Smart Power Distribution Network: Situation Awareness, Planning, and Operation (Power Systems) [1st ed. 2023] 9819967570, 9789819967575

Table of contents :
Preface
Acknowledgments
Contents
1 System Overview
2 Smart Power Distribution Network Situation Awareness
2.1 Introduction
2.2 Description of Situation Awareness
2.2.1 Concept of Situation Awareness
2.2.2 Objectives of Situation Awareness for Smart Distribution Networks
2.2.3 Challenges of Situation Awareness for Smart Distribution Networks
2.3 Comprehensive Framework of Situation Awareness
2.4 Key Technologies of Situation Detection
2.4.1 Big Data of Situation
2.4.2 5G Communication Technology
2.4.3 Virtual Acquisition Technology
2.4.4 Optimization Configuration of Measurement Technology
2.5 Key Technologies of Situation Comprehension
2.5.1 Uncertain Power Flow Calculation Technology
2.5.2 Hybrid State Estimation Technology
2.5.3 SPDN Self-Healing Technology
2.5.4 SPDN Characteristic Analysis Technology
2.5.5 Coordinated Dispatch Technology
2.5.6 Power Market Technology
2.5.7 Virtual Power Plant Technology
2.5.8 Renewable Energy Planning Technology
2.5.9 Edge Computing Technology
2.6 Key Technologies of Situation Prediction
2.6.1 Three-Phase Unbalanced Load Prediction Technology
2.6.2 Renewable Energy Output Prediction Technology Considering Uncertainty
2.6.3 Electric Vehicle Charging Prediction Technology
2.6.4 Intelligent Inspection Technology
2.6.5 Security Situation Prediction Technology
2.7 Conclusions
References
3 Photovoltaic Prediction and Virtual Collection
3.1 Photovoltaic Prediction
3.1.1 Introduction
3.1.2 Factor Analysis
3.1.3 Photovoltaic Output Forecasting Method
3.1.4 Short-Term Photovoltaic Output Forecasting Examples and Results Analysis
3.2 Photovoltaic Virtual Collection
3.2.1 Introduction
3.2.2 Virtual Collection Framework of DPVs
3.2.3 Deep Trained RDAE for DPVs Virtual Collection
3.2.4 Case Study
3.2.5 Conclusion
References
4 Multi-energy Load Forecasting of Integrated Energy System
4.1 Introduction
4.2 Problem Model
4.3 Choice of Load Prediction Influence Factors Based on Pearson Correlation Coefficient
4.4 Load Prediction Method Based on IPSO-WNN
4.4.1 WNN Model
4.4.2 Particle Swarm Optimization
4.4.3 Inertia Weight of Particles
4.4.4 Chaos Algorithm
4.5 Experimental Simulation and Analysis
4.5.1 Data Processing
4.5.2 Evaluating Indicators
4.5.3 Parameter Setting
4.5.4 Result Analysis
4.6 Conclusion
References
5 Optimal Planning of Energy Storage Considering Uncertainty of Load and Wind Generation
5.1 Introduction
5.2 Problem Formulation
5.2.1 Objective Function
5.2.2 Constraints
5.2.3 Uncertainty Reduction
5.3 Solving the Optimization Model
5.4 Case Study
5.4.1 The Benchmark System
5.4.2 Comparisons of Simulation Results
5.4.3 Comparison of Different Algorithm
5.5 Conclusion
References
6 Coupled Multi-network Constrained Planning of Energy Supplying Facilities for Hybrid Hydrogen-Electric Vehicles
6.1 Introduction
6.2 Modified Maximum Covering Location Method Regarding TN
6.2.1 Traffic Flow
6.2.2 Modelling of H2EVs
6.2.3 Modified MCLM
6.3 Multi-network Framework Considering Coupled Flow Constraints
6.3.1 Multi-network Framework
6.3.2 AC Power Flow Constrained PN with PV Integrated
6.3.3 HN Considering PV Driven SOEC
6.3.4 Coupled Section
6.4 Many-Objective Optimization Based Bi-level Planning Model for HVESF
6.4.1 Bi-level Many-Objective Planning Model
6.4.2 Solving Procedure
6.5 Case Study
6.5.1 Case Description
6.5.2 Analysis on HVESFs Planning Model and Relationship Among Many Objectives
6.5.3 Analysis on Effectiveness of Obtained Planning Solutions Considering Modified MCLM
6.5.4 Analysis on Effectiveness of Multi-network Framework
6.6 Conclusion
References
7 Multiple Equipment Planning for Integrated Energy System
7.1 Introduction
7.2 Introduction of Multi-energy Coupling in IES
7.3 Models for DG Output Uncertainty and Carbon Emission Reduction
7.3.1 DG Uncertainty Modeling Based on Matrix Form Affine Arithmetic
7.3.2 Charging Cost Model of Carbon Emissions
7.4 Optimal Planning Model of IES Considering Carbon Emissions and DG Uncertainty
7.4.1 Objective Function
7.4.2 Constraints
7.5 Solution Methodology
7.6 Case Study
7.6.1 Test System Introduction and Parameters Setting
7.6.2 Results and Discussion
7.6.3 Comparison of Optimization Algorithms
7.6.4 Sensitivity Analysis
7.7 Conclusion
References
8 Collaborative Operation Between Power Network and Hydrogen Fueling Stations with Peer-to-Peer Energy Trading
8.1 Introduction
8.2 Operation Model of HFSs Coupled Power-Traffic System Considering P2P Energy Trading
8.2.1 Operation Model of Power Network
8.2.2 Operation Model of Hydrogen Fueling Station with P2P Energy Trading
8.2.3 Operation Model of Traffic Network
8.3 Collaborative Operation Framework Considering P2P Energy Trading
8.3.1 Collaborative Operation Framework
8.3.2 P2P Energy Trading Strategy
8.4 Benefit Allocation Mechanism with Collaborative P2P Energy Trading Strategy
8.4.1 The Allocation Mechanism Based on Bilateral Shapley Value
8.4.2 The Formulation of Characteristic Function v(mathcalS)
8.4.3 Vthe Proof of Proposition
8.5 Case Study
8.5.1 Simulation Settings
8.5.2 Analysis on the Coupled System and Impact Relationship Among HFSs, PN and TN
8.5.3 Analysis on Effectiveness of Collaborative Framework with P2P Energy Trading
8.6 Conclusions
References
9 Coordinated Operation Between Electric Vehicle Charging Stations and Distribution Power Network Considering Energy and Reserve
9.1 Introduction
9.2 Formulations of Energy-Reserve Decision for Electric Vehicle Charging Stations
9.3 Operational Formulations of Distribution Power Network
9.3.1 Power Balance
9.3.2 Security Constraints
9.3.3 ESS Output Constraints
9.3.4 Reserve Constraints
9.3.5 Reactive Power Constraints
9.4 Shared Energy and Reserve Model for Charging Stations and Distribution Power Network Using Coalition Game
9.4.1 Shared Energy and Reserve Scheduling Model
9.4.2 Characteristic Function and Shapely Value Based on Participation Factors
9.5 Case Study
9.5.1 Simulation Settings
9.5.2 Simulation Results
9.6 Conclusion
References
10 Interactive Energy Management Between Electric Vehicle Charging Stations and Electricity Distribution System
10.1 Introduction
10.2 Decision Model of Electric Vehicle Charging Stations Considering Quality of Service Constraints
10.2.1 Electric Vehicle Charging Station
10.2.2 QoS of Electric Vehicle Charging Station
10.2.3 Decision Model of Electric Vehicle Charging Station
10.3 Decision Model of Distribution Power Network with Electric Vehicle Charging Stations
10.3.1 Decision Model of Distribution Power Network
10.3.2 Convex Relaxation
10.4 Interactive Energy Management for Electric Vehicle Charging Stations and Distribution Power Network Using Supply Function Equilibrium
10.4.1 Supply Function Equilibrium
10.4.2 Existence of Equilibrium Solutions
10.5 Hybrid Optimization Algorithm for Equilibrium Solution
10.6 Case Study
10.6.1 Case Description
10.6.2 Case study
10.7 Conclusion
References

Citation preview

Power Systems

Leijiao Ge Yuanzheng Li

Smart Power Distribution Network Situation Awareness, Planning, and Operation

Power Systems

Electrical power has been the technological foundation of industrial societies for many years. Although the systems designed to provide and apply electrical energy have reached a high degree of maturity, unforeseen problems are constantly encountered, necessitating the design of more efficient and reliable systems based on novel technologies. The book series Power Systems is aimed at providing detailed, accurate and sound technical information about these new developments in electrical power engineering. It includes topics on power generation, storage and transmission as well as electrical machines. The monographs and advanced textbooks in this series address researchers, lecturers, industrial engineers and senior students in electrical engineering. **Power Systems is indexed in Scopus**

Leijiao Ge · Yuanzheng Li

Smart Power Distribution Network Situation Awareness, Planning, and Operation

Leijiao Ge School of Electrical and Information Engineering Tianjin University Tianjin, China

Yuanzheng Li School of Artificial Intelligence and Automation Huazhong University of Science and Technology Wuhan, Hubei, China

ISSN 1612-1287 ISSN 1860-4676 (electronic) Power Systems ISBN 978-981-99-6757-5 ISBN 978-981-99-6758-2 (eBook) https://doi.org/10.1007/978-981-99-6758-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Preface

Due to the rapid development of emerging information and communication technologies and advanced metering infrastructure, distribution networks are in an evolvement from passive to active distribution networks, also called smart power distribution networks (SPDN). In addition, with the rapidly increasing penetration of distributed generations inspired by the smart grid concept, the SPDN integrates multiple renewable energy sources and focuses on reliable operation. To achieve the environmental objective of gas emission reduction and accommodate the high penetration of distributed generations, supervisory control and data acquisition systems are employed to monitor the SPDN, and distribution management systems and energy management systems act as decision-support information systems for the coordination of remote SPDN equipment. Additionally, the widespread application of devices such as distribution transformer terminal unit, feeder terminal unit, remote terminal unit, and distribution automation terminal contributes to the maturity of SPDN. Planning and operation cost is an economic factor that the SPDN management should consider. The planning and operation level of multi-terminal SPDN determines the power quality of end-users, to some extent. Among multiple planning and operation technologies, situation awareness (SA) emerges and is gradually integrated into the SPDN. Facing a high proportion of RES, adequate monitoring, analysis, and prediction of the SPDN operating status are urgent. Therefore, comprehensive SA, which contains detection, comprehension, and projection, becomes a significant guarantee for the optimal operation of SPDN. Due to the strong adaptability, SA can dynamically evolve with the future SPDN technology development to provide higher quality planning and operation of SPDN. This book is a monograph about the data-mechanism-driven methods for SPDN situation awareness, planning, and operation, which consists of 10 chapters. It begins with an overview of the basic concepts of SPDN situation awareness, planning, and operation in terms of problem statement and property. Since the data collection and state detection of SPDN are the foundation of planning and operation, the SA is introduced first. Then, the work of SPDN planning and operation are shown. To help readers have a better understanding, we would like to make a simple review of the 10 chapters in the following. v

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Preface

Chapter 1 conducts a brief introduction of SPDN issues, including the concept of SA, planning, and operation. Following the introduction of SPDN, the key problem statement and property are identified in this chapter. Chapter 2 provides a comprehensive review of SPDN situation awareness. The state-of-the-art knowledge of SA is discussed, a review of critical technologies is presented, and a five-layer visualization framework of the SA is constructed. Chapter 3 presents the data-based method for photovoltaic prediction and virtual collection in the SPDN. Some targeted neural networks are introduced in this chapter, which aim to achieve the short-term prediction of photovoltaic active power and low-cost collection of operational data. Chapter 4 proposes a wavelet neural network based on the improved particle swarm optimization method for short-term load prediction of integrated energy system. Chapter 5 proposes a novel optimal energy storage system capacity planning scheme, which is proposed to reduce the influence of uncertainty of both renewable energy and load demands. Chapter 6 presents a multinetwork framework considering coupled flow constraints for the planning issue of hybrid hydrogen-electric vehicles energysupplying facilities, involving all the power network, hydrogen network, and traffic network. Chapter 7 introduces an optimization planning model for integrated energy systems considering the carbon emission charging and distributed generation, in which affine model based on matrix form is first proposed and an optimal planning model is established. Chapter 8 establishes the operation model of hydrogen fueling station coupled power-traffic system. A collaborative operation framework with peer-to-peer energy trading is proposed to promote the interactive efficiency between the SPDN and the hydrogen fueling station. Chapter 9 proposes a coordinated operation method for electric vehicle charging stations and an SPDN, considering integrated energy and reserve regulation. We propose a shared energy and reserve scheduling model based on the coalition game and adopt a characteristic function to study allocations of economic benefits. Chapter 10 presents an energy management method for the operation of electric vehicle charging stations and an SPDN while considering their interaction. A game based on the supply function equilibrium model is adopted to analyze the energy interaction. In conclusion, this book provides various applications of the data-mechanismbased situation awareness, planning, and operation techniques for the SPDN operation. We hope this book can inspire readers to define new problems, apply novel methods, and obtain interesting results with massive history data in power systems. Tianjin, China Wuhan, China

Leijiao Ge Yuanzheng Li

Acknowledgments

This book made a summary of our research about smart power distribution network situation awareness, planning, and operation achieved in recent years. These works were carried out in the Key Laboratory of Smart Grid of the Ministry of Education, Tianjin University, Tianjin, China, and the School of Artificial Intelligence and Automation, Ministry of Education Key Laboratory of Image Processing and Intelligence Control, Huazhong University of Science and Technology, Wuhan, China. Many people contributed to this book in various ways. The authors are indebted to Mr. Hangxu Liu from Tianjin University and Mr. Jun Zhang from Huazhong University of Science and Technology, who have contributed materials to this book and thank them for their assistance in pointing out typos and checking the whole book. In addition, we appreciate the staff at Springer for their assistance and help in the preparation of this book. This work is supported in part by the National Natural Science Foundation of China (No. 51807134) and in part by the Tencent Rhinoceros Foundation of China (No. Tencent TEG RBFR20230705). The authors really appreciate their supports. Leijiao Ge Yuanzheng Li

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Contents

1

System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2

Smart Power Distribution Network Situation Awareness . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Description of Situation Awareness . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Concept of Situation Awareness . . . . . . . . . . . . . . . . . . . . . 2.2.2 Objectives of Situation Awareness for Smart Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Challenges of Situation Awareness for Smart Distribution Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Comprehensive Framework of Situation Awareness . . . . . . . . . . . 2.4 Key Technologies of Situation Detection . . . . . . . . . . . . . . . . . . . . . 2.4.1 Big Data of Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 5G Communication Technology . . . . . . . . . . . . . . . . . . . . 2.4.3 Virtual Acquisition Technology . . . . . . . . . . . . . . . . . . . . . 2.4.4 Optimization Configuration of Measurement Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Key Technologies of Situation Comprehension . . . . . . . . . . . . . . . 2.5.1 Uncertain Power Flow Calculation Technology . . . . . . . . 2.5.2 Hybrid State Estimation Technology . . . . . . . . . . . . . . . . . 2.5.3 SPDN Self-Healing Technology . . . . . . . . . . . . . . . . . . . . 2.5.4 SPDN Characteristic Analysis Technology . . . . . . . . . . . 2.5.5 Coordinated Dispatch Technology . . . . . . . . . . . . . . . . . . . 2.5.6 Power Market Technology . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.7 Virtual Power Plant Technology . . . . . . . . . . . . . . . . . . . . . 2.5.8 Renewable Energy Planning Technology . . . . . . . . . . . . . 2.5.9 Edge Computing Technology . . . . . . . . . . . . . . . . . . . . . . .

3 3 5 5 5 6 6 7 8 8 9 9 9 10 11 11 11 12 12 12 12 13

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2.6

3

4

Key Technologies of Situation Prediction . . . . . . . . . . . . . . . . . . . . 2.6.1 Three-Phase Unbalanced Load Prediction Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Renewable Energy Output Prediction Technology Considering Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.3 Electric Vehicle Charging Prediction Technology . . . . . . 2.6.4 Intelligent Inspection Technology . . . . . . . . . . . . . . . . . . . 2.6.5 Security Situation Prediction Technology . . . . . . . . . . . . . 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

Photovoltaic Prediction and Virtual Collection . . . . . . . . . . . . . . . . . . . 3.1 Photovoltaic Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Photovoltaic Output Forecasting Method . . . . . . . . . . . . . 3.1.4 Short-Term Photovoltaic Output Forecasting Examples and Results Analysis . . . . . . . . . . . . . . . . . . . . . 3.2 Photovoltaic Virtual Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Virtual Collection Framework of DPVs . . . . . . . . . . . . . . 3.2.3 Deep Trained RDAE for DPVs Virtual Collection . . . . . 3.2.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19 19 19 20 21

Multi-energy Load Forecasting of Integrated Energy System . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Problem Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Choice of Load Prediction Influence Factors Based on Pearson Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Load Prediction Method Based on IPSO-WNN . . . . . . . . . . . . . . . 4.4.1 WNN Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Inertia Weight of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Chaos Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Experimental Simulation and Analysis . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Evaluating Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Parameter Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Result Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 52

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5

6

Optimal Planning of Energy Storage Considering Uncertainty of Load and Wind Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Uncertainty Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Solving the Optimization Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 The Benchmark System . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Comparisons of Simulation Results . . . . . . . . . . . . . . . . . . 5.4.3 Comparison of Different Algorithm . . . . . . . . . . . . . . . . . 5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coupled Multi-network Constrained Planning of Energy Supplying Facilities for Hybrid Hydrogen-Electric Vehicles . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Modified Maximum Covering Location Method Regarding TN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Traffic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Modelling of H2EVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Modified MCLM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Multi-network Framework Considering Coupled Flow Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Multi-network Framework . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 AC Power Flow Constrained PN with PV Integrated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 HN Considering PV Driven SOEC . . . . . . . . . . . . . . . . . . 6.3.4 Coupled Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Many-Objective Optimization Based Bi-level Planning Model for HVESF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Bi-level Many-Objective Planning Model . . . . . . . . . . . . 6.4.2 Solving Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Case Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Analysis on HVESFs Planning Model and Relationship Among Many Objectives . . . . . . . . . . . 6.5.3 Analysis on Effectiveness of Obtained Planning Solutions Considering Modified MCLM . . . . . . . . . . . . . 6.5.4 Analysis on Effectiveness of Multi-network Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Multiple Equipment Planning for Integrated Energy System . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Introduction of Multi-energy Coupling in IES . . . . . . . . . . . . . . . . 7.3 Models for DG Output Uncertainty and Carbon Emission Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 DG Uncertainty Modeling Based on Matrix Form Affine Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Charging Cost Model of Carbon Emissions . . . . . . . . . . . 7.4 Optimal Planning Model of IES Considering Carbon Emissions and DG Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Test System Introduction and Parameters Setting . . . . . . 7.6.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.3 Comparison of Optimization Algorithms . . . . . . . . . . . . . 7.6.4 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collaborative Operation Between Power Network and Hydrogen Fueling Stations with Peer-to-Peer Energy Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Operation Model of HFSs Coupled Power-Traffic System Considering P2P Energy Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Operation Model of Power Network . . . . . . . . . . . . . . . . . 8.2.2 Operation Model of Hydrogen Fueling Station with P2P Energy Trading . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Operation Model of Traffic Network . . . . . . . . . . . . . . . . . 8.3 Collaborative Operation Framework Considering P2P Energy Trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Collaborative Operation Framework . . . . . . . . . . . . . . . . . 8.3.2 P2P Energy Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . 8.4 Benefit Allocation Mechanism with Collaborative P2P Energy Trading Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 The Allocation Mechanism Based on Bilateral Shapley Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 The Formulation of Characteristic Function v(S) . . . . . . 8.4.3 Vthe Proof of Proposition . . . . . . . . . . . . . . . . . . . . . . . . . .

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Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.2 Analysis on the Coupled System and Impact Relationship Among HFSs, PN and TN . . . . . . . . . . . . . . 8.5.3 Analysis on Effectiveness of Collaborative Framework with P2P Energy Trading . . . . . . . . . . . . . . . . 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Coordinated Operation Between Electric Vehicle Charging Stations and Distribution Power Network Considering Energy and Reserve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Formulations of Energy-Reserve Decision for Electric Vehicle Charging Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Operational Formulations of Distribution Power Network . . . . . . 9.3.1 Power Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Security Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 ESS Output Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.4 Reserve Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 Reactive Power Constraints . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Shared Energy and Reserve Model for Charging Stations and Distribution Power Network Using Coalition Game . . . . . . . . 9.4.1 Shared Energy and Reserve Scheduling Model . . . . . . . . 9.4.2 Characteristic Function and Shapely Value Based on Participation Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Simulation Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Interactive Energy Management Between Electric Vehicle Charging Stations and Electricity Distribution System . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Decision Model of Electric Vehicle Charging Stations Considering Quality of Service Constraints . . . . . . . . . . . . . . . . . . 10.2.1 Electric Vehicle Charging Station . . . . . . . . . . . . . . . . . . . 10.2.2 QoS of Electric Vehicle Charging Station . . . . . . . . . . . . . 10.2.3 Decision Model of Electric Vehicle Charging Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Decision Model of Distribution Power Network with Electric Vehicle Charging Stations . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Decision Model of Distribution Power Network . . . . . . . 10.3.2 Convex Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10.4 Interactive Energy Management for Electric Vehicle Charging Stations and Distribution Power Network Using Supply Function Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Supply Function Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Existence of Equilibrium Solutions . . . . . . . . . . . . . . . . . . 10.5 Hybrid Optimization Algorithm for Equilibrium Solution . . . . . . 10.6 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.1 Case Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.2 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

System Overview

With the increasing penetration of renewable energy and distributed energy resources, smart power distribution network (SPDN) is facing great challenges, which could be divided into two categories. On the one hand, the endogenous uncertainties of renewable energy and multi-energy load lead to great difficulties in SPDN forecast. On the other hand, massive electric devices as well as their complex constraint relationships bring about significant difficulties in SPDN operation and maintenance. The integration of intermittent renewable energy into SPDN presents significant challenges for the lean operation and maintenance of SPDN. As a vital guarantee for the observability improvement and stable operation of SPDN, situation awareness (SA) began to excite the significant interest of SPDN scholars and managers. In this paper, the state-of-the-art concept, issues, and challenges in SPDN SA are discussed, a review of key technologies and developing trends is presented, and a 5-dimensional visualization framework of the SPDN SA is constructed. Specific to lean operation and maintenance, the paper decomposes SA into three stages: detection, comprehension, and prediction, where SA detection aims to improve the SPDN observability, SA comprehension is associated with the SPDN operating status, and SA prediction pertains to the analysis of the future SPDN situation. We believe that the presented technical framework of SPDN SA can be used as a solid base for lean operation and maintenance in SPDN. And the carbon emission also comes with high environmental costs as the world is progressing toward clean and efficient renewable energy. These challenges are calling for alternative supplies to meet the demand of remote communities that have equal rights to access reliable energy. Meanwhile, it is notable that many areas are rich in natural renewable resources, an ideal condition for the adoption of integrated energy system (IES), which integrate various distributed renewable energy generation from, e.g., solar, wind, and biomass energy, to locally supply the energy demand in these areas. In this context, the capacity configuration of various energy storage and conversion devices has become a challenge. Providing larger capacity for SPDN planning will improve system stability. But strong conservatism can also

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_1

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reduce system economy. In addition, planning solutions can also affect the operational performance of the system. Therefore, the planning and operation of SPDN are also key points to be discussed in this book. Owe to the increasing attention paid to the economy and low-carbon of SPDN in recent years, several effective methods have been successfully applied in the SPDN and achieved good performances. Therefore, this book is concerned with the research on the key issues of economy and low-carbon for SPDN SA, planning, and control, which consist of three main parts. (1) Principle of SPDN situation awareness, in inclusion of reviewing previous contribution of various research methods as well as their drawbacks to analyze characteristics of SPDN situation awareness. (2) Artificial intelligence enabled computational methods for SPDN optimal planning problems, which are devoted to present the recent approaches of deep learning and machine learning as well as their availability to deal with the uncertainty of SPDN. (3) Multiple types of equipment and controllable loads bring adjustments to the operation and control of SPDN, but also provide the possibility of improving performance. Including control methods for electric vehicles, flexible loads, energy storage, and other equipment, which help determine the optimal solution of SPDN operation. The book is useful for university researchers, engineers, and graduate students in electrical engineering and computer science who wish to learn the situation awareness, planning, and control of SPDN.

Chapter 2

Smart Power Distribution Network Situation Awareness

2.1 Introduction The concept of Situation Awareness (SA) in the smart power distribution network (SPDN) is derived from human psychology involving sensory, perception, and behavioral habits. 1. In the field of psychology, the sensation is the brain’s reflection of various attributes in objective things that directly act on the human sensory organs [1]. Human cognition of objective things starts with sensation. It is the initial detection of complex things and the basis of complex cognitive activities such as perception and behavior. That is similar to the concept of SA detection. 2. Based on sensory information, perception processes multiple sensory information in a specific way, interprets the sensory information on individual experience, and taps the deep meaning of sensory information. That is similar to the concept of SA comprehension. 3. Based on sensory and perception, behavior refers to human activities after receiving internal and external stimuli. The theory of planned behavior can explain the human decision-making behavior from the perspective of perceptual information processing and the expectation value theory, and predict the future behavioral tendency [2]. That is similar to the concept of SA prediction. Therefore, the human collects multiple sensory information, and relies on perception to process the sensory information. The following behavior can be explained and predicted by the theory of planned behavior [3]. In general, human psychology corresponds to the basic principle of SA in the SPDN. SA refers to detecting, comprehending, and predicting various elements under certain space–time conditions [4]. Therefore, the process of SA can be divided into three stages: situation information collection, real-time situation analysis, and future situation prediction [5]. Anjaria et al. [6] investigates the relationship between the SA theory and cybernetics, and adopts this relationship to check the feasibility of

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_2

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SA-based information security risk management (ISRM) implementation in the organizational scenario. The authors of [7] investigate the influence of some variables on safety performance and examine the mediating effectiveness of SA. Considering existing models of SA and ontology-based approach for maritime SA, seaborne SA is applied to navigation safety control in [8]. Nowadays, SA has been identified as a critical skill in maintaining safety in high-risk industries. Irwin, A et al. explore SA among farmers in the United Kingdom when operating heavy agricultural machinery [9]. Based on the representative SA model, [10] presents the distributed swarm SA of unmanned aerial vehicle. Network Security SA becomes a security theory that can perceive the network threat globally [11]. As the power network hub, SPDN is directly connected to terminals, and its completeness will affect the power quality of end-users. Adequate monitoring and analysis of the SPDN operating status are urgent, so SA of the SPDN has emerged. However, the SPDN has diversified characteristics in terms of operating status, equipment types, and topology. The coverage of measurement devices in the remote areas cannot provide enough information for SA detection. Although SPDN SA has gradually integrated into the distribution network, the operation and maintenance of SA in the SPDN remains challenging. Therefore, it is necessary to explore the SA in SPDN. In the early stage of SPDN SA, Diez D et al. present a graphical user interface for power grid grounded on SA-oriented design principles [12]. Control room operators can achieve an appropriate SA level. In [13], two design strategies are summarized for SA in real-time distribution operation. One is the preparation of standardized data acquisition networks. The other is a real-time security analysis tool for SPDN. From the perspective of system access, The authors of [5] explain the key technologies of SA and orientation. Compared with the past, the architecture of SPDN has undergone tremendous changes. AC/DC hybrid [14], multi-energy complementarity [15], energy internet [16] and other distribution network forms emerge. As a result, SPDN has more complex operating conditions and fault types. The high proportion of clean energy and the disorderly access of DGs leads to a significant increase in the SPDN uncertainty. Meanwhile, regional electrical loads increase, power indicators are refined, and the demand for power quality improves. With the drastic changes in the SA operating environment, it is urgent to explore the SPDN SA from the perspective of lean operation and maintenance. The objective of this paper is to provide an updated picture of the SPDN SA technologies and assist in the lean operation and maintenance of SPDN. The paper begins with an overview of the concept, objectives, and challenges of SPDN SA. Following this, a 5-dimension comprehensive framework of SPDN SA is conducted. Ultimately, this paper analyzes and forecasts the key technologies of situation detection, comprehension, and prediction from the perspective of SPDN lean operation and maintenance. The overview contributes to address the challenges faced in the deployment of SPDN SA and, provide helpful information, and guidance in selecting suitable technologies for specific applications.

2.2 Description of Situation Awareness

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2.2 Description of Situation Awareness 2.2.1 Concept of Situation Awareness SA technology refers to the perception, understanding, and forecasting of various elements in the surrounding environment [5]. The concept of the three stages is as follows: 1. The situation detection stage. The task of the stage is to detect essential features in the environment. Multi-dimensional data and information can be collected. Besides, Situation detection is the data basis of situation comprehension and prediction. 2. Situation comprehension stage. The essence of this stage is to obtain an understanding of the environment through data analysis. Specifically, the data obtained in the situation detection is integrated, and the relationship between behaviors and objects in the information is analyzed. 3. Situation prediction stage. The core of situation prediction is to realize the practical application of SA knowledge. Based on the information basis of situation detection and comprehension, this stage predicts the future environmental situation.

2.2.2 Objectives of Situation Awareness for Smart Distribution Networks 1. The primary goal is to achieve real-time or quasi-real-time SA for SPDN, which can quickly determine the operating status of the distribution network. Based on the historical records of SPDN operation and maintenance data, SA provides managers with accurate SPDN situation information; 2. Observability is the key technical indicator of SA. High-level SA can provide SPDN with a visualized system situation and solve the shortcomings of insufficient measurement devices in the distribution network; 3. SA has a significant contribution to SPDN security. Specifically, conduct the security situation analysis, detect potential SPDN operational risks, predict possible failures in the future, and provide a scientific basis for the active defense of the power distribution system; 4. Through continuous innovation of intelligent algorithms, SA is cultivating SPDN adaptive capabilities. Based on the information obtained by SA, SPDN can independently recognize and improve the situation and guide the development of the distribution network situation in a good direction.

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2.2.3 Challenges of Situation Awareness for Smart Distribution Networks Due to SPDN’s diverse scenarios, massive data scale, and complex operating forms, traditional SA cannot adapt to the current SPDN environment. The severe operation and maintenance challenges faced are as follows: 1. Situational detection challenges. New measurement equipment such as advanced metering infrastructure [17], smart meters [18], and Phasor Measurement Unit (PMU) [19] are rapidly deployed in SPDN. Therefore, the data collected by SPDN increases sharply, which inevitably increases the processing pressure of SA redundant data. Although the collected power data can monitor the distribution network, it lacks information that reflects the poor operating status of the SPDN. Therefore, the input data of the SA system is asymmetric, and some missing data is necessary to be accurately completed by calculation. How to comprehensively detect SPDN status remains a challenging point in lean operation and maintenance; 2. Situational comprehension challenges. The phenomenon of reverse power transmission at the terminals of the distribution network is prominent. As a result, the risk of voltage fluctuations and power loss increases [20]. Large-scale DGs lead the traditional dispatch mode to unsuitable. There are considerable differences in SPDN’s topology, operation mode, energy structure, and automation level in different regions. Traditional situation comprehension technology is challenging to adapt to the current SPDN. As the decision center of SPDN, situation comprehension should assist the lean operation and maintenance of multi-form SPDN. How to accurately understand the operating situation of the SPDN is the focus of research. 3. Situation prediction challenges. The replacement of terminal energy leads to an imbalance between power supply and power consumption, and the stability margin of SPDN is challenging to determine. Unlike passive distribution networks, SPDN has a higher proportion of DG [21]. Although the integration of high-penetration new energy sources improves the SPDN flexibility, the uncertainty of SPDN also increases. It requires sufficient mathematical transformation ability and robustness for situation prediction. How to effectively predict the distribution network trend needs to be solved urgently.

2.3 Comprehensive Framework of Situation Awareness Promoting the application of SA technology in SPDN has a broad development space and high application value. This paper constructs a comprehensive framework of SPDN SA as shown in Fig. 2.1, which integrates Supervisory Control and Data Acquisition (SCADA) [22], 5G communication technology [23], energy management system [24], distribution automation system [25], SA system, data processing

2.4 Key Technologies of Situation Detection

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Fig. 2.1 A comprehensive framework of SPDN SA

system, and communication network. In order to clearly understand the relationship between SA and SPDN, the comprehensive framework of SPDN SA has been decomposed into a five-dimensional physical structure. SA stages, including situation detection, comprehension, and prediction, are combined to explore the organic combination of SPDN and SA. Besides, SA is an evolving technology, which will adapt to the development of SPDN through the update of smart algorithms and the introduction of new energy technologies.

2.4 Key Technologies of Situation Detection Situation detection is the data acquisition stage, which acquires SPDN data required for situation comprehension and prediction. To improve the SPDN visibility, the comprehensive perception of the SPDN is realized from depth and breadth. The situation detection structure is shown in Fig. 2.2. The key technologies of situation detection include big data of situation, 5G communication technology, virtual acquisition technology, optimization configuration of measurement technology.

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Fig. 2.2 The structure of situation detection

2.4.1 Big Data of Situation In the data-intensive era of SPDN, SA data presents the characteristics of largescale, multi-source, changeable, and heterogeneous. Recently, much research work has been done on SPDN SA. Most of the existing methods store different types of data in different ways, which makes data query and analysis inefficient. To store the situation information, Tao et al. propose a graph database-based hierarchical multidomain SA data storage method [26]. After data pre-processing, multi-dimensional data is fused to improve the visibility of SPDN. A new data-fusion method is proposed in [27] to detect incipient faults by integrating data collected from multiple sources instead of a single data source. Big data technology has gradually been applied to SPDN SA and integrated chaotic situation data.

2.4.2 5G Communication Technology Communication technology is the core factor that affects SPDN observability. Due to the characteristics of high data transmission speed and low transmission delay, advanced 5G communication technology has begun to be invested in the construction

2.5 Key Technologies of Situation Comprehension

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of SPDN and electric internet of things (IoT) [28]. In order to meet the high-capacity, high-bandwidth, and low-latency requirements of SA, 5G technology is gradually being applied to smart meters and condition monitoring systems.

2.4.3 Virtual Acquisition Technology To improve the comprehensiveness of operation and maintenance data, SPDN virtual collection technology is becoming a research hotspot. The technology is independent of SPDN measurement equipment such as sensors, collectors, and concentrators installed. For data that cannot be collected in real-time or is challenging to collect, virtual collection technology replaces traditional equipment collection through prediction and data extrapolation [29]. Based on the SPDN big data platform, real-time operation and maintenance data are used as the standard. According to part of the operation and maintenance data of the distribution network, similar areas of the distribution network to be collected are selected. By mining the inherent mapping relationship between the real-time data in the distribution network and similar areas, the unknown data in similar areas can be predicted or supplemented by existing data. The virtual collection contributes to the comprehensive collection of SPDN operation and maintenance data.

2.4.4 Optimization Configuration of Measurement Technology SPDN SA is inseparable from a complete hardware foundation of measurement devices. Advanced metering infrastructure includes measurement equipment configuration optimization, PMU configuration optimization, and data application technology [30]. Through the integration of smart meters, wide-area communication networks, measurement data systems, and indoor user networks, the intelligence of the SPDN measurement are realized, thereby ensuring the observability of the SPDN.

2.5 Key Technologies of Situation Comprehension Situation comprehension is the data analysis stage, which explores the potential information of the data collected in the situation detection. Besides, the stability domain, economy, load transfer capability, reliability, flexibility, power supply capability, load access capability, and DG absorption capability are integrated into the analysis of the SPDN situation. As the foundation of SPDN lean operation and maintenance, the structure of situation comprehension is shown in Fig. 2.3. The key technologies

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Fig. 2.3 The structure of situation comprehension

of situation comprehension include uncertain power flow calculation technology, hybrid state estimation technology, SPDN self-healing technology, SPDN characteristic analysis technology, coordinated dispatch technology, power market technology, virtual power plant technology, renewable energy planning technology, edge computing technology.

2.5.1 Uncertain Power Flow Calculation Technology Uncertain power flow calculation technology involves interval power flow [31], fuzzy power flow [32], probabilistic power flow [33], which estimates the influence of uncertain factors on the distribution network. The known and to-be-calculated quantities in deterministic power flow calculations are regarded as random variables. Based on fuzzy number or probability statistics theory, the uncertainty power flow calculation model of the distribution network is established. Only a single calculation can provide SPDN SA with more objective data analysis. Therefore, Uncertain Power

2.5 Key Technologies of Situation Comprehension

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Flow Calculation Technology reduces the burden of repeated calculations caused by uncertain factors.

2.5.2 Hybrid State Estimation Technology The current distribution network operation and maintenance data mainly come from the SCADA system. In order to further improve the accuracy, timeliness, and scope of measurement in the distribution network, PMU with more comprehensive measurement information has gradually become popular in SPDN. However, the current SPDN is in a state where many traditional and new measurement devices coexist. Therefore, there is an urgent need for Hybrid State Estimation Technology based on PMU/SCADA hybrid measurement to improve the accuracy and breadth of situational awareness [34]. Future research will focus on the differences between different measurement devices regarding frequency, time scale, structure, delay and explore suitable data processing methods.

2.5.3 SPDN Self-Healing Technology SPDN self-healing technology can effectively improve the resilience of SPDN, which mainly includes fault location technology, fault recovery technology, network reconfiguration technology, fast simulation technology [35]. In order to ensure the reliable power supply of infrastructure under various emergencies, SPDN self-healing technology can combine with SPDN SA to realize the pre-judgment analysis of disturbances.

2.5.4 SPDN Characteristic Analysis Technology Many characteristics exist in SPDN, such as reliability, flexibility, stability, and economy. SA establishes the mathematical model compatible with multiple types of SPDN terminal equipment, adopts the distribution network information provided by situation detection to evaluate the SPDN characteristics, and then realizes the flexible correction of SPDN operating status. Besides, self-learning evaluation technology gradually emerges, achieving dynamic evaluation and the objective balance of expert opinions [36].

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2.5.5 Coordinated Dispatch Technology In order to coordinate the complementarity of different energy sources and energy storage, coordinated dispatch technology has become the core of building the integrated energy system [37]. It cooperates with the primary and secondary systems, achieves precise control on the time scale and spatial layout, and guides SPDN’s lean operation and maintenance.

2.5.6 Power Market Technology Power market technology refers to the geometry of electricity production, transmission, consumption, and sale. Game theory [38] is used to establish a healthy bidirectional competition of electricity markets for electricity producers and users.

2.5.7 Virtual Power Plant Technology The development of DG has transformed end-users from passive price-takers into active market participants. In order to efficiently manage massive active end-users, virtual power plant becomes the focus of research [39]. It can provide necessary information to help consumers improve their profits and trade with the electricity market directly.

2.5.8 Renewable Energy Planning Technology SPDN multi-energy complementary technology effectively promotes the energy transformation of cities. Meanwhile, energy equipment such as wind power, photovoltaic, DC electrolysis of water into hydrogen, hydrogen-storage, AC ice-storage, and water-storage equipment have been gradually connected to SPDN. Therefore, how to optimize the configuration of renewable energy and improve the structure of SPDN energy is an urgent problem. Based on robust optimization theory, renewable energy planning technology can contribute to SPDN lean operation and maintenance, and reduce the blindness of uncertain decision-making [40].

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2.5.9 Edge Computing Technology The popularization of electric IoT makes IoT terminals tend to be miniaturized and intelligent. Edge computing technology [41] enables flexible collaboration between smart terminals and improves the response speed of SPDN SA.

2.6 Key Technologies of Situation Prediction Situation prediction is the stage of state prediction, which can predict the development trend of the SPDN state. Besides, situation prediction evaluates the operational risks of the SPDN, and provides theoretical support for the management department. With the intelligence of SPDN, the adaptation of SPDN relies on accurate situation prediction, and its architecture is shown in Fig. 2.4. The key technologies of situation prediction include three-phase unbalanced load prediction technology, renewable energy output prediction technology considering uncertainty, electric vehicle (EV) charging prediction technology, intelligent inspection technology, and security situation prediction technology.

2.6.1 Three-Phase Unbalanced Load Prediction Technology Under the background of big data, three-phase unbalanced load situation analysis and prediction method are proposed [42]. In order to adapt to the characteristics of the three-phase unbalanced distribution network, the three-phase unbalanced load calculation model is constructed. Furthermore, the asymmetric load and the unbalance degree of the SPDN can be accurately predicted.

2.6.2 Renewable Energy Output Prediction Technology Considering Uncertainty Despite the transformation of SPDN energy structure, the intermittency of renewable energy affects the stable operation of SPDN, and the renewable energy output prediction technology quantifies the impact of the renewable energy uncertainty in SPDN. Generally, algorithms such as probability and statistics laws, interval estimation, and fuzzy theory are employed to predict renewable energy output [43]. The prediction results are compatible with SPDN areas that contain various uncertain parameters.

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Fig. 2.4 The structure of situation prediction

2.6.3 Electric Vehicle Charging Prediction Technology EVs are rapidly spreading in cities, but their Spatio-temporal randomness poses a significant challenge for SPDN optimization scheduling strategies. How to simulate the EV travel chain, extract the characteristics of EV charging, and predict the Spatiotemporal distribution of EV load remains challenging. To solve the problem, the EV charging prediction technology emerges [44], which is one of the key technologies for situation prediction to accurately predict the Spatio-temporal distribution of EV load by fusing big data.

References

15

2.6.4 Intelligent Inspection Technology With the increasingly complex SPDN structure, there are many types of faults in the distribution network, and the redundancy of influencing factors has increased. Intelligent inspection technology faces the complex problem of extracting fault features and decoupling fault location layered [45]. In response to the problem, situation prediction combines situation detection and comprehension to realize in-depth data mining. According to the configuration of maintenance personnel, constructing a dynamic inspection strategy can provide reliable decision support for SPDN lean operation and maintenance.

2.6.5 Security Situation Prediction Technology To build a strong distribution network, security situation prediction technology has emerged. SA analyzes the operating status of SPDN, extracts potential security risks, predicts the security situation, and finally proposes a security correction method. Rapidly extracting SPDN security situation elements and identifying abnormal situations are the technical core [46].

2.7 Conclusions With the development of distribution network automation, SA has gradually been popularized and applied in SPDN. However, more SPDN operating technologies and energy forms appear. The key technologies of SA need to be adjusted to adapt to the progress of SPDN. Consolidating the key technologies of SPDN SA, promoting the organic integration of various technologies, and improving key technologies based on the implementation effect of SA are the future research directions. To provide technical support for the lean operation and maintenance of SPDN, this paper explains the background of SPDN SA, introduces the SA concept, establishes a 5-dimensional integrated framework for SA, and finally analyzes the key technologies of SA. We believe that the paper can provide a reference for the development of SPDN SA in the future.

References 1. Dundes A (2020) On the psychology of legend. University of California Press, In American Folk Legend, pp 21–36 2. Ajzen I (1991) The theory of planned behavior. Organ Behav Hum Decis Process 50(2):179–211

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3. Luiza Neto I, Matsunaga LH, Machado CC, Gunther H, Hillesheim D, Pimentel CE, Vargas JC, D’Orsi E (2020) Psychological determinants of walking in a Brazilian sample: an application of the theory of planned behavior. Transp Res Part F-Traffic Psychol Behav 73:391–398 4. Ge LJ, Li YL, Li SX, Zhu JB, Yan J (2021) Evaluation of the situational awareness effects for smart distribution networks under the novel design of indicator framework and hybrid weighting method. Front Energy 15(1):143–158 5. Wang S, Liang D, Ge L (2016) Key technologies of situation awareness and orientation for smart distribution systems. Autom Electr Power Syst 40(12):2–8 6. Anjaria K, Mishra A (2018) Relating wiener’s cybernetics aspects and a situation awareness model implementation for information security risk management. Kybernetes 47(1):58–79 7. Mohammadfam I, Mahdinia M, Soltanzadeh A, Aliabadi MM, Soltanian AR (2021) A path analysis model of individual variables predicting safety behavior and human error: the mediating effect of situation awareness. Int J Ind Ergon 84 8. Smirnova OV (2018) Situation awareness for navigation safety control. Transnav-Int J Mar Navig Saf Sea Transp 12(2):383–388 9. Irwin A, Caruso L, Tone I (2019) Thinking ahead of the tractor: driver safety and situation awareness. J Agromedicine 24(3):288–297 10. Gao Y, Li DS, Cheng ZX (2018) UAV distributed swarm situation awareness model. J Electron Inf Technol 40(6):1271–1278 11. Liu XW, Yu JG, Lv WF, Yu DX, Wang YL, Wu Y (2019) Network security situation: from awareness to awareness-control. J Netw Comput Appl 139:15–30 12. Diez D, Romero R, Tena S (2016) Designing a human supervisory control system for smart grid. IEEE Latin Am Trans 14(4):1899–1905 13. Song IK, Yun SY, Kwon SC, Kwak NH (2013) Design of smart distribution management system for obtaining real-time security analysis and predictive operation in Korea. IEEE Trans Smart Grid 4(1):375–382 14. Espina E, Cardenas-Dobson R, Simpson-Porco JW, Saez D, Kazerani M (2021) A consensusbased secondary control strategy for hybrid AC/DC microgrids with experimental validation. IEEE Trans Power Electron 36(5):5971–5984 15. Wu X, Li Y, Tan Y, Cao Y, Rehtanz C (2019) Optimal energy management for the residential MES. Iet Gener Transm Dis 13(10):1786–1793 16. Lv Z, Kong W, Zhang X, Jiang D, Lv H, Lu X (2020) Intelligent security planning for regional distributed energy internet. IEEE Trans Industr Inf 16(5):3540–3547 17. Choi JS, Lee S, Chun SJ (2021) A queueing network analysis of a hierarchical communication architecture for advanced metering infrastructure. IEEE Trans Smart Grid 12(5):4318–4326 18. Cunha VC, Freitas W, Trindade FCL, Santoso S (2020) Automated determination of topology and line parameters in low voltage systems using smart meters measurements. IEEE Trans Smart Grid 11(6):5028–5038 19. De Oliveira-De Jesus PM, Rodriguez NA, Celeita DF, Ramos GA (2021) PMU-based system state estimation for multigrounded distribution systems. Ieee T Power Syst 36(2):1071–1081 20. Zhou X, Farivar M, Liu Z, Chen L, Low SH (2021) Reverse and forward engineering of local voltage control in distribution networks. IEEE Trans Autom Control 66(3):1116–1128 21. Mohammadrezaee R, Ghaisari J, Yousefi G, Kamali M (2021) Dynamic state estimation of smart distribution grids using compressed measurements. IEEE Trans Smart Grid 12(5):4535– 4542 22. Taylor Z, Akhavan-Hejazi H, Cortez E, Alvarez L, Ula S, Barth M, Mohsenian-Rad H (2019) Customer-side SCADA-assisted large battery operation optimization for distribution feeder peak load shaving. IEEE Trans Smart Grid 10(1):992–1004 23. Ye J, Ge X, Mao G, Zhong Y (2018) 5G ultradense networks with nonuniform distributed users. IEEE Trans Veh Technol 67(3):2660–2670 24. Du Y, Li F (2020) Intelligent multi-microgrid energy management based on deep neural network and model-free reinforcement learning. IEEE Trans Smart Grid 11(2):1066–1076 25. Siirto OK, Safdarian A, Lehtonen M, Fotuhi-Firuzabad M (2015) Optimal distribution network automation considering earth fault events. IEEE Trans Smart Grid 6(2):1010–1018

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26. Tao XL, Liu Y, Zhao F, Yang CS, Wang Y (2018) Graph database-based network security situation awareness data storage method. Eurasip J Wirel Commun Netw 27. Wei YP, Wu DZ, Terpenny J (2020) Robust incipient fault detection of complex systems using data fusion. IEEE Trans Instrum Meas 69(12):9526–9534 28. Reka SS, Dragicevic T, Siano P, Prabaharan SRS (2019) Future generation 5G wireless networks for smart grid: a comprehensive review. Energies 12(11) 29. Ge L, Qin Y, Liu J, Bai X (2021) Virtual acquisition method of distributed photovoltaic data based on similarity day and BA-WNN. Electr Power Autom Equip 41(6):8–14 30. Akrami A, Doostizadeh M, Aminifar F (2020) Optimal reconfiguration of distribution network using mu PMU measurements: a data-driven stochastic robust optimization. IEEE Trans Smart Grid 11(1):420–428 31. Liu B, Huang Q, Zhao J, Hu W (2020) A computational attractive interval power flow approach with correlated uncertain power injections. Ieee T Power Syst 35(1):825–828 32. Aghili SJ, Saghafi H, Hajian-Hoseinabadi H (2020) Uncertainty analysis using fuzzy transformation method: an application in power-flow studies. Ieee T Power Syst 35(1):42–52 33. Wang ZW, Shen C, Liu F, Gao F (2017) Analytical expressions for joint distributions in probabilistic load flow. Ieee T Power Syst 32(3):2473–2474 34. Kabiri M, Amjady N (2019) A new hybrid state estimation considering different accuracy levels of PMU and SCADA measurements. IEEE Trans Instrum Meas 68(9):3078–3089 35. Ahmadi SA, Vahidinasab V, Ghazizadeh MS, Giaouris D (2021) A stochastic framework for secure reconfiguration of active distribution networks. Iet Gener Transm Dis 36. Ge L, Li Y, Zhu X, Zhou Y, Wang T, Yan J (2020) An evaluation system for HVDC protection systems by a novel indicator framework and a self-learning combination method. IEEE Access 8:152053–152070 37. Torbaghan SS, Suryanarayana G, Hoschle H, D’Hulst R, Geth F, Caerts C, Van Hertem D (2020) Optimal flexibility dispatch problem using second-order cone relaxation of AC power flows. Ieee T Power Syst 35(1):98–108 38. Fu Y, Zhang ZQ, Li ZK, Mi Y (2020) Energy management for hybrid AC/DC distribution system with microgrid clusters using non-cooperative game theory and robust optimization. IEEE Trans Smart Grid 11(2):1510–1525 39. Zhang R, Hredzak B (2021) Distributed dynamic clustering algorithm for formation of heterogeneous virtual power plants based on power requirements. IEEE Trans Smart Grid 12(1):192–204 40. Fathabad AM, Cheng J, Pan K, Qiu F (2020) Data-driven planning for renewable distributed generation integration. Ieee T Power Syst 35(6):4357–4368 41. Gong C, Lin F, Gong X, Lu Y (2020) Intelligent cooperative edge computing in internet of things. IEEE Internet Things J 7(10):9372–9382 42. Li H, Shi C, Liu X, Wulamu A, Yang A (2020) Three-phase unbalance prediction of electric power based on hierarchical temporal Memory. Cmc-Computers Materials & Continua 64(2):987–1004 43. Chen Y, Li T, Zhao C, Wei W (2021) Decentralized provision of renewable predictions within a virtual power plant. Ieee T Power Syst 36(3):2652–2662 44. Zhao Y, Wang Z, Shen ZJM, Sun F (2021) Data-driven framework for large-scale prediction of charging energy in electric vehicles. Appl Energy 282 45. Mao T, Yao J, Xin J, Kang T, Deng D, Zhao J (2013) Intelligent overhaul and safety check management system of 110kV distribution network. Autom Electr Power Syst 37(2):125–129 46. Xiao J, Zhang B, Luo F (2019) Distribution network security situation awareness method based on security distance. IEEE Access 7:37855–37864

Chapter 3

Photovoltaic Prediction and Virtual Collection

3.1 Photovoltaic Prediction 3.1.1 Introduction The output of photovoltaic (PV) power generation is random and intermittent, which has a strong impact on the safe and stable operation of power grids. To reduce the impact of large-scale PV penetration and ensure the security of power grids, it is imperative to accurately forecast the PV output by an effective and efficient manner [1, 2]. Currently, most PV output forecasting approaches can be categorized as physical and statistical methods. The physical methods leverage the solar radiation transfer equation, the PV module operating equation, and/or other physical equations to make the forecast. This category relies on detailed and precise geography, weather and solar radiation data of the PV plants, while the modeling process is often complicated. To overcome the challenge, Liu et al. proposed an ensemble technique [3] that creates a set of individual recursive arithmetic average models on the predictions of power outputs. The data-driven ensemble model can be applied to situations where large amount of data need to be processed, but the prediction effect of individual indicators is not satisfactory. The influence of weather types on the prediction effect has not been thoroughly analyzed in [4], which has lower prediction effect on cloudy and rainy weather is than that of sunny weather. The authors of [5] proposed a new method for forecasting PV output power using deep LSTM networks, which have good forecasting accuracy but some of the meteorological data such as irradiance are often not available. In this paper, we proposed a new end-to-end framework to extract features, predict PV outputs, and optimize model parameters through a three-phase method of a factor analysis (FA), a gray wolf optimization (GWO) and a generalized regression neural network (GRNN). Using the measured power of a real-world PV plant as an example, the prediction method is proven to have a high prediction accuracy and robustness. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_3

19

20

3 Photovoltaic Prediction and Virtual Collection

3.1.2 Factor Analysis Photovoltaic output has more meteorological input characteristics, and the correlation between different meteorological input characteristics is very strong. In this paper, FA method is adopted to reduce the dimension of meteorological input characteristics and reduce the complexity of forecasting. FA is a multivariate statistical method that simplifies multidimensional vectors through dimensionality reduction technology. It belongs to the generalization of principal component analysis (PCA). In power system, it is often used for dimensionality reduction and simplification of multidimensional vectors with complex correlation. The meteorological input characteristic after standardization is P = [P1 , P2 , . . . Pn ]T , n is the meteorological input feature dimension, and the general model of factor analysis is: P = AF + ε

(3.1)

|T | ( ) where, F = f1 , f2 , . . . fr is a common factor variable; A = aij n×r is the factor load matrix, which explains the correlation between the variables Pi , aij is the load of the variable Pi on the common factor fi , which reflects the importance of the common factor fi to the variable Pi . The load on the common factor, which reflects the importance of the common factor fi to the variable Pi . AF is the common component, which contains the common information of meteorological input characteristics. ε = [ε1 , ε2 . . . εn ]T is a special factor vector that represents the portion of the photovoltaic output forecasting input feature that cannot be interpreted by a common factor. Equation (3.1) requires the estimation of the estimated factor load matrix A and the special variance matrix Θ. The principal component estimation method is adopted: Aˆ =

|/

| / / ( ) λˆ 1 eˆ 1 , λˆ 2 eˆ 2 , . . . , λˆ r eˆ r = aij n×r

(3.2)

( ) ˆ = diag υˆ 12 , υˆ 22 , · · · , υˆ n2 o

(3.3)

υˆ i2 = sii −

r E

aˆ ij2 , i = 1, 2, . . . , n

(3.4)

j=1

where, λˆ 1 ≥ λˆ 2 ≥ · · · ≥ λˆ r ≥ 0 are the first r maximum eigenvalues of the sample covariance matrix Sn×n ; eˆ 1 , eˆ 2 , ... , eˆ r are the corresponding multivariate unit eigenvectors; υˆ i2 is the estimated variance of the special factor at time i; sii is the ith diagonal element in sample covariance matrix S; aˆ ij is the estimated value of the load matrix element in row i and column j. According to the historical observation sample, after obtaining the factor index A and the special variance matrix Θ estimation value from Eqs. (3.2) and (3.3). The common factor estimation vector Fˆ corresponding to the sample can be calculated,

3.1 Photovoltaic Prediction

21

as approximated by Eq. (3.4). Fˆ = Aˆ ' S −1 P

(3.5)

The dimension r of the common factor is usually obtained from the contribution rate of the total variance of the common factors. When the cumulative contribution rate of the top r principal components reaches over 85%, it can be considered that the first r common factors have basically included all the information of meteorological input characteristics.

3.1.3 Photovoltaic Output Forecasting Method 1. Generalized regression neural network Generalized Regression Neural Network (GRNN) is an improved algorithm of RBFNN. Compared with other neural network models, GRNN neural network has stronger nonlinear mapping ability and flexible network structure and high fault tolerance and robustness. It is a good explanation for the complex nonlinear relationship between the predicted object and multiple influencing factors. It is suitable for predicting the mixed load of commercial and residential people with many influencing factors and complex randomness. GRNN is composed of input layer, mode layer, addition layer and output layer, corresponding to network input [X1 , X2 , . . . Xn ], and output [h1 , h2 , . . . hm ]. The structure diagram of GRNN is shown in Fig. 3.1. The number of input layer neurons is the same as the vector dimension in the training sample, and each neuron transmits the input data directly to the pattern layer.

Fig. 3.1 GRNN structure diagram

22

3 Photovoltaic Prediction and Virtual Collection

The number of neurons in the pattern layer is consistent with the number of training samples n, and its transfer function is radial basis function: | | (X − Xi )T (X − Xi ) Ki = exp − 2σ 2

(3.6)

where, X is the network input variable; Xi is the learning sample corresponding to the ith neuron; i = 1, 2, . . . , n; σ represents the smoothing factor. The summation layer utilizes two summation methods: one is to calculate the weighted sum of the output of each neuron in the pattern layer; the other is to calculate the sum of the outputs of the neurons in the pattern layer. The two types of formulas are shown in Eqs. (3.1) and (3.2), respectively. Y1 =

n E i=1

Y2 =

| | (X − Xi )T (X − Xi ) hij exp − 2σ 2

n E i=1

|

(X − Xi )T (X − Xi ) exp − 2σ 2

(3.7)

| (3.8)

where, j = 1, 2, . . . , m; hij is the j-th element in the dependent variable of the i-th training sample, and the value of j is 1 during load prediction. The output layer adopts linear function to output the result, and the estimation result of the corresponding neuron j is: hj =

Y1 Y2

(3.9)

As can be seen, GRNN has only one parameter–smooth factor a needs to be determined. If σ is too large, the predicted value will approximate to the mean of the target value in all training samples. If σ is too small, the generalization ability of the prediction model will be poor. In this paper, GWO algorithm is used to find the optimal σ to improve the prediction accuracy of GRNN. 2. Grey Wolf optimization algorithm GWO is a swarm intelligence algorithm with good self-organizing learning ability, simple parameters, easy implementation and good global search ability. In this paper, GWO is adopted to optimize the selection of GRNN’s smoothing factor σ to enhance GRNN’s fitting regression ability. GWO mimicked the hunting behavior of the wolves and obtained three wolves α, β, δ and the remaining wolves ω, according to the hierarchy of the wolves, as shown in Fig. 3.2. Among them, Wolf α is the optimal solution for wolves, Wolf β and Wolf δ are the sub-optimal solution, and the remaining Wolf ω is the candidate solution. The Wolf pack approximates to the optimal solution of the objective function in the search space through the initial solution of three individual wolves α, β, δ. The wolf

3.1 Photovoltaic Prediction

Optimal solution

23

Wolf

: food and habitat selection

Wolf

Wolf : help wolf make decisions

Wolf Sub-optimal solution

Wolf : detection, alarm, suppression, guard Wolf

Remaining solution

Wolf follow the orders of higher wolves

Wolf

Predation process

Search and track prey

Chase and surround prey

Attack prey

Fig. 3.2 Wolf group hierarchy. Reprinted from Ref. [6], copyright 2023, with permission from IEEE

position is updated and evolved, and the distance from the optimal solution is changed to achieve optimality solution. In the hunting process, the main mathematical models of GWO are as follows: (1) Feeding distance. The distance D between the individual Wolf and the prey should be determined in advance before hunting: | | D = |C · Φ p (i) − Φ(i)|

(3.10)

where, i is the number of iterations, Φ p (i) is the position vector of the prey, Φ(i) is the location of the individual wolf, C is the coefficient vector, its expression is as follow: C = 2r1

(3.11)

where, r1 is the spatial distance coefficient and the random vector within [0,1]. (2) Update of wolf position. As the distance between the individual Wolf and the prey decreases, the position of the individual Wolf is constantly updated, as shown in Eq. (3.10): Φ(i + 1) = Φ p (i) − ξ D where, ξ is the convergence factor, and the expression is as follows:

(3.12)

24

3 Photovoltaic Prediction and Virtual Collection

ξ = 2ar2 − a

(3.13)

where, a decreases from 2 to 0 as the number of iterations increases, r2 is the same as r1 , and it is also a random vector in [0,1]. (3) Update of prey position. Wolf α, Wolf β and Wolf δ are the first wolves closest to the prey in the Wolf pack. The position of the remaining wolves ω is updated by three wolves: Dα = |C α Φ α (i) − Φ(i)|

(3.14)

| | Dβ = |C β Φ β (i) − Φ(i)|

(3.15)

Dδ = |C δ Φ δ (i) − Φ(i)|

(3.16)

Φ 1 = Φ α − ξ 1 Dα

(3.17)

Φ 2 = Φ β − ξ 2 Dβ

(3.18)

Φ 3 = Φ δ − ξ 3 Dδ

(3.19)

Φ P (i + 1) =

Φ1 + Φ2 + Φ3 3

(3.20)

where, Φ α , Φ β and Φ δ respectively represent the immediate positions of Wolf α, Wolf β and Wolf δ, and Dα , Dβ and Dδ respectively represent the distance between the individual Wolf and the head Wolf in the remaining wolves ω. GWO located the range of prey (optimal solution) through the locations of Wolf α, Wolf β and Wolf δ, and gradually narrowed the distance from the prey in the way of Wolf predation, and finally killed the prey. Compared with other intelligent algorithms that search for the optimal solution guided by the position of a single solution, GWO is a multi-position search algorithm that improves the global search ability of the algorithm. 3. The establishment of forecasting model and the flow of algorithm For the photovoltaic output, this paper proposed a short-term forecasting model based on FA-GWO-GRNN, which can be divided into the following five steps: (1) Data preprocessing; (2) FA algorithm was used to extract the main information of meteorological input features to realize the dimensionality reduction of input features; (3) The weather, temperature, and annual product data were used as indicators for selecting similar days. According to the meteorological data for predicted day

3.1 Photovoltaic Prediction

25

of the weather forecast, the samples with the same weather as the predicted day were selected from the historical day to constitute the set A. the samples in set A whose daily maximum temperature was within ± 3°C from the predicted day were selected from set A to form set B and the samples in set B whose annual product data was within ± 30 days from the predicted day were selected from set B to form set C. Then, set C is similar day set. (4) Similar to the above set C as the training sample set, the 10-fold cross validation, the training sample set is divided into 10 average, 1 in selected as the test set, the rest of the 9 as a training set GWO comes with GRNN model prediction error GWO comes as fitness function, the optimization on the parameter σ of the GRNN. GWO comes parameter Settings are as follows: number n = 20 wolves, the number of iterations n = 50, particle number 1, the final result to take 10 times the optimal value of cross validation. (5) After determining the optimal parameters of the GRNN model, the training sample set is used for offline training of the GRNN model, and the photovoltaic output forecasting model based on GWO-GRNN can be obtained. Input the input feature data of the predicted day into the forcasting model, and the load predicted value of each moment of the predicted day can be obtained. The overall algorithm flow chart is shown in Fig. 3.3.

3.1.4 Short-Term Photovoltaic Output Forecasting Examples and Results Analysis In this paper, the actual power data of a photovoltaic plant in 2016 and 2017 were used for example verification. 11 points (8:00–18:00) were collected in one day, and the time interval was 1 h. Historical load, time and meteorological factors were used as input characteristics of short-term prediction of photovoltaic output. The historical load was the PV output at the first two moments of the forecast time. The meteorological input characteristics included atmospheric pressure, maximum wind speed, maximum wind speed and direction, and maximum wind speed. Great wind speed, average temperature, maximum temperature, minimum temperature, relative humidity and precipitation. Firstly, input characteristic data was normalized and mapped to the interval [1, −1], as follows: Z∗ =

zmax +zmin 2 zmax −zmin 2

z−

(3.21)

where zmax , zmin are the maximum and minimum values of variables respectively. 1. Error Indicators In order to measure the accuracy and robustness of the prediction model, the standard deviation of mean absolute percentage error (MAPE) root mean square error (RMSE)

26

3 Photovoltaic Prediction and Virtual Collection

start

Initialization of the wolves by limits of the position of the gray wolf

FA algorithm was used to extract the meteorological input features to realize the dimensionality reduction of input features

Fitness value of each individual gray wolf was determined according to the fitness function

Select similar day as training sample set

GWO algorithm optimizes GRNN network parameters

Offline training of GRNN network

Rank wolves according to fitness, the top three are Wolf

, and

,

respectively

Location update

Parameter update

Establish a GRNN forecasting model Meet the condition?

Forecasting result

No

Yes over

Determine wolf

position and get result

Fig. 3.3 Short-term photovoltaic output forecasting method flowchart based on FA-GWO-GRNN. Reprinted from Ref. [6], copyright 2023, with permission from IEEE

and MAPE is adopted as the error standard in this paper, as shown in Eqs. (3.21), (3.22) and (3.23), respectively. | | n 1 E |yˆ t − yˆ st | EM = × 100% n 1 yˆ st | | n | 1 E( )2 yˆ t − yˆ st ER = | n 1 | | n | 1 E qM = | (mt − m)2 n−1 1

(3.22)

(3.23)

(3.24)

where, n is the number of predicted moments;ˆyt is the predicted load value at time t;ˆyst is the actual load value at time t; mi . is the absolute percentage error at time t; m

3.2 Photovoltaic Virtual Collection

27

is the average absolute percentage error at n times. MAPE and RMSE can evaluate the accuracy of model prediction results, and RMSE is sensitive to the maximum or minimal error in a group of results. The standard deviation of MAPE can be calculated to evaluate the fluctuation degree of prediction error and to test the robustness and stability of the model. 2. Dimension Reduction of Original Input Features Of screening after 10 meteorological input feature dimension reduction factor analysis, structural factor score matrix, the results are shown in Table 3.2. According to the common factor of factor score coefficient, linear function equation can be formed. Then, four common factors are extracted from meteorological input characteristics. Where, the common factor 1 represents temperature and atmospheric pressure. Common factor 2 represents wind speed. The common factor 3 represents the wind direction angle. The common factor 4 represents precipitation and relative humidity. The total variance contribution rate of the four common factors is 88.785% (> 85%), indicating that the common factors basically contain all the effective information of 10 meteorological input characteristics (Table 3.1).

3.2 Photovoltaic Virtual Collection 3.2.1 Introduction Compared with centralized PV, distributed PV (DPV) have attracted increasing attention in the world with the advantages of high energy utilization, low environmental pollution and flexible installation. Its installtion capacity is increasing annually, and developed rapidly as a promising solution to replace fossil energy. However, the development of DPV has gradually caused some problems. Due to its huge numbers, wide distribution range and big operation data, power company requires a large number of sensors to monitor DPVs operation status. It may causes problems such as a high collection device cost, insufficient data transmission bandwidth and geographical restrictions of data transmission in special locations, which makes the collection and transmission of DPVs operation data challenging. Moreover, it also requires specific communication channels, servers, databases and data monitoring platform, which leads to high operating costs and is not suitable to home PV users. Also, it is difficult to realize the accurate awareness of the DPVs operation state in a region only by improving the completeness of data collection devices. Therefore, it is significant to develop a new low-cost and efficient monitor method of DPVs. Currently, there are few researchs on regional DPVs data virtual collection. However, the researchs of PV output prediction and missing data repair can provide inspiration for the virtual collection of DPVs. For PV output prediction, Ref. [1]

28

3 Photovoltaic Prediction and Virtual Collection

Table 3.1 Factor analysis results of meteorological input characteristics after screening. Reprinted from Ref. [6], copyright 2023, with permission from IEEE Indicators

Common factor 1 Common factor 2 Common factor 3 Common factor 4

Atmospheric pressure

−0.132

−0.029

−0.017

−0.071

Average temperature

0.158

0.033

−0.002

−0.071

Highest temperature

0.158

0.039

−0.009

−0.075

Lowest temperature

0.158

0.048

−0.016

−0.071

Maximum wind speed

0.005

0.405

−0.002

0.146

Extreme wind speed

0.012

0.425

−0.030

0.174

Wind direction of maximum wind speed

0.021

−0.070

0.543

0.038

Wind direction of extreme wind speed

0.021

−0.126

0.575

0.021

Relative humidity −0.022

−0.243

0.080

0.355

Precipitation

−0.025

0.148

0.016

0.519

Variance contribution rate %

39.649

26.175

12.636

10.326

Contribution rate of total variance %

88.785

Table 3.2 Relationship between εI and meteorological conditions. Reprinted from Ref. [7], copyright 2023, with permission from IEEE Weather

Rain or snow

Overcast

Overcast to cloudy

Cloudy

Cloudy to clear

Clear

Range of εI

[−1.0, −0.7]

[−0.7, −0.5]

[−0.5, 0]

[0, 0.5]

[0.5, 0.7]

[0.7, 1.0]

realized the accurate prediction of PV output by simulating the physical properties of a photovoltaic panel and machine learning techniques. Ref. [2] proposed an improved random forest-based method for ultra-short-term prediction of PV cluster output power. For PV missing data repair, Ref. [3] used super-resolution perception convolutional neural network to recover the missing data and forecast PV generation. Ref. [4] implemented 11 univariate imputation methods to estimate missing values of PV dataset system.

3.2 Photovoltaic Virtual Collection

29

The above researchs aimed to predicting of PV (or PV cluster) output in the future with a complete data collection devices and completing the missing data of PV historical dataset. However, the above researchs can not accurately complete the missing data of DPVs in real time with the incomplete collection devices and realize the reducing of data collection devices amount. The utilization of artificial intelligence technology to deeply mine the spatial–temporal correlation of DPVs output in a region makes the economical and efficient collection of DPVs data promising. To overcome the limitations of the above studies, this study proposes a data virtual collection model of DPVs. By deep mining the spatial correlation of all regional DPVs in different geographical locations and the temporal correlation of each DPVs historical operation data, this method could obtain the dependency of their operation data. Therefore, the method has the ability to ensure the high-precision collection of DPVs operation data while reducing the number of acquisition devices. In essence, the method proposed in this paper is the system identification and state estimation for a large system which is consist of multiple subsystems. This method can infer the complete operation data of DPVs from the incomplete operation data. Therefore, the key of this process is the “selection” mechanism of finding the most important data. For instance, when reading articles related to renewable energy, we can easily guess that the obscured word “p**t*v*****c” is “photovoltaic” according to the previous and subsequent texts. But it is difficult to restore “****o*o**ai*”, especially when reading literary articles. Incomplete DPVs data equal to adding noise to the complete DPVs data, only the data of reference power stations (RPSs) in DPVs is not missing. The denoising autoencoders (DAE) is able to complete the corrupt data in real time through analysing the historical data [5], which can provide reference for the method proposed in this paper. However, the working process of traditional DAE is only to fit each group of data independently, and lack of the temporal correlation analysis of its historical data. To improve the DAE for large and complex data, Ref. [8] proposed the multiple imputation with denoising autoencoders to rebuilt damaged data. However, the working process of traditional DAE [5, 8] is only to fit each group of data independently, and there is a lack of time correlation analysis of its historical data. For this reason, Ref. [9] proposed the LSTM-SDAE neural network with the autoencoder hidden layers replaced by LSTM units to obtain the temporal relationship among multivariate variables. Ref. [10] proposed a deep denoising convolutional autoencoder to identify the Coronavirus disease 2019 by analyzing computed tomography images. However, the existing improvement of DAE [9, 10] can only analyze the given historical data set. They cannot analyze the time correlation of damaged data in real time. More importantly, the sample noise of existing DAE is selected randomly, there are few studies focused on the optimization of training set noise to improve the incomplete data repair ability. This makes the reasonable selection of RPSs is impossible. To overcome this defect, it is necessary to optimize the noise of DAE, and then find the optimal RPSs quickly. In addition, the operating state of PV is mainly affected by solar radiation. Due to the diverse installation positions and inclination angles of DPVs in the region, there are minute weather and solar altitude differences in all over a region. This

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3 Photovoltaic Prediction and Virtual Collection

phenomenon resulting in the diverse operation status of DPVs with the change of solar radiation intensity and time. Therefore, it is necessary to build an alternative RPSs set and install data collection devices for all DPVs in this set. In the process of virtual data collection, to reduce the calculation cost, some RPSs are selected in real time from the set of alternative RPSs for data collection. Unfortunately, the RPSs selected by the deterministic model of solar radiation is difficult to ensure the real-time and accurate estimation of all DPVs in a region. It is necessary to model the uncertainty of solar radiation to reduce the impact of uncertainty on the selection of RPSs. There are few studies on the output virtual collection of DPVs, and lack of consideration of the solar radiation intensity uncertainty. There are some studies have committed to reducing the influence of solar radiation uncertainty, such as stochastic optimization (SO), robust optimization (RO), and other optimization method. However, the traditional deterministic data shows some limitations in the analysis and calculation of systems with uncertain parameter [11], calling for advanced model that can efficiently describe the uncertainty and guarantee the reasonable selection of RPSs to support the accurate estimation of DPVs economically [12]. Interval model is a novel uncertainty modeling method which was developed to obtain the solutions based on the range of uncertainty and find the worst scenario and the most optimistic scenario. Still, the result range will be large after few calculation due to its strong conservatism. Result in the RPSs selection become challenge. As a better method than interval model, the affine model can overcomes the conservatism of interval model and deal with the uncertainty [11]. To this end, this paper aims to establish a DPVs virtual collection model to detect DPVs data with accuracy, efficiency and economy in a long term. Firstly, to reduce the amount of collection devices and ensure the virtual collection accuracy of DPVs operation data, this paper proposes the virtual collection model framework of DPVs. Then, to extract the spatial–temporal correlation of DPVs, a deep trainedrecurrent denoising autoencoder (DT-RDAE) is proposed. An improved optimization algorithm is used to optimize the noise signal of RDAE to obtain the optimal RPSs. Aiming to slove the complex high-dimensional optimization problem, an improved honey badger algorithm (IHBA) is developed deeply train DT-RDAE. To reasonably select RPSs from DPVs in the future and reduce the uncertainty impact of solar radiation, an affine artificial neural network (AANN) based on affine model of solar radiation intensity is proposed. Finally, we conducted simulations and analyzed the results on the 33 DPVs in Jiangsu Province of China to demonstrate the effectiveness of the proposed method compared to the other methods in the literature. Main contributions of this paper are shown as follows. (1) A DPVs virtual collection model is proposed to realize the accurate collection of DPVs output data with low equipment cost and calculation cost in a region. (2) A DT-RDAE assisted by optimizer is proposed to analyze the spatial–temporal correlation of DPVs and monitor its output data in real time. (3) IHBA is developed to optimize the input noise of DT-RDAE to optimize the RPSs. The tiered dynamic prey value evaluation mechanism is introduced to improve the global search ability of the honey badger.

3.2 Photovoltaic Virtual Collection

31

(4) The AANN based on affine mathematics is constructed to reduce the influence of the solar radiation intensity uncertainty, so as to ensure the real-time selection of some RPSs in the set of alternative RPSs is reasonable.

3.2.2 Virtual Collection Framework of DPVs The difference of solar radiation, meteorological state, ambient temperature and other factors at each location in a region makes DPVs actual output is various, and has spatial fluctuation. However, their output is correlate to the spatial distribution of DPVs. For each DPV, its output has a historical correlation in time, which is similar to the short-term prediction of PV output. This paper fully considers the spatial–temporal correlation of DPVs output, and propose a deeply trained recurrent denoising autoencoders (DT-RDAE), and use it to deeply explore the output characteristics of DPVs. The input noise of RDAE is constantly changed to find the optimal RPSs by deeply training. To reduce the training times of DT-RDAE, an improved optimization algorithm is developed to optimize the input noise. So that the training is accelerated, and realize the rapid searching of the optimal RPSs in various historical scenes, and capture the spatial–temporal correlation of DPVs output. The solar radiation intensity at each position in a region is mainly affected by the weather condition, which is not exactly the same as the overall solar radiation intensity in the region. Therefore, it is necessary to establish the uncertainty model of solar radiation intensity to improve the rationality of RPSs selection. Therefore, this paper establishes a solar radiation intensity model based on affine mathematics, and constructs an affine artificial neural network (AANN). Then, using the optimal RPSs of DPVs in various historical scenes to train the AANN, and obtain the selection mechanism of RPSs in different scenes. Accordingly, the DPVs output is collectted accurately, economically and efficiently by the virtual collection model. The virtual collection framework of DPVs is shown in Fig. 3.4.

3.2.3 Deep Trained RDAE for DPVs Virtual Collection Denoising autoencoders (DAE) is a kind of autoencoder that accepts damaged data as input. The powerful fitting ability of DAE can restore corrupt data [5]. Therefore, aiming the DPVs clusters equipped with only some data collection devices, DAE can conduct accurate data virtual collection of all DPVs in real time according to the output data of RPSs. However, the classical DAE is unable to remember the historical state of the input and output of each nodes, so it lacks the ability to analyze the time correlation of DPVs. To overcome this defect, recurrent denoising autoencoders (RDAE) is proposed in this paper. A memory recurrently update module is added on the basis of the classic DAE. In the training process, to find the optimal RPSs in the historical

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3 Photovoltaic Prediction and Virtual Collection

Distributed Photovoltaic Cluster Current Time and Meteorological State Historical Moments and Meteorological Scenes

Improved HBA

Optimize Historical RPSs

Global Search

Accelerating Deep Training

Population Location Update

High Dimensional Solution Space

Speed Up Convergence

All Historical Moments

Optimizer Assisted RDAE Deep Training Performance Calculation Iterative Update RPSs plan Spatio-temporal correlation analysis

RPSs Application Stage

Real Time Uncertainty Corrupt Spatial Diagnosis Data Input Correlation

1 Training Stage

Optimal RPSs in Historical Scenarios

Memory Individual Accurate Virtual Time Update Recurrently Correlation Collection

DT-RDAE

Affine BP Neural Network

Fig. 3.4 The virtual collection framework of DPVs. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

scenes, it is necessary to continuously adjust the noise of the input data for deeply training. This paper also constructs a deep training RADE, and uses IHBA to assist in the training of RDAE to reduce the number of training and realize the rapid search of the optimal RPSs. The structure and schematic of IHBA-assisted DT-RDAE is shown in Fig. 3.5. 1. RDAE Considering DPVs Spatial–Temporal Correlation Complete DPVs in tmax DPVs Data DPVs in t... DPVs in t2 DPVs in t1

Error Accuracy Improving Improved Honey Badger Algorithm Memory Updating

Optimize RPSs of DPVs in t1~tn New Deep Training Memory Noise Input Incomplete DPVs Data

Memory Recurrently Update Module

Previous Memory

Spatio-Temporal Coupling Analysis Module Virtual Collected DPVs Data

Fig. 3.5 The structure and schematic of IHBA-assisted DT-RDAE. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

3.2 Photovoltaic Virtual Collection

33

Virtual Collection Module

Incomplete DPVs data P*

P*PV1 (t) P*PV2 (t)

. . .

^

Output of DPVs P U1

^

P PV1(t)

U2

^

. . .

P PV2(t)

. . .

Un

P*PVn (t)

^

P PVn(t)

Un+1

S1

M1(t) S2

. . .

Previous Memory Vector M(t-1) M1(t-1)

R1

M2(t-1)

R2

. . . Mn(t-1) A

. . .

Rn Rn+1

New Memory Vector M(t)

M1(t-1)

Sn Sn+1

M2(t-1)

M2(t)

. . . Mn(t)

. . . Mn(t-1) B

Memory Refreshing Module

Memory Recall Module

Fig. 3.6 The topology of RDAE. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

The main function of RDAE is analysing the spatio-temporal correlation of historical data, and then obtain the ability of accurately estimating all DPVs according to the output data of RPSs. To retain the spatial correlation analysis ability of classical DAE and realizing the time correlation analysis of DPVs, this paper adds memory refreshing and recall modules to DAE. The topology of RDAE is shown in Fig. 3.6. Assumed that, the output of all DPVs at the current time t and the incomplete DPVs data input to RDAE are respectively: | | P(t) = P1 P2 ... Pi ... Pn

(3.25)

| | P∗ (t) = P1∗ P2∗ ... Pi∗ ... Pn∗

(3.26)

where Pi represents the output of i-th DPV and n represents the number of DPVs in the region. Since P∗ (t) is incomplete DPVs data, P∗ (t) ∈ P(t). As mentioned earlier, incomplete DPVs data is equivalent to a noise added to the complete DPVs data, so P∗ (t) can be expressed as:

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3 Photovoltaic Prediction and Virtual Collection

P∗ (t) = P(t) · N(t) | | N(t) = Nt,1 Nt,2 ... Nt,i ... Nt,n

(3.27)

where, N(t) represents the noise added to P(t) at time t; Nt,i is a binary variable, representing the noise added to i-th DPVs at time t. N(t) defaults to zero vector. When i-th DPV is selected as RPS, Nt,i is set to 1. Then, P∗ (t) becomes a vector which is only representing the output of RPSs. For the virtual collection module, the input is the incomplete DPVs data P∗ (t) and the recall vector of the previous memory vector processed by the memory playback module: | | ' ' ' ' M' (t − 1) = Mt−1,1 Mt−1,2 ... Mt−1,i ... Mt−1,n (3.28) = g(M(t − 1)) where, M(t − 1) is an abstract expression of the historical state of DPVs,but it does not represent the last time or historical average power of DPVs; g() represents the function of memory recall module. In particular, when t = 0, M(0) is a zero vector. Therefore, the output of the virtual collection module can be expressed as: | | ˆ = Pˆ 1 Pˆ 2 ... Pˆ i ... Pˆ n P(t) ( ) = f P∗ (t), M' (t − 1) ) ( = f P∗ (t), g(M(t − 1))

(3.29)

where, f() represents the function of virtual collection module. For the memory refreshing module, a new memory vector is formed by combining the previous memory vector and the virtual collection data of DPVs at the time t: ( ) ˆ M(t) = h P(t), M(t − 1)

(3.30)

where, h() represents the function of memory refreshing module. According to (3.28) and (3.29), the timing function of RDAE with the relationship of input–output at any time as follows: { ∗ ,))) t=1 ( f (P (1), ( (g(M(0))) ˆ P(t) = (3.31) ∗ ˆ − 1), M(t − 2) f P (t), g h P(t ,t ≥ 2 Furthermore, for RDAE with number of data sets is Tmax in the training set, the loss function is: LOSS =

tmax ( )2 1 E ˆ − P(t) P(t) 2tmax t=1

(3.32)

3.2 Photovoltaic Virtual Collection

35

Therefore, we get the RDAE model which considering the spatial–temporal correlation of DPVs. In the classical DAE, the value of N(t) is randomly determined according to a fixed probability. However, the random selection method will lead to the selected RPSs is unreasonable. Moreover, different N(t) will have an impact on the training results of RDAE and the accuracy of virtual collection. Therefore, it is necessary to reasonably adjust the N(t) at each time, so as to find the optimal RPSs in each historical scene. 2. Optimization Model of RPSs For all historical moments, the selection of RPSs can be expressed as: |T | AR = N(1) N(2) ... N(t) ... N(tmax ) ⎡ ⎤ N1,1 N1,2 . . . N1,i . . . N1,n ⎢ N ⎥ ⎢ 2,1 N2,2 . . . N2,i . . . . N2,n ⎥ ⎢ . ⎥ .. ⎢ . ⎥ . . . . ... ⎥ ⎢ . =⎢ ⎥ ⎢ Nt,1 Nt,2 . . . Nt,n ⎥ ⎢ ⎥ .. ⎢ .. ⎥ ⎣ . . . . . ... ⎦ Ntmax ,1 Ntmax ,2 ... Ntmax ,i ... Ntmax ,n

(3.33)

To reduce the amount of RPSs and improve the rationality of RPSs selection, the model selects the set of alternative RPSs PN. At time t, the actual RPSs will be selected from PN. To some extent, this approach gives RPSs selection flexibility. In practical engineering application, collection devices will be installed for all DPVs in PN. For different solar radiation intensities and time, a part of PN will be selected as RPSs at the current time according to the actual situation, so as to reduce the data calculation cost. Therefore, the scale of PN and the actual amount of RPSs at any time need to be limited. (1) Alternative RPSs Size Constraints The set of alternative RPSs can be expressed as: PN = N(1)|N(2)|...|N(t)|...|N(tmax ) | | = N1' N2' ... Ni' ... Nn'

(3.34)

The scale of PN is: NUM_PN =

n E

Ni' = mna

(3.35)

i=1

where, mna represents the maximum amount of collection devices that can be installed.

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3 Photovoltaic Prediction and Virtual Collection

(2) RPSs Amount Constraints The actual number of RPSs at any time can be expressed as: NUM_N(t) =

n E

Nt,i = mnr

(3.36)

i=1

where mnr represents the maximum amount of collection devices available at any time. It is worth noting that the constraint on the amount of actual RPSs here does not take “ ≤ ” but “ = ”. The reason is the essence of the DPSs virtual collection proposed in this paper is the state estimation with higher accuracy, and the collection accuracy is positively correlated with the data sources. To sum up, optimization model of RPSs is a binary ultra-high-dimensional (the dimension is tmax × n) nonlinear non differentiable optimization problem, which is difficult to solve. 3. HBA Based on ImprovedDynamic Opportunism For the above RPSs optimization problem, an improved honey badger algorithm (IHBA) is developed in this paper. The honey badger algorithm (HBA) [13] was proposed by Fatma A. Hashim et al. in 2021. As a new powerful optimizer, it shows stronger search accuracy than many classical optimization algorithms such as particle swarm optimization, harris hawks optimization (HHO) [14] and thermal exchange optimization [13]. However, the simulation of HBA on the predation behavior of honey badger is not enough. The position update strategy relies on the current global optimal position, resulting in insufficient global search ability. Aiming at the predation behavior of honey badger, this paper introduces dynamic opportunism to evaluate the current global optimal position. Thus, the dependence on the inferior global optimal position is reduced and the global search ability is improved. The position update strategy of honey badger in classic HBA is composed of digging phase and honey phase, which are respectively: xnew = F × r3 × α × di × |cos(2π r4 ) × [1 − cos(2π r5 )]| +(1 + F × β × I ) × xprey

(3.37)

xnew = F × r7 × α × di + xprey

(3.38)

where, xprey is the position of prey, that is, the current global optimal position; I, di and α respectively represent the smell intensity of prey, the distance between prey and i-th honey badger and the density factor, and their calculation method can refer to [13]; β is a preset parameter (default = 6); F, r3 , r4 , r5 and r7 are random numbers between 0 and 1. It can be seen from (3.36) and (3.37) that the position update of HBA mainly moves around the prey to select a suitable place to dig and capture the prey. However, the

3.2 Photovoltaic Virtual Collection

37

process does not consider the potential value of prey. With the iterative search of the algorithm, the ability of the global optimal position guiding honey badgers to find new prey will decline. As a result, the honey badger wil put rotten to the foraging behavior, and the algorithm trapping in local optimal location. As an opportunistic predator, honey badgers will adjust its food source according to the current extent of lack food, and its food composition will change seasonally. Therefore, this paper constructs a value evaluation method for prey to dynamically adjust the global optimal weight when the position of honey badger is updated. The value of prey is:

Vprey

⎧ R /(2∗R −R ) ⎪ Rdec ≤ Rc1 ⎨ GD (Rdec /Rc1 )(0.5 + γ e c1 | c1 dec ), GF (Rdec − Rc1 ) + Vprey |Rdec =Rc1 , = R < Rdec ≤ Rc2 c1 ⎪ ⎩ e(Rc2 /(Rc2 −Rdec )) G R + V || Rc2 < Rdec L c2 prey Rdec =Rc2 ,

(3.39)

where, GD , GF and GL represent the dynamic, normal and maximum evaluation coefficients of Vprey , respectively; γ represents sensitivity coefficient; RC1 and RC2 are opportunistic trigger thresholds of departure and approach, respectively; Rdec represents the change rate of the global optimal value, and its calculation as follows: ) ( Rdec = fj − fj−1 /fj−1

(3.40)

where fj and fj−1 represent the global optimal values of j-th and ( j−1)-th iterative processes, respectively. Thus, the position update calculation method of honey badger becomes: xnew = F × r3 × α × di × |cos(2π r4 ) × [1 − cos(2π r5 )]| ) ( +(1 + F × β × I ) × Vprey × xprey ) ( xnew = F × r7 × α × di + Vprey × xprey

(3.41) (3.42)

When Rdec is large, the honey badger will enter a positive stage, increase interest in the current prey and accelerate its approach; On the contrary, the honey badger enters the picky eating stage and try to change its food source to reduce its dependence on the current global optimal location. To prevent trapping in local optimal location, when Rdec > RC2 , it becomes a constant. The flowchart of IHBA assisted RDAE for deep training is shown in Fig. 3.7. 4. Affine Artificial Neural Network IHBA assisted RDAE in deep training to obtain the optimal RPSs in all historical scenes. These data and various scenes including solar radiation intensity and time data are used to form a training set to train the artificial neural network for real-time RPSs selection. As solar radiation is uncertain under different weather conditions, deterministic solar radiation intensity models may become unreliable [11], making it difficult to obtain a high virtual collection accuracy.

38

3 Photovoltaic Prediction and Virtual Collection Prey search

Deep training

Start

Retraining RDAE model using the new AR

Input the parameter

Correct prediction error

Define the fitness function (LOSS function of D-RDAE)

Calculate the virtual collection error Calculate honey badgers’s fitness

Initialize number of honey badgers and their respective positions

N Calculate the current honey badgers’s fitness Calculate the change rate of global optimal value based on (16) Calculate current prey value based on (15)

Whether to reach the IHBA iteration number

Y Output xbest (optimal RPSs) Construct a D-RDAE model using the RPSs of optimal AR Correct prediction error

Update honey badgers position baed on (17) and (18)

End

Well trained

Fig. 3.7 The flowchart of IHBA assisted RDAE for deep training. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

Interval mathematics is a potential uncertain data processing method, which can better overcome the influence of uncertain parameters in system [12]. However, interval mathematics has strong conservatism, and affine mathematics can overcome this defect [11]. Therefore, this papper developed an affine artificial neural network (AANN) based on the affine model of the uncertainty of solar radiation intensity for real-time RPSs selection. For the traditional artificial neural network, the input data can be expressed as: |T | X = X1 X2 . . . Xs

(3.43)

| | ˆ = Xˆ 1 Xˆ 2 . . . Xˆ s T X

(3.44)

Its affine form is:

For d-th affine elements Xˆ d (d = 1, 2, . . . , s): Xˆ d =x0,d + x1,d ε1,d + x2,d ε2,d + · · · + xp,d εp,d (d = 1, 2, 3, . . . , s)

(3.45)

3.2 Photovoltaic Virtual Collection

39

Therefore, (3.43) is: ⎡

x0,1 x1,1 ε1,1 x2,1 ε2,1 ⎢ x0,2 x1,2 ε1,2 x2,2 ε2,2 ˆ =⎢ X ⎣ ... ... ... x0,s x1,s ε1,s x2,s ε2,s

⎤ ... xp,1 εp,1 ... xp,2 εp,2 ⎥ ⎥ ... ... ⎦ ... xp,s εp,s

(3.46)

According to the reasonable simplification of the existing affine form, only the first noise element is extracted [11]. Therefore, (3.45) can be simplified as: |T | x0,2 ... x0,s x0,1 ˆ X= x1,1 ε1,1 x1,2 ε1,2 ... x1,s ε1,s

(3.47)

For neural networks without considering temporal correlation, the input layer can ˆ into the input layer of neural only be input with one-dimensional vectors. To input X network, it needs to be reshaped into one-dimensional vector. Reshape all line vectors ˆ into one line according to the line number: in X | | ˆ = x1 x2 T X | | x1 = x0,1 x0,2 ... x0,s | | x2 = x1,1 ε1,1 x1,2 ε1,2 ... x1,s ε1,s

(3.48)

ˆ train composed of m X, ˆ it can be expressed as: For the training set X | | ˆ trian = X ˆ2 ... X ˆ1 X ˆς ... X ˆm X | | ˆ ς = x1,ς x2,ς T , ς = 1, 2, . . . , m X

(3.49)

For the neural network with h and o neurons in the hidden layer and output layer respectively, the output is: ( ) ˆ ςT × ω + b × y + B Ooutput = activ X

(3.50)

where, activ represents the activation function of neural network; ω and b represent the weight value matrix from the input layer to the hidden layer and the offset vector of the input layer, respectively; y and B represent the weight value matrix from hidden layer to output layer and the offset vector of hidden layer, respectively. True value vector is: | | Yς = y1,ς y2,ς . . . yo,ς , ς = 1, 2, . . . , m

(3.51)

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3 Photovoltaic Prediction and Virtual Collection

The loss function is: ( )2 ) 1E 2 1 E( ˆ ςT × ω + b × y + B − Yς activ X E= /\ς = 2 ς=1 2 ς =1 m

m

(3.52)

Then, the weight of each layer of the network is corrected by using the error back propagation and gradient descent method. It can be seen from the above that the working process of AANN requires activ can calculate affine numbers and be derivable. However, at present, the arithmetical rules of affine number is only limited to the basic four arithmetic operations [15]. Therefore, this study selects parametric rectified linear unit (PReLU) [16] as the activation function. The arithmetic operation of this function is simple and can avoid the limitations of affine arithmetic operation. However, the input of affine numbers into AANN for calculation involves a large number of multiplication processes. The multiplication of affine number is: Xˆ d ∗ Xˆ d =x0,d x0,d + 2x0,d ε1,d )2 ( + x1,d ε1,d (d = 1, 2, 3, . . . , s)

(3.53)

It can be seen that affine multiplication calculation will make the order of noise elements increasing with the calculation times. As a result, when the value of noise element is not near −1 or 1, the calculation result is close to 0. It makes the variation range of output result of AANN very unstable and loses the significance of considering parameter uncertainty. Therefore, this paper introduces a new noise element into the calculation result to replace the high-order term, so as to obtain the following linear representation: 2 εk,d (d = 1, 2, 3, . . . , s) Xˆ d ∗ Xˆ d = x0,d x0,d + 2x0,d ε1,d + x1,d

(3.54)

In this study, the input data has only two dimensions: solar radiation intensity IS and time T, s = 2, and only former has uncertainty. For solar radiation intensity, its affine form is: Iˆ s = Is0 + Is1 εI ) ( Is0 = Is + Is /2 ) ( Is1 = Is − Is /2

(3.55)

where, IS and IS are the upper and lower bounds of IS , respectively. Further, (3.48) is simplified as: ⎡

ˆ trian X

⎤ Is0,2 . . . Is0,tmax Is0,1 = ⎣ Is1,1 εI ,1 Is1,2 εI ,2 . . . Is1,tmax εI ,tmax ⎦ T1 T2 . . . Ttmax

(3.56)

3.2 Photovoltaic Virtual Collection

41

Specially, the value of εI is determined by the weather, not according to the εI ∈ [−1, 1] of classical affine mathematics. The value of εI in different weather is shown in Table 3.2.

3.2.4 Case Study To verify the effectiveness of the method proposed in this paper, 33 DPVs in an administrative district of Nanjing, Jiangsu Province, China were selected for virtual collection test. The data collected from March 1, 2018 to December 31, 2018 are collected over a 15-min interval from 07:15 to 17:00. The solar radiation intensity, weather and DPVs output data from March 2018 to July 2018 are extracted for network training and error correction. The testing data are from August 2018 to December 2018 for DPVs virtual collection and effectiveness verification. The time resolution of the solar radiation intensity, weathe and DPVs output is 15 min. The parameters of mna and mnr are 10 and 8, respectively. The number of DT-RDAE and AANN hidden layer neurons Nh−RDAE and Nh−ANN are 16 and 20, respectively. The population size S of IHBA is 50 and the maximum number of iterations Tmax is 300. In this Section, 5 experiments are conducted to verify the accuracy of the virtual collection model, the effectiveness of DT-RDAE, the optimization ability of IHBA, the superiority of AANN and the stability of the proposed method in severe fluctuating weather. 1. Virtual Collection Results AANN and IHBA assisted DT-RDAE were trained with training set. For the verification set, the virtual collection is evaluated by mean absolute percentage error (MAPE) and mean absolute error (MAE) [17]. The overall situation of 33 DPVS throughout the year and the overall situation of DPVS at all times of the year are shown in Figs. 3.8 and 3.9 respectively. The annual virtual collection results of 33 DPVs and the overall results of all DPVs at each time are shown in Figs. 3.8 and 3.9 respectively. As shown in Fig. 3.5, the virtual collection accuracy of RPSs is the highest, which is lower than the overall MAPE average. It proves the rationality of RPSs selection. As shown in Fig. 3.9, the overall virtual collection accuracy of all DPVs is high, Fig. 3.8 The average MAPE throughout the year of 33 DPVs. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

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3 Photovoltaic Prediction and Virtual Collection

Fig. 3.9 The average MAPE among all DPVs of the year. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

and the MAPE at any time is no more than 6%. During November and December in winter, the accuracy of virtual collection is low, and the higher MAPE is mainly distributed at 07:00 and 17:00. This is mainly because the training data source of DT-RDAE and AANN is from March to July, and there is a lack of data similar to the climatic characteristics of November and December. 2. Verification of DT-RDAE To verify the effectiveness of DT-RDAE proposed in this paper, the classic DAE and RDAE without optimizer assisted deep training are selected and compared with DT-RDAE. The virtual vollection result in different method as shown in Table 3.3. It can be seen from Table 3.3 that DT-RDAE has the highest accuracy, and the MAPE and MAE of all DPVs are lower than RDAE and DAE. Meanwhile, the collection accuracy of RDAE is higher than DAE, which proves the superiority of DT-RDAE. Furthermore, we can see that among the results of RDAE, among the 10 DPVs with the lowest MAPE, there is a high coincidence with the RPSs of DTRDAE. There are 8 RPSs with the same number, while only 4 in DAEs as the same. This indicates that the ability of DAE to analyze the spatial correlation of DPVs output in a region is shortage. The addition of memory refreshing, recall modules and optimizier assisting deep training mechanism can greatly improve the input data coupling characteristic analysis ability of DAE. Considering the time-dependent of DPVs output, the MAE of RDAE is lower than DAE. This shows that the output characteristics of DPVs in a region have strong time correlation. This is similar to the prediction of PV. Although the PV prediction can also extract the time correlation

3.2 Photovoltaic Virtual Collection

43

Table 3.3 Virtual vollection result in different method. Reprinted from Ref. [7], copyright 2023, with permission from IEEE Number of DPV

DT-RDAE MAE

RDAE MAPE

MAE

DAE MAPE

MAE

MAPE

1

4497

0.6926

6959

1.0922

17,238

2.9379

2

5755

1.0093

7453

1.1637

17,511

3.0830

3

5630

0.9654

7154

1.1171

15,159

2.4148

4

5758

0.9037

8008

1.3296

10,617

2.0058

5

5363

0.8891

7641

1.2732

14,966

2.6669

6

5807

0.8779

7952

1.3129

17,124

2.8646

7

5335

0.8322

7712

1.1879

11,172

1.9906

8

4916

0.7834

5895

1.0242

15,029

2.8070

9

5776

0.9431

8171

1.3560

15,900

2.8710

10

5076

0.7865

8108

1.2453

17,557

2.7648

11

4325

0.6622

6663

1.0282

16,385

2.7361

12

4154

0.7755

6266

1.1290

12,969

2.4055

13

5354

0.8717

7952

1.2535

16,613

2.6757

14

3410

0.5654

6771

1.0564

15,883

2.3441

15

5366

0.9657

7649

1.3609

16,397

2.9721

16

3303

0.6330

5490

0.9948

17,757

2.6946

17

5758

0.8806

8252

1.2475

17,597

2.6977

18

5238

0.8433

7886

1.4051

13,862

2.1750

19

5432

0.8850

7899

1.2661

16,723

2.7265

20

5070

0.8279

7476

1.1977

15,750

2.5543

21

3449

0.6247

8154

1.2739

14,175

2.2764

22

4971

0.9550

7833

1.2288

16,451

2.5667

23

5161

0.9351

7499

1.3293

17,730

2.9041

24

3954

0.6955

6142

1.0584

12,400

2.1734

25

4829

0.8650

5731

0.9236

10,957

1.8044

26

4308

0.8234

6499

1.2013

13,307

2.5479

27

4921

0.9185

7220

1.3125

15,376

2.8277

28

6029

0.8899

8636

1.2724

18,435

2.7278

29

5075

0.7531

7355

1.1191

15,588

2.4360

30

4581

0.7363

7211

1.2641

13,574

2.0845

31

4636

0.7931

6929

1.1778

14,375

2.4683

32

4944

0.9316

6897

1.2664

16,214

2.6067

33

5625

0.9379

7162

1.3482

15,284

2.9456

44

3 Photovoltaic Prediction and Virtual Collection

of PV, it requires DPVs to have a complete data collection device and a period of historical data. It lack the real-time data estimation ability of DPVs cluster that the data collection device are incomplete. With the help of memory recurrent refreshing and recall, the time correlation can be fully exploited in the absence of collection device to realize high-precision virtual collection of DPVs. 3. Comparison of Optimization Algorithms To prove the effectiveness of IHBA developed in this paper, HBA, Coyote Optimization Algorithm (COA) [18], Grey Wolf Optimizer (GWO) [19] and HHO [14] are selected to optimize the RPSs of DT-RDAE. Due to the optimization and virtual collection results of IHBA had shown in Figs. 3.8 and 3.9 and Table 3.2, the other 4 algorithms results are shown in Tables 3.4 and 3.5, respectively. Figure 3.10 shows the global optimum of the DT-RDAE loss function obtained by IHBA, HBA, COA, GWO and HHO over 300 iterations. As shown in Fig. 3.10, IHBA has the highest search accuracy. Compared with HBA, IHBA has a slower convergence speed at the initial stage of iteration, but the global search ability is powerful. It overcomes the putting rotten phenomenon of honey badger when the agent is close to the local optimal position in the classical HBA. This is mainly because HHO, like HBA, belongs to the algorithm which is based on swarm intelligence behavior [20]. However, the position update formula of HHO considers the overall situation of all agents and does not completely rely on the global optimal position. From this point, it also indirectly proves the rationality of the improvement idea of HBA in this paper. Although COA has strong global search ability [18], for the RPSs optimization problem proposed in this paper, the search accuracy is ordinary due to the high dimension of solution space (Dimensions = C10 33 ). 4. Comparison of Uncertainty Modeling Methods To prove the superiority of the proposed AANN considering solar radiation uncertainty for optimizing RPSs, it is compared with other solar radiation uncertainty modeling methods. However, there are few studies on the virtual collection of DPVs, so it is difficult to find the RPSs optimization method considering the uncertainty of solar radiation. Therefore, SO [21] and RO [22] in the deterministic optimization method are selected to compare with AANN. The optimization results and virtual Table 3.4 Optimal RPSs based on different optimizers. Reprinted from Ref. [7], copyright 2023, with permission from IEEE Optimizer

1-th RPS

2-th RPS

3-th RPS

4-th RPS

5-th RPS

6-th RPS

7-th RPS

8-th RPS

9-th RPS

10-th RPS

GWO

3

4

7

18

21

24

25

29

30

31

HBA

4

7

12

18

24

25

29

30

31

32

COA

3

4

7

12

18

22

24

25

30

32

HHO

3

4

7

12

15

16

24

25

26

32

3.2 Photovoltaic Virtual Collection

45

Table 3.5 Virtual vollection result in different optimizers. Reprinted from Ref. [7], copyright 2023, with permission from IEEE Number of DPV

GWO MAE

HBA MAPE

MAE

COA MAPE

MAE

HHO MAPE

MAE

MAPE

1

11,949

2.1058

12,877

2.2693

10,514

1.8529

3991

0.7033

2

11,802

2.0818

10,346

1.8250

10,281

1.8135

4556

0.8036

3

8604

1.3086

9960

1.5148

8197

1.2467

2339

0.3557

4

5726

1.2986

4750

1.0774

4173

0.9465

1850

0.4195

5

10,196

1.8877

9991

1.8496

8259

1.5289

3372

0.6242

6

11,872

2.0840

10,347

1.8163

9751

1.7118

3077

0.5401

7

6701

1.3297

6012

1.1929

4911

0.9744

1561

0.3099

8

10,973

2.1959

10,462

2.0937

8138

1.6286

2267

0.4537

9204

1.7527

8728

1.6621

8825

1.6805

4026

0.7666

10

9

11,956

1.8950

11,245

1.7822

10,405

1.6492

3555

0.5635

11

12,423

2.1363

12,538

2.1562

10,197

1.7535

4024

0.6920

12

9657

1.7856

8185

1.5135

7477

1.3825

1966

0.3636

13

10,482

1.6796

10,051

1.6105

9808

1.5715

3973

0.6366

14

11,537

1.6453

11,549

1.6469

11,126

1.5866

4303

0.6136

15

10,148

1.8459

11,314

2.0579

9836

1.7891

2413

0.4389

16

15,631

2.2293

14,362

2.0484

11,816

1.6853

2974

0.4241

17

11,954

1.8347

10,801

1.6577

10,164

1.5600

4293

0.6589

18

7916

1.2224

7440

1.1489

7740

1.1952

2843

0.4390

19

13,096

2.1358

10,357

1.6892

9177

1.4967

3191

0.5205

20

11,132

1.7995

11,158

1.8038

9319

1.5065

4130

0.6676

21

9689

1.4920

9901

1.5246

9152

1.4094

3566

0.5491

22

12,104

1.6993

11,473

1.6107

9466

1.3290

4102

0.5759

23

13,631

2.1354

11,363

1.7801

10,239

1.6040

4230

0.6626

24

9399

1.6447

7916

1.3853

7568

1.3244

2367

0.4143

25

6145

0.9421

5907

0.9055

5298

0.8121

1265

0.1939

26

10,575

2.0265

8101

1.5523

7551

1.4471

1816

0.3479

27

11,917

2.1763

9552

1.7444

8905

1.6262

4022

0.7344

28

14,137

2.0943

12,829

1.9004

10,370

1.5362

4469

0.6621

29

10,274

1.6446

9049

1.4485

8734

1.3981

4139

0.6625

30

10,404

1.5596

8681

1.3013

7241

1.0854

2950

0.4422

31

8775

1.5093

8565

1.4733

8094

1.3922

3330

0.5728

32

11,229

1.6690

9843

1.4630

9176

1.3638

2295

0.3411

33

10,302

2.1414

8993

1.8692

8439

1.7542

2784

0.5786

46

3 Photovoltaic Prediction and Virtual Collection

Fig. 3.10 Comparison of algorithm results. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

collection accuracy of the three methods are shown in Table 3.6 and Fig. 3.11, respectively. As shown in Table 3.6, the RPSs of the three optimization methods are different, due to the different optimization characteristics of the three methods. As shown in Fig. 3.11, all DPVs and overall virtual collection accuracy of AANN method are the best. This proves the superiority of AANN proposed in this paper for system identification with uncertain parameters. Compared with SO, RO focuses on optimizing the worst scenario, while SO focuses on overall optimization. Therefore, the overall virtual collection accuracy of SO is higher than RO. However, for some special DPVs with terrible virtual collection result, RO will be more accurate than SO. 5. Extreme Test Due to the limited training data, it is impossible to include all meteorological scenarios and DPVs state in the region. Therefore, when the local meteorological scene changes, the virtual collection accuracy will be influenced. To test the antiinterference ability of the virtual collection technology proposed in this paper, this Table 3.6 Optimal RPSs based on different method. Reprinted from Ref. [7], copyright 2023, with permission from IEEE Optimizer

1-th RPS

2-th RPS

3-th RPS

4-th RPS

5-th RPS

6-th RPS

7-th RPS

8-th RPS

9-th RPS

10-th RPS

AANN

1

8

11

12

14

16

21

24

29

30

SO

4

7

12

18

24

25

29

30

31

32

RO

3

4

7

12

15

16

24

25

26

32

3.2 Photovoltaic Virtual Collection AANN

SO

47 AANN

SO 1 2 3 33 32

RO

33 1 2 3 3210000

4 31 5 8000 30 6 29 6000 7 28 4000 8 27 2000 9 26 0 10 25 11 24 23 12 13 22 14 21 15 20 19 18 17 16

MAE of different method

RO

2 4 31 5 30 1.5 6 29 1 7 28 8 27 0.5 9 26 0 10 25 24 11 23 12 13 22 14 21 20 19 15 18 17 16

MPAE of different method

Fig. 3.11 Virtual collection accuracy of different methods. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

Fig. 3.12 Virtual collection effect with different fluctuation ranges. Reprinted from Ref. [7], copyright 2023, with permission from IEEE

Number of DPV

paper randomly adds noise with different fluctuation ranges to the test set to verify the effect of virtual collection. To avoid contingency, each noise is tested 100 times, and the MAPE of each test result is averaged. Without considering the influence of weather, the PV output is directly proportional to the solar radiation intensity [23]. Therefore, the experiment can be reasonably simplified by adding the same noise to the solar radiation intensity and PV output. The effect of virtual collection with different fluctuation ranges is shown in Fig. 3.12. As shown in Fig. 3.12, with the increase of climate fluctuation range, the overall effect of virtual collection is still very good, especially RPSs. This is mainly because the DT-RDAE constructed in this paper has strong memory ability. For the memory refresh and recall modules, the input to the virtual collection module is a set of timevarying vectors determined by the historical state of DPVs. The introduction of this vector makes up for the lack of adaptability to climate change, which is caused by the inability of DAE to be trained in real time. However, the virtual collection accuracy of particular DPVs will decline sharply with the increase of climate fluctuation range.

33 29 25 21 17 13 9 5 1

MAPE(%) 2 1.5 1 0.5

10

20 30 40 Fluctuation Ranges of Solar(%)

50

0

48

3 Photovoltaic Prediction and Virtual Collection

In actual application, it can be considered to install data collection devices for such DPVs according to the degree of climate change in the region. To meet the demand of virtual collection accuracy.

3.2.5 Conclusion In this paper, an affine optimization of RPSs and data virtual collection model considering spatio-temporal coupling of DPVs is proposed to determine the DPVs that need to install the data collection device. It realizes the long-term low-cost and highprecision collection of DPVs output data. The DT-RADE is used to analyze the spatial–temporal correlation of DPVs output. An improved HBA is proposed to optimize the input noise of DT-RADE and determine the optimal RPSs. The AANN is used to reduce the number of RPSs in different scenes, which overcomes the influence of the uncertainty of solar radiation intensity. In summary, we can conclude that: (1) The virtual collection technology proposed in this paper reduced the number of DPVs data collection devices in a region and realize the high-precision estimation of DPVs output with slight loss of measurement accuracy. (2) Compared with traditional DAE, DT-RDAE can well capture the spatial– temporal correlation of time-varying input data. The using of optimizer to deeply train RDAE can increase the system perception ability of the network. (3) Through the dynamic evaluation of the value of prey, the proposed IHBA overcomes the problem that the position update of agent in HBA is completely dependent on the global optimal position. It has stronger global search ability than HBA, COA, GWO and HHO. (4) The AANN constructed by affine mathematics has stronger ability to overcome the influence of solar radiation intensity uncertainty than SO and RO, and provides the selection strategy of RPSs to DT-RDAE in different scenarios. The proposed study can reduce the amount of data collection devices and calculation cost for a region or system that needs a lot of data measurement and collection nodes. The AANN can provide a new idea for system state estimation with uncertain parameters. However, with the passing of time, the system characteristics may change tremendously. This leads to the decrease of virtual collection accuracy. In practical application, it is necessary to appropriately increase the number of data collection devices or the maximum real-time data collection scale according to the requirements of collection accuracy and the possible change range of the system. However, the relationship between virtual collection accuracy and the amount of RPSs is not clear. With the development of PV, the challenges of data collection and device cost will be serious increasingly. How to further reduce the amount of devices and the scale of data collection within the allowable error range of virtual collection is a possible research direction of virtual collection in the future.

References

49

References 1. Elsinga B, van Sark W (2017) Short-term peer-to-peer solar forecasting in a network of photovoltaic systems. Appl Energy 206:1464–1483 2. Akhter MN, Mekhilef S, Mokhlis H, Mohamed Shah N (2019) Review on forecasting of photovoltaic power generation based on machine learning and metaheuristic techniques. IET Renew Power Gener 13(7):1009–1023 3. Liu L, Zhan M, Bai Y (2019) A recursive ensemble model for forecasting the power output of photovoltaic systems. Sol Energy 189:291–298 4. Li L-L, Wen S-Y, Tseng M-L, Wang C-S (2019) Renewable energy prediction: a novel shortterm prediction model of photovoltaic output power. J Clean Prod 228:359–375 5. Abdel-Nasser M, Mahmoud K (2019) Accurate photovoltaic power forecasting models using deep LSTM-RNN. Neural Comput Appl 31(7):2727–2740 6. Li K, Cheng G, Sun X, Yang Z (2019) A nonlinear flux linkage model for bearingless induction motor based on GWO-LSSVM. IEEE Access 7:36558–36567 7. Delussu F, Manzione D, Meo R, Ottino G, Asare M (2022) Experiments and comparison of digital twinning of photovoltaic panels by machine learning models and a cyber-physical model in modelica. IEEE Trans Industrial Informatics 18(6):4018–4028 8. Yang M, Zhao1 M, Liu D, Ma M, Su X (2021) Improved random forest method for ultra-shortterm prediction of the output power of a photovoltaic cluster. Front Energy Res 9:749367. Art. no. 749367 9. Liu W, Ren C, Yan X (2021) PV generation forecasting with missing input data: a superresolution perception approach. IEEE Trans Sustain Energy 12(2):1493–1496 10. Mohamad NB, Lai AC, Lim BH (2022) A case study in the tropical region to evaluate univariate imputation methods for solar irradiance data with different weather types. Sustain Energy Technol Assess 50. Art. no. 101764 11. Vincent P, Larochelle H, Bengio Y, Manzagol PA (2008) Extracting and composing robust features with denoising autoencoders. In: Proceedings of the 25th international conference on machine learning. pp 1096–1103 12. Lall R, Robinson T (2022) The MIDAS touch: accurate and scalable missing-data imputation with deep learning. Polit Anal 30:179–196 13. Zhang C, Hu D, Yang T (2022) Anomaly detection and diagnosis for wind turbines using long short-term memory-based stacked denoising autoencoders and XGBoost. Reliab Eng Syst Saf 222. Art. no. 108445 14. Scarpiniti M, Ahrabi SS, Baccarelli E, Piazzo L, Momenzadeh A (2022) A novel unsupervised approach based on the hidden features of deep denoising autoencoders for COVID-19 disease detection. Expert Syst Appl 192. Art. no. 116366 15. Wang S, Han L, Wu L (2015) Uncertainty tracing of distributed generations via complex affine arithmetic based unbalanced three-phase power flow. IEEE Trans Power Syst 30(6):3053–3062 16. Wang B, Zhang C, Dong ZY (2020) Interval optimization-based coordination of demand response and battery energy storage system considering soc management in a microgrid. IEEE Trans Sustain Energy 11(4):2922–2931 17. Hashima FA, Housseinb EH, Hussainc K, Mabroukd MS, Al-Atabany W (2022) Honey badger algorithm: new metaheuristic algorithm for solving optimization problems. Math Comput Simul 192:84–110 18. Heidari A, Seyedali M, Hossam F, Ibrahim A, Majdi M, Huiling C (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872 19. Raj V, Kumar BK (2019) A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty. Electr Power Energy Syst 107:395–402 20. Niu G, Wang X, Golda M (2021) An optimized adaptive PReLU-DBN for rolling element bearing fault diagnosis. Neurocomputing 445:26–34 21. Yao T, Wang J, Haoyan W, Zhang P, Li S, Ke X, Liu X, Chi X (2022) Intra-hour photovoltaic generation forecasting based on multi-source data and deep learning methods. IEEE Trans Sustain Energy 13(1):607–618

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Chapter 4

Multi-energy Load Forecasting of Integrated Energy System

4.1 Introduction Integrated energy system (IES) is a kind of integrated energy supply platform based on “multi-energy complementation, energy cascade utilization” [1], which realizes the conversion of various energy sources, such as combined cooling, heating and power (CCHP) [2]. With the rapid development of the Energy Internet, the coupling of different types of energy is becoming higher and more common, which calls for more advanced load prediction with higher accuracy and efficiency. At present, energy load can be roughly divided into three categories: cooling load, thermal load and electric load [3–5]. The cooling load keeps indoor temperature and humidity at specified levels, including lighting heat dissipation, human body heat dissipation and other ways of heat dissipation. The thermal load refers to the amount of heat released per unit of time when the fuel burns in the burner. The sum of the electric power taken from the electric power system by the electric power user’s electric equipment at a certain time is called the electric load, whose related characteristics can be observed through some load curves. To accurately predict and analyze the IES performance, extensive research efforts have been carried out, with focuses on short-term load prediction. In Ref. [6], the correction factor is introduced into Kalman filter, which is used to modify the traditional Kalman prediction results and improve the accuracy of short-term load prediction. In Ref. [7], a chaos disturbance factor is introduced into Cuckoo search to improve the global search ability, and the Elman-IOC short-term load forecasting model is established using improved Cuckoo search. In Ref. [8], an autoregressivemoving average with exogenous terms (ARMAX) model is used to predict multiple loads of integrated energy system with temperature as external input. This prediction method is relatively simple in modeling and requires less data, but it does not consider the interaction between loads, and the prediction error is large. In Ref. [9], considering the influences among three types of loads are considered, a deep neural network model based on multi-layer restricted Boltzmann machine (RBM) is proposed. The prediction method has a high accuracy, but it is difficult to train the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_4

51

52

4 Multi-energy Load Forecasting of Integrated Energy System

model, with a long prediction time and a large amount of data for training. In Ref. [10], the wavelet neural network (WNN) is introduced to predict the cold, heat and electric loads of the IES with a competitive performance. Compared to other methods aforementioned, WNN has a strong ability in learning and feature extraction over a relatively simple structure, which is suitable for fast load forecasting of IES with many influence factors. As the traditional WNN prediction method is sensitive to the initial connection weights and wavelet parameters, poor selection of parameters will cause slow convergence rate or even non-convergence that will lead to poor prediction results. Also, there are many influence factors in the short-term load forecasting of IES, and the key is to choose the appropriate effecting factors. To improve IES load prediction, this paper proposes a new method named improved particle swarm optimization (IPSO)-WNN, where the key parameters are calculated by PSO and chaos algorithms. To improve the prediction, influence factors are selected using Pearson correlation coefficient and some factors are abandoned. The location parameter is produced by iterative formula of particle swarm positions to accelerate the optimization process. As PSO may be lost in the local optima, chaos algorithm is introduced to search for the global optimal particle. The remainder of this paper is structured as follows. In Sect. 4.2, the problem model is constructed and a detailed description of load prediction is presented. Section 4.3 uses the correlation coefficients to screen the important factors that affect the load prediction, which include historical data, meteorological data, typical daily parameters of IES. Section 4.4 introduces the methodology and procedures of IPSOWNN in detail. Section 4.5 presents and evaluates the performance of the proposed method via simulations.

4.2 Problem Model The IES load forecasting and optimization model is shown in Fig. 4.1. The loads to predict are composed of three types, i.e., electric load, thermal load and cooling load, whose predicted values are denoted as y i + /\yit (i = 1, 2, 3) respectively. The relevant data involved in the load forecasting process include historical load data, meteorological data and some daily parameters of IES, such as historical electric load P1 , wind speed V, week Z. The key influence factors of the three typical loads are determined by the Pearson coefficient ρ X Y . In order to reduce the prediction dimensions and forecast three kinds of load with high accuracy and efficiency, the indicators with correlation coefficient greater than 0.29 are taken as the consideration factors of all kinds of load prediction according to the actual situation. The training data is input into the prediction module for predictive outcome training and error correction yit , while related parameters are input to predict each type of load. To optimize the performance of WNN, PSO algorithm is adopted to replace the particle iteration velocity v(i, k) and position x(i, k) in WNN, and chaos search is conducted on the optimal particle after iteration to determine the optimal particle x(k, d). The output of electric load, thermal load and cooling load prediction through module is /\

4.3 Choice of Load Prediction Influence Factors Based on Pearson …

53

Prediction module

Foundation model

Influence factors Historical load data historical electric load P1 historical thermal load P2 historical cooling load P3 Meteorological data

ρ XY > 0.29

Related parameters

y i (i = 1, 2,3)

x(i,k) v(i,k)

3 Particle swarm optimization

prediction results y i + Δyit

Error correction

day R week Z month M

Wavelet neural network

P1 Historical P2 2 load T data P3 W R Z M

Daily parameters

1

Optimization module

wind speed V Historical load data temperature T wind direction D weather W

Pearson correlation coefficient

P1 P2 T W

x(k , d )

Chaos algorithm

Training data

Δyit = yit − y it

Fig. 4.1 The structure of the strategy for V2G /\

/\

recorded as y i (i = 1, 2, 3), and the final load prediction result y i + /\yit is obtained after training and correction.

4.3 Choice of Load Prediction Influence Factors Based on Pearson Correlation Coefficient Different from short-term load forecasting in power systems, IES has energy conversion equipment, and the three types of loads in IES have both high coupling and strong correlation. Reference [11] suggested that the load characteristics of each load and the relationship between them should be considered in the short-term load forecasting of IES. The short-term load prediction of IES is not only affected by the interaction between loads, but also by many other factors such as the operating environmental and daily types. Reference [12] pointed out that only by quantifying the influence factors reasonably can the influence degree of load prediction be better expressed. Therefore, Pearson correlation coefficient is introduced to verify the correlation between each factor and each load and to select the influence factors of short-term load of IES based on the correlation analysis. The Pearson coefficient is a widely-adopted metric to calculate the correlation between each influence factor and each load, it represents the strength of the correlation degree between two sequences in Ref. [13]. The calculation principle is shown in formula (4.1). ρX Y

(

)( ) X i − X Yi − Y =/ )2 /E I ( )2 EI ( X − X i i=1 i=1 Yi − Y EI

i=1

(4.1)

54

4 Multi-energy Load Forecasting of Integrated Energy System positive correlation

negative correlation

Fig. 4.2 Meaning of value of Pearson coefficient

0

-1

1

where X and Y represent the average value of sequence X and Y, respectively; ρ X Y represents the correlation between X and Y, and I is the number of data in the sequence. As a common method to measure the correlation between random variable X and Y, the value of Pearson coefficient ranges from −1 to 1, as shown in Fig. 4.2. The higher the absolute value of the correlation coefficient, the greater the impact on load prediction. If the two variables are positively correlated, the value range of their correlation coefficient is (0, 1]; if the variables are negatively correlated, the value range is [−1, 0); 0 means that the two variables are completely independent of each other. To further analyze the influence factors of different kinds of load in IES prediction and achieve predicted results efficiently, correlation analysis is conducted for some common influence factors, including historical electric load P1 , historical thermal load P2 , historical cooling load P3 , wind speed V, temperature T, wind direction D, weather W, day R, week Z and month M. The correlation coefficients between these factors and three target predicted loads are shown in Table 4.1. If too many factors are selected, it will make it difficult to create an effective model and decrease the forecasting speed. Based on this consideration, the factors with absolute value of correlation coefficient greater than 0.29 are selected, and some factors that have little influence on load forecasting can be ignored in the subsequent forecasting process. The selection of key influence factors of various loads can be referred to Fig. 4.3. From Fig. 4.3, it is obvious that historical electric load P1 , historical thermal load P2 , temperature T and weather W have great influence on the operation and Table 4.1 Pearson coefficients of three typical loads Factors

Electric load

Thermal load

Cooling load

Historical electric load P1

0.6741

0.4919

0.1945

Historical thermal load P2

0.2962

0.5737

−0.2437

Historical cooling load P3 Wind speed V

0.1168

−0.0820

0.7995

−0.0574

−0.0186

0.1097 −0.1415

0.4626

0.4676

Wind direction D

−0.2652

–0.1187

0.1177

Weather W

−0.2938

–0.1351

−0.5188

Temperature T

Day R

−0.2095

–0.0275

0.3967

Week Z

−0.2061

–0.0240

0.4009

Month M

−0.2089

–0.0249

0.3969

4.4 Load Prediction Method Based on IPSO-WNN

55

Fig. 4.3 Pearson coefficients of three types of load

prediction of electric load. Indicators such as historical electric load P1 , historical thermal load P2 and temperature T have much greater impact on thermal load than the other 7 factors. The main effecting factors of cooling load forecasting in IES include historical cooling load P3 , weather W, day R, week Z and month M.

4.4 Load Prediction Method Based on IPSO-WNN In this section, some related optimization methodologies are briefly introduced and its optimization flow chart is shown in Fig. 4.4. Then, the improved wavelet neural network is described in detail, and principles of the improved part are analyzed. In this paper, an improved PSO is used to optimize the connection weight, the translation and scaling of the wavelet function in WNN. The detailed steps of the prediction model are as follows: 1. Step 1—Input and normalize the data of key influence factors. 2. Step 2—Initialize the connection weight, the translation and expansion in the wavelet function. 3. Step 3—Obtain the initial individual and global optima by the PSO. 4. Step 4—Update the particle’s speed and position. The fitness of each particle is calculated and the individual optimal and global optimal are updated. Calculate the weight coefficient according to formulas (16)–(19). 5. Step 5—According to formula (20)–(22), perform chaos search for the current optimal particles. If the new particle generated by chaos search is better than the current optimal particle, replace the optimal particle. 6. Step 6—If the conditions for the next step are met, proceed. If not, return to step 3.

56

4 Multi-energy Load Forecasting of Integrated Energy System

Fig. 4.4 The flowchart of load forecasting

Input data

Output

Initialize weights and wavelet parameters

Correct prediction error

Prediction based on wavelet neural network

Initialize particle swarm

Get the best wavelet parameters and connection weights

Obtain individual and global optimization

Y Update particle speed and position

Fig. 4.5 Structure diagram of wavelet neural network

N

Whether the end condition is met

Calculate particle fitness

Chaotic search of the current optimal position

Calculate weight w according to fitness

Update individual best and global best

F1

x1

w y1 +

F2

.

x2

ys .

+

.

xn

FL

7. Step 7—The optimal initial connection weights and wavelet parameters are obtained. Combined with the training error to improve prediction results.

4.4.1 WNN Model A WNN uses wavelet function as the activation function in the hidden layer of neural network. With a structure shown in Fig. 4.5, WNN combines multi-scale resolution and time–frequency analysis of wavelet function with the learning ability of neural

4.4 Load Prediction Method Based on IPSO-WNN

57

networks [14]. Compared with generic neural networks, WNN has a stronger generalization ability and robustness [15]. There are many factors influencing the prediction of integrated energy system, and each factor is interrelated, so it is difficult to extract data features accurately. WNN makes use of the feature that wavelet function can translate and expand, which makes data feature more obvious and easy to extract. The mathematical model is shown in (4.2)–(4.5). Fm (x1 , x2 , . . . , xn ) =

n |

( ) τam ,bm x j

j=1

∀m = 1, 2 . . . , L

(4.2)

) ( ( ) x j − bm τam ,bm x j = τ am

(4.3)

τ (x) = e−0.5x cos(1.75x)

(4.4)

2

ys =

L E

wms Fm (x1 , x2 , . . . , xn )

(4.5)

m=1

where Fm is the output of the hidden layer m, τ (x) is the mother wavelet of the wavelet function, am is the scaling factor, bm is the translation factor of the wavelet function, x is the input, y is the model output, and wms (s = 1, 2, 3) is the connection weight.

4.4.2 Particle Swarm Optimization Traditional WNN uses error back propagation algorithm to optimize parameters in the model. Because of the gradient descent method, the transmission information of the neural network with complex structure will be sparse, which leads to the poor effect of load forecasting for the comprehensive energy system. PSO is a relatively mature optimization method, which has the characteristics of fast optimization speed and good optimization effect [12]. It is suitable for optimizing the connection weight and wavelet parameters in WNN. The updated formulas of its position and speed is shown in (4.6) and (4.7). Vik+1 = ω · Vik + c1 · rand1 · (Pbest − X i ) + c2 · rand2 · (G best − X i )

(4.6)

X ik+1 = X ik + Vik+1

(4.7)

58

4 Multi-energy Load Forecasting of Integrated Energy System

where Vik and X ik are the velocity and position of particle i in the kth iteration respectively, ω is the particle weight coefficient, rand1 and rand2 are randomly generated in [−1, 1], c1 and c2 are learning factors, G best is global optimal value, Pbest is individual optimal value.

4.4.3 Inertia Weight of Particles Weight coefficient is very important in the process of PSO optimization. A small weight coefficient indicates a strong local search ability of PSO, while a big weight coefficient represents a weak global search ability of PSO. The convergence speed and optimization effect of particle swarm are both influenced by the weight coefficient. Therefore, the optimization ability and convergence speed of PSO can be improved by selecting the appropriate weight coefficient ω [13]. According to different weight requirements of particles, different weight strategies are established in the paper. Pg is the fitness of the current global optimal particle, f and f p respectively represent the fitness mean of the current particle and the fitness mean of the particle better than f , f b is the fitness of particle b. When f b < f , particle b is far away from the optimal position, so the inertia weight coefficient should be larger. The inertia weight is calculated as (4.8) and (4.9). ω = ωavg +

ωmax − ωmin × rand 2

ωavg =

ωmax + ωmin 2

(4.8) (4.9)

where, ωmax and ωmin are the maximum weight and the minimum weight respectively, ωavg is the average weight, and rand is a random value in [0, 1]. When f b > f p , particle b is closer to the optimal position, so the inertia weight coefficient should be smaller, inertia weight is calculated by (4.10). | | | fi − f p | ( ) | × ωavg − ωmin | ω = ωavg − | | Pg − f p

(4.10)

When f < f b < f p , the non-linear decreasing method of weight should be used in the calculation of inertia weight, as shown in (4.11). ω = ωmax −

(ωmax − ωmin ) · iter maxgen

(4.11)

where iter represents the current number of iterations and maxgen is the total number of iterations.

4.5 Experimental Simulation and Analysis

59

4.4.4 Chaos Algorithm PSO has some shortcomings, such as easily lost in the local optimal solution, premature convergence in advance and so on, which results in large short-term load forecasting error [14]. In order to solve the above problems, chaos algorithm is introduced in PSO iterative process. Using the randomness, ergodicity and other characteristics of chaos algorithm to search deeper, to prevent the particle swarm optimization algorithm from converging in advance [15]. If every particle is searched by chaos, it will have a great impact on the prediction speed. Therefore, only the current optimal particle after each iteration is searched by chaos in this paper. If the new particle produced by chaos search is better than the optimal particle, then the optimal replacement is carried out. In this way, the influence of chaos algorithm on prediction speed can be reduced. The chaotic search process is shown in (4.12)–(4.14). Pbest = ( p1 , p2 , . . . , p D ) represent the optimal positions of individuals. Map each dimensional pi in the Pbest to the chaos variable δkd and δkd ∈ [0, 1], as shown in (4.12). δdk =

pdk − pmax,d pmax,d − pmin,d

(4.12)

In the above formula, d = (1, 2, . . . , D), Pmin,d , Pmax,d are the lower and upper limits of the d-dimensional variable search space. Use logistic iterative equation to deal with δdk , as shown in (4.13). ( ) δdk+1 = μδdk 1 − δdk

(4.13)

where, μ is the chaotic coefficient, and the iterative chaotic variable δdk is inversely mapped to the original spatial solution, as shown in (4.14). ( ) xdk = pmax,d − pmin,d δik + pmin,d

(4.14)

Then, a new solution xdk can be obtained. If the particle’s fitness is better than that of Pbest , it indicates that the new solution is better than the original solution and needs to be replaced.

4.5 Experimental Simulation and Analysis In order to verify the effectiveness of the prediction method constructed in this paper, an IES of the Binhai district in Tianjin is selected for analysis. The historical load data, temperature, weather data and daily parameters of the IES from January to December 2017 are extracted. The data of 2 months in each quarter is used for the training model and obtaining training errors. Simultaneously, the data of the remaining months (January, April, July, and October) is used for load forecasting and verifying the

60

4 Multi-energy Load Forecasting of Integrated Energy System

effectiveness and feasibility of the IPSO-WNN. To analyze the performance of the prediction method proposed in the paper, two sets of comparison models are put up. IES load forecast based on the traditional WNN method is recorded as model 1 [16, 17]. Prediction based on IPSO-WNN without error correction is recorded as model 2. Prediction based on IPSO-WNN with error correction is recorded as model 3, which is the model proposed above in this paper.

4.5.1 Data Processing In order to guarantee the integrity of the data sequence, the method of adding the missing value with the mean value is used to deal with the missing data in the data sequence. Due to the dimension of each influencing factor, different normalization treatment is required, as in (4.15). H' =

H − Hmin Hmax − Hmin

(4.15)

where Hmax and Hmin are the maximum and minimum values in the data sequence, which are the normalized data, and H represents the data before processing.

4.5.2 Evaluating Indicators Mean absolute percentage error (MAPE) and weighted mean accuracy (WMA) are selected as the evaluation indexes in the paper. WMA can reflect the performance of the prediction model to the integrated energy system load prediction as a whole, and the average absolute percentage error can reflect the prediction performance of the prediction model to each load, its calculation formula is as (4.16) and (4.17). MAPE

| N | 1 E || yt − yt' || × 100% = N t=1 | yt |

(4.16)

MA = 1 − MAPE

(4.17)

WMA = αe MAe + αh MAh + αq MAq

(4.18)

where yt is the actual value, yt' is the predicted value, αe , αh and αq are respectively the weights of electric, thermal and cooling loads. The weight coefficient is set to 0.6, 0.25 and 0.15.

4.5 Experimental Simulation and Analysis

61

4.5.3 Parameter Setting The time scale of the thermal load and electric load is 15 min, the time scale of cooling load is 30 min, if load prediction is carried out at time t, it is necessary to know the corresponding influence factors at time t − 1 and t − 2. The input vector has 30 dimensions and the output vector has 3 dimensions. Therefore, the input layer neurons of the IPSO-WNN model are 32, and the output layer neurons are 3. When the number of hidden layer neurons is 15, the effect is the best. Then the structure of the improved wavelet neural network is 32-15-3. The number of iterations is 3000, the number of particles is 50, and the learning factor is 0.06.

4.5.4 Result Analysis The forecast results of electric load, thermal load and cooling load in four different months are shown in Figs. 4.6 and 4.7 respectively. Some conclusions can be drawn from the figures: 1. According to the results of three kinds of load prediction, the errors of three kinds of load in peak and valley periods are large. 2. Compared with thermal load and electric load forecasting, the error of cooling load forecasting is larger and the fluctuation of cooling load during the day is frequent. The factors affecting cooling load in real life are complex., which is difficult to predict. 3. Due to the strong inertia and slight fluctuation of thermal and electric load, the prediction accuracy is high.

Fig. 4.6 Forecast results

62

4 Multi-energy Load Forecasting of Integrated Energy System

Fig. 4.7 Electric load prediction results

4. In general, the prediction accuracy in January (winter) and July (summer) is higher, and the prediction accuracy in April (spring) and October (fall) is lower. In order to have a deeper understanding of the relevant performance of different prediction models, MAPE and WMA are used to compare and analyze the prediction errors of different models. The detailed data are shown in Fig. 4.8 and Tables 4.2 and 4.3.

Fig. 4.8 WMA of three prediction models

4.6 Conclusion

63

Table 4.2 MAPE of three prediction modes Model Electric load type Jan Apr Jul

Thermal load Oct

Jan

Apr

Cooling load Jul

Oct

Jan

Apr

Jul

Oct

Model 0.089 0.098 0.061 0.063 0.057 0.183 0.073 0.125 0.047 0.043 0.060 0.146 1 Model 0.059 0.047 0.026 0.047 0.070 0.149 0.005 0.118 0.046 0.054 0.055 0.057 2 Model 0.022 0.010 0.008 0.004 0.048 0.174 0.004 0.057 0.056 0.132 0.038 0.035 3

Table 4.3 Prediction time of three prediction models

Model type

Model 1

Model 2

Model 3

Prediction time (s)

275

234

227

Several conclusions can be made from Tables 4.2 and 4.3 and Fig. 4.8: (1) Compared with the other two methods, the WNN prediction method based on improved IPSO has the highest prediction accuracy of 96.59%. It is verified that the introduction of chaos algorithm and adaptive weight selection strategy in the IPSO algorithm can overcome the shortcomings of poor convergence and easy to fall into local optimum of the traditional algorithm, and effectively improve the accuracy of WNN load forecasting for the comprehensive energy system. (2) The prediction speed of model 1 is the slowest, that of model 2 is the fastest, and that of model 3 is between them. To improve the convergence speed and reduce the prediction time, the weight selection method based on particle adaptive degree is adopted. However, due to the introduction of chaos algorithm, the complexity of PSO is increased and the convergence speed of PSO is reduced, which leads to the prediction time of model 3 is increased compared with model 2. The introduction of chaos algorithm to search only the current optimal particles reduces the impact of chaos algorithm on prediction speed, so the prediction time of model 3 is only 7 s longer than that of model 2, which has little impact on the overall performance of prediction method. However, compared with model 1, the convergence speed is obviously improved, and the prediction time is reduced by 48 s.

4.6 Conclusion In order to solve the problem of poor prediction accuracy of traditional WNN integrated energy system, a short-term load prediction method based on IPSO-WNN is put forward in the paper. By using Pearson coefficient to select the appropriate factors as the prediction input, chaos algorithm and adaptive weight selection strategy are introduced into PSO, and the improved PSO is used to optimize the connection weight

64

4 Multi-energy Load Forecasting of Integrated Energy System

and wavelet parameters in WNN prediction model, and the training errors are referenced for feedback correction. Through the case study, IPSO-WNN load prediction method in IES overcomes the problems of slow convergence speed and easy to fall into local optimum of traditional WNN forecasting method, effectively improves the forecasting accuracy and speed, and improves the performance of forecasting model.

References 1. Li Y, Huan J, Cao H, Gao C, Zhang X, Zhang J et al (2018) Distribution network planning strategy based on integrated energy collaborative optimization. Grid Technol 42(05):1393– 1400 2. Zhang W, Dong X, Sun W, Wu J (2017) Research on the integrated energy system in energy Internet. Process Autom Instrum 38(1):12–15 3. Jairath AK, Kumar S, Yadav G (2015) Thermal insulation—a method to reduce heat load and electricity consumption—a case study of cold storages. In: 2015 international conference on recent developments in control, automation and power engineering (RDCAPE), Noida, pp 309–313 4. Zhang K, Li XR, Liu JM (2019) Research on minimum schedulable power optimization of CCHP system. In: 2019 IEEE innovative smart grid technologies-Asia (ISGT Asia), Chengdu, China, pp 4210–4214 5. Cheng L, Liu C, Huang R, Li H (2016) An optimal operating strategy for CCHP in multi-energy carrier system. In: 2016 IEEE power and energy society general meeting (PESGM), Boston, MA, pp 1–5 6. Taylor JW (2012) Short-term load forecasting with exponentially weighted methods. IEEE Trans Power Syst 27(1):458–464 7. Ngo VC, Wu W, Zhang B, Li Z, Wang Y (Oct 2015) Ultra-short-term load forecasting using robust exponentially weighted method in distribution networks. In: 2015 IEEE power & energy society general meeting, Denver, CO, pp 1–5 8. Kotur D, Žarkovi´c M (2016) Neural network models for electricity prices and loads short and long-term prediction. In: 2016 4th international symposium on environmental friendly energies and applications (EFEA), Belgrade, pp 1–5 9. Yang J, Chai T, Luo C, Yu W (2019) Intelligent demand forecasting of smelting process using data-driven and mechanism model. IEEE Trans Ind Electron 66(12):9745–9755 10. Yujie L, Xiaoling Y, Jieyan X, Zheng C, Fei M, Haoming L (2018) Medium-term forecasting of cold, electric and gas load in multi-energy system based on VAR model. In: 2018 13th IEEE conference on industrial electronics and applications (ICIEA), Wuhan, pp 1676–1680 11. Billinton R, Khan E (1992) A security based approach to composite power system reliability evaluation. IEEE Trans Power Syst PS-7(1):65–72 12. Choi J, Kim H, Cha J, Billinton R (Jul 2001) Nodal probabilistic congestion and reliability evaluation of a transmission system under the deregulated electricity market. In: Proceedings of IEEE PES SM2001 conference, Vancouver, Canada 13. Wu F, Yang L (2017) Simulation of the integrated energy system for isolated Island. In: 2017 China international electrical and energy conference (CIEEC), Beijing, pp 527–531 14. Yilmaz S, Oysal Y (2010) Fuzzy wavelet neural network models for prediction and identification of dynamical systems. IEEE Trans Neural Netw 21(10):1599–1609 15. Lin F-J, Wai R-J, Chen M-P (2003) Wavelet neural network control for linear ultrasonic motor drive via adaptive sliding-mode technique. IEEE Trans Ultrason Ferroelectr Freq Control 50(6):686–698

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16. Liang W, Rutao Q, Daogang P, Hao Z (2013) Short-term load forecasting with WNN based on body amenity indicator. In: 2013 international conference on computer sciences and applications, Wuhan, pp 795–798 17. Fu Q, Han B (2019) Study on application of wavelet neural network (WNN) model in city gas load forecasting. In: 2019 IEEE 4th international conference on cloud computing and big data analysis (ICCCBDA), Chengdu, China, pp 317–320

Chapter 5

Optimal Planning of Energy Storage Considering Uncertainty of Load and Wind Generation

5.1 Introduction The high penetration of wind generations (WG) raises the risks of the secure and economical operation of distribution networks (DN) due to the intermittent wind speed and unexpected turbulence. To solve this problem, energy storage systems (ESS) have received increasing attention for their advantages in smoothing power fluctuations induced by the wind power while reducing the impact of uncertain load demands in DNs through proper demand response (DR) designs [1–5]. In this context, this study presents a new approach to the optimal capacity allocation of ESSs in DN, which introduces a comprehensive DR to reduce the uncertainty of high-penetration WG and load demand using computational swarm intelligence. Currently, several studies have explored solutions to accommodate the uncertainties from WGs and load demands. The uncertainty of wind power output has also been studied in the DN [6, 7]. In Ref. [8], WGs are precisely modeled in terms of timescale and uncertainty to research the correlation of multiple time-scale, uncertainty and simulation time. Simulation in a typical test system not only verifies the accuracy of the model proposed in this paper, but also obtains the best prediction time-scale considering the simulation time and cost. In Ref. [9], a stochastic programming was used to model WGs to reduce the uncertainty in a home energy management. The simulation results demonstrate the home energy management with the WGs model can greatly reduce costs. Reference [10] proposed a novel wind prediction model based on particle swarm optimization and support vector machine (PSO-SVR) and grey combination model to reduce the disadvantage of low prediction accuracy of the traditional grey system. Compared with the single grey system, the mean absolute error (MAE), mean absolute percentage error (MAPE) and root-mean-square error (RMSE) of the proposed model for WGs prediction are improved by 37.7%, 34.9%, and 34.4%, respectively. With the participation in DR programs, the roles of the consumers change from a passive entity to an active one that manages both local consumption and generation resources [11]. References [12–14] studied the role of DR in load adjustment. In Ref. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_5

67

68

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

[12], a method is proposed to adjust the load curve considering the uncertainty of DR. Using the different acting speed of the two types of DR and establishes a two-stage scheduling model to reduce the uncertainty of load. References [13, 14] proposed a new strategy using an optimal model of peak shaving and valley filling with electric vehicles for economic dispatching; the simulation results have demonstrated that the strategy is in improving load management under large integration of electric vehicles (EV). In Ref. [15], a DR optimization methodology for application in a generic residential house is proposed to find the optimal scheduling of minimal operating costs and reduce the uncertainty of load. There are also many studies on stochastic optimization of wind power in DR. A stochastic programming investment model combining continuous operational constraints and wind scenarios was proposed in Ref. [16] to research the impact of DR in WGs. The numerical results show that with the increase of DR capacity, wind power decreases and social surplus increases. In Ref. [17] a method was proposed to study the impact of WGs and DR on locational marginal prices. By shifting the proper amount of DR load from peak hours to off peaks, the utilization of WGs was enhanced and the investment cost was reduced. Reference [18] analysed the impact of WGs on electricity price. The scenario simulation was conducted in Monte-Carlo, then through the reduction and incorporation of scenarios to formulate stochastic uniform market price. There have been some research efforts on the optimal configuration of ESSs to maintain the stability of the DN and reduce the uncertainty of WG and load demands furthermore in Refs. [19–23]. In Ref. [20], a novel planning model for the ESSs in distribution network wherein both load leveling and voltage profile improvement applications are extracted. Simulation results demonstrate that not only the load profile tends to be flat and resulting lower energy cost but also the voltage profile can improve in some degrees without increasing planning and operation costs. ESSs can reduce power losses and improve the stability of a DN when ESSs were allocated at optimized locations in the network [21]. To ensure the minimum cost of substation expansion deferral, a novel multi-objective mixed integer linear programming model for ESSs operation was proposed in Ref. [22], and the proposed model is highly flexible with respect to the planner preferences, without increasing operation costs. Also, to accommodate the large penetration of wind energy, a multi-step method based on the optimal power flow is presented in Ref. [23] for the configuration of ESSs to minimize the annual electricity cost in DNs. Despite the extensive efforts, however, most of the works above relied on deterministic models to optimize ESS configuration in the DN. The deterministic models have not been able to consider the impact of load variations and adjustments under a comprehensive DR system, nor the impact of the uncertainty of high WG penetration on the optimal capacity allocation of ESSs. To fill this gap, an optimal capacity allocation model of ESSs is proposed in this paper to minimize the cost and loss of ESSs under the conditions of secure and stable operation of DN and ESSs. In this new model, all objectives are incorporated in a single cost function to select the global optimal solution. The uncertainty of WG and load demands is modelled using particle swarm optimization and backpropagation (PSO-BP) neural network

5.2 Problem Formulation

69

in a comprehensive DR, respectively, and an improved simulated annealing PSO (ISAPSO) algorithm is employed to optimize the ESSs capacity allocation with minimized investment costs and energy losses. The main contributions of this paper are as follows. 1. Proposing a new ESS optimal capacity allocation model to minimize the investment cost and power losses. 2. ISAPSO is used to optimize the capacity allocation. Compared with another two algorithms proposed in this paper, the investment costs have been reduced by 12.5% and 7.1% respectively, and the power losses have been reduced by 18.6% and 4.5% respectively. 3. A comprehensive DR system based on the time-of-use (TOU) and incentives are proposed to reduce the uncertainty of load. 4. To predict the WGs more accurately, a PSO-BP neural network is proposed. Compared with the BP method, the MAE, RMSE of the proposed model for WGs prediction is improved by 11.7%, 5.3% respectively.

5.2 Problem Formulation The problem formulation is presented throughout this section to derive the model for optimal capacity allocation of ESSs. The problem formulation ideas for the entire paper are shown in Fig. 5.1. The goal is to minimize the costs of investment and power losses, considering the uncertainty of load and wind generation, which is solved by the presented optimization model as a mixed-integer linear problem.

5.2.1 Objective Function For ESSs, the objective function of the proposed optimization model can be given as: TOU Based on

Reasonable Load

Incentives

Adjustment

Load Historic Data

Important Load

Costmin,

Load Management

Ploss, CDR

Accurate WGs WGs Historic Data

Prediction

PSO-BP

Data Processing

ESSs Position Determination

WGs Prediction

Fig. 5.1 The overall idea of the method in this paper

Wind Turbies

ISAPSO

Optimal Capacity Allocation of ESSs

70

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

min F = CINV + CLOSS + CDR − Bshift

(5.1)

where F is the total investment cost, CINV is the life-time cost of ESS, CLOSS is the cost of network loss, CDR is the cost of implementing DR, and Bshift is the load adjustment profit. 1. ESSs Investment Cost CINV , the first term in Eq. (5.1), represents the life-time investment cost. It is defined as: CINV =

N    c E E ess,i + c P Pess,i α + com E ess,i

(5.2)

i=1

where N is the number of ESS installed, c E is the unit capacity cost of ESS, c P is the unit power cost of ESS, com is the unit O&M cost of ESS, E ess,i and Pess,i are the capacity and power of the ith ESS, respectively. Meanwhile, α is the transformation coefficient from the present value to a uniform annual value, α=

γess (1 + γess )less (1 + γess )less − 1

(5.3)

where γess is the interest rate and less is the service life cycle of ESS. 2. Network Losses Cost CLOSS , the second term in Eq. (5.1), represents the costs of network power losses. It is defined as: CLOSS = t

NL 

closs Pi

(5.4)

i=1

where N L is the total number of branches, closs is the unit power loss cost of the network, Pi is the power loss on the ith line, and t is the duration. 3. Cost of Implementing DR CLOSS , the third term in Eq. (5.1), represents the costs of the DR system. It is defined as: CDR =

NL 

(cDR PDR − c0 P0 )t

(5.5)

i=1

where cDR and c0 are the incentive and initial costs of unit power, respectively. P0 and PDR are the total power before and after implementing DR, respectively.

5.2 Problem Formulation

71

4. Load Adjustment Profit Bshift , the benefits of load adjustments, can be calculated by the difference between the income from discharging the ESSs at peak hours and the cost of charging the ESSs at valley hours, Bshift =

N    λpeak Pdis,i − λoffpeak Pch,i t

(5.6)

i=1

where λpeak and λoffpeak are the peak and valley electricity prices, respectively; Pch,i and Pdis,i are the charging and discharging power of the ith ESS, respectively.

5.2.2 Constraints 1. Power Balance Constraint d c PWG,t + Pgrid,t + Pbess,t − Pbess,t = Pload,t + Ploss,t

(5.7)

where PWG,t is the power of WGs at time t, Pgrid,t is the power purchased from c d and Pbess,t represent the charging and discharging the upper system at time t. Pbess,t power at time t, respectively. Pload,t and Ploss,t represent the load power demand and network power loss at time t, respectively. 2 ESSs Operational Constraint ⎧ ⎪ ⎪ ⎪ ⎪ ⎨

c,t c,max Pbess,i ≤ Pbess,i d,t d,max Pbess,i ≤ Pbess,i c d ybess,i + ybess,i ≤1

⎪ ⎪ ⎪ ⎪ ⎩ SOCtbess,i = SOCt−1 bess,i +

c d ηc Pbess,i − η1 Pbess,i d

Pbess,i

t

(5.8)

c,t d,t where Pbess,i and Pbess,i are the charging and discharging power of ESS at time t, c,max d,max respectively. Pbess,i and Pbess,i are the maximum charging and discharging power c d are the binary charging and discharging state of ESS, respectively. ybess,i and ybess,i of the ith ESS, respectively; ηc and ηd are the charging and discharging efficiency of the ESS, respectively.

3. Energy Balance Constraint of ESSs T   t=1

c,t d,t Pbess,i ηc t + (Pbess,i t) ηd = 0

(5.9)

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5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

5.2.3 Uncertainty Reduction Due to the uncertainty of WG and load demand, it is difficult to obtain the optimal capacity allocation of ESSs at a high degree of accuracy. To reduce the impact of uncertainty on the proposed model, this study uses PSO-BP to improve the accuracy of WGs prediction, and use comprehensive DR to reduce the uncertainty of load demands based on load management. 1. WGs Prediction Based on PSO-BP Accurate WGs prediction can improve the security and reliability of DN [24]. Current WGs prediction methods include physical methods, statistical methods, and artificial intelligence methods. It is found that among many WGs prediction methods, the PSOBP neural network algorithm not only has higher prediction accuracy but also reduce calculation time. So, PSO-BP neural network algorithm is selected in this paper. In the neural network, the data are first linearly normalized to the valid input range of the network. Then, we use the PSO algorithm to optimize the weights and bias of BP neural network and improve the prediction accuracy. Given a BP neural network, the velocity v and position s of each particle in the PSO are updated as follows: 

    vil+1 = wvil + c1r1 pbest − sil + c2 r2 gbest − sil sil+1 = sil + vil+1

(5.10)

where i is the number of the current iteration, c1 and c2 are the cognitive factors and social factors, respectively; r1 and r2 are the random number distributed between [0, 1]; pbest is the individual optimal extremum, gbest is the global optimal. The total error of the samples is taken as the objective function as follows: f 2 1  ek = yk,i − Ck f i=1

fitness =

S 1 ek S k=1

(5.11)

(5.12)

where f is the total number of the actual values in sample k, and S is the total number of the mean square errors in all samples. ek , yk,i and Ck are the mean square error, the ith actual value, and the predicted value of sample k, respectively. The position of the optimal particle is used to assign the weight and bias of the corresponding neuron. The normalized data are used as the input to the neural network, and the relationship between the input layer and the hidden layer is, zj =

M  i=1

ωi j xi + b j

(5.13)

5.2 Problem Formulation

73

where xi is the input of the neuron i, and z j is the output of the neuron j, ωi j is the weight of the link between neuron i and neuron j, b j is the bias of neuron j, and M is the total number of neurons in the previous layer. With the activation function, the relationship between the hidden layer and the output layer can be obtained as:   yj = ϕ z j

(5.14)

where y j is the output of the neuron j and ϕ(x) is the activation function. In this paper, the Sigmoid function [25] is adopted, where ϕ(x) = 1+e1 −x . Finally, the output power of the WGs is PWT =

1 c p ρ Av3 2

(5.15)

where PWT is the output power of WGs, cp is the influencing factor of wind energy utilization coefficient of WGs, ρ is the air density, A is the swept air area, and v is the wind speed. The root mean square error (RMSE) and mean absolute error (MAE) are used in the objective functions to evaluate the prediction performance of PSO-BP. Backpropagation and gradient descent algorithms are used to update the weights and bias to minimize the objective function [26]. 2. TOU Model Based on Incentives The uncertainty of load will affect the stability of DN dispatch due to the randomness of participating users’ intentions. It is important for operators of DN to reduce the uncertainty of load [27]. Comprehensive DR generally refers to the use of both TOU and incentive measures for load management. According to the research, comprehensive DR has better performance than using TOU or incentive measures alone [28, 29]. So, we choose comprehensive DR as the approach to reduce the load uncertainty. In DR, the relationship between users’ load and electricity price is usually described using the demand elasticity coefficient (DEC) as follows:  li j li0  λi j = li j li0

(5.16)

li j = l j − li0

(5.17)

pi j = p j − pi0

(5.18)

where li j is the load difference between time j and time i, pi j is the electricity price difference between time j and time i, li0 and pi0 represent the load and electricity price before DR, respectively; l j and p j represent the load and electricity price of the period j after the DR, respectively.

74

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

When i and j are not equal, λi j represents the cross DEC in different periods: when the electricity price at time j is low and the load at time i is shifted to time j, thus the DEC is positive. When i and j are the same, λi j represents time i own self-elastic coefficient: when the price of electricity rises, the load of time i will be shifted to other periods, thus the DEC is negative. A DEC matrix E can be then composed of the self-elastic and mutual elastic coefficients, ⎡

λ11 λ12 ⎢ λ21 λ22 ⎢ E =⎢ . .. ⎣ .. . λ M1 λ M2

⎤ · · · λ1M · · · λ2M ⎥ ⎥ .. .. ⎥ . . ⎦ · · · λM M

(5.19)

where M represents the periods divided in one day. The main diagonal elements are self-elastic coefficients, while the others are mutual elastic coefficients. This DEC matrix can be obtained from the historical TOU data. Once E is obtained, the load matrix L in each period can be calculated from the historical TOU data:  ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ l10 0 · · · 0 p1  p10 l10 l1 ⎢ l2 ⎥ ⎢ 0 l20 0 0 ⎥ ⎢ p2 p20 ⎥ ⎢ l20 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ (5.20) L = ⎢ . ⎥ = ⎢ . . . . ⎥E ⎢ ⎥+⎢ . ⎥ .. ⎦ ⎣ .. ⎦ ⎣ .. ⎦ ⎣ .. .. .. .. ⎦ ⎣ . lT pT pT 0 lT 0 0 0 · · · lT 0 The optimized load model can be obtained by adding the following incentive mechanism based on the load matrix defined above: ⎡

l10 ⎢ 0 ⎢ L=⎢ ⎢ .. ⎣ . 0

0 ··· l20 0 .. .. . . 0 ···

  ⎤ ⎡  ⎤⎞ ⎡ ⎤ l10 p1 + a j1 p10 (p1 + a1 ) p10    ⎟ ⎢ ⎥⎜ ⎢ (p + a ) p ⎥ ⎢ p + a ⎥ p20 ⎥ 2 2 20 ⎥ 2 ⎥⎜ ⎢ ⎢ ⎥⎟ ⎢ l20 ⎥ j2 ⎥⎜ D 1 ⎢ ⎥ + D2 ⎢ ⎥⎟ + ⎢ . ⎥ .. .. ⎥⎜ ⎢ ⎥ ⎢ ⎥⎟ ⎢ . ⎥ ⎦⎝ ⎣ ⎦ ⎣ ⎦⎠ ⎣ . ⎦ . .    lT 0 pT + a j T pT 0 lT 0 (pT + aT ) pT 0 0 0 .. .

⎤⎛

⎡

(5.21) where D1 = diag[λ11 , λ22 , . . . , λT T ] is the main diagonal of the DEC matrix, that is, the matrix of self-elastic coefficients; D2 = E − D1 is the matrix of mutual elasticity coefficients, and aT is the incentive value at time period T, a j T is the incentive value to which the load is shifted.

5.3 Solving the Optimization Model

75

5.3 Solving the Optimization Model From a mathematical perspective, the proposed model is a nonlinear commitment optimization problem with mixed-integers. To tackle the challenge, PSO-BP is used for WGs prediction, and adjustable activation function and embedding chaos algorithm (BP-AAEC) is used for reducing the uncertainty of load demands based on reasonable load management. Then, ISAPSO is adopted to satisfy the demands of efficiency and convergence. The optimization solution mainly includes the following steps. 1. WGs Prediction Step 1.1: Generate an initial population of PSO-BP. The number of hidden nodes and the initial connection density for each network are generated. And normalize the original WGs data. Step 1.2: According to the input vector, the weight between an input-layer neuron and hidden-layer neuron ωi j , evaluate the output values of hidden-layer by Eq. (5.13). Calculate the output values of output-layer based on the weight between output-layer neuron and hidden-layer neuron bias b j by Eq. (5.14). Step 1.3: Initialize the position of each particle of PSO by means of weight ωi j and bias b j by Eq. (5.10). Evaluate the new fitness and update the global optimum. Step 1.4: Update the weight and bias according to an iterative number of PSO algorithm. The optimal parameters obtained by PSO are given to BP neural network model. Step 1.5: If t < tmax , then t = t + 1, and go back to Step 1.4; otherwise output the predictive result. 2. Load Scheduling Step 2.1: Initialize BP-AAEC and set the initial value of each parameter. Normalize the historical load data. Suppose the weight value is ω, and bias is b. Let e be the error function threshold; Set the initial value of the parameter as X 0 . Let X ∗ be the most optimum network parameter at present X ∗ = X 0 . Step 2.2: Run BP-AAEC, and get the parameter X k∗ ; let k = k + 1. Step 2.3: Evaluate the fitness in Eq. (5.20) and compare f (X k∗ ) with f (X ∗ ). Step 2.4: Calculate  f = f (X k∗ ) − f (X ∗ ): if  f < e, the prediction is convergent. If  f > e, return to Step 2.2. 3. Optimal Capacity Allocation of ESSs Step 3.1: Initialize the population of ISAPSO, including the position, velocity, and initial temperature. Step 3.2: Calculate the fitness by Eq. (5.1), with the constraints Eqs. (5.7)–(5.9).

76

5 Optimal Planning of Energy Storage Considering Uncertainty of Load … Start Input data of historical load, WG End Yes

Initialize PSOBP

Reach maximum iterations or error goals?

No Standardized processing

Initialize BPAAEC Annealing

Standardized processing Get analogue maxtrix

Accept the f ( xk +1 )

Get equivalence fuzzy maxtrix Get cluster No

Is beat cluster? Yes Obtain forecast load

Yes

Δf < 0

No Accept the f ( xk +1 ) by probability

Update the speed and position of each particle, calculate Δf = f ( xk +1 ) − f ( xk )

Establish the optimization function model and constraint function model Calculate forecast wind generations

Update the speed and position of each particle Update individual extremes and global extremes of nextgeneration particle swarm

Evaluate new particle and calculate the fitness value of objective function for every particle

Initialize ISAPSO, Input data of storage, population and iteration

Calculate individual extremes and global extremes of particle swarm

Obtain optimal Yes weights and offsets

Reach maximum iterations or error goals?

No

Fig. 5.2 The optimization procedure for finding optimal planning schemes

Step 3.3: Update the velocity and position by Eq. (5.10). Step 3.4: Calculate the new fitness in Eq. (5.1) for each particle. Step 3.5: Apply the annealing Tk+1 = λTk . Step 3.6: If the iteration conditions are met, stop the search; otherwise, return to Step 3.3. The flowchart of the entire algorithm is shown in Fig. 5.2.

5.4 Case Study 5.4.1 The Benchmark System The proposed method is evaluated on a modified IEEE 33-node test distribution system, as illustrated in Fig. 5.3 [30]. The rated voltage of the system is 12.6 kV with a peak load of 3.775 + j2.300 MVA. The important loads are set on Node 3, 10, 26. In order to serve the important loads continuously when the DN fails and to ensure the stability of the system, the WGs are allocated in Node 4 (800 kW) and Node 14

5.4 Case Study

77

(1000 kW), where the power factor is 0.8. The rated cut-in and cut-out wind speeds are 12 m/s, 4 m/s, and 20 m/s, respectively. The heuristic algorithm selected in this paper can be applied for different types of ESSs, such as the lead-acid battery (LAB), the sodium-sulfur battery (NaS), or the Li-ion battery (LIB), among others [31]. The parameters of the three types of batteries are provided in Table 5.2 [32]. Considering the service life and costs of investment, the sodium-sulfur battery is used. Also, considering the important loads and the stable operation of the DN, we assumed ESSs are allocated in Node 2, 6 and 12. The rest parameters refer to Table 5.1, and the other parameters of ESSs are the same as in Table 5.2. The price of electricity in different time periods and the incentive value are shown in Fig. 5.4. 19 20 21 22

Wind Turbine1

Superior grid

Wind

Important Load3

Turbine2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Important Load1

26 27 28 29 30 31 32 33 23 24 25

Important Load2

Fig. 5.3 The modified IEEE 33-bus distribution test system

Table 5.1 Parameters of the simulation

Table 5.2 Comparison of three different batteries

Parameter

Value

Number of charge/discharge cycles in storage life

10000

ESSs investment cost (¥/kWh)

1000

Interest rate

3%

Annual increment load rate

10%

Power losses cost (¥/kWh)

0.4

Parameter

LAB

NaS

LIB

Fixed O&M (¥/kW)

25.5

27

51.75

Efficient (%)

80

85

90

Range of SOC (%)

30–70

10–90

20–80

Service life (years)

10

15

12.5

78

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

Fig. 5.4 Elasticity coefficient of TOU electricity price and incentive value

5.4.2 Comparisons of Simulation Results In the ISAPSO, the number of population particles and iterations are set as 30 and 100, respectively. To evaluate the performance, the following cases are considered: Case A: Simulation of the IEEE-33 system of considering reducing the uncertainty of WGs and load, without ESSs. Case B: Optimize the capacity allocation of ESSs by only reducing the uncertainty of load, and the output of WGs is simply the rated power. Case C: Optimize the capacity allocation of ESSs by only reducing the uncertainty of WGs, and DR is not adopted to reduce the uncertainty of load. Case D: Optimize the capacity allocation of ESSs by reducing the uncertainties of WGs and load by the means of this paper proposed. The simulation results are shown in Fig. 5.5. In the absence of ESSs, even if the method of reducing the uncertainty of WGs and load mentioned in this paper is used in the simulation, there will be greater power loss and voltage deviation. Compared with Case A and Case B, although the comprehensive DR can introduce some costs in Case C, it improves the effect of load shifting and reduces the power losses (18.4% and 4.5%, respectively). Overall, Case C can reduce the uncertainty of load and WGs at the same time, making the DN more stable at a lower total cost of investment (12.5% and 7.1%, respectively) than Case A and Case B. Simultaneously, in order to prove that the position of ESSs and WGs selected in this paper is optimal, the following cases are performed: Case a: Optimize the capacity allocation of ESSs considering only changing the location of ESSs (they are set on Node 11, 19, 27, respectively), and the position of WGs does not change.

5.4 Case Study

79 2000

1811.74

400

354 3

1104.27

1400

1200 930.76 1000

972.32

300

1600

Power Loss

389 3

800 200

600 400

100 0

KW

KW

405 3

Capacity

1800

Capacity

500

Power Loss

600

200

0

0

CaseA

CaseB

CaseC

CaseD

(a)

Voltage Deviation 189.9

203.3

200

Cost (×104 ¥)

1.4

Cost 213.7

1.2

150 113.5

0.58

0.8 0.6

0.49

100

1

p.u.

1.21

Voltage Deviation

250

0.4 50 0.12 0

0.2 0

CaseA

CaseB

CaseC

CaseD

(b) Fig. 5.5 Comparison of optimization results of different schemes

Case b: Optimize the capacity allocation of ESSs considering only changing the location of WGs (they are set on Node 7, 16, respectively), and the position of ESSs does not change. Case c: Optimize the capacity allocation of ESSs considering changing the location of ESSs (they are set on Node 11, 19, 27, respectively) and WGs (they are set on Node 7, 16, respectively), simultaneously. Case d: Optimize the capacity allocation of ESSs according to the location of ESSs and WGs provided in this paper. The above simulation cases are all based on the methods proposed in this paper, and the selection of nodes is random. Table 5.3 presents comparison of the above four cases. As we can observed from Table 5.3, both the power losses and the voltage deviation of the DN will be increased when the location of the ESSs or the WGs changes. This is because the change of position makes the role of ESSs or WGs

80

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

Table 5.3 Simulation results of the above four cases Parameter

Case a

Case b

Case c

Case d

Capacity of ESSs (kW)

372 × 3

369 × 3

398 × 3

354 × 3

Power losses (kW)

987.17

970.33

1011.25

930.76

Cost (×104 yuan)

202.7

193.8

209.1

189.9

Voltage deviation (rad p.u.)

0.44

0.48

0.63

0.12

unable to radiate the entire DN, which increases the cost of ESSs and reduces the stability of the distribution network. Therefore, only when the optimal location is selected for ESSs and WGs in the DN can the cost and stability be minimized.

5.4.3 Comparison of Different Algorithm To evaluate the performance of the proposed algorithm, the section will first verify the feasibility of the proposed method to reduce the uncertainty of load demands and WGs prediction, respectively. After that, the validity of the optimal capacity allocation model is validated by comparing it with other methods. Finally, in order to prove the superiority of IASPSO, this paper selected PSO and NSGA-II to compare with ISAPSO. 1. Comparison of Uncertainty Reduction To illustrate the effectiveness of the proposed method, the uncertainty of load and WGs proposed in this paper is firstly evaluated. Two typical cases will be considered: Case 1 only considers load scheduling under TOU tariff, while Case 2 considers TOU based on incentives. The historical data of the total load and each important load are shown in Fig. 5.6. And the load adjustment under the two different DRs is shown in Fig. 5.7. It can be seen from the figure that the shifting load in the second case is better. As shown in Fig. 5.7, we can see that the peak load decreases, valley load rises and the difference between peak and valley decreases when we adopt the strategy of case 1. For a part of the load that cannot be transferred during the period, the peakto-valley difference can decrease further by the strategy of case 2 while giving some compensation and the load curve is more smooth. This is because case 2 adopts an TOU based on incentives strategy to enable load adjustment with the participation of the distribution network operator, which allows the load to be further adjusted compared to case 1. The detailed peak-to-valley difference is shown in Table 5.4. DGs have a great impact on the stability of the DN. In order to ensure the stable operation of the system, it is necessary to reduce the uncertainty of DGs. In this part, we will prove the effectiveness of the proposed method to reduce the uncertainty of DGs by comparing BP with the PSO-BP. The historical data of the total DGs and each DG are shown in Fig. 5.8.

5.4 Case Study

81

Fig. 5.6 Daily load curves of total load and important load

Fig. 5.7 Comparison of different load adjustment strategies

Table 5.4 Simulation results of the above four cases

Parameter

The original date

Case 1

Case 2

Total load

587

875

747

Important load 1

73

63

56

Important load 2

147

114

110

Important load 3

118

100

94

82

5 Optimal Planning of Energy Storage Considering Uncertainty of Load …

Fig. 5.8 Daily DGs curves of total DG and points load

5.5 Conclusion This paper proposed an optimal capacity allocation scheme for ESSs by reducing the influence of uncertainty of WGs and load demands in DNs. Furthermore, the combination of comprehensive DR and PSO-BP reduced the uncertainty of load demands and WG, respectively. The optimal capacity allocation of ESSs is solved by a cost-benefit analysis considering the reduction of power losses and load shift. In order to prove the generality of our model, we first compared the TOU with the comprehensive DR proposed in this paper for the load adjustment method. Based on the simulation results, the comprehensive DR has better performance in reducing the uncertainty of load than TOU with a slightly increased cost than the latter. Then, we compared BP with PSO-BP for more accurate DGs prediction. From the obtained results, we can see that the PSO-BP is more accurate than BP for WG prediction. The MAE and RMSE are 0.1337 and 0.1628 in PSO-BP, and 0.1494 and 0.1715 in BP, respectively. Finally, we got the optimal capacity allocation of ESSs by ISAPSO algorithm. The simulation results show that the optimal capacity allocation model of ESSs can better reduce the cost of investment and power losses and improve the stability of DNs when we combine the comprehensive DR and PSO-BP instead of using only one of them. What’s more, the proposed algorithm can reduce the computation time and obtain better results than other heuristic algorithms. For the future work, along with the expected continuing development in battery technology, we will choose batteries with better performance as the ESSs of the DN. In addition, the holidays and weather conditions will also be considered. And more efficient heuristic algorithms will also be used to solve the optimal allocation model of ESSs.

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Chapter 6

Coupled Multi-network Constrained Planning of Energy Supplying Facilities for Hybrid Hydrogen-Electric Vehicles

6.1 Introduction To achieve sustainable development of our society, electric vehicles (EVs) have been widely deployed throughout the world [1–3]. According to International Energy Agency, the total number of EVs is predicted to reach 245 million by the year of 2030 [4]. With the evolution of hydrogen technology, it is worth mentioning that hybrid hydrogen-electric vehicles (H2EVs) have been emerging [4–6]. H2EVs utilize not only renewable energy (RE) directly, but also hydrogen which could be also produced by such kind of energy. Therefore, using H2EVs is one of efficient approaches for RE utilization. Evidently, the planning of related energy supplying facilities are important to H2EVs development. Such facilities mainly consist of power charging and hydrogen refueling stations. They involve both the power network (PN) and hydrogen network (HN), simultaneously. Therefore, their abilities of supplying energy (i.e., electricity and hydrogen) and satisfying demands of H2EVs are significantly limited by operational constraints of PN and HN [7], such as the transmission power, mass flow of hydrogen pipelines, etc. This issue is more complex when RE is integrated into the PN, due to its uncertain power output [8]. Note that the energy demand of H2EVs is also impacted by structure of traffic network (TN), as it would change the behaviour of drivers. For instance, the driver would like to choose a shorter road than a longer one, and it may change the energy demand of H2EVs [9]. Therefore, under such a complex environment of the multinetwork including PN, HN and TN, it would be challenging to plan H2EVs energy supplying facilities (HVESFs). In other words, we should well satisfy energy demand of H2EVs for HVESFs planning while meeting operational constraints of the multi-network. Currently, previous researchers rarely devote to the planning issue of HVESFs. The existing related work mainly focus on the planning issue of EV charging facilities, which could be mainly divided into two catalogues. On the one hand, some work address power flow constrained planning. For instance, Ref. [10] proposes an algorithm for planning EV charging facilities, in order to balance the supply and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_6

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EV charging demand while considering power flow constraints. Similarly, Ref. [11] develops a multi-objective coordinated planning model for EVs. Furthermore, Ref. [12] establishes a power flow constrained two-stage stochastic programming model, which aims to obtain the planning solution of public parking charging stations. On the other hand, TN is introduced based on the mentioned work, in order to further consider impacts of traffic flow. In this aspect, Ref. [13] develops a coordinated planning strategy for EV charging facilities in the coupled traffic-power network. With the consideration of constructive budget, the issue of planning charging facilities considering both PN and TN is addressed in Ref. [14]. In addition, a robust optimization approach is introduced for the planning in the coupled traffic and power networks [15]. Besides, Ref. [16] presents a graph computing based planning method, considering the reliability of both PN and TN. Reference [17] proposes a planning model to satisfy the energy demand in TN, considering PN operational constraints. Furthermore, some researches take RE into account, in order to well investigate the planning impact on its utilization. For instance, a RE integrated framework is proposed to optimize the planning of charging facilities. It aims to enhance RE utilization using EV charging flexibility [18]. Similarly, Ref. [19] proposes a stochastic method for planning of EV charging facilities, with the consideration of uncertain RE and PN constraints. Besides, Ref. [20] presents a multidisciplinary approach for planning EV charging stations and distributed RE plants in a coupled transportation and power network. Also, Ref. [21] proposes a scheme to conduct joint planning of EV charging facilities and renewable power generation. With the development of gas-driven technology, the hydrogen vehicle, especially H2EVs, is regarded as a better option for RE utilization [22]. Accordingly, few recent work study the corresponding issue of planning. For instance, Ref. [22] shows a collaborative planning strategy for hydrogen refueling stations, considering the coupled power-traffic networks. Likewise, Ref. [23] evaluates the optimal planning of hydrogen refueling stations with consideration of interactions between the traffic and power networks. Note that above studies are based on the assumption that hydrogen is merely produced by renewable power in the refueling station. However, the hydrogen network (HN) is more important for large-scale application of hydrogen [4]. Therefore, the HN has been vigorously promoted for social development in many countries. Apparently, it could directly deliver hydrogen to refueling stations. Nevertheless, the integration of HN has not been considered for HVESFs planning, to the best of authors’ knowledge. It could be observed that existing studies have well addressed the planning problem of energy supplying facilities for vehicles, mainly considering TN and PN. Nevertheless, if we consider the planning of HVESFs, the coupled PN, TN and HN should be taken into account. This is because that the HVESF obtains electricity and hydrogen from PN and HN, respectively. Then, it charges and refuels H2EVs in TN to meet their energy demands. In this way, PN, HN and TN are coupled by HVESFs. However, this coupled multi-network based planning of HVESF is not taken into account, as far as authors are concerned.Regarding this point, we have investigated the following issues.

6.2 Modified Maximum Covering Location Method Regarding TN

87

1. Since HVESF couples energy networks of PN and HN, its maximum charging power would be limited by not only power flow of PN but also mass flow of HN. On the other hand, the maximum hydrogen refueling speed of HVESF is limited by the mass flow of HN. Also, the power flow has a significant impact on it, because hydrogen is generated by electrolysis as well, which consumes electricity from PN. Therefore, the maximum charging power and hydrogen refueling speed of HVESF may be reduced. 2. Existing work mainly considers the single network (PN or TN), or coupled two networks (PN and TN). Nevertheless, the H2EVs couples all the three networks, i.e., PN, HN and TN. Accordingly, it may be not easy to meet their operational constraints, simultaneously. Therefore, we propose a multinetwork framework considering such simultaneous constraints. 3. Based on the proposed framework, we think it shall be interesting to develop a many-objective planning model, and reveal relationships among various objectives, such as constructive cost, operational cost, RE utilization, voltage deviation, transmission loss, etc. It would be helpful for decision making in planning HVESFs. To solve above issues, we conduct the following work, which are main contributions of our paper. 1. We propose a modified maximum covering location method for HVESFs planning regarding TN, in order to well satisfy the energy demand of H2EVs. 2. On this basis, we develop a multi-network framework considering coupled flow constraints. It would help to satisfy operational constraints of the multi-network, and be better for planning HVESFs. 3. Furthermore, a many-objective optimization based bilevel planning model is proposed. It aims to reveal relationships among various objectives, which could assist in decision making for planning.

6.2 Modified Maximum Covering Location Method Regarding TN Note that the traditional maximum covering location method (MCLM) is an approach to address the planning issue of TN [24]. However, in order to well satisfy energy demand of H2EVs, the modified maximum covering location method is proposed in this paper. Regarding TN nodes, we first calculate traffic flows of H2EVs. Then, the energy demand of H2EVs is obtained, which can be satisfied via the modified MCLM. Details are presented as follows.

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

6.2.1 Traffic Flow As shown in Fig. 6.1a, the TN is separated into a series of O-D pair units [25]. Each unit consists of two TN nodes, which are connected by a single route to deliver H2EVs. Accordingly, the traffic flow regarding each TN node should be balanced, i.e., its net flow (in-flow minus out-flow) should be 0. E

si,dirj f i,r j = 0, i ∈ TN

(6.1)

j∈NNi

f i,r j ≥ 0

(6.2)

where TN and NNi are the set of TN nodes and the set of neighbour nodes of i, respectively. Besides, f i,r j denotes the traffic flow of H2EVs between TN nodes i, j, which is non-negative. Furthermore, si,dirj is the corresponding traffic direction between nodes i, j (1 for i from j, −1 otherwise).

Fig. 6.1 Modified MCLM regarding H2EVs, reprinted from Ref. [45], copyright2023, with permission from IEEE

6.2 Modified Maximum Covering Location Method Regarding TN

89

Also, the in-flow should equal to the out-flow regarding traffic node i. To this end, the node passing flow f in is the half of total traffic flow regarding the route connected to node i. f in =

1 E r f , i ∈ TN 2 j∈NN i, j

(6.3)

i

In addition, the averaged traffic flow can be obtained by the well-known gravity spatial interaction model [9], i.e., f i,r j =

wi w j , i ∈ TN, j ∈ NNi 1.5 · di, j

(6.4)

where wi and di, j are traffic weight of node i and the shortest distance between TN nodes i and j, respectively. Such weight manifests the extent of node attractiveness for traffic flow. For instance, a TN node located in commercial districts would correspond to a larger traffic weight.

6.2.2 Modelling of H2EVs Note that both electricity and hydrogen are consumed by H2EVs. It means the battery and hydrogen tank are equipped in the H2EV, as shown in Fig. 6.1b. In detail, from the storage tank, the hydrogen is firstly refueled into the solid oxide fuel cell (SOFC) for producing electricity. Then, such electricity would be injected into the battery. Finally, the motor uses energy from battery to drive the vehicle [26]. In terms of such energy operational structure, the formulation of H2EVs energy storage is expressed as follows. E v = E vele + ηSOFC E vhyd

(6.5)

hyd

where E v , E vele , and E v are total energy storage of H2EV v, as well as its electricity and hydrogen storage, respectively. Besides, ηSOFC denotes the efficiency of SOFC. The mentioned energy storage should satisfy corresponding constraints. In terms of the energy operational structure introduced above, electricity in the battery is full when the hydrogen energy storage is not empty, as the hydrogen is consumed first. That is, (

) ele E full − E vele E vhyd = 0

(6.6)

ele where E full denotes the full electricity storage of battery in the H2EV. Also, such battery should satisfy its limit of state of charge (SoC), while the hydrogen tank meets the capacity constraint. Accordingly, these limitations are formulated as follows.

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

SoCv =

E vele ele E full

SoC ≤ SoCv ≤ SoC hyd

0 ≤ E vhyd ≤ E full

(6.7) (6.8) (6.9)

Therein, SoCv represents the state of charge regarding H2EV v, which could be calculated via (6.7). Note that SoC and SoC are the maximum and minimum values hyd of SoCv , respectively. Specially, E full denotes the full hydrogen storage in H2EVs. Accordingly, the constraint of hydrogen tank storage is expressed as (6.9).

6.2.3 Modified MCLM The HVESF obtains energy from both PN and HN first, as shown in the Fig. 6.1c. Then, it not only charges batteries of connected H2EVs but also refuels their hydrogen tanks. It is indicated H2EVs may have different storage states of energy when arriving at HVESFs. Such states are usually assumed to follow Normal probabilistic distribution [9, 27]. Therefore, the following formulations hold. Ev E full | | 1 (SoEv − μ) f (SoEv ) = √ exp − 2σ 2 σ 2π SoEv =

(6.10) (6.11)

where SoEv represents the energy storage state regarding H2EV v. Besides, E full is the total energy storage of H2EVs when the battery and hydrogen tank are full. In addition, μ and σ represent the mean and deviation of the Normal probabilistic distribution, which are set to be 0.1 and 0.32, respectively. Based on the SoEv aforementioned, we calculate the SoC of battery SoEv and hyd hydrogen storage E v via (6.6), (6.7) and (6.10). Then, regarding traffic flow expressed by (6.3) and the H2EV model formulated by (6.5)–(6.9), electricity demand hyd ele E d,i and hydrogen demand E d,i of node i are expressed as follows. ele E d,i

) ele E fi n ( v=1 SoC − SoCv E full = , i ∈ TN ηc hyd

E d,i =

fi n ( E v=1

) hyd E full − E vhyd , i ∈ T N

(6.12)

(6.13)

6.2 Modified Maximum Covering Location Method Regarding TN

91

where ηc represents the efficiency of charging via HVESFs. In order to satisfy the energy demand of H2EVs calculated above, a modified MCLM is proposed and detailedly formulated as follows. Firstly, on the basis of traditional MCLM, the maximum covering range of the HVESF is expressed as Eq. (6.14). D=

E full eoc

(6.14)

where D denotes the maximum covering range, and eoc is the consumed energy of H2EVs per kilometer. It should be mentioned that only H2EVs within the maximum covering range could be charged and refueled. In other words, once a TN node is covered by HVESF planned ones, its corresponding H2EVs flow could access energy. Therefore, if the node j is to be planned with a HVESF, its covered set of TN nodes CN j is presented as follows. } { CN j = i ∈ TN|di, j ≤ D , j ∈ TN

(6.15)

Based on above description, the covering state of the TN node is expressed as (6.16). { csi, j =

1 i ∈ CN j , j ∈ TN 0i∈ / CN j

(6.16)

Therein, csi, j represents the covering state of node j on i. Specifically, if TN node i is within the covering set of j, the corresponding covering state is labeled by 1, otherwise it would be 0. In other words, if csi, j equals to 1, it means node j takes responsibility for satisfying energy demands of TN node i. Then, the number of HVESFs for energy demands of TN node i could be calculated as follows. ( ) E E ci = ts j,k , i ∈ TN csi, j (6.17) j∈TN

EE

k∈K

tsi,k = |K |

(6.18)

k∈K i∈TN

where tsi,k denotes the location state of kth energy facility on TN node j (1 represents that kth energy facility E locates at node j, 0 otherwise). In addition, K is the set of HVESFs. Accordingly, k∈K tsi,k indicates the number E of HVESFs located at node j. Therefore, among HVESFs located at node j, csi, j k∈K tsi,k in (6.17) represents the number of those taking responsibility for energy demands of TN node i. To this end, ci denotes the number of HVESFs for energy demands of node i in the whole TN, and it could be calculated via (6.17).

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

It is noted that to ensure the energy demands of H2EVs in TN, the modified MCLM is formulated considering the following two aspects. On the one hand, there should be more than one HVESF taking responsibility for energy demands of each TN node. ci ≥ 1, i ∈ TN

(6.19)

On the other hand, we modify the objective function (i.e. supplying ability) of MCLM as follows. E EE ele E d,i ≤T tsi,k Pkvc ηc (6.20) i∈TN

E

i∈TN

k∈K i∈TN

hyd

E d,i ≤ T

EE

tsi,k Skvr HVH2

(6.21)

k∈K i∈TN

where Pkvc and Skvr are the charging and refueling capacity of HVESF k, respectively. Furthermore, HVH2 represents the heat value of hydrogen. In addition, T is averaged parking time of H2EVs. In this way, we can guarantee the quantity of energy demand of TN nodes formulated in (6.12) and (6.13). Therefore, the energy demand of H2EVs is satisfied via our modified MCLM.

6.3 Multi-network Framework Considering Coupled Flow Constraints 6.3.1 Multi-network Framework It is noted that HVESFs provide electricity and hydrogen for H2EVs, which involve PN, HN and TN. It means power flow of PN, mass flow of HN, traffic flow of TN are coupled and required to be simultaneously considered. Regarding this issue, we propose a multi-network framework considering coupled flow constraints as shown in Fig. 6.2, in order to well address the planning issue of HVESFs. As shown in Fig. 6.2a, the thermal power unit and photovoltaic (PV) are adopted in PN for power generations, in order to meet the power demand of HVESFs, SOEC as well as traditional loads. Besides, it could be observed from Fig. 6.2b that the SOEC uses electricity to produce hydrogen, which is consumed by HVESFs. Also, the hydrogen supplier is employed in HN, which is regarded as a complement to provide limit quantity hydrogen [26]. Finally, the electricity and hydrogen consumed by HVESFs are delivered to the connected H2EVs for satisfying their energy demands, as shown in Fig. 6.2c.

6.3 Multi-network Framework Considering Coupled Flow Constraints

93

Fig. 6.2 Coupled multi-network flow framework, reprinted from Ref. [45], copyright2023, with permission from IEEE

In term of the above description, the power flow of PN and traffic flow of TN are coupled by the HVESF, which is also the coupling section between mass flow of HN and traffic flow. The mass flow of HN mainly stems from the solid oxide electrolyser cell (SOEC), which produces hydrogen by electrolyzing water. Therefore, the SOEC couples energy flow of PN and HN. Specially, uncertain RE (such as photovoltaic, which is commonly deployed in PN) has significant impacts on the power flow, and further influences the mass flow due to the coupled relationship. To this end, the integration of PV is also considered to address the planning issue of HVESFs. Note that above coupling relationships result in coupled flow constraints of the multi-network, which are required to be satisfied, simultaneously. Nevertheless, this might be hard to be achieved due to the complex coupling relationships [22], as well as the uncertainty of RE. Especially, the coupled power flow and hydrogen flow are difficult to be simultaneously met. Accordingly, two aspects are taken into account to tackle this issue. On the one hand, the SOEC in the proposed framework is mainly driven by PV. That is, the power output from PV can be directly used by SOEC, in order to produce hydrogen without delivery via PN. It means that such process is not constrained by power grid and could directly adjust the hydrogen flow. In this way, we can enhance the ability of adjusting the hydrogen flow to satisfy the mass flow constraints in HN, while guaranteeing the power flow in PN. Likewise, hydrogen suppliers could also provide hydrogen directly without constraints related to power flow. Therefore, hydrogen suppliers are introduced as a complement for providing hydrogen to satisfy the mass flow balance.

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

In the following part of this section, constraints of PN and HN, as well as the coupled flow constraints in the multinetwork framework are modeled and formulated in detail.

6.3.2 AC Power Flow Constrained PN with PV Integrated In this paper, both thermal power units and PV are employed in PN, to meet power demand of traditional loads, HVESFs, and SOECs. Specially, PV is deployed together with the SOEC, for transferring electricity to hydrogen. Note that it is necessary to take power flow into account, for supporting operational security of PN. Therefore, we take the AC power flow constrained PN as an example, and corresponding constraints are modelled as follows. 1. Power output constraints The active and reactive power outputs of thermal power units, as well as PV power outputs are limited by their upper and lower boundaries, which are formulated as follows. TG

TG P TG n,g ≤ Pn,g ≤ P n,g , n ∈ PN, g ∈ G TG

Q TG ≤ Q TG n,g ≤ Q n,g , n ∈ PN, g ∈ G n,g PV

0 ≤ Pn,PVp ≤ P n, p , n ∈ PN, p ∈ P

(6.22) (6.23) (6.24)

TG where Pn,g and Q TG n,g denote the active and reactive power outputs of thermal power unit g, which is located on PN node n. Besides, Pn,PVp is the power outputs of PV. Specially, (·) and (·) represent the corresponding upper and lower boundaries. In addition, PN is the set of PN nodes, while P and G denote sets of the PV and thermal power units, respectively.

2. Reserve constraints To tackle the possible fluctuation of PV power outputs and PN load demands, reserve requirements of thermal power units are taken into account [28]. Sup =

E E(

TG

TG P n,g − Pn,g

) (6.25)

n∈PN g∈G

Sup ≥ ωup

EE

Pn,PVp + βr

n∈PN p∈P

Sdn =

E E( n∈PN g∈G

E

PnD

(6.26)

n∈PN TG Pn,g − P TG n,g

)

(6.27)

6.3 Multi-network Framework Considering Coupled Flow Constraints

Sdn ≥ ωdn

EE

Pn,PVp

95

(6.28)

n∈PN p∈P

where Sup and Sdn denote the up and down reserves of thermal power units, respectively, and PnD represents the local power demand in PN. Besides, βr is the reserve coefficient of traditional power load, while ωup and ωdn represent the up and down reserve coefficients of PV power outputs, respectively. 3. AC power flow constraints The PV, SOEC and HVESF integrated in the PN indeed affect the distribution of the power flow. Therefore, we take power flow of PN into account. Specifically, the active and reactive power balance constraints are formulated as follows. E

TG Pn,g +

g∈G

= PnD +

E (

Pm,n − rm,n lm,n

m:m→n

E

Pn,l + psn,k Pkvc +

l:n→l

)

E(

) Pn,SOEC − Pn,PVp + gn vn , (l, m, n) ∈ PN p

p∈P

(6.29) E

Q TG n,g +

g∈G

= QD n +

E (

Q m,n − xm,n lm,n

)

m:m→n

E

Q n,l + bn vn , (l, m, n) ∈ PN

(6.30)

l:n→l

where Pm,n and Q m,n are active and reactive power delivered from PN node m to n, respectively, while lm,n represents the square of line current between node m, n. It is noted that rm,n as well as xm,n denote the corresponding resistance and reactance. Furthermore, vn is the square of voltage regarding PN node n, while gn and bn represent the corresponding conductance and susceptance, respectively. In addition, psn,k denotes the location state of the kth HVESF on PN node n. It should be mentioned that the SOEC could directly use the electricity generated by the corresponding PV. Therefore, they are deployed together and connected to the same PN node. Hence, the SOEC and PV are both indicated by p ∈ P. Accordingly, the pth SOEC could directly employ power output of the pth PV. On this basis, denotes the power demand of SOEC p, while Pn,PVp regrading PN node n, Pn,SOEC p represents the power output of PV p. Therefore, their net power demand on PN node − Pn,PVp , as shown in (6.29). In addition, following formulations related to n is Pn,SOEC p transmission power, line current and node voltage hold [29]. }( ) ) ( ( )2 } 2 vn = vl − 2 rn,l Pn,l + xn,l Q n,l + ln,l × rn,l + xn,l , (n, l) ∈ PN ( ln,l =

Pn,l

)2

( )2 + Q n,l , (n, l) ∈ PN vn

(6.31)

(6.32)

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

where vl is the voltage of PN node l. Besides, rn,l and xn,l are the resistance and reactance between nodes n, l, respectively. Furthermore, Pn,l represents the active power delivered from node n to l, and Q n,l denotes the reactive one. 4. Grid security constraints In order to ensure the operational security of the PN, we consider the following constraints for node voltage, line current and transmission power as well. ( )2 )2 ( vmin,n ≤ vn ≤ vmax,n , n ∈ PN

(6.33)

)2 ( ln,l ≤ lmax,n,l , (n, l) ∈ PN

(6.34)

} } } Pn,l } ≤ P n,l , (n, l) ∈ PN

(6.35)

Specifically, vmin,n and vmax,n represent the minimum and maximum voltage of PN node n. Besides, lmax,n,l is the maximum line current between PN node n, l. In addition, P n,l denotes the maximum allowed transmission power.

6.3.3 HN Considering PV Driven SOEC As shown in Fig. 6.2, both PV driven SOEC and hydrogen suppliers are employed in HN. For more details, the PV driven SOEC is installed in HN as the main hydrogen source, which could utilize PV power outputs directly and produce hydrogen to benefit PV utilizations. Afterwards, the hydrogen is distributed by the HN, and then refueled into the H2EV via HVESFs. It should be mentioned that hydrogen suppliers are regarded as a complement and provide the limited quantity of hydrogen, in order to adjust the hydrogen flow to satisfy the mass flow constraints while guaranteeing the power flow. Therefore, HN constraints are modelled and could be expressed as follows. 1. Hydrogen balance constraint Regarding the supply demand relationship of whole HN aforementioned, hydrogen injected to HN should equal to the consumption. EE p∈P d∈HN

SOEC Sd, + p

EE s∈S d∈HN

SLP Sd,s =

E

Skvr

(6.36)

k∈K

SOEC SLP where Sd, and Sd,s denote the hydrogen flow provided by the pth SOEC and sth p hydrogen supplier on HN node d, respectively. Specially, HN is the set of HN nodes. Besides, Skvr represents the refueling capacity of HVESF k.

2. Mass flow constraints

6.3 Multi-network Framework Considering Coupled Flow Constraints

97

The distribution of the hydrogen in the HN are limited by its mass flow constraints. Specifically, for each node in HN, its injected hydrogen flow should be balanced with the sum of its consumption and effusion. E

SOEC Sd, + p

p∈P

E

SLP Sd,s +

s∈S

E

hyd

f c,d =

c:c→d

E

hyd

f d,e + hsd,k Skvr , d ∈ HN

(6.37)

e:d→e

hyd

where f c,d is the hydrogen flow delivered from HN node c to d, and hsd,k represents the location state of k th HVESF on HN node d. Therein, the steady-state hydrogen flow of a pipeline without compressors is decided by Weymouth flow Eq. (6.38), based on gas pressure at both ends of pipelines [26]. /} } hyd f d,e = sgn(πd , πe )μd,e }(πd )2 − (πe )2 }

(6.38)

where πd denotes the pressure of HN node d, and μd,e is the pipeline constant between node d, e. 3. Boundary constraints The hydrogen flow of pipeline and HN node pressure are limited by their upper and lower boundaries, to ensure the operational security of the whole HN. hyd

hyd

hyd f min ≤ f d,e ≤ f max , π ≤ πd ≤ π , (d, e) ∈ HN hyd

(6.39)

hyd

Therein, f min and f max are maximum and minimum delivered hydrogen flow of pipeline, respectively. Likewise, π and π denote the lower and upper boundaries of node pressure. Also, the supplying hydrogen flow of hydrogen suppliers has its boundary constraints, i.e., SLP

SLP 0 ≤ Sd,s ≤ S d,s , d ∈ HN, s ∈ S

(6.40)

SLP

where S d,s represents the maximum hydrogen flow provided by hydrogen supplier s located at node d.

6.3.4 Coupled Section The HVESF integrates multiple flows among PN, HN and TN. Therefore, in this paper, the possible planning site of the HVESF should be connected to all the PN, HN and TN, simultaneously. To this end, coupled constraints regarding the HVESF are formulated as follows. K ⊂ {TN ∩ PN ∩ HN}

(6.41)

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

E

tsi,k =

E n∈PN

i∈TN

psn,k =

E

hsd,k = 1, k ∈ K

(6.42)

d∈HN

where tsi,k , psn,k , and hsd,k denote the location state of the kth HVESF on TN node i, PN node n and HN node d, respectively. For example, tsi,k (or psn,k , hsd,k ) would be labeled by 1 if the kth HVESF is located on TN node i (or PN node n, HN node d). Otherwise, it will be labelled by 0. On this basis, (6.42) indicates that a HVESF could be only planned on a network node. Moreover, since the SOEC utilizes electricity from PN to produce hydrogen, which would be further injected to HN, the following energy conversion constraint should be satisfied. E E SOEC HVH2 Sd, = ηSOEC Pn,SOEC (6.43) p p , p ∈ P d∈HN

n∈PN

where ηSOEC denotes the efficiency of SOEC. Consequently, Pn,SOEC represents the p SOEC power demand of SOEC p on PN node n, and Sd, p is the hydrogen supplied by SOEC p on HN node d. In addition, HVH2 stands for the heat value of hydrogen.

6.4 Many-Objective Optimization Based Bi-level Planning Model for HVESF 6.4.1 Bi-level Many-Objective Planning Model Regarding the planning issue of HVESFs, two aspects are required to be considered. On the one hand, the scheduling feasibility for the planning solution is necessary to be ensured. Specifically, we should satisfy operational constraints of the multiple networks, based on the planning solution. On the other hand, various objectives of both planning and scheduling shall be comprehensively considered. It would be very helpful to determine reasonable planning solutions. Regarding this issue, a manyobjective optimization based bi-level planning model is proposed as shown in Fig. 6.3, which is on the basis of the coupled flow constraints developed in Sect. 3. It could be observed from this figure that both levels for planning and scheduling are considered. In detail, the planning level is used to determine the planning solution, and the scheduling level is employed to evaluate its feasibility and scheduling performances. Especially, the many-objective optimization approach is introduced to consider objectives of this bi-level HVESFs planning model, including the constructive cost, operational cost, PV utilization, voltage deviation and transmission loss. For more details, the upper level shown in Fig. 6.3a mainly focuses on the planning solution of HVESFs. It aims to minimize the constructive cost directly, considering constraints of TN traffic flow. Besides, the scheduling performance based on the planning solution is also taken into account, which are evaluated and delivered back

6.4 Many-Objective Optimization Based Bi-level Planning Model for HVESF

99

Fig. 6.3 Many-objective optimization based bi-level planning model, reprinted from Ref. [45], copyright2023, with permission from IEEE

via the lower level. Specially, the planning solution (left red rectangle in Fig. 6.3a is regarded as decision variables of the upper level, and includes location and charging/ refueling capacity of HVESFs, as well as objective weights of scheduling. It should be mentioned that these weights mainly refer to the importance of scheduling objectives. Indeed, they have significant impacts on the optimized scheduling scheme. Therefore, these weights are regarded as decision variables to be obtained in the upper level, considering preferences of different scheduling objectives based on the planning. Consequently, the planning solution in the upper level model would be also fed into the lower one. On this basis, scheduling objectives (red rectangle in Fig. 6.3b are optimized in the lower level, which accounts the coupled multi-network flow constraints. Finally, these objective values would be delivered back to the upper level, and considered together with the constructive cost. In this way, we can evaluate not only the constructive cost but also feasibility and performances of planning solutions, regarding coupled flow constrained scheduling conditions. Specifically, the upper level for minimizing the constructive cost is formulated as follows. | | E ( )E c e vc h vr min F1 = tsi,k ci + ci Pk + ci Sk u (6.44) i∈TN k∈K s.t. (1) ∼ (21) } { vc vr u = Pk , Sk , tsi,k , psn,k , hsd,k , α1 , α2 , α3 , α4 , α5

(6.45)

100

6 Coupled Multi-network Constrained Planning of Energy Supplying …

where cic , cie and cih represent the constructive cost, power and hydrogen capacity installation cost of TN node i, respectively. Furthermore, u is the vector of decision variables of the upper level. Therein, α 1 ~ α 5 are weights for scheduling objectives in the lower level. Besides, the lower level model not only minimizes the operation cost, node voltage deviation and transmission loss, but also maximizes the PV utilization, in order to achieve better operational performance. Note that all the PN power flow, HN mass flow and TN traffic flow constraints are taken into consideration, and formulations are expressed as follows. min [α2 F2 + α3 F3 + α4 F4 − α5 F5 ] u∗ ⎧ } } } 1/2 } ⎪ − v ⎪ }v } n 0 ⎪ ⎪ ⎪ F = 2 ⎪ ⎪ v0 ⎪ ⎪ ( ) ⎪ ⎪ ⎪ E E ⎪ ⎪ ⎪ F3 = rm,n lm,n ⎪ ⎪ ⎪ ⎪ n∈P N m:m→n ⎪ ⎪ ⎡ ( ⎤ ⎨ )2 ( ) E E E E E s.t. TG TG SLP ⎣ag ⎪ Pn,g + bg Pn,g + cg ⎦ + Sd,s F4 = ps ⎪ ⎪ ⎪ ⎪ n∈PN n∈PN g∈G s∈S d∈HN ⎪ ⎪ ⎛ ⎞ ⎪ ⎪ ⎪ ⎪ E E ⎪ ⎪ ⎝ ⎪ Pn,PVp ⎠ ⎪ F5 = ⎪ ⎪ ⎪ n∈PN p∈P ⎪ ⎪ ⎪ ⎩ (22) ∼ (43) (6.46) { TG TG PV SOEC SOEC SLP } u ∗ = Pn,g , Q n,g , Pn, p , Pn, p , Sd, p , Sd,s , πd (6.47) where v0 denotes the normal voltage of PN nodes, and ag , bg , cg as well as ps represent operation cost coefficients of thermal power units [30] and price of hydrogen provided by the suppliers, respectively. It is noted that F2 ∼ F5 are objective functions of voltage deviation, transmission loss, operation cost as well as PV utilization. Note that F4 involves both generation cost of thermal power units and cost paid for hydrogen suppliers. Furthermore, α 2 ∼ α 5 are objective weights for scheduling objectives F2 ∼ F5 , respectively. Specially, the decision variable of this level u ∗ includes thermal active/reactive power outputs, PV power utilization, SOEC power demand and the corrsponding produced hydrogen flow, hydrogen supplier flow, and HN node pressure, as shown in Fig. 6.3b and expressed as (6.47) To conclude, these two levels are connected via planning solution as well as the scheduling objective values. In addition, the corresponding procedure for solving this many-objective optimization based bi-level planning model is presented in the next subsection.

6.5 Case Study

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6.4.2 Solving Procedure It is noted that the proposed model is a non-linear and nonconvex optimization problem. On the one hand, for (6.20) and (6.21) in the upper level model, both charging/refueling capacity (continuous variables) and location state (binary variable, labelled by 0/1) of HVESFs are decision variables. Specially, note that continuous variables times binary one makes the problem (6.44) non-convex and hard to be relaxed [31]. Regarding this issue, differential evolution (DE) algorithm is employed, which could effectively solve non-convex problems [32]. On the other hand, the lower level problem could be relaxed via cone relaxation approach [33], and then efficiently solved by interior point method (IPM). Therefore, to solve the developed bi-level optimization model, the corresponding hybrid DEIPM algorithm [28] is used and shown as Fig. 6.4. Generally, the upper level model is solved by DE algorithm [28], while the lower level is optimized on the basis of IPM by commercial solver CPLEX. Specifically, we firstly initialize the population of upper level decision variables. After that, the mutation and crossover operations are conducted. Then, the objective of upper level, i.e., constructive cost, is calculated. Furthermore, the lower level uses decision variables of upper level, which are passed by step (1) in Fig. 6.4, to optimize and obtain its objective functions. They include voltage deviation, transmission loss, operation cost, and PV utilization. It should be mentioned that both upper and lower level objectives are delivered to the operation of non-dominated sorting [28] via step (2). In this way, all the objectives are considered to conduct selection and generate the next population. After a preset iterations, we finally obtain the Pareto solutions 1 of the proposed model [34].

6.5 Case Study 6.5.1 Case Description In this paper, we employ the coupled multi-network shown in Fig. 6.5, in order to verify the feasibility and outperformance of our proposed planning model, modified MCLM and multinetwork framework. This multi-network includes a modified IEEE 33-bus PN [35], a 39-bus HN [36] and a 25-bus TN [9]. Specially, the overlapping relationship of TN, PN, and HN nodes is shown in Table 6.1. It could be observed from the figure that three PVs are integrated to buses 5, 7, and 20 of the PN, respectively, together with three corresponding SOECs. Note that these three SOECs are connected to bus 2, 10, and 24 of the 39-bus HN, and such overlapping relationships are indicated by gray lines in Fig. 6.5. Besides, the efficiency of SOEC is set as 0.80. In addition, three hydrogen suppliers locates at bus 1, 7, and 20, respectively. Note that in the coupled multi-network, three HVESFs are assumed to be installed, and its constructive cost coefficients are also shown in Table 6.1. Three cases are

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

Fig. 6.4 Solving procedure of proposed HVESF planning-scheduling model, reprinted from Ref. [45], copyright2023, with permission from IEEE

adopted in this paper to verify the effectiveness and reveal the impact of multinetwork on the performances of system planning and scheduling. In the IEEE 33-bus PN, the predicted errors of PV and traditional loads are set as 6% and 5%, respectively, in order to account uncertainties in the PN [37]. Besides, the upper boundary for the power outputs of PV is assumed to be 70 MW. Furthermore, pressure limitations of the HN node, hydrogen flow boundaries of the pipelines, as well as their lengths are referred to [38]. Specially, the price of hydrogen is set as 20 $/kg [36]. The total energy storage of H2EVs is set to be 2 MWh, and each H2EVs would consume 0.01 MWh energy per kilometer. Besides, both of electricity and hydrogen take 50% of the full energy storage. The efficiencies of charging and SOFC are set as 0.80 and 0.98, respectively.

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Fig. 6.5 Structure of the coupled multi-network, reprinted from Ref. [45], copyright2023, with permission from IEEE

Case 1: In this case, the power flow of PN, mass flow of HN and traffic flow of TN are required to be satisfied, simultaneously. This case aims to verify the feasibility of the proposed planning model. Case 2: Compared with Case 1, this case is set only without using the proposed modified MCLM. Therefore, it is compared with Case 1 to verify the effectiveness of modified MCLM. Case 3: In this case, only the power flow of PN and traffic flow of TN are required to be satisfied, which correspond to traditional EV charging station planning model [13]. This case is set to be compared with Case 1. It aims to verify the effectiveness of proposed multi-network framework with coupled flow constraints.

6.5.2 Analysis on HVESFs Planning Model and Relationship Among Many Objectives We conduct simulations on Case 1 to analyze the proposed HVESFs planning model, and reveal relationships among many objectives. Specially, simulations are conducted in MATLAB with 20 parallel pools on a 64-bit PC with two 2.91 GHz processors. It takes about 47 minutes for one independent run of the hybrid DE-IPM algorithm, considering 1800 iterations and a population scale of 100.

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Table 6.1 Data of the multi-network and corresponding coupling information, reprinted from Ref. [45], copyright2023, with permission from IEEE TN

Coupled

Coupled

Hydrogen

Electric

Node

HN node

PN node

Constructive

Constructive

Index

Index

Index

Cost (k$/kg/h)

Cost (k$/kW)

1

21

18

2.50

4.50

2

25

6

2.50

4.50

3

8

14

2.50

1.50

4

7

2

0.50

1.50

5

34

30

0.50

1.50

6

33

33

0.50

1.50

7

14

27

0.50

2.50

8

18

32

0.50

2.50

9

29

10

0.50

2.50

10

13

15

1.50

1.50

11

17

23

1.50

3.50

12

20

24

1.50

3.50

13

24

12

1.50

3.50

14

35

8

1.50

3.50

15

2

5

2.00

3.00

16

19

11

2.00

3.00

17

26

19

2.00

3.00

18

11

4

2.00

3.00

19

38

25

4.50

3.00

20

10

7

4.50

0.50

21

24

20

4.50

0.50

22

6

3

4.50

3.50

23

12

28

4.50

3.50

24

4

1

4.50

3.50

25

22

22

4.50

3.50

The convergent performance of the algorithm is firstly studied. This is mainly because the proposed many-objective bi-level planning model is feasible and efficient only if the corresponding solving algorithm is convergent [39]. Specifically, the hyper-volume (HV) indicator, which is widely used to evaluate optimization algorithms [40], is employed to evaluate such convergent performance. We calculate HV values of 10 independent runs regarding Case 1. The corresponding convergent curves are shown in Fig. 6.6, respectively. It is observed from this figure that the HV values fluctuate up and down from 0 to 60 iterations, approximately. Then, it keeps gradually increasing and is convergent

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105

Fig. 6.6 Convergent curves, reprinted from Ref. [45], copyright 2023, with permission from IEEE

at about 1100 iterations, in all 10 independent runs. This means that the model could satisfy its constraints and trend to be optimal with the development of iterations. Besides, it is indicated that the HV almost keeps steady during the following iterations, which means that the algorithm is already convergent. Specially, final value of HV is within [7:44 × 108, 7:85 × 108] with a maximum deviation of 5.2%. Therefore, the proposed algorithm is also with good stability. It verifies that the proposed many-objective optimization based bi-level planning model can be well solved via the hybrid DE-IPM algorithm. Based on above simulations, we obtain and present the best Pareto solutions among 10 independent runs (i.e., with highest HV value). Since five objectives are considered, it is difficult to show such Pareto solutions. Therefore, the parallel axis plot [41] is adopted. As shown in Fig. 6.7a, multiple axes present values of the 5 objectives, i.e., constructive cost (CC), operational cost (OC), PV utilization (PVU), transmission loss (TL), and voltage deviation (VD). Each line corresponds to a Pareto solution. It could be observed that the obtained Pareto front is irregular. This is mainly because the planning issue is discrete, and changes in planning (location and capacity) of HVESFs could make significant impacts on performances of the various objectives. For more details, note that there are massive lines in Fig. 6.7a, which makes it hard to conduct further analysis. Therefore, we extract two main tendentious in this figure and shown them in Fig. 6.7b, in order to reveal the relationship among many objectives. Specifically, it is noted that the two lines between axes of CC and OC are crossed. It means the constructive cost and operational cost are in the tradeoff relationship [42]. Besides, as indicated by the blue line in Fig. 6.7b, the lower operational cost, higher PV utilization, less transmission loss requires a higher constructive cost. On the contrary, as shown via the red line, the lower constructive cost leads to a higher operational cost and transmission loss. It means that the constructive cost impacts scheduling performances of the coupling networks.

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6 Coupled Multi-network Constrained Planning of Energy Supplying …

Fig. 6.7 Pareto solutions obtained by proposed model, reprinted from Ref. [45], copyright 2023, with permission from IEEE

Regarding the relationship among scheduling performances, analysis is conducted as follows. It is noted that the two lines among axes of OC, PVU and TL are noncrossed in Fig. 6.7b. This indicates the more PV utilization, the higher transmission loss, and the larger operational cost. The reason is that higher utilization of PV power is realized by delivering them to PN nodes. Therefore, the line current would increase since the node voltage is limited by its boundaries, as shown in Eq. (6.35). This leads to a larger transmission loss, and it means that the traditional power output would enhance to balance power flow. Finally, it results in a higher operational cost. In addition, the transmission loss and node voltage deviation are in trade-off relationship according to crossed lines between axes of TL and VD, as presented in Fig. 6.7b. The above analysis reveals the relationships among many objectives, and verifies the rationality of the obtained Pareto solutions. Therefore, the proposed manyobjective optimization based bi-level planning model is effective to consider various objectives. Nevertheless, we should choose a final planning solution. In this paper, the fuzzy decision-making method [43] is employed, details of which are presented in Appendix of the paper. Then, results with respect to the final planning solution are shown and discussed in the next subsection.

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107

6.5.3 Analysis on Effectiveness of Obtained Planning Solutions Considering Modified MCLM For the fuzzy decision making method, we set weights of these 5 objectives as the same, i.e., 0.2. Then, results of Case 1 are obtained, and values of objective functions, including constructive cost, operational cost, PV utilization, transmission loss as well as voltage deviation are 346.59 k$, 1.32 k$, 106.59 MW, 1.08 MW, 0.028 p.u., respectively. In addition, Fig. 6.8 shows the final planning solution for HVESFs. Specifically, note that these H2EVs are located at nodes 20, 3, 21 of TN, as shown in Fig. 6.8a. Besides, it is indicated in Fig. 6.8b, c that for three HVESFs, the installed capacities of electricity (and hydrogen) are 10.12 MW (61.89 kg/h), 4.69 MW (96.70 kg/h), 12.80 MW (51.47 kg/h), respectively. Furthermore, the data of PVs and SOECs are also shown in Fig. 6.8c. The three PVs use most of their power utilizations (i.e., 31.11 MW of 31.11 MW, 34.72 MW of 35.18 MW, 31.91 MW of 40.30 MW) for hydrogen production in SOECs. Therefore, our proposed model could obtain the planning solutions of HVESFs, which contribute to the PV utilization. To further verify the effectiveness of proposed modified MCLM, simulation results of Case 2 (without proposed modified MCLM) are compared to Case 1. Specifically, we show the total installed capacities (electricity and hydrogen) of HVESFs

Fig. 6.8 Planning of HVESFs as well as data of PV and SOEC in Case 1, reprinted from Ref. [45], copyright 2023, with permission from IEEE

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Table 6.2 total installed capacities of electricity and hydrogen in Cases 1 and 2 as well as energy demands of H2EVs, reprinted from Ref. [45], copyright 2023, with permission from IEEE Hydrogen flow (kg/h)

Items

Electric power (MW)

H2EVs demands

103.38

9.62

Case 1 supply

210.05

27.61

Case 2 supply

92.62

7.44

and energy demands of H2EVs in Table 6.2. It could be observed that the total supplement of hydrogen and electricity in Case 1 are 210.65 kg/h and 27.61 MW, which satisfies the energy demand of H2EVs, i.e., 103.38 kg/h and 9.62 MW. However, those of Case 2 are 92.62 kg/h and 7.44 MW, respectively. Accordingly, compared to energy demand of H2EVs, the total supplement of hydrogen and electricity in Case 2 is 10.76 kg/h and 2.18 MW lower. That is, the energy demands of H2EVs could not be satisfied. To this end, using the modified MCLM, such demand could be effectively fulfilled in Case 1. In conclusion, the proposed model with modified MCLM could support the planning of HVESFs while meeting the energy demands of H2EVs.

6.5.4 Analysis on Effectiveness of Multi-network Framework Note that Case 3 refers to the traditional planning model with two coupled networks, while Case 1 is our proposed one considering multi-network framework. Therefore, we conduct simulations on Case 3, and compare its results with those of Case 1. This aims to further verify the effectiveness of proposed multi-network framework considering coupled flow constraints. Results are given in Table 6.3, and Figs. 6.9, 6.10 and 6.11. It is indicated that Table 6.3 shows the objective values of both Case 1 and Case 3. Obviously, Case 1 corresponds to better planning and scheduling performances of the multinetwork, apart from PV utilizations. In detail, the constructive cost, operational cost, transmission loss and voltage deviation are 41.66%, 25%, 9.24%, 41.67% better, respectively. Specially, the PV utilization of Case 3 is 116.30 MW, which is larger than that of Case 1, i.e., 106.59 MW. This is mainly because that Case 3 is set without mass flow of HN, compared to Case 1 limited by all the power flow, mass flow, and Table 6.3 Objectives comparison of Cases 1 and 3, reprinted from Ref. [45], copyright 2023, with permission from IEEE Case

Constructive cost (k$)

Operational cost (k$)

PV utilization (MW)

Transmission loss (MW)

Node voltage deviation (p.u.)

Case 1

346.59

1.32

106.59

1.08

0.028

Case 3

594.10

1.76

116.30

1.19

0.048

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109

Fig. 6.9 Current comparison between Cases 1 and 3, reprinted from Ref. [45], copyright 2023, with permission from IEEE

traffic flow. Therefore, the quantity of hydrogen in HN of Case 3 is not limited, which means it can utilize more PV to produce sufficient hydrogen. Meanwhile, it is necessary to take secure performances of these two cases into account. For Cases 1 and 3, the line current, node voltage of PN, as well as mass flow of HN are shown in Figs. 6.9, 6.10 and 6.11, respectively. It is indicated from Fig. 6.9 that Case 1 has a smaller fluctuation and amplitude of line current, compared to Case 3. Specifically, its maximum point is (30, 31, 0.22 p.u.), while that of Case

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Fig. 6.10 Node voltage comparison between Cases 1 and 3, reprinted from Ref. [45], copyright 2023, with permission from IEEE Fig. 6.11 Hydrogen flow deviation of HN nodes in Cases 1 and 3, reprinted from Ref. [45], copyright 2023, with permission from IEEE

3 is (12, 13, 0.26 p.u.). Due to such a smaller line current of Case 1, its transmission loss would be decreased compared to Case 3, i.e., reducing from 1.19 to 1.08 MW, as indicated in Table 6.3. Furthermore, it could be observed from Fig. 6.10 that the voltage reaches its upper and lower boundaries at nodes 18 and 23 of PN in Case 3, respectively. However, note that Case 1 obtains a smaller maximum value, and neither reach the upper or lower boundaries of node voltage. To this end, the margin of node voltage in Case 1 is smaller than that of Case 3, corresponding to a narrower variational range. It means a lower voltage deviation, which is 0.028 in Case 1 compared to 0.048 in Case 3, as shown in Table 6.3. It further contributes to the enhancement of PN operational security. Therefore, Case 1 considering multi-network framework with coupled flow constraints could obtain securer and better performances of PN, for the planning of HVESFs. Finally, the hydrogen flow deviations of HN nodes regarding Cases 1 and 3 are shown in Fig. 6.11. Specially, such indicator refers to the hydrogen flow deviation

6.6 Conclusion

111

between the entering flow and leaving flow of HN nodes, which should be zero to ensure the system security. Since the mass flow constraint of HN is taken into consideration in Case 1, its flow deviations of HN nodes are all zeros, shown in the figure. It indicates that the mass flow could be well satisfied. On the contrary, it is noted that Case 3 without mass flow limitations has large deviations of hydrogen flow at HN nodes 2, 10, 17, 18, and 24. Specifically, the maximum value reaches as high as 80 kg/h, which should be zero in the normal condition. This issue indeed challenges the security of HN operation. Regarding this point, the operation of HN would break down due to the unbalance of its mass flow [44]. It means that the planning solution obtained in Case 3 is unfeasible. To this end, it is necessary to consider all the flow constraints in coupled multi-network. This also verifies the effectiveness of the proposed multi-network framework considering coupled flow constraints. In conclusion, the developed many-objective optimization based bi-level planning model could successfully obtain feasible solutions, via the hybrid DE-IPM algorithm. Then, the trade-off relationship among many objectives (constructive cost, operational cost, voltage deviation, RE utilization and transmission loss) are revealed. Regarding the obtained solution, it is indicated that the proposed modified MCLM could effectively ensure the energy demand of H2EVs. Finally, multi-network framework based planning model (Case 1) is verified to have better secure and economic performances, compared with traditional one (Case 3).

6.6 Conclusion This paper developed a uncertain RE integrated multinetwork framework considering coupled flow constraints for HVESFs planning by introducing power flow of PN, mass flow of HN and traffic flow of TN, simultaneously. Specially, the TN was established on the basis of modified maximum covering location method. In this way, the energy supplying ability of HVESFs, which is significantly constrained by the coupled multi-network, is ensured to satisfy the energy demand of H2EVs. Finally, a many-objective optimization based bi-level planning model is proposed for HVESFs, and a hybrid DE-interior point method algorithm is used to efficiently solve the issue. Case studies based on 25-bus traffic network, modified IEEE 33-bus power system, and 39-bus hydrogen network have been conducted, and the results verify the feasibility and effectiveness of our work. Specifically, the main findings are listed as follows. 1. Through considering constraints of modified MCLM, the energy demand of H2EVs is well satisfied, regarding multi-network constrained planning condition. 2. Based on the proposed multi-network framework considering coupled flow constraints, the developed HVESFs planning model is verified to have a better performance compared to exiting model with coupled two networks constraints.

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In detail, the constructive cost, operational cost, voltage deviation, and transmission loss are 41.66%, 25%, 9.24%, 41.67% lower, respectively. Besides, the operation security of both PN and HN is ensured by multi-network framework, while the existing model cannot guarantee the operational security of HN. 3. The proposed many-objective planning model could provide Pareto solutions, based on which the relationship among many objectives is revealed. Specially, the constructive cost is in trade-off relationship with the operational performance. Besides, operational cost, RE utilization and transmission loss have similar varying trends, but it is constrained by the voltage deviation. This relationship could be helpful for decision maker to determine solutions for the planning of HVESFs.

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Chapter 7

Multiple Equipment Planning for Integrated Energy System

7.1 Introduction With the growth of energy demand and concerns of environmental pollution, integrated energy system, as one of the latest energy technologies, has attracted increasing attention, because it can not only couple various energy sources for better energy efficiency, but also effectively accommodate distributed generation and reduce the utilization of conventional energy [1–3]. However, the integration of DG into the IES system will also bring forth challenges to the stable operation of IES due to the uncertainty of DG. In addition, considering the impact of increasing carbon emissions on the environment, more countries have started to limit the carbon emissions of energy systems [4]. These factors are posing new requirements on the further development of IES. There have been numerous efforts to tackle the challenges and optimize the planning of IES. Ref. [5, 6] summarized the basic concept, characteristics and structural framework of the Energy Internet, a promising direction that will significantly reshape the planning and management of future IES. In [7], a combined gas and electricity network expansion planning model is proposed to reduce the expansion cost by analyzing the gas and electricity infrastructure expansion requirements. A framework for optimal planning and sizing of interconnected energy hubs is proposed in [8] for optimal capacity allocation among various components. A bi-level, multistage expansion planning of the integrated natural gas and electrical power systems was proposed in [9] to minimize the investment and operational costs, based on a novel formulation of optimal economic dispatch under the operational constraints. Although the studies above can well reduce the installation and operation costs of IES, the types of energy sources considered therein are limited and cannot full play to the potential of IES that often need to manage a diversity of sources from the DGs. With increasing renewable energy-based DG connected to the IES, there is also a growing call to investigate IES planning considering the DG integration [10, 11]. In [12], a probability-interval-based IES planning considering wind power integration is proposed to reduce the impact of the uncertainty of wind power; a © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_7

115

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7 Multiple Equipment Planning for Integrated Energy System

piecewise linearization method is applied to address nonlinear integral terms in the proposed model to improve the computational efficiency. A novel distributed energy system with co-generation of photovoltaic and ground source heat pump is proposed in [13] to balance energy and flow; particle swarm optimization hybrid algorithm is proposed to develop an optimal operation strategy coupled with seasonal adjustment of the cooling/heating share. In [14], an optimal planning of energy hub with transformer, combined heat and power, boiler, wind turbine and energy storage is proposed; Monte Carlo simulation is used to generate scenarios of wind to analyze and reduce the uncertainty. A probabilistic planning approach based on chanceconstrained programming is proposed in [15] to plan the DG and natural gas network by reducing the uncertainty of distribution power generation and the real and reactive power demand. As environmental pollution and global warming becomes a world-wide concern, it is also becoming crucial to consider carbon emission reduction in the planning IES [4, 16, 17]. To this end, a matrix model of energy hubs of complex network is designed in [18] to optimize the financial viability and the reduction of greenhouse gas emissions under different scenarios, which found that a network composed of multiple energy hubs can improve economic efficiency and reduce the cost from carbon emissions. A reward and punishment ladder-type carbon trading cost model is introduced in [19] into electric-gas-integrated energy system planning model to reduce the carbon emissions. A dynamic two-stage model that considers DG and demand response is proposed in [20] to develop low-carbon, sustainable distribution systems; by cooptimizing the allocation of DG, gas turbines and smart meters simultaneously based on the two-stage model, the total cost and carbon emissions can be significantly reduced. In [21], a novel expansion co-planning framework of power system and natural gas system is proposed to reduce the total expansion and carbon emissions costs by modeling the planning process as a mixed integer nonlinear optimization problem. In [22], a bi-level integrated expansion planning model of multiple energy systems to consider district carbon emission constraints; in the bi-level model, the upper-level model studies the planning of various regional integrated energy systems, and the lower-level model investigates the minimum-cost planning of multiple energy infrastructures based the carbon emissions constraints. Although the above research improves the level of IES planning, the punishment mechanism for carbon emissions is relatively single. The fixed mechanism of reward and punishment or constraint conditions of carbon emission has limited effect on reducing carbon emissions, it is difficult to achieve the flexible adjustment of carbon emission. So, the tiered dynamic carbon emission charging model proposed in this paper. The carbon emission can be controlled at a lower level by controlling the adjustment coefficient. Especially for the uncertainty treatment of DG output model, no matter using fixed wind and solar energy historical data [30] or output prediction model [31] in the optimization planning process, the social benefit of planning scheme is not reliable enough, it is unable to ensure that the economy and carbon emission reduction effect have good performance under different climate conditions. The affine arithmetic in the form of matrix can make the DG output in a reasonable small interval

7.2 Introduction of Multi-energy Coupling in IES

117

according to the local scenery resources and weather conditions, which can ensure that the system has superior economy in most cases. To fill this gap, this paper proposes an optimal planning of IES considering carbon emissions and uncertainty of DG. An affine model in matrix form is introduced to reduce the influence of the uncertainty of DG output to IES. A tiered charging cost model is designed to reduce the carbon emissions. The two models are then combined into an optimal planning model for IES, whose objective function considers the costs of investment, operation, and carbon emission simultaneously. An improved Quantum particle swarm optimization (IQPSO) is employed to solve the planning model. The proposed method is evaluated on the 14-bus IES benchmark and compared with other planning models to demonstrate its effectiveness. The key contributions of this paper are summarized as follows: 1. To reduce the influence of the uncertainty of DG and calculation error, an affine model in matrix form is used to improve the economy and reliability of IES planning scheme. 2. To reduce environmental pollution from carbon emission, a tiered charging cost model is designed to reduce the carbon emissions and adopts the dynamic pricing mode in the third layer to further reduce carbon emission. 3. To achieve optimal planning of IES, an improved Quantum particle swarm algorithm (IQPSO) is developed to solve the planning model. A hierarchical automatic learning method improves the particle diversity of quantum particle swarm algorithm (QPSO) and enhance the global search ability.

7.2 Introduction of Multi-energy Coupling in IES With the development of energy technologies, the mutual conversion among different energies has become a hot topic [23]. As a complex networked system integrating multiple energies, IES can not only couple multiple forms of energy such as electricity, gas, and heat, but also improve the efficiency of all sources of energy via flexible energy conversion and coordination. A typical structure of IES is shown in Fig. 7.1. As can be seen from Fig. 7.1, the supply-side of IES includes both traditional power generation units, DG, and natural gas. IES also contains CCHP(Combined Cooling Heating and Power), gas boiler, P2G(Power to Gas), and other facilities for energy conversion. Different types of energy can be converted to meet the demands via IES. The conversion between different energy can be expressed as: Hgen,g = ηgh G con

(7.1)

Hgen, p = η ph Pcon

(7.2)

118

7 Multiple Equipment Planning for Integrated Energy System Optimal planning of IES

Traditional generators: Gas boilers: Capacity; Year Capacity; Year

Electric

Electric

DG

TG

Sourcenetwork-load interconnection PV

Heat

WT

CCHP: Capacity; Year

P2G: DG: Capacity; Year Capacity; Year Electrical load

Electric P2G Gas

Electric

Gas Gas station NG

Affine transformation based on (36) Input noise unit Supply-side

CCHP Gas Gas GB Heat Heat

Cold

Cooling load

Heating load Gas Network-side

Gas load Demand-side

EDG

EP2G + Ereal Objective Function Investment Cost Carbon Emission Cost

ECO2

-

Operation Cost

Load Power Shortage Penalty Cost

Fig. 7.1 The structure of IES. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

G gen, p = η pg Pcon, p2g

(7.3)

where G con and Pcon are the natural gas and electricity consumed in heat production, respectively; Pcon, p2g is the electricity consumed when Hgen, p = η ph Pcon natural gas is produced via P2G; Hgen,g and Hgen, p are the heating generated by natural gas and electricity, respectively; G gen, p is the natural gas generated by electricity via P2G; ηgh , η ph , and η pg are the natural gas to heating conversion efficiency, electricity to heating conversion efficiency and electricity to natural gas conversion efficiency via P2G [24], respectively. In practical IES, the supply often needs the collaborative conversion of multiple energies [25], which means that a more complex coupling among various energies, and the need for more efficient IES. The multi-energy coupling can be expressed as ⎤ ⎡ η11 E gen,1 ⎢E ⎥ ⎢η ⎢ gen,2 ⎥ ⎢ 21 ⎢ ⎥ ⎢ ⎢ . ⎥ ⎢ . ⎢ ⎥=⎢ ⎢ . ⎥ ⎢ . ⎢ ⎥ ⎢ ⎣ . ⎦ ⎣ . E gen,m ηm1 ⎡

⎤⎡ μ11 μ12 . . η12 . . . ηn1 ⎢μ μ η22 . . . ηn2 ⎥ ⎥⎢ 21 22 . . ⎥⎢ . . . . . ⎥⎢ . ⎥⎢ . . . . . ⎥⎢ . ⎥⎢ . . . . . . . ⎦⎣ . .. ηm2 . . . ηmn μm1 μm2 . .

⎤⎡ ⎤ μn1 E con,1 ⎢ ⎥ μn2 ⎥ ⎥⎢ E con,2 ⎥ ⎥⎢ ⎥ . ⎥⎢ . ⎥ ⎥⎢ ⎥ . ⎥⎢ . ⎥ ⎥⎢ ⎥ . . . ⎦⎣ . ⎦ E con,n . μmn (7.4) . .

where E gen,m and E con,n are the mth energy type generated and the nth type consumed, respectively; ηmn is the conversion efficiency of the mth type into the nth type, and μmn is the proportion of the mth type generated that will be converted into the nth type. The above formula can be expressed in the matrix form

7.3 Models for DG Output Uncertainty and Carbon Emission Reduction

Egen = ημEcon

119

(7.5)

7.3 Models for DG Output Uncertainty and Carbon Emission Reduction The uncertainty of DG in wind generator and photovoltaic systems is mainly caused by fluctuations in wind speed and solar radiation intensity. Interval mathematics can express the uncertainty of DG output, but if the interval model is directly used for modeling the DG output, the conservatism of interval mathematics will result in excessive error and even “interval explosion” after several interval calculations [26]. To overcome this limitation, Comba and Stolfi proposed the concept of affine mathematics in [32]. But affine mathematics is still too conservative. In [33], Ralph et al. Proposed the matrix form of affine arithmetic, and proved that the accuracy of this kind of affine arithmetic is better than affine arithmetic and interval arithmetic. Therefore, the paper uses matrix form affine mathematics to reduce the impact of DG outputs uncertainty on optimal planning.

7.3.1 DG Uncertainty Modeling Based on Matrix Form Affine Arithmetic A matrix form of affine model to consider the uncertainty of DG output in the system planning can improve the economy of the system. Meanwhile, formulating a reasonable carbon emission cost model can further reduce both investment costs and environmental pollution. Therefore, this section mainly introduces the matrix form affine model to reduce the impact of DG output uncertainty. In this section, the modified affine arithmetic based on matrix form is used to establish the uncertainty model of DG. 1. Modified Affine Arithmetic in Matrix Form The uncertainty of DG output has substantial impact on the system planning. For this reason, some scholars use interval number model to describe the uncertainty of DG. To overcome the accuracy problem of the interval number model, affine models are used in some research works. Although the affine arithmetic can usually get more accurate results than interval arithmetic, it can still be too conservative. For example, assume that the affine form of variables and can be expressed as: ∧

x = 0 + ξ1 + ξ2 ∧

y = 0 + ξ1 − ξ2

(7.6)

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7 Multiple Equipment Planning for Integrated Energy System

where ξ1 and ξ2 are the noise units, they are used to represent the uncertainty of variables, and they can be the uncertainty of input data, truncation error of formula, rounding error in operation and so on. Then, (

∧

∧

x × y = x0 +

n E

|) xi ξi

( × y0 +

i=1

= x0 y0 +

n E

(x0 yi + y0 xi )ξi +

n E

|) yi ξi

i=1 ( n E

i=1

|) xi ξi

×

i=1

( n E

|)

(7.7)

yi ξi

i=1

To express the above formula linearly, a new noise element ξk containing coefficient u, v is used to replace the last quadratic term of the (7.7) with respect to the n n E E |xi |, v = |yi |, ξk ∈ [−1, 1]. noise element ξi , where u = i=1

∧

∧

i=1

Therefore, x × y can be transformed into a new affine form: ∧

∧

x × y = x0 y0 +

n E

(x0 yi + y0 xi )ξi + uvξk

(7.8)

i=1 ∧

∧

so the range of x × y is [−4, 4]. However, ∧

∧

(

x × y = x0 +

n E

|) xi ξi

( × y0 +

i=1

= x0 y0 + = x0 y0 +

n E i=1 n E

(x0 yi + y0 xi )ξi + (x0 yi + y0 xi )ξi +

i=1

n E

|) yi ξi

i=1 ( n E i=1 ( n E

|) xi ξi

×

|) xi

×

( n E

i=1 ( n E

i=1

|) yi ξi |)

(7.9)

yi ξi

i=1

= (0 + ξ1 + ξ2 ) × (0 + ξ1 − ξ2 ) = ξ12 − ξ22 ∧

∧

The true range of x × y will be: ξ12 − ξ22 = [0, 1] − [0, 1] = [−1, 1]

(7.10)

As shown in the example above, if the multiplication rule of affine arithmetic is used, the range of value is exaggerated by 4 times. The underlying reason is that the multiplication of affine arithmetic is not accurate enough, and the affine arithmetic does not satisfy the distributive law.

7.3 Models for DG Output Uncertainty and Carbon Emission Reduction

121

To improve the accuracy of the conventional affine arithmetic, [33] have proposed a new modified affine arithmetic with more accurate matrix form. It was further proven that the modified affine algorithm in matrix form is more accurate than the affine algorithm in central form, which in turn is more accurate than the interval algorithm. Therefore, the modified affine algorithm in matrix form is more accurate than the interval algorithm in central form. Assume that a binary function is: f (x, y) =

m n E E

ai j x i y j = XAY

(7.11)

i=0 j=0

| | | | (x, y) ∈ x, x × y, y

(7.12) |

_

|

where the interval numbers of variables x and y are x ∈ x , x and y ∈ −

|

| y, y , _

−

respectively, their affine form are: ∧

x = x 0 + x 1 εx ∧

y = y0 + y1 ε y

(7.13) (7.14)

Similar to (7.6), εx and ε y the noise units, their affine form can be defined as vectors: ) ( ∧ n X = 1, εx , ..., εx

(7.15)

) ( ∧ m T Y = 1, ε y , ..., ε y

(7.16)

The transformation matrices B and C are defined as follows: ⎡ ⎤ 1 x0 . . . x0n x0n−1 ⎢ 0 x . . . (n − 1)x n−2 x nx n−1 x ⎥ 1 1 1⎥ ⎢ 0 0 ⎢. . . ⎥ . . ⎢ ⎥ ⎢ ⎥ B=⎢. . . . . ⎥ ⎢ ⎥ ⎢. . ⎥ . . . ⎢ ⎥ ⎣0 0 . . . nx0 x1n−1 ⎦ x1n−1 0 0 ... 0 x1n

(7.17)

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7 Multiple Equipment Planning for Integrated Energy System

⎡

1 y0 . . .

⎢ ⎢ ⎢ ⎢ ⎢ C =⎢ ⎢ ⎢ ⎢ m−1 ⎣ y0 y0m

0 y1 . . . (m − 1)y0m−2 y1 my0m−1 y1

0 ... 0 ... . . . . . . m−1 y ... 1 . . . my0 y1m−1

⎤ 0 0 ⎥ ⎥ . ⎥ ⎥ ⎥ . ⎥ ⎥ . ⎥ ⎥ 0 ⎦ y1m

(7.18)

In the formula, ⎧( ) ⎨ j x j−i x i , i≤ j 0 1 Bi j = i ⎩ 0, i > j i = 0, 1, ..., n, j = 0, 1, ..., n ⎧( ) ⎨ i y i− j y j , i≥ j Ci j = j 0 1 ⎩ 0, i < j

(7.19)

(7.20)

i = 0, 1, ..., m, j = 0, 1, ..., m The new coefficient matrix D can be obtained from the transformation matrices B and C with the original coefficient matrix A: D = BAC

(7.21)

Therefore, the affine form of function f (x, y) can be expressed by the following matrix calculation form: ) ( ∧ ∧ ∧ ∧ ∧ ∧ y = X D Y = X(BAC) Y f x, (7.22) Through the above modified matrix, the binary polynomial with uncertain variables can be transformed into the affine form, after which the calculation accuracy and speed can be improved. The output of photovoltaic system (PV) is mainly affected by solar radiation [27], and within a certain period, the solar intensity can be approximately regarded as a Beta distribution [28], and the PV output can be modeled as: PP V = I Sη P V f (I ) =

) ( ) ( I b−1 I a−1 |(a + b) 1− |(a)|(b) Imax Imax

(7.23)

(7.24)

7.3 Models for DG Output Uncertainty and Carbon Emission Reduction

123

where I is the solar radiation intensity, S is the solar panel area, and η P V is the photoelectric conversion efficiency; Imax is the maximum solar radiation intensity, a and b are the parameters of the Beta distribution. The uncertainty of wind turbine (WT) outputs is mainly caused by the variation of wind speed. The mathematical model of WT output can be given as [29]:

PW T =

⎧ ⎪ ⎨ ⎪ ⎩

0, v3 −v3 Pra v3 −vci3 ra ci

Pra ,

0 ≤ v < vci or v > vco , vci ≤ v < vra

(7.25)

vra ≤ v < vco

where vci , vra , and vco are the cut-in, rated, and cut-out wind speeds, respectively; v is the actual wind speed, and Pra is the rated power of WT. The short-term wind speed follows a two-parameter Weibull distribution [29], whose probability density function can be expressed as: f (v) =

( )( ) | | v k−1 −( vc )k k e c c

(7.26)

where c and k are shape and scale parameters, respectively; t is the time variable. 3. DG Output Model in the Matrix Affine Form When the wind speed meets the conditions of vci ≤ v ≤ vra , , according to (7.22) and (7.25), the DG output model of IES can be expressed as: PDG = PW T + PP V =

vci3 Pra 3 v − + I Sη P V (vci ≤ v ≤ vra ) 3 − v3 3 − v3 vra vra ci ci

(7.27)

= k1 v 3 + k2 I + a v3

ra ci where k1 = v3 P−v . To transform the binary 3 , k 2 = Sη P V , and a = − 3 vra −vci3 ra ci polynomial into the affine form with the transformation matrix, we have: ⎤ ⎡ ⎤ ⎡ 1 v0 v02 v03 a k2 | | 2 ⎢ ⎥ ⎢0 0⎥ ⎥, B = ⎢ 0 v1 2v0 v1 3v0 v1 ⎥, C = 1 0 , A=⎢ ⎣ 0 0 v2 3v0 v2 ⎦ ⎣0 0⎦ I0 I1 1 1 0 0 0 v13 k1 0 where I max and I min ( ) ∧ ( ) ∧ vra + vci 2 3 2 3 T , V = 1, εv , εv , εv , I = 1, ε I , ε I , ε I , v0 = 2 Imax + Imin Imax − Imin vra − vci , I0 = , and I1 = , v1 = 2 2 2 are taken from the variation range of local solar radiation intensity. The range of εv and ε I is determined by the weather of the day and the northern hemisphere polar vortex area index during the same period. The corresponding relationship between

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7 Multiple Equipment Planning for Integrated Energy System

Table 7.1 Relationship between value range of ε I and meteorological conditions. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Range of ε I

Weather Rain or snow

[−1.0, −0.7]

Overcast

[−0.7, −0.5]

Overcast to cloudy

[−0.5, 0]

Cloudy

[0, 0.5]

Cloudy to clear

[0.5, 0.7]

Clear

[0.7, 1.0]

Table 7.2 Relationship between value range of εv and meteorological conditions. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Polar vortex area index of the Northern hemisphere

Range of εv

[650, 670]

[−1.0, −0.55]

[670, 690]

[−0.55, −0.2]

[690, 715]

[−0.2, 0.2]

[715, 730]

[0.2, 0.7]

[730, 750]

[0.7, 1.0]

the range of ε I and εv , and the meteorological conditions can be found in Tables 7.1 and 7.2, respectively. Therefore, the DG uncertainty model based on matrix form affine model can be obtained as follows: ∧

∧

P DG = V(BAC) I

(7.28)

) ( ∧ Judge the data in the V = 1, εv , εv2 , εv3 , and transform the data that does not meet the condition vci ≤ v ≤ vra reasonably to ensure the correctness of the matrix form affine transformation in (7.28).

7.3.2 Charging Cost Model of Carbon Emissions On the cost of carbon emission control, the effect of DG integration and P2G operation in IES on reducing carbon emission can be expressed as, E DG =

ζgen PDG ηgen

E P2G = ζ P2G PP2G

(7.29) (7.30)

7.3 Models for DG Output Uncertainty and Carbon Emission Reduction

125

where E DG and E P2G are the reductions of carbon emission of DG integration and P2G operation, respectively; ζgen and ζ P2G are the carbon emission and carbon capture coefficients of traditional generators and P2G, respectively; ηgen is the generation efficiency of traditional generators. In this paper, in order to calculate the carbon emissions reduced by DG, we assume that the electricity generated by DG is provided by traditional generators, and calculate the carbon emissions of traditional generators according to the electricity generated, which is the carbon emissions reduced by DG. To accurately quantify the cost of carbon emissions and reduce carbon emissions, we set a step-by-step carbon trading price that varies according to different carbon emissions over three intervals. With the increase of carbon emissions, the carbon trading price is also increased to achieve the purpose of reducing carbon emissions. This paper discusses the three stages of carbon trading price step by step. Case 1: The lowest carbon trading price will be applied when the carbon emissions are below the allocated minimum allowable emissions. Case 2: When carbon emissions are above the minimum allowable emissions and below the maximum allowable emissions, a fixed carbon trading price will be adopted. Case 3: A dynamic carbon trading price will be used when carbon emissions are higher than the maximum allowable emissions. To sum up, the charging cost model of carbon emission can be expressed as,

Ccar =

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

PL Er eal

Er eal ≤ E L1

PF (Er eal − E L1 ) + PL E L1 , E L1 ≤ Er eal ≤ E L2 ⎪ ⎪ ⎪ Er eal ⎪ −1 ⎪ ⎪ P (1 + αe E L2 )(Er eal − E L2 ) ⎪ Er eal ≥ E L2 ⎩ D +PF (E L2 − E L1 ) + PL E L1

(7.31)

E real = E C O2 − E DG − E P2G

(7.32)

where PL , PF , and PD are the lowest carbon trading price, fixed carbon trading price and initial value of dynamic carbon trading price, respectively; E L1 and E L2 are the minimum and maximum allowable emissions, respectively; α is the adjustable parameter; Er eal is the actual carbon emissions, E C O2 is the difference between actual carbon emissions and the reduction in carbon emissions by DG integration and P2G operation.

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7 Multiple Equipment Planning for Integrated Energy System

7.4 Optimal Planning Model of IES Considering Carbon Emissions and DG Uncertainty Based on the coupling relationship between multi-energies formulated in Sect. 7.2 and the proposed models of DG uncertainty and carbon emission reduction in Sect. 7.3, this section establishes an optimal planning model considering various constraints. After that, the IPSO used to solve the model will also be presented.

7.4.1 Objective Function The main purpose of the optimal planning of the IES system is to minimize the total cost while ensuring all the constraints of the IES system. Therefore, the objective function of the optimal planning model is to minimize the total cost, including the investment cost, the operation cost, and the carbon emission cost, which can be expressed as: min F =

T E t=1

Cinv (t) =

( ) λt Cinv (t) + Cope (t) + Ccar (t) + Clack (t) E

Di Pi,t yt,i +

i∈yDG

+

E

⎛ E Cope (t) =

G j P j,t yt, j

j∈yG E

E

Cl Pl,t yt,l +

l∈yCC H P

8760 E

E

(7.33)

Di Pi,h,t +

⎜ i∈yDG ⎜ E ⎝ + h=1

E

G j P j,h,t

j∈yG E

Cl Pl,h,t +

l∈yCC H P

Clack (t) =

G Bm Pm,t yt,m

(7.34)

m∈yG B

E

G Bm Pm,h,t

⎞ ⎟ ⎟ ⎠

(7.35)

m∈yG B

T E 8760 E

Plack,h,t ylack− pun

(7.36)

t=1 h=1

λt =

1 (1 + τ )t−1

(7.37)

where Cinv (t), Cope (t), Ccar (t) and Clack (t) are the investment cost, the operation cost, the carbon emission cost, and the load power shortage penalty cost, respectively; T is the planning horizon (in the number of years); λt is the coefficient of present value. Di , G j , Cl and G Bm are the investment cost per capacity of DG, traditional generator, CCHP and gas boiler, respectively; Pi,t , P j,t , Pl,t and Pm,t are the installation capacity of DG i, traditional generator j, CCHP l and gas boiler m

7.4 Optimal Planning Model of IES Considering Carbon Emissions and DG …

127

in the year t, respectively; yt,i , yt, j , yt, j , and yt,m are the binary variables indicating whether to install DG, traditional generator, CCHP gas boiler in the year t, respectively; ylack− pun is penalty cost of unit load power shortage; Oi , O j , Ol and Om are the operation cost per capacity of capacity of DG i, traditional generator j, CCHP l and gas boiler m, respectively; y DG , yG E , yCC H P and yG B are the set of DG, traditional generator, CCHP and gas boiler, respectively.

7.4.2 Constraints To ensure the secure operations of the IES system with the minimum total planning cost, it is necessary to fully consider the constraints. The constraints of the optimal planning model mainly include four parts: investment constraints, electricity input/output constraints, operation constraints, energy coupling constraints. 1. Inestment Constraints ya,t ≤ ya,t+1 ∀a ∈ y DG , yG E , yCC H P , yG B , t < T

(7.38)

ya,t = 0 ∀a ∈ y DG , yG E , yCC H P , yG B , t < Ta,com

(7.39)

where ya,t are the binary variables indicating whether to install the candidate equipment in the year t; Ta,com is the first commission year of each candidate equipment. ya,t = 0 indicates that the equipment has not been installed, while ya,t = 1 means the equipment has been invested and will exist in the remaining planning horizon [12]. In addition, the investment and installation of equipment will only be carried out after the minimum commission year. 2. Electricity Input/Output Constraints min max Pgen,i ≤ Pgen,i ≤ Pgen,i

(7.40)

min max PDG,i ≤ PDG,i ≤ PDG,i

(7.41)

min max PCC H P,i ≤ PCC H P,i ≤ PCC H P,i

(7.42)

min max PP2G,i ≤ PP2G,i ≤ PP2G,i

(7.43)

min max where Pgen,i , Pgen,i and Pgen,i are the lower limit, upper limit and actual power min max , PDG,i and PDG,i are the lower output of traditional generator i, respectively; PDG,i min max limit, upper limit and actual power output of DG i, respectively; PCC H P,i , PCC H P,i and PCC H P,i are the lower limit, upper limit and actual power output of CCHP i,

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7 Multiple Equipment Planning for Integrated Energy System

min max respectively; PP2G,i , PP2G,i and PP2G,i are the lower limit, upper limit and actual power output of P2G i, respectively.

3. Operation Constraints Pgen + PDG + /PCC H P − PP2G = PLoad − Plack

(7.44)

HT her + HG B + /HCC H P = HLoad

(7.45)

CCC H P = C Load

(7.46)

G N G + G P2G − G CC H P − G G B = G Load

(7.47)

where Pgen and PDG are the total electric power output by traditional generators and DG, respectively; /PCC H P is the difference between the input and output electric power of all the CCHP units; PP2G is the total electric power input to all the P2G units; PLoad is the total electric load; Plack is the load power shortage; HT her and HG B are the total heat generated by all the traditional generators and gas boilers, respectively; /HCC H P is the difference between the total input and output heating power of all the CCHP units; HLoad is the total heat load; CCC H P is the total cooling power generated by all the CCHP units; C Load is the total cooling load and power loss, respectively; G N G and G P2G are the total natural gas input by all the natural gas plants and P2G units, respectively; G CC H P and G G B are the total natural gas flowing into CCHP units and gas boilers, respectively; G Load is the total natural gas load. 3. Energies Coupling Constraints The energy conversion process depends on the coupling constraints. The coupling relationship between electricity, heating and natural gas has been introduced in (7.1)– (7.6).

7.5 Solution Methodology The proposed optimization model of IES is a mixed- integer nonlinear programming problem (MINLP). We use Particle swarm optimization (PSO), a widely used intelligent algorithm to solve the MINLP. It does not need to analyze the objective function and constraints, but it is often unable to obtain the optimal solution because of the disadvantage of premature convergence and trapping in local minima easily. Moreover, IES optimal planning in this paper is a typical high-dimensional problem with multiple decision variables, which also increases the difficulty of PSO to solve the optimal solution.

7.5 Solution Methodology

129

To better solve the proposed optimal planning problem, this paper proposes an improved quantum particle swarm optimization algorithm to solve this problem. Quantum particle swarm optimization (QPSO) is a probabilistic particle swarm optimization (PSO) algorithm enhanced from the classical particle swarm optimization (PSO). In QPSO, each particle is attracted by a potential well gravitational field centered on the personal best value when it moves and getting close. Because the particle is in the quantum bound state, the velocity and position appear with a certain probability in the process of motion, and there is no definite trajectory, and there is no definite trajectory when the particles move, so the particles can explore in the whole solution space to find the global optimal solution, which makes a better global search ability of QPSO algorithm than that of traditional PSO algorithm. The QPSO algorithm has the following steps: 1. Initialization of particle population: The particle population with the size of S is generated randomly. 2. Calculate the personal optimal average position: m pbest =

S 1E plocal−i S i=1

(7.48)

In (7.48), m pbest represents the individual optimal average position; plocal−i represents the individual optimal position of the particle in this iteration. 3. Particle position update: ( ) | | 1 | | pi (t + 1) = Pi ± β m pbest − pi (t) · ln μ

(7.49)

where pi (t) and pi (t + 1) represent the positions of particles in tth and (t + 1)th iterations, respectively; μ is a random number on (0, 1); in the formula, the probabilities of taking the + and the − are both 0.5:, when μ > 0.5, the positive sign is taken while when μ ≤ 0.5 the negative will be taken. Pi is used to update the particle position and β is the contraction expansion factor, which are expressed as follows: Pi = ϕ · plocal−i + (1 − ϕ) pglobal ( β = 0.5 + 0.5 ×

Tmax − t Tmax

(7.50)

) (7.51)

where pglobal is the global optimal position; ϕ is the learning coefficient in [0, 1]. Tmax is the maximum number of iterations and t is the current number of iterations. The optimization problem in this paper is an integer nonlinear programming with constraints, so after finding the updated position of particles, it is rounded and its boundary is limited to ensure that the particle position is an integer.

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7 Multiple Equipment Planning for Integrated Energy System

4. Iterative Solution: After the position update, it is substituted into the simulation model to get the fitness value. If the calculation process violates the constraints, stop this iteration and proceed to the next iteration. The above process is repeated iteratively until the maximum number of iterations is reached, and the global optimal is the optimization result. To improve the diversity of particles, this paper has proposed several improvements to QPSO. The individual optimal particles are divided into upper, middle, and lower layers according to the fitness order, where the ratio of particle number is 1:3:6. The optimal position of the upper layer particle guides the position update of the upper, middle, and lower layers; the optimal position of the middle layer guides the position update of the middle and lower layers, while the optimal position of the lower layer only guides lower layer. The optimal position of the upper particle is the global optimal position. The location with the best fitness in each layer participates in the calculation of Pi with the global optimal location. The specific procedure to update the position of each layer is as follows: Upper layer: Pi = ϕ · plocal−i + (1 − ϕ) pglobal

(7.52)

) ( Pi = ϕ · plocal−i + (1 − ϕ) k1−2 pglobal + k2−2 pglobal−2

(7.53)

Middle layer:

Lower layer: ( ) Pi = ϕ · plocal−i + (1 − ϕ) k1−3 pglobal + k2−3 pglobal−2 + k3−3 pglobal−3 (7.54) where k1−2 and k2−2 represent the influence coefficients of the upper and middle layers, respectively, on the updating of the optimal corresponding particle position of the middle layer. Similarly, k1−3 , k2−3 , and k3−3 are the influence coefficients of the upper, middle, and lower layers on the updating of the optimal corresponding particle position of the lower layer, respectively; pglobal−2 and pglobal−3 represent the personal optimal in the middle and lower layers, respectively. After calculating the fitness value, the optimal position of the individual is updated; the upper, middle, and lower layers are updated at the same time. The above operation can prevent the global optimization from dominating the position update too much and reduce the diversity of particles, which makes the algorithm fall into local optimization and further improves the global search ability of QPSO. The solution is shown in Fig. 7.2.

7.6 Case Study Fig. 7.2 The flowchart of the IQPSO algorithm. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

131 Start Input the network data and form network topologies Obtaining large scale weather

Calculate the carbon emissions reduced by DG and P2G operation

Establish the output models of DG

Obtain the net carbon emissions involved in the cost calculation

Convert the output mode of DG to the input of load

Calculate the cost of carbon emissions at all levels

Input various data, initialize IQPSO,determine the Gbest,Pbest Update the position of each particle Compare and update Gbest,Pbest Whether to reach the maximum iteration?

No

Yes End

7.6 Case Study 7.6.1 Test System Introduction and Parameters Setting To better verify the proposed method, the IEEE 33-bus IES network established in is improved, as shown in Fig. 7.3. The exciting IEEE 33-nodes IES network comprises 5 traditional generators, 3 natural gas suppliers, 4 gas boilers, 1 power turbine, and 1 photovoltaic power generation system. During the planning period, 4 traditional generators, 3 gas boilers, 4 CCHP units, 5 P2G stations and 2 distributed generators are the candidate equipment, the specific parameter of the equipment are shown in Tables 7.3, 7.4, 7.5, 7.6, and 7.7 [25]. In this paper, the planning horizon is set to 8 years, and four cases are analyzed and compared to illustrate the effectiveness of the proposed planning method. The parameters are as follows in Table 7.8. The noise unit values of wind speed and solar radiation intensity are selected according to the annual meteorological forecast and referring to Tables 7.1 and 7.2. The four cases are as are shown in Tables 7.9, the specific description is as follows:

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7 Multiple Equipment Planning for Integrated Energy System

Fig. 7.3 The topology of 14-bus IES. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

CCHP2 19

G8 20

P2G3 21 22

GB2 G1 G2

P2G2 GB3

P2G1 G3

G4

G7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 18 GS1 GB1

GB5 WT

GB6 G6 PV GS3 CCHP1 GS2 G5 GB4 P2G4

26 27 2829 30 31 32 33 CCHP3 G9 CCHP4

GB7 23

24

25

Table 7.3 Parameter of candidate traditional generators. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Number Node Capacity (MW) Unit investment price ($ 103 / Unit operation price ($ 103 / MW) MW) G6

9

35

900

0.15

G7

16

30

900

0.15

G8

20

40

900

0.15

G9

24

30

900

0.15

Table 7.4 Parameter of candidate gas boilers. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Number Node Capacity (MW) Unit investment price ($ 103 / Unit operation price ($ 103 / MW) MW) GB5

4

25

800

0.032

GB6

12

30

800

0.032

GB7

23

30

800

0.032

Table 7.5 Parameter of candidate CCHP units. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Number Node Capacity (MW) Unit investment price ($ 103 / Unit operation price ($ 103 / MW) MW) CCHP1

14

25

600

0.085

CCHP2

19

30

600

0.085

CCHP3

24

30

600

0.085

CCHP4

29

25

600

0.085

7.6 Case Study

133

Table 7.6 Parameter of candidate P2G stations. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Number Node Capacity (MW) Unit investment price ($ 103 / Unit operation price ($ 103 / MW) MW) P2G1

5

15

500

0.07

P2G2

11

15

500

0.07

P2G3

21

25

500

0.07

P2G4

32

25

500

0.07

Table 7.7 Parameter of candidate DGs. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Number

Node

Capacity (MW)

Unit investment price ($ 103 / MW)

Unit operation price ($ 103 / MW)

DG1 (WT)

21

30

600

0.08

DG2 (PV)

33

25

800

0.09

Case 1: Coordinated planning the electricity, natural gas and CCHP system, without considering DG schema and carbon emission. Case 2: Coordinated planning the electricity, natural gas, DG and CCHP system, with a fixed charging cost for carbon emissions. Case 3: Coordinated planning the electricity, natural gas and CCHP system, with a tiered charging cost for carbon emissions and without considering DG schema. Case 4: Coordinated Planning the electricity, natural gas and CCHP system by the methods presented in this paper.

7.6.2 Results and Discussion The optimal planning results and costs for different cases are shown in Tables 7.10 and 7.11. In Table 7.10, X (x, y) represents the x-th candidate device X installed at y-th year. From Table 7.8, we can see that Case 4 has fewer traditional generator units than Cases 1, 2, and 3, as the tiered charging cost of carbon emissions proposed in this paper effectively reduced the emissions. However, lower carbon emissions also mean that Case 4 has more DGs to make up for the lost electricity due to lower carbon emissions. At the same time, the number of gas boiler and P2G in the Case 4 is relatively small due to the increase in the number of DG units. Tables 7.10 and 7.11 show the optimal planning scheme and its corresponding costs (including investment cost, operation cost, carbon emission cost, penalty cost for load loss and total cost) under different conditions. Compared with Case 1 and

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7 Multiple Equipment Planning for Integrated Energy System

Table 7.8 Parameter of IES. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Parameters

Symbol and unit

Value

Peak value of power load

Pload−max (MW)

178.8

Average value of power load

Pload−avr (MW)

88.4

Annual growth rate of power load

θ1

7%

Peak value of natural gas load

G load−max (m3)

88.5

Valley value of natural gas load

G load−min (m3)

10

Annual growth rate of gas load

θ2

3%

Peak value of heat load

Hload−max (MW)

120.3

Valley value of heat load

Hload−min (MW)

10

Peak value of cooling load demand

Cload−max (MW)

76.9

Average value of cooling load demand

Cload−avr (MW)

36.4

Carbon emission coefficients of traditional generators

ζgen (kg/kw/h)

0.997

Carbon capture coefficients of P2G

ζ P2G (kg/kw/h)

1.964

Generation efficiency of traditional generators

ηgen

30%

Penalty cost of unit load power shortage

ylack− pun ($/kw/h)

1.64

Minimum allowable emissions

E L1 (t)

50,000

Maximum allowable emissions

E L2 (t)

60,000

Lowest carbon trading price

PL ($/t)

4320

Fixed carbon trading price

PF ($/t)

5560

Initial value of dynamic carbon trading price

PD ($/t)

6800

Adjustable parameter

α

0.06

Coefficient of present value

λt

5%

Depreciation coefficient

τ

3.33%

Planning horizon

T (year)

8

Maximum number of iterations

Tmax

300

Population size of particles

S

30

Influence coefficients of the upper layer to middle layer

k1−2

2/3

Influence coefficients of the middle layer to middle layer

k2−2

1/3

Influence coefficients of the upper layer to lower layer

k1−3

3/5

Influence coefficients of the middle layer to lower layer

k2−3

3/10

Influence coefficients of the lower layer to lower layer

k3−3

1/10

Learning coefficient

ϕ

0.5

Cut-in wind speeds

vci (m/s)

5

Rated wind speeds

vra (m/s)

16

Cut-out wind speeds

vco (m/s)

22

Shape parameter

c

9.86

Scale parameter

k

1.56

Maximum solar radiation intensity

Imax (W/sr)

2.9 (continued)

7.6 Case Study

135

Table 7.8 (continued) Parameters

Symbol and unit

Value

Minimum solar radiation intensity

Imin (W/sr)

1.9

Parameter of the Beta distribution

a

7.5

Parameter of the Beta distribution

b

16.3

Table 7.9 Case features. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Case

DG schema

Carbon emission charge mode

Case 1

Without consideration

Without consideration

Case 2

Considered

Fixed charging cost

Case 3

Without consideration

Tiered dynamic charging cost

Case 4

Considered

Tiered dynamic charging cost

Table 7.10 Optimal planning of different cases. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Case

Case 1

Generators

G(9, 1) G(6, 4) G(7, G(7, 1) G(6, 3) G(8, G(6, 1) G(7, 4) G(9, G(8, 1) G(6, 6) G(8, 7) 7) 5) 7)

Case 2

Case 3

Gas Boilers

GB(5, 2) GB(7, 4) GB(6, 7)

P2G

GB(6, 2) GB(7, 6)

Case 4

GB(5, 1) GB(7, 5)

GB(7, 6)

P2G(1, 1) P2G(3, 4) P2G(1, 1) P2G(2, P2G(4, 5) P2G(4, 6) 5) P2G(3, 7)

P2G(4, 1) P2G(2, 3) P2G(1, 6)

P2G(2, 2) P2G(4, 7)

CCHP

CCHP(1, 3) CCHP(2, 5) CCHP(3, 7)

CCHP(3, 2) CCHP(1, 6)

CCHP(1, 4) CCHP(3, 7)

CCHP(2, 3) CCHP(1, 5)

DG

/

DG(1, 4)

/

DG(1, 2) DG(2, 5)

Table 7.11 Comparison cost of different cases. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Case

Total Cost ($, × 107 )

Investment Cost ($, × 107 )

Operation Cost ($, × 107 )

Carbon Emission Cost ($, × 107 )

Carbon Emission (t)

Load Power Shortage Penalty Cost ($, × 107 )

Case 1

195.29

28.05

156.78

\

91,651

10.46

Case 2

208.22

23.60

134.55

37.82

68,022

12.25

Case 3

187.70

19.45

110.75

45.61

84,873

11.89

Case 4

170.01

18.75

109.65

29.17

62,781

12.44

136

7 Multiple Equipment Planning for Integrated Energy System

Case 2, the total cost of Case 4 decreased by 12.95% and 18.36% respectively. This is mainly because compared with the fixed carbon emission cost, the tiered dynamic carbon emission charging model proposed in this paper can better reduce the capacity of traditional generating units and reduce the operation cost and carbon emission while ensuring load supply reliability. Case 1 does not consider DG and carbon emission cost, which makes the traditional generator set the largest installed capacity and maintains the best load supply reliability. However, due to the lack of carbon emission cost, it is difficult to guide the optimization algorithm to reduce the installed capacity of traditional generator set, which makes the operation cost the highest and the carbon emission is huge. In Case 2, the fixed carbon emission charging model is adopted, and the capacity of reducing carbon emission is insufficient. Therefore, more traditional generators are installed, and the operating cost also rises. The total investment cost of Case 4 is 9.43% lower than that of Case 3. The addition of DG reduces the carbon emission cost and operation cost. In addition, although DG is not considered in Case 3, due to the layered dynamic carbon emission model, the carbon emission is reduced by 7.4% and the carbon emission cost is reduced by 36.04% compared with Case 1, and the operating cost is not significantly improved, which indirectly proves the effectiveness of the proposed method for reducing the total cost and carbon emission.

7.6.3 Comparison of Optimization Algorithms To verify the effectiveness of the proposed IQPSO algorithm, in Case 4, it is compared with PSO and QPSO. Figure 7.4 shows the relationship between the global optimal value and the number of iterations when PSO, QPSO and IQPSO solve the IES optimization programming model.

Fig. 7.4 Comparison of algorithm results. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

7.6 Case Study

137

As shown in Fig. 7.4, QPSO has the fastest convergence, but because IQPSO adopts the hierarchical decision-making and increases the diversity of particles, it shows the best global search ability. Compared with the traditional planning method using wind and solar forecast data, this proposed DG uncertainty model based on matrix form affine arithmetic can reduce the impact of DG output uncertainty on IES planning and improve the ability of the system to adapt in a variety of wind and solar scenarios. Figures 7.5 and 7.6 show the typical daily forecast data of wind speed and solar radiation intensity respectively in 8 years. Table 7.12 shows the optimized planning scheme with wind and solar radiation forecast data planning method in Case 4 scenario. Table 7.13 shows the cost of this planning scheme. Fig. 7.5 Typical daily wind speed. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

Fig. 7.6 Typical daily solar radiation intensity. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

Table 7.12 Optimal planning scheme based on wind and solar forecast data. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Generators

Gas Boilers

P2G

CCHP

DG

G(2, 2) G(3, 1)

GB(2, 3)GB(1, 5)

P2G(1, 2) P2G(3, 7) P2G(2, 3)

CCHP(2, 6) CCHP(1, 2)

DG(1, 3) DG(2, 1)

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7 Multiple Equipment Planning for Integrated Energy System

Table 7.13 Cost of planning scheme using wind and solar forecast data. Reprinted from Ref. [34], copyright 2023, with permission from IEEE Total cost ($, × 107 )

Investment cost ($, ×107 )

Operation cost ($, ×107 )

Carbon emission cost ($, ×107 )

Load power shortage penalty cost ($, ×107 )

182.42

20.10

119.94

29.79

12.59

To verify the effectiveness of the proposed method to reduce the impact of distributed generation uncertainty on the planning scheme, Monte Carlo simulation method is used to compare the proposed planning method and the traditional wind and solar forecasting data planning method in Case 4. The number of simulations is 10000, and the average of the total cost of every 100 simulations is taken as the comparison data. The characteristic parameters are shown in Sect. 7.6.1, and the scenery data are generated according to the (7.23) and (7.25). Figure 7.7 show the comparison of operation effects of different planning schemes under different DG output models. It can be seen from Fig. 7.7 that the traditional planning method has lower total investment, load power shortage penalty and carbon emission costs in some specific scenarios, but the overall operation effect is not as good as the method proposed in this paper, which shows better adaptability of the proposed method in terms of total cost and environmental benefits.

Fig. 7.7 Comparison of carbon emissions of different DG models. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

7.6 Case Study

139

Fig. 7.8 Sensitivity analysis of adjustment parameter. Reprinted from Ref. [34], copyright 2023, with permission from IEEE

7.6.4 Sensitivity Analysis To obtain the optimal planning cost by the method proposed in this paper, different adjustment parameters α are studied. We study the change of planning cost with different values of α, as shown in Fig. 7.8. As can be seen from Fig. 7.8, when α is between 0.01 and 0.04, the total cost is rising. This is because the cost after exceeding the maximum allowable emissions has less impact on the overall planning horizon. When α is between 0.04 and 0.06, the overall cost is declining. This is because the rise of α has a significant constraint effect on the reduction of carbon emission cost. The cost of carbon emission plays a greater role in the scope of master plan, which can have a positive impact on reducing the total cost. At this time, the dependence of the system on traditional generators is reduced, the operation cost is reduced, the carbon emission cost is reduced, and the investment cost is reduced. With further increase of α, the cost of carbon emissions has become an important factor with a negative impact on the total planning cost. This is because the value of α is too large to limit carbon emissions, and the cost of carbon emissions increases. The dependence of the system on traditional generators will thus further decrease—so does the operating cost, promoting the expansion of P2G and DG. The investment cost thus increases significantly. Therefore, in this paper, we choose α = 0.06 for simulation analysis, as shown in Sect. 7.4.2. For different IES structure, wind and solar resources and load demand, the characteristic curve of α will also vary. The main reason is that the change of source α layout will have a key impact on the proportion of carbon emission cost in the total investment of the system. With the progress of science and technology and the growing public awareness of environmental protection, we can gradually increase the value of α to reduce carbon emissions.

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7 Multiple Equipment Planning for Integrated Energy System

7.7 Conclusion In this paper, an optimal planning approach for integrated energy system considering carbon emissions and uncertainty of DG is proposed to determine the optimal time and capacity of traditional generator units, gas boilers, P2G, CCHP and DG. The matrix form of affine number method is used to further reduce the influence of DG uncertainty. Considering the environmental pollution caused by high carbon emissions, a tiered dynamic charging cost model is proposed to reduce carbon emissions. Finally, an IQPSO is used to obtain the optimal planning scheme of IES. The simulation results show that compared with the traditional methods, the proposed planning method considering carbon emission and DG uncertainty can not only reduce the total cost, but also reduce the carbon emission cost. And through the sensitivity analysis of the adjustment parameter, the optimal parameter can be obtained. Overall, the method proposed in this paper can effectively perform optimal planning of IES.

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Chapter 8

Collaborative Operation Between Power Network and Hydrogen Fueling Stations with Peer-to-Peer Energy Trading

8.1 Introduction As a highly promising alternative to traditional vehicles within urban transportation systems, electric vehicles (EVs) have experienced rapid development primarily due to their minimal environmental impact [1–4]. Remarkably, the International Energy Agency’s data reveals that the global number of EVs surpassed 10 million by the year 2020 [5]. While EVs offer the enticing prospect of zero vehicle emissions, they do encounter certain challenges such as extended recharging durations and limited driving range [6]. However, there is a silver lining in the form of Hydrogen Fueling Electric Vehicles (H2EVs), which have witnessed a surge in popularity in recent years and are considered a viable solution for addressing the drawbacks of conventional EVs [7]. The power of H2EVs is generated by Fuel Cells (FCs), resulting in emissions that consist solely of water [8]. Moreover, H2EVs boast additional advantages, including an extensive driving range and a remarkably short refueling time [9]. However, the myriad advantages of the H2EV would be greatly diminished if the hydrogen used to power it were produced using electricity derived from fossil-fueled energy sources. This is primarily due to the low efficiency of converting energy from fossil fuels into electricity. Consequently, it is recommended that hydrogen be produced through electrolysis, a process powered by renewable energy obtained from the power network. By adopting this approach, the mass refueling of H2EVs at hydrogen fueling stations (HFSs) introduces a significant interaction between two interconnected physical systems: the power network (PN) and the transportation network (TN). This interaction arises because the charging behavior of EVs within the TN directly impacts the power distribution within the PN. Therefore, it is of utmost importance to establish an efficient and seamless interaction between HFSs and the PN, taking into account the operational constraints of both systems. Furthermore, with the inherent uncertainty associated with renewable energy sources, the optimal coordination of HFSs and the PN while satisfying the energy demands of H2EVs becomes an even more intricate and multifaceted challenge. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_8

143

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Therefore, in order to foster and propel the advancement of H2EVs, it becomes imperative to delve into a comprehensive investigation of the synergistic operation between PN and HFSs, all while ensuring the seamless integration of the coupled power-traffic system within the operational constraints. By undertaking this crucial endeavor, we can unravel the intricate dynamics and interdependencies between these entities, ultimately paving the way for an optimized and harmonious collaboration that propels the widespread adoption and efficient functioning of H2EVs. In the current landscape, the exploration of the interaction between HFSs and the coupled power-traffic system remains a scarcely addressed area, to the best of the authors’ knowledge. Nevertheless, drawing an analogy, existing literature predominantly concentrates on the collaboration between EVs, EVCSs, and PN, which can be categorized into two distinct realms. The first category revolves around the pursuit of profit maximization for all stakeholders involved. For instance, in Ref. [10], a win– win strategy is put forth, wherein EV users and the PN strive to achieve improved economic gains and enhanced stability, respectively. Considering the integration of renewable energy sources, Ref. [11] proposes an optimal operational strategy for EVs, effectively reducing energy costs for EV owners and mitigating power deviations within the PN. Reference [12], on the other hand, introduces a collaborative scheduling model aimed at enhancing the cost-effectiveness of EV charging power while facilitating the absorption of wind power within the PN. Meanwhile, Ref. [13] presents an energy management method based on a supply function game model, highlighting the cooperative nature between EVCSs and the PN, ultimately enhancing the utilities of EVCSs. To incentivize EVs to actively participate in such collaborations, Ref. [14] introduces an innovative pricing policy that ensures the PN’s profitability while motivating EV users to engage in the cooperative efforts. Lastly, Ref. [15] proposes an interactive operational model between EVs and the PN from an energy and reserve perspective, seeking to optimize the benefits for both EVs and the PN. The second category of research endeavors is dedicated to harnessing the flexibility of EV loads to provide ancillary services and bolster the operations of PN. An exemplary instance of this is found in Ref. [16], which introduces a game-theoretic approach aimed at incentivizing EVs to contribute frequency regulation services to the PN. Reference [17] explores the utilization of EVs to offer ancillary services in the form of reserves, taking into account the operational constraints of the PN. Furthermore, Ref. [18] highlights the untapped potential of EVCSs, emphasizing their capacity to leverage energy storage for the provision of ancillary services to the PN. In pursuit of secondary frequency regulation for the PN, Ref. [19] proposes a power management scheme that capitalizes on the active participation of EVs. Similarly, Ref. [20] puts forth a collaborative operational method for EVCSs and the PN, taking into consideration the comprehensive integration of energy and reserve regulation. Moreover, Ref. [21] pioneers the development of an effective real-time energy management strategy for EVCSs, incorporating photovoltaic (PV) assistance to facilitate the seamless participation of EVCSs in providing ancillary services to the PN.

8.1 Introduction

145

It is crucial to acknowledge that the widespread adoption of EVs on a large scale would undoubtedly have significant ramifications for both PN and TN, as evidenced by the increasing prevalence of EVs [22, 23]. Therefore, it becomes imperative to consider the spatial distribution of EV traffic flows across the TN while simultaneously optimizing the charging and discharging schedules of EVs. A notable example can be found in Ref. [24], which explores the influence of road congestion on route selection and characterizes the traffic flow pattern within a steady state obtained through the Wardrop user equilibrium. In Ref. [25], a comprehensive analysis of the collaborative operation between the electrified TN and PN is conducted, taking into account factors such as travel speed and the charge/discharge behavior of EVs. Reference [26] introduces an optimization-based multi-period traffic assignment model that captures the dynamic nature of vehicular flows, considering rational drivers with varying travel demands. Additionally, Ref. [27] focuses on optimizing route selection and charge/discharge scheduling to enhance the overall economic profitability of EVs. By integrating these considerations, we can effectively navigate the challenges and capitalize on the opportunities presented by the coexistence of EVs within the PN and TN. With the rapid advancement of hydrogen technology, hydrogen-powered vehicles, particularly H2EVs, have emerged as a promising solution for achieving emissionsfree transportation [28]. As a result, investigating the operational dynamics between hydrogen-powered vehicles and PN holds significant value and warrants further exploration. For example, Ref. [29] introduces an energy sharing model that encompasses the PN and HFSs, aiming to maximize the overall social welfare through the exchange of electricity and hydrogen. However, it is important to note that this model does not take into account the intricacies of traffic flow. Additionally, in the context of supplying energy for H2EVs, Ref. [30] presents an optimal scheduling framework for distributed HFSs to provide operating reserves (OR) to the electricity market. Regrettably, TN remains unconsidered in this particular model. Furthermore, Ref. [31] proposes an optimal operational strategy for an integrated electric power and hydrogen system, taking into consideration the operational constraints of the PN, TN, and the inherent uncertainty of stochastic renewable energy sources. By delving into these research avenues, we can gain valuable insights into the seamless coordination and optimization of hydrogen-powered vehicles within the PN, paving the way for a sustainable and efficient transportation ecosystem. However, the aforementioned works primarily rely on traditional centralized collaborative methods, which are plagued by several issues, including low efficiency and privacy concerns [32–34]. To address this challenge, P2P energy trading has emerged as a promising solution for enabling distributed and flexible control of energy among various participants [35]. For instance, Ref. [36] puts forward a P2P operational framework that facilitates energy trading between an EVCS and a business entity equipped with PV systems, aiming to optimize the benefits for all involved parties. In a similar vein, Ref. [37] introduces a novel P2P local electricity market model that seamlessly integrates PV power generation and the flexibility of loads. By considering both factors simultaneously, this model fosters a more efficient and sustainable energy exchange. Furthermore, ensuring a fair allocation of revenue

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8 Collaborative Operation Between Power Network and Hydrogen …

derived from P2P energy trading becomes essential to incentivize participants to engage in such transactions. Reference [38] explores the notion of fairness in profit allocation within a collaborative P2P energy market model, emphasizing the importance of equitable distribution. By embracing P2P energy trading and addressing the issue of fair revenue allocation, we can overcome the limitations of centralized approaches and unlock the potential for more efficient, secure, and participatory energy systems. It is evident that the existing body of literature has extensively explored the collaborative operations between PN and energy supplying facilities for vehicles, with a primary focus on EVCSs. However, in contrast to the comprehensive studies conducted on EVs, the research pertaining to the cooperation between the PN and HFSs remains relatively scarce. Nonetheless, recognizing the potential benefits of promoting the collaboration between the PN and HFSs, it becomes imperative to consider the interconnected nature of PN and TN through the utilization of HFSs. This is primarily due to the fact that HFSs rely on electricity from the PN to perform the electrolysis process, converting water into hydrogen. Subsequently, the produced hydrogen is stored within fueling stations equipped with storage facilities to meet the refueling demands of H2EVs within the TN. Thus, this interplay forms a coupled power-traffic system via hydrogen fueling stations, which serves the dual purpose of supplying power to end-users and fulfilling the refueling requirements of H2EVs. Moreover, in light of the evolving electricity market landscape, it is conceivable that different entities may operate various HFSs. Therefore, this paper takes into account the scenario where HFSs are affiliated with different corporations. To enhance operational efficiency, P2P trading mechanism emerges as an opportune avenue for HFSs to engage in energy transactions, potentially leading to increased profitability for these HFSs. By leveraging P2P trading, HFSs can seize the opportunity to optimize their energy exchange, thereby maximizing their overall financial gains. However, to the best of the authors’ knowledge, the investigation into the collaborative operation based on the coupled power-traffic system of HFSs remains unexplored. Firstly, delving into the intricate relationship between the PN, TN, and HFSs would pave the way for their simultaneous advancement. By thoroughly examining their impact on one another, we can drive optimal operations across the entire system. Secondly, there is considerable value in studying the efficient operation of HFSs and the coupled power-traffic system while taking into account both power and traffic constraints. This comprehensive approach holds the potential to minimize the overall operational costs of the system. Thirdly, the exploration of an internal P2P energy trading strategy among HFSs becomes crucial, particularly in meeting the energy demands of H2EVs. Embracing P2P energy trading has the potential to enhance the efficiency of collaborative operations, presenting an opportunity for HFSs to optimize their energy exchange within the network. Fourthly, it is imperative to design a fair allocation mechanism for collaborative revenue that considers the contributions of all participants. Such a mechanism would not only promote fairness but also fortify the successful application and adoption of collaborative operations. By addressing these aspects, we can unlock the full potential of the collaborative operation within

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147

the coupled power-traffic system, fostering greater efficiency, fairness, and success in the integration of HFSs into the overall energy landscape. To fulfill this objective, we embark on the following endeavors, which not only align with the overarching goals of this paper but also contribute significantly to the existing body of knowledge in this field. Through our research, we aim to make the following substantial contributions: 1. We establish an operation model for the coupled power-traffic system of HFSs that incorporates the dynamics of P2P energy trading. This model serves as a comprehensive framework to elucidate the intricate relationship between HFSs, the power flow of PN, and the traffic flow of TN, enabling a simultaneous analysis of their interdependencies. 2. Building upon the aforementioned model, we propose a collaborative operation framework that facilitates synergy between the PN and HFSs, while considering the constraints imposed by the coupled power-traffic system. This framework not only enables the provision of energy but also takes into account the supply of ancillary services. By optimizing the collaborative operations within this framework, the operational costs of the entire system can be significantly reduced. Moreover, this collaborative approach brings about mutual benefits for the PN, TN, and HFSs, fostering a more efficient and sustainable energy ecosystem. 3. In our quest to enhance the efficiency of collaborative operations, we introduce P2P energy trading among HFSs to meet the energy demands of H2EVs. This integration of P2P energy trading considers dynamic electricity prices and the energy stored within HFSs, ensuring a flexible and responsive energy supply system. By leveraging the advantages of P2P energy trading, we can optimize the allocation and utilization of available energy resources, further enhancing the overall efficiency and reliability of the collaborative operation. 4. To ensure a fair and equitable distribution of benefits, we introduce a revenue allocation mechanism based on the bilateral Shapley value. This mechanism is designed to allocate surplus in a manner that promotes fairness, incentivizes participation in collaborative operations, and encourages the sustainable growth of the energy ecosystem. Additionally, we provide a rigorous mathematical proof that demonstrates the collaborative benefits derived from considering P2P energy trading are no less than the profits obtained through independent operations, reinforcing the viability and attractiveness of collaborative endeavors.

8.2 Operation Model of HFSs Coupled Power-Traffic System Considering P2P Energy Trading As alluded to earlier, the coupled power-traffic system of HFSs materializes when we take into account the collaborative operation between PN and HFSs while adhering to the constraints imposed by TN. The intricate configuration of this interconnected system is vividly depicted in Fig. 8.1, where three principal components seamlessly converge: the PN, HFSs, and TN. Each component plays a pivotal role in enabling

148 (a)

8 Collaborative Operation Between Power Network and Hydrogen … (b)

H2 pump

(c)

H2 tank Electrolyzer

Fuel Cell PV

H2 pump

P2P energy trade Route 1

ESS

Fig. 8.1 The HFSs coupled power-traffic system: a power network, b hydrogen fueling stations, c transportation network, d P2P energy trading, reprinted from Ref. [57], copyright2022, with permission from IEEE

the efficient functioning of the coupled system, collectively forming a dynamic and integrated network that harmoniously caters to the power and transportation demands of modern energy ecosystems. Upon careful examination of Fig. 8.1a, a notable observation emerges: the strategic utilization of PV panels and energy storage systems (ESS) within the PN. Recognizing the economic infeasibility of producing hydrogen powered by fossil fuels, the integration of PV technology within the PN becomes indispensable. This deliberate deployment of PV panels serves the purpose of harnessing solar energy to supply the required electricity for the electrolyzer, enabling the efficient conversion of water into hydrogen. Furthermore, the incorporation of an ESS within the PN assumes a critical role in effectively managing the inherent uncertainties associated with PV power generation. By acting as a reliable reservoir, the ESS adeptly accommodates fluctuations in PV output, ensuring a stable and uninterrupted power supply to the electrolyzer. Moreover, the ESS serves a dual function by providing valuable OR capabilities, bolstering the overall resilience and flexibility of the PN. Furthermore, as depicted in the captivating illustration of Fig. 8.1b, HFS boasts an array of essential components including the electrolyzer, FC, and storage tank. Notably, the electrolyzer assumes a paramount role within the HFS as it harnesses the electricity supplied by the PN to facilitate the conversion of water into hydrogen. This process is instrumental in producing high-quality hydrogen that can be effectively stored in the dedicated storage tank, which serves two crucial functions. On one hand,

8.2 Operation Model of HFSs Coupled Power-Traffic System Considering …

149

the stored hydrogen within the HFS can be seamlessly channeled to FC, enabling the generation of electricity that is subsequently transferred back to the PN to serve as a valuable OR. Specifically, when the HFS receives a positive OR signal from the PN, it promptly taps into its hydrogen reserves, allowing the fuel cell to efficiently produce electricity. This electricity is then seamlessly injected back into the PN, augmenting the positive reserve and enhancing the overall operational capabilities of the energy system. On the other hand, the stored hydrogen within the HFS assumes a pivotal role in directly fulfilling the energy demands of H2EVs within TN, as elegantly portrayed in Fig. 8.1c. Through the utilization of a hydrogen pump, the HFS expertly caters to the energy requirements of H2EVs, providing a reliable and sustainable source of power. This dynamic interplay between the HFS and TN ensures smooth and efficient refueling operations, further facilitating the widespread adoption and utilization of hydrogen as a clean and viable energy source. Nevertheless, the economic benefits derived from HFSs solely through the provision of OR services remain limited. The financial rewards associated with supplying OR are often constrained by relatively lower returns. To overcome this challenge and unlock greater profitability, an innovative and promising approach emerges: the establishment of a coalition among HFSs, fostering bilateral energy trading within their network. This transformative strategy, embodied in Fig. 8.1d, introduces P2P electricity trading among HFSs, signifying a groundbreaking paradigm shift. Diverging from the conventional mutual trading methods between HFSs and the PN, the introduction of P2P energy trading opens up a novel avenue for HFSs to engage in direct energy transactions with one another. This transformative approach capitalizes on the inherent imbalances in hydrogen demand arising from the uneven distribution of traffic flow among H2EVs. The heterogeneous hydrogen demand across HFSs often gives rise to a scenario where certain thriving HFSs must resort to purchasing electricity from external sources to meet the soaring hydrogen requirements of H2EVs. Conversely, some HFSs find themselves with an abundance of hydrogen stored within their storage tanks, amply satisfying the demand of H2EVs. In this fortuitous circumstance, HFSs with more modest hydrogen demands can seize the opportunity to directly engage in P2P energy trading, where they act as sellers of electricity to the prosperous HFSs. Moreover, the implementation of HFS with P2P energy trading would significantly enhance the functionality of the coupled power-traffic system, thereby yielding a multitude of benefits. Firstly, by establishing interconnections between various HFSs, the burden on PN buses is effectively alleviated, offering a notable respite. This is primarily due to the fact that a considerable portion of the electricity required is supplied by other HFSs, resulting in a more balanced distribution of power flow as compared to the scenario where P2P energy trading is absent. Secondly, the introduction of this innovative system leads to a remarkable reduction in refueling queuing time. This can be attributed to the fact that the prosperous HFSs are able to maintain a steady supply capacity with the assistance of other interconnected HFSs. The significance of this reduction in queuing time extends beyond mere convenience, as it directly contributes to mitigating congestion levels experienced on TN. As a result,

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the overall travel expense of H2EVs is significantly reduced, making the utilization of this sustainable mode of transportation even more appealing. When analyzing the impact on TN, it becomes apparent that the distribution of traffic flow and fluctuating refueling demands are contingent upon the route choices made by drivers, thereby exerting an influence on the operation of PN. Hence, to accurately capture the rational behavior of individual drivers and determine the hydrogen demand of HFSs, the distribution of vehicular flows in a steady state is represented by the Wardrop user equilibrium [39]. This equilibrium concept not only accounts for the preferences and decision-making of drivers but also serves as a basis for estimating the hydrogen demand at HFSs. In the subsequent part of this section, a comprehensive description of the operational models for PN, HFSs incorporating P2P energy trading, and TN is provided, respectively. Each model is examined individually, shedding light on their distinct functionalities and contributions to the overall system.

8.2.1 Operation Model of Power Network Within the scope of this research paper, the integration of both PV systems and ESS within the PN infrastructure plays a pivotal role in meeting the electricity requirements of conventional loads as well as the electrolyzer within HFSs. Consequently, it becomes imperative to carefully examine and address the constraints pertaining to power balance and the reliable operation of PV and ESS. Furthermore, to effectively manage potential fluctuations in PN load demands and account for the inherent uncertainties associated with PV power outputs, reserve constraints are also taken into careful consideration. The subsequent section delves into the intricate details of these constraints, providing a comprehensive understanding of their significance and implications within the context of the study. 1. Power balance In power system operations, it is crucial to maintain a balance of active and reactive power between the power sources and the demand. This balance is represented as follows. g

p j = P jPN + P jPV + P jESS,dc − P jESS,c g

PV ESS q j = Q PN j + Qj + Qj g

Pilj + p j − ril j Iilj =

E

(8.1) (8.2)

l P jk + p dj , ∀l ∈ E L

(8.3)

Q ljk + q dj , ∀l ∈ E L

(8.4)

k∈π( j) g

Q li j + q j − xil j Iilj =

E k∈π( j )

8.2 Operation Model of HFSs Coupled Power-Traffic System Considering …

151

) ( )2 ( U j = Ui − 2 ril j Pilj + xil j Q li j + z li j Iilj , ∀l ∈ E L

(8.5)

( )2 ( )2 Iilj Ui = Pilj + Q li j , ∀l ∈ E L

(8.6)

g

where, at a bus j, p j represents the total active power generation, which is the sum of PN, PV, and ESS. P jPN and P jPV indicate the active power of PN and PV output power, respectively. P jESS,dc and P jESS,c represent the discharging and charging power g of ESS. Similarly, at the same bus, q j represents the total reactive power generation, PN ESS represent the reactive while Q j denotes the reactive power of PN. Q PV j and Q j power of PN and ESS, respectively. The nodal active and reactive power balance constraints are represented by Eqs. (8.3) and (8.4), where Pilj and Q li j denote the active and reactive power flow in a branch l connecting buses i and j, respectively. Additionally, ril j , xil j , and z li j represent the corresponding resistance, reactance, and impedance of line l. Iilj represents the square magnitude of current in line l, while U j denotes the square magnitude of voltage at bus j. Furthermore, Eq. (8.5) illustrates the voltage drop in power transmission, and Eq. (8.6) defines the apparent power at the head node of each branch. In this paper, considering the inclusion of ESS, it is necessary to ensure that the energy stored during the current time interval /t is equal to the difference between the charged and discharged energy. This equality constraint can be expressed as follows. ESS ESS E i,t = E i,(t−1) + Pi,tESS,c ηc /t −

Pi,tESS,dc ηdc

/t

(8.7)

ESS where E i,t represents the energy stored in ESS i at the end of time step t. Additionally, our model takes into account the charging and discharging efficiencies of ESS, denoted by ηc and ηdc , respectively.

2. Security constraints To ensure the operational security of PN, the following magnitude constraints are considered: voltage, branch current, and apparent power.

/

U min ≤ U j ≤ U max , ∀ j ∈ EN j j

(8.8)

Ii j ≤ Iimax j , ∀l ∈ E L

(8.9)

(

Pilj

)2

( )2 + Q li j ≤ Slmax , ∀l ∈ E L

(8.10)

where U min and U max represent the minimum and maximum square magnitudes j j represents the maximum square of voltage at a specific bus j, respectively. Iimax j

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8 Collaborative Operation Between Power Network and Hydrogen …

magnitude of current on a branch l connecting two buses i and j. Additionally, Slmax denotes the maximum allowed apparent power of the branch l. Furthermore, there is a specified range within which the active and reactive power output of the PV unit and ESS must be limited, as expressed below. 0 ≤ PiPV ≤ PiPV,max

(8.11)

ESS,max ESS 0 ≤ Pdc,i ≤ Pdc,i

(8.12)

ESS,max ESS 0 ≤ Pc,i ≤ Pc,i

(8.13)

ESS ESS Pdc,i (t)Pc,i (t) = 0

(8.14)

ESS ESS E iESS,min + POR,i,t ≤ E iESS ≤ E iESS,max − POR,i,t

(8.15)

ESS,max where PiPV,max represents the maximum output power of PV unit i. Pdc,i and ESS,max Pc,i denote the maximum discharging and charging power of ESS i, respectively. It should be noted that simultaneous charging and discharging are prohibited, as stated in Eq. (8.14). Additionally, the energy stored in ESS must be within a specified range, as described in Eq. (8.15). E iESS,min and E iESS,max represent the minimum and maximum allowable energy storage levels of ESS, respectively. Furthermore, Eq. (8.15) also considers the supplied OR (Operating Reserve) from ESS to PN, ESS . denoted by POR,i,t

3. Reserve constraints To account for potential load demand fluctuations and uncertainties in PV power, reserve requirements for PN are taken into consideration. ORup ≥ ωup

E

PiPV + βr

i∈E N

ORdn ≥ ωdn

E

pid

(8.16)

i∈E N

E

PiPV

(8.17)

i∈E N

where ORup and ORdn represent the required up and down reserves for PN, respectively. Additionally, ωup and ωdn denote the up and down reserve coefficients for PV power outputs. Furthermore, βr represents the reserve coefficient for traditional active power demand in PN.

8.2 Operation Model of HFSs Coupled Power-Traffic System Considering …

153

8.2.2 Operation Model of Hydrogen Fueling Station with P2P Energy Trading Figure 8.1 vividly illustrates the intricate interplay between the operation of HFS and the interconnected PN and TN systems. From a comprehensive perspective, it becomes evidently clear that various factors exert mutual influence and engender a complex relationship. On one hand, the fluctuating electricity prices within the wholesale market wield a direct impact on the electricity purchase schedules of HFS. In a reciprocal manner, the distinct electricity demands of HFSs effectively shape the power distribution within the PN infrastructure. On the other hand, the route choices made by drivers bear a profound influence on the distribution of traffic flow within TN, thereby directly impacting the hydrogen fueling demands of HFS. Furthermore, the selling price of hydrogen fuel assumes a pivotal role in the decision-making process of drivers, as they are inclined to select HFSs offering lower prices and opt for paths that minimize travel expenses. It is crucial to consider both aspects, effectively integrating them to form the HFSs coupled power-traffic system. Consequently, the operation of HFS is meticulously subjected to a set of constraints that encompass both power flow within PN and traffic flow within TN. The subsequent formulations expound upon these constraints, providing a detailed framework for understanding their implications within the system. 1. Operation constraints The electrolyzer is installed to produce hydrogen, and the hydrogen supply is restricted by the output flow of the electrolyzer. Similarly, the OR service provided by HFS is also constrained by the output power of the fuel cell. Elz 0 ≤ Q Elz s,t ≤ Q max

(8.18)

FC FC 0 ≤ Ps,t ≤ Pmax

(8.19)

Elz Elz Q Elz · ηElz · Ps,t s,t = λ

(8.20)

FC Ps,t = λFC · ηFC · Q FC s,t

(8.21)

H H H SOCs,min ≤ SOCs,t ≤ SOCs,max

(8.22)

where Q Elz s,t represents the hydrogen flow generated by the electrolyzer at time step t, denotes the maximum output flow of the electrolyzer. The output power of and Q Elz max FC , while the maximum output power of the fuel cell at time step t is indicated by Ps,t FC . Additionally, ηElz and ηFC denote the efficiency the fuel cell is represented by Pmax of the electrolyzer and fuel cell, respectively. ηElz and ηFC represent the efficiency of electrolyzer and fuel cell. The hydrogen state of charge (SOC) at time step t is

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8 Collaborative Operation Between Power Network and Hydrogen …

H represented by SOCs,t . Furthermore, for security concerns, the SOC of the tank is H H and the maximum state SOCs,max . limited by the minimum state SOCs,min

2. Hydrogen balance constraint Like the ESS in PN, hydrogen is balanced based on the difference between hydrogen production and consumption within the current time interval /t. ) ( H H H,Dmd SOCs,t = SOCs,(t−1) + Q Elz − Q FC s,t − Q s,t s,t · /t

(8.23)

H,Dmd where Q s,t and Q FC s,t represent the hydrogen demand of HFS s and hydrogen feedback to FC at time step t, respectively.

3. Reserve constraints Since the hydrogen demand of HFSs varies, the capacity of HFSs supplying OR service differs and is restricted by the minimum and maximum SOC of the hydrogen tank. H HFS H H HFS SOCs,min + POR,s,t ≤ SOCs,t ≤ SOCs,max − POR,s,t

(8.24)

HFS where POR,s,t denotes the OR that HFS s could provide for PN at time step t.

8.2.3 Operation Model of Traffic Network The distribution of traffic flow relies on factors such as road congestion and route choices. Considering the rational behavior of drivers, they will opt for the route that offers the lowest travel expenses, leading to a traffic flow equilibrium. In transportation theory, the stable traffic flow pattern in a congested TN is known as the Wardrop user equilibrium. In this equilibrium, the travel expenses on all active paths are equal, and no driver can reduce their expenses by unilaterally changing routes. To characterize the equilibrium in the TN, we outline several assumptions in this section. Firstly, all H2EVs aim to select the route with the lowest travel expenses, considering factors like travel time and refueling costs. Secondly, each H2EV has the capability to reach any HFS in the TN without running out of energy. The fundamental operational model of the TN is represented by a connected directional graph denoted as G T = [TN , T A ], where TN represents the set of nodes including origins, intersections, and destinations. Additionally, T A represents the set of links, which refers to the roads in the TN. Typically, the driving pattern in the TN is segmented into a series of O–D pairs (r, s), where an EV departs from the origin node r and travels to the destination node s. The diagram of the O–D pair (r, s) is depicted in Fig. 8.2a. Typically, each origin–destination O–D pair (r, s) is connected by multiple paths instead of just one. A path represents a series of connected links between the origin r and the destination s. In our TN model, the link-path incidence matrix

8.2 Operation Model of HFSs Coupled Power-Traffic System Considering …

(a)

linki

...

(c)

linkj

r

s

Origin

path

(b) Refuel IN

HFS

155

HFS node

Destination

link

OUT

Bypass link

Fig. 8.2 Traffic network model: a O–D pair, b hydrogen fueling station, c traffic flow of O–D pair with multiple feasible paths, reprinted from Ref. [57], copyright2022, with permission from IEEE

/ = [/r s ], ∀(r, s) depicts the path topology, where /r s refers to the subset related to the O–D pair (r, s). If link a is a segment of path k, its corresponding element in rs rs = 1; otherwise, it is δak = 0. the matrix is δak To describe the decision-making process of a H2EV, specifically whether to stop for refueling or continue driving, the HFS is represented by a simplified module consisting of two nodes and two links [40]. Figure 8.2b illustrates this module, which includes an entrance node IN, an exit node OUT, a refueling link IN → HFS → OUT, and a bypass link IN → OUT. Based on this representation, the links within the urban transportation network can be classified into three categories. 1. Regular link without HFS The travel time on regular links without HFS can be represented by the Bureau of Public Roads function [41]. This function is commonly used to assess travel time in the presence of congestion [42]. | ta (xa ) =

ta0

( )4 | xa 1 + 0.15 , ∀a ∈ T AR ca

(8.25)

where ta (xa ) represents the travel time of link a given the traffic flow xa . ta0 denotes the ideal travel time, which is the minimum time under speed constraints without congestion. Additionally, ca represents the capacity of traffic flow on link a. 2. Refueling link with a HFS The time spent on the refueling link IN → HFS → OUT in Fig. 8.2b can be divided into two components: refueling time and queuing time. The refueling time is considered a constant ta0 since it has a minor impact on the overall travel time for H2EVs. The queuing time, on the other hand, is described by the Davidson function, which is based on queuing theory [43]. The Davidson function can be expressed as follows.

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8 Collaborative Operation Between Power Network and Hydrogen …

| ( ta (xa ) = ta0 1 + J

xa ca − xa

)| , ∀a ∈ T AC

(8.26)

where ca represents the service capacity of HFS on the fueling link a ∈ T AC , while J is the parameter used in the Davidson function. 3. Bypass link The travel time of bypass link, i.e., IN → OUT in Fig. 8.2b could be neglected as drivers pass the HFS without staying for refueling. ta (xa ) = 0, ∀a ∈ T AB

(8.27)

As mentioned previously, there can be several possible paths between an origin– destination O–D pair. Consequently, the traffic flow for an O–D pair is the sum of H2EV flows f kr s on all feasible paths K r s , as depicted in Fig. 8.2c. Furthermore, using the H2EV flow f kr s and the link-path incidence matrix, we can calculate the traffic flow on each link as follows. E E rs xa = f kr s δak , ∀a ∈ T A (8.28) r s k∈K r s

E

f kr s = q r s , ∀(r, s)

(8.29)

k∈K r s

f kr s ≥ 0, ∀k ∈ K r s , ∀(r, s)

(8.30)

where the relationship between link flow and path flow is expressed in Eq. (8.28), and xa represents the traffic flow on link a. f kr s denotes the vehicular flow on path k for the O–D pair (r, s). q r s represents the total traffic flow from origin r to destination s. Furthermore, the constraints on traffic flow are defined in Eqs. (8.29) and (8.30) respectively. Furthermore, the travel time tkr s and travel expense ckr s of H2EVs on path k between O–D pair (r, s) could be derived based on link flow xa as follows. tkr s =

E

rs ta (xa )δak , ∀k ∈ K r s , ∀(r, s)

(8.31)

ckr s = ωtkr s + λa E B , ∀k ∈ K r s , ∀(r, s)

(8.32)

a∈T A

where ω and λa are the monetary value of travel time and the hydrogen price at fueling link a ∈ T AC , respectively. It is evident that when drivers have the opportunity to minimize their travel expenses by selecting alternate routes, the resulting traffic flow within TN undergoes a corresponding shift. This is primarily due to the inherent rationality of drivers seeking to minimize their individual travel expenses. As a consequence, a state of stable traffic

8.3 Collaborative Operation Framework Considering P2P Energy Trading

157

flow equilibrium emerges, wherein the travel expenses of H2EVs traversing all viable paths are equivalent. Typically, under such circumstances, drivers lack the incentive to deviate from this established pattern since the travel expenses across all routes remain the same. Thus, this equilibrium state is not only achieved but also naturally sustained over time. As outlined in Ref. [44], the concept of traffic network equilibrium can be effectively translated into an optimization problem, which can be mathematically expressed as follows.

min

xa E{

ωta (θ )dθ + λa E B xa

(8.33)

a∈T AC 0

s.t. Eq.(28 ∼ 32)

(8.34)

where the objective of Eq. (8.33) is to minimize the overall travel expense of TN by adjusting the distribution of traffic flow on each link. In this paper, the traffic network equilibrium is computed using PSO, a widely adopted optimization algorithm known for its simplicity [45]. To encapsulate the essence of this section, an intricate model is meticulously constructed to represent the HFSs coupled power-traffic system. This model takes into account the intricate interdependencies that exist between HFSs, the power flow within PN, and the traffic flow within TN. By simultaneously considering these vital elements, a holistic understanding of the system dynamics is achieved. Furthermore, in a bid to maximize the advantages offered by HFSs and foster the seamless operation of the integrated system, the concept of P2P energy trading is introduced. This innovative approach serves as a catalyst, propelling the system towards enhanced efficiency and effectiveness. By leveraging the potential of P2P energy trading, the benefits derived from HFSs are magnified, further reinforcing the seamless operation and optimal performance of the coupled power-traffic system.

8.3 Collaborative Operation Framework Considering P2P Energy Trading Upon careful examination of the aforementioned HFSs coupled power-traffic system, a noteworthy observation emerges: the energy demands of H2EVs are proficiently met through a symbiotic relationship between PN and HFSs. This harmonious interaction yields manifold benefits, including a reduction in operational costs and an amplification of the overall system efficiency. Moreover, it is essential to acknowledge that the operation of HFSs is intrinsically intertwined with the dynamics of TN, as it directly shapes the distribution of energy demand within both PN and HFSs. Put simply, optimizing the operation between PN and HFSs necessitates a thorough consideration of the constraints imposed by TN. Hence, to delve deeper into the

158

8 Collaborative Operation Between Power Network and Hydrogen …

exploration of this efficient interaction while duly accounting for TN constraints, a collaborative operation framework is introduced in this section. By embracing this framework, a comprehensive investigation can be conducted, shedding light on the intricate interplay between PN and HFSs while ensuring a cohesive integration with the constraints imposed by TN. In the pursuit of establishing an effective collaborative framework, the coalition game emerges as a widely adopted approach known for its practical effectiveness and manageable complexity [46]. With the primary objective of maximizing the individual benefits of all participants, a collaborative operation framework is meticulously formulated in this section, integrating the realms of PN, HFSs, and TN, while encompassing both energy and reserve considerations. Within this framework, the provision of OR for PN is facilitated through the collective efforts of three key entities: ESS, the wholesale market, and HFSs. Notably distinct from ESS and the wholesale market, HFSs contribute to the OR service by harnessing the power of hydrogen fuel. This unique process involves the conversion of hydrogen fuel to electricity within the fuel cell of the HFS. Subsequently, the generated electricity is seamlessly fed back into PN as positive reserves, effectively fulfilling the required OR. Conversely, when the HFSs receive a negative OR signal from PN, they strategically respond by increasing their electricity consumption through electrolysis, thereby acting as negative reserves. This intricate orchestration of energy flow and reserve management exemplifies the collaborative prowess of the framework, underscoring its capacity to optimize the interplay between PN, HFSs, and TN while ensuring efficient utilization of available resources. As highlighted earlier, the potential benefits derived from providing OR services to PN are inherently limited, as the OR reward typically falls below the prevailing electricity price. Moreover, the centralized nature of collaborative operation raises concerns surrounding efficiency and privacy. To address these challenges, we propose the implementation of P2P energy trading within the collaborative operation framework. By introducing P2P energy trading, we effectively tackle the aforementioned issues, fostering enhanced efficiency and alleviating privacy concerns. Acting as the central hub for interaction between PN and TN, HFSs are strategically distributed across various locations, often under the ownership of different entities. This decentralized and diverse landscape lends itself well to P2P energy trading, making it an ideal solution. Consequently, our research paper applies a novel P2P energy trading strategy to HFSs, serving as a cornerstone of the proposed framework. Departing from the conventional P2P energy trading market, which typically operates on a fixed transaction price, we develop a dynamic pricing mechanism that takes into account the variable electricity prices observed in both PN and HFSs. This dynamic approach not only improves the collaborative efficiency but also ensures adaptability to changing market conditions. Additionally, to ensure the sustainability of the P2P trade market, we introduce a tailored control mechanism designed to prevent arbitrage. This mechanism effectively safeguards against participants exploiting price differentials by purchasing energy from low-price markets and simultaneously selling it at higher price markets, thus maintaining fairness and integrity within the trading ecosystem.

8.3 Collaborative Operation Framework Considering P2P Energy Trading

159

In the rest part of this section, detailed content of collaborative energy and reserve operation model and P2P energy trading strategy are presented, respectively.

8.3.1 Collaborative Operation Framework This paper considers two aspects of the collaborative operation between PN and HFSs. Firstly, the energy demand of HFSs is a priority to meet the hydrogen requirements of H2EVs. Secondly, OR is taken into account to support the PN’s operations. To address these requirements, we propose a collaborative framework, illustrated in Fig. 8.3, that considers both energy and reserve within operational constraints simultaneously. We can observe two types of flows between PN and HFSs: the energy flow depicted by a solid blue line and the reserve flow represented by a dotted green line. Specifically, electricity is procured from the wholesale market and then transferred from PN to HFSs to meet the energy needs of H2EVs. Additionally, HFSs have the capability to offer OR services to PN in exchange for financial rewards. Figure 8.3 highlights that the OR service of PN is supported by both ESS and HFSs, which can be expressed as follows. ESS ORup = PtPN,RT + POR,t +

S E

HFS POR,s,t

(8.35)

HFS POR,s,t

(8.36)

s=1 ESS ORdn = PtPN,RT + POR,t +

S E s=1

Electricity Wholesale Market

Energy

Reserve

P2P energy trade

Power Network

Hydrogen Fueling Stations

PV ESS

Fig. 8.3 The collaborative operation framework considering P2P energy trading, reprinted from Ref. [57], copyright2022, with permission from IEEE

160

8 Collaborative Operation Between Power Network and Hydrogen …

Furthermore, acknowledging the varying energy demands of HFSs caused by imbalanced traffic flow, HFSs from different entities have the opportunity to engage in direct energy trading with one another. This allows HFSs to potentially generate higher revenue compared to providing OR services to PN, especially when the energy prices in the P2P trading market exceed the rewards offered by PN. From the PN’s perspective, the operational cost can be divided into five components: energy procurement costs from the day-ahead and real-time markets, penalty costs associated with deviations from the day-ahead plan, and discharging and charging expenses. The formulation of the PN’s operational cost can be expressed as follows. CPN =

T E {

| } epn | PN,DA PN,RT ESS ESS ESS λDA /t + λRT + λt | PtPN,RT | + λESS t Pt t Pt dc Pdc,t + λc Pc,t

t=1

(8.37) where λDA represents the day-ahead electricity price, while λRT t t represents the realtime market electricity price. PtPN,DA and PtPN,RT denote the electricity purchased by epn PN from the day-ahead and real-time markets, respectively. Additionally, λt is the penalty cost coefficient for the deviation between real-time power and the day-ahead ESS represent the cost coefficients for discharging and charging plan [47]. λESS dc and λc the ESS, respectively. From the perspective of the HFS, the operation cost consists of several components. These include the cost of purchasing energy from the wholesale market and P2P trade market, the financial reward received by the HFS for providing OR to PN, and the revenue generated from selling electricity to the P2P trade market. CHFS =

S E T E {

} HFS OR HFS P2P P2P P2P P2P λDA t Pin,s,t − λt POR,s,t + λin,s,t Pin,s,t − λout,s,t Pout,s,t /t

s=1 t=1

(8.38) where λOR is the financial reward coefficient of HFS supplying OR service to t HFS HFS and Pout,s,t represent the consumed energy and provided OR of HFS. λP2P PN.Pin,s,t in,s,t P2P and λout,s,t denote the purchasing and selling price of P2P energy trading market, P2P P2P and Pout,s,t represent the amount of purchasing and respectively. In addition, Pin,s,t selling electricity of HFS from P2P energy trading market In summary, the collaborative operation cost of PN and HFSs is expressed as follows. min CPN + CHFS

(8.39)

{ ⎨ (1) ∼ (24) s.t. (28) ∼ (32) ⎩ (35) ∼ (36)

(8.40)

8.3 Collaborative Operation Framework Considering P2P Energy Trading

161

where CPN and CHFS denote the operation cost of PN and HFS, respectively. By this ESS ESS , Pc,t , means, the decision variables of Eq. (8.39) contain PtPN,DA , PtPN,RT , Pdc,t ESS HFS HFS HFS P2P P2P POR,t , Pin,i,t , Pout,i,t , POR,i,t , Pin,i,t and Pout,i,t .

8.3.2 P2P Energy Trading Strategy In recent years, P2P energy trading has gained significant attention in various commercial sectors, aiming to facilitate the wider adoption of EVs and distributed renewable energy. Compared to traditional centralized trade mechanisms, P2P energy trading is considered a flexible and economically beneficial alternative [48–50]. In this market, participants, known as prosumers, have the ability to directly buy or sell energy from each other, enabling mutually beneficial transactions. Within our article, HFSs can generate revenue through three primary avenues: (1) converting water into hydrogen using low-cost electricity and then selling it to H2EVs at a higher price, (2) receiving financial rewards from the PN for supplying OR services, and (3) engaging in P2P energy trading with other HFSs at a suitable price that is higher than the OR reward but lower than the PN’s retail price. Essentially, HFSs involved in P2P energy trading decide whether to trade electricity with the wholesale market or other HFSs based on the energy prices. When the financial rewards for OR services exceed the electricity selling price in the P2P market, HFSs are inclined to provide OR services to the PN. Conversely, if the purchasing price in the P2P market is lower than the wholesale market or the selling price in the P2P market exceeds the OR rewards, HFSs prefer to trade energy within the P2P market. Through the collaborative operation framework with P2P energy trading, HFSs can achieve higher profits compared to operating independently. Simultaneously, the entire system benefits from reduced operational costs for the PN and decreased congestion in the TN. While there have been studies on P2P energy trading between different prosumers, the internal energy trading strategy among HFSs from different entities has not been explored. Establishing an appropriate pricing mechanism is crucial for the successful and sustainable implementation of P2P trading. In this section, we propose an innovative P2P energy trading strategy among HFSs that determines the transaction price in the P2P market while ensuring fair practices and preventing arbitrage. Typically, the electricity selling price in the wholesale market varies due to different production costs. Consequently, the monetary value of hydrogen stored in the HFS fluctuates as well, reflecting the variable electricity prices obtained from the wholesale market. Hence, it is logical to consider the average cumulative price of energy stored in the HFS when determining the transaction price in the P2P market. In other words, if the stored energy is not properly evaluated, HFSs may choose not to participate in P2P energy trading. Some existing P2P trading methods employ pre-defined energy transaction prices using contracts [49]. However, this approach fails to account for the dynamic monetary value of hydrogen stored in HFSs, specifically the cost variation resulting from fluctuating electricity purchasing prices.

162

8 Collaborative Operation Between Power Network and Hydrogen …

To address this issue and improve the overall operational efficiency of the framework, it is essential to consider the dynamic monetary value of stored hydrogen. Fortunately, the average price of stored energy in EVs has already been introduced through the concept of Energy Price Tag (EPT) in Ref. [51]. The EPT suggests that the charging energy for any energy storage system can be supplied by different energy resources, each associated with a specific price. Unlike electricity, which is challenging to store in large quantities for extended periods, hydrogen offers convenient storage and utilization on a larger scale. Therefore, we leverage insights from the EPT and establish the monetary value of hydrogen stored in HFSs. The calculation of the EPT is based on the operational conditions of the HFS, specifically its roles as a consumer and a producer. As a consumer, the HFS purchases electricity from the wholesale and P2P markets. Conversely, as a producer, it sells its excess energy. By considering these factors, we can calculate the EPT for the HFS at each time step, which can be expressed as follows. { EPTs,t =

Consumer λRT t , EPTs,t−1 , Producer

(8.41)

where EPTs,t represents the average price of energy stored in the HFS s at time step t. Besides, λRT t denotes the energy price that HFS purchases form PN real-time wholesale market. Building upon the concept of EPT, we have developed a dynamic pricing strategy for the P2P energy trading market. In this strategy, consumers aim to purchase electricity at the lowest price from other HFSs, while producers intend to sell energy based on their EPT. The equation for calculating the trade price in the P2P market is as follows. P2P λP2P in,s,t = min λout, p,t p∈S\s

λP2P out,s,t =

Et−1 i=1

EPTs,i

(8.42) (8.43)

P2P where λP2P in,s,t and λout, p,t represent the purchase and selling price in the P2P energy trading market, respectively. Furthermore, arbitrage typically occurs between markets with different prices, enabling participants to profit by purchasing commodities from low-priced markets and selling them in high-priced markets. However, for HFSs, their primary responsibility is to meet the hydrogen demand of H2EVs. Engaging in arbitrage instead of providing services to H2EVs is not suitable for HFSs. To address this, a specialized control mechanism is proposed in this section to prevent arbitrage. To achieve this, we establish a rule that prosumers in our P2P market can only assume a single role at any given time. This means that HFSs are not allowed to simultaneously buy and sell electricity. Specifically, when operating in consumer mode, HFSs are prohibited from selling electricity. Similarly, when functioning as producers and selling

8.3 Collaborative Operation Framework Considering P2P Energy Trading

163

excess energy, they are not permitted to purchase low-priced energy. This ensures the sustainable application of collaborative operations with P2P energy trading. In conclusion, we present the flowchart of our proposed P2P energy trading strategy with dynamic pricing and an arbitrage prevention mechanism, as depicted in Fig. 8.4. Through our proposed collaborative operation framework with P2P energy trading, both HFSs and PN can enjoy increased revenue. However, it is important to examine how this revenue is allocated to encourage collaboration. If the benefits are not distributed fairly, participants may be reluctant to engage in collaborative operations. Hence, the design of a benefit allocation mechanism is discussed in the following section.

Fig. 8.4 Flowchart of the proposed P2P energy trading strategy with dynamic pricing and arbitrage prevention mechanism, reprinted from Ref. [57], copyright2022, with permission from IEEE

164

8 Collaborative Operation Between Power Network and Hydrogen …

8.4 Benefit Allocation Mechanism with Collaborative P2P Energy Trading Strategy 8.4.1 The Allocation Mechanism Based on Bilateral Shapley Value Once the collaboration payoff is determined, it becomes crucial to fairly allocate the benefits for the successful implementation of collaborative operations. This is because each participant’s contribution within the coalition is unequal. Therefore, revenue distribution is closely tied to coalition fairness, which ultimately impacts the participants’ motivation to actively engage in the collaboration. In this context, the traditional method of benefit allocation, such as the Shapley value method, is commonly used to address the revenue assignment problem within collaborative frameworks [52]. However, the Shapley value method can be computationally complex. To overcome this limitation, an enhanced benefit allocation mechanism based on the bilateral Shapley value is introduced. To better understand this improved mechanism, we will briefly introduce the formulations of the Shapley value. Building upon the Shapley value method, the allocated profit of member k within a collaborative union M can be represented as ’k(v), which is calculated as follows. ϕk (v) =

E

|S|!(M − |S| − 1)! [v(S ∪ {k}) − v(S)] M! S⊆M\{k}

(8.44)

where S ⊆ M\{k} represents all subsets S of M excepts player member k. |S|! and M! denote the number of members in subset S and the whole union M, respectively. Besides, v(S ∪ {k}) − v(S) and v(S) are the collaborative benefit of union S ∪ {k} and S. The contribution of member k under different scenarios is presented by v(S ∪ {k}) − v(S). Moreover, |S|!(M − |S| − 1)!/M! represents the probability of corresponding scenarios. In this way, Eq. (8.44) could be interpreted as the expectation of contribution over the possible permutations, in which the coalition can be formed. However, calculating the Shapley value can be computationally burdensome, especially when the size of union M becomes O(M!). To address this concern, the bilateral Shapley value (BSV) is introduced as a solution to manage the exponential increase in complexity with the growing number of players [53, 54]. The formula for BSV is expressed as follows. 1 1 v({k}) + [v(M) − v(M\{k})] 2 2 E /ϕk = v(M) − ϕkBSV (v)

ϕkBSV (v) =

k∈M

(8.45) (8.46)

8.4 Benefit Allocation Mechanism with Collaborative P2P Energy Trading …

165

ϕkBSV (v) /ϕk BSV (v) k∈M ϕk

ϕk (v) = ϕkBSV (v) + E

(8.47)

where ϕkBSV (v) represents the allocated profit of member k, while /ϕk represents the profit difference between the entire coalition and its members. The final equation for the allocated profit of member k is expressed in Eq. (8.47). Notably, the calculation of BSV is directly proportional to the number of members, which is significantly lower than the exponential complexity of the traditional Shapley value method. Furthermore, the bilateral Shapley value ensures that players in the coalition, namely PN and HFSs in our scenario, do not receive less revenue from the collaborative operation compared to independent operation. This property is called super additive in mathematics, which is proofed in subsection C.

8.4.2 The Formulation of Characteristic Function v(S) In the coalition game, each union S aims to generate profits for its player members, which is determined by the value of the characteristic function v(S). The characteristic function is established based on the components of the coalition S. If the set S is empty, the benefit of the union S is equal to zero, which is expressed as follows. v(S) = 0, if S = ∅

(8.48)

If PN is not included in the union S, which means PN does not take part in the collaboration with HFS. In this way, the profit of union S is only the sum of the revenues of HFSs with P2P energy trading strategy. v(S) = −CHFS = −

S E T E

{

s=1 t=1

if {PN} ∩ S = ∅

HFS OR HFS λDA t Pin,s,t − λt POR,s,t P2P P2P P2P +λP2P in,s,t Pin,s,t − λout,s,t Pout,s,t

} /t, (8.49)

If the union S consists solely of PN, the collaborative profit of S is equal to the net profit of PN. In this scenario, the collaborative framework with P2P energy trading is not implemented, and the characteristic function is defined as follows.

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8 Collaborative Operation Between Power Network and Hydrogen …

v(S) = −CPN = −

T E t=1

{

} PN,DA PN,RT λDA + λRT t Pt t Pt | /t, epn | +λt | P PN,RT | + λESS P ESS + λESS P ESS t

dc

dc,t

c

c,t

if {PN} = S

(8.50)

If union S contains the PN and HFSs, the collaborative operation framework with P2P energy trading can be implemented in union S. Therefore, the collaborative profit of union S can be obtained as follows. } PN,DA PN,RT λDA + λRT t Pt t Pt | v(S) = − /t epn | ESS ESS ESS +λt | PtPN,RT | + λESS dc Pdc,t + λc Pc,t t=1 { DA HFS } S E T HFS E λt Pin,s,t − λOR t |POR,s,t | /t, − P2P P2P P2P +λP2P in,s,t Pin,s,t − λout,s,t Pout,s,t s=1 t=1 T E

{

if {PN} ⊂ S

(8.51)

8.4.3 Vthe Proof of Proposition To demonstrate the stability of the collaborative framework with P2P energy trading, the proof of superadditivity is provided as follows. Proposition: The proposed collaborative operation framework with P2P energy trading is superadditive. Proof: The net profit of alliance S ∪ {k} in the collaborative framework, as discussed in the previous subsection, depends on the composition of union S and member k. In essence, the calculation of net profit relies on three specific circumstances, which cover all cases except the empty set mentioned in Section B. If player member k belongs to PN and the coalition S comprises HFSs, the symbol v(S ∪ {k}) represents the total revenue after implementing the collaborative framework with P2P energy trading. The contribution of member k can then be derived.

8.4 Benefit Allocation Mechanism with Collaborative P2P Energy Trading …

167

v(S ∪ {k}) − v(S) =−

T E | epn | PN,DA PN,RT {λDA + λRT + λt | PtPN,RT | t Pt t Pt t=1

ESS ESS ESS + λESS dc Pdc,t + λc Pc,t }/t − HFS − λOR t |POR,s,t |

+

+

P2P λP2P in,s,t Pin,s,t

S E T E

HFS {λDA t Pin,s,t

−

−

S E T E

HFS {λDA t Pin,s,t

s=1 t=1 P2P λP2P out,s,t Pout,s,t }/t

HFS λOR t |POR,s,t |

+

(8.52)

P2P λP2P in,s,t Pin,s,t

s=1 t=1 P2P − λP2P out,s,t Pout,s,t }/t

=−

T E | epn | PN,DA PN,RT {λDA + λRT + λt | PtPN,RT | t Pt t Pt t=1

ESS ESS ESS + λESS dc Pdc,t + λc Pc,t }/t

where HFSs provide the OR service for PN under the collaborative framework so that PN could purchase less reserve from the wholesale market. This means that the value of PtPN,RT within the coalition is lower than that of the independent operation mode. Additionally, HFSs can also buy electricity from the P2P energy trading market, further reducing the quantity of energy PN needs to purchase from the wholesale market. Consequently, the value of PtPN,DA is lower than the amount of purchased electricity in the absence of P2P energy trading. As a result, Eq. (8.52) can be further expressed as follows. v(S ∪ {k}) − v(S) ≥ v(k), if k ∈ {PN}

(8.53)

In other words, the benefit of member k is more than that of the independent operation, which illustrates the collaborative framework with P2P energy trading can increase the total revenue. If player k is an HFS and the PN is not part of the union S, it implies that coalition S ∪{k} consists solely of HFSs. Consequently, there is only peer-to-peer (P2P) energy trading among the HFSs, and no collaborative operation takes place between the PN and HFS.

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8 Collaborative Operation Between Power Network and Hydrogen …

v(S ∪ {k}) − v(S) =−

S∪{k} T EE

HFS OR HFS P2P P2P P2P P2P {λDA t Pin,s,t − λt |POR,s,t | + λin,s,t Pin,s,t − λout,s,t Pout,s,t }/t

s=1 t=1

+

S E T E

HFS P2P P2P OR HFS P2P P2P {λDA t Pin,s,t + λin,s,t Pin,s,t − λt |POR,s,t | − λout,s,t Pout,s,t }/t

(8.54)

s=1 t=1

=

T E HFS OR HFS P2P P2P P2P P2P {λDA t Pin,s,t − λt |POR,s,t | + λin,s,t Pin,s,t − λout,s,t Pout,s,t }/t t=1

= v(k), if k ∈ S &{PN} ∈ /S From Eq. (8.54), it is evident that the contribution of member k is equivalent to the benefit achieved in independent operations. This implies that without implementing the collaborative framework, the total revenue cannot be increased. If the player k is a HFS and PN is participated in the collaborative operation, the benefit function of S ∪ {k} is expressed as follows. v(S ∪ {k}) =−

T E

| epn | PN,DA PN,RT ESS ESS ESS {λDA + λRT + λt | PtPN,RT | + λESS t Pt t Pt dc Pdc,t + λc Pc,t }/t

t=1

−

S∪{k} T EE

HFS OR HFS P2P P2P P2P P2P {λDA t Pin,s,t − λt |POR,s,t | + λin,s,t Pin,s,t − λout,s,t Pout,s,t }/t

s=1 t=1

(8.55) On this basis, the contribution of player k is formulated as follows. v(S ∪ {k}) − v(S) =−

T E

HFS OR HFS P2P P2P P2P P2P {λDA t Pin,s,t − λt |POR,s,t | + λin,s,t Pin,s,t − λout,s,t Pout,s,t }/t

(8.56)

t=1

= v(k), if k ∈ S & {PN} ∈ S According to the proof above, for any member k and any set S, the following inequality always holds. v(S ∪ {k}) − v(S) ≥ v({k})

(8.57)

The adoption of the collaborative framework with P2P energy trading leads to an increase in the benefits of member k, regardless of the coalition’s composition. By combining Eq. (8.57) with the enhanced bilateral Shapley value method, we derive the following equation.

8.5 Case Study

169

1 1 1 1 v({k}) + [v(M) − v(M\{k})] ≥ v({k}) + v({k}) = v({k}) 2 2 2 2 BSV (v) ϕ ϕk (v) = ϕkBSV (v) + E k BSV /ϕk ≥ v({k} (v) k∈M ϕk (8.58) ϕkBSV (v) =

In summary, the profit of collaborative union S ∪ {k} is equal to or greater than the combined profit of S and member k. This means that when implementing the collaborative framework with P2P energy trading, the net profit of PN and HFSs is always higher than or equal to their net profits in independent operations.

8.5 Case Study 8.5.1 Simulation Settings To explore the impact relationship within the coupled system and validate the effectiveness of our proposed collaborative operation framework featuring P2P energy trading, we perform case studies on a test power-traffic system incorporating three hydrogen fueling stations. This coupled system comprises a 16-node TN with three HFSs and a modified IEEE 33-bus PN [55]. The details of this system are outlined below. The TN’s network topology, shown in Fig. 8.5, consists of 16 nodes and 20 links, including three refueling links. For regular links in the TN, the road capacity is set at ca = 100 p.u., with a corresponding free travel time of ta0 = 10 min. In the HFS’s node-link module, the fixed refueling time for the refuel link is ta0 = 20 min, and its capacity is set to ca = 60 p.u. The bypass link has a free travel time of zero and its ca capacity is equal to the adjacent regular link, which is ca = 100 p.u. in our case. Additionally, the monetary value assigned to travel time is ω = $10 per hour. To simulate the steady traffic flow in the equilibrium model, we select five O–D pairs along with their corresponding traffic demands, which are listed in Table 8.1. In the table, the traffic flow of traditional gasoline vehicles and H2EVs between each O–D pair (r, s) is represented by symbols qgr s and qer s , respectively. The modified IEEE 33-bus PN is characterized by a specific network topology. In this configuration, three PVs are installed at buses 6, 23, and 30 to generate power. To account for the uncertainty in PV output power and ensure a reliable power supply for the PN, an ESS with a capacity of 1 MWh is integrated at bus 1. Additionally, three HFSs are connected to buses 6, 23, and 30, respectively. Furthermore, the PV capacities are set as follows: 1 MW, 0.5 MW, and 0.5 MW for buses 6, 23, and 30, respectively. The ESS has a maximum charging and discharging power of 0.5 MW, with an efficiency of 0.9. The charging and discharging cost coefficients for the ESS are set at 0.35 $/kWh [56]. Moreover, anticipated errors in PV outputs and loads are considered, with predicted errors of 30% and 10%, respectively.

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8 Collaborative Operation Between Power Network and Hydrogen …

Fig. 8.5 Network topology of coupled 16-node TN and 33-bus PN, reprinted from Ref. [57], copyright2022, with permission from IEEE Table 8.1 O–D pairs and their trip information, reprinted from Ref. [57], copyright2022, with permission from IEEE O–D pair

Route selection

qg rs (p.u.)

qe rs (p.u.)

T1–T6

T1 → I1 → T3 → T6 T1 → I1 → E1 → T6 T1 → I1 → T3 → I2 → E2 → T6

75

5

T1–T10

T1 → I1 → T3 → T6 → I3 → E3 → T10 T1 → I1 → E1 → T6 → I3 → E3 → T10 T1 → T3 → I2 → E2 → T6 → I3 → E3 → T10

50

5

T3–T6

T3 → T6 T3 → I1 → E1 → T6 T3 → I2 → E2 → T6

85

10

T4–T8

T4 → I3 → T6 → T3 → I2 → T8 T4 → I3 → T6 → E2 → I2 → T8 T4 → I3 → T6 → E1 → I1 → T3 → I2 → T8

60

5

T5–T7

T5 → I2 → T3 → T6 → I3 → E3 → T7 T5 → I2 → E2 → T6 → I3 → E3 → T7 T5 → I2 → T3 → I1 → E1 → T6 → I3 → E3 → T7

40

10

8.5 Case Study

171

To ensure clarity, we have divided the simulation analysis into two aspects: the study of the coupled system and the evaluation of our proposed collaborative framework. Firstly, from the perspective of the coupled system, we investigate the impact relationship between PN and TN through HFS. This analysis reveals that the operation of HFS is influenced by the constraints of the coupled power-traffic system. Conversely, the operation of HFS also affects the distribution of power flow in PN and traffic flow in TN. Secondly, we examine the effectiveness of our proposed collaborative framework with P2P energy trading. This verification demonstrates that collaborative operation can reduce operational costs and enhance financial benefits. Additionally, the P2P energy trading strategy contributes to the improved operation of the coupled power-traffic system. In the remaining part of this section, we present three cases designed to verify the performance of both the coupled system and the collaborative framework. Case 1: In this case, PN and HFSs operate independently within the constraints of PN and TN, respectively. HFSs do not provide OR for PN or engage in energy trading with other HFSs. The purpose of this case is to verify the feasibility of the operation model and investigate the impact relationship between HFS, PN, and TN. Case 2: Unlike Case 1, PN and HFSs in this case are operated cooperatively using a centralized approach. HFSs are capable of supplying OR for PN, and in return, PN provides financial rewards to the HFSs. P2P energy trading is not considered in this case due to the centralized framework. It is compared to Case 1 to evaluate the effectiveness of the collaborative framework. Case 3: In this case, we simulate collaborative operation with P2P energy trading to validate the effectiveness of our developed P2P energy trading mechanism based on Case 2. Specifically, HFSs can earn benefits by providing OR services for PN and participating in energy transactions within the P2P trade market. The objective of this case is to verify the effectiveness of our proposed P2P energy trading strategy.

8.5.2 Analysis on the Coupled System and Impact Relationship Among HFSs, PN and TN We conducted simulations on Case 1 to verify the feasibility of the coupled powertraffic system and to understand the impact relationship between HFS, PN, and TN. In this case, we examine the traffic network equilibrium in two scenarios to illustrate the interplay within the coupled power-traffic system. In Scenario 1, we assume a consistent hydrogen selling price (λ = 100 $/MWh) across all HFSs. As mentioned earlier, the traffic network equilibrium is formulated as an optimization problem that aims to minimize the overall travel expense within TN. Under this assumption, the steady equilibrium pattern in Scenario 1 is depicted in Fig. 8.6. The figure illustrates the traffic flow across each link in our 16-node TN. For instance, consider the O–D pair (T3, T6). It can be observed that the traffic flow reaching T6 is

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8 Collaborative Operation Between Power Network and Hydrogen …

Fig. 8.6 The distribution of traffic flow at user equilibrium pattern in Scenario 1, reprinted from Ref. [57], copyright2022, with permission from IEEE

symmetrically distributed, given the symmetrical network topology surrounding T6. When TN reaches a user equilibrium pattern, the travel expense for all paths from T3 to T6 becomes equal, which ensures that rational drivers are not concerned with route selection. Consequently, the steady traffic flow of T3 → I1 → E1 → T6 and T3 → I2 → E2 → T6 are equal in this scenario. To examine the influence of HFS operations on route selection, we introduce Scenario 2, where different HFSs offer varying hydrogen selling prices. In this scenario, the hydrogen prices for HFSs are set at $100/MWh, $200/MWh, and $150/MWh, respectively. This variation arises because some HFSs may choose to attract drivers by lowering their selling prices. The updated traffic network equilibrium is illustrated in Fig. 8.7, revealing that more drivers prefer refueling at the first HFS, namely HFS1, due to its lower hydrogen price. Notably, the distribution of traffic flow in Scenario 2 differs from that of Scenario 1, demonstrating the impact of HFS operations on drivers’ path choices. Furthermore, Table 8.2 presents the trip information of traffic network equilibrium for each O–D pair in both scenarios. It is evident that the travel expenses for all feasible paths, regardless of the O–D pair, are equal. Based on the traffic flow data obtained from both scenarios, we can determine the energy demand of HFSs, as depicted in Fig. 8.8. The graph illustrates that the hydrogen demand of HFSs varies due to the fluctuating traffic flow in TN over time. Notably, the peak hydrogen demand at 8:00 and 17:00 aligns with the rush hour traffic in TN. Additionally, the graph reveals that the demand differs among the various HFSs since the traffic flow passing through each HFS in TN is not equal. Furthermore, a noticeable disparity in hydrogen demand can be observed between the two scenarios. In Scenario 1, the hydrogen demand for HFS1 and HFS2 overlaps

8.5 Case Study

173

Fig. 8.7 The distribution of traffic flow at user equilibrium pattern in Scenario 2, reprinted from Ref. [57], copyright2022, with permission from IEEE

Table 8.2 Trip information of equilibrium pattern in our 16-node TN, reprinted from Ref. [57], copyright2022, with permission from IEEE O–D pair

Route selection

Travel expense ($) Scenario 1

Scenario 2

T1–T6

T1 → I1 → E1 → T6 T1 → I1 → T3 → I2 → E2 → T6

6.76

7.51

T1–T10

T1 → I1 → T3 → T6 → I3 → E3 → T10 T1 → I1 → E1 → T6 → I3 → E3 → T10 T1 → T3 → I2 → E2 → T6 → I3 → E3 → T10

6.56

7.31

T3–T6

T3 → T1 → E1 → T6 T3 → I2 → E2 → T6

3.01

3.92

T4–T8

T4 → I3 → T6 → E2 → I2 → T8 T4 → I3 → T6 → E1 → I1 → T3 → I2 → T8

6.60

7.63

T5–T7

T5 → I2 → T3 → T6 → I3 → E3 → T7 T5 → I2 → E2 → T6 → I3 → E3 → T7

4.48

5.82

due to the symmetric TN topology and the same hydrogen selling price. On the other hand, in Scenario 2, the hydrogen demand for HFS1 is significantly higher than the other two HFSs. This discrepancy arises because HFS1 offers a lower hydrogen selling price, attracting more H2EV drivers to refuel at that particular station. In summary, the operation of HFSs impacts the distribution of traffic flow in TN, which subsequently determines the hydrogen demand for each HFS. Furthermore, the varying hydrogen demand of HFSs in these two scenarios results in different power consumption, which in turn impacts the power distribution of PN.

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8 Collaborative Operation Between Power Network and Hydrogen …

Fig. 8.8 Hydrogen demand of three hydrogen fueling stations: a Scenario 1, b Scenario 2, reprinted from Ref. [57], copyright2022, with permission from IEEE

This impact on PN’s operation is illustrated in Fig. 8.9, considering the dispatch plan of HFSs and the traffic flow in TN. To assess the operational state of PN, we compare four parameters: average active power, reactive power, magnitude of branch current, and bus voltage. Comparing the two scenarios, it can be observed that, except at 20:00, the average active and reactive power in Scenario 1 are higher than those in Scenario 2. However, the magnitude of branch current is nearly the same in both scenarios, indicating that the current on the branch is not significantly affected by the variation in traffic flow or the different hydrogen demand of HFSs, as shown in Fig. 8.9b. Moreover, the average magnitude of bus voltage in Scenario 1 is noticeably lower than that in Scenario 2, suggesting a reduced voltage burden in Scenario 2. The only exception is at 20:00, where the average magnitude of bus voltage is the same in both scenarios, reaching 0.9913 p.u., which is the peak value over the 24-h period. The results obtained highlight the interplay between PN and TN through HFS, where the operation of HFSs is influenced by fluctuating electricity and hydrogen

Fig. 8.9 The distribution of traffic flow at user equilibrium pattern in Scenario 2, reprinted from Ref. [57], copyright2022, with permission from IEEE

8.5 Case Study

175

prices. Simultaneously, the operation of HFSs impacts the distribution of power flow in PN and traffic flow in TN. These findings shed light on the interconnected nature of the coupled system. Having examined the impact relationship within this interconnected system, the subsequent subsection focuses on discussing the effectiveness of the collaborative framework with P2P energy trading.

8.5.3 Analysis on Effectiveness of Collaborative Framework with P2P Energy Trading To validate the effectiveness of our proposed collaborative framework with P2P energy trading, we conducted simulation studies on Cases 1–3 using Scenario 1 as an example. Taking into account the energy demand in Scenario 1, along with the electricity prices from the wholesale market and our proposed P2P trade pricing mechanism, we obtained the energy transaction prices within the collaborative P2P trade framework, as depicted in Fig. 8.10a. From the consumer’s perspective, it can be observed that the purchasing price from the P2P trade market is higher than the price during 1:00–7:00 and 23:00–24:00. This is because from the wholesale market λDA t the energy demand from users during these time intervals is low, prompting PN to sell electricity at a lower price to encourage energy consumption. However, from 9:00 to 22:00, the purchasing price from the P2P trade market is lower than the wholesale market price λDA t . This indicates that HFSs are inclined to procure energy from the P2P trade market rather than the wholesale market, as it helps reduce operational costs. Looking from the producer’s perspective, the selling prices in the P2P trade market generally surpass the financial rewards offered by PN, except during the time periods of 6:00–9:00 and 16:00–19:00, as indicated in Fig. 8.10b. During these specific periods, HFSs prioritize trading energy with others to maximize their profits. It is

Fig. 8.10 Energy transaction prices under collaborative P2P trade framework: a purchasing price ($/MWh), b selling price ($/MWh), reprinted from Ref. [57], copyright2022, with permission from IEEE

176

8 Collaborative Operation Between Power Network and Hydrogen …

Fig. 8.11 Operating parameters of hydrogen fueling stations: a input power of electrolyzer (MW), b output power of fuel cell (MW), reprinted from Ref. [57], copyright2022, with permission from IEEE

worth noting that the trade prices in the rush hour of TN are set at zero, indicating that HFSs do not engage in energy exchange with others during this time. This is because the energy demand in TN is high during these hours, and HFSs need to prioritize meeting the demand of H2EVs in TN. Additionally, our developed control strategy prohibits HFSs from simultaneously buying and selling energy, thereby preventing arbitrage opportunities. Based on this foundation, the schedules of HFSs in the three cases are obtained and depicted in Fig. 8.11. In Case 1, HFSs generate profits by purchasing electricity at a low cost, converting it into hydrogen, and supplying it to H2EVs at a higher price. Consequently, the input power for the electrolyzer in HFSs is higher compared to the other cases, particularly during periods when electricity prices are relatively low, as shown in Fig. 8.11a. Since HFSs operate independently, they do not provide operating reserve (OR) services to PN, resulting in a fuel cell output power of zero. In Case 2, a notable departure from Case 1 is the collaborative operation between PN and HFSs. Here, HFSs provide PN with OR services, and in return, PN offers financial rewards to the HFSs. Consequently, the operation of HFSs becomes depenbut also on the financial rewards λOR they dent not only on electricity prices λDA t t receive. As depicted in Fig. 8.11b, HFSs in Case 2 display a preference for supplying OR services to PN in order to maximize their financial rewards. Furthermore, taking into account the integration of P2P energy trading, HFSs in Case 3 enjoy increased flexibility compared to Case 1 and Case 2. They have the option to purchase electricity from either the wholesale market or the P2P market, selecting the option with the lower price. Additionally, HFSs can sell OR to PN or sell electricity to other HFSs, depending on the prevailing prices. Consequently, it is observed that HFSs in Case 3 strategically choose to procure electricity from the wholesale market during the price is lower compared to the transaction 1:00–9:00 and 23:00–24:00, as λDA t price in the P2P market. From 10:00 to 23:00, the primary source of input power for the electrolyzer is obtained through P2P trading, ensuring reduced operation costs, as depicted in Fig. 8.11a. Similarly, HFSs prioritize transferring energy to other HFSs

8.5 Case Study

177

Fig. 8.12 Operating parameters of power network: a OR provided by ESS to PN (MW), b OR purchased from wholesale market and HFS (MW), reprinted from Ref. [57], copyright2022, with permission from IEEE

via fuel cells, as the transaction price in the P2P market is higher than the OR rewards offered by PN, as demonstrated in Fig. 8.11b. The optimal control of PN’s operation is demonstrated in Fig. 8.12 across the three cases. In Case 1, PN’s required OR can only be provided by its affiliated ESS or purchased from the wholesale market. Notably, the ESS, being part of PN, offers OR services to PN free of charge. Consequently, it is observed that PN solely relies on the ESS for OR acquisition before 8:00, as the cost coefficient of discharging the ESS is notably lower than the electricity price in the wholesale market. However, after 8:00, the capacity of the ESS falls short, forcing PN to purchase OR from the expensive wholesale market due to the lack of alternatives. In comparison to Case 1, both Case 2 and Case 3 exhibit the ability of HFSs to procure OR from both the wholesale market and other HFSs. Consequently, as depicted in Fig. 8.12a, ESS in Case 2 and Case 3 supplies a reduced amount of OR to PN before 5:00, in contrast to Case 1, where PN solely relies on purchasing OR directly from HFSs. Similarly, Fig. 8.12b illustrates that PN procures a decreased amount of OR from the wholesale market, as the OR prices offered by HFSs are occasionally lower than those in the wholesale market. Additionally, Table 8.3 presents the operation costs for the three cases. Notably, the independent case incurs the highest operation cost, amounting to $15, 259.73. However, with the implementation of the collaborative framework in Case 2, the cost decreases to $14, 610.52. This reduction is achieved through the transaction of OR between PN and HFSs at a comparatively lower price. In this cooperative arrangement, without P2P energy trading, the calculated benefit function amounts to $649.21. Consequently, the coalition formed by PN and HFSs realizes an additional profit of $649.21 in comparison to Case 1. Furthermore, when considering the integration of P2P energy trading, the operation cost further decreases to a remarkable $13, 841.39 within the collaborative operation framework. This substantial reduction is primarily attributed to the ability of HFSs to engage in energy trading with each other using

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8 Collaborative Operation Between Power Network and Hydrogen …

Table 8.3 Operation cost of coalition under three cases, reprinted from Ref. [57], copyright2022, with permission from IEEE

Operation cost ($)

Benefit function of coalition ($)

Case 1

15259.73

0

Case 2

14610.52

649.21

Case 3

13841.39

1418.34

a P2P approach, thereby securing lower prices and consequently minimizing operational expenses. Consequently, the resulting profit amounts to $1, 418.34, the highest among the three cases. The augmentation of profit can be directly attributed to the advantageous P2P energy trading, which effectively reduces operational costs while maximizing economic gains. Employing our meticulously designed benefit allocation mechanism based on bilateral Shapley value, the allocation of economic profits among PN and the three HFSs in Cases 1∼3 is meticulously presented in Table 8.4. A careful analysis of the allocation reveals that the distribution of revenues is predicated on the individual contributions made to the collective welfare of the coalition. Notably, in Case 1, where independent operation prevails, the benefit allocated to the participants is observed to be zero, as no additional benefits are derived from this mode of operation. Conversely, in Case 2, where collaborative operation is actively pursued, participants are rewarded with profits in direct proportion to their respective contributions to the unified endeavor. A notable example is the remarkable gain of $216.13 accrued by PN, the largest benefit obtained by any player in Case 2. This compelling outcome unequivocally demonstrates the allure and incentive for participants within the collaborative framework to actively engage in the pursuit of increased economic benefits. This tangible evidence serves as a powerful motivator, effectively encouraging greater participation and fostering a deep sense of commitment among the participants. Furthermore, by harnessing the potential of P2P energy trading, the allocated benefits of all members in Case 3 surpass those of Case 1 and 2. Remarkably, the benefits obtained in Case 3 amount to $614.69, $283.17, $260.49, and $259.99 for the respective participants. These substantial gains serve as a testament to the undeniable superiority of our proposed collaborative framework, enriched by the integration of P2P energy trading. This remarkable outcome further underscores the pivotal role played by our framework in unlocking enhanced economic benefits, solidifying its position as a transformative and advantageous approach to collaborative operations. Table 8.4 The allocation of economic benefit of PN and HFSs, reprinted from Ref. [57], copyright2022, with permission from IEEE Allocation ($)

PN

HFS1

HFS2

HFS3

Case 1

0

0

0

0

Case 2

216.13

146.42

149.71

136.95

Case 3

614.69

283.17

260.49

259.99

8.6 Conclusions

179

In a comprehensive analysis, this study delves into the intricate relationship between PN and TN, leveraging the coupled power-traffic system as a foundational framework. By examining various scenarios with different hydrogen selling prices, the investigation sheds light on the profound impact of HFS operation on both PN and TN. Notably, through a meticulous comparison of two distinct scenarios, it becomes apparent that the operation of HFSs possesses the potential to significantly influence the status and dynamics of both PN and TN. Building upon these insightful findings, the efficacy of the proposed collaborative operation framework between PN and HFSs is rigorously verified under the constraints of the coupled system. Impeccably designed simulations showcase the remarkable cost reduction capabilities inherent within our developed collaborative framework. These results underscore the transformative potential of our approach, as it effectively minimizes operational costs while fostering enhanced cooperation and synergy among the participants.

8.6 Conclusions This paper presents the establishment of a comprehensive HFSs coupled powertraffic system, taking into account P2P energy trading, with the aim of exploring the intricate relationship between HFSs, power flow of PN, and traffic flow of TN. To enhance the effective interaction between PN and HFSs, a novel collaborative operation framework incorporating P2P energy trading, based on coalition game theory, is proposed. This framework takes into consideration the simultaneous supply of energy and reserve, thereby promoting efficiency. Building upon this foundation, a dynamic pricing and arbitrage prevention mechanism is developed for the P2P energy trading strategy, further reducing the operational costs of the coalition. In addition, a profit allocation method based on bilateral Shapley value is introduced, offering a computationally efficient approach for allocating economic benefits compared to traditional methods. Moreover, the stability of the coalition formed by PN and HFSs is ensured through the derivation of the super additive properties of the collaborative operation framework with P2P energy trading. This guarantees that each participant within the coalition can attain increased benefits. Extensive case studies have been diligently conducted to empirically validate the efficacy of our meticulously developed coupled model and the innovative collaborative framework incorporating P2P energy trading. The results obtained from these comprehensive simulations convincingly demonstrate the interdependence between the operation of HFSs and the coupled power-traffic system. Notably, the operation of HFSs is inherently influenced by the intricate dynamics of the coupled powertraffic system, while simultaneously exerting a profound impact on the overall status of both PN and TN. Furthermore, the case studies conducted to evaluate the collaborative framework with P2P energy trading shed light on the substantial benefits that can be derived from the cooperative interaction between HFSs and PN in terms of energy generation and reserve allocation. Remarkably, the findings underscore the

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8 Collaborative Operation Between Power Network and Hydrogen …

remarkable advantage of collaboration, as both HFSs and PN can effectively maximize their respective gains through this synergistic approach. Moreover, a meticulous analysis of benefit allocation has been diligently executed, serving as a catalyst for fostering increased participation and cooperation. This insightful analysis effectively underscores the inherent advantages offered by our proposed collaborative operation framework with P2P energy trading, thereby motivating and encouraging active engagement among the participants. The allocation of benefits is thus meticulously orchestrated to ensure fairness and encourage sustained involvement within the collaborative ecosystem.

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Chapter 9

Coordinated Operation Between Electric Vehicle Charging Stations and Distribution Power Network Considering Energy and Reserve

9.1 Introduction As an important technology for saving energy and reducing emissions in transportation systems, electric vehicles (EVs) and their charging stations have drawn much attention in recent years [1–5]. Indeed, the International Energy Agency has predicted that the number of EVs worldwide will reach 245 million by 2030, including about 4.6 million in China [6, 7]. Due to the large-scale adoption of EVs, the transportation system needs more charging power, and the controllable characteristic of EV charging loads also provides a favorable opportunity for improving the security, economy, and reliability of power systems [8]. Apparently, EVs as charging demand affect the spatial and temporal distribution of electrical loads in a power system. Therefore, it is important for EVs and the power system to interact with each other in an efficient way, which could enhance both the power system performance and renewable utilization. As an important form of power system, distribution power networks (DPNs) is considered for its efficient coordinated operation with EVs in existing works. On the one hand, it is indicated that large-scale EV charging could lead to various operational issues in a DPN, such as voltage deviations and line losses, which reduce the power system performance [9]. For instance, an Internet of Things-based centralized control strategy was proposed in Ref. [10] to coordinate EV and DES distribution, which can significantly improve the network performance, including energy loss and voltage imbalance. Besides, Ref. [11] develops static and dynamic scheduling frameworks for optimal EV coordination, which aims for better energy management. Ref. [12] presented a robust power management scheme between EVs and a DPN, considering voltage deviations and line overloading. On the other hand, EVs could also help the DPN accommodate renewable energy. In Ref. [13], an optimal operation strategy of the DPN system was proposed to improve the accommodation of solar energy by EVs. In Ref. [14], an optimal decentralized EV charging control was proposed to deal with uncertainties of wind power, and the economic benefits of EVs and the DPN were maximized. In addition, Ref. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_9

183

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9 Coordinated Operation Between Electric Vehicle Charging Stations …

[15] developed an optimized EV charging strategy to mitigate the fluctuation of wind power generation, and simulation results verified the outperformance of the strategy for better interaction between EVs and wind energy. What is more, Ref. [16] proposed a new multistage distribution expansion planning model, which can minimize the investment cost of renewable energy with the help of scheduling EVs. Especially, note that EVs and a DPN interact with each other through EV charging stations (EVCSs) [17], which could be regarded as aggregators of EVs to cooperate with the DPN. Therefore, their interactions in terms of energy management with storage systems is significant to achieve an efficient cooperation. In this aspect, Liao et al. [18] proposed an optimization algorithm for the economic dispatch of an EVCS combined with energy storage systems. Simulation results showed that adequate dispatch could reduce the impacts of charging demands on the DPN. Besides, Chaudhari et al. [19] presented a combined deterministic and rule-based approach for energy storage management in the EVCS, which is verified could effectively satisfy EV charging loads and conduct energy transfer between the EVCSs and the DPN. Moreover, Bao et al. [20] proposed a bi-level optimization approach for energy management of an EVCS, and a battery system was introduced for charging load control. Case studies based on real data in the Huairou District of Beijing verified the effectiveness of the proposed approach. The works mentioned above focused on energy interactions. However, EVs could also provide the DPN with ancillary services, such as reserve supply [21–26]. For instance, Ref. [21] showed that EVCSs participated in offering reserve, and a rulebased decision-making method was applied to simultaneously support the ancillary service for DPN and the charging service for EVs. Ref. [22] reported a charging model of EVCSs, by which reserve was provided for the DPN to deal with fluctuations of wind power. In addition, Ref. [23] pointed out that EVCSs could offer reserve to compensate for active power in the DPN, and a decentralized coordination algorithm was proposed to lessen computational complexity, compared with that of the centralized approach. Similarly, charging demands of EVCSs were deemed as responsive loads that provided reserve for the DPN in Ref. [24], and an energy and reserve scheduling method was presented to mitigate negative effects regarding uncertainties of renewable power in the DPN. Ref. [25] studied the impacts of EVCSs on the operation of DPN when they provided reserve services, and the results indicated reductions in operational cost and wind curtailment as well as an increase in environmental benefits. Also, Ref. [26] considered that EVCSs supplied reserves for the power network, and their coordination was studied via a robust optimization approach. Simulation results verified that the total operational cost was reduced when reserve services were provided. According to the above literature review, it is seen that the DPN and EVCSs can reduce their dependency on the third entity, e.g., the wholesale market, when they cooperate in energy and reserve regulation. In detail, such cooperation could effectively utilize renewable energy in the DPN and reduce the energy purchased from the wholesale market. Besides, EVCSs receive energy from the DPN to meet EV charging demands, while the DPN reduces its operating cost when EVCSs provide reserve services for it. In other words, EVCSs and the DPN as a whole, can obtain

9.2 Formulations of Energy-Reserve Decision for Electric Vehicle Charging …

185

economic benefits, e.g., reduction of the total operation cost, compared with the situation that they directly purchase energy or reserve from the wholesale market. However, to the best of authors’ knowledge, the issue of how to quantitatively allocate such benefits to EVCSs and the DPN has not been reported, which is the main motivation of our work. Meanwhile, it is noted that with the development of EVCSs, their quality of service (QoS) shall be paid attention when they interact with the DPN, i.e., the charging demands of EVs are satisfied within a guaranteed period of time [27]. In order to solve the above issues, this paper proposes a method for the coordinated operation of energy and reserve in a system containing EVCSs and the DPN, in which the coalition game is used to analyze and allocate economic benefits among EVCSs and the DPN. Specifically, (i) we firstly apply the network calculus theory to describe the QoS of EVCSs and propose an optimization objective to maximize the QoS, then the formulation about the economic cost for the shared energy and reserve scheduling in the system are described, thus a multi-objective optimization model is established to help the economic operation of EVCSs and the DPN; (ii) we adopt a characteristic function of the coalition between EVCSs and the DPN based on the coalition game, and offered an improved allocation mechanism for fairly distributing economic benefits. These two aspects are main contributions of our paper.

9.2 Formulations of Energy-Reserve Decision for Electric Vehicle Charging Stations In this Section, we propose formulations of energy-reserve integrated decisions for EVCSs with QoS constraints, which are described based on the network calculus theory [28]. In detail, the network calculus theory based charging QoS model of EVs are shown as follows, which could be referred to [29] for more details. Besides, an optimization objective about QoS is proposed to describe the behavior of EVCS better. We denote Pev,j (t) as the charging power of EV j at time t, and /t as the time step. In this way, formulations of its arrival curve Aj (t), the departure curve Dj (t), and the minimum departure curve Dmin,j (t) of EV j are given as follows. A j (t) = min{E re, j , Pmax,i (t − tar, j ) · /t} D j (t) = { Dmin, j (t) =

t E

(9.1)

Pev, j (t) · /t

(9.2)

0 tar, j ≤ t ≤ tch, j Pmax,i (tdep, j − t) · /t tch, j ≤ t ≤ tdep, j

(9.3)

tar, j

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9 Coordinated Operation Between Electric Vehicle Charging Stations …

where t ch,j = t dep,j − E re,j /Pmax,i . Specially, arriving time and the latest departure time set by the user are denoted as t ar,j and t dep,j , respectively. In addition, E re,j and Pmax,i represent the required charging energy for EV j and the maximum charging power from the charging station i, respectively. Notes that when EVCS i provides charging service, it shall satisfy the energy demand of EVs, i.e., guaranteeing the QoS of charging service. Therefore, this paper characterizes the QoS of EVCS i, shown as follows. Ai (t) =

E

A j (t), ∀i ∈ N

(9.4)

D j (t), ∀i ∈ N

(9.5)

Dmin, j (t), ∀i ∈ N

(9.6)

j∈i

Di (t) =

E j∈i

Dmin,i (t) =

E j∈i

where Ai (t), Di (t), Dmin,i (t) represent arrival curve, departure curve and minimum departure curve of EVCS i, respectively. Besides, N is the set of charging stations, and i ∈ N . It should be mentioned that the arrival, departure, and minimum departure curves shall satisfy the following relationship, i.e., Ai (t) ≥ Di (t) ≥ Dmin,i (t), to ensure the QoS of EVCSs Moreover, since all EVs want their electricity demands to be satisfied quickly, an optimization objective about QoS can be described as follows. {T max F Q i = {0T 0

Di (t)−Dmin,i (t) Ai (t)−Dmin,i (t)

(9.7)

where F Q i ∈ [0, 1] [0, 1], and a larger value of F Q i means a higher service efficiency of EVCS. For example, when F Q i = 1, the arrival and departure curves of the EVCS would coincide, which means that EVCS satisfies all electricity demands when EVs arrive, and it is a behavior of high QoS. When Eq. (9.7) is introduced to the whole model as one of optimization objectives, the impacts of QoS on the economic cost could be further explored. When an EV arrives at the charging station at time tar,j, it will report its own needed energy Ere,j and the estimated departure time tdep,j to the operator of EVCS i. Then the station optimizes the charging and reserve plans based on the energy and reserve prices in the wholesale market to minimize its cost. The cost function can be expressed in the following formulation. min Ui =

T E

[λe,DA (t)Pi (t) − λ r (t)Ri (t)]/t, ∀i ∈ N

(9.8)

t=1

Pi (t) + Ri (t) ≤ Pmax,i

(9.9)

9.3 Operational Formulations of Distribution Power Network

187

where Pi (t) and Ri (t) are the charging power and the reserve of EVCS i at time interval t. Pmax,i is the maximum charging power of EVCS i. In addition, λe,DA (t) and λr (t) are the energy and reserve prices, respectively. It can be seen from Eq. (9.8) that EVCS i shall pay the wholesale market for charging energy, and obtain benefits as it provides reserves to the market. In our work, we consider that EVCSs provide reserve services. Note that the battery storage of EVCSs shall have enough energy to maintain its output for a time period αs, which could be qualified for providing spinning reserves [30]. Thus, the following constraints shall be satisfied. Pi (t) ≥ Ri (t) ≥ 0, ∀i ∈ N , t ∈ T

(9.10)

Ai (t) ≥ Di (t) + Ri (t)αS , ∀i ∈ N , t ∈ T

(9.11)

Di (t) − Ri (t)αS ≥ Dmin,i (t), ∀i ∈ N , t ∈ T

(9.12)

9.3 Operational Formulations of Distribution Power Network In order to satisfy its load demands, the DPN needs purchase energy and reserve from the wholesale market. Meanwhile, the DPN can use energy storage systems (ESSs) to well accommodate uncertainties of renewable energy, e.g., photovoltaic cells (PVs), in order to reduce its cost. Therefore, the total operation cost of DPN is expressed as follows. UD P N =

T E

{λ e, D A (t)PD P N , D A (t) + λ e,RT (t) p D P N , RT (t)

t=1

+ e P E N | p D P N , RT (t)| +

E

}/t

(9.13)

i∈E SS

where PDPN,DA (t) and pDPN,RT (t) are the purchased energy and reserve from the wholesale market, respectively. PESS,dc,i (t) and PESS,c,i (t) stand for the discharging and charging power of ESS i at time interval t, respectively. λe,RT is the reserve price of the wholesale market, and ePEN is the penalty cost coefficient of the offset between real-time power and day-ahead plan [31]. cESS,i denotes the charging and discharging cost coefficient of ESS i. ESS stands for the ESS set of the DPN. In addition, for the operation of DPN, we shall consider constraints of power balance, voltage amplitude, etc. Also, the uncertainty of PV outputs is also taken into account. Details are presented in the following subsections.

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9 Coordinated Operation Between Electric Vehicle Charging Stations …

9.3.1 Power Balance For any node i in the DPN, formulations of power balance are expressed as follows. E

PDPN,i (t)+

i∈G j

E

E

PPV,i (t)+

i∈PV j

[PESS,dc,i (t) − PESS,c,i ] −

i∈ESS j

Pi j (t) − ri j li j (t) −

E

E

PL,i (t) =

i∈L j

P jk (t), ∀ j ∈ B, t ∈ T

k:( j,k)∈E

(9.14) E i∈G j

Q DPN,i (t) +

E

E

Q PV,i (t) +

i∈PV j

Q ESS,i (t) −

i∈ESS j

Q i j (t) − xi j li j (t) −

E

E

Q L,i (t) =

i∈L j

Q jk (t), ∀ j ∈ B, t ∈ T

(9.15)

k:( j,k)∈E

v j (t) = vi (t) − 2[ri j Pi j (t) + xi j Q i j (t)] + (ri2j + xi2j )li j (t) li j (t) =

Pi j (t)2 + Q i j (t)2 vi (t)

, ∀(i, j ) ∈ E, i ∈ B, t ∈ T

(9.16)

(9.17)

where PDPN,i (t) and QDPN,i (t) are the active and reactive power which are injected into the node i of DPN in time interval t. PPV,i (t) and QPV,i (t) represent the predicted active and reactive power outputs of PV. QESS,i (t), PL,i (t), and QL,i (t) denote the reactive power output of ESS i, the predictive active and reactive power consumption of load i, respectively. Pij (t) and Qij (t) stand for the active and reactive power of the branch ij from node i to node j. l ij (t) is the square of current amplitude flowing through the branch. vi (t) is the square of voltage amplitude of node i. r ij and x ij are the resistance and reactance of branch ij. B is the set of nodes in the DPN, and E is the set of lines. G j , L j , ESS j and PV j represent the sets of the external system, loads, ESS and PV which are accessed at node j in the DPN.

9.3.2 Security Constraints In order to guarantee operational security of the DPN, the operator needs to consider voltage amplitude constraints of each node and power flow constraints of branches in the DPN. 2 2 Vmin,i ≤ vi (t) ≤ Vmax,i , ∀i ∈ B, t ∈ T

(9.18)

2 li j (t) ≤ Imax,i j , ∀(i, j ) ∈ E, t ∈ T

(9.19)

9.3 Operational Formulations of Distribution Power Network

189

where V min,i and V max,i are lower and upper bounds of voltage amplitude at node i, respectively. I max,ij is the upper bound of current in the branch ij.

9.3.3 ESS Output Constraints 0 ≤ PESS,dc,i (t) ≤ PESS,dc,max,i

(9.20)

0 ≤ PESS,c,i (t) ≤ PESS,c,max,i

(9.21)

PESS,dc,i (t)PESS,c,i (t)= 0

(9.22)

E ESS,i (t) = E ESS,i (t − /t) + PESS,c,i (t)ηc /t −

PESS,dc,i (t) /t ηdc

E ESS min,i ≤ E ESS,i (t) ≤ E ESSmax,i , ∀i ∈ ESS, t ∈ T

(9.23) (9.24)

where PESS,dc,max,i and PESS,c,max,i are the maximum discharging and charging power of ESS i, and E ESS,i (t) is the energy stored at the end of t. E ESSmin,i and E ESSmax,i denote the minimum and maximum stored energy that ESS i allows, respectively. ηc and ηdc are the charging and the discharging efficiencies, respectively. It is noted that Eq. (9.22) indicates that the ESS cannot charge and discharge at the same time.

9.3.4 Reserve Constraints It is difficult to obtain actual values of PV outputs and load demands, due to the existence of forecasting errors. However, such errors can be quantified via certain ranges [32, 33], which are formulated as follows. /PPV,i (t) ∈ [−δPV,i (t), δPV,i (t)], ∀i ∈ PV, t ∈ T

(9.25)

/PL,i (t) ∈ [−δL,i (t), δL,i (t)], ∀i ∈ L, t ∈ T

(9.26)

where /PPV,i (t) and /PL,i (t) stand for deviations between actual and predicted values of PV outputs and loads, respectively. δ PV,i (t) and δ L,i (t) are their maximum prediction errors, respectively. Specially, ESSs can provide reserves and the DPN can purchase/sell electricity from/to the real-time wholesale market, to compensate uncertainties of PV outputs and load demands and realize the real-time power balance [34, 35]. In this paper, we use the participation factors method [36], to determine the contributions of ESSs and

190

9 Coordinated Operation Between Electric Vehicle Charging Stations …

the power exchange between the DPN and the real-time wholesale market. pESS,i (t) = PESS,dc,i (t) − PESS,c,i (t) − βESS,i (t)ζ (t)

(9.27)

pDPN,RT (t) = −βRT (t)ζ (t)

(9.28)

βRT (t) +

E

βESS,i (t) = 1

(9.29)

i∈ESS

βRT (t), βESS,i (t) ≥ 0, ∀i ∈ ESS, t ∈ T

(9.30)

where β ESS,i (t) and β RT (t) are the participation factors for ESSs and real-time market. pESS,i (t) is the actual output of the ith ESS, and pDPN,RT (t) represents the exchanged power. In addition, ζ(t) is the summation of deviations between actual and forecast values in terms of PV outputs and loads, which is expressed as follows. ζ (t)=

E

/PPV,i (t) +

i∈PV

ζmin (t) = −

E

E

δPV,i (t) −

i∈PV

ζmax (t) =

E

/PL,i (t), ∀t ∈ T

(9.31)

i∈L

δPV,i (t) +

i∈PV

E

δL,i (t), ∀t ∈ T

(9.32)

i∈L

E

δL,i (t), ∀t ∈ T

(9.33)

i∈L

where ζmin (t) and ζmax (t) are the minimum and maximum values of ζ(t), respectively.

When ESS i provides reserve to the DPN, its actual charging/discharging power pEES,i (t) and the stored energy shall satisfy the following constraints. −PESS,c,max,i ≤ pEES,i (t) ≤ PESS,dc,max,i , ∀i ∈ ESS, t ∈ T

(9.34)

max{ pEES,i (t), 0} /t, ∀i ∈ ESS, t ∈ T ηdc

(9.35)

E ESS,i (t) + max{− pEES,i (t), 0}ηc /t ≤ E ESSmax,i , n ∈ N , t ∈ T

(9.36)

E ESS min,i ≤ E ESS,i (t) −

9.3.5 Reactive Power Constraints If power outputs of PVs and charging/discharging powers of ESSs are not binding at the rated capacities of power converters, the DPN operator can adjust their reactive

9.4 Shared Energy and Reserve Model for Charging Stations …

191

power outputs [37]. They shall satisfy the following constraints. 2 (PESS,dc,i (t) − PESS,c,i (t))2 + Q ESS,i (t)2 ≤ SESS,i , ∀i ∈ ESS, t ∈ T 2 PPV, j (t)2 + Q PV, j (t)2 ≤ SPV, j , ∀ j ∈ PV, t ∈ T

(9.37) (9.38)

where S ESS,i and S PV,j are capacities of the converters connecting ESS i and PV j. Therefore, the decision variables of Eq. (9.13) consist of PDPN,DA (t), PESS,c,i (t), QESS,i (t), QPV,j (t), β ESS,i (t), and β RT (t). Meanwhile, constraints Eqs. (9.15)-(9.38) shall be satisfied for the secure operations of DPN.

9.4 Shared Energy and Reserve Model for Charging Stations and Distribution Power Network Using Coalition Game In game theory, a coalition game is the one with cooperation between groups of players, using possible external enforcements, such as a contract law. Because of its well-recognized advantage on enhancing the whole benefit of all players, the coalition game has been widely used in studying offer prices in power markets [38], profit allocation to power producers [39], economic dispatch [40], demand side management [41], etc. Therefore, in this paper, we plan to use the coalition game to realize the optimal operations for EVCSs and the DPN.

9.4.1 Shared Energy and Reserve Scheduling Model To well use this game, it is necessary to explain how these two entities cooperate with each other in a system. Figure 9.1 shows energy and reserve transfer among EVCSs, the DPN, and the wholesale market. In detail, the black solid and dotted lines represent energy and reserve, and the arrow in these lines indicates transfer direction. In this way, it is seen that EVCSs and the DPN can individually interact with the third entity, i.e., the wholesale market, in terms of both energy and reserve. For instance, EVCSs purchase energy from the wholesale market to satisfy their EV charging demands, while EVCSs can provide reserve for the market in turn. Also, the DPN may purchase/sell energy and reserve from/to the wholesale market when the excessive or deficient electricity happens. However, when EVCSs are integrated into the DPN, it is natural to study the issue as of how these two entities share the energy and reserve resources as a whole to reduce their dependency on the wholesale market. That is, EVCSs can directly provide reserve to the DPN so that it will purchase less reserve from the wholesale market. On the other hand, the energy can also be transferred from the DPN to EVCSs, which

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9 Coordinated Operation Between Electric Vehicle Charging Stations …

Wholesale Market PV

ESS

DPN

EVCS 1 Energy flow from wholesale market

EVCS 2 Reserve flow from wholesale market

EVCS 3 Cooperation energy/reserve flow

Fig. 9.1 The operation of the system containing EVCSs and the DPN for energy and reserve, reprinted from Ref. [49], copyright2023, with permission from IEEE

reduce the amount of electricity purchased from the wholesale market. In this way, cooperation of EVCSs and the DPN could lead to reduction of their total operational cost. Therefore, in order to well study the coalition game, it is necessary to establish a shared energy and reserve scheduling model for coalitions among EVCSs and the DPN. This game can be expressed as {M,v,φ}, where M represents the set of all members, i.e., all EVCSs and the DPN, and the number is denoted as M. v: 2M → R is the characteristic function of any coalition S ⊂ 2M , which means the cooperation of coalition S leads to economic benefits, i.e., reduction of operation cost, compared with that of no coalitions. φ stands for the vector of benefits that will be allocated to individual players in each coalition. Consequently, to study the characteristic function, we formulate the shared energy and reserve scheduling model regarding coalition S, and its operation cost CS is shown as follows.

9.4 Shared Energy and Reserve Model for Charging Stations …

193

ET { λ e, DA (t)PDPN, DA (t) + λ e,RT (t) pDPN, RT (t) + ePEN | pDPN, RT (t)| t=1 min CS = E } + [cESS,i PESS,dc,i (t) + cESS,i PESS,c,i (t)] /t i∈ESS ~~ ~ ~ +

Operation cost of DPN

ET E ~

t=1

{

i∈S

} [λ e,DA (t)Pi (t) − λ r (t)Ri (t)] /t ~~ ~

Operation cost of EVCSs

(9.39) It is observed that Eq. (9.39) is the summation of the operation cost of DPN and EVCSs (which are players in the coalition), based on Eq. (9.8) and Eq. (9.12). Note that each charging station and the DPN can realize the power balance in real-time through sharing reserves during their cooperation. We can also introduce participation factors of EVCSs, thus the following constraints shall be considered. E i∈S

βi (t) + βRT (t) +

E

βESS,i (t) = 1, ∀S ⊂ N , t ∈ T

(9.40)

i∈ESS

Pi (t) − βi (t)ζ (t) ≥ 0, ∀i ∈ N , t ∈ T

(9.41)

Pi (t) + βi (t)ζ (t) ≤ Pmax,i , ∀i ∈ S, t ∈ T

(9.42)

Ai (t) ≥ Di (t) + αS βi (t)ζ (t)/t, ∀i ∈ S, t ∈ T

(9.43)

Di (t) − αS βi (t)ζ (t)/t ≥ Dmin,i (t), ∀i ∈ S, t ∈ T

(9.44)

0 ≤ βi (t) ≤ 1, ∀i ∈ S, t ∈ T

(9.45)

where β i (t) is the participation factor of EVCS i at time interval t. In this way, the decision variables of Eq. (9.39) include PDPN,DA (t), PESS,dc,i (t), PESS,c,i (t), Pi (t), QESS,i (t), QPV,j (t), β RT (t), β ESS,i (t), and β i (t). As a result, considering the economic cost and QoS described in Sections II and III, the multi-objective problem about the cooperation for EVCSs and the DPN can be expressed as follows ⎧ E ⎪ Ui ⎨ min CS = UDPN + ⎪ ⎩ max F Q i =

{T

{0T 0

i∈S Di (t)−Dmin,i (t)

(9.46)

Ai (t)−Dmin,i (t)

s.t. (9.9)–(9.12), (9.14)–(9.24), (9.34)–(9.38), (9.40)–(9.45) where CS and F Q i means the total economic cost and QoS of each EVCS, respectively. Usually, we can use the weighting summation method2 to transform (9.46) to a

194

9 Coordinated Operation Between Electric Vehicle Charging Stations …

single objective optimization model. For instance, when the weight of one objective is set up to 1 and the other 0, the model can be only used for optimizing CS or F Q i . However, it shall be mentioned that Eq. (9.46) is an uncertain optimization problem, as PV outputs and load demands in the DPN are presented as interval variables, shown as in Eqs. (9.25)–(9.26). Therefore, we use the robust optimization to solve it. This approach converts the uncertainty optimization problem into a deterministic robustness counterpart [42]. Besides, since the optimization objects of Eq. (9.46) are not of the same order of magnitude, it is improper to sum them with different weights to form a total object. Therefore, we employed the AUGMECON ε-constraint algorithm [43] to solve the problem to obtain the Pareto soultions2, which is further discussed in the Appendix with a method to select a harmony solution.

9.4.2 Characteristic Function and Shapely Value Based on Participation Factors After obtaining the optimal operation cost of the coalition, we need to measure the value generated by the coordinated operations between EVCSs and the DPN. This is related to the characteristic function. Therefore, we define this function v(S) of the coalition S ⊂ 2 M as the economic benefit by the coordinated operation, i.e., reduction of the total operational cost, compared with the situation that EVCSs and the DPN are not in coordinated operation. Therefore, the characteristic function is formulated as follows. E v(S) = Ui − CS (9.47) i∈S

For any two disjoint coalitions S andV in the coalition game (S ∩ V=∅), when the DPN is not involved in the coalition S or V, i.e., only EVCSs are players, then CS =

T E E {

} [λ e,DA (t)Pi (t) − λ r (t)Ri (t)] /t

(9.48)

t=1 i∈S

which means each EVCS in or purchases energy from and sells reserve to the wholesale market, and EVCSs do not cooperate with each other in terms of energy and reserve provision. In other words, an EVCS does not provide energy or reserve to others in our paper. Therefore, we can obtain the following equation. CS + CV = CS∪V

(9.49)

9.4 Shared Energy and Reserve Model for Charging Stations …

195

When the DPN is a member of coalition S or V, without loss of generality, we assume the DPN is in S. Then CS∪V represents the operation cost with cooperation of DPN and all EVCSs in S and V. On the contrary, CS + CV stands for the total costs of these two coalitions without cooperation i.e., the DPN does not cooperate with EVCSs in V. Notes that the more fully coordinated operation among the DPN and EVCSs, the less their dependency on the wholesale market. That is, the DPN could provide energy from PV to EVCSs. Besides, EVCSs could also adjust charging demands by energy and reserve cooperation with the DPN, in order to reduce electricity purchased from the wholesale market. Therefore, the total cost of S and V will be no less than the coordinated one when the DPN is cooperated with all EVCSs of S and V. CS∪V ≤ CS + CV

(9.50)

For any two disjoint coalitions S and V, the function satisfies the formulations. v(S) + v(V) E E Um − C S + Um − C V = m∈S

=

E

m∈V

Um − C S − C V ≤

m∈S∪V

E

Um − CS∪V

(9.51)

m∈S∪V

= v(S ∪ V) Therefore, the coalition game is super additive, and it has the following characteristics [44]. 1. The Shapely value of the coalition is its core, and it should be modified by participation factors for they represent the contribution of each player. 2. The coalition is stable. That is, EVCSs and the DPN in the coalition will not be willing to operate independently. This issue will be further verified in the Case Study Section of this paper. At present, the Shapely value has been widely used in the payoff allocation problem under the context of coordinated game [45]. When the Shapely value is employed to measure contributions of EVCSs and the DPN to the coalition, it can be expressed as follows. SVm (v) =

E

|S|!(M − |S| − 1)! [v(S ∪ {m}) − v(S)] M! S⊆M\{m}

(9.52)

where M represents the set of all players, and M is a subset of S. Their numbers are denoted as M and |S|, respectively. In this way, Eq. (9.51) can be explained as follows: considering the coalition being formed one player at a time, each player demands its contribution v(S ∪ {m}) − v(S) as a fair compensation, then it takes the average of this contribution over possible different permutations in which the coalition can be

196

9 Coordinated Operation Between Electric Vehicle Charging Stations …

formed. It is a proper method to allocate benefits when the contribution is hard to express. However, since the participation factor means the interaction degree of one player with others in a certain period, it can represent the contribution of the play in this coalition game. The summation of participation factors of the player m can be expressed as follows. {

T

ωm =

/ βm (t)

0

E {

T

βm (t)

(9.53)

m∈M 0

Based on the above equation, the player with a large participation factors should obtain an economic compensation from others. Therefore, the cost of an entity can be expressed as follows. φm (v) = SVm (v) − (ωi − 1/M) · min {Cm − SVm (v)} m∈M

(9.54)

With the help of Eq. (9.53), the allocation of economic benefits should be more fair, which would promote each player to collaborate with others. The detailed results will be discussed in the Section V, and two proposition about the proposed benefits allocation method should be proved. Proposition 1 The summation of economic costs of all players cannot be changed by the benefits allocation. Proof 1 The Shapely value should satisfy the following constraint. E

SVm (v) = CM

m∈M

Then, φm (v) obeys the following mathematical property.

(9.55)

9.4 Shared Energy and Reserve Model for Charging Stations … E

φm (v) =

m∈M

=

E

=

{SVm (v) − (ωi − 1/M) · min {Cm − SVm (v)}} m∈M

m∈M

E

SVm (v) −

m∈M

E

E

(ωi − 1/M) · min {Cm − SVm (v)} m∈M

m∈M

SVm (v) − (

m∈M

197

E

ωi − M/M) · min {Cm − SVm (v)} m∈M

m∈M

⎫ ⎤ / {T T {T ⎪ ⎪ E { ⎪ ⎪ ⎢ β (t) ⎥ ⎪ βm (t) βm (t)⎥ m ⎪ ⎢ ⎪ ⎪ ⎢ ⎥ ⎬ E E ⎢0 m∈M 0 ⎥ 0 ⎢ ⎥ −1 = SVm (v) − min {Cm − SVm (v)} · ⎢ ⎥ ⎪ ⎪ T m∈M ⎥ ⎪ ⎪ ⎪ ⎪ E { m∈M m∈M ⎢ ⎢ ⎥ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎣− ⎦ β (t) m ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ m∈M 0 ⎡ ⎤ / {T T {T E { ⎢ βm (t) βm (t) βm (t) − 1⎥ ⎢ ⎥ ⎢ ⎥ E E m∈M 0 ⎢ ⎥ 0 0 ⎥ SVm (v) − min {Cm − SVm (v)} · ⎢ = ⎢ ⎥ T m∈M { ⎢ ⎥ E m∈M ⎢m∈M ⎥ ⎣ ⎦ − βm (t) − 1 ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

⎡

m∈M 0

(9.56) As a result, the summation of φm (v) is equal to the total costs of all players, which means the total benefits never be changed by the allocation method. Proposition 2 The benefits allocated to each players should be no less than zero. Proof 2 Based on Eqs. (9.47)–(9.51), the characteristic function satisfies following formulations. v(M) = CM −

M E

Cm ≤ 0

(9.57)

i=1

As a result, M E

Cm ≥ CM

(9.58)

i=1

In addition, the Shapely value of each player is no greater than their economic costs without the cooperation, which is expressed as follows. SVm (v) ≤ Cm Therefore, when wm ≥ 1/M,

(9.59)

198

9 Coordinated Operation Between Electric Vehicle Charging Stations …

φm (v) = SVm (v) − (ωi − 1/M) · min {πm − SVm (v)} m∈M

≤ SVm (v) − (1/M − 1/M) · min {πm − SVm (v)} m∈M

(9.60)

≤ SVm (v) ≤ Cm Besides, when wm < 1/M φm (v) = SVm (v) − (ωi − 1/M) · min {Cm − SVm (v)} m∈M

= SVm (v) − Cm + Cm − (ωi − 1/M) · min {Cm − SVm (v)} m∈M

= Cm + SVm (v) − Cm − (ωi − 1/M) · min {Cm − SVm (v)} m∈M

= Cm − [Cm − SVm (v)] − (ωi − 1/M) · min {Cm − SVm (v)} m∈M

≤ Cm − min {Cm − SVm (v)} m∈M

−(ωi − 1/M) · min {Cm − SVm (v)} m∈M

= Cm − (1 + ωi − 1/M) · min {Cm − SVm (v)} m∈M

(9.61)

= Cm − (1 − 1/M) · min {Cm − SVm (v)} m∈M

−ωi · min {Cm − SVm (v)} m∈M

≤ Cm − (1 − M/M) · min {Cm − SVm (v)} m∈M

−ωi · min {Cm − SVm (v)} m∈M

= Cm − ωi · min {Cm − SVm (v)} m∈M

≤ Cm Based on Eqs. (9.60)–(9.61), φm (v) is never be greater than Cm , i.e., the cost of each player could be reduced with the help of the benefits allocation method.

9.5 Case Study 9.5.1 Simulation Settings In this section, we use an IEEE-33 bus DPN [46] and 3 EVCSs to conduct simulation studies. The maximum charging power of the stations are set as 1.2 MW, 2.4 MW, and 2.4 MW, respectively. Moreover, numbers of charging outlets of these 3 EVCSs are 10, 20, and 20, respectively. In the DPN, 3 PVs are located at buses 6, 23, and 30, respectively. In addition, one ESS is installed and its capacity is 1 MWh. Its maximum charging and discharging power are both 0.5 MW, and the efficiencies

9.5 Case Study

199

are both set as 0.9. The charging and discharging cost coefficients of the ESS are both set as 0.35 $/kWh [47]. The forecast values of PV outputs and loads in the DPN, as well as the energy and reserve prices of the wholesale market are shown in Table 9.1. Maximum forecast errors of PV outputs and loads are set as 30% and 10%, respectively. To verify effectiveness of the proposed shared energy and reserve scheduling model based on the coalition game, we obtain and analyze operational plans of EVCSs and the DPN in the non-coordinated and coordinated modes, respectively. Note that EVCSs and the DPN do not exchange energy or reserve in the non-coordinated mode. In comparison, they are operated in the coordinated mode. In this way, the impact of QoS on the operation cost are not discussed, i.e., the weight of cost is set up to 1 as described in Section VI. Table 9.1 Forecasted load and photovoltaic generation output together with prices information, reprinted from Ref. [49], copyright 2023, with permission from IEEE t(h)

PPV, (t) (MW)

PL (t) (MW)

λe,DA (t) ($/MWh)

λr (t) ($/MWh)

01:00

0.00

2.0728

155.12

0.63

02:00

0.00

1.8156

135.87

0.63

03:00

0.00

1.7810

133.28

0.63

04:00

0.00

1.6921

126.63

0.63

05:00

0.00

1.7828

133.42

0.63

06:00

0.00

2.0999

157.15

0.63

07:00

0.03

2.3310

174.44

0.63

08:00

0.05

2.3768

177.87

0.63

09:00

0.17

2.4797

185.57

0.63

10:00

0.41

2.5433

190.33

0.63

11:00

0.63

2.6452

197.96

0.63

12:00

0.86

2.8566

213.78

0.63

13:00

0.94

3.0587

228.90

0.63

14:00

1.00

3.0905

231.28

0.63

15:00

0.95

3.3374

249.76

0.63

16:00

0.81

3.8771

290.15

0.63

17:00

0.59

3.9258

293.79

0.63

18:00

0.35

4.1213

308.42

0.63

19:00

0.14

4.1484

310.45

0.63

20:00

0.02

4.4580

333.62

0.63

21:00

0.02

3.8070

284.90

0.63

22:00

0.00

3.0746

230.09

0.63

23:00

0.00

2.8211

211.12

0.63

24:00

0.00

2.4703

184.87

0.63

200

9 Coordinated Operation Between Electric Vehicle Charging Stations …

In addition, we assume that EVCSs 1 and 2 provide service for taxis, and EVCS 3 gives service for public buses. Detailed data about the regular usage of EVs are referred to from Reference [48]. According to the calculation method of the arrival curve and the minimum departure curve presented in Section II, they are obtained as shown in Fig. 9.2. To reveal the impacts of QoS on the charging plan and reserve, especially the system operation cost, the Pareto front of Eq. (9.46) should be solved and shown. Specially, it could be observed from Fig. 9.2 that EVCS 1 and EVCS 2 for taxis require a high QoS. Therefore, Eq. (9.7) is only applied to be calculated the QoS of EVCS 3 to analyze the impacts of different QoS requirements on results. Then we investigate the simulation results in the non-coordinated and coordinated modes, as well as different QoS values, which are presented in following subsections. 40

18 Arrival curve Minimum departure curve

16

Energy (MWh)

Energy (MWh)

12 10 8 6

30 25 20 15

4

10

2

5

0

5:00

10:00 15:00 Time (h)

20:00

Arrival curve Minimum departure curve

35

14

0

10:00 15:00 Time (h)

5:00

(a) Charging station 1

20:00

(b) Charging station 2

12

Energy (MWh)

10 Arrival curve Minimum Departure curve

8 6 4 2 0

20:00

1:00 6:00 Time (h)

11:00

(c) Charging station 3

Fig. 9.2 Arrival curve and departure curve of each charging station, reprinted from Ref. [49], copyright2023, with permission from IEEE

9.5 Case Study

201

5

PDPN,DA(t) (MW)

4.5

PESS,dc(t) -PESS,c(t) (MW)

0.15 Coordinated

4

Non-coordinated

3.5 3 2.5 2

Coordinated Non-coordinated

0.05 0 -0.05 -0.1 -0.15

1.5 1

0.1

5:00

10:00

15:00 Time (h)

20:00

(a) Day -ahead energy purchase plan

-0.2

5:00

10:00

15:00

20:00

Time (h)

(b) Charging and discharging plan of ESS

Fig. 9.3 Day-ahead energy purchase plans of DPN, charging and discharging plans of ESS in the coordinated and non-coordinated modes, reprinted from Ref. [49], copyright 2023, with permission from IEEE

9.5.2 Simulation Results 1. Results analysis of the coordinated mode compared to non-coordinated mode In the coordinated operation between EVCSs and the DPN, their operation plans are obtained and shown in Fig. 9.3 and Fig. 9.4, respectively. As shown in Fig. 9.3, purchase plans of the DPN changes in 4:00 and 22:00–24:00, compared with those of the non-coordinated mode. Also, the charging and discharging plans of the ESS are altered in these time intervals. Furthermore, Fig. 9.4 shows charging plans of individual EVCSs when they cooperate with the DPN. It is also observed that their plans are different from those obtained by the non-coordinated operation. This means the energy and reserve cooperation between EVCSs and the DPN puts impacts on the charging plans of each station. In addition, participation factors of the real-time market and EVCSs are presented in Table 9.2. Compared with the results of non-coordinated mode (NC-mode), we can see that the number of time intervals in which the value of βDPN,RT(t) is 0 has increased to 17 in coordinated mode (C-mode). It means that the purchased reserve from the real-time market is significantly reduced during these time intervals. Meanwhile, we observe that EVCSs also provide reserve service to the DPN when they are in the coordinated operations. For instance, EVCS 3 provides reserve during 20:00–21:00, 24:00 and 1:00, as the participation factors is not 0 during these time intervals. Furthermore, we compare the values of characteristic function for all coalitions, i.e., {DPN}, {EVCS 1}, {EVCS 2}, {EVCS 3}, {DPN & EVCS 1}, {DPN & EVCS 2}, {DPN & EVCS 3}, {EVCS 1 & EVCS 2}, {EVCS 1 & EVCS 3}, {EVCS 2 & EVCS 3}, {DPN, EVCS 1 & EVCS 2}, {DPN, EVCS 1 & EVCS 3}, {DPN, EVCS 2 & EVCS 3}, {EVCS 1, EVCS 2 & EVCS 3}, and {DPN, EVCS 1, EVCS 2 & EVCS

202

9 Coordinated Operation Between Electric Vehicle Charging Stations … Coordinated

1.2

2.5

Non-coordinated

2

P2(t) (MW)

P1(t) (MW)

1 0.8 0.6

1.5 1

0.4 0.2

0.5

0

0

Coordinated Non-coordinated

5:00

10:00

15:00

20:00

5:00

10:00

15:00

20:00

Time (h)

Time (h)

(a) Charging station 1

(b) Charging station 2

2.5

P3(t) (MW)

2 1.5

Coordinated Non-coordinated

1 0.5 0 5:00

10:00

15:00

20:00

Time (h)

(c) Charging station 3

Fig. 9.4 Charging plans of EVCSs in the coordinated and non-coordinated modes, reprinted from Ref. [49], copyright2023, with permission from IEEE

3}. In this way, the optimal coalition group can be obtained, and the allocation of economic benefits among members of the optimal group is calculated by Eq. (9.53). In detail, Table 9.3 presents the operation costs and values of the characteristic function of different coalitions. It can be seen that for the non-coordinated case, the operation cost for the DPN is $14,579, and the costs for individual EVCSs are $3,329, $8,094, and $1,492, respectively. Then the operation cost for the DPN and charging stations are the summation of these values, i.e., $27,494. On the contrary, for the coordinated case, the total cost is $26,672, which is 2.99% lower than that of the non-coordinated mode. It is noted that the DPN cooperates with more EVCSs, and the characteristic function value of the coalition is increased in a fully coordinated operation. This means the DPN and EVCSs pay less cost to the wholesale market, i.e., less dependency on the wholesale market. On the basis of Eq. (9.53), the detailed allocation of economic benefits of the DPN and these three EVCSs is shown in Table 9.4. The details values are $500.8,

9.5 Case Study

203

Table 9.2 Participation factors among DPN and EVCSs, reprinted from Ref. [49], copyright2023, with permission from IEEE t(h)

β DPN,RT (t) C-mode

β 1 (t) NC-mode

β 2 (t)

β 3 (t)

C-mode

1:00

0.00

0.00

0.00

0.00

0.13

2:00

0.00

0.00

0.00

0.00

0.00

3:00

0.00

0.00

0.00

0.00

0.00

4:00

0.00

0.00

0.00

0.00

0.00

5:00

0.00

0.00

0.00

0.00

0.00

6:00

0.00

0.00

0.00

0.00

0.00

7:00

0.00

0.00

0.00

0.00

0.00

8:00

0.00

0.00

0.00

0.00

0.00

9:00

0.16

0.16

0.00

0.00

0.00

10:00

0.37

0.37

0.00

0.00

0.00

11:00

0.49

0.49

0.00

0.00

0.00

12:00

0.39

0.58

0.10

0.08

0.00

13:00

0.00

0.61

0.23

0.38

0.00

14:00

0.00

0.63

0.18

0.45

0.00

15:00

0.63

0.63

0.00

0.00

0.00

16:00

0.63

0.63

0.00

0.00

0.00

17:00

0.08

0.58

0.24

0.26

0.00

18:00

0.00

0.52

0.22

0.30

0.00

19:00

0.00

0.44

0.15

0.28

0.00

20:00

0.00

0.42

0.00

0.00

0.42

21:00

0.00

0.32

0.12

0.00

0.20

22:00

0.00

0.14

0.15

0.18

0.00

23:00

0.00

0.06

0.14

0.18

0.00

24:00

0.00

0.27

0.00

0.00

0.27

$104, $156.5 and $60.7, respectively. As seen from the fourth row, when the Shapely value is employed, the values would be $492.5, $107, $154.2 and $68.3, respectively. However, though they obey the rule that high participation factor values are worth more benefits, the percentage of the cost reduction does not (as shown in the sixth row). Especially, the value of EVCS 3 is 4.58% which is much higher than others, but its participation factor is only 0.14. Therefore, it is necessary to give entities with a high participation factor some economic compensation, shown in the seventh row. In this way, though the percentage of the cost reduction of EVCS 3 is still higher than others, the willingness of DPN and EVCS2 to join the coalition game would be increased since they can obtain economic compensations. Besides, it can be observed that the value of characteristic function increases if more EVCSs cooperate with the DPN, which means that the whole coalition can

204

9 Coordinated Operation Between Electric Vehicle Charging Stations …

Table 9.3 Operation cost and characteristic function value of each coalition, reprinted from Ref. [49], copyright2023, with permission from IEEE Participants in coalition

Operation cost of coalition ($)

Characteristic function value of coalition ($)

DPN

14,579

0.00

EVCS 1

3,329

0.00

EVCS 2

8,094

0.00

EVCS 3

1,492

0.00

DPN & EVCS 1

17,384

524

DPN & EVCS 2

22,065

609

DPN & EVCS 3

15,846

225

EVCS 1 & EVCS 2

11,423

0.00

EVCS 1 & EVCS 3

4,821

0.00

EVCS 2 & EVCS 3

9,586

0.00

DPN, EVCS 1 & EVCS 2

25,296

706

DPN, EVCS 1 & EVCS 3

18,760

640

DPN, EVCS 2 & EVCS 3

23,426

739

EVCS 1, EVCS 2 & EVCS 3 12,915

0.00

DPN, EVCS 1, EVCS 2 & EVCS 3

822

26,672

Table 9.4 The allocation of economic benefits of the DPN and EVCSs, reprinted from Ref. [49], copyright2023, with permission from IEEE Entity

DPN

EVCS 1

EVCS 2

EVCS 3

Cm ($)

14,579

3329

8094

1492

ωm

0.37

0.21

0.28

0.14

SVm (v)($)

14,086.5

3222

7939.8

1423.7

Cm − SVm (v)($)

492.5

107

154.2

68.3

1 − SVm (v)/Cm (%)

3.38

3.21

1.9

4.58

φm (v)($)

14,078.2

3225

7937.5

1431.3

Cm − φm (v)($)

500.8

104

156.5

60.7

1 − φm (v)/Cm (%)

3.44

3.12

1.93

4.07

obtain more economic benefits. In addition, when EVCSs cooperate with the DPN, the departure curves of the three charging stations are shown in Fig. 9.5. It is observed that the departure curves are above the minimum ones for all the three EVCSs, which means they can provide EVs with charging services while satisfying the QoS. Therefore, for the coordinated operation of DPN and EVCSs, their operational costs are reduced and the QoS of charging could also be guaranteed. To conclude, the

9.5 Case Study

205

effectiveness of the proposed coordinated operation method is verified, and it is encouraged that all EVCSs are cooperated with the DPN in operations. 2. Results analysis of the QoS In terms of mentioned relationship between QoS and system operation cost, simulation results are shown as follows. In detail, Fig. 9.6 shows the Pareto front with the two optimization objectives, which is obtained by the AUGMECON ε-constraint algorithm shown in the Appendix. It is seen that the cost increases from $26,672 to $28,008, with the value of QoS varying from 0.35 to 0.93. That is, a higher QoS requirement derives a larger cost. This is mainly because the distance between the arrival curve and the departure curve is narrowed with the increase of QoS. In Fig. 9.7, we take EVCS 3, two extreme solutions and a harmonic solution for analysis, which are denoted as S1, S2, and S3 in Fig. 9.6, respectively. Regarding extreme solutions, they mean one of the objectives is optimal. As for the harmonic 20 Arrival curve Minimum departure curve Departure curve

Arrival curve Minimum departure curve Departure curve

30

Energy (MWh)

Energy (MWh)

15

40

10

5

20

10

0 5:00

10:00 15:00 Time (h)

20:00

0

5:00

(a) Charging station 1

10:00 15:00 Time (h)

20:00

(b) Charging station 2

12

Energy (MWh)

10 8 6 4

Arrival curve

2

Minimum departure curve Departure curve

0

20:00

1:00 6:00 Time (h)

11:00

(c) Charging station 3

Fig. 9.5 Departure curves of individual EVCSs when they and the DPN are in the coordinated mode, reprinted from Ref. [49], copyright2023, with permission from IEEE

206

9 Coordinated Operation Between Electric Vehicle Charging Stations …

Fig. 9.6 Pareto solutions about QoS and operation cost, reprinted from Ref. [49], copyright2023, with permission from IEEE

solution, it is the optimal result when all weights of objectives are the same. For ease of expression, the three solutions are marked as S1, S2, and S3, respectively. It is noted that the improvement in QoS would lead to the less flexibility in the charging scheme for EVCS, i.e., the departure curves should be advanced to ensure the QoS, compared to S2 shown in Fig. 9.7, which further contributes to increasing the cost of the whole system. The charging plans of EVCS 3 in S1 and S2 and the electricity price curve are further compared in Fig. 9.8. It could be observed that the charging plan of S1 is advanced compared to S2, because it should satisfy all electricity demands earlier for high QoS. Specifically, the charging load of S2 between 2:00 and 5:00 is shifted to 20:00, 21:00, 22:00, 23:00 and 24:00 in S1, respectively. Since the prices of these time intervals are higher than that of 2:00 to 5:00, the cost would increase. Figure 9.9 shows the participation factors of EVCS 3 with different weights of QoS, which is represented by α. Based on this setting, S4 and S5 are produced to explore the relationship between the participation factors and QoS furthermore, and their values of α are 0.4 and 0.6, respectively. It is evident that S3 has the highest participation factor. On the one hand, the higher QoS leads to a larger participation factors of EVCS 3, which shows additional benefits to joining the game. On the other hand, when EVCS aims to achieve the optimal QoS, it would satisfy all electricity demands from EVs as quickly as possible, which leads to a low reserve of EVCS 3 to provide services.

9.5 Case Study

207

Fig. 9.7 Arrival/Minimum departure curves and departure curves of EVCS 3 regarding different QoS values, reprinted from Ref. [49], copyright2023, with permission from IEEE

Fig. 9.8 Market day ahead price curve and charging plans for S1 and S2, reprinted from Ref. [49], copyright2023, with permission from IEEE

208

9 Coordinated Operation Between Electric Vehicle Charging Stations …

Fig. 9.9 Participation factors of EVCS 3 with different weights of QoS, reprinted from Ref. [49], copyright2023, with permission from IEEE

9.6 Conclusion This paper has proposed a coordinated operation method for a system containing EVCSs and the DPN, considering the energy and reserve regulations. Firstly, a multiobjective optimization model of energy-reserve integrated decisions for the system considering the economic cost and the QoS is established based on the network calculus theory. Then, a characteristic function of the coalition between EVCSs and the DPN based on the coalition game is proposed, and the Shapley value modified by the participation factors is used to allocate the economic benefits obtained by the cooperation. Simulation studies have verified that the coordinated operation method can reduce the operation cost of EVCSs and the DPN, compared with the situation that they directly purchase energy and reserve from the wholesale market. This means the DPN and EVCSs can lessen their dependency on the wholesale market when they cooperate in terms of energy and reserve regulation. Besides, operation costs of different coalitions are analyzed, and the coalition consisting DPN and all EVCSs can obtain the most economic benefits. Therefore, it can be concluded that EVCSs and the DPN are encouraged to participate in the coordinated operations. In addition, it is verified that a higher QoS requirement would lead to an increase in coalition cost, which further encourages EVSCs to participate in the proposed game in a certain. Moreover, both energy and reserve are planned for day-ahead scheduling in the proposed method based on forecast values and their uncertain deviations. Then, actual deviations are addressed by using shared reserve or purchasing energy from the real-time market, and model prediction control is considered as a suitable option to conduct the real-time scheduling, which could be explored in our future work. Furthermore, we will investigate how to set up an economic mechanism for EV users who want to leave earlier from EVCSs, and a more proper compensation method for

References

209

the EVCSs which have to terminate the arranged charging services based on the reported departure time.

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19. Chaudhari K, Ukil A, Kumar KN et al (2018) Hybrid optimization for economic deployment of ESS in PV integrated EV charging station. IEEE Trans Industr Inf 14(1):106–116 20. Yan B, Luo Y, Zhang W, Huang M, Wang LY, Jiang J (2018) A bi-Level optimization approach to charging load regulation of electric vehicle fast charging stations based on a battery energy storage system. Energies 11(1):229 21. Chen Q, Liu N, Hu C, Wang L, Zhang J (2017) Autonomous energy management strategy for solid-state transformer to integrate PV-assisted EV charging station participating in ancillary service. IEEE Trans Ind Inf 13(1):258–269 22. Xia S, Bu SQ, Luo X, Chan KW, Lu X (2018) An autonomous real time charging strategy for plug-in electric vehicles to regulate frequency of distribution system with fluctuating wind generation. IEEE Trans Sustain Energy 9(2):511–524 23. Peng Z, Hao L (2017) Decentralized coordination of electric vehicle charging stations for active power compensation. In: 2017 IEEE 86th vehicular technology conference (VTC-Fall). pp 1–5 24. Zakariazadeh A, Jadid S, Siano P (2015) Integrated operation of electric vehicles and renewable generation in a smart distribution system. Energy Convers Manag 89:99–110 25. Pavi´c I, Capuder T, Kuzle I (2015) Value of flexible electric vehicles in providing spinning reserve services. Appl Energy 157:60–74 26. Bai X, Qiao W (2015) Robust optimization for bidirectional dispatch coordination of large-scale V2G. IEEE Trans Smart Grid 6(4):1944–1954 27. Sun B, Tan X, Tsang DHK (2014) Optimal charging operation of battery swapping stations with QoS guarantee.In: IEEE international conference on smart grid communications, pp 13–18 28. Le Boudec JY, Thiran P (2001) Network calculus: a theory of deterministic queuing systems for the internet. Springer Science & Business Media 29. Li YZ, Ni ZX, Zhao TY et al (2020) Supply function game based energy management between electric vehicle charging stations and electricity distribution system considering quality of service. IEEE Trans Ind Appl 56(5):5932–5943 30. Li N, Uckun C, Constantinescu EM et al (2016) Flexible operation of batteries in power system scheduling with renewable energy. IEEE Trans Sustain Energy 7(2):685–696 31. Botterud A, Zhou Z, Wang J et al (2012) Wind power trading under uncertainty in LMP markets. IEEE Trans Power Syst 27(2):894–903 32. Liu G, Xu Y, Tomsovic K (2016) Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization. IEEE Trans Smart Grid 7(1):227–237 33. Zhang Y, Gatsis N, Giannakis G (2013) Robust energy management for microgrids with highpenetration renewables. IEEE Trans Sustain Energy 4(4):944–953 34. Alharbi W, Raahemifar K (2015) Probabilistic coordination of microgrid energy resources operation considering uncertainties. Electr Power Syst Res 128:1–10 35. Nguyen DT, Le LB (2015) Risk-constrained profit maximization for microgrid aggregators with demand response. IEEE Trans Smart Grid 6(1):135–146 36. Jabr RA (2013) Adjustable robust OPF with renewable energy sources. IEEE Trans Power Syst 28(4):4742–4751 37. Cagnano A, DeTuglie E, Liserre M et al (2011) Online optimal reactive power control strategy of PV inverters. IEEE Trans Industr Electron 58(10):4549–4558 38. Ferrero R, Shahidehpour S, Rames V (1997) Transaction analysis in deregulated power systems using game theory. IEEE Trans Power Syst 12(3):1340–1347 39. Dabbagh SR, Sheikh-El-Eslam MK (2015) Risk-based profit allocation to DERs integrated with a virtual power plant using cooperative Game theory. Electr Power Syst Res 121:368–378 40. Zhou B, Chan K, Yu T, Chung C (2013) Equilibrium-inspired multiple group search optimization with synergistic learning for multi-objective electric power dispatch. IEEE Trans Power Syst 28(4):3534–3545 41. Sheikhi A, Rayati M, Bahrami S, Ranjbar AM, Sattari S (2015) A cloud computing framework on demand side management game in smart energy hubs. Int J Electr Power Energy Syst 64(1):1007–1016 42. Li Y, Huang J, Liu Y, Wang H, Wang Y, Ai X (2021) A multi-criteria optimal operation framework for renewable energy integrated data center microgrid with waste heat recovery. In:

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Chapter 10

Interactive Energy Management Between Electric Vehicle Charging Stations and Electricity Distribution System

10.1 Introduction Electric vehicles (EVs) have rapidly gained significant traction and sparked widespread interest in recent years [1, 2]. Projections indicate that by 2020, the number of EVs on the roads is expected to soar to an impressive 12.9 million [3], a statistic that underscores the growing prominence of electric vehicle charging stations (EVCSs). Undoubtedly, EVs and EVCSs play a pivotal role in the advancement of the energy internet, serving as a crucial catalyst for seamless energy exchange between electric vehicles and power systems. This synergy creates a robust platform that fosters efficient and impactful interactions between EVs and the broader energy landscape. The charging demands of EVs exert a profound influence on the intricate spatial and temporal distribution of loads within the power system. However, different driving rules and charging characteristics make it difficult for EVs and the power system to interact friendly with each other. That is, we should ensure the quality of EV charging service to promote electrification of the transportation system, while stimulating efficient interaction between EVs and the power system, especially during the charging process of Evs. Indeed, the interactive energy consumption management between EVs and power systems of different scales had been studied, mainly in terms of microgrids (MGs) [4–8] and electricity distribution systems (EDSs) [9–12]. As for the energy interaction between EVs and the MG, Ref. [4] proposes an optimal centralized scheduling method, which can jointly control the charging process of EVs and electricity consumption of home appliances in the MG. Reference [5] introduces a stochastic optimal network reconfiguration method for an MG with EVs, in order to reduce the operational cost while satisfying energy requirements of EVs. In Reference [6], an optimal energy management model is proposed to manage a residential MG including EVs and renewable energy sources, with a daily cost saving of around 10%. In Reference [7], the first stage of this framework is dedicated to determining optimal prices for the parking deck operators, and in the second stage, a cutting-edge model © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 L. Ge and Y. Li, Smart Power Distribution Network, Power Systems, https://doi.org/10.1007/978-981-99-6758-2_10

213

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predictive control-based operation strategy comes into play. References [8] proposes an optimal operation method for an MG with multiple EVs, in which a stochastic optimization decision model with EVs is constructed based on the MG operations. When it comes to the dynamic energy management interaction between electric vehicles (EVs) and an Electric Distribution System (EDS), Reference [9] presents an innovative approach that revolutionizes the charging arrangement of EVs while taking into account the operational constraints of the EDS. This groundbreaking method not only ensures the fulfillment of individual EV owners’ energy needs but also effectively mitigates the risk of distribution grid congestion. Furthermore, Reference [10] introduces a robust energy management scheme that establishes a harmonious relationship between EVs and the EDS. Employing a non-linear programming approach, this scheme yields an optimal solution by considering a diverse array of operational constraints. It is worth emphasizing that appropriately adjusting the charging plans of EVs can significantly enhance the operational efficiency of the EDS. For instance, Reference [11] delves into the realm of multi-stage EV charging optimization models, presenting an effective strategy to minimize line losses within the EDS. In a similar vein, Reference [12] proposes an optimal operational strategy for the EDS system, designed to bolster the integration of EVs. This results in the transformation of the EDS into a dynamic system, with the traditional layer catering to existing system loads, while the innovative layer seamlessly interfaces with renewable energy and EVs, fostering a symbiotic relationship. As the realm of EVCSs continues to progress, the intricacies of energy management between EVCSs and EDSs have garnered considerable attention. Notably, Hafez et al. [13] present a comprehensive model that accurately captures the aggregate charging load at an EVCS. This model seamlessly integrates within an EDS operation framework, enabling the simultaneous determination of optimal EDS operation strategies and EVCS charging plans. In a similar vein, Liao et al. [14] propose a highly effective and intelligent dispatch scheme for EVCSs, specifically designed to alleviate the adverse impacts of charging demands on the EDS, all while optimizing the operational costs of the EVCS itself. Building on this concept, Amir et al. [15] introduce a groundbreaking strategy for coordinated management between EVCSs and the EDS, with the primary objectives of peak demand shaving, enhancing voltage profiles, and minimizing power losses. Furthermore, Suganya et al. [16] contribute to the field by introducing a sophisticated smart energy management system for EVCSs operating within the EDS environment. This innovative approach aims to achieve the lowest possible operational costs for the EVCSs, while ensuring seamless integration with the broader EDS infrastructure. However, the above works consider EVCSs and the EDS as a whole for pursuing the maximum social welfare, which neglects the fact that they belong to different entities, and have not investigated the detailed process of interactions. Indeed, the EDS and EVCSs could achieve higher utilities when interacting with each other. In addition, it is noted that the quality of service (QoS) of EVCSs should be guaranteed when they interact with the EDS in terms of energy management, i.e., charging demands of EVs are satisfied during a certain period of time [17].

10.2 Decision Model of Electric Vehicle Charging Stations Considering …

215

In order to solve the issues mentioned above, we propose an interactive energy consumption management method for EVCSs and the EDS in this paper. First, we present the formulations of EVCSs while considering QoS constraints. Then, we use supply function equilibrium (SFE) based game theory to analyze the process of interactive energy management between EVCSs and the EDS, which derives an interactive model to accurately describe the interaction between EVCSs and the EDS. Afterwards, a hybrid optimization algorithm is applied to solve the model and obtain the equilibrium point.

10.2 Decision Model of Electric Vehicle Charging Stations Considering Quality of Service Constraints 10.2.1 Electric Vehicle Charging Station Illustrated in Fig. 10.1, EVCS denoted as i establishes a crucial connection with EDS, enabling it to deliver essential charging services to arriving electric vehicles (EVs). When an EV, identified as j arrives at the designated charging station at a specific time t ar,j , it promptly communicates its energy demand E re,j and the anticipated departure time t dep,j to the operator overseeing EVCS i. This transparent information exchange allows for a comprehensive understanding of the requirements and preferences of the EV user. Subsequently, EVCS i shares vital data, including the arrival curve, minimum departure curve, and demand curve, with the EDS. Armed with this valuable information, the EDS engages in strategic decision-making, promptly procuring electricity from the wholesale market based on prevailing wholesale energy prices. Furthermore, the EDS diligently engineers optimal charging plans for EVCS i, ensuring seamless satisfaction of the diverse demands presented by EV users.

10.2.2 QoS of Electric Vehicle Charging Station In this subsection, we propose a QoS constrained decision model for EVCSs, which is formulated based on the network calculus theory [18]. Firstly, we denote the arriving time and the latest departure time set by the user of EV j as t ar,j and t dep,j , respectively. Also, E re,j and Pmax,i stand for the required charging energy for EV j and the maximum charging power from EVCS i, respectively. In this way, the arrival, departure, and minimum departure curves for EV j are presented as follows. Definition 1: The arrival curve of EV j is its cumulative energy requirements during time interval [t ar,j , t]. Definition 2: The departure curve of EV j is the cumulative received energy of EV j during time interval [t ar,j , t].

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Wholesale market Energy price Electricity distribution system 1) Arrival curve 2) Minimum departure curve 3) Demand curve

Charging plan

Charging station 1

Charging station i

...

Charging station N

1) Arrival time 2) Departure time 3) Energy demand

Charging power

Information flow

Fig. 10.1 Information flow between EVCSs and the EDS, reprinted from Ref. [32], copyright 2023, with permission from IEEE

Definition 3: For an designated arrival curve, the minimum departure curve of EV j is the minimum cumulative energy that should be received by EV j on the premise of satisfying QoS during time interval [t ar,j , t]. Based on the Definition 2, the departure curve includes the situation that the EV has received the minimum required energy but still not left the charging station. In this way, formulations of the arrival, departure, and minimum departure curves of EV j are presented as follows. A j (t) = min{Pmax,i (t − tar, j )/t, E re, j } D j (t) =

t E

Pev, j (t)/t

(10.1)

(10.2)

tar, j

Dmin, j (t) = min{E re, j , max[E re, j − Pmax,i (tdep, j − t)/t, 0]}

(10.3)

where Pev,j (t) is the charging power of EV j at time t, /t is the time step. These curves should satisfy the following relation, i.e., Aj (t) ≥ Dj (t) ≥ Dmin,j (t). On the other hand, when EVCS i provides charging service, its QoS needs to be met, i.e., the charging demands of EVs need to be satisfied within a guaranteed

10.2 Decision Model of Electric Vehicle Charging Stations Considering …

217

period of time [17]. Based on the network calculus theory, this paper characterizes the QoS of the designated EVCS i as follows. We denote the set of charging time intervals as T = [1, 2, …, T ], where T is the length of time intervals. Concepts of arrival, departure, and minimum departure curves of EVCS i are defined as follows. Definition 4: The arrival curve of EVCS i is its cumulative required energy during time interval [1, t]. Definition 5: The departure curve of EVCS i is the cumulative energy supplied by EVCS i during time interval [1, t]. Definition 6: For the designated arrival curve, the minimum departure curve of EVCS i is the minimum cumulative energy that should be supplied by EVCS i on the premise of satisfying QoS in the time interval [1, t]. In this way, formulations of the arrival curve, departure curve, and minimum departure curve of EVCS i are presented as follows. Ai (t) =

E

min{Pmax,i (t − tar, j )/t, Er e, j }, ∀i ∈ N , t ∈ T

(10.4)

j∈i

Di (t) =

t EE

Pev, j (t)/t, ∀i ∈ N , t ∈ T

(10.5)

j∈i tar, j

Dmin,i (t) =

E

min{E re, j , max[E re, j − Pmax, j (tdep, j − t)/t, 0]}, (10.6)

j∈i

∀i ∈ N , t ∈ T where N is the set of charging stations. It can be seen from (10.1)–(10.6) that the arrival, the departure, and the minimum departure curves of EVCS i can be obtained by the time aggregation of the corresponding curves of EV j, respectively. Additionally, the three curves (10.4)–(10.6) meet the following relationship, i.e., Ai (t) ≥ Di (t) ≥ Dmin,i (t).

(10.7)

In this way, energy demands of EVs are guaranteed before their departure.

10.2.3 Decision Model of Electric Vehicle Charging Station It is noted that EVCSs are electricity consumers, and they can be regarded as virtual firms in the supply function equilibrium based game theory. Therefore, in this paper, we use the virtual bidding curves for EVCSs, i.e., these charging stations want to purchase electricity from the EDS at certain prices. Consequently, bidding curves of EVCSs will affect the marginal price in the EDS, which in turn influence the optimal

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charging plans for EVCSs. In this paper, bidding curve of EVCS i is expressed as a linear function [19–21]: S Di (t) = ki (t)[ci (t) − di (t)Pi (t)], ∀i ∈ N , t ∈ T

(10.8)

where SDi (t) represents the price that EVCS i is willing to pay for the charging power Pi (t) during time period t, and ci (t) is the maximum price. d i (t) is positive coefficient, indicating the linear decreasing relationship between the marginal price of EVCS i and charging power Pi (t). Note that the k-parameterization is usually used as exercise of market power by offering optimized supply functions that are scaled versions of the true marginal cost functions [21]. Therefore, we adopt the k-parameterization in (10.8), and k i (t) is called the rate coefficient of EVCS i during time period t. It is set by the EVCS operator, which will affect the marginal price. In this way, the utility function of EVCS i is shown as follows. . max Ui = ki (t)

T E

1 [ci Pi (t) − di (t)Pi (t)2 − λi (t)Pi (t)]/t, ∀oi ∈ N 2 t=1

(10.9)

where λi (t) is the marginal price of time period t of the node in the EDS that EVCS i is connected to. The decision variable of (10.9) is k i (t), which is bounded by the pair of values k min,i and k max,i , denoting as the lower and upper bounds of the rate coefficient, respectively. Note that ci stands for the maximum price that EVCS i is willing to pay, then the second term of (10.9), ci Pi (t), can be deemed as the budget cost. In addition, the price that EVCS i is willing to pay will be reduced by d i with an increase in one unit of charging power. Therefore, (10.9) can be understood as the budget surplus, which is set as the utility function of EVCS i in this paper.

10.3 Decision Model of Distribution Power Network with Electric Vehicle Charging Stations 10.3.1 Decision Model of Distribution Power Network Operating as an autonomous entity, the operator of EDS assumes the role of an astute decision-maker, driven by the relentless pursuit of optimizing both its purchase plan from the wholesale market and the charging plans meticulously devised for EVCSs. The ultimate objective lies in maximizing the welfare of the EDS, a term that encompasses a comprehensive cost-benefit analysis. In this context, welfare, as defined in this paper, refers to the dynamic cost-benefit function that quantifies the disparity between revenue generation and the incurred costs associated with the provision of power supply to users. With this perspective in mind, the utility function of the EDS, denoted as U EDS , can be succinctly expressed as follows.

10.3 Decision Model of Distribution Power Network with Electric Vehicle …

max

PDPN (t),Pi (t)

UEDS

⎧ |⎫ | T ⎪ ⎬ ⎨E ki (t)ci (t)Pi (t) − 1 ki (t)di (t)Pi (t)2 ⎪ E 2 = ⎪ ⎪ ⎭ t=1 ⎩i∈N − C e (t)PEDS (t)/t

219

(10.10)

where C e (t) and PEDS (t) are the purchase price and power from the wholesale market during time period t. In addition, operational constraints of EDS should be satisfied, including power balance and network security constraints, which are presented as follows. 1. Power balance For each node i of EDS during time period t, the active and reactive power balance equations are expressed as follows. PEDS,i (t) −

E

PL,i (t) −

i∈L j

Pi j (t) − ri j li j (t) −

E

Pi (t) =

i∈N j

E

P jk (t), ∀ j ∈ B, t ∈ T

(10.11)

k:( j,k)∈E

Q EDS,i (t) −

E

Q L,i (t) = Q i j (t) − xi j li j (t) −

i∈L j

E

Q jk (t), ∀ j ∈ B, t ∈ T

k:( j,k)∈E

(10.12) v j (t) = vi (t) − 2[ri j Pi j (t) + xi j Q i j (t)] + (ri2j + xi2j )li j (t), ∀(i, j) ∈ Eo, t ∈ T (10.13) li j (t) =

Pi j (t)2 + Q i j (t)2 vi (t)

, ∀(i, j ) ∈ E, i ∈ B, t ∈ T

(10.14)

where PEDS,i (t) and QEDS,i (t) are the active and reactive power injected into the EDS through node i during time period t. PL,i (t) and QL,i (t) represent the active and reactive power consumption of load i. Pij (t) and Qij (t) stand for the active and reactive power transmitted from node i to node j through the branch ij. lij (t) and vi (t) are squared current of branch ij and squared voltage amplitude of node i, respectively. r ij and x ij denote resistance and reactance of branch ij, respectively. B and E are the sets of nodes and lines in the EDS, respectively. In addition, L j and N j are sets of loads and EVCSs connected to node j, respectively. 2. Security constraint In order to ensure the secure operation of the EDS, voltage magnitude of each node and power flow of each branch need to meet the following constraints. 2 2 Vmin,i ≤ vi (t) ≤ Vmax,i , ∀i ∈ B, t ∈ T

(10.15)

2 li j (t) ≤ Imax,i j , ∀(i, j ) ∈ E, t ∈ T

(10.16)

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10 Interactive Energy Management Between Electric Vehicle Charging …

where vi (t) is squared voltage amplitude of node i, and its lower and upper bounds are denoted as V min,i and V max,i , respectively. l ij (t) stands for the squared current amplitude of branch ij, and its maximum value is expressed as I max,ij .

10.3.2 Convex Relaxation Upon careful examination, it becomes evident that constraint (10.14) exhibits nonlinearity and non-convexity, rendering the attainment of a globally optimal solution for the decision model of DPN a formidable challenge. The intricate nature of this constraint introduces complexities that hinder straightforward optimization. Consequently, in order to surmount these challenges, a relaxation technique is employed, precisely in the form of a rotating cone as described in reference [22]. By relaxing constraint (10.14) using this innovative approach, the optimization process gains newfound flexibility and adaptability, paving the way for enhanced computational tractability and the potential for more efficient solutions. li j (t) ≥

Pi j (t)2 + Q i j (t)2 vi (t)

, ∀(i, j ) ∈ ε, i ∈ β, t ∈ T

(10.17)

In this way, the decision model of the EDS becomes convex, which is expressed as the following form. max UEDS =

{ T E E t=1

i∈N

} 1 [ki (t)ci (t)Pi (t) − ki (t)di (t)P i (t)] − Ce (t)PEDS (t) /t 2

⎧ M xEDS = N (λ) ⎪ ⎪ ⎪ ⎨R x EDS ≤ S (μ) s.t. ⎪ xEDS ∈ C(sx ) ⎪ ⎪ ⎩ xEDS ∈ K(sn )

(10.18) where x EDS stands for the decision variables which consist of power purchase plan from the wholesale market and charging plans of each EVCS, and the auxiliary variable P i (t). Mx EDS = N represents constraints (10.12) and (10.13). Rx ≤ S stands for the constraint (10.15), (10.16) and (10.7). x EDS ∈ C means that x EDS satisfies the second order rotating cone constraint (10.17). λ, μ, sx and sn represent the Lagrange multipliers of the corresponding constraints. x EDS ∈ K indicates that x EDS satisfies the following regular cone. Pi (t)2 ≤ P i (t), ∀i ∈ N , t ∈ T

(10.19)

10.4 Interactive Energy Management for Electric Vehicle Charging Stations …

221

We can observe that (10.18) is a linear conic programming (LCP) problem. According to the strong duality condition of the LCP problem [23], the first order optimality conditions of (10.18) are shown as follows. −L + M T λ + R T μ + sx + sn = 0 N T λ + S T μ = L T x E DS M x E DS = N Rx E DS ≤ S μ≥0

(10.20)

x E DS ∈ C x E DS ∈ K sx ∈ C ∗ sn ∈ K ∗ where L is the first order derivative of the objective function in (10.18) against x EDS . C* and K∗ represent dual cones of C and K, respectively.

10.4 Interactive Energy Management for Electric Vehicle Charging Stations and Distribution Power Network Using Supply Function Equilibrium 10.4.1 Supply Function Equilibrium In order to study the interactive energy management for EVCSs and the EDS, we use the supply function equilibrium based game theory to provide a mathematical description. We define the SFE game as Γ = N , S, |, EDS, S E DS, | E DS, where S is the set of operation strategies of EVCSs, and | represents N utility functions corresponding to individual EVCSs, as presented in (10.9). S E DS stands for the set of operation strategies of EDS, and | E DS is the utility function, shown in (10.10). As depicted in the illuminating Fig. 10.2, an enthralling exploration of interactive energy management unfolds by strategically designating EVCSs and EDS as leaders and followers, respectively, within this intricate game. The rationale behind positioning the EVCSs as leaders stems from the imperative need to accord their energy requirements utmost significance, thereby facilitating the widespread adoption and proliferation of both EVs and EVCSs. Delving deeper into the dynamics, each EVCS exerts its influence by transmitting a compelling bidding curve to the discerning EDS operator, subsequently shaping the marginal price. In response, the EDS diligently optimizes the power delivery to EVCSs and adeptly crafts purchase plans from the wholesale market, all with the overarching aim of maximizing its own utility while steadfastly satisfying the energy demands of EV users prior to their

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Quality of service Charging station 1

Quality of service Charging station i

Demand curve

Charging stations (Leaders) Quality of service Charging station N

Charging plans

Utility Electricity distribution system (Follower) Fig. 10.2 Interactive progress of energy management between EVCSs and the EDS using supply function equilibrium based game, reprinted from Ref. [32], copyright 2023, with permission from IEEE

scheduled departures. Concurrently, the game also entails the pursuit of finding the optimal bidding curve for each EVCS, a pursuit achieved through judicious adjustments of its rate coefficient. By skillfully manipulating this coefficient, the EVCSs strive to achieve the pinnacle of utility, harmonizing their own objectives within the broader framework of the game.

10.4.2 Existence of Equilibrium Solutions In this subsection, the existence of equilibrium solution of the SFE game is discussed, and the following definition is given. Definition: For the SFE game defined in Sect. 10.3. A, if a solution x * satisfies the following condition, ∗ ∗ Ui (xi∗ , x−i ) ≥ Ui (xi , x−i ), ∀xi ∈ Si , i ∈ N ∪ EDS

(10.21)

x * is an equilibrium of the SFE game |. Based on the first order optimality conditions, the SFE game can be transformed into the following mathematical program with equilibrium constraints (MPEC) problem [24].

10.5 Hybrid Optimization Algorithm for Equilibrium Solution

max

E

ki (t),xEDS

{

s.t.

223

Ui

i∈N

kmin,i ≤ ki (t) ≤ kmax,i , ∀i ∈ N , t ∈ T

(10.22)

(20)

When k i (t) is given, both L and Q are constants, then the equilibrium constraint (10.20) is a linear conic constraint. In this way, there exists an solution in (10.22), which is an equilibrium in the SFE game [25].

10.5 Hybrid Optimization Algorithm for Equilibrium Solution The attainment of the equilibrium point in SFE game | lies in the solution of optimization problem (10.22). Notably, it is essential to acknowledge that equation N T λ + S T μ = L T xDPN in (10.20) encompasses the presence of a bilinear function, specifically denoted as L T x EDS . Consequently, the non-convexity of (10.22) becomes evident. A powerful technique that emerges as a viable solution to tackle such non-convex optimization problems is the esteemed DE, one of many evolutionary algorithms renowned for its profound effectiveness [26]. Not only does DE stand as a reliable choice, but it also boasts the distinct advantages of a straightforward coding process and widespread applicability, distinguishing it from other evolutionary algorithms that may be more intricate or specialized in nature. Generally, the steps of DE are population initialization, crossover, mutation, and selection. Detailed procedures can be referred to Ref. [26]. In the mutation and crossover operation of DE, control parameters F and C R affect search step of the algorithm and succession ability of offspring to parents, respectively, i.e., these parameters determine the performance of DE to certain extent. Note that it is difficult to select the optimal values for F and C R , which are usually problem specific. In this way, we adopt the DE with self-adapting control parameters [27]. In the case of limited prior knowledge, F and C R can be embedded into the individual, and the parameters can be adaptively adjusted among evolution of the population. It has been verified that the adaptive parameter control has good searching performance and robustness, and the adaptive F and C R are expressed as follows [27]. { Fi,g+1 =

Fmin + r1 Fmax , r2 < τ1 Fi,g , {

C R,i,g+1 =

r2 ≥ τ1 r3 , r4 < τ2 C R,i,g , r2 ≥ τ1

(10.23)

(10.24)

where F i,g and C R,i,g represent the values of F and C R when individual i is at generation g. r 1 , r 2 , r 3 and r 4 are uniformly distributed random numbers between [0, 1].

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10 Interactive Energy Management Between Electric Vehicle Charging …

τ 1 and τ 2 are the individual probability corresponding to F and C R in the adjusted population. In this paper, F min , F max , τ 1 and τ 2 are set as 0.1, 0.9, 0.1 and 0.1, respectively. An intriguing observation arises when considering the scenario where the knowledge of k i (t) is available in Eq. (10.22). In this context, Eq. (10.20) transforms into a linear conic constraint, thereby rendering it amenable to a resolution through the esteemed interior point method [28]. The captivating flowchart depicted in Fig. 10.3 unveils a remarkable hybrid algorithm that seamlessly merges the prowess of DE technique with the precision of the interior point algorithm, collectively employed to unravel the intricacies of solving optimization problem (10.22). This innovative approach presents a compelling pathway towards achieving an optimal solution, effectively navigating the complexities inherent in the interplay between DE and the interior point method.

10.6 Case Study 10.6.1 Case Description In this captivating section, we embark on an enthralling journey of simulation studies utilizing the illustrious IEEE 33-bus Electric Distribution System (EDS) [29] as our experimental backdrop. Within this intricate network, three EVCSs grace the landscape, each meticulously connected to buses 3, 19, and 23, respectively. An intriguing aspect lies in the charging capabilities of these three EVCSs, collectively catering to a staggering number of 200, 800, and 1000 EVs, granting them the power to meet the charging demands of a multitude of electric vehicles. As we delve deeper into the realm of simulations, our time frame spans from 15:00 to 15:00 the following day, capturing the charging behaviors exhibited by the EVs throughout this captivating period. To ensure the utmost accuracy, we rely on comprehensive survey data sourced from the vibrant Beijing region, effectively encapsulating the usage patterns of EVs as they arrive at and depart from the EVCSs, while also providing valuable insights into the corresponding mileages covered [30]. This meticulous attention to detail allows for a truly immersive simulation experience, where realworld dynamics seamlessly merge with the virtual environment. f (tar,i ) =

1 0.75π [1 + 3(tar,i − 17.2)2 ]

f (tdep,i ) = √

1 2π × 0.8

f (ds,i ) =

e

α (α β

−

(tdep,i −18.2)2 2×0.82

0 ≤ tar,i ≤ 24 , i ∈ N 0 ≤ tdep,i ≤ 24 , i ∈ N

1 α−1 − βα e ds,i ds,i ≥ 0 , i ∈ N − 1)!

(10.25) (10.26) (10.27)

10.6 Case Study

225

Start

Population initialization

Termination conditions

Yes

Equilibrium solution

No Mutation

Optimization of EDS

Overlapping

Solution of (20)

Individual evaluation

Marginal node price of EDS

Choice

Utility of EVCSs

Optimization of bidding curve of each EVcharging station Fig. 10.3 The flowchart of the hybrid algorithm using DE and interior point method, reprinted from Ref. [32], copyright2023, with permission from IEEE

where f (•) stands for the probability density function. d s,i is the mileage between two successive charging. α and β are the parameters in the corresponding probability density, which are set as 5 and 3, respectively. The energy demand of each EV can be determined by the following formulation. E re,i = ds,i eav /ηc , i ∈ N

(10.28)

where eav and ηc are the power consumption per kilometer and the charging efficiency, the values of which are 0.15 kWh/km and 0.9, respectively. The parameters governing the charging process of EVs, such as the maximum charging power and the time step, have been carefully configured. With a charging power limit of 3 kW and a time step of 1 h, the arrival curve and minimum departure

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10 Interactive Energy Management Between Electric Vehicle Charging …

curve for each EVCS have been meticulously derived and are visually represented in Fig. 10.4. To establish a realistic pricing framework, the electricity prices from the wholesale market have been adopted, specifically referring to the esteemed California electricity market in the United States [31]. These prices have been converted to the local currency symbol “¥” and are concisely summarized in Table 10.1. To reflect the economic considerations, the cost function ci (t) for each charging station has been set at twice the energy price of the corresponding period, while the discharge rate d i (t) has been established at 0.1¥/kWh2. Furthermore, the algorithm parameters have been meticulously selected, with a population size of 20 in the Differential Evolution (DE) algorithm and a total of 100 iterations to ensure an effective optimization process. In order to verify the effectiveness of the proposed interactive energy method, we compare its performance with the following methods that do not explicitly consider interactions between the EDS and EVCSs. 1. Uncontrolled charging method In the context of uncontrolled charging, where each EVCS operates autonomously, their primary objective is to fulfill the energy demands of EVs promptly. Adhering to their respective arrival curves, EVCSs diligently offer charging services, aiming to cater to the energy needs of EVs at the earliest possible time. This prioritization 1

4

Energy (MWh)

Energy (MWh)

0.8 0.6 0.4 0.2 0

3 2 1 0

Time(h)

Time(h)

(a) Charging station 1

(b) Charging station 2

5

Energy (MWh)

4 3 2 Arrival curve

1

Minimum departure curve 0

Time(h)

Fig. 10.4 Arrival curve and minimal departure curve of each charging station, reprinted from Ref. [32], copyright 2023, with permission from IEEE

10.6 Case Study

227

Table. 10.1 Energy prices in the wholesale market, reprinted from Ref. [32], copyright 2023, with permission from IEEE t (h)

C e (t) (¥/kWh)

t (h)

C e (t) (¥/kWh)

t (h)

C e (t) (¥/kWh)

1

0.1359

9

0.1903

17

0.3084

2

0.1333

10

0.1980

18

0.3105

3

0.1266

11

0.2138

19

0.3336

4

0.1334

12

0.2289

20

0.2849

5

0.1572

13

0.2313

21

0.2301

6

0.1744

14

0.2498

22

0.2111

7

0.1779

15

0.2902

23

0.1849

8

0.1856

16

0.2938

24

0.1551

ensures that the operations of the EVCSs take precedence, guaranteeing efficient and timely charging services for the EVs in question. 2. Social welfare maximization charging method Under the charging method of social welfare maximization, each EVCS reports its bidding curve without using k-parameterization. The aim of this method is to maximize total utilities of the EDS network and EVCSs, which is shown as follows. ⎧ | |⎫ 1 ⎪ T 2 ⎬ ⎨ E E ci (t)Pi (t) − di (t)Pi (t) ⎪ 2 (10.29) max Uuti = ⎪ ⎪ ⎭ t=1 ⎩i∈N − C e (t)PEDS (t)/t s.t. (10.7), (10.11)–(10.13), (10.15)–(10.17). where U uti stands for the social welfare.

10.6.2 Case study 1. Uncontrolled charging In this case, to verify the effect of uncontrolled charging on the EDS operations, load curves of the EDS with and without charging loads are compared in Fig. 10.5. Note that the no-charging load curve presents the original load of the EDS without participations of EVCSs. It is evident from Fig. 10.5 that the load curve under uncontrolled charging is different from the no-charging one, and the peak load of about 6 MW happens at around 23:00 as EVCSs provide charging services for EVs. However, it can be seen from Fig. 10.6 that the charging load significantly impacts operational security of the EDS. For instance, voltage amplitudes of node 19 during the peak load time period 22:00–23:00 are lower than the lower limit (0.95 p.u.). Furthermore, the

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10 Interactive Energy Management Between Electric Vehicle Charging …

utilities of individual charging stations and the EDS are ¥693.36, ¥2821.09, ¥3431.08, and ¥6222.23, respectively. Therefore, the overall utility of EVCSs and the EDS is the sum of above values, i.e., ¥13,167.76. 2. Analysis on supply function equilibrium Figure 10.7 shows the convergence curve of the utility of EVCSs when the hybrid algorithm is used to solve the optimization problem (10.22). It is observed that after 50 iterations, the utility converges to ¥8866.80, and the utility of three charging stations are ¥885.99, ¥3562.15 and ¥4418.66, respectively. Compared with those of uncontrolled charging, the utilities of these EVCSs are increased by 27.78%, 26.27% and 28.78%, respectively. Meanwhile, the utility of the EDS is ¥4323.11. Consequently, the total utility of EVCSs and the EDS is ¥13,189.90, which is higher than that of 7

Fig. 10.5 Load curve under uncontrolled charging, reprinted from Ref. [32], copyright 2023, with permission from IEEE

No -charg ing load Load curve under uncontrolled charging

Load (MW)

6 5 4 3 2 1

20 00

1 00

6 00

11 00

) (h e m Ti

Fig. 10.6 Voltage magnitude of each bus in the EDS under uncontrolled charging, reprinted from Ref. [32], copyright 2023, with permission from IEEE

Voltage amplitude

Time(h)

Node

10.6 Case Study

229

the uncontrolled charging ¥13,167.76. In addition, the load curve of EDS in the SE state and the no-charging load curve are compared in Fig. 10.8. It clearly shows the proposed SFR interactive energy management method could effectively mitigate peak load, in comparison with the uncontrolled charging presented in Fig. 10.5. Furthermore, in Fig. 10.9, a comprehensive depiction of the voltage magnitude curves for individual nodes within EDS over a span of 24 h is provided. Notably, the figure showcases that the voltage magnitudes of all nodes consistently remain within the secure voltage range, specifically denoted as [0.95 p.u., 1.05 p.u.]. This remarkable observation indicates that SFE approach effectively mitigates any potential security violations pertaining to voltage limits within the EDS operations. The coordination of charging loads in EVCSs plays a pivotal role in achieving this desirable outcome. Moreover, Fig. 10.10 enlightens us with the departure curves of the EVCSs. 8900

)

8800 Utility of EVCSs (

Fig. 10.7 Convergence curve of utility of EVCSs obtained by the hybrid optimization algorithm, reprinted from Ref. [32], copyright 2023, with permission from IEEE

8700 8600 8500 8400 8300 8200 10

4.5

Fig. 10.8 Load curve under SFE state, reprinted from Ref. [32], copyright 2023, with permission from IEEE

20 30 Generation

40

No -charg ing load curve Load curve under SFE state

4

Load (MW)

3.5 3 2.5 2 1.5 1

20:00

1:00

6:00 Time(h)

11:00

50

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10 Interactive Energy Management Between Electric Vehicle Charging …

It is evident that all three departure curves remain well-bounded by the arrival and minimum departure curves. This compelling visualization signifies that the charging plans devised for each charging station diligently adhere to the constraints specified by Eq. (10.7). Consequently, QoS offered by each charging station is unequivocally satisfied, further reinforcing the effectiveness of the implemented system. Additionally, in Fig. 10.11, the values of the coefficient k i (t) for each EVCS in the SFE state are presented. This insightful depiction reveals that each EVCS dynamically adjusts this parameter in real-time, strategically optimizing their utility during interactions with the EDS. The adaptability showcased by the EVCSs in maximizing their efficacy further underscores the sophistication and efficiency of the SFE methodology. 3. Analysis on the results of social welfare maximization

h) e( m Ti

Fig. 10.9 Voltage magnitude of each bus under SFE state, reprinted from Ref. [32], copyright 2023, with permission from IEEE

Voltage amplitude p.u.

When the maximum social welfare of EVCSs and the EDS is pursued, the corresponding departure curve of each charging station is shown in Fig. 10.12. The departure curve of each EV charging station is consistent with that of the SFE state. Furthermore, the utility under the social welfare maximization is obtained as ¥13,189.90, which is the same as that of the SFE state. This verifies that our proposed interactive energy management method for EVCSs and the EDS based on the SFE game is lossless, because the maximal social utility is consistent with that of SE. However, under the method of the social welfare maximization, we cannot obtain the interaction process of energy management between EVCSs and the EDS. Therefore, in this sense, our proposed method is advantageous for analyzing energy interaction, while also achieving the maximum social welfare.

Node

10.6 Case Study

231

1

4

3

Energy (MWh)

Energy (MWh)

0.8 0.6 0.4

1

0.2 0

2

20:00

1:00

6:00 Time (h)

0

11:00

20:00

(a) Charging station 1

1:00

6:00 Time (h)

11:00

(b) Charging station 2

5

Energy (MWh)

4 3 Arrival curve

2

Departure curve Minimal departure curve

1 0

20:00

1:00

6:00 Time (h)

11:00

(c) Charging station 3

Fig. 10.10 Departure curve of each charging station under SFE state, reprinted from Ref. [32], copyright 2023, with permission from IEEE 2

EVCS 1 EVCS 2 EVCS 3

1.8 1.6

ki(t)

1.4 1.2 1 0.8 0.6

20 00

1 00

6 00

11 00

Time(h)

Fig. 10.11 Bidding parameter of each charging station under SFE state, reprinted from Ref. [32], copyright 2023, with permission from IEEE

232

10 Interactive Energy Management Between Electric Vehicle Charging … 1

4

3 Energy (MWh)

Energy (MWh)

0.8 0.6 0.4

1

0.2 0

2

20 00

1 00

6 00

0

11 00

20 00

Time (h)

1 00

6 00

11 00

Time (h)

(a) Charging station 1

(b) Charging station 2

5

Energy (MWh)

4 3 2

Arrival curve

1

Minimal departure curve

Departure curve

0

20 00

1 00

6 00

11 00

Time (h)

(c) Charging station 3

Fig. 10.12 Departure curve of each charging station under social welfare maximization, reprinted from Ref. [32], copyright 2023, with permission from IEEE

10.7 Conclusion In order to facilitate the harmonious collaboration between EVCSs and EDS, this paper presents a sophisticated and interactive energy management approach based on the supply function game. The proposed methodology is designed to optimize the overall performance by integrating the energy decision model for EVCSs, which adheres to stringent quality-of-service constraints and leverages the network calculus theory. Subsequently, the EDS endeavors to maximize its utility by strategically orchestrating charging plans for the charging stations and formulating purchase plans from the wholesale market. To comprehensively analyze the intricate interplay between EVCSs and the EDS, we employ SFE game framework. This game-theoretic model not only guarantees the existence of an equilibrium solution but also enables us

References

233

to elucidate the interactive process involved in energy management. To identify this equilibrium solution, a hybrid optimization algorithm, combining the power of differential evolution and the precision of the interior point method, is diligently applied. Through rigorous simulation studies, we have meticulously compared the performance of our proposed interactive method with uncontrolled charging and social welfare maximization strategies. The compelling results unequivocally demonstrate that the proposed interaction mechanism between EVCSs and the EDS yields superior operational outcomes. These benefits include a significant reduction in peak load, an enhanced voltage profile within the EDS, increased utilities for each EVCS, and an unwavering commitment to delivering exceptional quality of service. Importantly, these findings also validate that the equilibrium solution achieved through the SFE game corresponds to the maximization of social welfare, thereby confirming the economic efficiency of our innovative and interactive energy management approach.

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