to be injected into the controller [2]. Digital twins are digital models of existing or future physical entities. Real-time perception, diagnosis, and prediction of the state of physical entities are realized through actual measurement, simulation and data analysis, and the physical entities are controlled through performance and state optimization and command transmission. To evolve itself through mutual learning between related digital models, and at the same time improve the decision-making of stakeholders in the life cycle of physical entities [3]. Using the concept of digital twins, by comparing the output signals of digital twins and physical twins in real time, fault diagnosis of power converters can be realized [4]. This paper takes the boost converter as an example, and proposes a method of boost converter parameter identification based on digital twin. First of all, this digital twin model is a virtual copy of the mathematical analytical model, which can continuously update itself based on the data from the mathematical analytical model. Then, use the data obtained by analyzing the particle swarm algorithm to make the difference between the digital twin model and the mathematical analytical model smaller than the preset threshold. Finally, by comparing the output signals of the digital twin model and the mathematical analytical model, key parameters such as the inductance and capacitance of the boost converter are identified.

2 Mathematical Analysis Model of Boost Converter Figure 1 shows the circuit diagram of boost converter and the equivalent circuit diagram of MOSFET in on state and off state. Where V in is the input voltage, V f is the forward diode voltage; L is inductance and C is capacitance; iL is the inductor current, vc is the capacitor voltage, and vo is the output voltage; RD , RL and RC are the parasitic resistance of MOSFET, inductor and capacitor respectively; D is 1 when MOSFET is on and 0 when MOSFET is off. When the MOSFET is in the on state, as shown in Fig. 1b, the calculation shows that: ⎧ 1 di L ⎪ ⎪ = [−(R L + R D )i L + Vin ] ⎪ ⎪ L d t ⎪ ⎪ ⎨d 1 1 vC (1) =− vC ⎪ C R + RC dt ⎪ ⎪ ⎪ ⎪ R ⎪ ⎩ vo = vC R + RC

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Fig. 1 Equivalent circuit of boost converter: a General circuit diagram of boost converter; b MOSFET is on-state; c MOSFET is off-state

When the MOSFET is in the off state, as shown in Fig. 1c, the calculation shows that: ⎧    1 R RC R di L ⎪ ⎪ = vC + Vin − V f − RL + iL − ⎪ ⎪ ⎪ L R + RC R + RC dt ⎪ ⎪  ⎨ dvC 1 1 R (2) = iL − vC ⎪ C R + RC R + RC dt ⎪ ⎪ ⎪ ⎪ R RC R ⎪ ⎪ ⎩ vo = iL + vC R + RC R + RC According to the state space averaging method, by synthesizing the on state and off state of MOSFET, from (1) and (2), it can be concluded that:

   ⎧ 1 R RC di L ⎪ ⎪ = + + R − 1) R − D(R iL (D ) L L D ⎪ ⎪ L R + RC dt ⎪ ⎪  ⎪ ⎪ ⎪ R ⎪ ⎪ vC + Vin + (D − 1)V f +(D − 1) ⎨ R + RC  ⎪ d 1 1 R vC ⎪ ⎪ = iL − vC (1 − D) ⎪ ⎪ ⎪ C R + RC dt R + RC ⎪ ⎪ ⎪ ⎪ R ⎪ ⎩ vo = (1 − D) R RC i L + vC R + RC R + RC

(3)

In order to get iL and vC , Eq. (3) must be solved. Linearize the differential equation, and within the acceptable accuracy range, the output voltage vo can be described by discrete time steps:

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vo,n+1 = (1 − D)

R RC R i L ,n+1 + vC,n+1 R + RC R + RC

(4)

where the nth time step is defined as the current time interval, the (n + 1)th time step represents the next one. iL,n+1 represents the inductor current of the (n + 1)th step, vC,n+1 represents the capacitor voltage of the (n + 1)th step, vo,n+1 represents the (n + 1)th step The output voltage. In this paper, a typical fourth-order Runge–Kutta method [5] is used to linearize the differential equation, and it is considered that the modeling error of the converter is negligible. In order to simplify the analysis process, (3) Rewrite as follows: ⎧ di L ⎪ ⎪ ⎨ f 1 (i L , vC ) = dt dvC ⎪ ⎪ ⎩ f 2 (i L , vC ) = dt

(5)

Therefore, iL,n+1 and vC,n+1 can be expressed as: ⎧ h ⎪ ⎨ i L ,n+1 = i L ,n + (K a1 + 2K a2 +2K a3 + K a4 ) 6 h ⎪ ⎩v C,n+1 = vC,n + (K b1 + 2K b2 +2K b3 + K b4 ) 6

(6)

where h is the calculation step time from the nth step to the (n + 1)th step, k a1 -k a4 and k b1 -k b4 are the average change rates of the nth and (n + 1)th steps. The calculation is as follows: ⎧ K a1 = f 1 (xn , yn ) ⎪ ⎪ ⎪ ⎪ ⎪ K b1 = f 2 (xn , yn ) ⎪ ⎪ ⎪   ⎪ ⎪ h h ⎪ ⎪ ⎪ K a2 = f 1 xn + K a1 , yn + K b1 ⎪ ⎪ 2 2 ⎪ ⎪   ⎪ ⎪ h h ⎪ ⎪ ⎪ ⎨ K b2 = f 2 xn + 2 K a1 , yn + 2 K b1   (7) ⎪ h h ⎪ ⎪ K a3 = f 1 xn + K a2 , yn + K b2 ⎪ ⎪ 2 2 ⎪ ⎪ ⎪   ⎪ ⎪ h h ⎪ ⎪ K b3 = f 2 xn + K a2 , yn + K b2 ⎪ ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ ⎪ K a4 = f 1 (xn + h K a3 , yn + h K b3 ) ⎪ ⎪ ⎩ K b4 = f 2 (xn + h K a3 , yn + h K b3 ) After the calculation of (5)–(7), the final expression of vo can be obtained:

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vo,n+1 = ai L ,n + bvC,n + c a, b, c = f 3 (L , C, R L , RC , R D )

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(8)

The coefficients a, b and c are composed of seven parameters: L, C, RL , RC , RD , D and V in . Among them, L, C, RL , RC , and RD are unknown parameters, input voltage V in can be measured from boost converter, and switching state D of MOSFET can be determined by (9)–(10) comparing modulation signal vm and triangular carrier signal vtri . ⎧ ve,n = ve,n+1 ⎪ ⎪ ⎪ ⎨ vm,n = vm,n+1 ⎪ ve,n+1 = Vr e f − vo ⎪ ⎪

 ⎩ vm,n+1 = vm,n + K P ve,n+1 − ve,n + K I hve,n+1  1 vm,n+1 ≥ vtri,n+1 

Dn+1 = 0 vm,n+1 ≤ vtri,n+1

(9)

(10)

where V ref is the reference value of the output voltage vo , ve is the difference between the output voltage and its reference value, K P and K I are the parameters of PI controller.

3 Parameter Identification of Boost Converter The final model of the Boost converter is represented by (8). Because the coefficients a, b, and c are highly nonlinear functions of five variables, it is impossible to estimate the model in this paper with traditional least squares method and other algorithms [6]. This paper chooses particle swarm algorithm as the solution, its realization process is simple, and it has good versatility for different models. Particle swarm optimization (PSO) algorithm is a population-based iterative optimization algorithm, which simulates the behavior of birds and fish swarm and guides particles to search the global optimal solution [7]. In order to realize particle swarm optimization, an objective function must be constructed first. The objective function of this paper is as follows:  N  2  i Ld, j − i L p, j + (vod, j − vop, j )2 f obj =

j=1

N

(11)

where iLd,j and vod,j are the inductance current and output voltage calculated in the digital twin boost converter. iLp,j and vop,j are the inductance current and output

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Fig. 2 Parameter identification flow chart of digital twin technology in boost converter

voltage measured from the physical boost converter, and N is the sample size of the measured data. The parameters of key components in physical boost circuit can be obtained by minimizing the objective function defined in (11) by particle swarm optimization. Figure 2 shows the parameter identification flow chart of the digital twin technology in the boost converter. First, the initial time step n is 0, and the parameters L, C, RL , RC , RD , iL , vC and switch state D are initialized. Then, the time step is updated according to n = n + 1, and the next step is to calculate the inductor current iL , capacitor voltage vC and output voltage vo through (1)–(8). Finally, update D through (9)–(10) and perform the calculation of the next loop. If the obtained f obj is less than the preset threshold, the output parameters of the digital twin circuit represent the working state of the physical boost converter. Otherwise, the relevant parameters are updated according to the following formula:



 vi, j = wvi−1, j + c1r1 pi, j − xi−1, j + c2 r2 pg, j − xi−1, j xi, j = xi−1, j + vi, j

(12)

where i is the number of iterations, j is the number of particles, x i,j is the position of the jth particle in the ith iteration, vi,j is the velocity of the jth particle in the ith iteration, pi,j is the individual optimum of the jth particle, and pg,j is the global optimum. w is inertia weight, c1 and c2 are acceleration number, r 1 and r 2 are weight factors. The corresponding parameter settings in this paper are shown in Table 1. Finally, the updated parameters are brought back to the digital twin circuit of boost converter for further calculation until the found f obj is less than the preset threshold.

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Table 1 Specification of update objective function Specification

Value

w

0.9

c1 /c2

2/2

r 1 /r 2

0.5/0.5

4 Simulation Verification In order to verify the proposed method, the inductor, capacitor and parasitic resistance of boost converter are simulated by using digital twin technology in Matlab/Simulink environment. Table 2 shows the parameter values in the mathematical analysis model, reflecting the parameter information in the physical converter. Figure 3 shows the descending process of the objective function, reflecting the convergence information of the parameters. From the simulation diagram, we can Table 2 Specification of boost converter Specification

Value

V in /V ref

50 V/95 V

Vf

0.8 V

RL /RC /RD

0.2Ω/0.224Ω/0.01Ω

Ro

40Ω

L

1 mH

C

200uF

Fig. 3 Descent process of objective function

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see that after the program runs for 3.7 s, the value of the objective function is less than the preset threshold of 0.1, which indicates that the parameter identification is over and reaches a stable state. Figure 4 shows the process of using digital twin technology to simultaneously identify the inductance parameter L and the capacitance parameter C in the converter. Figure 4a shows the identification process of the inductor parameters. The final identified parameter value is about 1.02 mH, which is 0.02 mH away from the value of the inductor in the converter, 1mH, with an error of 2%. Figure 4b is the process of identifying capacitance parameters. The final identified parameter value is about 0.201 mF, which is 1uF different from the value of the converter capacitance 200 uF, and the error is 0.5%. Figure 5 shows the identification process of the parasitic resistance of the converter. Figure 5a shows the identification process of the inductor parasitic resistance RL . The final identified parameter value is 0.2Ω, which is the same as the value

Fig. 4 The identification process of converter inductance and capacitance parameters: a Inductance parameter identification process; b The identification process of capacitance parameters

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Fig. 5 The identification process of the parasitic resistance of the converter: a The identification process of inductance parasitic resistance RL ; b The identification process of capacitor parasitic resistance RC ; c Identification process of MOSFET parasitic resistance RD

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of the inductor parasitic resistance in the converter, with almost no error. Figure 5b shows the identification process of the capacitor parasitic resistance RC . The final identified parameter value is about 0.226Ω, which is 0.002Ω different from the capacitor parasitic resistance 0.224Ω in the converter, and the error is about 0.9%. Figure 5c shows the identification process of the MOSFET parasitic resistance RD . The final identified parameter value is 0.001Ω, which is the same as the value of the MOSFET parasitic resistance in the converter, with almost no error. The above simulation results show that the identification of parasitic resistance parameters using digital twin technology is still effective. Figure 6 shows the process of digital twin technology tracking the inductor current, capacitor voltage, and output voltage in the converter. Among them, the blue line represents the parameters in the converter, and the red line represents the parameters in the digital twin. Figure 6a shows the tracking process of the inductor current. At 7.00005 s, the value identified by the digital twin inductor current iLd is about 5.6A, which is 0.3A different from the value 5.9A of the converter inductor current iLp , so the error is 5.08%. The error range is 0–5.08%. Figure 6b shows the process of identifying the capacitor voltage. At 7.00015 s, the value identified by the digital twin capacitor voltage vcd is 96.34 V, which is 0.24 V different from the value 96.58 V of the converter capacitor voltage vcp , so the error is 0.25%. The range is 0–0.25%. Figure 6c shows the identification process of the output voltage. At 7.00005 s, the value recognized by the digital twin output voltage vod is 95.8 V, which is 0.25 V different from the value 96.05 V of the physical converter capacitor voltage vcp , so the error is 0.26%. The error range is 0–0.26%. The above simulation results show that the use of digital twin technology to identify the inductor current, capacitor voltage, and output voltage is also very effective.

5 Conclusion This paper takes the boost converter as an example, and proposes a method of boost converter parameter identification based on digital twin. A digital twin model was built in the Matlab/Simulink environment, and the inductance and capacitance of the converter were simulated at the same time, and the parasitic resistance of the converter was also simulated separately. The simulation results show that the digital twin technology can not only identify parameters such as inductance, capacitance, and parasitic resistance in the converter, but also has relatively small identification errors. In addition, the inductor current, capacitor voltage, and output voltage identified by the digital twin are also very close to the corresponding parameters in the converter. The above simulation results demonstrate the effectiveness of the boost converter parameter identification method based on the digital twin. In the verification process of this article, although parameters such as inductance, capacitance, and parasitic resistance have been identified, there are still certain errors, especially inductance current errors. In addition, parameters such as environment and

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Fig. 6 Digital twin technology tracks the process of inductor current, capacitor voltage, and output voltage in the converter: a Tracking process of inductor current; b Capacitor voltage tracking process; c Tracking process of output voltage

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temperature will also have an impact on the converter, which needs to be carefully considered in actual use. The work is supported by the National Natural Science Foundation of China (51777001), Educational Commission of Anhui Province (KJ2020A0031).

References 1. Peng Y, Zhao S, Wang H (2021) A digital twin based estimation method for health indicators of DC–DC converters. IEEE Trans Power Electron 36(2):2105–2118 2. Poon J, Jain P, Spanos C, Panda SK, Sanders SR (2017) Fault prognosis for power electronics systems using adaptive parameter identification. IEEE Trans Ind Appl 53(3):2862–2870 3. Tian F, Duan H, Yang X (2019) Digital twins white paper. [Online]. Available: https://www. 3mbang.com/p-16276163.html 4. Milton M, De La O C, Ginn HL, Benigni A (2020)Controller-embeddable probabilistic real-time digital twins for power electronic converter diagnostics. IEEE Trans Power Electron 35(9):9850– 9864 5. Hult J (2007) A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers. J Lightwave Technol 25(12):3770–3775 6. Kimball JW, Krein PT (2008) A current-sensorless digital controller for active power factor correction control based on Kalman filters. In: 2008 twenty-third annual ieee applied power electronics conference and exposition, pp 1328–1333 7. Zhan Z, Zhang J, Li Y, Chung HS (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern Part B(Cybernetics) 39(6):1362–1381

Transmission Line Tower Fault Identification Based on Image Processing Technology Wencheng Sun, Lingyun Wu, Jiaxin Yuan, Nuochun Liu, Liwen Peng, and Xianfeng Zheng

Abstract At present, the safety of transmission lines has attracted much attention from the power sector. In order to solve the problem of bird’s nest identification and insulator failure on transmission line towers, this paper studies a monitoring system using video image processing technology. Firstly, the image is gray-scaled, and then the edge of the image is extracted based on the Canny algorithm. Finally, a detection method based on the histogram of orientation gradient (HOG) and support vector machine (SVM) is proposed. This method improves the utilization efficiency of the online monitoring system and has important practical significance. Keywords Image processing technology · HOG · SVM

1 Introduction Transmission lines play a very important role in the power system, which is related to the power consumption of thousands of households [1]. Large-scale power outages will bring great losses to the national economy [2]. Therefore, the power sector pays great attention to the safety of transmission lines [3]. The impact of bird activities on transmission lines is mainly manifested in the following aspects: birds will often build nests on the transmission line towers, and the drop of nest materials can easily cause short circuits around the towers. Insulators are one of the important components of transmission lines [4]. According to statistics, more than half of the accidents caused by insulator failures which have brought great safety hazards to the stable operation of transmission lines [5]. Therefore, for the safe and reliable operation of the power grid, we must monitor the nesting behavior of birds on the transmission line towers and the working status of the insulators [6, 7].

W. Sun (B) · L. Wu Southwest Branch of State Grid Corporation of China, Chengdu 610041, China e-mail: [email protected] J. Yuan · N. Liu · L. Peng · X. Zheng School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_62

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Traditional power transmission line monitoring methods are mainly manual inspections [8]. When a bird’s nest or insulator failure is found, the staff will eliminate the risk. Such monitoring measures are inefficient and difficult to ensure their safety. Although helicopter inspection can improve inspection efficiency, its high cost and low flexibility cannot be applied on a large scale. The on-line monitoring technology of the transmission line based on the video image monitoring and identification system directly transmits the collected video images to the monitoring center through the camera installed on the transmission tower, the video image processing and recognition system of the monitoring center is used to automatically recognize the state of the transmission line tower and give an alarm [9]. Compared with the traditional manual inspection method, it is simpler, more accurate, real-time and economical. This article intends to use video image processing technology to research the bird’s nest identification and insulator failure on the transmission line tower, which can quickly and intelligently locate and monitor it, greatly saving manpower and material resources, making the entire monitoring system efficient and practical, improving the utilization efficiency of the online monitoring system and provide a new intuitive and accurate method for ensuring the safe operation of the power system, which has very important practical significance.

2 Image Preprocessing 2.1 Image Grayscale Image preprocessing technology [10] is a common part of pattern recognition systems. The images captured by video are often color images. Although the information reflected by color images is more delicate, the amount of data is too large, which is not suitable for direct image feature extraction. Therefore, it needs to be grayed out first to reduce the data information of the picture. In addition, from the actual identification purpose of bird’s nest and insulator, generally there is no need for color information about the tower, bird’s nest and insulator. Therefore, it is necessary to perform grayscale processing first to reduce the data information of the picture. Generally, color images are generally in RGB format, and the proportions of red, green, and blue components in the image are different. Grayscale image is an image format that only contains brightness information but no color information. It is often stored in 8-bit unsigned integers. The conversion from RGB image to grayscale image follows Eq. (1). I = 0.220R + 0.587G + 0.114B

(1)

The size range of R, G, B, V is from 0 to 255. The image sample after graying is shown in Fig. 1.

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Fig. 1 a The grayscale image of the transmission line tower with bird’s nests. B The grayscale image of the transmission line tower with damaged insulators

2.2 Edge Detection Based on Canny Algorithm The Canny edge detection operator uses the first-order directional derivative in any direction of the two-dimensional Gaussian function as a noise filter, and convolves with the image f (x, y) for filtering; then finds the local maximum value of the filtered image gradient, and uses this to determine the edge of the image. First take the following two-dimensional Gaussian function equation: G(x, y) =

( 2 ) 1 x + y2 exp − 2π σ 2 2σ 2

(2)

In the above equation, σ is the standard deviation of the Gaussian function. Then, find the first-order directional derivative of the Gaussian function G(x, y) in a certain direction K as: G n = K · ∇G(x, y)  Among them, K is the direction vector, K =   vector, ∇G(x, y) =

∂G ∂x ∂G ∂y

(3)

 cos θ ; ∇G(x, y) is the gradient sin θ

.

The Canny operator is based on a two-dimensional convolution (∇G(x, y)) ∗ f (x, y), and the edge strength is determined by |(∇G(x, y)) ∗ f (x, y)| and the (∇G(x,y))∗f(x,y) . direction K = |(∇G(x,y))∗f(x,y)| The image after edge processing with Canny algorithm is shown in Fig. 2.

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Fig. 2 Image filtered by Canny algorithm of the transmission line

3 Feature Extraction Histogram of Oriented Gradient (HOG) [11, 12] is used to calculate the statistical value of the direction information of the local image gradient. It divides the image into small connected areas, which are called cell units, and then collects the histogram of the gradient or edge direction of each pixel in the cell unit. Finally, these histograms can be combined to form a feature descriptor. The flow chart of hog feature extraction is shown in Fig. 3.

3.1 Gradient Calculation First, regardless of the size of the original image, the original image is divided into 8 × 8 small blocks. In the HOG algorithm, this 8 × 8 small block is called a cell. In a cell, the horizontal and vertical gradients of all pixels are calculated. The specific method is to use the following two spatial filters to filter the image: (

⎛ ⎞ ) −1 −1 0 1 ; ⎝ 0 ⎠ 1

Input image

Normalise gamma & color

Compute gradients

Collect HOGs for all blocks over detection window

Normalise contrast within overlapping blocks of cells

Accumulate weighted votes for gradient orientation over spatial cells

Fig. 3 HOG feature extraction process

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An 8 × 8 cell passes the above two filters to obtain two 8 × 8 matrices, which represent the horizontal and vertical gradients on the image block respectively. In this way, the gradient dx and dy in two directions at each position can be obtained. Then convert the dx and dy of each point into angle and amplitude. The specific algorithm is as follows: / magnitude =

dx2 + dy2

direction = arctan

dx dy

(4) (5)

Finally, each cell can get an 8 × 8 amplitude matrix and an 8 × 8 angle matrix.

3.2 Gradient Histogram Statistics Through gradient calculation, an 8 × 8 amplitude matrix and an 8 × 8 angle matrix are calculated from each 8 × 8 cell. If this is a feature, the feature has 8 × 8 × 2 = 128 dimensions. HOG is based on these 128-dimensional original features and calculates a 9-dimensional histogram. The histogram is based on angles and is divided every 20°. These nine dimensions represent 0, 20, 40, 60, 80, 100, 120, 140, and 160, respectively. HOG comprehensively considers the gradient assignment and angle to vote, and finally determines the weight of each dimension of the histogram. The mathematical equation for this process is expressed as follows: δl = g

θ − θl 20

(6)

δr = g

θr − θ 20

(7)

In the equation, θ represents the direction angle of the point, the subscript l represents the angle closest to the point on the left of the point, the subscript r represents the angle closest to the point on the right of the point, δl represents the increase in the histogram of the left dimension, δr represents the increase in the histogram of the left dimension, and g indicates the magnitude of the point.

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4 Support Vector Machine(SVM) and Convolutional Neural Network (CNN) Support vector machine (Machine learning algorithm) is a neural network mainly used for pattern classification and nonlinear regression [13, 14]. It is often applied to binary classification problems. Specific to this problem, since the final result of bird’s nest identification is only the binary problem of judging whether there is a bird’s nest on the transmission tower, its basic idea is to treat the input data as a point in the space, find a hyperplane in space according to the mark of each point, make the points with the same mark on the same side of the hyperplane, and try to increase the distance from the data point to the hyperplane. At this time, the entire space is divided into two parts, each with a mark corresponding to them. When the data needs to be classified, just calculate its position on the plane. The learning process of SVM is as follows: (1) (2)

(3)

(4)

Perform feature extraction on the sample test set; Select a suitable kernel function for transformation, and convert the input sample space to a high-dimensional RKHS (Reproducing Kernel Hilbert Space); Construct the optimal separation hyperplane in the RKHS space, that is, search for SVM, construct the learning machine from the obtained SVM, and complete the training of the sample; The unknown category data after the same preprocessing is input into the learning machine for classification and discrimination, the learning result is obtained, and the learning process ends.

For self-explosive insulators, unlike the bird’s nest, we can use CNN to identify them.

5 Conclusion In this paper, a set of applied video image processing technology is studied for the identification of bird’s nest on transmission line towers and insulator faults. The project uses digital images intercepted in the video stream of the transmission line transmitted to the monitoring center and the tower picture library obtained by the helicopter patrol as the research object, and performs a series of image processing and recognition on the collected digital image information. The realization of the scheme includes image preprocessing, feature extraction and machine learning training. This scheme provides a new intuitive and accurate means to ensure the safe operation of the power system, which has very important practical significance. Acknowledgements This work was supported by State Grid Corporation of China (SGSW0000AQJS2100060).

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References 1. Hu Y (2021) Analysis of influencing factors of transmission line operation safety and prevention countermeasures. IOP Conf Ser Earth Environ Sci 781(4) 2. Fang J, Hou J, Dai C (2021) Study on safety management of guy wires in the construction of UHV (EHV) transmission lines. J Phys Conf Ser 2005(1) 3. Ekici S (2012) Support vector machines for classification and locating faults on transmission lines. Appl Soft Comput J 12(6) 4. Han J, Yang Z, Zhang Q, Chen C, Li H, Lai S, Hu G, Xu C, Xu H, Wang D, Chen R (2019) A method of insulator faults detection in aerial images for high-voltage transmission lines inspection. Appl Sci 9(10) 5. Liu C, Wu Y, Liu J, Sun Z, Xu H (2021) Insulator faults detection in aerial images from high-voltage transmission lines based on deep learning model. Appl Sci 11(10) 6. Gopakumar P, Mallikajuna B, Reddy MJ, Mohanta DK (2018) Remote monitoring system for real time detection and classification of transmission line faults in a power grid using PMU measurements. Prot Control Modern Power Syst 3(1) 7. Fahim SR, Sarker SK, Muyeen SM, Das SK, Kamwa I (2021) A deep learning based intelligent approach in detection and classification of transmission line faults. Int J Electr Power Energy Syst 133 8. Jin Y, Wang W, Pei L, Chen X, Song B (2021) The research and implementation transmission line tower rod and monitoring system using reverse network RTK technology. J Phys Conf Ser 1894(1) 9. Li C, Wang Q, Jing Z, Zhu H, Wang P, Yu C (2021) A method of data transmission technology for line condition monitoring in smart transmission grid. E3S Web Conf 252 10. Kastrinaki V, Zervakis M, Kalaitzakis K (2003) A survey of video processing techniques for traffic applications. Image Vis Comput 21(4) 11. Savio MM, Deepa T, Bonasu A, Anurag TS (2021) Image processing for face recognition using HAAR, HOG, and SVM algorithms. J Phys Conf Ser 1964(6) 12. Wang Y, Zhu X, Wu B (2018) Automatic detection of individual oil palm trees from UAV images using HOG features and an SVM classifier. Int J Remote Sens 40(19). Taylor & Francis 13. Mao Y, Liu H, Ye R, Shi Y, Song Z (2014) Detection and segmentation of virus plaque using HOG and SVM: toward automatic plaque assay. Bio-Med Mater Eng 24(6) 14. Xi HY, Xiao ZT, Zhang F (2011) Study on pedestrian detection method based on HOG features and SVM. Adv Materi Res 1289

Uniformly Observability of the Semi-discrete Schrödinger Equation Kunyi Yang, Lei Chen, and Jietao Zou

Abstract In this paper, we consider the uniformly observability of the semi-discrete scheme for Schrödinger equation. Firstly, for the Schrödinger equation, it is shown to be exponentially stable and the observability inequality has been stated in the paper. Secondly, the researcher constructs the numerical scheme for the Schrödinger equation, and presents the observability inequality of the discrete scheme. Keywords Schrödinger equation · Semi-discrete scheme · Observability inequality

1 Introduction Over the past decades, much research has been focused on the stabilization and convergence properties of the distributed parameter systems. Unfortunately, little progress has been made in the related research in recent years. Tebou and Zuazua [1] show that the locally damped wave equation is exponentially stable by adding the vanishing numerical viscosity term, and prove the stability property by discrete multiplier techniques. Tebou and Zuazua [2] further solve the problem of stabilization for the wave equation with the boundary dissipation through the same method. And [3] shows the boundary observability of the semi-discrete schemes for the onedimensional Schrödinger equation. Recently Liu and Guo [4] argue that Euler–Bernoulli beam is exponentially stable through constructing the semi-discretized scheme using the finite volume method. And the uniformly exponential decay of the discrete system has been proved by Lyapunov function, a crucial method of energy multiplier technique. Later on Liu and Guo [5, 6] consider the wave equation, also find that the same finite difference scheme is uniformly exponentially stable. In view of the wave equation with local viscosity damping, Guo and Xu [7] obtain the uniformly exponential convergence by adopting the same semi-discrete scheme

K. Yang (B) · L. Chen · J. Zou College of Science, North China University of Technology, Beijing 100144, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 C. Hu et al. (eds.), Conference Proceedings of 2021 International Joint Conference on Energy, Electrical and Power Engineering, Lecture Notes in Electrical Engineering 899, https://doi.org/10.1007/978-981-19-1922-0_63

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For the one-dimensional Schrödinger equation with vanishing viscosity, its uniform controllability has been considered in the references [8] and [9]. This paper considers the Schrödinger equation with the dissipative boundary condition which is shown to be exponentially stable and the observability inequality has been obtained. And then the semi-discretized scheme has been constructed by using the finite volume method. The corresponding observability inequality has been proved for the discrete system. In the paper, we consider the Schrödinger equation as follows ⎧ wt (x, t) = −i wx x (x, t), 0 < x < 1, t > 0, ⎪ ⎪ ⎨ w(0, t) = 0, t ≥ 0, ⎪ wx (1, t) = −kwt (1, t), t ≥ 0, ⎪ ⎩ w(x, 0) = w0 (x), 0 ≤ x ≤ 1,

(1)

where x and t denote the position and time respectively, w denotes the state, w 0 (x) denotes the initial value of w and k is a positive constant. Machtyngier and Zuazua [10] proved that the high-dimensional Schrödinger equation has been exponentially stable. In this paper we will analyze the one-dimensional Schrödinger equation. The paper contains the following sections. In the second section, we show that the one-dimensional Schrödinger equation is exponentially stable and the observability inequality is proven. The next section is focused on the semi-discrete scheme for the Schrödinger equation and the decay property for the discrete system, and the observability inequality for the semi-discrete Schrödinger equation has been shown. The last section is devoted to the summary of this paper.

2 Exponential Stability and Observability Inequality of the Schrödinger Equation For the one-dimensional Schrödinger Eq. (1), its energy is naturally defined as that E(t) =

1 2

1 0

|wx (x, t)|2 d x, t ≥ 0,

(2)

whose decay property can be easily inferred below ˙ = −k|wt (1, t)|2 , k > 0, t > 0. E(t)

(3)

Then the paper presents the exponential stability of the system (1) by using the energy multiplier technique stated in the theorem below. Theorem 1 There exist positive constants M and ω such that the energy E(t) of the system (1) satisfies that

Uniformly Observability of the Semi-discrete …

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E(t) ≤ Me−ωt E(0),

∀t ≥ 0.

(4)

Proof Define the multiplier 

1 ρ(t) = · Im 2

1

xw(x, t)wx (x, t)d x,

t ≥ 0,

(5)

0

which together with the inequality   |w(x, t)| = 

x

2

0

2  wξ (ξ, t)dξ  ≤ 2E(t), t ≥ 0,

(6)

give that |ρ(t)| ≤ E(t), ∀t ≥ 0.

(7)

After the simple process of integration by parts, we have that k2 ρ(t) ˙ = −2E(t) + |wt (1, t)|2 + Re 2





 i −k w(1, t)wt (1, t) , 2

∀t ≥ 0, (8)

by using the boundary conditions of (1). Moreover, since 



 3 2  i −k  ≤ |w(1, t)|2 + k + 1 |wt (1, t)|2 ,  (1, t) w(1, t)w t   6 8 2

∀t ≥ 0,

(9)

by Cauchy’s inequality, and   |w(1, t)| =  2

0

1

2  wx (x, t)d x  ≤ 2E(t), ∀t ≥ 0,

(10)

thus, altogether with (8) we find that   ρ(t) ˙ ≤ −E(t) + k 2 + 1 |wt (1, t)|2 ,

∀t ≥ 0.

(11)

t ≥ 0,

(12)

Now define the Lyapunov function L(t) = E(t) + ερ(t), 0 < ε < 1, which together with (3) and (11) tell us that    ˙ L(t) ≤ − k − ε k 2 + 1 |wt (1, t)|2 − εE(t), ∀t ≥ 0.

(13)

758

When 0 < ε
0, then we have the

Next we consider the observability inequality of the system (1) shown for the following conservative system ⎧ ⎨ u t (x, t) = −iu x x (x, t), 0 < x < 1, t > 0, u(0, t) = u x (1, t) = 0, t ≥ 0, ⎩ u(x, 0) = u 0 (x), 0 ≤ x ≤ 1.

(19)

Its energy is naturally defined as that 1 E (t) = 2



u

1

|u x (x, t)|2 d x, t ≥ 0,

(20)

0

which results apparently that E˙ u (t) = 0, t > 0. Then we find that the observability inequality can be obtained. Theorem 2 When T > 43 , the observability inequality

(21)

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1 E (0) ≤ 2(3T − 4)



T

u

|u t (1, t)|2 dt

(22)

0

holds. Proof Define the function 

1

ρ (t) = Im u

xu(x, t)u x (x, t)d x,

t ≥ 0,

(23)

0

which together with the inequality   |u(x, t)| = 

x

2

0

2  u η (η, t)dη ≤ 2E u (t), t ≥ 0,

(24)

give that  u  ρ (t) ≤ 2E u (t), ∀t ≥ 0.

(25)

Then after the processes of integration by parts, we have that   ρ˙ u (t) = 4E u (t) + Im u(1, t)u t (1, t) ,

∀t ≥ 0,

(26)

by using boundary conditions of the system (19). Now for any T > 0, integrating for time t from 0 to T in the Eq. (26) shows that 

T



4

T

E (t)dt = ρ (T ) − ρ (0) − Im u

u

u

0

u(1, t)u t (1, t)dt,

∀T > 0,

(27)

0

which together with the following estimate   |u(1, t)| = 

1

2

0

2  u x (x, t)d x  ≤ 2E u (t), 0 ≤ x ≤ 1, t ≥ 0,

(28)

and the inequality (25) give that 

T

1 E (t)dt ≤ 2E (T ) + 2E (0) + 2 u

3 0

u



T

u

|u t (1, t)|2 dt,

∀T > 0.

(29)

0

Also from the conservative property (21), we obtain the observability inequality (22). ❚

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3 Decay Property of the Semi-discrete Scheme and Its Observability Inequality In the section, we construct the semi-discretized schemes for the systems (1) and (19) by using the finite volume method. Then the energies of the systems have been presented, and the inequality which the system (19) satisfies has been displayed. For a large natural number N , make the space variable x difference 0 = x0 < x1 < · · · < x N < x N +1 = 1,

(30)

which can be signed as that x j = j h,

j = 0, 1, · · · , N + 1,

(31)

and h = N 1+1 is the space step. Then we introduce the notations subsequently v j+ 21 =

v j +v j+1 , 2

δx v j+ 21 =

v j+1 −v j h

, δx2 v j =

δx v j+ 1 −δx v j− 1 2

2

h

.

(32)

The discrete scheme of the system (1) can be constructed as ⎧   1   ⎪ + w = −iδx2 w j , w ⎪ 1 1 ⎨ 2 j+ j− 2

w0 = 0, ⎪ ⎪ ⎩ δx w N + 1 + 2

2

ih  wN + 1 2 2

j = 1, · · · , N , (33)

=

−kw N +1 ,

where w j ( j = 0, 1, · · · , N + 1) represent the discretization value of w(x j , t). ( j = 0, 1, · · · , N + 1). The energy of the system (33) is defined as N 2 h    E h (t) = δx w j+ 21  , 2 j=0

t ≥ 0.

(34)

Lemma 1 The energy E h (t) is dissipative in the sense that 2  E˙ h (t) = −k w N +1  ,

t > 0, k > 0.

(35)

Proof Multiply the first equation of the system (33) by hw j  and take the addition by j from 1 to N , then we have that N    1 j=1

2

wj+ 1 2

+

wj− 1 2



 +

iδx2 w j

hw j = 0

(36)

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which results that h

 N  N    h   2 δx w j+ 21 δx w j+ 1 + i δx w N + 21 − w N + 1 wN +1 = 0. w j+ 1  − i h 2 2 2 2 j=0 j=0 (37)

Thus, from the definition of the energy (34), it is indicated that E˙ h (t) = Re



δx w N + 21 +

  ih  w N + 1 wN +1 , 2 2

(38)

which together with the second boundary condition of the system (33) lead apparently to (35). ❚ Next we construct the semi-discretized scheme for the system (19) ⎧   1   2 ⎪ ⎪ ⎨ 2 u j+ 21 + u j− 21 = −i δx u j , u 0 = 0, ⎪ ⎪ ⎩ δx u N + 1 + i h u  1 = 0, 2 N+ 2

j = 1, · · · , N , (39)

2

where u j ( j = 0, 1, · · · , N + 1) represent the discretization value of u(x j , t). ( j = 0, 1, · · · , N + 1). The energy of the system (39) is defined as E hu (t) =

N 2 h    δx u j+ 21  , t ≥ 0, 2 j=0

(40)

whose properties can be obtained naturally as follows. Lemma 2 The energy E hu (t) satisfies that E˙ hu (t) = 0,

∀t > 0.

(41)

Theorem 3 When T > 43 , the inequality below holds E hu (0) ≤

1 2(3T − 4)



T 0

|u N +1 |2 dt.

(42)

  Proof Multiply the first equation of (39) by j h 2 δx u j+ 21 + δx u j− 21 , make the sum for j from 1 to N and integrate for t from 0 to T , then we have that

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 N   T h j=1

0

= −i h

2

   u j+ 1 + u j− 1 j h δx u j+ 21 + δx u j− 21 dt 2

N   T j=1

0

2

  δx2 u j j h δx u j+ 21 + δx u j− 21 dt

(43)

which together with the boundary conditions of (39) result that 2     T   j h u j+ 21 + u j− 21 u j+ 21 − u j− 21 |0T − 2 0 δx u N + 21  dt j=1 T T −2i 0 u N + 21 u N + 1 dt + 8 0 E hu (t)dt = 0.

i

N 

(44)

2

Multiply the second boundary condition of (39) by 2δx u N + 21 and integrate for t from 0 to T , then we have that 

T

2 0

 2    T 1 1 1 δx u N + 2  dt + i hu N + 2 δx u N + 2 |0 − i

T 0

  u N + 21 u N +1 − u N dt = 0. (45)

Therefore,    j h u j+ 21 + u j− 21 u j+ 21 − u j− 21 |0T + i hu N + 21 δx u N + 21 |0T j=1 T T −2i 0 u N + 21 u N +1 dt + 8 0 E hu (t)dt = 0.

i

N 

(46)

At the same time, simple computations can show the following estimates           N u i 1 1 − u 1 1 δx u 1  ≤ 4E (t), 1 + u j h u u + i hu j+ 2 j− 2 j+ 2 j− 2 N+ 2 N+ 2  h    j=1

(47)

and  2   u N + 21  ≤ 2E hu (t).

(48)

In conclusion, it is found that 

T

6 0

 E hu (t)dt

≤

8E hu (t)

T

+ 0

  u

N +1

2  dt

(49)

which together with the conservative property (41) show that the inequality (42) holds. ❚

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4 Summary In this paper, we consider the one-dimensional Schrödinger equation with dissipative boundary condition. Firstly we show that the system is exponentially stable and the observability inequality holds. Secondly, the semi-discretized scheme of the Schrödinger equation has been constructed by using the finite volume method. And the observability inequality of the discrete system has been proven subsequently. The conclusion of the paper means that the semi-discrete scheme based on the finite volume method has been effective for the observability inequality, which may bring about the stability or controllability results of the discrete system for our possible future work.

References 1. Tebou LT, Zuazua E (2003) Uniform exponential long time decay for the space semidiscretization of a locally damped wave equation via an artificial numerical viscosity. Numer Math 95:563–598 2. Tebou LT, Zuazua E (2007) Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation. Adv. Copmut. Math. 26:337–365 3. Infante JA, Zuazua E (1999) Boundary observability for the space semi-discretizations of the 1-D wave equation. Math Model Numer Anal 33:407–438 4. Liu JK, Guo BZ (2019) A novel semi-discrete scheme preserving uniformly exponential stability for an Euler-Bernoulli beam. Syst Control Lett 134:104518 5. Liu JK, Guo BZ (2020) A new semi-discretized order reduction finite difference scheme for uniform approximation of 1-d wave equation. SIAM J Control Optim 58:2256–2287 6. Liu JK, Wu BB (2018) A uniformly approximated semi-discretized finite difference scheme for exponential stabiliy of 1-d wave equation with damped boundary. Acta Math Appl Sin 41:832–845 7. Guo BZ, Xu BB (2020) A semi-discrete finite difference method to uniform stabilization of wave equation with local viscosity. IFAC J. Syst. Control. 13:101000 8. Micu S, Roventa I (2012) Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity. In: ESAIM: COCV, vol 18, pp 277–293 9. Bugariu IF, Roventa I (2014) Small time uniform controllability of the linear one-dimensional Schrödinger equation with vanishing viscosity. J Optim Theory Appl 160:949–965 10. Machtyngier E, Zuazua E (1994) Stabilization of the Schrödinger equation. Portugallae Math 51:243–256