The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023): Volume II (Lecture Notes in Electrical Engineering, 1159) 9819708761, 9789819708765

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Lecture Notes in Electrical Engineering 1159

Chunwei Cai · Xiaohui Qu · Ruikun Mai · Pengcheng Zhang · Wenping Chai · Shuai Wu   Editors

The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023) Volume II

Lecture Notes in Electrical Engineering

1159

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

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Chunwei Cai · Xiaohui Qu · Ruikun Mai · Pengcheng Zhang · Wenping Chai · Shuai Wu Editors

The Proceedings of 2023 International Conference on Wireless Power Transfer (ICWPT2023) Volume II

Editors Chunwei Cai Harbin Institute of Technology Weihai, Shandong, China

Xiaohui Qu Southeast University Nanjing, Jiangsu, China

Ruikun Mai Southwest Jiaotong University Chengdu, Sichuan, China

Pengcheng Zhang Tsinghua University Beijing, China

Wenping Chai Harbin Institute of Technology Weihai, Shandong, China

Shuai Wu Harbin Institute of Technology Weihai, Shandong, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-97-0876-5 ISBN 978-981-97-0877-2 (eBook) https://doi.org/10.1007/978-981-97-0877-2 © Beijing Paike Culture Commu. Co., Ltd. 2024 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.

Contents

Operation Optimization of the Cold End System with Dual-Pressure Condenser of 1000 MW Coal-Fired Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Liu, Yan Liu, Guoqing Li, Pan Qin, Diping Zhao, Xiao Chen, and Shenglong Zeng Water Content Monitoring of Two-Phase Flow in Oil Pipeline Based on Electromagnetic Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiawei Shi, Da He, Jiajie Deng, Mofan Gao, and Junjie He Design of Hilbert Fractal Antenna for Partial Discharge Detection in Cable Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yang Yin, Shi-qiang Li, Xiao-heng Yan, Xiao-he Zhao, Zhi-guang Lv, and Yi-miao Liu

1

11

19

Study of Resonance Suppression Strategy and Its Adaptability for Grid-Connected Inverters in High Permeability Environment . . . . . . . . . . . . . Meimei Sun, Xuezhi Xia, Changzhou Yu, and Chenggang Wang

28

The Feedback Control of the −200 kV High Voltage Power Supply for CRAFT NNBI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shengmin Pan, Baocan He, Hulin Feng, Denghui Wang, Hongfei Yong, Yiyun Huang, and Quanguo Tang

40

Modeling and APP Development for the Evaluation of the Electromagnetic Disturbance of Modular Multilevel Converter Towers . . . . . . . . . . . . . . . . . . . . . . . Lijing Yi, Xikui Ma, Ru Xiang, Haoyu Lian, Huifu Wang, and Jiawei Wang

49

Theory and Method of Non-contact Electrostatic Gait Detection Based on Human Body Electrostatic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sichao Qin, Weiling Li, Yu Qiao, Jie Bai, Jiaao Yan, Ruoyu Han, Pengfei Li, and Xi Chen Statistical Indicator System for New Generation Power System Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jucong Li, Rongming Li, Chao Xun, Xiangyu Wu, Xiaofu Jiang, Zhijun Tang, Longcan Zhou, and Changxu Jiang A Fault Dictionary Diagnosis Method for Photovoltaic Array Based on Maximum Fuzzy Fault Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Chen, Xinyin Zhang, Tingting Pei, and Cong Ding

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Contents

An DC Overvoltage Surge Suppression Circuit for Airborne High-Current Avionics Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dong Gao, Xinyu Gao, Zihe Li, Fei Feng, and Guofei Teng Comparison and Analysis of Full Power Inverter Topology for Large Capacity Variable Speed Pumped Storage Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fengyuan Tian, Kaiguo Wang, Jinwu Gong, Bo Zhao, Qichao Zhang, Youzong Jian, and Hemin Yang

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Optimization of Non-destructive Detection Method for Metal Pipelines Based on Magnetic Induction Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Jiawei Shi, Yi Lv, and Jiawei Jiang Analysis of Transient Voltage Stability Under the Interaction Between HVDC Receiving End and New Energy Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Zunmin Liu, Deping Ke, Jian Xu, Xin Sun, and Xiaojiu Ma Optimal Scheduling of VPP with Carbon Capture and P2G Considering Demand Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Mingzhao Xie, Li Kang, Jiekang Wu, Zikang Fang, Weiming Luo, and Jianan Liu Methodology for Analysis of Safety Improvements of SSCs for Operation License Extension of Nuclear Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Rui Liu Laying Technology and Scenario Applicability Analysis of High Temperature Superconducting Cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Ting Jiao, Shuaibo Li, Lei Su, Hua Huang, and Guoqi Li An Implementation Method of Energy Harvesting CT Based on Double-Winding Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Qiaozhi Xue, Nanzhe Wei, Xinqi Li, Ziqian Ren, Jiang Shang, and Chunguang Ren A Novel Six-Element Multi-resonant DC-DC Converter for Wide Input Voltage Range Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 Nanzhe Wei, Qiaozhi Xue, Jiang Shang, Ziqian Ren, Xinqi Li, and Chunguang Ren Topology and Hysteresis SVPWM Fault-Tolerant Control Strategy of the Novel Multilevel Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Guohua Li, Yutang Ma, and Liangjun Wang

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Evolutionary Game Analysis of Commercial Building Participation in Demand Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Zheng Wang and Jie Yu Research and Practice of Power Demand Response Market Mechanismtion . . . . 192 Yu Zhang, Tao Xu, Yan Zhang, Zhen Li, and Jia Yin Research on MPC Fault-Tolerant Control of Five-Level Inverter . . . . . . . . . . . . . . 202 Guohua Li, Rongyu Dong, and Guangda Liu Characteristic Analysis of Quasi-Power-Frequency Sequence Oscillations in DFIG Wind Farms Integrated via MMC-HVDC . . . . . . . . . . . . . . . . . . . . . . . . . 215 Hui Liu, Wenkai Dong, Xiao Wang, Yunhong Li, Xiaoyang Deng, Yina Ren, and Xiaorong Xie Research on Multi-level Distributed Photovoltaic Consumption Strategies Photovoltaic Based on AC/DC Hybrid Distribution Network . . . . . . . . . . . . . . . . . 224 Guanglin Sha, Qing Duan, Lu Liu, Jian Gao, Genqi Chen, and Xiaolei Li Research on the Influence of Harmonics on Interruption Performance of High-Voltage Circuit Breaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Han Zhang, Gang Wang, Renjie Yu, Ze Guo, and Xingwen Li Sensorless Control of Permanent Magnet Synchronous Motor Based on Adaptive Sliding Mode Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Xu Shizhou, Jia Xinxin, Fan Jingsheng, and Chang Jinhai Research on Capacity Configuration of Wind Storage Hydrogen Production Plant Considering “Source-Load” Double Disturbance . . . . . . . . . . . . 254 Lei Xu, Ji Li, Yuying Zhang, Xiqiang Chang, Wenyuan Zheng, Jixuan Yu, and Dongyang Sun High-Gain Feed Antenna for Improved Travelling-Wave Excitation Efficiency in Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Tong Liu and Yang Gao High-Sensitivity Microwave Sensor Based on Slot Structures for Permittivity Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Han Xiao and Yang Gao Simplified Space Vector Modulation Algorithm for Modular Multilevel Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Zhanhao Zhao, Cui Wang, Yunhe Wang, Chenhang Wu, Zuojia Niu, Tengwei Zhu, and Hongwei Wang

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Operation of Integrated Energy System Based on Heating System . . . . . . . . . . . . 292 Rui Ma, Hui Fan, Xiaoguang Hao, Jianfeng Li, and Hui Wang Optimization of ESS Configuration and Operation Strategy for PV DC Collection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Ke Guo and Xiaolin Yang Novel Open Circuit Voltage Clamp Protection Method Based on Microsecond Pulse Current Source for DBD Application . . . . . . . . . . . . . . . . . 314 Zhenyu Guo, Shanshan Jin, and Zhi Fang High-Precision Current Source with Lumped Current Outer Loop-Distributed Current Inner Loop for the Application of Sintered Powder Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Songyang Zhao, Shanshan Jin, and Zhi Fang Voltage Regulation Method for Active Distribution Networks Based on Rotary Voltage Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 Xiangwu Yan, Chen Shao, Weifeng Peng, Bingzhen Li, and Weilin Wu Active Power Decoupling Control Strategy for MMCs with Split-Capacitor Sub-modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 Fuyuan Zhuang, Xinmig Hu, Yunshan Wang, and Shunfeng Yang Research on the Short-Term Power Interval Prediction Method for Distributed Power Sources in Distribution Networks Based on Quantile Random Forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 Zhen Lei, Qiangsheng Bu, and Jing Wang Load Forecasting Based on Data Mining and Improved Stacking Ensemble Learning Under Load Aggregator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Zhishuo Zhang, Xinhui Du, Wenxuan Zhang, Kun Chang, and Rixin Zhang Research on Short-Term Electric Load Forecasting Based on VMD-FGRU . . . . 372 Junjie Shen, Xuan Zeng, Cui Wang, Shihan Deng, and Xing Lin Analysis of the Depth of Positive Sequence Voltage Sags in Distribution Network Faults and Their Effects on New Energy-Type Equipment . . . . . . . . . . . 381 Zhichang Liu, Qinghui Lu, Xin Yin, Xianggen Yin, Jiaxuan Hu, and Jian Qiao Measuring Method for Strand Current in Formed-Parallel Coil of Flat-Wire Motor Based on Hall Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 Ni Lei and Yanping Liang

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Research on Low and High Voltage Interlocking Fault Ride-Through Control Strategy for Doubly-Fed Wind Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 Darui Zhu, Jiakang Cheng, Jie Chen, and Jiandong Duan A Hybrid Multi-objective Optimization Algorithm Based on NSGA-II and MOGWO and Its Application to Optimal Design of Electromagnetic Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 Xinyu Wang and Yilun Li Application of TRIZ Theory in Power Electronic Circuits . . . . . . . . . . . . . . . . . . . 424 Yonggao Zhang, Zhongyi Sun, and Peng Liu Is Pollution Internalized? A Study of the Impact of Environmental Administrative Penalties on Companies’ Earnings in China’s Thermal Power Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 Wu Sun Master Slave Game Optimization Scheduling of Park Comprehensive Energy System Based on Stepped Demand Response . . . . . . . . . . . . . . . . . . . . . . . 444 Xinhe Zhang, Songcen Wang, Yichuan Xu, Xin Yu, Chenyang Xia, and Aiwen Xing Visualization and Detection Method for Surface-Mounted Evaporative Cooling Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454 Zhang Kexin, Liu Guoqiang, and Liu Jing Research on the Regionalization Development of China’s Power Transmission Projects Considering Spatial Correlation . . . . . . . . . . . . . . . . . . . . . . 466 Yuhui Ma and Panxin Mao A Model for Evaluating Science and Technology Innovation Capability of Energy Internet Firms Based on Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Rui Li Site Selection and Capacity Determination of Photovoltaic Generation Based on Nodal Inertia Constrained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Chengbin Chi, Shan Liu, Qi Liu, Fan Li, Guanghua Wang, and Jun Mei Research on Optimal Chimeric Morphology of Flexible DC Interconnect Topology Considering Node Inertia Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Chengbin Chi, Shan Liu, Qi Liu, Fan Li, Xuan Liu, and Jun Mei

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Calculation of Node Critical Inertia Compensation of Multi-machine System Based on Inertia Spatio-Temporal Distribution Characteristics . . . . . . . . 503 Chengbin Chi, Shan Liu, Qi Liu, Fan Li, Lei Liu, and Jun Mei A Comparative Study of Trading Mechanisms in China’s Reserve Auxiliary Services Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Yue Guo, Yuming Huang, Yanru Liu, Yi Song, Yaxuan Han, and Dunnan Liu Bidding Strategy Among Multi-party Electricity Sellers Based on Zero-Sum Game Theory in Complex Electricity Market Environment . . . . . . 523 Qingkai Sun, Menghua Fan, Chen Lv, Qiuyang Ma, and Su Yang Research on Reactive Power Compensation Method of Long-Distance and Large-Capacity Offshore Wind Farm High Voltage AC Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Wanrong Chen and Longfu Luo Research on the Sealing Efficiency of Downhole Electromagnetic Barriers Based on COMSOL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 Zhongjian Kang, Peng Liu, Yuchen Liu, and Chenghuang Zhang Solar Photovoltaic Penetration into the Grid Based on Energy Storage Optimization Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 Sothearot Vann, Hongyu Zhu, Chen Chen, and Dongdong Zhang Electricity Price Prediction Framework Based on Two-Stage Time Series Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Yuzhe Huang, Chenwei Wu, Chenghan Li, Zizheng Wang, and Kan Li Optimization Design of Self-powered Coil for Wireless Sensor of Three Core Cable Based on Spatial Electromagnetic Energy . . . . . . . . . . . . . . . . . . . . . . . 571 Xu Lu, Ran Hu, Jie Tian, Zhifeng Xu, and Feng Tang Research on Photovoltaic Grid-Connected Control of New Quasi-Z-Source Inverter Based on VSG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 Xin Mao, Hongsheng Su, and Jingxiu Li Impedance Analysis of Supercapacitor DC-DC Converter in Two-Cascade System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Tao Lin, Jun Liu, and Peng Weifa Electromagnetic Characteristic Analysis of Superconducting Cables . . . . . . . . . . 597 Dong Ding, Wenze Si, Sisi Peng, Jiaqi Cai, Lingxuan Chen, Xianhao Li, and Ying Xu

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Hardware-In-The-Loop Simulation of High Voltage Modular Multilevel Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 Zhu Ruijun, Dong Yanbo, Yang Haiying, Liang Shuaiqi, Zhang Xuejun, Zhang Qingjie, and Tian Anmin Preliminary Scheme of the High Precision RF Impedance Measurement for the Negative Ion Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 Xin Tian, Dong Li, Dezhi Chen, and Chen Zuo Research on the Organizational System of Multi-level and Grid-Based Power Trading Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Qiu Li, Xu Lin, and Yanling Wang Hierarchical Optimal Scheduling Strategy for Electric Vehicles with Dynamic Time-of-Use Tariff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632 ChuangXin Wang and Zhong Chen Design of Suppressor Grid Power Supply for Neutral Beam Injector . . . . . . . . . . 640 Junjun Pan, Zhimin Liu, Caichao Jiang, Sheng Liu, and Shiyong Chen Optimization Design and Research of Control Strategy Based on Dual Closed-Loop Three-Phase Voltage PWM Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . 648 Feng Liu and Yihui Xia Dynamic Forecasting of Hydroelectric Engineering Price Index Using Multidimensional Conditional Autoregressive Model: A Case Study in Southwest China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657 Li Ma and Huaqi Xiang Multiple Benefits Evaluation of Mechanized Construction of 110 kV Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Yuhui Ma and Panxin Mao Short-Term Photovoltaic Power Prediction Based on 3DCNN and CLSTM Hybrid Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679 Tengqi Luo, Yueming Ding, Rongxi Cui, Xingwang Lu, and Qinyue Tan Pathways and Key Technologies for Zero-Carbon Industrial Parks: A Concise Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687 Guihong Zhang, Cunqiang Huang, Qiang Zhang, Xiangcheng Zhang, Jinliang Mi, and Peng Zhang

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Research on Voltage Stability of Distributed Photovoltaic Active Distribution Network with High Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 Haifeng Zhan, Jianwei Wang, Yueming Ding, Jun Lu, Rongxi Cu, Qinyue Tan, and Xinming Lu Multi-stage Robust Unit Commitment Considering Renewable Energy Uncertainty and Nonanticipativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707 Zijiao Han, Kai Kang, Guangyu Na, Qiang Zhang, Qi Jia, and Feng Liu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721

Operation Optimization of the Cold End System with Dual-Pressure Condenser of 1000 MW Coal-Fired Unit Li Liu(B) , Yan Liu, Guoqing Li, Pan Qin, Diping Zhao, Xiao Chen, and Shenglong Zeng China Power Huachuang Electricity Technology Research Co., Ltd., Suzhou 215000, China [email protected]

Abstract. Taking the cold end system with dual-pressure condenser of a 1000 MW coal-fired unit as the research object, considering real-time parameters during operation, the full working conditions real-time optimization model was established. Based on the historical operation data, the accuracy of the model was verified, the influence of changes in real-time state parameters such as load, circulating water inlet temperature and clean coefficient on the optimization calculation results was analyzed, and the optimal circulating pump operation mode and energy saving potential under calculated working conditions were obtained. The calculation results showed that, 63.44% of the calculation conditions had achieved energy saving effect, and the cumulative income could reach 604.16 MW·h, the optimal operation modes of the circulating water pump were more necessary to reasonably determine Under the working conditions of high load and high inlet water temperature. Keywords: dual-pressure condenser · cold end system · full working conditions · operation optimization

1 Introduction The purpose of the cold end system of the power plant is maintaining the vacuum of the condenser. And the output of the unit increases with the increase of the condenser vacuum. However, whether from the design or operational perspective, it’s not the higher the vacuum, the better. There is an optimal vacuum. Therefore, optimizing the cold end to ensure the optimal vacuum state of the condenser is an important measure to ensure the economic operation of the unit and achieve energy conservation and consumption reduction in the power plant. At present, many scholars have conducted analysis and research on the optimization of the cold end of power plants, and have achieved some results [1–5]. However, existing research includes the following issues in the actual operation process of the unit, which may lead to the actual operating conditions not being in the optimal operating state.

© Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 1–10, 2024. https://doi.org/10.1007/978-981-97-0877-2_1

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(1) In the actual operation process of the unit, it is generally possible to operate according to the pre prepared operating instructions for the circulating pump. The boundary conditions are mostly the inlet temperature and load of the circulating water, but these two parameters change according to a certain step law and cannot be continuously changed, which means that the refinement of the operating instructions cannot be achieved. (2) During the operation process, the relevant parameters change in real time, and currently, most cold end optimization studies take some key parameters, such as cleanliness coefficient, specific enthalpy difference, as fixed values, which will result in certain errors between the calculation results and the actual situation. Although the above will not have a significant impact on the operational safety of the unit, it may deviate from the optimal operating state under certain operating conditions, especially boundary conditions where the combination of circulating pumps changes. Therefore, this article establishes a real-time cold end optimization analysis method for all operating conditions, and takes the cold end system of a dual pressure condenser of a 1000 MW coal-fired unit as the research object to analyze the energy-saving potential of the cold end optimization of the unit.

2 Optimization Principle The pressure of the condenser is an important factor affecting the output of the unit, and the output of the unit increases with the decrease of the condenser pressure. The pressure of the condenser is mainly affected by the parameters of the circulating water. When the inlet water temperature of the circulating water remains constant, the pressure of the condenser will decrease with the increase of the circulating water flow rate. However, an increase in the circulating water flow rate will lead to an increase in the power consumption of the water pump. Therefore, there exists an optimal circulating water flow rate that maximizes the difference between the increase in unit output and the increase in pump power consumption when the pressure of the condenser changes, resulting in the best economic efficiency, as shown in formula (1): N = Nt − Np

(1)

Among them,  N is the increase in revenue, MW;  Nt is the unit output increment, MW;  Np is the incremental power consumption of the water pump, in MW. Therefore, the purpose of cold end optimization is to obtain the optimal flow rate, which is the optimal combination scheme for water pump operation.

3 Thermodynamic Model The problems that need to be solved in cold end optimization mainly include three aspects: the relationship between condenser pressure and circulating water volume, the relationship between unit output increment and condenser pressure, and the relationship between circulating water pump power consumption and circulating water volume.

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Therefore, the optimization of the cold end system involves three main equipment and models, namely the circulating water pump, condenser, and steam turbine, which have a certain coupling relationship with each other based on the circulating water flow rate, as shown in Fig. 1.

Fig.1. Schematic diagram of cold end optimization model

3.1 Relational Model of Condenser Pressure Changing with Circulating Water Volume The characteristic of condenser pressure changing with the circulating water volume is the most core content in cold end optimization, which mainly depends on the thermodynamic characteristics of the condenser. The pressure of the condenser is determined by the saturation temperature of the condensate, which is mainly affected by the circulating water flow rate and the inlet temperature of the circulating water. However, in actual operation, other factors such as condenser load and cleanliness can also affect the working performance of the condenser. The corresponding condenser pressure pc (kPa) can be calculated by looking up the table based on the saturation temperature ts (°C) of the condensate or by using the following equation:  7.46 ts +100 × 9.81 57.66 (2) pc = 1000 The saturation temperature of condensate is determined by formula (3): ts = tw,in + t + δt

(3)

Among them, tw, in is the inlet temperature of cooling water, °C;  T is the temperature rise of cooling water, °C; δ T is the heat transfer end difference of the condenser, °C. The cooling water temperature rise can be obtained from the condenser Thermal equilibrium equation:   Qc = Dk (hc − hwc ) = KAtm = Dw cp tw,out − tw,in (4) t =

Dk (hc − hwc ) cp Dw

(5)

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Among them, Qc is the thermal load of the condenser, kW; Dk is the condensing capacity of the condenser, t/h; Hc is the exhaust enthalpy of the steam turbine, kJ/kg; Hwc is the specific enthalpy of condensed water, kJ/kg; K is the total Heat transfer coefficient, kW/(m2 · °C);  Tm is the Logarithmic mean temperature difference, °C; A is the cooling area, m2; Dw is the cooling water flow rate, kg/s; Cp is the specific heat at constant pressure, kJ/(kg · °C); Tw, out is the outlet temperature of the cooling water, °C. (1) In general, the condensing capacity of the condenser is equal to the sum of the Engine displacement of the steam turbine and the small turbine, which will decrease with the decrease of the group load. In this example, it is a double pressure condenser. The condensing capacity of the low-pressure and high-pressure condensers is shown in Fig. 2. (2) The specific enthalpy difference hc hwc is also an important input parameter in condenser pressure prediction. At present, there are two main methods to deal with this parameter in most of the literature on cold end optimization. One is to establish a complete thermodynamic system simulation model of the unit through the Thermal equilibrium method and solve the exhaust enthalpy value [4, 5]. This method is more accurate, but the calculation process is complex, and many parameters need to be known; One approach is to assume that a condenser under high vacuum has a small range of value variation, taking a fixed value from 2140 to 2220 kJ/kg [6]. Although this method is simple, it may increase the calculation error due to the fact that ➀ the actual specific enthalpy difference varies with the load, and ➁ the actual unit specific enthalpy difference may also exceed this range. Figure 3 shows the variation of specific enthalpy difference between low-pressure and high-pressure condensers with unit load in this calculation example.

Fig. 2. Shows the condensing capacity of Fig. 3. Shows the specific enthalpy difference low-pressure and high-pressure condensers in between low-pressure and high-pressure the calculation example condensers in the calculation example

The heat transfer end difference can be determined by Eq. (6): t

δt = e

KA cp D w

−1

(6)

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It can be seen that the heat transfer end difference of condenser is related to heat transfer, cooling area, Heat transfer coefficient and cooling water flow. For the operating unit, the cooling area has been determined. Under a certain steam load and cooling water flow, its size mainly depends on the Heat transfer coefficient. The HEI standard can be used to calculate the total Heat transfer coefficient, K = K0 βc βt βm

(7)

wherein, K0 is the basic Heat transfer coefficient, W/(m 2 °C); β C is the cleanliness coefficient of the condenser tube; β T is the correction coefficient for the inlet temperature of the cooling water; β M is the correction factor for the wall thickness of the condenser tube material. The condenser tube side cleaning coefficient is defined as the ratio of the actual total Heat transfer coefficient of the condenser to the calculated Heat transfer coefficient under the ideal cleaning state, that is, βc =

K K0 βt βm

(8)

The actual Heat transfer coefficient of the condenser is not only related to the operating parameters and load, but also related to the cleanliness of the tube side, the amount of air leakage, and the rubber ball cleaning. Therefore, the cleanliness coefficient is a real-time variable value, and within a rubber ball cleaning cycle, its value may vary widely [7, 8]. If the cleaning coefficient is set to a fixed value (such as the design cleaning coefficient) in the calculation, the calculation error will also increase. At present, there are few literature reports that Real-time computing of the cleaning coefficient is adopted in the cold end optimization research. 3.2 Relational Model Between Unit Output Increment and Condenser Pressure The influence of condenser pressure on unit output can be determined by Thermal equilibrium calculation, thermodynamic method or test method. It can also be obtained by fitting the correction curve of the exhaust pressure provided by the manufacturer on the turbine output, as shown in Eq. (9): Nt = FN (Q, pc )

(9)

Among them, Q is the unit load, MW. 3.3 Relational Model of Circulating Water Pump Power Consumption Changing with Circulating Water Volume The power consumption characteristics of circulating water pumps can be obtained by calculating models or changing the operation mode of circulating water pump combinations through experiments, to obtain the power consumption of circulating water pumps under different combinations and different circulating water flows: Np = Fp (Dw )

(10)

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In this example, the circulating water pump consists of three constant speed pumps. The water flow regulation is achieved by changing the combination of pumps, which cannot be continuously adjustable and is a discrete variation. Therefore, the objective function formula (1) has been transformed into the maximum difference obtained by solving for discrete changes in circulating water volume N max corresponds to the circulating water volume, thus determining the operating combination mode of the circulating water pump.

4 Research Subjects 4.1 Research Subjects This article takes the 1050 MW condensing steam turbine generator unit of a certain power plant as the research object. The condenser is an N-55500 dual back pressure, single process, dual shell surface type condenser. The rated back pressure of the high and low pressure condensers is 4.8 and 5.6kPa respectively, with a designed cooling water flow rate of 109440m3/h and a designed cleanliness coefficient of 0.9. Each unit is equipped with three constant speed circulating water pumps, with a single circulating pump flow rate of 13.44m3 /h and a power of 2855.5kW. The correction curve of exhaust pressure on turbine output is shown in Fig. 4.

Fig. 4. Correction Curve of Exhaust Pressure on Turbine Output

Fig. 5. Changes in Unit Power, Circulating Water Inlet Temperature, and Pump Start over Time

4.2 Model Validation Select the on-site operation data of the unit from March 1 to 21, 2023 for calculation and analysis, with a step length of 10 min and a total of 2957 effective calculation conditions. Figure 5 shows the historical data of the unit’s load, circulating water inlet temperature, and pump startup. The maximum load of the unit is 1002.61 MW, the minimum load is 392.30MW, and the inlet temperature of the circulating water is between 10.33 ~ 24.68 °C. In most operating conditions, one circulating water pump is opened, accounting for 90.63%. The operating condition of two circulating pumps is to have a minimum power of 604.44 MW, corresponding to a circulating water inlet temperature of 17.27

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°C; The minimum circulating water inlet temperature is 16.57 °C, corresponding to a unit power of 969.32 MW. Figure 6 shows the error between the power calculated by the model and the actual operating output power under the same number of pumps opened in actual operation. From the graph, it can be seen that the maximum relative error is 0.49%, the average relative error is 0.09%, and the number of operating conditions with errors between − 0.3% and 0.3% accounts for 94.25%, verifying the accuracy of the model.

Fig. 6. Power Calculation Error Distribution Fig. 7. Calculation of optimal pump start and actual pump start mode

4.3 Analysis of Optimization Results Figure 7 shows the comparison between the calculated optimal pump operation and the actual pump operation mode. In the calculation of the optimal pump starting method, there are 805 operating conditions for one pump and 2152 operating conditions for two pumps, which is 1875 more than the operating conditions. The number of operating conditions that match the number of pumps started is 1081, while the number of operating conditions that do not match is 1876, accounting for 63.44%. Both are operating with one pump, and the optimal number of two pumps is calculated. In the inconsistent working conditions, the minimum power is 392.30MW, and the corresponding circulating water inlet temperature is 19.98 °C; The minimum inlet temperature of circulating water is 11.74 °C, and the corresponding unit power is 603.59 MW. Taking a load of 500 MW (495 MW~505 MW) as an example, the number of calculation conditions is 561, and the inlet temperature of the circulating water is between 11.82~22.13 °C. The change in pump startup with the inlet temperature of the circulating water is shown in Fig. 8. During actual operation, one circulating water pump is operated; Under the condition of a constant cleaning coefficient of 0.9, the optimal pump start result is calculated as: when the circulating water temperature is less than 18.15 °C, start one pump, and vice versa, start two pumps. However, during the actual operation of the unit, the cleanliness coefficient will deviate from the design cleanliness coefficient under most conditions. It can be seen from 2.1 that when the cleanliness coefficient is less than the design cleanliness coefficient, the total Heat transfer coefficient will become smaller, and the heat transfer end difference will increase. To ensure that the saturation temperature

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of condensate, i.e. the pressure of condenser, remains constant, under the condition that the inlet temperature of circulating water remains constant, it is necessary to reduce the temperature difference between the inlet and outlet of circulating water, increase the flow of circulating water, and increase the number of pumps to be opened. Therefore, when considering the changes in the cleanliness coefficient during actual operation, even when the inlet temperature of the circulating water is low, there will still be a situation of starting two pumps. From this, it can be seen that the optimal operating state of the cold end system is not only affected by the inlet temperature and load of the circulating water, but also greatly affected by the real-time cleaning coefficient of the condenser. Increasing the number of pump units will increase the power consumption of the circulating pump, but the slight increase in unit power caused by the decrease in back pressure is greater than the increase in power consumption of the circulating pump. Therefore, the net profit of unit power after optimization is positive. Figure 9 shows the revenue values and cumulative revenue values for each operating condition during the calculation period. Among them, the operating condition where the number of pump starts is consistent with the calculated number of pump starts is 0. Among other operating conditions, the maximum profit is 7947.56 kW, and the corresponding unit load and circulating water inlet temperature are 733.21 MW and 21.31 °C, respectively. The cumulative profit is 604.16 MW ·h.

Fig. 8. Changes in the number of pumps opened with the inlet temperature of circulating water under a 500 MW load

Fig. 9. Calculation of Revenue Value and Accumulated Revenue Value under Operating Conditions

Figure 10 shows the variation relationship of the optimized revenue random group load, where the size of the bubble represents the percentage of revenue to the corresponding operating load, i.e. the revenue ratio. From the graph, it can be seen that the revenue and revenue ratio generally increases with the increase of load and circulating water inlet temperature. The maximum revenue operating condition mentioned above also has the highest revenue ratio, which is 1.09%. Figure 11 shows the relationship between revenue and circulating water inlet temperature under six typical loads (with a high proportion of loads). From the figure, it can be clearly seen that under the same load, the revenue increases linearly with the inlet temperature of the circulating water. The lower the load, the higher the linear compliance (the number of calculated operating conditions for 400 MW is relatively small, so R2 is small). Moreover, as the load increases, the maximum revenue and maximum revenue

Operation Optimization of the Cold End System

Fig. 10. Relationship between Revenue Random Group Load and Circulating Water Inlet Temperature

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Fig. 11. Relationship between revenue and circulating water inlet temperature under typical loads

ratio also increase, and the amplitude of revenue increase is also greater, as shown in Table 1. Therefore, under high load and high inlet temperature conditions, it is more necessary to reasonably determine the optimal operating mode of the circulating water pump. Table 1. Relationship between Revenue and Circulating Water Inlet Temperature under Typical Load proportion, %

string formula

R2

Power (MW)

Power range, (MW)

400

395~405

0.74

y = −1158 + 80.88x0.63

20.68

0.17

0.23%

450

445~455

4.43

y = −2975 + 178.07x0.95

22.73

1079.9

0.24

4.43%

500

495~505

13.56

y = −3088 + 207.34x0.97

22.13

1619.15

0.32

7.70%

700

695~705

1.66

y = −2232 + 288.99x0.88

22.47

4475.54

0.64

3.58%

800

795~805

2.23

y = −9723 + 669.20x0.85

23.58

7678.12

0.95

4.49%

880

875~885

5.24

23.73

7762.92

0.88

17.79%

y = −20476 + 1203x

0.83

inlet temperature, °C

maximum return, kW

677.39

• The • maxiProportion mum of cumushare of lative benefits, income, % %

5 Conclusion This article establishes a real-time optimization model for the cold end system of a dual pressure condenser of a 1000MW coal-fired unit under all operating conditions. The historical data from March 1 to March 21, 2023 were calculated and analyzed, and the following conclusions were obtained:

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(1) Based on the comparison of unit load, the maximum relative error calculated by the model is 0.49%, and the average relative error is 0.09%. (2) During the operation of the unit, in addition to the load and circulating water inlet temperature, the change in cleanliness coefficient also has a significant impact on the optimal number of pumps to be started. (3) 63.44% of the calculated operating conditions achieved energy-saving effects, with a maximum revenue of 7947.56 kW and a cumulative revenue of 604.16 MWh. (4) The benefit to benefit ratio basically increases with the increase of load and circulating water inlet temperature, and the benefit increases linearly with the circulating water inlet temperature under the same load. Under high load and high inlet temperature conditions, it is even more necessary to reasonably determine the optimal operating mode of the circulating water pump.

References 1. Yang, Q.: Quantitative analysis of the influence of circulating cooling water inlet temperature on condenser pressure. Steam Turbine Technol. 62(5), 393–395 (2020). (in Chinese) 2. Zhao, W.: Optimization of the circulating water system of dual pressure condensers. Steam Turbine Technol. 59(2), 145–147+150 (2017). (in Chinese) 3. Li, P.: Operation optimization of circulating water system of Cogeneration unit based on adaptive model. Chinese J. Electr. Eng. 38(18), 5500–5509 (2018). (in Chinese) 4. Meng, L.: Research on cold-end optimization and cooling system configuration of 1000 mw ultra supercritical unit with wide load. Electr. Power Surv. Design 10, 13–18 (2022). (in Chinese) 5. Wei, J.: Research and application of cold end optimal control system of direct air cooling unit based on multi parameter monitoring. Power Syst. Eng. 39(2), 15–18 (2023). (in Chinese) 6. Guo, J.: Research on optimization of circulating water system operation for 630MW Coal-fired Units. Thermal Turbines 51(2), 110–116 (2022). (in Chinese) 7. Miao, D.: Coupled calculation and analysis method for pressure characteristics of direct air-cooled condensers. Steam Turbine Technol. 63(5), 377–381 (2021). (in Chinese) 8. Wang, X.: On line performance monitoring and optimization of steam turbine cold end system. Southeast University, Nanjing (2016). (in Chinese) 9. Lin, Y.: Analysis of frequency conversion optimization operation of circulating pumps considering cleanliness coefficient. Steam Turbine Technol. 56(04), 299–302 (2014). (in Chinese) 10. Zhou, L.: The effect of pipe wall cleanliness coefficient on the vacuum of dual back pressure condensers. East China Power, (07), 17–19+69 (2002). (in Chinese)

Water Content Monitoring of Two-Phase Flow in Oil Pipeline Based on Electromagnetic Induction Jiawei Shi, Da He, Jiajie Deng, Mofan Gao, and Junjie He(B) Shenyang Aerospace University, Shenyang 110000, China [email protected]

Abstract. Oil energy is very important for national development, but with the exploitation of oil resources, the emergence of high water content oil reduces the combustion efficiency. Therefore, timely monitoring of oil moisture content is very important for subsequent oil exploitation. Based on the principle of electromagnetic induction, a sensor array consisting of 8 excitation coils and 12 detection coils is designed to monitor the oil water content in the pipeline. The experiment verifies that the induced voltage is proportional to the moisture content. The experimental results show that the presence of pipeline defects increases the value of induced voltage, but does not change the trend of induced voltage. At the same time, when the number of coils in the sensor array is between 500 and 1000 turns, the sensitivity of the overall monitoring system reaches the best, and too much or too little will affect the result. This is of great significance for improving the efficiency of oil extraction and ensuring energy supply. Keywords: Electromagnetic induction · Two-phase flow · Pipelines · Moisture content

1 Introduction Oil is an important resource for national war readiness, and its efficient long distance transportation is very important. Pipeline transportation has become the preferred method because of its advantages of large transportation volume and low cost. However, as the exploitation of most oil fields has entered the middle and later stages, the water cut in oil is relatively high [1]. Oil with high water content will reduce subsequent refining quality and combustion efficiency [2]. Therefore, it is urgent to accurately detect the water content in the oil inside the pipeline without damaging the pipeline structure and affecting the pipeline transportation. Density detection, ultrasonic detection and other methods have been widely used, but they are sensitive to pressure and temperature changes, and high moisture content detection is limited [3]. As a non-invasive detection method, electromagnetic induction technology can accurately detect water content according to the different electrical conductivity of oil and water, and it has the advantages of safety, low cost, non-contact and good penetration depth [4]. Therefore, the application of electromagnetic induction detection technology to the detection of oil-water two-phase flow in oil pipeline can realize the monitoring of water content. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 11–18, 2024. https://doi.org/10.1007/978-981-97-0877-2_2

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Domestic and foreign scholars have done a lot of research on oil-water two-phase flow. In 1981, Mukherjee discovered the corresponding relationship between the middle pressure drop and the horizontal inclination Angle of the near-horizontal oil-water twophase flow pattern [5]. In 1997, Trallero put forward a new classification method, which divided oil-water flow patterns in horizontal pipelines into six types [6]. These studies enable scholars to have a more comprehensive understanding of the flow pattern and flow state change law of oil-water two-phase flow, and begin to study the detection of water-oil two-phase water content. In 2003, Jin proposed a new type of conductance probe that can be used to measure water volume fraction and axial velocity in oil-water two-phase pipeline flow [7]. In 2012, Liang proposed an optimally designed parallel wire conductance probe that could accurately distinguish the volume fraction of oilwater two-phase flow [8]. In 2015, Wang Jie studied the error of water content in oil, and improved the accuracy of measuring water content in oil produced liquid by increasing the distillation temperature and other methods [9]. In 2021, Zhang Zhenyuan proposed a new method of measuring water content by radio frequency method under oil-water twophase spiral flow, and the error was controlled within 6.29% [10]. In 2021, Yiguang found a flow-through microwave resonator sensor for predicting water content in oil-water twophase flow [11]. In 2023, Bao Yong proposed a method based on ultrasonic nonlinear parameters to detect the phase fraction of oil-water mixture, and built a measurement model to achieve accurate measurement [12]. This paper studies the monitoring of water content of two-phase flow in oil pipeline based on electromagnetic induction method. Firstly, a mathematical model is established to analyze the influence of different water content on the relative height of oil phase and water phase. Then the sensor array and two kinds of pipeline monitoring system models with or without defects are built, and the change law of the induced voltage of the detection coil is analyzed. Finally, the effects of pipeline defects and coil turns of sensor array on water content monitoring are compared and analyzed.

2 Principle 2.1 Electromagnetic Induction Maxwell’s equations are the basic equations of electromagnetism theory, and the differential form of Maxwell’s equations is expressed as: ⎧ ∇ × H = J + ∂D ⎪ ∂t ⎪ ⎨ ∇ × E = − ∂B ∂t ⎪ ∇ ·D =ρ ⎪ ⎩ ∇ ·B=0

(1)

where H and E are magnetic field strength and electric field strength; J is the current density; D is the electric displacement vector; B is the magnetic induction intensity; ρ is the density of charge. According to Maxwell’s equations and the quasi-static magnetic field used by Griffiths [13] et al. to describe the electromagnetic induction of the two-coil structure, it can

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be concluded that: B ∝ (ωε0 εr − jσ )ω B

(2)

where B is the induced secondary magnetic field, B is the main magnetic field, ε0 is the dielectric constant of vacuum, εr is the relative dielectric constant of the target conductor, and σ is the conductivity of the target conductor. Because in the actual detection, the change of the induced voltage and the change of the magnetic field are proportional. Combined with formula (2), it can be concluded that the imaginary part of the induced voltage is related to the conductivity and frequency. Therefore, based on the difference in electrical conductivity between water and oil, the water content inside the pipeline can be inferred indirectly by measuring the imaginary part of the induced voltage. 2.2 Moisture Content When oil-water two-phase flow is transported in the pipeline, different fluid structure modes are often produced due to the geometric differences of flow rate and pipeline. But because oil is less dense than water, it floats on top of the water, forming layers for storage in the pipe. When the transport speed is low, the stratification phenomenon is more obvious. The two-phase planar distribution of oil and water in a cylindrical pipeline is shown in Fig. 1.

(a) Side view of the pipe

(b) A cross-section of the pipeline

Fig. 1. Oil-water two-phase planar distribution.

Among them, the volume proportion of water phase occupying the whole is the water content of the two phases of oil and water. The formula of water content is as follows: ∂=

V1 V1 + V2

(3)

where ∂ is the water content, V1 is the volume of the water phase and V2 is the volume of the oil phase. And because the pipes are cylindrical. Therefore, according to its pipeline, the following mathematical model can be inferred: ◦

θ 1 2 ◦ 2 r sin θ = nπ ◦ πr − 360 2

(4)

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where r is the radius of the cylinder section, θ is the Angle corresponding to the water phase, h is the height of the water phase, and n is the water content of the oil and water phases. Through the approximate solution of the above formula (3), the Angle and height h of the water phase corresponding to different water content can be obtained, as shown in Table 1. Table 1. Data corresponding to different moisture content. Moisture content

0

0.2

0.4

0.6

0.8

1.0

Angle (°)

0°

120°

162°

198°

240°

360°

Height(mm)

0

0.5r

0.84r

1.16r

1.5r

2r

3 Methods 3.1 Design of Sensor Array In order to more accurately monitor the water content inside the oil pipeline, this paper designed a sensor array using COMSOL Multiphysics, as shown in Fig. 2. The sensor array consists of 8 excitation coils and 12 detection coils. The excitation coil has a radius of 18 mm, a number of turns of 50, and is arranged at equal intervals on rings with a radius of 60 mm. The detection coils have a radius of 8 mm and a number of turns of 50, and are also arranged at equal intervals on rings with a radius of 45 mm. To form an array of detection coils, either of the detection coils can be rotated by 30°. Similarly, to form an array of excitation coils, rotate any excitation coil by 45°.

(a) Two-dimensional planar graph

(b) Three dimentional stereogram

Fig. 2. MIT pipeline inspection 3D model.

3.2 Oil-Water Two-Phase Flow Model Construction The sensor array in Sect. 3.1 above is used to build a three-dimensional model of the oil pipeline water content monitoring system, as shown in Fig. 3(a). The system consists of

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a 300 mm length aluminum pipe and sensor array. The radius of the aluminum pipe is set to 26 mm, the thickness is 10 mm, and the conductivity is. In order to simulate oil-water two-phase flow, a working plane division domain space was established in the middle of the aluminum pipeline, as shown in Fig. 3(b). By constantly changing the height of the working plane to adjust the size of the water cut, the conductivity of water is set to 1, and the conductivity of oil is set to 1. The coil material of the sensor array is set to copper, the excitation frequency is 100 kHz, and the excitation current size is 10 A.

(a) Pipeline construction model

(b) Working plane segmentation domain

Fig. 3. Monitoring system model.

3.3 Construction of Defective Pipelines for Oil-Water Two-Phase Flow During the transportation of metal pipes, defects may occur on the surface of the pipes due to physical damage or chemical corrosion. These defects can cause changes in the conductivity of the pipeline and may affect the monitoring results of the water content. To verify this conjecture, a cylindrical aluminum pipe with a rectangular defect is used without changing the other conditions set out in Sect. 3.2 above. The rectangular defect has a length of 40 mm, a width of 10 mm and a height of 5mm, and the conductivity is set to 0, as shown in Fig. 4(a). The two-dimensional plane screenshot of the pipeline monitoring model is shown in Fig. 4(b).

(a) Three dimensional diagram of the pipeline

(b) Two-dimensional plan of pipeline

Fig. 4. Pipeline monitoring model with defects.

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4 Results 4.1 The Influence of Different Moisture Content on Induced Voltage Based on the data corresponding to different water content in Table 1 and combined with the monitoring system model in Sect. 3.2 above, simulation calculation can be performed to obtain the induced voltage of the detection coil under different water content. As shown in Fig. 5(a). A clear trend can be observed from the line plot drawn in Fig. 5(a): as the moisture content increases, the value of the induced voltage obtained by the detection coil also increases. This shows that there is a proportional relationship between the induced voltage and the moisture content. Therefore, we can use the numerical value of the induced voltage to infer the size of the water content, which provides feasibility support for the subsequent further study. Induced voltage with different moisture content (V)

12.375

Induced voltage with different moisture content (V)

induced voltage(V)

induced voltage (V)

12.3515 12.3505 12.3495 12.3485 12.3475

12.37 12.365 12.36 12.355 12.35

12.3465

12.345

12.3455 0

0.2

0.4

0.6

0.8

1

moisture content

(a) Detect the induced voltage of the coil

0 0.2 0.4 0.6 no defect moisture content defecve

0.8

1

(b) Comparison of induced voltage with or without defect.

Fig. 5. Detect the induced voltage of the coil.

4.2 The Influence of Pipeline Defects on Moisture Content Monitoring In the case of different moisture content, the induced voltage of the pipe without defect and the pipe with rectangular defect are measured respectively. These measurements are then plotted as a line chart, as shown in Fig. 5(b). By looking at Fig. 5(b), it can be concluded that the induced voltage of a defective pipeline will increase overall compared to a non-defective pipeline. This is because the defect changes the conductivity of the pipe, resulting in a stronger induced current in the pipe, which further leads to an overall increase in induced voltage. However, with the increase of water content, the water inside the pipeline will have a certain attenuation effect on the electromagnetic induction process. This keeps the trend of changes in the induced voltage constant, even in defective pipes. Therefore, although a defective pipe will show an overall higher induced voltage, its tendency to change with water content is still similar to that of a pipe without defects.

Water Content Monitoring of Two-Phase Flow in Oil Pipeline

17

4.3 The Influence of Sensor Coil Turns on Moisture Content Monitoring When the moisture content is 0.4, the coil turns of the sensor array are studied, and the coil turns are set to 100 turns, 200 turns, 500 turns and 1000 turns respectively. Then the induced voltage is calculated at the frequency of 100 kHz, and the induced voltage value is relatively reduced. The induced voltage values under the four conditions are plotted in a line chart, as shown in Fig. 6. This can better show the effect of different coil turns on the induced voltage.

relative induced voltage (V)

Induced voltage with different coil turns (V) 2 1.5 1 0.5 0 0.2 100 turns

0.4

0.6

0.8

500 turns

1000 turns

moisture content

200 turns

Fig. 6. The induced voltage of different coil turns

Under ideal conditions, with the increase of water content, the change of induced voltage should show a linear increasing relationship. According to the results in Fig. 6, it can be concluded that when the number of turns of the coil increases, the induced voltage gradually approaches a straight line with the increase of water content. However, when the number of coil turns reaches 1000, the value of the induced voltage at the moisture content of 0.8 is lower than that at the number of coil turns is 500. This indicates that the coil 1000 turns may have added noise and interference to the monitoring system model, resulting in the induced voltage change is no longer close to the linear increase form. In addition, the influence of coil position and frequency will cause the induced voltage change can not be completely linearly increased. Therefore, the optimal number of coil turns should be between 500 and 1000 turns. This can minimize the impact of noise and interference, making the change of induced voltage and the change of water content more accurate and reliable.

5 Conclusion This paper studies the influence of water content on induced voltage by constructing a water content monitoring model of two phases of oil and water and using a sensor array consisting of 8 excitation coils and 12 detection coils. The experimental results show that the induced voltage of the detection coil is proportional to the moisture content. In addition, pipeline defects increase the overall value of the induced voltage, but do not

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change the trend of change between the induced voltage and water content. Finally, it is found that in the monitoring system of this experiment, when the number of turns is less than 500, the change of induced voltage gradually approaches the line with the increase of the number of turns, but when the number of turns reaches 1000, the change trend of induced voltage changes. Therefore, the optimal number of coil turns should be between 500 and 1000 turns. Too many turns will reduce the value of the induced voltage.

References 1. Wang, K.: Optimization of oil recovery engineering technology in the middle and late stage of oilfield development. Petrochemical Technol. 30(05), 214–216 (2023). (in Chinese) 2. Zhao, S., Ding, Z., Meng, Y., et al.: Combustion characteristics of red light heavy oil in porous media under dynamic air flow. Contemporary Chem. Ind. 51(06), 1294–1297+1301 (2022). (in Chinese) 3. Tang conscription, Gao, Z.: Design of detector for measuring water content of crude oil based on density method. Modern Electron. Tech. 34(23), 137–139 (2011). (in Chinese) 4. Mahindra, G., Maryam, R., K. R A.: Electromagnetic induction imaging at multiple depths with a single coil. IEEE Trans. Instrumentation Measur. 70 (2021) 5. Mukherjee, H., Brill, J.P., Beggs, H.D.: Experimental study of oil-water flow in inclined pipes. J. Energy Res. Technol. 103(1), 56–66 (1981) 6. Trallero, J.L., Sarica, C., Brill, J.P.: A study of oil-water flow patterns in horizontal pipes. SPE Prod. Facil.Facil. 12(3), 165–172 (1997) 7. Jin, N.D., Wang, N.J., Xu, L.J.: Optimization of a conductance probe with vertical multielectrode array for the measurement of oil-water two-phase flow. In: Proceedings of the Second International Conference on Machine Learning and Cybernetics, pp. 899–905 (2003) 8. Liang, X., Jin, N., Yu, Z., et al.: The measurement characteristics of parallel-wire conductance probe used in horizontal oil-water two-phase flow. In: IEEE Proceedings of the 31st Chinese Control Conference, pp. 6888–6893 (2012) 9. Wang, J., Li, L., Zhang, R., et al.: Error analysis of water cut measurement in oil well production fluid in Shengli Oilfield. Tech. Supervision Petrol. Ind. 31(05), 12–14 (2015). (in Chinese) 10. Zhang, Z., Zhang, X., Wang, W., et al.: Measurement of water cut of crude oil by radiofrequency method under oil-water two-phase spiral flow. Oil Gas Chem. Ind. 50(01), 101– 107+118 (2021). (in Chinese) 11. Yiguang, Y., Ying, X., Chao, Y., et al.: Water cut measurement of oil–water two-phase flow in the resonant cavity sensor based on analytical field solution method. Measurement, 174 (2021) 12. Bao, Y., Dong, F., Tan, C.: Phase holdup detection of oil-water two-phase flow based on ultrasonic nonlinear parameters. Chin. J. Eng. Thermophysics 44(06), 1583–1586 (2023). (in Chinese) 13. Griffiths, H., Stewart, W.R., Gough, W.: Magnetic induction tomography: a measuring system for biological tissues. Ann. N. Y. Acad. Sci. 873(1), 335–345 (1999)

Design of Hilbert Fractal Antenna for Partial Discharge Detection in Cable Joints Yang Yin1,2 , Shi-qiang Li2,3,4(B) , Xiao-heng Yan1 , Xiao-he Zhao5,6 , Zhi-guang Lv1,2 , and Yi-miao Liu2,3 1 Faculty of Electrical and Control Engineering, Liaoning Technology University,

Huludao 125000, China 2 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

[email protected]

3 University of the Chinese Academy of Sciences, Beijing 100049, China 4 Institute of Electrical Engineering and Advanced Electromagnetic Drive Technology,

Qilu Zhongke, Jinan 250000, China 5 Henan Institute of Technology, Xinxiang 453000, Henan, China 6 Henan Key Laboratory of Cable Structure and Materials, Xinxiang 453000, Henan, China

Abstract. Effective detection of partial discharge faults is of vital importance for ensuring efficient power transmission. Currently, there are various partial discharge signal detection methods, such as the differential method and highfrequency current detection method. However, these methods suffer from low detection accuracy and narrow signal bandwidth. In this paper, the Hilbert fractal antenna is chosen as the research subject. The Hilbert antenna is an ultra-wideband, small-sized antenna that offers high detection accuracy and a broad detection bandwidth. As the location of the feed point affects the impedance matching and antenna parameters, optimizing the feed point position can significantly impact antenna performance. Through simulation and optimization using HFSS software, the feed point of the fourth-order Hilbert fractal antenna is selected and optimized. Additionally, the lengths of three different conductors, substrate thickness, and conductor width are also optimized. The optimization results demonstrate that within the frequency range of 0.3 GHz to 3 GHz, there are four resonant points. The overall bandwidth reaches 400 MHz within the range of 0.3 GHz to 1 GHz, and the antenna exhibits good overall directivity. The antenna exhibits suitable dimensions and excellent performance, making it suitable for capturing ultra-high-frequency signals of partialdischarges in cables. Keyword: Partial Discharge · Cable Connector · UHF · Hilbert Forming · antenna

1 Introduction In recent times, as economies have grown, the need for electrical power has surged. Ensuring the dependability of this power has become paramount, particularly in maintaining the safety and stability of power transmission lines. Among these lines, the use © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 19–27, 2024. https://doi.org/10.1007/978-981-97-0877-2_3

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of underground power cables has gained favor due to their benefits in urban aesthetics and installation flexibility [1]. These cables have found extensive usage due to their outstanding performance. Presently, the prevalent choice for underground power lines is cross-linked polyethylene cables. However, due to their intricate structure, meticulous steps are necessary during the manufacturing of cable joints. These cables must pass tests according to the GB-50120—2016 standards before being commissioned. Additionally, the cable joints require manual installation on-site. Operational issues often lead to faults in these cables over time. Examination of these failures reveals that most are caused by partial discharge defects stemming from the manufacturing process. Common problems encompass insufficient polishing after joint compression, flaws in insulation ring peeling, the presence of air gaps during conductor surface processing, and even the inclusion of metallic particles in the insulation surface [2]. The advantages of ultra-high frequency (UHF) detection techniques in identifying partial discharges (PD) are increasingly evident. More research is necessary to effectively implement UHF methods for on-site PD detection in cable joints. UHF PD signals span a broad frequency range (300–3000 MHz) [3]. Currently, various UHF antennas are used for PD detection, including Archimedean spiral antennas, Sierpinski carpet fractal antennas [4], Peano fractal antennas [5], loop antennas, and microstrip patch antennas. These antennas, compared to Hilbert fractal antennas, have larger sizes and lower detection frequencies. For instance, Lu et al. explored the application of Archimedean spiral antennas for detecting cable PD faults [6], although their larger size makes them unsuitable for confined spaces. Zhang et al. investigated the use of ultra-wideband monopole patch antennas for PD detection in electrical equipment [7], but these antennas possess a narrow detection bandwidth and are ill-suited for wideband UHF signals. Chongqing University studied the effectiveness of third-order Hilbert fractal antennas for transformer PD detection [8], yet their accuracy was limited, resulting in imprecise detections. Regarding Hilbert fractal antennas, design optimization was carried out using HFSS simulation software. The simulation analysis explored how varying wire segment lengths influenced antenna performance, factoring in wire width and dielectric substrate thickness. Employing an enumeration method for optimization yielded a proficient signal acquisition antenna. Hilbert fractal antenna. 1.1 Hilbert Antenna Theory Fractals are characterized by their morphology of filling space in a non-integer dimension. In 1973, Benoit Mandelbrot introduced the concepts of fractal dimension and fractal geometry during his lectures at the French Academy. The term "fractal" originally meant irregular and fragmented. Hilbert antennas are a type of planar fractal antennas. Through multiple iterations of self-similarity, the Hilbert fractal antenna increases its curve order (n) as the number of iterations increases, thereby increasing the utilization of space(9). As shown in Fig. 1, with the same outer dimensions, the total length of the Hilbert fractal antenna curve increases in a geometric progression as the fractal antenna order increases, highlighting its advantages in miniaturization and multi-band operation(10).

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Fig. 1. Hilbert fractal antenna impedance equivalent plot

1.2 Calculation of Resonant Frequency of Hilbert Fractal Antenna The Hilbert antenna wire segment can be divided into three categories. As shown in Fig. 2, for a 3rd order Hilbert fractal antenna with an outer dimension of L, it consists of parallel wire segments of length M, short-circuit terminal segments of length N, and additional wire segments of length W. The wire width is denoted as d.

Fig. 2. Hilbert fractal antenna simulation model

The Hilbert fractal antenna is a recursively iterated filling curve, which determines its multiple resonant frequencies. The method for calculating the resonant frequencies of the Hilbert fractal antenna is derived from the calculation method of resonant frequencies for bent-wire antennas. As the order of the antenna increases and the outer boundary L remains unchanged, the lengths of the parallel wire segments M, short-circuit terminal segments N, and additional wire segments W gradually decrease. Let O denote the logarithmic length of the parallel double wire, S denote the total length of the short-circuit terminal segments, and C denote the total length of the additional wire segments. According to reference [11], all resonant frequencies of an n-th order Hilbert fractal antenna can be obtained. In Eq. (2), c represents the speed of light, c = 3 × 108 m/s. This paper mainly discusses the first resonant frequency of the Hilbert fractal antenna. All mentioned resonant frequencies refer to the first resonant frequency of the Hilbert fractal antenna. In the equation, we expand Eq. (2) using the third-order Taylor series and L, J, Sinto Eq. (2) to obtain an approximate system of equations for solving the fourth-order Hilbert

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fractal antenna resonant frequency.Therefore, by varying the lengths of the three types of wires, the optimal values for the resonant frequency can be found. Parameter settings to improve antenna performance. In this article, the HFSS electromagnetic field simulation software is used to model the antenna, taking into account the different lengths of different wires, and optimizing the design of a high-performance fourth order Hilbert antenna.

2 Simulation Analysis Based on the analysis above, it can be concluded that the three wire lengths of the Hilbert fractal antenna have an impact on the antenna’s resonant points. Based on this analysis, the author conducted simulation modeling and optimization design of the Hilbert fractal antenna by considering five variables: wire width (d), dielectric substrate thickness (H), and the three wire lengths. Introduction. According to the functions of the HFSS electromagnetic simulation software, parameter optimization is carried out through the parameter sweep function.   ⎧ Ze 2N N μ0 S + C 4(S + C) ⎪ ⎪ O log tan β + · · log −1 ⎪ ⎪ πω d 2 π 2 d ⎪ ⎪ ⎨   4kl μ0 kλ (2) · log −1 = ⎪ ⎪ π 4 d ⎪ ⎪ ⎪ ⎪ ⎩ fr = c λ  ⎧   ⎪ Ze 2N N 1 N 3 μ0 64M + 64W ⎪ ⎪ 64 log tan β + β · × + ⎪ ⎪ πω d 2 3 2 π 2 ⎪ ⎪ ⎨    4(64M + 64W ) μ0 kλ 4kl(8M + 7A) (3) log −1 = · log −1 ⎪ ⎪ ⎪ d π 4 d ⎪ ⎪ ⎪ ⎪ ⎩ fr = c λ

2.1 Construction of Hilbert Mode Antenna Model Using the HFSS software, the antenna can be designed based on the wire layer shapes and types shown in Fig. 1 and Fig. 2, respectively. The length of the parallel wire is denoted as M, the length of the short circuit termination is denoted as N, and the length of the additional wire segment is denoted as W. The longer side of the antenna is given by L = 7W + 8M, and the shorter side is given by J = 5N + 3M + 7W, Total length of conductive layerS = 64M. The boundary lengths of the wire layer, dielectric substrate, and ground layer are set to be equal. The dielectric substrate has a thickness of H. The wire layer and the ground layer are located on opposite sides of the dielectric substrate. For the Hilbert antenna, the dielectric substrate material is FR-4, and both the wire layer and the ground layer are made of copper. The coaxial feeding method (backfeeding)

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23

is used, and the excitation source is a lumped port. The UHF frequency range for the sweep is set to be 0.3 GHz to 3 GHz. The position of the antenna feeding point affects the matching between the antenna’s input impedance and the impedance of the feeding line. Different feeding point positions result in different antenna input impedances. The actual feeding point of the antenna is chosen based on various factors, taking into consideration practical considerations, as referenced in other literature [11]. The selection of the feeding point is shown in Fig. 3

The feeding point is at position 0

The feeding point is at position 1

The feeding point is position2

Fig. 3. HFSS simulation diagram of fourth order Hilbert antenna

. 2.2 Optimization Analysis of Feeding Points The position at which the antenna is connected to the feed line is known as the feeding point. The choice of feeding point location directly affects the matching between the antenna’s input impedance and the impedance of the feed line [12]. Additionally, an antenna can have multiple resonant points, meaning there are multiple frequency values at which the antenna can effectively match with a 50  coaxial cable. In order to study the impact of the feeding point location on the overall performance of the antenna, three typical feeding point locations shown in Fig. 3 were selected for simulation. The other geometric antenna dimension parameters are as follows: FR4 material with a dielectric constant of 4.4, substrate thickness of 1.6mm, and a conductor width of 2mm for the wire layer. The voltage standing wave ratio (VSWR) curves for different feeding points are shown in Fig. 6. The antenna simulation sweep range is from 300 MHz to 3000 MHz, with frequency on the x-axis and VSWR on the y-axis representing the magnitude of the power received by the antenna at different operating frequencies [13]. When optimizing the design of an antenna, the variables under study include the wire width (d), dielectric board thickness (H), parallel wire length (M), short-circuit terminal length (N), and additional wire segment length (W)., Conductive layer (h) In comparison to reference [13], the author has added four variables: dielectric board thickness (H), parallel wire length (M), short-circuit terminal length (N), and additional

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wire segment length (W). The optimization aims to improve the parallel wire length, short-circuit terminal length, additional wire segment length, and the outer boundary (L) of the antenna, thereby enhancing the antenna’s spatial utilization and ensuring more reasonable and effective optimization results. This will result in more accurate acquisition of local discharge signals by the Hilbert antenna (Table 1). Table 1. Parameter scan settings variable

range

Step length

Take points

M

(3 mm, 8 mm)

0.5 mm

9

N

(3 mm, 8 mm)

0.5 mm

9

W

(3 mm, 8 mm)

0.5 mm

9

d

(1 mm, 3 mm)

0.2 mm

11

H

(1 mm, 2 mm)

0.5 mm

6

h

(0.005 mm, 0.05 mm)

0.005 mm

10

3 Analysis of Simulation Optimization Results After the optimization process, Obtain the final fourth order Hilbert fractal day parameters: N = 9 mm,M = 7 mm, W = 5 mm, d = 2 mm, H = 1.6 mm, h = 0.005 mm. By comparing the VSWR curves for different feeding point locations, it can be observed that the antenna achieves the best VSWR value at the feeding point location 0.

Fig. 4. Standing Wave Ratio of Original 4-order Hilbert Fractal Antenna

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According to the VSWR plot of the optimized fourth-order Hilbert fractal antenna shown in Fig. 6, the antenna’s bandwidth can be determined as shown in Table 2. Based on the analysis, the antenna has a bandwidth of 2131.3 MHz. Compared to the original Hilbert fractal antenna with a bandwidth of 1560 MHz, there is a significant improvement in performance. This indicates that the optimized fourth-order Hilbert fractal antenna has a wider frequency range and demonstrates enhanced performance (Fig. 5).

Fig. 5. Optimized 4-order Hilbert fractal antenna standing wave ratio

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Y. Yin et al. Table 2. Optimized Hilbert Antenna Pass Band Statistics

frequency band range

bandwidth

0.3546 GHz~0.3947GHz

30 MHz

0.4249 GHz~0.4568 GHz

31.9 MHz

0.5423 GHz~0.5618 GHz

19.5 MHz

0.5753 GHz~0.6386 GHz

63.4 MHz

0.6475 GHz~0.7886 GHz

141.1 MHz

0..9105 GHz~1.1178 GHz

207.3 MHz

1.1803 GHz~1.4716 GHz

291.3 MHz

1.5386 GHz~1.7829 GHz

234.3 MHz

1.8330 GHz~2.4361 GHz

603.1 MHz

2.4615 GHz~2.5219 GHz

60.4 MHz

2.5560 GHz~3.000 GHz

444 MHz

4 Simulation Analysis The paper focuses on designing a fourth-order Hilbert fractal acquisition antenna to detect partial discharge signals in cable joints. The analysis starts by investigating how the antenna’s resonant frequency is affected by varying wire segment lengths and widths. Next, a model of the fourth-order Hilbert fractal antenna is created using HFSS software, considering how the substrate thickness impacts its performance. The modeling and optimization process takes into account five parameters and the feeding point’s position. The simulation results highlight that the optimized fourth-order Hilbert fractal antenna displays enhanced characteristics. Through a comparison of different feeding point positions, the antenna’s VSWR performance is evaluated across various levels. Across the 0.3 GHz to 3 GHz frequency range, placing the feeding point at position 0 evenly distributes the antenna’s four resonant points and achieves favorable VSWR distribution. Notably, a bandwidth of almost 400 MHz exists between 300 MHz and 1 GHz, and within the 1 GHz to 3 GHz range, three segments offer bandwidths surpassing 600 MHz. Additionally, the antenna showcases favorable directional properties. Acknowledgements. This research is supported by the Henan Key Laboratory of Cable Structure and Materials, Henan Institute of Technology (No. HKL-CSM2022002), Henan Science and Technology Projects Fund in 2022 (No. 222102220102)), National Natural Science Foundation of China (Grant NO. 52077210).

References 1. Qi, X., Liu, L., Lv, Z., Huang, X., Wang, W., Yu, S.: Research on a novel online monitoring system for cable partial discharge. Electr. Power Supply Utilization 37(01), 51–56 (2020)

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2. Li, X., Xu, Y., Li, J.: Analysis of electrical performance of 10kV cross-linked polyethylene cable joint with minor defects. Electric Power Technol. 569(11), 128–130 (2022) 3. Xie, Y., et al.: HFSS Principles and Engineering Applications. Science Press (2009) 4. Canes, P.-B.: On the behavior of the Sierpinski multiband fractal antenna. IEEE Trans. Antennas Propag.Propag. 46(4), 517–524 (1998) 5. Wu, T., Yang, Q., Jiang, C., Shao, S., Wang, Y., Liu, B.: Design of partial discharge UHF microstrip antenna based on LS peano fractal structure. In: 2021 IEEE 5th Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), Xi’an, China, pp. 556–560 (2021) 6. Lu, C., Ren, P.: Design of UHF sensor antenna for power cable partial discharge detection. Ship Electron. Technol. 42(12), 11–16 (2022) 7. Zhang, A., Xu, W., Xing, D., et al.: Design of ultra-wideband monopole antenna for partial discharge detection based on curved current technology. Electr. Appl. 41(01), 85–90 (2022) 8. Li, J., Ning, J., Jin, Z., et al.: Study on UHF Hilbert fractal antenna for online monitoring of transformer partial discharge. Electric Power Autom. Equipment 158(06), 31–35 (2007) 9. Cheng, C.: Research on UHF monitoring of transformer partial discharge with fourth-order fractal antenna and signal processing and recognition. Chongqing University (2009) 10. Wu, T., Yang, Q., Jiang, C., Shao, S., Wang, Y., Liu, B.: Design of partial discharge UHF microstrip antenna based on LS peano fractal structure. In: 2021 IEEE 5th Information Technology, China, pp. 556–560 (2021) 11. Wang, C.: Design and development of ultra-high frequency antenna for discharge detection and detection system. Southwest Jiaotong University (2020) 12. Li, M.: HFSS Antenna Design (2nd Edition). Electronic Industry Press (2011) 13. Ning, J.: Research on ultra-high frequency online monitoring method for partial discharge of power transformer. Chongqing University (2007) 14. Yan, X.: Study on electromagnetic radiation characteristics of bow net arc based on Hilbert fractal antenna. Southwest Jiaotong University (2019) 15. Ji, S., Wang, Y., Li, J.Y., Liang, N., Sun, D., Wang, W., He, W.: Research status and development of ultra-high frequency antenna for GIS partial discharge detection. High Voltage Apparatus 51(04), 163–172+177 (2015) 16. Sun, C., Xu, G., Tang, J., Shi, H., Zhu, W.: Model and performance research on built-in sensor for GIS partial discharge detection. Proc. Chin. Soc. Electr. Eng. 08, 92–99 (2004)

Study of Resonance Suppression Strategy and Its Adaptability for Grid-Connected Inverters in High Permeability Environment Meimei Sun1(B) , Xuezhi Xia2 , Changzhou Yu3 , and Chenggang Wang1 1 Naval Aviation University, Zhifu Road. 188, Yantai 264001, China

[email protected]

2 Wuhan Digital Engineering Institute, Luoyu Road. 718, Wuhan 430074, China 3 Hefei University, Jinxiu Road. 99, Hefei 230601, China

Abstract. In the high permeability environment, the use of LC (LCL) filters on the AC side of grid-connected photovoltaic inverters can effectively reduce the size and capacity of the filters. However, it can lead to filter resonance issues. The active damping control method can avoid filter resonance problems. This study take focuses on the three-level photovoltaic grid-connected inverter by using a virtual resistor based on the differential of capacitor voltage to generate capacitor current, the active damping scheme suppresses the resonance of the inverter output current without additional sensors. The robustness of this scheme under different grid short-circuit capacities is analyzed. Finally, the feasibility of the algorithm is validated on a 30 kW three-level grid-connected inverter experimental platform. Keywords: Active damping · Capacitor voltage differential · Grid-connected inverter

1 Introduction With the rapid development of the distributed renewable energy industry, grid-connected photovoltaic inverters have been widely applied. Due to the pressure for grid current quality, efficiency, and cost, the filter design of grid-connected inverters has increasingly adopted higher-order LC or LCL filters [1] and three-level non-isolated transformerless configurations [2]. Compared to the L-type filter, the LC (LCL) filter has advantages in terms of cost and volume, especially in low-switching-frequency high-power systems, where its advantages are more prominent. However, the LCL filter introduces a complex pole pair unwanted into the transfer function of the closed-loop system, which can easily lead to system resonance and stability issues [3]. Therefore, it is necessary to study methods to increase the damping of the inverter to suppress resonance. Resonance suppression strategies can be approached from both hardware configuration and control strategy perspectives, including passive damping and active damping methods. However, passive damping schemes have drawbacks such as additional system losses, increased overall cost, and poor adaptability to grid environments. In practical applications, it is desirable to increase system damping through control algorithms without introducing additional system losses, which is known as active damping [4]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 28–39, 2024. https://doi.org/10.1007/978-981-97-0877-2_4

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Common active damping methods include virtual resistor method [5], lead-lag compensation method [6], notch filter method [7], dual current loop control [8], triple current loop control [9], state feedback method [10], and combined passive and active damping methods [11] and designing a series phase-lead compensation in the capacitive current feedback loop [12]. However all these methods require additional sensors to detect state variables and increase system damping. Due to the relatively easy detection of capacitor voltage, active damping methods utilizing capacitor voltage as a feedback variable have advantages. In this paper, a virtual resistor active damping scheme based on the differential of capacitor voltage to generate capacitor current is employed, and the robustness of active damping with respect to grid short-circuit capacity is analyzed. Finally, experimental verification is conducted.

2 Basic Principles of Three-Level Grid-Connected Photovoltaic Inverter 2.1 Structure of Three-Level Grid-Connected Photovoltaic Inverter The topology of a three-phase three-level grid-connected inverter is shown in Fig. 1. L 1 represents the bridge arm inductance, L g is the grid impedance, C 1 is the return midpoint capacitor, C 2 is the differential mode capacitor, iL is the bridge arm current, ig is the grid-side current, E is the three-phase grid voltage, and Cbus is the positive and negative bus capacitors. Based on the MPPT algorithm, the DC voltage command signal is obtained, and the active power command signal for the current loop is obtained through a PI controller. The main issue regarding grid current resonance lies in the control of the current loop and the control of the voltage control. Fortunately, the bandwidth of the current loop is significantly different from that of the voltage loop, so the current loop and voltage loop can be considered separately [13]. Therefore, this paper focuses on the analysis of the closed-loop control system of the current loop.

iL

Lg

L1

ig

E

CBus o

C1 C2 MPPT

SVPWM +

PI

+ abc

PI

Id_ref

PLL

Ea,b,c

PI

Iq_ref

θ dq

id abc - iq dq

Fig. 1. Basic Structure Diagram of Three-Level Grid-Connected Inverter

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2.2 Controlled Model and Characteristics of LCL Filter When considering the decoupling between the three-phase systems, the analysis of the controlled object can be focused on the single-phase LCL filter. The basic control structure diagram of the current loop is shown in Fig. 2. iL

i

*

uinv

ref

PI(s) uC

1 sL1 1 s  C1  C2

ic

1 sLg

ig

Fig. 2. Diagram of grid inverter current loop control structure

To eliminate the need for sensors and ensure system stability, the current loop control method based on inverter-side current feedback is commonly used, as shown in Fig. 2. The current error regulator adopts a PI controller, where K pwm represents the PWM gain and is given by Kpwm = U dc /U cm , with Udc being the DC bus voltage, U cm being the modulation wave amplitude, Uinv being the inverter-side voltage, U c being the voltage across capacitor C 2 , ic being the current flowing through capacitor C 2 , iL being the inverter-side current, i* ref being the desired inverter-side current, and ig being the grid-side current. Based on the basic control structure diagram in Fig. 2, the open-loop transfer function of the system can be derived. Gopen (s) = PI (s)Kpwm (s)

s2 Lg (C1 + C2 ) + 1   s3 L1 Lg (C1 + C2 ) + s L1 + Lg

(1)

The discrete zero-pole plot (Fig. 3) and Bode plot (Fig. 4) of the open-loop system are as follows: From the Z-plane pole-zero plot in Fig. 3 of the open-loop system, it can be observed that the system has poles located on the unit circle, indicating the presence of critically unstable poles. Similarly, from the Bode plot in Fig. 4, it can be seen that this introduces a resonance peak to the system. This can easily lead to system resonance, posing a challenge to the design of the entire system controller. If the gain of the regulator is set too high, it can easily lead to system resonance, while setting the gain too low may result in poor control performance, unable to guarantee the requirements for output current waveform quality and dynamic characteristics. The overall stability margin of the system is relatively low.

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Pole-Zero Map 1 0.6S/T 0.8

0.5S/T

0.4S/T 0.1 0.3S/T 0.2 0.3 0.4 0.2S/T 0.5 0.6 0.7 0.1S/T 0.8 0.9

0.7S/T

0.6

0.8S/T

Imaginary Axis

0.4 0.9S/T

0.2

1S/T 1S/T

0 -0.2

0.9S/T

0.1S/T

-0.4 0.8S/T

-0.6

0.2S/T 0.7S/T

-0.8

0.3S/T 0.6S/T

-1 -1.5

-1

-0.5

0.5S/T

0.4S/T

0

0.5

1

1.5

Real Axis

Fig. 3. Discrete zero-pole plot of the system Bode Diagram

Magnitude (dB)

200

0

Phase (deg)

-200 90 45 0 -45 -90 3 10

4

10

5

10

Fig. 4. Bode plot of the system

2.3 LCL Undamped Current Loop Control Furthermore, by establishing the closed-loop transfer function of the system, the stability margin and the effect of active damping can be analyzed. Without incorporating active damping, as shown in Fig. 2, the transfer function of the closed-loop output current with respect to the reference current can be obtained based on inverter-side current. Ig (s) PI (s)Kpwm (s)   = Iref (s) s3 L1 (C1 + C2 )Lg + s2 (C1 + C2 )Lg PI (s)Kpwm (s) + s L1 + Lg + PI (s)Kpwm (s)

(2)

2.4 Active Damping Control For LC-type grid-connected inverters, the filtering capacitor has voltage sampling capability. This sampling can be utilized to differentially reconstruct the capacitor current and feed the reconstructed value back into the control forward path, forming a virtual resistor. This virtual resistor increases system damping to suppress resonance peaks. However, the differentiation process can introduce high-frequency noise, potentially causing system instability. To address this issue, the differentiated capacitor voltage is

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-

PI(s)

Kpwm

-

1+GAD(s)

E

-

Fig. 5. Block diagram of current loop control structure with active damping

passed through a low-pass filter to eliminate the high-frequency disturbances introduced by differentiation. Additionally, a coefficient K is introduced to adjust the size of the virtual resistor. The transfer function of GAD (s) in Fig. 5 is as follows. GAD (s)=

Ks 1 + Tfitler s

(3)

In this equation, K = (C1 + C2 )Rd , Rd represents the resistance value of the corresponding virtual resistor, which needs to be multiplied by the capacitance value due to the differentiation of the capacitor voltage to reconstruct the capacitor current. T filter is the time constant of the first-order low-pass filter. This time constant should be set smaller than the resonance time constant to ensure that the signals in the resonance frequency range are not attenuated by the filter. The open-loop transfer function of the system is as follows: Ig (s) PI (s)Kpwm (s)   = Iref (s) s3 L1 (C1 + C2 )Lg + s2 (C1 + C2 )Lg PI (s)Kpwm (s) + s L1 + Lg + PI (s)Kpwm (s) − sLg GAD (s)Kpwm (s)

(4)

2.5 Comparison Between Active Damping and Undamped Control The pole-zero plots and Bode plots of the closed-loop transfer functions for both undamped and actively damped control are shown in Fig. 6 and Fig. 7, respectively. From Fig. 6, it can be observed that by introducing a certain virtual resistor, the critical stable pole of the system moves inside the unit circle, increasing the damping ratio and avoiding resonance. At the same time, a pair of low-frequency poles gradually transition from non-dominant poles to dominant poles. The same conclusion can be drawn from Fig. 7. With the introduction of the virtual resistor, the resonance peak at the resonant frequency of the system decreases, effectively suppressing resonance. Additionally, as the virtual resistor is further increased, it may lead to harmonic amplification at frequencies lower than the resonant frequency, consistent with the gradual dominance of low-frequency poles observed in Fig. 6.

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33

1

0.5

0

-0.5

-1 -1

-0.5

0

0.5

1

Fig. 6. Zero-pole plots of undamped control and active damping with different virtual damping values 50

0

-50

Magnitude (dB)

(dB)

10

Without Damping

0 -10 -20

Active Damping 4.13

4.09

-100

10

10

4

3

10

10

(Hz)

Fig. 7. Bode plots of undamped control and active damping with different virtual damping values

3 Robustness Analysis of Active Damping 3.1 Comparison of Control Loop Gain The above analysis of active damping was conducted under ideal conditions. In practice, the grid-side impedance is a variable that may affect the effectiveness of active damping in suppressing resonance. Typically, the grid impedance is often represented by the short-circuit capacity of the grid. Here, the closed-loop system pole-zero plots with active damping are plotted for varying grid short-circuit capacities ranging from 100:1 to 10:1. The direction of the arrows in the figure represents the decreasing direction of the short-circuit capacity.

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Imaginary Axis

0.5

0

-0.5

-1 -1

-0.5

0

0.5

1

Real Axis

Fig. 8. Zero-pole plot of active damping under different short-circuit capacities Bode Diagram

Magnitude (dB)

50

0

-50

-100

3

10

4

10

Frequency (Hz)

Fig. 9. Bode plot of active damping under different short-circuit capacities

From the pole-zero plot in Fig. 8, it can be observed that as the grid short-circuit capacity decreases, the change in damping ratio of the system is relatively small, but the oscillation frequency increases. Similarly, Fig. 9 reflects that as the grid short-circuit capacity decreases, the resonant peak of the system’s closed-loop response shifts towards lower frequencies. Although the resonant peak magnitude increases slightly, the increase is not significant, indicating a certain robustness of active damping to changes in grid impedance.

Study of Resonance Suppression Strategy

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4 Simulation and Experiment Results To verify the effectiveness of the proposed method, a 30 kW three-level grid-connected inverter experimental platform (Fig. 10) was built based on the information provided in Table 1. The DSP chip used was the TMSF2808 from Texas Instruments, with a sampling period of 62.5 µs.

Fig. 10. Experimental platform

The simulation and experiment parameters are shown in Table 1. Table 1. Simulation and experiment parameters Parameter

Value

Parameter

Value

Power

30 Kw

Line impedance

0.6 mH

Grid Voltage (Line Voltage)

400 V

Filtering Capacitor C1

3.5 uF

Switching Frequency

16 kHz

Filtering Capacitor C2

3.2 uF

DC Bus Voltage

660 V

Short Circuit Capacity

60:1

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Figure 11(a) shows the grid voltage and grid-side current under the undamped control scheme, while Fig. 11(b) displays the zoomed-in waveform. Due to resonance effects, the grid-side current waveform exhibits oscillations. From the zoomed-in waveform, it can be observed that the resonance frequency is between 4 kHz and 5 kHz. This oscillation phenomenon can lead to performance degradation and potentially have adverse effects on the grid. To address this issue, the introduction of active damping control scheme can effectively suppress resonance and improve the stability and performance of the system. a) 100V/div

5A/div

b)

Fig. 11. Output current waveform and local amplification diagram under undamped control

Figure 12 shows the waveform of the instantaneous switching when active damping control is applied. From the dashed box in the figure, it can be seen that before active damping is introduced, the current exhibits resonance. However, after the activation of active damping control, the resonance phenomenon in the current is effectively suppressed. Figure 13(a) displays the grid voltage and grid-connected current after the implementation of active damping control, while Fig. 13(b) shows the zoomed-in waveform. With active damping control in place, the current resonance is well suppressed. In the zoomed-in waveform, it can be observed that the current waveform contains almost no resonance frequency but only the switching frequency ripple at 16 kHz.

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Figure 14(a) represents the FFT analysis of the grid-connected current without damping control. From the figure, it can be seen that the system resonance occurs around 5 kHz, with an amplitude close to 2% of the fundamental frequency. After the implementation of active damping control, the FFT analysis of the grid-connected current is shown in Fig. 14(b), where the amplitude at 5 kHz is reduced to 0.2% of the fundamental frequency, indicating effective control of the resonance peak.

100V/div

5A/div

Acving Damping

Fig. 12. Instantaneous output current waveform with active damping added

a) 100V/div

5A/div

b)

Fig. 13. Output current waveform and local amplification diagram under active damping control

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Mag

1.5

1

0.5

0

0

2000

4000 6000 Frequency (Hz)

8000

10000

8000

10000

(a) 2

Mag

1.5

1

0.5

0

0

2000

4000 6000 Frequency (Hz)

(b) Fig. 14. Frequency spectrum of output current waveform under undamped and active damping control.

5 Conclusion This paper addresses the resonance issue in three-level LC-type inverters and proposes an active damping control scheme based on the first-order derivative of the capacitor voltage, without the need for additional sensors. By comparing and analyzing the undamped and damped control schemes, it is concluded that the active damping scheme is effective in suppressing resonance in grid-connected inverters. The robustness of this active damping scheme under different grid short-circuit capacities is also analyzed. Finally, the correctness of the proposed scheme is validated through experiments conducted on a 30 kW three-level grid-connected inverter experimental platform. Acknowledgement. This work was supported in part by The National Natural Science Foundation of China (Grant No. 51907064).

References 1. Hu, W., et al.: Improved current control for LCL-filter-based inverter connected to weak grid. Power Electron. 03, 120–122 (2017)

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2. Zhuang, G., Zhang, X., Liu, W., Zhuang, J.: Overvoltage and overcurrent protection of SiC MOSFET in three-level topology with flying capacitor. Trans. China Electrotech. Soc. 36(2), 341–351 (2021) 3. Dannehl, J., Wessels, C., Fuchs, F.W.: Limitations of voltage-oriented PI current control of grid-connected PWM rectifiers with filters. IEEE Trans. Ind. Electron. 56(2), 380–388 (2009) 4. Xu, H., et al.: A reactive power sharing strategy of VSG based on virtual capacitor algorithm. IEEE Trans. Industr. Electron.Industr. Electron. 64(9), 7520–7531 (2017) 5. Dahono, P.A.: A control method to damp oscillation in the input LC filter. In: Power Electronics Specialists Conference, 2002. pesc 02. 2002 IEEE 33rd Annual. IEEE, 4, pp. 1630–1635 (2002) 6. Gullvik, W., Norum, L., Nilsen, R.: Active damping of resonance oscillations in LCL-filters based on virtual flux and virtual resistor. In: 2007 European Conference on Power Electronics and Applications. IEEE, pp. 1–10 (2007) 7. Yu, C., et al.: Modeling and resonance analysis of multiparallel inverters system under asynchronous carriers conditions. IEEE Trans. Power Electron. 32(4), 3192–3205 (2016) 8. Yu, C., et al.: Stability margin analysis of multi-inverter grid-connected system considering asynchronous control period under high penetration. In: 2021 IEEE 12th Energy Conversion Congress & Exposition-Asia (ECCE-Asia). IEEE (2021) 9. Zomood, N.: Stationary frame current regulation of PWM inverters with zero steady-error. IEEE Trans. Power Electron. 18(3), 814–822 (2003) 10. Dannehl, J., Liserre, M., Fuchs, F.W.: Filter-based active damping of voltage source converters with filter. IEEE Trans. Ind. Electron. 58(8), 3623–3633 (2011) 11. Zhang, X., Yu, C., Liu, F., et al.: Stability improvement of grid-connect inverter using combination of passive and active damping. In: 2012 7th International Power Electronics and Motion Control Conference (IPEMC). IEEE, 4, pp. 2809–2813 (2012) 12. Shan, T., Zhang, Y.: A delay conpensation method for active damping LCLLC-type gridconnected inverter. Power Electron. 57(4), 1–4 (2023)

The Feedback Control of the −200 kV High Voltage Power Supply for CRAFT NNBI Shengmin Pan(B) , Baocan He, Hulin Feng, Denghui Wang, Hongfei Yong, Yiyun Huang, and Quanguo Tang Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China [email protected]

Abstract. The −200 kV high-voltage power supply serves as the acceleration power supply for the Comprehensive Research Facility for Fusion Technology neutral beam injector (CRAFT NNBI) system, and its operation entails strict requirements to ensure its dynamic and steady-state performance. This article proposes a power supply topology for its application based on phase-controlled rectification, a three-level NPC inverter, a boost converter transformer, and highvoltage uncontrollable rectification (AC-DC-AC-DC). This topology provides a structural advantage by enabling control functionality on the low-voltage side, thereby eliminating the need for control functions on the high-voltage side. The boost converter transformer ensures electrical isolation between the high-voltage and low-voltage sides, while the precise control of the output voltage is coordinated by the phase-controlled rectifier and NPC inverter. Coarse adjustment is achieved through regulation of the DC bus voltage while the duty cycle of the NPC can be adjusted for fine-tuning. The quality of the DC output voltage is controlled through a combination of phase-controlled rectification and the NPC inverter to ensure the stability, accuracy, and ripple requirements of the final high-voltage DC side. This article also provides a detailed analysis of the hardware selection and feedback control of the system through a simulation of the power supply using MATLAB/Simulink software. The experimental tests and simulation results consistently indicated that the power supply meets the stability and dynamic response requirements necessary for the CRAFT NNBI system’s implementation. Keywords: High Voltage Power Supply · Pulse · NPC Converter · Converter Transformer · High Voltage Uncontrolled Rectifier · PID

1 Introduction The Thirteenth Five-Year Plan of the National Key Project, “Comprehensive Research Facility for Fusion Technology (CRAFT),” aims to develop various key subsystems or components for future fusion reactors in China. This includes the development of a world-leading 200 keV/1000 S high-power negative ion source equipped with a −200 kV high voltage accelerator power system to ensure the stable and reliable operation of the NNBI system. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 40–48, 2024. https://doi.org/10.1007/978-981-97-0877-2_5

The Feedback Control of the −200 kV High Voltage Power Supply

41

Fig. 1. Topology of CRAFT NNBI Power Supply

The CRAFT NNBI accelerator power supply is based on a Neutral-Point-Clamped (NPC) inverter and operates as an ultra-high voltage DC power supply. The power supply system comprises a phase-controlled rectifier„ an NPC inverter [1–5], a converter step-up transformer [6–8], a high-voltage uncontrolled rectifier, and an RC filter for high-voltage output [9–12]. The power supply topology is illustrated in Fig. 1.

2 Key Component Selection and Parameter Determination 2.1 Selection of DC Bus Voltage (Vdc ) and Inverter Frequency (finv ) a Subsection Sample The impact of the DC bus voltage (Vdc ) on the rectification and inverter stages is primarily reflected in variations in current flow and the operating voltage of the NPC inverter semiconductor switches. Once performance, cost, and various parameters of the semiconductor switches in different stages of the power supply were factored in, 5 kV was determined to be the optimal DC bus voltage Vdc . The inverter frequency (finv ) refers to the output frequency of the inverter. Taking into account the performance and cost aspects required of the power supply, the final decision was made to set the inverter output frequency (finv ) at 150 Hz. 2.2 A Subsection Sample Step-Up Transformer Parameter Selection The transformer is the core component of the power supply, enabling the conversion of low voltage into high voltage while providing electrical insulation between the highvoltage and low-voltage sides. There are four winding configurations for the transformer: Y/Y, /, /Y, Y/. Uout_0 represents the no-load output voltage of the accelerator’s high-voltage power supply, and the conversion ratio of the converter step-up transformer is expressed as V1n :V2n = 1:n. D denotes the duty cycle of the inverter. To provide a visual comparison of the isolation converter step-up transformer’s transformation ratio across different connection modes, n0 is defined as the reciprocal of the unit value of the transformation ratio. The /Y connection mode not only need to smallest n, but also Uout_0 can be controlled across the entire range of D ∈ [0, 1]. Therefore, the /Y connection mode was determined to be the optimal connection mode for the CRAFT NNBI high-voltage power step-up transformer.

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2.2.1 RMS Value Calculation of the Primary Side Voltage The Root Mean Square (RMS) value of the voltage applied to the primary side of the converter step-up transformer is determined by equating it with the maximum magnetic flux density generated by the imposed sinusoidal voltage. When the modulation factor falls within the range 2/3 < m < 1, the line voltage output from the NPC inverter reaches its highest point, with the average value of its positive half-cycle equaling 2/3 Vdc. The equivalent RMS value of the converter step-up transformer’s primary side voltage, U1, can be obtained using Eq. (1) π (1) U1 = √ Vdc 3 2 where Vdc represents the DC bus voltage. When the DC bus voltage is equal to 5000 V with a fluctuation range of ±5%, the corresponding U1 range lies between 3.52 kV and 3.89 kV. 2.2.2 The Selection of the Step-up Transformer Leakage Inductance Value The selection of a leakage inductance value for a converter step-up transformer entails the consideration of two factors. Firstly, it aims to limit the rate at which the inverter output current increases during load ignition, wherein a larger leakage inductance results in an inverter current that rises at a slower rate. Secondly, a larger leakage inductance causes a greater phase voltage drop, leading to a decrease in the output voltage of the power supply. Therefore, choosing the appropriate leakage inductance value for a converter step-up transformer requires a compromise between these two factors. (a) The turns ratio (n) of the converter step-up transformer winding is 1/23.6. The inverter output current rises at its fastest rate when one of the phases outputs Vdc/2 and the other two phases output - Vdc/2 (or vice versa). Furthermore, the maximum current during normal inverter operation occurs at the end of this interval, and ignition near the end of this period results in the most severe overcurrent condition for the inverter. The change in inverter output current (I) during the ignition period can be expressed as follows: 2Vdc Vdc td = 2 td (2) I = 1.5Ls1 n × Ls2 where Ls1 represents the leakage inductance of the converter step-up transformer referred to the primary side and Ls2 represents the leakage inductance referred to the secondary side; td represents the shutdown time of the inverter after ignition occurs, with a duration of 100 μs. The calculation of I ignores the inductance of the transmission line between the inverter and the step-up transformer. The selected insulated-gate bipolar transistor (IGBT) for the inverter has a safe shutdown current of 3000 A. Assuming ignition occurs near the inverter output current’s peak value and the peak current during normal operation is 1739 A, it becomes necessary to limit I to a value ≤ 1261 A. Using Eq. (2), we determined that Ls2 should be greater than or equal to 441.6 mH. Considering a margin and ease of design, a value of 500 mH is chosen for Ls2. Uo = Udio − 6fLs2 Io

(3)

The Feedback Control of the −200 kV High Voltage Power Supply

43

2Vdc n

(4)

Udio =

where Udio represents the ideal no-load output voltage of the high-voltage power supply under a modulation index (m) of 1; f denotes the frequency (150 Hz); Io represents the output current of the high-voltage power supply. Assuming a fluctuation range of ±5% for the DC bus voltage (Vdc ) at 5000 V and an output current (Io ) of 28 A for the highvoltage power supply, the corresponding output voltage range (v) of the high-voltage power supply was estimated to be between 211.6 kV and 235.2 kV. Similarly, the range of the ideal no-load voltage (Udio ) was estimated to be between 224.2 kV and 247.8 kV.

3 Simulation and Modeling Based on the operating principle of the three-phase three-level NPC inverter, the relationship between the phase voltage VAN of inverter phase A and time can be expressed by Eq. (5):

VAN

⎧V dc ⎪ , 0 < t < dT ⎪ ⎪ ⎪ 2 ⎪ ⎨ 1 1 = 0, dT < t < T , ( + d )T < t < T ⎪ 2 2 ⎪ ⎪ ⎪ ⎪ ⎩ − Vdc , 1 T < t < ( 1 + d )T 2 2 2

(5)

Equation (5) shows that the phase voltage of the inverter output is a discrete quantity in terms of time. Since its value is determined by the pulse width of the output voltage, it is unsuitable for analyzing the high-voltage rectifier or obtaining the transfer function between the output voltage Uo and the duty cycle (d). To overcome this, the Fourier transform was used to convert the phase voltage of the inverter output into a Fourier series consisting of the fundamental and harmonic frequencies. By applying the principle of impulse equivalence, only the fundamental 150 Hz frequency is extracted. This transforms the relationship between the duty cycle (d) and the pulse width of the phase voltage into a relationship between the duty cycle (d) and a fundamental sinusoidal signal. According to the basic formula of the Fourier transform, ∞

a0  + an cos nωt + bn sin nωt 2 n=1   2 t0 +T 2 t0 +T f (t) cos nωtdt bn = f (t) sin nωtdt, n ∈ (1, ∞) an = T t0 T t0

f (t) =

(6)

By combining Eq. (5) and Eq. (6), we can obtain the Fourier transform coefficients: an =

Vin [(cos nπ − 1) sin(2d + 1)nπ ] nπ

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bn =

Vin [(cos(2d + 1)nπ − cos nπ )(1 − cos nπ )] nπ

Based on the above description, with n = 1, we can calculate the fundamental coefficient: a1 = − b1 =

2Vin [sin(2d + 1)π ] π

2Vin [cos(2d + 1)π + 1] π

Therefore, the fundamental frequency of the inverter phase A output voltage can be calculated according to Eq. (7):  2Vin [− sin(2d + 1)π ] cos ωt VAN = a1 cos ωt + b1 sin ωt = (7) +[1 + cos(2d + 1)π ] sin ωt π Since the difference between the two adjacent phases is 120°, the output phase voltages of phases B and C can likewise be obtained according to Eq. (7), as shown in Eqs. (8) and (9):  2Vin [− sin(2d + 1)π ] cos(ωt + 23 π ) (8) VBN = +[1 + cos(2d + 1)π ] sin(ωt + 23 π ) π  2Vin [− sin(2d + 1)π ] cos(ωt − 23 π ) VCN = (9) +[1 + cos(2d + 1)π ] sin(ωt − 23 π ) π The output voltage signals of the NPC inverter can be transformed into a three-phase voltage source format, represented by Eqs. (7), (8), and (9). These three-phase voltage sources can be further simplified and are illustrated in Fig. 2, which shows the converter step-up transformer, high-voltage rectifier system, and DC filter schematic. The converter step-up transformer is connected in a /Y configuration [13–15]. Therefore, the phase voltage of the secondary winding is equal to the product of the line voltage of the primary winding and the turns ratio of the step-up transformer. In other words, Va = nVAB

(10)

The output voltages for phases B and C can be obtained according to the same method. The output phase voltage Va amplitude |Va | on the secondary side of the converter step-up transformer can be obtained using Eqs. (7), (8), and (10) with a trigonometric function, resulting in the combined formula shown in Eq. (11): √ 2 6nVin

|Va | = 1 + cos(2d + 1)π (11) π Hence, in an ideal no-load condition, the average output voltage of the three-phase uncontrolled rectifier circuit can be calculated using the formula Ud = 1.414|Va |, where

The Feedback Control of the −200 kV High Voltage Power Supply

45

Ud represents the output voltage of the high-voltage rectifier. Treating Ud as the input voltage source, the leakage inductance of the converter step-up transformer can be modeled as a series inductor in the circuit. By analyzing the simplified equivalent circuit shown in Fig. 2 in terms of signal behavior over time (time domain analysis), we can derive the transfer function G1 (s) using Eq. (12). G1 (s) =

Uo (s) RL RCs + RL = Ud (s) (RCL + RL CL)s2 + (RL RC + L)s + RL

(12)

d

Fig. 2. Equivalent Circuit of CRAFT NNBI Power Supply

Furthermore, by taking the IGBT control signal as the input and the load output voltage as the output, we can obtain the overall transfer function GO (s) of the inverterbased DC high-voltage power supply system. √ RL RCs + RL 2 6nVin × Go (s) = π (RCL + RL CL)s2 + (RL RC + L)s + RL The control diagram consists of the PI controller transfer function, Gpi (s), and the system transfer function, GO (s). The output voltage is fed back to the input and compared with the reference voltage, Vref , to generate an error signal (H(s) = 1). Consequently, the closed-loop transfer function of the control system, (s), is expressed by Eq. (13). φ(s) =

G(s)H (s) 1 + G(s)H (s)

(13)

In Eq. (13), G(s) represents the open-loop transfer function, and Gpi (s) represents the PI transfer function. They can be defined as follows: G(s) = Gpi (s)Go (s) Gpi (s) = kp +

ki s

Based on the above analysis, the closed-loop transfer function of the system can be obtained using Eq. (14): φ(s) =

s3

as2 + bs + c + As2 + Bs + c

(14)

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In Eq. (14): a= b=

XRL Rf Cf kp 2Rf Cf L

X (RL Rf Cf ki + RL kp ) 2Rf Cf L

A=

RL Rf Cf + L + XRL Rf Cf kp 2Rf Cf L

B=

RL + X (RL Rf Cf ki + RL kp ) 2Rf Cf L XRL ki 2Rf Cf L √ 4 3nVin X = π C=

The closed-loop transfer function (s) of the system can be expressed in the normalized form of a third-order minimum-phase system, as demonstrated by Eq. (15). φ(s) =

ωn3 s3 + αωn s2 + βωn2 s + ωn3

(15)

According to the table of typical coefficients and response performance indexes of the standardized transfer function of the minimum-phase system [16–18], when the order of the closed-loop transfer function is 3, the coefficient values are α = 1.9 and β = 2.2. Moreover, for a third-order system, the standardized regulation time should be ωn ts . In the present power control system, a requirement was set, limiting the rise time ts to 50.5.

Fig. 3. Power Simulation Waveforms

Figure 3 illustrates the simulated waveform of the power supply’s output voltage. The output voltage reached the set maximum value (80 ms) without any overshoot and

The Feedback Control of the −200 kV High Voltage Power Supply

47

remained stable thereafter. This indicates that when the DC bus voltage is 5000V and the output voltage is 200 kV, the output voltage ripple remains within the anticipated ±5% range. Hence, the adoption of PI control is indeed feasible.

4 Experimental Verification The power supply test waveform is presented in Fig. 4, with the power supply output voltage waveform represented by the yellow curve and the current waveform represented by the blue curve. The voltage can be directly read from the graph, while the current is scaled such that 1V represents 30 A. From Fig. 4, it can be observed that at 200 kV voltage, the current is approximately 28 A, the voltage rise time is around 80 ms, and the peak-to-peak ripple voltage is approximately 8 kV, all of which indicate that the system satisfies the design requirements.

Fig. 4. Output Voltage and Current Waveforms of CRAFT NNBI Power Supply

5 Conclusion This paper presented a comprehensive analysis of the CRAFT NNBI high-voltage power supply, including the selection of key parameters, circuit topology analysis, simulation, and modeling. The proposed power supply system’s feasibility was validated through experimental testing. The waveforms obtained from the experimental tests demonstrated that both the dynamic and static parameters of the system meet the design requirements. Notably, the ignition protection time, a mere 17 μs, was significantly below the system’s 100 μs requirement. This demonstrated the power supply system’s capability to rapidly disconnect high voltage during load ignition, ensuring the safe and reliable operation of the load ion source.

References 1. Sheianov, A., Xi, X.: Highly efficient three level sparse NPC inverter for ultra-high-speed PMSM. In: 2022 IEEE 5th International Electrical and Energy Conference (2022)

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2. Wang, Y., Zhang, Z., Huang, W., Kennel, R., et al.: Encoderless Sequential Predictive Torque Control with SMO of 3L-NPC Converter-fed Induction Motor Drives for Electrical Car applications 3. Pandey, P., Barai, M.: A comprehensive performance study of three-level NPC VSI with induction motor load in closed-loop. In: 2022 2nd Asian Conference on Innovation in Technology, Pune, India, 26–28 Aug (2022) 4. De Victor, M.R., Renner, S.: Camargo.Field Oriented Predictive Current Control on NPC Driving an Induction Motor 5. Payami, S., Behera, R.K.: Common-mode voltage and vibration mitigation of a five-phase three-level npc inverter-fed induction motor drive system. IEEE J. Emerging Sel. Top. Power Electron. 03(2), 349–361 (2015) 6. Xiang, C., Zhang, L., Cheng, S.: Duty VV-MPTC for post-fault eight switch three-phase inverter fed induction motor drives with reduced neutral point voltage fluctuation. IEEE Trans. Power Electron. 36(10), 11691–11700 (2021) 7. Bubert, A., Swain, S., De Doncker, R.W.: Desigh Considerations of DC-Link Capacitors in NPC Inverters for Electric Vehicles 8. Shukla, D.M.: Control and operation of multifunctional NPC inverter for Grid-connected solar PV. In: International Conference on Electrical, Computer and Energy Technologies, 20–22 July 2022, Prague-Czech Republic 9. Srirattanawichaikul, W., Kumsuwan, Y., Premrudeepreechacharn, S., Wu, B.: A Vector Control of a Grid-Connected 3L-NPC-VSC with DFIG Drives 10. Yong, W., Gen, C., Fei, W.: A novel gybrid three-level NPC topology with digital driven serial connected IGBTs for medium voltage multi-MW wind power converter 11. Li, Y., Shi, L., Li, Y.: A novel Control Strategy of Rectifier for NPC Back-to-Back Converter in HIL system 12. Wang, S., Song, W., Feng, X.: A novel CBPWM strategy for single-phase three-level NPC rectifiers in electric railway traction 13. Xie, L.: Design of High Power Quasi Optical Mode Converter, Master’s thesis 14. Xuan, W., Yao, L., Li, Q., Mao, X., et al.: Development of ECRH Main High Voltage Power Supply for HL_ 2A Device, Nuclear Fusion and Plasma Physics, Volume 28, Issue 2, June 2008 15. Wang, Y., Li, Q., Wang, S.: High voltage power supply for HL-2A low hybrid wave heating system. Nuclear fusion and Plasma Physics, vol. 25, No. 3, September 2005 16. Ma, S.: Research and System Implementation of 100kV PSM High Voltage Power Supply, Doctoral Dissertation, Huazhong University of Science and Technology 17. Li, M.: Development and application of J-TEXT Tokamak continuous frequency conversion rotating disturbance field system, doctoral thesis, Huazhong University of Science and Technology 18. Yang, Z., Zhang, J., Huang, Y., et al.: Transient Analysis of High Power High Voltage DC Power Output Short Circuit Fault. Nuclear fusion and Plasma Physics, vol. 34, Issue 4, December 2014

Modeling and APP Development for the Evaluation of the Electromagnetic Disturbance of Modular Multilevel Converter Towers Lijing Yi1 , Xikui Ma1 , Ru Xiang1 , Haoyu Lian2 , Huifu Wang1 , and Jiawei Wang1(B) 1 School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

[email protected] 2 School of Electrical and Electronic Engineering, Hubei University of Technology,

Wuhan 430068, China

Abstract. Compared with traditional high voltage direct current (HVDC) transmission, flexible HVDC transmission offers numerous advantages in technology, economy, and environmental protection. However, flexible HVDC systems involve many semiconductor devices such as the insulated gate bipolar transistors (IGBT) and power diodes, which often operate under high-frequency switching, causing severe radiated electromagnetic interference. Accurate forecast of such electromagnetic disturbance is crucial for ensuring the safe and reliable operation of the flexible HVDC transmission systems. To achieve this goal, a three-dimensional finite element model of the valve towers of the modular multilevel converters (MMC), which are the elementary components of the HVDC transmission systems, has been built. By utilizing the IGBT mathematical model and the direct frequency domain method, the time profiles as well as the frequency spectra of the transient currents of the IGBTs are extracted and imposed to the finite element model as the excitations inducing electromagnetic interference. Furthermore, the finite element model is integrated in a dedicated APP. Taking into account the widely used capacitor voltage sequencing method of sub-modules, a user-friendly and efficient interface was designed based on the Simdroid platform. This interface allows for parametric modelling, straightforward meshing, calculation, and post-processing. The App provides a comprehensive prediction of the electromagnetic disturbance level of the flexible HVDC transmission systems including the near field distribution pattern and far field propagation characteristics under various operation conditions, which is favorable to the design and optimization of the shielding and protection structure of the converter. Keywords: Flexible HVDC transmission system · Valve tower · Electromagnetic disturbance · APP development

1 Introduction Compared with traditional high voltage direct current (HVDC) transmission, flexible HVDC transmission offers significant advantages in technology, economy, and environmental protection, making it a crucial component in the development of smart grids [1]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 49–57, 2024. https://doi.org/10.1007/978-981-97-0877-2_6

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The Modular Multilevel Converter (MMC), which is the core part of HVDC transmission systems, is a novel voltage source converter topology introduced by A. Lesnicar and R. Marquardt [2, 3]. With its broad potential in new energy grid integration, grid interconnection, and long-distance power transmission, the modular multilevel converter plays a vital role in future energy systems. However, the flexible HVDC converter station experiences numerous electromagnetic interferences, and the propagation path is intricate. Due to the high-frequency switching operation of the insulated gate bipolar transistors (IGBT) and power diodes, the high-frequency disturbances are significantly higher compared with those of traditional DC converter valves [4]. Therefore, accurate prediction of the electromagnetic interference in flexible HVDC transmission holds great importance for the success of flexible HVDC transmission projects. Significant efforts have been made both in studying the electromagnetic compatibility of flexible DC converter systems. To simplify the problem and reduce computational complexity, many analysis and prediction methods rely on electromagnetic transient models based on circuit theory and electromagnetic theory. Researchers from Wuhan University exploit dipole theory to derive the model parameters of the equivalent dipole model for the converter valve, taking into account the behavior characteristics of IGBT. This approach enables the calculation of the converter system’s radiation field based on a simple model, yet the overall system’s operating characteristics is neglected [5]. Researchers from North China Electric Power University propose a method that combines the moment method and antenna theory to measure the electromagnetic interference sources generated by the converter valve. They calculate the radiated electromagnetic interference produced by the three-phase two-level VSC-HVDC converter system in FEKO, but the near field has not been analyzed [6, 7]. In [8], the electromagnetic radiation disturbance of an 800 kV UHVDC converter station converter valve is measured and analyzed. In summary, most existing efforts have focused on the electromagnetic interference problem of the entire valve hall and have greatly simplified the model without considering the operating status of the converter system, leading to a large error. This paper begins with the IGBT mathematical model to analyze the response of IGBT switch transients. The direct frequency domain method is employed for this purpose. Furthermore, working characteristics of the converter valve tower is investigated, taking into account the most commonly used capacitor voltage sequencing algorithm. An APP for analyzing the electromagnetic disturbance is then developed based on the Simdroid platform. Finally, the electromagnetic disturbance characteristics of the converter valve tower are calculated for each working state and harmonic.

2 MMC-HVDC System 2.1 Operation Situation Analysis Figure 1 illustrates the fundamental structure of the half-bridge type MMC system. The three-phase MMC comprises highly modular power modules with six legs, where each leg consists of n power modules and a series DC reactor, denoted by Ls. The configuration and operating state of the converter system determine the radiation electromagnetic interference.

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Fig. 1. Three-phase MMC topology

The power module serves as the core component of the MMC-HVDC system. Through the switching of the power module, the MMC regulates the output voltage and power. The input and cutoff of the power modules are controlled by managing the turn-on and turn-off of the two IGBT devices, S1 and S2, as depicted in Table 1. During regular power transmission operations, a latching state is prohibited. Hence, under normal circumstances, the power modules operate in two distinct states: input and cutoff, as shown in Table 1. Table 1. MMC switch working state Mode

S1

S2

U0

I

State

1

1

0

Uc

+

Input

2

1

0

Uc

−

Input

3

0

1

0

+

Cut-off

4

0

1

0

−

Cut-off

5

0

0

Uc

+

Latching

6

0

0

0

−

Latching

2.2 Mathematical Model of IGBT Switch Transients The high-frequency operation of IGBT is the primary cause of electromagnetic disturbance in converter valves. To obtain the current waveform of IGBT action transients, an algebraic model method is employed [9, 10]. The necessary parameters for the equation can be obtained from the manufacturer’s data table, making the modeling process more practical and significantly reducing the requirements and complexity of experimental conditions for simulation preparation (Figs. 2 and 3).

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0.1 0

0.9

0

d on

0.1 0 on

0

1 on

2 on

3 on

4 on

Fig. 2. The current turn-on transient waveforms

0

0.9

0

d

0.1 0

1

0

2

Fig. 3. The current turn-off transient waveforms

The current turn-on transient of the IGBT is segmented into four time durations, while the turn-off transient is divided into two time durations. The transient waveforms can be expressed by formulas (1) and (2), respectively. ⎧ ⎪ Ices [t0(on) , t1(on) ] ⎪ ⎪ ⎨ Ices + Kir (t − t1(on) ) [t1(on) , t2(on) ] Ic (t) = (1) 2 ⎪ Ic0 + Kir (t − t2(on) )e−α2(on) (t−t2(on) ) [t2(on) , t3(on) ] ⎪ ⎪ 2 ⎩ [t3(on) , t4(on) ] Ic0 + Irrm e−α3(on) (t−t3(on) )  Ic0 [t0(off) , t1(off) ] (2) Ic (t) = 2 2 0.9Ic0 e−α1(off ) (t−t2(off) ) + 0.1Ic0 e−α2(off ) (t−t2(off) ) [t1(off) , t2(off) ] The Infineon’s FZ1500R33HE3 IGBT is considered in our context. The turn-on and turn-off process lasts for 3 us. Using the direct frequency domain method, the switching transient is expanded. The resulting frequency domain characteristics of the switching transient are depicted in Fig. 4 and Fig. 5, respectively. It is observed that the frequency range of the turn-on current and shutdown current is concentrated within 0.3–5 MHz. The maximum harmonic components of the turn-on transient and turn-off transient occur at 0.3 MHz, with amplitudes of 1466 A and 531 A, respectively.

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Turn-on transient Turn-off transient

I/A

1000

500

0

0

5

10

15

20

f/MHz

Fig. 4. The Fourier series of the time profiles of the transient currents.

3 Electromagnetic Simulation Analysis of Converter Valve Tower 3.1 Valve Tower Model and Capacitor Voltage Sorting Algorithm The structure of the valve tower is intricate. Some geometry details are neglected to simplify the model. The influence of the insulation shed is disregarded, and the insulator is simplified as a cylinder. Additionally, the impact of the waterway is ignored, as well as the effect of the round chamfer of the valve tower fittings. The simplified model, as depicted in Fig. 5, encompasses 12 pillar insulators, 4 shields, and 168 power modules. The entire valve tower model has dimensions of approximately 11 m in length, 4.5 m in width, and 11.5 m in height.

Fig. 5. 3D geometry of a valve tower

Considering the widely used capacitor voltage sorting algorithm [11, 12], during the transition from one state to another, it is essential to arrange the discharge capacitance

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of each power module in ascending order. The power module with the highest ranking is given priority, while the power module with the lowest ranking is cut off first. The model comprises 7 power modules per valve section, with one module serving as a redundant component. Consequently, there are a total of 24 valve segments, resulting in 144 modules available for operation in the working condition. 3.2 APP Development Utilizing the Simdroid platform, which is a general purpose Multiphysics simulation platform, this work adopts a “PaaS platform+APP application” approach. This approach provides users a unified graphical interactive simulation environment. It facilitates engineers with straightforward simulation and APP development. The scheme design is illustrated in Fig. 6. Key variable parameters of flexible HVDC transmission are defined. These parameters are then linked to the excitation and solution frequency settings. By inputting the parameters corresponding to each working state of the valve tower, the results under different working conditions can be obtained automatically.

3

Fig. 6. Schematic diagram of the design scheme

3.3 Implementation of Each Function This professional tool consists of three distinct functional areas. The first area is the shortcut menu bar, which includes six function buttons. These buttons are responsible for generating geometry, creating a mesh, performing calculations, executing one-click calculations, displaying logs, and exiting the tool. The first four buttons are primarily used for operational calculations once the key parameters are set. The display log function is utilized to monitor the progress and convergence of the calculation process, as well as the calculation duration. The introduction and parameter setting ribbon provides an overview of the App’s engineering background and application scenarios. It also allows for the modification of key parameter settings. These key parameters include the simulation solution frequency band, encompassing the start frequency, end frequency, frequency step size, and interval

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step size for discrete sweeps. In addition, this area enables the configuration of the current working status of each power module within the six valve sections of the four valve layers in the converter valve tower. The interface of this functional area is depicted in Fig. 7 and Fig. 8. Model and results visualization ribbon offers three visualization options: geometry visualization, mesh visualization, and calculation result visualization. Geometry visualization allows users to view the regenerated geometry. Mesh visualization enables the observation of the mesh splitting effect when it is re-divided, as demonstrated in Fig. 9.

1

2 3

4

m

v

Fig. 7. Solving the frequency band setting interface

1

2

3

4

5

6

Fig. 8. Modification interface for setting excitation parameters

When the simulation is completed, the results can be viewed in Model and Results Visualization ribbon, including the electric field intensity distribution and far-field distribution of the valve tower under different working states at various frequency points. The electromagnetic distribution characteristic of the two cases is presented below. In the first case, the excitation amplitude of all modules, except for the redundant module, is set to unity. In the second case, there is an input transient in the first valve segment module on the first floor of the valve tower, while the states of other modules remain unchanged, with an excitation amplitude of 0. The observation from Fig. 10 and Fig. 11 reveals that, irrespective of the operating state of the valve tower, the electric field distribution tends to concentrate in the middle of both sides of the tower. In order to mitigate electromagnetic interference between modules, the installation of a shielding device in the middle of the valve tower can

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Fig. 9. Mesh visualization

(a) Distribution of Electric field

(b) Distribution of far field

Fig. 10. Electromagnetic distribution of case1

(a) Distribution of Electric field

(b) Distribution of far field

Fig. 11. Electromagnetic distribution of case2

be considered. Furthermore, regardless of specific action scenarios, the far-field electromagnetic radiation of the valve tower yields similar outcomes. As the number of modules in the operating state increases, the radiation characteristics of the entire valve tower become more akin to dipoles. Consequently, reinforcing lateral and top shielding becomes crucial for the suppress of electromagnetic interference of the overall valve tower.

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4 Conclusions This manuscript provides a comprehensive introduction to a specialized parametric simulation app that has been developed. By simply entering the parameters into the designated visualization window, users can easily configure the model and generate various post-processing results after the calculation process. This user-friendly app eliminates the need for simulation expertise, making it straightforward to unexperienced engineerings. The APP enables systematic prediction of the electromagnetic interference of the valve tower under different operating conditions. It serves as a valuable reference for the electromagnetic interference analysis and shielding design of converter valve systems. Furthermore, the app can be promoted and implemented within operation and maintenance units of flexible HVDC converter stations, playing a significant role in the development of smart grids.

References 1. Qiao, W., Mao, Y.: Overview of shanghai flexible HVDC transmission demonstration project. East China Electric Power 39(7), 1137–1140 (2011). (in Chinese) 2. Marquart, R., lesnicar, A.: New concept for high voltage-modular multilevel converter. In: Proceedings of the IEEE 35th Annual Power Electronics Specialist, vol. 6, pp. 25–26 (2004) 3. Lesnicar, A., Marquardt, R.: An innovative modular multilevel converter topology suitable for a wide power range. Power Technology Conference, p. 6. IEEE (2003) 4. Sun, H., Du, L., Liang, G.: Antenna model of MMC-HVDC converter valve system and its radiated electromagnetic disturbance analysis. Proc. CSEE 36(03), 879–888 (2016). (in Chinese) 5. Yu, S., Ruan, J., Liu, B.: Calculation of electromagnetic radiation of VSC-HVDC converter stations. High Volt. Eng. 35(08), 1980–1985 (2009). (in Chinese) 6. H. Sun, L. Du, G. Liang. Calculation of electromagnetic radiation of VSC-HVDC converter system. IEEE Transactions on Magnetics, 52(3),1–4 (2016) 7. Liang, G., Zhu, R.: Predictive analysis for radiated electromagnetic disturbance in MMCHVDC valve hall. CPSS Trans. Power Electron. Appl. 5(2), 126–134 (2020) 8. Ni, X.-J., Zhang, B.-H., Qiu, P., He, S.-Y., Xie, Y.-Z.: Radiated disturbance measurement and analysis for ±800 kV DC converter valve. In: 2022 4th International Conference on Power and Energy Technology (ICPET), Beijing, China, pp. 364–368 (2022) 9. Jin, M., Weiming, M.: Power converter EMI analysis including IGBT nonlinear switching transient model. IEEE Trans. Industrial Electron. 53(5), 1577–1583 (2006) 10. Rajapakse, A.D., Gole, A.M., Wilson, P.L.: Electromagnetic transient simulation models for accurate representation of switching losses and thermal performance in power electronic systems. IEEE Trans. Power Deliv. 20(1), 319–327 (2005) 11. Wang, K., Li, Y., Zheng, Z., Xu, L.: Voltage balancing and fluctuation-suppression methods of floating capacitors in a new modular multilevel converter. IEEE Trans. Ind. Electron. 60(5), 1943–1954 (2013) 12. Joshi, S.D., Ghat, M.B., Shukla, A., Chandorkar, M.C.: Improved balancing and sensing of submodule capacitor voltages in modular multilevel converter. IEEE Trans. Ind. Appl. 57(1), 537–548 (2021)

Theory and Method of Non-contact Electrostatic Gait Detection Based on Human Body Electrostatic Field Sichao Qin(B)

, Weiling Li, Yu Qiao, Jie Bai, Jiaao Yan, Ruoyu Han, Pengfei Li, and Xi Chen

School of Mechanical and Electrical Engineering, Beijing Institute of Technology, Beijing 100081, China [email protected], {r.han,pfli,chenxi}@bit.edu.cn

Abstract. Gait analysis is an important means for diagnosing related diseases, guiding rehabilitation, and assessing mobility. Compared with existing methods, the non-contact electrostatic induction detection method for obtaining gait signals has the advantages of being non-wearable, low-cost, and capable of directly obtaining full-cycle gait signals for a long time. This paper proposes a theory and method of non-contact electrostatic gait detection based on the human body’s electrostatic field. The change law of the equivalent capacitance of the human foot to the ground was analyzed and the kinematic equations of the human foot during movement was established. Based on this, a non-contact electrostatic gait signal detection model based on the human body’s electrostatic field was established. Both the simulation curve of the theoretical model and the measured electrostatic gait signal can reflect the gait information of the foot movement, especially initial contact (IC), toe-off (TO), and swing phase, and have high consistency. This research provides a new theoretical basis and feasible technical approach for gait measurement and analysis. Keywords: Non-Contact Detection · Electrostatic Gait · Equivalent Plantar Capacitance · Gait Analysis

1 Instruction Human gait is a complex coordinated movement achieved by the control of the nervous system over more than 400 muscles and more than 200 bones. Human gait carries rich body characteristics and health information [1, 2]. Gait analysis is an important method for studying human walking characteristics, explaining the key links and influencing factors of gait, and can provide important guidance for the early diagnosis and treatment of patients [3]. Current gait analysis techniques can be mainly divided into gait analysis techniques based on machine vision, based on foot pressure information, and based on inertial measurement units, according to different measurement principles. Gait analysis methods based on machine vision refer to the use of cameras or infrared detection systems to © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 58–65, 2024. https://doi.org/10.1007/978-981-97-0877-2_7

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extract relevant parameters of human motion from their spatiotemporal motion trajectories [4, 5]. The gait signal obtained by this method is obtained after complex algorithm extraction of the obtained image signal, and the obtained motion image is easily affected by external factors. In addition, the VICON system, which is considered as the “gold standard” in the field of motion analysis, requires high costs and the collection and analysis of data requires professional staffs, making it unsuitable for gait detection and analysis in low-level hospitals or patients’ homes [6]. The gait measurement method based on pressure plates and pressure sensors is often used to verify the accuracy of other measurement methods [7, 8]. However, it cannot obtain the gait signal after the subject’s foot leaves the ground. Gait measurement systems based on Inertial Measurement Units (IMUs) usually consist of accelerometers and micro-gyroscopes. These sensors are placed on fixed parts of the subject’s body, and information such as the threeaxis acceleration and angular velocity of the body parts is measured by the sensors. This method has the advantages of low cost, miniaturization, low consumption, and simple system structure [9]. However, its measurement accuracy is also easily affected by the sensor fixation method and fixation location [10], and it affects the subject’s ability to walk in the most natural state. In summary, the existing three measurement methods all have certain limitations in detecting the full-cycle gait signals of the test subjects while walking in their most natural state. In contrast, non-contact electrostatic induction detection technology is an economical, non-contact, long-term monitoring technology that can obtain fine full-cycle human gait signals in the most comfortable walking state. According to Ficker T.‘s research, when a person walks, the equivalent capacitance between their body and the ground changes, creating a sinusoidal oscillation-like pattern in their body’s potential [11, 12]. Reference [13] first proposed that a non-contact electrostatic detection system can be used to achieve human movement detection. Professor Kurita established an equivalent capacitance model of the human body, and experimentally tested the induced electrostatic signals of the human body when stepping, walking and binding part of the lower limbs, and a convolutional neural network is used to classify gait signals and complete identity recognition [13–16]. Li Mengxuan accurately divided the gait cycle, support period, and swing period on the obtained electrostatic gait signals, and used multimodal information fusion to achieve the division of mobility levels [17]. The above research has greatly promoted the development of non-contact electrostatic detection technology. However, the theory and methods of non-contact gait detection based on the human body’s electrostatic field still need further research. Therefore, this paper proposes a non-contact electrostatic gait detection theory and method based on human body electrostatics. By analyzing the regularity of the change of the equivalent capacitance between the human body and the ground during movement, a theoretical model of non-contact gait detection based on the human body’s electrostatic field is established. According to the regularity of human stepping movement, the kinematic equations of the distance between the heel and the ground, toe and the ground, the contact area between the foot and the ground, and the relative angle between the foot and the ground are fitted, and simulation curves are obtained. By comparing with the measured signals, the correctness of the theoretical model is verified. This research

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work has laid a foundation for obtaining electrostatic gait signals through non-contact methods and performing gait analysis.

2 Principles and Methods 2.1 Analysis of the Equivalent Capacitance Between Human Foot and Ground When the human body is standing, As shown in Fig. 1, the series coupling capacitance of the sole capacitance and the surface capacitance of the floor can be expressed by Eq. (1). Where Cs1 and Cs2 are the capacitances of the left and right soles, respectively. Cf1 . And Cf2 are the capacitances of the left and right soles in contact with the ground, respectively. Csjfj =

Csj · Cfj , (j = 1, 2). Csj + Cfj

(1)

Fig. 1. Schematic diagram of human body capacitance when standing

In the above formula, the capacitance of the sole Cs1 = Cs2 = εs Ss /ds , where εs , Ss , and ds represent the dielectric constant, the sole’s area and thickness, respectively. The capacitance caused by the part of the sole in contact with the ground is Cf 1 = Cf 2 = εf Sc /df , where εf , Sc , and df indicate the average dielectric constant, the area where the sole touches the floor’s surface, and the distance between the floor’s surface and the ground where a potential difference exists, respectively. There is a coupling capacitance Cri (i = 1, 2, 3) between other parts of the body and other grounded surfaces (such as walls) and the surrounding environment (such as tables, chairs, bookshelves, etc.) in space. Therefore, the total capacitance CB of the human body when standing is formed by the parallel connection of Cr and Csf , as shown in the following formula: CB = Csf + Cr ,Csf =

2  j=1

Csjfj , Cr =

∞ 

Cri

(2)

i=1

When the human body is in the process of stepping or walking, the feet move alternately in a regular manner. During the double-foot support period, the contact area SC

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between the sole and the surface of the floor changes with the movement of the foot, causing the capacitance Cf1 and Cf2 to change accordingly. During the swing period, after the foot is completely off the ground, an equivalent capacitance Ch(t) is formed between the sole and the surface of the floor, consisting of a non-ideal parallel plate capacitor with air as the medium and an inclination angle, as shown in Fig. 2. Equation (3) can be used to represent the equivalent instantaneous capacitance of a walking human body. ⎧ 1 1 1 ⎪ + + support period ⎪ ⎨ Cs1f 1 + Cr Cs2 Cf 2 1 = (3) 1 1 1 ⎪ CB(t) ⎪ ⎩ + + swing period Cs1f 1 + Cr Cs2 Ch(t) where Ch(t) is the equivalent capacitance of the human foot to the ground under the influence of the edge effect of the entire sole edge, according to literature [18], the mathematical calculation model is:  

a sin θ ε0 b π a sin θ ε0 b ln( + 1) + ln ln( + 1) + 1 + 1 Ch(t) = θ h π θ h  

(4) 1 πb πb H + πb ε0 H ln( + 1) − h ln( + 1) + π b ln( ) +a + π sin θ H h h + πb

Fig. 2. Schematic diagram of equivalent capacitance between human foot and ground when walking

2.2 Non-contact Electrostatic Gait Signal Detection Model Based on Human Electrostatic Field As shown in Fig. 3, when a person stepping, their equivalent capacitance changes, which alters the potential of their body and the electric field around them. The detection electrode produces an induced charge, which it amplifies before converting to a voltage signal through I/V. The real-time gait signal is acquired after filtering. The formula below can be used to represent the potential of the human body as it moves in front of the detecting electrode: UB = QB /(CB (t) + Cg )

(5)

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The charge of the human body, which can be estimated as a constant after a few seconds of continuous movement, the following induced charge is observed on the detection electrode: QE = Cg (UB − VE )

(6)

The electrostatic induction current passing through the detection electrode plate can be described as Eq. (7), where k = Cg · d(QB )/dt. ⎧ d 1 d 1 ⎪ ⎪ ⎨ k dt ( C ) ∝ k dt ( S (t) ) support period d 1 dUB dQE C f2 = Cg ∝k ( )= I (t) = ⎪ 1 d dt dt dt CB (t) ⎪ ⎩k ( ) swing period dt Ch (t) (7)

Fig. 3. Experimental layout diagram of non-contact electrostatic detection system

As can be observed in Eq. (7), the change in the equivalent coupling capacitance of the human body is the principal cause of the induced current on the detection electrode. During the support and swing periods, many factors have varied effects on the change in human coupling capacitance. It mostly pertains to the contact area between the sole and the floor’s surface throughout the support phase. The primary factor affecting the non-ideal parallel plate capacitor created by the foot and the floor’s surface throughout the swing phase is the change in the distance and angle between the sole and the ground. 2.3 Kinematic Equations of Human Foot During Stepping The kinematic equations of the foot in the human electrostatic gait signal detection model is the change of the distance h(t) between the toe and the ground, the distance H (t) between the heel and the ground, the angle θ (t) between the plane where the sole is located and the horizontal ground, and the contact area SC (t) between the sole and the surface of the floor during movement. Taking stepping as an example, in the gait cycle of a healthy human body, the support period of stepping can be further divided into toe contact, heel contact, mid-stance, heel off, and toe off stages. The swing period can be

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further divided into toe off, accelerated lifting, decelerated lifting, accelerated falling, decelerated falling, and toe contact stages. The distance h(t) between the toe and the ground changes during the swing period. Let α be the proportion of the support period in the gait cycle, β be the proportion of the swing lifting period in the entire swing period, and h0 be the maximum distance between the toe and the ground during stepping. The distance between the toe and the ground can be expressed by a piecewise function h(t). Let θ0 be the maximum angle between the plane where the sole is located and the horizontal ground during the movement, and γ be the proportion of the time from toe contact to opposite heel contact in the double-foot support period. The relationship between the angle θ (t) between the plane where the sole is located and the horizontal ground during movement is as Eq. (9). Let the length of the sole be a, and combining the function expressions of h(t) and θ (t) above, the relationship between the height H (t) of the heel from the ground can be obtained as Eq. (10): Let the area of the sole be S0 , inspired by the research on the contact area between the foot and the ground in reference [14], the relationship between the change in the contact area between the sole and the ground is fitted as Eq. (11): ⎧ ⎪ 0, (n − ⎪  1)T ≤ t ≤ (n − 1)T + αT ; ⎨ 1 h(t) = h0 sin 2π · 4β(1−α)T · (t − αT ) , (n − 1)T + αT ≤ t < (n − 1)T + αT + β(1 − α)T ;

 ⎪ ⎪ 1 ⎩ h cos 2π ·  4(1−β)(1−α)T · [t − (αT + β(1 − α)T )] , (n − 1)T + αT + β(1 − α)T ≤ t < nT ; ⎧θ 0 γ (2α−1) 1 ⎪ T; ⎪ 40 1 + cos 2π · γ (2α−1)T · t , (n − 1)T ≤ t < (n − 1)T + 2 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ )(2α−1)) ⎪ ⎪ 0, ⎧(n − 1)T⎡+ (2α−1) T ≤ t < (n − 1)T +⎤(1+(1−γ T; ⎪ 2 2 ⎨   ⎫ (1+(1−γ )(2α−1))T ⎬ ⎨ t− θ(t) = θ0 (1+(1−γ )(2α−1)) 2 ⎦ , (n − 1)T + ⎣ ⎪ T ≤ t < (n − 1)T + αT ; ⎪ 4 ⎩1 − cos 2π · 2 (2α−1)T ⎪ ⎭ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪  ⎪ ⎪ θ0 1 ⎩ θ0 sin 2π · 2 2(1−α)T · (t − α)T + 2 , (n − 1)T + αT ≤ t < nT ;

H (t) = h(t) + a · sin θ (t)

(8)

(9)

(10)

⎧ 

 ⎪ (t+ γ (2α−1)T ) 1 2 ⎪ S , (n − 1)T ≤ t < (n − 1)T + γ (2α−1) − cos 2π · T; ⎪ 0 2 ⎪ 3γ (2α−1)T 2 ⎪ ⎪ ⎪ ⎪ ⎪ (n− 1)T + (2α−1) < (n − 1)T + (1+(1−γ2)(2α−1)) T; ⎪ 2 T ≤ t  ⎨ S0 , 1 1 T SC (t) = S0 2 + cos 2π · (2α−1)T (t − 2 ) , ⎪ ⎪ ⎪ (n − 1)T + (1+(1−γ2)(2α−1)) T ≤ t < (n − 1)T + αT ; ⎪ ⎪ ⎪ ⎪ ⎪ 0, (n − 1)T + αT ≤ t < nT ; ⎪ ⎪ ⎩ (11)

3 Simulation and Measurement Data Analysis By using the kinematic equations of the human foot during stepping established in the principles and methods and substituting it into the non-contact electrostatic gait signal detection model based on the human electrostatic field, the simulated stepping

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electrostatic gait signal can be obtained. At the same time, using the experimental layout diagram shown in Fig. 3, the electrostatic gait signals of multiple subjects were collected. The simulated waveform and measured signal are shown in Fig. 4.

Fig. 4. Simulated and measured electrostatic gait signals

In Fig. 4, (a) is the induced current waveform of human foot movement obtained by simulation, and (b), (c), (d), (e), and (f) are the induced current waveforms obtained by 5 different test subjects. By comparing the simulated and measured signals, it can be seen that the measured signals all show similar characteristics to the simulated signals, that is, the waveform has obvious local extreme points, and there is a decaying transition curve between the maximum and minimum points. As can be known from the previous analysis, the local extreme points of the waveform are mainly caused by the human foot touching and leaving the ground, while the transition waveform between the extreme points is caused by the movement of the foot during the swing period. The theoretical model simulation waveform has high consistency with the measured signal, can reflect the gait information of foot movement, and provides theoretical support for the extraction of relevant gait characteristics.

4 Conclusion This paper proposes a non-contact electrostatic gait detection theory and method based on the human body’s electrostatic field, and verifies the correctness of the theoretical model through measured gait signals. This method can obtain the full-cycle time-domain signal of the natural gait of the subject in a non-contact manner, and is expected to provide an important basis for gait detail parameters in the early diagnosis, treatment, and rehabilitation guidance of patients with neurological diseases (such as hemiplegia, Parkinson’s disease, etc.).

References 1. VanDe Port, I.G.L., Kwakkel, G., Van Wijk, I., Lindeman, E.: Susceptibility to deterioration of mobility long-term after stroke: a prospective cohort study. Stroke 37(1), 167–171 (2006)

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2. Chen, S., Lach, J., Lo, B., Yang, G.Z.: Toward Pervasive Gait Analysis With Wearable Sensors: A Systematic Review. IEEE J. Biomed. Heal. Informatics 20(6), 1521–1537 (2016) 3. Ornetti, P., Maillefert, J.F., Laroche, D., Morisset, C., Dougados, M., Gossec, L.: Gait analysis as a quantifiable outcome measure in hip or knee osteoarthritis: A systematic review. Jt. Bone Spine 77(5), 421–425 (2010) 4. Kang, K., Jeong, S., Yu, H., Park, J.: Vision-based gait analysis system utilizing deep learning algorithms in idiopathic normal-pressure hydrocephalus patients. Alzheimer’s Dement. 17(S5), 53139 (2021) 5. Jeon, S., Lee, K.M., Koo, S.: Anomalous Gait Feature Classification From 3-D Motion Capture Data. IEEE J. Biomed. Heal. Informatics 26(2), 696–703 (2022) 6. Carse, B., Meadows, B., Bowers, R., Rowe, P.: Affordable clinical gait analysis: an assessment of the marker tracking accuracy of a new low-cost optical 3D motion analysis system. Physiother. (United Kingdom) 99(4), 347–351 (2013) 7. Daniluk, A., Hadamus, A., Ludwicki, M., Zagrodny, B.: Backward vs. forward gait symmetry analysis based on plantar pressure mapping. Symmetry (Basel) 14(2), 203 (2022) 8. Lorentzen, J., Frisk, R., Willerslev-Olsen, M., Bouyer, L., Farmer, S.F., Nielsen, J.B.: Gait training facilitates push-off and improves gait symmetry in children with cerebral palsy. Hum. Mov. Sci. 69, 102565 (2020) 9. Steinmetzer, T., Wilberg, S., Bönninger, I., Travieso, C.M.: Analyzing gait symmetry with automatically synchronized wearable sensors in daily life. Microprocess. Microsyst. 77, 103118 (2020) 10. Anwary, A.R., Yu, H., Vassallo, M.: Optimal foot location for placing wearable IMU sensors and automatic feature extraction for gait analysis. IEEE Sens. J. 18(6), 2555–2567 (2018) 11. Ficker, T.: Charging by walking. J. Phys. D Appl. Phys. 39(2), 410–417 (2006) 12. Ficker, T.: Electrification of human body by walking. J. Electrostat. 64(1), 10–16 (2006) 13. Takiguchi, K., Wada, T., Toyama, S.: Human body detection that uses electric field by walking. J. Adv. Mech. Des. Syst. Manuf. 1(3), 294–305 (2007) 14. K. Kurita: Differences between individuals with temporal change in plantar surface contact area in walking motion. In: Proceedings - 2013 International Conference on Biometrics Kansei Engineering ICBAKE 2013, pp. 87–90 (2013) 15. Kurita, K.: New estimation method for the electric potential of the human body under perfect noncontact conditions. IEEJ Trans. Electr. Electron. Eng. 4(2), 309–311 (2009) 16. Kurita, K.: Novel detection technique for triboelectricity under perfect noncontact condition. Appl. Mech. Mater. 36, 355–359 (2010) 17. Li, M., Li, P., Tian, S., Tang, K., Chen, X.: Estimation of temporal gait parameters using a human body electrostatic sensing-based method. Sensors Switzerland 18(6), 1737 (2018) 18. Qin, S., et al.: Modeling and evaluating full-cycle natural gait detection based on human electrostatic field. Minor revision required for publication. IEEE Trans. Instrum. Meas. (2023)

Statistical Indicator System for New Generation Power System Construction Jucong Li1 , Rongming Li1 , Chao Xun1 , Xiangyu Wu2 , Xiaofu Jiang2 , Zhijun Tang2 , Longcan Zhou3 , and Changxu Jiang3(B) 1 State Grid Fujian Electric Power Co., Ltd., Fuzhou 350100, China 2 Fujian Power Co., Ltd., Electric Power Research Institute, Fuzhou 350007, China 3 Fuzhou University, Fuzhou 350108, China

[email protected]

Abstract. With the advancement of carbon peak and carbon neutrality process, the new generation power system will change in terms of energy structure, load characteristics, power grid form, technical basis and operation characteristics. This brings new requirements and changes to the statistical work of the power grid. To adapt to the new situation of the new generation power system, this paper constructs a scientific and comprehensive set of statistical indicators for the new generation based on the principles of feasibility, universality, systematization and science. Corresponding to the five characteristics of the new generation power system, the statistical indicator system constructed in this paper focuses on the five dimensions as its core: clean and low-carbon, safe and reliable, flexible and intelligent, open and interactive, economic and efficient. It includes a total of 18 secondary indicators and 75 tertiary indicators. The proposed statistical indicator system for the new generation power system covers various aspects of production, operation and decision-making, to accurately reflect the construction of provincial demonstration areas for the new generation power system, as well as a reference value for guiding the efficient and scientific construction of the new electricity system. Keywords: New generation power system · statistical indicator system · clean and low-carbon · flexible and intelligent

1 Introduction In September 2020, President Xi Jinping officially announced at the general debate of the 75th UN General Assembly that China strives to peak its CO2 emissions before 2030 and achieve carbon neutrality before 2060. In March 2021, President Xi Jinping proposed the construction of a new generation power system, indicating the fundamental role of the new generation power system in achieving the “dual carbon” goals [1]. In July of the same year, three provinces, namely Fujian, Qinghai, and Zhejiang, were designated as provincial demonstration areas for the new generation power system. Since then, starting with these three provincial demonstration areas, multiple provincial grid companies have actively explored the construction path for the provincial-level new electricity system [2, 3]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 66–78, 2024. https://doi.org/10.1007/978-981-97-0877-2_8

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The new generation power system bears the historical mission of energy transformation, serving as an important component of a clean, low-carbon, safe, and efficient energy system. It possesses fundamental characteristics such as cleanliness, low carbon emissions, safety and controllability, flexibility and efficiency, intelligence and userfriendliness, as well as openness and interactivity. However, the power system faces challenges related to power source structure, load characteristics, grid topology, and technological foundations in the process of constructing the new generation power system. These challenges have prompted the need for new requirements and exploration in terms of statistical indicators [4, 5]. To address the increasing share of renewable energy in the new generation power system, research on exploring statistical indicators has been conducted, both domestically and internationally. In Ref. [6], an analytic hierarchy process and fuzzy comprehensive evaluation method were employed to analyze the flexibility resources (such as energy storage and interruptible loads) in the power system, establishing a comprehensive evaluation indicator system suitable for assessing these flexibility resources. Ref. [7] constructed an evaluation indicator system for smart grids based on three characteristics of intelligent power grids, using rough set theory to analyze the indicator system. The proposed indicator system provides reference and scientific guidance for the construction of intelligent power grids. In Ref. [8], a set of indicators was proposed to examine the coordination between the power system and new energy sources. Ref. [9] addressed the limitations of applying traditional risk assessment methods in the new electricity system and identified key points for assessing risks in the new system, offering essential references for its development and safe operation. Ref. [10] constructed a comprehensive evaluation indicator system for key technologies in constructing a modern power grid, with dimensions including pilot projects, technicality, and expected benefits, providing a data foundation for the scientific and efficient construction of a modern power grid. Ref. [11] aimed to evaluate the operational risks of the new electricity system, analyzing typical risk characteristics on both the supply and demand sides, and establishing a risk assessment theoretical system suitable for ensuring the safe and reliable operation of the system. Ref. [12] conducted research on the investment benefits of power grid projects and constructed an investment evaluation indicator system consisting of five dimensions, including economic benefits and construction management. These studies provide theoretical foundations and reference guidance for the development of the new electricity system, facilitating its transformation and upgrading, as well as the enhancement of overall operational efficiency. The above literature constructs various evaluation indicator systems for new generation power systems from the perspectives of intelligent construction, coordinated development, operational risks, and investment efficiency. However, due to different emphasis in the process of the study of evaluation indicator systems, a single indicator system lacks the ability to comprehensively evaluate the processes of investment, construction, development, production, operation, risks, and benefits of new power systems. This paper is based on the current changes in the energy structure, load characteristics, grid morphology, technical foundation, and operation characteristics of the new generation power system, and constructs a scientific and comprehensive statistical indicator system for new power systems, with the core dimensions of clean and low carbon,

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safe and reliable, flexible and intelligent, open and interactive, economic and efficient. By constructing the system of statistical indicator system of the new generation power system, it can reflect the changes of important elements of the power system such as generation, network, load, storage, electricity market and transactions, as well as the construction of the new generation power system, and provide support for the production and operation and development decision of the new generation power system.

2 Current Statistical Indicator System Analysis Electric power production statistics is an important part of industrial statistics and national economic statistics. It has three functions of statistical information, consultation and supervision. The existing power production statistics of the power system include seven aspects: power generation statistics, power supply statistics, power consumption statistics, power balance, load statistics, equipment statistics and energy consumption statistics. The service objects include internal statistics, government statistics and industry statistics, as shown in Fig. 1. Among them, internal statistics refers to the internal statistics of electric power enterprises. Through the statistical investigation and analysis of the production and operation activities of electric power enterprises, the statistical information obtained can provide a reference and guide for the development of electric power enterprises. Government statistics and industry statistics refer to the use of various statistical methods to conduct statistical investigation and analysis of the daily electricity consumption of social residents and social enterprises, which is used to guide the construction of power system and load distribution. The introduction of various statistical contents is shown in Table 1.

Fig. 1. Classification of Production Statistical Services

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Table 1. Various Types of Statistical Content Situation Production statistics

Business Contents

Generation statistics

Statistics of production equipment, production capacity, product output and technical and economic indicators of power plants

Supply statistics

Statistics of power supply quantity, electricity sales quantity, line loss quantity, power supply quality, and operational related indicators

Consumption statistics

Statistics of electricity consumption in various industries of the national economy and electricity consumption indicators for urban and rural residents’ living

Power balance

Conducting balanced calculations for electricity product quantity indicators from the production and consumption perspectives

Load statistics

Statistics of different caliber maximum and minimum loads, as well as load factors and other information

Equipment statistics

Statistics of relevant indicators for generation, transmission, distribution, and utilization of electric power equipment

Energy consumption statistics Statistical analysis of physical and monetary energy consumption in the company’s production and operations processes

3 Thoughts on the Construction of the Statistical Index System In July 2021, State Grid Corporation of China officially released the “Action Plan for Constructing a New Generation Power System with Renewable Energy as the Main Body (2021–2030)”. The report points out that the new generation power system has five fundamental characteristics: clean and low-carbon, safe and controllable, flexible and efficient, intelligent and friendly, and open and interactive. The statistical indicator system of the new generation power system should be able to comprehensively and accurately reflect these fundamental characteristics. Therefore, based on the five characteristics and in accordance with the principles of feasibility, universality, systematic and scientific, this paper proposes a five-dimensions indicator system architecture consisting of clean and low carbon, safe and reliable, flexible and intelligent, open and interactive, economic and efficient. Simultaneously, it adopts the overall approach of “existing as the main, supplemented by additions, complementing each other” to construct the statistical indicator system of the new power system. This means that the indicators in the statistical indicator system mainly rely on existing indicators and meet new statistical requirements by supplementing indicators. During the process of constructing the statistical indicator system for the new generation power system, we were based on the requirements of the action plan related to the new power system. After an extensive review of research achievements by domestic and

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foreign scholars, a large number of indicators were identified by combining the characteristics and connotations of the new generation power system. Following the principles of feasibility, universality, systematicity, and scientificity, the indicators were preliminarily selected. Subsequently, a review of relevant literature and consultations with multiple experts and scholars were conducted to further refine the indicators, resulting in a scientifically structured and comprehensive statistical indicator system for the new power system. The construction process of the new generation power system statistical indicator framework is illustrated as in Fig. 2. a

Fig. 2. Construction process of a new generation power system statistical indicator framework

4 Construction of Statistical Indicator System

low

Fig. 3. The statistical indicator system of the new generation power system

The new power system is crucial to a clean and low-carbon, safe and efficient energy framework. It is based on new energy sources as the primary supply, ensuring energy and power safety as a fundamental prerequisite, and prioritizing meeting the electricity

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demands for economic and social development. The system revolves around a robust and intelligent power grid, supported by the interactive integration of generation, grid, load, and storage, as well as the complementarity of multiple energy sources. It exhibits fundamental characteristics of being clean, low-carbon, safe, controllable, flexible, efficient, intelligent, user-friendly, and open for collaboration. Based on these features, the statistical indicator system of the new generation power system is constructed around five primary indicators: clean and low-carbon, safe and reliable, flexible and intelligent, open and interactive, economic and efficient. This system includes a total of 18 secondary indicators and 75 tertiary indicators, as illustrated in Fig. 3. 4.1 Clean and Low-Carbon Related Indicators Clean and low-carbon characteristics are important characteristics of the new generation power system and the direction of future social development. Clean and low-carbon, as primary indicators, include four secondary indicators and nineteen tertiary indicators: new energy grid integration performance, new energy consumption capacity, energy saving and emission reduction, and social energy consumption level. The clean and low-carbon related indicators are shown in Table 2. Table 2. Clean and low-carbon related indicators Secondary indicators

Tertiary indicators

Unit

Frequency

(1) New energy grid integration performance

1) Distributed photovoltaic installed capacity

MWh

Monthly/Annual

2) Renewable energy generation

MWh

Monthly/Annual

3) Utilizing hourly h indicator

Monthly/Annual

4) Distributed power generation installed capacity

MWh

Annual

5) Wind power installed capacity

MW

Annual

6) Hydrogen production from offshore wind power

Tonne

Monthly

(continued)

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Secondary indicators

Tertiary indicators

Unit

7) Permeation rate % of renewable energy

Monthly

8) Capacity of new energy storage

Monthly

MWh

(2) New energy 9) Penetration rate % consumption capacity of renewable energy electricity

(3) Energy-saving and emission reduction

Frequency

Monthly

10) Penetration rate of renewable energy capacity

%

Monthly

11) Wind curtailment rate

%

Monthly

12) Curtailed solar % energy rate

Monthly

13) Wind and MWh solar curtailed electricity amount

Monthly

14) Carbon dioxide emission reduction

Tonne

Monthly

15) Clean energy emission reduction

Tonne

Monthly

16) Electricity substitution quantity

MWh

Monthly

17) Electric substitution emission reduction

Tonne

Monthly

(continued)

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Table 2. (continued) Secondary indicators

Tertiary indicators

Unit

Frequency

(4) Social energy consumption level

18) Energy consumption per unit of GDP

Tonne of standard coal/ ten thousand Yuan

Annual

19) Proportion of % electric energy to terminal energy consumption

Monthly

4.2 Safe and Reliable Related Indicators In modern society, almost all production activities, entertainment activities and family life have been inseparable from the support of electricity, so improving the power quality and stabilizing the reliability of power supply is the eternal task of power supply enterprises. Safe and reliable related indicators include three secondary indicators: electric energy quality, reliability indicators, and operational status, along with fifteen tertiary indicators. The safe and reliable related indicators are shown as Table 3. Table 3. Safety and reliability related indicators Secondary indicators

Tertiary indicators

Unit

Frequency

(1) Electric power quality

1) Voltage qualified rate

%

Monthly

2) Average voltage unqualified time of the city network

h

Monthly

(2) Reliability indicators

3) Reliability rate of urban power supply %

Monthly

4) Voltage qualified rate of rural network %

Monthly

5) Average voltage unqualified time of the rural network

h

Monthly

6) Rural power supply reliability rate

%

Monthly

7) N-1 pass rate

%

Monthly

8) Increased reliability of urban power supply

%

Monthly

9) Increase in urban power supply reliability

%

Monthly

10) Increased reliability of rural power supply

%

Monthly

11) Increase in rural power supply reliability

%

Monthly (continued)

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J. Li et al. Table 3. (continued)

Secondary indicators

Tertiary indicators

Unit

Frequency

(3) Operational status

12) Peak electricity generation load

MW

Monthly

13) Peak electricity consumption load

MW

Monthly

14) Maximum peak-to-valley difference MW

Monthly

15) Average electricity load rate

Monthly

%

4.3 Flexible and Intelligent Related Indicators The new generation power system has the characteristics of high proportion of renewable energy and high proportion of power electronic equipment [6]. To deal with the randomness, volatility, and intermittency of renewable energy problems, the power system needs to enhance its capability for forecasting new energy output and load, strengthen grid construction, improve the adjustment ability, and elevate the level of intelligence. Therefore, the new generation power system statistical indicator system includes flexible and intelligent related indicators. Among them, there are four secondary indicators: regulating ability, electricity exchange capacity, level of marketization, and intelligent application indicators, as well as sixteen tertiary indicators. The flexible intelligence related indicators are shown in Table 4. Table 4. Flexible intelligence related indicators Secondary indicators

Tertiary indicators

Unit

Frequency

(1) Regulating ability

1) Unified dispatchable capacity

MW

Monthly

2) Reserve capacity

MW

Monthly

3) Proportion of flexible power sources

%

Monthly

4) Power plant peak-shaving capacity

MW

Monthly

5) Inter-provincial electricity trading volume

MWh

Monthly

6) Electric power exchange capacity

MW

Monthly

7) Carbon emissions trading volume

Tonne

Monthly

8) Green energy trading volume

MWh

Monthly

(2) Electricity exchange capacity

(3) Level of marketization

(continued)

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Table 4. (continued) Secondary indicators

(4) intelligent application

Tertiary indicators

Unit

Frequency

9) Electricity sales volume through third-party intermediaries

MWh

Monthly

10) Clean energy generation rights trading volume

MWh

Monthly

11) Effective perception rate of distribution transformer

%

Monthly

12) Number of smart integrated terminals

/

Monthly

13) Distributed photovoltaic % group adjustment and control capability

Monthly

14) Coverage rate of feeder automation lines

%

Monthly

15) Reliability of communication % network transmission

Monthly

16) Coverage rate of backbone communication network optical fibers

Monthly

%

4.4 Open and Interactive Related Indicators In the process of the construction of the new generation power system, facing the requirements of large-scale integration of renewable energy sources with randomness, volatility, and intermittency characteristics, the new power system needs to have the ability to accommodate these renewable energy sources, which means the power system should be more open. At the same, the emergence and development of new equipment and business models such as energy storage, electric vehicles, and virtual power plants, which serve as both electricity producers and consumers, require enhancing the interactive capabilities between the existing power generation and demand. As a characteristic of the new generation power system, open and interactive related indicators include two secondary indicators of generation-load integration and interaction, as well as eleven tertiary indicators. The open interaction related indicators are shown in Table 5. 4.5 Economic and Efficient Related Indicators Meanwhile, economic and efficient characteristics are crucial to the investment and construction of a new generation power system. Within the primary indicator of economic and efficient, there are five secondary indicators, including equipment utilization rate, comprehensive line loss rate, investment status, comprehensive energy services and benefit indicators. And it is also subdivided into fourteen tertiary indicators. The economic and efficient related indicators are shown in Table 6.

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Secondary indicators

Tertiary indicators

Unit

Frequency

(1) Generation-load integration indicators

1) Number of power plant voltage level connections

/

Monthly

2) Number of load voltage level connections

/

Monthly

3) Pumped storage hydropower generation

MWh

Monthly

4) New energy storage generation

MWh

Monthly

5) V2G online power

MWh

Monthly

6) Electric vehicle charging amount

MWh

Monthly

7) Number of electric vehicle charging stations

/

Monthly

(2) Generation-load interaction indicators

8) Automotive IoT user interaction %

Monthly

9) Proportion of adjustable load resources

%

Monthly

10) Cumulative demand response adjusted grid load

MW

Monthly

11) Cumulative demand response total energy reduction

MWh

Monthly

5 Statistical Indicator System Analysis After an extensive review of numerous domestic and international research literature and conducting surveys with multiple experts and scholars, this paper has developed a comprehensive set of statistical indicators for the new generation power system. The statistical indicator system for the new generation power system can reflect various aspects of the power system, including investment and benefits (indicators like investment status and benefits indicators), construction and development (indicators like total investment in special projects for the new power system, cumulative allocations, and completed investments), production and operation (indicators like new energy installed capacity and penetration rate, electricity generation and penetration rate), as well as operation and risk (indicators like power quality, reliability metrics, and operational status). This evaluation serves as a decision-making reference for the subsequent construction and development of the new generation power system. It also has contributed to grid enterprises in further exploring the development model and implications of the new generation power system, essentially understanding the new requirements of the “dual carbon” goals for the future development of the grid.

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Table 6. Economic and efficient related indicators Secondary indicators

Tertiary indicators

Unit

Frequency

(1) Equipment utilization rate

1) Average load ratio of transformer

%

Monthly

2) Average load ratio of Line

%

Monthly

(2) Comprehensive line loss 3) Comprehensive line loss rate rate

%

Monthly

(3) Investment status

4) Total investment in specialized projects

Yuan

Monthly/Annual

5) Issued plan for specialized projects

Yuan

Monthly/Annual

6) Completion of investment in specialized projects

Yuan

Monthly/Annual

(4) Comprehensive energy services indicators

(5) Benefit indicators

7) Investment in pumped storage Yuan hydropower plant construction

Monthly

8) Investment in grid-side energy Yuan storage project construction

Monthly

9) Investment in grid modernization projects

Yuan

Monthly

10) Completion status of comprehensive energy services projects

Yuan

Monthly/Annual

11) Comprehensive benefits of integrated energy services

Yuan

Monthly

12) Investment return rate of new energy power stations

%

Annual

13) Energy storage equipment return on investment

%

Annual

14) Engineering cost reduction rate

%

Annual

6 Conclusion Following the principles of feasibility, universality, systematicity, and scientific principles, this paper has meticulously reviewed and refined the existing statistical indicator system, aligning it with the five core attributes of the new power system. This meticulous enhancement was achieved by ensuring the scientific selection of indicators through extensive literature research. In culmination, a pioneering statistical indicator framework for the new power system has been established. It prominently features the five dimensions of being clean and low-carbon, safe and reliable, flexible and intelligent, open and interactive, economic and efficient, which function as primary benchmarks.

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This comprehensive system effectively mirrors the progress of constructing provincial demonstration zones for the new power system and provides substantial assistance for operational management and strategic decision-making. It stands as a valuable point of reference for the efficient and scientifically grounded advancement of the new power system, thus guiding its overall development.

References 1. Lopes, J.A.P., Madureira, A.G., Matos, M., et al.: The future of power systems: challenges, trends, and upcoming paradigms. Wiley Interdiscipl. Rev. Energy Environ. 9(3), 368 (2020) 2. Zhang, T., Liu, S., Qiu, W., et al.: KPI-based real-time situational awareness for power systems with a high proportion of renewable energy sources. CSEE J. Power Energy Syst. 8(4), 1060–1073 (2020) 3. Zhang, B., Hao, R., Shao, C., et al.: Research on the evaluation index system of the rational utilization rate of Gansu new energy under the background of double-carbon. In: 2021 International Conference on Power System Technology: Carbon Neutrality and New Type of Power System, pp. 171–175 (2021) 4. Li, T., Guo, Y.: Environmental efficiency measurements for new type thermal power enterprises considering carbon peak and neutrality (2022) 5. Hou, Y., Tai, S., Li, X., et al.: Evaluation on key technologies for the construction of lowcarbon index of electric power based on “double carbon”. Int. J. Emerg. Electr. Power Syst. (2023). 10.1515/ ijeeps-2023-0061 6. Yang, Y., Hou, J., Bian, X., et al.: Comprehensive evaluation of flexible resources for high penetration of renewable energy sources integrated to the distribution network. Distrib. Util. 38(11), 68–76 (2021). (in Chinese) 7. Huang, Z., Song, X., Liu, S.: Study on the evaluation index system and the key indexes of grid intelligence development. Distrib. Util. 33(02), 43–47+42 (2016). (in Chinese) 8. Li, Q., Aai, H., Wang, X.: Study on assessment indicators system of coordinated development between new energy and smart grid. Energy China 33(05), 25–28 (2011). (in Chinese) 9. Guo, C., Liu, Z., Feng, B., et al.: Research status and prospect of new-type power system risk assessment. High Volt. Eng. 48(09), 3394–3404 (2022). (in Chinese) 10. Liu, Y.: Evaluation methodology of key technologies in modern power grid construction. Popular Util. Electr. 37(08), 41–42 (2022). (in Chinese) 11. Hu, B., Xie, K., Shao, C., et al.: Commentary on risk of new power system under goals of carbon emission peak and carbon neutrality: characteristics, indices and assessment methods. Autom. Elect. Power Syst. 1–15 (2023). (in Chinese). http://kns.cnki.net/kcms/detail/32.1180. TP.20230107.1325.001.html 12. Yang, B.: Construction and application of post evaluation system for provincial major power grid engineering investment projects. Money China 34, 72–74 (2022). (in Chinese)

A Fault Dictionary Diagnosis Method for Photovoltaic Array Based on Maximum Fuzzy Fault Number Wei Chen(B) , Xinyin Zhang, Tingting Pei, and Cong Ding School of Electrical Engineering and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, Gansu, China [email protected]

Abstract. Aiming at the problem that the fault type of PV array is difficult to detect, a fault diagnosis method of PV array fault dictionary based on the maximum number of fuzzy faults is proposed. Firstly, the test point with the most fault information is obtained according to the “maximum number of fuzzy faults”, the node voltage is collected as a new fault characteristic before measurement, and then the node voltage value is divided into a fuzzy domain, the center value of the fuzzy domain is calculated, the fault phenomenon set is established, the working code corresponding to each node is obtained, and the fault dictionary is constructed. In the process of fault diagnosis after testing, it is only necessary to measure the new node voltage value and determine the range of its central value to realize the fault diagnosis of the photovoltaic array. The simulation results show that the proposed method has high accuracy, which proves the feasibility and effectiveness of the method. Keywords: Photovoltaic array · Fault diagnosis · Maximum number of fuzzy failures · Symptom set · Failure dictionary

1 Introduction In recent years, due to the growing demand for renewable energy. Photovoltaic power generation technology has developed rapidly. However, the changing use environment makes the photovoltaic array failure frequently, which seriously affects the safe operation of photovoltaic power generation. At present, the main methods for fault diagnosis of photovoltaic power generation system are infrared image method [1–3], Circuit structure method [4–6], I-V curve method [7–10] and intelligent algorithm [11–13]. In Reference[1], an automatic stitching algorithm of infrared photovoltaic images based on fast robust feature detection operator is used to realize the automatic stitching process from image sequence to panoramic image, so as to realize the detection of abnormal heating of photovoltaic modules. Reference [2] realized fault identification and location through neural network and wavelet transform. Based on U-Net network and HSV space, Reference [3] proposed a photovoltaic infrared image segmentation and hot spot detection method. Reference [4–6] © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 79–88, 2024. https://doi.org/10.1007/978-981-97-0877-2_9

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is based on the optimization of sensor configuration to achieve fault location. Reference [7–10] based on the I-V characteristics of the photovoltaic array, the fault of the photovoltaic module is diagnosed and some fault types are identified. Reference [11–13] achieves accurate detection of faults by optimizing intelligent algorithms. In summary, this paper proposes a new fault dictionary diagnosis method for photovoltaic array based on the maximum fuzzy fault number. This method uses the “maximum fuzzy fault number” to select the best test node set. By determining the voltage value of each node in each fault state, the corresponding test value interval of each branch is determined, that is, the fuzzy domain [14], The construction of fault dictionary is completed, and the detection of hard fault (short circuit and open circuit) and soft fault (aging) can be realized after testing, and the fault area can be located, which can provide theoretical support for the fault detection of photovoltaic power generation system.

2 Output Characteristics and Simulation Analysis of Photovoltaic Modules 2.1 Mathematical Model of Photovoltaic Module This paper uses a single diode model. Figure 1 is the equivalent circuit.

I

I ph Id

Rsh

I sh

RS U

VD1

Fig. 1. Solar cell equivalent circuit with single diodes model

The output characteristic equation can be obtained from Kirchhoff’s current law, as shown in Eq. (1). I = Iph − Id − Ish

(1)

In the formula, I ph −photogenerated current. I sh − leakage current on parallel resistors. I d −the current flowing through the diode is proportional to the reverse saturation current of the diode, as shown in Eq. (2).     U + IRs −1 (2) Id = IO exp aNs UT In the formula, I O -diode reverse saturation current, A. U-output voltage of photovoltaic cells, V. a-diode ideality factor. Ns -Number of series photovoltaic cells. U T -thermal voltage of photovoltaic cells. The expression is shown in (3). UT =

kTC q

(3)

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In the formula, q−electron charge constant, q = 1.602 × 10−19C. k− Boltzmann constant, k = 1.38 × 10−23 J/K. T C− photovoltaic cell temperature. According to the above formula, further derivation can be obtained:     U + IRs U + IRs −1 − (4) I = Iph − Io exp akT Rsh where, Rs -equivalent series resistance. Rsh - equivalent parallel resistance. 2.2 Analysis of Output Characteristics of Photovoltaic Modules Under Different Fault States The single diode simulation model of photovoltaic cell is built. The I-V and P-V characteristics of 4 × 3 PV array under different faults are analyzed, as shown in Fig. 2(a) and Fig. 2(b). 2000

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25

1RUPDO 6KDGRZ IDXOW 2SHQFLUFXLW 6KRUWFLUFXLW $JLQJ

1800 1600 1400

20

P/W

I/A

1200 15

1000 800

10

600 400

5

200 0 0

20

40

60 U/V

80

100

(a)

0 0

20

40

60 U/V

80

100

120

(b)

Fig. 2. Output characteristics of each fault state of the PV array (a) I-V (b) P-V

It can be seen from the above figure, when the open circuit and abnormal aging state of the component only consider the voltage as the fault feature, the fault cannot be completely isolated. Therefore, this paper proposes the concept of “maximum fuzzy fault number”, optimizes the measurable nodes, and uses the node voltage values of each fault type set by the pre-test simulation to construct the fault dictionary. After the test, the fault detection and fault location are completed in the form of finding the fault dictionary.

3 Fault Dictionary Diagnosis Strategy Based on Maximum Fuzzy Fault Number 3.1 Build a Fault Dictionary Before Testing The process of establishing the dictionary is actually the analysis process before the test. It is necessary to complete the determination of the fault set, the selection of the measurable nodes, the segmentation of the fuzzy domain of the fault feature, the accurate isolation of the fault type and the generation of the fault feature code.

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3.1.1 The Introduction of the Maximum Fuzzy Fault Number and the Optimization of Measurable Nodes The traditional test node selection is based on the number of fuzzy sets, and the node is selected to isolate the fault. However, the isolation effect of this method is poor and the process is complicated. Therefore, the concept of “fuzzy set fault number” is proposed to improve the traditional node voltage selection method. That is, excluding the node nj with (Max(Max(NFij))), where NFij is the number of faults contained in the fuzzy set of finding test nodes. Taking the fuzzy set of Fig. 3 as an example, Fj represents different fault types, and the node nj with the maximum number of faults Max(N Fij ) is excluded by using the above strategy. Let St = {n1 , n2 , n3 , n4 , n5 }, the maximum values of all five nodes in this example are as follows: Max(NF12) = 4, Max(NF13) = 7, Max(NF14) = 2, Max(NF15) = 4. In this way, an effective set Sn = {n1 , n4 , n5 } is obtained, and it is a minimal set to meet the requirements of node optimization. Therefore, the fuzzy domain divided by node voltage is more accurate, so that all faults can be completely isolated, and the diagnostic accuracy is also improved. The comparison results with the traditional method are shown in Table 1. In this paper, a 4 × 3 photovoltaic array is taken as an example. Different nodes in the array are selected to form the corresponding fuzzy sets. A total of 6 nodes are selected, and four working states are set, which are normal state FN , short-circuit fault FS , open-circuit fault FO and aging fault FD . The specific node selection diagram and sensor configuration are shown in Fig. 3, and the fuzzy sets are shown in Table 2. Table 1. Comparison results between traditional methods and optimization methods Reference standard

Number of isolated faults

Hop count

Diagnosis precision

Maximum number of fuzzy sets

2

4

60%

Maximum number of fuzzy set faults

3

3

100%

Applying the above strategy, excluding nodes 4 and nodes 6. In this paper, the selected node set is {n1 , n2 , n3 , n5 }. They are ➀➁➂➃ nodes in Fig. Fig. 4. 3.1.2 Build a Fault Phenomenon Set After the selection of nodes is completed by the corresponding strategy, the pre-test simulation analysis is carried out to construct a new fault phenomenon set (fuzzy set). When all fuzzy sets can isolate all fault states, the center values of each fuzzy domain are stored to construct a fault dictionary. The center value of each fuzzy domain is determined as follows. Taking the first node as an example, the remaining nodes can

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Table 2. Fuzzy sets of each node 1

2

3

4

n1

FS

FN

FD

FO

n2

FN

FS

FD

FO

n3

FN

FD

FO

FS

n4 n5

FN FS

FS, FD FN

FO FD

FO

n6

FS

FN, FD

FO

/

/



n1 n2

n3 n4 n5

3

1

2

F1F2 F3

F0 F6

1

2

F2 F3 F4 F7

F 0 F8

4

F5 F7

F4 F8

F5 F1 F6

F0 F8

V



V2

1

2

3

4

F0 F1

F5 F7

F2 F3

F4

1

V5 V1

2

1 F1 F2 F3 F4 F5 F6 F7

F0 F1 F7 F2



3

2

3

F3F8

F4 F5 F6

5



V3

F6 F8

Fig. 4. Schematic diagram of PV array node selection

Fig. 3. Example of a fuzzy set

determine the center value by analogy. n 1  U1j = UC N

(5)

j=1

In the formula, U 1j - the value of voltage element in each fuzzy domain. N-the total number of node voltages collected for a node under different working conditions. U C -the center value of the fuzzy domain. 3.2 Fault Diagnosis After Measurement The interval of the measured point T is determined by the pre-test fault dictionary. The test interval composed of the test data of each test point is V to form a workspace, and the K faults in the fault set are equivalent to the K subspaces of the entire workspace. The center of these subspaces is actually the fuzzy domain center value of the test data of each test point. A test is performed on the photovoltaic array to be measured, and a simulation analysis is performed for different working states to obtain the corresponding test interval V. The sum of squared deviations SSD(Fj ) corresponding to the fault is defined, and the

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following calculations are performed: n      2 SSD Fj = Uit − Ui Fj

(6)

i=1

In the formula, U it − the t−th voltage value at the i−th test point under a certain working condition. U i (Fj )−the center value of the fuzzy domain of the fault Fj at the i−th test point.   If SSD(FT ) = minSSD Fj , j = 1, 2, ..., K, indicating that U it falls in the subspace FT , the current fault state can be determined to be FT . The fault detection is realized and the fault of a branch is accurately located at the same time. The specific process is shown in Fig. 5. 3.3 Fault Diagnosis Steps The online fault diagnosis method proposed in this paper can be summarized as follows: 1) Three common single faults are selected as fault sets. 2) The minimum test node set is selected, and the corresponding fuzzy set is established. The fault dictionary is constructed before the test. 3) The technical personnel measure the node voltage value. According to the defined sum of squared deviations, the current fault state (short circuit, open circuit or abnormal aging) is determined by comparing with the fault dictionary to complete the fault diagnosis. The steps of the whole fault diagnosis method are shown in Fig. 6.

U it

n

SSD (Fj )

[U it

U i ( F j )] 2

i 1

SSD(FN ) SSD(FD ) SSD(FO ) SSD(FS )

N

Y

Fig. 5. Flow chart of post-test analysis process

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(U11,U12 ,...,U1n ) (U21,U22,...,U2n )

(U31,U32,...,U3n ) (U51 ,U52 ,...,U5n )

U it U i ( Fj ) SSD(Fj )

n

SSD(FT )

min

[U it

U i (Fj )]2

N

i 1

Y

FT Aging

Fig. 6. Flow chart of the PV array fault diagnosis

4 Simulation Verification In order to verify the feasibility of the fault dictionary method proposed in this paper, a 4 × 3 photovoltaic array simulation model is built. The photovoltaic module model used in the simulation process is 1So1tech 1STH-215-P. According to the method described above, this paper mainly sets up four working states of normal (FN ), short circuit (FS ), open circuit (FO ) and aging (FD ) for analysis. According to the selected nodes in this paper, the node voltage value is obtained, the fault phenomenon set of the construction node is shown in Table 3. Table 3. Set of node symptoms Fault parameter

Fault phenomenon set number

Faults contained in fault phenomenon set

Parameter ranges

n1

1

FS

[84.7272,88.7272]

2

FN

[97.3945,101.3945]

3

FD

[117.6372,121.6372]

4

FO

[176.8328,180.8328]

1

FN

[47.6972,51.6972]

2

FS

[53.2061,57.2061]

3

FD

[57.5235,61.5235]

4

FO

[87.4164,91.4164]

1

FN

[22.8486,26.8486]

2

FD

[27.8035,31.8035]

n2

n3

(continued)

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Fault parameter

n4

Fault phenomenon set number

Faults contained in fault phenomenon set

Parameter ranges

3

FO

[42.7100,46.7100]

4

FS

[54.0203,58.0203]

1

FS

[54.9556,58.9556]

2

FN

[72.5458,76.5458]

3

FD

[87.7953,91.7953]

4

FO

[132.1246,136.1246]

In this paper, 4 × 3 photovoltaic array is taken as an example. Therefore, each fault is divided into three corresponding sub-faults F1, F2 and F3. For example, the first branch has a short-circuit fault, which is defined as FS1, and the second branch has a shortcircuit fault as FS2. By analogy, the three common fault states are divided into nine different faults {FS1, FS2, FS3; FO1, FO2, FO3; FD1, FD2, FD3}, and construct a new fault dictionary, as shown in Table 4. Table 4. PV array fault dictionary Faulty condition

Fault Set Category

Fault code n1

n2

n3

n4

FS

FS1

1

1

1

1

FS2

2

2

1

2

FS3

2

1

4

2

FD1

3

1

1

3

FD2

2

3

1

2

FD3

2

1

2

2

FO1

4

1

1

4

FO2

2

4

1

2

FO3

2

1

3

2

FD

FO

It can be seen from Table 4 that the fault code corresponding to each fault type is unique, which also meets the initial requirements of the fault dictionary. The environmental parameters are set, and the three fault states of open circuit fault, short circuit fault and aging fault are simulated respectively. The test data is directly compared with the fault dictionary to find out whether the specific fault code is consistent and realize the fault diagnosis. The simulation results are shown in Table 5, Table 6 and Table 7.

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Table 5. Open circuit fault test data Experimental serial number

n1

n2

n3

n4

Theoretical fault code

Actual fault code

1

180.4

48.4

24.2

135.3

4114

4114

2

99.9

90.2

24.9

74.9

2412

2412

3

97.6

48.8

45.1

73.2

2132

2132

Table 6. Short circuit fault test data Experimental serial number

n1

n2

n3

n4

Theoretical fault code

Actual fault code

1

86.5

48.6

24.3

58.9

1111

1111

2

98.5

54.0

24.0

72.7

2212

2212

3

99.8

48.7

55.7

73.0

2142

2142

Table 7. Aging fault test data Experimental serial number

n1

n2

n3

n4

Theoretical fault code

Actual fault code

1

121.6

50.5

25.2

91.3

3113

3113

2

98.6

59.9

24.7

73.9

2312

2312

3

101.3

51.2

30.7

76.3

2122

2122

The simulation results show that the constructed fault dictionary is effective for fault diagnosis of photovoltaic array.

5 Conclusion In this paper, a fault dictionary diagnosis method for photovoltaic array based on “maximum fuzzy fault number” is proposed, and the following conclusions are obtained: 1) According to the basic output characteristics of photovoltaic modules, the node voltage is selected as a new fault feature, the concept of fuzzy domain is introduced, the fuzzy set (fault phenomenon set) is constructed, and a complete fault dictionary is established. 2) Based on the “maximum fuzzy fault number”, the measurable nodes are selected to ensure the complete isolation of the selected nodes from the fault, so as to reduce the calculation and the dimension of the fault dictionary, and the diagnostic accuracy is also improved.

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3) In combination with pre-test simulation (SBT), after-test analysis, technicians can directly measure on the spot and complete fault diagnosis by finding fault dictionary. Without calculation, fault detection, fault type identification and accurate location of fault branches of photovoltaic array can be realized. Acknowledgments. This research was supported by the National Natural Science Foundation of China (51767017) and the Basic Research Innovation Group Project of Gansu Province (18JR3RA133).

References 1. Xia, M., Yahao, L.: UAV infrared image stitching in PV array fault detection. Acta energiae solaris sinica 41(03), 262–269 (2020). (in Chinese) 2. Haque, A., Bharath, K.V.S., Khan, M.A., et al.: Fault diagnosis of photovoltaic modules. Energy Sci. Eng. 7(3), 622–644 (2019) 3. Liu, J., Ji, N.: A bright spot detection and analysis method for infrared photovoltaic panels based on image processing. Front. Energy Res. 10, 978247 (2023) 4. Hu, Y., Chen, H., Xu, R., et al.: PV array fault diagnosis based on optimal sensor configuration. Proc. CSEE 31(33), 19–30 (2011). (in Chinese) 5. Qi, T., Yongqiang, Z., Jiacheng, H.: Shadow diagnosis and positioning of PV array based on optimal sensor arrangement. Acta energiae solaris sinica 39(02), 513–519 (2018). (in Chinese) 6. Pei, T., Zhang, J., Li, L., et al.: A fault locating method for PV arrays based on improved voltage sensor placement. Sol. Energy 201, 279–297 (2020) 7. Qiang, L., Ke, G., Mingxuan, M., et al.: A photovoltaic fault detection method based on series equivalent resistance. Acta energiae solaris sinica 41(10), 119–226 (2020). (in Chinese) 8. Chen, Z., Wu, L., Cheng, S., et al.: Intelligent fault diagnosis of photovoltaic arrays based on optimized kernel extreme learning machine and IV characteristics. Appl. Energy 204, 912–931 (2017) 9. Liu, Y., Ding, K., Zhang, J., et al.: Intelligent fault diagnosis of photovoltaic array based on variable predictive models and I-V curves. Sol. Energy 237, 340–351 (2022) 10. Spataru, S., Sera, D., Kerekes, T., et al.: Diagnostic method for photovoltaic systems based on light I-V measurements. Sol. Energy 119, 29–44 (2015) 11. Dai, S., Chen, Z., Wu, L., et al.: PV array fault diagnosis method using LSTM and steady-state time series. J. Fuzhou Univ. (Nat. Sci. Edn.) 50(01), 54–60 (2022). (in Chinese) 12. Wang, Y., Li, Z., Wu, C.: A four-parameter online fault diagnosis method for photovoltaic modules. Proc. CSEE 34(13), 2078–2087 (2014). (in Chinese) 13. Wang, J., Gao, D., Zhu, S., et al.: Fault diagnosis method of photovoltaic array based on support vector machine. Energy Sour. Part A: Recov. Util. Environ. Effect. 45(2), 5380–5395 (2023) 14. Jinyan, C., Shengjian, C., Qiang, H.: A fault dictionary method that implements fault location step by step. J. Electron. Measur. Instrument. 02, 48–52 (1997). (in Chinese)

An DC Overvoltage Surge Suppression Circuit for Airborne High-Current Avionics Equipment Dong Gao(B) , Xinyu Gao, Zihe Li, Fei Feng, and Guofei Teng Xi’an Aeronautics Computing Technique Research Institute, AVIC, Xi’an 710065, China [email protected]

Abstract. The avionics equipment used in harsh environment needs to meet the requirements of corresponding overvoltage surge test. The traditional avionics equipment uses two kinds of overvoltage surge suppression circuit, electromagnetic compatibility suppression and linear power limiting, which can meet the requirements of the product, but cannot solve the application problem of highcurrent avionics equipment. In this paper, two kinds of traditional circuits are explained and compared, the limitations and shortcomings of their application are pointed out, and an improved type of overvoltage surge suppression circuit is proposed and verified by experiment. The circuit passed the 50 V/12.5 ms overvoltage surge test in accordance with the overvoltage surge requirements of GJB181A2003 and worked normally. In addition, the experimental test results show that the maximum impedance is only 0.98 W in the input voltage range of 18 V–32 V under 400 W load condition. The hybrid improved circuit can solve various problems of traditional overvoltage surge suppression circuit in high current applications, and the performance index and reliability of avionics equipment can be significantly improved by using this circuit. Keywords: Overvoltage Surge Suppression · High-Current · Airborne Avionics Equipment

1 Introduction The airborne avionics equipment is used in the harsh working environment, and the power supply compatibility test such as overvoltage surge should be completed according to the requirements before installation. Military field test conditions and criteria generally follow the national military standard GJB181-86 or GJB181A-2003, some models also adopt the U.S. military standard MIL-STD-704, the new model is based on its power supply environment to develop special specifications. The civil aircraft sector generally follows RTCA’s DO-160F/G standard. These standards are basically similar in the requirements for electrical equipment, and the specific index requirements vary [1, 2]. For DC 28 V power supply overvoltage surge, GJB181-86 requires to withstand 80 V/50 ms surge voltage and normal operation, while GJB181A-2003 requires to withstand 50 V/12.5 ms surge voltage in normal surge test and the whole process works normally. The abnormal surge test requires that the equipment needs to withstand 50 V/50 ms © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 89–96, 2024. https://doi.org/10.1007/978-981-97-0877-2_10

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surge voltage without any damage, and should be able to automatically resume normal work after resuming normal power supply [3–6]. In this paper, the realization of two traditional surge suppression circuits is introduced, and the limitations and shortcomings of their practical applications are pointed out. A surge suppression circuit that can meet the requirements of high current applications is proposed.

2 Traditional Overvoltage Surge Suppression Circuit In general, the overvoltage surge exceeds the working range of the power converter, so it is also necessary to set up a special overvoltage surge suppression circuit to solve the problem [7–10]. In the existing avionics products, the main realization methods are electromagnetic compatibility suppression and linear power limiting [11, 12]. This section mainly introduces the traditional surge suppression circuit and its disadvantages in application. 2.1 Electromagnetic Compatibility Type Overvoltage Surge Suppression Circuit In some traditional avionics equipment, the overvoltage surge test is realized by adjusting the electromagnetic compatibility circuit. The principle is to suppress the absorption of higher harmonics in the rectangular wave overvoltage surge voltage, so as to reduce the voltage peak of the electromagnetic compatibility output to meet the working conditions of the back-end electrical circuit. This method has great application limitations, overvoltage surge is generally tens of ms time, the frequency of fundamental wave is only tens of Hz, electromagnetic compatibility filter has obvious suppression effect on high frequency, but for the rectangle wave rich in 10 Hz–10 kHz low frequency component basic attenuation is very small. In order to meet the requirements of surge test, it is necessary to increase the LC value of the filter, which not only significantly increases the volume and weight of the filter, but also brings the impedance matching problem between the power supply source and the power load. These problems make the method of adjusting the electromagnetic compatibility circuit unsuitable for avionics applications. 2.2 Linear Power Limiting Type Overvoltage Surge Suppression Circuit The realization of the linear power limiting surge suppression circuit takes advantage of the linear operating characteristics of semiconductor devices. By dynamically adjusting the impedance of the circuit, the output voltage of the surge suppression circuit is limited, so as to ensure the normal operation of the post-stage electrical equipment. Specifically, the circuit monitors the output voltage of the circuit, if the output voltage exceeds the limit value, through a reasonable setting, the power semiconductor such as the triode/MOSFET connected in the main circuit is changed from the previous saturation conduction work to the linear amplification area work. Dynamically adjust its own impedance according to the input, thus limiting the input voltage of the post-stage equipment, so that the product can meet the requirements of overvoltage surge test.

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Through reasonable device selection, the normal operation of the product during the overvoltage surge can be ensured. With simple adjustments, the circuit can also be transformed into a switching circuit. If there is a fault or no need to work, you can turn off the power semiconductor switch to disconnect the power supply of the system to the back-end circuit, the relevant circuit schematic diagram is shown in Fig. 1. This method is small in size and good in performance, and has been widely used in the surge suppression circuit of avionics equipment.

Fig. 1. Traditional overvoltage surge suppression circuit schematic.

The core of the traditional surge suppression circuit is the power semiconductor device such as transistor/MOSFET, which is controlled by the acquisition control circuit to achieve overvoltage surge suppression. In the normal working process, the surge suppression tube should have a minimum on-voltage drop in order to reduce the line voltage drop and reduce product loss. During the overvoltage surge period, the power semiconductor is in a linear working area, and it needs to withstand very large power itself, so the selection of power semiconductor devices is particularly important. The on-voltage drop of the transistor V CE(SAT) is basically about 0.3 V, and the onvoltage drop of MOSFET is related to its load, which is basically proportional to its on-state impedance RDS(ON) , and the on-voltage drop is almost negligible when the load is small, and the selection is convenient, so the MOSFET is used as a power switch in general occasions. The power of conventional avionics control equipment is mostly below 100 W, and the maximum output voltage when overvoltage surge is generally set to the normal working limit of 32 V, so the maximum working current does not exceed 3 A. By checking the voltage, current and time parameters of SOA curve, MOSFETs that meet the requirements are selected. Taking the typical 100 V-MOSFETs in Fig. 2 as an example, the MOSFETs that meet the requirements are selected by checking the voltage, current and time parameters of the SOA curve. It can be seen from Table 1 that its VDSS can reach 100 V, and its maximum onstate impedance of 2.3  hardly brings additional on-state loss, which can meet the requirements of conventional applications.

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Fig. 2. Safe operating area (SOA) curve of 100 V-MOSFETs (I D = f (V DS ), TC = 25 °C, D = 0). Table 1. Key performance parameters of 100 V MOSFET.

Parameter

Value

Unit

VDS

100

V

RDS(ON), MAX

2.3

mΩ

ID

120

A

Profile

3 High Current Overvoltage Surge Suppression Circuit With the development of aircraft, 28 V DC power supply is also introduced in some highpower avionics equipment (between 300 W and 650 W) to improve its power supply reliability, and the overvoltage surge suppression circuit has created new problems in the application of traditional circuits. The working current of the above-mentioned highpower avionics equipment during overvoltage surge can reach 15 A, and the maximum working current in normal operation is close to 30 A. Although MOSFETS in the range of 100 V can show good on-state characteristics, due to the limitation of their own PN junction thickness, the SOA region is too small to meet the high power/high current applications (Table 2).

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Table 2. Key performance parameters of 650 V MOSFET.

Parameter

Value

Unit

VDS

650

V

RDS(ON), MAX

99

mΩ

ID

109

A

Profile

In order to fit the requirements of the SOA region, it is generally necessary to select 650 V and above grade pressure-resistant MOSFETS as Table shown. This kind of MOSFET has a larger SOA area, which can fit the application scenario of 15 A and fit the requirements of overvoltage surge test. But correspondingly, its on-state impedance characteristics have become a new problem. Taking a typical 650 V-MOSFET in Fig. 3 as an example, its maximum impedance reaches 99 , which could bring a maximum power consumption of about 76.4 W in normal operation. Although multiple MOSFET can be used in parallel to expand power and reduce on-state impedance in practical applications, there are still great application limitations, and new requirements are put forward for device heat dissipation, PCB layout, and MOSFET consistency.

Fig. 3. Safe operating area (SOA) curve of 650 V-MOSFETs (I D = f (V DS ), TC = 25 °C, D = 0).

Based on the above analysis and summary, we design and propose a surge suppression circuit suitable for high-power airborne equipment, which can take into account the

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existing surge suppression and on-state loss. The main method is to adopt a parallel mode of 100 V-MOSFET and 650 V-MOS in the main power circuit, and adopt a hierarchical control mode on the control circuit. In normal operation, both 100V-MOSFET and 650 V-MOSFET are saturated on. Because the on-state impedance of 100 V-MOSFET is much smaller than that of 100 V-MOSFET, the 100 V-MOSFET bears most of the working current and reduces the on-state loss to the greatest extent. When overvoltage surge occurs, the 100 V-MOSFET is shut down quickly, and the SOA characteristics of 650 V-MOSFET and its control circuit are used to realize overvoltage surge suppression. In this way, the respective advantages of 100 V-MOSFET and 650 V-MOSFET will be utilized to the maximum, and their insufficient characteristics will be avoided to achieve a high-power over-voltage surge suppression circuit. The circuit schematic diagram is shown in Fig. 4.

Fig. 4. Schematic diagram of hybrid surge suppression circuit.

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4 Experimental Verification By testing the hybrid overvoltage surge suppression circuit designed for high current application, the experimental results are shown in Fig. 5. The circuit passed the 50 V/12.5 ms overvoltage surge test in accordance with the overvoltage surge requirements of GJB181A-2003 and worked normally. When the input surge voltage reaches more than 40 V, the output voltage of the hybrid surge suppression circuit is still stable at 28 V. In addition, the experimental test results show that the maximum impedance is only 0.98 W in the input voltage range of 18 V–32 V under 400 W load condition.

Fig. 5. Test results of overvoltage surge test of hybrid surge suppression circuit (Channel 1: Input overvoltage surge, Channel 2: Surge suppression circuit output voltage).

5 Conclusions In this paper, firstly, the method of solving overvoltage surge for existing products is explained, two traditional realization methods and circuits are introduced, and the limitations and shortcomings of practical application are pointed out by analyzing the circuits. For the application of high current, a hybrid improved overvoltage surge suppression circuit is proposed and tested. Experiments show that this improved circuit can solve various problems of traditional surge suppression circuit in high current applications, and can significantly improve the performance index and reliability of the product.

References 1. Wei, J.F., Li, B.M.: A novel surge suppression scheme for capacitive pulsed power supply. IEEE Trans. Plasma Sci. 50(8), 2396–2402 (2022) 2. Fukunaga, S., Takayama, H., Hikihara, T.: A study on switching surge voltage suppression of SiC MOSFET by digital active gate drive. In: 2021 IEEE 12th Energy Conversion Congress and Exposition - Asia (ECCE Asia), pp. 1325–1330 (2021) 3. Yamaguchi, D., Cheng, Y.S., Mannen, T., et al.: Digital active gate control for a three-phase inverter circuit for a surge voltage suppression and switching loss reduction. In: 2020 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 3782–3787 (2020)

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4. Proenca, F., Pereira, R.F.R., Costa, E.C.M., et al.: Overvoltage suppression in half-wavelength transmission systems using line surge arresters. In: 2019 International Symposium on Lightning Protection (Xv Sipda) (2019) 5. Fukunaga, S.H., Funaki, T.: Switching surge voltage suppression in SiC half-bridge module with double side conducting ceramic substrate and snubber capacitor. IEICE Electronics Express 14(11) (2017) 6. Fu, L., Liu, P.Z., Chai, W.Y.: Design of high voltage surge suppression circuit for unmanned ground vehicle computer system. In: Proceedings of 2017 IEEE International Conference on Unmanned Systems (ICUS), pp. 539–543 (2017) 7. Narita, K., Shimizu, T.: Suppression method of motor-surge-voltage using the surge suppression cable. In: 2015 9th International Conference on Power Electronics and Ecce Asia (ICPE-Ecce Asia), pp. 1355–1361 (2015) 8. Kadoshima, Y., Koiwa, K., Itoh, J., et al.: Surge voltage suppression methods for three-phase to single-phase matrix converter. In: 2015 Thirtieth Annual Ieee Applied Power Electronics Conference and Exposition (Apec 2015), pp. 115–121 (2015) 9. Liu, T.L., Jin, H.B., Wu, Q.D., et al.: Surge voltage suppression circuit design of on-board SCR controller. Measur. Technol. Eng. Res. Ind. Pts 1–3, 33–335: 2358-+ (2013) 10. Wagner, C.L., Bankoske, J.W.: Evaluation of surge suppression resistors in high-voltage circuit breakers. IEEE Trans. Power Apparatus Syst. Pa86(6): 698-& (1967) 11. Tanaka, Y., Kitabata, T., Nasu, K., et al.: Suppression of cavitation surge in turbopump with inducer by reduced-diameter suction pipe with swirl brake. J. Fluids Eng.-Trans. ASME 144(7) (2022) 12. Li, W.S., Wen, X.H., Zhang, J., et al.: Neutral point voltage balance and surge voltage reduction for three-level converters in PMSM starting process based on narrow pulse suppression. J. Power Electron. 22(6), 1033–1046 (2022)

Comparison and Analysis of Full Power Inverter Topology for Large Capacity Variable Speed Pumped Storage Units Fengyuan Tian1 , Kaiguo Wang1 , Jinwu Gong1(B) , Bo Zhao2 , Qichao Zhang2 , Youzong Jian3 , and Hemin Yang3 1 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

[email protected]

2 Pumped Storage Technological and Economic Research Institute of State Grid Xinyuan

Company, Beijing 100000, China 3 State Grid Electric Power Research Institute Co., Ltd., Nanjing 211106, China

Abstract. Variable speed pumped storage units have significant advantages over traditional fixed speed pumped storage units in terms of efficiency and adaptability to operating conditions. Full power frequency converters are key equipment for variable speed pumping and storage units, and studying the application of various frequency converter topologies in large capacity variable speed pumping and storage units is of great significance. This article takes a 100 megawatt variable speed pumped storage unit as an example, and based on existing devices, compares and analyzes three-level back-to-back converter (NPC), five-level back-to-back converter (SMC) The design schemes of Modular Multilevel Converter (MMC) and Modular Multilevel Matrix Converters (M3C) with four topologies applied to high-power, 13.8 kV connected variable speed pumped storage units are compared and analyzed in terms of cost and topology advantages and disadvantages. It can be concluded that NPC and SMC are more suitable for low-voltage situations, and transformers need to be added to increase voltage in high-voltage situations, MMC and M3C have more advantages in high-pressure situations. Keywords: three level back-to-back converter · five level back-to-back converter · back-to-back modular multilevel converter · modular multilevel matrix converter

1 Introduction With the increasing penetration rate of renewable energy, the grid connection of a large number of new energy sources, mainly photovoltaic and wind, has brought unprecedented challenges to the safe and stable operation of the power grid. Pumped storage power stations are a type of energy storage method with a long lifespan, reliability, economy, and environmental friendliness. They have the characteristics of fast start-up and flexible operation, and can both reduce peak load and fill valley. Traditional pumped storage units generally operate at a fixed speed, with relatively slow power regulation © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 97–106, 2024. https://doi.org/10.1007/978-981-97-0877-2_11

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speed. They can only pump at full load under pump conditions and cannot adjust the pumping power according to system requirements, thus unable to accurately meet the requirements of grid frequency regulation. The current variable speed pumped storage units have the advantages of high efficiency, wide adjustment range, and flexible operation. They can quickly adjust active and reactive power, and have a wide range of reactive power compensation capabilities, which helps the safe and stable operation of the new power system [1, 2]. The topology in the full power frequency converter of large capacity variable speed pumped storage units is an important foundation for the autonomous construction of large capacity variable speed pumped storage units. The basic requirement of its pumped storage system for frequency converters is to achieve three-phase to three-phase AC power conversion, while also having the ability to operate in four quadrants. Due to the high system power of large capacity units, in order to match the motor voltage levels, a multi-level topology is usually used to achieve high voltage output [3–5]. At present, the full power frequency converter of large capacity variable speed pumped storage units has been pilot applied in Switzerland and Austria. One of the original fixed speed units in Unit 2 of Grimse 1 Power Station in Switzerland has been transformed into a 100 MW full power frequency converter unit, and the Kaprun berstufe pumped storage power station in Austria is currently undergoing full power frequency conversion transformation for two 85 MW units [6]. At present, there is relatively little research on this aspect in China, and there is a lack of demonstration projects. The design and operating principles of the station system are not yet clear. Therefore, it is necessary to study the topology of large capacity and full power frequency converters, serving the pumped storage units under construction and to be renovated, and providing key basic support for the development of China’s pumped storage industry. At present, commonly used high-voltage high-capacity multi-level converter topologies with four quadrant AC-AC power conversion capabilities include three-level backto-back NPC, five-level back-to-back SMC, back-to-back MMC, and M3C. Triple level NPC has the advantages of low device usage, high power density, and simple control, and has been widely used in the fields of power transmission, new energy generation, and energy storage systems [7]. ABB’s renovation plan for Unit 2 of the Grimsel Power Station in Switzerland is to connect two sets of back-to-back three-level NPC converters in parallel and then connect them in series with another set to achieve a 100MVA variable frequency speed control system. Back-to-back five level SMC is composed of two five level SMCs connected through a common DC bus, which contains some redundant switch states and can be adjusted more flexibly [8]. Back-to-back MMC is composed of two MMC connected through a common DC bus, consisting of 12 bridge arms, each consisting of a cascaded half bridge power unit and bridge arm inductance. Similar to the back to back three-level NPC, the network side and machine side of the back to back MMC converter can also be modeled and controlled separately [9]. Each bridge arm in M3C contains a set of cascaded full bridges and a bridge arm inductance, but unlike back-to-back MMC, M3C is directly connected to two three-phase systems through 9 bridge arms, without intermediate DC links, and can achieve direct AC-AC power conversion [10].

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This article takes a 100 megawatt variable speed pumped storage unit as an example to list the design schemes of using four topologies: three-level back to back NPC, fivelevel back to back SMC, back to back MMC, and M3C to apply to 100 megawatt variable speed pumped storage units. The advantages and disadvantages of their cost and topology are analyzed, providing a reference for the selection and design of 100 megawatt variable speed units.

2 Topology The frequency converter for full power variable speed pumped storage systems needs to achieve basic four quadrant AC-AC energy conversion. Three level back to back NPC, five level back to back SMC, back to back MMC, and M3C are several classic topologies, and their topology structure and basic working principle are shown below. 2.1 Three Level Back to Back NPC

Fig. 1. Topological structure of three-level back-to-back NPC.

The circuit structure of a three-level back-to-back NPC is shown in Fig. 1. Two three-level NPCs are connected through a common DC bus, and their network side and machine side can be separately modeled and controlled. The switching states of single-phase three-level NPC are shown in Table 1, and carrier stacking modulation is required. Table 1. Switching State Table of Three Level NPC. S1

S2

S3

S4

Vo

1

1

0

0

E

0

1

1

0

0

0

0

1

1

-E

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2.2 Five Level Back-to-Back SMC

Fig. 2. Topological Structure of Five Level Back-to-Back SMC.

The circuit structure of a five level back-to-back SMC is shown in Fig. 2, consisting of two five level SMCs connected through a common DC bus. Due to its inclusion of redundant switch states, its control strategy is more flexible. 2.3 Back-to-Back MMC The circuit structure of the back-to-back MMC is shown in Fig. 3, which is composed of two MMC connected through a common DC bus. The network side and machine side of the converter can be modeled and controlled separately.

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u

i i N

i

Fig. 3. Back-to-back MMC topology.

2.4 Matrix Converter (M3C) The circuit structure of matrix converter M3C is shown in Fig. 4, where U, V, and W represent the input of the converter, which is connected to the power grid in the pumped storage power station. R, S, and T represent the output of the converter, and are connected to the motor in the pumped storage power station.

u

S

Fig. 4. Matrix converter M3C.

3 Design Scheme List the design schemes for applying four topologies, namely three-level back-to-back NPC, five-level back-to-back SMC, back-to-back MMC, and M3C, to a 100 megawatt variable speed pumped storage unit, with a power level of 100MW and an input voltage of 13.8 kV.

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3.1 Back-to-Back NPC Design Scheme For the back to back NPC three-level, in order to achieve a high-voltage output of 13.8 kV, two schemes can be adopted: device series technology (without the need for a transformer) or high low high (with the need for a transformer). When using 4500V/3000A IGBT devices, if twice the voltage margin is left, five of the above devices need to be connected in series, which is technically difficult to achieve. Therefore, this scheme is abandoned and a high low high (transformer required) scheme is adopted. In order to achieve a power level of 100 MW, 5 power units are used in parallel, with each power unit being 20 MW. In addition, in order to achieve flow capacity, the switch units within each power unit are composed of two switch tubes in parallel. Each power unit has 6 bridge arms, a total of 30 bridge arms. According to the back-to-back NPC topology, each bridge arm contains 8 IGBTs and 2 clamping diodes, resulting in a total of 240 IGBTs and 60 clamping diodes; Each power unit requires 2 DC side support capacitors, totaling 10 DC side support capacitors; Each power unit requires 3 grid connected inductors, totaling 15 grid connected inductors; Each power unit has a transformer before and after it, and 5 power units are connected in parallel, so the number of transformers is 10. The types, parameters, and quantities of the main devices required are shown in Table 2. Table 2. Main Parameters of NPC Scheme. device

parameter

Quantity (pieces)

transformer

13.8kV/2.5kV(20MVA)

10

DC side support capacitor

18mF/2800V/2100A

10

IGBT

4500V/3000A

240

Clamp diode

4500V/5000A

60

Grid connected inductance

185uH/4184A

15

3.2 Back-to-Back SMC Design Scheme The back-to-back SMC adopts 5 power units in parallel, each with a power unit of 20MW. A transformer is required before and after each power unit, so the number of transformers is 10; Each power unit contains 6 bridge arms, totaling 30 bridge arms. According to the back-to-back SMC topology, each bridge arm contains 12 IGBTs and 2 floating capacitors, resulting in a total of 360 IGBTs and 60 floating capacitors. The types, parameters, and quantities of the main devices required are shown in Table 3.

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Table 3. Main Parameters of SMC Scheme. device

parameter

Quantity (pieces)

transformer

13.8kV/5.52kV(20MVA)

10

IGBT

4500V/3000A

360

Floating capacitor

13mF/2800V/1075A

60

Grid connected inductance

490uH/2092A

15

DC bus support capacitor

7mF/5600V/1500A

10

3.3 Back-to-Back MMC Design Scheme Each bridge arm of the back-to-back MMC consists of 12 cascaded half bridge power units, with 12 bridge arm inductors, 288 IGBTs, 144 submodule capacitors, and 3 grid connected inductors. The types, parameters, and quantities of the main devices required are shown in Table 4. Table 4. Main Parameters of MMC Scheme. device

parameter

Quantity (pieces)

Bridge arm inductance

1.69mH/2410A

12

Submodule capacitance

18mF/2800V/2100A

144

Grid connected inductance

350uH/4184A

3

IGBT

4500V/3000A

288

3.4 M3C Design Scheme Each bridge arm of M3C is composed of 11 cascaded full bridge power units. In order to achieve flow capacity, the switch units within each power unit are composed of 2 switch tubes in parallel, so the number of IGBTs is 792. In addition, the number of bridge arm inductors is 9, and the number of grid connected inductors is 3. The types, parameters, and quantities of the main devices required are shown in Table 5.

4 Comparative Analysis This article will compare and analyze the design schemes of various topologies in the third section from aspects such as cost, topology advantages and disadvantages.

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device

parameter

Quantity (pieces)

Grid connected inductance

700uH/4184A

3

Submodule capacitance

11mF/2800V/950A

99

Bridge arm inductance

400uH/2900A

9

IGBT

4500V/3000A

792

4.1 Costing Consult relevant equipment manufacturers and inquire about relevant information, and the cost is shown in Table 6. From the table, it can be seen that MMC has the lowest cost price at 27.924 million yuan, while back-to-back SMC has the highest cost price at 54.44 million yuan. Table 6. Cost of Different Design Schemes. Scheme

Cost (Ten thousand yuan)

Back-to-back NPC

4688

Back-to-back SMC

5444

Back-to-back MMC

2792.4

M3C

3315.6

4.2 Advantages and Disadvantages of Topology The advantages of a three-level back-to-back NPC topology are that it requires fewer switching devices, a mature topology, and a relatively simple control algorithm. But the challenges faced include the balance of capacitor voltage midpoint potential and lowfrequency fluctuations of midpoint potential; Lack of control freedom makes it difficult to cope with power grid failures; When the number of levels is low and the switching frequency is not high, the harmonic content of the output voltage is high, resulting in a high THD of the grid side current; Parallel connection of multiple modules may lead to issues of circulation and uneven power distribution; The high low high mode requires a large number of transformers. The advantages of a five level back-to-back SMC topology are simple output level expansion, small clamping capacitor capacity required, high power density, and easy modular design. However, the challenges faced are the voltage imbalance of the floating capacitor, which requires more switching devices and more complex control compared to three-level NPC. In high voltage and high-power scenarios, device series and parallel connections are also required, resulting in device voltage and current sharing issues. In

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addition, due to the voltage level of existing IGBT and other power devices, back-toback SMC cannot directly meet the line voltage output demand of 10kV and above. Transformers are also required in 100 megawatt level full power variable speed pumped storage units. The advantage of a back-to-back MMC topology is its modular structure, strong scalability, and ability to meet high-power requirements. At the same time, it can achieve the output effect of traditional topology with higher frequencies at lower switching frequencies. For variable speed pumped storage applications, the main problem with the back-to-back MMC topology is that when starting under pump operating conditions, the capacitance voltage fluctuation of the motor side MMC is relatively large, and control algorithms need to be used to suppress the capacitance voltage fluctuation. This algorithm is only used during the unit startup phase and does not affect the operation of the unit within the conventional speed range. The advantage of M3C topology is that its H-bridge cascade structure can solve DC fault traversal; M3C solves the control defects of ordinary matrix converters by connecting an inductor in series with each bridge arm, which is independent of each other and can be flexibly controlled and processed. Unlike back-to-back MMC, the main problem encountered when applying M3C to variable speed pumped storage is that the capacitor voltage fluctuates significantly when the motor frequency is close to the grid frequency. Therefore, when applying M3C to pumped storage, it is necessary to consider designing the rated frequency of the motor to be a certain value lower than the grid frequency.

5 Conclusion At present, large capacity and full power variable speed pumped storage units are still a new field in China, and large capacity and full power frequency converters are the core equipment of full power variable speed pumped storage units. This article takes a hundred megawatt level variable speed pumped storage unit as an example, and designs a scheme for applying three-level back to back NPC, five-level back to back SMC, back to back MMC, and M3C to a variable speed pumped storage unit with a power level of 100MW and an input voltage of 13.8 kV. By comparing and analyzing their cost and topology advantages and disadvantages, it can be concluded that NPC and SMC are more suitable for low voltage situations. In high voltage situations, it is necessary to add transformers to increase the voltage; Due to their modular design, strong scalability, flexible configuration, and ease of achieving high voltage output, MMC and M3C are more suitable for high voltage applications. Acknowledgments. This work was funded by the Science and Technology Project of State Grid Corporation of China (No. 4000-202343072A-1–1-ZN).

References 1. Rufei, H., Fang, W., Hao, Z.: Technical route and key parameter selection of seawater variable speed pumped storage units. Water Resour. Hydropower Technol. 51(S2), 184–189 (2020). (in Chinese)

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2. Li Tao, H., Weihao, L.J., et al.: Intelligent economic dispatch for PV-PHS integrated system: a deep reinforcement learning-based approach. Trans. China Electrotechnical Soc. 35(13), 2757–2768 (2020). (in Chinese) 3. Zhu, X., Wang, H., Zhang, W., et al.: A novel single-phase five-level transformer-less photovoltaic (PV) inverter. China Electrotechnical Soc. Trans. Electr. Mach. Syst. 4(4), 329–338 (2020) 4. Jun, Z., Li, Z., Cheng, Y.: Review of the lifetime evaluation for the IGBT module. Trans. China Electrotechnical Soc. 36(12), 2560–2575 (2021). (in Chinese) 5. Sun, P., Tian, Y., Pou, J., Konstantinou, G.: Beyond the MMC: extended modular multilevel converter topologies and applications. IEEE Open J. Power Electron. 3, 317–333 (2022) 6. Chuanbao, Y., Mei, Y., Tingting, L., et al.: Analysis of the technical application of full power variable frequency pumped storage units. J. Hydropower Pumped Storage 6(05), 56–61 (2020). (in Chinese) 7. Xu, X., Zheng, Z., Wang, K., Yang, B., Li, Y.: A carrier-based common-mode voltage elimination method for back-to-back three-level NPC converters. IEEE Trans. Power Electron. 37(3), 3040–3052 (2022) 8. Weilun, P., Jianguo, J., He, L., et al.: A space vector modulation strategy for five level stacked multi unit converters based on capacitor voltage balance. Electr. Measur. Instrum. 54(13), 24–29 (2017). (in Chinese) 9. Chongbin, Z., Qirong, J., Haiquan, F., et al.: Broadband frequency coupled impedance model and small signal stability analysis of back-to-back asynchronous interconnection system based on MMC. Chin. J. Electr. Eng. 43(10), 3691–3705 (2023). (in Chinese) 10. Wang, C., Zheng, Z., Wang, K., et al.: Analysis and control of modular multilevel matrix converters under branch fault conditions. IEEE Trans. Power Electron. 37(2), 1682–1699 (2022)

Optimization of Non-destructive Detection Method for Metal Pipelines Based on Magnetic Induction Tomography Jiawei Shi, Yi Lv(B) , and Jiawei Jiang Shenyang Aerospace University, Shenyang 110000, China [email protected]

Abstract. Pipeline transportation has become an indispensable way in production and life. However, the emergence of pipeline defects causes great harm, so timely detection of pipeline defects is crucial for all fields. At present, Magnetic Induction Tomography technology is applied to non-destructive health inspection of metal pipelines, which can infer the location of pipeline defects and visually reconstruct them. However, the traditional sensor array consisting of 12 coils can’t accurately recognize the defects categories when detecting defects of different shapes and depths. In order to solve this problem, the sensor array design is improved, which is composed of a pair of Helmholtz coils and 24 side-by-side detection coils. The experimental results show that the optimized sensor array can better recognize the variation amplitude of different defects and improve the identification degree of defects. Keywords: Magnetic Induction Tomography (MIT) · Sensor array · Metal pipelines · Optimization

1 Introduction Pipelines play an important role in industrial transport, transporting oil, water and natural gas. However, pipelines are vulnerable to physical damage and chemical corrosion, and defects such as cracks, pits and perforations may occur [1]. Consequently, there is an urgent need for non-destructive detection of pipeline health. However, the traditional X-ray, ultrasonic and magnetic flux leakage detection has some problems such as difficult detection [2], environmental pollution and application limitations [3]. Magnetic Induction Tomography (MIT) is a non-invasive imaging technique that was originally used in the medical field and had less application in the industrial field. MIT uses the conductivity distribution characteristics to reconstruct the information inside the measured object, which has the advantages of non-contact, safety, low cost and good penetration depth [4]. Therefore, the application of MIT to pipeline non-destructive detection can realize the visual inspection of pipeline interior. MIT has an early start abroad. In 1968, Peter realized MIT imaging of human body for the first time, laying the foundation for its application in medical research [5]. Subsequently, MIT was gradually applied to the industrial field. In 1993, Al-Zeibak designed © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 107–114, 2024. https://doi.org/10.1007/978-981-97-0877-2_12

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an MIT system based on metal salt solution and reconstructed it using filtered back projection [6]. In 1996, Peyton put forward a time-sharing multiplexing method for excitation coil and detection coil [7]. In 2001, Binns used electromagnetic imaging to monitor the flow of molten steel in pipelines in real time and verified its feasibility [8]. In 2006, Yin designed a new planar MIT system that can detect non-magnetic metal plate defects [9]. In 2012, L. Ma studied pipeline inspection and proposed a defects detection method for metal pipelines [10]. Although the domestic pipeline inspection field started late, it has made rapid progress in recent years. In 2014, Qian Hongliang developed a pipeline corrosion detector based on electromagnetic ultrasound to detect pipeline wall corrosion through reflected waves [11]. In 2018, Li Zhonghu found that when the depth of pipeline defects increased, the impedance amplitude was linearly proportional to the corrosion defects [12]. In 2019, Hu Tiehua used the online detection technology to realize the detection of pipeline metal loss under the condition of 8m/s [13]. In 2020, Wang Qi put forward a method based on Bayesian theory to realize the imaging of aluminum plate defects [14]. In 2022, Yuan Xin ‘an proposed a method based on the uniform eddy current effect to display the defects in the inner wall of pipelines [15]. In the same year, Shen Changyu developed a pipeline magnetized by a low-frequency electromagnetic sensor to detect internal defects in pressure-bearing pipelines [16]. This paper optimizes the non-destructive detection method of metal pipelines based on MIT. Firstly, the sensor array is composed of a pair of Helmholtz coils and 24 sideby-side detection coils by improving the traditional 12-plane coil array. Secondly, the variation rule of induced voltage data is analyzed, the approximate location of defects is located, and the filter backprojection algorithm is used to perform two-dimensional imaging of pipeline defects. Finally, the influence of the two sensor arrays on detecting different defect shapes and depths is compared and analyzed.

2 Principle 2.1 MIT Signal in Pipeline Non-destructive Detection According to Maxwell’s equations, MIT’s theoretical solution model can be obtained: ∇×

1 ∇ × A + jσ ωA = Js μ

(1)

where μ and σ are the permeability and conductivity, A is the vector magnetic potential, ω is the angular frequency, Js is the source current density. The forward problem of MIT is to obtain the detected data of the induced voltage, while the inverse problem is to reconstruct the distribution of the conductivity. The induced voltage can be derived from the vector magnetic potential A:  (2) V = A · dl c

where V is the induced voltage, and c is the integral path of the detection coil.

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Griffiths[17] used a quasi-static magnetic field to describe MIT with a two-coil structure. If the skin depth of electromagnetic wave is greater than the thickness of the target, it can be concluded that: B ∝ (ωε0 εr − jσ )ω B

(3)

where B is the secondary magnetic field, B is the major magnetic field, ε0 is the dielectric constant of vacuum, εr and σ are the relative permittivity and conductivity of the target conductor.  In the actual MIT detection, the voltage signal V V and the magnetic field signal  B B are proportional. However, there are differences in electromagnetic properties when applying MIT to metal pipelines and biological tissues detection. Compared to the biological tissues, the metal pipelines possess high conductivity. Also, it is recommended to use a lower frequency than the applying for medical detection under the premise of meeting the skin depth. 2.2 MIT Sensor Array for Pipeline Detection Traditional sensor array is in the form of planar symmetry, as shown in Fig. 1(a). Coil array is obtained by rotating one of the coils by 30°. An array of 12 coils is formed around the metal pipeline, among which the d1 coil is the excitation coil and the rest are the detection coils. According to the induced voltage data obtained by the detection coils, the defects of the metal pipeline are studied. 2.3 Optimization Methods of Sensor Array In the traditional sensor array, the excitation coil size is small, which may cause the excitation not to cover the entire model. To optimize the coil array, a pair of Helmholtz coils were used as excitation and 24 side-by-side coils were tested, as shown in Fig. 1(b). This design expands the excitation range and makes the excitation magnetic field distribution more uniform. In addition, the increased number of detection coils makes the induced voltage data denser, improving the accuracy of MIT image reconstruction.

Fig. 1. Three-dimensional diagram of coil array.

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2.4 Pipeline Defect Because pipeline defects are mostly caused by chemical corrosion of internal substances or external physical damage, these defects usually show a concave shape. Therefore, the defect is defined as the difference set between a cylindrical pipeline and a cuboid. Among them, the width of the cuboid defect is 10 mm, the depth is 4 mm and the depth is 20 mm. The defect is located at the intersection of the positive direction of the y axis and the pipeline in the xy plane. The defective pipeline is shown in Fig. 2.

Fig. 2. Defective pipeline plan.

2.5 Applied Reconstruction Algorithm MIT’s image reconstruction is based on induced voltage data to infer the conductivity distribution inside the object. The common algorithms include filter back projection algorithm, which uses the central slice theorem to reflect the conductivity distribution at different angles through projection data. In order to eliminate artifacts caused by backprojection, it is necessary to filter the projection data. The relationship between the induced voltage and the projected data can be inferred using the Radon transform:  ∞ S(t)eiγ Gst ds (4) p(θ, s) = −∞

where S(t) is the induced voltage signal, p(θ, s) is the projected data, γ is the gyromagnetic ratio, G is the gradient magnetic field.

3 Methods 3.1 Traditional Sensor Array MIT Inspection for Pipelines COMSOL Multiphysics was used to establish a three-dimensional metal pipeline system model, as shown in Fig. 3(a). The system consists of a 2.2 sensor array and a cylindrical aluminum pipeline of 100 mm length, with an outer radius of 31.4 mm and an inner radius of 25.6 mm, and an electrical conductivity of 3.774 × 107 S/m. The coil in the sensor array has a radius of 6 mm, a height of 1mm, and a thickness of 2 mm. A total of 12 coils are evenly distributed outside the metal pipeline with a radius of 36 mm. The frequency of the excitation coil is 1 kHz, the size is 10A, and the material is copper.

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3.2 Optimized Sensor for MIT Pipeline Detection The optimized coil is applied to the MIT pipe inspection, as shown in Fig. 3(b). The system uses the sensor array in 2.3 for detection, and the pipeline setup is the same as in 3.1. The radius of the excitation coil is 80 mm, the height is 2 mm, the width is 1 mm, and the vertical distance from the symmetrical center of the pipe is 46 mm. The detection coils are distributed side by side with 12 coils on both sides 36 mm away from the symmetric center of the pipeline, the radius is 4 mm, the height is 2 mm, and the width is 1 mm. The size and frequency of the excitation coil are consistent with the above.

Fig. 3. MIT pipeline inspection 3D model.

4 Results 4.1 MIT Inspection of Pipeline Defects In order to research the influence of defects on pipeline performance, the induced voltage of detection coil is analyzed. By longitudinally scanning the coil array along the pipeline direction, and taking the induced voltage data of one coil in the range of 20 mm to 80 mm, as shown in Fig. 4. Detect coil inducced voltage

Deteect coil induced d voltage

20

30

40

50

60

70

80 0

4.35

induced voltage(mV)

induced voltage(mV)

-0.19

3.85

-0.2

3.35

-0.21

2.85

-0.22

coil heeight(mm) defecve

(a) Traditional see

defect-free

20 0

30

40

50

60

70

80

coil heigh ht(mm)

defecve

defect-free

O Optimized sensorr array

Fig. 4. Coil induced voltage.

In Fig. 4, the endpoint position of the conventional coil array causes the induced voltage data to mutate, while the optimized coil array avoids this situation. Because the

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optimized coil size is larger, it has a wider range of eddy current detection. At the same time, the variation of induced voltage is axisymmetric, and the defect position is just within the symmetry axis. The experiment was performed by changing the length of the pipeline to 200 mm, and the results showed that the defects usually appeared on the axis of symmetry with the greatest range of induced voltage changes. Next, a two-dimensional pipeline section with a radius of 25.4 mm and a thickness of 6.2 mm was built using MATLAB, and a rectangular defect with a length of 5 mm and a width of 4 mm was created on the positive half-axis of the Y-axis. The conductivity of the pipeline is 3.774 × 107 S/m. Then, the filtered back projection algorithm is used for image reconstruction, as shown in Fig. 5. The results show that the reconstruction effect without filter is very poor, but the overall reconstruction effect is improved after adding filter, among which Ram-Lak filter has the best effect.

Fig. 5. Filter back projection algorithm for image reconstruction

4.2 MIT Measurement Results for Traditional Pipelines

-2.58

Three kinds of shape defect induced voltage -20 10

40

70 100 130 160 190 220

-2.68

coil height (mm)

-2.78 rectangle

trapezoid

(a) Traditional sensor array

Three kinds of shape defect induced voltage induced voltage (mV)

induced voltage (mV)

The defect shape of metal pipelines is usually rectangular, triangular and trapezoidal. The thickness of the defect is 10 mm and the volume is 1600 cubic mm. The pipeline radius is 100 mm, the thickness is 50 mm, and the length is 200 mm. The defects are located at 0 mm, 20 mm and 40 mm from the pipeline surface.

1.85

1.35 40

70

100

130

160

coil height(mm) triangle

rectangle

trapezoid

(b) Optimized sensor array

Fig. 6. 20 mm depth of different defects induced voltage.

triangle

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As shown in Fig. 6(a), at a depth of 20 mm, the induced voltage trend of the three defects is roughly the same, but the rectangle is larger than the trapezoid, and the trapezoid is larger than the triangle. Although the three defects have the same area, they are different in shape and have different degrees of interference with the magnetic field. 4.3 MIT Measurement Results for Sensor Optimization It is difficult for traditional sensor arrays to recognize defects of different depths and shapes when detecting defects. Therefore, the optimized sensor array was used for MIT measurement analysis without changing the pipeline settings. Figure 7 shows the influence of different depths on the induced voltage, while Fig. 6(b) shows the influence of different defects on the induced voltage at a depth of 20 mm. Rectangular defect induced voltage

Depth is 0 Depth is 20 Depth is 40

(a) rectangle

Triangular defect induced voltage

Trapezoidal defect induced voltage

Depth is 0 Depth is 20 Depth is 40

(b) triangle

Depth is 0 Depth is 20 Depth is 40

(c) trapezoid

Fig. 7. Optimized induction voltage at different depths.

Through comparative analysis, because the optimized sensor array can generate strong enough excitation signal, the change of measurement results is more obvious. In addition, increasing the number of detection coils can improve the resolution and sensitivity of the system, making the measurement results easier to recognize.

5 Conclusion By improving the traditional sensor array, a sensor array consisting of a pair of Helmholtz coils and 24 side by side detection coils is used to optimize the non-destructive detection method for metal pipelines. The experimental results show that the pipeline defects usually appear on the symmetry axis of the maximum range of induced voltage change. The effect of Ram-Lak filter is better in image reconstruction. The induced voltage of rectangular defect is larger than that of trapezoid defect, and trapezoid defect is larger than that of triangle defect, and the induced voltage decreases gradually with the increase of depth. The optimized sensor array increases the variation amplitude of induced voltage and improves the discrimination of different defects. This proves that the optimized sensor array can substantially improve the detection of pipeline defects. Acknowledgments. This work was supported in part by Foundation of Liaoning Educational Committee under Grant JYT2020049.

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References 1. Tian, C., Ma, Y., Tian, J.: Application analysis of MT and PT testing in heat supply pipeline. In: Proceedings of the Workshop on Construction and Efficient Operation of Heat Supply Engineering in 2022, pp. 1161–1172 (2022). (in Chinese) 2. Li, J., Hao, X., Guang, R.: Application status and role of non-destructive testing technology in natural gas pipelines. China Pet. Chem. Stand. Qual. 40(01), 62–63+66 (2020). (in Chinese) 3. Xianming, L., Ping, L., Jiangtao, C., et al.: Research progress of leak detection and location technology in long distance oil and gas pipelines. Control. Eng. 25(04), 621–629 (2018). (in Chinese) 4. Ganesh, M., Ravan, M., Amineh, R.K.: Electromagnetic induction imaging at multiple depths with a single coil. IEEE Trans. Instrum. Measur. 70, 1–9 (2021). https://doi.org/10.1109/TIM. 2021.3050659 5. Tarjan, P.P., McFee, R.: Electrodeless measurements of the effective resistivity of the human torso and head by magnetic induction. IEEE Trans. Biomed. Eng. BME-15(4), 266–278 (1968). https://doi.org/10.1109/TBME.1968.4502577 6. Al-Zeibak, S., Saunders, N.H.: A feasibility study of in vivo electromagnetic imaging. Phy. Med. Biol. 38(1), 151–160 (1993) 7. Peyton, J.A., Yu, Z.Z., Lyon, G., et al.: An overview of electromagnetic inductance tomography: description of three different systems. Meas. Sci. Technol. 7(3), 261–271 (1996) 8. Binns, R., Lyons, A.R.A., Peyton, J.A., et al.: Imaging molten steel flow profiles. Meas. Sci. Technol. 12(8), 1132–1138 (2001) 9. Yin, W., Peyton, J.A.: A planar EMT system for the detection of faults on thin metallic plates. Meas. Sci. Technol. 17(8), 2130–2135 (2006) 10. Ma, L., Wei, H.Y., Soleimani, M.: Pipelines inspection using magnetic induction tomography based on a narrowband pass filtering method. Prog. Electromagnet. Res. M 23, 65–78 (2012). https://doi.org/10.2528/PIERM11111109 11. Qian, H., Wang, Y., Yan, C., et al.: Development of Metal pipeline corrosion detector based on electromagnetic ultrasound. Non-destructive Test. 37(06), 24–28+32 (2015). (in Chinese) 12. Li, Z., Tian, W.: Research on eddy current detection of corrosion defects on inner wall of pipeline. Comput. Simul. 35(07), 331–334+403 (2018). (in Chinese) 13. Hu, T., Guo, J.: Development and application of new detection technology and equipment in oil and gas pipelines. Nat. Gas Ind. 39(01), 118–124 (2019). (in Chinese) 14. Qi, W., Jingwei, Z., Ronghua, Z., et al.: Research on electromagnetic imaging of metal defects based on Bayesian statistical model. Chin. J. Sci. Instrument 41(01), 47–55 (2020). (in Chinese) 15. Xin’an, Y., Guangtai, Z., Wei, L., et al.: Development of electromagnetic imaging teaching experimental system for pipe inner wall defects. Lab. Res. Explor. 41(03), 169–173 (2022). (in Chinese) 16. Changyu, S., Yongqi, W., Yang, L., et al.: Low frequency electromagnetic detection of inner wall damage defects of pressure bearing pipelines. Non-Destr. Test. 44(09), 45–51 (2022). (in Chinese) 17. Griffiths, H., Stewart, W.R., Gough, W.: Magnetic induction tomography: a measuring system for biological tissues. Ann. New York Acad. Sci. 873(1), 335–345 (1999)

Analysis of Transient Voltage Stability Under the Interaction Between HVDC Receiving End and New Energy Station Zunmin Liu1 , Deping Ke1(B) , Jian Xu1 , Xin Sun2 , and Xiaojiu Ma3 1 School of Electrical Engineering and Automation, Wuhan University, Wuhan 430072, China

{kedeping,xujian}@whu.edu.cn

2 Electric Power Research Institute of Henan Power Grid Co.,Ltd. Grid State,

Zhengzhou 450052, China 3 Henan Power Grid Co.,Ltd. Grid State, Zhengzhou 450003, China

[email protected]

Abstract. When Short-circuit fault occurs at the receiving end of High Voltage Direct Current (HVDC), it is easy to cause voltage instability of the new energy station at HVDC receiving end. Therefore, the mechanism of the interaction between the new energy station and the HVDC receiving end and its influence on the voltage stability are analyzed. Firstly, the mathematical model of the new energy station is established by taking the photovoltaic (PV) station as an example, and its active power-voltage and reactive power-voltage characteristics are deduced. The active-voltage characteristics determine the upper limit of voltage recovery rate at the receiving end. The reactive power-voltage characteristics show that the reactive power characteristics of the new energy station are similar to that of the capacitor. Secondly, through the power flow equation of the HVDC receiving end, the influence of the active power-voltage characteristics on the voltage stability of the receiving end is analyzed. Finally, the deduced active power-voltage and reactive power-voltage characteristics of the new energy station are verified by simulation, and the output active power of the new energy station will affect the voltage recovery rate at HVDC receiving end, and thus affect the voltage stability. Keywords: HVDC · New energy station · Transient voltage stability · Receiving network

1 Introduction In years of development, China has strengthened the construction of a strong power grid with UHVDC network as the core of the million-volt AC-DC system, and HVDC technology has been widely used in the layout of “west-east power transmission, North-South mutual supply, and national networking” [1]. However, with the large-scale photovoltaic station and wind farm linked to the grid, the HVDC receiving end presents the characteristics of low inertia and low damping, and its voltage stability is also greatly challenged. Therefore, it is necessary to study the interactive coupling between new energy and HVDC receiving end and its essence of transient voltage instability. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 115–127, 2024. https://doi.org/10.1007/978-981-97-0877-2_13

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In present-day conditions, there are two categories of the voltage stability of HVDC receiving end which are static voltage stability and transient voltage stability. When it comes to the static voltage stability problem, its research has been relatively mature. Literature [2] puts forward the analytical expression of the AC and DC voltage stability criterion, and theoretically verifies the compatibility of the criterion and the generalized Jacobian matrix criterion. Literature [3] deduces the voltage stability criterion of the multi-fed LCC-HVDC system based on the eigenvalue decomposition of the generalized Jacobian matrix. Based on sensitivity analysis, literature [4] divides the physical quantities of HVDC system into state variables and control variables, and analyzes the voltage stability of the HVDC receiving end under different control modes in turn. To solve the transient voltage stability problem, literature [5] analyzes the stability problem of HVDC system based on transient energy function method, and gives its stability margin. However, due to the complex construction and calculation of transient energy function, this method is not suitable for engineering application. Literature [6] proposes an S-type VDCOL control curve. The consequence of the simulation shows that the raised VDCOL curve is able to promote the voltage stability at the HVDC receiving end, but the mechanism of the influence of the VDCOL curve on the voltage stability is not pointed out. Literature [7] verifies that the inverter station can inject reactive power into the receiving end of the HVDC under certain conditions through time-domain simulation method, and designs a new HVDC system control strategy accordingly, which can improve the voltage stability of the HVDC receiving end, but lacks the setting method of the parameter in the control strategy. In literature [8], the singular induced bifurcation criterion based on the Differential Algebra Equation (DAE) is used to estimate the voltage stability of the system. However, the computation time of this method is longer and further optimization is needed. Based on the eigenvalue analysis method of transient dynamics, literature [9] analyzes the voltage stability problem in the medium time scale. However, it is more difficult and complicated for large power systems to calculate eigenvalue, therefore the abovementioned method could only be applicable to the voltage stability analysis of small power systems. The dynamic reactive power-voltage characteristics of new energy station have become a research hotspot in the interaction between new energy station and HVDC receiving end [10]. On the basis of the dual analysis method, literature [11] proposed the reactive power-power angle equation of grid-following inverters, which provided a theoretical basis for analyzing the reactive power supporting capability of grid-following inverters. Reference [12] deduces the transient reactive power analytic expression of permanent magnet synchronous generator (PMSG) and doubly-fed induction generator (DFIG), which provides theoretical support for computing analytic solution of reactive power and voltage characteristics of PMSG or DFIG and HVDC system in the transient process of reference [13]. Based on the superposition theorem, literature [14] established the transient reactive power characteristics of PMSG and DFIG under the condition of voltage step. Literature [15] derived the analytical expression of the stator transient voltage of DFIG under threephase short-circuit fault but did not consider the transient voltage characteristics of DFIG under asymmetric fault. Based on the method of equivalent fault source, literature [16] solves the analytical expression of the current of DFIG when the grid voltage drops.

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To sum up, most of the research on voltage stability analysis of HVDC system in the existing literature focused on improving HVDC control mode to increase voltage stability. By contrast, few studies threw light on the essence of transient voltage instability. On the other hand, a great number of existing literature studies on the reactive power-voltage characteristics of new energy station focus on the transient reactive power-voltage characteristics of PV station and wind farm during the LVRT, and few studies on the transient active power-voltage characteristics of PV station and wind farm while connecting to the HVDC receiving end. In this paper, the active power-voltage and reactive power-voltage characteristics of new energy station (NES) are established, and its influence of the output active power and reactive power on the voltage stability is analyzed. Secondly, on the ground of the power flow equation, this paper deduces the analytical expression of the bus voltage in the transient process under the condition of NES connected to HVDC receiving end and analyzes the effect of the output active power of NES on the voltage of the HVDC receiving end. The influence is mainly manifested as that the active powervoltage characteristics of NES determine the upper limit of the voltage recovery rate at the receiving end. Then the transient voltage stability of HVDC receiving end is affected.

2 Active Power-Voltage and Reactive Power-Voltage Characteristics of New Energy Station 2.1 Theoretical Analysis In this paper, the transient active power-voltage and reactive power-voltage characteristics of the new energy station are established by taking the photovoltaic station as an example. The typical PV station main circuit topology and its control block diagram are shown in Fig. 1. In Fig. 1, the inverter is linked to the power grid through LC filter. L, Cf and R are filter inductance, resistance, and capacitance respectively. Ua , Ub , Uc , Ia , Ib and Ic are output voltage and current for grid-connected inverter. ICa , ICb and ICc are the current of the capacitor. Uga , Ugb , Ugc , Iga , Igb and Igc are the grid voltage and current. θ is the phase angle of the phase-locked loop(PLL) at grid side. Lg is the equivalent inductance of the grid. Us is the equivalent voltage at grid side. Idref and Iqref are current instructions (given by outer power loop or LVRT) in the dq coordinate system. The voltage equation of the filter capacitor in dq coordinate system is as follows:  sugd = ωugq − (1/Cf )igd + (1/Cf )id (1) sugq = −ωugd − (1/Cf )igq + (1/Cf )iq In the formula (1), s is the differential operator in the Laplace transform. ugd and ugq are the grid voltage. igd and igq are the grid current. id and iq are the current of the inverter. The subscript ‘d’ and ‘q’ means d axis and q axis in the dq conversion. ω is the grid angular frequency. The current equation of the filter inductor is:  sid = ωiq − RL id − L1 id − L1 ugd + L1 ud (2) siq = −ωid − RL iq − L1 iq − L1 ugq + L1 uq

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Fig. 1. PV station main circuit topology and control block diagram

In the Eq. (2), ud , uq , id and iq are the voltage and current of the inverter. Feedforward decoupling control is adopted for the inverter, and its equation is as follows: ⎧   ⎨ udref = Kp + Ki (idref − id ) + ugd − ωLiq s   (3) ⎩ uqref = Kp + Ki (iqref − iq ) + ugq + ωLid s In the Eq. (3), Kp and Ki are the proportional coefficient and integral coefficient of the inner current loop respectively. By substituting formula (3) into formula (1) and tuning the relation with the parameters of a typical type I system [17], we can obtain:  1 id = 4.5T 2 s2 +3T idref s s+1 s (4) 1 iq = 4.5T 2 s2 +3T s+1 iqref s

s

In the formula (4), Ts is the PWM switching period. Since the PWM switching frequency is very high, and the voltage stability is mostly studied in electromechanical transient models, formula (4) can be simplified as follows:  id ≈ idref (5) iq ≈ iqref By substituting formula (5) into formula (1) and (2), we get:  igd = idref + ωCf ugq − sCf ugd igq = iqref − ωCf ugd − sCf ugq

(6)

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In formula (6), if the output voltage vector of the PLL aligns with the d-axis projection of grid voltage vector, then:    du P = 23 ugd igd = 23 ugd idref − Cf dtgd (7) 2 − 3u i Q = − 23 ugd igq = 23 ωCf ugd 2 gd qref Equation (7) shows that the output active power of PV station is related to the voltage recovery rate at the grid side, and its reactive power-voltage characteristic is similar to capacitor’s, which is a quadratic function of the voltage. 2.2 Active Power-Voltage and Reactive Power-Voltage Characteristic Analysis of New Energy Station According to the active-voltage characteristics of NES, when the grid voltage meets formula (8), the NES injects active power into the power grid, while when the grid voltage meets formula (9), the NES absorbs active power from the grid. idref dugd < dt Cf

(8)

dugd idref > dt Cf

(9)

According to the reactive power-voltage characteristics of NES, its reactive power and the grid voltage show quadratic function characteristics, similar to the characteristics of the capacitor, as shown in Fig. 2. Therefore, when iq is constant, if the grid voltage drops, the NES will reduce the output reactive power, resulting in further voltage drop at the grid side; if there is overvoltage at the grid side, the NES will increase the output reactive power, further aggravating the overvoltage at the grid side.

Fig. 2. Reactive-voltage characteristics of new energy station

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3 Analysis of Interactive and Coupling Between HVDC Receiving End and New Energy Station 3.1 Mathematical Model Building The typical interactive and coupling system between HVDC receiving end and new energy station is shown in Fig. 3. Ud is the DC voltage, Id is the DC current, Pd and Qd is HVDC transmission power, Qc is the reactive power of the compensated capacitor at the receiving end, UP is the bus voltage, PG and QG are the output active and reactive power of synchronous generator. PPV and QPV are the output active power and reactive power of the photovoltaic station, XG and XPV are the equivalent inductance of the branch of the synchronous generator and the equivalent inductance of the branch of the photovoltaic station, UG and UPV are the voltage of the synchronous generator the photovoltaic station, respectively.

Fig. 3. Typical interactive and coupling system of HVDC receiving end and new energy station

When commutation failure occurs, the power of the system meets the following requirements: ⎧  2 U ⎪ ⎨ Qc = QcN UpNp (10) Q = Qc + QG + QPV ⎪ ⎩ d Pd + PG + PPV = 0 In formula (10), QcN and UpN are respectively the output reactive power emitted by the compensating capacitor and the bus voltage of receiving end under rated working conditions. The AC bus transient voltage of receiving end meets: ⎧

2 2 ⎪ ⎨ Up = (UG + (UG ) + (δUG ) QG XG UG = UG (11) ⎪ ⎩ δU = PG XG G UG In formula (11), UG is the vertical component of the terminal voltage of the synchronous machine, and δUG is the horizontal component of the terminal voltage of the synchronous machine.

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By substituting Eqs. (10) into (11), the AC bus transient voltage of receiving end Up in the transient process can be obtained as follows: 

A + B − C(Pd + PPV )2 (12) Up = D where the expression of A, B, C and D is: ⎧ XG QcN ⎪ ⎪ A = 2 + 2 ⎪ UpN ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ B = 4 XG QcN + 2 UpN ⎪ XG4 QcN ⎪ ⎪ ⎪ 4 U4 ⎪ C = 4 UpN ⎪ G √ XG Q ⎪ ⎪ ⎩ D = 2 2 cN U U pN

XG2 QcN (Qd −QPV ) 2 U2 UpN G XG2 QcN (Qd −QPV ) 2 U2 UpN G



+1 +1

(13)

G

According to Eq. (13), the AC bus voltage Up in the transient process is related to Pd and Qd transmitted by HVDC inverter and the output active power PPV and reactive power QPV of the photovoltaic station. Combined with active power-voltage and reactive power-voltage characteristics of PV station derived from formula (7), the interactive coupling mechanism between the HVDC receiving end and PV station can be analyzed in detail. 3.2 Mechanism Analysis of the Influence of Active Power-Voltage Characteristics on Voltage Stability of HVDC Receiving End In formula (13), taking the partial derivative of PPV , we get: C(P +P

)

PV  √d 2D A+ B−C(Pd +PPV )2 ∂Up =−

√

PN n2 2π fn2 Bm Ac n3

(14)

Under this condition, the VSR works in the inductive state and adjusts the secondary voltage to the rated voltage U N at the working point. Then the equivalent inductance X P of VSR in inductive state and the X eq of secondary side are: 2  (15) XP = n3nU2 N /PN LP =

XP ω

(16)

4 Analysis of Simulation Characteristics of Double Winding CT Following the design approach outlined previously, the core parameters adopted in this paper are shown in Table 1. First of all, several different primary currents are set to verify the compensation effect of VSR on the measuring and power harvesting equipment. As shown in Fig. 5, the output load voltage of the measuring and power harvesting equipment is compared with that of the traditional current transformer under different currents. As can be seen from Fig. 5, when the input current undergoes fluctuations, the secondary side voltage of the conventional current transformer is reduced when the input current is low; when the primary current is large, the core is saturated, the voltage waveform is distorted, and the output voltage cannot be stable. In contrast, measuring and power-harvesting equipment with VSR can sustain a relatively consistent voltage amidst current fluctuations.

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Name

Parameter size

Material

Silicon lamination

Load side turn number

180

Load side turn number

90

Inner diameter (mm)

50

Outer diameter (mm)

90

High (mm)

100

Rated voltage (V)

80

Rated power (W)

30

Fig. 5. Simulation results of the load simulator

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5 Conclusion In this paper, the power harvesting transformer in transmission line is designed based on double winding control method. The VSR is dynamically regulated by this method to output and stabilize the voltage according to the current on the primary side. When the primary side current is small, the excitation compensation mode is adopted to increase the output power and voltage; when the primary side current is too large, the demagnetization mode is used to reduce the voltage and output the desired power. Finally, the simulation and experimental results show that the integrated equipment of measurement and induction based on VSR proposed in this paper can maintain the stable output voltage of 80V in the range of 60A-500A. Acknowledgement. This work was supported by Key Research and Development Program of Shanxi Province (202102060301012).

References 1. Ashraf, N., Sheikh, S.A., Khan, S.A., Shayea, I., Jalal, M.: simultaneous wireless information and power transfer with cooperative relaying for next-generation wireless networks: a review. IEEE Access 9, 71482–71504 (2021) 2. Zhuang, Y., Xu, C.: Improving current transformer-based energy extraction from AC power lines by manipulating magnetic field. IEEE Trans. Ind. Electron. 67(11), 9471–9479 (2020) 3. Wang, Z., et al.: A self-sustained current sensor for smart grid application. IEEE Trans. Ind. Electron. 68(12), 12810–12820 (2021) 4. Bhuiyan, R.H., Dougal, R.A., Ali, M.: A miniature energy harvesting device for wireless sensors in electric power system. IEEE Sensors J. 10(7), 1249–1258 (2010) 5. Davarpanah, M., Sanaye-Pasand, M., Iravani, R.: A saturation suppression approach for the current transformer—Part I: Fundamental concepts and design. IEEE Trans. Power Deliv. 28(3), 1928–1935 (2013) 6. Davarpanah, M., Sanaye-Pasand, M., Iravani, R.: Saturation suppression approach for the current transformer—Part II: Performance evaluation. IEEE Trans. Power Del. 28(3), 1936– 1943 (2013) 7. Saeed, S., Alinejad-Beromi, Y.: Prevention of the current transformer saturation by using negative resistance. IET Gener. Transm. Distrib. 15(3), 508–517 (2021) 8. Hu, J., Luo, J., Zheng, Y., Li, K.: Graphene-grid deployment in energy harvesting cooperative wireless sensor nerworks for green IOT. IEEE Trans. Ind. Informat. 15(3), 1820–1829 (2019) 9. Ruan, T., Chew, Z., Zhu, M.: Energy-aware approaches for energy harvesting powered wireless sensor nodes. IEEE Sens. J. 17(7), 2165–2173 (2017) 10. Dobzhanskyi, O., et al.: Axial-flux PM disk generator with magnetic clear for oceanic wave energy harvesting. IEEE Access 7, 44813–44822 (2019)

A Novel Six-Element Multi-resonant DC-DC Converter for Wide Input Voltage Range Applications Nanzhe Wei(B) , Qiaozhi Xue, Jiang Shang, Ziqian Ren, Xinqi Li, and Chunguang Ren College of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan, China [email protected]

Abstract. A multi-element wide gain resonant converter with trap function is proposed in this paper. Compared with the conventional LLC converter, the converter proposed in this paper can maintain the output voltage stable in a wider input voltage range. Besides, the third harmonic is used to deliver power, improving efficiency of the converter. The operating principle, voltage gain characteristics and impedance characteristics of the converter is described and analyzed in detail, and the main circuit parameters is designed in the paper. The simulation results demonstrated that the wide voltage gain can be realized by the proposed converter. Meanwhile ZVS for the primary side switches and ZCS for the secondary side switches can be achieved, and great soft-start performance can be displayed. Keywords: DC-DC converter · multi-resonant structure · wide input voltage range · third harmonic

1 Introduction In recent years, with the shortage of traditional fossil fuels and the worsening of environmental pollution, traditional non-renewable energy sources such as coal and oil are gradually being replaced by renewable energy sources such as solar and wind energy. However, in solar and wind power generation systems, there is a wide range of fluctuation in output voltage, which can vary greatly with the change in weather conditions [1, 2]. The supply voltage is usually varied for the electric motor of electric vehicle and hybrid vehicle applications. Portable electronic products also need to adapt to different battery voltages and load requirements. All of these applications require the DC-DC converters with a wide voltage gain range. LLC resonant converter can achieve zero voltage switching (ZVS) for primary side switches and zero current switching (ZCS) for secondary side switches, therefore switching losses is reduced and conversion efficiency is improved [3–5]. In addition, the resonant inductor can be replaced by the leakage inductance of the transformer to promote magnetic integration and further improve power density. Typically, the LLC converter adopts variable frequency control. When operating in the under-resonant state, the converter’s gain quickly responds to frequency variations, but when operating in the overresonant state, the voltage gain decreases slowly with increasing frequency. Therefore, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 164–171, 2024. https://doi.org/10.1007/978-981-97-0877-2_18

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a wide frequency adjustment range is required to meet the gain requirements when the LLC converter is applied in a wide voltage range situation, which is not friendly to the design of magnetic components. In order to balance the voltage gain and efficiency of the LLC converter, a lot of research on the control strategy and topology of the LLC converter have been conducted by domestic and foreign scholars. In [6], the converter’s voltage gain is increased by adding resonant branches. In [7] and [8], the converter switches between the half-bridge and full-bridge LLC to achieve wider voltage gain. However, it faces the problem of smooth switching between the two states. A three-level LLC converter proposed in [9], which is composed of two half-bridges to achieve wide voltage gain. However, when the voltage gain increase, the switch loss also increases accordingly. In [10] and [11], some five-element multi-resonant converters were proposed, which can not only achieve wide gain, but also use the high harmonics to transmit power and achieve efficiency improvement. However, the voltage gain characteristics at over-resonance is mainly improved and the wide voltage gain at under-resonance is not achieved in these multiresonant converters. To overcome the drawbacks of LLC converter in balancing wide voltage gain and high efficiency, a six-element-based multi-resonant LLC converter is proposed in this paper. It can achieve a wider range of input voltage while ensuring higher efficiency through frequency control. The working principle and characteristics of the converter is introduced, and a simulation model is constructed. The simulation results indicate that the converter has the significant advantages in terms of wide voltage gain.

2 Six-Element Resonant Converter 2.1 Circuit Topology The proposed six-element resonant converter is shown in Fig. 1. Based on the traditional LLC structure, the fundamental branch L r1 C r1 is connected in parallel with the third harmonic branch L r3 C r3 , and series branch L p C p is used instead of the transformer excitation inductance. S1 ~ S4 forms a full bridge inverter structure, D1 ~ D4 forms a full bridge rectifier structure. The fundamental branch L r1 C r1 , the third harmonic branch L r3 C r3 , and the series branch L p C p form the resonant tank together.

Fig. 1. The topology of the proposed converter.

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2.2 Operation Principles Similar to LLC converter, frequency modulation method is used in this converter. It is divided into three kinds of operating sates based on the relationship between series resonant frequency of the L r1 and C r1 and the switching frequency. Only the waveform at the under-resonant state is analyzed here. The working principles of the quasi-resonant and over-resonant sates are similar to the under-resonant state and will not be described here. When the operating frequency of the converter is lower than the series resonant frequency of L r1 and C r1 , the waveform of the converter is shown in Fig. 2. There are a total of 12 operating modes within one switching period.

0

0

p 0

0

0

1

2

3

4 5

6

7 8 9 10

11

12

Fig. 2. Operation waveforms of the proposed converter.

2.3 Characteristics Analysis The AC equivalent circuit based on fundamental wave analysis method is shown in Fig. 3. Where Req is the equivalent resistance. Req =

8n2 Ro π2

where: n is the transformer ratio, Ro is the output resistance.

(1)

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Fig. 3. Equivalent FHA model of the proposed converter.

From Fig. 3, it can be seen that compared to traditional LLC converters, the multiresonant converter has four different resonant frequencies. When operating at the resonant frequency, the impedance of the LC series resonant branch is 0, and the impedance of the LC parallel resonant branch is infinite. Based on this, the normalized resonant frequency can be obtained as formula (3). Definition: h=

Lp Cp Cr3 Lr3 ,g = ,k = ,q = Lr1 Cr1 Lr1 Cr1

⎧ ⎨ fr1 = ⎩ frn =

√1 , f = √1 fr1 Lr1 Cr1 r3 hg 1+g √1 fr1 (1+h)g fr1 , frp = kq

2π

(2)

(3)

Among them, f r1 represents the resonant frequency of the fundamental wave branch L r1 C r1 , f r3 represents the resonant frequency of the third harmonic branch L r3 C r3 , f rn represents the notch frequency of the parallel resonant branch L r1 C r1 L r3 C r3 , and f rp represents the resonant frequency of the serious branch L p C p . From the fundamental wave equivalent model, the voltage gain of the proposed converter is: M =     1+

1

2



 f ∗ − f1∗ hf ∗ − gf1∗



 kf ∗ − qf1∗ f ∗ − f1∗ +hf ∗ − gf1∗

+



 2 Q f ∗ − f1∗ hf ∗ − gf1∗

 f ∗ − f1∗ +hf ∗ − gf1∗

(4)

In formula (4), f s is the switching frequency of multi-resonant converters, f * is the is the youngest value of the switching frequency; Q is quality factor;Z o is the characteristic impedance. According to formula (5)(6)(7), the voltage gain characteristic graph is shown in Fig. 4.

f ∗ = fs fr1 (5)

Q = Z0 Req Z0 =



Lr1 Cr1

(6) (7)

From Fig. 4, it can be seen that when f s is higher than f r1 , the gain characteristics of the proposed converter is greater than that of the LLC converter. Between f r1 and

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2f r1 , the voltage gain can achieve a monotonic variation from 1 to 0. Within a smaller range of switching frequency, lower voltage gain can be achieved, and additional third harmonic can be transmitted. When f s is lower than f r1 , the proposed converter has a higher voltage gain compared to the LLC converter within a narrower range of switching frequency. Taking all the above analysis into consideration, the proposed converter has a wider voltage gain throughout the entire operating frequency range.

2 p

1

0

1

2

3

4

Fig. 4. Comparison of voltage gain between LLC and the proposed converter.

3 Parameter Design 3.1 Influence of k and Q on Gain Characteristics 7

6 q

6

q

5

q

5 4

q

4 3

3 2

2

1

1 0 0

0.5

1

1.5

2

2.5

3

3.5

0 0

0.5

1

1.5

2

2.5

3

3.5

Fig. 5. Influence of k, q and Q on gain.

It can be seen from Fig. 5 that when the f s is higher than f r1 , the voltage gain characteristics almost is not affected by k and q. When f s is lower than f r1 , the maximum value of voltage gain increases with the decrease of q and k. Therefore, we should choose smaller values for k and q as much as possible. 3.2 Influence of Q on Gain Characteristics As shown in Fig. 5, with the value of Q decreased, the maximum voltage gain increases, but the response of the gain following frequency decreases when the frequency is higher

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than the resonant frequency. Therefore, from the perspective of wide voltage gain, a smaller Q value is better. While from the perspective of frequency response, a larger Q value is preferred. Therefore, a compromise is needed. Based on the above analysis, the final selection is h = 0.6, g = 0.185, k = 15, q = 0.2, Q = 0.18.

4 Simulation Result The design targets and related parameters are shown in Table 1. Table 1. The parameters of the simulation model. Parameter

Value

Input voltage V in /V

200 ~ 400

Output voltage V o /V

48

Output Power Po /W

500

Resonant inductance L r1 /μH

38.4

Resonant inductance L r3 /μH

23.04

Parallel branch inductance L p /μH

576

Resonant capacitance C r1 /nF

66

Resonant capacitance C r3 /nF

12.2

Parallel branch capacitance C p /nF

13.2

Transformer turns ratio n

36: 6

Figure 6 show the simulation waveforms under full load conditions with different input voltages. It can be seen that throughout the voltage range, the primary side devices achieve ZVS and secondary side devices achieve ZCS.

Fig. 6. Full-load simulation waveform with different input voltage.

Figure 7 presents the soft-start waveforms of the converter. The converter starts at the notch frequency using a control strategy that adjusts the duty cycle before the frequency modulation. It can be seen that during the start-up, the converter exhibits minimal current impact and the voltage rises smoothly, indicating excellent soft-start performance.

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Fig. 7. Soft-start simulation waveforms.

5 Conclusion A wide-gain six elements based multi-resonant converter is proposed in this paper. Compared with LLC converter, the proposed converter achieves a wider range of input voltage adjustment. In addition, the third harmonic can be used for power transmission, which can improve the efficiency of the converter. Theoretical analysis and parameter design of the converter are conducted. Finally, the voltage gain and soft-switching characteristics of the converter are verified through simulation. Acknowledgment. This work was supported by the National Nature Science Foundation of China under grant 51807130 and Key Research and Development Program of Shanxi Province (202102060301012).

References 1. Lasseter, R.H.: Smart distribution: coupled microgrids. In: Proceedings of the IEEE, vol. 99, no. 6, pp. 1074–1082 (2011). https://doi.org/10.1109/JPROC.2011.2114630 2. Nejabatkhah, F., Li, Y.W.: Overview of power management strategies of hybrid AC/DC microgrid. In: IEEE Transactions on Power Electronics, vol. 30, no. 12, pp. 7072–7089 (2015). https://doi.org/10.1109/TPEL.2014.2384999 3. Kundu, U., Yenduri, K., Sensarma, P.: Accurate ZVS analysis for magnetic design and efficiency improvement of full-bridge LLC resonant converter. In: IEEE Transactions on Power Electronics, vol. 32, no. 3, pp. 1703–1706 (2017). https://doi.org/10.1109/TPEL.2016.260 4118 4. Yang, B., Lee, F.C., Zhang, A.J., Huang, G.: LLC resonant converter for front end DC/DC conversion, APEC. In: Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.02CH37335), Dallas, TX, USA, 2002, pp. 1108–1112, vol. 2 (2002). https://doi.org/10.1109/APEC.2002.989382 5. Kim, J.-W., Park, M.-H., Lee, B.-H., Lai, J.-S.: Analysis and design of LLC converter considering output voltage regulation under no-load condition. In: IEEE Transactions on Power Electronics, vol. 35, no. 1, pp. 522–534 (2020). https://doi.org/10.1109/TPEL.2019.2914375 6. Kim, C.-E., Baek, J., Lee, J.-B.: Three-switch LLC resonant converter for high-efficiency adapter with universal input voltage. In: IEEE Transactions on Power Electronics, vol. 36, no. 1, pp. 630–638 (2021). https://doi.org/10.1109/TPEL.2020.3002383

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7. Sun, W., Xing, Y., Wu, H., Ding, J.: Modified high-efficiency LLC converters with two split resonant branches for wide input-voltage range applications. In: IEEE Transactions on Power Electronics, vol. 33, no. 9, pp. 7867–7879 (2018). https://doi.org/10.1109/TPEL.2017.277 3484 8. Liang, Z., Guo, R., Wang, G., Huang, A.: A new wide input range high efficiency photovoltaic inverter. In: 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, USA, 2010, pp. 2937–2943 (2010). https://doi.org/10.1109/ECCE.2010.5618217 9. Lee, I.-O., Moon, G.-W.: Analysis and design of a three-level LLC series resonant converter for high- and wide-input-voltage applications. In: IEEE Transactions on Power Electronics, vol. 27, no. 6, pp. 2966–2979 (2012). https://doi.org/10.1109/TPEL.2011.2174381 10. Zhang, X., Jing, J., Guan, Y., Dai, M., Wang, Y., Xu, D.: High-efficiency high-order CL-LLC DC/DC converter with wide input voltage range. In: IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10383–10394 (2021). https://doi.org/10.1109/TPEL.2021.3067715 11. Zhao, Q., Liu, W., Wang, Y., Wang, D., Wu, N.: A novel multiresonant DC–DC converter with wide output-voltage range. In: IEEE Transactions on Power Electronics, vol. 35, no. 6, pp. 5625–5638 (2020). https://doi.org/10.1109/TPEL.2019.2948217

Topology and Hysteresis SVPWM Fault-Tolerant Control Strategy of the Novel Multilevel Inverter Guohua Li1 , Yutang Ma1(B) , and Liangjun Wang2 1 Liaoning University of Engineering and Technology, Huludao, China

[email protected] 2 State Grid Jibei Electric Power Company Limited Smart Distribution Network Center,

Beijing, China

Abstract. Large number of power electronic devices will increase the volume of multilevel inverter and increase the probability of failure; on the other hand, more redundant switching states can be provided to improve the fault tolerance of the inverter. Reduced Device Count Multilevel Inverters (RDC-MLIs) have tried to minimize the number of power electronic devices, but failed to take into account the fault tolerance of the inverter. A novel multilevel inverter topology and its hysteresis SVPWM fault-tolerant control strategy are proposed. This method not only realizes the multilevel output of the inverter, but also realizes effective fault-tolerant control for single-switch open-circuit fault and large-number doubleswitch open-circuit fault of the system without reducing or slightly reducing the output performance of the system. It ensures the direct switching of the driving signal to the variable structure unit, and abandons the main switching device and backup switching device operating in the inverter, which not only reduces the difficulty of implementation, but also has high stability. Through simulation and experimental results, the reliability of the topology and fault-tolerant control strategy is effectively verified. Keywords: Multilevel inverters · Reduced device count · Hysteresis SVPWM · Current tracking · Fault tolerant

1 Introduction Security and stability are two major indicators for evaluating the performance of power electronic systems. According to research statistics, the proportion of inverter faults in many power electronic system faults is in the forefront [1]. Among them, the semiconductor switch is the most vulnerable, and the failure rate is as high as about 21% [2, 3]. The system usually connects hardware protection circuits such as fast fuses in series, which can convert short-circuit faults into open-circuit faults for processing [4]. In order to further improve the reliability of the inverter and achieve fault-tolerant control while reducing the number of switches, References [5, 6] proposed fault-tolerant multilevel inverters that reduce the number of components. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 172–183, 2024. https://doi.org/10.1007/978-981-97-0877-2_19

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For multilevel inverters, its main fault-tolerant control methods include software method and hardware method. Adding redundant units or auxiliary modules to the topology of multilevel inverters is called the hardware method [7]; When the toilet is under fault-tolerant control, the relatively complex operation will lead to a significant decrease in reliability. The software method abandons the cumbersome topology operation, and relies entirely on the control algorithm to achieve the purpose of fault tolerance. The first method is to cut the faulty cell or device out of the circuit and maintain the inverter derated output with the remaining switching devices [8]. The second method is to offset the neutral point, which is essentially the basic zero-sequence voltage input to the circuit [9], which has the advantage of obtaining the maximum symmetrical line voltage from the bypass fault. The third method is to change the voltage on the DC side of the inverter, so that the maximum voltage output before and after the fault is equal [10]. In summary, a new single-phase five-level variable structure inverter is proposed. On this basis, a current tracking hysteresis SVPWM reconfigurable fault-tolerant control method is proposed. The equivalent replacement and reconstruction of the topology structure of redundant voltage vectors is used to complete the purpose of fault tolerance; The principle of vector substitution is: first select redundant vector equivalent substitution with the same vector position, and then select the redundant vector with the closest vector position. The advantage of this method is that it abandons the cumbersome process of traditional hardware fault tolerance, and does not need to switch between the main switching device and the backup switching device, but changes the instantaneous topology of the main circuit by changing the driving signal. The operation is simple, and the requirements for the device are not high, and the stability is good.

2 Single-Phase Five-Level Variable Structure Inverter Topology 2.1 New Inverter Topology and Its Operating State

Fig. 1. The topology of main circuit of five level inverter.

Figure 1 is composed of two DC power supplies and six sets of switches, including four sets of switches in the two branches of the H-bridge inverter and two additional switch groups. The additional switch group can be composed of a bidirectional IGBT switch group or a IGBT in parallel with a single-phase bridge uncontrollable rectifier module.

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The inverter has a total of 9 sets of switching states and voltage space vectors, as shown in Table 1. In the fault state, the redundant voltage vector and topology reconstruction can lay the foundation for the fault-tolerant control algorithm. Table 1. Inverter switching state and voltage vector. vector

T1

T2

T3

T4

T5

T6

u0

V1

1

0

0

1

0

0

2E

V2

1

0

0

0

0

1

E

V3

0

0

0

1

1

0

E

V4

1

1

0

0

0

0

0

V5

0

0

1

1

0

0

0

V6

0

0

0

0

1

1

0

V7

0

0

1

0

0

1

−E

V8

0

1

0

0

1

0

−E

V9

0

1

1

0

0

0

−2E

2.2 Hysteresis SVPWM Current Tracking Control 2

2h h *

0

h 2h

u 2

Fig. 2. Hysteresis SVPWM current tracking control algorithm flow chart.

Fig. 3. The schematic diagram of hysteresis current control.

Figure 2 and Fig. 3 are the control method flowchart and current tracking hypothetical diagram used in this article, respectively, where i0 is the input current, if is the feedback

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current, i* is the reference current, the hysteresis widths of the next stage correspond to h and 2h, and the resistors and inductors on the load side are symbolized L and R. Firstly, the current tracking error i is determined by hysteresis comparison: Vi = i ∗ − i f

(1)

Next, change the working state of the switch and reasonably select the voltage vector transformation so that the tracking current is always kept within the hysteresis range. The relationship between ring width and output voltage is: ⎧ ⎪ 2E 2h < i ⎪ ⎪ ⎪ ⎪ h < i ≤ 2h ⎨E (2) u0 = 0 −h ≤ i ≤ h ⎪ ⎪ ⎪ −E −2h ≤ i < −h ⎪ ⎪ ⎩ −2E i < −2h The relationship between output voltage and output current is: u0 = Ri0 + L

di0 dt

(3)

When the output current is positive, the special solution of formula (3) is: i0(t) =

−t u0 (1 − e /τ ) R

(4)

Or if (t) = ifm (1 − e

−t/

τ)

(5)

In the formula, τ is the load time constant τ = L/R; ifm is the steady-state maximum of the feedback current, and ifm = E/(K i *R); K i is the current transmission coefficient, and K i = i0 /if0 . When switching occurs, since the current of the inductor is a non-transcendental variable, i0L(t0+) = i0L(t0-) for the inductor, at this time, the circuit is equivalent to a zero input response of a resistor and inductor. Therefore, according to Kirchhoff’s voltage law, there is Ri(t) + L

diL(t) =0 dt

(6)

The special solution of Eq. (6) is: iL(t) = iL(0+) e

−t/

τ

(7)

When the output current is negative, the particular solution of Eq. (3) is: i0(t) = −

−t u0 (1 − e /τ ) R

(8)

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Or if (t) = −ifm (1 − e

−t/

τ)

(9)

When a path change occurs, there is also: iL(t) = iL(0+) e

−t/

τ

(10)

3 Open-Circuit Fault Analysis and Its Fault-Tolerant Operation When the power switch of the inverter fails, one or more switching states will become a fault state, and the corresponding voltage level will fail, so the control performance of the inverter will be seriously affected. In order to maintain the stable operation of the inverter when the switch fails, it is necessary to replace the fault vector with a redundant voltage vector that is coincident or adjacent to the spatial position, so that the inverter can output symmetrical positive and negative levels and zero levels to maintain relatively stable operation. The topology has 6 kinds of single-tube faults and 15 kinds of double-tube faults. The probability of open-circuit fault of three or more tubes is very small, which is not analyzed in this paper. As shown in Table 2 and Table 3, if the inverter is in the case of switch fault, different voltage vector replacement√strategies are adopted for single-switch faults and double-switch faults; Among them, ‘ ’ means that under the fault state, the voltage vector does not have a corresponding fault, that is, it is not affected, and there is no need for other voltage vector replacement operations; ‘–’ indicates that a voltage vector could not be found that could be replaced. Table 2. Inverter voltage vector is represented under single open-circuit fault. fault tube

level value and voltage vector −2E

T1

V7

T2

V7

T3

V6

T4

V7 √

T5 T6

√

−E √

0 √

E √

√

√

√

V6 √ √ V6

V4 V4 √ √

√ V2 V2 √

2E V3 V3 V3 V2 √ √

When a single switch fault occurs, it is divided into two types, that is, from the additional switch group side and the H-bridge inverter side. Firstly, taking the T5 singleswitch open-circuit fault on the side of the additional switch group as an example, the five voltage vectors of V1 , V3 , V5 , V7 and V9 selected by the original algorithm, when

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the T5 open-circuit fault occurs, it can be seen from Table 2 that only the voltage vector V3 becomes the fault vector, and other voltage vectors are not affected. According to Table 1, it can be seen that by using V2 with equal vectors as its replacement amount, the inverter can still maintain the same level of output in the fault condition. The H-bridge side takes the T1 single-tube open-circuit fault as an example. When the switch tube T1 has an open-circuit fault, only V1 becomes a fault vector that needs to be replaced, and the remaining voltage vectors will not be affected by the fault and can continue to be used. However, the voltage vector V1 has no vector replacement with the same level value. In order to ensure the voltage balance, the corresponding −2E level can only be discarded. It is necessary to replace 2E and-2E with E and-E levels, that is, when 0 < i ≤ 2h, select the vector V3 ; when 0 < i ≤ −2h, select the vector V7 . After the fault vector appears, the voltage vector with the closest spatial position is selected by the modulation method and replaced. At this time, the inverter is reduced to three-level, and the short-term sustainable operation is waiting for maintenance. Table 3. Inverter voltage vector is represented under double open-circuit fault. fault tube

level value and voltage vector −2E

T1 and T2

V7

T1 and T3 T1 and T4

V8

−E √

0 √

V8 √

V6

V7 √

√

T1 and T6 T2 and T3

V8

V8

—

T2 and T4

V7

— √

T2 and T5 T2 and T6

V7 —

—

T3 and T4 T3 and T5

V8

T1 and T5

V6 √ √ V6

√

2E V3 V3

—

—

— √

—

√

V3 V3

V2

V2

√

V2 √

V2

V8

V4

V2

V2

—

—

V4

V2

T3 and T6

V8

V4

T4 and T5 T4 and T6

V7

V8 √

V2 √

V4

V2

V2

V8

V4 √

—

— √

T5 and T6

V8 √

√

V9

V6 √

E √

V1

V3

V3

When the double-tube open-circuit fault occurs, there are three types, as shown in Table 4. Type ➀ takes the simultaneous fault of switch tube T1 and T2 as an example. When a fault state occurs, half of the normal vector translates to a failure vector. As shown in Table 3, the vectors V3 , V5 and V7 are not converted to fault vectors; V1 and V9 are converted to fault vectors, but there is no corresponding voltage vector to replace. The analysis method is the same as that of T1 single-tube open-circuit fault. When 0
S2 and (C + C0 )Q > S1 . For the location of the mixed strategy point is discussed according to the following five scenarios, only in scenario 1 the equilibrium point E5 (x0 , y0 ) is in the equilibrium point space N {(x, y)|0 ≤ x, y ≤ 1}, and in the remaining four scenarios the equilibrium point E5 (x0 , y0 ) is not in the equilibrium point space N {(x, y)|0 ≤ x, y ≤ 1}. 3.1 Scenario 1 Constraints: (C + C0 )QT < S2 < (C + C0 )Q (C + C0 )QI + R < S1 < (C + C0 )Q (C + C0 )(Q − QI ) − R > 0 By means of a symbolic analysis of the determinant and trace of each equilibrium point, the stabilizing equilibrium points are E2 (1, 0), E3 (0, 1), E4 (1, 1). In this scenario, the equilibrium point E5 (x0 , y0 ) is in the strategy space N {(x, y)|0 ≤ x, y ≤ 1}, but is derived as a saddle point from the sign analysis of the Jacobi matrix determinant and the trace, which is an unstable state.

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3.2 Scenario 2 Constraints: (C + C0 )QT < S2 < (C + C0 )Q S1 < (C + C0 )Q < (C + C0 )QI + R By means of a symbolic analysis of the determinant and trace of each equilibrium point, there is only one stable equilibrium point E2 (1, 0), i.e., the intelligent building chooses to participate in demand response and the traditional building chooses not to participate in demand response. 3.3 Scenario 3 Constraints: (C + C0 )QT < S2 < (C + C0 )Q S1 < (C + C0 )QI + R By means of a symbolic analysis of the determinant and trace of each equilibrium point, there is only one stable equilibrium point E2 (1, 0), i.e., the intelligent building chooses to participate in demand response and the traditional building chooses not to participate in demand response. 3.4 Scenario 4 Constraints: S2 < (C + C0 )QT < (C + C0 )Q (C + C0 )QI + R < S1 < (C + C0 )Q (C + C0 )(Q − QI ) − R > 0 By means of a symbolic analysis of the determinant and trace of each equilibrium point, there is only one stable equilibrium point E3 (0, 1), i.e., the intelligent building chooses not to participate in demand response and the traditional building chooses to participate in demand response. 3.5 Scenario 5 Constraints: S2 < (C + C0 )QT < (C + C0 )Q S1 < (C + C0 )QI + R By means of a symbolic analysis of the determinant and trace of each equilibrium point, there is no stable equilibrium when the cost of participating in demand response is too low for both intelligent and traditional buildings.

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4 Cost Analysis of Commercial Building Participation in Demand Response The cost of a single participation in demand response in commercial buildings is categorized as the sum of fixed and variable costs. For the intelligent building, in the early stage of construction need to install a variety of sensors, equipment, integrated systems and automatic control devices, the cost is high, this cost as a fixed cost, but with the help of the above facilities intelligent building can automatically meet the demand response, single participation in demand response variable cost is 0. As the number of times the intelligent building to participate in the demand response becomes more and more, will be fixed cost As the number of times the intelligent building participates in the demand response becomes more, the fixed cost will be divided equally into each time the value will be less, and S1 is the sum of the variable cost and the fixed cost divided equally into each time the value, so the more times the intelligent building participates in the demand response, the lower the cost of a single participation in the demand response S1 . For traditional buildings, due to the lack of need to install a variety of sensors and automation control systems, the fixed cost of 0, each time to participate in demand response requires human resources, equipment, system management costs, this as a variable cost. Therefore, the cost of a single participation in demand response S2 is considered basically unchanged. Taking scenario 1 and scenario 2 as an example, under the premise that the benefit Y ,Y = of traditional building when both parties participate in demand response ProfTB C ∗ QT + C0 ∗ QT − S2 < 0 remains unchanged, and S1 decreases if the number of times it participates increases, i.e., from scenario 1, (C + C0 )QI + R < S1 < (C + C0 )Q reduces to Scenario 2, S1 < (C + C0 )Q < (C + C0 )QI + R. The equilibrium point is also reduced from E2 (1, 0), E3 (0, 1), and E4 (1, 1) in Scenario 1 to E2 (1, 0) in Scenario 2, i.e., the stabilizing strategy gradually converges from any one party participating in the demand response and the other not to participate in the demand response to the intelligent building meeting all the demand response, and the traditional building will no longer tend to participate in the demand response.

5 Conclusions With the continuous progress of science and technology and the rapid development of society, building architecture plays an increasingly important role in people’s lives. This paper constructs a game model of the evolution of two types of commercial buildings under load integrators: intelligent buildings and traditional buildings when participating in demand response, and analyzes the trend of commercial buildings’ choices to participate in demand response when the subsidy price of demand response, real-time tariffs, and the cost of single participation in demand response change, as well as the change of the relationship between them, according to the actual situation. It provides a reference for the future development trend of buildings under the premise of satisfying demand response. Acknowledgements. Funded projects: Research on the operation mechanism and key technology of integrated energy system based on the theory of institutional effectiveness (U1966204);

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Research on information-driven flexible energy management and operation strategy for integrated energy-efficient power plants (51977032).

References 1. Zhou, X.: Research on the application of demand response in energy management of largescale intelligent commercial buildings. Huazhong University of Science and Technology (2020). https://doi.org/10.27157/d.cnki.ghzku.2019.004557. (in Chinese) 2. Zhang, R.: Research and Design of Power Demand Response Terminal for Intelligent Buildings. North China Electric Power University (2016). (in Chinese) 3. Ye, H.: Research on automatic demand response system for intelligent buildings. North China Electric Power University (Beijing) (2016). (in Chinese) 4. Wang, D.: Research on automatic demand response system for electricity consumption in intelligent buildings. Anhui University of Technology (2019). (in Chinese) 5. Khorram, M., et al.: Office building participation in demand response programs supported by intelligent lighting management. Energy Inform. 1(1), 9 (2018) 6. Chandra, R., Radhakrishnan, K.K., Panda, S.K.: Transactive control of air-conditioning systems in buildings for participation in Singapore’s Demand Response market through load curtailment. Sustain. Energy Grids Netw. 31, 100742 (2022) 7. Elkadeem, M.R., Abido, M.A.: Optimal planning and operation of grid-connected PV/CHP/battery energy system considering demand response and electric vehicles for a multi-residential complex building. J. Energy Storage 72, 108198 (2023) 8. Shang, M., Gao H., He, S., et al.: Low carbon planning for buildings considering stepped carbon rewards and penalties and integrated demand response. In: Journal of Shanghai Jiao Tong University, pp.1–31 (2023).https://doi.org/10.16183/j.cnki.jsjtu.2022.527. (in Chinese) 9. Cheng, L., Yu, T.: Analysis of typical scenarios of equilibrium stability of multi-group asymmetric evolutionary game in open electricity market environment. Chin. J. Electr. Eng. 38(19), 5687–5703+5926 (2018). https://doi.org/10.13334/j.0258-8013.pcsee.172219. (in Chinese) 10. Peng, C., Qian, K., Yan, J.: Differential evolution game bidding strategy for generation side in new energy grid-connected environment. Grid Technol. 43(06), 2002–2010 (2019). https:// doi.org/10.13335/j.1000-3673.pst.2018.2084. (in Chinese) 11. Sun, Y., Song, Y., Yao, L., et al.: Research on the behavior of power users in choosing power sales companies under the environment of power sales market. Grid Technol. 42(04), 1124–1131 (2018). https://doi.org/10.13335/j.1000-3673.pst.2017.2338. (in Chinese) 12. Ovalle, A., Hably, A., Bacha, S., et al.: Escort evolutionary game dynamics approach for integral load management of electric vehicle fleets. IEEE Trans. Ind. Electron. 64(2), 1358– 1369 (2017) 13. Cao, Y., Jie, Y., Li, Y., et al.: An evolutionary game-based approach to retail-side competitive strategy selection in regional integrated energy markets. Power Syst. Autom. 47(05), 104–113 (2023). (in Chinese)

Research and Practice of Power Demand Response Market Mechanismtion Yu Zhang1 , Tao Xu2(B) , Yan Zhang1 , Zhen Li1 , and Jia Yin1 1 Power Grid Planning and Research Center, Guizhou Power Grid Corporation,

Guiyang 550003, China 2 Guizhou University, Guiyang 550025, China

[email protected]

Abstract. The safe and stable operation of the new power system is facing serious challenges. The establishment and improvement of demand response incentive mechanism is one of the important ways to balance the system. Firstly, the classification of power demand response and the benefits of implementing demand response are summarized. Secondly, the paper summarizes the theoretical achievements of power demand response mechanism construction from different market backgrounds and market subjects. Thirdly, based on the experience of overseas power demand response implementation, the investigation explores the status quo and development path of domestic demand response implementation; Finally, the paper summarizes the challenges faced by Chinese demand response market mechanism, and puts forward the prospect of the development of Chinese demand response market mechanism construction. Keywords: Power demand response · Market mechanism · Incentive mechanism · Power auxiliary services · Load aggregator

1 Introduction A large amount of intermittent and fluctuating renewable energy enters the network, the peak-valley difference continues to increase and the seasonal peak load phenomenon is prominent, and the risk of safe and stable operation of the new power system rises sharply [1]. It has become an important way to balance the system by deeply exploring the flexibility resources on the demand side, promoting the scheduling of “multi-load storage and coordination of the source network”, fully absorbing renewable energy [2], and establishing and improving the incentive mechanism of demand response (DR). During the “13th Five-Year Plan” period, China carried out demand response and achieved outstanding results in peak reduction and valley filling, promoting the consumption of new energy, and promoting the development of the electricity market [3]. However, under the long-term monopoly state of the electricity market, the development of demand response is greatly affected by the power policy, and the lack of incentive mechanism hinders the development of demand response [4]. It is urgent to establish and © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 192–201, 2024. https://doi.org/10.1007/978-981-97-0877-2_21

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improve the DR Market mechanism that is suitable for the development of the electricity market. This paper aims to summarize the experience of the construction of DR Market mechanism at home and abroad through research, combine the current situation of China’s electricity market and the problems faced by the implementation of DR, and put forward suggestions on the construction of China’s DR Market mechanism.

2 Classification and Benefit of Demand Response Power demand response generally refers to the behavior that users adjust their power consumption patterns to gain benefits according to market price changes or in response to incentive messages from system operators. 2.1 Response Type At present, China has developed a large number of DR-related theoretical research and practice, according to the incentive mode can be divided into price-based, incentive-based and policy-based. Price-based DR Is often involuntary, such as using time pricing, real-time pricing, peak pricing, and so on. Market prices guide the participation of demand-side resources, and users adjust the demand to control the cost of electricity, transferring the load during peak hours to off-peak hours. Incentive-based DR Is usually voluntary, with users adjusting their electricity consumption based on incentive information in order to receive direct compensation or preferential prices. Typical incentive based DRS includes direct load control, interruptible load, demand side bidding and so on. Policy DR Is usually mandatory, such as orderly electricity consumption, which is a major theoretical and practical innovation based on the actual situation of the development of China’s power market [5]. It is usually achieved through legal, administrative, economic, technical and other means, such as over-peak power consumption, power rationing, emergency switches, etc., to avoid unplanned power outages. 2.2 Response Benefits The benefits of demand response are embodied in power system, users and society. The benefits of the system. 1) Reduce the overall peak load of the system and ensure reliable power supply of the system [6]. Reduce the non-emergency load of the user, reduce the peak load of the system, and reduce the operation risk of the system. 2) DR Resources are characterized by high reliability, fast response and low cost [7], and can provide auxiliary services such as peak regulation, frequency modulation and backup. 3) Reduce or postpone power investment. Shifting short periods of peak load, alleviating system capacity shortfalls, delaying or reducing investment in new power plants and transmission grids. 4) Reduce losses caused by transmission line blockage or failure during peak load hours.

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User benefits. User demand response can generate direct economic benefits, such as access to subsidies or preferential electricity prices. In addition, demand response improves demand elasticity, making market prices lower and more stable, mitigating the impact of soaring electricity prices. In addition, the ability of large manufacturers to manipulate electricity prices [8] can also be limited to promote electricity prices to reach the price equilibrium point with optimal social benefits. Social benefits. Demand side response can provide backup reserve and balance service for new energy power generation access system, and promote new energy consumption. At the same time, it can also reduce the use of primary energy such as fossil and natural gas, reduce greenhouse gas emissions, and reduce the degree of environmental pollution caused by energy use.

3 The Theoretical Research Status of Demand Response Market Mechanism 3.1 The Research Results of Demand Response Mechanism (1) Research on mechanism based on market background Power medium and long term market. Price DR, such as TOU price, is mainly divided into peak and valley periods by clustering method, and the price elasticity matrix is usually used to describe the relationship between supply and demand [9], and the dynamic TOU price mechanism can better reflect the relationship between user response and electricity price [10]. It is worth noting that compared with the actual load curve, the TOU tariff mechanism based on the power output net load curve has better adaptability to the absorption of renewable energy [11]. For the invitation incentive DR, the operator releases the demand response invitation information according to the operation needs, and the user chooses whether to participate. For example, based on the purpose of peak cutting and valley filling, literature [12] designed the incentive DR Of Anhui Province from the aspects of organizational model, start-up conditions, salary standard and fund source. Spot market for electricity. Demand-side resources participate in the power market mainly through bidding. Literature [13] designed a DR Mechanism with trigger conditions considering user response behavior. Literature [14] designed the trading mechanism and clearing model of incentive-type DR Under the power spot market, treating the source load resources equally and jointly clearing. Literature [15] proposed that demand-side and genset bidding at the same stage, and adopted the two-time clearing mode to price the generation side. Literature [16] proposes to establish a demand response trading market for DR Aggregators to compete with other participants in the day-ahead wholesale electricity market. Electric auxiliary services market. Foreign demand-side resources participate in the market competition of the combination of main and auxiliary markets, and the market price is cleared through bidding. Literature [17] incorporates DR Into dayahead collaborative optimization of energy and rotating reserve markets based on uniform marginal prices. However, the coupling degree of domestic power energy and auxiliary service market is low, and resource allocation is not completely determined by the market. Literature [18] proposes an optimal model for contract-based

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load aggregators to participate in day-ahead ancillary services market. Literature [19] put forward the bidding and clearing model and trading framework of load distributor and thermal power unit in the peak load regulating market, but did not consider the game behavior of bidding between the two. (2) Research on mechanism based on market subject The power grid company. As the leader of demand response implementation, power grid companies develop different DR Incentive mechanisms according to the needs of system operation. Literature [20] proposes a stepped DR Incentive mechanism considering the strong uncertainty of user behavior to adapt to the changes of user uncertainty. Literature [21] optimized the reward and punishment scores of actual power consumption of residential users at various periods, and proposed a score-based DR Incentive mechanism for residential users. Literature [22] proposes a hybrid DR Mechanism that combines real-time pricing and real-time incentives to provide monetary incentives to retailers at the optimal incentive rate. The company that sells electricity. It mainly considers the callability of demandside resources, incentive pricing and avoiding market risk. Literature [23] presents a real-time price decision model DRiven by DR project historical accumulation data based on real-time price model.Literature [24] designed a ladder incentive pricing model for electricity retailers to sell electricity in the day ahead market based on nonlinear pricing theory. In reference [25], a two-level optimization model based on information gap decision theory is developed to determine the power purchase and demand response incentive strategies of risk-averse retailers. For power retailers, price-based DR peaking is more effective, while incentive-based DR controllability and valley filling are better, and the complementary combination of the two can ensure better response effect [26]. Load aggregator. It mainly focuses on the uncertainty of aggregate resource scheduling and the pricing mechanism of incentive price. Literature [27] designed an incentive mechanism based on credit to guide users to declare reasonable capacity and reduce revenue loss caused by response deviation. Literature [28] proposes a scheduling method to achieve refined residential aggregate load without obtaining detailed power information of users, and improve its bargaining power in the market. Literature [29] establishes a demand response mechanism with electricity price and subsidy incentives, and aggregates park load to participate in optimal scheduling. Virtual power plant (VPP). Focus on dealing with internal and external interest relations to achieve fair distribution of DR Interests. Literature [30] describes the flexible interval of source, load and storage distribution in the form of fixed values and deviation quantities, and proposes a flexible optimal planning method for virtual power plants. Literature [31] proposes a demand response strategy of VPP, which is used to simulate energy trading in the internal power market of VPP. 3.2 Demand Response Mechanism Response Effect Evaluation The evaluation of the demand response mechanism considers the contribution of each entity to the power system. It is difficult to evaluate DR Directly based on price, but the accurate estimation of price elasticity coefficient can reflect the user’s response to price under different energy consumption characteristics. The evaluation based on incentive

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demand response mechanism is mainly evaluated from the perspective of relative contribution and absolute contribution. Compared with the basic linear DR, the quasi-linear demand response is more suitable for the development needs of new power systems [32]. In addition, the evaluation indicators include response speed, duration, credit rating, etc. Literature [33] designed a user credit rating evaluation system based on the single response effect as an index. Literature [34] proposes a two-tier pricing mechanism consisting of fixed base price and variable penalty price to distinguish the contribution to peak grid demand. Literature [35] considers response speed, duration and number of successful responses, and proposes a demand response scheme with “power integration” as the core.

4 The Implementation Status of DR Market Mechanism 4.1 Foreign Demand Response Market Mechanism At present, foreign power demand response mainly focuses on three aspects: energy, auxiliary service and capacity [36], and there are four different ways to participate. The first approach is price-based DR: users respond to price by adjusting demand. Second, design mechanisms that allow users to bid or quote directly to the wholesale market and participate in dispatching and power plants. Third, according to the nature and technical design of auxiliary service products, system operators purchase different auxiliary service products. Fourth, design a capacity procurement mechanism separate from the energy market, that is, the capacity mechanism (Table 1). Table 1. Typical national demand response project. Area

Project type

Implementation plan

PJM

Economic demand response

Demand-side resources bid in the market

Emergency demand response A demand response subsidy mechanism combining fixed-rate compensation and price fluctuation Japan

Negative Watt market

Britain Time-of-use tariff Interruptible load France Time-of-use tariff

Demand-side resources bid in the market Offer a variety of time-of-use rates The contract provides for standby and FM auxiliary services According to weather conditions to establish three-color electricity prices, daily implementation of peak and valley electricity prices

4.2 Domestic Demand Responds to Market Mechanism At present, various regions in China have explored and established price-based disaster recovery mechanisms, such as peak-valley time-of-use price, seasonal price, feng-valley

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price, peak-valley price, and deep-valley price. Scientifically guide users to cut peaks and compensate valleys, improve power supply and demand, promote the consumption of new energy, give full play to the role of the market in determining prices, form an effective market-based TOU price signal [37], and constantly optimize the peak-valley period, and gradually widen the peak-valley price difference. At the same time, carry out the invitation and incentive DR Project. In terms of market players, there are mainly power users and load aggregators, and some areas include energy storage and virtual power plants. In terms of response income, it mainly consists of response electricity price subsidies and assessment fees. Generally, electricity price subsidies are related to response speed, response time and response deviation, and capacity subsidies are also increased for projects with fast response speed and high regulatory requirements. For the sources of funds, there are spot surplus, peak electricity price rise, market-oriented user distribution or beneficiary distribution. In addition, from the perspective of national policy changes, the future demand side can be aggregated into different types through its characteristics, as a third party to participate in electricity market transactions, such as medium-and long-term, ancillary services, spot, full mobilization and utilization of demand-side resource capacity.

5 Challenges and Prospects of DR Mechanism Construction 5.1 Challenges (1) Lack of investment recovery mechanism. The profit of the power grid company directly depends on the total delivery volume of electricity, and the implementation of demand response will affect its economic interests. The operation cost of power companies participating in demand response is too high [38]; It is difficult to quantify the income of users participating in demand response, and they face high economic risks of unpredictable investment and profits. (2) Pricing of subsidized electricity prices. Peak-valley TOU is an important means to improve load characteristics and absorb renewable energy, but the difference of peak-valley price is small in our country [39]. Incentive DR Has low marketization degree, unreasonable pricing scheme structure, small proportion of electricity cost in production cost and lack of willingness to respond. (3) Profitability of emerging market members. Emerging market players such as electricity selling companies, distributed power supplies, electric vehicles, virtual power plants, and energy storage systems do not match their contributions in the process of participating in demand response, and their forms of profit are relatively simple [40]. There is no clear business case to show that DR Projects can maintain the operation of aggregation middlemen, and small users on the demand side have insufficient ability to respond to resource aggregation. (4) Lack of mature market-oriented incentive mechanism. The coupling degree between the power spot market and the auxiliary service market is low, the real-time price of power commodities is not transmitted to the demand side [41], market barriers lead to the demand response is not realized market incentives, and the market value of the user response is not reflected.

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(5) Effect evaluation of demand response and responsibility allocation. Due to the lack of appropriate demand response evaluation system, it is difficult to quantitatively estimate the benefits and costs generated by demand response [42]. At present, the division of responsibility and obligation of power demand response is not clear, for example, the fairness and rationality of the subject of contribution response funds and its contribution ratio are still controversial. 5.2 Outlook (1) Reasonable formulation of subsidies or preferential prices. Calculate electricity price cost to carry out price DR, and design incentive DR Mechanism according to system needs. At the same time, adhere to the market-oriented, through market-based means to formulate subsidies or preferential prices, scientific allocation of resources [43]. (2) Enrich the types of DR Projects and fine manage demand response users [44]. Users have different characteristics in the demand for electricity, and the classification of DR Projects can maximize the enthusiasm of users to participate in demand response. At the same time, coordinate and integrate various types of DR Resources to achieve complementary advantages and promote the optimal development of various demand-side resources such as demand response and distributed power. (3) Attach importance to the market function expansion of business models such as load integrators and virtual power plants. Aggregators discuss with users the implementation mode and revenue sharing mechanism of demand response, explore the integrated management of users’ electric energy, carry out value-added service functions in various fields, and share the results of demand response [45]. (4) Incorporate demand response into market competition. Establish a joint operation mechanism of demand response and power spot market, integrate demand-side resources in the form of aggregators such as virtual power plants, and participate in the power day-ahead market, real-time market, and auxiliary service market [46], so as to improve the optimal allocation level of electric energy through market mechanism. In addition, timely exploration should be made to establish a capacity trading market with demand-side participation or establish a corresponding capacity mechanism [47]. (5) Strengthen demand response supervision and evaluate demand response comprehensively and effectively. Develop a scientific performance evaluation index system to accurately evaluate the implementation process, efficiency, effect and influence of demand response [48]. Explore the demand elasticity and response characteristics of participating customers, improve customer satisfaction and response rate, and ensure that the net present value of the benefits obtained by the demand response entities is greater than zero. Acknowledgments. This work was funded by Department of Science and Technology of Guizhou Province (Guizhou Science and technology contract support [2021] General 409), China Southern Power Grid Company Limited (GZKJXM20210385).

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Research on MPC Fault-Tolerant Control of Five-Level Inverter Guohua Li, Rongyu Dong(B) , and Guangda Liu Institute of Electrical and Control Engineering, Liaoning Technical University, Huludao 125105, China [email protected]

Abstract. In order to ensure the reliable work of UPS equipment with long-term and stable work requirements. Among the many control methods of multi-level inverters, this paper chooses Model Predictive Control (MPC) method to study. MPC method has unique rolling optimization ability and high dynamic response ability, which can ensure that the inverter is in a high-quality working state for a long time. When the fault of the switch tube is detected, the fast fault-tolerant control is carried out by changing the reference current and switching the voltage vector participating in the rolling optimization, so as to ensure that the output current of such equipment is not distorted and maintain the safe operation of the equipment and its load. Keywords: Multilevel Inverter · MPC · Failure-tolerant Control

1 Introduction With the continuous progress of the industrial field, the remote control system has been continuously developed, and the remote switch cabinet has penetrated into various industrial fields [1]. However, the high integration of the control system has led to the reduction of system reliability [2], and the system is more vulnerable to regional power outages and power outages [3]. So in today’s remote control room, Uninterruptible Power Supply (UPS) ushered in the rapid development. When the mains power is normal, the power frequency voltage is provided to the communication equipment through the AC distribution cabinet and the DC distribution cabinet, and the UPS power supply is used to supply the battery pack [4]. UPS in the main power failure, through the multi-level inverter to the battery pack to provide DC inverter for AC power supply AC distribution cabinet and room air conditioning environment equipment, to maintain the normal operation of the room [5]. In order to ensure the reliable operation of UPS, among the many control methods of multi-level inverters, this paper chooses Model Predictive Control (MPC) method for research. MPC is a kind of computer control algorithm proposed in the 1970 s, which has been widely used in the field of chemical industry [6]. It was not until 1983 that the German scholar J. Holtz first applied MPC to the field of motor control [7]. MPC technology was applied in the three-phase inverter system by Rodriguez in 2004.Compared with other © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 202–214, 2024. https://doi.org/10.1007/978-981-97-0877-2_22

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control technologies, it has obvious advantages, strong dynamic response ability and excellent robustness. It is easy to increase the constraint term of input signal through the design of cost function [8]. However, MPC technology also has its own shortcomings. As an enumeration method, MPC technology optimizes each switching state when tracking the output current in the application and multi-level inverter system, and the calculation amount is too large [9]. Aiming at the problem of excessive calculation in optimization, Reference [10] proposed to directly use voltage instead of current as the tracking target, and directly perform cost function operation with voltage vector, which simplifies the number of optimizations. The experimental results show that the operation speed is increased by 50%. After the inverter power tube fails, the number of voltage vectors available to the inverter will be reduced. What is reflected in the multi-level inverter is that the number of levels corresponding to the voltage vector in the output phase voltage is missing, resulting in serious distortion of the current waveform output by the inverter, which greatly increases the harmonic content in the output current [11]. Fault-tolerant control technology enables the system to have a certain degree of redundancy, that is, the system can ‘tolerate’ part of the fault [12]. After the fault occurs, by adopting the fault-tolerant control strategy, the output current and phase voltage of the inverter are restored to the state before the fault occurs or the amplitude of the output current of the inverter is reduced but the sinusoidal degree of the output current is maintained to reduce the harmonic content of the output, so as to ensure that the circuit system of the inverter has the basic output function. In 1995, researchers proposed fault-tolerant control using the redundant vector of the inverter topology. In Reference [13], the residual voltage vector of the clamping diode of the three-level NPC inverter is analyzed, and the fault-tolerant control is carried out by the remaining redundant vector. After fault diagnosis according to the fault diagnosis method proposed in literature [14], a hysteresis space vector pulse width modulation (SVPWM) fault-tolerant control method for current tracking singlephase voltage source multilevel inverter is proposed in literature [15], which can ensure that the output current of the inverter can track the reference current more accurately. In this paper, the MPC method with strong dynamic response ability and low output harmonic content is selected for research. Through the vector reconstruction after vector substitution and topology reconstruction, the MPC fault-tolerant control strategy is determined according to the residual voltage vector. The rolling optimization of the inverter output is completed under the premise of ensuring the sinusoidal output of the inverter, and the output effect after fault tolerance is evaluated. The reliability and feasibility of the MPC fault-tolerant method proposed in this paper are verified by simulation and experiment.

2 Topology and Working Principle 2.1 Introduction of Single-Phase Five-Level MPUC Inverter Topology The five-level MPUC inverter is composed of six sets of IGBTs with reverse parallel diodes and two independent DC power supplies. Each pair of complementary switching tubes is defined as the function Sn, and the three-bit binary number S 1 S 2 S 3 is formed

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by the conduction state of three pairs of complementary switching tubes, Define Vi (i = S1 S2 S3 → Decimal conversion). The two independent DC source outputs of the five-level MPUC inverter system are both E, and the reference direction of the output current is from M point to N point. There are eight switching states in the three pairs of complementary switching tubes of the single-phase five-level MPUC inverter. The output levels are arranged from top to bottom according to 2E, E, 0, −E, −2E, as shown in Table 1. Table 1. MPUC Inverter switch status and voltage. Vector

S1

S2

S3

uo

V5

1

0

1

2E

V4

1

0

0

E

V1

0

0

1

E

V0

0

0

0

0

V7

1

1

1

0

V6

1

1

0

−E

V3

0

1

1

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Fig. 1. Vector V 5 , V 2 , V 3 , V 4 , V 1 , V 6 , V 7 , V 0 circuit flow chart

(1) When the voltage vector is V 5, V 2. According to the switching state and voltage vector table of the inverter in Table 1, when the output voltage vector is V5 , the corresponding three-bit binary number of the conduction state is S1 S2 S3 = 101.At this time, the switching tubes T1 , T4 and T5 of the inverter are in the conduction state, and the output level of the inverter system is 2E. The

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current flow diagram of the inverter is shown in Fig. 1.(a). According to the definition of V i , the conduction state of the switch tube of V2 is complementary to that of V5 , and the output level is -2E. The current flow diagram is shown in Fig. 1. (b). (2) The remaining voltage vectors correspond to the switching state as shown in Fig.1. According to Table 1, the voltage vector is V3 conduction state binary number S1 S2 S3 = 011, V4 switch tube conduction state is complementary to V3 , and the output level value is E; the binary number of the conduction state of the voltage vector V1 is S1 S2 S3 = 001, and the output level is E. The conduction state of the switch tube of V6 is complementary to V1 , and the output level is -E. The binary number of the conduction state of the voltage vector V7 is S1 S2 S3 = 111, and the output level is 0. The conduction state of the switch tube of V0 is complementary to that of V7 , and the output level is 0. 2.2 Analysis of Normal Working State of MPUC Inverter According to the MPC method under the normal working state of the MPUC inverter, the system parameters of the Matlab/Simulink simulation system are as follows (Table 2): Table 2. MPUC inverter system simulation parameters. Parameter

Numerical value

DC regulated voltage source voltage E/V

12

Load resistance R/ 

5

Load inductance L/mH

5

Forecast cycle TS /S

5 × 10–4

Reference current amplitude i∗ /A

4

Reference current frequency f /Hz

50

Because the DC power supply of the inverter in UPS is generally 12 V lead-acid battery in series for the output of 220 V battery group or in parallel for 12 V battery group after the output transformer boost to 220 V two ways, as the main load of UPS power loop system, high precision air conditioning in the motor equipment as the main load. Therefore, the DC voltage source in the simulation parameters is selected as 12 V, and the load is selected as the resistance-inductance load to simulate the inverter in the UPS system.

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Fig. 2. MPUC inverter simulation output voltage and current diagram

The MPC control simulation is used for the five-level MPUC inverter topology, and the output effect of hysteresis control is verified by the output voltage and current waveform and FFT analysis diagram. Figure 2. is the voltage and current waveforms of the MPUC inverter simulation output. Figure 3. is the output current harmonic content diagram of MPC control mode. MPC predicts the optimal switching state for output. The harmonic content of the output current is low, the tracking effect of the reference current is good, and the control accuracy is high. It is suitable as a fault-tolerant control method for inverters in UPS power supply.

Fig. 3. Inverter MPC method simulation current THD diagram

3 Analysis of Fault and Fault-Tolerant Control Method for MPUC Inverter 3.1 Single-Switch Open-Circuit Fault Analysis of Single-Phase Five-Level MPUC Inverter The three pairs of switching tubes (T1 , T2 )、(T3 , T4 ) and (T5 , T6 ) of the single-phase five-level MPUC inverter are always in the complementary conduction state, and the switching states corresponding to the eight voltage vectors of the inverter are complementary to each other. The output values of the three complementary voltage vectors are opposite to each other, except that the output effects of the two voltage vectors V 0 and V 7 are the same. As a result, once a single tube fault occurs in the MPUC inverter, four of the eight voltage vectors cannot be output, which becomes the fault vector, resulting in the loss of the corresponding level of the output voltage. The single-tube fault state

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of the inverter is analyzed. Table 3 is made according to the voltage vector affected by √ the single-tube fault of the inverter, in which indicates that the voltage vector can still work normally after the open-circuit fault of the switch tube occurs. × indicates that this voltage vector cannot work normally after an open-circuit fault, resulting in the failure to output the number of levels corresponding to the voltage vector. According to the influence table of single tube fault on MPUC inverter in Table 3, the single tube fault can be divided into two types: T1 , T2 , T5 and T6 fault state results are similar, and the output voltage is reduced from five-level to four-level operation after fault. The fault state results of T3 and T4 are similar, and the output voltage is reduced from five-level to three-level operation after fault. According to Table 3, the voltage vector diagram of MPUC inverter under normal operation and single tube fault operation is drawn. The voltage vector of the red dotted line is a voltage vector that is affected by the open circuit of the switch tube and cannot participate in the rolling optimization process. The black voltage vector indicates that the voltage vector is not affected and can participate in the rolling optimization process of the MPC normally. Table 3. The Influence of Single Transistor Fault on MPUC Inverter. Vector

T1

V5

×

V4

× √

V1 V0

√

V7

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V6

× √

V3 V2

√

T2 √

T3 √

√

√ √

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√

× √

×

√

×

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2E

T4

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×

× √

× ×

× √

× √

× √

√ √

× √

√

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uo

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-2E

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V4(T1,T4,T6) 0 V7(T1,T3,T5)

-E -E

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-2E

(b)T1 fault

Fig. 4. MPUC inverter normal and T1 single transistor fault voltage vector diagram

According to Fig. 4.(b), when the switch tube T1 fails, the voltage vectors V4 , V5 , V6 and V7 fail. The remaining four voltage vectors of the inverter can still output a positive level, a zero level and two negative levels. Although the inverter is a four-level output state, the control of the increase and decrease of the output current of the inverter is

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maintained. The output voltage and current of the simulation are shown in Fig. 5. When the fault occurs in T1 , and the output current THD of the inverter is 15.1%.

Fig. 5. Simulated output voltage and current diagram after T1 single transistor failure

Fig. 6. MPUC inverter T2 and T4 single transistor fault voltage vector diagram

According to Fig. 6.(a), when the switch tube T2 fails, the voltage vectors V 0 , V 1 , V 2 and V 3 fail, and the inverter maintains the four-level output state of increasing the output current of the inverter and reducing the control. The voltage and current waveforms of the simulation output under T2 fault state are shown in Fig. 7(a)At this time, the output current THD of the inverter is 13.9%.

Fig. 7. The simulation output voltage and current diagram of T2 and T3 single tube fault

According to Fig. 6.(b), when the switch tube T3 fails, the voltage vectors V 2 , V 3 , V 6 and V 7 cannot be used. The remaining four voltage vectors of the inverter can only

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output three positive levels and one zero level. The inverter becomes a three-level output state, and the output current value cannot be reduced by the on-off of the switch tube, and the inverter loses the control of the output current. The voltage and current waveforms of the simulation output in the T3 fault state are shown in Fig. 7(b)At this time, the output current THD of the inverter is 43.5%. 3.2 Fault-Tolerant Control Analysis of Single Open-Circuit Fault When the corresponding fault occurs in the switch tube of the inverter, according to the above analysis of the single tube fault, when the fault of the switch tube T1 , T2 , T5 , T6 occurs, the switching reference current value is used in the vector diagram. The voltage in the same direction as the fault vector, or the projection of the similar direction vector along the direction of the fault vector, replaces the original fault vector, maintains the waveform of the output current, so that it can still be maintained as a sinusoidal type after a single tube fault occurs, without excessive current distortion. According to the voltage vector fault after the T1 fault, the three-level MPC method is used to control the MPUC inverter to obtain a sinusoidal output current with low harmonic content. The voltage vector affected by T2 , T5 and T6 faults is similar to that of T1 , and the output after fault-tolerant control is similar to that of T1 , without too much repetition. After the fault-tolerant control of T1 , the harmonic content of the output is reduced to 1.42% of that after the fault-tolerant control, and the maximum output of the output current is reduced to 55.6% of that before the fault, which verifies the faulttolerant control effect of MPC on T1 single-tube fault. The change of output current before and after fault-tolerant control of other types of faults is the same as that of T1 single-tube fault-tolerant control. In the event of a switch tube T3 , T4 fault, because the inverter can only carry out positive level, zero level or negative level, zero level output, can not control the output current of the inverter, the inverter topology needs to be reconstructed to carry out faulttolerant control of the inverter. The equipotential points of T1 and T2 connected to M points are defined as A and B, and the positive and negative poles of the two DC regulated power supplies are defined as C, F, D and E, respectively. The equipotential points of T5 and T6 connected by N points are defined as G and H. In the event of a T3 , T4 fault, as shown in Fig. 8, the C and F two points are shorted and the T4 is cut off between the D and F points to realize the reconstruction of the inverter topology. A T1 C

B

VD1

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Fig. 8. T3 single transistor fault topology reconstruction diagram

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In the T3 fault-tolerant control, the reconstructed voltage vector is added to the prediction sequence, and all the pre-reconstructed voltage vectors are removed from the MPC’s prediction of the next cycle and the sequence of cost function optimization. The reference current value is used to perform the three-level MPC method output with the reconstructed voltage vector. The output voltage waveform is changed from a half-wave sine wave to a sine wave after the capacity reduction output. The output voltage and current waveforms of T3 after fault-tolerant control are shown in Fig. 9. The harmonic content of the output is reduced to 1.42% after fault-tolerant control, which verifies the fault-tolerant control effect of MPC on T3 single-switch fault.

Fig. 9. Single transistor fault tolerant control simulation output voltage and current diagram.

4 Experimental Analysis A system experimental platform is built to verify and analyze the method. The system parameters are as follows: the two power supply voltages on the DC side of the inverter are 12 V; the reactor at the output end is 5mH, the resistance is 5, the reference current is a sine wave with an amplitude of 4A and a frequency of 50Hz, and the expected prediction period of MPC is set to 5e-3s. The inverter power switching device IGBT model is BSM50GB120DN2; the driving circuit adopts the falling wood source integrated IGBT drive module DA962D6; the main control chip of the system adopts 32-bit DSP TMS320F28335; the inverter dead time is set to 1µs; in the experiment, the oscilloscope model is DS1052 E, and the power quality analyzer is HIOKI PW3198; the experimental prototype is shown in Fig. 10.

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Fig. 10. Experimental prototype

4.1 Experimental Analysis of MPC

Fig. 11. MPC output voltage, current waveform and current THD diagram

Figure 11.(a) is the output voltage and current waveform of MPUC inverter under non-fault state. It can be seen from the figure that when all switching devices are normal, MPC suppresses the voltage and current waveform distortion between different level switching of MPC under the premise of high-precision control of output current by MPC control. Through the periodization, the harmonic content generated by the MPC control mode is further reduced, and the current waveform output by the inverter changes according to the sine law. At this time, the output voltage is 5 level, and the output current can accurately track the reference value. As shown in Fig. 11.(b), the current harmonic distortion rate is 1.42%. 4.2 Experimental Analysis of MPC Single-Tube Fault Tolerance When the switch tube T1 fails, the level corresponding to the voltage vectors V 4 , V 5 , V 6 and V 7 cannot be provided to the inverter. When T1 fails, the V 2 voltage vector is abandoned, and the three levels of V 0 , V 1 , and V 3 are selected as the three levels of 0, E, and -E output of the inverter to perform three-level MPC fault-tolerant control. Through the output voltage and current waveforms of T1 single-tube fault shown in Fig. 12.(a) and the THD of the inverter output current shown in Fig. 13.(a) is 16.3%, the output waveform after single-tube fault T1 is verified. The output voltage and current waveforms of T5 single-tube fault are similar to those of T1 single-tube fault. Similarly,

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Fig. 12. Output voltage and current waveform of inverter T1 , T2 and T3 fault

Fig. 13. Current THD diagram at T1 , T2 and T3 fault

when the switch tube T2 fails, as shown in Fig. 12(b) and Fig. 13(b), the inverter output current THD is 15.1%, which verifies the output waveform after the single-tube fault T2 .When a single-tube fault occurs, T6 and T2 output voltage and current waveforms are similar. After analysis, when the T3 single tube fault occurs, the whole circuit can only output negative level and zero level. At this time, the fault-tolerant control method is to short C and F points, the switching state of zero vector is T1 and T6 , the switching state of level E is T1 and T5 , and the switching state of level -E is T2 and T6 . After fault-tolerant control, the inverter is in three-level output state. The output voltage and current waveforms of the T3 single-tube fault shown in Fig. 12.(c) and the output current THD of the inverter shown in Fig. 13.(c) are 47.1%, which verifies the output effect of the inverter after the single-tube T3 fault occurs. The output voltage and current waveforms of T4 and T3 before and after fault tolerance are opposite when the inverter has a single-tube fault. After a single-tube fault occurs in the inverter, the number of levels available to the inverter is reduced from 8 before the fault to 4, and the inverter can optimize the reference current rollingly. However, due to the remaining four voltage vectors, the output ripple rate is significantly increased, and the output current THD of the inverter is 16.3%, 15.1% and 47.1%, respectively. According to the fault-tolerant control scheme mentioned above, the corresponding three-level MPC fault-tolerant control is carried out. As shown in Fig. 14.(a), the output current waveform of the inverter returns to normal after fault-tolerant control, and the sine degree is good. Figure 14.(b) shows that

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Fig. 14. Three-level fault-tolerant control output voltage, current waveform and current THD diagram

the current harmonic distortion rate under fault-tolerant operation is 1.65%. After the T3 and T4 double-switch faults, the fault-tolerant control of the voltage vector reconstruction after the topology reconstruction, the three-level MPC output effect is the same as the fault-tolerant effect after the single-switch fault.

5 Conclusion The power supply part of the inverter for the UPS power supply system is often powered by two sets of batteries respectively. In this paper, a five-level MPUC inverter with two DC power supplies is selected for research. Under the long-term, stable operation and high-precision control required by the UPS power supply system, through the theoretical comparison of various multi-level inverter control methods, the MPC control method with high control accuracy and stronger dynamic response ability is selected for research. According to the hysteresis control THD analysis of the MPUC inverter, it is confirmed that the output current harmonic content of the MPC control mode is low and the control accuracy is high. The output voltage, current waveform and current THD of the five-level MPUC inverter under single-tube fault state are analyzed by simulation, and the output effect of the MPC control mode is confirmed by experimental verification. The corresponding fault-tolerant control scheme is designed to ensure that the inverter can operate with fault capacity reduction under fault condition and increase the stability of UPS power supply system. The fault-tolerant control method is verified by simulation and experiment, and the effectiveness of the method is verified. Acknowledgment. This work was supported by the Natural Science Foundation of Liaoning Province (20180550268), the Natural Science Foundation of Liaoning Provincial Department of Science and Technology (2021-BS-273), the subject innovation team project of Liaoning University of Engineering and Technology ’ Intelligent Electrical Equipment and Control Technology ’ (LNTU20TD-32) and the Foundation of Liaoning Provincial Department of Education (20–1067).

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References 1. Xiangning, X., Yonghai, X.: Analysis of power quality problems. Grid Technol. (03), 66–69 (2001). (in Chinese) 2. Zhenxiang, H., Family, C.: Security and prevention measures of power system. Grid Technol., (09), 1–6 (2004). (in Chinese) 3. Choi, U.-M., Lee, J.-S., Blaabjerg, F., Lee, K.-B.: Open-Circuit fault diagnosis and f aulttolerant control for a grid-connected NPC inverter. IEEE Trans. Power Electron. 31(10), 7234–7247 (2016) 4. Family, C., Yudong, Z., Zhejing, B.: Cascading failure analysis under the interaction of power system and communication network. Power Autom. Equip. 33(01), 7–11 (2013). (in Chinese) 5. Zhengkun, L., Yan, Z.: Uninterruptible power supply direct parallel machine and automatic switching redundancy power supply mode. Huadian Technol. 32(02), 69–71+80+84 (2010). (in Chinese) 6. Zou, Ding, Z.: Introduction to the application of model predictive control engineering. Chemical Industry Press, Beijing (2010). (in Chinese) 7. Holtz, J.,Stadtfeld, S.: A predictive controller for the stator current vector of ac machines fed from a switched voltage source. In: Proceedings of the International Power Electronics Conference,Tokyo,Japan, pp. 1665–1675 (1983) 8. Trabelsi, M., Bayhan, S., Ghazi, K.A., et al.: Finite-control-set model predictive control for grid-connected packed-u-cells multilevel inverter. IEEE Trans. Industr. Electron. 63(11), 7286–7295 (2016) 9. Xiaoyu, Z., Dan, W., Zhouhua, P.: Asynchronous motor model predictive direct torque control. Motor Control Appl. 43(02), 6–12 (2016). (in Chinese) 10. Miao, X.: Research on current control and optimization of permanent magnet synchronous motor based on model prediction. China University of Mining and Technology (2022). (in Chinese) 11. Jung, J.-H., Hyun-Keun, K., Son, Y.-D., Kim, J.-M.: Open-switch fault diagnosis algorithm and tolerant control method of the three-phase three-level NPC active rectifier. Energies 12(13), 1–17 (2019) 12. Research on fault-tolerant control strategy of three-level inverter. Xi‘an University of Technology (2023). https://doi.org/10.27391/d.cnki.gxagu.2023.000647. (in Chinese) 13. Jinggang, Z.: Research on modulation and fault-tolerant control strategy of dual three-level inverter. China University of Mining and Technology (2022). (in Chinese) 14. Research on open circuit fault diagnosis of voltage source inverter in UPS system. Power Syst. Protect. Control 48(23), 148–153 (2020). (in Chinese) 15. Guohua, L., Feng, L., Jiaxin, L.: Single-phase MPUC five-level inverter hysteresis SVPWM fault-tolerant control method. Power Electr. Technol. 56(04), 109–112 (2022). (in Chinese)

Characteristic Analysis of Quasi-Power-Frequency Sequence Oscillations in DFIG Wind Farms Integrated via MMC-HVDC Hui Liu1 , Wenkai Dong2(B) , Xiao Wang1 , Yunhong Li1 , Xiaoyang Deng1 , Yina Ren1 , and Xiaorong Xie2 1 State Grid Jibei Electric Power Co. Ltd., Research Institute, North China Electric Power

Research Institute Co. Ltd., Beijing, China 2 State Key Laboratory of Power System, Department of Electrical Engineering, Tsinghua

University, Beijing, China [email protected]

Abstract. The quasi-power-frequency sequence oscillation is a new type of oscillation issue observed in practical renewable energy integrated power systems via MMC-HVDC in recent years. In this paper, characteristics of quasi-powerfrequency oscillations in DFIG wind farms integrated power systems via MMCHVDC are studied. Frist, state-space model of the system is established. Then impact of control parameters on the quasi-power-frequency oscillation is analyzed based on the root locus method. Finally, effectiveness of conclusions drawn based on the linearized model is verified via non-linear simulations. It is found that this new type of oscillation is mainly relative with the dynamics of phase lock loop of the DFIG, current inner loop of RSC of the DFIG and AC voltage outer loop of the MMC. In addition, increase of active power outputs of the DFIGs can also decrease damping of the oscillation. Keywords: Quasi-power-frequency Sequence Oscillation · DFIG · MMC-HVDC

1 Introduction 1.1 A Subsection Sample Due to the economic advantages in large-capacity and long-distance power transmission, modular multilevel converter based high voltage direct current transmission (MMCHVDC) has been widely used in the integration of large-scale renewable power generation stations [1]. However, sending end of the renewable energy integrated power system via MMC-HVDC is of high penetration of power electronic interfaced technologies, and hence stability of the system is challenged. In recent years, oscillation stability This work is supported by the State Grid Corporation of China (KJZ2022056). © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 215–223, 2024. https://doi.org/10.1007/978-981-97-0877-2_23

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has become one of the key bottlenecks for the stable operation of renewable energy integrated power systems via MMC-HVDC, such as the high frequency resonance in Germany [2] and the sub-synchronous oscillation in North China [3]. Besides, quasipower-frequency sequence oscillations have monitored in North China recently, which has not been observed before. The quasi-power-frequency oscillation can reduce the power transfer capacity of MMC-HVDC. Since it is a new type of oscillation, it is necessary to study the characteristics of quasi-power-frequency oscillation, to provide basis for the planning and oscillation mitigation of renewable energy integrated power system via MMC-HVDC. The quasi-power-frequency oscillation is observed in sequence current and voltage with a frequency between 40 ~ 60Hz. Then based on the relationship between the abc and d-q coordinates, this new type of oscillation appears as an oscillation with a frequency between 0 ~ 10Hz. Therefore, the quasi-power-frequency oscillation can be clarified as low frequency oscillation in line with the newly released definition and classification of power system stability by IEEE and CIGRE [4]. According to the existing studies on low frequency oscillations of grid-connected converters, quasi-power-frequency oscillation is mainly relevant with the dynamics of outer control loops or phase lock loops of the converter control systems [5]-[7]. The studies mentioned above provide theoretical basis for understanding the causes of quasi-power-frequency oscillations. However, these studies mainly focus on the low frequency oscillation of converters under weak grid. For a renewable energy integrated power system via MMC-HVDC, characteristics of the quasi-power-frequency oscillation is not clear enough, which is unfavorable to study of oscillation mechanism and mitigation. This paper focuses on the characteristics of quasi-power-frequency oscillation in DFIG wind farms integrated power systems via MMC-HVDC. State-space model of the system is established at first. Then impact of control parameters and operating conditions on the quasi-power-frequency oscillation is studied based on mode analysis. Finally, effectiveness of conclusions obtained is verified via time-domain simulation.

2 Modelling of DFIG Wind Farms Integrated via MMC-HVDC

Fig. 1. Topology of a DFIG wind farm integrated power system via MMC-HVDC.

The general topology of a DFIG wind farm integrated power system via MMCHVDC is shown in Fig. 1. Oscillation stability of the gird can be studied based on the linearized model. In this paper, state-space modelling is adopted, and the mostcommonly-used vector control is considered for the converters. Then the DFIGs and

Characteristic Analysis of Quasi-Power-Frequency Sequence Oscillations

MMC converter can be modelled as [8]-[10], ⎧ ⎨ d X = A X + B V di di di di di dt ⎩ Idi = Cdi Xdi + Ddi Vdi ⎧ ⎨ d X = A X + B V m m m m m dt ⎩ Im = Cm Xm + Dm Vm

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(1)

(2)

where  denotes micro increment of a variable vector; Xdi and Xm are respectively the   T T state vectors of the ith DFIG and the MMC; Vdi = Vdix Vdiy , Idi = Idix Idiy , Vdix + jVdiy and Idix + jIdiy are respectively the terminal voltage and output current of  T the ith DFIG expressed in the common x-y coordinate of AC grid; Vm = Vmx Vmy , T  Im = Imx Imy , Vmx + jVmy and Imx + jImy are respectively the terminal voltage and output current of the MMC in x-y coordinated; Adi , Bdi , Cdi and Ddi (or Am , Bm , Cm and Dm ) are respectively the state-space matrix, control matrix, output matrix and feedback matrix of the ith DFIG (or the MMC); i = 1, 2, . . . , N , N is the total number of DFIGs. From (1) and (2), state-space models of all the DFIGs and the MMC converter can form the following representation, ⎧ ⎨ d X = A X + B V g g dt (3) ⎩ I = Cg X + Dg V   T T  T T T  T T T T T; I = where X = XD Xm , XD = Xd1 Xd2 . . . XdN ID Im , ID =  T T T   T T T  T T T T T; A = Id1 Id2 . . . IdN ; V = VD Vm , VD = Vd1 Vd2 . . . VdN g       diag[Adi ] 0 diag[Bdi ] 0 diag[Cdi ] 0 , Bg = , Cg = , Dg = 0 Am 0 Bm 0 Cm   diag[Ddi ] 0 ; diag[Adi ], diag[Bdi ], diag[Cdi ], diag[Ddi ] respectively denotes a 0 Dm block diagonal matrix with the diagonal elements to be Adi , Bdi , Cdi and Ddi , i = 1, 2, . . . , N ; 0 denotes a zero matrix with a proper dimension. By using the node admittance matrix and cancelling the passive nodes, network equation of the gird can be expressed as, I = Ynet V

(4)

where Ynet is the node admittance matrix. By combining (3) and (4), state-space matrix of the system can be obtained as, d X = AX dt

(5)

where A = Ag + Bg (Ynet − Dg )−1 Cg is the state-space matrix of the power system. It should be noted that the state-space model in (5) is expressed in d-q (or x-y) coordinate and the quasi-power-frequency oscillation mentioned before is observed in

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the phase current and voltage i.e., in abc coordinate. In this paper, power frequency is considered to be 50Hz. Then according to the relationship between abc and d-q coordinates, quasi-power-frequency oscillations of 40 ~ 60Hz in abc coordinate will appear as oscillations of 0 ~ 10Hz in d-q coordinate, i.e., frequency of the dominant oscillation mode should be 0 ~ 10Hz.

3 Characteristic Analysis of Quasi-Power-Frequency Oscillation To study the characteristics of quasi-power-frequency oscillation, a typical power grid with multiple DFIGs integrated via MMC-HVDC is constructed as shown in Fig. 2. At initial state, there are sixty DFIGs in the wind farm, each of which is with a rated capacity of 5 MW.

Fig. 2. A typical power grid with multiple DFIGs integrated via MMC-HVDC.

3.1 Impact of Control Parameters In this subsection, impact of control parameters of the DFIG and MMC on the quasipower-frequency oscillation is analyzed. According to the multi-time-scale characteristics of converter control system, bandwidths of the outer loop, phase lock loop and inner loop are respectively around 20Hz, 50Hz and 200Hz in general (d-q coordinate) [9]. First, mode analysis was conducted considering different parameter settings and operating points. The preconditions considered in the mode analysis are as follows. 1) Bandwidths of the outer loop and phase lock loop are within 50Hz. 2) Power outputs of the DFIGs were considered to be 25%, 50%, 75% and 100% of the rated capacity and power factor was considered to be ± 0.95 and 1. According to the oscillation modes obtained and their participation factor, the quasipower-frequency oscillation were mostly likely to be induced by the dynamics of phase lock loops of the DFIGs and voltage outer loop of the MMC. Then, mode analysis was conducted with control parameters for phase lock loop of the DFIG being increased from (1, 10) to (15, 150) and control parameters for voltage outer loop of the MMC respectively to be (2, 20), (6, 60) and (10, 100). Root loci of the dominant quasi-power-frequency oscillation mode obtained are shown in Fig. 3. In Fig. 3, arrow denotes direction for the root locus with the change of parameters for the phase lock loops. It should be noted that the DFIGs were set to be operated at the rated capacity with a power factor of 1. From Fig. 3, the following conclusions can be drawn. 1) The quasi-power-frequency oscillation is prone to be induced when proportional and integral coefficients for the MMC are 2 and 20, i.e., when the bandwidth of the voltage outer loop is relatively low. 2) In general, with the increase of bandwidths of the phase

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lock loop and the voltage outer loop, damping and frequency of dominant oscillation mode also increase. Finally, three quasi-power-frequency modes were selected as representative modes, to further study impact of other control parameters on the oscillation. The representative modes selected were respectively λ1 = 9.65 + j13.49 (control parameters for phase lock loops of the DFIGs and voltage outer loop of the MMC are respectively (1, 10) and (2, 20)), λ2 = 0.01+j30.07 (control parameters for phase lock loops and voltage outer loop are respectively (3, 30) and (6, 60)) and λ3 = −20.59 + j45.33 (control parameters for phase lock loops and voltage outer loop are respectively (12, 120) and (10, 100)). The dominant oscillation mode was calculated when each of the control parameters for the DFIG and MMC varies from 10% to 190% of the initial value and the root loci obtained are shown in Fig. 4, where starting point of the root locus is marked in green and end is marked in yellow.

Fig. 3. Root loci of the dominant quasi-power-frequency oscillation mode considering impact of the phase lock loop and voltage outer loop.

From Fig. 4, the control parameters of phase lock loops of the DFIGs and voltage outer loop of the MMC have a significant impact on the quasi-power-frequency oscillation. Besides, when the bandwidth of voltage outer loop of the MMC is low, the quasi-power-frequency oscillation can also be affected by the control parameters for outer and inner loops of the RSCs of the DFIGs. 3.2 Impact of Operating Conditions In this section, impact of operating conditions on the quasi-power-frequency oscillation is studied. The analysis was also conducted by taking λ1 , λ2 and λ3 as examples. The dominant oscillation mode was calculated when active power output for each of the DFIGs increased from 10% to 100% of the rated capacity. The root loci of λ1 , λ2 and λ3 are shown in Fig. 5, where starting point is marked in green and end is in yellow. It can be seen that with the increase of active power output, damping of the dominant oscillation mode decreases.

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(a) 1

(c)

(b)

2

3

Fig. 4. Root loci of the dominant quasi-power-frequency oscillation mode considering impact of the control parameters for the DFIGs and MMC.

1

2 3

Fig. 5. Root loci of the dominant quasi-power-frequency oscillation mode considering impact of operating conditions.

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4 Simulation Verification

(4, 40)

(3, 30)

(2, 20)

2.595 2.585 2.575 0

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2

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4

5

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2.605

2.615 (10, 100) 2.585 2.565 0

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2.591

2.358

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(a) Scenario 1 Active power output of the MMC/p.u.

Active power output of the MMC/p.u.

In this section, conclusions drawn based on the linearized model will be verified via non-linear simulation. Due to the limitation of space, in the simulation verification, only the following scenarios are taken into consideration. Scenario 1: From Fig. 3, under the condition that control parameters for voltage outer loop of the MMC are (6, 60), the system is respectively stable, critically stable and unstable when parameters for the phase lock loop of the DFIG are (2, 20), (3, 30) and (4, 40). Besides, the corresponding dominant oscillation mode is respectively λ11 = 0.45 + j25.86, λ12 = 0.01 + j30.07 and λ13 = −0.67 + j33.14. Scenario 2: From Fig. 3, under the condition that control parameters for the phase lock loop of the DFIG are (1, 10), the system is stable/unstable when control parameters for voltage outer loop of the MMC are (10, 100)/(6, 60). The corresponding dominant mode are respectively λ21 = −0.88 + j18.41 and λ22 = 0.52 + j19.07. Scenario 3: From Fig. 5, under the condition that control parameters for phase lock loop of the DFIG and voltage outer loop of the MMC are respectively (3, 30) and (6, 60), the system is critically stable when active power output of each DFIG is the rated capacity and stable when active power output is 90% of the rated capacity. The dominant oscillation modes is respectively λ31 = 0.01 + j30.07 and λ32 = −0.32 + j30.76. In the simulation, active power outputs of the DFIGs decreased by 5% due to a sudden change of the wind at 0.5s and recovered in 0.1s. The active power output of the MMC under the scenarios mentioned above are presented in Fig. 6. It can be seen that, non-linear simulation results are consistent with the results of mode analysis, and hence effectiveness of the conclusions drawn based on linearized model is verified.

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5 Conclusions The quasi-power-frequency oscillation is a new-type of oscillation observed in practical renewable energy integrated power system via MMC-HVDC recently. Characteristics of the quasi-power-frequency oscillation in DFIG wind farms integrated power systems via MMC-HVDC are studied in this paper. The main conclusions drawn are as follows. 1) The quasi-power-frequency oscillation is mostly likely to be induced by the dynamics of phase lock loops of the DFIGs and voltage outer loop of the MMC. In general, damping and frequency of the quasi-power-frequency oscillation increase with the increase of bandwidths of the phase lock loop and AC voltage outer loop. 2) Damping of the dominant quasi-power-frequency oscillation mode is mainly affect by the proportional coefficients of phase lock loop of the DFIG, current inner loop of RSC of the DFIG, AC voltage outer loop of the MMC and operating conditions of the system. In general, with the increase of the proportional coefficients, damping of the oscillation mode also increases. Besides, damping of the dominant quasi-powerfrequency oscillation mode increases with the decrease of active power outputs of the DFIGs. 3) Frequency of the dominant oscillation mode is mainly affected by the integral coefficients of phase lock loop of the DFIG, current inner loop of RSC of the DFIG and AC voltage outer loop of the MMC. The oscillation frequency increases with the increase of integral coefficients.

References 1. Li, R., Yu, L., Xu, L., et al.: Coordinated control of parallel DR-HVDC and MMC-HVDC systems for offshore wind energy transmission. IEEE J Emerg. Selected Top. Power Electr. 8(3), 2572–2582 (2020) 2. Li, Y., An, T., Zhang, D., et al.: Analysis and suppression control of high frequency resonance for MMC-HVDC system. IEEE Trans. Power Deliv. 36(6), 3867–3881 (2021) 3. Li H., Xie X., Liu R., et al.: Analysis and mitigation of the subsynchronous oscillation in renewable energy system connected to the MMC-HVDC. In: Proceedings of the CSEE (2023). Early access 4. Hatziargyriou, N., Milanovic, J., Rahmann, C., et al.: Definition and classification of power system stability-revisited & extended. IEEE Trans. Power Syst. 36(4), 3271–3281 (2021) 5. Fan, L., Miao, Z.: An explanation of oscillations due to wind power plants weak grid interconnection. IEEE Trans. Sustain. Energy 9(1), 488–490 (2018) 6. Fan, L., Miao, Z.: Wind in weak grids: 4Hz or 30Hz oscillations? IEEE Trans. Power Syst. 33(5), 5803–5804 (2018) 7. Du, W., Wang, Y., Wang, H., et al.: Small-disturbance stability limit of a grid-connected wind farm with PMSGs in the timescale of DC voltage dynamics. IEEE Trans. Power Syst. 36(3), 2366–2379 (2021) 8. Huang, Y., Yuan, X., Hu, J., et al.: Modeling of VSC connected to weak grid for stability analysis of DC-link voltage control. IEEE J. Emerg. Selected Top. Power Electr. 3(4), 1193– 1204 (2015)

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9. Ma, N., Xie, X., He, J., et al.: Review of wide-band oscillation in renewable and power electronics highly integrated power systems. Proc. CSEE 40(15), 4720–4732 (2020) 10. Ji, K., Liu, S., Pang, H., et al.: Generalized impedance analysis and new sight at damping controls for wind farm connected MMC-HVdc. IEEE J. Emerg. Selected Top. Power Electron. 9(6), 7278–7295 (2021)

Research on Multi-level Distributed Photovoltaic Consumption Strategies Photovoltaic Based on AC/DC Hybrid Distribution Network Guanglin Sha1 , Qing Duan1 , Lu Liu1 , Jian Gao1(B) , Genqi Chen2 , and Xiaolei Li2 1 Distribution Technology Center, China Electric Power Research Institute, Beijing 100192,

China {Shaguanglin,duanqing,liulu,gaojian}@epri.sgcc.com.cn 2 Shaoxing Power Supply Company, State Grid Zhejiang Electric Power Company, Shaoxing 312000, China

Abstract. Due to the characteristics of volatility, intermittence and uncertainty of distributed photovoltaic, when large-scale distributed photovoltaic is connected to the power grid, it will cause photovoltaic power curtailed. Therefore, a multi-level consumption strategy for access to distributed photovoltaic distribution network is proposed. Firstly, this paper studies the topology of a new energy router, and proposes a new AC/DC hybrid distribution network architecture based on it. Then, according to the operation characteristics of AC/DC hybrid distribution network, the coordinated control strategy of four-level consumption including bus consumption, cross-bus consumption, cross-area consumption and energy return to the grid is studied in detail, which avoids the direct injection of photovoltaic power into the distribution network and reduces the energy exchange between the station areas and the grid. Finally, in the Matlab/Simulink simulation environment, the distributed photovoltaic four-level consumption is simulated and verified, and the results prove the effectiveness of the proposed multi-level consumption strategy. Keywords: Energy router · AC/DC hybrid distribution network · distributed photovoltaic · consumption

1 Introduction In recent years, the problem of environmental pollution caused by the depletion of fossil energy and its combustion has become increasingly prominent. In order to improve this situation, countries focus on the development and utilization of clean energy such as solar energy and wind energy, and actively explore clean energy power generation technology [1–5]. However, there are also many problems in new energy power generation. Taking distributed photovoltaic power generation as an example, because of its intermittent, fluctuating and random characteristics, it will have a negative impact on the voltage level and harmonic content of the access point after being connected to the distribution network [6, 7]. Therefore, more and more scholars have studied how to improve the photovoltaic consumption capacity of the distribution network. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 224–234, 2024. https://doi.org/10.1007/978-981-97-0877-2_24

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Reference [8] introduced a novel distributed energy storage management strategy to improve the photovoltaic consumption capacity of the distribution network through the energy storage system. Reference [9] effectively alleviated the problem of voltage fluctuation and reverse power flow by using energy storage system and optimal control of distribution network. In reference [10], the interaction between AC/DC distribution network and micro-energy network is fully considered, and the optimal scheduling strategy of AC/DC distribution network considering dynamic network reconfiguration and multi-energy coordination is studied to improve the absorptive capacity. Aiming at the grid-connected microgrid with electric vehicles and high-permeability photovoltaics, a dynamic EV interactive response control strategy is proposed to improve the photovoltaic absorption capacity [11]. Most of the above methods rely on the coordinated control of the energy storage system to achieve photovoltaic consumption. It is necessary to configure different capacity energy storage systems for different photovoltaic systems. Therefore, the photovoltaic consumption is greatly affected by the parameters of the energy storage system and has great limitations. In order to improve the distribution network’s ability to absorb distributed photovoltaics, this paper proposes a new topology of energy router. The structure has both grid-connected ports, mutual aid ports, and AC and DC load ports. It can be connected to the distribution network upwards and can accept distributed photovoltaics downwards. In the new AC/DC hybrid distribution network composed of energy routers as the basic unit, each energy router constitutes a station area, and the interconnection between the stations is formed through the DC system, which can realize the multi-level consumption of distributed photovoltaic.

2 AC/DC Hybrid Distribution Network Architecture Based on Energy Router 2.1 The Proposed Energy Router Topology Structure As mentioned above, due to the constraints of power quality, the traditional distribution network has very limited capacity for photovoltaic consumption. On the basis of previous studies, this paper proposes to use the multi-port energy router shown in Fig. 1 as the basic unit of the new AC/DC hybrid distribution network, and studies the distributed photovoltaic consumption strategy under this topology. As shown in Fig. 1, each energy router forms a station area to power the local load. The topology consists of four ports: grid-side converter port, mutual aid port, lowvoltage three-phase AC load port and low-voltage DC load port. The whole system can realize the interconnection and bidirectional energy transfer between different AC and DC systems and different voltage levels through power electronic conversion technology, and can provide standardized interface for electrical equipment through decentralized autonomous control strategy, and realize the bidirectional transmission of electric energy in the system. 2.2 AC/DC Hybrid Distribution Network Architecture The single energy router described in the previous section has a DC bus, an AC load port and a DC load port. As a station area, it can supply power to the AC and DC loads

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in the region. If distributed photovoltaics are added to the AC load port or DC load port of a single energy router, only the three-level consumption of distributed photovoltaics can be achieved, that is, internal consumption of the bus, cross-bus consumption, and energy return to the grid. In order to realize the four-level consumption of distributed photovoltaics, it is necessary to interconnect multiple energy routers through DC mutual aid buses to form an AC/DC hybrid distribution network architecture based on energy routers, as shown in Fig. 2.

Fig. 1. Topology of multi-port bidirectional energy router.

Fig. 2. AC/DC hybrid distribution network architecture.

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3 Control Strategy of AC/DC Hybrid Distribution Network Based on Energy Router 3.1 System-Level Control Strategy The schematic diagram of decentralized autonomous control proposed in this paper is shown in Fig. 3. The positive direction of energy flow from the grid to the DC bus and from the bus to the load port is defined. Both AC and DC load ports adopt constant voltage control. When the distributed photovoltaic output is insufficient or there is no light, the voltage level of the load port tends to decrease. At this time, the offset of the voltage outer loop is positive, the converter is running in the positive direction, and the insufficient power of the load port is supplemented by the DC bus. On the contrary, when the photovoltaic output is surplus, the voltage level of the load port tends to increase. At this time, the offset of the voltage outer loop is negative, the converter runs in the opposite direction, and the surplus power of the load port is sent back to the DC bus. Therefore, the increase and decrease of photovoltaic output are transformed into the upward and downward trend of DC bus voltage.

Fig. 3. Decentralized autonomous control diagram.

The gateway converter also adopts constant voltage control, which is responsible for maintaining the stability of the DC bus voltage. If the DC bus voltage rises, the offset obtained by the voltage outer loop is negative, and the gateway converter runs in the opposite direction, and the surplus power on the DC bus is sent back to the grid. If the DC bus voltage drops, the offset obtained by the voltage outer loop is positive, and the gateway converter runs in the positive direction, injecting power into the DC bus to maintain the bus voltage constant. In this way, each converter maintains the voltage at the outlet, and realizes the power balance inside the energy router while providing power for the AC and DC loads, and realizes the decentralized autonomy of the router. For the mutual port, the total output of the distributed photovoltaic and the total load of the AC and DC are transmitted to the mutual port converter of the station area by the communication system. Taking the sum of photovoltaic output greater than the sum of

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load as an example, at this time, there is power surplus in this station area. If there is a power shortage in other stations at this time, the mutual aid port will send the surplus power to other stations for consumption. At this time, the residual power of the station area will be partially or completely transmitted to other stations, and the energy returned to the power grid will be reduced. At the same time, the area receiving mutual energy can also reduce the energy absorbed from the power grid, so as to realize the cross-area consumption of photovoltaic and improve the utilization rate of distributed photovoltaic. 3.2 Cascaded H-bridge Converter Control Scheme As the input stage of the whole device, the cascaded H-bridge converter is directly connected to the power grid. Its main function is to realize the power conversion from AC to DC, and maintain the balance of its DC side voltage, so as to provide stable DC input for the DC/DC converter in the next link. In this paper, a three-stage DC voltage stabilization control strategy is adopted for the three-phase cascaded H-bridge converter. The first stage is the global DC voltage regulation control, so that the average value of the DC side capacitor voltage of all Hbridge units is equal to the reference value; the second stage is the inter-phase voltage balance control, so that the average DC voltage of all H-bridge units in each phase is equal to the global average DC voltage in the first stage. The third-stage in-phase voltage balance control is a DC voltage stabilization control for each H-bridge unit, so that the DC side voltage of each H-bridge unit is equal to the average DC voltage of all units in the phase. Global DC Voltage Stabilization Control. The schematic diagram of global DC voltage regulation control is shown in the Fig. 4. When the capacitor voltage deviates from the set value, the active current reference value of the inner loop current decoupling is adjusted by the capacitor voltage closed loop on the DC side, so that the DC side of the converter is charged and discharged by the active current, so as to adjust the average value of the DC side capacitor voltage, and then meet the needs of global DC voltage regulation.

Fig. 4. Global DC voltage stabilization control block diagram.

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Interphase DC Voltage Stabilization Control. The phase-to-phase voltage balance means that the sum or average value of the DC-side capacitor voltage of each phase is equal between phases in the three-phase system. When the energy exchanged by the converter is different from the internal loss of the bridge arm, it is easy to cause the unbalance of the three-phase DC side capacitor voltage. In order to solve this imbalance, the power angle between the grid voltage and the AC side voltage of the converter can be adjusted. However, the power angle of the cascaded H-bridge converter in steady-state operation is very small, so directly adjusting the power angle is likely to cause system instability. In this paper, the active power transmitted between each phase bridge arm and the grid side is indirectly adjusted by correcting the reference voltage command value of the bridge arm output. The control block diagram is shown in the Fig. 5.

Fig. 5. Interphase DC voltage stabilization control block diagram.

In-phase DC Voltage Regulation Control. In-phase DC voltage regulation control refers to the DC side voltage balance control of each H-bridge unit in each phase of the three-phase cascaded H-bridge converter. For each H-bridge unit in the single-phase bridge arm, the current flowing through the AC side is the same, so the active power absorbed by each unit should be adjusted by correcting its AC side voltage. In this paper, the voltage balance control strategy based on reactive current in-phase is adopted, as shown in Fig. 6.

Fig. 6. In-phase DC voltage stabilization control block diagram.

3.3 Isolated DC-DC Converter Control Scheme The high-voltage DC generated by the cascaded H-bridge converter needs to pass through the DC/DC converter again to generate a low-voltage DC bus voltage. The change of

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low-voltage DC bus voltage reflects the change of power demand in the AC and DC ports of the low-voltage side of the energy router. Therefore, as the intermediate stage of the energy router, the main control goal of the isolated half-bridge DC/DC converter is to keep the low-voltage side DC bus voltage constant. The control principle is shown in Fig. 7.

Fig. 7. Isolated DC-DC converter control block diagram.

3.4 Mutual Converter Control Scheme The function of the mutual aid port is to transmit the excess power of the station area to other stations when the sum of the photovoltaic output in the station area is greater than the sum of the local load, there is excess power in the station area, and there is a power shortage in other stations. When there is a power shortage in the station area and there is excess power in other stations, the excess energy of other stations is absorbed into the station area to realize mutual support between the stations, so as to realize the multi-level consumption of photovoltaic. Taking two stations as an example, assuming that in the first station area, the sum of photovoltaic output is Ppv, and the sum of AC load and DC load is Pload , the excess power in the first station area is P1 = Ppv -Pload . If P1 > 0, there is excess power in the station area; if P1 < 0, there is a power shortage in the station area. Similarly, P2 is used to represent the excess power in the second station area. P1 * is used to represent the power instruction of the first zone mutual converter. The power relationship between the two areas has the following situations: (1) When P1 > 0 and P2 > 0, the two stations have excess power, and the mutual converter does not transmit power. At this time, the power instruction P1 * = 0. There is no energy exchange between the two stations, and the respective excess power is returned to the grid separately. (2) When P1 > 0, P2 < 0, and P1 ≥ | P2 |, the station area 1 has excess power, while the station area 2 has a power deficit, and the excess power of the station area 1 is greater than the power of the station area 2. At this time, let P1 * = | P2 |, station area 1 transmits power to station area 2, completely supplements the power deficit of station area 2, and returns the remaining power to the power grid. (3) When P1 > 0, P2 < 0, and P1 < | P2 |, station 1 has excess power, while station 2 has power shortage, but the excess power of station 1 is less than the power shortage of station 2, and P1 * = P1 . The station area 1 transmits all the excess power in the station area to the station area 2, but it still cannot fully supplement the power shortage of the station area 2, and the remaining insufficient power of the station area 2 is supplemented by the power grid. (4) When P1 < 0, P2 < 0, there is a power shortage in the two stations, and the mutual converter does not transmit power. At this time, the power instruction P1 * =

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0, there is no energy exchange between the two stations, and the insufficient power is supplemented by the grid connected to each station. (5) When P1 < 0, and | P1 | < P2 , the power of station area 1 is deficient, while station area 2 has excess power, and the excess power of station area 2 is greater than the power of station area 1. At this time, let P1 * = P1 , station area 1 absorbs power from the mutual bus, and completely supplements the power shortage of station area 1. Area 2 will return the remaining power to the grid. (6) When P1 < 0, and | P1 | ≥ P2 , the station area 1 power shortage, and the station area 2 has excess power, but the excess power of the station area 2 is less than the power shortage of the station area 1. At this time, let P1 * = -P2 , the station area 1 absorbs power from the mutual bus, and the station area 2 transmits the excess power to the station area 1 completely, but it still can not fully supplement the power shortage of the station area 1, and the insufficient power of the station area 1 is replenished by the power grid. The mutual converter of station area 2 adopts constant voltage control to maintain the stability of DC bus voltage. At the same time, it cooperates with the mutual aid converter of station area 1. When station area 1 injects power into the mutual aid bus, station area 2 can absorb this part of power. When the station area 1 to the mutual bus absorption power, can realize the station area 2 to the mutual bus to supplement this part of the power, so as to realize the mutual aid of energy between the two stations, to achieve cross station consumption of photovoltaic.

4 Simulation Results

Table 1. System simulation parameters. Symbol

Parameter

Value

V bus

DC bus voltage

800V

V mutual

Mutual aid bus voltage

16kV

PG

Gateway converter power

0-200KW

PM

Mutual converter power

0-200KW

Pac

AC load power

100KW

Pdc

DC load power

100KW

In order to verify the four-level consumption strategy of distributed photovoltaic and obtain the power flow waveform of the energy router, this paper builds a simulation model of the energy router in the Matlab/Simulink environment. Some parameters of the simulation are shown in Table 1.

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The distributed photovoltaic is connected to the DC load port, and the photovoltaic power of the station area 1 is gradually increased. The photovoltaic power of the station area 2 is constant. The power conversion curves of the station area 1 and the station area 2 are shown in Fig. 8 and Fig. 9, respectively. From 0s to 0.1s, the photovoltaic power is 0, and all the loads in the station area are powered by the power grid. Considering the power loss of each converter, the power absorbed by the gateway converter from the grid is about 210 kW. From 0.1s to 0.2s, the photovoltaic power increases continuously, and the first stage of photovoltaic consumption, that is, the bus consumption, begins to be realized. The power absorbed by the DC port begins to decrease, and the power absorbed by the gateway converter from the grid also begins to decrease, and the part of the absorbed power reduction is equal to the photovoltaic power. From 0.2s to 0.3s, this period of time just to achieve the first level of photovoltaic consumption. The photovoltaic power is exactly supplied to the DC load in the bus, and the power absorbed by the DC port is 0, as shown in the figure. From 0.3s to 0.4s, the photovoltaic power continues to increase. At this time, the photovoltaic power is already greater than the load power in the bus. After the bus is consumed, there is still a power surplus. Therefore, the power absorbed by the DC port becomes negative, and the external power is emitted. The power is the difference between the photovoltaic power and the load power of the bus. During this period, the power absorbed by the gateway converter from the grid continues to decrease. Photovoltaics not only supply power to the bus load, but also provide a part of the power for the AC bus load, achieving cross-bus consumption. From 0.4s to 0.5s, the photovoltaic power is constant at 200 kW. During this period of time, the photovoltaic power is equal to the total load power of the station area, which just fully realizes the in-bus consumption and cross-bus consumption. At this time, the power absorbed by the gateway converter from the grid is reduced to 0, and the power self-sufficiency is fully realized inside the station area. From 0.5s to 0.7s, the photovoltaic power continues to increase, and the photovoltaic power is already greater than the total load of the station area. The station area 2 has always had a power shortage of 100 kW, so the mutual converter is started at this time, and the excess power of the station area 1 is sent to the station area 2 to realize the cross-station consumption of photovoltaics, that is, the third-level consumption. After 0.8s, the photovoltaic power continues to increase, and the station area 2 can not be absorbed at this time. Therefore, the power waveform of the gateway converter is reversed, and the excess power is returned to the power grid to realize the fourth-level consumption. Figure 10 shows the voltage waveform of the DC bus in the energy router. It can be seen from the figure that the DC bus voltage is stable at 800 V, and the fluctuation of photovoltaic does not affect the fluctuation of DC bus voltage.

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5 Conclusion In order to improve the consumption capacity of distributed photovoltaic in distribution network, this paper studies the topology and working principle of an energy router, as well as the working characteristics of each port converter. The advantages of a new AC/DC hybrid distribution network architecture composed of energy routers as basic

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units are described. On this basis, the coordinated control strategy to realize the four-level consumption of distributed photovoltaic is studied. The simulation model is built, and the simulation results verify the effectiveness of the four-level consumption coordination control strategy of distributed photovoltaic. Acknowledgements. This work is supported by the State Grid Corporation of Headquarter Science and Technology Project under Grant 5400-202255484A-2–0-KJ. ( Research and development of key technologies of flexible distribution secondary system integration for energy interconnection).

. References 1. Walling, R.A., Saint, R., Dugan, R.C., Burke, J., Kojovic, L.A.: Summary of distributed resources impact on power delivery systems. IEEE Trans. Power Deliv. 23(3), 1636–1644 (2008). https://doi.org/10.1109/TPWRD.2007.909115 2. El Shafei, A., Ozdemir, S., Altin, N., Jean-Pierre, G., Nasiri, A.: Development of a medium voltage, high power, high frequency four-port solid state transformer. CES Trans. Electr. Mach. Syst. 6(1), 95–104 (2022) 3. Hanbin, D., Peiqiang, L., Jifei, W., Dan, W., Zhensheng, L.: Optimal dispatch of integrated energy system considering complementary coordination of electric/thermal energy storage. Trans. China Electrotech. Soc. 35(21), 4532–4543 (2020). (in Chinese) 4. Xuechun, W., Hongkun, C., Lei, C.: Multi-player interactive decision-making model for operational flexibility improvement of regional integrated energy system. Trans. China Electrotech. Soc. 36(11), 2207–2219 (2021). (in Chinese) 5. Hui, S., Haibao, Z., Xin, W.: Research and application of multi-energy coordinated control of generation, network, load and storage. Trans. China Electrotech. Soc. 36(15), 3264–3271 (2021). (in Chinese) 6. Abdelrahman, Milanovi´c, J.V.: Practical approaches to assessment of harmonics along radial distribution feeders. IEEE Trans. Power Deliv. 34(3), 1184–1192 (2019) 7. Torquato, R., Salles, D., Pereira, C.O., Meira, P.C.M., Freitas, W.: A comprehensive assessment of PV hosting capacity on low-voltage distribution systems. IEEE Trans. Power Deliv. 33(2), 1002–1012 (2018). https://doi.org/10.1109/TPWRD.2018.2798707 8. Jayasekara, N., Wolfs, P., Masoum, M.A.S.: An optimal management strategy for distributed storages in distribution networks with high penetrations of PV. Electr. Power Syst. Res. 116, 147–157 (2014) 9. Zhicheng, X., Bo, Z., Ming, D., et al.: Photovoltaic hosting capacity evaluation of distribution networks and inverter parameters optimization based on node voltage sensitivity. Proc. CSEE 36(06), 1578–1587 (2016). (in Chinese) 10. Zhong, Z., Shihong, M., Chao, L., Di, Z., Ji, H.: Coordinated optimal dispatching strategy of AC/DC distribution network for the integration of micro energy internet. Trans. China Electrotech. Soc. 37(1), 192–207 (2022). (in Chinese) 11. Xiaodong, Y., Youbing, Z., Yangchang, J., Xieluyao, Z.B.: Renewable energy accommodation-based strategy for electric vehicle considering dynamic interaction in microgrid. Trans. China Electrotech. Soc. 33(02), 390–400 (2018). (in Chinese)

Research on the Influence of Harmonics on Interruption Performance of High-Voltage Circuit Breaker Han Zhang1 , Gang Wang1 , Renjie Yu1 , Ze Guo2 , and Xingwen Li1(B) 1 State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong

University, Xi’an 710049, China [email protected] 2 State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300401, China

Abstract. In the context of the new electric power system, the large-scale access of renewable energy source and power electronic devices has led to an increase of harmonic components in the main grid. High-voltage circuit breakers, as crucial switching devices in the power system, will be influenced during their breaking performance under harmonic conditions. Therefore, investigating the breaking performance of high-voltage circuit breakers under harmonic conditions is essential for preventing the serious consequences that could arise from breaking failures. In this study, a harmonic breaking experimental platform was constructed using a synthetic circuit to simulate actual operating conditions of the power system. Through conducting breaking experiments under both fundamental frequency conditions and harmonic conditions, the influence of harmonics on arc energy and the erosion condition of contacts in high-voltage circuit breakers was analyzed. The experimental results indicate that, in comparison to fundamental frequency currents, harmonic currents cause significant fluctuations in arc voltage during the breaker interruption process. When the arcing time is same, the arc energy of harmonic conditions is higher, leading to more severe erosion of the contacts. Keywords: New power system · Harmonics · High voltage circuit breaker · Breaking performance

1 Introduction In recent years, China has vigorously promoted the "carbon peak carbon neutral", in order to achieve this goal, the power system towards a clean, low-carbon, intelligent direction to accelerate the construction. In this context, with the large-scale access of renewable energy sources such as wind power and photovoltaic and nonlinear loads such as electric vehicle charging piles, the harmonic components in the power system are increasing, and the transmission mechanism is becoming more complex. Harmonics cause distortion of current waveform in power system, and the zero crossing slope of distorted harmonic current increases compared with the fundamental wave, which © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 235–244, 2024. https://doi.org/10.1007/978-981-97-0877-2_25

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makes the breaking condition of high-voltage circuit breaker worse, and the probability of breaking failure increases accordingly. At the same time, the larger arc energy under harmonic condition causes serious contact erosion and shortened electrical life. In order to study the breaking performance of circuit breakers, many scholars have done a lot of useful work. Shi Y [1] et al. calculated the electric conductivity of arc plasma under different SF6 gas pressure and temperature by using the non-equilibrium small current arc mathematical model, and applied it to the calculation of the airflow field of 1100kV filter group circuit breaker to study the influence of different breaking phase angle, different contact burning degree, different charging pressure and different breaking speed on the recovery characteristics of the circuit breaker’ s back-arc medium. Peng Z [2], Liu K [3] et al. studied the breaking characteristics of circuit breakers under harmonic currents by establishing an arc magnetohydrodynamic model under harmonic currents. The research shows that the existence of harmonics in the system will cause the current change rate di/dt to increase significantly when the current flows through zero during the breaker breaking process, which affects the breaker breaking process and is not conducive to the successful breaker breaking. Zhou Y [4, 5] et al. studied the ablation of contacts by electric arc. Yin J [6] et al. studied the effect of frequency on dynamic characteristics of arc through the combination of experiment and simulation. Based on the operation status of the distribution network, Li Z [7] et al. described the impact of new energy power generation on the safe and stable operation of the grid, and proposed solutions. Lee S [8], Wang W [9] used a synthetic circuit to generate harmonics and obtained ideal results in simulation and experiment. Kuzmin S.V [10] et al. considered the influence of higher harmonics of current and voltage on the degree of switching overvoltage, and finally determined that the 5th and 7th current harmonics had the greatest influence on the value of switching overvoltage. Based on the above research, this paper uses synthetic circuit to build a harmonic breaking experiment platform, which is used to simulate the actual operating conditions of power system, and carry out the breaking experiment of high-voltage circuit breaker, so as to analyze the influence of harmonics on arc energy and contact erosion during the arc burning stage.

2 Experimental Platform 2.1 Synthetic Circuit and Test Prototype High voltage circuit breaker direct breaking test needs large short circuit capacity, and the experiment cost is high, synthetic circuit test is an equivalent test method, so the synthetic circuit test is usually used. The synthetic circuit is mainly composed of current source loop and voltage source loop. In general, the current source generates the breaking current, and the voltage source generates the recovery voltage. In this paper, in order to study the breaking performance of circuit breakers under harmonic conditions, fundamental current is generated by current source and harmonic current is generated by voltage source. The zero crossing slope caused by harmonic current in real power system is simulated by overlapping the zero crossing of fundamental current and harmonic current. The schematic diagram of harmonic breaking test circuit based on synthetic circuit is shown in Fig. 1.

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Ls AB R01

G1

TO

R1

G2 A

C C01

C1

G3 Cs

Fig. 1. Schematic diagram of harmonic breaking test circuit.

Among them, C and L constitute the fundamental current source oscillation circuit; Cs and Ls constitute the harmonic current source oscillation circuit; R01 and C01 limit the recovery voltage of the auxiliary switch AB. G1 is the closing circuit breaker; TO is the trial circuit breaker; G3 is the ignition ball gap. According to the collected operation data, harmonics in the power system are mainly consisted of the 3rd, 5th, 7th and 11th harmonics. In order to remove the influence of harmonic frequency on the results, only the 7th harmonics are selected for the test. The inductance and capacitance parameters in the experiment can be calculated by formula (1), f =

1 √

(1)

2π LC

By calculating the value of inductance and capacitance, the harmonic current source can generate harmonics of the expected frequency. At the same time, in order to avoid the current limiting problem, the capacitor value should be reduced as much as possible at a small current level, so as to increase the charging voltage, in this way, the reduction of current waveform period which is caused by arc voltage higher than the charging voltage can be avoided. After calculation, the selection of the inductance and capacitance parameters of the fundamental current source loop and the voltage source loop are shown in Table 1. Table 1. Selected Synthetic Circuit Parameters. Current source

Current level

Inductance

Capacitance

Charging voltage

Fundamental current source

4kA

0.34mH

25mF

0.8kV

12kA

0.17mH

50mF

1.25kV

Harmonic current source

24kA

0.09mH

84mF

1.7 kV

0.4kA

1.8mH

97.5 µ F

2.5kV

1.2kA

1.8mH

97.5µF

7.2kV

2.4kA

1.8mH

97.5µF

8.0kV

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The physical layout of the synthetic circuit experimental platform is depicted in Fig. 2. Rogowski coils and high-voltage probes are employed to measure the arc current and arc voltage of the circuit breaker during the interruption process. Data is captured using an oscilloscope with a sampling frequency of 500 kHz. To investigate the impact of harmonics on arc voltage and current during the interruption process, this study consists of two sets of experiments: a fundamental frequency control group and a harmonic test group. Each group of experiments involves 36 interruption trials at current levels of 4kA, 12kA, and 24kA, resulting in a total of 108 interruptions in each group.

(a)

(b)

Fig. 2. (a) Synthetic circuit experiment platform (b) SF6 porcelain column circuit breaker.

The circuit breaker prototype used for the experiments is an SF6 porcelain column circuit breaker, as illustrated in Fig. 2(b). The model of this circuit breaker is LW25A126, which features a rated current of 3150A, a rated voltage of 126kV, and a rated short-circuit breaking current of 40kA. 2.2 Breaking Test To simulate the most severe operating conditions in actual power systems, the experiments achieve alignment between the zero-crossings of the seventh harmonic and the fundamental frequency by controlling the moment of triggering the arcing gap. The timing coordination of multiple circuit breakers is involved during the interruption process, primarily involving the synchronization between the closing breaker G1, the test object breaker TO, and the arcing gap G3. Based on measurements, the inherent closing time of breaker G1 is 45.3ms, the inherent opening time of test object breaker TO is 40ms, and the delay time of arcing gap G3 is 250 µ s. The timing coordination between these circuit breakers is controlled as depicted in Fig. 3.

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Fig. 3. Circuit breaker control sequence diagram.

3 Result Analysis 3.1 Comparative Analysis of Fundamental and Harmonic Breaking Waveform Based on the experimental setup described above, a total of 108 tests were conducted under both fundamental frequency and fundamental frequency superimposed with harmonic conditions. Selected experiment waveforms are depicted in the figure provided. From Fig. 4, it can be observed that when the circuit breaker interrupts fundamental frequency current, the arc voltage begins to rise at the moment of arcing initiation. There is a significant arc extinction peak before the arc is extinguished, ultimately leading to successful breaking at the first zero-crossing of the current waveform. During interruption of harmonic current, due to the distortion in arc current, the arc voltage experiences substantial fluctuations. A notable arc extinction peak is also observed before the arc is extinguished, with successful break occurring at the zero-crossing point. This indicates that even under conditions of increased fluctuation in arc voltage caused by the distortion of harmonic current, the circuit breaker can still successfully break short-circuit current when the rate of change near the zero-crossing point is heightened, particularly at lower current levels.

(a)

(b)

Fig. 4. 4kA current level breaking waveform (a) Only fundamental wave (b) Harmonics contained.

From Fig. 5, it is evident that an increase in current levels results in higher voltages across the contacts. Thus, even in the closed state, higher voltages are observed. Following arcing initiation, the generation of arc leads to an increase in the measured voltage.

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(a)

(b)

Fig. 5. 12kA current level breaking waveform (a) Only fundamental wave (b) Harmonics contained.

(a)

(b)

Fig. 6. 24kA current level breaking waveform (a) Only fundamental wave (b) Harmonics contained.

Similar to the 4kA current level, a higher arc extinction peak can be seen before the zerocrossing point, ultimately leading to arc extinguishment in the first cycle of the current waveform. With further escalation in current levels, as demonstrated by the waveform for 24kA in Fig. 6, the influence of harmonics continues to cause sustained fluctuations in arc voltage, which is the same as the situations of 4kA and 12kA. Moreover, at the 24kA current level, the magnitude of the arcing peak under harmonic conditions far exceeds that of the fundamental frequency, posing a greater challenge to the circuit breaker’s interruption. Using formulas (2), (3) and (4), various parameters such as arc energy, transfer charge, and Joule energy during the circuit breaker interruption process were calculated for both fundamental frequency and fundamental frequency superimposed with seventh harmonic conditions. The results are presented in Fig. 7.  (2) Earc = I · U dt  C1 =

I dt

(3)

I 2 dt

(4)

 C2 =

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It can be seen that under each current level, the amount of transferred charge and Joule energy in the arc burning stage under harmonic condition are significantly higher than that under fundamental condition. Therefore, under the influence of harmonic condition, the erosion of contacts will increase, thus greatly shortening the electrical life of the circuit breaker.

Fig. 7. Transfer charge in the arc burning stage.

3.2 The Erosion Degree of Circuit Breaker Contacts In order to contrast the impact of interrupting fundamental frequency and harmonic currents on contact erosion, after the completion of each interruption test at various current levels, the moving and static arc contacts were disassembled and their erosion conditions were observed. The contact erosion conditions are illustrated in the provided figure. From the Figs. 8, 9 and 10, it can be observed that at the 4kA current level, which is relatively low, after 36 interruptions, the erosion on the contacts caused by both fundamental frequency and harmonic interruptions is roughly similar. At the higher current level of 12kA, it is evident that contact erosion due to harmonic interruptions is significantly more severe compared to fundamental frequency interruptions. To investigate the variation in contact quality, the mass of the moving and static contacts was measured after the completion of each interruption experiment at different current levels. A comparison of the contact erosion mass is presented in the Tables 2 and 3. It is evident that the arc energy is higher under harmonic conditions. Consequently, in the same current level, contact erosion is notably more severe compared to the fundamental frequency scenario, which leads to a reduced lifespan of the circuit breaker.

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(a)

(b)

Fig. 8. Contact ablation condition (a) Only fundamental wave (b) Harmonics contained.

(a)

(b)

Fig. 9. Contact ablation condition (a) Only fundamental wave (b) Harmonics contained.

(a)

(b)

Fig. 10. Contact ablation condition (a) Only fundamental wave (b) Harmonics contained.

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Table 2. Mass of contact after experiment under fundamental condition. Serial number

Static arc contact

Moving arc contact

1

442.498g

642.27g

2

440.144g

640.14g

3

420.870g

625.00g

Table 3. Mass of contact after experiment under harmonic condition. Serial number

Static arc contact

Moving arc contact

1

442.391g

636.20g

2

439.754g

633.95g

3

412.865g

613.09g

4 Conclusion This study used an SF6 porcelain column circuit breaker as the experimental prototype and established a harmonic interruption experiment platform based on a synthetic circuit. By conducting tests at three current levels: 4kA, 12kA, and 24kA, for both fundamental frequency and fundamental frequency superimposed with a 10% seventh harmonic, the influence of harmonics on circuit breaker interruption performance was investigated. The results indicate that under harmonic interruption conditions, arc energy, transfer charge, and Joule energy are all higher than under fundamental frequency interruption conditions. Besides, contact erosion is more severe. This study establishes a theoretical foundation for the operational maintenance of circuit breakers under harmonic conditions in power systems.

References 1. Shi, Y.: Study on breaker breaking characteristics of 1100kV filter group. Shenyang Industrial University (2023). (in Chinese) 2. Peng, Z., Liu, K., Nan, Y.W., et al.: Coupling model of AC filter branch in SF6 circuit breaker during the break process. Plasma Sci. Technol. 2020, 22(12), 125402 (2023) 3. Liu, K., Li, R., Peng, Z., Chen, J., Yu, X., Chen, S.: Research on breaking arc characteristics of circuit breakers under harmonic current. In: 2021 International Conference on Advanced Electrical Equipment and Reliable Operation (AEERO), Beijing, China, pp 1–4 (2021) 4. Zhou, Y., et al.: Surface average temperature measurement of Cu-W contact material burning in CO2: preliminary study. Plasma Phys. Technol. 10(1), 20–23 (2023) 5. Zhou, Y., et al.: Experimental study of arc erosion in gas-blasting and free-burning conditions in high-voltage circuit breakers. Plasma Phys. Technol. 10(1), 32–35 (2023) 6. Yin, J., Li, X., Liu, C., et al.: Experimental study on effect of frequency on air arc ignition characteristics of low voltage circuit breaker. High Voltage Technol. 47(11), 10 (2021). (in Chinese)

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7. Li, Z.: The influence of new energy power generation on the operation of distribution network and the corresponding measures. Electric Age, 2022(6), 3 (2022) 8. Lee, S., Yoo, J., Jeon, H.J., Choe, G.H.: Design and development of distorted source device for circuit breakers failure analysis. In: 2007 7th International Conference on Power Electronics, Daegu, Korea (South), pp. 411–413 (2007) 9. Wang, W., et al.: Harmonic current simulation and test based on synthetic circuit. In: 2023 IEEE 6th International Electrical and Energy Conference (CIEEC), Hefei, China (2023) 10. Kuzmin, S.V., Umetskaia, E.V., Zavalov, A.A.: Influence of power quality on value of switching overvoltages in networks 6–10 kV. In: 2020 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), pp. 1–4. IEEE (2020)

Sensorless Control of Permanent Magnet Synchronous Motor Based on Adaptive Sliding Mode Observer Xu Shizhou, Jia Xinxin(B) , Fan Jingsheng, and Chang Jinhai Henan Normal University, Xinxiang 453007, Henan, China [email protected]

Abstract. For the sensorless control method of traditional sliding mode observer, the high frequency harmonic content in the fundamental wave of Counterelectromotive force is high, the dither is serious, and The error of rotor position estimation is relatively large. In this paper, a sensorless control method of PMSM with adaptive sliding mode observer is proposed. Firstly, the adaptive rate of Counter-electromotive force is constructed, and the adaptive rate satisfies the stability of Lyapunov function. The adaptive sliding mode observer is constructed, which can rapidly reduce the observation error of Counter-electromotive force. In the rotor position estimation process, a phase-locked loop method is adopted, and a rotation impact elimination link is added to the traditional phase-locked loop, the effect of speed change is eliminated and the observation accuracy of sliding mode observer is improved. Finally, set up in Matlab/simulink simulation model. The results show this approach can effectively suppress sliding mode dither, reduce high-frequency harmonics in Counter-electromotive force, the high frequency harmonics in the Counter-electromotive force are reduced and the precision of rotor position observation is to improve. Keywords: PMSM · sliding mode observer · adaptive rate · Phase-locked loop

1 Introduction As an important electromechanical conversion device in daily life and industrial production, electric motors have a wide range of applications [1, 2]. In current industrial applications, the rotor speed and position information of PMSM are still obtained by mechanical sensors, so as to carry out efficient vector control of PMSM. The use of mechanical sensors increases installation costs, and has poor stability and low signal reliability in harsh environments. Sensorless control technology can enhance the reliability of permanent magnet synchronous motor control systems and the inclusiveness of the working environment [3–5]. In response to the problems of low observation accuracy and severe jitter in traditional sliding mode observers, this article proposes an adaptive sliding mode observer (ASMO) based sensorless control method. On the premise of satisfying the stability of Lyapunov function, this article constructs an ASMO for the Counter-electromotive force, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 245–253, 2024. https://doi.org/10.1007/978-981-97-0877-2_26

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which quickly attenuates the observation error of the back electromotive force. This article adopts a phase-locked loop method with a link to eliminate the influence of rotation to get the rotor position, and eliminates the influence of speed changes to improve observation accuracy. Set up in Matlab/simulink simulation model. The results show this approach can effectively suppress sliding mode dither, reduce high-frequency harmonics in Counter-electromotive force and improve rotor position observation accuracy compared with traditional sliding mode observer. At present, there are two sensorless methods for PMSM. High frequency signal injection method is usually used at low speed stage, and Counter-electromotive force and flux estimation method are usually used at medium and high speed stage [7]. The high frequency signal injection method utilizes the saliency effect of permanent magnet synchronous motors, the high frequency signal is injected between two adjacent windings of PMSM [8, 9]. The high frequency signal excites the magnetic field in the stator winding, resulting in a high frequency response current that differs significantly from the fundamental current frequency at low speeds. By separating the response current through a filter, the rotor position information of the motor is obtained. The SMO method is a usually used method in the medium to high speed operation stage [10]. As a nonlinear observer, its structure will change as the state changes, It is similar to hysteresis control and belongs to discontinuous control. The SMO method is not affected by external disturbances and has strong robustness and adaptability [11]. Because of its simple structure and easy implementation, it is widely used for position sensorless control. Literature [12], this paper presents a sensorless control of fuzzy control algorithm, the method can effectively decrease the error of speed control and improve control accuracy; Reference [13] proposes a sensorless control method for parallel sliding mode observers, which can effectively reduce the dependence of control algorithms on motor parameters and enhance the observation accuracy of the observer; In reference [14], an error compensation control method is proposed to improve the precision of rotor position estimation by compensating the error of rotor position estimation. This article proposes an adaptive SMO based sensorless control method. On the premise of satisfying the stability of Lyapunov function, this article constructs an adaptive SMO for the Counter-electromotive force, which quickly attenuates the observation error of the Counter-electromotive force. This article adopts a phase-locked loop method with a link to eliminate the influence of rotation to get the rotor position, and eliminates the influence of speed changes to improve observation accuracy. Set up in Matlab/simulink simulation model. The results show this approach can effectively suppress sliding mode dither, reduce high-frequency harmonics in Counter-electromotive force and improve rotor position observation accuracy compared with traditional sliding mode observer.

2 Design of Sliding Mode Observer In this article, the surface mount PMSM is taken as the control object, and the mathematical model is established in a two-phase stationary coordinate system:         1 uα Rs iα 1 d iα −sin θe = − − f ωe (1) cos θe dt iβ Ls uβ Ls iβ Ls

Sensorless Control of Permanent Magnet Synchronous Motor



Eα Eβ



 = f ωe

− sin θe cos θe

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 (2)

In formula (1), uα and uβ are the stator voltage on the α and β coordinate axis; iα and iβ are the stator current on the α and β coordinate axis; Rs and Ls are stator resistance and inductance on the α and β coordinate axis; Eα and Eβ are counter-electromotive force component on the α and β coordinate axis; ωr and f are rotor electrical angular velocity and rotor magnetic flux. It can be seen from Eqs. (1) and (2) that the rotor position information is only included in the Counter-electromotive, so the rotor position information can be get through the back EMF, and the differential equation of Eq. (2) is satisfied:       d −f ωe sin θe d Eα −f ωe sin θe = = ωe −f ωe cos θe dt Eβ dt f ωe cos θe   −Eβ = ωe (3) Eα The stator current error is defined as the sliding mode surface of the SMO: (4) When the SMO reaches the sliding film switching surface, the Counter-electromotive force observation will converge to the true value, thus the rotor flux angle can be calculated. The adaptive sliding mode observer is designed: (5) In Eq. (5), k is the SMO gain coefficient and satisfies the following equality. (6) According to Eqs. (1) and (5), the error equation for the current can be obtained as: (7)

Due to the system entering the sliding surface,

, from Eq. (7), it can be

concluded that: ∼

Eβ = Ls ksign(s) Therefore, the adaptive rate of Counter-electromotive force is designed as: ⎧ d ⎪ Eα ⎨ dt E α = −ωe E β − l d dt E β = ωe E α − l Eβ ⎪ ⎩ d ω = Eα E β + E α Eβ dt e 









(8)









(9)

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To prove the stability of the adaptive SMO, the Lyapunov function is defined as: V =

1 2 2 ( E + Eβ + ω2e ) 2 α

(10)

Due to the fact that the mechanical time constant is much greater than the electrical time constant, it is assumed that the rotational speed remains constant within an estimated period. From Eq. (9), it can be concluded that: ⎧ d ⎪ Eα = −ωe E β + ωe Eβ − l Eα ⎨ dt d (11) E = ω E − ω E − l E e α e α β dt β ⎪ ⎩ d ω = Eα E β − E α Eβ dt e 















Substituting Eq. (11) into Eq. (10) yields: (12) Therefore, Eq. (12) satisfies the Lyapunov stability theorem, indicating that the algorithm formula is stable.

3 Estimation of Rotor Position and Velocity According to Eq. (2), the SMO Counter-electromotive force contains the information of rotor and speed position, the position information of the rotor is usually get using the arctangent function. 

∼

θ = −tan

−1

(

Eα



Eβ

)

(13)

However, the sliding mode variable structure may experience shaking during operation, This will lead to high-frequency dither of Counter-electromotive force. If the inverse tangent function is used to estimate the rotor position, it will be affected by highfrequency dither during the operation process, and the error of rotor estimation will increase. In this article, the PLL is used to estimate the position and velocity information of the rotor. The Counter-electromotive force observation—eα and eβ can be obtained from the adaptive sliding mode observer: 



(14) In Eq. (14), ke = ωe f . The error signal of Counter-electromotive force is adjusted by PI controller to get the rotor speed, and the rotor position is get through integration. In Eq. (14), ke = ωe f . The error signal of Counter-electromotive force is adjusted by PI controller to obtain the rotor speed, and then the rotor position is obtained through integration. The open loop transfer function of the PLL is as follows: 

GPLL

ke kp s + ke ki θe = = 2 θe s + ke kp s + ke ki

(15)

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In Eq. (15), kp and ke are Proportional and integral coefficients of PI regulators. Due to the inclusion of speed information in ke , changes in speed can have an impact on the performance of the desired position estimation. Adding a rotation influence link to the traditional phase-locked loop can eliminate the influence of rotor speed and improve observation accuracy. The structure of the PLL is shown in Fig. 1.

Fig. 1. Block diagram of phase-locked loop structure

Equation (8) can be written in the following form: − Eˆ α cosθˆe − Eˆ β cosθˆβ = ωˆ e f sinθe cosθˆe − ωe f cosθe sinθˆe = ωˆ e f sin(θe − θˆe )

(16)

After adding the process of eliminating the influence of rotation, the error information of the rotor position can be expressed as: 



 E = ωe f sin θe − θ e / eα 2 −eβ 2 = sin θe − θ e (17) 









The speed information obtained by the phase-locked loop is fed back to the adaptive algorithm, which forms the adaptive SMO as shown in Fig. 2.

Fig. 2. Adaptive sliding mode observer

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4 Simulation and Analysis To verify the proposed adaptive SMO position sensorless control system, the author builds a simulation model on Matlab/Simulink based on Fig. 3.

Fig. 3. Adaptive sliding mode observer sensorless control system

The arguments of PMSM used in the simulation are shown in Table 1. Table 1. Parameters of permanent magnet synchronous motor. Parameter

Numeric value

Number of phases (m)

3

Number of pole pairs (p)

4

Rated speed (r/min)

1000

Stator resistance ()

2.875

Armature inductance (H)

0.0085

Rotational inertia (kg·m2 )

0.001

Flux linkage (Wb1)

0.175

When the motor speed reaches 1000 r/min, the parameter curve of the motor operation using a traditional SMO is as follows, as shown in Fig. 4, 4-(a) is Motor speed variation curve, 4-(b) is error variation curve of actual and observed motor speed values, 4-(c) is variation curve of actual and observed motor rotor position values, 4-(d) is error variation curve of actual and observed motor rotor position values.

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4-(a)

4-(c)

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4-(b)

4-(d)

Fig. 4. Traditional sliding mode observer operating curve

When the motor speed reaches 1000 r/min, the parameter curve of the motor operation using an adaptive SMO is as follows, as shown in Fig. 5, 5-(a) is Motor speed variation curve, 5-(b) is error variation curve of actual and observed motor speed values, 5-(c) is variation curve of actual and observed motor rotor position values, 5-(d) is error variation curve of actual and observed motor rotor position values. From the two images above, the rotor position estimated by traditional SMO contains harmonics and exhibits significant jitter. Compared to traditional SMO, when using an adaptive SMO, the estimation of position is more accurate, the tracking performance is significantly improved, and the position waveform of the rotor contains almost no harmonics.

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5-(a)

5-(b)

5-(c)

5-(d)

Fig. 5. Adaptive sliding mode observer operating curve

5 Conclusion In response to the problems of low observation precision and severe jitter in traditional SMO, this article proposes an adaptive SMO based sensorless control method. On the premise of satisfying the stability of Lyapunov function, this article constructs an adaptive SMO for the Counter-electromotive force, which quickly attenuates the observation error of the back electromotive force. This article adopts a phase-locked loop method with a link to eliminate the influence of rotation to get the rotor position, and eliminates the influence of speed changes to improve observation accuracy. Set up in Matlab/simulink simulation model. The results show this approach can effectively suppress sliding mode dither, reduce high-frequency harmonics in Counter-electromotive force and improve rotor position observation accuracy compared with traditional sliding mode observer.

References 1. Shanmao, G., Fengyou, H., Guojun, T., Shengwen, Y.: A review of sensorless control technology of permanent magnet synchronous motor. Trans. China Electrotech. Soc. 24(11), 14–20 (2009). (in Chinese)

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2. Qian, W., Zhang, X., Jin, F., Bai, H., Lu, D., Cheng, B.: Using high-control-bandwidth FPGA and SiC inverters to enhance high-frequency injection sensorless control in interior permanent magnet synchronous machine. IEEE Access 6, 42454–42466 (2018) 3. Jin, A., Xiang, S., Li, S.: Sensorless control strategy of PMSM in full speed range. Packag. Eng. 2020, 1011–3563 (2020). (in Chinese) 4. Fatu, M., Teodorescu, R., Boldea, I., Andreescu, G.D., Blaabjerg, F.: IF starting method with smooth transition to EMF based motion-sensorless vector control of PM synchronous motor/generator. In: 2008 IEEE Power Electronics Specialists Conference, pp. 1481–1487. IEEE, June 2008 5. Kommuri, S.K., Defoort, M., Karimi, H.R., Veluvolu, K.C.: A robust observer-based sensor fault-tolerant control for PMSM in electric vehicles. IEEE Trans. Ind. Electron. 63(12), 7671– 7681 (2016) 6. Ren, X., Huang, B., Yin, H.: A review of the large-scale application of autonomous mobility of agricultural platform. Comput. Electron. Agric. 206, 107628 (2023). (in Chinese) 7. Wang, G., Valla, M., Solsona, J.: Position sensorless permanent magnet synchronous machine drives—a review. IEEE Trans. Ind. Electron. 67(7), 5830–5842 (2019) 8. Zhu, Z.Q., Liang, D., Liu, K.: Online parameter estimation for permanent magnet synchronous machines: an overview. IEEE Access 9, 59059–59084 (2021) 9. Gong, C., Hu, Y., Gao, J., Wang, Y., Yan, L.: An improved delay-suppressed sliding-mode observer for sensorless vector-controlled PMSM. IEEE Trans. Ind. Electron. 67(7), 5913– 5923 (2019) 10. Xu, W., Qu, S., Zhao, L., Zhang, H.: An improved adaptive sliding mode observer (2020) 11. Wang, Y., Xu, Y., Zou, J.: Sliding-mode sensorless control of PMSM with inverter nonlinearity compensation. IEEE Trans. Power Electron. 34(10), 10206–10220 (2019) 12. Gu, J., You, S., Kim, W., Moon, J.: Fuzzy event-triggered super twisting sliding mode control for position tracking of permanent magnet synchronous motors under unknown disturbances. IEEE Trans. Ind. Inform. (2023) 13. Zhong, Y., Lin, H., Wang, J., Yang, H.: Improved adaptive sliding-mode observer based position sensorless control for variable flux memory machines. IEEE Trans. Power Electron. 38(5), 6395–6406 (2023) 14. Ding, H., Zou, X., Li, J.: Sensorless control strategy of permanent magnet synchronous motor based on fuzzy sliding mode observer. IEEE Access 10, 36743–36752 (2022)

Research on Capacity Configuration of Wind Storage Hydrogen Production Plant Considering “Source-Load” Double Disturbance Lei Xu1 , Ji Li1(B) , Yuying Zhang1 , Xiqiang Chang1 , Wenyuan Zheng2 , Jixuan Yu2 , and Dongyang Sun2 1 Electric Power Research Institute of State Grid Xinjiang Electric Power Co., Ltd.,

Urumqi 830011, China [email protected] 2 School of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China

Abstract. Hydrogen production from wind power is an important method to solve the problem of wind abandonment and improve the utilization rate of wind power. However, the “source” turbulence caused by unstable wind speed and the “load” turbulence caused by sudden load change will adversely affect the stable operation of power-to-hydrogen system and the grid connection stability of wind farm. To solve this problem, a synergistic control strategy between supercapacitor and power-to-hydrogen system is proposed. The strategy is based on the Ensemble empirical mode decomposition algorithm. By making the supercapacitor stabilize the high-frequency component in the turbulence of “source-load”, the stability of power-to-hydrogen system is improved, and an optimal allocation method of supercapacitor capacity suitable for the control strategy is proposed. Finally, the effectiveness of the strategy is verified by Simulink simulation. Keywords: wind-storage-hydrogen station · energy storage type doubly-fed induction generator · wind power fluctuations mitigation · grid frequency modulation · capacity allocation

1 Introduction The total installed capacity of renewable energy power generation in China reached 930 million kW by the end of 2020, with wind power accounting for 280 million kW, 12.7% of the total installed capacity [1]. President Xi Jinping of the People’s Republic of China announced at the Climate Ambition Summit that the total installed capacity of China’s wind and solar power will reach more than 1.2 billion kW in 2030 [2]. However, with the vigorous development of wind and solar power, problems such as the high volatility of renewable power generation and insufficient grid inertia have emerged [3]. Some areas have been forced to abandon wind to protect the security and stability of the grid, limiting low-carbon and emission reduction targets [4]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 254–263, 2024. https://doi.org/10.1007/978-981-97-0877-2_27

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Power-to-hydrogen (P2H) is an important method to solve the problem of wind abandonment and improve the wind power consumption capacity of the power grid [5]. P2H has broad development prospects and will undergo large-scale development and application under China’s “double carbon” goal. A P2H device configured for abandoned wind can help stabilize the turbulence of the “source-load” and improve the frequency stability of the power grid and the grid connection stability of wind farms. The main methods can be divided into two categories. The first is to convert hydrogen into electric energy and retransmit it to the power grid through fuel cells or steam turbines [6]. The second is to treat P2H as a controllable load and realize demand-side response by starting or shutting down the electrolysis cell [7]. However, both methods still experience issues when stabilizing the turbulence of the “source-load” in P2H auxiliary wind farms. For example, the first method has many energy conversion links, low overall conversion efficiency, and insufficient energy utilization [8]. The second method will cause frequent startup and shutdown of the electrolysis cell, which will have an adverse impact on the service life and stable operation of the P2H system [9]. This paper proposes a “source-load” turbulence suppression method based on P2H and an energy storage system (ESS) to solve the above problems. The high-frequency component in the turbulence of the “source-load” is suppressed by a supercapacitor to improve the operation stability of the P2H system. The power output characteristics of the supercapacitor and P2H are analyzed. The optimal configuration capacity and output power of the supercapacitor and the load reduction of the P2H system are then determined using the ensemble empirical-mode decomposition (EEMD) algorithm. A P2H power grid simulation model and supercapacitor energy storage system doubly-fed induction generator (SCESS-DFIG) is built based on Simulink. The simulation results show that the proposed strategy can effectively improve the ability of the wind farm to suppress the “source-load” turbulence.

2 The Mechanism of “Source-Load” Turbulence and Smoothing Method P2H technology is one of the important means to solve the problem of wind abandonment. Its schematic diagram is shown in Fig. 1. As shown in box 1 of Fig. 1, P2H converts the wind power generated beyond the grid’s capacity to chemical energy, which is stored in the form of hydrogen. The stored hydrogen can be sold through synthetic natural gas or hydrogen pipelines for industrial use and hydrogen-energy vehicles. Thus, wind energy utilization is improved, the economic benefits for wind farms are enhanced, and carbon emissions are reduced. Currently, there are three main electrolysis technologies: alkaline electrolysis, proton exchange membrane (PEM) electrolysis, and solid oxide electrolysis. Their chemical equations are provided in Eq. (1). Electrolyze 2H 2 O   2H 2 +O 2

ΔH =+570 kJ/mol

(1)

As shown in box 2 in Fig. 1, the P2H system consists of multiple electrolytic cells, each of which can be started and stopped independently. The total power of the P2H

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system is shown in Eq. (2). PP2H =

n 

si PP2H_N

(2)

i=1

where si represents the start-stop state of the electrolytic cell, and its value is 0 or 1 (1 when the electrolytic cell is powered on, and 0 when the power is off); PP2H_N is the rated power of the electrolysis cell.

Fig. 1. Schematic diagram of P2H.

As shown in box 3 in Fig. 1, the mechanical power Pwind captured by the fans is represented as follows: Pwind =

1 ρπ R2 v3 Cp 2

(3)

where λ, β, R, ρ, v, Cp , and  are the tip speed ratio, blade angle, radius of the blades, air density, wind speed, wind energy utilization coefficient, and angular velocity of the blade, respectively. In order to make full use of wind energy, the fan operates normally in the maximum power point tracking (MPPT) state. Thus, Pwind obtains the maximum value PMPPT , i.e., the wind energy utilization coefficient reaches the maximum value C p_MPPT , at which time the fan output power is represented as follows: 1 PMPPT = ρπ R2 Cp_MPPT v3 = kMPPT v3 2

(4)

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where k MPPT is the intermediate variable. It can be seen from Eq. (4) that when the fan is running steadily in the MPPT state, its output power is only related to the wind speed and decoupling with the frequency of the power grid. Therefore, the output power of the wind turbine will fluctuate with the wind speed, i.e., there is a “source” turbulence. At the same time, the wind turbine cannot respond to the frequency change of the grid nor address the turbulence of the “load”. Taking the more mature alkaline electrolytic cell as an example, frequent start-stop will endanger its service life and operational safety [3]. Therefore, when it is regarded as a controlled load to suppress the “source-load” turbulence, an additional energy storage devices should be added to match it. Figure 2 compares the electrical and economic characteristics of supercapacitors, batteries, and P2H [10, 11]. As shown in the figure, supercapacitors complement the P2H in flexibility and maximum output power. Therefore, using supercapacitors can compensate for the flexibility and maximum output power of the P2H system. The problem of frequent start-stop of the electrolytic cell is solved by processing the high-frequency component of the power fluctuation with the supercapacitor. At the same time, because supercapacitors are only required to handle high-frequency components, they do not require high capacity configuration, and the one-time investment cost is small.

Fig. 2. Comparison of parameters for supercapacitors, batteries, and P2H.

3 “Source-Load” Turbulence Suppression Methods Based on Wind-Storage-Hydrogen Station In order to determine the capacity configuration of the supercapacitor, it is necessary to calculate the amount of capacity required for the high-frequency component in the power instruction processed by the supercapacitor. Historical data of the power instructions to be decomposed by EEMD is also employed, and the high-frequency component is extracted as the basis for the capacity configuration of the supercapacitor. The specific steps for EEMD are as follows: 1) Add a different white noise wi (n) from group M to the historical data x(n), and set its sum to X i (n): Xi (n) = x(n) + wi (n)

(i = 1, 2, · · · , M )

(5)

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2) The X i (n) is broken down into multiple IMF via the EMD algorithm: Xi (n) =

m 

cij + ri

(i = 1, 2, · · · , M )

(6)

j=1

Where cij is the jth IMF obtained by the decomposition of the ith group data, and r i is the remaining amount obtained by the decomposition of the ith group data. 3) Take the mean of the group M decomposition result as the final result: cj =

M 1  cij M

(j = 1, 2, · · · , m)

(7)

i=1

M 1  r= ri M

(8)

i=1

The calculation steps of EMD are as follows: 1) Calculate all extremum points s(n) and upper and lower envelope curves emax (n), emin (n) of the data to be decomposed using cubic spline interpolation function, and calculate the mean m(n): m(n) =

emax (n) + emin (n) 2

(9)

2) Subtract the mean m(n) from the data to be decomposed X i (n): h(n) = Xi (n) − m(n)

(10)

3) Repeat steps 1 and 2 with the calculation error h(n) as the data to be decomposed until the standard deviation of the calculation error is less than the preset value σ:   N  |hk−1 (n) − hk (n)|2 SD = 2, mnrr −m −n0 ≤ 1

II III IV V VI

0 (mr + nr − m0 − n0 ) ≤ 2, mnrr −m −n0 > 1

0 (mr + nr − m0 − n0 ) ≤ 2, mnrr −m −n0 ≤ 1, nr ≥ (n0 + 1)

0 (mr + nr − m0 − n0 ) ≤ 2, mnrr −m −n0 ≤ 1, nr < (n0 + 1)

0 (mr + nr − m0 − n0 ) > 2, mnrr −m −n0 > 1, nr ≥ (n0 + 1)

0 (mr + nr − m0 − n0 ) > 2, mnrr −m −n0 > 1, nr < (n0 + 1)

The three space vectors closest to the reference vector can be determined by judging the region where the reference vector is located according to Table 1. When the reference vector V r falls into region I, it can be synthesized by three space vectors, V 1 , V 3 and V 4 , whose action times are t 1 , t 3 and t 4 . When the reference vector V r falls into region II, it can be synthesized by three space vectors, V0 , V 2 and V 4 , whose action times are t 0 , t 2 and t 4 . When the reference vector V r falls into region III or IV, synthesizing with V 0 , V 1 and V 4 may result in a 2-level jump when the three space vectors are switched. In order to avoid 2-level jumps, at least two space vectors should be on the same side of the layer, so it is necessary to determine the space vector V 5 (m0 − 1, n0 + 1), which is 2 less than the distance of the horizontal coordinates of V 4 , and has the same vertical

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coordinates. Similarly, when the reference vector V r falls into the region V or VI, it is necessary to determine another space vector V 6 (m0 + 3, n0 + 1), and V 6 is 2 more than the horizontal coordinate distance of V 4 , and the vertical coordinate is the same. The positional relationship between V 5 and V 6 and the square is shown in Fig. 3(b).

Fig. 3. Reference vector localization.

According to the volt-second equilibrium principle, a system of equations is listed to find the action time of each space vector. 4.2 Solving for Switching States Since the number of space vectors is smaller than the number of switching states, one space vector may correspond to multiple switching states. When the condition of zerosequence voltage is introduced, the space vectors can only correspond to one set of switching states. The zero sequence voltage is N 0 = (a + b + c)/3, let N = 3N 0. N =a+b+c

(6)

From Eq. (4) and (6), the correspondence between the switching state S(a, b, c) and the space vector V (m, n) is obtained as follows. ⎤ ⎡ ⎤ ⎡ m+N a 3 ⎣ b ⎦ = ⎣ a + n−m ⎦ c

a−

2 n+m 2

(7)

Since the number of levels output from the MMC are all integers, that is to say, a is an integer. Substituting different values of N into Eq. (7) gives the switching state as follows Table 2, mod (m, 3) means that m is divided by 3 to get the remainder.

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mod (m, 3) 0

1

2

switch status ⎧ ⎪ N =0 ⎪ ⎪ ⎪ ⎨ a = m/3 ⎪ ⎪ b = a + (n − m)/2 ⎪ ⎪ ⎩ c = a − (n + m)/2 ⎧ ⎪ N = −1 ⎪ ⎪ ⎪ ⎨ a = (m + N )/3 ⎪ ⎪ b = a + (n − m)/2 ⎪ ⎪ ⎩ c = a − (n + m)/2 ⎧ ⎪ N =1 ⎪ ⎪ ⎪ ⎨ a = (m + N )/3 ⎪ b = a + (n − m)/2 ⎪ ⎪ ⎪ ⎩ c = a − (n + m)/2

The a, b and c obtained by calculating according toTab2 may not satisfy the condition a, b, c ∈ [0, ±1, · · · , ±x/2], At this point, a, b, and c need to be further corrected. If min(a, b, c) < −x/2, then h = min(a, b, c) + x/2, if max(a, b, c) > x/2, then h = max(a, b, c) − x/2, otherwise, h = 0. ⎧  ⎨a = a − h (8) b = b − h ⎩  c =c−h S  (a , b , c ) corresponds to the switching state of the space vector V (m, n). 4.3 Steps to Implement the Simplified Algorithm for Space Vector Modulation 1) Sample the reference voltage in one sampling period, Determine the coordinates of V 0 in the square where the reference vector V r (mr , nr ) is located. Further obtaining other spatial vector coordinates. 2) According to the region judgment formula in Table 1, the region where the reference vector V r (mr , nr ) falls into the square can be found. 3) Determine the three space vectors nearest to the reference vector V r (mr , nr ) from the region, and find the action time of each space vector according to the principle of volt-second equilibrium. 4) Calculate the set of switching states corresponding to each space vector. 5) According to the five-segment algorithm, the specific a , b and c values are converted into switching states of the MMC bridge arms. When the reference vectors are synthesized in this cycle, it is necessary to sample the reference vectors for the next cycle and repeat the above process.

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5 Analysis of Simulation Results In order to verify the effectiveness of the modulation strategy proposed in this paper, a three-phase MMC system simulation model is constructed in Matlab/Simulink, comparing the Phase Disposition PWM (PD-PWM) and the SVM simplification algorithm proposed in this paper, and analyzing the quality of output voltage waveforms and the DC voltage utilization rate of the two modulation strategies. The specific simulation parameters of the system are shown in Table 3. Table 3. Simulation parameters of MMC system. Parameter type

Numerical value

DC side bus voltage U dc /V

2000

Number of bridge arm submodules x/ each

10

Submodule Capacitance C/mF

4

Bridge Arm Inductors L/mH

6

Equivalent inductance on AC side L s /mH

10

Load resistance Rs /Ω

20

Sampling frequency f s /Hz

5000

When the modulation coefficient is p = 0.86. The output phase voltage waveform of PD-PWM is shown in Fig. 4(a), and then FFT analysis is performed on the a-phase voltage, which leads to the phase voltage fundamental amplitude shown in Fig. 4(b) as 832.5 V, and THD is 10.52%. The output phase voltage waveform of the SVM simplified algorithm proposed in this paper is shown in Fig. 5(a), and the amplitude of the phase voltage fundamental wave shown in Fig. 5(b) is 959.1 V, and the THD is 8.14%. Figure 4(c) shows the waveforms of three line voltages of the PD-PWM, and Fig. 4(d) shows the FFT analysis of the line voltage, and the base amplitude of the line voltage is 1442V and the THD is 6.27%. Figure 5(c) shows the waveforms of three line voltages for the simplified SVM algorithm proposed in this paper, and Fig. 5(d) shows the line voltage fundamental amplitude of 1660 V with a THD value of 5.57%. According to the simulation results obtained from Fig. 4, Fig. 5, comparing the two modulation strategies, it can be concluded that the voltage utilization of the SVM simplified algorithm proposed in this paper is about 15% higher than that of the PDPWM, and the quality of its voltage waveforms is also superior to that of the PD-PWM.

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(a) Output phase voltage waveform

(c) Output line voltage waveform

(b) FFT analysis of phase voltage uA

(d) FFT analysis of line voltage uAB

Fig. 4. Simulation waveforms and FFT analysis results of PD-PWM (p = 0.86).

(a) Output phase voltage waveform

(c) Output line voltage waveform

(b) FFT analysis of phase voltage uA

(d) FFT analysis of line voltage uAB

Fig. 5. Simulation waveforms and FFT analysis results of the proposed SVM algorithm (p = 0.86).

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6 Conclusion In this paper, the positioning of reference vector and the action time of space vector are mainly derived and calculated, and finally the SVM simplified algorithm is implemented. In order to verify the effectiveness of the algorithm, a three-phase MMC system simulation model is built according to the working principle of MMC. By simulating and comparing different modulation strategies, it is concluded from the simulation results that the SVM simplified algorithm has certain advantages. Acknowledgments. This work was funded by the Natural Science Foundation of Jiangxi under Grant (No. 20224ACB204016).

References 1. Liang, Y., Huo, Y., Zhao, F.: An accelerated distance protection of transmission lines emanating from MMC-HVDC stations. IEEE J. Emerg. Sel. Top. Power Electron. 9(5), 5558–5570 (2021) 2. Xiang, W., Yang, S., Adam, G.P., Zhang, H., Zuo, W., Wen, J.: DC fault protection algorithms of MMC-HVDC grids, fault analysis, methodologies, experimental validations, and future trends. IEEE Trans. Power Electron. 36(10), 11245–11264 (2021) 3. Yang, R., Shi, G., Zhang, C., Li, G., Cai, X.: Internal energy based grid-forming control for MMC-HVDC systems with wind farm integration. IEEE Trans. Ind. Appl. 59(1), 503–512 (2023) 4. Lin, L., Lin, Y., He, Z., et al.: Improved nearest-level modulation for a modular multilevel converter with a lower submodule number. IEEE Trans. Power Electron. 31(8), 5369–5377 (2016) 5. Yi, L., Huang, X., Huang, S., et al.: Operation control of high voltage variable frequency speed regulating system in modular multilevel converter based on nearest level approximation modulation. Trans. Electrotech. Soc. 35(06), 1303–1315 (2020). (in Chinese) 6. Wang, K., Jin, L., Li, G., Deng, Y., He, X.: Online capacitance estimation of submodule capacitors for modular multilevel converter with nearest level modulation. IEEE Trans. Power Electron. 35(7), 6678–6681 (2020) 7. Bai, Z., Zhou, Y.: Analysis and improvement of carrier Cascade pulse width modulation strategy for modularized multilevel converter. Power Syst. Autom. 42(21), 139–144 (2018). (in Chinese) 8. He, L., Shuai, Z., Shan, J., et al.: Comparative analysis of multi-carrier modulation strategies in MMC. J. Power Sour. 17(05), 56–64 (2019). (in Chinese) 9. Ronanki, D., Williamson, S.S.: Discontinuous space vector modulation schemes for modular multilevel converters. IEEE Trans. Power Electron. 36(4), 3987–3994 (2021) 10. Muthavarapu, A.K., Biswas, J., Barai, M.: An efficient sorting algorithm for capacitor voltage balance of modular multilevel converter with space vector pulsewidth modulation. IEEE Trans. Power Electron. 37(8), 9254–9265 (2022) 11. Tang, X., Feng, Q., Wang, C., et al.: Zero-sequence voltage optimal control algorithm for multilevel converters in stretched αβ coordinate system. High Volt. Technol. 43(01), 23–29 (2017). (in Chinese)

Operation of Integrated Energy System Based on Heating System Rui Ma1(B) , Hui Fan2 , Xiaoguang Hao1 , Jianfeng Li1 , and Hui Wang1 1 State Grid Hebei Electric Power Research Institute, Shijiazhuang 050021, China

[email protected]

2 State Grid Hebei Electric Power Company, Shijiazhuang 050021, China

[email protected]

Abstract. As the demand for energy increases, the integrated energy system (IES) has developed rapidly. The IES includes various types of energy, which can help to realize the mutual coupling and transformation of electricity, gas, wind and other energy. The existing basic theory cannot adapt to the energy coupling relationship in the energy system anymore, so other aspects are needed to reveal the principle of energy transmission and transformation in the IES. This paper has studied the operation of the IES based on the heating system, and has found that compared with the energy system based on the energy network theory, the accuracy of the prediction of the electricity consumption for the selected industrial park heating was higher, more than 97%, while the accuracy of the prediction of the heating electricity consumption of the system based on the energy network theory was less than 94%. Meanwhile, based on the heating system, the utilization rate of all kinds of energy could also be improved, and the utilization rate of all kinds of energy was above 91%. The IES based on heating system can help to reduce the cost of energy system operation, improve the speed break of operation and increase the conversion rate of various types of energy, which can meet the needs of the times for resources, and also help to protect the environment. Therefore, it is meaningful to study the operation of IES based on heating systems in this paper. Keywords: Integrated Energy System · Heating System · Operating Cost · Electricity Consumption Forecast

1 Introduction Energy is fundamental to keep human life, the progress of social civilization and the development of different industries. It always determines human daily life, and is an indispensable material condition for social and economic development. After the outbreak of the energy crisis, the word “energy” is gradually becoming a hot issue in the global focus. The traditional non-renewable resource energy is usually animal fossil energy, which contains a lot of aspects, playing an important role in the energy system. The increasing demand of energy are urgent problems to be solved at this stage, but while meeting the consumption needs of social and economic development, advocating green environmental protection and achieving sustainable energy development, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 292–304, 2024. https://doi.org/10.1007/978-981-97-0877-2_31

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countries around the world also need to solve other problems. In order to cope with the current energy dilemma, it is necessary to find a way to use green energy for economic development, which can help to alleviate the energy dilemma. The complementarity of several energy sources including electricity and heat helps to improve the flexibility and rationality of the IES and to achieve multiple benefits for economic development and the environment. The IES is a new carrier integrating multiple energy complements. It is highly concerned by people for its higher energy supply efficiency and flexibility of system operation, which leads it to become a main methods of energy supply in the future. In this paper, an in-depth study of the IES based on the heating system is conducted to further improve the utilization of various types of energy and to improve the accuracy of the prediction of electricity consumption for heating in industrial parks. The establishment and optimization of IES has been intensively studied by researchers in many countries in recent years, providing theoretical basis and feasibility verification for the establishment and implementation of energy systems and achieving a series of research results. Ruiming Fang proposed an IES and discussed the construction of a multi-objective daily power dispatch for IES in terms of both operational and environmental costs [1]. Yang Chao proposed an energy efficiency modeling approach to reduce the energy consumption of IES in coastal areas. He focused on energy networks based on IES and analyzed the energy conversion relationships of IES [2]. Liu Sai proposed a method for advance operation optimization of building-level IES considering the additional potential benefits of energy storage. On the basis of the characteristics of energy storage for peak and valley reduction, this approach further considered the changes in system load and real-time electricity prices [3]. Zhou Suyang proposed an optimal scheduling model for electric, thermal and gas networks that integrated the thermal inertia of gas lines and heating systems. He also developed an optimal scheduling model that could be applied to IES [4]. The above researchers have carried out various researches on the IES and also used different methods, but few experts and scholars have considered the use of heating systems for research. Therefore, this paper studies it based on the heating system. Other scholars have different research views on the establishment and optimization of IES. Zuo Xue conducted a study in order to model the load on the electric heating and cooling system of an IES in a coastal area. The power flow values for the electric heating and cooling system of the IES were obtained by calculating the grid, natural gas network and integrated energy flow. Meanwhile, the load model of the electric heating and cooling system was constructed according to the coupling relationship of the electric heating and cooling system [5]. Zhang Ning believed that the IES composed of a group of energy hubs should properly adjust the system parameters with a great impact on the safety performance. Therefore, he proposed an event-triggered distributed hybrid control scheme for safe and economical operation of the system [6]. Sun Yonghui proposed an optimal advance optimization plan for an integrated gaselectric energy system considering bidirectional energy flow to minimize the day-ahead operating cost of the system, using a second-order cone planning approach to solve the optimization problem. The problem is actually a nonlinear programming problem with the addition of cutting planes to ensure the accuracy of the global optimal solution

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[7]. Jiang Tao investigated the multi-cycle optimal energy flow and energy pricing of a carbon-emission embedded IES, and proposed an optimal scheduling model for the IES. For the optimization problem, he also proposed and linearized models for DC flows, natural gas pipeline flows and heating network energy flows [8]. These scholars have studied various aspects of IES, which have laid the theoretical foundation for the research in this paper. Energy is not only the basis of human indispensability and development, but also the root of socio-economic development. Improving energy efficiency, ensuring energy security, promoting the centralized treatment of renewable energy and promoting ecological environmental protection have become the inevitable choice to deal with the increasingly prominent contradiction between energy demand growth, energy shortage and environmental protection in the rapid development of social economy. In this context, the concept of IES comes into being. The IES is an operation model that breaks away from the separate planning and independent operation of various energy supply systems [9, 10]. In this paper, the heating system is used to optimize the IES, improve the accuracy of the system for electricity consumption prediction, and also improve the utilization of various types of energy. The application of heating system can reduce the operation cost of energy system, and use lower cost to transform various energy sources, which can improve economic benefits and protect the environment at the same time.

2 Methods of Exploration of Optimization of IES 2.1 IES The IES is a complex network that contains multiple energy sources that complement each other and interact with each other. The connection relationship between its networks is based on the integration effect of heating system energy, which can further improve the accuracy of energy scheduling and energy utilization efficiency [11]. The IES is usually a collection of energy integrated networks in a relatively large range in a certain region, which puts forward higher requirements in many aspects. The IES is an integrated system with relatively high coupling and cooperation among energy sources, including four parts [12]. Energy conversion equipment includes gas turbines, heating furnaces and other facilities, which generate electricity by igniting fossil fuels such as natural gas. Energy transmission network contains the electric network, heating and cooling network, etc. Energy consumption network refers to the energy consumption link in the IES. Figure 1 is a schematic diagram of IES. There are some differences between the IES and the previous conventional grid. In IES, the flow of various energy sources is more complex and changeable, and the operation optimization of the system involves more subjects [13]. At this stage, the heating system and other systems are independent of each other, and their operation is carried out independently by the units they undertake. IES is an energy supply system with many advantages based on excellent electronic control technology of power engineering and advanced communication and collection technology [14]. Generally speaking, the IES has three structural features: trans-regional, regional and industrial park-level IES. Trans-regional IES is mainly composed of long-distance and large-space machinery and

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Fig. 1. Schematic diagram of IES

equipment. Regional IES is mainly composed of medium-voltage distribution network and heating network. The IES’s framework is shown in Fig. 2.

Fig. 2. Structure diagram of IES

2.2 Optimization Modeling of IES Analysis. The operation of the IES provides customers with various forms of energy, including electricity and heat, in a timely and flexible manner. The types of equipment involved in the system are complex and diverse. In full consideration of the diversified working principles and operating characteristics of this equipment, as well as the role of various energy production, transmission, storage and consumption in the IES, relevant equipment participating in the system operation must be sorted and classified according

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to certain specifications. For the equipment in the IES, some classification standards have been provided by the literature research. Through sorting out the basic composition and network topology of the IES, it is found that the power system, heating internet, cooling network and natural gas in the system are closely related. The differentiation of devices according to the type of energy substances carried can effectively represent the coupled interactions between different types of energy networks. Using this as a criterion for classification, the equipment in an IES is divided into independent and coupled equipment. On this basis, the principle analysis and mathematical model of different types of equipment are carried out respectively to build a complete analysis framework for the improvement and operation of the IES. Figure 3 shows the physical structure of the IES.

Fig. 3. Physical structure of IES

Optimization Model. The heating network model is the most complex model with the largest number of connected equipment in the industrial zone. The heating network model not only needs to connect a variety of heating equipment, but also provides heat to customers in the industrial park [15]. The most important equipment in the heat network model is the three equipment of water collector, water distributor and heat storage tank, and some piping distribution lines of different apertures and lengths. The main parameters of equipment and pipeline in the heating network model are also set according to the power energy data information. Water distributor and water collector models are indispensable equipment for all industrial parks with heat supply network. The function of the water collector is to connect the return water pipeline in the user area, collect the ultra-low temperature intelligent return water in the heating area to the water collector, and distribute the water to each equipment according to the power of each equipment. The water distributor and water collector are the key equipment of the

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heating network. They can distribute the cooling circulating water required by consumers and equipment as required to maintain the heating network’s stability. The comprehensive operation optimization research of the IES refers to that it can help the system to be improved in the short term, meet the energy market demand of the end product users, and clarify the energy transmission and distribution mode [16]. In the comprehensive energy flow calculation of the IES, the heat load of the primary heating network is usually given immediately. After the iterative calculation, because of the characteristics of the heat exchanger and radiator, the heat load changes with the change of the operating conditions. At the same time, the heat load is generally expressed in the customer’s requirements for temperature, which is closely related to the user’s ambient temperature and the main structure of the building. Therefore, during the specific operation, the heat exchanger and radiator may be affected by some factors, thus affecting the thermal load output power of the primary heating network. The energy transmission and exchange of the heating system is realized by the flow of steam in the heating pipe network, and then the heat exchange is carried out through the heat exchanger, heat pipe radiator and other systems. The thermal system mainly includes three parts: pyrogen, heat network and heat load. The heat energy generated by the pyrogen is transmitted according to the primary heating network, and the heat energy is exchanged between the heat exchange station and the secondary heating network, and then transmitted to the heat load through the secondary heating network to generate a closed loop. Figure 4 shows the structural diagram of the heating system.

V

Fig. 4. Structure diagram of heating system

The key function of the heating network model is to connect the heating equipment in the IES and have the effect of heat storage. The most important equipment is the heat storage tank and heat exchanger. The power balance constraint of power network is calculated as follows:      Qi = Qg − QTi − Wi 5j=1 Wj Hij cosθij + Aij sinθij     (1) Fi = Fg − FTi − Wi 5j=1 Wj Hij cosθij − Aij sinθij In the energy flow calculation of the IES, the thermal load of the primary heating network is usually directly given. When performing the iterative calculation, the calculation

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formula is as follows: Tv =

  μ1 V1y μ2 V2 qW   qg − qv W μ1 V1y μ2 V2 + μ1 V1y + μ2 V2 − μ1 μ2 V1y q

(2)

The modeling subject establishes the conversion matrix based on the research of the conversion relationship among electric energy, thermal energy and natural gas energy, and further develops into an energy hub. The mathematical expression of its basic model is:  Hi = eij qj , ∀i (3) j

To optimize the IES, the optimization objective of the model is to minimize the total energy loss of the system, and the calculation formula is as follows:  ⎧  2 2 ⎪ ⎨ Qloss = i,j∈Hel Hij Ri + Rj − 2Ri Rj cosθij   (4) Wloss = Win − Wout ⎪  ⎩ 2 Lloss = 2 ∗ j∈Hel VRi pRi In Formula (4), Qloss represents the active power loss of the power system and W loss represents the heat loss of the heating system. The operating costs include the operation and maintenance costs of the equipment as well as the fuel costs. They can be calculated from the following formula: Bope = Bom + Bfuel =

G g=1

I i=1

g

ci Qi +

G g=1

I

g g t E i=1 j j

(5)

In Formula (5), ci represents the unit variable operation and maintenance cost of the equipment. According to the power flow model of power grid and natural gas network, their calculation formulas are as Formulas (6) and (7): m βi − βj k + Qij j=1 j=1 Yij

 n Nij pij pij πi2 − πj2 + Fij,P2G

Qi = Fi =

m j=1

j=1

(6) (7)

The relationship between heat energy provided by heat source and water flow and temperature is expressed as follows:   H + H C,djts C,djts i∈Hp j∈Hp H  H Wnts = (8) H bm ∗ snts − rnts

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2.3 Heating System There are many types of heating systems, and the specific forms of different types of systems are also different. There are four common types. For these different types of heating systems, experts and scholars who have conducted this research agree that cogeneration heating is superior to other heating systems in many aspects. However, they have not reached a unified standard on the unified measurement standard of heating system. Even if only the energy consumption is considered as a separate factor, there are different opinions. The cogeneration heating system is composed of many aspects, but the main reason for its difficulty in scientific evaluation is the evaluation of energy consumption [17, 18]. As far as the evaluation of energy consumption is concerned, if only the individual index value is used to measure the energy consumption of the system, the first law of thermodynamics is generally used to explain, but the first law of thermodynamics ignores the difference between heat and electricity.

3 Optimization Experiment of IES Based on Management System Using the heating system to study the operation of the IES can better help to predict the use of various kinds of energy in the integrated system in advance, improve the accuracy of energy prediction such as electricity, gas and heat, and reduce the error between the actual value and the actual value. This paper selected an industrial park and forecast the electricity used by the industrial park for heating from December 1 to 10, 2022, and finally the predicted results were compared with the actual values. To better verify the accuracy of electricity consumption prediction based on heating system, it was compared with the energy system based on energy network theory. Table 1 shows the predicted and true values of heating supply in December of the industrial park. Table 1. Details of predicted and true values of the two systems Time

True value (KW)

Predicted value of the system based on heating system (KW)

Predicted value of the system based on energy network theory (KW)

1

5815

5875

5372

2

7896

7802

8484

3

8897

8807

9718

4

5471

5528

5005

5

6028

6151

6507

6

6555

6427

6025

7

7159

7001

6682

8

6089

6159

6502

9

7248

7195

6701

10

7512

7388

8281

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As shown in Table 1, the industrial park used the most electricity for heating on December 3, with 8897/KW, while the less electricity was only 5471/KW on December 4. By studying the predicted value of the heating system and the theoretical predicted value of the energy network with the real value, the error between the predicted value and the real value of the two systems can be calculated. The smaller the error rate, the higher the prediction accuracy and the better the system performance. The accuracy of the two systems for the power consumption prediction of the industrial park is shown in Fig. 5.

(a)

(b)

Fig. 5. Comparison of accuracy of power consumption prediction between the two systems (a) IES based on heating system (b) IES based on energy network theory

As shown in Fig. 5, the prediction accuracy of the IES based on the heating system for the selected industrial park heating power consumption was much higher than that of the energy system based on the energy network theory, and the accuracy of continuous prediction fluctuated less, with stronger stability than that of the energy system based on the energy network theory. In Fig. 5(a), the prediction accuracy of heating power consumption of the system based on heating system was above 97%, while in Fig. 5(b), the prediction accuracy of heating power consumption of the system based on energy network theory was below 94%. Among them, the IES based on heating system had the highest accuracy of power consumption forecast on the 9th day, with 99.27%, which was 6.82% higher than the system based on energy network theory. The system based on the heating system had the lowest accuracy of power consumption prediction on the 7th day, only 97.79%, but it was still 4.45% higher than the system based on the energy network theory. At the same time, the 7th day was also the time when the system based on the energy network theory had the highest accuracy of power consumption prediction. The system based on energy network theory had the lowest accuracy of power consumption

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forecast on the 10th day, only 89.76%, which was 8.59% lower than the system studied in this paper. The above data showed that the research on the IES using the heating system can improve the accuracy of its prediction of the heating power consumption, and can help enterprises better predict the electricity consumption and adjust the energy, with strong prediction stability. Whether the system has advantages or not is an important factor of its operation cost. For the IES, even though some systems have good performance and high prediction speed and accuracy, if the operation cost is too high, the possibility of selecting these systems for the vast majority of people is not high. To study the impact of the heating system on the operation cost of the IES, it was compared with the energy system based on the energy network theory, mainly comparing the operation cost of one thermal power plant, one natural gas plant, one wind farm, two wind farms and two thermal power plants. The specific comparison results are shown in Fig. 6.

(a)

(b)

Fig. 6. Comparison of operating costs of two systems for different energy plants (a) IES based on heating system (b) IES based on energy network theory

As shown in Fig. 6, the operation cost of the IES based on the heating system for different thermal power plants or wind farms was lower than that of the energy system based on the energy network theory. In Fig. 6(a), the operating cost of one thermal power plant based on the heating system was 4.1525 million yuan, and the operating cost of two thermal power plants was 7.0418 million yuan, a difference of 2.8893 million yuan. In Fig. 6(b), the operating cost of one thermal power plant and two thermal power plants based on the energy network theory was 4.5544 million yuan. The system based on the heating system could reduce the operating costs of each plant. With the increase of electric heating plants, the gap between the operating costs was relatively reduced. The operating cost of a natural gas plant based on the heating system was 3.8205 million

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yuan, which was 282.4 thousand yuan lower than the system based on the energy network theory. The operating cost of a wind farm based on energy network theory was 3.0514 million yuan, which was 157.8 thousand yuan higher than the system studied in this paper. The above data showed that based on the heating system, the operation cost of each energy plant can be reduced, and the establishment and optimization of the IES can be carried out at a lower cost. The establishment of IES is to make full use of all kinds of energy. The energy systems based on different methods have different energy utilization rates. The heating system studied in this paper has improved the utilization rate of all kinds of energy, compared with the energy system based on the energy network theory. To further reflect this improvement, this paper used these two systems to study the utilization rate of electric energy, natural gas, wind energy, thermal energy, light energy and other energy. The specific comparison results are shown in Fig. 7.

(a)

(b)

Fig. 7. Comparison of utilization rates of different energy sources between the two systems (a) IES based on heating system (b) IES based on energy network theory

As shown in Fig. 7, the IES based on heating system had higher utilization rate for different types of energy than the energy system based on energy network theory. In Fig. 7(a), the energy system based on the heating system had a utilization rate of more than 91% for all kinds of energy. In Fig. 7(b), the utilization rate of energy systems based on energy network theory for all kinds of energy was below 86%. Among them, the energy system based on heating system had the highest utilization rate of heat energy, 93.88%, 9.99% higher than that of the energy system based on energy network theory. The energy system based on heating system had the lowest utilization rate of wind energy, only 91.78%, but it was 7.23% higher than that of the energy system based on energy network theory. The energy system based on energy network theory had the

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highest utilization rate of light energy, 85.74%, but it was still 7.3% lower than that of the system studied in this paper. The energy system based on energy network theory had the lowest utilization rate of natural gas, only 82.78%, which was 9.69% lower than that of the system studied in this paper. The above data showed that the department studied in this paper has a higher utilization rate of all kinds of energy. The IES based on the heating system can effectively improve the utilization rate of all kinds of energy and improve the conversion rate of energy. It is not only conducive to cost saving, but also conducive to environmental protection, which is suitable for the era of energy shortage.

4 Conclusion To better achieve sustainable socio-economic development and efficient use of energy, there has been an increasing interest in IES in recent years. The IES is an energy system with high efficiency, low carbon and green environmental protection, which can effectively improve the utilization rate of energy and promote the centralized treatment of renewable energy. The dynamic simulation modeling of IES plays a vital role in the scientific research of the optimal control and energy scheduling of IES. The IES can improve the energy utilization rate, but its relatively high coupling characteristics add some difficulties to the scheduling operation of the IES. This paper integrated the latest research results of various countries in the world, expounded the most basic composition of the IES and analyzed the modeling of the IES. Considering the advantages and difficulties of various system establishment methods, this paper studied the operation of IES based on the heating system. Through the comparative study with the energy system based on the energy network theory, different types of energy utilization rates were studied. It has been found that the heating system improved the utilization rate of all kinds of energy and also helped to reduce the operating cost of the system. At the same time, the accuracy of the system prediction was also improved. Acknowledgements. This work is supported in part by the Science and Technology Project of Hebei Electric Power Company (kj2021-002).

References 1. Fang, R.M.: Multi-objective optimized operation of integrated energy system with hydrogen storage. Int. J. Hydrog. Energy 44(56), 29409–29417 (2019) 2. Yang, C., Gao, F.K., Dong, M.Y.: Energy efficiency modeling of integrated energy system in coastal areas. J. Coast. Res. 103(SI), 995–1001 (2020) 3. Liu, S., et al.: Operational optimization of a building-level integrated energy system considering additional potential benefits of energy storage. Prot. Control Mod. Power Syst. 6(1), 1 (2021). https://doi.org/10.1186/s41601-021-00184-0 4. Zhou, S.Y.: Integrated energy system operation optimization with gas linepack and thermal inertia. IET Renew. Power Gener. 15(15), 3743–3760 (2021) 5. Zuo, X.: The modeling of the electric heating and cooling system of the integrated energy system in the coastal area. J. Coastal Res. 103(SI), 1022–1029 (2020)

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6. Zhang, N.: Event-triggered distributed hybrid control scheme for the integrated energy system. IEEE Trans. Ind. Inf. 18(2), 835–846 (2021) 7. Sun, Y.H.: Day-ahead optimization schedule for gas-electric integrated energy system based on second-order cone programming. CSEE J. Power Energy Syst. 6(1), 142–151 (2020) 8. Jiang, T.: Optimal energy flow and nodal energy pricing in carbon emission-embedded integrated energy systems. CSEE J. Power Energy Syst. 4(2), 179–187 (2018) 9. Zhao, X.J.: Matching model of energy supply and demand of the integrated energy system in coastal areas. J. Coastal Res. 103(SI), 983–989 (2020) 10. Wang, Y.L.: Optimal scheduling of the regional integrated energy system considering economy and environment. IEEE Trans. Sustain. Energy 10(4), 1939–1949 (2018) 11. Keshavarzzadeh, A.H., Ahmadi, P., Safaei, M.R.: Assessment and optimization of an integrated energy system with electrolysis and fuel cells for electricity, cooling and hydrogen production using various optimization techniques. Int. J. Hydrog. Energy 44(39), 21379–21396 (2019) 12. Xiao, H.: Bi-level planning for integrated energy systems incorporating demand response and energy storage under uncertain environments using novel metamodel. CSEE J. Power Energy Syst. 4(2), 155–167 (2018) 13. Habibollahzade, A.: Multi-criteria optimization of an integrated energy system with thermoelectric generator, parabolic trough solar collector and electrolysis for hydrogen production. Int. J. Hydrog. Energy 43(31), 14140–14157 (2018) 14. Liu, X.O.: Research on decentralized operation scheduling strategy of integrated energy system based on energy blockchain. Int. J. Energy Res. 46(15), 21558–21582 (2022) 15. Zhang, S.H.: Dynamic security control in heat and electricity integrated energy system with an equivalent heating network model. IEEE Trans. Smart Grid 12(6), 4788–4798 (2021) 16. Davis, M., Ahiduzzaman, M., Kumar, A.: How to model a complex national energy system? Developing an integrated energy systems framework for long-term energy and emissions analysis. Int. J. Glob. Warm. 17(1), 23–58 (2019) 17. Pan, P.Y., Wu, Y.Y., Chen, H.: Performance evaluation of an improved biomass-fired cogeneration system simultaneously using extraction steam, cooling water, and feedwater for heating. Front. Energy 16(2), 321–335 (2022) 18. Alayi, R.: Technical and environmental analysis of photovoltaic and solar water heater cogeneration system: a case study of Saveh City. Int. J. Low-Carbon Technol. 16(2), 447–453 (2021)

Optimization of ESS Configuration and Operation Strategy for PV DC Collection System Ke Guo1 and Xiaolin Yang2(B) 1 State Key Laboratory of Power Transmission Equipment and System Security and New

Technology, Chongqing University, Chongqing 400044, China [email protected] 2 School of Electrical Engineering, Chongqing University, Chongqing 400044, China [email protected]

Abstract. Configuring energy storage system (ESS) in photovoltaic (PV) DC collection systems can suppress PV fluctuations. For PV DC collection systems, this article considers the system output power characteristics and configuration ESS costs, and designs a double-layer solution model for multi-objective optimization. The overall optimization objective is to minimize the system configuration ESS cost, and the outer layer determines the configuration power and capacity of the ESS. Particle swarm optimization algorithm is used to solve the problem; The inner layer determines the optimal operating strategy for energy storage, using yalmip and cplex for optimization solution. The example analysis shows that the proposed model can improve the output power characteristics and economic performance of the PV DC collection system. The model is feasible and effective, and it also demonstrates that the model can provide theoretical support for the rationality of ESS configuration in the PV DC collection system, which is conducive to the perfect development of the PV DC collection system. Keywords: PV DC Collection System · Optimization of ESS Configuration · Double-layer Model · Multi-objective Optimization · Particle Swarm Optimization

1 Introduction Currently, PV power is transmitted in the form of DC convergence, which can significantly improve its energy utilization and transmission characteristics, and has gradually become a hot research topic for scholars worldwide [1–4]. In the PV DC collection system, the PV array is affected by external lighting conditions, and its output has randomness and volatility. In this regard, energy storage technology can improve the volatility and intermittent impact of new energy on system performance, and promote complementary energy development [5]. Related scholars [3] propose that the combination of PV modules and energy storage can effectively optimize the output power characteristics of PV collection systems. Due to its short development time, there is a lack of in-depth © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 305–313, 2024. https://doi.org/10.1007/978-981-97-0877-2_32

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research on the proportion of energy storage configuration in this collection system both domestically and internationally. In order to improve the economic performance and overall coordination of ESS configuration, this article studies the capacity configuration of energy storage units in the optical storage DC collection system, providing theoretical support for the rationality of energy storage configuration proportion in the system. At present, intelligent optimization algorithms are effective methods for solving energy storage configuration capacity both domestically and internationally [6–9]. In essence, the optimization configuration of ESS can be transformed into multi-objective optimization problems based on reliable demand response [6, 10], battery health [11], economic efficiency [9], and other aspects. For multi-objective optimization problems, domestic and foreign researchers often solve them by constructing a double-layer model [12–14]: Reference [12] designed a double-layer model based on a scoring system, which utilizes genetic optimization algorithms, cplex, and the distance between superior and inferior solutions scoring system to achieve energy storage optimization; The doublelayer optimization model constructed in reference [13] aims to minimize the cost of distributed energy storage configuration, and is solved through an improved genetic algorithm; Reference [14] considers regional peak shaving demand and marginal node power costs, implements a dual layer model of “scale optimization and spatial deployment” to achieve optimal deployment of energy storage. This article considers the output power characteristics and configuration energy storage cost of PV DC collection systems, and designs a double-layer solution model for multi-objective optimization: The overall optimization objective is to minimize the energy storage cost of the system configuration, and the outer layer determines the power and capacity of the ESS configuration, and particle swarm optimization algorithm is used to solve the problem; The inner layer determines the optimal operating strategy for energy storage, by using Matlab’s built-in yalmip toolbox for modeling and IBM’s developed cplex technology for solving, the efficiency of the solution is improved. The example analysis demonstrates the scientific and reliable nature of the established model.

2 ESS Optimization Configuration Model for PV DC Collection Systems 2.1 System Structure Selection For PV DC collection system, the input independent output series (IIOS) cascade type is selected as the topology form, which is widely applicable in PV power plant DC collection and grid connection scenarios. Figure 1 shows the structure diagram of the IIOS type PV DC collection system with ESS configuration.

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#1

#2

#

Fig. 1. System structure diagram

2.2 Objective Function The objective function is set as the cost of configuring ESS in the system, which is the sum of initial construction costs, charging and discharging costs, and maintenance costs. The specific formula is shown in Eq. (1). F = Cb + Cch + Cf

(1)

In the formula: F, Cb , Cch and Cf are the total cost, initial construction cost, charging and discharging cost, and maintenance cost of the ESS module, respectively. The initial construction cost is related to the power and capacity of ESS. Cb =

n 

(Q1 · Pess + Q2 · Eess ) ·

1

s · (1 + s)J (1 + s)J − 1

(2)

In the above formula, n is the number of ESS modules configured for the system, Q1 represents the unit power cost of ESS configuration, Q2 represents the unit capacity cost, Pess and Eess are respectively the configured power and capacity of ESS, s is the Bank rate, and J represents the service life of ESS. The cost equation for ESS charging and discharging is Cch =

24 365   1

{Pch (x) − Pdch (x)} · t · Co (x)

(3)

1

Where: Pch (x) is the charging power of ESS at time x, and Pdch (x) is the discharge power at time x, t represents the sampling interval time, and Co (x) represents the corresponding electricity price at time x. The cost of ESS and maintenance in the later stage is generally calculated based on the proportional value of the initial investment cost. Cf = kCb In the formula, k is the cost coefficient of ESS operation and maintenance.

(4)

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2.3 Constraint Condition The ESS configuration constraints in the collection system are shown below. (i) ESS charging and discharging power constraints To avoid excessive charging and discharging power of ESS, it is necessary to constrain the charging and discharging power of ESS, based on the following inequality. 0 ≤ Pch (x) ≤ Pess

(5)

0 ≤ Pdch (x) ≤ Pess

(6)

Where: gch (x) and gdch (x) represent the charging and discharging states of ESS at time x. (ii) Continuity constraints on ESS capacity Eess (x + 1) = Eess (x) + ηch · Pch (x) −

Pdch (x) ηdch

(7)

In the formula, Eess (x + 1) and Eess (x) represent the ESS capacity values at time x + 1 and x respectively. ηch is the ESS charging efficiency, and ηdch represents the discharging efficiency. (iii) State of Charge Constraint Overcharging and discharging of batteries in ESS are two important factors that threaten battery safety [15]. To ensure good ESS performance and extend the service life of ESS, the state of charge (SOC) of ESS is constrained. SOCmin ≤ SOC(x) ≤ SOCmax

(8)

As expressed in (8): SOCmin and SOCmax each represent the minimum and maximum values of the ESS state of charge. SOC(x) is the SOC of ESS at time x. (iv) energy conservation Ppv (x) + Pdch (x) − Pch (x) = Pg(x)

(9)

Where: Pg(x) and Ppv (x) show the System output power and total PV output power. (v) System output power characteristic constraints To optimize the output power characteristics of the collection system, constraints are imposed on the system output period and power size. 24 

(1 − λ) ·

24 

Ppv (x)

1

μ

≤ Pg(θ ) ≤ (1 + λ) ·

Ppv (x)

1

μ

(10)

In the formula: λ is the fluctuation rate of output power of the collection system, μ stand for the output hours, θ is the output power time point.

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3 Double-Layer Optimization Model 3.1 Solution Flowchart The solution process of the double-layer optimization model is shown in Fig. 2.

o

Fig. 2. Solution flowchart

3.2 Configuration Ideas This article constructs a double-layer optimization model, exploring the optimal configuration and operation strategy of ESS power and capacity based on improving the output characteristics of the collection system and minimizing the investment cost of ESS. The outer layer of the double-layer model determines the configuration power and capacity of the ESS, and uses particle swarm optimization algorithm to solve it; The inner layer transforms the charging and discharging operation of ESS into a mixed integer linear programming problem under the peak-valley time-of-use (TOU) electricity tariffs. The inner layer objective is solved using the yalmip toolbox provided by Matlab and the cplex technology developed by IBM, which improves the solving efficiency.

4 Example Analysis 4.1 Example Overview This article adopts the IIOS type PV DC collection system as the basic model, consisting of 7 identical PV modules and 1 ESS module connected in series.1 PV module is composed of a PV system and a DC-DC converter; The ESS module consists of a lithium-ion battery with a rated operating time of 4 h and a bidirectional DC-DC converter. Select the peak-valley TOU electricity tariff data of a northern region of China in autumn.

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The following figure shows the output power curve of a single PV array in a typical day of the system. And the model setting parameters are shown in Tables 1 below (Fig. 3). Single PV Array Output

Power/kW

150

100

50

0

5

10

15

20

Time/h

Fig. 3. Output diagram of single PV array

Table 1. Model parameters parameter

value

n

1

Q1

300 yuan/kW

Q2

800 yuan/kWh

s

5%

J

12 years

t

1h

k

0.5%

ηch

88%

ηdch

88%

Socmin

0.2

Socmax

0.8

λ

5%

μ

10 h

θ

08:00–19:00

4.2 Results Analysis Figure 4 (a) shows the fitness curve of ESS cost and (b) shows the operation power diagram in a typical day of the collection system. According to the double-layer model, the optimal configuration of ESS in the collection system is 486.4 kW/1861.7 kWh. As shown in Fig. 4, after 25 iterations, the total cost of ESS reached convergence, with a minimum value of 56300 yuan/year. The above

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8

PV Output ESS Discharge Power ESS Charging Power System Output Power

1500 7.5

Power/kW

Cost Fitness Value/yuan

311

1000

7 6.5 6 5.5

500

0

0

10

20

30

40

50

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figure verifies the feasibility and superiority of the double-layer model method designed in this article, which is suitable for solving the ESS configuration and operation strategy in PV DC collection systems. Figure 5 shows the comparison of the total output power of the collection system before and after the ESS configuration. System Output after Configuration System Output before Configuration

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From Fig. 5, it can be seen that the reasonable configuration of ESS in the collection system results in a concentrated PV power output between 08:00 and 19:00, with controllable output power and smooth operation, reducing the fluctuation of power integrated into the grid and effectively improving the controllability of the output power of the PV DC collection system.

5 Summary On the premise of improving the output power characteristics of PV DC collection systems and reducing system investment costs, this paper designs a double-layer optimization model for ESS configuration, which uses particle swarm optimization algorithm, yalmip, and cplex to solve the capacity, power, and ESS operation strategy of ESS configuration. The calculation example shows that the double-layer optimization model for ESS configuration proposed in this article is scientific and reliable, and can be used to optimize the operation status of the IIOS DC collection system, making its system

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output power characteristics excellent, and improving the economic performance of the system.

References 1. Xi, X., Huang, W., Zhang, L., et al.: Comprehensive protection method for low-voltage cable of PV plant DC collection system based on series reactance. Trans. China Electrotech. Soc. 33(S2), 608–615 (2018). (in Chinese) 2. Zhuang, Y., Liu, F., Huang, Y., et al.: A multiport DC solid-state transformer for MVDC integration interface of multiple distributed energy sources and DC loads in distribution network. IEEE Trans. Power Electron. 37(2), 2283–2296 (2022) 3. Luo, Y., Qing, X., Peng, R., et al.: Influence of different factors on fault current under DC side fault of photo voltaic grid connected system. In: 2021 IEEE 5th Conference on Energy Internet and Energy System Integration (EI2), Taiyuan, China, pp. 835–838 (2021) 4. Li, X., Zhu, M., Hu, H., et al.: Coordinated power control for distributed hybrid energy storage in DC PV power collection system. In: 2020 IEEE 9th International Power Electronics and Motion Control Conference (IPEMC2020-ECCE Asia), Nanjing, China, pp. 1734–1739 (2020) 5. Li, Z., Zhang, R., Sun, H., et al.: Review on key technologies of hydrogen generation, storage and transportation based on multi-energy complementary renewable energy. Trans. China Electrotech. Soc. 36(3), 446–462 (2021). (in Chinese) 6. Li, Q., Zhao, S., Pu, Y., et al.: Capacity optimization of hybrid energy storage microgrid considering electricity-hydrogen coupling. Trans. China Electrotech. Soc. 36(3), 486–495 (2021). (in Chinese) 7. Meng, D., Yu, W.: Capacity optimization configuration of hybrid energy storage system using a modified grey wolf optimization. In: 2022 7th International Conference on Power and Renewable Energy (ICPRE), Shanghai, China, pp. 1043–1047 (2022) 8. Boonraksa, T., Pinthurat, W., Wongdet, P., et al.: Optimal capacity and cost analysis of hybrid energy storage system in standalone DC microgrid. IEEE Access 11, 65496–65506 (2023) 9. Liu, Y., Yang, Z., Lin, F., et al.: Study on adaptive energy management and optimal capacity configuration of urban rail ground hybrid energy storage system. Trans. China Electrotech. Soc. 36(23), 4874–4884 (2021). (in Chinese) 10. Bian, X., Shi, Y., Pei, C., et al.: Bi-level collaborative configuration optimization of integrated community energy system considering economy and reliability. Trans. China Electrotech. Soc. 36(21), 4529–4543 (2021). (in Chinese) 11. Zhang, X., Chen, C., Zhang, Y., et al.: Optimal configuration of wind farm energy storage capacity considering battery operation state. Autom. Electr. Power Syst. 46(18), 199–207 (2022). (in Chinese) 12. Ma, S., Wu, Y., Li, J., et al.: Research on optimal configuration of centralized battery energy storage for multiple service objectives. High Volt. Appar. 59(07), 75–86 (2023). (in Chinese) 13. Yu, H., Rong, H., Xu, Y., et al.: Double-layer planning configuration with distributed PV power and energy storage system. In: 2022 IEEE 5th International Conference on Automation, Electronics and Electrical Engineering (AUTEEE), Shenyang, China, pp. 37–41 (2022)

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14. Guo, Z., Liu, P., Gong, D., et al.: Deployment of independent energy storage in urban area based on double -layer optimization methodology. In: 2022 IEEE 6th Conference on Energy Internet and Energy System Integration (EI2), Chengdu, China, pp. 775–779 (2022) 15. Wei, Y., Li, Y., Cao, B., et al.: Research on power equalization of lithium-ion batteries with less loss buck chopper. Trans. China Electrotech. Soc. 33(11), 2575–2583 (2018). (in Chinese)

Novel Open Circuit Voltage Clamp Protection Method Based on Microsecond Pulse Current Source for DBD Application Zhenyu Guo, Shanshan Jin(B)

, and Zhi Fang

College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing 211816, China [email protected]

Abstract. The microsecond pulse supply based on flyback has the advantages of a simple circuit structure, few power components, a simple drive circuit, and convenient modular expansion. It has a wide application prospect in applying dielectric barrier discharge (DBD) plasma drive. However, the output of this type of microsecond pulse supply is a pulse current source, which, by C load under DBD equivalent capacitive load conditions, charges the load capacitor, and generates a high voltage pulse voltage U pulse , generating discharge plasma. The smaller the load capacitance, the higher the amplitude of the pulse voltage generated. In practical engineering applications, inevitably, the load electrode connection is not strong. Still, it is fatal for the microsecond pulse current source, which will cause the output pulse voltage amplitude to be too high damaging the power supply and causing human contact safety problems. This paper proposed a resistor-capacitordiode (RCD) branch, in which the voltage amplitude of the output terminal can be effectively limited by reasonably designing the voltage on the RCD energy storage capacitor C s and the amplitude of the pulse output voltage U pulse by controlling the secondary opening mode of diode Ds . Finally, the effectiveness of the proposed method is verified by simulation experiments. Keywords: Absorbing circuit · voltage clamp · MPPM · DBD

1 Introduction Low-temperature plasma is widely used in biomedicine, energy conversion, and industrial material processing because of its rich variety of active particles, which can promote biochemical reactions that are difficult to occur under normal temperature and pressure conditions [1–3]. Especially in the field of biomedical applications, the electrode temperature characteristics, safety characteristics and discharge stability of discharge plasma have more stringent requirements, so the development of DBD discharge plasma sources has been widely developed. At the same time, professional plasma biomedical researchers summarized that DBD plasma sources had significant effects on some skin surface treatment diseases including the surface disinfection of medical devices [4]. Similar DBD wound treatment devices used in medical and domestic applications require plasma source devices to become smaller, safer, and more reliable [5]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 314–320, 2024. https://doi.org/10.1007/978-981-97-0877-2_33

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Many kinds of high-voltage power supplies can be used to drive DBD discharge, all of which are outside the medium and form gas breakdown discharge through high pressure to produce plasma [6]. However, the discharge characteristics of different driving pulse power are very different. Due to the capacitance-like equivalent load form of the DBD electrode, the discharge efficiency of the high-frequency bipolar AC power supply is relatively low, and the electrode temperature is too high with a large amount of heat consumption [7, 8]. Compared with a high-frequency AC power supply, a unipolar pulse supply [9] can generate higher discharge efficiency under a relatively low pulse frequency condition with a lower electrode temperature, electrical safety [10] more suitable for human contact [11], and lower electromagnetic noise interference. Among them, the microsecond pulse power supply has more application prospects because of its simple structure, low cost, and easy miniaturization. Open circuits will cause the output pulse voltage amplitude to be too high damaging the power supply and causing human contact safety problems. This paper proposed a resistor-capacitor-diode (RCD) branch, in which the voltage amplitude of the output terminal can be effectively limited by reasonably designing the voltage on the RCD energy storage capacitor C s and the amplitude of the pulse output voltage U pulse by controlling the secondary opening mode of diode Ds .

2 Proposed Open Circuit Voltage Clamp Protection Method for MPPM

Fig. 1. Proposed MPPM with RCD. (a) Equivalent circuit diagram. (b) Key point waveform analysis.

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The proposed pulse power formation unit of MPPM and the key point analysis waveform are shown in Fig. 1. Figure 1 (a) shows a similar flyback topology. The pulse power is formed by the pulse transformer T, which can be equivalent to the primary inductor L p , the ideal energy transmission transformer, the primary leakage inductor L pri_lk, and the secondary leakage inductor L sec_lk . The high voltage RDD branch, consisting of D1 , D2, and R1 , is a pulse shaping circuit to ensure that the high voltage pulse waveform of the DBD load is generated without resonance. The RCD circuit is composed of Ds , C s, and Rs , and has two functions, one is to absorb the energy stored in leakage L pri_lk , and the other is to realize the open-circuit voltage clamp function. The circuit operating in the OFF state has four stages, the OFF-Stage I–IV. During OFF-Stage I: at the ON-Stage stage, the T stores energy. At the moment t 1–1 , the energy stored by L p is transferred to the secondary side. In contrast, the energy stored by leakage sensing L pri_lk will continue to flow through the Ds , charging the C s , and transferring quickly. The voltage variation, U cs is:  Llk Ucs = · Ipri_peak (1) Cs If the U pulse_peak is limited, the voltage threshold of C s can be obtained as U cs_limit , with the maximum and minimum voltage, U cs_max , U cs_min are: Np Upulse_peak Ns  Np 1 Llk Upulse_peak + · Ipri_peak Ucs_max = Ns 2 Cs  Np 1 Llk Upulse_peak − · Ipri_peak Ucs_min = Ns 2 Cs Ucs_limit =

(2) (3) (4)

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The Ds enters the on-state again when U pulse is high enough, and the U ce_tra is as follows: Uce_tra = Ucs + Uout

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With the U pulse keep decreasing and Ds is still in the cutoff state. In practical engineering applications, inevitably, the load electrode connection is not strong; the proposed RDC branch can suppress the U pulse voltage amplitude effectively by connecting C s equivalent to the load port by controlling the Ds avoiding the human contact safety problem.

3 Simulation Results and Discussion Through the above theoretical analysis, the paper puts forward the RCD branch can not only effectively reduce the heat loss on the switching transistor, but also can have the effect of pulse output voltage limiting protection, this is because the RCD branch of Ds on the state is different, the Ds of conduction is leaking energy transfer for the first time, the Ds conduction is limited pulse output voltage for the second time. Here, we conducted Saber circuit simulation verification for the two working modes of the proposed RCD branch. The simulation schematic diagram and the names of key electrical nodes are shown in Fig. 2. In the simulation, the leakage inductance is replaced by 107 μH inductance with an independent series connection on the primary side, which is also the measured leakage inductance of the pulse transformer. The simulation waveforms of the key points are shown in Fig. 3, where the dashed lines are the simulation results without adding the RCD branch, and the solid lines are the simulation results with adding the proposed RCD branch. As can be seen from the waveform of the simulation result in Fig. 3(a), when switch transistor Q is off, the leakage energy of the primary side L pri_lk is stored in C s of the RCD branch in a very short time, and the turn-on time of diode Ds of the RCD circuit is shaded area ➀ in Fig. 3. Since the total leakage energy is stored in the C s , the power switching switch transistor Q has almost no switching loss during the switching process, so in theory, Q does not need additional design heat sink to dissipate heat, which is conducive to the volume optimization.

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Fig. 2. Simulation schematic diagram and the names of key electrical nodes

Fig. 3. Simulation waveforms of the key points with and without RCD

As the U pulse continues to increase, if the increase is too high, greater than the voltage on the C s on the RCD branch, Ds will enter the open state again and enter the secondary turn-on stage, shaded area ➁ in Fig. 3(a). This stage is the voltage clamp protection stage proposed in this paper, which will occur under open output conditions in practical engineering applications. The introduction of C s in the RCD branch ensures that the high-voltage output end is equivalent to accessing a large load capacitor, transferring the secondary energy of the secondary side to C s . When the load capacitance is larger, the U pulse amplitude is smaller, and the secondary conduction mode duration of Ds gradually decreases, as shown in Fig. 4 (a). However, when the pulse amplitude voltage is too high under light load conditions, Ds will quickly enter the secondary on-state and perform the clamp protection function, as shown in Fig. 4(b).

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Fig. 4. The limited voltage protection function of the proposed RCD branch. (a) Different load capacitors C load . (b) Pulse voltage limiting function under light load conditions.

4 Conclusion In this study, based on the MPPM, an RCD circuit for reducing power consumption of the transistor Q and reducing the high pulse amplitude voltage at low loads for output voltage limiting protection function for human contact safety. Unlike the RCD spike absorption circuit in the conventional flyback, the proposed RCD circuit has two conduction times due to the presence of Ds in one pulse time. During the first conduction of Ds , the RCD branch absorbs the energy from the transformer’s primary leakage inductance to reduce the thermal loss of the switching transistor, and this step will be completed in a very short period. As U pluse continues to rise, Ds will start the next conduction. During the second conduction, the energy on the secondary side will be partially reflected on the primary side, therefore limiting the increase of the pulse voltage amplitude, which is most obvious at low loads. The reduction of power consumption of transistor Q greatly improves the performance of the MPPM, while the switching transistor does not require additional heat dissipation. The function of limiting the pulse amplitude voltage for the RCD branch can greatly improve the output safety of MPPM under low load conditions, and it also provides greater protection for some DBDs that are accessible to the human body.

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Acknowledgment. This work was supported by the National Natural Science Foundation of China, Natural Science Youth Foundation Project of Jiangsu Province of China, Jiangsu Provincial Natural Science Foundation for Colleges and Universities, and Jiangsu Provincial Double-Innovation Doctor Foundation, under Grants: 52107153, BK20210548, 21KJB470022 and JSSCBS20210389.

References 1. Park, G.Y., et al.: Atmospheric-pressure plasma sources for biomedical applications. Plasma Sour. Sci. Technol. 21(4), 043001 (2012) 2. Mei, D., Liu, S., Tu, X.: CO2 reforming with methane for syngas production using a dielectric barrier discharge plasma coupled with Ni/γ-Al2 O3 catalysts: process optimization through response surface methodology. J. CO2 Utili. 21, 314–326 (2017) 3. Metropolis, S., Rassias, G., Bekiari, V., Aggelopoulos, C.A.: Structure-degradation efficiency studies in the remediation of aqueous solutions of dyes using nanosecond-pulsed DBD plasma. Sep. Purif. Technol. 274(1), 119031 (2021) 4. Saleh, S.A., Allen, B., Ozkop, E., Colpitts, B.G.: Multistage and multilevel power electronic converter-based power supply for plasma DBD devices. IEEE Trans. Ind. Electron. 65(7), 5466–5475 (2018) 5. Bárdos, L., Baránková, H.: Cold atmospheric plasma: sources, processes, and applications. Thin Solid Films 518(23), 6705–6713 (2010) 6. Daeschlein, G., et al.: Skin decontamination by low-temperature atmospheric pressure plasma jet and dielectric barrier discharge plasma. J. Hosp. Infect. 81(3), 177–183 (2012) 7. Lee, K., et al.: Plasma skincare device based on floating electrode dielectric barrier discharge. Plasma Sci. Technol. 21(12), 125403 (2019) 8. Liu, Y., Hu, P., Qiu, H., Wang, R.: Development of a hand-held FE-DBD plasma device. In: He, J., Li, Y., Yang, Q., Liang, X. (eds.) The proceedings of the 16th Annual Conference of China Electrotechnical Society. LNEE, vol. 891, pp. 566–572. Springer, Singapore (2022). https://doi.org/10.1007/978-981-19-1532-1_60 9. Wiley, J.S., Shelley, J.T., Graham Cooks, R.: Handheld low-temperature plasma probe for portable “point-and-shoot” ambient ionization mass spectrometry. Anal. Chem. 85(14), 6545– 6552 (2013) 10. Ho, K.N., Chaijaruwanich, A: Development of a battery-operated plasma device using dielectric barrier discharge plasma in ambient air. CMU J. Nat. Sci. 17(1), 47–59 (2018) 11. Liu, Y., Wang, S., Zhou, R., Fang, Z., (Ken) Ostrikov, K.: Development of a battery-operated floating-electrode dielectric barrier discharge plasma device and its characteristics. Plasma Sci. Technol. 23(6), 064008 (2021) 12. Sanabria, C., Florez, D., Piquet, H., Diez, R.: Sizing equations for a square voltage pulse power supply for dielectric barrier discharges. IEEE Trans. Power Electron. 37(4), 4374–4384 (2022) 13. Deng, Z., Liu, X., Qiu, Q., Jia, H., Deng, Y., He, X.: Nonlinear resonance characteristics analysis of DBD load based on state plane trajectory. IEEE Trans. Power Electron. 38(4), 4760–4770 (2023) 14. Wang, Q., Liu, F., Miao, C., Yan, B., Fang, Z.: Investigation on discharge characteristics of a coaxial dielectric barrier discharge reactor driven by AC and ns power sources. Plasma Sci. Technol. 20(3), 035404 (2018) 15. Duan, G., Fang, Z., Fu, J., Yu, P., Mei, D.: Influence of water cooling for the outer electrode on the discharge characteristics of an atmospheric coaxial DBD reactor. IEEE Trans. Plasma Sci. 49(3), 1173–1180 (2021)

High-Precision Current Source with Lumped Current Outer Loop-Distributed Current Inner Loop for the Application of Sintered Powder Materials Songyang Zhao, Shanshan Jin(B)

, and Zhi Fang

College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing 211816, China [email protected]

Abstract. Pulse electric current sintering is a new powder material synthesis technology. Due to the limited output accuracy of the current source, it is difficult to precisely control the amount of charge that passes through the sample and the mold, to precisely adjust the temperature rise rate of the target sample. Based on the topology of the linear current source, a high-precision current source with lumped current outer loop and the distributed current inner loop is designed in this paper, which consists of two parts: the distributed current inner loop power stage unit and the current outer loop feedback calibration unit. The working principle and characteristic parameters of the double closed loop current source are analyzed through the circuit structure. The influence of the power transistor on the output current accuracy is analyzed through verification experiments, and it is proved that the current source can output extremely high current accuracy, achieve a static error of mA level, and realize rapid temperature rise during sintering. Keywords: Pulse electric current sintering · Linear current source · double closed-loop structure · high precision

1 Introduction Since ancient times, material synthesis has always been a hot topic. Powder metallurgy is the most extensive method for preparing composite materials, and sintering, as one of the most basic processes in the production process of powder metallurgy, plays an extremely critical role [1]. Sintering refers to the process of heating the powder or powder compact to a temperature below its basic components and holding it at this temperature for a while and then cooling it to room temperature according to a certain method and speed. Through this process, powder particles are combined to obtain materials with desired properties [2]. Sintering is the general term for the densification process and phenomenon of powder or embryo body at high temperatures. As a new sintering method, pulse electric current sintering (PECS) is to apply pulse or constant current strong current to the sample and the mold and uses the Joule thermal effect of the current © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 321–329, 2024. https://doi.org/10.1007/978-981-97-0877-2_34

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and other electric field effects to make the sample quickly hot compacting [3, 4]. Its remarkable feature is the rapid and low-temperature preparation of materials, which can be used for the preparation of sintered metals, ceramics, and nanomaterials. Compared with conventional sintering methods, pulsed current sintering has a higher degree of material densification and smaller grain size, which has wider application scenarios [5, 6]. Because PECS needs to accurately calculate the amount of charge entering the sample and the mold after determining the mold and the target sample for sintering, this allows precise calculation of the exact rate of temperature rise of the sintered target sample. Therefore, high-precision current source is one of the key technologies of this technology. At present, there are two common ways to realize high-precision power current sources. One is the switching mode scheme in which the transistor works in the switching state, which adopts peak current control, average current control, or subsequent current control to adjust the output. The second is the linear mode scheme in which the transistor works in the linear amplification region and adjusts the gate voltage of the power switch through negative feedback control [7]. In this paper, a high precision current source with aggregate current outer loopdistributed current inner loop is proposed for the application field of PECS technology. The dual negative feedback-double closed-loop structure of distributed inner loop and collector current outer loop can significantly reduce the output current error of the current source system, improve the overall output accuracy of the current source, and ensure the rapidity of the PECS temperature control.

2 Proposed High-Precision Current Source with Double Closed-Loop Structure 2.1 Double Closed-Loop System Frame Diagram The overall system frame of the lumped current outer loop-distributed current inner loop high precision current source based on the double closed-loop feedback architecture is shown in Fig. 1, which consists of two parts: the distributed current inner loop power stage unit and the current outer loop feedback calibration unit. The distributed current inner loop power stage unit for the whole system to provide power output, which is mainly composed of N (N  1) linear current source modules in parallel, through the input side of the parallel form, can realize each linear source by the same DC input voltage control. Parallel connection of outputs enables power superposition in the form of N-mode linear sources with N-fold current. The input voltage can be adjusted according to the user’s actual current demand. The current outer loop feedback calibration unit is based on the inner loop power stage unit, adding the lumped outer loop negative feedback adjustment and calibration link, to further improve the output accuracy of the current source and reduce the error superposition brought about by the superposition of multiple power stage units. 2.2 System Architecture and Analysis N line linear source connected in parallel equivalent circuit diagram shown in Fig. 2 (a), where a single linear current source module topology shown in Fig. 2 (b), using a

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Fig. 1. Double closed-loop system frame diagram

dual high-speed voltage feedback amplifier, dual high-speed voltage feedback amplifier with positive and negative power supply VEE and VCC for power supply, in the input side of the input is given a reference voltage U ref , the use of op-amps, “virtual short and virtual broken” characteristics, the circuit by differential sampling to detect the voltage on the sampling resistor, sent to the reverse side of the feedback op-amp, compared with the given reference voltage U ref makes the sampling resistor voltage is equal to U ref Using the op-amp’s “false short and false break” feature, the circuit detects the voltage on the sampling resistor through differential sampling, sends it to the inverse end of the feedback op-amp, and compares it with the given reference voltage U ref so that the voltage on both ends of the sampling resistor is equal to U ref , and then it will get a sampling resistor branch current I path , and realizes the linear control of the output current through the given input voltage. Among them: Rf 2 = Rf 4 , Rf 1 = Rf 3

(1)

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(2)

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(3)

Compared with the traditional linear current source [8], the drive circuit and compensation circuit are added to the structure, the drive circuit through the combination of transistors and field effect tubes can not only protect the operational amplifier but also enhance the stability of the system, which is conducive to the realization of the parallelism of the multiple current sources [9]; and the compensation circuit in the dynamic change of the environment to play a key role, which greatly improves the dynamic response performance of the system. The structure of the lumped current outer loop circuit’s role is to collect the output current and then compared it with the input reference control voltage signal for correction,

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(a) Parallel equivalent diagram

(b) Linear current source circuit structure diagram

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to further improve the output linear current accuracy. The total collector current outer loop circuit can accurately collect the output current of the current source power stage unit and convert it into the corresponding voltage signal, correct and calibrate it and compare it with the input control voltage signal to form a negative feedback loop, and the final output voltage signal is used as the input control voltage signal of the current source power stage unit. Using a frequency network analyzer, the dynamic frequency characteristics of the above collector current outer loop circuit link simulation [10], the output of the openloop logarithmic frequency response characteristics of the curve is shown in Fig. 3, from the figure, the collector current outer loop circuit link is approximated as a second-order oscillation link.

Fig. 3. Open-loop logarithmic frequency characteristic of lumped current outer loop circuit

3 Experimental Results and Discussion A dual closed-loop current source hardware experimental platform is built to validate the feasibility and effectiveness of outputting high-precision current as proposed in this paper. Figure 4 shows the linear source hardware platform used for experimental verification. The experimental verification is divided into four parts: the study of the

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influence of power linear transistor parameters on current accuracy, the double closedloop current control accuracy test experiment, the current source edge editing function experiment, and the sintering temperature rise test experiment.

Fig. 4. Linear source experimental platform

3.1 Effect of Power Linear Transistor Parameters on Current Accuracy The power transistor [11] is the core component of the linear source, in the case of the same adjustment range of the operational amplifier as well as the driver circuit, the degree of nonlinearity in the nonlinear region of the power transistor with different parameters has a large gap, i.e., the characteristics of the transistor affects the accuracy of the linear source in the small current output. To investigate the influence of different parameters on the accuracy of power output in the nonlinear region, the experimental platform shown in Fig. 5 (c) is built. The effects of transmission characteristics, and output characteristics on output accuracy are tested separately. Since the transistor’s through-current and withstand-voltage capabilities can reflect the transmission characteristic curve and output characteristic curve of the transistor to a certain extent, the transistor with the desired characteristics can be selected by comparing the through-current and withstand-voltage values of the transistor. 50

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The transfer characteristic of a power transistor, shown in Fig. 5 (a), is the relationship between the drain current I D and the voltage U GS between the gate-source, reflecting

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the relationship between the input voltage and the output current. Figure 6 shows the waveforms of the oscillation regulation process of three transistors with large differences in the degree of nonlinearity of the transfer characteristic curves reflecting different degrees of nonlinearity at small current outputs, and the parameters of the selected transistors are 60 V/8 A, 60 V/60 A, and 60 V/140 A, respectively, and the parameters measured at U ref = 0.1 V and U bus = 10 V.

o

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(b) 60V/8A

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Fig. 6. Effect of transistors with different degrees of transmission characteristic curve nonlinearity on output current accuracy

It can be found that the degree of oscillation of the measured output AC component increases as the transistor through-current capability increases, i.e., the degree of nonlinearity increases. This is because as the degree of nonlinearity increases, the range of variation of the transistor’s drain current I D gradually increases under the modulating effect of the same gate drive voltage U GS , so that it exhibits a greater amplitude of oscillation, and also affects the accuracy of the output current to some extent. The output characteristic curve of the power transistor is shown in Fig. 5 (b), reflecting the relationship between the drain current I D and the drain voltage U DS . Figure 7 shows the waveforms of the oscillation regulation process with different degrees of nonlinearity reflected in the small current output of three transistors with large differences in the degree of nonlinearity in the output characteristic curves, and the parameters of the selected transistors are 60 V/8 A, 500 V/8 A, and 1200 V/8 A, respectively, which are measured under the conditions of U ref = 0.2 V and U bus = 2 V. As the transistor’s voltage withstand capability increases, i.e., the degree of nonlinearity increases, results similar to those described above can be obtained.

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3.2 Dual Closed-Loop Current Control Test Experiment Figure 8 (a) shows the comparison graph of the influence of the external loop on the output accuracy. It can be clearly seen that after adding the external loop feedback of the collector current, the actual output current value is basically the same as the trend of the ideal output current, and the output accuracy is also improved very significantly, realizing the high-precision power current output, and there is only the mA level of the static error. Figure 8 (b) shows the collector output current at N = 10 measured at the input reference voltage in the form of a triangle wave, where the reference value U max = 1.5 V, U min = 0.3 V, and the frequency is f = 1 kHz. it can be found that the highest peak value and the lowest peak value of the output current are the current values corresponding to the input reference voltage signal, and the output current frequency is the same as the input voltage frequency. It shows that the current source power stage unit can accurately follow the edge change of the input reference control voltage signal, can correctly reflect the change frequency of the voltage signal, and output the corresponding linear current with certain dynamic response performance. The current source is connected with the boron nitride loosely connected to the carbon paper through the wire to test the temperature change and luminescence of the boron nitride and the carbon paper after passing into different pulse forms of current. The pulse current parameters are set to period T = 10 s, pulse width = 1 s, rising edge

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t r = 1 ms, falling edge t f = 1 ms, and pulse current amplitude I pulse = 35 A. The results are shown in Fig. 9.

(a) Real-time material temperature profile

(b) Material Luminescence Images

Fig. 9. Application of double closed-loop current source in sintering

4 Conclusions To better apply the PECS, this paper proposes a high-precision current source with lumped current outer loop and distributed current inner loop. Firstly, a dual-closed-loop dual-feedback system-based frame is proposed and structurally analyzed. Secondly, it was analyzed experimentally that the output current oscillations increase with the degree of nonlinearity of the transistor characteristic curve. Finally, the validity of the whole current source system was verified, and the static error of the output current was obtained to be at the mA level, and the temperature rise of 2400 °C in 1s could be realized. Acknowledgments. This work was supported by the National Natural Science Foundation of China under Grant 52107153, the Natural Science Youth Foundation Project of Jiangsu Province of China under Grant BK20210548, Jiangsu Provincial Natural Science Foundation for Colleges and Universities under Grant 21KJB470022 and Jiangsu Provincial Double-Innovation Doctor Foundation under Grant JSSCBS20210389.

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References 1. Manohar, G., Pandey, K.M., Maity, S.R.: Effect of sintering mechanisms on mechanical properties of AA7075/B4C composite fabricated by powder metallurgy techniques. Ceram. Int. 47(11), 15147–15154 (2021) 2. Zhang, L., Peng, J., Zhang, S.: New application of plasma activated sintering in material preparation. Rare Metals 24(6), 5 (2000). (in Chinese) 3. Milanese, C., et al.: Hydrogen storage in magnesium–metal mixtures: reversibility, kinetic aspects, and phase analysis. J. Alloys Compd. 465(1–2), 396–405 (2008) 4. Manohar, G., Pandey, K.M., Maity, S.R.: Aluminium (AA7075) metal matrix composite reinforced with B4C nano particles and effect of individual alloying elements in Al fabricated by powder metallurgy techniques. J. Phys. Conf. Ser. 1451(1), 012024 (2020) 5. Tokita, M.: Progress of spark plasma sintering (SPS) method, systems, ceramics applications, and industrialization. Ceramics 4(2), 160–198 (2021) 6. Liu, Z., Xu, J., Xi, X., Zhou, J.: High-strength Ti2AlN ceramics prepared by pulse electric current sintering based on powders synthesized by molten salt method. J. Eur. Ceram. Soc. 42(4), 1302–1310 (2022) 7. Liu, H., Zhang, D., Wang, Z., Zhang, H., Liu, Q.: Design consideration of a high precision and stability linear current source. In: 2019 4th International Conference on Power and Renewable Energy (ICPRE), pp. 173–179. IEEE (2019) 8. Li, D., Rodríguez, M., Zai, A., Sardin, D., Maksimovi´c, D., Popovi´c, Z.: RFPA supply modulator using wide-bandwidth linear amplifier with a GaN HEMT output stage. In: 2013 IEEE 14th Workshop on Control and Modeling for Power Electronics (COMPEL), pp. 1–6. IEEE (2013) 9. Jin, S.: Research on key technologies of space solar array simulator. (Doctoral dissertation, Harbin Institute of Technology) (2017). (in Chinese) 10. Li, J., Wan, W., Liu, Z.: A frequency characteristic analysis method for control systems based on time-domain response. Proc. CSEE 32(29), 116–122 (2016) 11. Guo, J.: Research on novel SiC field-effect power transistor. (Doctoral dissertation, University of Electronic Science and Technology of China) (2022). (in Chinese)

Voltage Regulation Method for Active Distribution Networks Based on Rotary Voltage Regulator Xiangwu Yan, Chen Shao(B) , Weifeng Peng, Bingzhen Li, and Weilin Wu Key Laboratory of Distributed Energy Storage and Micro-Grid of Hebei Province, North China Electric Power University, Baoding, China [email protected]

Abstract. Due to the dominant resistive component in distribution lines, the voltage upper and lower limits may occur in the same scenario. The voltage upper limit is caused by daytime photovoltaic power injection, while the voltage lower limit is caused by nighttime line voltage drop. Load tap changer (LTC) voltage regulation and dynamic reactive power compensation voltage regulation devices have certain limitations. A method using a Rotary Voltage Regulator (RVR) is proposed, which injects a constant amplitude and continuously adjustable phase voltage phasor into the line by controlling the relative angle of the rotor. Regarding the four-quadrant bidirectional voltage regulation characteristics of RVR, the method to improve the power factor under the premise of voltage regulation is studied. Furthermore, the overshoot problem caused by the mechanical structure during the voltage regulation process is analyzed, and a variable speed control scheme for RVR is designed. Finally, a 380 V/40 kVA RVR prototype is developed, and experimental results show that RVR can effectively improve the power factor at the access point while satisfying the voltage regulation requirements, thus verifying the effectiveness and correctness of the proposed control strategy. Keywords: Rotary voltage regulator · Active distribution network · Bidirectional voltage regulation · Power factor regulation

1 Introduction In the context of the energy crisis and environmental pollution, research and development of renewable energy generation have been promoted. Among various renewable energy sources, distributed power generation plays a significant role [1]. However, with the integration of scaled distributed energy sources and the diversification of user loads on the distribution grid, the traditional one-way power flow is transforming into a two-way flow, impacting the voltage distribution across the entire network, and potentially leading to voltage violations [2]. To address the voltage control issue in active distribution networks, several studies have been conducted, including distribution network reconfiguration [3], on-load © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 330–337, 2024. https://doi.org/10.1007/978-981-97-0877-2_35

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tap changer (OLTC) voltage regulation [4], application of distribution network synchronous compensators (DSTATCOM) [6], and participation of energy storage in voltage regulation [7]. In the 1990s, General Electric introduced a novel rotary power flow controller (RPFC) [8], consisting of series and parallel transformers and sets of rotary phase-shifting transformers. This system flexibly controls compensating voltage in lines, enabling flexible power control. Analyzing its compensation characteristics revealed that when applied to distribution network voltage regulation scenarios, only a set of rotary phase-shifting transformers is needed to achieve bidirectional voltage regulation at connection points, effectively reducing equipment costs. Building on this concept, a new rotary voltage regulator (RVR) was designed. This RVR injects a constant amplitude and phase-adjustable voltage phasor into the line by controlling the relative angle between the rotor and stator, achieving bidirectional control of connection point voltage [9, 10]. Building on this, research was conducted on RVR-based active distribution network voltage regulation and power factor improvement methods, analyzing the topology and operation principles of the RVR and establishing a simplified circuit model. To address the mechanical structural voltage regulation deficiencies, a variable-speed control scheme for RVR was designed, effectively reducing system steady-state errors and improving response speed. Finally, a prototype RVR with specifications of 380 V/40 kVA was developed. Experimental results demonstrate that the RVR exhibits favorable voltage regulation and power factor adjustment characteristics, confirming the effectiveness and correctness of the proposed topology and control strategy.

2 Mechanism Analysis of Voltage Exceedance in Active Distribution Networks The integration scheme for the distribution system is illustrated in Fig. 1. 35kV busbar 35/10.5kV Us U1 Voltage regulation device 1#10/0.4kV R1+jX1 P1+jQ1

2#10/0.4kV

Grid connection point 1 User load

Grid connection point 2 User load

P1,DG1 +jQ1,DG1 1#Photovolt aic inverter P1,L1+jQ1,L1 P1,DG2 +jQ1,DG2 2#Photovolt aic inverter

P1,L2+jQ2,L2

Fig. 1. Active distribution grid system with distributed PV

In the diagram, U˙ s represents the voltage at the starting point of the 10 kV busbar section, U˙ 1 denotes the grid-connected point voltage, R1 + jX 1 signifies the line

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impedance, and P1 + jQ1 stands for the line transmission power. The transverse component of the feeder voltage drop has a minimal effect on the voltage drop. Therefore, considering only the longitudinal component of the voltage drop, the relationship between the grid-connected point voltage and the line transmission power can be expressed as follows: P1 R1 + Q1 X1 (1) U1 = Us − Us Hence, when distributed power sources generate a substantial amount of power that cannot be fully absorbed on-site, the direction of power flow will change. In the context of P1 R1 + Q1 X 1 < 0, the grid-connected point voltage will rise, possibly resulting in voltage exceedance.

3 RVR-Based Voltage Regulation and Loss Reduction Optimization Strategy in Active Distribution Networks 3.1 RVR Topology and Operating Principles As shown in Fig. 2, the RVR topology consists of the rotor side paralleling with the primary side of the transformer and connecting to the power supply line.

Fig. 2. Topology of RVR

The single-phase equivalent circuit of the RVR is depicted in Fig. 3(a), while the simplified circuit model is shown in Fig. 3(b).  + I˙s ZRVR U˙ RVR = U˙ RVR

(2)

 = k1 ejα U˙ s U˙ RVR

(3)

The simplified serial part of the RVR can be represented by a controlled ideal voltage source and an equivalent internal impedance. By altering the relative angle α between the stator and rotor, continuous adjustment of the injected line voltage can be achieved.

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Fig. 3. Working principle of RVR

3.2 Bidirectional Voltage Regulation Method of the RVR Referring to the structure of the active distribution network in Fig. 1, the grid-connected point voltage after the integration of the RVR can be expressed as follows:  2 P1 R + Q1 X P1 R1 + Q1 X1 Us2 + URVR − − (4) U1 =   −2Us URVR cos α U1 U1 − URVR  In the equation, URVR = k1 ejα U˙ s , R and X represent the equivalent resistance and reactance of Z RVR , while R1 and X 1 represent the line impedance. According to the “Voltage Deviations for Power Quality in Electricity Supply” (GB/T12325-2008) regulations, different voltage levels of lines have varying permissible limits for voltage deviations. For the 10 kV supply voltage, the allowable voltage deviation is within ±7% of the nominal voltage. Combining Eq. (3), when the grid-connected point voltage exceeds the limits, there’s a voltage regulation requirement for the RVR. Figure 4(a) illustrates the upper voltage limit control mode, while Fig. 4(b) shows the lower voltage limit control mode.

Fig. 4. Voltage regulation vector diagram of RVR

In the diagram, R and X represent the RVR impedance. It can be observed that positions A and B achieve effective voltage regulation for upper limit control, while positions C and D do the same for lower limit control. Furthermore, the voltage vector of the RVR integrated into the line at different positions will affect the power factor at the connection point. It is considered that when

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there is a small phase difference between voltage and current, the RVR connection point will have a higher power factor. Therefore, the design in Eq. (5) calculates the magnitude of the RVR voltage vector for voltage exceedance regulation:   θ − ϕs < θD − ϕs URVR = URVR C U1 < UN C  θC − ϕs > θD − ϕs URVR = URVR D  (5)  θA − ϕs < θB − ϕs URVR = URVR A U1 > UN  θA − ϕs > θB − ϕs URVR = URVR B In the equation, θ A , θ B , θ C , and θ D represent the angles of the RVR voltage vector     at points A, B, C, and D respectively. URVR A , URVR B , URVR C and URVR D are the corresponding voltage vectors at these points. ϕ s stands for the angle of the line current vector. By ensuring voltage regulation, this approach effectively enhances the power factor at the connection point. As shown in Fig. 5, the RVR control block diagram includes three main components: ➀ Main circuit structure, ➁ Variable-speed control module, and ➂ Main control strategy module.

Fig. 5. RVR control block diagram

4 Experimental Verification To validate the effectiveness and correctness of the proposed rotational voltage regulator (RVR) control strategy, a 380V experimental prototype of the RVR was constructed in the laboratory for verification purposes. To enhance the voltage regulation capacity of the RVR device, two sets of RVRs were connected in series for regulation. The experimental hardware setup is illustrated in Fig. 6.

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(a) Internal structure of RVR

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(b) Main Structure of RVR and Load Cabinet

(c) Relationship between servo motor, turbine worm, and rotor gear

(d) Motor drive module

Fig. 6. Experimental platform of RVR

4.1 RVR Variable Setpoint Voltage Regulation Experimental Verification Under the condition of keeping the load at the end of the line and line resistance constant, the voltage of the RVR integrated into the line is adjusted to achieve bidirectional voltage regulation at the grid-connected point. The effectiveness and robustness of the RVR variable setpoint voltage regulation experiment are validated through a four-stage experimental condition. Table 1 presents the set voltage values for the four stages, and Fig. 7 illustrates the voltage regulation control strategies considering power factor and the conventional voltage regulation control strategy. Table 1. Dynamic voltage regulation experiment parameters The process of voltage regulation/s

t0− t1

t1− t2

t2− t3

t3− t4

The set voltage/V

220

230

240

210

Load power/kVA

0.5+j0.5

3.3 + j1.2

0.1 + j0.1

–

Comparing Fig. 7 (a) and Fig. 7 (b), in terms of voltage control, both control strategies effectively regulate the voltage below the right end of the RVR connection point without affecting the voltage at the left end of RVR. However, the conventional voltage regulation control strategy achieves voltage regulation but only maintains a power

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Fig. 7. RVR variable set point voltage regulation experiment

factor of around 0.36–0.4, which does not meet the power supply requirements. On the other hand, the power factor-based voltage regulation control strategy proposed in this paper significantly improves the power factor while effectively regulating the voltage (achieving a power factor above 0.98 at the RVR connection point). This validates the effectiveness of the proposed control strategy.

5 Conclusion In response to the issue of voltage violations caused by the high penetration of distributed photovoltaic systems into the grid, a solution involving a rotary voltage regulator (RVR) is proposed. Through theoretical analysis and experimental verification, the following conclusions are drawn: 1) The proposed control strategy for the novel rotary voltage regulator achieves effective power factor improvement while enabling bidirectional regulation of line voltages. Within a 1% deviation range, the control strategy effectively regulates the voltage at the connection point and maintains a power factor above 0.97. 2) A simplified circuit model of the RVR is constructed, and the electromagnetic relationships within its internal components are analyzed. It is evident that the main circuit parameters of the RVR and the rotor angle directly influence the compensating voltage injected into the line, thereby affecting the line voltage. 3) The transformer structure of the RVR provides better resistance to system faults like short circuits, enhancing its resilience and reliability while maintaining costeffectiveness. Consequently, for the future construction of active distribution networks, the RVR holds extensive applicability and substantial value.

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References 1. Ma, Q., Hao, Z., Zhang, Y., et al.: Network partitioning and voltage coordination control of distributed photovoltaic distribution networks with high permeability 39(03), 93–102+108 (2023) 2. Zhang, J., Lv, Q., Guo, X., et al.: Research on maximum photovoltaic access capacity of distribution network considering reasonable light abandonment. Acta Energiae Solaris Sinica 44(02), 418–426 (2023) 3. Zheng, S., Deng, Z., Fan, R., et al.: Research on maximum power supply capacity of distribution network including distributed new energy site selection. China South. Power Grid Technol. 12(05), 71–79 (2018) 4. Chen, Y., Yang, P., Zeng, Z., et al.: Distributed energy planning of distribution network considering operation domain of microgrid. Autom. Electr. Power Syst. 43(03), 83–91 (2019) 5. LvV, S., Ye, L., Li, J., et al.: An evaluation index of medium and long term voltage stability considering the influence of dynamic regulation of on-load regulator transformers. J. Electr. Power Sci. Technol. 33(03), 86–92 (2018) 6. Wu, X., Mo, J., Wei, J.: Voltage support operation strategy of active distribution network based on district coordinated control. Mod. Power, 1–12 (2023) 7. Zhang, T., Yu, L., Yao, J., et al.: Reactive power optimization of distribution network based on improved multi-objective difference gray wolf algorithm. Inf. Control 20, 49(01), 78–86 8. Yan, X., Shao, C., Wu, M., et al.: Multi-scene control method of active distribution network based on electromagnetic rotating power flow controller. J. China Electrotech. Soc. 1–12 (2023) 9. Yan, X., Peng, W., Shao, C., et al.: User side voltage control method based on rotating power flow controller. Trans. China Electrotech. Soc., 1–11 (2023) 10. Yan, X., Jia, J., Wang, D., et al.: User side voltage regulation method of low voltage platform based on power spring. Trans. China Electrotechn. Soc. 20, 35(12), 2623–2631

Active Power Decoupling Control Strategy for MMCs with Split-Capacitor Sub-modules Fuyuan Zhuang1 , Xinmig Hu1 , Yunshan Wang1 , and Shunfeng Yang1,2(B) 1 National Rail Transit Electrification and Automation Engineering Technique Research Center,

Southwest Jiaotong University, Chengdu 61000, China {zhuangfuyuan,13018210152,yswang}@my.swjtu.edu.cn, [email protected] 2 School of Electrical Engineering, Southwest Jiaotong University, Chengdu 61000, China

Abstract. Although modular multilevel converters (MMCs) are more and more widely used, low frequency ripple voltage appears in sub-module (SM) capacitors due to the operating mode, and the fundamental frequency and double frequency are the main ones. Based on the split-capacitor sub-module (SC-SM) structure, an easy double closed loop active power decoupling control strategy is proposed in this paper. Firstly, the ripple power of MMC arm is deeply analyzed, and the operation principle of split-capacitor is introduced accordingly. Then, a mathematical model based on MMC split-capacitor is established in detail. Finally, the control strategy of voltage outer loop and current inner loop is proposed, and the AC and DC voltage decoupling is realized. The effectiveness and accuracy of the control scheme are verified by simulation experiments. The experiment results show that the voltage ripple of the split-capacitor sub-module is well suppressed in the steady state, and the voltage ripple is reduced to 3%. Keywords: Modular multilevel converters · split capacitor · active power decoupling

1 Introduction Modular multilevel converters (MMC) have become the preferred converter topology for high voltage direct current (HVDC) transmission due to their modular design, good harmonic characteristics and flexible expansibility, and many HVDC transmission demonstration projects have been built in China [1]. Sub-module (SM) capacitors have fundamental and double frequency ripple voltages. Capacitors with large volume are used to suppress voltage ripple in engineering applications, so it is particularly important to suppress the low frequency ripple voltage of capacitors. Active power decoupling technology is an effective method to solve the secondary ripple power in single-phase converter by transferring the specific frequency ripple power to decoupled inductors and capacitors [2]. Common decoupling circuits include Buck [3], Boost [4], buck-boost [5], Split-Capacitor (SC) [6], and so on. In the [7], at the output end of the AC-DC single-phase converter, an additional arm composed of a switching © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 338–346, 2024. https://doi.org/10.1007/978-981-97-0877-2_36

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tube and a diode is added, and a decoupling circuit is formed by an inductor. Because the power density of inductors is much lower than that of capacitors, the ability to reduce hardware volume is limited. The SC is used to decouple the active power in the single-phase converter to solve the inherent double frequency ripple power, and only one voltage closed loop is used for control in the [6]. The transition period is long and the dynamic tracking effect is limited when the load changes. In recent years, some scholars have applied the active power decoupling technology to the SM of MMC to decouple the arm ripple power and suppress the SM ripple voltage. An additional Buck circuit is attached to all SMs for power decoupling in the [8], and the ripple power is transferred to the capacitor of the Buck circuit. The repetitive controller is used to suppress the fundamental frequency and double frequency ripple voltage, but the SM voltage fluctuates greatly when the load changes. In the [9], only an extra Buck decoupling SM is attached in the middle of the upper and lower arm of the traditional half-bridge SM (HB-SM). This scheme can only eliminate even harmonic power, so the effect of suppressing the SM voltage ripple is limited. And all the above decoupled circuit control must have independence, that is, it does not affect the main circuit control. In this paper, the split-capacitor structure decouples the ripple power of MMC arm to suppress the low frequency ripple voltage of SM. The arm ripple power is derived, and the operation principle of the SC is analyzed. For the SC-SM, the corresponding mathematical model and equivalent circuit model are established, and the double closedloop control strategy is proposed. The simulation results show that, compared with the HB-SM, the voltage ripple is well suppressed.

2 Arm Ripple Power Analysis of the MMC This paper takes the study of single-phase MMC inverter as an example, and its topology is shown in Fig. 1. The output voltage uo and current io can be expressed as follows:  uo = Uo sin ωt (1) io = Io sin(ωt + θ ) where ω is the fundamental frequency 50Hz, and θ is the phase difference. Ignoring the voltage on L arm and Rarm , the upper and lower arm voltages and currents can be expressed as: ⎧ io ⎪  ⎨ iu = Idc + Idiff2 sin(2ωt + θdiff2 ) + Udc uu = 2 − uo 2 (2) , i ul = U2dc + uo ⎪ o ⎩i = I + I l dc diff2 sin(2ωt + θdiff2 ) − 2 where I dc represents the DC component of the circulating current, I diff2 represents the peak of AC double frequency, and θ diff2 represents the phase difference. The upper and lower arm power can be expressed as the multiplication of the corresponding arm voltage and current. Considering that the circulating current double

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frequency component has been well suppressed in practical applications, and I diff2 is a small value, so the arm power can be expressed as: ⎧ Udc Io Uo Io ⎪ sin(ωt + θ ) − Uo Idc sin ωt + cos(2ωt + θ ) ⎨ pu = uu iu = 4 4 (3) ⎪ ⎩ p = u i = − Udc Io sin(ωt + θ ) + U I sin ωt + Uo Io cos(2ωt + θ ) l l l o dc 4 4 According to (3), the arm power ripple is mainly based on 50 Hz and 100 Hz, and the ripple power will lead to the SM ripple voltage with the same frequency. When the SM voltage ripple is too large, it will affect the stress of the switching devices, the circulating current and output characteristics of the system AC and DC ports [10], so the voltage ripple must be suppressed by certain methods.

Fig. 1. Structure of a single-phase MMC

3 Operating Principle of the SC-SM In this paper, the SC-SM is used to replace the traditional HB-SM. Its specific topology is shown in Fig. 2. The ideal voltage waveforms SC are shown in Fig. 3. As can be seen from Fig. 3, uC1 and uC2 contain two parts respectively, which are DC component and AC component. Through the active power decoupling, the AC voltages of uC1 and uC2 are equal in magnitude and opposite in direction, and the sum of DC voltages of that is a constant value, which is DC voltage of the original HB-SM. In this way, the effect of suppressing the voltage ripple of the SM is achieved. When the SC-SM is used to replace the traditional HB-SM, the arm ripple power cannot be eliminated, but can only be transferred to the new SC structure. Taking a SM of the upper arm as an example, there are the following equations:  uC1 (t) + uC2 (t) = USM (4) pC1 (t) + pC2 (t) = pSM

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Fig. 2. Structure of the SC-SM

uC 2

U SM 2

Fig. 3. Idealized voltage waveforms of the SC-SM

where U SM is DC voltage of the SM, pSM is the power of the SM, i.e. U SM = U dc /N, pSM = pu /N. The specific expressions of uC1 (t) and uC2 (t) can be obtained as follows:  ⎧ ⎪ 2 C 2 ⎪ ⎪ uC1 (t) = USM − (WSM + b) ⎪ ⎨ C1 + C2 C1 + C2 (5)  ⎪ ⎪ 2 C ⎪ 1 ⎪ ⎩ uC2 (t) = USM + (WSM + b) C1 + C2 C1 + C2 WSM = −

Uo Idiff Uo Io Udc Io cos(ωt + θ ) + cos ωt + sin(2ωt + θ ) 4N ω Nω 8N ω

(6)

where b is an artificially given DC bias constant to ensure that the root sign must always be greater than zero, while also ensuring the capacitor voltage operating range, i.e. 0 ≤ uC1 (t) ≤ U SM , 0 ≤ uC2 (t) ≤ U SM . It can be seen from the (5) that the capacitor voltage consists of two parts: DC and AC, and the two AC component are completely opposite. At the same time, the (5) is completely consistent with the ideal voltage waveform shown in Fig. 3.

4 Modeling of the SC-SM In Fig. 2, according to the average equation of space state, the inductance voltage expression can be obtained based on the KVL principle: Lf

diL = d2 uC1 − d2 uC2 dt

where d 2 is the duty cycle of S3 and d2 + d2 = 1.

(7)

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According to the above analysis, the (5) can be simplified as follows:  uC1 = UC1 + u˜ C1 uC2 = UC2 + u˜ C2

(8)

where u˜ C1 + u˜ C2 = 0, UC1 + UC2 = USM . Assuming that iL and d 2 are composed of their DC and AC component, i.e. iL = IL + ˜iL , d2 = D2 + d˜ 2 , and bringing (8) into (7), it can get the following expression: diL dIL d ˜iL = Lf + Lf = (D2 UC1 − D2 UC2 ) dt dt dt +(D2 u˜ C1 − D2 u˜ C2 + d˜ 2 UC1 + d˜ 2 UC2 + d˜ 2 u˜ C1 + d˜ 2 u˜ C2 ) Lf

(9)

where D2 + D2 = 1. When the system is in stable operation, iL contains only AC component, i.e. I L = 0. By further simplifying (9), the AC and DC decoupling expressions can be obtained respectively:  UC1 = D2 USM (10) UC2 = D2 USM diL d ˜iL = Lf = d˜ 2 USM + u˜ C1 = d˜ 2 USM − u˜ C2 (11) dt dt The switching frequency of S3 and S4 is much higher than S1 and S2 , so iSM can be considered as a constant. Based on the KCL principle, the SC current can be expressed as follows: ⎧ duC1 ⎪ = −d2 iL + iSM ⎨ iC1 = C1 dt (12) ⎪ ⎩ i = C duC2 = d  i + i C2 2 SM 2 L dt The equivalent mathematical model based on SC is shown in Fig. 4. It can be seen that through d 2 firstly controls iL , and it realizes the control of uC1 and uC2 . Lf

d2

d 2U SM

d2

uC 2

U C1

iL d 2

uC1 uC1

1 sL

iL

iC1 iSM

iC 2

iL d 2

1 sC1

1 sC2

uC1

uC1

uC 2

uC 2

UC 2

Fig. 4. Mathematical model of split-capacitor

Applying the KCL principle to point A in Fig. 2, it can be obtained: iL = C2

duC2 duC1 d u˜ C1 − C1 = −(C2 + C1 ) dt dt dt

(13)

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And (12) can also be expressed as: ⎧ d u˜ C1 C1 ⎪ ⎪ = iC1 = − iL ⎨ C1 dt C1 + C2 d u˜ C2 ⎪ ⎪ ⎩ C2 C2 = iC2 = iL dt C1 + C2

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(14)

where ignoring the impact of iSM on the SC structure. However, iSM can be regarded as a disturbance to the SC-SM, i.e. iSM = ˆiSM . Finally, the equivalent circuit based on the SC-SM can be obtained, as shown in Fig. 5. D2U SM

D2U SM

d 2U SM

d 2U SM

uC1 uC 2

iˆSM

uˆC1 uˆC 2

Fig. 5. Equivalent circuit

5 Control Design of the System For the traditional control of MMC, such as output current, circulating current, SM voltage average and balance control, the original control mode remains unchanged, and it is independent from the active power decoupling control of the SC-SM [11]. The decoupling control diagram is shown in Fig. 6. First, the SM voltage reference ∗ is compared with its feedback u USM SM , through a Quasi-Proportional Resonant (QPR) ∗ controller, the 50 Hz and 100 Hz signals are amplified, and the reference voltage u˜ C1 is obtained. Then through differentiator and proportional amplification, the inductor current reference can be obtained, i.e. iL∗ . Then the difference with its feedback value iL is made and amplified by the proportional controller k p to obtain d˜ 2 . According to the calculation of the system parameters, D2 can be directly given, and finally S3 and S4 control signals are generated by means of modulation. The mathematical model of AC transfer function of the overall control system is ∗ can be composed of DC and AC, it can be shown as the shown in Fig. 7. Since USM following formula: ∗ ∗ ∗ = UC1 + u˜ C1 + UC2 + u˜ C2 USM

(15)

∗ +u ∗ = 0, U  ˜ C2 where u˜ C1 C1 and U C2 are related to D2 and D2 . Because D2 is given directly in the control system, it is not included in Fig. 7. It can be seen from (14) that the two AC transfer function are only opposite, so the mathematical model of the control loop in this paper only takes the upper part of Fig. 4 as an example for analysis, i.e.d2 − u˜ C1 . According to (15), it can be assumed that the given ∗ in Fig. 7. Since the real u ∗ can not be given directly, ˜ C1 reference of SM voltage is u˜ C1 it is obtained by the error signal between the assuming given value and the fee- d-back value, and then through QPR in Fig. 6.

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d2

kp iL

C1 C2 C1

C2

d dt

uC1

QPR

U SM

Fig. 6. Active power decoupling diagram

uC1

GQPR

C2 s

k1

iL

kp

k2

z

1

Gi

L d2

iL

G u C 1i L

uC1

Fig. 7. Mathematical model of control system

6 Simulation Results In order to verify the accuracy of the established model and control system, a singlephase MMC system is built in the simulation software PLECS, and SC is used for power decoupling in all SMs. Specific system parameters and control parameters were shown in Table 1. In addition, the same parameters MMC system is built with the all HB-SM with 470 µF capacitor. Table 1. Parameters of the MMC system Parameter

Value

Parameter

Value

DC voltage U dc

200 V

S1 /S2 carrier frequency

2 kHz

No. of SM N

2

S3 /S4 carrier frequency

20 kHz

Modulation index m

0.8

SC capacitor C1

82 µF

Load resistance Ro

15 

SC capacitor C2

220 µF

Arm inductance L arm

5 mH

SC inductor L f

0.5 mH

The simulation steady-state current waveform of the MMC system with SC-SM is shown in Fig. 8, and the voltage waveform of the SC-SM is shown in Fig. 9. As can be seen from Fig. 8, the system can still operate stably when the traditional HB-SM is completely replaced by SC-SM. As can be seen from the voltage comparison between the HB-SM and the SC-SM in Fig. 9, they both fluctuate around 100 V. The voltage fluctuation range of the SM is 14 V and 6 V respectively, and the ripple rate drops

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from the original 7% to 3%. Low frequency voltage ripple is obviously suppressed, and 6 V is mainly the high frequency harmonics introduced by the switching devices. The capacitance values of the SC are 82 µF and 220 µF respectively, which are much smaller than the 470 µF of the HB-SM. As shown in Fig. 9, the SC voltages uC1 and uC2 are symmetrical at the center line 50 V, and the AC components of them are equal in magnitude and opposite in direction, which can cancel each other out. The DC voltages operate based on their DC bias respectively, and the sum of DC voltages is 100 V. It fully demonstrates that the SC-SM does operate according to the operating principle analyzed above.

Fig. 8. Simulated steady-state current waveforms of MMC system

Fig. 9. Simulated steady-state voltage waveforms of split-capacitor

7 Conclusion In this paper, based on SC-SM of MMC, a double closed-loop active power decoupling control strategy is proposed to suppress the low frequency voltage fluctuation of the SM. The voltage ripple of SM and operating mechanism of SC-SM are analyzed in detail. Based on the established mathematical model, the equivalent circuit and the active power decoupling control strategy of voltage-current double closed loop are proposed. And the AC-DC voltage decoupling is realized. A single-phase MMC system with SC with different capacitance values is simulated, and low frequency voltage ripple is obviously suppressed. The experimental results prove the effectiveness of the mathematical model and control strategy. Acknowledgments. This works was supported by Chengdu Guojia Electrical Engineering Co., Ltd (Grant No. NEEC-2022-A05), Scientific Research Project of China State Railway Group Co., Ltd (No. L2023J002) and National Natural Science Foundation of China (Grant No. 52177196).

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References 1. Yin, T., Wang, Y., Duan, G., et al.: Zero DC voltage control based DC fault ride-through strategy for hybrid modular multilevel converter in HVDC. Trans. China Electrotechnical Soc. 34, 343–351 (2019). (in Chinses) 2. Liu, Y., Yuan, Y., Wang, H., et al.: Cooperative control strategy of modular decoupling circuit. Trans. China Electrotechnical Soc. 1–11 (2023). (in Chinese) 3. Li, H., Zhang, K., Zhao, H., et al.: A high power density single rectifier with power decoupling function. Trans. China Electrotechnical Soc. 26, 72–82 (2011). (in Chinese) 4. Wang, L., Cui, S., Chen, M.: Parallel compensation control of power factor corrector without electrolytic capacitor by power decoupling. Trans. China Electrotech. Soc. 34(3), 516-528 (2019). (in Chinese) 5. Wang, S., Ruan, X., Yao, K., et al.: A novel LED driver without electrolytic capacitor and flicker. Trans. China Electrotechnical Soc. 27(4), 173–178 (2012). (in Chinese) 6. Tang, Y., Blaabjerg, F., Loh, P.C., et al.: Decoupling of fluctuating power in single-phase systems through a symmetrical half-bridge circuit. IEEE Trans. Power Electron. 30(4), 1855– 1865 (2015) 7. Su, M., Pan, P., Long, X., et al.: An active power-decoupling method for single-phase AC-DC converters. IEEE Trans. Industr. Inf. 10(1), 461–468 (2014) 8. Kong, Z.H., Huang, X., Wang, Z., et al.: Active power decoupling for submodules of a modular multilevel converter. IEEE Trans. Power Electron. 33(1), 125–136 (2018) 9. Jia, G.L., Chen, M., Tang, S., et al.: Active power decoupling for a modified modular multilevel converter to decrease submodule capacitor voltage ripples and power losses. IEEE Trans. Power Electron. 36(3), 2835–2851 (2021) 10. Song, Q., Meng, J., Zhou, Y., et al.: Analysis of ripple effect of submodule capacitor voltage and its influence on optimal design of MMC. Power Syst. Technol. 45(11), 4478–4490 (2021). (in Chinese) 11. Yang, J., Hou, J., Liu, Y., et al.: Distributed cooperative control method and application in power system. Trans. China Electrotechnical Soc. 36(19), 4035–4049 (2021). (in Chinese)

Research on the Short-Term Power Interval Prediction Method for Distributed Power Sources in Distribution Networks Based on Quantile Random Forests Zhen Lei1 , Qiangsheng Bu1 , and Jing Wang2(B) 1 State Grid Jiangsu Electric Power Company Limited, Jiangsu, China 2 Tsinghua University, Beijing, China

[email protected]

Abstract. With the widespread application of Distributed Generation (DG) in new energy power systems, accurate prediction of its power output has become a key issue. To address this problem, this study proposes a short-term power interval forecasting method for distributed power generation in distribution networks based on Quantile Random Forests. Initially, in-depth processing was performed on historical photovoltaic and wind power active power data, as well as meteorological data. This included the imputation of missing values via KNN, the handling of outliers, and normalization, as well as the selection of major influencing factors on the output of distributed power through correlation analysis. Subsequently, we employed advanced technologies such as quantile regression, random forests, and confidence intervals to construct a Quantile Random Forest interval forecasting model tailored to distributed power in distribution networks. After the model’s construction, adjustments were made to the model parameters, followed by crossvalidation and further debugging and optimization. Lastly, the key meteorological information for future prediction was input into the optimized model for forecasting. The forecasting method in this study takes full advantage of the Quantile Random Forest’s strengths in dealing with non-linear, high-dimensional data, and handling missing data, enhancing prediction accuracy and reducing prediction bias, providing significant guidance for actual network operation and dispatching. Future research will continue to deepen the understanding and application of the Quantile Random Forest model in hopes of improving forecasting results and optimizing grid operation. Keywords: New Energy Power System or Advanced Power System · Distributed Generation (DG) · Quantile Random Forests · Power Interval Forecasting

1 Introduction In the context of the “dual carbon” goal, China’s extensive utilization of new energy sources has seen significant development, and building a new type of power system that adapts to the gradually increasing proportion of new energy has become the primary goal © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 347–360, 2024. https://doi.org/10.1007/978-981-97-0877-2_37

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[1, 2]. With the rapid development of renewable energy and distributed power generation systems, power prediction of distributed power sources in the distribution network has become the core link in the operation and control of the new power system [3]. Traditional point prediction methods [4–7] have been widely used in many application scenarios, but as the requirements for system stability and flexibility increase, the limitations of these methods in capturing power load fluctuations and uncertainties in renewable energy sources have become increasingly apparent. Interval forecasting, as a method that provides information about forecasting uncertainty, has received extensive attention in many fields. Compared with traditional point prediction, interval forecasting not only provides the expected value of future power, but also describes the potential fluctuation range of these predicted values, thus providing decision-makers with richer and more comprehensive information. Literature [7] proposed a super network method based on deep neural networks, which estimates prediction intervals and probabilities, and the results showed that the estimated prediction interval is narrower (up to 20%) than the prediction interval estimated by quantiles, with a target coverage rate of 70%– 80% for all areas. Depending on the area, the target coverage rate is 85%, 90%, and 95%, while the super network (HN) always achieves the required coverage for a higher target coverage rate. Literature [8] proposed a method based on Quantile Regression Long Short-Term Memory Neural Network (QR-LSTM), and the interval coverage rate obtained tends to the confidence level. Literature [9] proposed a method based on similar day clustering and QR-CNN-BiLSTM model, to achieve short-term interval probability prediction of photovoltaic power. This model, by integrating convolutional neural networks and recurrent neural networks, can enhance the prediction resolution to 5 min. Although the accuracy of prediction has been greatly improved by the above methods, they perform rather poorly in dealing with non-linear, high-dimensional data and handling missing data. Therefore, this paper proposes a method for interval prediction of distributed power sources based on quantile random forests. The main contributions of this paper’s method are as follows: It combines random forests and quantile regression: 1) This combination provides a powerful method for interval prediction, which not only retains the non-linear modeling capability of random forests, but also can describe the entire distribution of predicted values; 2) It is suitable for short-term prediction: for the short-term power prediction problem of distributed power sources, this method fully considers the characteristics of power fluctuation and uncertainty, providing accurate interval estimation; 3) Comprehensive evaluation method: by using evaluation indicators including Prediction Interval Coverage Probability (PICP) and Prediction Interval Normalized Average Width (PINAW), the reliability and degree of uncertainty of the model are comprehensively measured.

2 Fundamental Principles 2.1 Random Forests The working principle of Random Forests is to construct multiple decision trees, and make the final prediction by averaging the prediction results of these trees. Each decision tree is trained on a randomly selected subset of samples, and a randomly selected subset

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of features is also used when choosing splitting attributes. This randomization process helps to improve the robustness and accuracy of the model. Suppose there is a dataset D, which includes n samples and p features. Random Forest consists of B decision trees, each of which is constructed through the following steps: 1) Bootstrap sampling: Randomly draw the nth sample from the original dataset D with replacement, forming a new dataset Db . 2) Construct decision tree: Use dataset Db to construct a decision tree. Each time a node is split, randomly select m features from p features, and choose the best splitting feature from them. The prediction of the decision tree can be expressed as: Tb (x) = fb (x; θb )

(1)

Where Tb (x) is the prediction of the bth tree, fb (x; θb ) is the structure of the tree, and θb are the parameters learned from the datasetDb . The final prediction of the Random Forest is the average of the predictions of all trees (for regression problems) or the majority vote (for classification problems). Mathematically, the prediction of the Random Forest can be expressed as: For regression problems: 1 Tb (x) B B

yˆ (x) =

(2)

b=1

For classification problems: yˆ (x) = mode{T1 (x), T2 (x), . . . , TB (x)}

(3)

This ensemble approach of Random Forests, by averaging the predictions of multiple trees, helps to reduce the variance of the model, improving the accuracy and robustness of the predictions. Its strategy of randomly selecting samples and features also helps to reduce the risk of overfitting, making the model perform better on unseen data (Fig. 1). 2.2 Quantile Regression Quantile Regression (QR) is a flexible statistical analysis method aimed at estimating different quantiles of the dependent variable. Unlike ordinary least squares regression (OLS), quantile regression is not only concerned with the mean of the response variable, but also has interpretability for its entire distribution. This property is particularly important in photovoltaic forecasting, because it can reveal the relationship between photovoltaic output power and influencing factors (such as solar radiation, temperature, etc.) at different output levels. Assuming our goal is to predict the photovoltaic power generation at the qth quantile, this quantile regression model can be represented as: QY |X (q) = X β(q)

(4)

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Fig. 1. Random forest prediction diagram

Where QYX (q) is the conditional quantile, X is the explanatory variable matrix, and β(q) is the coefficient vector of the qth quantile. The estimation of quantile regression is based on the solution to the following optimization problem: ˆ β(q) = arg min β

Where:



n 

  ρq yi − xi β

(5)

i=1

q · u, if u ≥ 0 −(1 − q) · u, if u < 0

Here, yi and xi are the observed values of the response variable and the explanatory variable, respectively, and ρq is the quantile loss function. ˆ By solving the above problem, a set of estimated coefficients β(q) can be obtained, and any quantile of the photovoltaic output power can be predicted. This allows us to more comprehensively predict the distribution characteristics of photovoltaic output power, thereby more effectively carrying out energy dispatching and risk management. In general, quantile regression provides a powerful statistical tool for photovoltaic interval prediction, which can not only capture the central tendency of the data, but also analyze and predict the performance of photovoltaic output power at different quantiles. This is of great significance for formulating more accurate and reliable energy policies and operation strategies. 2.3 Confidence Interval Confidence interval is a method of statistical inference used to estimate the range of unknown parameters (such as population mean, proportion, etc.). A confidence interval

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provides an interval estimate that reflects the possible range of parameter values and corresponds to a given confidence level. Suppose you want to calculate the population parameter θ, and we have a sample statistic (such as the sample mean) that can be used to estimate this parameter. Therefore, we hope to construct a confidence interval for θ with a confidence level of (1–α). The steps are as follows: 1) Calculate point estimate: First, calculate the point estimate of parameter θ. For the case of the population mean of a normal distribution, the point estimate is usually the sample mean x, calculated as follows: 1 xi n n

x=

(6)

i=1

2) Calculate standard error: Then, calculate the standard error (SE) of the sample statistic. For the case of the mean, the standard error can be calculated as: s SE = √ (7) n In the formula, s is the sample standard deviation, and n is the sample size. 3) Determine the confidence level: After that, choose a confidence level, such as 95%, which corresponds to α of 0.05. Therefore, the probability that the confidence interval contains the true value of the population parameter is 95%. 4) Find the critical value: Find the critical value Zα/2 by looking up the Z-score table of the standard normal distribution or the corresponding t-distribution table (if the sample size is small and/or the population standard deviation is unknown). For a 95% confidence level, Zα/2 is usually about 1.96. 5) Calculate the confidence interval: Finally, calculate the confidence interval using the following formula:   x − Zα/2 · SE, x + Zα/2 · SE (8) This interval is the confidence interval for the parameter θ. The width of the confidence interval reflects the precision of the estimate. A wider confidence interval may reflect a greater level of uncertainty or a smaller sample size.

3 Quantile Random Forest Interval Prediction Model 3.1 Data Process When conducting interval prediction for distributed power sources, some preprocessing steps are needed for the raw data to reduce noise, eliminate seasonality and trends, deal with missing values, and minimize the impact of outliers. 1) Handling missing values. In power data sets, there are often some missing values, which might be caused by sensor failures or data transmission problems. There are many methods to handle missing values, such as filling in with previous or next values, using the mean or median to fill in, or using more complex methods like KNN filling or interpolation.

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2) Data normalization. As the scale and characteristics of distributed power sources may vary greatly, it is necessary to standardize the data so that all data is on the same scale. Commonly used standardization methods include Min-Max normalization and Z-Score normalization, the formulas of which are: Min-Max normalization formula: Xnorm =

X − Xmin Xmax − Xmin

(9)

Z-Score normalization formula: X −μ (10) σ In the formula: X represents the original data, Xmin and Xmax respectively are the minimum and maximum values of the data, μ and σ are the mean and standard deviation of the data. Xnorm =

3.2 Correlation Analysis Kendall’s rank correlation is a non-parametric test that measures the strength of dependence between two variables. It’s often denoted as Kendall’s tau (τ). Unlike Pearson’s correlation, Kendall’s τ does not assume that the relationship between variables is linear, nor does it require the variables to be normally distributed. Therefore, it can capture both linear and nonlinear relationships. The method works based on the concordant and discordant pairs of observations in the data. If you have a pair of observations (x1 , y1 ) and (x2 , y2 ): The pair is considered concordant if the ranks for both elements obey the same inequality: (x1 > x2 and y1 > y2 or (x1 < x2 and y1 < y2 ). The pair is considered discordant, if the ranks for the elements obey the opposite inequality: (x1 > x2 and y1 < y2 ) or (x1 < x2 and y1 > y2 ). Kendall’s τ is calculated as the difference between the proportion of concordant and discordant pairs divided by the total number of pairs. If τ is positive, it indicates that the rank of y tends to increase as the rank of x increases. If τ is negative, it indicates that the rank of y tends to decrease as the rank of x increases. In the context of predicting distributed power generation, Kendall’s rank correlation can be a useful tool for identifying and quantifying relationships between different variables, even when those relationships are not linear. The Kendall’s τ coefficient can be calculated using the following formula: τ=

(nc − nd )   (nc + nd + ntx ) nc + nd + nty

(11)

In the formula, nc represents the number of concordant pairs, nd represents the number of discordant pairs, ntx and nty are the numbers of tied pairs in x and y, respectively (Fig. 2). The range of Kendall’s τ is from –1 to 1. When τ = 1, it indicates a perfect positive correlation; when τ = –1, it indicates a perfect negative correlation; and when τ = 0, it indicates no linear relationship at all.

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Fig. 2. Analysis of Relationship

3.3 Confidence Interval Given the high volatility and uncertainty of distributed power output, the complex nonlinear series of distributed power output is handled by the random forest method. Therefore, this method combines random forest with quantile regression for prediction. This paper will take advantage of the quantile regression’s ability to output multiple quantile point predictions, and combine random forest with quantile regression to construct a quantile regression forest model. This is in order to quantify the uncertainty information existing in distributed photovoltaic power output. The specific steps are as follows: 1) Data preprocessing. This includes operations such as missing value completion, outlier handling, normalization, etc. on the original photovoltaic power output data. In addition, it also includes the division of the dataset and the selection of feature dimensions for data input. 2) Correlation analysis. Based on the Kendall correlation analysis method, calculate the correlation coefficient of the factors influencing photovoltaic power output, and select the most significant coefficient as the feature input. 3) Building a quantile regression random forest prediction model. This part includes model training and prediction, as well as comparing actual values and predicted values using metrics such as MAE, RMSE and MAPE. 4) Use different quantile points to predict the distributed photovoltaic values at different quantile points using the quantile random forest model. 5) Prediction interval construction. This part calculates the mean and variance of the conditional quantile prediction values at different quantile points, and the predicted values of different quantile points follow a Gaussian distribution. 6) Interval prediction model evaluation. Use PICP and PINAW to evaluate the performance of the interval model (Fig. 3).

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Fig. 3. Quantile Random Forest Interval Prediction Model Process

4 Model Evaluation Since the error between the actual value of photovoltaic power output and the predicted value obtained by the regression model directly reflects the performance of the model, choosing appropriate evaluation indicators is extremely critical for the evaluation and selection of the model. In order to comprehensively evaluate the performance of the point prediction model, multiple evaluation criteria such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) can be used to measure the prediction accuracy and reliability of the model [11]. 1) Mean Absolute Error (MAE). The MAE quantifies the average level of absolute differences between model predictions and actual values. The smaller the value, the higher the accuracy of the model. 1 |yi − yˆ i | n n

MAE =

(12)

i=1

2) Root Mean Square Error (RMSE). Compared with MAE, RMSE gives higher penalties to larger errors. Therefore, if the model’s prediction for certain observations is particularly poor, RMSE will increase correspondingly. The smaller the value, the

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higher the accuracy of the model.



n

1  RMSE =  (yi − yˆ i )2 n

(13)

i=1

3) Mean absolute percentage error ( MAPE). MAPE is a scale-independent evaluation index, which represents the error in the form of percentage. This allows predictions of different ranges or units to be directly compared. The smaller the value, the higher the accuracy of the model. n 1  yt − yˆ t (14) MAPE = y × 100% n t t=1

In Eq. (12–14): yi is the actual value, yˆ i is the predicted value, n is the number of observations. In addition, to evaluate the credibility and uncertainty level of the forecast interval, two key indicators are usually used to measure the performance of the interval forecast model: Prediction Interval Coverage Probability (PICP) and Prediction Interval Normalized Average Width (PINAW) [12]. 1) Prediction Interval Coverage Probability (PICP) measures the probability that the actual observed value falls within the predicted interval. This reflects the reliability of the forecast interval. The formula is as follows: 1 I (yi ∈ [Li , Ui ]) n n

PICP =

(15)

i=1

In the formula: I is the indicator function, yi is the i-th actual value, Li and Ui are respectively the lower and upper limits of the forecast interval, and n is the number of observations. Ideally, PICP should be close to the chosen confidence level. 2) The Prediction Interval Normalized Average Width (PINAW) takes into account the average width of the prediction interval, and normalizes it through the maximum possible width, thereby evaluating the relationship between the interval width and overall volatility. The formula can be represented as: 1  Ui − Li n Ymax − Ymin n

PINAW =

(16)

i=1

In the formula, Li and Ui are the lower and upper limits of the prediction interval, Ymax and Ymin are the maximum and minimum values of the observed values. A smaller value indicates less uncertainty.

5 Example Analysis The method in this paper was experimentally validated on a dataset of distributed photovoltaic power output in a certain region of North China in January 2022. The distributed photovoltaic power output dataset in this area was collected at intervals of 15 min, and the experimental dataset was divided in a ratio of 8:2.

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In addition, to highlight the applicability of this paper’s method for interval prediction of distributed photovoltaic power output in the region, a comparative analysis was conducted with SVR, GRU, LSTM, and CNN, and interval prediction models of these models were also constructed for comparative analysis. The analysis results are as follows. Table 1. Comparison of point prediction results among different models Forecasting Model

MAE

RMSE

MAPE

SVR

13.53

19.46

0.86

LSTM

67.92

88.61

4.48

GRU

94.52

115.29

6.37

CNN

66.69

83.07

4.77

This paper

14.12

23.16

4.43

It can be seen from Table 1 that the support vector regression model (SVR) has the best prediction effect at the deterministic point; on the test set, the value of the random forest prediction model (RF) is 4.43, and the prediction accuracy is relatively high. The QS value was 13.71, which was 17.76 and 59.12 lower than that of GRU model and CNN model, respectively. Table 2. Comparison of interval prediction results among different models Forecasting Model

PICP 85

PINAW 90

95

85

90

95

QR-SVR

74.59

78.44

81.85

22.65

25.77

28.93

QR-LSTM

90.71

87.44

93.23

87.53

99.69

119.14

QR-GRU

75.62

78.30

88.15

119.38

139.27

162.64

QR-CNN

65.97

73.68

83.79

115.32

130.65

157.30

This paper

90.91

88.35

93.79

124.58

131.64

158.33

From Table 2, it can be seen that the Quantile Random Forest (QR-RF) model has a high coverage rate on the actual distributed photovoltaic output dataset and has the best interval prediction performance. When the confidence level is 95%, the PICP value of the QR-RF model is 94.36%. The model in this paper is 16.32%, 0.2%, 15.29%, 24.94% higher than the QR-SVR, QR-LSTM, QR-GRU, QR-CNN models respectively. Similarly, it can be seen that at the 90% and 85% confidence levels, the PICP value of the model in this paper is higher than the comparison models. The results show that the model has a high interval prediction coverage rate, close to the confidence level, strong interval coverage capability, and optimal prediction performance. It can be used

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for short-term prediction of distributed photovoltaic output. It quantifies the interference caused by external uncertainties in the distributed photovoltaic output power sequence, making the prediction result within an interval range, which can measure the uncertainty of distributed photovoltaic output. In order to make the interval prediction results of the model used in this paper more intuitive, the interval prediction results of the QR-RF model on the distributed photovoltaic output power dataset in the capital region of New York State at different confidence levels were plotted, as shown in Figs. 4, 5 and 6. The horizontal axis represents the predicted time points, at intervals of every 15 min, and the vertical axis represents the distributed photovoltaic power values. The figure mainly analyzes the interval prediction results when the confidence level is 80%, 85%, 90%, and 95%.

Fig. 4. Interval prediction results with a confidence interval of 85%

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Fig. 5. Interval prediction results with a confidence interval of 90%

Fig. 6. Interval prediction results with a confidence interval of 95%

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6 Conclusion In this paper, a short-term power interval prediction method of distributed power supply based on quantile random forest is proposed. This method not only provides accurate prediction, but also estimates the uncertainty of prediction, which is of great significance in the planning and operation of new power systems. For the data set used in the experiment, the prediction results of this method are significantly better than the traditional methods. This method combines quantile regression with random forest, and makes effective interval prediction of distributed photovoltaic output by using the diversity of random forest model and the advantages of quantile regression. The experimental results show that the prediction accuracy and stability of this method are obviously better than the traditional random forest prediction method, which can accurately reflect the trend and fluctuation range of distributed photovoltaic power. Further research can explore how to improve the quantile random forest algorithm to further improve the prediction accuracy and stability. Acknowledgments. This work is supported by the science and technology project of SGCC(5108202218280A-2–371-XG, Research on Key Technologies of Perception Control and Regulation for Low-Voltage Distributed Generation Dispatching under the New Electric Power System).

References. 1. A Glimpse Makes Mountains Look Small - Sustainable City and Transportation Team, 2050 Net Zero Emissions: A Roadmap for the Global Energy Sector. Beijing Planning and Construction, (05), pp. 31–39 (2022) 2. Jinping, X.: Speech at the 75th session of the united nations general assembly. Gazette State Counc. People’s Repub. China 28, 5–7 (2020) 3. Gao, H., et al.: Review of power balance analysis in the new type of power system. High Volt. Technol. 49(07), 2683–2696 (2023) 4. Liao, Q., et al.: Distributed photovoltaic net load prediction in new energy power systems. J. Shanghai Jiao Tong Univ. 55(12), 1520–1531 (2021) 5. Ma, M., et al.: An adaptive interval power forecasting method for photovoltaic plant and its optimization. Sustain. Energy Technol. Assess. 52, 102360 (2022) 6. Li, H., et al.: A multi-step ahead point-interval forecasting system for hourly PM2.5 concentrations based on multivariate decomposition and kernel density estimation. Expert Syst. Appl. 226, 120140 (2023) 7. Alcántara, A., Galván, I.M., Aler, R.: Direct estimation of prediction intervals for solar and wind regional energy forecasting with deep neural networks. Eng. Appl. Artif. Intell. 114, 105128 (2022) 8. Li, M., et al.: Power load forecasting model based on explainable deep learning. Foreign Electron. Measur. Technol. 42(04), 66–73 (2023) 9. Wang, K., et al.: Short-term interval probability forecasting of photovoltaic power based on similar day clustering and QR-CNN-BiLSTM model. High Volt. Technol. 48(11), 4372–4388 (2022) 10. McNeil, A.J., Nešlehová, J.G., Smith, A.D.: On attainability of Kendall’s tau matrices and concordance signatures. J. Multivar. Anal. 191, 105033 (2022)

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11. Jiang, B., et al.: Transformer hot spot temperature prediction based on ACO optimized BP neural network. J. Electr. Measur. Instrum. 36(10), 235–242 (2022) 12. Zhao, S., et al.: Day-ahead photovoltaic output forecasting error distribution model based on numerical feature clustering. Autom. Electr. Power Syst. 43(13), 36–45 (2019)

Load Forecasting Based on Data Mining and Improved Stacking Ensemble Learning Under Load Aggregator Zhishuo Zhang, Xinhui Du(B) , Wenxuan Zhang, Kun Chang, and Rixin Zhang School of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan 030000, Shanxi, China [email protected]

Abstract. In the process of demand response, in order to manage resources in the load side better and solve the problems of large amount of data, unclear data characteristics and many invalid data, the load aggregator proposed a load forecasting model based on data mining and improved stacking ensemble learning. Firstly, analyze the energy consumption behavior of loads agented by load aggregators, and models for various loads participating in demand response are established; Then, the data processing feature engineering based on data mining model is established to extract the features of the original data and form the load forecasting feature data set; Finally, through improving stacking ensemble learning model, all kinds of loads under the load aggregator are predicted. To verify the effectiveness of the model, the article conducts experiments using real load data from a certain location. And compare it with other algorithms. The experiment shows that the model proposed in the article improves the prediction speed and accuracy, providing a reliable basis for load aggregators to participate in the demand response market. Keywords: Load aggregator · Load forecasting · Data mining · Feature extraction · Improve stacking ensemble learning

1 Introduction With the proposal of the “double carbon” goal, a large number of new energy sources have been incorporated, affecting the stability of power grid operation [1]. Simply relying on adjusting the output of the power generation side is no longer sufficient to solve the problem. The load side resources have enormous response potential, so calling on demand side resources has become an effective measure to solve the above problems [2]. However, there are issues with multi types, dispersed layout, and uncertainty in response to load side resources. So load aggregators(LA) emerged. LA is a polymer with adjustable loads. LA itself cannot perform demand response(DR). This entity aggregates dispersed load side resources, solving the problem of poor response effect caused by uneven response of adjustable loads. LA gains revenue from the DR resources aggregated through agents. In order to maximize profits, LA need © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 361–371, 2024. https://doi.org/10.1007/978-981-97-0877-2_38

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to master the electricity consumption information of the response resources of agent. Therefore, load forecasting for response resources is of great significance. In recent years, the research on power load prediction remains a hot topic. Traditional load forecasting mainly uses mathematical statistics and time series methods. With the development of artificial intelligence, machine learning algorithms are gradually applied to load forecasting, such as neural networks, SVM, etc. [3] uses neural networks to predict loads with nonlinear mapping capabilities, but this model is prone to trapping the results into local optima; [4] uses a random forest algorithm for load forecasting, but this algorithm is prone to overfitting; [5] proposes a ultra short term load forecasting based on the double-layer XGBoost algorithm, aiming to solve the problem of large load data volume and unclear feature relationships between data. Compared to single algorithm prediction, combined algorithms have higher prediction accuracy. [6] improves the LSTM algorithm by extracting features from input signals using CNN to improve the prediction accuracy of the model. However, the accuracy of load prediction during peak hours is not high; In order to fully explore the temporal features between data. [7] proposes a short-term power load prediction method based on a feature screening CNN-BiLSTM, which improves the prediction accuracy; [8] uses the CNN-GRU to train and forecast a group of actual power load examples, and the results show that the prediction accuracy of the combined model is better than that of the single model; [9] proposes a method for ultra short term load forecasting based on CNN-BiLSTM-Attention, targeting the nonlinear and temporal characteristics of loads. However, the above research still has shortcomings: (1) The literature has not considered the impact of LA participating in DR on load forecasting; (2) The models established in the above research is only applicable to a certain region or a load with the same pattern, without considering the applicability of the model for multiple regular loads under the LA; (3) Although the above research conducted feature screening, there were issues with not considering the correlation between load characteristics and load characteristics, as well as the cumbersome implementation process. Based on this, the article proposes a multiple load forecasting model considering the influence of multiple features under load aggregation quotient. Firstly, establish a load model under DR for the load under the agent of the LA; Then, based on feature engineering, a data mining model is established to analyze the correlation and redundancy between load features, as well as the mapping relationship between load features and loads; Finally, for multiple loads under LA, an improved stacking ensemble learning model is established to improve the applicability of the model while ensuring the accuracy of load prediction. The article verifies the feasibility of the algorithm by analyzing and simulating data from a certain location.

2 Establishing Load Models for LA Participating in DR In the DR market, the demand side will determine the demand based on its future electricity consumption behavior. Then, the demand side releases relevant DR information to the DR market; The market will proceed with clearance based on marginal clearance, determining the price and successful bidder. In this market, LA is the responders of DR, who will bid based on the electricity consumption and response volume of the adjustable load they represent; As the main

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body of load side resource aggregation, LA participate in the DR market in the regulatory market and conduct transactions on a daily basis. The participation of LA in the DR market mainly relies on adjustable resources on the load side to respond to regulatory demands released by the power grid in the DR market, thereby benefiting from grid interaction. The specific operating mechanism is shown in Fig. 1.

Fig. 1. Operating mechanism of LA

2.1 Establishment of Charging Load Model for Electric Vehicles The ownership of private cars accounts for the largest proportion among electric vehicles, with short dwell time and short driving time, making charging regulation the most feasible. The article takes private cars as an example to establish a model. According to [10], the initial state of charge(SOC) of an electric vehicle is related to the driving range of the vehicle, and the calculation formula is as follows: SOC0 = (1 −

L ) ∗ 100% Lm

(1)

where, L is the daily driving mileage; Lm is the maximum driving distance. The charging duration is positively correlated with the battery capacity. The specific representation is as follows: Tc =

(SOCe − SOC0 ) ∗ Bc ηp

(2)

where, SOCe represents the expected charging capacity of the user; Bc is the battery capacity; η is charging efficiency; p is charging power. The charging efficiency is related

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to the charging mode, which can be divided into conventional charging mode and fast charging mode. The corresponding charging efficiency is as follows:  90% slow charging (3) η= 80% fast charging The charging power of electric vehicles under LA during the k time period is: Pev,k =

N1 

ev pi,k

(4)

i=1 ev is the charging power of the where, N1 is the ownership of electric vehicles and pi,k electric vehicle i during period k.

2.2 Establishment of Commercial Load Model In the commercial load electricity consumption, the proportion of air conditioning electricity consumption has almost reached 90%. Therefore, the article replaces commercial load electricity with air conditioning electricity. For LA, studying the power consumption of a single air conditioner is meaningless. LA is more concerned about the power of multiple air conditioners. The specific representation is as follows: Pac =

N2 

ac si,k ∗ pi,k

(5)

i=1

where, N2 represents the total amount of air conditioning under LA, si,k represents on/off ac status of time k of air conditioning i, with 0 representing off and 1 representing on; pi,k represents the power of air conditioning i during period k. Because the electricity consumption of air conditioning is related to indoor, outdoor, and initial set temperatures. So, when the initial setting temperature of the air conditioning remains unchanged, the air conditioning power can be calculated using the air conditioning duty cycle [11]. The representation of the duty cycle is as follows: D=

ton ton + toff

δ ) QR + Tset − 0.5δ − To δ ) = ln(1 + To − Tset − 0.5δ

ton = ln(1 + toff

(6)

where, ton is the startup time; toff is the downtime; δ is a temperature dead zone; Q represents the exchange of heat between air conditioning and indoor air conditioning; R is the equivalent thermal resistance; Tset is the starting temperature for the air conditioner; To indicates the outdoor temperature.

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So, when LA agents enough air conditioners, the aggregated power of the air conditioners under LA during period k is: Pac,.k =

N2 

ac Di ∗ pi,k

(7)

i=1

where, Di represents the duty cycle of air conditioner i operation. 2.3 Establishment of Industrial Load Model According to the characteristics of industrial load, industrial loads can be divided into two types: continuous adjustable loads and non-continuous adjustable loads. Due to the high scheduling flexibility and high power of continuous adjustable loads, there is no need to participate in the market through LA. Therefore, the article mainly considers non-continuous adjustable loads, taking electric arc furnaces as an example [12]. The operating state of electric arc furnaces is mainly divided into two types: lowtemperature drying state and smelting state. Low temperature oven drying is to ensure the temperature of the furnace body when there are no production tasks; The goal of energy conservation has been achieved; The smelting state is the working state. The specific operating status is shown in Fig. 2. From the Fig. 2, it can be seen that the working state of the electric arc furnace is discontinuous, and there is a power gap period between the drying state and the smelting state. So, the power of the electric arc furnace is expressed as follows: Pin,k =

N3 

adj

int on (pi,k ∗ (1 − xi,k ) + pi,k ∗ xi,k + pi,k )

(8)

i=1

P

Power Cap Smelting Power Oven Power

t

Fig. 2. Working status of electric arc furnace

Where, N3 is the total amount of electric arc furnaces under LA; xi,k is the smelting state of electric arc i furnace during period k, 1 is working smelting state, and 0 is drying int is the baking power of electric arc furnace i during period k; pon is the initial state; pi,k i,k adj

smelting power of electric arc furnace i during period k; pi,k is the power of adjustment for the smelting of electric arc furnace i during period k.

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3 Feature Engineering Based on Data Mining Data mining is an interdisciplinary field that is a product of big data research in the Internet era, including data engineering, artificial intelligence, machine learning, etc. [13]. Among them, time series data mining is the theory and method of discovering information and knowledge from time series data [14]. When conducting multi load forecasting, LA need to consider the impact of multiple factors on the load horizontally, such as weather, date, etc.; Vertical consideration should be given to the impact of time series on load, such as the first 1 moment, the first 2 moments, etc. Firstly, the article uses the Ensemble Empirical Mode Decomposition(EEMD) to decompose various influencing factors; Then, Pearson correlation coefficient(PCC) analysis is used to analyze the redundancy between features and the correlation between features and load values; Finally, form the input dataset for prediction model. 3.1 Time Series Decomposition Based on EEMD Algorithm The algorithm utilizes the statistical characteristics of Gaussian white noise with uniform frequency distribution, and changes the extreme point characteristics of the signal by adding different white noise of the same amplitude each time. Then, the corresponding IMF obtained from multiple EMDs is overall averaged to counteract the added white noise, effectively suppressing the generation of modal aliasing. The flowchart for actual load based on the EEMD algorithm is shown in Fig. 3.

Fig. 3. Decomposition flowchart based on EEMD

3.2 Redundancy and Correlation Analysis Based on PCC Correlation reflects the mapping relationship between features or between features and results. The stronger the mapping relationship, the greater the correlation. Redundancy is an evaluation indicator of the correlation between features, which preserves one of the two features with high correlation. Its purpose is to reduce the number of features

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and improve the computational accuracy and efficiency of the model while ensuring that information is not lost in large quantities. The article uses PCC to analyze the redundancy between feature quantities. The calculation formula is as follows: m 

RPCC = 

(ai − a)(bi − b)

i=1 m 

(9) (ai − a)2 (bi − b)2

i=1

Through correlation and redundancy analysis, the input feature set of the prediction model is ultimately formed.

4 Load Forecasting Model Based on Improved Stacking Ensemble learning Currently, research on load forecasting mostly relies on neural networks for load prediction. However, a single neural network (BP, LSTM, BiLSTM, etc.) may have poor practicality for different load types, which means that the prediction effect for one type of load is good, but the prediction effect for another type of load is poor. Based on this, the article proposes a model based on improved Stacking ensemble learning for load forecasting of adjustable resources. The improved Stacking ensemble learning model uses a single neural network as a base learner to cross validate the predicted results of each base learner, achieving secondary learning and improving the accuracy of the prediction model. The advantage of this model is to utilize the weight allocation of secondary learning to increase the weight of base learners suitable for predicting loads and reduce the weight of non suitable base learners. The specific formula for the predicted value Lm (t) at time t on day m based on the above model is as follows: Lm (t) = a1 B1m (t) + a2 B2m (t) + ... + an Bnm (t)

(10)

where, B1 , B2 , ..., Bn are different base learners, and a1 , a2 , ..., an are the weights of the corresponding base learners.

5 Example Analysis Conduct simulation analysis using data from 100 adjustable loads (including electric vehicles, commercial loads, and industrial loads) in a certain location in February. 5.1 Analysis of Feature Extraction Results Based on Data Mining (1) Decomposition feature analysis After processing the raw data, first perform EEMD decomposition. Figure 4 shows the load decomposition curve based on the EEMD algorithm. The horizontal axis represents the charging time of the electric vehicle charging station.

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Fig. 4. Load Decomposition Curve

The load is decomposed into four components. According to the characteristics of the EEMD algorithm for decomposing curves, the actual meaning represented by each component is as follows: For the load curve, the fluctuation frequency and discrete type of IMF1 are relatively large, reflecting the main response behavior of the adjustable resource; IMF2 has significant volatility, reflecting users’ electricity consumption behavior in a short period of time and their unique electricity consumption behavior; IMF3 reflects the electricity consumption behavior of users over a longer time scale;, IMF4 generally represents an upward trend in electricity consumption. (2) Redundancy analysis Based on the decomposed features mentioned above, the redundancy relationship between features is explained through PCC. The specific results are shown in Fig. 5.

Fig. 5. Redundancy Analysis Result Chart

Figure 6 shows the analysis of redundancy between various features in the obtained decomposed features. From the graph, it can be seen that there is a strong correlation between feature input and potential value output, so a mapping relationship can be formed between potential features and potential values; Among various features, feature 1 has a strong correlation with feature 2, feature 3, and feature 4, so only data from feature 1 can be taken. As a result, the number of features in the feature set is reduced, and the computational efficiency of the model is improved.

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(3) Analysis of the advantages of data mining Being able to explore the internal relationships of data avoids the problem of requiring a large amount of data during the evaluation process. Solved the efficiency issue of the running process, and significantly improved computational efficiency through data mining. Improved the accuracy of predicted values. Figure 6 shows the results of Gaussian regression calculation without data mining. Table 1 compares the indicators after data mining with those without data mining.

Fig. 6. Probability distribution map without data mining

From Table 1, it can be seen that after data mining, the prediction effect will be significantly improved through point prediction evaluation indicators, and the prediction of intervals will be more accurate through interval prediction indicators; The larger the amount of data, the better the effectiveness of potential assessment. However, for data that has undergone data mining processing, although the size of the data volume has an impact, it is lower than that of data that has not undergone data mining. Table 1. Comparison between data mining and without data mining

Without data mining With data mining

MAE

RMSE

PICP

MPIW

184.81

274.31

0.47

0.47

9.71

17.23

0.91

0.34

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5.2 Improving Stacking Ensemble Learning Results Analysis (1) Load prediction results based on improved Stacking ensemble The article selects the first 4 h of historical load data from a certain electric vehicle charging station in February as the input of the model to verify the accuracy of the improved Stacking ensemble learning established in the article. As shown in Fig. 4, the sampling cycle of this data is 15 min (Fig. 7).

Fig. 7. Forecast result chart based on improved stacking Ensemble learning

(2) Comparative analysis of load forecasting results Table 2 compares the results of the article’s method with Stacking ensemble learning and LSTM methods. Table 2. Comparison of Different Load Forecasting Methods and Results Index

Load Type

MAE

RMSE

LSTM

electric vehicle

16.7

388.5

commercial load

13.8

362.4

industrial load

20.9

410.6

electric vehicle

11.9

231.4

commercial load

24.7

436.8

industrial load

16.9

394.5

electric vehicle

9.5

205.6

8.4

204.5

10.2

210.9

Stacking Integrated Learning

Improving Stacking Integrated Learning

commercial load industrial load

6 Conclusion At present, load forecasting has become an essential technology for DR research. Through theoretical analysis and simulation verification, the following conclusions are obtained:

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I) The article takes into account the computational efficiency and accuracy of the model, as well as the difficulty in obtaining large amounts of data. Using data mining methods, it extracts the internal relationships of features, removes redundant information and noise information, and solves the above problems to obtain load prediction values with an error of no more than 1%. II) The article establishes a load forecasting model based on improved stacking ensemble learning using the load forecasting feature dataset obtained from data mining, providing the possibility for one model to predict multiple loads.

References 1. Buddhadeva, S., Sangram, K.R., Pravat, K.R.: Application of mathematical morphology for power quality improvement in microgrid. Int. Trans. Electr. Energy Syst. 30(5), 12329 (2020) 2. Yang, J., Li, Q., Zhang, Y., et al.: Peak shaving optimization modeling for demand response of multiple EV aggregators considering matching degree of power grid demand. Electr. Power Autom. Equip. 41(8), 125–134 (2021) 3. Master-slave game based optimal pricing strategy for LA in day-ahead electricity market. Autom. Electric Power Syst. 45(1), 159−167 (2021). (in Chinese) 4. Li, G., Liu, Z., Jin, G., et al.: Ultra short-term power load forecasting based on randomly distributive embedded framework and BP neural network. Power Syst. Technol. 44(2), 437– 445 (2020). (in Chinese) 5. Li, Y., Jia, Y., Li, L.: Short term power load forecasting based on a stochastic forest algorithm. Power Syst. Protect. Control 48(21), 117–124 (2020). (in Chinese) 6. Ultra-short-term power load forecasting based on two-layer XGBoost considering the influence of multiple features. High Volt. Eng. 47(8), 2885–2898 (2021) 7. Lu, J., Zhang, Q., Yang, Z., et al.: Short-term load forecasting method based on CNN-LSTM hybrid neural network model. Autom. Electr. Power Syst. 43(8), 131–137 (2019). (in Chinese) 8. Zhu, L., Xun, Z., Wang, Y., et al.: Short term power load forecasting based on CNN Bi LSTM. Power Grid Technol. 45(11), 4532–4539 (2021). (in Chinese) 9. Wei, J., Zhao, H., Liu, D., et al.: Short-term power load forecasting method by attention-based CNN-LSTM. J. North China Electr. Power Univ. 48(1), 42–47 (2021). (in Chinese) 10. Ren, J., Wei, H., Zou, Z.: Ultra-short term power load forecasting based on CNN-BiLSTM attention. Power Syst. Protect. Control 50(8), 108–116 (2022) 11. Gong, C., Lin, S., Bian, X., et al.: Economic optimization model of a load aggregator based on the multi-agent stackelberg game. Power Syst. Protect. Control 50(2), 30–40 (2022). (in Chinese) 12. Fan, D., Zhang, S., Wang, Y., et al.: Day ahead scheduling strategy for air conditioning load aggregators considering user regulation behavior diversity. Power Syst. Protect. Control 50(17), 133–142 (2022). (in Chinese) 13. Zhang, B., Si, D., Li, W., et al.: Economic dispatch strategy for power systems considering multiple types of dispatchable flexible load responses. New Technol. Electr. Energy 42(04), 39–47 (2023). (in Chinese) 14. Zheng, J., Gao, D.: Analysis of the causes of low voltage in distribution networks based on data mining. Electr. Mater. 185(02), 63–67 (2023). (in Chinese)

Research on Short-Term Electric Load Forecasting Based on VMD-FGRU Junjie Shen, Xuan Zeng(B) , Cui Wang, Shihan Deng, and Xing Lin Nanchang Institute of Technology, Nanchang 330099, China [email protected], [email protected]

Abstract. In order to improve the accuracy of short-term load forecasting, a hybrid forecasting model based on variational mode decomposition (VMD), fuzzy logic and gated recurrent unit (GRU) is proposed. Firstly, the original load sequence is decomposed into several modal components by VMD algorithm, then the decomposed modal components are combined with the fuzzy processed meteorological information, and then the combined data are inputted into the GRU model for prediction, and finally the prediction results of each modal component are superimposed to obtain the final load prediction results. Through simulation experiments and comparison with other models (SVR, LSTM, GRU, VMD-FGRU), the hybrid model proposed in this paper has better prediction accuracy. Keywords: Short-Term Electricity Load Forecasting · Gated Recurrent Unit · Fuzzy logic · Variational Mode Decomposition

1 Introduction Accurate load forecasting of the power system helps the power system to formulate reasonable power generation planning and improve the economy of power system operation; it also helps power market participants to make wise trading decisions, improve resource utilization efficiency, and maximize revenue [1]. In recent years, deep learning methods have become a research hotspot in the field of load forecasting due to their powerful learning ability [2, 3]. For example, Long Short-Term Memory (LSTM) [4, 5] alleviates the problem of gradient vanishing by increasing the gating structure, but the LSTM network structure is relatively complex and time-consuming to compute. Gated Recurrent Unit (GRU) network [6] is a variant of LSTM network, compared with LSTM, GRU has a smaller number of parameters and lower computational complexity. However, when utilizing GRU for load forecasting, only the historical data of the electricity load itself is considered, while other factors that may cause load fluctuations, such as date and climate, are ignored. Fuzzy logic is a method that can accurately describe the fuzzy relationship between multiple influencing factors. Combining it with GRU, not only retains the intuitiveness of fuzzy logic, but also makes use of GRU’s ability to deal with complex relationships, which can realize more accurate and effective power load forecasting. Variational modal decomposition [7] is an adaptive and fully recursive method of modal variational and signal processing, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 372–380, 2024. https://doi.org/10.1007/978-981-97-0877-2_39

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which can effectively solve the problem of nonlinear and nonsmoothed load sequence by signal decomposition of the load sequence and obtaining different intrinsic modal functions (IMF). Therefore, this paper proposes a short-term power load forecasting model based on VMD-FGRU to reduce the overall computational complexity reduction of the model and improve the forecasting accuracy and forecasting effect.

2 Theoretical Foundations of Mixed Models 2.1 Variational Modal Decomposition Variational modal decomposition (VMD) is a signal processing method used to decompose complex nonsmoothed signals into multiple modal components [8]. The decomposition process of VMD is a solution process that transforms the signal decomposition into non-recursive variational modes by performing an iterative search for the optimal center frequency and effective bandwidth of the variational problem [9]. In this paper, the expression for performing the variational mode decomposition is:     2  j ∗ uk (t)]e−jωk t  σt [ δ(t) + (1) min k {uk },{ωk } πt 2 s.t.

K k=1

uk = f

(2)

where k is the number of IMFs, {uk } and {ωk } are the kth IMF and its center frequency, δ(t) is the Dirac function, f is the original load sequence, ∗ is the sign of the convolution operation. 2.2 Variational Modal Decomposition The GRU network is an improved version of the LSTM network, with a chain structure. It combines the memory unit of LSTM into an update gate, reducing parameters in the network. This gating mechanism enables more efficient information transmission and memory capacity [10]. The basic structure of GRU network is shown in Fig. 1. The GRU calculation process is shown below: ⎧ rt = σ (Wr xt + Ur ht−1 ) ⎪ ⎪ ⎨ zt = σ (Wz xt + Uz ht−1 ) ⎪ h˜ = tanh(Wh xt + Uh (rt  ht−1 )) ⎪ ⎩ t ht = zt  ht + (1 − zt )  ht−1

(3)

where xt , zt , rt , ht−1 , ht and h˜ t are the input information, the reset gate state, the update gate state, the network memory variable at the previous moment, the network memory variable at the current moment and the hidden state of the candidate set. σ is the sigmoid activation function. Wr , Ur , WZ , Uz , Wh and Uh are the weight matrices of the corresponding gates and the candidate set.  denotes the dot-product operation.

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Fig. 1. GRU network basic structure diagram

2.3 Variational Modal Decomposition Fuzzy logic is a mathematical theory and computational method capable of handling information of a fuzzy nature [11]. It is based on fuzzy set theory and fuzzy reasoning, which can provide an accurate description of fuzzy relationships between multiple influencing factors. It has the advantage of dealing with fuzzy and uncertainty problems and has a wide range of applications in several fields. The affiliation function is a mathematical function that describes fuzzy sets and fuzzy rules in fuzzy logic.

3 Prediction Model Based on VMD-FGRU Network 3.1 Structure of the Prediction Model In the hybrid VMD-FGRU network proposed in this paper, the historical load data are first decomposed into multiple modal components using the VMD method. Next, the decomposed modal components are combined with meteorological factors and then input into the model for training. The specific process is shown in Fig. 2. 3.2 Structure of the Prediction Model For the evaluation of load forecasting accuracy, Mean Absolute Error (MAE), Mean Square Error (MSE), R-Square (R2) and Explained Variance Score (EVS) are selected as the evaluation criteria in this paper. Their expressions are shown as follows: 1 m |(yi − yˆ i )| MAE = (4) i=1 m 1 m (yi − yˆ i )2 (5) MSE = i=1 m  (ˆyi − yi )2 R2 = 1 − i (6) 2 i (y i − yi ) Var{yi − yˆ i } (7) EVS(yi , yˆ i ) = 1 − Var{yi } where m is the number of forecast data points. yi is the actual load data at moment i and yi is the forecast load data at moment i.



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Fig. 2. VMD-FGRU model flow chart

4 Algorithm Analysis 4.1 Experimental Dataset and Environment Configuration In this paper, data including actual electrical load, temperature, humidity, cloud type, precipitation, dew point, wind speed, wind direction, barometric pressure, and surface albedo are selected from January 1, 2020–December 31, 2020 for a region in Arizona, USA. The data collection interval is 1 h, and a day can be divided into 24 time series, totaling 8784 data. The dataset is divided into training and test sets in the ratio of 8:2. 4.2 Selection of Important Parameters of VMD Algorithm In this paper, the center frequency method is used to select the number of decomposed modes k. The center frequency of each modal component of the load data decomposed by VMD is shown in Table 1. The penalty factor α is taken to be the default value of 2000, and ε is taken to be 10–6 . As can be seen from Table 1, when k = 4, 5, 6, there is still important information in the last IMF that has not been completely decomposed. When k = 8, the center frequencies of IMF3 and IMF4 are very close to each other, so it can be assumed that there is a modal aliasing. After comprehensive analysis, this paper takes k = 7 as the appropriate number of decomposed modal components. After determining the number k of modal components of the VMD decomposition, the value of the noise tolerance τ can be further determined. The residual error index (REI) method is used to determine the value of τ, which ranges from 0 to 1. τ is optimized according to the Root Mean Square Error (RMSE) between the denoised time series and the original time series, which can be simplified to REI, whose mathematical expression is shown in Eq. (8) is shown, and the REI value after the operation is shown in Fig. 3. From Fig. 3, it can be seen that the value of τ is 0.15 when the REI value reaches the

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component

4

5

6

7

8

IMF1

9.52 × 10–6

8.91 × 10–6

8.8 × 10–6

8.81 × 10–6

8.79 × 10–6

IMF2

0.046

0.042

0.041

0.041

0.041

IMF3

0.148

0.096

0.094

0.093

0.093

IMF4

0.312

0.175

0.161

0.141

0.122

0.321

0.223

0.208

0.184

0.318

0.28

0.269

0.399

0.333

IMF5 IMF6 IMF7 IMF8

0.425

minimum value of 87.96. Therefore, τ = 0.15 is taken as the appropriate noise tolerance value. According to the parameter values obtained from the above analysis, the original load sequence is decomposed using the VMD algorithm, and the modal components obtained are shown in Fig. 4. REI = min

1 m k [ Uk − f ] i=1 k=1 m

(8)

where Uk denotes the number of modes decomposed and m denotes the number of signals.

Fig. 3. REI value

4.3 Fuzzy Logic Processing In this paper, a fuzzy function is initially defined to fuzzify various weather characteristic data and represent them as fuzzy sets. The k-means clustering algorithm is employed for clustering, with the number of cluster categories set to 5 in order to assign labels to each data point. Data sets with different cluster labels are then divided into distinct fuzzy sets. The choice of membership functions significantly influences the prediction performance of the model. Therefore, diverse membership functions are selected for model training, and the effectiveness of the prediction model is evaluated using RMS

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Fig. 4. VMD decomposition result

and R2 metrics. The membership function that yields optimal predictive performance is identified, and the results are presented in Table 2. Specifically, Gauss2mf is chosen as the most suitable membership function (Table 3). Table 2. Comparison of prediction effect of different membership degree functions function type

RMS

R2

Trimf

0.811

0.9833

Trapmf

0.791

0.9734

Gbellmf

0.933

0.9898

Gaussmf

1.743

0.9987

Gauss2mf

0.675

0.9998

Psigmf

0.872

0.8754

Table 3. Mean square error loss of different GRU layers Network Layers

Number of iterations

Mean Square Loss Error

2

1000

0.00325

3

1000

0.00211

4

1000

0.00263

5

1000

0.00268

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4.4 Selection of GRU Parameters In this paper, the selection of the number of layers of the GRU network is discussed in focus. Under the condition that the number of iterations is kept 1000 times, the number of GRU network layers is deepened step by step, the mean square error loss of the model is calculated, and the layer with the smallest mean square error loss is selected. The results are shown in Table 4. From the table, it can be seen that the mean square loss of the model is minimized when the number of GRU network layers is selected as 3, so the number of GRU network layers is selected as 3. The GRU network was trained using the Adam optimization algorithm to optimize the parameters, and the mean square error loss function was used as the empirical risk function. The learning rate was set to 0.01, the decay coefficient to 0.9, and Dropout to 0.4 to prevent model overfitting. 4.5 Analysis of Results In order to reflect the superiority of the performance of the model proposed in this paper, the model in this paper is compared with the LSTM model, GRU model, SVR model, and VMD-GRU model, and the experimental conditions are exactly the same. In order to make the curves more intuitively show the difference between each model, the load forecast curves of each model for a total of thirty days from April 1, 2020 to April 30, 2020 are taken as shown in Fig. 5, and the evaluation of the forecast performance of each model is shown in Table 4. As can be seen from Fig. 5, the SVR model can only roughly predict the trend of the actual load curve, but the prediction of the spikes in the curve is poorly fitted, the LSTM model and the GRU model, for the change of the actual load curve can be well fitted, but the prediction of the existence of hysteresis phenomenon, the stability of the poorer, the VMD-GRU model for the actual load curve is well fitted, but failed to fully tap the key information in the load sequence, the model proposed in this paper is very good for the actual load curve is well fitted, more closely related to the actual load value, the accuracy of the high. As can be seen from Table 4, the MAE value of the model is reduced by 1.3025 MW, 0.5333 MW, 0.5353 MW, 0.2766 MW, and the MSE value is reduced by 0.6391 MW, 0.3629 MW, 0.372 MW, compared to the load forecasting of the SVR model, the LSTM model, the GRU model, and the VMD-GRU model, respectively, 0.2246 MW, which indicates that the model proposed in this paper has strong stability. The EVS value reaches 98.08% and the R2 reaches 98.06%, which indicates that the model proposed in this paper has better prediction and higher accuracy.

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Fig. 5. Prediction graphs for each model Table 4. Evaluation of prediction performance of each model Model

MAE/MW

MSE/MW

R2 /%

EVS/%

SVR

1.4266

0.9159

77.62

77.65

LSTM

0.6574

0.6397

89.69

90.56

GRU

0.6594

0.6488

89.66

91.94

VMD-GRU

0.4007

0.5014

93.72

94.72

VMD-FGRU

0.1241

0.2768

98.06

98.08

5 Conclusion This paper presents a novel power load forecasting approach based on VMD-FGRU, which integrates the strengths of VMD, fuzzy logic, and GRU to effectively address the nonlinear relationships among multivariate variables while preserving temporal dependencies, thereby enhancing forecast accuracy. The proposed model is applied to real power load data from Arizona, USA and incorporates weather factors such as temperature, humidity, cloud type, and precipitation that influence user’s power consumption. Experimental results demonstrate superior accuracy and stability of the proposed model compared to alternative approaches. Acknowledgment. This study was supported by the Key Project of Natural Science Foundation of Jiangxi Province (20224ACB204016).

References 1. Zhao, Y., Wang, H., Kang, L., et al.: Short-term power load forecasting based on temporal convolutional network. J. Electrotechnology, 37(5), 1242–1251 (2022). (in Chinese) 2. Aurangzeb, K., Alhussein, M., Javaid, K., et al.: A pyramid-CNN based deep learning model for power load forecasting of similar-profile energy customers based on clustering. IEEE Access 9, 14992–15003 (2021)

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3. Lv, L., Wu, Z., Zhang, J., et al.: A VMD and LSTM based hybrid model of load forecasting for power grid security. IEEE Trans. Industr. Inf. 18(9), 6474–6482 (2021) 4. Cai, C., Tao, Y., Zhu, T., et al.: Short-term load forecasting based on deep learning bidirectional LSTM neural network. Appl. Sci. 11(17), 8129 (2021) 5. Lei, Y., Yang, S.: Mid-long term load forecasting model based on support vector machine optimized by improved sparrow search algorithm. Energy Rep. 8(5), 491–497 (2022) 6. Li, W., Wu, H., Zhu, N., et al.: Prediction of dissolved oxygen in a fishery pond based on gated recurrent unit (GRU). Inf. Process. Agri. 8(1), 185–193 (2021) 7. Yang, T., Hu, D., Tang, C., et al.: Prediction of dissolved gas content in transformer oil based on SMA-VMD-GRU modeling. Trans. China Electrotechnical Soc. 38(1), 117–130 (2023). (in Chinese) 8. Quan, Y., Yu, M., Wang, W., et al.: Short-term wind speed prediction based on fractal optimization with VMD and GA-BP. J. Solar Energy 44(7), 436–446 (2023). (in Chinese) 9. Zhou, J., Xiao, M., Niu, Y., et al.: Rolling bearing fault diagnosis based on WGWOA-VMDSVM. Sensors 22(16), 6281 (2022) 10. Jung, S., Moon, J., Park, S., et al.: An attention-based multilayer GRU model for multistepahead short-term load forecasting. Sensors 21(5), 1639 (2021) 11. Serrano-Guerrero, J., Romero, F.P., Olivas, J.A.: Fuzzy logic applied to opinion mining: a review. Knowl.-Based Syst. 222, 107018 (2021)

Analysis of the Depth of Positive Sequence Voltage Sags in Distribution Network Faults and Their Effects on New Energy-Type Equipment Zhichang Liu1

, Qinghui Lu1 , Xin Yin2(B) , Xianggen Yin1 , Jiaxuan Hu1 , and Jian Qiao1

1 State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong

University of Science and Technology, Wuhan 430074, China 2 School of Automation, Wuhan University of Technology, Wuhan 430070, China

[email protected]

Abstract. With the proposal of the “double carbon” goal, the proportion of distributed generation in the power grid is gradually increasing, distribution network faults will lead to voltage sags, which may make the distributed generation into the low voltage ride-through process or even off-grid, and sensitive loads to work abnormally, affecting the normal operation of the power grid. This paper takes a typical radial distribution network as an example and analyzes the depth of voltage sags at new energy-type equipment points of common coupling (PCC) in different grounding methods and at different locations where various faults with transition resistance occur. Theoretical analysis and PSCAD/EMTDC simulation analysis results show that the closer the fault is to the PCC, the deeper the positive sequence voltage sag at the PCC, and the lowest positive sequence voltage is lower than 0.2 pu in a three-phase short circuit, and the obtained conclusions provide some guidance for the fault voltage compensation strategy such as Dynamic Voltage Restorer (DVR). Keywords: Distribution network · voltage sag · distributed generation · small current neutral grounding system

1 Introduction Distributed new energy has the advantages of cleanliness, low carbon, and high efficiency, and it is an important part of the new power system mainly based on new energy. With the proposal of the “double carbon” goal, the installed capacity of distributed new energy has been steadily increasing, and distributed generation (DG) system is mainly connected to the distribution network [1]. When a fault occurs, voltage sag will occur at the DG PCC, and the DG goes through the low-voltage ride-through process, and maybe the voltage sags are severe enough to cause the DG to go off-grid, which affects the normal transmission of electric energy [2]. Besides, some new energy units have insufficient © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 381–393, 2024. https://doi.org/10.1007/978-981-97-0877-2_40

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low-voltage ride-through capability, and will also get off-grid during mild voltage sags [3]. In addition, when the voltage sags to a certain extent, voltage-sensitive loads will be seriously affected or even get off-grid [4, 5]. Therefore, power quality, power supply reliability, security, economy, and other aspects related to distribution networks have gradually been emphasized. For distribution network voltage sags, some studies have been conducted in the literature. Literature [6] discussed the transfer of voltage sags between transformers, but did not consider the sequential component, and literature [7] simulated and analyzed the amplitude of distribution network voltage sags with DG connected, but did not analyze it theoretically and did not consider the transition resistance. Literature [8, 9] established a transient model reflecting phase and magnitude and an uncertainty model for unbalanced voltage sags, but it did not consider the effect of the distribution network neutral grounding method on voltage sags. Literature [10] discusses the suppression measures of voltage sags, but the methods are not combined with the depth of voltage sags. Literature [11–13] used dynamic voltage regulators to compensate for voltage fluctuation, which can compensate for a certain degree of voltage fluctuation, but its design parameters and power are related to the depth of voltage sags, and further research on the depth of voltage sags is needed. In this paper, firstly, the positive, negative, and zero sequence network of the radial distribution network is constructed according to different neutral grounding methods, different fault locations, and different transition resistances, and then the voltage sag depth of new energy type equipment ports in radial distribution network with different neutral grounding methods, different fault locations, and different transition resistances is analyzed by using the sequence network analysis method. Finally, the PSCAD/EMTDC electromagnetic transient simulation model is used to verify the correctness of the theoretical analysis.

2 Distributed New Energy Low Voltage Ride Through Strategies and Grid Integration Requirements According to the Chinese national standards Technical Requirements for GridConnected Inverters for Photovoltaic Power Generation (GB/T 37408–2019) and Technical Provisions for Wind Farm Access to Power Systems (GB/T 19963.1–2021), the new energy power supply is required to have LV ride-through capability: when the voltage at the PCC falls to 20% of the nominal voltage, the new power supply unit should continuously operate without going off-grid for 625 ms. When the voltage at the PCC of the new energy power supply can be restored to 90% of the nominal voltage within 2 s after a sag, the new energy power supply unit should guarantee continuous operation without going off-grid (Fig. 1).

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Fig. 1. Requirements for low voltage ride-through capability of new energy units.

At the same time, new energy units should also meet the reactive power support requirements of the grid system without overcurrent in the inverter, and the residual current should be active current [14]. The common wind and solar storage new energy units use the phase-locked loop to follow the positive sequence voltage of the grid [15], and their low voltage ride-through control strategies are shown in Eqs. (1)–(2) [16, 17]. ⎧ + + U ≥ 0.9(pu) ⎨ idf = idm ,  T  + (1) i + 2 − i +2 , U < 0.9(pu) ⎩ idf = min Udm∗ , Imax T qf T

⎧ + + ⎪ ⎨ iqf = iqm + iqf = kq (0.9 − |UT∗ |) · In ⎪ ⎩ i+ = I max qf

UT > 0.9(pu) 0.2(pu) ≤ UT ≤ 0.9(pu) UT ≤ 0.2(pu)

(2)

where idf + , iqf + is d, q-axis current command value, idm + , iqm + is the normal operating conditions d, q-axis current command value, I max is the maximum output current of the inverter, U T * is the inverter port voltage nominal value, I max is the maximum output current of the inverter, k q is the reactive power compensation coefficient, generally be 1.5–2.

3 Analysis of Voltage Sag at PCC of Distributed New Energy Equipment With the continuous emergence of new technology industries, power quality has received increasing attention. Among them, voltage sags have been recognized as the most important dynamic power quality problem that affects the normal and safe operation of power equipment. There are two main parameters of the degree of voltage sags: the magnitude and the duration of voltage sags [18]. The IEEE defines voltage sags as follows: the supply voltage RMS drops rapidly to 90%−10% of the rated value and lasts for 0.5−30 rated frequency cycles. For distributed new energy sources, the control strategy uses phase-locked loops to track the phase amplitude of the grid positive sequence voltage, and the LVRT strategy also uses the positive sequence voltage as a reference. The voltage sags are usually caused by short-circuit faults within the power supply system or users, and the sequence network analysis method is used to analyze the positive sequence voltage of the distributed new energy PCC after the fault.

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3.1 Typical Radial Distribution Network Model The most common radial distribution network structure is used for analysis, as shown in Fig. 2. Among them, the 10 kV system is considered to be ungrounded, grounded via the neutral arcing coil or small resistance of the grounding transformer. In the figure, the 700 V port is connected to distributed new energy or voltage-sensitive loads, and the load side may be distributed new energy, providing a certain short-circuit current. In this paper, we consider the most serious case of voltage sags at the 700 V port, i.e., there is no distributed new energy at the load side, and the 700 V side does not provide short-circuit current.

Fig. 2. Typical radial distribution network structure.

3.2 Single-Phase Short Circuit

Fig. 3. 10 kV side single-phase short circuit sequence network diagram.

Due to the short transmission line, the positive and negative sequence impedance of the load is much larger than the power supply and line impedance, while the line capacitive impedance is much larger than the power supply and line impedance, it can be assumed that the fault current is approximated to be equal to the current flowing through the power supply [19]. According to the short circuit sequence network, the positivesequence fault current and the positive-sequence voltage at the port are calculated to be (Fig. 3):

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385

Es1 (3) 2(Zs1 + ZL11 + ZT 11 + αZL21 ) + [Zg2 + (1 − α)ZL20 ]//(αZL20 + (ZL30 + Zg3 )//(ZL10 + Zg1 )) + 3Rf Zs1 + ZL11 + ZT 11 + 2αZL21 + [Zg2 + (1 − α)ZL20 ]//(αZL20 + (ZL30 + Zg3 )//(ZL10 + Zg1 )) + 3Rf UG1 = Es1 ∗ ≈ Es1 2(Zs1 + ZL11 + ZT 11 + αZL21 ) + [Zg2 + (1 − α)ZL20 ]//(αZL20 + (ZL30 + Zg3 )//(ZL10 + Zg1 )) + 3Rf If 1 ≈

(4) ⎧ grounded with resistence ⎨ 3XiRg where Zgi = 3XiLg grounded with arc suppression coil , i = 1, 2, 3 ⎩ ∞ not grounded Similarly, it can be obtained that the positive sequence fault current in case of singlephase short-circuit on the 110 kV side is: Es1 2Zs1 + Zs0 //ZT 10 + 3Rf Zs1 + Zs0 //ZT 10 + 3Rf = Es1 ∗ > 0.5Es1 2Zs1 + Zs0 //ZT 10 + 3Rf If 1 ≈

UG1

(5) (6)

According to Eqs. (3)–(6), when a single-phase fault occurs on the 110 kV side, the port positive-sequence voltage is not less than 0.5pu. However, when a single-phase fault occurs on the 10 kV side, the port positive-sequence voltage is approximated as the power supply voltage, which does not affect the new energy operation. 3.3 Two-Phase Short Circuit

Fig. 4. 10 kV side two-phase short circuit sequence network diagram.

According to the short circuit sequence network, the positive sequence fault current and the port positive sequence voltage are calculated as (Fig. 4): Es1 2(Zs1 + ZL11 + ZT 11 + αZL21 ) + Rf (Zs1 + ZL11 + ZT 11 + 2αZL21 ) + Rf = Es1 ∗ ≥ 0.5Es1 2(Zs1 + ZL11 + ZT 11 + αZL21 ) + Rf If 1 ≈

UG1

(7) (8)

According to Eqs. (7)–(8), after a two-phase short-circuit fault, the port positivesequence voltage will be greater than 0.5 times the supply voltage, and the closer to the new energy bus, the smaller the transition resistance is, the lower the voltage is, and the lowest is 0.5 times the supply voltage, so that if no countermeasure strategy is taken, the new energy will enter into a low-voltage ride-through process, and the sensitive loads will also not work normally.

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3.4 Two-Phase Short Circuit Grounding

Fig. 5. 10 kV side two-phase short-circuit grounding sequence network diagram.

According to the short circuit sequence network, the positive sequence fault current and the port positive sequence voltage are calculated as Eqs. (9)−(10) Similarly, the positive sequence fault current in case of a two-phase short circuit grounding at 110 kV side is obtained as Eqs. (11)−(12) (Fig. 5): If 1 ≈

Es1 Zs1 + ZL11 + ZT 11 + αZL21 + Rf + (Zs1 + ZL11 + ZT 11 + αZL21 )//[Zg2 + (1 − α)ZL20 + 3Rfg ]

UG1 ≈ Es1 ∗

(Zs1 + ZL11 + ZT 11 + 2αZL21 ) + Rf ≥ 0.5Es1 2(Zs1 + ZL11 + ZT 11 + αZL21 ) + Rf

If 1 ≈ UG1 = Es1 ∗

Es1 Zs1 + Zs1 //(Zs0 //ZT 10 + 3Rfg )

Zs1 //(Zs0 //ZT 10 + 3Rfg ) < 0.5Es1 Zs1 + Zs1 //(Zs0 //ZT 10 + 3Rfg )

(9) (10) (11) (12)

According to Eqs. (9)−(12), when a two-phase short-circuit ground fault occurs on the 110 kV side, the port positive sequence voltage is not higher than 0.5 pu; However, when a two-phase short-circuit ground fault occurs on the 10 kV side, the port positive sequence voltage is similar to that of the two-phase short-circuit case, which will be greater than 0.5 times the power supply voltage. Moreover, the closer the fault is to the bus of the new energy or sensitive loads, the smaller the transition resistance is, the lower the voltage is and the lowest is 0.5 times the power supply voltage. If no countermeasure strategy is taken, the new energy will enter the low-voltage ride-through process, and the voltage-sensitive loads will not work normally. 3.5 Three-Phase Short Circuit According to the short circuit sequence network, the positive sequence fault current and the port positive sequence voltage are calculated as (Fig. 6) If 1 ≈

Es1 Zs1 + ZL11 + ZT 11 + αZL21 + Rf

(13)

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387

Fig. 6. 10 kV side two-phase short-circuit grounding sequence network diagram.

UG1 = Es1 ∗

αZL21 + Rf Zs1 + ZL11 + ZT 11 + αZL21 + Rf

(14)

According to Eqs. (13)−(14), when a three-phase short circuit fault, the closer the fault point is to the new energy or sensitive load bus, the lower the transition resistance is, and the lower the positive sequence voltage at the port is. If no countermeasure strategy is taken, the new energy will enter the low-voltage ride-through process or even get off-grid, and the voltage-sensitive load will also work abnormally or go off-grid.

4 Simulation Analysis of Voltage Sag at PCC of Distributed New Energy Equipment The radial distribution network shown in Fig. 2 is simulated and modeled using PSCAD/EMTDC electromagnetic transient simulation software. Where the lines are all overhead lines, F4 and F6 faults are set at line midpoints, and the specific parameters are shown in Table 1. Table 1. Simulation system parameters System impedance ()

L1 length(km)

L2 length (km)

L3 length (km)

T1 short circuit impedance

1.2 + 11.4j

6

6

3

10%

T2 short circuit impedance

T3 short circuit impedance

Load (kW)

Grounding arc suppression coil (H)

Grounding resistance()

6%

6%

3.24 + 1.98j

1.3H

15

4.1 Single-Phase Short Circuit From Fig. 7 and Table 2, it can be seen that when single-phase short-circuit grounding occurs at the 110 kV side, the port voltage is not less than 0.5 pu; when single-phase short-circuit grounding occurs at the 10 kV side, there is almost no sag in port voltage, which is in line with the theoretical analysis.

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U1

1

U+/pu.

U/kV

0.5

0

0.5

-0.5 0

0.1

0.2

0.3

0.4

0

0.5

0

0.1

0.2

0.3

t/s

t/s

(a)

(b)

0.4

0.5

Fig. 7. Single-phase short-circuit port (a) three-phase voltage; (b) positive sequence voltage nominal value. Table 2. Positive sequence nominal voltage at the port when a single-phase ground fault occurs at different locations with different neutral grounding methods Fault position\grounding method

F1

F2

F3

F4

F5

F6

F7

ungrounded

0.665

1.003

1.046

1.041

1.037

1.04

1.051

Arc suppression coil grounded

0.654

0.986

1.024

1.02

1.016

1.034

1.047

Small resistance grounded

0.654

0.984

0.994

0.973

0.974

0.966

0.954

4.2 Two-Phase Short Circuit From Fig. 8 and Table 3, it can be seen that when a two-phase short circuit occurs, the lowest port voltage drops to 0.5 pu, which is consistent with the theoretical analysis. A B C

1

U1

0.8

U+/pu.

U/kV

0.5

0

0.6 0.4 0.2

-0.5 0

0.1

0.2

0.3

0.4

0.5

0

0

0.1

0.2

0.3

t/s

t/s

(a)

(b)

0.4

0.5

Fig. 8. Two-phase short-circuit port (a) three-phase voltage; (b) positive sequence voltage nominal value.

4.3 Two-Phase Short Circuit Grounding From Fig. 9, and Table 4 it can be seen that when a two-phase short-circuit grounding occurs on the 110 kV side, the port voltage will fall to lower than 0.5 pu; When a twophase short-circuit grounding occurs on the 10 kV side, and the lowest port voltage falls to 0.5 pu, which is consistent with the theoretical analysis.

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389

Table 3. Positive sequence nominal voltage at the port when a two-phase short circuit occurs at different locations with different neutral grounding methods. Fault position\grounding method

F1

F2

F3

F4

F5

F6

F7

ungrounded

0.5

0.5

0.5

0.664

0.748

0.5

0.5

Arc suppression coil grounded

0.491

0.491

0.491

0.654

0.737

0.491

0.491

Small resistance grounded

0.476

0.476

0.476

0.639

0.722

0.476

0.476

U1

0.8

U+/pu.

U/kV

1

A B C

0.5

0

0.6 0.4 0.2

-0.5 0

0.1

0.2

0.3

0.4

0

0.5

0

0.1

0.2

0.3

t/s

t/s

(a)

(b)

0.4

0.5

Fig. 9. Two-phase short circuit grounding port (a) three-phase voltage; (b) positive sequence voltage nominal value.

Table 4. Positive sequence nominal voltage at the port when two-phase short circuit grounding occurs at different locations with different neutral grounding methods. Fault position\grounding method

F1

F2

F3

F4

F5

F6

F7

ungrounded

0.331

0.501

0.506

0.673

0.756

0.518

0.527

Arc suppression coil grounded

0.328

0.493

0.501

0.663

0.745

0.508

0.516

Small resistance grounded

0.317

0.477

0.472

0.632

0.713

0.466

0.46

4.4 Three-Phase Short Circuit From Fig. 10 and Table 5, it can be seen that when a three-phase short-circuit occurs at the 10 kV side, and the closer it is to the new energy-type equipment grid-connected bus, the deeper the port voltage drops, and in the most severe condition, it drops to close to 0, which is consistent with theoretical analysis (Table 6).

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0.8

U+/pu.

U/kV

1

A B C

0.5

0

0.6 0.4 0.2

-0.5 0

0.1

0.2

0.3

0.4

0

0.5

0

0.1

0.2

0.3

0.4

0.5

t/s

t/s

(a)

(b)

Fig. 10. Three-phase short-circuit port (a) three-phase voltage; (b) positive sequence voltage nominal value. Table 5. Positive sequence nominal voltage at the port when a three-phase short-circuit occurs at different locations with different neutral grounding methods. Fault position\grounding method

F1

F2

F3

F4

F5

F6

F7

ungrounded

0

0

0

0.329

0.497

0

0

Arc suppression coil grounded

0

0

0

0.327

0.492

0

0

Small resistance grounded

0

0

0

0.327

0.492

0

0

Table 6. Positive sequence nominal voltage at the port when a three-phase short-circuit with transition resistance occurs at different locations, neutral point ungrounded. Fault position\transition resistance()

F1

F2

F3

F4

F5

F6

F7

ungrounded

0.01

0.665

1.003

1.046

1.041

1.037

1.04

1.051

1

0.805

1.003

1.044

1.04

1.036

1.037

1.042

10

0.958

1.001

1.023

1.022

1.02

1.021

1.025

100

0.995

0.999

0.999

0.999

0.999

0.999

0.999

1000

0.999

0.999

0.999

0.999

0.999

0.999

0.999

3000

0.999

0.999

0.999

0.999

0.999

0.999

0.999

0.01

0.654

0.986

1.024

1.02

1.016

1.034

1.047

1

0.791

0.986

1.023

1.019

1.015

1.032

1.041

10

0.942

0.984

1.006

1.004

1.002

1.017

1.026

100

0.978

0.983

0.983

0.983

0.983

0.983

0.983

1000

0.982

0.982

0.982

0.982

0.982

0.982

0.982

3000

0.982

0.982

0.982

0.982

0.982

0.982

grounded with arcing coil

0.982 (continued)

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391

Table 6. (continued) Fault position\transition resistance()

F1

F2

F3

F4

F5

F6

F7

grounded with small resistance

0.01

0.654

0.984

0.994

0.973

0.974

0.966

0.954

1

0.791

0.983

0.99

0.974

0.981

0.968

0.954

10

0.942

0.983

0.981

0.977

0.982

0.975

0.966

100

0.978

0.983

0.982

0.982

0.982

0.982

0.982

1000

0.982

0.983

0.983

0.983

0.983

0.983

0.983

3000

0.982

0.983

0.983

0.983

0.983

0.983

0.983

4.5 Single-Phase Short Circuit With Transition Resistance Due to the short phase-to-phase arc in the distribution network, the phase-to-phase shortcircuit transition resistance can be ignored, so only the single-phase grounding transition resistance is considered. The simulation results are shown in Table 7. The simulation results show that the larger the transition resistance, the lower the voltage sag when a fault occurs on the 110 kV side, and the transition resistance has almost no effect on the voltage sag when a fault occurs on the 10 kV side. 4.6 New Energy Sources Provide Short-Circuit Current Scenarios Considering the case that the new energy source provides short-circuit current, the simulation results are shown in Table 7. The comparison of the simulation results with Table 3 shows that the degree of positive sequence voltage sag at the port is reduced after the new energy source provides short-circuit current. Table 7. Positive sequence nominal voltage at the port when a two-phase short circuit occurs at different locations with different neutral grounding methods, DG operating. Fault position\grounding method

F1

F2

F3

F4

F5

F6

F7

ungrounded

0.554

0.553

0.542

0.695

0.773

0.536

0.53

Arc suppression coil grounded

0.546

0.545

0.534

0.686

0.763

0.528

0.521

Small resistance grounded

0.546

0.545

0.534

0.686

0.763

0.528

0.521

5 Conclusion In this paper, the positive sequence voltage sag of new energy-type equipment ports when various faults with transition resistors occur in typical radial distribution networks under different non-effective grounding methods is analyzed by using the sequential network

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analysis method. The analysis results show that, for the directly grounded 110 kV system, the positive sequence voltage is not lower than 0.5 pu when a single-phase grounding fault occurs, and the positive sequence voltage is not higher than 0.5 pu when a two-phase short-circuit is grounded. Meanwhile, in a non-effectively grounded 10 kV system, there is almost no sag in the positive sequence voltage in the case of a single-phase grounding fault, and the positive sequence voltage is higher than 0.5 pu when a two-phase grounded short-circuit occurs. Besides, the positive sequence voltage is higher than 0.5 pu in the case of two-phase short-circuits for all voltage levels of the distribution network and the lowest voltage of a three-phase short circuit will be close to 0. Moreover, when the short circuit occurs in the branch line, the closer the short circuit point is to the bus of new energy class equipment, the smaller the transition resistance is, and the deeper the positive sequence voltage sag of the port is. The electromagnetic transient simulation of PSCAD/EMTDC verifies the accuracy of the conclusions. The positive sequence voltage sag analysis in this paper provides a kind of capacity and design parameter guidance for blocking the short-circuit loop for series voltage compensation, such as DVR, to ensure that the new energy equipment is in normal working condition after the fault. Acknowledgments. This work is supported by Youth Fund of the National Natural Science Foundation of China 52007010.

References 1. Qiao, Y., Wu, H., Wu, T., et al.: A partitioned current protection scheme of distribution network with inverter interfaced distributed generator. Trans. China Electrotechnical Soc. 37(S1), 134–144 (2022). (in Chinese) 2. Shen, Z., Sun, H., Zhong, W., et al.: Key event based analysis of evolution law of cascading failures in power system with high proportion of renewable energy. Autom. Electric Power Syst. 46(24), 57–65 (2022). (in Chinese) 3. Wang, N., Ma, Y., Ding, K., et al.: Analysis on root reasons of WTGs nuisance tripping in Jiuquan wind power base. Autom. Electric Power Syst. 36(19), 42–46 (2012). (in Chinese) 4. Vilathgamuwa, D.M., Perera, A.A.D.R., Choi, S.S.: Voltage sag compensation with energy optimized dynamic voltage restorer. IEEE Trans. Power Delivery 18(3), 928–936 (2003) 5. Wang, X., Tang, Z., Liu, X.: Evaluation of the operating status of voltage sensitive equipment considering the protective action mechanism of low voltage release under the random influence of voltage sag. Trans. China Electrotech. Soc. 37(15), 3794–3804 (2022). (in Chinese) 6. Tao, S., Xiao, X.: Voltage sags types under different grounding modes of neutral and their propagation: part II. Trans. China Electrotech. Soc. 10, 156–159 (2007). (in Chinese) 7. Zhao, Y., Hu, X.: Impacts of distributed generation on distribution system voltage sags. Power Syst. Technol. (14), 5–9+18 (2008). (in Chinese) 8. Zhang, L., Bollen, M.H.J.: Characteristic of voltage sags (sags) in power systems. IEEE Trans. Power Deliv. 15(2) (2000) 9. Jia, D., Liu, K., Sheng, W., et al.: Voltage sag simulation and evaluation in active distribution network with fault cases. In: Proceedings of the CSEE, vol. 36, no. 5, pp. 1279-1288 (2016). (in Chinese) 10. Jin, Z., Liu, B.: Voltage sag analysis & solution. Electr. Equip. 4, 63–66 (2006). (in Chinese) 11. Han, M., You, Y., Liu, H.: Principle and realization of a dynamic voltage regulator (DVR) based on line voltage compensating. In: Proceedings of the CSEE, vol. 12, pp. 52–56 (2003). (in Chinese)

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12. Tu, C., Li, Q., Guo, Q., et al.: Fusion design and control method of bridge current limiter and dynamic voltage restorer. Trans. China Electrotechnical Soc. 35(20), 4384–4396 (2020). (in Chinese) 13. Rauf, A.M., Khadkikar, V.: An enhanced voltage sag compensation scheme for dynamic voltage restorer. IEEE Trans. Industr. Electron. 62(5), 2683–2692 (2015) 14. Qiao, J., Yin, X., Wang, Y., et al.: A multi-terminal traveling wave fault location method for active distribution network based on residual clustering. Int. J. Electr. Power Energy Syst. 131, 107070 (2021) 15. Yang, M., Yang, C., Li, Y., et al.: A new phase-locked loop design method based on impedance remodeling of grid-connected inverter under high permeability. Trans. China Electrotech. Soc. 1–13 (2023). (in Chinese) 16. Kabiri, R., Holmes, D.G., McGrath, B.P.: Control of active and reactive power ripple to mitigate unbalanced grid voltages. IEEE Trans. Ind. Appl. 52(2), 1660–1668 (2016) 17. Xu, K., Zhang, Z., Liu, H., et al.: Study on fault characteristics and its related impact factors of photovoltaic generator. Trans. China Electrotechnical Soc. 35(02), 359–371 (2020). (in Chinese) 18. Costa, F.B., Driesen, J.: Assessment of voltage sag indices based on scaling and wavelet coefficient energy analysis. IEEE Trans. Power Delivery 28(1), 336–346 (2013) 19. Zeng, X., Yin, X., Zhang, Z., et al.: Study for negative sequence current distributing and ground fault protection in middle voltage power systems. In: Proceedings of the CSEE, vol. 21, no. 6, pp. 85-90 (2001). (in Chinese)

Measuring Method for Strand Current in Formed-Parallel Coil of Flat-Wire Motor Based on Hall Sensors Ni Lei

and Yanping Liang(B)

College of Electrical and Electronic Engineering, Harbin University of Science and Technology, Harbin 150080, China [email protected]

Abstract. Formed-parallel coil is a new stator coil type of flat-wire motor. It is designed to reduce the eddy current loss in the stator coil and decrease the difficulty of coil production. In the experiments, it can only detect the total current of each stator coil instead of the current distribution of each strand. Aiming to solve the problem, this paper proposes a strand current measuring method based on Hall sensors without destroying the coil structure. The end leakage magnetic field (ELMF) and strand current are analyzed by finite element solution (FEM). The relationship between the strand currents, ELMF and Hall output signal is derived. The coil strand current test platform is built and the experimental verification is carried out by a 15 kW flat-wire motor. The result shows that the current measuring method can measure the current distribution in the strands accurately. It provides an experimental evaluation basis for analyzing the reasonableness of the strand current distribution and the design of the formed-parallel coil. Keywords: Flat-wire motors · Formed-parallel coil · Hall sensor · Magnetic Field Measurement · Current Measurement

1 Introduction The rapid development of the new energy automotive industry has put higher requirements on the performance of drive motors. The drive motor must have a high power density to satisfy the vehicle can run in different conditions, and the heat problem must be small enough. Therefore, flat-wire motors become the drive motors to reduce motor copper loss and reduce heat problems. The common form of flat-wire motor coil is distributed winding [1]. Compared to the concentrated winding [2], it has better performance in terms of cogging torque, output torque and NVH. The distributed winding can be divided into two types according to different mounting techniques, which are continuous wave windings and axially mounted hairpin windings [3]. The continuous wave winding is difficult to preform, although it does not need twisting and welding in the process. Hairpin windings need to be processed by twisting and welding processes, which makes production more difficult. Therefore, paper [4] proposed the Diamond coil. This coil is a diamond-shaped coil formed by twisting a continuous rectangular wire. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 394–402, 2024. https://doi.org/10.1007/978-981-97-0877-2_41

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The advantage of this coil compared to regular coils is that it has fewer weld points. And its turns have more flexible selectivity. However, higher eddy current loss is generated at high speed conditions due to the large rectangular conductor cross-sectional area [5]. Therefore, this paper proposed a new type of stator coil by dividing the rectangular wire. Due to the compact end structure of flat wire motors, it is not possible to measure the strand current directly by clamped-wire current transformers. Therefore, the strand current can only be measured in an indirect way. Indirect current measuring method usually uses Rogowski coil [6, 7] and Hall sensors [8–11]. In [6], the paper describes the working principle of different types of electronic current transformers based on Rogowski coil. In [7], the authors measured the three-phase busbar current by Rogowski coil and analyzed the effect of the measurement positions on the results. However, the large size of the Rogowski coil makes it difficult to apply them to measure flat-wire winding currents. Hall sensors have become the research point due to their small size, high measurement accuracy and stability. In [8], this work presented a measurement method based on circular arrays of magnetic sensors. This sensor has a large structure and is only suitable for single conductor current measurement. In [9], this author presented a current detection method based on Hall sensors. The method is able to measure the current of a multiphase conductor of arbitrary cross-section. In [10], this paper used thermopile sensor array and Hall-effect sensor array to detect novel stator inter-turn fault. This method can only detect the status of motor operation. In [11], this paper proposed Hall sensors with linear array structure to measure the current in strands. But the size of the unit is too large to be applied to the end of the flat-wire motor. This paper proposed a current measuring method to solve the problem that only the total current of the formed-parallel coil can be detected instead of the each strand current. Firstly, the ELMF and the strand current of the formed-parallel coil are analyzed. Then, the relationship between the strand currents, the ELMF and the Hall output signal is derived. Finally, a current measurement platform based on Hall sensors is built. Take a 15 kW flat wire motor as an example. The reliability and accuracy of the measuring method are proved by comparing the results.

2 Analysis of the Strand Current and ELMF 2.1 Physical Model The physical models of the 15 kW flat-wire motor are shown in Fig. 1 and Fig. 2. The stator slot type of the research motor is open slot. The formed-parallel coil consists of 5 flat copper wires. One side of the coil is the twisted end and the other side is the welding end. The straight sections of the coil in the slot are the upper layer in one slot and lower layer in the other slot. The flat-wire motor parameters are in Table 1. 2.2 Numerical Model In order to simplify the calculation, some basic assumptions are as follows: a) Ignore the wedge, interlayer insulation and main insulation made of non-magnetic materials.

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(a) Stator.

(b) Rotor.

Fig. 1. The physical models of flat-wire motor.

Fig. 2. The physical model of formed-parallel coil.

Table 1. The parameters of the flat-wire motor. Parameter

Value

Parameter

Value

Rated power/kW

15

Outer diameter/mm

260

Rated current/A

64.35

Pitch

4

Rated speed/rpm

2550

Turns per slot

6

Slot number

36

Conductors per slot

30

b) Ignore the effect of neighboring slot coils on the calculation results. According to the above assumptions, a single coil and stator core are chosen as the solution domain to calculate the ELMF and current. The solution domain is shown in Fig. 3 (a). The coil is divided into eddy current region ζ1 . The other part is noneddy current region ζ2 . Based on the Biot-Savart law, the equation of the magnetic field ˙ s and the source current density J˙s is: intensity H ˚ ˙ Js × r ˙s = 1 H dv (1) 4π r3 V

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The mathematical model of the ζ1 and is: (2)

The mathematical model of the ζ2 is: ˙ s) ˙ = ∇ · (μH ∇ · (μ∇ ψ)

(3)

where V is the conductor volume, T˙ is the electric vector potential, ψ˙ is the magnetic scalar potential, ρ is the electrical resistivity, and μ is the magnetic permeability. Figure 3(a) shows the boundary conditions. The outer surfaces are S1 , S2 , and S3 . The boundary conditions are:

(4)

where n is the normal vector. 2.3 Calculation Result Due to the compact end space structure of the flat-wire motor, the target section as shown in Fig. 3 (b) is selected to analyze the ELMF under rated condition. The ELMF of the target section under rated condition is shown in Fig. 3 (b). In Fig. 3 (b) that the magnetic field intensity of strand 1−3 is larger than strand 4−5 due to the skin effect. According to the Ampere circuital law, the magnetic field distribution has influence on the current. The results of the current are in Table 2. Table 2. The results of the strand current. Strand number

RMS current/A

1

9.94

2

9.31

3

9.30

4

8.83

5

8.87

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(a) Solving domain.

(b) The magnetic field of the target section

Fig. 3. Solving domain and the magnetic field.

3 Relationship Between Current And ELMF 3.1 The Relationship Derivation Take a single strand as an example to solve for the magnetic field density generated by the strand at the point P. The strand current I is divided into m current elements as shown in Fig. 4 (a). According to the Biot-Savart law, the direction of the magnetic field density dB produced by either current element Ia is the same. The magnetic field density B at point P is:  μ0 θ2 Ia sin θ dθ μ0 Ia = (cos θ1 − cos θ2 ) (5) B = 4π θ1 r0 4π r0 The total magnetic field density B produced by the strand current I at point P is: m  μ0 Ia (cos θa1 − cos θa2 ) = MI B= 4π ra

(6)

a=1

where θa1 , θa2 are the angles from the point P to the ends of the current element I a respectively, r a is the distance from the point P to the current element I a , M is the magnetic flux density per unit ampere of the current source determined by the distance between measuring point and current source. From the Fig. 4 (a), the B of the calculation points is calculated in the case of several current sources is: ⎤⎡ ⎤ ⎡ ⎤ ⎡ M1,1 M1,2 M1,3 M1,4 M1,5 I1 B1 ⎢ B ⎥ ⎢ M M M M M ⎥⎢ I ⎥ ⎢ 2 ⎥ ⎢ 2,1 2,2 2,3 2,4 2,5 ⎥⎢ 2 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ (7) ⎢ B3 ⎥ = ⎢ M3,1 M3,2 M3,3 M3,4 M3,5 ⎥⎢ I3 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎣ B4 ⎦ ⎣ M4,1 M4,2 M4,3 M4,4 M4,5 ⎦⎣ I4 ⎦ B5 M5,1 M5,2 M5,3 M5,4 M5,5 I5 where M 1,1 is the magnetic flux density per ampere generated by the current of strand 1 at the measurement position P1 , and so on.

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3.2 The Result of ELMF The ELMF comparison of the FEM and analytic solution (AM) is shown in Fig. 4 (b). The two results have the same trend. The maximum relative error of them is –3.95%.

(a)

The point positions.

(b) The comparison of the results.

Fig. 4. The point positions and the comparison of the ELMF results.

4 Experimental Verification 4.1 Hall Sensors The Hall sensor used for the experiment is A1324. Its size is 1.5 mm × 4 mm × 3 mm. The specifications are in Table 3. The supply voltage of the sensor is 5 V. The Hall sensitivity is 5 mV/G. Its operating temperature range is −40 °C−150 °C. Table 3. The specifications of Hall sensor. Model

A1324

Supply voltage/V

5

Sensitivity/mV/G

5

Operating temperature /°C

−40–150

The equation between the Hall sensor signal and the leakage magnetic field is: E = kH B where k H is the Hall sensor sensitivity.

(8)

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So, the relationship between the output signal of all Hall sensors and the leakage magnetic field of all calculation points is: ⎤⎡ ⎤ ⎡ ⎤ ⎡ N1,1 N1,2 N1,3 N1,4 N1,5 I1 E1 ⎢ E ⎥ ⎢ N N N N N ⎥⎢ I ⎥ ⎢ 2 ⎥ ⎢ 2,1 2,2 2,3 2,4 2,5 ⎥⎢ 2 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ (9) ⎢ E3 ⎥ = ⎢ N3,1 N3,2 N3,3 N3,4 N3,5 ⎥⎢ I3 ⎥ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎣ E4 ⎦ ⎣ N4,1 N4,2 N4,3 N4,4 N4,5 ⎦⎣ I4 ⎦ E5 N5,1 N5,2 N5,3 N5,4 N5,5 I5 where N 1,1 = M 1,1 /k H , and so on. 4.2 Experimental Platform The experimental platform built based on the Hall sensor principle is shown in Fig. 5. The experimental objects are a stator core and a single formed-parallel coil. The power supply applies the current to a single formed-parallel coil, and the current level is monitored by the current transformer. The Hall sensors are mounted in the middle of the coil twisted end. The data acquisition card inputs the collected signal to the computer. The ELMF and current are obtained by reprocessing. 4.3 Experimental Result To verify the reliability of the measuring method, the experimental platform as shown in Fig. 5 is used for verification. The RMS value of the experimental current is 45.5 A, and the frequency is 170 Hz. The Hall sensor output voltage is in Fig. 6 (a). The experimental results of ELMF and currents are obtained from the experiment data. The comparison of leakage magnetic field is shown in Fig. 6 (b) and the comparison of strand currents is shown in Table 4. The maximum relative error between the experimental and simulation results of the ELMF is 3.46%. From Table 4, that the maximum relative error of the strand current is −7.46%.

Fig. 5. Experimental platform.

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(a) Hall sensor output voltage signal.

401

(b) The comparison of results.

Fig. 6. Experimental results.

Table 4. The comparison of strand currents. Strand number

Simulation result/A

Simulation Result/A

Relative error/%

1

9.94

9.70

−2.44

2

9.31

8.73

−6.24

3

9.30

9.69

4.17

4

8.83

8.17

−7.46

5

8.87

9.21

3.87

5 Conclusion This paper presented a measuring method to detect the strand current of formed-parallel coil based on Hall sensor without destroying the structure. The method is able to measure the formed-parallel coil current accurately. The conclusions are as follows. a) This measuring method is using Hall sensors to measure the ELMF at the end of the formed-parallel coil. By comparing the results, the maximum relative error of the strand current is –7.46%. This method is suitable to measure the strand current and the ELMF. b) Due to the complicated ELMF at the end of the formed-parallel coil, the experimental results are affected by the surrounding coils. Therefore, the middle position of the twisted end of the coil is the best measurement area. c) This method provides an experimental evaluation basis for analyzing the reasonableness of the strand current distribution and the design of the formed-parallel coil. Acknowledgments. This work was funded by National Natural Science Foundation of China under Grant 51977053.

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References 1. Sa, Z., Feng, Z., Jianbo, L., Yu, J., Liang, X.: Simplified engineering calculation of efficiency map of interior permanent magnet synchronous machines with hairpin windings considering PWM-induced harmonic losses. Trans. China Electrotechnical Soc. 37(22), 5687–5703 (2022). (in Chinese) 2. Wang, X., Yin, H., Yu, R.: Analytical calculation and parameter optimization of eddy current loss for coreless axial flux permanent magnet synchronous machine with multilayer flat wire winding. Trans. China Electrotechnical Soc. 3. Xie, Y., Li, H., Cai, W., He, Z.: Design and research of double layer internal permanent magnet synchronous motor with hairpin winding. Electr. Mach. Control 26(04), 47–56 (2022). (in Chinese) 4. Ishigami, T., Tanaka, Y., Homma, H.: Motor stator with thick rectangular wire lap winding for HEVs. IEEE Trans. Ind. Appl. 51(4), 2917–2923 (2015) 5. Liu, J., Liang, Y., Yang, P., Wang, W., Zhao, F., Xu, K.: Analysis on circulating current loss in the formed winding of permanent magnet synchronous motors. IEEE Access 9, 113403– 113414 (2021) 6. Di, Z., Sun, T.: Development status and application prospect of electronic current transformer. Instrum. Technol. 361(05), 37–40+44 (2019). (in Chinese) 7. Wang, P., Zhang, G., Zhu, X., Luo, C.: Planar rogowski coil current transducer used for three-phase plate-form busbars. In: 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007, pp. 1–4. Warsaw, Poland (2007) 8. Weiss, R., Itzke, A., Reitenspieß, J., Hoffmann, I., Weigel, R.: A novel closed loop current sensor based on a circular array of magnetic field sensors. IEEE Sens. J. 19(7), 2517–2524 (2019) 9. D’Antona, G., Di Rienzo, L., Ottoboni, R., Manara, A.: Processing magnetic sensor array data for AC current measurement in multiconductor systems. IEEE Trans. Instrum. Meas. 50(5), 1289–1295 (2001) 10. Kumar, P.S., Xie, L., Halick, M.S.M., Vaiyapuri, V.: Stator end-winding thermal and magnetic sensor arrays for online stator inter-turn fault detection. IEEE Sens. J. 21(4), 5312–5321 (2021) 11. Liang, Y., Wan, Y., Wang, C., Bian, X., Wang, D.: Study on measuring method of stator transposed strand current in AC generator. Chin. J. Sci. Instrum. 39(4), 161–169 (2018)

Research on Low and High Voltage Interlocking Fault Ride-Through Control Strategy for Doubly-Fed Wind Turbines Darui Zhu(B) , Jiakang Cheng, Jie Chen, and Jiandong Duan School of Electricial Engineering, Xi’an University of Technology, Xi’an 710048, Shanxi, China [email protected]

Abstract. In recent years, after the voltage at the grid-connected point drops due to the failure of the wind turbine, there are frequent cascading failures caused by the sudden rise of voltage due to excessive reactive power compensation. In order to enable wind turbines to provide suitable power support in case of grid failure. The wind turbines connected to the grid are required to have LVRT ability and HVRT ability according to the national standard. In this paper, a low-high voltage interlocking FRT strategy for reactive power input control of RSC and GSC by a DFIG is used. The limit values of reactive currents issued by RSC and GSC when chain faults occur and the allocation principles are discussed. It is verified through simulation that the continuous low and high voltage ride-through ability of DFIG during operation can be effectively ensured, which in turn ensures the stable operation of DFIG. Keywords: DFIG · low-high voltage interlocking faults · reactive power support · coordinated control

1 Introduction Under the trend of rapid global economic development, the wind power market has also been fully supported, and the global capacity for mounted wind power has expanded rapidly [1, 2]. As the installed capacity of WTGs continues to increase, the operational requirements for WTGs connected to the grid are becoming more and more stringent. Wind farms not only need to provide frequency and voltage regulation similar to that of conventional power plants, but also need to provide some degree of low-voltage operation capability for WTGs. DFIG have become a mainstream model in the wind energy market because of many advantages, such as low converter capacity, large speed regulation range, active-reactive decoupling control, and low cost [3]. At present, a number of large-scale wind turbine off-grid accidents have occurred in China, which have adversely affected people’s lives and the smooth operation of the power system as well as the reliable power supply [4]. In view of meeting the requirements of the national grid for grid-connected WTGs to be able to provide reactive power to help with voltage restoration in the event of a fault, it is necessary to ensure that they are capable of LVRT and HVRT. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 403–411, 2024. https://doi.org/10.1007/978-981-97-0877-2_42

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For LVRT, a lot of research has been carried out at home and abroad, and the control technology of LVRT has been relatively mature. Literature [5] attempts to utilize the reactive power adjustment ability of RSC and GSC with a view to injecting reactive power into the grid during low voltage crossing for voltage recovery. Literature [6] used the dynamic variation of stator equivalent excitation current as a rotor voltage compensation term to improve the transient response of DFIG in HVRT. Literature [7, 8] analyzed the dynamic process of GSC under voltage surge and proposed the DC link voltage optimization control strategy of GSC and GSC reactive power optimization control strategy, respectively. Literature [9] proposed a collaborative control for DFIG, and the LVRT performance of the proposed control strategy was verified by simulation. Literature [10] proposes cooperative control algorithms, system stability constraints, and optimization methods of control parameters that can improve the high/low voltage fault ride-through capability of DFIG. Literature [11] reveals the essential difference between the transient characteristics of chained and single faults. On this basis, a low and high voltage chained fault ride-through scheme based on rotor transient induced electromotive force suppression is given. Literature [12] proposes a LVRT method consisting of virtual inertia control and a modified GSC method. It provides frequency support to the grid through synthesized inertia while realizing fault crossing ability according to the grid code requirements. Although, the research on low and high voltage interlocking fault crossing control strategies for DFIG has received wide attention. However, all of the above are researches on the overcurrent and overvoltage phenomena caused by a single voltage dip or rise, and do not consider the research on the chain problem of voltage rise triggered by excess reactive power compensation due to voltage dips. Therefore, further research and improvement of the low and high voltage chain fault crossing control strategy of DFIG are needed for better suppression of overcurrent and overvoltage. Therefore, the reactive current extremes of RSC and GSC is derived according to the formula. The reactive current distribution schemes of GSC and RSC are also determined. Based on this, a collaborative control strategy of GSC and RSC is proposed to restrain rotor overcurrent and DC bus overvoltage, so as to augment the operation ability of DFIG system without off-grid crossing.

2 Reactive Power Regulation Capability of Doubly-Fed Turbines During Low and High Voltage Interlocking Faults 2.1 DFIG Structure In view to better analyze the distribution rules of reactive power and the current magnitude constraints, it is necessary to construct the structure diagrams of RSC and GSC, and the DFIG network infrastructure and the power stream are shown in Fig. 1. Among them, Ps and Qs are the active power and reactive power output of stator side; Pr and Qr are the active power and reactive power input of RSC; Pg and Qg are the active power and reactive power input of GSC; and Pt and Qt are the total active power and reactive power output of DFIG. It can be shown that the reactive power requirement during a fault condition to be supported by the reactive power contribution from the RSC and GSC.

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Fig. 1. DFIG system structure diagram

During normal operation, the magnitude of the reactive power referred to the DFIG is usually based on system demand and operating conditions and can be specifically controlled and adjusted. Typically, the DFIG is operated at a power factor of 1 to maximize system power output and efficiency. The ability of RSC and GSC reactive power regulation can be utilized during low and high voltage interlocking faults to meet the grid regulation requirements for reactive power support. 2.2 GSC Reactive Power Regulation Capability By changing the control strategy and parameter settings of the GSC, it can be made to supply an appropriate current to meet the grid-connected conditions. The GSC can actively emit reactive power when extra reactive power is needed in the larger grid, and it can actively absorb reactive power when there is excess reactive power in the larger grid. By regulating the output of reactive power, the GSC helps to maintain a stable voltage level in the grid. The following correlation is observed between the current values of the GSC and the GSC current threshold: 2 2 + Igd ≤ Ig2 max Ig2 = Igq

(1)

Using grid voltage-directed vector control as the control of the GSC, the following correlation is observed between the power of the network side output and the netword side dq-axis current:    Pg = − 23 ugd igd + ugq igq  = − 23 Us igd (2) Qg = 23 ugd igd + ugq igq = 23 Us igq Associating (1) and (2), the reactive current issuing and absorbing limits of GSC can be obtained, i.e.: ⎧  2P ⎨I = I2 − ( 3Ugs )2 gq_out  g max (3) 2P ⎩I = − I2 − ( g )2 gq_in

g max

3Us

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2.3 RSC Reactive Power Regulation Capability The reactive power adjustment ability of the RSC is critical to maintaining network stability and balance. In the occasion of a network fault, the RSC can respond quickly to keep the grid voltage and frequency within acceptable limits. The RSC injects or absorbs the required reactive current through rational regulation to meet the reactive power demand of the network. The following correlation is observed between the RSC current and the RSC current threshold: 2 2 + Ird ≤ Ir2max Ir2 = Irq

(4)

Vector control based on stator voltage orientation is used as the basic control strategy for the RSC. The following correlation is observed between the power output from the stator side and the stator and rotor currents: Ps = 23 usd isd = 23 Us LLms ird

2  (5) U Qs = − 23 usd isq = 23 ωe sLs + ULs Ls m irq After expressing Eq. (5) in the form of a sum, substituting into Eq. (4) yields: (

2Ls 2Ls Us 2 Ps )2 + ( Qs − ) ≤ Ir2max 3Lm Us 3Lm Us ω1 Lm

(6)

Substituting the Qs = − 23 usd isq in Eqs. (5) into (6) yields the stator-side reactive current emitting limit and absorbing limit, viz: ⎧

2 ⎪ 2Ps ⎪ ⎨ Isq_out = ( LLm Irmax )2 − 3U − ωUe Lsm s s

(7)

2 ⎪ ⎪ ⎩ Isq_in = − ( Lm Irmax )2 − 2Ps − Us Ls 3Us ωe Lm Associative Eqs. (3) and (7) give the total reactive current emitted and absorbed limit of the turbine, i.e.:  Iq_out =Isq_out +Igq_out (8) Iq_in =Isq_in +Igq_in The correlation is observed between the reference value of reactive current of RSC and the reference value of reactive current on the stator side can be introduced according to Eq. (8), i.e.: Irq_ref = −

Us Lm − Isq_ref ω1 Lm Ls

(9)

Both RSC and GSC have reactive power adjustment ability, so both can furnish reactive power to the electric network. When RSC gives priority to provide reactive power, it makes the q-axis current increase. Since the RSC prioritizes the reactive power supply, it causes the q-axis current to increase, which in consequence leads to the rotor current to surpass the threshold value making the system more unstable. So, in this paper, the GSC is made to prioritize the supply of reactive power and when it supplied by the GSC is saturated, then it is supplied through the RSC.

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3 Coordinated Control Strategy of Converter Considering Reactive Current Support 3.1 Distribution Scheme for Reactive Current The voltage of the network point is first judged. When the voltage at the grid point is less than 0.9 p.u. (the lower limit of normal floating), it is necessary to provide reactive current to the network to make it rise; when the voltage at the network point is greater than 1.1 p.u. (the upper limit of normal floating), it is necessary to absorb reactive current from the network to make it fall. The wind farm test requirements have specified that the wind farm should provide dynamic reactive current to support the grid voltage at LVRT and HVRT. The reactive current magnitude (standardized value) is respectively:  ≥ K1 (0.9 − Us ), 0.2 ≤ Us ≤ 0.9 I (10) Iref = LVRT IHVRT ≥ K2 (Us − 1.1), 1.1 ≤ Us ≤ 1.3 The required reactive current reference (Iref ) is obtained by calculation and then the dq-axis component of the GSC current reference (Igd_ref and Igq_ref ) is determined. Specify the reactive current by judging the Us , and the reactive current allocation scheme is shown in Fig. 2.

Fig. 2. Flow chart of reactive current distribution

3.2 GSC Reactive Power Support Mode The reactive power control mode of GSC is shown in Fig. 3. During the steady state period, the GSC operates at unit power factor and the reactive current is 0. During the fault phase, it is necessary to switch to the reactive support mode to obtain the value of the reactive current to be emitted by the GSC according to the reactive current allocation scheme. This is because there may be DC bus voltage fluctuations leading to an increase in Igd_ref . A limiter is usually used to limit the reactive current in the q-axis to ensure that the GSC can provide sufficient reactive power to guarantee the reliable operation of the grid.

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Fig. 3. Reactive support mode of GSC

3.3 Distribution Scheme for Reactive Current The control mode on the rotor side is shown in Fig. 4. The RSC uses a stator voltage targeted vector control strategy as a basis. When the reactive current provided by the GSC does not reach the upper limit, the RSC operates in the conventional control mode. When the reactive current provided by the GSC reaches the upper limit, the remaining reactive current is provided through the RSC. That is, it runs in the collaborative control strategy mentioned in this paper.

Fig. 4. Reactive support mode of RSC

4 Simulation Analysis A 3MW DFIG is built in Matlab/Simulink simulation platform for simulation verification. The parameters are shown in the following Table 1. Table 1. DFIG parameters Parameter

Value

Parameter

Value

Rated power

3

High Through Reactive Current Coefficient

2

Stator resistance/p.u

0.013

Rated Voltage/V

690

Rotor resistance/p.u

0.024

DC side voltage/V

1200 (continued)

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Table 1. (continued) Parameter

Value

Parameter

Value

Magnetization/p.u

3.99

Stator leakage reactance/p.u

0.239

Low-throughput reactive current factor

1

Rotor leakage resistance/p.u

0.231

Maximum rotor current

1.5

Maximum value of network side current

0.8

Setting at t = 1 s, the occurrence of fault makes the voltage of the grid voltage fall from 1 p.u. to 0.7 p.u., with a duration of 200 ms, and after the fault is removed, it triggers the phenomenon of voltage surge, and the voltage is lifted to 1.2 p.u., which lasts for 200 ms and then restores to the normal value.

(a) Grid-side point voltage

(b) Grid-side active reactive power

(c) DC bus voltage

(d) Reactive power

Fig. 5. Simulation waveforms

Figure 5 shows the simulated waveform of the coordinated control of GSC and RSC proposed in this paper. When a low-high voltage interlocking crossing fault occurs, the GSC and RSC are switched to reactive power support mode. In the voltage dip phase, the GSC first supplies 0.3 p.u. of reactive power to the grid from (b), and according to (f) about 0.4 p.u. of total reactive power is emitted, so the rest of the reactive power is supplied by the RSC. During the voltage lift, the grid flows about 0.1 p.u. and 0.3 p.u. of reactive power from the GSC and RSC to support the rapid recovery of the large grid. The coordinated control of GSC and RSC allows continuous operation without disconnection from the grid during interlocking faults, ensuring the safe operation of the turbine as well as the converter.

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5 Conclusion The DFIG structure is briefly analyzed. The allocation principle of q-axis current reference value of RSC and GSC is deduced and analyzed according to the formula, on the basis of which a collaborative control strategy is raised in which RSC and GSC cooperate with each other for reasonable reactive power allocation, and the effectiveness of the control strategy proposed in this paper is substantiated according to the simulation results. The control strategy can improve the voltage and current overrun problem. However, it is only for the chain fault under mild voltage dips, and when the voltage dips deeply, it is necessary to consider adding the improvement of the hardware part. Acknowledgments. This work was funded by Natural Science Basic Research Plan in Shaanxi Province of China (2023-JC-YB-359), Postdoctoral Research Foundation of China (2020M683685XB) and National Natural Science Foundation of China (U2106218), and by Science and Technology Project of State Grid Shaanxi Electric Power Company Limited 5226KY220013.

References 1. Lu, Z., Li, W., Xie, B., et al.: Study on China’s wind power development path-based on the target for 2030. Renew. Sustain. Energy Rev. 51, 197–208 (2015) 2. Sun, S., Liu, F., Xue, S., et al.: Review on wind power development in China: current situation and improvement strategies to realize future development. Renew. Sustain. Energy Rev. 45, 589–599 (2015) 3. Li, W.: Research on high-voltage ride-through of doubly-fed wind turbine with normal and stator winding turn-to-turn short-circuit faults. Micro motor 53(05), 67–72+99 (2020) (in Chinese) 4. Xu, H., Zhang, W., Chen, J., et al.: High-voltage ride-through control strategy for doublyfed wind turbines considering dynamic reactive power support. Chin. J. Electr. Eng. 33(36), 112–119+16 (2013) (in Chinese) 5. Li, H., Fu, B., Yang, C., et al.: Reactive current allocation and control strategies improvement of low voltage ride though for doubly fed induction wind turbine generation system. In: Proceedings of the CSEE, vol. 32, no. 22, pp. 24–31 (2012) (in Chinese) 6. Sun, L., Wang, Y.: Analysis and performance evaluation for transient whole process of improved control strategy for doubly-fed induction generator crossed by high voltage ride through. High Voltage Eng. 45(2), 593–599 (2019) (in Chinese) 7. Zheng, Z., Geng, H., Yang, G.: High voltage ride-through control strategy of grid-connected inverter for renewable energy systems. In: Proceedings of the CSEE, vol. 35, no. (6), pp. 1463– 1472 (2015) (in Chinese) 8. Xu, H., Zhang, W., Chen, J., et al.: A high-voltage ride-through control strategy for DFIG base wind turbines considering dynamic reactive power support. In: Proceedings of the CSEE, vol. 33, no. (36), pp. 112–119 (2013) (in Chinese) 9. de Nguimfack–Ndongmo, J.D., Kenné, G., Nfah, E.M.: Design of nonlinear synergetic controller for transient stabilization enhancement of DFIG in multimachine wind power systems. Energy Procedia 93, 125–132 (2016). https://doi.org/10.1016/j.egypro.2016.07.160 10. Zhen, Y., Su, N., Li, M.: Cooperative control strategy of doubly-fed wind turbine applicable to high/low voltage ride-through and its stabilization technology. Grid Technol. 45(01), 39–49 (2020). https://doi.org/10.13335/j.1000-3673.pst.0199a (in Chinese)

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11. Jiang, H., Wang, S., Li, X., et al.: Accurate analysis of transient characteristics and ridethrough scheme for doubly-fed asynchronous wind turbine with low and high voltage chain faults. Grid Technol. 45(10), 4076–4083 (2020). https://doi.org/10.13335/j.1000-3673.pst. 2137 (in Chinese) 12. Verma, P., Seethalekshmi, K., Dwivedi, B.: A cooperative approach of frequency regulation through virtual inertia control and enhancement of low voltage ride-through DFIG-base wind farm. J. Mod. Power Syst. Clean Energy 10(6), 1519–1530 (2022)

A Hybrid Multi-objective Optimization Algorithm Based on NSGA-II and MOGWO and Its Application to Optimal Design of Electromagnetic Devices Xinyu Wang and Yilun Li(B) College of Information Science and Technology, Donghua University, Shanghai 201620, China [email protected], [email protected]

Abstract. Due to the increasingly fierce competition in science, technology and economy, optimization algorithms play a crucial role in the design of electromagnetic devices. At present, optimization methods based on evolutionary algorithms are widely used in social development, but many algorithms still reflect the problems of insufficient global search ability, easy to fall into local optimal solutions, and insufficient diversity of solutions when dealing with objective functions with multi-modal landscape, discontinuities and other characteristics. A new hybrid multi-objective optimization algorithm is proposed to solve the above problem, which is based on Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-objective Grey Wolf Optimizer (MOGWO) algorithm. In this new optimization algorithm, NSGA-II is chosen as the core, and leader decision-making mechanism of MOGWO and other techniques are adopted, which improves the convergence performance of the hybrid algorithm, and enhances the diversity of the Pareto solutions. Performance testing of the new hybrid algorithm for convergence and diversity, and it is applied to the optimal design problem of electromagnetic devices. The results obtained demonstrate that the algorithm has correctness and effectiveness. Keywords: Multi-objective optimization · Non-dominated Sorting Genetic Algorithms · Multi-Objective Grey Wolf Optimizer · Superconducting Magnetic Energy Storage

1 Introduction In the field of electromagnetic devices design optimization, many factors need to be considered, in addition to the performance factors such as the structure, materials and some specific parameters of the electromagnetic device, the cost factor of the devices also needs to be considered. There is a non-linear relationship between device performance and cost, which restricts and conflicts with each other. You cannot pursue high performance regardless of cost, nor can you pursue low cost regardless of device performance. This demonstrates that electromagnetic device optimization problems are generally complex multi-objective optimization (MOO) problems. Nowadays, MOO algorithms are © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 412–423, 2024. https://doi.org/10.1007/978-981-97-0877-2_43

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widely used in the optimal design of electromagnetic devices. For example, in the device design of overload magnetic field generator [1], NSGA-II was used as the optimization design kernel to reduce the cost and the difficulty of recycling; In order to improve calculation accuracy and optimization efficiency of the air-gap magnetic field analysis of the permanent magnet synchronous motor used in the electric vehicle, Yuansheng An et al. [2] applied NSGA-II to optimize the structural parameters of the prototype of the motor; and for purpose of individual requirements of substation equipment parameters and performance optimization of substation equipment, Hongjiang Wang et al. [3] used a hybrid genetic algorithm to optimize the structural design of substation equipment. NSGA-II [4], as a widely applied MOO algorithm, has good global search ability, but its convergence accuracy is unsatisfied when facing complex high-dimensional nonlinear MOO problems, and the uniformity of the distribution of Pareto solutions needs to be improved; MOGWO algorithm [5], which possesses strong local search ability, have issues such as slow convergence and prone to fall into local optimal solutions [6]. A new hybrid MOO algorithm based on NSGA-II and MOGWO is proposed, which further improves the convergence and diversity while ensuring the advantages of the original NSGA-II algorithm by introducing the leader update mechanism of MOGWO. Typical test functions are used to verify the convergence and diversity performance of the proposed algorithm, and it is applied to the optimal design of a superconducting energy storage device.

2 Multi-objective Optimization Problems A multi-objective optimization (MOO) problem involves the simultaneous optimization of multiple objective functions. Generally, a MOO problem consists of n decision variables and m objective variables [7]. min y = F(x) = [f1 (x), f2 (x), . . . , fm (x)]T  Si (x) ≤ 0, i = 1, 2, . . . , p s.t. Tj (x) = 0, j = 1, 2, . . . , q

(1)

where x = (x1 , x2 , . . . , xn ) ∈ X ⊂ Rn is an n-dimensional decision vector and y = (y1 , y2 , . . . , ym ) ∈ Y ⊂ Rm is an m-dimensional objective function vector. F(x) defines m mapping functions from the decision space X to the objective function space Y; p inequality constraints represented by Si (x); and q equality constraints represented by Tj (x). Definition 1. Feasible solutions and the set of feasible solutions: an x is said to be a feasible solution if and only if it satisfies all the constraints in Eq. (1), and X f is said to be the set of feasible solutions if and only if all x ∈ X f ⊂ Rn are all feasible solutions. Definition 2. Pareto domination: for any two decision vectors xα , xβ ∈ X f , the corresponding function values are f (xα ) and f (xβ ) in the space of objective functions, and are labelled as xα xβ if xα dominates xβ , denoted by the formula:    fi (xα ) ≤ fi xβ , ∀i ∈ {1, 2, . . . , m} (2) fj (xα ) < fj xβ , ∃j ∈ {1, 2, . . . , m}

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Definition 3. Pareto optimal solution: if the decision vector xa is a Pareto optimal solution, it means that there is no other decision vector xb in the decision variable space X f that can dominate xa . In simpler terms, xa is the best solution and cannot be outperformed by any other feasible solution. The set of dominating solutions is referred to as PS, which comprises all the Pareto optimal solutions. PS includes all the solutions that are not dominated by any other feasible solution in the decision variable space.    (3) PS = xa ∈ X f ∀xb ∈ X f , xa ≺ xb Definition 4. Pareto Frontier (PF): the set consisting of the objective function of the Pareto dominated solution set is called the Pareto Frontier. PF = { F(x)|x ∈ PS}

(4)

3 A New Hybrid MOO Algorithm 3.1 NSGA-II NSGA-II [4] is a MOO algorithm which is designed with the basic framework of genetic algorithm, and the iteration of the algorithm mimics the evolutionary process in nature. The algorithm used non-dominated sorting method to reduce complexity; and by adopting the elite retention technique, the best individuals in the population are reserved to improve the robustness and convergence speed of the algorithm [8]; and to avoid the algorithm from falling into the local optimal solution by proposing the concept of crowding distance to maintain the diversity of the population. However, its convergence accuracy and the distribution uniformity of the population still need to be improved. Figure 1 shows the basic flowchart of NSGA-II, population is firstly initialized to generate N individuals. Non-dominated sorting and crowding distance calculation are performed to determine the quality of individuals in the population; next, appropriate individuals are chosen from the initial parent population for crossover and mutation to generate N offspring population individuals; then, the parent and offspring populations are combined to a new population, non-dominated sorting and crowding distance calculation are carried out to screen out the same number of good individuals as parent populations to form the next generation; and in the end, termination conditions are judged to determine whether the algorithm would be stopped. If the conditions are satisfied, the population of the last generation will be output as the final optimization result. 3.2 MOGWO MOGWO is a meta-heuristic algorithm designed for multi-objective optimization problems. It is based on the single-objective grey wolf algorithm and takes inspiration from the hunting behavior of wolves to find optimal solutions. In MOGWO, the social hierarchy of wolves is divided into four classes. The best solution obtained so far is referred to as the alpha (α) wolf, while the second and third best solutions are known as the beta (β) wolf and delta (δ) wolf, respectively. These three solutions are considered leaders

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Fig. 1. Flowchart of NSGA-II.

within the algorithm. The remaining solutions are referred to as omega (ω) wolves. The optimization process in MOGWO involves updating the positions of the ω wolves by utilizing information from the positions of the leaders. This mimics the way in which wolves surround their prey and attack it collectively. In the wolf surrounding phase, the algorithm simulates surrounding behavior of wolves during hunting by proposing the following formula:    D = C · X p (t) − X(t) (5) X (t + 1) = X p (t) − A · D where D is the distance between the grey wolf and the prey, A and C are two different vector coefficients, t is the current iteration number, X p is the prey position and X is the grey wolf position,  A = 2a · r1 − a (6) C = 2 · r2 where the value of a is linearly reduced from 2 to 0 depending on the number of iterations, and r1 and r2 are two random values between 0 and 1. During the wolf hunting, the position of each grey wolf is continually updated by the following equation, looking for better solutions to the problem: ⎧ ⎨ Da = |C1 · X a − X| (7) D = |C2 · X b − X| ⎩ b Dc = |C3 · X c − X| ⎧ ⎨ X α = X a − A1 · (Da ) (8) X = X b − A2 · (Db ) ⎩ β X δ = X c − A3 · (Dc )

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X(t + 1) = (X α + X β + X δ )/3

(9)

Parameter A ensures the global search ability of the grey wolf algorithm; when |A| > 1, the grey wolf will move away from the prey and conduct a wide search; when |A| < 1, the grey wolf will move closer to the prey and attack. Parameter C represents the random weight factor that influences how the grey wolf’s position affects the prey’s position. This parameter aids in preventing the algorithm from being trapped in a local optimal solution, thereby ensuring the diversity of the algorithm’s results. 3.3 Hybrid Algorithm The proposed hybrid algorithm is illustrated in Fig. 2. It combines the NSGA-II framework with the MOGWO algorithm to enhance its performance. In this hybrid algorithm, NSGA-II is chosen as the main framework for optimization. The MOGWO algorithm is introduced as a complementary component. During each iteration of the algorithm, the elite solution set method is employed. This means that the optimal solution obtained in each iteration is stored in the elite solution set. The elite solution set serves two purposes: firstly, it acts as an evolutionary population for the MOGWO algorithm, and secondly, it preserves the non-dominated solutions that will be considered as the final optimization results of the hybrid algorithm. The hybrid algorithm adopts a search strategy that leverages the strengths of both NSGA-II and MOGWO. NSGA-II focuses on exploring the entire search space to find optimal solutions, ensuring good global search ability and diversity in the obtained Pareto solutions. On the other hand, the MOGWO algorithm selects three leaders from the elite solution set and conducts a local search near these leaders. This approach improves the algorithm’s search accuracy and strengthens its local search ability. By combining these two algorithms, the hybrid algorithm aims to achieve a balance between global exploration and local exploitation, resulting in improved optimization performance and the discovery of high-quality solutions in multi-objective optimization problems. 3.4 Performance Testing Test Function The performance of hybrid algorithm is evaluated using the ZDT series of classical test functions, Namely ZDT1, ZDT2, ZDT3, ZDT4, ZDT6. The results obtained from the hybrid algorithm are then compared with two well-known algorithms. Performance Indicators The performance metrics of MOO algorithms include three metrics, γ (convergence metric),  (diversity metric) [4] to evaluate convergence, diversity, and Non-dominated Individual Ratio (NDR), NDR [9] to determine the quality of the resulting PF. The convergence metric γ is used to quantify the distance between the Pareto front obtained by the algorithm and the set of true Pareto optimal solutions. A smaller value of γ indicates a higher level of convergence. NQ dm (10) γ = m=1 NQ

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p by

nd

Fig. 2. Flowchart of proposed hybrid algorithm.

where dm is the closest distance of the ith non-dominated solution of the algorithm to the true PF. NQ denotes the number of PF solution sets in the algorithm. The diversity metric  is used to measure the uniformity of the solution set obtained by the algorithm across the entire objective space. It serves as an indicator of the algorithm’s diversity, where a smaller value of  signifies a more diverse solution set.  NQ −1   dr + ds + n=1 dn − d  (11) = dr + ds + (NQ − 1)d where dr and ds are the distances between the endpoints of the algorithm obtained Pareto front and the endpoints of the true Pareto front, dn is the Euclidean distance between two neighbouring points in the non-dominated solution set obtained by the algorithm, and d is the mean of the distances between neighbouring points.

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The NDR metric serves as a comparative measure to assess the quality of solutions obtained by multiple algorithms. It quantifies the number of non-dominated solutions in a set, with a higher NDR indicating a greater number of non-dominated solutions and thus higher quality of the solution set produced by the algorithm. ⎧ 1  ratio(A) = |PS| ⎪ x∈A |x ∈ PS| ⎪ ⎪ ⎨ ratio(B) = 1  |x ∈ PS| |PS| x∈B (12) 1 ⎪ ratio(C) = |PS| ⎪ x∈C |x ∈ PS| ⎪  ⎩ 1 ratio(D) = |PS| x∈D |x ∈ PS| where A, B, C and D are four Pareto solution sets obtained by different algorithms in some MOO problems, and PS is the set of non-dominated solutions consisting of A, B, C and D. Test Results The performance of the hybrid algorithm is validated by conducting tests using standard test function problems. The results obtained from these tests are used to compare the PF obtained by the hybrid algorithm with those obtained by NSGA-II and MOGWO. The comparison is presented in Fig. 3. From the optimization results of the hybrid algorithm for different test function problems shown in Fig. 3, observing all test function problems, the hybrid algorithm yields result very close to the true PF. This denotes a high convergence rate for the hybrid algorithm across all test function problems. In comparison, NSGA-II algorithm is unstable in ZDT4, which is a multi-peak function that is highly easy to local convergence, and MOGWO is also unable to find an optimal solution, but the overall performance of the hybrid algorithm is better that the two counterparts, which demonstrates that the hybrid algorithm has a strong global search ability. As seen in Fig. 3, the optimization outcomes of the hybrid algorithm for various test function problems are remarkably close to the actual PF. This denotes a high convergence rate for the hybrid algorithm across all test function problems. Comparatively, the NSGAII algorithm exhibits instability in ZDT4, a multi-peak function known for its ease of local convergence, and MOGWO also fails to find an optimal solution. However, the overall performance of the hybrid algorithm surpasses these two, confirming the hybrid algorithm’s superior global search capability. The hybrid algorithm, NSGA-II, and MOGWO are each independently run 20 times. From these runs, the mean value E(γ ) and standard deviation σ (γ ) of the convergence metric for each algorithm are calculated. Additionally, the mean value E() and standard deviation σ () of the diversity metric are also calculated. From Table 1, it can be seen that for the five test functions with different characteristics, the convergence metric of hybrid Algorithm is significantly better than that of NSGA-II and MOGWO, indicating that the algorithm has better convergence accuracy, better convergence stability. From Table 2, it can be seen that E() of the hybrid algorithm is slightly worse than MOGWO in ZDT3 and ZDT6, and σ () does not perform as well as MOGWO in ZDT1, the hybrid algorithm does not perform as well as NSGA-II in ZDT2 and ZDT4. However, as a whole, the hybrid algorithm is better in terms of diversity, and yields a more uniform distribution of the PF.

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(a)

419

(b)

(c)

(d)

(e)

Fig. 3. Comparison of PF obtained by different algorithms (a) ZDT1, (b) ZDT2, (c) ZDT3, (d) ZDT4, (e) ZDT6.

4 Optimal Design of Superconducting Magnetic Energy Storage Device Superconducting Magnetic Energy Storage (SMES) [10] optimization problem is a MOO design problem who optimizes the design of the parameters of the device to obtain the required stored energy at a certain stray magnetic field. The structure of the device is shown in Fig. 4, two concentric coils are operated under superconducting conditions with opposite current. The optimization of the device requires that the magnetic energy stored in the magnetic field it creates is as close as possible to the size of the standard energy storage, while limiting the size of their stray magnetic field.

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f (·)

Hybrid

NSGA-II

MOGWO

E(γ )

σ (γ )

E(γ )

σ (γ )

E(γ )

σ (γ )

ZDT1

0.00006

0.00003

0.003

0.003

0.00014

0.00006

ZDT2

0.00005

0.00001

0.021

0.033

0.00006

0.00002

ZDT3

0.00018

0.00002

0.006

0.010

0.00023

0.00004

ZDT4

0.00296

0.00802

2.715

1.159

-

-

ZDT6

0.026

0.052

0.151

0.062

0.032

0.030

Table 2. Comparison of statistical diversity metric of different algorithms. f (·)

Hybrid

NSGA-II

MOGWO

E()

σ ()

E()

σ ()

E()

σ ()

ZDT1

0.487

0.076

0.796

0.022

0.710

0.032

ZDT2

0.460

0.099

0.797

0.022

0.700

0.031

ZDT3

0.933

0.024

0.930

0.045

0.853

0.049

ZDT4

0.692

0.029

0.510

0.316

-

-

ZDT6

0.690

0.029

0.394

0.170

0.617

0.050

Moreover, two constraints of the device need to be satisfied, one is the physical condition of the industrial superconducting material, i.e., the given current density and the maximum flux density on the coils must not violate this condition, which is expressed in the following equation. 6.4 ∗ |Bm | + |J | ≤ 54

(13)

where Bm is the maximum flux density on the coils and J is the current density flowing through the coil. The second constraint is coil position constraint, the positions of the coils cannot overlap each other in practical applications, which requires that. R1 +

d1 d2 ≤ R2 − 2 2

(14)

where R1 and R2 are the radius of the coil, d1 and d2 are the thickness of the coil. The variables of the three-variable optimization problem are the height h2 , radius R2 and thickness d2 of the outer coil, and the specific parameters of the three-variable optimization design are shown in Table 3. The fixed parameter values are inner coil height h1 = 1.6m, radius R1 = 2.0m, thickness d1 = 0.27m and current densities J1 = 22.5A/mm2 for the inner coil and J2 = −22.5A/mm2 for the outer coil.

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d1 d2 1

J1

J2

2

1 2

Fig. 4. Structure diagram of superconducting magnetic energy storage device. Table 3. Three-variable optimization parameter design table. R2 (m)

h2 /2(m)

d2 (m)

Maximum limit

2.6

0.204

0.1

Minimum limit

3.4

1.1

0.4

The mathematical model of the SMES three-variable optimization problem is given in the following equation: ⎧  2 ⎨ f1 R2 , h2 , d2 = Bstray 2 2 B norm

 min ⎩ f R , h2 , d = |E−Eref | (15) 2

2

2

2

Eref

s.t.|Bm | ≤ 4.92T 2 where Eref = 180MJ is the standard stored energy, Bnorm = 9μT is standard the stray field, and E, Bstray are the actual stray field energy around the device and the actual energy stored by the device, respectively. The above model is computed using FEA software and the proposed hybrid algorithm is applied to solve the above problem and then NSGA-II and MOGWO are run separately for comparison. The hybrid algorithm’s initial population is set with 20 individuals and the iteration count is capped at 50. On the other hand, for the rest of the algorithms, while the initial population also consists of 20 individuals, the number of iterations is set to 100. The Pareto solutions obtained by the three algorithms for the optimization problem are compared in Fig. 5. To be noted, the green markers in Fig. 5 are the typical solutions (minF = f1 + f2 ) obtained by different algorithms. In addition, the NDR metric of the Pareto solutions of NSGA-II, MOGWO and the hybrid algorithm in Fig. 5 are 13.8%, 34.5% and 51.7%, respectively, the hybrid algorithm has the highest NDR metric, which means its solution quality is the best. The typical solutions in Table 4 further demonstrate that the hybrid algorithm achieves better overall performance and better optimization accuracy when solving the

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Fig. 5. Comparison results of three-variable optimization for superconducting magnetic energy storage devices.

SMES three-variable optimization problem. The actual energy store corresponding to the typical result of the hybrid algorithm optimization is 179.51 MJ, which is only 0.49 MJ short of the required 180 MJ. It indicates that after the optimization of the structure by the hybrid algorithm, the device meets the requirement that the energy storage should be as close as possible to 180 MJ. Table 4. Comparison of typical results of three variable optimization. NSGA-II

MOGWO

Hybrid

R2 (m)

3.085

3.050

3.090

h2 /2(m)

0.633

0.734

0.270

d2 (m)

0.149

0.131

0.346

2 Bstray (μT)

0.657

0.572

0.770

E(MJ)

167.01

162.13

179.51

f1

0.073

0.064

0.086

f2

0.072

0.099

0.003

F

0.145

0.163

0.089

5 Conclusion A new hybrid MOO algorithm based on NSGA-II and MOGWO is proposed. The selection, recombination and mutation operator of NSGA-II ensure the diversity of the algorithm, while the leader update mechanism and elite solution retention strategy of MOGWO facilitate the algorithm to converge fast and enhance the local search ability in the meanwhile. The numerical results demonstrate that the proposed algorithm has better convergence and diversity performance. When solving the MOO problem of SMES

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device, the hybrid algorithm yields more superior solutions, which further verifies the correctness and effectiveness of the proposed hybrid algorithm. Acknowledgments. This work was Sponsored by Shanghai Sailing Program (21YF1400300).

References 1. Lee, X., Lu, J., Zhang, X., et al.: Optimized design of NSGA-II based overload magnetic field generator. J Electrotechnology 36(21), 4399–4407 (2021). (in Chinese) 2. An, Y., Ma, Z., Lee, X., et al.: Analytical modelling and multi-objective optimization of airgap magnetic field in built-in permanent magnet synchronous motors for electric vehicles. Chin. Highw. J. 36(1), 253 (2023). (in Chinese) 3. Wang, H., Zhao, T., Ren, N., et al.: Conceptual design of multi-objective optimization of substation equipment using hybrid genetic algorithm. J. Liaon. Univ. Eng. Technol. (Nat. Sci. Ed.) 40(03), 270–274 (2021). (in Chinese) 4. Deb, K., Pratap, A., Agarwal, S., et al.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002) 5. Mirjalili, S., Saremi, S., Mirjalili, S.M., et al.: Multiobjective grey wolf optimizer: a novel algorithm for multi-criterion optimization. Expert Syst. Appl. 47, 106–119 (2016) 6. Yi, Y., Liu, C., He, Q., et al.: Optimization of reactive power in wind-containing distribution networks based on an improved wolf pack algorithm. Inner Mongolia Power Technol. 41(3), 1–7 (2023). (in Chinese) 7. Deb, K.: Multi-objective optimization using evolutionary algorithms: an intro-duction//Multiobjective evolutionary optimization for product design and manufacturing, pp. 3–34. Springer, London, London (2011) 8. Huang, C., Xu, M., Liu, Z., et al. (2019). Research on ATREX engine performance optimization method based on NSGA II algorithm distribution degree improvement. In: propulsion technology, 40(11), pp .2420–2427. (in Chinese) 9. Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2008) 10. Alotto, P., Baumgartner, U., Freschi, F., et al.: SMES optimization benchmark extended: Introducing Pareto optimal solutions into TEAM22. IEEE Trans. Magn. 44(6), 1066–1069 (2008)

Application of TRIZ Theory in Power Electronic Circuits Yonggao Zhang, Zhongyi Sun(B) , and Peng Liu School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China [email protected]

Abstract. TRIZ theory of invention, as a theory of invention and innovation, has been widely used in various fields. In this paper, the contradiction matrix of TRIZ theory is combined with power electronic topologies to systematically illustrate the construction laws and methods of new topologies. Taking the power electron conversion topology of DC-DC circuit as an example, the construction principles of several common topologies are analyzed, and the feasibility of the construction method is verified. In addition, combined with TRIZ theory to guide the regularity of the new topology of power electronics, a new type of soft switching high-gain enhanced converter is proposed, which provides a new idea for the construction of power electronic circuits with better performance. Keywords: TRIZ · The contradiction matrix · Power electronic topology

1 Introduction Power electronics is a technology that uses power electronics effectively to achieve efficient conversion and control of electrical energy [1], and the design and improvement of power electronics topologies is an important aspect of theoretical research in power electronics. A good new power electronic converter can not only make good use of electrical energy but also greatly improve the efficiency of electrical energy conversion, which will also bring about different degrees of progress in power electronics technology [2]. However, for a long time, the process of creating the topology of many new power electronic converters has relied on researchers to build them according to circuit requirements and experience [3], without a rigorous logic and pattern that can be followed, making the design of the circuit topology highly random [4]. In response to the problems in the construction of power electronic converter topology, many experts and scholars at home and abroad have been carrying out extensive research work [5].Currently, there are mainly graph theory method [6], analogy method [7], pairwise method [8] and so on in the construction and innovative guidance of power electronic converters. The graph theory method abstracts electrical components into directed line segments according to the direction of current flow, represents circuit diagrams as directed graphs [9], and analyses them according to the properties of the graphs. S. LINDER et al. were the first to apply graph theory to the study of the characteristics © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 424–432, 2024. https://doi.org/10.1007/978-981-97-0877-2_44

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of circuits containing switching devices. The analogy method in power electronics is a method that uses the similarity of a certain type of circuit topology to derive other topologies of the same type. Lin applied the circuit analogy method to a passive lossless circuit by analogizing a passive lossless LC resonant circuit to a transformer circuit to obtain a new passive soft switching technology that incorporates a charge pump energy regeneration network. In power electronics, the topology of a new circuit can be obtained by replacing elements in an existing topology using the elements of the dyad. The first application of the dyadic method in power electronics was proposed by Bloch scholars in 1946, using ideal transformers to construct dyadic circuit gates for non-planar circuits. The above studies show that there are certain rules for the construction of power electronic topologies, but they are all limited to a particular converter topology or a particular class of converter topologies, and the study of guiding methods for the construction of all power electronic converter topologies is still in its infancy in the field of power electronics. This paper proposes a method of applying the contradiction matrix of Theory of Inventive Problem(TRIZ) to guide the topological construction of power electronic transformations, starting from the disadvantages of the existing design of electronic topology construction which is highly random and requires relatively high experience of the designer. Analyze the technical conflicts existing in traditional power electronic circuits, and use the TRIZ invention principle to attempt logical reasoning to obtain the general principles of power electronic circuit topology invention.

2 The Power Electronic Language of Contradiction Matrix Table The TRIZ theory believes that whether a new technology is innovative depends on whether the technology can solve or transfer conflicts in the design [17], thereby obtaining a completely optimized solution. Power electronic systems are usually complex and composed of multiple components, and there are numerous technical conflicts in the design and optimization process of the entire system. For power electronic converters, not all of the 48 engineering parameters and 40 invention principles of TRIZ theory are applicable. In order to introduce TRIZ theory into power electronics, it is necessary to analyze and screen these parameters and invention principles, and reinterpret them in the language of power electronics. Table 1 describes the meaning of some general engineering parameters in the TRIZ theory corresponding to the parameters in power electronics. Based on the power electronics parameters in Table 1, a suitable contradiction matrix table for power electronics can be obtained, as shown in Table 2. The vertical axis represents the parameters that need improvement, and the horizontal axis represents the parameters that deteriorate with it. When using the contradiction matrix to solve technical conflicts in power electronic converters, it can be divided into the following steps: (1) By analyzing the function and topology of the converter, the problems in the system are clearly identified. For example, how to balance load adaptation and output ripple size in the design of switching power supplies.

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Number

Technical parameters in TRIZ

Technical parameters in power electronics

14

Speed

Voltage amplitude

32

Adaptability

Dynamic response

45

Complexity of device

Complexity of converters

46

Complexity of control

Complexity of control

Table 2. Conflict matrix in power electronics Improve

Deteriorate 14

32

45

46

Voltage amplitude

Dynamic response

Complexity of device

Complexity of control

14

Voltage amplitude

–

5,13

5,10,13

10,13

32

Dynamic response

10,13

–

6,17

1

45

Complexity of device

10,13

13,10

12

–

46

Complexity of control

10,5

13

13

–

(2) Analyze the problems that exist in the system, identify one or more pairs of technical conflicts, and determine the parameters that need improvement and those that deteriorate accordingly. (3) Based on the specific parameters determined, query the power electronic contradiction matrix table in Table 2 to find the corresponding matrix elements at the intersection grid of the improved and deteriorated engineering parameters. (4) Use the obtained inventive principle as a reference for theoretical guidance to construct a new topology. (5) If there are multiple pairs of contradictions, repeat steps 2–4 until all suitable invention principles are found. Some of the inventive principles in the table of the power electronic contradiction matrix are described in the language of power electronics, see Table 3. For example, the inventive principle ‘5-merger principle’, which means the merging together of similar or different classes of operational objects in space or time, and in the case of power electronic converters means ‘combining the circuit characteristics of two or more circuit elements (such as inductors, capacitors, diodes, etc.) into a new circuit.

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Table 3. Application of invention principle to power electronics. Number

Principle of invention in TRIZ

Meaning in power electronics

5

Merger

By combining the same or different devices, converters, etc.

6

Versatility

The converter device has multiple functions or shares components between bridge arms

10

Pre-action

Add components to offset the impact of adverse factors in advance

13

Reverse

Shifting or reversing the relationship of the converter device positions

3 The Validity of Power Electronic Contradiction Matrix The TRIZ general parameters have been converted into power electronics language and the contradiction matrix table applicable to power electronics has been constructed. In the following, the topology will be constructed using the obtained power electronics contradiction matrix table and the common dc-dc converter circuits will be used as examples to verify the logical rationality and validity of the topology derivation. For dc-dc chopper circuits, the simplest topologies are Buck circuits and Boost circuits, as shown in Fig. 1(a) and 1(b) below. These two circuits can perform the buck and boost functions independently, respectively. A series of dc-dc chopper circuits, such as Cuk circuits, Sepic circuits, Zeta circuits, etc., will be derived from these two most common topologies in the following.

L

L

VT

VD

E (a)

C

R

VD

VT

C

E

R

(b)

Fig. 1. Basic dc/dc circuits. (a) Buck chopper circuit. (b) Boost chopper circuit.

The boost and buck circuits topology is relatively simple, but in practice the need for a separate step-up function or step-down function for applications with different voltage levels no longer meets the demand. If a circuit is capable of both boost and buck, it can be adapted to the changing state of the external circuit, but to achieve two voltage changes in one circuit would make the circuit complex. This means that the parameter to be improved is ‘dynamic response’ and the parameter to be deteriorated is ‘complexity of the converters’. By looking up the power electronics contradiction matrix, the ‘versatility principle’ can be obtained. The inductor combines the boost function in the boost circuit

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with the freewheeling function in the buck circuit, and the inductor components can be used in both the boost topology and the buck topology, so as to realize the versatility of the components, and the Buck-Boost circuit and the Cuk circuit with the buck-boost function can be obtained, as shown in Fig. 2.

C

L

E

L1

VD

VT

VT

R

VD

E

(a)

L2

C

R

(b)

Fig. 2. The circuit with both Boost and Buck. (a) Buck-Boost circuit. (b) Cuk chopper circuit.

Although the input and output currents of the Cuk circuit are continuous and the pulsation is small, its output voltage is negative. The parameters that can be improved are ‘reliability of converters’ and deteriorated are ‘complexity of control’. By searching the power electronic contradiction matrix table, we can obtain the ‘pre-action principle’. Using the ‘pre-action principle’, a capacitor is connected in parallel to the output side of the Cuk circuit to achieve isolation between the input and the output, thus realizing a positive polarity output and an isolated output, which results in a Sepic circuit, as shown in Fig. 3(a). This circuit has continuous supply current but intermittent load current, and in order to make the load current continuous, the components of the system are mobilized using the ‘reverse principle’, so that a Zeta circuit with continuous input current and positive output voltage can be obtained, as shown in Fig. 3(b).

L1

C1

VT

L2

E (a)

VD C2

C1

VT R

E

L2 C2

L1

R

VD (b)

Fig. 3. Two improved Cuk circuits. (a) Sepic chopper circuit. (b) Zeta chopper circuit.

A logical demonstration of the dc-dc converter topology derivation using the TRIZ power electronics paradox matrix is shown in Fig. 4.

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1

1

2

2

429

2

2

1

2

1

Fig. 4. Logic diagram of dc-dc converter topology development change.

4 Application of Contradiction Matrix in Constructing New Topology The previous chapter provided a explanation of two common transformation topologies using TRIZ contradiction matrices. This theoretical method will be used to derive the construction and improvement of a new type of high-gain DC-DC converter circuit. By using the ‘merge principle’, the output of the previous stage converter is merged with the input of the next stage to obtain a traditional cascaded boost converter, as shown in Fig. 5(a). Using the ‘low cost replacement principle’ replace the power side switch S1 in Fig. 5(a) with a diode to achieve cost savings. By utilizing the previously obtained ‘reverse principle’ and changing the position of the newly added diode on the parallel circuit of inductor L, an improved cascaded boost converter can be obtained, as shown in Fig. 5(b).

L1 E

VT1

VD1 L2

VD2

VT2

C2

C1 (a)

VD2 L1 R

E

VD1

L2

VD3

C1

VT1

C2

R

(b)

Fig. 5. Topology of cascaded Boost converter. (a) conventional cascaded boost converter. (b) Improved.

According to the construction process of the improved cascaded Boost converter in Fig. 2, it is possible to combine the Buck, Boost, Buck-boost converters and boost circuits with the combination principle, so as to obtain a variety of combination converter topology. By combining the Buck boost and Boost circuits, a dual switch cascaded converter can be obtained as shown in Fig. 6(a).According to the ‘low-cost replacement

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principle’, one switch tube can be replaced by two diodes, and the ‘reverse principle’ can be used to change the position of the newly added diode, so that VD2 is connected in parallel with the energy storage inductor L2 , and VD3 provides a channel for the discharge of inductor L1 , resulting in the topology structure shown in Fig. 6(b). Although the improved cascaded Buck-boost in Fig. 6(b) solves the problem of high voltage stress of the energy storage capacitor, the power switch of the converter will still produce large instantaneous voltage and current changes, resulting in energy loss and switching loss. Using the ‘equipotential principle’, the efficiency of the system is improved and the energy loss is reduced by creating a negative energy effect related to loss at some time of the working cycle. Specifically, the resonant circuit and an auxiliary switch tube can be introduced into the circuit to make the switch and resonant circuit in a suitable resonant state, thus reducing the amplitude of the switching transient voltage and current, as shown in Fig. 6(c). The delay time between the main switch VT1 and the auxiliary switch VT2 is relatively short and they are complementary switches. By driving the signal through the control circuit and the resonance circuit, the zero voltage opening of the auxiliary switch and the main switch can be achieved. Buck-boost C L1 1

VD1 VT2

E

C1

boost VD2 L2 C2

VD3 VD2

L1 R

E

L2

VD1

VD3

C2

R

VT1

VT1

(a)

(b) L2

C1

VD 3

L1 VD VD 2 1 E

VT2 C2

VT1

Lr

C3

R

Cr

(c) Fig. 6. Construction process of a new soft switching cascaded converter (a) Cascaded Buck-boost converter; (b) Improved cascaded Buck-boost converter; (c) Soft switching cascade converter.

This new soft-switching cascaded Boost converter not only has high voltage gain, but also reduces the voltage stress of capacitor and the hard switching problem of main and auxiliary switches, and reduces the switching loss of the converter. According to the above characteristics of constructing topology by using TRIZ contradiction matrix, new cascaded soft-switching converters such as Boost-Cuk, Cuk-Boost and Sepic-Boost can also be constructed, which provides a new idea for constructing more practical high-gain dc-dc converters in the future.

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Table 4. Summary of topological development change Circuit DC-DC

High gain Boost

Original

Diffraction

parameters

Principle

Improve

Deteriorate

Fig. 2a

Dynamic response

Complexity of control

Versatility

Fig. 2b

Dynamic response

Complexity of converters

Merger

Fig. 2

Fig. 3(a) Fig. 3(b)

Reliability of converters

Complexity of converters

Segmentation pre-action

Fig. 5(a)

Fig. 5(b)

Complexity of Harmonic control content Loss of converters

Fig. 1

Fig. 6(a) Fig. 6(b) Fig. 6(c)

Low-cost alternative Merger Low-cost alternative Equipotential

5 Conclusion In this paper, TRIZ theory is applied to the field of power electronics, and a contradiction matrix table applicable to power electronics is derived by analyzing the technical conflicts existing in the topology of power electronics circuits and elaborating the general parameters and invention principles of TRIZ in the language of power electronics. In order to verify the validity of the newly obtained contradiction matrix table, this paper takes common dc-dc circuits as examples. The process of constructing topology with the help of power electronics contradiction matrix table is illustrated. In addition, a new soft-switching cascaded boost converter is constructed in this paper using power electronic paradox matrix, and the proposed circuit reduces the switching losses while ensuring high voltage gain. Table 4 summarizes the technical conflicts in the construction of different topologies, the invention principles used and the connection between each topology, which is used to visually analyze the topology evolution. The contradiction matrix in TRIZ theory can provide more possibilities for power electronics topology design, and future trends will focus on features such as intelligence, environmental protection and energy conservation, sustainability, cost reduction and reliability improvement. In future research, explore how to better use advanced technological tools such as computer simulation in combination with power electronics, so as to better exploit the advantages of the paradox matrix. In addition, cooperation with professionals in other fields is needed to jointly address the practical needs of power electronics topology design in order to provide more scientific and stable and credible guidance for future power electronics topology design. Acknowledgement. This research was supported by the Fund for National Natural Science Foundation of China (Grant No.52267015).

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References 1. Mansouri, M., Aghay Kaboli, S.H., Selvaraj, J., Rahim, N.A.: A review of single phase power factor correction A.C.-D.C. converters. In: IEEE Conference on Clean Energy and Technology (CEAT), pp 389–394. Langkawi, Malaysia (2013) 2. Jang, Y., Jovanovic, M.M.: A bridgeless PFC boost rectifier with optimized magneticutilization. IEEE Trans. Power Electron. 24(1), 85–93 (2009) 3. Abdulkareem, A., Somefun, T.E., Oguntosin, V., Ogunade, F.: Development and construction of automatic three-phase power changeover control circuit with alarm. IOP Conf. Ser. Mater. Sci. Eng. 1036(1), 012081 (2021). https://doi.org/10.1088/1757-899X/1036/1/012081 4. Xinping, D.: A high-performance Z-source inverter operating at wide-range load. Trans. China Electrotechnical Soc. 23(2), 615–620 (2008) 5. Zhang, G., Zhang, B., Li, Z., et al.: A graph theory-based topology construction method for power electronics. In: 20th Annual Conference of China Power Supply Society, pp. 610–615. Hangzhou (2013) (in Chinese) 6. Tse, C.K., Lee, Y.S., So, W.C.: An approach to modelling DC-DC converter circuits using graph theoretic concepts. Int. J. Circuit Theory Appl. 21(4), 371–384 (1993). https://doi.org/ 10.1002/cta.4490210407 7. Zhang, Y., Wang, Q., Li, C., et al.: Generalized construction method and phase-disposition PWM for SiC & Si hybrid multilevel active-neutral-point-clamped converter. In: 9th IEEE International Power Electronics and Motion Control Conference (IPEMC), pp. 2032–2038. Nanjing (2020) 8. Das, B., Chatterjee, D., Bhattacharya, A.: Multilevel converter topology suitable for separate and variable magnitude of DC sources. Int. J. Power Electron. 15(2), 194–215 (2022) 9. Borgianni, Y., Fiorineschi, L., Frillici, F.S., et al.: The process for individuating TRIZ inventive principles: deterministic, stochastic or domain-oriented. Design Science 7, E12 (2021) 10. Liu, P., Zhu, K.: Design of structure and control system of intelligent parking equipment based on TRIZ and cloud platform. J. Phys. Conf. Ser. 1750, 012020 (2021) 11. Jalil, N.A., Khalid, N.I., Sulaiman, N.S., et al.: Conceptual design of portable electrolyzed water cleaning rig using TRIZ method. Food Res. 5(S1), 188–192 (2021)

Is Pollution Internalized? A Study of the Impact of Environmental Administrative Penalties on Companies’ Earnings in China’s Thermal Power Industry Wu Sun1,2(B) 1 International Business College, Shandong Technology and Business University, Yantai, China

[email protected] 2 School of Economics and Management, Shihezi University, Xinjiang, China

Abstract. Under the background of green development, China actively promotes environmental protection policies, and the pressure of transformation of highly polluting industries increases accordingly. This paper chooses the thermal power industry, which consumes relatively more coal and pollutes relatively more, as the research object, analyzes listed companies from the perspective of environmental protection administrative penalties, and proposes the environmental protection administrative penalties constraint effect and the pollution externalization effect, which are the two reaction pathways of companies when facing the possibility of pollution. By analyzing the financial statements of 25 thermal power companies and the number of environmental administrative penalties during the period from 2013 to 2020, it is found that the net profits of listed companies in the thermal power industry that are subject to more environmental administrative penalties are more sensitive to the number of environmental administrative penalties, which suggests that environmental administrative penalties play a role in restraining the polluting behaviors of companies. This means that in the thermal power industry, the administrative penalty constraint effect is greater than the pollution externalization effect, and the supervision of our environmental protection department is appropriate and the guiding role is obvious. Keywords: Environmental Administrative Penalties · Financing Constraints · Internalization · Thermal Power Industry

1 Introductory The continuous progress of human society and rapid economic development have posed a great challenge to global energy consumption. In order to obtain energy, especially clean energy, the use of coal to obtain electricity has been the most common method for a long time. According to the report of the World Energy Organization [1], as of September 9, 2020, CO2 emissions in 2020 is the most is the energy production industry, followed by industry, transportation, construction and other industries. With the rapid © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 433–443, 2024. https://doi.org/10.1007/978-981-97-0877-2_45

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development of China’s economy, in order to reduce costs, the pursuit of excessive profits, The production of ecological pollution caused by more and more. 2019, China’s GDP growth rate of 6.1%, contributing to the world’s economic growth rate of 30%. Economic growth inevitably requires the support of energy, and China has always been a large energy consumer, with imports of crude oil, coal and natural gas growing year by year, importing 510 million tons, 300 million tons and 100 million tons respectively in 2019. According to the National Bureau of Statistics (NBS) in 2019, total energy consumption for the year amounted to 4.86 billion tons of standard coal, an increase of 3.3% over the previous year. Coal consumption accounted for 57.7% of total energy consumption, while clean energy consumption such as natural gas, hydropower, nuclear power and wind power accounted for 23.4% of total energy consumption [2]. In the consumption of coal, the national power industry consumed 2.29 billion tons of coal in 2019, accounting for 62.7% of all coal consumption in that year [3]. Thermal power companies require less investment and have relatively low power generation costs, making them ideal for use in coal-rich developing countries.In order to develop a green economy, China needs the support of green, clean energy, so nuclear power, wind power, solar photovoltaic power generation industry is developing rapidly, but the thermal power is still the main supply of electricity. In 2019, thermal power generation accounted for 69.6% in China. (See Fig. 1).

Fig. 1. Composition of Total National Power Generation from 2009 to 2019 (%)

Thermal power generates electricity by burning coal, but the pollution caused by combustion has increased accordingly. According to the Second National Pollution Source Census Bulletin issued by the Ministry of Ecology and Environment of the People’s Republic of China, the top 3 industries in terms of sulfur dioxide emissions are: electric power, heat production and supply industry, 1,462,600 tons; non-metallic mineral product industry, 1,245,900 tons; and ferrous metal smelting and rolling industry, 82,315,000 tons, with the above 3 industries accounting for a combined total of 66.75% of sulfur

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dioxide emissions from industrial sources [4]. It can be seen that the electric power industry causes a lot of pollution to the air. The improvement effect of environmental pollution after energy efficiency improvement has a large impact on the transformation of economic development mode (Bai J.H. and Nie L., 2018) [5]. Chinese President Xi Jinping made a solemn promise to the world at the general debate of the 75th United Nations General Assembly that China’s carbon dioxide emissions would strive to peak by 2030 and work towards carbon neutrality by 2060. As a result, the thermal power industry has begun to transition to cleaner energy, with thermal power companies either increasing R&D investment in waste-to-energy generation, stepping up pollution control efforts, or introducing technology to improve productivity. However, with the business goal of maximizing profits, there are still some companies that discharge untreated or incompletely treated pollutants in the course of their operations, causing pollution to the environment. China’s government environmental protection departments monitor companies through inspections, spot checks and whistleblower reports, and promptly impose administrative penalties for polluting behavior. This to a certain extent combats corporate pollution behavior, punishes polluting companies and inhibits the occurrence of pollution, guides companies to increase investment in research and development, scientific and technological investment and technological progress, and plays a corresponding role in promoting the improvement of green productivity of China’s thermal power industry. This paper studies 25 list companies in the thermal power industry, and finds that the net profit of listed companies with polluting behaviors is more sensitive to the number of environmental protection administrative penalties, which indicates that the environmental protection administrative penalties play a certain role in constraining the polluting behaviors, but the type of shareholders does not have a significant effect on the net profit of listed companies. In summary, the analysis of this paper implies that in the thermal power industry, the administrative penalty constraint effect is greater than the pollution externalization effect, and the supervision of China’s environmental protection department is appropriate and the guiding effect is obvious. China’s environmental protection administrative departments should actively conduct environmental protection administrative penalties, fully utilize its constraining effect, guide the industries to environmental protection, green production, and contribute to the development of green economy in China. The rest of this paper is arranged as follows: The second part is the literature review, which analyzes the viewpoints of the existing literature; the third part studies the response mechanism of listed companies under environmental protection administrative penalties, and puts forward two effects - the environmental penalties constraint effects and the pollution externalization effect, describes the source of the data at the same time. The forth part is the empirical test based on the hypotheses and models, and the heterogeneity and robustness tests; the fifth part is the conclusion.

2 Literature Review Most scholars analyze the excess return after the SEC penalty, financial violation penalty or auditor’s opinion, for example, Xin Y. et al. (2019) [6], Ding X. et al. (2019) [7],Liu W.J. et al. (2019) [8], Zhang Jia (2019) [9], Tao X.H. et al. (2019) [10] and Lili Lu (2017)

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[11]. Lou S.D. et al. (2019) argues that the regulation of listed companies in backward areas will be relatively weaker [12]. Xin Y. et al. (2019) found that if an company within a group is penalized for violations, there is an information contagion effect within the group, and the group can will support the company [13]. In the study of environmental penalties, scholars’ research is mainly divided into two aspects: studying the theoretical role (Jiang N., 2019) [14] and empirically impact of environmental protection penalties (Yin J.H. et al., 2020) [15]. In terms of the impact of environmental penalties, some scholars analyzed the impact of environmental administrative penalties on companies (Yao S. and Li S.Y., 2017)[16], and found that environmental penalties have a negative impact on the level of corporate finance and green innovation, showing an “inverted U-shape”(Fan F. et al., 2021; Jiang T. and Li L., 2020)[17][18]. Zhu X. et al. (2023) found that the level of enforcement, measured by the total number of penalties, was significantly higher in counties with higher per capita GPD and larger government budget deficits higher [19]. Wang Y. et al. (2020) suggesting that the larger size of penalized firms, the more severe the penalties, and the presence of media reports would lead to stronger deterrence effects on peer firms [20]. It is generally believed that for firms in heavily polluting industries, environmental penalties reduce their revenues (Tang S., et al. 2019; Brady J. et al., 2019) [21, 22]. Environmental administrative penalty is a strong tool for the government to regulate environmental protection, it will control pollution and emissions reduction that is beneficial for the development of green and low-carbon industries (Zhang K. et al., 2023; Ding X.G. et al., 2022) [23, 24], but at the same time, othersf believe that environmental administrative penalties have a limited effect on green innovation (Wang A.L. et al., 2023) [25]. To summarize, the research of various scholars in China has focused on the analysis of environmental penalties, and concluded that it have a certain penalty effect, but certain heterogeneity will weaken the effect. Most articles take whether the rectification is completed as explanatory variables to analyze the role of each factor in influencing environmental penalties, there are few researches on the number of environmental administrative penalties. As the relative difficulty of collecting environmental protection data, all data are collected almost from top to bottom, i.e., looking for all environmental protection penalty data first, and then filtering them, this method will prone to selection bias. If the bias cannot be reasonably dealt with, the results of empirical analysis will not be credible. Therefore, according to the scholars’ previous analysis, this paper selects the relatively more polluted thermal power generation industry and specifically collects its environmental administrative penalty data for research. Therefore, in the sample data of this paper, there are both thermal power companies that have not been subjected to environmental administrative penalties and thermal power companies that have been subjected to environmental administrative penalties, and there will no sample selection bias.

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3 Model Assumption and Data Sources 3.1 Effect Analysis This paper assumes that there are two effects, Environmental penalties constraint effects, and Pollution externalization effects, that firms will weigh their own interests between these two effects and make optimal choices. 1. Environmental Penalties Constraint Effects Through the monitoring of environmental protection monitoring equipment, government departments will regularly investigate and discover non-compliant companies that do not discharge pollutants in accordance with the regulations, and will impose appropriate administrative environmental protection penalties. The administrative environmental penalties will increase the non-operating costs of the company after the violation, and urge the company to invest in research and development, actively participate in pollution control, and improve the technological progress of the company; in the short term, the cost of the company will be increased, and the profit will be decreased, but in the long term, it will increase the profitability of the company, and improve the overall social environment. 2. Pollution Externalization Effects From the perspective of the company, since the company intentionally carries out the polluting behavior in order to obtain excess profit, if it is not discovered, it can obtain excess profit. Therefore, firms will only refrain from polluting if environmental protection is more stringent and administrative penalties are stronge. So the pollution externalization effects refers to the fact that companies are more likely to pollute because they know that they will not be detected, or the cost of administratively penalized after detection is relatively low, and that they can still make a profit (See Fig. 2).

Environmental penalties constraint effects pollution externalization

Make Profits from Pollute production

Pollution and profit

Pollution will increase

Cost increase

Profit decline in short term

Pollution

Corporate Pollution Behavior

Administrative penalties for environmental protection

Profits rise in long run

Increased in R&D

Pollution reduction

Increasing productivity

Regulation by Government Departments

Fig. 2. Environmental Penalties Constraint Effects and Pollution Externalization Effects

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3.2 Hypothesis Based on the analysis, this paper assumes the existence of the following hypotheses: Hypothesis 1: It is assumed that China’s environmental protection administrative penalties for the thermal power industry there is a pollution constraint effect, that is, the cost of pollution after the relatively high cost, the company will reduce pollution and improve productivity, that is, the environmental protection administrative penalties constraint effect is greater. Hypothesis 2: Assuming that China’s environmental protection administrative penalties for thermal power industry binding insufficient, corporate pollution externalization effect, that is, after the implementation of corporate pollution, environmental protection administrative penalties are insufficient, resulting in the company to obtain the net pollution profits, will continue to implement the pollution behavior in the production chain, that is, the pollution externalization effect is strong. Hypothesis 3: This paper also examines the impact of the first largest shareholder on administrative penalties at the same time. That is, the shareholding shareholders for the state-owned nature of the background, then shareclass 1, if non-state, then 0. This paper assumes that the higher the proportion of shareholding, the stronger the constraints on the behavior of the company, then the possibility of administrative penalties is smaller; such as the first major shareholder for the state-owned nature of the shareholders of the listed company from the point of view of social responsibility, the influence of shareholders on the listed company is more, the smaller the violation of the possibility of less administrative penalties. 3.3 Data Sources This paper according to the industry classification of ShenYin & WanGuo, selected a total of 25 listed companies in the thermal power industry. Through CSMAR database, related data in quarterly financial statements are exported and organized according to the list of 25 thermal power listed companies. The data of environmental administrative penalties of 25 thermal power listed companies and their subsidiaries from 2014 to 2021 were collected through the website of Aiqicha.com. The basic description of each variable is shown in the Table 1 below: Table 1. Basic Description of Each Variable for Listed Companies in Thermal Power Industry Variable

hidden meaning

Mean

Std. Dev

Min

Max

n_ep

Number of environmental administrative penalties

1.06

2.29

0

14

otherp

Administrative penalties other than environmental protection

3.08

5.04

0

29 (continued)

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Table 1. (continued) Variable

hidden meaning

Mean

Std. Dev

Min

Max

netprofit

Net profit for the year

19.75

27.93

-20.39

175.49

lnshare

Logarithm of total equity

21.81

1.04

19.21

23.70

sharep

Shareholding ratio of the largest shareholder

47.90

15.10

16.91

83.43

shareclass

State-owned nature of the first largest shareholder

0.86

0.34

0

1

often

Firms with a high number of administrative penalties

0.36

0.481

0

1

lincome

Logarithm of operating income

23.38

1.06

20.90

25.88

lcost

Logarithm of operating costs

23.31

1.06

20.88

25.85

lncofo

Logarithm of non-operating costs

16.89

1.78

11.29

20.95

4 Empirical Findings 4.1 Model Assumption According to hypothesis 1 and hypothesis 2, the model designed in this paper is. netprofit = a + b*n_ ep + e

(1)

That is, the net profit of listed companies will be affected by the environmental protection administrative penalties in its year. If the net profit of listed companies subject to more administrative penalties is still higher than the net profit of other listed companies not subject to penalties, then it is considered that the binding force of China’s thermal power industry environmental protection administrative penalties is weaker, and the company will get net excess pollution profits from the implementation of polluting behaviors, and the society will bear the cost of governance for its pollution, which is the effect of externalization of pollution. Since the company’s net profit is mainly affected by operating revenue and operating costs, and also affected by certain financial indicators; at the same time, according to Assumption 3, this paper obtains the following formula: netprofit = a + b*n_ ep + c*sharep + d*shareclass + e*lnshare + f*lincome = g*lcost + k*lcostofout + e

(2)

That is, the higher the proportion of shares held by the first largest shareholder of the listed company (sharep), the less the listed company is subject to administrative penalties; at the same time, if the first largest shareholder is state-owned (shareclass), the less the listed company is subject to administrative penalties. This paper controlled the share capital size lnshare at the same time. In addition, this paper also considered non-operating costs(lcofo), to see is whether the environmental protection administrative penalties will affect the net profit through the non-operating expenses.

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4.2 Empirical Findings The results show that in most cases, the impact of environmental administrative penalties on the company’s net profit is significant at the 1% confidence level, only when adding the logarithmic value of the listed company’s revenues and costs for the year, although the degree of significance decreases slightly, but still significant at the 5% confidence level. It can be seen that the environmental administrative penalty for listed companies in the thermal power industry has a certain environmental penalty constraint effect, the effect is significant. The results are shown in Table 2. Table 2. Reporting of Regression Results with Control Variables Added in Stages Netprofit n_ep

otherp

(1) otherp

(2) lnshare

(3) sharep

(4) shareclass

(5) lincome

(6) lcost

(7) lncofo

−2.045***

−2.159***

−2.121***

−2.113***

−2.132***

−1.033***

−1.008***

(−4.35)

(−4.20)

(−4.18)

(−4.13)

(−4.13)

(−2.72)

(−2.60)

−0.608

−0.799

−0.782

−0.763

−0.853

−0.678

−0.661

(−1.49)

(−1.74)

(−1.60)

(−1.64)

(−1.75)

(−1.86)

(−1.84)

lnshare

14.27***

13.17**

13.49**

5.706

9.622**

9.503**

(3.78)

(2.84)

(3.09)

(1.94)

(2.88)

(2.97)

sharep

0.131

0.158

0.116

−0.215

−0.205

(0.61)

(0.72)

(0.68)

(−1.00)

(−0.93)

shareclass

−4.181

−5.265

−7.043

−7.112

(−0.26)

(−0.45)

(−0.71)

(−0.73)

lincome

12.95***

129.3***

129.3***

(5.11)

(4.33)

(4.48)

lcost

−119.2***

−119.6***

(−4.10)

(−4.14)

lncofo

0.399 (0.40)

_cons

N

23.79***

−286.7***

−269.1**

−273.8***

−403.7***

−414.8***

−412.0***

(3.86)

(−3.66)

(−3.00)

(−3.48)

(−5.69)

(−7.18)

(−8.35)

200

200

200

200

200

200

199

Note: ***, ** and * represent significant at the 1%, 5% and 10% levels, respectively. Robust t-values are in parentheses

From the coefficient, the impact of environmental administrative penalties on the net profit of companies listed in the thermal power industry is negative, i.e., with the increase of environmental administrative penalties, it will cause the net profit of companies in the thermal power industry to decline. However, it should also be seen that, with the addition of income and cost, the coefficient of environmental administrative penalties, although still negative, but has been significantly reduced, indicating that the net profit is affected by the total income and total cost of the larger, environmental administrative penalties have a slightly smaller impact, and negative.

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In terms of other variables, except for the number of share capital (lnshare), which has a positive and significant effect on net profit, other administrative penalties, the proportion of shareholding of major shareholders and the nature of major shareholders do not have a significant effect on net profit, which shows that the more capitalized the company is, the more it obtains net profit, whereas the other factors do not have a very significant effect on net profit. It should be noted that the impact of non-operating expenditures on net profit is not significant, which indicates that the fine caused by pure environmental costs, which is included in non-operating costs, and does not have a real impact on net profit, but environmental penalties on net profit is a significant impact. That through the previous analysis can be seen that environmental penalties on the net profit of the impact of two ways, one is the administrative penalty fines, and the other is to improve product quality and R&D level. Therefore, it means that the impact of environmental penalties on net profit is likely to be through the listed companies in order to reduce pollution, thereby improving the production level, R&D capabilities of this pathway and the decline in net profit. 4.3 Robustness Check This paper chooses DID method to conduct robustness test to observe whether environmental administrative penalties have a significant impact on net profit. Since China published the Decree of the Ministry of Environmental Protection and revised the Environmental Protection Law in 2015, which effectively improved the effectiveness and strength of environmental administrative penalties, this paper sets the year of policy implementation as 2015 for the parallel trend test. The results of the robustness test are shown by Fig. 3. It can be seen that in 2015, the year of policy implementation, the implementation of environmental protection policies has a significant impact on the profits of polluting companies in the thermal power industry, playing a binding role, and the policy effect continues up to 2020. Therefore, the environmental protection administrative punishment has an obvious constraining effect on listed companies in the thermal power industry, and the environmental protection policy is more effective.

5 Conclusion This paper analyzes listed companies in the thermal power industry through the perspective of environmental protection administrative penalties, and proposes the environmental protection penalty constraint effect and the pollution externalization effect of the two reaction pathways of companies facing the possibility of pollution, and gives the corresponding theoretical explanations. This paper chooses the thermal power industry, which consumes relatively more coal and pollutes relatively more, for research, and by analyzing the financial statements of 25 thermal power companies and the number of environmental protection administrative penalties during the period from 2013 to 2020, it is found that the net profits of listed companies in the thermal power industry that are subject to more environmental protection administrative penalties are more sensitive to the number of environmental

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Fig. 3. Policy Effects of Environmental Administrative Penalties

protection administrative penalties, which suggests that the environmental protection administrative penalties have played a certain effect, but the type of shareholders did not have a significant effect. In summary, the analysis of this paper implies that in the thermal power industry, the administrative penalty constraining effect is greater than the pollution externalization effect, and our environmental protection departments have appropriate regulatory efforts and obvious guiding role. China’s environmental protection administrative departments should actively carry out environmental protection administrative penalties, make full use of its constraining effect, guide the industries to carry out environmental protection and green production, and contribute to the development of green economy in China.

References 1. International Energy Organization, Energy Technology Perspectives 2020. https://webstore. iea.org/energy-technology-perspectives-2020 (2020) 2. National Bureau of Statistics, People’s Republic of China 2019 National Economic and Social Development Statistics Bulletin. http://www.stats.gov.cn/tjsj/zxfb/202002/t20200228_172 8913.html, Accessed 28 Feb 2020. (In Chinese) 3. China Coal Industry Association: 2019 coal industry development annual report, (2020). (In Chinese) 4. Ministry of Ecology and Environment of the People’s Republic of China, Second National Pollution Source Census Bulletin (2020). (In Chinese) 5. Bai, J.H., Nie, L.: Energy efficiency, environmental pollution and the transformation of China’s economic development mode. Financ. Res. 10, 1–18 (2018). (In Chinese) 6. Xin, Y., Teng, F., Gu, X.L.: Research on information and performance transfer effects of violation penalties in company groups. Manage. Sci. 32(01), 125–142 (2019). (In Chinese) 7. Ding, X.: A review of research on the governance effects of securities regulatory penalties. Farm Econ. Manage. 10, 58–59 (2019). (In Chinese) 8. Liu, W.J., Liu, T., Li, X.Z.: Research on the spillover effect of auditor’s penalty in the industry. Audit. Res. 04, 83–91 (2019). (In Chinese)

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9. Zhang, J., Fei, C.M., Yi, Y.: The “deterrent” effect of administrative penalties on the behavior of IPO insurance agents. Friends Account. 24, 39–48 (2019). (In Chinese) 10. Tao, X.H., Cao, S.W.: Non-punitive regulation and audit quality of stock exchanges-an analysis based on the information effect and supervision effect of annual report inquiry letters. Audit. Econ. Res. 34(02), 8–18 (2019). (In Chinese) 11. Lu, L.L.: Empirical analysis of government audit treatment penalty effect. Finance Account. Newsl. 19, 22–25 (2017). (In Chinese) 12. Lou, S.D., Zhang, M., Liu, Y.S.: Is there a poverty alleviation effect” in regulation–a study based on the penalization of listed companies in China. Econ. Theory Econ. Manage. 11, 87–100 (2020). (In Chinese) 13. Xin, Y., Teng, F., Gu, X.L.: Research on information and performance transfer effects of violation penalties in enterprise groups. Manage. Sci. 32(01), 125–142 (2019). (In Chinese) 14. Jiang, N.: Can environmental penalties deter and remediate corporate violations? –analysis based on national key monitoring companies. Econ. Manage. Res. 40(07), 102–115 (2019). (In Chinese) 15. Yin, J.H., Bow, L.D., Wang, S.: Loss of trust punishment and chilling effect-an empirical analysis from regional environmental protection penalty records. Res. Manage. 41(01), 254– 264 (2020). (In Chinese) 16. Yao, S., Li, S.Y.: Does environmental information disclosure have a penalizing effect? Econ. Manage. 31(02), 68–75 (2017). (In Chinese) 17. Fan, F., Lian, H., Liu, X.Y., Wang, X.L.: Can environmental regulation promote urban green innovation efficiency? an empirical study based on Chinese cities. J. Clean. Prod. 287, 125060 (2021) 18. Jiang, T., Li, L.: Research on the linkage mechanism of environmental penalty and financing effect to promote green development of companies. Theory Explor. 03, 104–109 (2020). (In Chinese) 19. Zhu, X., Ding, L., Li, H.Y., Gong, Y.Z.: A new national environmental law with harsh penalties and regulated discretion: Experiences and lessons from China. Resour. Conserv. Recycl. 181, 106245 (2022) 20. Wang, Y., Li, Y.X., Ma, Z., Song, J.B.: Can environmental administrative penalties serve as a warning to others? –A study on the deterrent effect of environmental regulation from the perspective of peer influence. J. Manage. Sci. 23(01), 77–95 (2020). (In Chinese) 21. Tang, S., Shi, W., Sun, A.Q.: Environmental pollution and firm value: theory and empirical evidence. J. Financ. Res. 08, 133–150 (2019). (In Chinese) 22. Brady, J., Evans, F.M., Wehrly, W.E.: Reputational penalties for environmental violations: A pure and scientific replication study. Int. Rev. Law Econ. 57, 60–72 (2019) 23. Zhang, K., Liu, Y.T.: A review of the system of “daily continuous penalty” in China’s environmental protection practice-from the perspective of law and economics. Environ. Impact Assess. Rev. 98, 106976 (2023) 24. Ding, X.G., Appolloni, A., Shahzad, M.: Environmental administrative penalty, corporate environmental disclosures and the cost of debt. J. Clean. Prod. 332, 129919 (2022) 25. Wang, A.L., Si, L.L., Hu, S.: Can the penalty mechanism of mandatory environmental regulations promote green innovation? Evidence from China’s company data. Energy Econ. 125, 106856 (2023)

Master Slave Game Optimization Scheduling of Park Comprehensive Energy System Based on Stepped Demand Response Xinhe Zhang1 , Songcen Wang1 , Yichuan Xu2 , Xin Yu2 , Chenyang Xia3 , and Aiwen Xing3(B) 1 Institute of China Electric Power Research, Beijing 100192, China 2 Institute of Changzhou Power Supply Branch of State Grid Jiangsu Electric Power,

Changzhou 213000, China 3 China University of Mining and Technology, Xuzhou 221008, China

[email protected]

Abstract. In order to deeply understand the interactive process of various subjects in the park’s integrated energy system, effectively guide the demand-side load optimization and promote energy low-carbon, this paper puts forward a masterslave game optimization scheduling model of the park’s integrated energy system based on ladder demand response, with the park operator as the leader and the user aggregator as the follower. First of all, a master-slave game structure with park operators and user aggregators as the main body is constructed, and a stepped demand response incentive mechanism is established to guide the energy use behavior of the user side; Secondly, based on the Stackelberg game theory and taking into account the carbon trading mechanism, with the goal of maximizing the comprehensive income of the park operators and the consumer surplus of the user aggregators, the optimal scheduling model of the comprehensive energy system considering the master-slave game of the park operators and the user aggregators is constructed; Finally, the theoretical research is analyzed and demonstrated through a numerical example, and the results show that the game interaction model proposed in this paper can effectively improve the benefits of the principal and subordinate parties, and reduce the carbon emission level of the system. Keywords: Comprehensive energy system of the park · Stackelberg game · Differential evolution algorithm · Demand response · Optimize scheduling

1 Introduction With the increasing consumption of energy and the increasingly serious problem of environmental pollution, energy and environmental issues have become a hot topic of concern [1]. The independent operation of traditional energy systems can lead to low energy utilization and resource waste. The Integrated Energy System (IES), coupled with multiple energy systems, can effectively solve the problem of low energy efficiency [2, 3, 4], which has received attention and research. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 444–453, 2024. https://doi.org/10.1007/978-981-97-0877-2_46

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At present, multiple loads are widely integrated into the comprehensive energy system of the park. Integrated demand response (IDR), improves the stability of the operation of the multi energy system by changing the user’s own load, promoting interaction between the demand side and the supply side [5]. IDR has transformed from a single electrical load to a comprehensive IDR that includes multiple loads such as electricity, heat, and gas [6]. The above research did not consider the mutual substitution between multiple loads, and the subsidies in the demand response incentive mechanism were fixed at a unit price, failing to fully tap the potential of the user side to fully participate in IDR. The optimization and scheduling of the comprehensive energy system in the park involves multiple interests, and the interaction between the interests of all parties is complex. Game theory can be used to solve such problems. Reference [7] proposes a comprehensive energy system collaborative optimization model based on master-slave game.Reference [8] establishes a master slave game model with multiple masters and slaves, and solves for the equilibrium interaction strategy of each participant. Reference [9] establishes a master-slave game for electricity trading between operators and users. Reference [10] proposes a mathematical model for the Stackelberg relationship between operators and followers in a dynamic pricing environment.Reference [11] introduces a cooperative game model in the construction cogeneration system. Reference [12] proposes a two-level optimization model method based on Stackelberg games. The paper first constructs a comprehensive energy system for the park, which includes a carbon capture system-electricity to gas coupled cogeneration unit. Subsequently, a stepped demand response incentive mechanism was established to guide user side energy consumption behavior. Then, based on Stackelberg game theory, with the goal of maximizing the comprehensive income of park operators and consumer surplus of user aggregators, a master-slave game interaction model between park operators and user aggregators is constructed. Finally, the effectiveness of the proposed scheduling model was verified through numerical analysis.

2 A Comprehensive Energy System Model for the Park and a Stepped Demand Response Incentive Model 2.1 Integrated Energy System for Parks Containing Carbon Capture and Electricity to Gas Conversion The energy supply and demand relationship of the park studied in this article is shown in Fig. 1. The energy demand on the user side is provided by the park operator, who purchases electricity and natural gas from higher-level energy sources to meet the energy demand of internal users in the park. The park operators include traditional conversion equipment such as combined heat and power (CHP), gas boiler (GB), power to gas (P2G), carbon capture system (CCS). Operators supply electricity through photovoltaic, wind, CHP, or directly purchase electricity from the grid to meet users’ energy needs; Thermal energy is mainly supplied through CHP and GB; Natural gas is mainly purchased from gas networks or obtained through P2G.The system includes batteries (ES), heat storage (HS), and hydrogen storage (GS).

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Electric Network

wind Gas network

photo voltaic

ES

CHP

heat load GB

CO2

HS GS

CO2 CCS

P2G

gas load

CHP-CCS-P2G system electric energy flow

heat energy flow

gas energy flow

Fig. 1. Game Structure of integrated energy system

1) CHP model for carbon capture and electric to gas conversion systems The electrical energy generated by CHP units can be divided into the following three categories based on their power usage, as shown in Eq. (1): t t t t PCHP = PCHP + PCCS + PP2G

(1)

t Among them, PCHP

means the generating power of the CHP unit, PEt means electricity t means the electrical power consumed by electricity demand, Pccs

supply for CHP’s t means the electrical power consumed for P2G. CCS, PP2G 

t t t t t t t t = PCHP,g ηCHP QCH4 , PP2G,g = αPP2G , ECO = βPP2G , PCCS = ωECO PCHP 2 2 t t 0 t t max{PCHP,min − h1 PCHP,h , hm (PCHP,h − PCHP,h )} ≤ PCHP ≤ PCHP,max − h2 PCHP,h

(2) t means the amount of natural gas consumed by CHP, ηCHP Among them, PCHP,g means the power generation efficiency of the gas turbine, QCH 4 means the combustion heat value of natural gas, α means electric conversion power for P2G gas production power, β means the coefficient of the calculation quantity, ω means the conversion coefficient that captures the consumed electrical energy, h1 and h2 means CHP unit electric heat conversion coefficients corresponding to the minimum and maximum output power are respectively, hm means linear supply slope of thermot the thermoelectric power corresponding to electric power for cogeneration; PCHP,h the lowest generation power of the CHP unit. The electrical power of CCS, P2G, and CHP should all be within their corresponding upper and lower power limits: t t t t t t t ≤ PCHP ≤ PCHP,max , PP2G,min ≤ PP2G ≤ PP2G,max , PCCS,min PCHP,min t t ≤ PCCS ≤ PCCS,max

(3)

2) Multivariate energy storage equipment model The diversified energy storage equipment includes batteries and heat storage tanks, and the two are uniformly modeled here. ⎧ t t ⎪ ⎨ 0 ≤ Pchar,e/h ≤ μn Pchar,max,e/h , 0 ≤ Pdis,e/h ≤ (1 − μn )Pdis,max,e/h t = H t−1 + (η t t He/h (4) char,e/h Pchar,e/h − Pdis,e/h /ηdis,e/h ) e/h ⎪ ⎩ H min ≤ H t ≤ H max , H 24 = H 1 e/h e/h e/h e/h e/h

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Where, e/h represents the battery and heat storage respectively, μn is a binary variable to ensure that the charging and discharging processes do not occur simultaneously, ηchar,e/h , ηdis,e/h means the charging and discharging efficiency of batteries and heat min , H max means minimum and maximum energy storage capacity storage tanks, He/h e/h of the battery and heat storage tank respectively. 3) Gas boiler model The gas boiler GB generates heat energy by burning natural gas: t t t t = δGB PGB,g QCH4 , 0 ≤ PGB,h ≤ PGB,h,max PGB,h

(5)

t Among them, PGB,g means the natural gas consumption of gas boilers, δGB means t heat generation efficiency of gas boilers, PGB,h,max means Maximum thermal power output for GB.

2.2 Stepped Demand Response Incentive Mechanism The electricity, heat, and gas loads considered in this article have the ability to achieve horizontal and vertical IDR, and can each achieve their own dimensional transfer and mutual substitution at the same time period. Therefore, the three types of loads can be divided into four parts, namely fixed load, transferable load, reducible load, and substitutable load. 2.2.1 Comprehensive Demand Response Model 1) Transferable load Transferable load refers to the transfer of the usage time of the load from the peak price range to the low price range within a certain range. The constraints of transferable load are shown in Eq. (6): ⎧ T T   ⎪ ⎨ Pt t t t t Pshift,in,e/h/g = Pshift,out,e/h/g shift,s,e/h/g = Pshift,in,e/h/g − Pshift,out,e/h/g , t=1 t=1 ⎪ t t t ⎩ 0 ≤ Pt shift,in,e/h/g ≤ Pshift,in,max,e/h/g , 0 ≤ Pshift,out,e/h/g ≤ Pshift,out,max,e/h/g (6) Where, Ptshift,in,e/h/g and Ptshift,out,e/h/g respectively represent the incoming and outgoing loads of electricity, heat, and gas loads, Ptshift,in,max,e/h/g and Ptshift,out,max,e/h/g represent the transferable load and the maximum transferable load, respectively, with T being the total number of time periods. 2) Can reduce load The load can be reduced based on the original load, which can directly interrupt the load with low importance. The following constraints need to be met: t t ≤ Pcut,max,e/h/g 0 ≤ Pcut,e/h/g

(7)

3) Substitutable load Alternative load refers to the load that users convert between electricity, gas, and heat demand based on their own conditions. The relationship between the amount

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of alternative electricity load and the corresponding amount of substituted gas load, as well as the relationship between the amount of alternative electricity load and the amount of substituted heat load, is as follows: ⎧ t t t t ⎪ ⎨ Prep1 = −λPgrep , Prep2 = −εPhrep WE ·ηE E ·ηE λ= W ,ε = W (8) WR ·ηR G ·ηG ⎪ ⎩ Pt t t t t t grep,min ≤ Pgrep ≤ Pgrep,max , Phrep,min ≤ Phrep ≤ Phrep,max Where, λ represents the substitution coefficient between electrical and gas loads, ε represents the substitution coefficient between electricity and heat load, WE , WG , WR represent the calorific value of electrical load, unit gas load, and unit heat load respectively, ηE , ηG , ηR represent the utilization rates of electrical load, gas load, and heat load respectively. 2.2.2 Stepped Demand Response Incentive Mechanism Model On the basis of a demand response incentive mechanism with fixed standards as subsidy prices, a stepped demand response incentive mechanism model is established to further promote user side participation in demand response. This model defines several incentive intervals, and the interval with a smaller demand response corresponds to a smaller subsidy amount. Conversely, the subsidy amount increases with an increase in demand response. ⎧ ⎪ δ, Ep0 − Ep1 ≤ lp ⎪ ⎪ ⎪ ⎪ δl ⎨ p (1 + α), lp ≤ Ep0 − Ep1 ≤ 2lp (9) CDRX = δlp (1 + 2α), 2lp ≤ Ep0 − Ep1 ≤ 3lp ⎪ ⎪ ⎪ δlp (1 + 3α), 3lp ≤ Ep0 − Ep1 ≤ 4lp ⎪ ⎪ ⎩ δl (1 + 4α), 4l ≤ E − E p p p0 p1 Where, CDRX is the subsidy amount per unit of peak shaving electricity, EP0 − Ep1 means peak shaving response electricity for users during peak load periods, δ responds to compensation prices for benchmark demand; α means the increase in peak shaving prices, lp means the interval length of peak shaving electricity during peak load periods. The peak shaving electricity compensation model is similar to the above equation and will not be elaborated here.

3 A Comprehensive Energy System Optimal Dispatching Model Considering Master Slave Game Theory 3.1 Master Slave Game Architecture Between Park Operators and User Aggregators The interactive framework of the DIES supply and demand bilateral game studied in this article is shown in Fig. 2, where a master-slave game is used to analyze the interest relationship between park operators and user aggregators. The park operator formulates energy purchase and sales prices based on market information and the supply and

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demand relationship with user aggregators. User aggregators respond to the load demand through comprehensive demand based on energy prices. Both parties in the game can share information, the operator obtains the energy consumption information of the user aggregator, and the user aggregator obtains the energy price information published by the operator. This game belongs to an information dynamic game, and there is a sequential order between the two games. In this process, multiple energy transactions engage in game interaction simultaneously, and after one or several iterations, until neither the operator nor the user aggregator can individually adjust the decision variables to improve their own efficiency.

Fig. 2. Game interaction framework of park operators

3.2 Optimization Scheduling Model for Each Entity This article proposes a master-slave game optimization scheduling model for a comprehensive energy system that takes park operators as leaders and user aggregators as followers. User aggregation of commercial energy is provided centrally by park operators, who purchase electricity and natural gas from higher-level energy networks to meet their internal energy needs. 3.2.1 Park Operators On the basis of considering energy sales revenue, maximum operating costs, environmental costs, and demand response costs, park operators maximize their own profits. The operator’s objective function can be expressed as: ⎧ l,g l,e l,h max CMNO = CIER + CIER + CIER − Cgrid − Cg − CCO2 − Cs,DR ⎪ ⎪ ⎪ l,e l,g l,h ⎪ t t t t t t ⎪ ⎪ ⎪ CIER = Pload ,e ce,s t, CIER = Pload ,h ch,s t, CIER = Pload ,g cgas,s t ⎨ T  t t t t t + Pt [PsGrid cg,s Cgrid = bGrid cg,b + Pbuy,g cgas,b ] t ⎪ ⎪ t=1 ⎪ ⎪ ⎪ T T   ⎪ ⎪ ⎩ Cs,DR = [CDRX (Ep0 − Ep1 ) − CDRT (Ev0 − Ev1 )], Com = ck Pkt t=1

t=1

(10)

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l,e l,h Where, CIER , CIER , CIER represent the electricity transactions between the park operator and the user aggregator, the income generated by heating and gas supply for the user aggregator, Cgrid is the cost incurred in transactions with the power grid; Cg means is cost of purchasing gas from the gas network; Com means cost of system operation and maintenance; CCO2 means the cost of carbon trading; Cs,DR refers to the stepped demand response cost. Regarding the cost of carbon trading, the initial carbon emission quota in China’s carbon trading market currently mainly adopts a free allocation method. As a microgrid operator of carbon emitting enterprises, their carbon emissions mainly come from cogeneration CHP units and gas boilers. ⎧ ⎨ EIES,a = ε1 (PCHP + h11 PCHP,h ) + ε2 PGB,h + ε3 − ECO2 (11) E = θ1 (PCHP + wt + pv + h11 PCHP,h + θ2 PGB,h ) ⎩ IES CCO2 = ςCO2 (EIES,a − EIES )

Where, ε1 , ε2 , ε3 is the carbon dioxide emission coefficient of CHP units and gas boilers, h11 is the electric heating conversion coefficient of the CHP unit corresponding to the minimum output power, θ1 means allocation of carbon emissions per unit; Is the conversion coefficient of electricity to heat for gas boilers. 3.2.2 User Aggregator The user aggregator adjusts its own load based on the energy price information released by the park operator, taking into account the demand response of electricity, heat, and gas loads, to achieve the highest objective function. max Cuser = Csa + CDR − Cenergy

(12)

1) User utility function Csa =

T 

t ve Pload ,e −

t=1 t +vg Pload ,g

αe t αh t t (Pload ,e )2 + vh Pload (P )2 ,h − 2 2 load ,h

αg t (P − )2 2 load ,g

(13)

Where, ve , αe , vh , αh , vg , αg respectively represent the preference coefficients for consumption of electricity, thermal energy, and gas energy, which can reflect the user’s preference for energy demand and affect the magnitude of demand. 2) Energy purchase cost Cenergy =

T  t=1

t t t t t t (Pload ,e ce,s + Pload ,h ch,s + Pload ,g cgas,s ) t

(14)

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4 Example Analysis This article takes 24 h a day as the scheduling cycle and takes 1 h as the step size for simulation. The price of gas energy is 3.23 yuan/m3 The calorific value of natural gas is 9.97 kW·h/m3 , The price is equivalent to 0.324 元/(kW·h). The replaced heat load and replaced gas load are 2% of the electricity consumption during time t, the reference value for stepped IDR grading is 10% of the electricity consumption during peak and valley load periods. 4.1 IDR Energy Analysis The changes in electricity, heat, and gas loads before and after the user side demand response are shown in Fig. 3. The original electricity load curve has two peaks during the 10–13 pm and 18–22 pm. At this time, the electricity price is relatively high. Under the stimulation of the time of use electricity price and the stepped demand response mechanism, the user side transfers the electricity from peak periods to valley periods (0– 8 am), and reduces the electricity load during peak periods (21–22 pm), thus achieving the goal of peak shaving and valley filling, reduce the fluctuation of electrical load, thereby reducing the cost of purchasing electricity for the system.

Fig. 3. Change of electricity, heat, gas load at user side

As shown in Fig. 3, it can be seen that for electrical loads, during periods of high electricity prices and peak electricity loads during the day, electricity is replaced by thermal and gas energy, thereby reducing the cost of purchasing electricity from operators. 4.2 Optimal Dispatching of Parks Under the Game of Both Supply and Demand To meet the diverse energy needs of users, user aggregators purchase energy from park operators. Figure 4 shows the supply of electricity, heat, gas, and carbon in the comprehensive energy system. In terms of electricity supply, the electricity load demand of users is provided by wind power, photovoltaic, CHP, and power grid purchasing. During the periods of 1 to 5am and 16 to 24am, wind resources are abundant, while photovoltaic resources are abundant during the periods of 8 to 17pm. When the electricity load on the user side is in

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Fig. 4. System electricity, heat, gas and carbon balance diagram

the low electricity prices of 1 to 9am, 10 to 12am, and 17 to 20pm, the lower electricity prices are used to charge the battery. During peak electricity load periods, the operator’s energy supply cannot meet the electricity load, and the battery discharges during peak electricity consumption and electricity prices from 13 to 16pm, 21 to 23pm. The heating load is mainly provided by gas boilers and gas turbines. To improve the energy utilization efficiency of gas turbines and fully utilize the thermal energy generated during power generation to provide heat to the user side. Gas energy is mainly purchased from park operators, not only for the user side, but also for GT and GB. During the periods of 0am to 7am and 13am to 16pm, P2G consumes electricity from cogeneration and generates gas power, while also reducing the cost of purchasing gas loads and reducing the cost of system energy purchase. The carbon balance diagram of the system is shown in Fig. 4, CCS supplies the captured carbon dioxide to P2G during the periods of 0–5am, and 18–19pm. The operation of P2G consumes the carbon dioxide generated by the system, thereby reducing the carbon trading cost of the system.

5 Conclusion This article proposes a master-slave game optimization scheduling model for park comprehensive energy systems based on stepped demand response. Through example analysis, the following conclusions are drawn: 1) Renewable energy and energy coupling equipment can achieve multi energy complementarity, user aggregators can be used to achieve peak shaving and valley filling of loads, optimize energy consumption strategies, and achieve mutual benefit and win-win situation between park operators and user aggregator.

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2) Establish a tiered demand response incentive mechanism, iteratively optimize subsidy unit prices, increase the enthusiasm of user side participation in response and the economy of the system, and fully tap into the potential of user side demand response. 3) Establishing a CHP model for carbon capture and electricity to gas systems, can effectively reduce carbon emissions during system operation. The optimization scheduling method proposed in this article can better promote user participation in demand response, make the results of demand response more close to user needs, and improve the economic benefits of the system while considering low-carbon characteristics. Acknowledgments. This work was funded by State Grid Technology Project, China (5400202218162A-1-1-ZN).

References 1. Lewandowska-Bernat, A., Desideri, U.: Opportunities of power-to-gas technology in different energy systems architectures. Appl. Energy 228, 57–67 (2018) 2. Jia, H., Wang, D., Xu, X., et al.: Research on some key problems related to integrated energy systems. Autom. Electric Power Syst. 39(7), 198–207 (2015). (in Chinese) 3. Jia, H., Xiao, Q., He, J.: An improved grid current and DC capacitor voltage balancing method for three-terminal hybrid AC/DC microgrid. IEEE Trans Smart Grid 10(6), 5876–5888 (2019) 4. Jiang, Z., Ai, Q., Hao, R.: Integrated demand response mechanism for industrial energy system based on multi-energy interaction. IEEE Access 7, 66336–66346 (2019) 5. Chen, J., Hu, Z., Chen, J., et al.: Optimal dispatch of integrated energy system considering ladder-type carbon trading and flexible double response of supply and demand. High Volt. Eng. 47(9), 3094–3104 (2021). (in Chinese) 6. Zeng, A., Zou, Y., Hao, S., et al.: Comprehensive demand response strategy of industrial users in the park considering the stepped carbon trading mechanism. High Volt. Eng. 48(11) (2022). (in Chinese) 7. Shuai, X., Ma, Z., Wang, X., et al.: Research on optimal operation of shared energy storage and integrated energy microgrid based on master-slave game theory, pp. 1–12, 27 November 2022. (in Chinese) 8. Wu, L., Jing, Z., Wu, Q., et al.: Equilibrium strategies for integrated energy systems based on stackelberg game mode. Autom. Electr. Power Syst. 42(4), 142–150 (2018). (in Chinese) 9. Maharjan, S., Zhu, Q., Zhang, Y., et al.: Dependable demand response management in the smart grid: a Stackelberg game approach. IEEE Trans. Smart Grid 4(1), 120–132 (2013) 10. Zugno, M., Morales, J.M., Pinson, P., et al.: A bilevel model for electricity retailers’ participation in a demand response market environment. Energy Econ. 36, 182–197 (2013) 11. Lozano, M.A., Serra, L.M., Pina, E.A.: Optimal design of trigeneration systems for buildings considering cooperative game theory for allocating production cost to energy services. Energy 261, 125299 (2022) 12. Bashir, A.A., Lund, A., Pourakbari-Kasmaei, M., et al.: Minimizing wind power curtailment and carbon emissions by power to heat sector coupling-a Stackelberg game approach. IEEE Access 8, 211892–211911 (2020)

Visualization and Detection Method for Surface-Mounted Evaporative Cooling Systems Zhang Kexin1,2(B) , Liu Guoqiang1,2,3 , and Liu Jing1,2,3 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China

[email protected]

2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Qilu Zhongke Electric Advanced Electromagnetic Drive Technology Research Institute,

Jinan 250101, China

Abstract. As power electronic devices move towards higher power density, miniaturization, and integration, traditional cooling methods are no longer sufficient to meet their cooling needs. The Power Equipment New Technology Laboratory of the Institute of Electrical Engineering, Chinese Academy of Sciences (CAS), has proposed a new surface-mounted evaporative cooling technology. However, existing research on the heat transfer characteristics of surface-mounted evaporative cooling systems still has significant shortcomings. To address the real-time visualization issue of the operating state of the liquid box in the surfacemounted evaporative cooling system, this paper applies Electrical Capacitance Tomography (ECT) technology to detect the capacitance signal of the liquid box during operation. In response to the differences between the liquid box structure and traditional pipelines, two sets of sensors are designed for comparison.To mitigate the ill-posedness of ECT, a pixel interpolation method is employed to improve the image reconstruction algorithm. Simulation results indicate that compared to traditional algorithms, the relative error of the pixel interpolation method mostly decreases by more than 0.1. The image correlation coefficient increases by more than 0.05, significantly enhancing image quality. Compared to traditional twophase flow detection methods, the approach presented in this paper exhibits higher accuracy and robustness. Keyword: Liquid box · Two-phase flow · Electrical Capacitance Tomography (ECT) · Bilinear interpolation

1 Introduction 1.1 A Subsection Sample With the rapid advancement of electronic devices, heat dissipation issues are becoming increasingly prominent [1]. The demand for high-performance cooling and the wide market space for practical applications have driven research into high heat flux cooling, © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 454–465, 2024. https://doi.org/10.1007/978-981-97-0877-2_47

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making it a crucial and active field. Surface-mounted evaporative cooling systems are commonly used thermal management technologies that effectively lower the operating temperature of electronic devices. In such systems, heat is carried away by the liquid through flow evaporation, achieving cooling of electronic components [2]. The liquid box is a component within the surface-mounted evaporative cooling system, typically utilized for containing and circulating the liquid coolant.

Fig. 1. Physical Structure of the Liquid Box

However, the flow state of the cooling medium inside the liquid box has a significant impact on cooling effectiveness. Therefore, in order to gain a deeper understanding of the heat transfer characteristics of boiling two-phase flow of organic coolant within the fin array of a surface-mounted self-circulation evaporative cooling system and to acquire insights into the heat transfer behavior within the liquid box channels, this study undertook a visualization investigation of boiling two-phase heat transfer flow within the liquid box [3]. Electrical Capacitance Tomography (ECT) is a visualization technique suitable for multiphase flow monitoring. It reconstructs the distribution of dielectric constants within the sensitive field by measuring boundary capacitance values, thereby obtaining corresponding material distributions [4]. Compared to other detection techniques, ECT offers advantages such as non-radiation, non-invasiveness, rapid response, easy installation, and low cost. Currently, ECT has been applied to multiphase flow measurement in small-scale pipelines. Applying ECT technology to visualize and detect surface-mounted evaporative cooling systems holds significant potential value [5]. However, conventional ECT sensors are not suitable for the geometry of the liquid box [6]. In traditional ECT sensors, electrodes are often uniformly arranged in enclosed spaces, which is suitable for circular pipelines. The liquid box pipelines differ from traditional ECT pipelines in the following three aspects:The bottom of the liquid box is in direct thermal contact with the heat source metal, treating it as a solid electrode plate, which introduces interference to the imaging results [7]. The liquid box has a rectangular shape, resulting in non-uniform measurement areas. Under conditions of small-scale pipelines, a higher number of electrodes in the ECT setup can lead to low data signal-to-noise ratio, and the process of fabrication and installation can be challenging.

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Fig. 2. Conventional Pipeline-Type ECT Sensor

Conventional capacitance design is not suitable for addressing the aforementioned issues. Therefore, this study specifically designed two sets of sensors with 9 electrodes and 11 electrodes respectively, tailored to the structure of the liquid box. Furthermore, ECT faces two main challenges: ill-posedness and ill-conditioning. To address the ill-conditioning of ECT, this paper applies bilinear interpolation to the image reconstruction process of ECT imaging results, building upon the classical LBP (Landweber-Bregman-Proximal) and Tikhonov regularization. This helps to reduce artifacts and noise, resulting in more accurate and realistic images. This approach effectively enhances the visualization of the flow state of the cooling medium within the liquid box, providing a more accurate reference for liquid box design and optimization. Finally, this paper compares the pixel interpolation method with traditional image reconstruction algorithms and validates them through numerical simulations. Evaluation metrics such as relative error and correlation coefficient are employed to analyze and compare the imaging results between commonly used imaging algorithms and the improved algorithms [8].

2 Related Work 2.1 Principle of ECT Operation An ECT system typically consists of three components: sensors, data acquisition system, and image reconstruction computer. The structural principle of an ECT system is illustrated in the diagram below:

Fig. 3. Schematic Diagram of ECT System Principle

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The workflow of an ECT system is as follows: By applying excitation voltages to the electrode array in a specific sequence, capacitance values between the excitation electrode and various detection electrodes are measured. The data acquisition system converts these measured signals into digital quantities and sends them to the computer. The computer, combining the received signals with image reconstruction algorithms, generates an image representing the distribution of dielectric constants within the conduit [6]. The voltage signal is applied to one of the electrodes while the remaining electrodes are grounded to obtain the capacitance between that electrode and the others. This process is repeated for each electrode, sequentially applying voltage signals and measuring the capacitance between all pairs of independent electrodes. There are multiple methods to solve the mathematical model of ECT, with numerical methods based on finite element methods being commonly used. The finite element method divides the object into numerous small finite element regions, establishes discrete equation systems, and utilizes numerical methods for solving. Additionally, regularization techniques and inversion algorithms can be employed to enhance imaging quality and reduce noise interference. ECT primarily involves forward and inverse problems. The forward problem determines the capacitance between independent electrode pairs based on the distribution of dielectric constants within the sensitive region. Conversely, the inverse problem uses measured boundary capacitance values to determine the distribution of dielectric constants within the sensitive region. The linear model of an ECT system can be expressed as follows: C = Sg

(1)

In the equation, Cis the normalized capacitance vector, S is the normalized sensitivity field matrix with respect to normalized dielectric constants. g represents the normalized dielectric constant vector, which corresponds to the grayscale values of the reconstructed image pixels. To address the ill-posedness and ill-conditioning issues in ECT technology, various image reconstruction algorithms have been proposed both domestically and internationally. Currently, ECT image reconstruction algorithms can be categorized into noniterative methods and iterative methods. Non-iterative methods include linear backprojection, Tikhonov regularization, singular value decomposition (SVD), among others. These methods share the characteristic of single-step imaging, resulting in fast image reconstruction but with limited accuracy. Iterative algorithms include Landweber, conjugate gradient (CG), etc., which offer better image resolution but may have slower convergence rates and less real-time capability. 2.2 Bilinear Interpolation Linear interpolation refers to an interpolation method where the interpolation function is a first-degree polynomial, resulting in zero interpolation error at the interpolation nodes. Linear interpolation can be used to approximate the original function or to calculate values not present in a lookup table.

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Bilinear interpolation, also known as bilinear interpolation, involves performing linear interpolation in two directions. It is a widely used interpolation technique in numerical analysis, applied in fields such as signal processing, digital image processing, and video processing [9].

3 Sensor Design and Algorithm 3.1 Sensor Design In traditional electrical capacitance tomography (ECT) sensors, electrodes are often uniformly arranged in enclosed spaces. Different-shaped ECT systems have varying numbers of measuring points, leading to different numbers of electrodes installed around the object under study. Common configurations include 6 electrodes, 8 electrodes, and 12 electrodes. Despite the rapid development of ECT, scholarly research has mostly focused on ECT sensors with uniformly distributed electrodes. ECT sensors with non-uniformly distributed electrodes have not received widespread attention. Considering the unique non-enclosed geometry of the liquid box, the metallic bottom side, serving as an electrode, is utilized. Three other sides are equipped with arranged electrodes. In the sensor design presented in this study, four key considerations were addressed: (1) Electrode Geometry: Number and Length The more electrodes used in the sensor, the more data can be collected. However, in situations with limited spacing, smaller electrode widths intensify edge effects between electrodes. Thus, electrode geometry is a matter of balance. (2) Electrode Arrangement: Placement on Each Side The liquid box cross-section has a height of 11mm and a width of 22mm, with a wall thickness of 1mm. The sides available for electrode design are one long side and two short sides. (3) Shielding and Grounding The shielding electrode comprises a shielding cover and radial electrodes. The shielding cover shields the internal field strength from external electric field interference. During measurements, the shielding cover is grounded to eliminate excessive interference from stray capacitance. Radial electrodes are connected to the shielding cover and arranged parallel to the detection electrodes. The shielding cover also separates measuring electrodes from each other, shielding mutual interference between adjacent electrode pairs. (4) Distance from the Bottom Electrode In preliminary work, we observed that large-area metal electrodes can impact image quality. Therefore, the distance from the bottom electrode is a key consideration in electrode design. In this study, electrodes were installed around the liquid box in a non-uniform distribution. Two sensor models were established with different electrode arrangements and quantities: 11-electrode arrangement and 9-electrode arrangement.

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Li Xiaolin and others introduced bilinear interpolation and applied it to visualize the gasification process of small satellite propellants, presenting a fast and effective optimization algorithm [10]. In this study, the bilinear interpolation method is applied to visualize the evaporation and boiling heat transfer process within the liquid box, with improvements made to its parameters. Compared to other interpolation methods, bilinear interpolation not only enhances image resolution but also reduces artifacts and noise, resulting in more accurate and realistic images. Therefore, by applying the bilinear interpolation method to the image reconstruction process of ECT imaging results, the visualization of the flow state of the cooling medium within the liquid box can be effectively improved, providing a more accurate reference for liquid box design and optimization (Fig. 4).

Fig. 4. Electrode Arrangement Diagram of the Liquid Box. Left: 11-Electrode Configuration, Right: 9-Electrode Configuration"

In the configuration with 11 electrodes on the left side, the lengths of the electrodes on the two shorter sides are 2.5mm, and the length of the electrode on the longer side is 4mm. The distance between these electrodes and the bottom edge is 0.9mm. In the arrangement depicted on the right, featuring 9 electrodes, the lengths of the electrodes on three sides are 4mm, and the distance from these electrodes to the bottom edge is 1.45mm. Two types of sensors were employed to conduct flow regime reconstruction for four distinct flow patterns. This approach aimed to explore the impact of sensor electrode distribution and quantity on the quality of reconstructed images. By means of comparative analysis of the final imaging outcomes, this investigation scrutinized the characteristics of sensors with varying electrode arrangements and quantities in the context of image reconstruction for different flow patterns. This endeavor offers an avenue for further enhancing sensor design [11]. 3.2 Image Reconstruction Algorithms The linear back projection (LBP) algorithm represents an early entrant in the realm of electrical capacitance tomography (ECT) imaging techniques. It operates under the premise that sensitivity distribution is independent of medium distribution, assuming a linear relationship between pixel grayscale values and the measured capacitance values. Accordingly, the capacitance measurement values are subjected to sensitivity weighting and then back-projected across the entire test plane to yield a depiction of medium distribution [12]. The strength of the LBP algorithm resides in its simplicity and swift computation, rendering it widely utilized for real-time image reconstruction. However, it comes with

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a trade-off in image quality, as it tends to yield inferior imaging results and may generate notable artifacts. The Tikhonov regularization algorithm is a recurrent choice for solving inverse problems. This approach is known as the Tikhonov regularization algorithm. Tikhonov regularization effectively reconstructs images, often achieving superior results compared to LBP. In this study, a weighted average of Tikhonov regularization and LBP reconstruction outcomes was adopted to serve as the final reconstructed image. The weighting coefficients are determined based on the image reconstruction context. Addressing the characteristics of gas-liquid two-phase flow within the liquid box, this research incorporates an interpolation-based image reconstruction algorithm. This method involves arranging the normalized reconstruction image elements into a vector, denoted as g, in a sequence from left to right and top to bottom. Furthermore, boundary points are cyclically selected from the image to divide it into a grid of 44 × 24 regions. Setting both horizontal and vertical periodicities at 2, the bilinear interpolation technique is employed to perform three consecutive linear interpolations in each direction. A portion of these points is set as unknowns, subject to constraints imposed by the nearest four points. This approach introduces novel constraints that mitigate the problem’s indeterminacy to a certain extent. Additionally, the method extends to vectors and matrices, incorporating prior knowledge. Consequently, it serves as a comparative validation measure in this study.

4 Simulation 4.1 Sensitivity Field In the context of Electrical Capacitance Tomography (ECT) systems, the sensitivity field refers to the distribution of sensitivity. It can be understood as the variation in capacitance values when the permittivity of a small element within the pipeline changes from low to high. This sensitivity field represents the degree to which capacitance values are responsive to changes in permittivity and serves as prior data for image reconstruction, directly impacting the quality of reconstructed images. The elements within the sensitivity field matrix define the sensitivity of the capacitance between electrode pairs i and j at a specific point within the sensitivity field, as the permittivity changes. The calculation is as follows: ˜ p(x,y) ∇φi (x, y) · ∇φi (x, y)dxdy (2) Sij = − Vi · Vj where Vi and Vj are the excitation voltages applied to electrodes i and j, respectively, ∇φi (x, y) and ∇φi (x, y) are the applied voltage differences, and represents the potential distribution at the point (x, y). The sensitivity distribution between selected electrodes of the 11-electrode sensor is illustrated in the accompanying figure (Fig. 5).

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1-2

1-5

1-10 Fig. 5. Conventional Pipeline-Type ECT Sensor

4.2 Image Reconstruction A simplified bubble and other typical simulation models were established using COMSOL Multiphysics and MATLAB to test and validate the pixel interpolation method. Table 1 presents a comparison of the results between pixel interpolation and other image reconstruction algorithms using the 11-electrode sensor in a simulated bubble scenario. Similarly, Table 2 illustrates a comparison of results for the 9-electrode sensor using pixel interpolation and other image reconstruction algorithms in the simulated bubble scenario.

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In these tables, LBP and Tikhonov are commonly used imaging algorithms. The pixel interpolation method is actually based on solving the inverse problems using LBP and Tikhonov. Therefore, the fusion of LBP and Tikhonov without the addition of pixel interpolation is also included. The planar structure of surface-mounted evaporative cooling systems can seamlessly conform to the surface of devices, as illustrated in Fig. 1. Heat is transferred through the bottom of the liquid box to the cooling medium inside, and when the liquid medium reaches its saturation temperature, it undergoes phase change, thus dissipating the heat from the chip. This effectively reduces the chip temperature, stabilizing the operational temperature around 60 °C. Additionally, the liquid box maintains full contact with the entire chip surface, ensuring uniform chip temperature distribution. The narrow and rectangular channel structure of the liquid box not only allows for a greater number of chip placements within limited space conditions for power electronic devices, but also minimizes coolant usage, enhancing the economic efficiency of the cooling system. Furthermore, the system features self-circulation, eliminating the need for a circulating pump and resulting in lower overall energy consumption. This bears significant importance for overall energy savings and efficiency enhancement in power electronic devices. Table 1. Comparison of Image Reconstruction using Pixel Interpolation Method for the 11Electrode Sensor and Other Image Reconstruction Algorithms

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Table 2. Comparison of Image Reconstruction using Pixel Interpolation Method for the 9Electrode Sensor and Other Image Reconstruction Algorithms

From the tables, it can be observed that the pixel interpolation method holds a certain advantage compared to other algorithms. In scenarios involving a single bubble and two bubbles within the bubbly flow, the pixel interpolation method exhibits more accurate reconstruction positions compared to other algorithms. 4.3 Image Quality Assessment This study employs the metrics of relative error and image correlation coefficient to evaluate the extent of deviation between the actual permittivity distribution and the reconstructed images (Tables 3, 4, 5 and 6). Table 3. Table captions should be placed above the tables.

LBP

Figure 1

Figure 2

Figure 3

0.6565

0.5926

0.6102

Tikhonov

0.5203

0.4356

0.4229

LBP + Tikhonov

0.5517

0.4709

0.5536

Pixel Interpolation Method

0.3230

0.3358

0.4271

From the reconstructed images and the aforementioned evaluation metrics, it is evident that the LBP algorithm produces reconstruction images that are barely recognizable to the naked eye, exhibiting poor discernibility. The images reconstructed using the Tikhonov algorithm display relatively blurred edges but offer better discernibility. On the other hand, the images reconstructed using the bilinear interpolation algorithm exhibit clearer edge information, fewer reconstruction artifacts, higher discernibility, and a closer resemblance to the actual distribution.

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Figure 2

Figure 3

LBP

0.6182

0.5595

0.5674

Tikhonov

0.4793

0.4423

0.4539

LBP + Tikhonov

0.5291

0.4233

0.5124

Pixel Interpolation Method

0.3301

0.2778

0.4432

Table 5. Table captions should be placed above the tables. Figure 1

Figure 2

Figure 3

LBP

0.4100

0.4335

0.4053

Tikhonov

0.5253

0.4556

0.6528

LBP + Tikhonov

0.6334

0.6239

0.5738

Pixel Interpolation Method

0.7229

0.7036

0.6993

Table 6. Table captions should be placed above the tables. Figure 1

Figure 2

Figure 3

LBP

0.4435

0.4923

0.4400

Tikhonov

0.4793

0.4423

0.4539

LBP + Tikhonov

0.7020

0.6623

0.6575

Pixel Interpolation Method

0.7525

0.6933

0.7240

5 Conclusion Addressing the visualization and monitoring of gas-liquid two-phase flow in the operational state of a liquid box, this study designed two sets of sensors with 9 and 11 electrodes respectively, and utilized the pixel interpolation method for image reconstruction. Through simulation and error analysis, the results demonstrate that the pixel interpolation method outperforms other methods in terms of image reconstruction quality for the ECT system. The relative errors in the images are mostly reduced by over 0.1, and the image correlation coefficients increase by over 0.05. The 9-electrode sensor features uniform electrode distribution and greater distance from the bottom electrode, resulting in smaller errors and higher image correlation coefficients compared to the 11-electrode sensor. This configuration is well-suited for the forthcoming liquid box experiments.

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References 1. Radamson, H., Thylén, L.: Chapter 4 - Moore’s Law for Photonics and Electronics 2. Radamson, H., Thylén, L.: Monolithic Nanoscale Photonics–Electronics Integration in Silicon and Other Group IV Elements, pp. 121–150. Oxford, Academic Press (2015) 3. Experimental Study on Boiling Heat Transfer Performance of Surface-mounted In-line SelfCirculation Evaporative Cooling System with Inner Fins 40(06), 1997-2006 (2020). https:// doi.org/10.13334/j.0258-8013.pcsee.191273. (in Chinese) 4. Kandlikar, S.G.: Review and projections of integrated cooling systems for three-dimensional integrated circuits. Journal of Electronic Packaging (2014); [6] Zhang, Y.P., Yu, X.L., Feng, Q.K., et al.: Thermal performance study of integrated cold plate with power module. Applied Thermal Engineering 29(17–18), 3568–3573 (2009) 5. Xiaolin, L., Jiangtao, S., Wenbin, T., et al.: Visual detection method for gasification process of cryogenic propellant in microsatellites. Space Control Technology and Applications 47(04), 93–102 (2021). (in Chinese) 6. Yang, W.Q., Nguyen, V.T., Betting, M., et al.: Ima ging wet gas separation process by capacitance tomo graphy [C] Electronic Imaging. SPIE, International Society for Optics and Photonics. California (2002) 7. Yang, L., Zhu, K.: Study on gas-liquid two-phase flow during vaporizing in LNG device. Gas & Heat 37(12), 11–15 (2017) 8. A Brief Discussion on the Development Prospects of the Post-HFC-134a Era. Organic Fluorine Industry 03, 45–47+64 (2010). (in Chinese) 9. Chi-Yeh, H., Griffith, P.: The mechanism of heat transfer in nucleate pool boiling—Part I: Bubble initiaton, growth and departure. Int. J. Heat and Mass Transfer 8(6), 887–904 (1965); [35] Cooper, M.G., Lloyd, A.J.P.: The microlayer in nucleate pool boiling. Int. J. Heat and Mass Transfer 12(8), 895–913 (1969) 10. Revellin, R., Dupont, V., Ursenbacher, T., et al.: Characterization of diabatic two-phase flows in microchannels: Flow parameter results for R-134a in a 0.5mm channel. Int. J. Multiph. Flow 32(7), 755–774 (2006) 11. Zhang, Y., Wei, J., Kong, X., et al.: Confined Submerged Jet Impingement Boiling of Subcooled FC-72 over Micro-Pin-Finned Surfaces. Heat Transfer Eng. 37(3–4), 269–278 (2016) 12. Xu, H., Si, C., Shao, S., et al.: Experimental investigation on heat transfer of spray cooling with isobutane (R600a). Int. J. Therm. Sci. 86, 21–27 (2014)

Research on the Regionalization Development of China’s Power Transmission Projects Considering Spatial Correlation Yuhui Ma(B) and Panxin Mao Hunan Electric Power Transmission and Transformation Engineering Company LTD., Laodong West Road, Changsha, Hunan 410015, China [email protected]

Abstract. The construction of smart grid transmission projects and UHV projects plays an important role in promoting the formation of inter-provincial spatial connectivity and allocation and the optimal allocation of energy resources on a large scale in provinces and regions. Based on relevant data, this paper first sorts out the construction and development history of China’s regional power grid and UHV transmission projects, and clarifies the connection of inter-provincial transmission projects and the characteristics of cross-provincial and cross-regional power transmission in recent years. Secondly, combined with the characteristics of the transmission and configuration of renewable energy power in transmission projects in China, the spatial connection weight matrix of power grid projects in different years is constructed, and the connectivity characteristics of transmission projects in the spatial dimension are compared and studied, and the development and change law of transmission power grid projects in China is analyzed, so as to provide reference for the construction of transmission projects. Keywords: Transmission Projects · Regional Power Grids · Spatial Correlation · Spatial Weights Matrix · Optimal Allocation of Resources

1 The Construction and Development History of Regional Power Grid Projects In the early stage of China’s power grid construction, it was a local power grid covering the province, and the distribution network between cities was gradually interconnected through the main network frame of 220 kV lines [1]. Since then, the scale, grid structure, and voltage technology of the power grid have continued to improve, and a larger range of provincial power grids and cross-provincial power grids have emerged [2]. In May 2001, the Northeast-North China Power Grid realized regional synchronous AC interconnection, marking that China’s power grid has entered a new stage of large-scale cross-provincial and cross-regional power transmission and national power grid interconnection [3]. After 2005, China formed a complete long-distance transmission grid framework and the basic structure of six major regions, as shown in Table 1. National © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 466–473, 2024. https://doi.org/10.1007/978-981-97-0877-2_48

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interconnection has promoted the optimal allocation of power resources on a larger scale, alleviated the difficulty of power transmission in the western and northern regions and the tight power supply in the eastern region, and is of great significance for promoting energy transformation [4]. In 2009, China’s power grid scale surpassed the United States to become the world’s largest power grid [5]. Table 1. Six regional power grids and its component. Regional power grid

Provincial power grid

Central Power Grid

Hubei, Hunan, Henan, Sichuan, Chongqing, Jiangxi

Northern Power Grid

Beijing, Tianjin, Hebei, Jibei, Shanxi, Mengxi, Shandong

Northwestern Power Grid

Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang, Xizang

Eastern Power Grid

Shanghai, Jiangsu, Zhejiang, Anhui, Fujian

Southern power grid

Guangdong, Guangxi, Yunnan, Guizhou, Hainan

Northeastern Power Grid

Liaoning, Jilin, Heilongjiang, Mengdong

During the Twelfth Five-Year Plan period, it is a stage of rapid development of China’s power grid construction, with an average annual growth rate of 4.5% in power grid investment projects, continuous improvement of regional power grid capacity, steady advancement of national interconnection, ranking first in the world in the scale and configuration capacity of power grid, and basically forming the basic framework of national interconnection. In 2011, the power configuration pattern of “west-to-east power transmission” and “north-south power transmission” was formed [6]. During the Thirteenth Five-Year Plan period, the construction of cross-regional and cross-provincial transmission projects across the country was accelerated, the regional power grid framework was continuously improved, and the configuration capacity and safe operation level were steadily improved. Investment in power grid projects showed a downward trend during this period, with an average annual growth rate of -3.53% [7]. The construction of UHV AC/DC transmission channels has promoted the increasing scale of cross-regional power transmission [8, 9]. China’s power grid structure will continue to maintain the six regional power grid patterns of Northeast, North China, Northwest China, Central China, East China and South, which are relatively independent between regions, and cross-regional long-distance transmission should be dominated by DC lines, and the network structure will be further optimized in the region to form a clear and reasonable, hierarchical partition of the main grid [10]. In the long term, it will gradually develop from centralized large power grids to smart grids with distributed and comprehensive energy utilization, and technologies such as energy storage, microgrids, intelligent communications, and energy Internet will be widely promoted and applied, and the intelligent level of the power grid will be comprehensively upgraded [11].

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2 China’s Cross-Regional and Inter-provincial Power Transmission Layout In terms of spatial layout, China has maintained the reverse distribution characteristics of hydroenergy, wind energy and solar energy resource enrichment areas and electricity load areas for a long time. Inter-provincial and cross-regional transmission is the link and bridge to achieve the goal of clean energy utilization, and its transmission capacity mainly depends on regional power grid interconnection lines and UHV transmission projects. Figure 1 shows the national cross-regional transmission capacity and growth rate from 2016 to 2022, and it can be seen from the figure that the cross-regional transmission capacity has increased year by year, and the national cross-regional transmission of electricity will be 765.4 billion kWh in 2022, an increase of 6.3%.

18815

20000

17215

36.98% 15000 10000 5000

12445 24.54% 9085

13615

14815

40.00%

15615 30.00% 20.00%

9.40%

10.25%

8.81%

10.00% 9.30%

5.40% 0 2016 2017 2018 2019 2020 Cross-zone transmission capacity/10,000 kW

0.00% 2021 2022 Annual growth rate

Fig. 1. Cross-regional transmission capacity and annual growth rate from 2016 to 2022.

In general, China’s cross-regional power transmission situation, Northwest Power Grid, Southwest Power Grid, Northeast Power Grid belong to typical sending end power grids, East China Power Grid and North China Power Grid are typical receiving end power grids. North China Power Grid and China Southern Power Grid have Hong Kong, Macao and international transmission business due to their geographical location and infrastructure conditions. Due to its geographical location and the core grid function of the transmission network, Central China Power Grid is basically balanced in its power transmission situation, and it undertakes the hub function of regional power grid dispatching configuration while meeting its own power demand. With the rapid development of inter-provincial and cross-regional transmission projects, there are problems such as high safety risks of channel transmission and large gaps between actual transmission and design capabilities. The proportion of electricity transmitted outside the power grid at the sending end is relatively high, which requires the coordinated development of local resource endowment and industrial economy. The cross-regional electricity consumption of some receiving power grids accounts for a high proportion of local electricity consumption, and it is necessary to consider the coordinated allocation of power within provinces, between provinces and across regions. In

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the process of inter-provincial and cross-regional power transmission, give full play to the driving force of resource endowment, policy factors, market mechanism and infrastructure, coordinate the construction progress of transmission projects and supporting facilities, and ensure the realization of design capacity and utilization rate.

3 Construction Principle of the Spatial Weight Matrix The spatial weights matrix introduces spatial effects into econometric modeling studies by describing the spatial relationships between study units. The spatial weights matrix W is a non-negative matrix of order n by n, which can depict the relationship between regions in space. Each element in W, wij represents the relationship between the ith and jth regions of the space and the degree of relationship, as in Eq. (1). Among them, the spatial weight matrix setting requires that the spatial element does not have a spatial spillover effect on itself, and specifies the symmetry of the diagonal wii = 0 and the spatial spillover effect of the matrix [12, 13]. ⎡

w11 ⎢ w21 ⎢ wij = ⎢ . ⎣ .. wn1

⎤ w12 · · · w1n w22 · · · w2n ⎥ ⎥ .. . . .. ⎥ . . ⎦ . wn2 · · · wnn

(1)

The core idea of the spatial weight matrix setting is to investigate the various relationships between the regions in the space, and specifically measure the degree of relationship. When the two regions are closely connected, the corresponding wij in the spatial weight matrix will also be larger; When the connection between the two regions is loose, the corresponding wij in the spatial weight matrix will also be smaller [14]. The first law of geography states that everything between regions is related to each other [15]. The spatial correlation formed by power grid transmission projects is the main carrier of cross-regional and inter-provincial power transmission and power market transactions, which is different from the geographical adjacency and location relationship between provinces, and accurately depicts the inter-provincial transmission project connectivity relationship, which can be used as an important basis for studying regional power planning issues.

4 Spatial Correlation Study of Power Transmission Projects in China 4.1 Analysis of the Spatial Distribution of Transmission Projects Based on the connection relationship between regional grid unified dispatching and UHV transmission projects, each province realizes cross-regional power grid connection, and the spatial connection relationship is no longer limited by whether the geographical location between provinces is adjacent or not, and the UHV project also realizes the correlation between provinces with remote geographical locations in power production

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and consumption [16]. The transmission and dispatch of renewable energy electricity can be realized between provinces in the regional grid through the regional dispatch and control center; Among them, Hebei and Hebei Power Grid belong to Hebei Province and North China Power Grid; Through the Mengdong and Mengxi power grids, the Inner Mongolia Autonomous Region is closely related to the provinces in the North China Power Grid and the Northeast Power Grid; The Tibet Autonomous Region belongs to the Northwest Power Grid and passes through Tibet. The Sichuan-Chongqing line has close connection with Sichuan Province and Chongqing Municipality. UHV DC transmission projects are connected to the sending and receiving end provinces, and the provinces along the UHV AC transmission project have close power grid connections. 4.2 Regional Grid Connectivity Analysis Connectivity is an important indicator for characterizing network datasets, which can be analyzed by the grid spatial weights matrix, which is defined as Eq. (2).  n i and j belong to the same regional grid or are connected by UHV lines WE = 0 i and j are not in same regional grid and not connected by UHV lines (2) Among them, n is the number of connections between the two provinces through regional grids and UHV projects. According to the assumption of the spatial weight matrix of power grid projects, the transmission lines of 32 provinces in six regions during the 13th Five-Year Plan period are used to establish the spatial weight matrix of five-year power grid projects W2016 , W2017 , W2018 , W2019 , and W2020 according to the commissioning schedule. Adjacency matrix A matrix that represents the adjacency relationship between vertices. According to the direct geographical corner adjacency relationship of the province, the corner adjacency weight matrix WC is established. The inverse distance weighting matrix, Wl is a distance-based spatial weighting matrix that determines the spatial relationship between each point by calculating the distance between them and others. ArcGIS 10.2 was applied to analyze the connectivity of China’s regional power grids, and the results are shown in Table 2. Comparing the three types of spatial weight matrices, the connectivity of the grid spatial weight matrix is between the corner adjacency matrix WC and the inverse distance matrix Wl . The corner adjacency matrix WC has the least number of spatial connectivity and the weakest spatial connectivity of 14.5%, among which Hainan has no geographical adjacency relationship with other provinces. From 2016 to 2020, the average connectivity of the spatial weight matrix of the power grid was 16.8%, which was close to the geographical adjacency matrix relationship, but the connectivity level was significantly improved. From the variation characteristics of the spatial weight matrix of power grid projects from 2015 to 2019, the connectivity increased from 16.4% in 2016 to 17.0% in 2020, an increase of 0.6 percentage points. The number of connections increased from 198 to 227, an increase of 14.6%. It can be seen that power grid connectivity is affected by factors such as geographical location and construction costs, which has broken the barriers of administrative divisions to a certain extent, but at present, it is still based on geographical

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Table 2. Connectivity of spatial weight matrixes. Spatial weight matrix

Spatial connectivity

Number of connections

WC

14.5%

139

W2016

16.4%

198

W2017

16.6%

210

W2018

17.0%

210

W2019

17.0%

222

W2020

17.0%

227

Wl

35.0%

336

adjacency and initially expands regional connectivity. The level of regional connectivity continues to increase, but the growth rate is gradually flattening, and no new UHV transmission lines were expanded and put into operation in 2018. At the beginning of the 13th Five-Year Plan, the commissioning and construction of UHV projects gradually slowed down, and technical demonstration and planning adjustments were carried out, ushering in a new round of construction climax after 2018. In 2020, the construction of the UHV ‘Ri(in Chinese)’ zigzag AC ring network in central China entered a comprehensive construction stage, and the North China UHV AC backbone network with the highest voltage level and the strongest grid structure in the world was basically formed. At the same time, the power interconnection and mutual assistance complex formed in the Southern Power Grid area, Yunnan and Guizhou provinces, and the power flow distribution of power collection channels in all directions tends to be balanced and reasonable in the Northeast Power Grid area. Table 3. Province connectivity within regional power grids from 2016 to 2020. Year

2016

2017

2018

2019

2020

Central Power Grid

39

40

40

40

41

Northern Power Grid

53

58

58

62

63

Northwestern Power Grid

34

36

36

37

37

Eastern Power Grid

38

40

40

47

47

southern power grid

25

27

27

27

29

Northeastern Power Grid

9

9

9

9

10

Total

198

210

210

222

227

The statistics of connections by regional grid during the 13th Five-Year Plan period are shown in Table 3. From the perspective of regional power grid, the power grid connection and development are greatly affected by the geographical location and the characteristics of the sending and receiving ends, and the planning and growth of regional

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transmission network projects with relatively partial geographical location and small power demand is relatively slow. The Northeast Power Grid does not include the grid connections established in Inner Mongolia, and the level of connectivity is the worst among the six major power grids. At the beginning of the period, the construction and interconnection of power grid in central China was relatively developed, but the growth was the slowest during the period. On the basis of better connectivity, North China Power Grid has the fastest growth in grid connection strength, and the peak of line operation was in 2016, mainly because North China Power Grid includes large energy supply bases in Inner Mongolia and Beijing-Tianjin-Hebei Shandong and other energy demand areas, and the internal power grid connection intensity and external connection number have been rapidly improved. East China Power Grid and Northwest Power Grid are respectively the main power receiving power grid and the sending end power grid, and East China mainly accepts the hydropower transmission of Southern Power Grid, and the transmission line planning and operation growth rate is relatively fast. Affected by geographical location and unified planning of enterprises, China Southern Power Grid has close internal connectivity, but lacks line expansion with other regional power grids.

5 Conclusion The power supply is distributed and the power supply is nearby, the power grid is layered and zoned, and the local balance is balanced, and the receiving power grid accepts external power in multiple channels and directions to build an intrinsically safe future power grid. The construction of transmission projects is based on the transformation of China’s power grid form. Therefore, in order to clarify the future development direction of China’s transmission project construction, this paper analyzes the characteristics of China’s transmission network construction and operation through detailed data based on the development history of China’s regional power grid and UHV transmission project, focusing on the transmission capacity, the characteristics of the power grid at the sending and receiving ends, and the operation of UHV lines at the national and regional levels. On this basis, the spatial weight matrix of power grid projects is established, the adjacency matrix and inverse distance matrix are compared, the change trend of matrix connectivity is studied, and the connectivity evolution characteristics of regional power grids are analyzed, which provides reference for the analysis of spatial pattern and evolution characteristics of transmission grid projects.

References 1. Wei, Q., Kaiqi, S., Huangqing, X.: Advances in urban power distribution system. Energies 15(19), 7329 (2022) 2. Yongming, T., Chenyu, M., Jie, L., et al.: Research on power security in key areas of urban distribution network. J. Phys: Conf. Ser. 2409(1), 1–4 (2022) 3. Wencheng, S., Wentao, C., Yuhui, P., et al.: Research on the application of smart site management for cross-regional power grid project based on the basic framework of digital power grid. IOP Conference Series: Earth and Environmental Science 440(3), 1–11 (2020)

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4. Zhou, L., Sun, L., Sun, W., et al.: Digital power grid construction research of the cross-regional core power transmission grid in southwest china based on ubiquitous electric internet of things. IOP Conference Series: Materials Science and Engineering 677(4), 042107 (2019) 5. Research and Markets Offers Report: Power Grid Construction in China. Wireless News (2012) 6. Zhu, Y., Ke, J., Wang, J., et al.: Water transfer and losses embodied in the west-east electricity transmission project in China. Appl. Energy 275, 115152 (2020) 7. Hui, W., Yunyun, Z., Weifen, L., et al.: Transregional electricity transmission and carbon emissions: evidence from ultra-high voltage transmission projects in China. Energy Economics 123, 106751 (2023) 8. Shi, J., Tang, B., Hao, B., et al.: Application of adaptive sampling algorithm in solving the scattering field of UHVAC/DC transmission lines. The Journal of Engineering 16, 1404–1407 (2019) 9. Minhu, X., Yun, G., Yubo, S., et al.: Measurement and analysis of 220 kV overhead transmission line parameters. J. Phys: Conf. Ser. 1754(1), 012078 (2021) 10. Zhang, X., Zhu, Q., Zhang, X.: Carbon emission intensity of final electricity consumption: assessment and decomposition of regional power grids in china from 2005 to 2020. Sustainability 15(13), 9946 (2023) 11. Giannelos, S., Borozan, S., Aunedi, M., et al.: Modelling smart grid technologies in optimisation problems for electricity grids. Energies 16(13), 5088 (2023) 12. Francesca, R., Offer, L.: Spatial autoregressions with an extended parameter space and similarity-based weights. Journal of Econometrics 235(2), 1770–1798 (2023) 13. Zhengzheng, C., Yanli, Z., Xiaoyi, H.: Bayesian analysis of spatial dynamic panel data model with convex combinations of different spatial weight matrices: A reparameterized approach. Econ. Lett. 217, 110695 (2022) 14. Haiqi, W., Liuke, L., Lei, C., et al.: Geospatial least squares support vector regression fused with spatial weight matrix. ISPRS Int. J. Geo Inf. 10(11), 714 (2021) 15. Friedmann, J.R.P.: Regional development policy : a case study of Venezuela. MIT Press, Cambridge Mass (1966) 16. Xiaohua, S., Peng, W.: Effectiveness of carbon emissions trading and renewable energy portfolio standards in the Chinese provincial and coupled electricity markets. Utilities Policy 84, 101622 (2023)

A Model for Evaluating Science and Technology Innovation Capability of Energy Internet Firms Based on Analytic Hierarchy Process and Fuzzy Comprehensive Evaluation Rui Li(B) State Grid Energy Research Institute Co., Ltd., Beijing 102209, China [email protected]

Abstract. Rapid decarburization of energy sector is critical in the transition to global net zero, and building Energy Internet (EI) relies on a new technology revolution. In this paper, a model for evaluating science and technology (S&T) innovation capability of EI firms is introduced, in which Analytic Hierarchy Process (AHP) is used to determine the weight of each index and Fuzzy Comprehensive Evaluation (FCE) is adopted to obtain rational assessment results. Qualitative indicators and quantitative indicators, process indicators and outcome indicators, common features and individual characteristics, are effectively taken into account in the assessment process by the full combination and effective application of AHP and FCE. Finally, seven EI firms were investigated as case studies, and the viability of the suggested model are successfully validated. Keywords: Energy Internet · science and technology innovation · capability evaluating model · analytic hierarchy process · fuzzy comprehensive evaluation

1 Introduction The effects of climate change are becoming more apparent from year to year, highlighting the urgent need to take action to limit climate change. Currently, more than 130 countries and regions around the world have set ambitious net zero emission targets. Global energy policies and discussions have recently concentrated on the significance of decarbonizing energy system and the transition to net zero since a carbon pollution-free energy sector is a key for reducing emissions [1–3]. Rifkin introduced the idea of EI and the vision to achieve a sustainable reduction in carbon emissions. First of all, to promote the transformation of energy sector, which is dominated by fossil fuels, into one that is dominated by carbon-free energy. Secondly, to address the widespread integration of large-scale distributed generations (DGs) into EI, several approaches such as building energy carrying, are being adopted. And a third point, employing energy storages, such as electrochemical energy storages and hydrogen storages, to deliver electricity to consumers. Fourthly, using digital technologies like machine learning, and artificial intelligence, to make energy systems flexible and efficient. Fifthly, to actualize the wide © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 474–484, 2024. https://doi.org/10.1007/978-981-97-0877-2_49

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link between transportation system and power system through electric vehicles. It is clear that EI represents a transformation of the conventional energy sector, with S&T innovation serving as the driving force. Currently, Universities and institutions have done a lot of theoretical studies on EI concept, critical technology, and commercial strategies. Reference [3] provided the concept and architecture of EI, and key issues are discussed in depth. Reference [4] analyzed the fundamental connotation of EI, sorted out development trends of EI, and elaborated on S&T issues that need to be focused on in the researches of EI. Literature [5] and [6] conduct theoretical and case studies on firms engaged in new energy business and their comprehensive energy business models of EI. Reference [7] and [8] conducted case studies on micro-grid and virtual power plant. Net-zero targets rely on several technologies such as renewables, smart grid, energy storages, hydrogen, energy efficiency. Additionally, a variety of innovations are required for EI like commercial strategies. However, S&T innovation capacities of EI firms are not given enough attention in present literatures. Therefore, this study conducts the research on EI S&T innovation issue based on an overall analysis of energy business and the similarity of organizational capabilities. An evaluation model and corresponding approach are proposed for S&T innovation capability of EI firms. And then availability and effectiveness are confirmed by case studies.

2 Connotations of EI Firms and S&T Innovation Capacity 2.1 Connotation of EI The essence of EI is a highly integrated intelligent system including energy system, transportation system, natural gas system and digital system, where power system is a hub or a bridge, variable renewable energies (VERs) are the main forms of energy supply, large-scale DGs and various types of energy storages can be widely connected to power grid, and digital technologies are key tools [2, 8]. When it comes to the issue of technology, EI is undergoing rapid reformation in a scenario where digital technologies are widely used. Energy technologies upgrades are also being carried out. When it comes to the issue of morphologic, EI has a strong network structure and vast distribution where centralized power bases, DGs, and energy storages are widely connected. When it comes to the issue of functionality, EI possesses excellent resource allocation abilities that can guarantee intelligent energy service requirements. 2.2 Connotation of S&T Innovation Capability of EI Firms S&T innovation is a broad phrase for original scientific research and technology innovation. In order to produce new products, enhance the quality of existing products, and offer new services, it is necessary to create and use new knowledge, technologies, and processes as well as adopt new production techniques and management models. When it comes to capacity, that is the all-encompassing characteristic demonstrated in successfully achieving a task or a goal. For businesses, capability refers to all of the firm’s strengths in terms of capital, management, sales, technology, and production.

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Overall, the ability of EI firms to use S&T resources, such as talent, financial, and other resources, to conduct research and development, create S&T achievements, and translate achievements into productivity, is referred to as S&T innovation capability.

3 Capacity Evaluation Modeling 3.1 Principles of Capability Evaluation Modeling First, both qualitative and quantitative indicators must be used in the evaluation modeling for S&T innovation capabilities, where qualitative analysis for the objective description, quantitative indicator analysis for the intuitive display and the in-depth discussion of the evaluation outcomes. Second, the process indicators and outcome indicators must be effectively combined in the modeling of S&T innovation capabilities of EI firms. The evaluation model should place equal emphasis on process aspects such enterprise management, internal operation, and growth momentum. Process indicators stand out among them because they concentrate more on following the path of S&T innovation, which can aid in our analysis of the factors that contribute to the gap in S&T innovation skills. Third, the evaluation model should not only concentrate on the general components to conduct S&T research, such as S&T talent, R&D funding, research infrastructure, etc., but also take into account the particular needs of EI firms, such as the safe and reliable supply of energy through technologies, promoting low-carbon transformation through technologies, and broadly deploying digital technologies. 3.2 Dimensions of Capability Evaluation Modeling S&T capability and the innovation capability are the two key dimensions. S&T capabilities, according to EI business, refer to the following four fields: power supply, power grid, demand-side, and the complementary technologies, such as digital and materials. Meanwhile, the innovation capacity may be broken down into the following four links: S&T decision-making, S&T input, S&T execution, and S&T output. (1) S&T capability: S&T capability is used to assess how basic research is organized, how well technologies are understood, and how well projects are constructed. In the field of power-supply, in response to the grid-connected demands for VER bases and large-capacity offshore wind power, EI firms should pay attention to the significant needs to enhance grid-support capabilities and operational risk prevention for VERs, such as key technologies and devices of grid-forming, the technologies of collection and delivery of large-capacity VER bases. In the field of power-grid, to effectively address the significant challenges of EI with high proportions of VERs and power electronic devices, EI firms should conduct more researches on the theory of power system stability, the key technologies and the core devices of resilient power grid. In the field of demand-side, in response to the development trend of the complementary utilization among multiple energy sources and the intelligent interaction of flexible loads, EI firms should conduct more researches on key technologies and

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devices of energy router, mathematical modeling and optimal scheduling of integrated energy systems, the use of low-carbon hydrogen and hydrogen-based fuels, etc. In the field of complementary technologies, new materials, new digital technologies will be widely used, and corresponding theories, materials, and devices should be research hotspots. For EI firms, the modeling method and real-time simulation technologies for power electronics, the preparation of high performance insulating materials, the development of power electronic chips and devices, should all be prioritized. (2) Innovation capability: To evaluate soft power of EI firms, including their capacity for S&T decision-making, S&T input, S&T execution, and S&T output. When it comes to S&T decision-making capacity, it refers the ability to capture the cutting-edge technical requirements that are driving the field integrate them into the framework of the S&T development plan and S&T project guidelines. For instance, storages is an important consideration for China, as the areas with the largest potential for VERs appear to be far from the main industrial hubs and city centers. Therefore, EI firms should explore technological needs, such as electrochemical energy storage, hydrogen energy storage, and flexible DC transmission, and promote all these technological needs in long-term planning or the major S&T project guidelines. When it comes to S&T input capacity, it refers to the ability of EI firms to increase the R&D efficiency by the accurately allocation of innovation resources, which can be measured by specific indicators like the quantity and structure of R&D investment, the quantity and structure of S&T talents, and the quantity and arrangement of major S&T infrastructures. For example, EI firms should enhance their S&T contributions to technological domains such smart grid, energy storage, artificial intelligence, etc. This involves growing the talent pool, acquiring new labs, and increasing R&D spending. When it comes to S&T execution capability, it refers to the ability to to transform innovation resources into achievements effectively. For example, due to the widespread application of digital technologies in EI, the research paradigm has undergone significant changes. Choosing digital technologies would most likely result in high efficiency and high quality than it would if using more conventional R&D methodology. However, the new technologies also come with potential risks. EI firms should consider these risks and how best to mitigate them [10]. The ability of EI firms to effectively convert innovation inputs into outputs is referred to as S&T output capability. On the one hand, S&T output capacity is reflected in the application of S&T advancements to safeguard the affordability of energy, to boost energy efficiency, and to strengthen energy’s resilience. On the other hand, S&T output capacity is also reflected in the application of S&T achievements to create new business models, such as comprehensive energy services, virtual power plant. Table 1 presents the model for S&T innovation capability of EI firms.

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R. Li Table 1. Evaluation indicators for S&T innovation capacity of EI firms.

Target layer

Rule layer

Function layer

Factor layer

Index layer

S&T innovation capability (A)

S&T capability (B1)

S&T capability of power-supply (C1)

Performance of basic research (D1)

Arrangement of basic research (E1)

Performance of applied research (D2)

Competences in technologies and equipment (E2)

Performance of experimental development (D3)

Strength of S&T demonstration projects (E3)

Performance of basic research (D4)

Arrangement of basic research (E4)

Performance of applied research (D5)

Competences in technologies and equipment (E5)

Performance of experimental development (D6)

Strength of S&T demonstration projects (E6)

Performance of basic research (D7)

Arrangement of basic research (E7)

Performance of applied research (D8)

Competences in technologies and equipment (E8)

Performance of experimental development (D9)

Strength of S&T demonstration projects (E9)

Performance of basic research (D10)

Arrangement of basic research (E10)

Performance of applied research (D11)

Competences in technologies and equipment (E11)

Performance of experimental development (D12)

Strength of S&T demonstration projects (E12)

Decision-making capacity in S&T strategy and planning (D13)

Role in the major issues of S&T innovation policies (E13)

Decision-making capacity in S&T innovation tasks (D14)

Role in the major issues of S&T innovation tasks (E14)

Performance of S&T talents (D15)

Number of R&D personnel (E15)

S&T capability of power-grid (C2)

S&T capability of demand-side (C3)

S&T capability of complementary technologies (C4)

Innovation capability (B2)

S&T decision-making capacity (C5)

S&T input capacity (C6)

Proportion of R&D personnel (E16) Proportion of S&T talents and teams at top level (E17) Performance of R&D investment (D16)

R&D intensity (E18) R&D expenditure (E19)

(continued)

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Table 1. (continued) Target layer

Rule layer

Function layer

Factor layer

Index layer R&D expenditure of basic research (E20)

Performance of S&T infrastructure (D17)

Major infrastructures for S&T innovation (E21) Major laboratories for developing technologies (E22)

S&T execution capability (C7)

Capability of S&T policy and strategy (D18)

Performance of S&T strategy and planning (E23) Performance of S&T innovation incentive Policy (E24)

Capability of R&D activities (D19)

Performance in major S&T special projects (E25) Strength in technologies and equipment (E26)

S&T output capacity (C8)

Capability of S&T collaboration (D20)

S&T joint institutions (E27)

Capability of Technologies adoption (D21)

New product development and adoption (E29)

Industry-university-institute cooperation (E28)

Industrial alliances (E30)

Capability of knowledge Patents by origin (E31) and technology outputs, PCT patents by origin (E32) and creative outputs (D22) International standard (E33) Performance of IEC (E34)

3.3 Evaluation Methods and Mathematical Modeling (1) AHP: Due to its capacity to effectively integrate expertise and logical analysis, AHP is frequently used in comprehensive evaluation [11]. Step 1: Create a judgment matrix A. The opinions of experts determine the priorities of each index. The elements of the same layer are compared pairwise to the judgment matrix obtained. The values in the judgment matrix indicate the importance of the inferior factors with respect to the factors in the superior layers, shown as (1). Step 2: Determinate weights. In the judgment matrix A, determine the geometric mean of the product of each row element. The fraction of each factor in the hierarchical single sorting is calculated after normalization, shown as (2) and (3). Step 3: Verify consistency. If CR < 0.1, the judgment matrix satisfies the requirement of consistency; otherwise, the matrix should be modified., shown as (4) to (5), where CI is the index used for measuring the amount by which a judgment matrix deviates from consistency, CR represents the random consistency ratio, and RI is used to reconcile the

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different requirements of the relevant CI. ⎞ α11 · · · · · ·α1n   ⎟ ⎜ A = αij n×n = ⎝ · · · · · · · · · · · · ·⎠ αn1 · · · · · ·αnn

  n n wi = αij ⎛

(1)

(2)

j=1

wi wi = n

(3)

  n n wi = αij

(4)

i=1 w i

j=1

λmax =

n  (AW )i i=1

CR =

(5)

nWi CI RI

(6)

(2) FCE: FCE utilizes fuzzy mathematics theory to quantify factors with unclear boundaries and difficulty in quantification. In this paper, FCE is used to evaluate the qualitative indicators. Meanwhile, the efficacy coefficient method is adopted to incorporate quantitative indicators into the fuzzy evaluation set [11]. Step 1: Set a fuzzy evaluation set. U is the set of factors. V is an evaluation set consisting of n types of comments representing the state of each factor ui of the evaluated object. In this paper, V is divided into five grades, shown as Table 2. Table 2. Judgment levels and their scores. Judgment

Better

Good

Normal

Bad

Worse

Score

100–90

90–80

80–70

70–60

60–50

Step 2: Create a fuzzy evaluation matrix. The weights and membership vectors of each factor are determined separately, and then a fuzzy evaluation matrix, represented as (7), should be obtained. A total evaluation matrix R is produced, shown as (8). Step 3: Single factor fuzzy evaluation. Perform fuzzy transformation on each single factor evaluation matrix and weight set separately, where Ai is the weight matrix, and ‘◦’ represents the generalized synthesis operation of Ai and Ri , which is the combination of fuzzy operators, shown as (9). Ri = (ri1 , ri2 , · · ·, rin )

(7)

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⎤ ⎡ ⎤ r11 , r12 , · · ·, r1n R1 ⎢ R ⎥ ⎢ r , r , · · ·, r ⎥ 2n ⎥ ⎢ 2 ⎥ ⎢ 21 22 =⎢ ⎥=⎢ ⎥ ⎣ · · ·⎦ ⎣ · · ··, · · ·, · · ·, · · ··⎦

481

⎡

  R = rij m×n

(8)

rm1 , rm2 , · · ·, rmn

Rm

Bi = Ai ◦ Ri = (b1 , b2 , · · ·, bn )

(9)

Step 4: Multi-factor fuzzy evaluation. Combine the evaluation vectors of the next level indicators into the evaluation matrix of the previous level indicators, and perform a synthesis operation with the weights of the previous level, and so on, until the target layer is reached. Finally, the S&T innovation capabilities of EI firms are evaluated.

4 Case Studies The seven businesses, which involves power production and power grid, are chosen as case studies to demonstrate the effectiveness and viability of the suggested models and approaches. During the process, twenty specialists were invited to calculate the weights of indicators and perform a thorough analysis of each indication of the sample firms. The relevant information of all these invited specialists is shown in Table 3. The weights of each index are calculated by AHP, as indicated in Table 4. Table 3. The relevant information of the experts. Ages

Fields

35–45 45–60 60Ratio 25%

50%

Affiliations

power-supply power-grid power-sales Firm colleges institutes

25% 35%

40%

25%

45% 30%

25%

Seven firms are assessed for S&T innovation capabilities after careful analysis, some public data, and experts’ evaluation. The results based on the aforementioned approach are displayed in Table 5, Fig. 1, and Fig. 2, respectively.

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A

B1

B2

C1

C2

C3

C4

C5

C6

C7

1.0000

0.4583

0.5417

0.3111

0.3317

0.2256

0.1317

0.1340

0.2694

0.1867

C8

D1

D2

D3

D4

D5

D6

D7

D8

D9

0.4098

0.1778

0.3558

0.4664

0.1869

0.3553

0.4578

0.2110

0.3973

0.3918

D10

D11

D12

D13

D14

D15

D16

D17

D18

D19

0.3069

0.3288

0.3643

0.5133

0.4867

0.4184

0.3590

0.2226

0.4609

0.3825

D20

D21

D22

E1

E2

E3

E4

E5

E6

E7

0.1565

0.6850

0.3150

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

E8

E9

E10

E11

E12

E13

E14

E15

E16

E17

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

0.2980

0.2581

0.4439

E18

E19

E20

E21

E22

E23

E24

E25

E26

E27

0.4710

0.3731

0.1559

0.6333

0.3667

0.4583

0.5417

0.3367

0.6633

0.6683

E28

E29

E30

E31

E32

E33

E34

/

/

/

0.3317

0.7133

0.2867

0.2018

0.1653

0.2673

0.3656

/

/

/

Table 5. Evaluation results of firms. Better

Good

Normal

Bad

Worse

100–90

90–80

80–70

70–60

60–50

score

Firm 1

0.4126

0.3334

0.2093

0.0401

0.0045

91.09

Firm 2

0.1753

0.3087

0.4004

0.0963

0.0193

85.24

Firm 3

0.2453

0.4075

0.2252

0.0986

0.0234

87.53

Firm 4

0.2645

0.3311

0.2864

0.0976

0.0204

87.22

Firm 5

0.1349

0.2477

0.4350

0.1590

0.0310

83.57

Firm 6

0.2085

0.3645

0.2832

0.1143

0.0294

86.08

Firm 7

0.0652

0.1836

0.3598

0.3351

0.0563

78.66

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483

Fig. 1. Evaluation results of Firm A.

(a) S&T capability of firms

(b) Innovation capability of firms

Fig. 2. Evaluation results of all these firms.

5 Conclusion The transition to low-carbon energy has gained support on a worldwide scale, and EI firms have emerged as key players to attain the net zero emissions goal. The evaluation of the S&T innovation capabilities of EI firms is of major significance since energy technologies and digital technologies have emerged as significant driving forces. In this research, an evaluation model and the associated approach are introduced for S&T innovation capabilities of EI firms using AHP and FCE. The aforementioned approach adequately takes into account both qualitative and quantitative indicators, process indicators and outcome indicators, common traits and individual characteristics. The effectiveness and viability of the suggested planning model and optimization techniques are confirmed by simulation results. Meanwhile, additional studies show that S&T execution skill is a relative advantage while S&T decision-making capacity is the current weakness of the EI firms in the case study. Acknowledgments. This work was supported by the science and technology project of State Grid Corporation of China, “Research on promotion path, power transitive model and empirical research of Energy Internet firms’ innovation capability” (1400-202157233A-0-0-00).

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References 1. Evans, M.A., Bono, C., Wang, Y.: Toward net-zero electricity in Europe: what are the challenges for the power system. IEEE Power Energ. Mag. 20(4), 44–54 (2022) 2. Beckstedde, E., Meeus, L.: From “fit and forget” to “flex or regret” in distribution grids: dealing with congestion in European distribution grids. IEEE Power Energ. Mag. 21(4), 45–52 (2023) 3. Wu, J., Zhou, Y., Gan, W.: Smart local energy systems towards net zero: practice and implications from the UK. CSEE Journal of Power and Energy Systems 9(2), 411–419 (2023) 4. Hussain, H.M., Narayanan, A., Nardelli, P.H.J., Yang, Y.: What is energy internet? concepts, technologies, and future directions. IEEE Access 8, 183127–183145 (2020) 5. Qin, J., Wan, Y., Yu, X., Li, F., Li, C.: Consensus-based distributed coordination between economic dispatch and demand response. IEEE Transactions on Smart Grid 10(4), 3709–3719 (2019) 6. Wu, Z., Wang, J., Zhong, H., et al.: Sharing economy in local energy markets. J. Modern Power Sys. Clean Ener. 11(3), 714–726 (2023) 7. Hui, H., Chen, Y., Yang, S., et al.: Coordination control of distributed generators and load resources for frequency restoration in isolated urban microgrids. Appl. Energy 327, 120116 (2022) 8. Bhuiyan, E.A., Hossain, M.Z., Muyeen, S.M., et al.: Towards next generation virtual power plant: technology review and frameworks. Renew. Sustain. Energy Rev. 150, 111358 (2021) 9. Kang, C.: Towards net-zero emission power system: deploy long-duration electricity storage technology for power systems with high penetration of renewables. iEnergy 1(1), 11–11 (2022) 10. Guo, H., Yang, J., Han, J.: The fit between value proposition innovation and technological innovation in the digital environment: implications for the performance of startups. IEEE Trans. Eng. Manage. 68(3), 797–809 (2021) 11. Li, Y., Sun, Z., Han, L., Mei, N.: Fuzzy comprehensive evaluation method for energy management systems based on an Internet of Things. IEEE Access 5, 21312–21322 (2017)

Site Selection and Capacity Determination of Photovoltaic Generation Based on Nodal Inertia Constrained Chengbin Chi1(B) , Shan Liu2 , Qi Liu1 , Fan Li3 , Guanghua Wang4 , and Jun Mei4 1 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., Beijing 102209, China [email protected] 2 Beijing Key Laboratory of DC Grid Technology and Simulation, State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China 3 State Grid Shanghai Municipal Electric Power Company, Shanghai 200120, China 4 School of Electrical Engineering, Southeast University, Nanjing 210096, China

Abstract. Aiming at the stochasticity of PV output power, and considering the influence of node critical inertia when system disturbance occurs, in this paper, a calculation method of PV power station siting capacity taking into account the node inertia constraints is proposed. Firstly, the primary embedding location of the PV plant is confirmed based on the results of the node critical inertia calculation when the disturbance occurs; Then, taking the minimum voltage deviation, the maximum total capacity of accessed PV and the minimum network loss as the planning objectives, the node voltage qualification rate as the main constraints to construct the calculation model. At the same time, the hierarchical analysis method is used to establish the optimal total objective function for the coordination of the three planning objectives and the particle swarm optimization (PSO) is used to solve the model. Taking the IEEE39 system as an example for simulation analysis, the results show that the network node voltage deviation and reduced by 26.9%, the total amount of renewable energy access is 707 MW and the node voltage qualification rate meets the planning requirements. Keywords: Photovoltaic generations · Nodal critical inertia · Voltage deviation · Probabilistic load flow

1 Introduction In recent years, photovoltaic has developed rapidly under the guidance and support of national policies and renewable energy-related technologies. As the country puts forward the strategic policy of building a new type of energy system, the penetration rate of photovoltaic in the power grid is also increasing, and the problem of photovoltaic carrying capacity limit has become a hotspot of concern in power grid planning. However, it is limited by the randomness of photovoltaic power output with weather conditions, the timeliness of time changes and the spatial inconsistency of light intensity in different © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 485–493, 2024. https://doi.org/10.1007/978-981-97-0877-2_50

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regions. The large-scale access of photovoltaic is bound to further increase the uncertainty of the power system, such as increasing the probability of voltage overruns at certain nodes of the power system. Among the existing studies, literature [1] had used purely mathematical calculations to analyze the new energy siting and capacity determination problem to optimize the target using network losses and network voltage levels. Literature [2] comprehensively considered the uncertainty factors such as load, renewable energy output, and power market price, established a dynamic probability model, and used genetic algorithm based on Pareto optimality theory to optimize the objective function. Literature [3] quantifies the annual power consumption and power abandonment, and proposed an access system planning model for multi-cluster renewable energy via aggregation station and multi-return DC grid-connection under the economic optimality objective. Literature [4] had proposed the PV center of gravity theory and applied it to the PV maximum access capacity calculation. Literature [5] had proposed a C-type Gram-Charlier series expansion method based on maximum entropy improvement to improve the computational accuracy efficiency. Literature [6] had proposed a PV power interval prediction technique based on parameter optimization of the Extreme Learning Machine (ELM) model to reduce the effect of PV output uncertainty. Literature [7] had solved the new energy siting and capacity determination problem under non-unit power factor by stochastic fractal search algorithm. The photovoltaic power station is connected to the grid through power electronic devices, which are decoupled from the system frequency and cannot provide inertia for the system. The growth rate of the photovoltaic power station is higher than that of the synchronous generator set or the replacement of the synchronous unit by the photovoltaic power station will cause a decrease in system inertia. At the same time, due to the limitation of power generation resources, PV power stations are geographically nonuniformly distributed, which makes the uneven distribution of grid inertia characteristics prominent. However, in the current research, fewer scholars have considered the inertia of the connected system when grid-connecting the PV. Therefore, in this paper, on the basis of considering the stochasticity of PV output, further considering the influence of the node critical inertia when the system is perturbed, a method of calculating the capacity of PV power plant siting taking into account the node inertia constraint is proposed. This paper establishes a siting and capacity model taking into account the node inertia constraints, constructs constraints such as the node voltage qualification rate, and solves the model using the PSO. The IEEE39 system model is used as an example to validate the effectiveness of the proposed approach.

2 First Site Selection According to special relativity, inertia is an inherent property of energy (objects) and any inertia should be attributed to energy. The inertia of a power system is the property of the system that suppresses energy fluctuations [8]. Synchronous generator sets are a major component of power supplies in conventional power systems. Because its rotating axis can provide a significant amount of inertia, it can provide the system with sufficient inertial resources. However, in the power system with high converter ratio, the inertia

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ratio on the power supply side decreases, and the importance of inertia on the load side becomes prominent. When the power disturbance occurs in the system, the power disturbance magnitude, inertial time constant and frequency satisfy the swing equation. 2Hsys

dfcoi = P dt

(1)

where fcoi , P denote the system center of inertia frequency, and the power inequality measure respectively. Because PV does not have virtual inertia, it is unable to release energy after a disturbance in the system. Therefore, it needs to be connected to the node that satisfies the critical inertia of the node in the system. In the case of target frequency change rate and disturbance power, the inertia of all nodes in the system is calculated by swing equation and arranged in descending order. Then the critical inertia is obtained and the calculated data set is used as the primary location set of PV.

3 Probabilistic Load Flow 3.1 Probabilistic Model of PV An important component of photovoltaic power generation is solar cells. The research shows that the light intensity has randomness and regularity, and follows Beta distribution in a certain period of time. The probability density function is shown in the following equation [9].     P b−1 P a−1 (a + b) 1− f (P) = (2) (a)(b) Pmax Pmax where r is the light intensity; rmax is the maximum light intensity; P is the PV output power; Pmax is the maximum PV output power; a and b are the shape parameters of the Beta distribution. 3.2 Expansion of Gram-Charlier Series If two random variables are independent of each other, their linear sums corresponding to convolution operations can be transformed into algebraic operations for the corresponding semi-invariants. Then the semi-invariants and corresponding moments of the desired random variables are obtained. Afterwards, the Gram-Charlier series expansion can be used to approximate the probability density function and cumulative distribution function of the random variable. If f (x) is the probability density function of a random variable x, and F(x) is its corresponding cumulative distribution function, which satisfies F’(x) = f (x), then f (x) and F(x) can be expressed as: k6 + 10k32 (6) k3 (3) k4 k5 ϕ (x) + ϕ (4) (x) − ϕ (5) (x) + ϕ (x) 3! 4! 5! 6! k8 + 56k3 k5 + 35k42 (8) k7 + 35k3 k4 (7) − ϕ (x) + ϕ (x) + · · · 7! 8!

f (x) = ϕ(x) −

(3)

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∞

k6 + 10k32 (5) k3 (2) k4 k5 ϕ (x) + ϕ (3) (x) − ϕ (4) (x) + ϕ (x) 3! 4! 5! 6! x (4) k8 + 56k3 k5 + 35k42 (7) k7 + 35k3 k4 (6) − ϕ (x) + ϕ (x) + · · · 7! 8!

F(x) =

ϕ(x)dx −

where ϕ(x) is the probability density function of the standard normal distribution and ϕ (i) (x) is the i-th order derivative of ϕ(x).

4 Optimal Chimeric Morphological Planning Models 4.1 Objective Function Under the premise of minimum voltage deviation, maximum access capacity and minimum network loss, different weights are assigned to the three objectives. (1) Minimum voltage deviation The voltage deviation can reflect the voltage level and power quality of the whole network, so the first optimization objective function f 1 is to minimize the voltage deviation. Nb    Ui − Uiref  f1 =

(5)

i=1

where U iref represents the reference voltage of the node voltage U i ; N b represents the number of nodes in the distribution network; U i represents the calculated voltage at node i. (2) Maximum capacity of PV The second optimization objective function f 2 is the maximum weighted sum of the connected PV power capacity. f2 =  n

1

i=1 xi Si

(6)

where x i is set to 1 or 0, 1 indicates that the i node is connected to the PV power supply, and 0 indicates that the node is not connected; n is the number of grid nodes; Si is the PV capacity connected to the node i. (3) Minimum network loss The third optimization objective function f 3 is the lowest network loss after the access. f3 =

NL 

 Gi,j Uj2 + Ui2 − 2Ui Uj cos θij

(7)

l=1

where θ ij represents the voltage phase angle difference between node i and node j; Gij represents the conductance between node i and node j; N L represents the total number of network lines; U i represents the voltage per unit value of node i.

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The weight analysis is carried out for the three objectives of coordinated optimal to achieve the normalization of multiple objectives and unify the dimension. The voltage deviation is set as the primary target, the access capacity is set as the secondary target, and the network loss is set as the tertiary target. After consistency checking, the multiobjective function is expressed as: min F = 1 f1 + 2

PDGall PDGloss + 3 Pbefore Ploss

(8)

where PDGall is the inverse of the total capacity of the access to PV; Pbefore is the total active capacity of the system before PV connection; PDGloss is the network loss generated when PV is connected to the grid; Ploss is the initial network loss of the grid. 4.2 Restrictive Condition (1) equational constraint When planning for distributed power, the first step is to ensure a reasonable distribution of tidal currents. ⎧ Nb ⎪    ⎪ ⎪ ⎪ P = U Uj Gij cos θij + Bij sin θij i i ⎪ ⎪ ⎨ j=1 (9) Nb ⎪  ⎪   ⎪ ⎪ ⎪ Q = Ui Uj Gij sin θij − Bij cos θij ⎪ ⎩ i j=1

where Pi and Qi are the injected active and reactive power of node i; U i and U j are the voltage amplitudes of nodes i and j; Gij and Bij are the conductance and susceptance of branch ij; θ ij is the voltage phase angle difference between nodes i and j. (2) inequality constraint Node voltage amplitude constraint: Vi min ≤ Vi ≤ Vi max

(10)

Branch circuit power constraint: 0 ≤ Si ≤ Si max

(11)

PV capacity constraint: 

PDG · ni ≤ Pi,D max PDG · N ≤ Ptotal

(12)

Active power constraint of equilibrium node: 0 ≤ Pslack ≤ Pslack max

(13)

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Distributed inertial primary siting constraint: HRocof =0.25 = {H1 , H2 , H3 , . . . , Hn }

(14)

where V imin and V imax represent the upper and lower voltage limits of node i; S imax is the upper limit of emergency operating power for branch circuits; Pi,Dmax is the upper limit of PV access for a single node; Ptotal is the total capacity of PV; Pslackmax is the upper limit of active power at the balancing node; H Rocof =0.25 is the dataset of distributed inertial primary site selection results. The power grid voltage is probabilistic under the influence of PV access. Therefore, this paper applies chance constraints to the power grid voltage under the influence of random factors:  PU {min[Ui ] ≤ Ui ≤ max[Ui ]} ≥ δ (15) min[Ui ] ≥ 0.94(pu) ∪ max[Ui ] ≤ 1.06(pu) In this paper, the inequality constraint of grid voltage over limit with photovoltaic power generation is expressed as the voltage qualification rate constraint in the form of chance constraint. Where PU is the probability of a qualifying event; δ is the confidence level. According to the actual requirements of the power grid, the appropriate confidence level δ can be selected, generally take 0.90 ~ 0.99 [10].

5 Example Analysis In this paper, the IEEE39-node system is taken as an example, and its system structure is shown in Fig. 1. The voltage level of the system is 345 kV, the reference power is 100 MW, the total active load of the system is 6254.23 MW and the total reactive load is 1387 MVAR. Because PV does not have virtual inertia, it cannot release energy after the disturbance of the system. Therefore, it needs to be connected to nodes that meet the critical inertia of nodes in the system. When the frequency change rate Rocof is 0.25Hz /s and the disturbance power P is 100MW, the critical inertia is calculated by the swing equation: Hmin =

1 P = = 100 2Rocof 2 × 0.005

(16)

where the critical node that can satisfy the lowest critical inertia of 100 is the 29th node. Based on the results of the primary embedding location siting of the PV plant, the range of access node locations is 1–29 nodes. The total number of distributed power access nodes is 2, and the access capacity of each PV does not exceed 600 MW. The amplitude of the voltage at each node ranges from 0.94 p.u. to 1.06 p.u. The sum of the voltage deviations at each node before connecting to PV is 0.8284 p.u. The confidence level is chosen to be 0.95. Under the MATLAB simulation environment, PSO is used to optimize and solve the multi-objective model established in the previous section for the siting and capacity determination of PV. The PSO algorithm populations are all 300, the maximum number of iterations is 25, the variable dimension is 4, the inertia weight w is 0.8, the learning factor c1 is 0.5 and c2 is 0.5.

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Fig. 1. IEEE39 System Diagram

Table 1. PV planning scheme Optimal location for PV

Maximum access capacity(MW)

22

560

23

147

The results of PV power station location and capacity planning solved by the PSO algorithm are shown in Table 1. In the IEEE39 node system, the voltages at each node solved by the PSO algorithm are shown in Fig. 2.

Fig. 2. Comparison of voltage amplitude before and after PV access

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After combining the obtained PV access capacity with the probabilistic power flow, the threshold crossing probability of voltage of each node can be obtained, and the probability density curve of voltage of each node is shown in Fig. 3. The cumulative probability curve of voltage at each node is shown in Fig. 4. From Fig. 3 and Fig. 4, it can be seen that under the constraints of the voltage magnitude at each node, each node voltage satisfies the overrun probability requirement.

Fig. 3. 1–29 node voltage probability density curve

Fig. 4. 1–29 node voltage accumulation probability curve

6 Conclusion In this paper, a method of calculating the siting capacity of PV is proposed, which takes into account the node inertia and PV output uncertainty. Firstly, the critical inertia nodes that can still maintain the stability condition when the system is perturbed are calculated by the critical inertia calculation, and this result is used as a one-time embedding site selection ensemble. Secondly, considering the uncertainty of PV output, and at the same time comprehensively considering a variety of factors such as node voltage deviation and, the total capacity of PV power plant access and active network loss, the objective

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function and constraints are established. Finally, the IEEE39 system is used for simulation verification. The results show that under the calculation method proposed in this paper, the total capacity of PV can be accessed up to 707 MW, and the voltage of each node after accessing meets the overrun probability requirement. Acknowledgments. Funded by Technology Project of the State Grid Corporation Headquarters Management “Research on network topology construction of dc power grid and its coupling with ac power grid/ 5100-202158467A-0-0-00”. This paper is also supported by the National Natural Science Foundation of China under Grant 52077037.

References 1. Muttaqi, K.M., Le, A.D.T., Negnevitsky, M., et al.: An algebraic approach for determination of dgs parameters to support voltage profiles in radial distribution networks. IEEE Trans. Smart Grid. 5(3), 1351–1360 (2014) 2. Soroudi, A., Caire, R., Hadjsaid, N., et al.: Probabilistic dynamic multi-objective model for renewable and nonrenewable distributed generation planning. IET Gener. Transm. Distrib. 5(11), 1173–1182 (2011) 3. Li, Z., Li, G., Zhou, M., et al.: Comprehensive optimization method for location and capacity of new energy access system based on fermat-weber problem. Power System Technology. 44(6), 2118–2126 (2020). (in Chinese) 4. Wei, X., Wu, J., Ding, R., et al.: Distributed PV hosting capacity calculation of distribution network based on PV barycenter theory. Power System Technology (2022). https://doi.org/ 10.13335/j.1000-3673.pst. 2004. (in Chinese) 5. Cao, R., Xing, J., Li, Z., et al.: Improved series expansion based probabilistic load flow calculation for power system with wind power. Power System Technology. 46(9), 3447–3455 (2022). (in Chinese) 6. He, Z., Zhang, Y., Zheng G., et al.: Interval prediction technology of photovoltaic power based on parameter optimization of extreme learning machine. J. Shanghai Jiaotong Univ. 338 (2022) https://doi.org/10.16183/j.cnki.jsjtu. (in Chinese) 7. Nguyen, T.P., Vo, D.N.: A novel stochastic fractal search algorithm for optimal allocation of distributed generators in radial distribution systems. Appl. Soft Comput. 70, 773–796 (2018) 8. Bian, Y., Wyman-Pain, H., Li, F., et al.: Demand side contributions for system inertia in the GB power system. IEEE Trans. Power Syst. 33(4), 3521–3530 (2018) 9. Zhang, X., Kang, C., Zhang, N., et al.: Analysis of mid/long term random characteristics of photovoltaic power generation. Automation of Electric Power Systems. 38(6), 6–13 (2014). (in Chinese) 10. Zhou, X., Ke, D., Sun, Y.: DG planning based on chance constraint of distribution network static voltage quality for renewable energies. Electric Power Automation Equipment. 35(9), 143–149 (2015). (in Chinese)

Research on Optimal Chimeric Morphology of Flexible DC Interconnect Topology Considering Node Inertia Constraints Chengbin Chi1(B) , Shan Liu2 , Qi Liu1 , Fan Li3 , Xuan Liu4 , and Jun Mei4 1 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., Beijing 102209, China [email protected] 2 Beijing Key Laboratory of DC Grid Technology and Simulation, State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China 3 State Grid Shanghai Municipal Electric Power Company, Shanghai 200120, China 4 School of Electrical Engineering, Southeast University, Nanjing 210096, China

Abstract. In order to solve the security risks between different power grids, it is necessary to use flexible interconnection devices to interconnect with each other to improve the security and reliability. With the development of dual-high power grids, the optimization of flexible DC interconnection topology should not only consider the location and capacity of traditional zonal interconnection devices, but also take into account the influence of node distributed inertia. In this paper, the first selection is carried out through the node-distributed inertia. Secondly, the active demand of the receiving grid is determined based on the change of the total supply capacity after the N-1 fault and the reactive demand is obtained through the sensitivity method, so as to put forward the scope of determining the capacity and obtain the optimal results of the site. Finally, the methodology is verified by the example, and the safety calibration is carried out for the obtained results. After the input of the flexible DC interconnection device, the power supply pressure of heavy partition can be alleviated, the power support can be carried out when the fault occurs, and the voltage of the partition grid can be stabilized. Keywords: Partition interconnection · flexible DC · location and volume · particle swarm optimization · distributed inertia

1 Introduction The power grid is a significant infrastructure and strong guarantee for social construction and development. In order to prevent excessive short-circuit current in the power grid and avoid the hidden dangers of the electromagnetic ring network, the traditional largescale power grid usually operates in the mode of zoning and sharding, but there are still some problems. During the normal operation of the sub-districts, the mutual influence between the sub-district power grids is small, but the sub-district power grids cannot realize mutual © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 494–502, 2024. https://doi.org/10.1007/978-981-97-0877-2_51

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energy supply in time; When a short circuit occurs in the sub-district grid, the shortcircuit current will be too large. Moreover, land shortage and environmental factors make it difficult to increase capacity [1]. After adding a high proportion of new energy, it adds more unstable factors to the power grid and brings more security risks to the regional power grid. As a new generation of DC transmission technology, flexible DC transmission can solve many problems in the operation of the power grid [2], so it is necessary to add flexible zoning interconnection devices to flexibly control the power flow, effectively improve the transmission and transformation capacity, and solve the potential safety and stability problems of the power grid [3]. At present, the research on the operation of power grid zoning interconnection has made some progress. Literature [4] determines the power support amount of the device by sensitivity method, and models and analyzes the static safety of the sub-district grid. In the literature [5], by analyzing the relationship between the capacity and reactive power output of the partition interconnection device, a fixed capacity method for flexible DC partition interconnection system is proposed. Literature [6] proposes a site selection method for flexible interconnection system through preliminary selecting and final selecting. Flexible interconnection can solve the problems in the operation of existing power grid partitions, and site selection and capacity are the key factors affecting the effectiveness and economy of interconnection devices. And it is necessary to consider the distributed inertia and its influence on the stability of the power grid.

2 Zonal Flexible Interconnection Site Selection Model 2.1 Sending Site Selection Model The optimal location of the sending grid of the flexible DC device must first meet the safety requirements, and meet the constraints of static safety and transient voltage stability when the sending grid runs normally and N-1 failure occurs, and no overtripping or overload occurs. The site selection of the sending grid mainly considers its economic indicators. The model of the sending grid is as follows. GBest−S = min(FS1 , FS2 , · · · , FSn ) fSn =

NL 

(1)

Gi,j (Ui2 + Uj2 − 2Ui Uj cos θij )

(2)

Gi,j0 (Ui02 + Uj02 − 2Ui0 Uj0 cos θij0 )

(3)

l=1

fS0 =

NL  l=1

FSn =

fSn fS0

(4)

where, GBest - S is the score of the optimal location scheme; fSn is the active network loss value of the optimal scheme. fS0 is the initial active network loss of the sending grid system. FSn is the objective function score after normalization of the optimal scheme.

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2.2 Receiver Site Selection Model The selection of the receiving grid position of the flexible DC device must first meet the safety requirements. During the selection, the primary index is determined to be the total supply capability of the receiving grid after providing power support. And the voltage deviation is set as the receiver site selection model of the second-level target. Considering the practical economy problem, the active power loss of the receiving grid is regarded as the third-level target. The receiver site setting model is as follows. GBest−R = min(GR1 , GR2 , · · · , GRn ) GRn =

3 

λi FRi

(5)

(6)

i=1

fR1 = PR0 (1 + λR ) FR1 = FR2 =

PR0 fR1

Nb    Ui − Uiref 

(7) (8)

(9)

i=1

fR3 =

NL 

Gi,j (Ui2 + Uj2 − 2Ui Uj cos θij )

(10)

Gi,j0 (Ui02 + Uj02 − 2Ui0 Uj0 cos θij0 )

(11)

l=1

fR0 =

NL  l=1

FR3 =

fR3 fR0

(12)

where, GBest - R is the score of the optimal location scheme; fR1 total supply capacity score for this scheme; fR3 active power loss score for this scheme; fR0 is the initial active network loss of the receiving grid system. F1 is the normalized index of total supply capacity; F2 is the normalized index of voltage deviation. F3 is the normalized index of active power loss. 2.3 Constraints The restrictive form of constraints is to add all constraints in the form of penalty functions to form a new objective function, and then the optimal solution of the new objective function is obtained by site selection models. 1. Short-circuit current constraint The size of the system short-circuit current is related to the impedance of the sequence network. After the grid is determined, the system short-circuit current can

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be calculated according to the actual operation mode. Due to the large difference between the rated voltage of the transformer and the nominal voltage, the correction factor is introduced to calculate the short-circuit impedance of the grid. The impedance of the synchronous generator needs to be corrected, and the correction factor is also introduced. Z is the short circuit current at the fault point of the corrected node impedance matrix, which can be simplified as: (0)

If =

Uf

Zff + Zf

(13)

(0)

where, Uf is the voltage value of the fault point f before the short circuit occurs; Zff is the self-impedance of node f , that is, the f diagonal value of node impedance matrix. Zf is the transition resistance of the short circuit fault of node f . 2. Node voltage constraints Ui ≤ Ui ≤ Ui

(14)

where: Ui is the bus voltage of the node i (kV); Ui is the upper voltage limit of the bus of node i (kV); Ui is the lower limit of bus voltage of node i (kV). 3. Line capacity constraints PL,i ≤ PL,i

(15)

where: PL,i is the transmission power (MW) of line i; PL,i is the thermal stability limit of line i (MW). 4. Generator output constraint  PG,i ≤ PG,i ≤ PG,i (16) QG,i ≤ QG,i ≤ QG,i where: PG,i 、QG,i are the active and reactive power output (MW, MVAR) of the generator respectively; PG,i 、QG,i are the upper limits of active and reactive power output of the generator (MW, MVAR), respectively; PG,i 、QG,i are the lower limits.

3 Location and Capacity Determination Method for Zoned Flexible Interconnection 3.1 First Time Location Taking into Account Distributed Inertia Inertia of a power system refers to the property of the system to suppress energy fluctuations [7]. Flexible DC engineering can optimize the power flow distribution of the system and improve the stability level of voltage and frequency, but at the same time, it will bring about the problem of reducing the moment of inertia of the system. Therefore, taking the moment of inertia as a constraint condition to ensure the frequency stability of the system. The expression of node inertia is: Hmin =

P 2Rocof

(17)

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where, Hmin is the calculated inertia of the node, ΔP is the magnitude of the disturbance power at the node, and Rocof is the frequency change rate at the node. Considering the adjustable power constraints of the unit, Rocof is set to 0.25 Hz/s, power disturbance is set to 100 MW, and its critical inertia is calculated to be 200 through the swing equation. Therefore, a location can be selected in the partition system, and the selected node set is used as the variable of the optimal chimeric morphology location problem. 3.2 Reactive Power Support In this paper, we focus on analyzing the sensitivity of bus voltage to nodal reactive power injection through the sensitivity approach [8]. The cartesian coordinate system is selected as an example, by the derivative rule of multiple functions, the derivative of the voltage Ui of bus node i to the reactive power injection Qm of node m is: SQj =

dUi ∂Ui dei ∂Ui dfi = + dQm ∂ei dQm ∂fi dQm

(18)

In formula (18), dei /dQm , dfi /dQm can be obtained from the Jacobian matrix J inverse matrix J −1 of the network. Therefore, the reactive power support Qi can be calculated as:   dUj dU1 dUn ,··· , ,··· , Qi = max ,1 ≤ j ≤ n (19) SQ1 SQj SQn

3.3 Active Power Support The rated range of flexible DC power is determined according to the characteristics of the power network at the transmitting and receiving grid: 1. The lower limit of flexible DC rated power is determined by the receiving grid. In order to ensure the safe power supply of the receiving grid, it is necessary to increase the power supply capacity until the fault occurs, so as to determine the lower limit of the rated power of the flexible DC.    (20) PdcN min = PTSC−R − min PTSC−R−i 1≤i≤n

 is the power supply capacity of the receiving grid In the formula, PTSC−R−i network after the loss of component i. 2. Determine the upper limit of the rated power of the flexible DC through the transmission zone network. Under normal circumstances, the power support to other zones should not affect the safe power supply of the power grid of the local zone. Therefore, the upper limit of the rated power of the flexible DC is:

PdcN max = PTSC−S − PS0 where, the total initial load of the sending grid is PS0 .

(21)

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3. Combined with the different requirements of the sending and receiving grids, the rated power of the flexible DC can be satisfied: PdcN min ≤ PdcN ≤ PdcN max

(22)

In this paper, we obtain the optimal chimera morphology by using a multi-objective particle swarm optimization (PSO) in a continuous iterative process [9]. And we construct a multi-objective function to build three indicators, and after normalization through analytic hierarchy process (AHP) [10].

4 Security Checks Step 1: Modification of the power flow equation of the device connection AC node: Assuming that the active power and reactive power transmitted by the AC bus node i to the zonal interconnection device are respectively PS , QS , the power flow equation at this point can be modified as follows.   Pi − Ui j∈i Uj (Gijs sin θj − Bijs cos θj ) − Ps = 0  (23) Qi − Ui j∈i Uj (Gijs sin θj − Bijs cos θj ) − Qs = 0 Step 2: Calculate power flow after power support: The calculated location and capacity determination results are substituted into the power flow equation to check whether the static security constraints are met. If not, the power support value is iteratively calculated until the calculated results meet the security constraints. Step 3: In the process of solving, the N-1 constraints in Sect. 2.3 and the capacity constraints of the device are also met. Ps2 + Qs2 ≤ Smax (24)

5 Application Example 5.1 Power Grid Overview In this study, the reference capacity of the system is 100 MVA, the reference voltage is 345 kV, the total active load of the sending system is 6254.23 MW and the total reactive load is 1387 MVAR. The total active load of the receiving grid is 5628.81MW, and the total reactive load is 1248.3 MVAR. And the results of the primary siting of the flexible interconnection device are shown in Fig. 1. In the MATLAB simulation environment, PSO algorithm was used to optimize the multi-objective model. And a total of two variables are encoded by integer coding. The first variable is the access location of the flexible partition interconnection device, and the second variable is the capacity of the flexible and straight partition interconnection device.

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Fig. 1. The results of one-time site selection of flexible interconnection devices

5.2 Optimal Chimeric Morphology Sensitivity analysis is carried out on the receiving grid, and the reactive power support amount required when setting the generator N-1 fault. The power flow calculation results after multiple N-1 faults, the per unit value of all node voltages of the receiving grid system is within the constraint range, that is, the voltage threshold is 0, so the calculated reactive power support required at the receiving grid is 0 MVAR. Besides, the total supply capacity of the sending grid partition is 7630.16 MW. The total supply capacity of the receiving grid is 6111.76 MW. N-1 fault occurs in the receiving system, and the minimum power supply capacity after the fault is calculated as 5685.10 MW. Therefore, the lower limit of active power support is: 426.9 MW. And the final calculation result of the upper power supply capacity is: 1375.9 MW. Through the method of combining PSO and penalty function, the target weight value of the location selection index is calculated by AHP, and the final objective function can be obtained. The optimal chimeric morphology is that the zonal interconnection device is connected to 8 nodes of the receiving zonal system, and the capacity is determined to be 606 MVA. When the sending grid is selected, the final result is that the partitioned interconnection device is connected to 6 nodes of the sending grid.

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5.3 Security Correction N-1 safety and stability check was carried out on the sending and receiving grid system connected to the flexible DC partition interconnection device, power flow equation correction and power flow calculation were carried out, and N-1 fault was set for safety check. The bus voltage of the receiving grid partition grid was shown in Fig. 2. And the location selection and capacity determination results meet all constraints, and the result is the optimal chimeric morphology.

Fig. 2. The voltage of the terminal bus when N-1 fault before and after the flexible direct interconnection is connected

6 Conclusion This paper mainly introduces the optimal chimeric morphology of the flexible DC interconnection, proposes a site and capacity determination method, and verifies with examples. And the following conclusions were obtained: 1) The first site selection taking into account the inertia is proposed, and the final site selection and capacity setting scheme is obtained based on PSO and AHP algorithms. 2) The sub-district grid achieves power support through a flexible DC interconnection system, relieving the pressure on the heavy-duty sub-district power supply and maximizing the total supply capacity. Acknowledgments. Funded by Technology Project of the State Grid Corporation Headquarters Management “Research on network topology construction of dc power grid and its coupling with ac power grid/ 5100-202158467A-0-0-00”. This paper is also supported by the National Natural Science Foundation of China under Grant 52077037.

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References 1. Marquardt, R., Lesnicar, A.: New concept for high voltage–modular multilevel converter. Power Electronics Specialists Conference 2004, 1–5 (2004) 2. Cai, Y., Guo, W., Zhao, C.: Accurate calculation and analysis of DC fault overcurrent in modular multilevel converters. Trans. Electr. Mach. Sys. 36(07), 1526–1536 (2021). (in Chinese) 3. Rao, H., Zhou, Y., Li, W.: Engineering Application and Development Prospects of Flexible DC Transmission Technology. Automation of Electrics Power Systems 47(01), 1–11 (2023). (in Chinese) 4. Xiao, J., Guo, W., Li, Y.: Static security analysis of zoned flexible interconnected urban grids. Power System Technology 40(10), 3140–3148 (2016). (in Chinese) 5. Xiao, J., Jiang, X., Huang, R.: Capacity-setting method for flexible interconnection devices in urban grid zones. Auto. Elect. Power Sys. 42(02), 99–105 (2018). (in Chinese) 6. Xiao, J., Li, S., Huang, R.: Siting method and demonstration application of flexible interconnection in urban power grid partition. Electric Power Construction 37(05), 10–20 (2018). (in Chinese) 7. Bian, Y., Wyman-Pain, H., Li, F., Bhakar, R., Mishra, S., Padhy, N.P.: Demand side contributions for system inertia in the GB power system. IEEE Trans. Power Syst. 33(04), 3521–3530 (2018) 8. Lof, P.A., Smed, T., Andersson, G.: Fast calculation of a voltage stability index. IEEE Trans on Power Systems 7(1), 54–64 (1992) 9. Xiong, Z., Yang, J., Hu, Z.: Evolutionary many-objective optimization algorithm based on angle and clustering. Appl. Intell. 51(4), 2045–2062 (2021) 10. Liu, X., Tan, Z., Yuan, Z.: Comprehensive optimization of access point selection for offshore wind farm integrated with voltage source converter high voltage direct current. Power Generation Technology 43(6), 892–900 (2022). (in Chinese)

Calculation of Node Critical Inertia Compensation of Multi-machine System Based on Inertia Spatio-Temporal Distribution Characteristics Chengbin Chi1(B) , Shan Liu2 , Qi Liu1 , Fan Li3 , Lei Liu4 , and Jun Mei4 1 State Key Laboratory of Advanced Power Transmission Technology, State Grid Smart Grid

Research Institute Co., Ltd., Beijing 102209, China [email protected] 2 Beijing Key Laboratory of DC Grid Technology and Simulation, State Grid Smart Grid Research Institute Co., Ltd., Beijing 102209, China 3 State Grid Shanghai Municipal Electric Power Company, Shanghai 200120, China 4 School of Electrical Engineering, Southeast University, Nanjing 210096, China

Abstract. Aiming at the frequency distribution of different nodes of the new energy power system when perturbation occurs, the node computational inertia index is defined to characterize the ability of a single node in the grid to resist the system frequency change after perturbation, and to quantify the inertia distribution characteristics of the system. Considering the physical structure and parameters of the power grid, the expression of the node calculation inertia of the multimachine system is deduced, and an example simulation is carried out through the IEEE39 node system, which verifies the correctness of the node calculation inertia, with an average error of 8.7%, and the lowest can reach 0.1%, and the simulation results show that the proposed node calculation inertia can accurately characterize the inertia distribution of the new energy power system, and the final calculation result proposes a new node inertia index for the multi-machine system based on the node inertia. Finally, a critical inertia compensation calculation method for multi-machine system is proposed based on the nodal inertia calculation results, and the results show that the proposed method can improve the level of nodal inertia very well. Keywords: New energy · Multi machine system · Node inertia · Critical inertia

1 Introduction New energy generating units through the power electronic device access to the power grid, and system frequency decoupling, can not provide inertia for the system, while the new energy units in the geographic non-uniform distribution, so that the uneven distribution of grid inertia characteristics highlights the perturbation of the system frequency after the system presents an obvious spatial and temporal distribution characteristics, the low inertia areas after the fault occurred in the system initial frequency change rate is © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 503–512, 2024. https://doi.org/10.1007/978-981-97-0877-2_52

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greater, easy to trigger the new energy units off the grid, anti-islanding protection, etc. System protection measures. Therefore, it is very important to analyze the phenomenon of new energy power system inertia decline and distribution characteristics, and refine the assessment of the system inertia level for the analysis of the regional frequency response characteristics of the system and frequency stability control research. Among the existing studies, literature [1, 2] quantitatively analyzed the frequency characteristics of nodes by considering the spatial and temporal distribution characteristics of frequency, and proposed metrics to reflect the differences in frequency performance of different nodes. Literature [3] simulated and analyzed the frequency response of the system when the overall inertia is constant but the distribution is different, pointing out that the inertia distribution will affect the system frequency characteristics. Literature [4] analyzed the influence of the inertia distribution of the units on both sides on the center of inertia and frequency characteristics of the system through the derivation of the center of inertia of the system of two machines. Literature [5] defines the node inertia characteristic index as the relative magnitude of the deviation of the node frequency from the center of inertia frequency from the relationship between frequency and inertia, but it is not possible to quantify the inertia characteristics of the node. Literature [6] defines the node inertia as the ratio of the size of the power change of each unit and the rate of change of the frequency of different nodes to obtain the system node inertia matrix, but obtaining the node inertia requires real-time monitoring of the information of the different nodes in the system, which requires a large amount of data, and is difficult to be applied in the actual engineering. Literature [7] points out that in the case of new energy unit access, the node perturbation propagation speed increases and the inertia level decreases in its neighborhood. In summary, current related studies lack quantitative characterization of inertia distrib ution properties of different nodes in the system. In this paper, considering the physical structure of the grid, network parameters and unbalanced power distribution coefficients, we theoretically derive the node calculation inertia expressions of the multi-machine system, calculate the inertia of each node by taking the IEEE39 node system as an example, and simulate it through PSASP to analyze the inertia distribution characteristic of the system and the influence of new energy access. Finally, a new energy unit with virtual inertia is added at the weak point of inertia and recalculated to obtain the required critical compensation inertia of the node to improve the inertia level of each node of the system.

2 Characterization of Power System Inertia Distribution 2.1 Inertia Distribution Characterization Indicator Proposed When a power perturbation occurs in the system, the power perturbation magnitude, inertia time constant, and frequency satisfy the swing equation [8]: 2Hsys

dfcoi = P dt

(1)

Among them, f coi , ΔP denote the system center of inertia frequency, and power inequality measure, respectively.

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Referring to the response of the system equivalent inertia to changes in system power and frequency in Eq. (1), the computed inertia at node k is defined as the ratio of the magnitude of the power perturbation to the rate of change of the initial frequency at the node after a power perturbation occurs at node k: Hck =

P 2 ∗ dfk /dt

(2)

Among them, H ck is the computational inertia at node k, ΔP is the magnitude of the perturbation power at node k, and f k is the frequency at node k. The computed inertia at node k is numerically equivalent to the inertial time constant that a virtual synchronous generator at node k has, as shown in Fig. 1 below. k k

1

2

1

2

1

d1

2

d2

Fig. 1. Schematic diagram of calculated inertia of nodes

2.2 Derivation of Inertia for Nodal Calculations of Multi-Machine Systems As shown in Fig. 2, it is a schematic diagram of a multi-machine system with n + m network nodes, where n is the number of nodes at the generator end and m is the number of other nodes. This system is used as an example to derive the computational inertia of any node k in the multi-machine system.

...

...

Fig. 2. Schematic diagram of multi machine system

Literature [9] states that the synchronizer frequency can be used to represent the network node frequency, and the relationship between the network node frequency and

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the synchronizer frequency in a multi-machine system is first derived in the following. The derivation matrix of the system is shown as follows:   Ynn Ynm (3) Y = Ymn Ymm Among them, Y nn , Y mm are the self-conductance of the generator node, other nodes respectively, and Y nn , Y mm are the mutual conductance between them. Neglecting the effect of conductance, taking into account the generator transient reactance and simplifying the load to an equivalent conductance, the system broadening conductance matrix is obtained as follows: ⎡ ⎤ −Yn 0 Yn ⎦ (4) Ys = ⎣ −Yn Ynn + Yn + Yln Ynm 0 Ymn Ymm + Ylm Among them, Y s denotes the generalization matrix of the system, Y n is the diagonal array formed by the generator transient reactance, and Y ln and Y lm are the load-equivalent derivatives at the generator node and other nodes, respectively. Express the above augmented matrix in the following form:   Y1 Y2 (5) Ys = Y3 Y4 Among them, Y1 

=

 .

Yn , Y2

=





−Yn 0 , Y3

 =

 −Yn , Y4 0

Ynn + Yn + Yln Ynm Ymn Ymm + Ylm The corresponding network equations are shown below:        In Ue Y1 Y2 Ue = = Ys 0 Unet Y3 Y4 Unet

=

(6)

Among them, Y n is the current vector injected into the system by the generator, and U e , U net are the voltage vectors at the potential nodes and network nodes within the generator, respectively. Based on the above network equations, the voltage relationship between the network nodes and the generator nodes is obtained as shown below: Y3 Ue + Y4 Unet = 0

(7)

Express the voltage of the network node from the generator node voltage as: Unet = R ∗ Ue

(8)

Among them, R = −Y4−1 Y3 , denotes the correlation matrix between the network node voltages and the potential node voltages within the generator The correlation matrix depends on the conductivity matrix of the system.

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In the above equation, the voltage magnitude and phase angle vectors at the network nodes are denoted as V net , δ net , and the corresponding magnitude and phase angle vectors of the potential in the generator are denoted as V e , δ e , as follows: Vnet · ejδnet = R ∗ (Ve · ejδe )

(9)

Extracting the part of Eq. Related to node k, after a fault at node k, the voltage at the point of fault can be represented by the potential within each generator as follows:

rkj Vj ejδj (10) Vk ejδk = j∈k

Among them, δ j is the phase angle corresponding to the internal potential of generator j; r kj is the element of matrix R that represents the relationship between node k and the voltage of generator j; and j ∈ k denotes the element corresponding to the row in which node k is taken from R. The voltage of node k expressed in Eq. (10) is deformed and simplified as shown in Eq. (11), and the voltage angle of node k is finally obtained as shown in Eq. (12). ⎧  ⎪ Vk = rkj Vj ej(δj −δk ) ⎪ ⎪ ⎪ j∈k ⎪       ⎪ ⎪ ⎨ Vk = rkj Vj cos δj − δk + j rkj Vj sin δj − δk j∈k (11)   j∈k  ⎪ ⎪ = V r V sin δ − δ ⎪ j j 0 kj k ⎪ ⎪ j∈k ⎪ ⎪  ⎩  sin δj − δk ≈ δj − δk  rkj Vj δj j∈k

δk = 

rkj Vj

(12)

j∈k

The frequency of node k is obtained from Eq. (12) as shown in Eq. (13), it is realized that the frequency of the network nodes is expressed using the frequency of the synchronous machine.  rkj Vj fj j∈k

fk = 

rkj Vj

(13)

j∈k

Among them, f j is the frequency of generator j. If a power disturbance occurs at node k, ignoring the load response to the unbalanced power, the unbalanced power will be distributed to each synchronous generator node according to the synchronous power coefficients, which are shown as follows: Djk = Vj Vk Bjk cos δjk0

(14)

Among them, Djk is the synchronous power coefficient of the generator, V j , V k are the internal potential amplitude of the generator j and the voltage amplitude of

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node k, respectively, and Bjk is the conductance in the system conductance matrix after contracting to the internal potential node of the generator and the fault node. When a power disturbance ΔP occurs at node k, the unbalanced power is distributed to each generator node according to the synchronized power coefficients shown in Eq. (14), and the unbalanced power picked up by generator j is: Djk P Pj =  Djk

(15)

j∈k

Among them, Djk and ΔPj are the synchronizer power coefficient corresponding to generator j and the unbalanced power picked up, respectively. Combining the generator swing equation and Eq. (15), the frequency rate of change of generator j is obtained as follows: Djk P dfj  = dt 2Hj ∗ Djk

(16)

j∈k

Among them, H j is the inertia time constant of the generator j. Substituting Eqs. (14) and (16) into the node computational inertia definition Eq. (2), mainly taking into account the influence of electro-conductivity, considering the system voltage around the rated value, and simplifying the power distribution coefficients, etc., the computational inertia of the node is obtained:   rkj Bjk j∈k

Hck =   j∈k

j∈k 1 Hj rkj

∗ Bjk



(17)

3 Example Analysis and Simulation 3.1 Characterization of the Distribution of Inertia Computed at the Nodes of a Multi-machine System In order to further illustrate the inertia distribution characteristics in the system and the impact of new energy access on the computed inertia of the multi-machine system, this paper adopts the computed inertia of the IEEE39 node system to analyze, which has 10 generators, 39 busbars, 19 loads, and 34 transmission lines; the rated frequency is 50 Hz, and the main voltage level is 345 kV, of which the No.1 machine is the equivalent of the external grid, and the No.2 is the balancing machine. Neglecting the effect of conductance, the theoretical derivation results from Eq. (17) are first used to obtain the computed inertia of each node in the IEEE39-node system, and then verified by comparing the theoretical derivation with the computed inertia of the nodes obtained from the transient simulation, and the results of the transient simulation are obtained in the following way: the corresponding system model is established in PSASP (Power System Analysis and Synthesis Program), and the corresponding system

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models are obtained by setting perturbations at each node and measuring the size of perturbations. Setting perturbations at each node, measuring the size of the perturbation and the initial frequency rate of change, and finding the calculated inertia according to the definition. Since the inertial response dominates the frequency stability for about 2s after the perturbation [10], in order to avoid the influence of the initial transient process and the incidental error of a single measurement point, the average frequency rate of change within the initial 0.2s after the perturbation occurs is taken as the initial frequency rate of change here. A line graph comparing the theoretical calculation results with the simulation results is drawn as shown in Fig. 3:

Fig. 3. Comparison of IEEE39 node inertia calculation and simulation results

The error between the theoretical calculations and the simulation results is calculated, and the three points with the smallest error and the three points with the largest error are taken as shown in Table 1, where the largest error is 24.7%, the smallest error is 0.1%, and the average error is 8.7%. From the above results, it can be seen that the theoretically derived results obtained by using MATLAB calculation are closer to the simulation results obtained by using PSASP simulation, which can prove the correctness of the theoretical derivation. At the same time, the simulation results are generally larger than the theoretical derivation results, which is due to the fact that the average frequency rate of change obtained by the simulation is smaller than the theoretical initial Rocof , which ultimately makes the measured results larger.

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Node

Inaccuracies (%)

Node

Inaccuracies (%)

23

0.104

36

19.899

39

0.211

29

21.621

14

0.297

37

24.743

3.2 Critical Inertia Compensation Calculation for Multi-Machine System Nodes Based on the results of distributed node inertia calculations for the IEEE39-node system in Sect. 3.1, they are sorted, and the critical inertia of the nodes in the system can be calculated based on the rocking equation by considering a certain amount of Rocof and the perturbation power ΔP. In this way, the nodes that meet the requirements of this critical inertia and those that do not can be determined. Considering that wind, light and other renewable energy units have virtual inertia after being configured with virtual inertia control technology, the system can be compensated for inertia. Therefore, it can be connected at the smallest non-generator node that does not satisfy the critical inertia of the system as described above as an inertia compensation device, so as to enhance the inertia of that node and nearby nodes. After connecting to the new energy unit, it can be used as the 40th node (the 11th generator node), counting its virtual inertia, and re-perform the distributed node inertia computation, and through the step-by-step approximation method, calculate and find out the lowest compensated inertia that can make the above mentioned smallest non-generator inertia node satisfy the requirement of the critical inertia. Considering the frequency rate of change Rocof 0.125 Hz/s and the disturbance power ΔP of 100 MW, the critical inertia is calculated by the swing equation as: Hmin =

1 P = = 200 2Rocof 2 × 0.0025

(19)

From Sect. 3.1, the smallest non-generator node in the IEEE39-node system that does not satisfy the critical inertia of the system to be 200 is the 29th node (H = 130.54), where a new energy unit is added as an inertia compensator, and the new node is designated as the 40th node.After adding the 40th node, recalculate the node inertia of each node in the whole network, set the initial value of the virtual inertia of the new energy unit to 100, and recalculate it again after lowering it by 1 each time by utilizing the step-by-step approximation method to search for the lowest compensating inertia that will make the inertia of the 29th node to reach 200, as shown in Fig. 4. When the inertia of the 29th node is reduced to 72, the lowest critical compensation inertia can be reached.

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Fig. 4. Trend of inertia change at node 29

4 Conclusion In order to analyze the inertia distribution characteristics of the new energy power system, this paper proposes the node computational inertia as an index to characterize the ability of the nodes to impede the frequency change of the system and to quantify the inertia distribution characteristics of the system for the frequency distribution of different nodes of the new energy power system when they are perturbed. On this basis, considering the physical structure and parameters of the power grid, the expression of node computational inertia of the multi-machine system is derived, and the system inertia distribution characteristics are verified through simulation examples. Finally, on the basis of the computed distributed node inertia, new new energy nodes are added to provide virtual inertia in order to enhance the inertia of the nodes of the nondynamo generator, so as to improve the frequency stability of the system. The main conclusions are as follows: the node calculated inertia can characterize the inertia distribution characteristics of the system, and the size of its value mainly depends on the electrical distance from the node to each inertia source and the size of each inertia source. The node inertia of the inertia system will affect the frequency characteristics of the system, and the frequency stability of the system can be improved by adding the virtual inertia compensation. Acknowledgments. Funded by Technology Project of the State Grid Corporation Headquarters Management “Research on network topology construction of dc power grid and its coupling with ac power grid/ 5100-202158467A-0-0-00”.

References 1. Gao, H., Yuan, H., Xin, H., et al.: Nodal frequency performance of power networks. 2019 IEEE 8th International Conference on Advanced Power System Automation and Protection (APAP), pp. 1838–1842. Xi’an, China (2019)

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2. Gao, H., Xin, H., Huang, L., et al.: Characteristic analysis and quantification of common mode frequency in power systems with high penetration of renewable resources. Proceedings of the CSEE. 41(03), 890–900 (2021). (in Chinese) 3. Xu, T., Jiang, W., Overbye, T.J.: Investigation of inertia’s locational impacts on primary frequency response using large-scale synthetic network models. In: 2017 IEEE Power and Energy Conference at Illinois (PECI), pp. 1–7. Champaign, IL, USA (2017) 4. Pulgar-Painemal, H., Wang, Y., Silva-Saravia, H.: On Inertia Distribution, Inter-Area Oscillations and Location of Electronically-Interfaced Resources. IEEE Transactions on Power Systems 33(1), 995–1003 (2018) 5. Wang, Y., Silva-Saravia, H., Pulgar-Painemal, H.: Estimating inertia distribution to enhance power system dynamics. In: 2017 North American Power Symposium (NAPS), pp. 1–6. Morgantown, WV, USA (2017) 6. Zeng, F., Zhang, J.: Temporal and spatial characteristics of power system inertia and its analysis method. Proceedings of the CSEE 40(01), 50–58+373 (2020). (in Chinese) 7. Ma, N., Wang, D.: Extracting spatial-temporal characteristics of frequency dynamic in largescale power grids. IEEE Trans. Power Syst. 34(4), 2654–2662 (2019) 8. Wei, F., Zhang, H., Wang, X., et al.: Transient stability analysis of virtual synchronous generator considering voltage dynamic characteristics. Power System Technology, 0987 (2023). https://doi.org/10.13335/j.1000-3673.pst. (in Chinese) 9. Milano, F., Ortega, Á.: Frequency Divider. IEEE Transactions on Power Systems 32(2), 1493–1501 (2017) 10. Li, D., Liu, Q., Xu, B., et al.: New energy power system critical inertia estimation method considering frequency stability constraints. Power System Protection and Control. 49(22), 24–33 (2021). (in Chinese)

A Comparative Study of Trading Mechanisms in China’s Reserve Auxiliary Services Market Yue Guo1 , Yuming Huang2,3(B) , Yanru Liu1 , Yi Song1 , Yaxuan Han2,3 , and Dunnan Liu2,3 1 State Grid Economic and Technological Research Institute Co., Ltd., Beijing, China 2 North China Electric Power University, Beijing, China 3 Beijing Huadian Energy Internet Research Institute Co., Ltd., Beijing, China

[email protected]

Abstract. With the increasing proportion of renewable energy in the power system, the increasing uncertainty on the generation side, the increasing demand for system reserve capacity, and the increasing abundance of reserve auxiliary service market players, the research on reserve capacity and reserve auxiliary service market trading rules is a hot topic at present. This paper takes Northwest China and East China as examples, summarizes the trading rules of reserve auxiliary service market in each region, analyzes the similarities and differences of the rules in each region, and researches the market signals released by the rules, expecting that it will help to formulate and improve the trading rules of reserve auxiliary service market in other regions. Keywords: Reserve ancillary services market · Reserve capacity · Trading rules · Market clearing

1 Introduction The introduction of the concepts of carbon peaking and carbon neutrality has progressively increased the proportion of new installed capacity and reduced carbon emissions, but it has also increased the variability of power generation and limited the availability of power during peak hours. To ensure reliable and efficient operation of the power system, the development of a standardised market for reserve capacity services cannot be delayed. Currently, pricing incentives are still used in China, and with the gradual increase in new energy sources, it is necessary to improve the incentives of traditional units through market mechanisms to provide reserve services to users and ensure system security and stability. In recent years, various regions have enacted or piloted policies related to the participation of reserve capacity in the auxiliary service market, providing policy support to ensure adequate reserve capacity supply. Literature 1 discusses the design and operation practice of the market mechanism for thermal power reserve capacity in Yunnan, and proposes the operation mechanism of the thermal power reserve capacity market in clean energy-rich areas with regard to the regional characteristics of Yunnan’s power © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 513–522, 2024. https://doi.org/10.1007/978-981-97-0877-2_53

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demand. Based on the VSC-MTDC system [1], Literature 2 proposes an optimal allocation method for shared FM reserve in interconnected power systems considering the cost of ancillary services, and FM control under emergency frequency deviation events [2]. Literature 3 Aiming at the characteristics of new energy reserve capacity, the allocation and optimization method of power system reserve capacity is studied, and the generation power of each generating unit is optimized based on the immune particle swarm optimization algorithm considering the reliability index [3]. Literature 4 analyzes the principles, characteristics and applicability of the strategic reserve mechanism according to the actual situation in China [4]. Meanwhile, a strategic reserve trigger mechanism based on the day-ahead spot market is designed to solve the problem of power supply shortage in special periods and alleviate high electricity prices. This paper can be divided into three parts. The first part introduces the definition and categorization of reserve capacity and gives an overview of the current status of reserve capacity development. The second part gives an overview of the current situation of China’s reserve capacity auxiliary service market, and based on the policies introduced in East China and Northwest China, it compares and analyzes the similarities and differences of the trading rules in the two regions, and summarizes the current trading mode of the reserve auxiliary service market; and the third part is to summarize the whole paper.

2 Reserve Capacity 2.1 Reserve Capacity Overview Reserve capacity refers to the available unit capacity reserved by the power system for the purpose of ensuring the normal operation of the power system even in the event of equipment maintenance, accidents, frequency regulation and so on. Reserve capacity enables the power grid to withstand random equipment shutdowns, load fluctuations and other perturbations, and to establish a balance between generation and load as quickly as possible to ensure that the frequency is within the prescribed range and that no chain of accidents or even large-scale blackouts occur. Reserve capacity in the power system is usually provided by thermal power units, hydropower units, gas-fired units and pumped storage. With the gradual increase in the installed capacity of new energy sources and the increasing emphasis on energy-saving scheduling in power grids, new energy generation systems such as wind power and photovoltaic power are gradually participating in the market to provide reserve capacity, but due to the uncertainty of the new energy output, there are still certain problems in realising the large-scale substitution of new energy generation systems for conventional units. 2.2 Classification of Reserve Capacity by Purpose Load Reserve. Load reserve refers to the reserve capacity set up to accommodate shortterm fluctuations in load in the system and to cover unplanned load fluctuations within a short period of time (one day), which is used to balance the load forecasting error and load fluctuations.

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Accident Reserve. Accidental reserve is the reserve capacity required to maintain the normal operation of the power system in the event of a fortuitous accident of a generating plant in the system so that the consumers are not seriously affected, and is also used to balance the system power deficit after the withdrawal of the most serious single unit failure in the grid. Maintenance Reserve. Maintenance reserve is the reserve capacity that the grid reserves for balancing when certain units are scheduled for maintenance [5].

2.3 Classification by Reserve Response Time Rotating Reserve. The rotating reserve is provided by a generator set operating online, synchronised with the system, which provides the declared reserve capacity within 10 min after dispatch and maintains this operating condition for at least 2 h. Non-rotating Reserve. Non-spinning reserve power shall be provided by independent generating units capable of providing non-energy reserve power, which are not synchronised with the system, and which, in the event of a system failure, can provide the declared reserve power within 10 min of dispatch and maintain this state of operation for at least 2 h to maintain system reliability. Alternate Reserve. Alternate reserve shall be provided by an offline unit capable of providing reserve power that does not operate in a mode synchronised with the system, that is capable of providing the advertised reserve power within 60 min of dispatch when the unit is repaired or taken offline, and that is capable of maintaining that state for at least 2 h [6].

3 Summary and Analysis of Trading Rules in the Reserve Ancillary Services Market 3.1 Reserve Auxiliary Services Market Overview Market Entities. The reserve ancillary services market players consist of four main components, namely reserve service purchasers, reserve service providers, market trading organisations and market management committees. Purchasers of Reserve Services. Reserve buyers are the responsible parties in the reserve capacity market and can be divided into three categories: grid-side customers, generationside customers, and use test customers. The buyer is usually the grid side, and the cost of the purchase is ultimately passed on to the USE or generation side. Reserve Service Providers. Reserve service providers are market entities that provide reserve services and can be categorised as generation vendors on the generation side and customers on the load side. This includes interruptible loads, energy storage, etc.

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Market Trading Organisations. There are two main types of trading institutions in the ancillary services market, namely power trading centres and power dispatch agencies. The power trading centres are mainly responsible for all aspects of trading in the power market, while the main task of the power dispatch agencies is to maintain the balance of the power system and ensure grid security. Market Management Committees. The Market Management Committee (MMC) mainly performs alternate auxiliary services market regulation, coordinates the main relationship between markets and drafting and revising relevant texts [7]. The specifics of each component are shown in Fig. 1:

Fig. 1. Alternative market structure

Transaction Models. The trading methods in the reserve market are mainly divided into bilateral contract type and centralised bidding type. Among them, bilateral contract-type trading refers to bilateral trading between reserve buyers and sellers through a third-party platform, whereby supply and demand parties decide on the contract content, including contract duration, default penalties, etc., through negotiation; Centralised bidding type means that, after the system dealer has announced the reserve requirement, the sellers of reserve capacity submit their bids and the bidding takes place on the trading floor in accordance with the market rules; the system dealer usually selects the bid with the lowest offer after taking into account the constraints related to the principle of the lowest cost of purchasing electricity for clearing purposes, the reserve plan and the clearing price, and all the successful bidders are settled uniformly in accordance with the market clearing tariffs, and the trading principle is shown in Figs. 2 and 3. Clearance Methods. Reserve market clearing mainly has the following two ways: First, according to the unified tariff clearing that is, power producers reported a trading session available to call the capacity and offer, the market trader according to the offer from low to high allocation of generating load, the final transaction of the unit offer for the marginal price of the time period, all the selected units will be settled in accordance

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Fig. 2. Alternate market trading principle

Fig. 3. Alternative market clearing process

with the price; Second, according to the unit offer clearing, and the unified tariff clearing is different from the way that all the winning units clearing the use of their own price, this way may increase the speculative behaviour of the power producer is not conducive to the suppression of its market power, the reserve market clearing the majority of the current first way.

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3.2 Reserve Auxiliary Services Market Level Segmentation Each province (region) from the market main body, the intra-day market, the day before the market three levels of reserve auxiliary services market provisions, the three levels work together to ensure the safe operation of the regional power grid, the establishment of market-based reserve auxiliary services across the provincial transfer mechanism, give full play to the market in the allocation of resources in the decisive role, and comprehensively enhance the regional power grid power safety and security capabilities [8]. Market players are the main participants in the electricity market, and the rules elaborate on the members of the market players, their rights and obligations, etc., with the aim of restraining the behaviour of the market players in the reserve auxiliary services market and guaranteeing the normal operation of the electricity market; The day-ahead market is the main trading platform of the reserve ancillary services market, and its rules stipulate the quotation and clearing periods, clearing principles, settlement rules, etc., so as to ensure that clean energy is given priority in clearing, and to respond positively to the “dual-carbon” programme; Intraday markets include quote adjustments, announcement of clearing results, etc., to achieve efficient use of reserve resources. 3.3 Overview of the Current Status of China’s Reserve Auxiliary Services Market In recent years, China has attached great importance to the marketisation of reserve capacity, and many regions across the country have introduced relevant policies, reflecting the trend of standardisation of China’s reserve market. In 2023, The Shanxi Positive reserve Auxiliary Services Market Trading Implementation Rules (Trial) issued in May implemented the market-based model while making better connection with other markets. It clarified the articulation relationship with the spot market, the medium- and long-term market and other auxiliary service markets in terms of transaction declaration, transaction timing, etc., and clarified the mechanism for independent settlement of various types of markets. The Northwest Regional reserve Auxiliary Service Market Trading Rules, issued in May of the same year, establishes a guarantee mechanism for the consumption of surplus clean energy and ensures that clean energy is utilised efficiently. In 2023, The Third Party Independent Subjects Participating in the Electricity Auxiliary Service Market in Zhejiang Province, which was launched on a trial basis in January 2023, specifies that the third party subjects participating in the reserve auxiliary service market include new types of energy storage, electric vehicles (charging piles), high-energy-carrying enterprises, load-side regulation resources, load aggregation enterprises, and other auxiliary service providers. In January 2022, the Guiding Opinions on Accelerating the Construction of a National Unified Electricity Market System proposed to follow the laws of operation of the electricity market and the laws of the market economy, optimise the overall design of the electricity market, realise the sharing of electric power resources and optimal allocation of electric power resources across the country, and accelerate the formation of

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a unified, open, competitive, orderly, safe, efficient and well-governed electricity market system. The Central China Inter-provincial Power Peaking and reserve Auxiliary Services Market Trading Rules issued in October 2022 set out the entry conditions for market players with abundant reserve capacity, with the single capacity of the grid-connected coal-fired thermal power units required to be 300MW or above, and the provinces with the necessary conditions can include the grid-connected hydropower stations with a capacity of 100MW or above (except for hydropower owned by the grid enterprises and run-of-river hydropower).) are included. 3.4 Summary, Comparison and Analysis of Trading Rules in the Reserve Ancillary Services Market In this paper, we will take the policies of East China and Northwest China as an example to list and compare and analyse the trading rules of the reserve auxiliary service market, as shown in Table 1: Table 1. East China vs. Northwest China

Market Entities

Day market

Eastern China

Northwestern

buyers

Provincial (municipal) grid enterprises with insufficient spinning reserve

Provinces (districts) power companies, DC supporting power supply, self-provided enterprises

sellers

Provinces (municipalities) with abundant rotating reserve and East China direct escrow with Daily regulation capacity of the unit

transmission side

grid company

grid company

Unit regulation capacity(MW)

≥ 300

≥ 350

Minimum unit of declared price(yuan/MW·h)

1

1

Buyer’s offer period/min

15

15

Seller’s offern(yuan/MW·h)

0 ≤ n ≤ 1000

≥1

(continued)

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Intraday market

Eastern China

Northwestern

Quotation time

Before 11: 30

Before 11: 00

clearance time

Before 13: 00

Before 14: 30

clearance time

T + 3.5 h

T+2h

clearance method

normal situation

Proportionate distribution according to needs

Buyer’s quantitative offer

High-Low Matching

quoted prices are the Clean Energy same Priority Clearance

The buyer quotes the quantity and not the price

Pmax prioritisation

Unmet buyer’s declared needs

The higher of the “guaranteed supply” willingness price, the buyer’s, or the seller’s spot purchase price

Non-declaration of buyer’s needs

120 percent* price of power supply guarantee

As a whole, the regional sub-centres of the State Grid are responsible for the operation of the reserve auxiliary service market, and the National Energy Administration carries out supervision to ensure that the reserve transactions are fair and efficient, adhere to the reserve market orientation, and ensure that the market operation is standardised and tranreservent. By comparing and analysing the trading rules of the two regions, it can be seen that the reserve auxiliary service market consists of the day-ahead market and the intra-day market, and in the market connection, through the provincial grid to forecast the rotating reserve capacity in the day-ahead, if the rotating reserve capacity fails to meet the requirements, then start the day-ahead reserve market; in the case of the provincial grid, when the day-ahead forecast of the rotating reserve capacity fails to meet the requirements, then start the intra-day reserve market [9]. In terms of market subjects, each region distinguishes between buyers and sellers by the adequacy of spinning reserve capacity as an indicator. Northwest China stipulates that thermal power plants and hydropower plants can only participate in the market as sellers, and puts forward the requirement of deep regulation capacity for thermal power units to participate in the market; East China stipulates that the seller unit that has won the bid in the previous day’s reserve market is not allowed to participate in the market of auxiliary services for peak shifting as a seller subject. From the market a few days ago, East China and Northwest China divided the working days into 96 periods, with each offer period lasting 15 min. East China set a cap on the seller’s offer, which is intended to constrain the market power of the large power companies and safeguard the buyer’s rights and interests; Northwest China’s offer closes earlier than East China’s, and clears later than East China. In addition, East China emphasises the priority of clean energy units for clearing.

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From the intraday market, the intraday reserve market is cleared using segmented marginal tariffs, with seller units sorted from low to high offer and buyer units sorted from high to low offer, matched one to one. Settlement in both East China and Northwest China is on a day-ahead and month-ahead basis, with slightly different time limits on offer adjustments, before 17:00 in East China and before 18:00 in Northwest China.

4 Conclusion This paper firstly gives an overview of the research and development status of reserve capacity, then summarises the trading rules of the reserve capacity auxiliary service market in East China and Northwest China, and refers to the trading rules of other provinces, and finds that the reserve capacity auxiliary service market emphasises the priority of clearing clean energy, and guarantees the efficient use of clean energy. The trading rules propose that buyers and sellers adopt the “high and low matching” method of centralised bidding and marginal clearing, thus encouraging sellers to quote low prices and buyers to quote high prices. Market players are encouraged to participate in the reserve capacity auxiliary service market to cope with sudden changes in grid power caused by events such as the shutdown of equipment other than generation, transmission and transformation equipment [10]. The market for auxiliary services for reserve capacity is still in its infancy in China, and regions still need to refer to advanced foreign experience in policy formulation and improvement. In order to encourage more market players to participate in the market, regions can appropriately increase compensation and provide certain incentives for market players participating in the market. Acknowledgment. This work is supported by the management science and technology project of State Grid Corporation of China (5100-202356016A-1-1ZN)

References 1. Duan, P.: Market mechanism design and operation practice of thermal power reserve capacity in Yunnan Province. In: China International Conference on Electricity Distribution, CICED. p. 57 (2021) 2. Sun, K.: Optimized allocation method of the VSC-MTDC system for frequency regulation reserves considering ancillary service cost. In: CSEE Journal of Power and Energy Systems, pp. 53–63 (2022) 3. Wu, W.: Reserve capacity allocation and optimization method of power systems with renewable energy. In: IEEE International Conference on Smart Grid and Smart Cities (ICSGSC), pp. 22–24 (2022) 4. Du, Y.: Strategic reserve mechanism design under the power market environment. In: IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), p. 56 (2022) 5. Shu, L., Liu, J., et al.: Study on the classification management method of active reserve in regional power grids. Zhejiang Electr. Power 40(09), 16–23 (2021). (in Chinese) 6. Feng, B.: Alternative ancillary services market clearance modelling study. China Outstanding Master’s Degree Thesis Full Text Database, vol. 3, pp. 1–72 (2021). (in Chinese)

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7. Li, Y.: Research on the optimal decision-making method of flexible standby under the new situation of power grid operationy. In: China Outstanding Master’s Degree Thesis Full Text Database, vol. 3, pp. 1–61 (2021). (in Chinese) 8. Guo, X., Zhou, J., et al.: Calculation method of system reserve capacity considering new energy uncertainty in source-grid-load-storage scheduling mode. In: IEEE Conference on Energy Internet and Energy System Integration (EI2), pp. 11–13 (2022) 9. Xiang, L., Shao, S., et al.: A fully distributed optimization method for reserve capacity of multi-area interconnected power systems considering reserve sharing. In: Chinese Control Conference (CCC), pp. 26–28 (2021) 10. Wang, W.: Analysis of the development direction of electricity ancillary services under the “dual carbon” goal. New Energy Technol. 4, 16–19 (2021). (in Chinese)

Bidding Strategy Among Multi-party Electricity Sellers Based on Zero-Sum Game Theory in Complex Electricity Market Environment Qingkai Sun(B) , Menghua Fan, Chen Lv, Qiuyang Ma, and Su Yang State Grid Energy Research Institute Co., Ltd., Beijing 102209, China [email protected], {fanmenghua,lvchen,maqiuyang, yangsu}@sgeri.sgcc.com.cn

Abstract. With the continuous development of the electricity market and the intensification of competition, the price competition among electricity suppliers is becoming increasingly intense. This kind of competition not only significantly impacts the survival and development of power suppliers but also directly affects the interests of power users and the stability of the social economy. Therefore, understanding the price competition mechanism of the electricity market and predicting the price change trend is of great significance to the healthy development of the electricity market. This study uses the zero-sum game model in game theory to simulate the price competition between two electricity sellers in the electricity market. In our model, the response strategies of electricity retailers in the early and late stages significantly impact their final economic benefits. In addition, the demand pattern of electricity buyers and the response strategies of electricity sellers have an essential impact on the bidding results. This study provides a new perspective for understanding the price competition in the electricity market and provides valuable enlightenment for regulating and managing the electricity market. Keywords: Electricity market · Price game · Zero-sum game · Multi-agent electricity retailer

1 Introduction The bidding mechanism of the electricity market is an essential part of the economic operation of the power system, and its research is of great significance for understanding the operation mechanism of the power market and improving the economic benefits of the power system [1, 2]. As early as the 1990s, with the gradual opening of the electricity market, scholars began to pay attention to and study the bidding problem in the electricity market. Schweppe put forward the bidding theory of electricity market, which laid the foundation for the follow-up research [3]. Since then, a lot of research work has conducted an in-depth discussion on the bidding mechanism of the electricity market, such as the work of Mohammad E. Khodayar [4], Ehsan Nekouei [5], and Iman Taheri Emami [6]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 523–530, 2024. https://doi.org/10.1007/978-981-97-0877-2_54

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Although many studies have conducted in-depth discussions on the bidding mechanism of the electricity market, most of them mainly focus on ideal market conditions, and few studies consider that electricity sellers may adjust their response strategies according to market conditions. For example, in their research, Hossein Mehdipourpicha [7] mainly focused on the electricity market bidding problem under ideal market conditions, but did not consider the response strategies of electricity sellers. In addition, most of the existing research analyzes the bidding problem in the electricity market from a macro perspective, and pays less attention to the bidding behavior at the micro level, such as the strategy selection and behavior changes of electricity sellers. For example, the research of Rahim Ghorani [8] and Oveis [9] mainly analyzed the bidding mechanism of the electricity market from a macro perspective. However, they paid less attention to the micro behavior of electricity sellers. Therefore, this study aims to simulate the bidding behavior of electricity sellers in the electricity market through a game theory model to deeply understand the impact of electricity sellers’ response strategies on the bidding results of the electricity market under different market conditions. The main contribution of this paper is: for the first time, the zero-sum game model in game theory is introduced into the bidding problem of the electricity market. Simulating the strategy selection and behavior changes of electricity retailers provides a new perspective for understanding the price competition in the electricity market. The methods and findings of this study have significant reference value for the management and supervision departments of the electricity market, which will help to maintain better the fairness and competition order of the electricity market and further promote the healthy development of the electricity market.

2 Bidding Game Model Among Multiple Electricity Sellers 2.1 Electricity Market Environmental Parameter Setting This paper aims to study and quantify the price game behavior of two electricity sellers A and B, in the electricity market. To this end, we construct a mathematical model based on zero-sum game theory to describe how the two electricity sellers respond to the complex market environment. Changes to adjust the price of electricity sales to compete with electricity buyers. First of all, to simulate the response of electricity retailers in different market environments, we first introduced the parameter of the response factor. The response factor describes the sensitivity of electricity sellers to price changes. This parameter is critical because it can affect the response strategies of electricity sellers when market prices change. We set two reaction factors for each electricity retailer, corresponding to the early and late market reactions, denoted as αA1 , αA2 , αB1 , and αB2 . The purpose of this design is to capture the differences in the behavior of the market that may exist in different periods. Second, this paper determines the price ceiling and expected price floor of each electricity retailer, denoted as PA,max , PA,min , PB,max and PB,min . In order to simulate market behavior more realistically, we also introduce the probability of price rise and fall, expressed as πup and πdown . These two parameters can simulate the market economy’s uncertainty and the randomness of price rise and fall. Finally, we simulate the distribution

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of user needs. In our model, user demand is assumed to be normally distributed with mean and standard deviation denoted as μ and σ , respectively. Such an assumption can better simulate the distribution of user demand in the actual market [10]. 2.2 Bidding Strategies of Multiple Electricity Sellers in the Electricity Market Environment In the model proposed in this paper, the pricing strategies of retailers A and B need to follow the following rules [11, 12]: 1) At the beginning of each period, electricity retailers will determine their electricity prices based on the current electricity prices, reaction factors, and the probability of price increases and decreases. 2) If a random number is less than the probability of a price drop and the current electricity price exceeds the expected minimum electricity price, the electricity retailer will reduce the electricity price. The amount by which the electricity price falls equals the reaction factor multiplied by (current electricity price – expected minimum electricity price). 3) If a random number is less than the probability of a price increase and the current electricity price is lower than the upper price limit, the electricity retailer will increase the electricity price. The electricity price increase equals the reaction factor multiplied by (price ceiling – current electricity price). 4) In each period, the electricity seller with the lower price will win the electricity purchase users in this period. If the prices of electricity sellers A and B are the same, we default that electricity seller A wins users. 5) The income of electricity sellers is equal to their electricity price multiplied by the demand of electricity buyers. Through the above description, we can get the following electricity price adjustment formula: For electricity seller A:   ⎧ ⎨ PA (t) − αA1 × PA (t) − PA,min  if rand < πdown and PA (t) > F PA (t + 1) = PA (t) + αA1 × PA,max − PA (t) if rand < πup and PA (t) < PA ⎩ PA (t) otherwise (1) For electricity seller B:   ⎧ ⎨ PB (t) − αB1 × PB (t) − PB, min  if rand < πdown and PB (t) > 1 PB (t + 1) = PB (t) + αB1 × PB, max − PB (t) if rand < πup and PB (t) < PB ⎩ PB (t) otherwise (2) Among them, t represents the current period. Rand is a random number uniformly distributed in the interval [0, 1].

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This model can simulate the price game process between electricity sellers A and B within 24 h and observe the impact of their price strategies on electricity sales revenue. In addition, we also conducted detailed simulations of daily peak hours further to deepen our understanding of the price game process. This model has important theoretical and practical significance for understanding the operating mechanism of the electricity market and optimizing the operation strategy of electricity retailers. 2.3 The Bidding Game Solution Process Among Multi-party Electricity Sellers in the Electricity Market Environment In a complex electricity market environment, the bidding game process between electricity seller A and electricity seller B is shown in the following figure: Start Initialization parameters: Set the initial parameters of the model, including the response factor of the retailer, the upper and lower limits of the price, the probability of price adjustment, etc. Set the demand mode for 24 hours a day: set the demand mode of electricity purchase users according to different periods of the day (morning peak, evening peak, off-peak hours) Start the simulation of each time period: simulate how multiple electricity sellers conduct price games within a time period Adjust the prices of electricity sellers A and B: Adjust your own price according to the response factor and price adjustment probability of the electricity seller, as well as the price of the other party Determine the supplier of the electricity purchaser: According to the new prices of electricity sellers A and B, determine which electricity seller chooses as the supplier within this time period Calculate the economic benefits of electricity sellers A and B: Calculate the economic benefits of electricity sellers based on their prices and the demand of electricity purchasing users

N

T>24? Y End

Fig. 1. The bidding game process between electricity seller A and electricity seller B.

3 Case study 3.1 Case Parameters Setting The game model constructed in this paper is the competitive behavior of two electricity sellers A and B, in the electricity market. Electricity retailers gain market share by adjusting electricity prices to snatch electricity buyers. In the calculation example of

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this paper, the initial electricity price of the two electricity retailers is set to be 100 yuan, and the expected minimum electricity price is 50 yuan, respectively. In order to describe the characteristics of demand changes in the electricity market, we divide 24 h a day into three periods: morning peak, evening peak, and non-peak. The user’s intraday demand pattern is generated by a normal distribution with a mean of 70 and a standard deviation of 30. The response factors of electricity sellers A and B are different in the morning peak and off-peak hours, and the response factor in the morning peak period is more significant, reflecting the sensitivity of electricity retailers to the increase in market demand. 3.2 Dynamic Analysis of Price Competition Between E-commerce Merchants A and B at Peak Hours In order to simulate and analyze the complex game competition process between electricity sellers A and B in the electricity market environment in detail, a typical time during peak hours is selected as an example for analysis. The detailed bidding process is shown in Fig. 1 below:

Fig. 2. Price competition between two sellers during peak hour over 100 iterations.

From the analysis in Fig. 2, it can be seen that during the peak period (the morning peak period is taken as an example in this example), the detailed electricity price game competition situation of electricity sellers A and B. 1) In the early stage of the bidding game, the electricity prices of the two electricity retailers changed more frequently and sharply, which reflected that they adjusted their electricity price strategies more actively when faced with significant demand. At the same time, the supplier choices of electricity buyers also change more frequently, which indicates that the impact of electricity price strategies on market share is more significant during peak hours. Both electricity sellers A and B hope to seize the market by lowering prices in the early stage of the game. 2) In the later stage of the bidding game, electricity sellers A and B’s prices tended to be stable, at 63 and 69, respectively. This shows that after the initial fierce bidding game, electricity sellers A and B have mastered each other’s bidding information and have made an optimal bidding strategy based on their conditions at the current moment.

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3.3 Dynamic analysis of price competition between electricity sellers A and B within 24 h After analyzing the bidding game between electricity seller A and B during the selected typical peak hours, the dynamic process of bidding game between electricity seller A and B within 24 h is analyzed, and the results are shown in Fig. 2:

Fig. 3. Price competition between two sellers over 24 h.

From the analysis in Fig. 3, it can be seen that the electricity price changes of electricity sellers A and B within 24 h and the supplier selection of electricity buyers. It can be seen that during the morning peak and evening peak hours, the electricity prices of electricity sellers A and B increased due to the increase in market demand. However, during off-peak hours, their electricity prices are reduced accordingly due to reduced market demand. In addition, electricity buyers always tend to choose electricity retailers with lower electricity prices, which verifies our hypothesis that electricity buyers will choose suppliers based on electricity prices. At the same time, it can be seen which electricity retailer has seized the market 24 h a day. Electricity retailer A has the lowest electricity price at 1:00, 2:00, and 11:00–24:00. Seize the market share; electricity seller B seized the market share from 4:00 to 10:00. 3.4 Analysis of the Cumulative Economic Benefits of Electricity Sellers A and B Within 24 h The cumulative economic analysis results of electricity sellers A and B within 24 h are shown in Fig. 3 below: Figure 4 depicts the cumulative economic benefits of electricity sellers A and B within 24 h. We can see that the cumulative revenue of the two e-commerce retailers grows faster during the morning peak and evening peak hours but slower during off-peak hours. This reflects the impact of market demand on the revenue of e-commerce retailers. It is worth noting that although the electricity price strategies of electricity sellers A and B are different, their cumulative income is quite close. This may be because their electricity price strategies can better adapt to changes in market demand, thus achieving effective market share snatching.

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Fig. 4. Cumulative revenues of two sellers over 24 h.

4 Conclusion In the complex environment of the electricity market, this paper constructs a bidding game strategy between two electricity sellers based on the zero-sum game theory, and the following conclusions can be obtained through the analysis of actual examples: (1) In the electricity market, the electricity price strategy and market demand of electricity sellers significantly impact the economic benefits of electricity sellers. (2) During the peak hours when the demand is greater, the impact of the electricity price strategy on the market share is more significant. In non-peak hours, due to the small market demand, the impact of the electricity price strategy on market share is relatively small. (3) Electricity sellers need to reasonably adjust their electricity price strategies according to market demand changes to maximize their economic benefits. Acknowledgments. This research was supported by SGCC Science and Technology Project “Research on Key Technologies for Deepening Design, Simulation and Analysis Evaluation of Multilevel Unified Power Market under the New Power System” (5108-202218280A-2-254-XG).

References 1. Zhao, Y., Cai, Q., Wang, L., et al.: Changes in the electricity market under the participation of diverse participants and its supervision necessity analysis. Energ. Reports 9, 2013–2023 (2023). https://doi.org/10.1016/j.egyr.2023.04.141 2. Bashi, M.H., Gharibpour, H., Lyons, P., et al.: Price formation in short-term electricity market scheduling. Electr. Power Syst. Res. 223, 109670 (2023) 3. Schweppe, F.C., Caramanis, M.C., Tabors, R.D., Bohn, R.E.: Spot Pricing of Electricity. Springer, US (1988) 4. Khodayar, M.E., Shahidehpour, M., et al.: Optimal strategies for multiple participants in electricity markets. IEEE Trans. Power Syst. 29(2), 986–997 (2014) 5. Nekouei, E., Alpcan, T., Chattopadhyay, D., et al.: Game-theoretic frameworks for demand response in electricity markets. IEEE Trans. Smart Grid 6(2), 748–758 (2015)

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6. Emami, I.T., Samani, E., Abyaneh, H.A., et al.: A Conceptual analysis of equilibrium bidding strategy in a combined oligopoly and oligopsony wholesale electricity market. IEEE Trans. Power Syst. 37(6), 4229–4243 (2022) 7. Mehdipourpicha, H., Bo, R., et al.: Optimal bidding strategy for physical market participants with virtual bidding capability in day-ahead electricity markets. IEEE Access 9, 85392–85402 (2021) 8. Ghorani, R., Fotuhi-Firuzabad, M., Moeini-Aghtaie, M., et al.: Main challenges of implementing penalty mechanisms in transactive electricity markets. IEEE Trans. Power Syst. 34(5), 3954–3956 (2019) 9. Abedinia, O., Ghasemi-Marzbali, A., et al.: A new reconfigured electricity market bidding strategy in view of players’ concerns. IEEE Trans. Ind. Appl. 58(6), 7034–7046 (2022) 10. Li, Q., Yang, Z., Yu, J., et al.: Impacts of previous revenues on bidding strategies in electricity market: a quantitative analysis. Appl. Energ. 345(1), 121304 (2023) 11. Xun, D., Jun, W., Ping, S., et al.: Purchase-sale strategy of power retailers considering user contribution degree. Power Syst. Technol. 43(8), 2752–2760 (2019). (in Chinese) 12. Yi, C., Han, W., Zheng, Y., et al.: Inter-and intra-provincial electricity market clearing and pricing model under the evolution of national unified electricity market. Trans. China Electrotech. Soc. Online. (in Chinese)

Research on Reactive Power Compensation Method of Long-Distance and Large-Capacity Offshore Wind Farm High Voltage AC Transmission System Wanrong Chen(B) and Longfu Luo College of Electrical and Information Engineering, Hunan University, Changsha 410082, Hunan Province, China [email protected]

Abstract. The overvoltage and reactive power imbalance issues brought on by the large charging reactive power of transmission submarine cables are becoming more and more noticeable as the offshore wind farm alternating current (AC) transmission system moves toward long distance, high voltage, and large capacity. This paper presents a reactive power compensation approach that takes into account the system’s steady-state reactive power requirements as well as power frequency overvoltage with the goal to increase the safety and reliability of system operation. Firstly, the offshore wind power high-voltage AC transmission system simulation model is built in PSCAD/EMTDC. Secondly, in order to configure the capability of the fixed high-voltage shunt reactors placed in the onshore control center, different kinds of power frequency overvoltage are investigated and compared. Then, the steady-state reactive power demands are analyzed, the compensation capacity and switching stages of the adjustable shunt reactor are determined with the goal of no reactive power flow at the point of common coupling (PCC), and a reasonable control strategy is formulated. Finally, the simulation verification shows that the reactive power compensation method can limit power frequency overvoltage to the specified range and compensate the steady-state reactive power demand in real time. Keywords: Offshore wind farm · AC transmission · Power frequency overvoltage · Reactive power compensation · Adjustable shunt reactor

1 Introduction Against the backdrop of the strategic goals of “carbon peak” and “carbon neutrality” and the construction of new-generation power systems, the penetration of wind power as a clean renewable energy source is growing rapidly. Offshore wind power has the advantages of good wind energy quality, not occupying land resources, being locally consumed, having a large single-machine capacity, etc. Compared to other power transmission methods, the structure of high voltage alternating current (HVAC) is simpler, engineering experience is more abundant, and it has obvious economic advantages in the offshore wind farm transmission system above 500 MW and within 100 km [1]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 531–542, 2024. https://doi.org/10.1007/978-981-97-0877-2_55

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Because of the unique insulation design, the distributed capacitance of AC submarine cable is up to tens of times higher than the overhead line. A large amount of charging power from the capacitance will take up the transmission capacity of the line, which means the reactive power cannot be balanced locally and may produce more serious and complex overvoltage, thus threatening the safe and stable operation of the grid [2]. As a preferred limiter in the field of renewable energy generation [3], reactive power compensation devices can stabilize the system voltage, improve transmission efficiency, balance three-phase power, etc. Therefore, studying the reactive power compensation method of large-scale offshore wind farm HVAC transmission systems is essential to ensuring the safety and reliability of offshore wind farm operations. The main compensation method for submarine cables is the parallel connection of fixed reactors in the line. [4] simulated the overvoltage of the 220 kV offshore wind farm transmission system before and after configuring the high-voltage reactor. [5] calculated the optimum fixed reactor capacity required for submarine cable with the objective of enhancing the maximum transmission capacity. Due to the strong randomness and volatility of wind power, the power flow of grid-connected lines will be constantly changing, so real-time reactive power compensation devices must be installed. [6] considered the influencing factors, such as generation mode, the current carrying capacity of the cable, and the reactive power output of wind turbines, to configure dynamic reactive power compensation devices. However, the dynamic compensation device is more expensive. The adjustable reactor is also capable of tracking the randomly varying power demand. [7] combined a fixed shunt reactor with an on-load switching reactor for compensation but did not consider the transient reactive power demand. This paper suggests a reactive power compensation approach to address the reactive power issue of long-distance and large-capacity offshore wind farm high-voltage AC transmission systems. First, a simulation model of the offshore wind farm AC transmission system is established. Then, the steady-state reactive power demand and the power frequency overvoltage are comprehensively analyzed. Finally, reactive power compensation is carried out in combination with fixed shunt reactors and adjustable shunt reactors to increase the system’s operational safety and dependability.

2 Model of the Offshore Wind Farm AC Transmission System 2.1 Structure of the AC Transmission System for the Offshore Wind Farm In the paper, a 500 MW offshore wind farm is selected as the arithmetic example. The AC transmission system of the wind farm adopts a two-stage boosting method, and the output voltage of the wind turbines is 0.69 kV. Each wind turbine is boosted to 35 kV by the boxtype transformer in the tower drum and then gathered to the offshore substation through the collecting submarine cable. After boosting to 330 kV at the offshore substation, it is transported to the onshore switching station by the 100 km submarine cable and boosted to 500 kV. Finally, it is linked to the onshore power grid from the point of connection of the offshore wind farm through the overhead line. The structure of the system is shown in Fig. 1.

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Fig. 1. Structure diagram of the AC transmission system for the offshore wind farm

2.2 Parameter Calculation of Submarine Cable The section parameters of the 330 kV three-core submarine cable are shown in Table 1. In order to facilitate the study of the impact of the length of the cable, the entire cable is divided into 10 sections, each of which is 10 km in length. Table 1. Section parameters of the 330 kV three-core submarine cable Structure name

Nominal thickness (mm)

Approximate outer diameter (mm)

Copper conductor

/

30.0

Conductor screen

2.4

34.8

XLPE insulation

29.0

92.8

Insulation screen

1.2

95.2

In this paper, a three-core submarine cable is simulated using the pipe-type cable model in PSCAD/EMTDC. Since the model does not contain the semi-conductor layer, the relational parameters need to be corrected to improve the model’s accuracy [8]. The corrected positive sequence parameters of the submarine cable through simulation and calculation are shown in Table 2. Table 2. Corrected positive sequence parameters of the 330 kV three-core submarine cable Parameter

Resistance (/mm)

Inductance (mH/mm)

Capacitance (µF/mm)

Value

0.0459

0.3132

0.1489

As shown in Table 2, the capacitance of submarine cable is greater than that of ordinary overhead lines. The calculation formula for charging power is as follows: QC = BlU 2

(1)

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where B is the ground susceptance of the submarine cable, l is the length of the cable, and U is the voltage level of the system. The charging power of this 100-km cable is calculated at 509.76 Mvar, which requires reactive power compensation. 2.3 Wind Turbines and the 35 kV Collector System In order to decrease the modeling difficulty and enhance the speed of simulation analysis of the system effectively, the wind turbines and the 35 kV collector system are equivalent to a synchronous generator with 500 MW of rated active power. As shown in Fig. 2. In Fig. 2, XS is the leakage reactance of the equivalent system. The power fluctuation of the wind farm is simulated by adjusting the power output of the generator. In order to make the wind turbines generate more active power when the wind is abundant, this paper does not take into account their ability to regulate reactive power.

Fig. 2. Equivalent schematic diagram of wind turbines and the 35 kV collector system

3 Reactive Power Compensation 3.1 Reactive Power Compensation Device The fixed high-voltage shunt reactor can increase the submarine cable’s transmission capacity, reduce the insulation level of the high-voltage system, and thus effectively improve the transmission efficiency [9]. The compensation degree of a shunt reactor is defined as the percentage of the compensation capacity and the charging power of the positive sequence capacitor under power frequency: K=

QL · 100% QC

(2)

where QL is the compensation capacity of the shunt reactor. The adjustable shunt reactor is composed of a fixed shunt reactor and an on-load tap changer; its power output is adjusted by changing the number of turns. With the appropriate control strategy, the adjustable reactor can track the output change of the wind power and the voltage control requirements of PCC to stabilize the excess charging reactive power caused by the change in power flow.

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3.2 Position of Reactive Power Compensation Restricted by construction conditions, the compensation devices are generally arranged at both ends of the submarine cable. Due to the inconvenient installation and maintenance of offshore substations and in order to improve the response speed and accuracy of reactor dynamic regulation, in this paper, the reactive power compensation devices are installed at the onshore control center. 3.3 Method of Reactive Power Compensation In order to improve the utilization of the adjustable shunt reactor at all grades, the adjustable reactor in this paper is only used to balance the changes in reactive power at PCC during normal operation, while the fixed shunt reactor plays the role of limiting the power frequency overvoltage and balancing part of the basic reactive power at the same time. The framework of the method is shown in Fig. 3.

Fig. 3. Flow diagram of the reactive power compensation device configuration method

4 Analysis of Power Frequency Overvoltage The problem of power frequency overvoltage in offshore wind farms is extremely important for the safe operation of the system, and the problem of reactive power compensation affects the power quality of the system. Therefore, while formulating the reactive power

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compensation method, the overvoltage limit must be taken into account. From [10], it is known that the power frequency overvoltage should not be greater than 1.3 p.u., where the reference voltage is calculated as follows: Um V0 = √ 3

(3)

where U m is the maximum voltage of the system. The maximum voltage of the 330 kV voltage level system is 363 kV, so the reference voltage V 0 is 209.578 kV. 4.1 Overvoltage Caused by the Capacitance Effect of the No-Load Long Line Due to the presence of capacitance to ground in submarine cables, the capacitive current of the line increases when AC current flows through it, and the superposition of the voltage drop generated by the capacitive current flowing through the series inductor and the voltage drop across the capacitance causes an increase in voltage at the no-load line’s termination. The maximum values of power frequency overvoltage generated at different lengths of submarine cable in this situation are shown in Fig. 4.

Fig. 4. Power frequency overvoltage caused by the capacitance effect of the no-load long line

As seen in Fig. 4, the longer the submarine cable is, the greater the terminal overvoltage is. Under each length of cable, the overvoltage capacity effect caused by no load on the grid side is greater than the case of no load on the wind farm side. When the length of the cable exceeds 39 km, the overvoltage will not meet the restriction. In this calculation example, the cable length is 100 km. At this time, the terminal voltage rises to 1.9522 p.u., which must be limited by installing shunt reactors. 4.2 Overvoltage Caused by Trouble-Free Load Rejection During normal operation of the system, when a fault-free load rejection occurs at the end of the cable, the superposition of the capacitance effect of the no-load line and the overspeed of the generator leads to a rise in potential, which results in a rise in the power

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Fig. 5. Power frequency overvoltage caused by trouble-free load rejection

frequency voltage. The maximum values of the power frequency overvoltage generated at different lengths of submarine cable in this situation are shown in Fig. 5. As seen in Fig. 5, with the increase in submarine cable length, the trouble-free load rejection overvoltage will increase, and the overvoltage on the grid side is much larger than that on the wind farm side. When the cable length exceeds 33 km, the power frequency overvoltage will exceed the limit requirements. When the cable length is 100 km, the maximum overvoltage is 2.5769 p.u., necessitating the use of a shunt reactor. 4.3 Overvoltage Caused by the Asymmetrical Short Circuit Asymmetrical short-circuit is the most common form of fault in transmission lines, and the zero-sequence current caused by it will increase the non-faulted phase voltage, which generates power frequency overvoltage. In this paper, single-phase and two-phase grounding fault conditions are simulated at points a and b, as shown in Fig. 6. The amplitudes of single-phase and two-phase grounding overvoltages are shown in Figs. 7 (a) and (b) in sequence. In Fig. 7, the dashed and solid lines represent the measurement results of the end and head of the submarine cable, respectively.

Fig. 6. Diagram of the fault location

From Fig. 7, it can be seen that when the length of submarine cable increases, the overvoltage caused by an asymmetrical short-circuit will increase, and the overvoltage

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Fig. 7. Power frequency overvoltage generated by the asymmetrical fault

generated by a single-phase grounding fault will be more severe. When the cable is longer than 49 km, the overvoltage caused by the two-phase grounding fault will be greater than the limit range, and when the cable is longer than 21 km, the overvoltage caused by the single-phase grounding fault will exceed the limit. The position of the maximum overvoltage is closely related to the position of the fault. When the fault occurs at point a, the maximum value occurs at the end of the cable; when the fault occurs at point b, the maximum value occurs at the head end of the cable. When the cable length is 100 km, the maximum value generated by the single-phase grounding fault is 2.7291 p.u., and the maximum value generated by the two-phase grounding fault is 1.5727 p.u., which are all over 1.3 p.u. and should be taken to inhibit measures. 4.4 Configuration of the Fixed High-Voltage Shunt Reactor As already stated, when the 330 kV submarine cable is longer than 21 km, the reactive power compensation device must be configured. When the length of the submarine cable is 100 km, under the identical configuration, the power frequency overvoltage generated by a single-phase ground fault is the highest, at 2.7291 p.u., followed by the overvoltage generated by trouble-free load rejection on the grid side. With the goal of obtaining the most appropriate compensation capacity, a multistage compensation capacity from 300 Mvar to 450 Mvar is simulated. The maximum values of the overvoltage caused by the two most serious fault forms under different compensation capacities and degrees are shown in Table 3. In Table 3, U 0 and U 1 indicate the maximum values of overvoltage after compensation caused by fault-free load rejection and the single-phase grounding fault, respectively. As can be seen from Table 3, after installing 375 Mvar of fixed reactor, the overvoltage caused by fault-free load rejection has met the regulation; after installing 400 Mvar of fixed reactor, the overvoltage generated by the single-phase grounding fault can be limited within the prescribed scope; the degree of compensation at this time is 78.84%. In order to avoid the resonance zone where the cable is not in full phase operation, the compensation capacity of shunt reactors is generally not greater than 80% [11]. Therefore, it is chosen to install a fixed reactor with a compensation degree of 78.84% in the onshore control center, that is, a reactor with a capacity of 400 Mvar. At this time, the power frequency overvoltage is effectively limited to the regulation range.

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Table 3. The maximum values of the two most severe power frequency overvoltages Compensation capacity (Mvar)

Compensation degree (%)

U 0 (p.u.)

U 1 (p.u.)

0

0

2.5769

2.7291

300

58.85

1.5239

1.6987

325

63.76

1.4284

1.4834

350

68.66

1.3351

1.3992

375

73.56

1.2587

1.3265

400

78.47

1.2072

1.2794

425

83.37

1.1707

1.2368

450

88.28

1.1596

1.2034

5 Analysis of Steady State Reactive Power Demand 5.1 Analysis of System Steady-State Reactive Power Demand Due to the continuous changes in wind speed, the active output of wind turbines is constantly changing, and the reactive power is also ever-changing. The voltage of PCC should be controlled at no more than −3% to +7% of the nominal voltage [12], and it is related to the capacitance of the cable and the active output of wind turbines. Since the extreme value of reactive power demand occurs at zero and the rated active output, it is analyzed under the two most typical operation modes when the voltage of PCC is 0.97–1.07 p.u. (at this time, 1 p.u. = 330 kV) in this paper. Before installing the fixed reactors, the reactive power demand of PCC is shown in Fig. 8. In Fig. 8, U pcc denotes the voltage at PCC; Pw denotes the active output of the wind turbines; Pe denotes the rated active power of the wind turbines; and the negative and positive values of the ordinate denote the inductive and capacitive reactive power requirements, respectively.

Fig. 8. Reactive power demands of PCC under different submarine cable lengths

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From Fig. 8, it can be seen that under the same cable length, the inductive reactive power requirement of the wind farm at rated active output is less than that at zero active output. When Pw = 0, the inductive reactive power demand with a cable length of 10– 100 km is inductive, and the longer the length, the larger the demand is. When Pw = Pe , the main requirement is capacitive reactive power if the cable length is smaller; if U pcc is 0.97 p.u. and the cable length reaches 33 km, or if U pcc is 1.07 p.u. and the length of the cable reaches 27 km, the reactive power demand begins only to be inductive. Basic reactive power compensation can be provided by fixed reactors, while the remainder is provided by adjustable reactors. When the cable length is 100km, the reactive power demand after the addition of a 400 Mvar fixed reactor is shown in Fig. 9.

Fig. 9. Reactive power demands of PCC after installing a 400 Mvar fixed shunt reactor

As seen in Fig. 9, after installing the fixed shunt reactor, the system reactive power demand corresponding to the 100 km submarine cable under the rated and zero active output of the wind turbines is always inductive, and it has a basically linear relationship with the voltage at PCC. Therefore, the reactive power demand during steady operation ranges from -2.41 Mvar to -121.91 Mvar, which is basically in the shadow part. 5.2 Configuration and Control Strategy of the Adjustable Shunt Reactor In order to minimize the impact of offshore wind farm operation on the grid voltage, it is best to control the reactive power of PCC to 0. Therefore, the adjustable reactor with a total compensation capacity of 120 Mvar and ten-grade switching is selected. Since the reactive power demand changes continuously with time and the adjustable reactor can only be operated in a graded manner, a reasonable control strategy is required. The control strategy is shown in Fig. 10. In Fig. 10, q denotes the compensation capacity of each reactor grade, and QPCC denotes the reactive power of PCC monitored in real time. This paper simulates the changes in reactive power demand caused by changes in the active output of the wind turbines based on the fluctuation characteristics of different typical wind speed models, and the efficacy of the configuration and control strategy of the reactor is verified [13]. The compensation effect is shown in Fig. 11. As seen in Fig. 11, when the reactive power demand changes due to the change in wind turbine active output from 0% to 100%, the reactive power at PCC only fluctuates in a small range near 0 after compensation. Therefore, the adjustable reactor can quickly track changes in reactive power demand, effectively reducing the exchange of reactive power.

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Fig. 10. Control strategy for adjustable shunt reactors

Fig. 11. Compensation effect of adjustable shunt reactors

6 Conclusion A method applied to the long-distance AC transmission system of the 330 kV offshore wind farm for reactive power compensation is presented in this paper. Considering the limitations of power frequency overvoltage and steady-state reactive power demand, a 400 Mvar fixed reactor and an adjustable shunt reactor with a compensation capacity of 120 Mvar and 10-stage switching are installed in the onshore control center, and a reasonable control strategy for the adjustable reactor is formulated. The verification shows that the reactive power compensation method can limit the overvoltage to the specified range and compensate the reactive power demand in real time, so as to improve the safety and reliability of the system.

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References 1. Wang, X.F., Wei, X.H., Ning, L.H.: Integration techniques and transmission schemes for offshore wind farms. Proc. CSEE 34(31), 5459–5466 (2014). (in Chinese) 2. Tan, H.T., Li, H., Yao, R.: Reactive-voltage coordinated control of offshore wind farm considering multiple optimization objectives. Int. J. Electr. Power Energy Syst. 136(1), 107602 (2022) 3. Cheng, P., Li, K., Wu, C.: Flexible power regulation and limitation of voltage source inverters under unbalanced grid faults. CES Trans. Electr. Mach. Syst. 6(2), 153–161 (2022) 4. Jin, Z.L., Chen, X.Y., Wen, X.S.: Study on power frequency and operating overvoltage of 220 kV long submarine cable in offshore wind farm. Insulators Surge Arresters 2020(1), 47–53 (2020). (in Chinese) 5. Zhang, J.H., Jiang, Y.W.: Reactive power compensation strategy for improving capacity of submarine cable. Electr. Eng. 20(5), 19–23 (2019). (in Chinese) 6. Chen, M., Tang, X.J., Chen, D.Z.: Reactive power compensation configuration of offshore wind power based on economic differential pressure theory. J. Phys: Conf. Ser. 2401(1), 012061 (2022) 7. Zhang, Z.G., Yu, D., Xu, Y.: Design study on reactive power compensation of long and high voltage submarine cable. Power Capacitor React. Power Compensation 31(6), 1674–1757 (2010). (in Chinese) 8. Zhang, W.J., Wang, S., Chen, X.Y.: Shunt reactor configuration of offshore wind farm transmission system with submarine cable. High Voltage Apparatus 58(1), 38–45 (2022). (in Chinese) 9. Zhou, H., Qiu, W.Q., Sun, K.: Ultra-High Voltage AC/DC Power Transmission, 1st edn. Zhejiang University Press, China (2018) 10. GB/T 50064–2014: Code for design of overvoltage protection and insulation coordination for AC electrical installations. China Electricity Council, China (2014). (in Chinese) 11. Lu, Y., Tan, J.: A discussion on the integration of offshore wind farm into Jiangsu power grid. Jiangsu Electr. Eng. 33(5), 55–58 (2014). (in Chinese) 12. GB/T 12325–2008: Power quality—Deviation of supply voltage. Chinese National Standardization Technical Committee for Voltage Current Ratings and Frequencies (2008). (in Chinese) 13. Liu, Y., Zhou, D.Y., Wang, C.W.: Model design and dynamic simulation of offshore Wind Turbines. Ship Eng. 42(S1), 554–557 (2020). (in Chinese)

Research on the Sealing Efficiency of Downhole Electromagnetic Barriers Based on COMSOL Zhongjian Kang1 , Peng Liu1(B) , Yuchen Liu2 , and Chenghuang Zhang2 1 College of New Energy, China University of Petroleum (East China), Qingdao 266580, China

[email protected] 2 Center for Basic Education, Ocean University of China, Qingdao 266100, China

Abstract. In order to examine the impact of downhole electromagnetic energy barriers on the energy utilization efficiency of shale spectral resonance devices, a simulation analysis of the sealing effect of these barriers is performed. Using COMSOL Multiphysics software along with the principles of elastic wave propagation and nonlinear finite element algorithm, the propagation process of shock waves in the presence of electromagnetic energy barriers in downhole environments is analyzed. The simulation results demonstrate that following pulse discharge from the discharge unit of the shale spectral resonance device, the resulting shock waves propagate through the water and casing. By comparing the pressure of the shock waves detected at the specific point on the inner wall of the casing with and without the downhole electromagnetic energy barrier, the effectiveness of the barrier in sealing the shock waves is confirmed. Consequently, the energy utilization efficiency of the shale spectral resonance device is improved by 46.8%. This analysis provides a theoretical foundation for the practical implementation of downhole electromagnetic energy barriers in unconventional oil and gas production operations. Keywords: Shale gas · COMOL · Partial discharge · Shock waves · Finite element simulation

1 Introduction The “Dual Carbon” objective has placed increased demands on China’s low-carbon energy transformation in terms of quality and progress. Petroleum and natural gas, as relatively clean and low-carbon energy sources, are crucial in achieving the “Dual Carbon” target and ensuring energy security. However, China’s current status in the development and utilization of oil and gas resources does not align with its strategic position in advancing the “Dual Carbon” target and securing energy security. China faces limitations in conventional oil and gas resources, along with challenges in exploration and production with high costs. Additionally, there is limited potential for stable growth in crude oil production and reserves [1, 2]. In 2020, China’s recoverable petroleum reserves amounted to 3.5 billion tons, with a per capita recoverable reserve of 2.48 tons, representing only 7.7% of the global average. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 543–553, 2024. https://doi.org/10.1007/978-981-97-0877-2_56

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China possesses significant potential in unconventional oil and gas resources, including shale gas, coalbed methane, and tight sandstone gas, compared to conventional reserves. In the past decade, China has achieved strategic advancements in exploring and developing these unconventional resources by leveraging technological knowledge and experience gained from North America [3]. However, the tight reservoirs, poor pore permeability, and low natural productivity pose challenges to effective production. To overcome these challenges, reservoir stimulation techniques are necessary to create fractures and enhance permeability [4, 5]. The China University of Petroleum (East China) has conducted research and development on a downhole electromagnetic energy barrier as an enhancement to the existing shale spectral resonance generator [6]. This energy barrier aims to further improve reservoir properties and achieve higher recovery rates of shale oil and gas. It addresses the challenge of effectively sealing the system by combining existing downhole isolation technologies with the shale spectral resonance generator. The shale spectrum resonance device operates by generating elastic waves through pulse discharge. These waves propagate within unconventional reservoirs, resulting in changes to their porosity [7]. Figure 1 illustrates the overall schematic diagram of the shale spectrum resonance device. A key characteristic of this method is its ability to achieve resonance by matching the discharge frequency with the reservoir’s natural frequency. Remarkably, only a small amount of electrical energy is necessary to significantly enhance the reservoir’s porosity and improve the efficiency of extracting unconventional shale gas. However, an obstacle faced by the device is the dissipation of shock waves into the surrounding free medium due to the open discharge space. To address this issue, it becomes imperative to investigate the propagation of elastic waves and the energy utilization efficiency of the device when an underground electromagnetic energy barrier

Fig. 1. Experimental platform of downhole electromagnetic energy barrier.

Fig. 2. Schematic diagram of cooperation between electromagnetic energy blocker and pulse discharge unit

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is installed. Figure 2 presents a schematic diagram of this underground electromagnetic energy barrier.

2 Analysis of the Mechanism of Shock Wave Propagation 2.1 Mechanism of Shock Wave Propagation in Shale Spectral Resonance Device In water, the shock wave generated by pulsed discharge during the process of expansion propagates outward at a velocity higher than the speed of sound in water. Similar to shock waves generated by explosions, the propagation and attenuation of shock waves generated by pulsed discharge in water exhibit similar characteristics [8]. However, the existing theories regarding the propagation of shock waves specifically generated by pulsed discharge in water are limited, resulting in a lack of substantial evidence. Therefore, it is reasonable to draw upon the relevant theories regarding the propagation of shock waves generated by explosions in water for analysis. This approach can provide valuable insights into understanding the mechanism of shock wave propagation induced by pulsed discharge in water. The transmission of shock waves generated by underwater pulsed discharge is characterized by a high-pressure, high-density wave front that rapidly moves through the water. Physical properties such as particle velocity, density, and pressure experience abrupt changes across the wave front. In an ideal scenario, the wave front of the shock wave would be a perfectly thin plane. However, due to the effects of fluid viscosity and thermal conductivity, these properties still undergo continuous but minute changes in the region immediately before and after the wave front, resulting in a thin but finite thickness of the wave front. The variations of these physical properties before and after the wave front can be seen in Fig. 3:

Fig. 3. Shock wave front

The three basic equations for the shock wave can be obtained from the initial state of undisturbed water ahead of the wave front, denoted as pressure p0 , density ρ0 , particle velocity u0 , temperature T0 , and specific internal energy E0 , and the disturbed state of water behind the wave front, denoted as pressure p1 , density ρ1 , particle velocity u1 , temperature T1 , and specific internal energy E1 . These equations include: ρ1 (DW − u1 ) = ρ0 DW

(1)

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p1 − p0 = ρ0 DW u1 E1 − E0 =

1 1 1 (p0 + p1 )( − ) 2 ρ0 ρ1

(2) (3)

E0 and E1 are the specific internal energies per unit mass for the initial and disturbed states respectively. These equations describe the conservation of mass, momentum, and energy across the shock wave. DW represents the wave speed of the shock wave [9]. Based on the aforementioned basic equations, by simultaneously solving the equation of state and adiabatic equation for water under hydrostatic pressure, it can be theoretically derived that for weak shock waves in water with peak pressure less than 0.1 GPa (assuming the propagation process to be isentropic), there is the following relationship between the wave speed DW and the peak pressure PM : DW = c0 (1 +

n + 1 PM 1/2 ∼ n + 1 PM ) = c0(1 + ) 2n B 4n B

(4)

In the equation,c0 represents the speed of sound in water before the disturbance n = 7.15 B = 299MPa. From the above equation, it can be inferred that there is a positive correlation between the peak pressure of weak shock waves in water and the wave speed. The wave speed will increase with the enhancement of the peak pressure. 2.2 Mechanisms of Shock Wave Attenuation When shock waves propagate in water, their intensity attenuates approximately exponentially. In shale spectrum resonance devices, the shock waves generated by pulse discharge are spherical waves. The relationship between the peak pressure, p, of the spherical waves and the propagation distance can be described as follows: p ∝ r −1 . During the near-field propagation of the shock waves generated by underwater explosion through pulse discharge in shale spectrum resonance devices, 40% to 60% of the energy of the shock waves is converted into internal energy of the water medium along the way. Previous studies have found that there is a relationship between the shock wave pressure, p, the discharge energy, and the distance, r, to the discharge electrode as follows: p = 2.59E · e−0.4836r

(5)

In the study, we investigate the propagation of shock waves and the sealing efficiency of downhole electromagnetic energy barriers. To analyze the shock wave propagation, we utilize a finite element method and utilize an empirical formula that relates the peak pressure, p, of the shock waves to the distance between the shock wave and the discharge electrode, denoted as r, and the discharge energy, denoted as E [10]. Through the finite element analysis, we can examine how the shock wave pressure varies with the distance between the shock wave and the discharge electrode. This relationship is depicted in Fig. 4, which shows a graph illustrating the function of shock wave pressure as a function of the distance.

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The purpose of this analysis is to gain insights into the behavior of shock waves and assess the effectiveness of the downhole electromagnetic energy barrier in containing and attenuating their pressure.

Fig. 4. The relationship between shock wave pressure and the distance between the discharge electrodes.

3 Simulation Analysis of Shock Wave Propagation During the operation of the shale resonator, shock waves are generated through pulse discharge in water. The detection of shock waves mainly relies on installing ultrasonic sensors on the outer wall of the equipment chamber to measure local discharge signals. Since the sensors have no electrical connection with the shale resonator’s electrical circuit, they are not affected by electrical signal interference, resulting in high accuracy in locating the shock wave source [11]. However, during on-site operations, the accuracy of the sensors can be affected by surrounding environmental noise and equipment mechanical vibrations. Additionally, the shock wave signal experiences significant attenuation in the free medium, which limits the detection range of the ultrasonic detection method. COMSOL Multiphysics is a powerful simulation software that utilizes the finite element method to accurately simulate a wide range of mathematical, physical, and engineering problems governed by partial differential equations. Within the software, the solid mechanics (elastic wave) physics module enables precise analysis of the propagation of shock waves generated by pulse discharge [12, 13]. In this study, the researchers utilized COMSOL 6.1 to perform a comprehensive three-dimensional simulation analysis of the downhole electromagnetic energy barrier. The main objective was to investigate the effectiveness of the barrier in containing the shock waves generated by the pulse discharge of the shale resonator. To achieve this, the simulation employed the minimum residual method as a linear iterative solver. By using the transient analysis mode, the researchers examined the propagation process from the initial stage up to 2 ms, with a time interval of 2 µs. The simulations also imposed an absolute error limit of 1 microsecond to ensure accuracy.

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By comparing the propagation processes of shock waves with and without the installation of the downhole electromagnetic energy barrier, the study aimed to evaluate the sealing effect of the barrier on the pulse discharge of the shale resonator. This analysis provides valuable insights into the barrier’s performance and its potential for effectively mitigating and containing shock waves in such applications. 3.1 Simulation and Modeling Methodology In the three-dimensional simulation model, solving the propagation problem of shock waves involves solving the velocity-strain equation under the specified boundary conditions. The velocity-strain equation can be utilized to solve the governing equation for general linear elastic materials, which is applicable to both isotropic and anisotropic material data. The velocity-strain equation is given as follows: ∂v − ∇ · S = FV ∂t

(6)

∂E 1 − [∇v − (∇v)T ] = 0 ∂t 2

(7)

S=C:E

(8)

ρ

In the equation, v represents velocity, ρ represents density, S is the stress tensor, E is the strain tensor, C is the elasticity tensor (or stiffness tensor), and FV is the possible volume force. The shock wave generated by pulse discharge is simulated by imposing an outward load on a boundary within the spatial model. As a result of the external load, different types of elastic waves propagate through the free medium and casing, traveling along the top surface of the linear elastic half-space. Specifically, these waves consist of compressional waves, shear waves, P-waves (Von Schmidt waves), and Rayleigh waves. The free boundary is particularly important because it generates Rayleigh waves, which propagate at a velocity lower than that of shear waves in the outer region of the casing. The classical estimate for the velocity of Rayleigh waves vR is: vR 0.87 + 1.12v ≈ cs 1+v

(9)

where v is the Poisson’s ratio. Hence, when constructing the overall grid for downhole electromagnetic energy barrier and shale spectral resonance devices, the grid size must be calculated using the velocity of Rayleigh waves to correctly solve for the propagation of Rayleigh waves.

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3.2 Establishment of the Simulation Model Due to the extended length of the shale spectral resonance device and the primary role of the downhole electromagnetic energy barrier in isolating its pulse discharge unit, it becomes possible to streamline the COMSOL simulation calculation by focusing solely on modeling and simulating the discharge unit of the shale spectral resonance device and the overall downhole electromagnetic energy barrier. This approach allows for a significant reduction in the number of mesh divisions while maintaining accuracy. Consequently, the calculation results converge more rapidly, resulting in more stable solutions. Based on the actual materials used in the discharge unit of the shale spectral resonance device and the downhole electromagnetic energy barrier, the material parameters for each component in the COMSOL simulation can be determined. Please refer to Table 1 for the properties of each material. Table 1. The properties of each material. Name

Material

Density (g/cm3 )

Young’s modulus (MPa)

Poisson’s ratio

Pressure wave velocity (m/s)

Shear wave velocity (m/s)

Shell

316L

7.9

193e3

0.3

5790

2240

Discharge electrode

Copper

8.96

125e3

0.33

3560

2156

Sealing section

Silicone gel

1.1

1.5

0.49

1000

200

Free medium

Water

1

2.2e3

0.5

1482

850

Casing

Concrete

2.5

30e3

0.2

4000

2000

Figure 5 illustrates the three-dimensional model and mesh partition of the discharge unit of the shale spectral resonance device, both in standalone operation and in conjunction with the downhole electromagnetic energy barrier. To facilitate the threedimensional simulation calculation, a free tetrahedral mesh partition is utilized. Through error analysis and iterative calculation, precise and dependable data on shock wave propagation is obtained. This solving method proficiently emulates the diffusion process of shock waves resulting from the pulsed discharge of the discharge unit in the shale spectral resonance device.

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Fig. 5. The three-dimensional model and mesh partitioning of the overall device.

4 Analysis of Simulation Results 4.1 Analysis of the Propagation Process of Shock Waves After Pulse Discharge In the case of the shale sonic resonance device situated within the casing of unconventional reservoirs, the outer casing is constrained by the reservoir while the interior of the casing is filled with water or other free media. When the pulse discharge unit of the shale sonic resonance device is activated, it produces shockwaves that travel through the water, resulting in complex propagation with multiple reflections within the casing. To analyze this phenomenon, a three-dimensional model was created using the pulse discharge unit and downhole electromagnetic energy barrier in COMSOL. Finite element simulation analysis was conducted, utilizing the initial position of the discharge unit as the starting point for the applied pressure load. Figure 6 provides an illustration of the propagation process of the shockwave in the water and casing when a single pulse discharge is initiated by the shale sonic resonance device. Figure 7 illustrates the propagation process of shockwaves in water and casing when the shale sonic resonance device’s pulse discharge unit is equipped with a downhole electromagnetic energy barrier.

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Fig. 6. The propagation process of shock waves without the barriers.

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Fig. 7. The propagation process of shock waves after installing the barrier.

From Figs. 6 and 7, it can be observed that during the propagation of shockwaves generated by the pulse discharge in water and casing, without the downhole electromagnetic energy barrier installed in the shale sonic resonance device, the shockwaves exist in an open space. In the vicinity of the pulse discharge and instantaneously, the shockwaves propagate through the water in a relatively simple path. However, after approximately 80 µs of propagation, the shockwaves reach the casing wall and are influenced by reflection, leading to a more complex propagation path. With increasing propagation distance, the peak overpressure of the shockwaves gradually decreases, and the propagation speed slows down. By comparing Figs. 6 and 7, it can be observed that during the propagation process, the downhole electromagnetic energy barrier reflects the shockwaves back into the corresponding enclosed area within the casing, resulting in the convergence of shockwave energy within the enclosed area. This helps to reduce the attenuation of the shockwaves in the free media.

Fig. 8. The pressure magnitude of the shockwaves on the casing wall at 300 µs. The left side represents the casing with the downhole electromagnetic energy barrier installed, while the right side depicts the casing with only the shale sonic resonance device operating independently.

Based on the information presented in Fig. 8, it is evident that the installation of the downhole electromagnetic energy barrier effectively seals off the shockwaves generated by the pulse discharge. This containment results in a concentration of the shockwaves

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within the enclosed space set apart by the downhole electromagnetic energy barrier. Consequently, the casing wall experiences a significantly higher pressure from the shockwaves compared to situations where only the shale sonic resonance device is in operation independently. 4.2 Analysis of the Sealing Effect of the Downhole Electromagnetic Energy Barrier To conduct a qualitative analysis of the enhanced energy utilization efficiency of the shale sonic resonance device after the installation of the downhole electromagnetic energy barrier, a finite element simulation analysis is performed on the propagation model of shockwaves generated by a single pulse discharge. By monitoring the pressure at a specific point near the pulse discharge, a schematic representation of the shockwave pressure, as demonstrated in Fig. 9, can be obtained.

Fig. 9. The variation of shockwave pressure over time at a specific point within the enclosed space during a single pulse discharge of the shale sonic resonance device, both without and with the installation of the downhole electromagnetic energy barrier.

Based on Fig 9, it is apparent that during the initial 100 µs, the pressure measured at the monitoring point within the enclosed space remains at 0, irrespective of whether the downhole electromagnetic energy barrier is installed or not. This is due to the shockwave not reaching that particular point. However, between 100 and 300 µs, it is evident from the figure that the measured pressure is higher when the energy barrier is installed compared to when it is not. Calculations reveal that the integrated pressure measured within 300 µs after the installation is 252.54 MPa, whereas the integrated pressure measured without the installation is only 172.02 MPa. These findings highlight that the downhole electromagnetic energy barrier can effectively enhance the energy utilization efficiency of the shale sonic resonance device by 46.8%.

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5 Conclusion (1) A thorough understanding of the propagation process of shockwaves generated by a single pulse discharge in the shale sonic resonance device has been achieved. COMSOL finite element analysis was employed to analyze the propagation and attenuation of shockwaves, laying the groundwork for studying the propagation of shockwaves generated by multiple pulse discharges. (2) Two comparative models were proposed: the standalone pulse discharge unit of the shale sonic resonance device and the combined model of the pulse discharge unit with the downhole electromagnetic energy barrier. COMSOL finite element simulations clearly demonstrate that the installation of the downhole electromagnetic energy barrier effectively seals the pulse discharge unit, leading to a remarkable 46.8% improvement in energy utilization efficiency.

References 1. Zheng, M., Li, J., Wu, X., et al.: China’s conventional and unconventional natural gas resources: potential and exploration targets. J. Nat. Gas Geosci. 3(6), 295–309 (2018) 2. Jiao, F.Z.: Recognition of “unconventional” in unconventional oil and gas. Pet. Explor. Devel. 46(5), 803–810 (2019). (in Chinese) 3. Gao, D.: Some research advances in well engineering technology for unconventional hydrocarbon. Nat. Gas Ind. B 9(1), 41–50 (2022) 4. Yuan, G., Fu, L., Wang, Y.: The up-to-date drilling and completion technologies for economic and effective development of unconventional oil & gas and suggestions for further improvements. Petrol. Drilling Tech. 50(01), 1–12 (2022). (in Chinese) 5. Akiyama, H., Akiyama, M.: Pulsed Discharge Plasmas in Contact with Water and their Applications. IEEJ Trans. Electr. Electron. Eng. 16(1), 6–14 (2021) 6. Nie, Y., Kang, Z., Wang, C.: Electrodes erosion characteristics of pulse discharge in water. High Voltage Eng. 47(07), 2607–2614 (2021). (in Chinese) 7. Huang, K., Li, X., Zhu, X.: Research on pulse discharge shock wave device for shale gas production enhancement. Petrol. Drilling Tech. 50(04), 97–103 (2022). (in Chinese) 8. Zhang, M.K.A.: Thesis Submitted to Southwest University of Science and Technology for the Degree of Master. Beijing University of Civil Engineering and Architecture, Beijing (2022). (in Chinese) 9. Lei, P., Zhang, Z., Wang, X.: Demonstration of transversely pumped Ar* laser with continuous-wave diode stack and repetitively pulsed discharge. Optics Commun. 513, 128116 (2022) 10. Jiao, K., Yun, F., Yan, Z.: Optimization and experimental study of the subsea retractable connector rubber packer based on Mooney-Rivlin constitutive model. J. Marine Sci. Eng. 9(12), 1391 (2021). https://doi.org/10.3390/jmse9121391 11. Li, C., Yang, G.T., Huang, Z.Z.: Constitutive equations of incompressible nonlinear superelastic material. Trans. Beijing Inst. Technol. 31(19), 30–34 (2011). (in Chinese) 12. Lei, W., Lina, D.: Simulation Analysis of Stray Current Corrosion based on COMSOL Multiphysics. New Technol. New Process 46(3), (2014) 13. Li, H., Li, G., Wang, Q.: Friction torque field distribution of a permanent-magnet spherical motor based on multi-physical field coupling analysis. IET Electric Power Appl. 15(8), 1045– 1055 (2021)

Solar Photovoltaic Penetration into the Grid Based on Energy Storage Optimization Technology Sothearot Vann, Hongyu Zhu, Chen Chen, and Dongdong Zhang(B) School of Electrical Engineering, Guangxi University, Nanning, China {hongyuzhu,cchen}@st.gxu.edu.cn, [email protected] Abstract. Solar energy is a potential renewable energy that is very important for the increasing energy needs of people living in modern life and contributing to reducing environmental pollution in energy production. To contribute to solving the above problem, existing fossil fuel power plants replaced by solar PV power and increasing the capacity of solar energy to meet the growing energy demand is a key role which can reduce climate change problem and reduce electricity production costs. However, the potential of Solar PV is closely related to the geographical location installed because the energy emitted from Solar PV depends on the amount of sunlight received, so the solar PV power output has variations. Therefore, energy storage is significant in power systems that use a large portion of solar energy in the grid. When the power supply exceeds the energy demand is charged into the storage and discharged during periods of power demand exceeding the power supply. It means that energy storage is a tool to balance the power system with unpredictability and fluctuations in renewable energy resources. The energy storage system is significant, but a high-capacity energy storage system has a high cost, so the electrical manufacturing sector can benefit from technologies that reduce energy storage. This paper presents the energy storage optimization technology to achieve solar PV penetration into the gride base on the ramping of power source generators. Keywords: Ramping Capability source · Power system imbalance · Energy storage · Optimization

1 Introduction Energy storage is a crucial component in maintaining the stability of the power system for a significant proportion of variable renewable energy, particularly solar photovoltaic energy. The deployment of battery storage in power systems to provide different grid services that directly assist variable renewable energy generation integration is becoming more popular as the cost of batteries drops and new technologies are updated. In addition, the storage system has decreased energy curtailment with a high proportion of variable renewable energy penetration and energy shifting on both sides (demand and supply). On the other hand, the availability of technologies that can decrease the value of energy storage systems may be a determining factor in the ability of the power grid to use renewable energy at lower costs [1]. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 554–562, 2024. https://doi.org/10.1007/978-981-97-0877-2_57

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However, a large-scale portion of solar PV also requires large-scale energy storage that affects the project plant’s economy. Solar PV power output is affected by weather, which occasionally causes power production unpredicted. For a large-scale portion of solar PV planning, the technology to balance the power system from fluctuations in solar PV output is a challenge that requires more exploration of new methods to overcome this problem. Advanced intelligence solutions have been looked at to respond with solar energy sources integration into the power grid to deal with the power system balance and economics and restrict carbon emissions into the environment. Future studies on the planning of expanding renewable energy interconnection and penetration into the existing electric power grid, as well as revenue and cost analyses of renewable energy integration, can benefit from the reliability evaluation of wind and solar energy resources for grid connection. The study also helps in the development of business plans for the electrical sector that have utilized to include renewable energy sources in the existing power system. Any weak system components used in the power production of solar and wind energy can be examined and addressed [2]. When the power grid is configured with a large share of variable renewable energy determining the optimum size of the battery energy storage system is essential. Energy storage system design should optimize to reduce the investment costs of energy storage with a high share of solar PV grid integration [3, 4]. The related literature views on power system research with significant penetration of variable renewable energy have increased significantly. Several papers have been presented, regarding the future of power systems with renewable energy, including the optimization of energy storage systems that use renewable energy with hydro pump storage, flexibility, and stability requirements [4–8]. Numerous studies on large-scale solar energy integrated into the power grid have confirmed that solar energy has confirmed its benefits more than side effects. The challenges research technology has reviewed for planers to address the grid system more efficiently or avoid the impacts on the grid on current and future projects. Balancing the supply and demand sides becomes crucial when integrating a high share of renewable energy into the grid. This review also provided data for researchers, security for the power grid, and scientists on the feasibility of integrating solar energy into the national grid for the new project preparation [9]. The 2025 Israel Electricity Grid Model studies and provides recommendations for maintaining stable frequencies in the power grid as it becomes more integrated with the location and capacity of renewable energy and energy storage systems. This study provides significant recommendations for addressing power systems at safe frequencies that provide designers to use existing pumped storage hydro systems over charging operations [10]. More flexibility is needed to maintain the balance of the power system, given the availability of highly variable renewable energy penetration in European countries. This study defined residual load variation and covered it with the dispatchable plant. The practical framework was to evaluate flexibility. The analysis demonstrates not only manages the balancing of the electricity system but also lowers carbon emissions [11]. However, there are very few studies and practical applications conducted in Cambodia. Based on a review of the relevant literature on the global energy grid, this paper aims to highlight the optimization of energy storage system requirement for Cambodia’s power grid when increasing the share of solar photovoltaic energy and to identify the available

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flexible resources that provide the ideal capacity’s energy storage. This study focuses on the hydropower industry’s ramping capabilities to optimal the necessary energy storage capacity for Cambodia’s national grid.

2 Power System with A High Share of Solar Photovoltaic 2.1 Solar Photovoltaic 10 MW With a 10 MW solar farm that provides data that may use as a guide for creating further solar plans in the region, Cambodia has been developing solar energy plans since 2017. Even though solar power capacity has increased significantly over the past two years, from 10 MW to more than 100 MW, it is still insufficient to meet the country’s fastincreasing electricity demands and the policy to reduce greenhouse gas emissions [12]. In particular, during the dry season, Cambodia’s geographic location has given rise to a high potential for solar energy. In Cambodia, the year-round availability of solar irradiation is gone for an average of approximately eight hours per day. The data on solar irradiation that has been measured and recorded has significant potential, with daily average levels of 5 kWh/m2 and peaks as high as 5.6 kWh/m2 in the central region of Cambodia. These levels are around twice as higher as Germany’s, and some of the top countries for solar development, such as Thailand and China [13]. 2.2 High Share of Solar Energy with Energy Storage System Energy storage systems can play a critical role due to their characteristic to maintain the power system’s balance when injecting a large amount of solar energy. The energy storage system can handle the fluctuation of applications across the distinct requirements in the electrical system chain, depending on its potential and technical characteristics, such as charge or discharge capacity and geographic location. The researcher needs to find the optimal strategy to develop the many practical options for an energy storage system effectively. Batteries storage technologies, which have several commercial scales in MW of installed capacity and a response time of less than seconds, have been classified as a mature technology. The most prevalent and developed method is hydro storage pumped, which has a response time of a few seconds. Pumped storage Hydropower can store substantial amount of energy, thus significantly supporting cascaded hydropower and solar projects’ complementarity and combined power generation. [14–16].

3 Energy Storage Optimization Method 3.1 Residual Load Model After considering the disparity between the load and weather-dependent renewable production in the power system, the residual load represents the remaining load. The residual load change from positive to negative when weather-dependent renewable production (must-run production) exceeds the load. If the residual load is negative, there is an excess

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power supply. In such instances, adjustments must be made by storing the surplus power or modifying the demand or supply. One approach to implementing these adjustments is by increasing the utilization of flexible loads or curtailing power production [17–19]. Below is the equation of the residual load RL(t):  RL(t) = L(t) − (MR)(t) (1)  (MR)(t) = W (t) + S(t) + R(t)

(2)

where: L(t) is Load (MW), MR is renewable must-run production (MW), W is wind energy (MW), S is solar energy (MW), R is run-of-river energy (MW) at time t. 3.2 Data Preparation Seven power sources were selected as input data for the Cambodia electricity power system in 2023. These sources were collected by Electricité du Cambodge (ECD). As an example of irradiation in the country, the output data of a solar farm with a 10 MW installation capacity, installed in 2017 and located in Svay Rieng Province in Southeast Cambodia, was utilized. The entire year data has divided into two different time scales: the dry season November to April and the rainy season May to October. The input data used in this study are shown in Table 1, which lists the seven installation capacity sources that the Cambodian power system chosen in 2023 for this study. Table 1. The seven installation capacity sources that Cambodian power system chose in 2023. Source

Installation Capacity

Energy

MW

%

GWh

%

Coal

525.00

19

3047.994

40

Fuel Oils

245.00

9

742.023

10

1328.00

48

1615.554

21

Hydro Biomass

34.00

1

88.148

1

Thailand

227.00

8

806.413

11

Vietnam

323.00

12

1248.908

16

Laos

76.00

3

112.837

1

Total

2758.00

100

7661.887

100

3.3 Research Flow Diagram Using the research flow diagram to do the optimization methodology, as shown in Fig. 1, was designed in this study.

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• Energy Storage without hydropower ramp up/down The energy storage (ES) without the hydropower ramping capability have depicted in the flow diagram. The steps procedure are as follows: 1. Concerning research instances, substitute the electricity import from the neighboring country and fuel oil power plant by supplying with the adjustable PV plan. 2. The residual load (RL) is calculated by subtracting the demand (D) and supply (S). The total capacity of hourly energy supply from all resources and loads was collected. 3. If supply exceeds demand, the result is a negative residual load, known as desertion. When supply is less than demand, the residual load will be positive. 4. If the system is not balanced, go to step 3. Otherwise, go to energy storage and end.

Fig. 1. Methodology for energy storage calculation and optimization

• Energy Storage with hydropower ramp up/down Energies storage (ES) optimization by hydropower ramping capability generators have depicted in this study flow diagram. The steps procedure are as follows: 1. Concerning research instances, substitute the electricity import from the neighboring country by supplying solar photovoltaics. Therefore, energy storage (ES) is needed to resist power supply fluctuation that depends on weather conditions. 2. The residual load’s capacity illustrates the imbalance between supply and demand. The residual load (RL) has calculated by subtracting the power demand (PD) from the power supply (PS). The historical hourly power supply and load data had recorded in the holding year. 3. If supply exceeds demand, there is a negative residual load, also known as desertion. In contrast, the residual load is positive. The ramping characteristics of

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hydropower are employed to compensate for the residual load. When the capability to ramp up (HRU) or ramp down (HRD) exists in hydropower systems, and the reservoir’s water level is at the operational threshold or not at full capacity, hydropower generators are employed to adjust the power output to meet the residual load.; otherwise, the residual load is curtailment to energy. 4. If the system is imbalanced, go to energy storage; Otherwise, end.

4 Case Study and Result One of the power system flexibilities used in this study for energy storage optimization is the hydropower plan ramping capacity, which intends to promote a clean energy transition and sustainable development in Cambodia. In addition, the hydro power plant ramping rate has the ability to respond to the changing of residual load. Energy storage optimization requirements for 2023, it is considered that achieving self-sufficiency and lower-cost power system operation is the best use for this nation’s resources, including grid connectivity. Figure 2 shows the average demand and supply profile during the dry and wet seasons with seven sources from the national grid in 2023. About 328 MW more power is generated during the dry season than during the wet, which is due to the increase in cooling system demand.

Fig. 2. Average demand and supply in dry and rainy season

Case study 1 substituted 12% of the total capacity in Table 1 with solar PV capacity, deducting 50% of the power imported from Thailand and 100% from Laos, respectively, from the national grid. In Fig. 3 (a), the peak power output of solar PV is produced at midday and generated between 7:00 and 17:00 in the rainy season. In the dry season, solar PV generated less than in the rainy season one hour. In the dry season, the power supply by hours exceeded the power demand in the daytime, and the excess energy was 733 MWh. It peaked at 11:00 with a 137 MW charge. The energy surplus could charge to the energy storage. Due to solar PV power’s inability to generate electricity throughout the night, there was a 937 MWh shortage in the energy supply. In the rainy season, the energy supply had a shortage of 685 MWh at night and an energy surplus of 884 MWh during the day. The peak charge of 155 MW occurred at 11 o’clock. Energy

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storage save as the source of supply to fulfill the gap that requires its capacity to meet the requirements. Case study 2 replaced the power import from Thailand at 50% and the Fuel Oils power at 50% with solar PV power. Solar PV power, which considers 18% of the total installation capacity sources chosen from EDC, was used in this case study to replace the power imported from neighboring countries. Energy storage was employed to manage the energy surplus during the daytime, which amounted to approximately 917 MWh in the dry season, but during the night energy storage discharged around 1539 MWh conversely. It peaked at 11:00 with a 186 MW charge. In the rainy season, the power supply had an energy shortage of 842 MWh at night and an energy surplus of 1366 MWh during the day. The peak charge of 237 MW occurred at 11 o’clock. This simulation shows in Fig. 3 (b). As shown in Fig. 3 (c), Solar PV power, which considers 23% of the total installation capacity sources chosen from EDC in Table 1, was utilized in case study 3 to replace the power imported from neighboring countries. Energy storage necessary to charge the excess energy during the daytime was about 1229 MWh, and discharge was around 1958 MWh at night in the dry season. The peak charge of 249 MW was observed at 11:00. Conversely, during the rainy season, there was an energy shortage of 1083 MWh during the night and an energy surplus of 1711 MWh during the day. The peak charge of 309 MW occurred at 11 o’clock.

Fig. 3. Average hourly energy storage characteristics of dry season and rainy season under different solar photovoltaic generation replacement ratio.

The energy storage capacity decreased after the energy storage optimization, which has launched by ramping the hydropower generator. The water in the reservoirs have reserved for later use during the dry season, and the hydropower generator’s operating hours were decreased in the daytime and increased at night. In case study 1, a significant amount of solar PV power was injected into Cambodia’s power grid after did hydropower plant ramping, reducing the energy storage from 733 MWh to 63 MWh in the dry season and 884 MWh to 0 MWh in the rainy season. Case study 2 has a larger reduction capacity than Case Study 1 since the energy storage has decreased from 917 MWh to 201 MWh dry season and 1366 MWh to 0 MWh in rainy season. In case study 3, Energy storage has decreased from 1229 MW/h to 429 MW/h in the dry season and 1711 MW/h to 22 MW/h in the rainy season, which is the largest decrease but in the rainy season has the energy surplus needed to store.

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5 Conclusion Energy storage is a crucial component of power system security planning with the high shear of variable solar PV capacity for integration into power systems. The optimization of energy storage in this study has significance for being economical with the solar PV planned energy. A fundamental aspect of this optimization technique is the ability of hydropower to ramp up or down, making it essential to manage reservoir water levels effectively. Currently, electricity imported to Cambodia from neighboring countries represents 30% of the total installed power in the country’s power grid. Projected with the high share of solar PV power grid integration can reduce the percentage of imported power, which makes the electrical power sector self-sufficient. This paper tested solar PV power capacity by substrate the power import from neighboring. For a more residual was estimated to be clear that the system balance or not if not was resolved by flexibility with hydropower plan generators and the energy storage system if hydropower plant generators were not capable of ramping. Finally, selecting the appropriate energy storage capacity depends on the testing and evaluation results. However, the research has assumed that the hydro pump level can provide ramping capabilities due to the hydraulic is complicated. Future research can concentrate on the hydraulic water levels in the reservoir to improve this optimization.

References 1. Mallapragada, D.S., Sepulveda, N.A., Jenkins, J.D.: Long-run system value of battery energy storage in future grids with increasing wind and solar generation. Appl. Energy 275, 115390 (2020) 2. Akhtar, I., Kirmani, S., Jameel, M.: Reliability assessment of power system considering the impact of renewable energy sources integration into grid with advanced intelligent strategies. IEEE Access 9, 32485–32497 (2021) 3. Garip, S., Ozdemir, S.: Optimization of PV and battery energy storage size in grid-connected microgrid. Appl. Sci. 12(16), 8247 (2022) 4. Yao, M., Cai, X.: Energy storage sizing optimization for large scale PV power plant. IEEE Access 9, 75599–75607 (2021) 5. Hassan, Q., Pawela, B., Hasan, A., Jaszczur, M.: Optimization of large-scale battery storage capacity in conjunction with photovoltaic systems for maximum self-sustainability. Energies 15(10), 3845 (2022) 6. Guerra, K., Haro, P., Gutiérrez, R.E., Gómez-Barea, A.: Facing the high share of variable renewable energy in the power system: flexibility and stability requirements. Appl. Energy 310, 118561 (2022) 7. Xu, X., Hu, W., Cao, D., Huang, Q., Chen, C., Chen, Z.: Optimized sizing of a standalone PV-wind-hydropower station with pumped-storage installation hybrid energy system. Renew. Energy 147(1), 1418–1431 (2020) 8. Alvarez, G.E.: Operation of pumped storage hydropower plants through optimization for power systems. Energy 202, 117797 (2020) 9. Nwaigwe, K.N., Mutabilwa, P., Dintwa, E.: An overview of solar power (PV systems) integration into electricity grids. Mater. Sci. Energy Technol. 2, 629–633 (2019) 10. Yosef, G.B., et al.: Frequency stability of the Israeli power grid with high penetration of renewable sources and energy storage systems. Energy Rep. 7, 6148–6161 (2021)

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11. Yan, X., Jiang, H., Gao, Y., Li, J., Abbes, D.: Practical flexibility analysis on europe power system with high penetration of variable renewable energy. In: 2020 IEEE Sustainable Power and Energy Conference (iSPEC) (2021) 12. Midat.org, https://www.mindat.org/climate.php. Last accessed 13 July 2022 13. Say Samal, H.E.: Harnessing the Solar Energy Potential in Cambodia. UNDP (2019) 14. Ekman, C.K., Jensen, S.H.: Prospects for large scale electricity storage in Denmark. Energy Convers. Manage. 51(6), 1140–1147 (2010) 15. Hedegaard, K., Meibom, P.: Wind power impacts and electricity storage–A time scale perspective. Renew. Energy 37, 318–324 (2012) 16. Guo, Y., Wu, Q., Zeng, Q.: WP3: flexibility and ramping requirements. DTU Electr. Eng. (2018) 17. Zhang, S., et al.: A regulating capacity determination method for pumped storage hydropower to restrain PV generation fluctuations. CSEE J. Power Energy Syst. 8, 304–316 (2020) 18. Bökenkamp, G.: The Role of Norwegian Hydro Storage in Future Renewable Electricity Supply Systems in Germany: Analysis with a Simulation Model. Universität Flensburg Interdisziplinäres Institut für Umwelt- Sozial-und Humanwissenschaften, Flensburg (2014) 19. Schill, W.P.: Residual load, renewable surplus generation and storage requirements in Germany. Energy Policy 73, 65–79 (2014)

Electricity Price Prediction Framework Based on Two-Stage Time Series Decomposition Yuzhe Huang1 , Chenwei Wu2 , Chenghan Li3

, Zizheng Wang4 , and Kan Li5(B)

1 Henan University of Technology, Zhengzhou 450001, China 2 University of Rochester, Rochester, NY 14642, USA 3 ZJU-UIUC Institute, Zhejiang University, Haining 314400, China 4 University of Miami, Oxford 45056, USA 5 China Datang Corporation, Handan 056044, China

[email protected]

Abstract. This research tackles the issue of insufficient accuracy in short-term electricity price forecasting. The novel approach combines a dual-stage signal decomposition technique using CEEMDAN and VMD, alongside a bidirectional gated cyclic unit network. The historical electricity price dataset is initially subjected to decomposition and entropy analysis. Subsequently, a KNN-driven clustering process partitions the data into distinct frequency-based signals. These separated signals then undergo further decomposition through VMD, enhancing the capture of intricate patterns. The enriched features are then channeled into a bidirectional gated cyclic unit network to facilitate comprehensive pattern learning. Rigorously evaluated using real-world US electricity data, the model exhibits a notable enhancement in predictive accuracy, showcasing its potential for practical application. Keywords: CEEMDAN,VMD · BiGRU · Electric price · time series decomposition

1 Introduction Amidst the steady and methodical evolution of China’s electricity market system, a diversified landscape of competition has begun to emerge. The market’s electricity sales have experienced significant growth, further accentuating the market’s pivotal role in optimal resource allocation. As an indispensable element within the power market, precise electricity price prediction not only offers guidance to market participants but also enhances comprehension of power market dynamics. Moreover, it furnishes regulatory authorities with an objective foundation for decision-making. The prediction of electricity prices assumes a crucial role in the seamless operation of the power system, underscoring the imperative of ensuring accurate forecasts to maintain the stability and efficiency of the power market. Y. Huang, C. Wu and C. Li—Contribute equally to this work. © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 563–570, 2024. https://doi.org/10.1007/978-981-97-0877-2_58

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At present, statistical methods and machine learning methods are the main methods for predicting electricity price in electricity market. Statistical methods mainly include Autoregressive Integrated Moving Average model (ARIMA) [1]. Traditional statistical methods have poor performance when dealing with nonlinear problems or time series with large fluctuations. With the development of artificial intelligence and big data technology, machine learning methods have been widely applied in the research direction of electricity price prediction. Machine learning methods mainly include Support Vector machines (support vector machines). SVM) [3], Random Forest (RF) [4], long short-term memory (LSTM) [5], Gated Recurrent Unit (GRU) [6] and other methods. The model employs intricate yet efficient steps for electricity price prediction. It initiates by decomposing historical data using CEEMDAN, extracting diverse mode signals to capture frequency and amplitude variations. Sample entropy evaluates these modal signals, enhancing insight into complexity. KNN clustering then reconstructs modes, yielding an explanatory and predictable price sequence. For complex timing, VMD further decomposes, yielding distinct frequencies for multi-scale trend capture. Modal time series feed into a bidirectional gated cyclic unit network. Compared to various models in predicting US electricity market prices, the proposed framework demonstrates heightened accuracy and stability.

2 Methods This section provides a detailed description of the proposed hybrid deep learning model, outlining its key features and components. The model is built using CEEMDAN and VMD methods. The framework of the proposed method is shown in Fig. 1, and its methodology includes the following steps: Decompose Co-IMF0 by VMD Decompose by CEEMDAN

Forecast by GRU Prediction result

Original sequence matrix GRU

Integrate by the K-Means and Sample entropy

vector GRU

Fig. 1. The framework of electrical price forecasting using CEEMDAN and VMD

Step 1: CEEMDAN was used to decompose the electricity price time series, and the IMF sample entropy obtained from each decomposition was calculated separately. Step 2: According to different IMF values, KNN clustering method was used to aggregate IMF into three sequences, namely Co-IMF1,Co-IMF2 and Co-IMF3, according to different IMF sample entropy values. Step 3: The Co-IMF1 was decomposed by VMD, and the IMF obtained after decomposition and the original Co-IMF1 and Co-IMF2 were predicted by BiGRU. Step 4: The final electricity price forecast result is obtained by adding different IMF forecast results. To evaluate the validity of the proposed prediction model, several widely used performance metrics were used, including root mean square error (RMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), and R2.

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2.1 CEEMDAN and VMD I. CEEMDAN The Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise) (CEEMDAN) with self-adaptive noise is developed from EMD, EEMD and CEEMD. EMDn (•) is defined as the modal component of the NTH stage generated by the application of EMD algorithm, and the nth modal component generated by CEEMDAN algorithm is denoted as IMFn. The implementation process of the algorithm is as follows: (a): The signal f (t) to be decomposed is added with n Gaussian white noise sequences whose mean is 0. f i (t) = f (t) + ε0 ωi (t), i = (1, 2, . . . , n)

(1)

ε0 is the signal to noise ratio, ωi is the white noise sequence added for the ith time. (b): Each f i (t) is decomposed by EMD algorithm, and the first modal component (IMF) and the first unique residual component r1 (t) are obtained IMF1 (t) =

1 n

n  i=1

  IMF1i (t) = 1n EMD1 f i (t)

(2)

r1 (t) = f (t) − IMF1 (t) (c): The residual components obtained after decomposition are added with noise and then decomposed by EMD. IMFk (t) =

1 n

n  i=1

   Ek D1 rk−1 (t) + εk−1 EMDk−1 ωi (t) , k = 2, 3 . . . , n

(3)

rk (t) = rk−1 (t) − IMFk (t)

(d): Finally, the CEEMDAN algorithm is terminated when the residual does not exceed two extreme points and the decomposition cannot continue. At this point, the residual trend is obvious and direct, and the original signal sequence is decomposed into n modal components and the residual term R(t): n IMFk (t) + R(t) (4) f (t) = k=1

II. VMD VMD is a signal decomposition method. In the process of obtaining the decomposition component, the center frequency and finite bandwidth of each component are determined by iteratively searching the optimal solution of the variational model, so as to realize the frequency domain division of the signal and the effective separation of each component. The VMD minimizes the sum of the estimated bandwidths for each component and extracts the corresponding center frequency using the alternating direction multiplier method. (a): In order to solve the optimization problem, Lagrange multipliers and secondorder penalty factors are introduced, and then the constrained variational problem

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is transformed into an unconstrained variational problem, and the augmented Lagrange expression is obtained: L({u }, {ωk }, λ) 2  k

    = α k ∂t ∂(t) + πj t ∗ uk (t) ejωk t  2   +f (t) − k uk (t) + λ(t), f (t) − k uk (t)

(5)

(b): The saddle point is the optimal solution of the original problem by using alternate direction multiplier method uˆ kn+1 (ω) = ωkn+1

=

 ˆ fˆ (ω)− i=k uˆ i (ω)+ λ(ω) 2 1+2α(ω−ωk )2 ∫∞ uk (ω)|2 d ω 0 =ω|ˆ 2 ∫∞ |ˆ u k (ω)| d ω 0

(6)

Repeat the above steps until iteration conditions are met. 2.2 BiGRU Gate recurrent unit (GRU) network is an improved structure of long short-term memory (LSTM) network, which can effectively solve the problems of network gradient disappearance and explosion. At the same time, the number of network learning parameters and the risk of model overfitting are reduced to some extent. The GRU structural unit contains an update gate and a reset gate, the former is used to update the hidden state by paying attention to the load information, and the latter is used to forget some nonimportant hidden state. The GRU structure is one-way input and output. However, when extracting the deep features of the load, it is necessary to establish a connection between the current state information and the hidden state before and after the moment. BIGRU performs well in this scenario. BIGRU consists of two one-way, opposite direction GRUs, and its structure is shown in Fig. 2.

Fig. 2. BIGRU unit structure diagram

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At each moment, the hidden state in the network is determined by two opposing GRUs, namely:   · x(t)  · h(t−1) + U = δ h(t) W 1 ← 1 ← (t) (7) + U ·x(t) h2 = δ W ·h(t+1) 2

 (t) (t) H (t) = h1 , h2 (t)

(t)

h1 is the hidden state of forward propagation, h2 is the hidden state of backward (t−1) (t+1) is the hidden state relative to a moment before a moment, h2 is propagation, h1 (t) the hidden state relative to the next moment. δ is activation function, x is the input at the time t, H (t) is the output at the time t, U, W are the weight matrix, and arrows are the direction of propagation.

3 Case study 3.1 Dataset The data set selected 6 years of historical electricity price data from January 1, 2015 to August 31, 2020 in the US electricity market. The data was sampled once a day, with an interval of 1day. The data set was divided according to 8:1:1 to obtain the training set, test set and verification set respectively.

Fig. 3. US market annual electricity price curve

Figure 3 shows the electricity price of the United States from May 2018 to May 2020. It can be seen that the electricity price series of the United States electricity market has nonlinear characteristics, and the fluctuations of electricity price are caused by many factors, such as the electricity price of the previous cycle, load, various energy prices, temperature, air pressure, precipitation, holidays, etc. 3.2 Data Processing Individual outliers and missing values are processed in the original data set. Direct deletion, average completion and K-Nearest Neighbor (KNN) are commonly used to

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better learn the potential rules in the historical electricity price series and improve the accuracy of prediction. In order to map the data in [−1,1], eliminate the adverse impact of abnormal samples on the prediction results, and reduce the error of training results, it is necessary to normalize the data. In this paper, Min-Max normalization method is adopted, and the formula is as follows: x=

xi − xmin xmax − xmax

(8)

3.3 Metrics In this paper, Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (Mean Absolute Percentage Error) were selected. MAPE and Mean Absolute Error (MAE) are used as evaluation indexes of the algorithm. For this experiment to predict electricity prices in the United States, the smaller the RMSE, MAPE and MAE of the model, respectively, the more accurate the prediction result.

4 Results and Analysis Table 1 shows the predicted results of the proposed model architecture compared to other baseline models. It can be seen from the table that NSTformer leads other baseline models in forecasting accuracy, possibly because NSTformer can better extract the unstable series in electricity prices. The proposed architecture is ahead of the NTsformer in each index, which indicates the effectiveness of the proposed architecture in electricity price prediction task (Figs. 4 and 5). Table 1. Comparison of prediction performances using different methods. RMSE

MAE

MAPE (%)

ARIMA

15.982

10.411

4.94

LSTM

13.410

12.325

3.42

CNN-LSTM

8.931

6.074

1.04

NSTformer [6]

7.832

5.953

0.55

Our

7.034

5.115

0.16

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Fig. 4. Prediction result of the Co-IMF0,Co-IMF1 and Co-IMF2

Fig. 5. Prediction result of the US electric price

5 Conclusion In this paper, an electricity price prediction architecture based on two-stage time series decomposition is proposed to improve the accuracy of electricity price prediction. Through the experiment and analysis of the real electricity price data set in the United States, the following conclusions are drawn: (1) In view of the strong volatility and instability of the electricity price series, the twostage signal decomposition method can better extract the electricity price volatility characteristics and fully excavate the relevant features to further improve the accuracy of the prediction model. This decomposition can effectively decouple the trend, period and residual components of the electricity price series, making the prediction model more able to grasp the complex dynamic changes of electricity price. (2) In the training of prediction model, BIGRU model has obvious advantages compared with the traditional GRU model. BIGRU model can realize the bidirectional transmission of information, learn the changing law of electricity price series more fully, and improve the accuracy of prediction model. Through bidirectional learning, the model can better capture the long-term dependence relationship and timing pattern of electricity price series, which helps to improve the accuracy of prediction.

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Future research can further consider the influence of policy changes and user behavior on electricity price, so as to further improve the accuracy of prediction. This will provide electricity market participants with more reliable electricity price forecast information, help them make more informed decisions and planning, and also play a positive role in promoting the balance between electricity supply and demand.

References 1. Karabiber, O.A., Xydis, G.: Electricity price forecasting in the Danish day-ahead market using the TBATS, ANN and ARIMA methods. Energies 12(5), 928 (2019) 2. Girish, G.P.: Spot electricity price forecasting in Indian electricity market using autoregressive-GARCH models. Energ. Strat. Rev. 11, 52–57 (2016) 3. Syah, R., Davarpanah, A., Elveny, M., Karmaker, A.K., Nasution, M.K., Hossain, M.A.: Forecasting daily electricity price by hybrid model of fractional wavelet transform, feature selection, support vector machine and optimization algorithm. Electronics 10(18), 2214 (2021) 4. Zhao, P., Dai, Y.: Power load forecasting of SVM based on real-time price and weighted grey relational projection algorithm. Power Syst. Technol 44(04), 1325–1332 (2020) 5. Bouktif, S., Fiaz, A., Ouni, A., Serhani, M.A.: Multi-sequence LSTM-RNN deep learning and metaheuristics for electric load forecasting. Energies 13(2), 391 (2020) 6. Liu, Y., Wu, H., Wang, J., Long, M.: Non-stationary transformers: Exploring the stationarity in time series forecasting. Adv. Neural. Inf. Process. Syst. 35, 9881–9893 (2022) 7. Tschora, L., Pierre, E., Plantevit, M., Robardet, C.: Electricity price forecasting on the dayahead market using machine learning. Appl. Energy 313, 118752 (2022) 8. Yang, W., Sun, S., Hao, Y., Wang, S.: A novel machine learning-based electricity price forecasting model based on optimal model selection strategy. Energy 238, 121989 (2022) 9. J˛edrzejewski, A., Lago, J., Marcjasz, G., Weron, R.: Electricity price forecasting: the dawn of machine learning. IEEE Power Energ. Mag. 20(3), 24–31 (2022) 10. Jan, F., Shah, I., Ali, S.: Short-term electricity prices forecasting using functional time series analysis. Energies 15(9), 3423 (2022) 11. Li, C., et al.: Prediction of EV charging load using two-stage time series decomposition and DeepBiLSTM model. IEEE Access 11, 72925–72941 (2023)

Optimization Design of Self-powered Coil for Wireless Sensor of Three Core Cable Based on Spatial Electromagnetic Energy Xu Lu(B) , Ran Hu, Jie Tian, Zhifeng Xu, and Feng Tang China Southern Power Grid Shenzhen Power Supply Co.Ltd, Shenzhen 518000, China [email protected]

Abstract. The energy of the cable status monitoring system comes from the selfpowered coil of system sensor, and the energy harvesting efficiency of this coil will directly determine the operation of cable status monitoring system. Considering that the failure of traditional self-powered coil caused by uneven spatial magnetic field distribution in three core cables, this paper based on the idea of spatial electromagnetic energy conversion, and proposed a simplified calculation model for spatial magnetic field distribution in three core cables, to guide the optimization design of self-powered coil in cable sensors. Firstly, according to the structural characteristics of three core cable, a simplified calculation model of cable space magnetic field is proposed, and the magnetic field at any position in the space around the cable is solved based on the basic Electromagnetism theories such as Ampere’s Law, and then the output voltage of self-powered coil is derived; Then, based on the above model and theory, the magnetic field distribution of the three core cable and the output voltage of self-powered coil were analyzed, thereby achieving the optimization design of the self-powered coil for three core cable. Keywords: Space electromagnetic energy · three core cable · wireless sensor · self-powered coil · electromagnetic induction

1 Introduction Wireless sensor networks, as an important component of power cable operation status monitoring systems, have always been a research hotspot in academia and industry. However, wireless sensor nodes have distribution and harsh working environments, making it difficult to provide wired power to them. Therefore, wireless sensor self-powered technology has been vigorously developed [1]. Considering that the self-powered coil is a key device in the aforementioned technology [2], its optimized design will undoubtedly be of great significance for the normal operation of the power cable operation status detection system. A large number of scholars and enterprises have conducted relevant research on the issue of self-powered power supply along power cables. Based on the principle of electromagnetic induction, closed iron core self-powered coils have been used to achieve fault, temperature, and other status monitoring under self-powered conditions in single © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 571–580, 2024. https://doi.org/10.1007/978-981-97-0877-2_59

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core cables and overhead lines [3]. However, when applying the same closed iron core self-powered coil on a three core cable line, the superposition distribution of the threephase magnetic field seriously weakens the magnetic field in the iron core, which limits the efficiency of energy extraction [4]. Considering that the uneven spatial magnetic field of three core power cables, this paper proposes a simplified calculation model for the spatial electromagnetic field distribution of the cable, and derives the output voltage of the self-powered coil from this model, achieving predictive analysis of the coil output voltage. On the basis of the above model and theory, the influence of key structural parameters of the self-powered coil on its output voltage was analyzed, and thus the optimal design of the self-powered coil for a three core power cable was achieved.

2 The Self-powered Principle and Problem of Cable Sensor 2.1 The Self-powered Principle of Cable Sensor The self-powered cable wireless sensors is mainly achieved by placing induction coils (i.e. self-powered coils) in a changing magnetic field. According to Faraday’s law of induction [5, 6], the changing magnetic field will generate an induced electromotive force in the coil, thus realizing the collection of magnetic field energy in space. Then, the energy management module is used to adjust the output voltage to meet the energy supply requirements of wireless sensors. Here, a brief explanation of the basic principle is provided using a self-powered coil for collecting magnetic field energy around a single core cable. The structural diagram of the self-powered coil is shown in Fig. 1. The main structural parameters of the coil include the inner diameter a and outer diameter b of the iron core, the number of coil turns N. When the coil is energized, the cable should be passed through its middle. In order to gather more magnetic field around the cable inside the coil, an iron core needs to be added inside the coil, and the induction coil should be evenly wound around the iron core. High permeability ferromagnetic materials will effectively improve the output voltage of self-powered coil.

Fig. 1. Structure diagram of cable sensor self-powered coil.

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2.2 The Self-powered Problem of Cable Sensor Due to its relatively simple internal structure, single core cables only have power frequency AC current flowing through a single conductor, so there is no magnetic field superposition. According to Biot-Savart’s law [7, 8], the magnetic field in the surrounding space is uniformly distributed. The structure of a three core cable differs greatly from that of a single core cable, and the comparison of the two structures is shown in Fig. 2.

Fig. 2. Structure diagram of cable sensor self-powered coil

When the three core cable in Fig. 2 passes through the three-phase current, since the sum of the three core cable three-phase current vector is 0, the magnetic fields generated by the three current carrying conductors in the surrounding space will be superimposed, resulting in the integration of the magnetic field loop in the surrounding space of the cable being 0. At this time, the induced voltage cannot be obtained through the traditional selfpowered coil in Fig. 1. In order to explore the possibility of electromagnetic induction energy harvesting in three core cables, further research is needed on the magnetic field distribution in the surrounding space of the three core cables, in order to design the most suitable self-powered coil.

3 The Solution to Output Voltage of Self-powered Coil for Wireless Sensor of Three Core Cable 3.1 The Simplified Calculation Model for Spatial Magnetic Field Distribution in Three Core Cables From Sect. 2.2, it can be seen that the magnetic field distribution in the surrounding space of a three core cable is also more complex for a single core cable. Therefore, in order to obtain an optimization method for energy harvesting coils suitable for the application scenario of a three core cable, it is necessary to start with the magnetic field distribution in the surrounding space of three core cable. In order to study the spatial magnetic field distribution of three core cables and guide the optimization design of self-powered coils, this paper proposes a simplified cable model as shown in Fig. 3, which simplifies the three-phase current carrying wire to an infinite line current located at the center of each phase wire.

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According to electromagnetism theory, the magnetic flux density B generated around an infinite parallel straight wire is: B=

μ0 I eφ 2πρ

(1)

C-phase conductor Cable center Cable outer surface B-phase conductor

A-phase conductor

Fig. 3. The simplified calculation model for spatial magnetic field distribution in three core cables.

The three-phase conductors A, B and C are regarded as infinite straight conductors respectively, and the three-phase power frequency current is connected, so that the Magnetic flux density BA , BB and BC generated by the three-phase conductors in the surrounding space are respectively: BA =

μ0 IA μ0 IB μ0 IC eφA , BB = eφB , BC = eφC 2π RA 2π RB 2π RC

(2)

In the equation, RA , RB and RC are the distances from the field point P(r, φ) to the center of the wire, respectively:  ⎧ ⎪ ⎪ R = (r sin φ)2 + (r cos φ − a)2 A ⎪ ⎪ ⎨  (3) R = [r + a cos(π/3 − φ)]2 + [a sin(π/3 − φ)]2 B ⎪ ⎪  ⎪ ⎪ ⎩ RC = [a sin(2π/3 − φ)]2 + [r − a cos(2π/3 − φ)]2 where, r and φ are respectively the coordinates of the field point P in the Polar coordinate system, and a is the distance from the cable center to the wire center. Substitute Eq. (3) into Eq. (2), and decompose the magnetic field generated by the three-phase wire at the field point P(r, φ) into the directions of ρ and φ, and then obtain BA , BB and BC as follows:

Optimization Design of Self-powered Coil for Wireless Sensor

⎧ ⎪ ⎪ ⎪ BA = ⎪ ⎪ ⎪ ⎪ ⎨ BB = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ BC =

575

  r − a cos φ a sin φ μ0 IA eφ 2 − e ρ 2 2π r + a2 − 2ar cos φ r + a2 − 2ar cos φ   r + a cos(π/3 − φ) a sin(π/3 − φ) μ0 IB − e eφ 2 ρ 2π r + a2 + 2ar cos(π/3 − φ) r 2 + a2 + 2ar cos(π/3 − φ)   r − a cos(2π/3 − φ) a sin(2π/3 − φ) μ0 IC eφ 2 + e ρ 2π r + a2 − 2ar cos(2π/3 − φ) r 2 + a2 − 2ar cos(2π/3 − φ) (4)

The spatial magnetic field distribution around the three core cable can be obtained by calculating Eq. (4). Considering the power frequency AC current in the three-phase conductor, the change of the magnetic flux density of the field point P with time can also be obtained. 3.2 Solution to the Output Voltage of Self-powered Coil Using the simplified calculation model proposed in Sect. 3.1, the magnetic flux density at any position around the cable can be obtained. Considering that the purpose of optimizing the design of self-powered coils is to achieve higher output voltage by effectively utilizing the spatial magnetic field around the three core cable. Therefore, this section will further calculate the output voltage of self-powered coil on the basis of Sect. 3.1, to further guide its optimization design. Assuming that the self-powered coil is square and has no iron core, l is the crosssectional length of coil, b is the cross-sectional width of the coil, d is the diameter of the copper wire in the coil, n is the number of turns in the single layer coil, n1 is the number of winding layers, and N is the total number of turns in the self-powered coil. The relationship between self-powered coil and cable position is shown in Fig. 4.

Fig. 4. The relationship between self-powered coil and cable position.

According to Fig. 4, the magnetic flux density perpendicular to the cross section of self-powered coil is: BPz (r, φ) = BPφ cos φ + BPρ sin φ In the equation, BPφ and BPρ can be obtained by Eq. (4).

(5)

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Assuming that the initial angle position of the self-powered coil is φ0 , calculate the magnetic flux ϕi of the ith coil (with values of ± 1 and ± 2 ···· ± n/2 long the positive and negative directions of z-axis, respectively), and Bz in the y-direction remains unchanged within the cross-section of the coil, but Bz will change along the x and z directions. In order to calculate the magnetic flux ϕi of any turn of the coil, it is needed to integrate the differential elements. Taking the area element dS = y·dx, we can obtain the magnetic flux element d ϕi as: dϕi = BPz (r, φ) · y · dx

(6)

 m+b/2 In the equation, ϕi = m−b/2 BPz (r, φ) · y · dx, r = x2 + h2k . Thus, the magnetic linkage of self-powered coil domain can be obtained as:  = n1 ×

±n/2

ϕi

(7)

i=±1

From this, the induced voltage e of the self-powered coil can be obtained as: e=−

d(t) dt

(8)

4 Optimization Design of Self-powered Coil for Three Core Cable Sensor 4.1 Calculation of Magnetic Field Distribution for 10kV Three Core Cross-Linked Polyethylene Cable Taking the common 10 kV three core cross-linked polyethylene cable in the distribution network as an example [9, 10], its model is YJLV22 8.7/10 kV-3 * 50 mm2 . When a three-phase AC current with an effective value of 100 A is introduced into a three core cable, the simplified calculation model for the spatial magnetic field distribution of the three core cable proposed in Sect. 2.1 and the COMSOL software are used to calculate the magnetic field distribution around the cable, thereby guiding the optimization design of the self-powered coil. Simplify the actual cable according to the simplified calculation model proposed in Sect. 3.1, and then calculate the magnetic field distribution around the three core cable according to Eq. (4). Compare the calculation results with the COMSOL simulation software, as shown in Fig. 5 and Fig. 6.

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Calculation model COMSOL

Calculation model COMSOL

Phase(°)

Modulus of Magnetic flux density(mT)

It can be seen from Fig. 5 and Fig. 6 that the simplified calculation model in Sect. 3.1 and the solution results of COMSOL simulation software show that the modulus of magnetic flux density changes continuously along the circumferential direction of the cable surface, and the tangential magnetic flux density Bφ reaches maximum values at 0°, 120° and 240°, and the radial magnetic flux density Bρ reaches maximum values at 60°, 180° and 300°. From this, it can be seen that the simplified calculation model for the spatial magnetic field distribution of three-core cables proposed in Sect. 3.1 is accurate, laying the foundation for solving the output voltage of the self-energy coil of the three-core cable.

Angle(°)

Fig. 5. The modulus and phase of tangential magnetic flux density Bφ at each point on the cable surface.

Calculation model COMSOL

Phase(°)

Modulus of Magnetic flux density(mT)

Calculation model COMSOL

Angle(°)

Fig. 6. The modulus and phase of radial magnetic flux density Bρ at each point on the cable surface.

4.2 Solution to the Output Voltage of Self-powered Coil Assuming that the cross-sectional length l of the self-powered coil is 40 mm and the width b is 30 mm, the diameter d of copper wire in the coil is 0.5 mm, the number of turns n of the single layer coil is 80, the number of winding layers n1 is 4, and the total number of turns N of the powered coil is 320. Calculate the output voltage of the

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Induced voltage of self- powered coil(mV)

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Calculation model COMSOL

Fig. 7. Induced voltage of self-powered coil.

self-powered coil according to Eq. (8) and compare it with the finite element COMSOL simulation results, as shown in Fig. 7. From Fig. 7, we can see that under the condition without an iron core, the output voltage modulus of the self-powered coil is about tens of millivolts. At the same time, the output voltage of the self-powered coil constantly changes with the initial angle φ0 , and reaches its maximum value at 0°, 120°, and 240° angles, respectively. 4.3 Optimization Design of Self-powered Coils Considering the low modulus of Magnetic flux density of the magnetic field around the three core cable, it is difficult to obtain the output voltage that meets the load requirements simply by relying on the self-powered coil, so it is necessary to wind the self-powered coil onto the iron core and use the common intrusive iron core layout to increase the collection efficiency of magnetic energy. According to the analysis of the magnetic field distribution around the three core cable in Sect. 4.1, along the circumferential direction of the cable surface, the modulus of magnetic flux density has maximum values at three positions, and the phase of Magnetic flux density at each position is also different, so the winding method of the self-powered coil should be optimized. When using an invasive iron core layout and winding a coil on the iron core, the magnetic field that generates magnetic flux on the coil cross-section is mainly the tangential component Bφ of the field point magnetic field. Therefore, the optimization of the iron core layout is mainly based on the changes Bφ around the cable. According to Fig. 5, it can be analyzed that the tangential magnetic flux density Bφ around the three core cable has extreme values at three locations, and it decays rapidly after reaching the extreme value along the circumference of the cable. When it rotates 30° from the extreme point, it reduces to half of the extreme value. In order to improve the energy collection efficiency and consider the space required for coil winding, and minimize the gap distance between the iron core and the cable, the Central angle corresponding to the coil area is determined as 30°. That is, taking the extreme point as the benchmark, offset 15° to the left and right respectively, and at this time, only 12.5% decrease. In addition, according to the phase diagram of Bφ , wrapping a complete single coil on the iron core will cause the induced voltage generated by the internal coils to cancel

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out each other, making it impossible to obtain the output voltage. In order to obtain the induced voltage of the coil, three independent energy tapping coils should be wound respectively at three positions where the maximum value of tangential magnetic flux density Bφ is taken, and the corresponding Central angle of the coil domain is 30°. The final designed self-powered coil is shown in Fig. 8.

Induction coil Toroidal core Fig. 8. Layout diagram of self-powered coil.

5 Conclusion Considering that the complex internal structure and uneven spatial magnetic field of three core cables, this paper proposes a simplified calculation model for the spatial magnetic field distribution of three core cables, calculates and analyzes the characteristics of the magnetic field distribution around the three core cables, as well as the output voltage of the induction coil. On this basis, a self-powered coil optimization design method suitable for magnetic energy collection of three core cables is proposed, that is, the invasive core layout is adopted, and three independent tapping coils are wound respectively at three positions where the tangential magnetic flux density of the three core cable takes the maximum value, and the corresponding Central angle of the coil area is 30°. Acknowledgments. This work is supported by Research on Live Detection Technology of Distribution Network Cable Insulation State Based on Harmonic Component Characteristics (Project NO. 090000KK52220013).

References 1. Cetinkaya, O., Akan, O.B.: Electric-field energy harvesting in wireless networks. IEEE Wirel. Commun. 24(2), 34–41 (2007) 2. Abasian, A., Tabesh, A., et al.: Design optimization of an energy harvesting platform for self-powered wireless devices in monitoring of ac power lines. IEEE Trans. Power Electron. 33(12), 10308–103162 (2018) 3. He, N., Hao, J., Sha, W., et al.: Design and realization of energy source of cable temperature monitoring device. Electrotech. Appl. 34(4), 73–76 (2016)

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4. Liu, G., Hu, F., Qu, H., et al.: Optimization design of magnetic coupling coil for wireless power transmission. Smart Power 47(12), 66–72 (2019) 5. Wang, F., Mi, D., Xu, Z.: Measurement of high pulse magnetic field basedon Faraday electromagnetic induction. High Volt. Eng. 34(04), 674–677 (2008) 6. Zhou, Y., Song, K., Fan, Y.: A novel waveguide-to-coaxial transition with embedded magnetic closed loop. IEEE Microw. Wirel. Comp. Lett. 32(8), 939–942 (2022) 7. Zhuang, Y., et al.: Improving current transformer-based energy extraction from AC power lines by manipulating magnetic field. IEEE Trans. Industr. Electron. 67(11), 9471–9479 (2020) 8. Tanaka, T., Ebihara, Y., Watanabe, M., et al.: Reproduction of ground magnetic variations during the SC and the substorm from the global simulation and Biot-Savart’s law. J. Geophy. Res. Space Phys. 125(2) (2020) 9. Jia, Z., Fan, W., Yuan, Y.: Thermal analysis of cold-shrinkable terminal joint of 10 kV XLPE based on temperature-rise tests. High Volt. Eng. 40(3), 795–800 (2014) 10. Wang, O., Chen, X., Wang, G.: Thermo-electric coupling simulation for 10 kV AC XLPE cable in DC operation. J. Southwest Jiaotong Univ. 57(1), 46–54 (2022)

Research on Photovoltaic Grid-Connected Control of New Quasi-Z-Source Inverter Based on VSG Xin Mao(B) , Hongsheng Su, and Jingxiu Li School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China [email protected]

Abstract. As more and more photovoltaic power generation systems are integrated into the power grid, it has brought a huge test to the stability of the power grid. For the purpose of reduce adverse effects of photovoltaic grid-connected on the grid, the paper proposes a novel quasi-Z-source inverter grid-connected structure on the strength of Virtual Synchronous Generator (VSG). The structure can be divided into two parts. The first part is the control part based on virtual synchronous generator technology. The second part is the boost part based on the novel quasi-Z-source fabric. That proposal of this structure not only simplifies the structure of the traditional two-stage step-up inverter, but also significantly improves the step-up capability. At the same time, it also solves the problem of low inertia and non-damping characteristics the grid-connected photovoltaic power generation system. The combination of the two improves the dynamic performance and stability of the system. Finally, through analysis of this results that the simulation experiment, the feasibility is verified. Keywords: Virtual Synchronous Generator · New Quasi-Z-Source Inverter · Inertia · Damping

1 Introduction Follow the global depletion of fossil energy, increasing attention has been given to the exploitation and make use of renewable energy, like wind energy, solar energy, etc., all of which have clean characteristics, and their development and utilization will not have a huge adverse impact on the natural environment. In recent years, the use of clean energy has entered a period of rapid development, followed by the proposal of various technologies to solve various problems caused by the use of clean energy. For solar energy, wind power and other distributed power generation grid-connected system, in the grid before the need to boost the inverter, the circuit structure is generally a twostage inverter structure, this structure for the number of electronic components more requirements, resulting in higher costs. In 2002, Professor Fangzheng Peng proposed the structure of Z-source inverter. This structure can avoid the generation of dead zone time, and it has a voltage boost effect. The structure is only composed of inductors and © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 581–588, 2024. https://doi.org/10.1007/978-981-97-0877-2_60

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capacitors [1]. Compared with the traditional two-stage booster inverter, its structure becomes simpler and the cost is correspondingly reduced. However, the traditional Zsource inverter has some disadvantages of high capacitive voltage stress and high impulse current. To solve this problem, scholars at home and abroad have carried out in-depth research and proposed several quasi-Z-source inverter structures. Literature [2] proposes a quasi-Z-source inverter structure continuous input current, which can reduce voltage of the capacitor and thus make the capacitor volume smaller and more economical when selecting the capacitor. Literature [3] proposed a novel of quasi-Z-source inverter structure based on switching inductance to solve the problem of insufficient lift pressure of traditional Z-source inverters, and verified that the boost ratio of this structure has been greatly improved. In reference [4], a novel eight-segment SVPWM modulation strategy is proposed to solve the problem that the traditional six-segment SVPWM modulation strategy with straight through zero vector has low utilization rate of zero vector time. This modulation strategy makes the zero-vector time utilization reach 100% and improves the voltage boost capability about quasi-Z source inverter. Of late years, with incorporation of a large number of new energies generating units into the power grid, that inertia and damping characteristics of power system have declined sharply, making the power grid system extremely unstable. So as to solve this problem, some scholars put forward the concept of virtual synchronous generator (VSG), VSG technology is through power electronic components to simulate the operating characteristics of synchronous generator, so that distributed power supply can provide inertia and damping support for grid after grid connection, so that the fluctuations generated by the power system during grid connection within the specified standards. With the in-depth study of VSG technology, more and more scholars have proposed improved virtual synchronous generator control technology to further improve the problems of active power and frequency oscillation [5, 6]. By establishing a small signal model and proving that active and reactive power are approximately decoupled, literature [7] further proposes a new VSG parameter design method, which has the characteristics of fast, accurate and stable. Literature [8–10] further studies the design that VSG’s rotary inertia, damping coefficient with other parameters, and proposes a relatively novel parameter design method, which can improve the rapidity, accuracy and stability of VSG control. Literature [11–13] is published in recent three years on the combination of quasi-Z-source inverter and virtual synchronous generator, and discusses the feasibility of combining quasi-Z-source inverter and virtual synchronous generator from different angles. Based on the content of the above literature, this paper combines the advantage of novel quasi-Z-source inverter with virtual synchronous generator, proposes a novel quasiZ-source inverter photovoltaic grid-connected system based on virtual synchronous generator. Firstly, the principle of novel quasi-Z-source inverter VSG system is introduced. Then, the control strategy of novel quasi-Z-source inverter VSG system is introduced. Finally, the simulation model is built by MATLAB to validate scheme. The simulation results show that the structure not only has boost effect of new quasi-Z-source inverter, but also has inertia and damping characteristics of virtual synchronous generator.

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2 A Novel Quasi-Z-Source Inverter VSG Grid-Combined System The construction topology the new quasi-Z-source inverter VSG control grid-combined system is shown in Fig. 1. This system mainly contains two parts. The part one is boosting part based on novel quasi-Z source structure. The second part is control part based on VSG control structure. The research content of this paper is mainly based on quasi-Zsource inverter and VSG structure, so photovoltaic power generation part is replaced by a simple DC power supply.

Fig. 1. A new quasi-Z-source inverter VSG control grid-combined system

2.1 Basic Principle of New Quasi-Z-Source Inverter The circuit topology of new quasi-Z-source inverter used in this paper is shown in Fig. 1. It is mainly covering five energy storage inductors L1 -L5 , two energy storage capacitors C1 , C2 and seven diodes. Compared with the traditional quasi-Z-source inverter, biggest difference between that two is the change of the boost capacity. The energy storage inductance of traditional quasi-Z-source inverter is replaced by a switching inductance structure, so that this structure can save many energies in the shoot-through state. Under same duty cycle, the voltage gain is higher than that of traditional quasi-Z-source inverter. The following introduces the two working states of novel quasi-Z-source inverter. Figure 2 ( a) is the circuit diagram of shoot-through state. On this working state, the power supply and the capacitor C2 charge and store energy for the inductor L1 meanwhile, and capacitor C1 is charged by the L2 -L5 inductor. According to the equivalent circuit

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diagram, the equation can be obtained: ⎧ ⎨ UPV = UL1 + UC2 ⎩ UL2 = UL3 = UL4 = UL5 = UC1 2

(1)

Figure 2(b) is the circuit diagram of non-through state. On this working state, the inductors L1 -L5 charge the load and capacitors C1 , C2 . According to the equivalent circuit diagram, the equation can be obtained: ⎧ UPV = UL1 + UC1 ⎪ ⎪ ⎨ UC2 UL2 = UL3 = UL4 = UL5 = ⎪ 4 ⎪ ⎩ UPN = UC1 − UC2

(2)

Fig. 2. The circuit diagram of new quasi-Z-source inverter on two working states

From Eq. ( 1 ), Eq. ( 2 ) and the volt-second balance theorem of inductance voltage, it can be obtained that: ⎧ (UPV − UC2 )T0 + (UPV − UC2 )T1 ⎪ ⎪ =0 ⎨ U L1 = T (3) UC2 ⎪ T + U4C2 T1 ⎪ ⎩ U L2 = 2 0 =0 T In the formula: T0 is direct time; T1 is non-direct time; T is the cycle. Substituting the shoot-through duty cycle D = T0 /T into above equation, we obtain: UPN =

3−D UPV = BUPV 1 − 4D + D2

(4)

In the formula: B is the boost factor, we can change the size of B to change the output voltage.

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2.2 Mathematical Modeling of Virtual Synchronous Generator In this paper, the voltage-type virtual synchronous generator is selected as the research object. Referring to the second-order classical model of synchronous generator, its mathematical model includes two parts: rotor motion equation and electromagnetic equation. The rotor motion equation reflects the inertia and damping peculiarity of synchronous generator; therefore, it is the core part of VSG technology. The mathematical expression is as follows: ⎧ dω Pm Pe ⎪ ⎪ J = − − DP (ω − ωref ) ⎪ ⎪ dt ω ω ⎨ E˙ = U˙ + I˙ (R + jX ) (5) ⎪ ⎪ ⎪ ⎪ ⎩ dθ = ω dt In the formula, J is rotational inertia, Pm is mechanical power, Pe is electromagnetic power, ω is running angular velocity, ωref is rated angular velocity, Dp is damping coefficient, E˙ is excitation electromotive force, I˙ is equivalent stator current, U is terminal voltage, R and X are the equivalent armature resistance and reactance respectively.

3 Control Strategy of New Quasi-Z-Source Inverter VSG Grid-Combined System The control strategy of new quasi-Z-source inverter virtual synchronous generator gridconnected system mainly includes the control of new quasi-Z-source inverter and the control of VSG. In this text, the control of new quasi-Z-source inverter is based on that existing eight-segment SVPWM control strategy, which is not described here. For VSG control technology, it mainly includes active power control and reactive power control. 3.1 Active Power Control Strategy of Virtual Synchronous Generator After introducing the idea that droop characteristics and the characteristics that inertia and damping into the virtual synchronous generator, the virtual synchronous generator has the primary frequency modulation characteristics of synchronous generator. Combined with active-frequency droop characteristics and the rotor mechanical equation, it can be obtained: ⎧ ⎨ Pm − Pref = Kf (ωref − ω) (6) ⎩ J d ω = Pm − Pe − DP (ω − ωref ) dt ω ω In the formula, Kf is active power droop coefficient, Pref is active power given value.

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3.2 Reactive Power Control Strategy of Virtual Synchronous Generator In synchronous generator, the system reactive power balance and voltage stability are realized by excitation regulator. The reactive power-voltage control equation of virtual synchronous generator may be obtained by referring to the principle of excitation regulator:  1  Qref + Dq (Uref − U ) − Q (7) Ks In the formula, K is the integral coefficient, Dq is the droop coefficient, Qref is given value of reactive power, Q is actual measured value of reactive power, Uref is given value of voltage, and U is actual value of voltage. E = U0 +

4 Simulation Verification and Result Analysis So as to verify feasibility of above theory, the MATLAB/SIMULINK simulation model is built to simulate. The following are the main parameters in the text, as shown in Table 1. Table 1. Virtual synchronous generator simulation parameters. Parameter

Description

Value

UPN /V

DC-link voltage

750

Rf / 

Inverter side resistance

0.1

Lf /mH

Inverter side inductance

3.2

Cf /μF

Smoothing capacitance

20

Lg /mH

The grid-side inductance

1.5

So as to verify inertia and damping characteristics of new quasi-Z-source inverter virtual synchronous generator grid-connected structure, the method of controlling variables is adopted. When other quantities are not changed, the values of inertia and damping coefficient are changed respectively, and influence of each parameter on the system is judged by the dynamic response of active power. As shown in Fig. 3, the dynamic response of different rotational inertia to the active power of the system is shown. We can conclude that as rotational inertia becomes larger, the oscillation frequency of active power response curve of the system is larger, the response speed is slower, and the system has a stronger inhibitory effect on the impact. As shown in Fig. 4, the dynamic response of different damping coefficients to active power of system is shown. It should be seen that as damping coefficient becomes larger, the oscillation frequency of system’s active response curve is lower, the response speed is faster, and the system’s suppression of the impact is weaker. On the whole, the moment of inertia and damping coefficient should not be too high or too low. So as to make system in an optimal state, rotational inertia and damping coefficient should match each other.

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Fig. 3. Active dynamic response of system under different rotational inertia

Fig. 4. The active dynamic response of the system with different damping coefficients

5 Conclusion and Foresight This text combines a novel quasi-Z-source inverter construction with virtual synchronous generator technology, and proposes a novel quasi-Z-source inverter virtual synchronous generator photovoltaic grid-connected system. This system can not only boost the voltage before grid connection through the new quasi-Z source structure, but also support inertia and damping characteristics of grid connection through virtual synchronous generator support system. Finally, the feasibility of this structure is verified by MATLAB/SIMULINK simulation. This structure has characteristics of providing good boost, inertia and damping support. At the same time, due to the existence of new quasi-Z source

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structure, current ripple of system is greatly improved, and the current harmonic distortion rate is low. However, this paper also has the situation that the research is not in place. For the control strategy of new quasi-Z-source inverter structure, that content of other scholars used has not been further analyzed. For this point, follow-up research needs to be further analyzed.

References 1. Peng, F., Fang, X., Gu, B.: Z-source converter. J. Electr. Technol. 19(2) (2016). (in Chinese) 2. Anderson, J., Peng, F.: Four quasi-Z-source inverters. In: 2008 IEEE Power Electronics Specialists Conference, pp. 2743–2749. Rhodes, Greece (2008) 3. Sun, D., Su, H., Jiang, K.: A novel quasi-Z-source inverter. J. Jinan Univ. (Nat. Sci. Ed.) 33(3), 199–206 (2019). (in Chinese) 4. Guo, H.: Improvement of SVPWM shoot-through modulation strategy for quasi-Z-source inverter. Electr. Technol. 5, 67–70 (2022). (in Chinese) 5. Wang, X., Chen, Q.: Research on grid-connected inverter control based on improved virtual synchronous generator. J. Electr. Eng. (2023). (in Chinese) 6. Chen, S., Sun, Y., Han, H.: A modified VSG control scheme with virtual resistance to enhance both small-signal stability and transient synchronization stability. IEEE Trans. Power Electron. 38(5), 6005–6014 (2023) 7. Wu, H., Ruan, X., Yang, D.: Modeling and parameter design of virtual synchronous generator power loop. Proc. CSEE 35(24), 6508–6518 (2015). (in Chinese) 8. Zhu, Z., Huang, S.: Stability control of microgrid based on adaptive moment of inertia VSG. J. Electr. Eng. 15(01), 41–47 (2020). (in Chinese) 9. Tao, L., Cheng, J., Wang, W.: Parameter design and optimization method of virtual synchronous generator. Power Syst. Protect. Control 46(12), 128–135 (2018). (in Chinese) 10. Gao, H.: Research on Parallel/off-grid Switching Control Strategy of Virtual Synchronous Generator. China University of Petroleum ( East China ), (2018). (in Chinese) 11. Liang, W., Liu, Y., Shen, Y.: Active power control integrated with reactive power compensation of battery energy stored quasi-Z source inverter PV power system operating in VSG mode. IEEE J. Emerg. Sel. Top. Power Electr. 11(1), 339–350 (2023) 12. Zhang, Y., Liu, Y., Luo, B.: Variable weight coefficient MPC control strategy for QZSI-VSG wind power grid-connected system. IET Renew. Power Gener. (2023) 13. Xiong, J., Zheng, B., Wang, T.: Predictive control of VSG photovoltaic grid-connected model based on improved Quasi-Z source inverter. Electr. Power Sci. Eng. 38(8), 12–21 (2022). (in Chinese)

Impedance Analysis of Supercapacitor DC-DC Converter in Two-Cascade System Tao Lin1,2

, Jun Liu1,2(B) , and Peng Weifa2

1 State Key Laboratory of Performance Monitoring and Protecting of Rail Transit

Infrastructure/SEAE, Nanchang 330013, China [email protected] 2 Electrical and Automatic Engineering School, East China Jiao Tong University, Nanchang 330013, China

Abstract. The supercapacitor can form a double cascade system with other converters. When the scheme of the other party that constitutes the cascading system with itself is unknown, it must be able to meet the cascading stability requirements. In order to achieve the corresponding stability, the input and output impedance of the supercapacitor DC-DC converter under two types of cascade conditions are analyzed, the influence of different control parameters on the impedance is analyzed, and the design rules related to the cascade stability are proposed. Due to the influence of magnetic core saturation, the filter inductance changes and the circuit parameters change, so the variable parameter control scheme is adopted for the ultracapacitor DC-DC converter to meet the control needs. After the corresponding analysis, simulation is carried out and experimental results are given to prove the correctness of the analysis. Keywords: Dual Cascade System · Ultra capacitor DC-DC Converter · Impedance Analysis · Variable Control Parameters

1 Introduction Supercapacitors (UC) are widely used in the field of rail transit [1, 2]. When the supercapacitor is used for bidirectional energy flow, a suitable supercapacitor bidirectional DC converter is needed. The supercapacitor bidirectional DC converter needs to relate to other converters to form a cascade system, which introduces the stability problem of the cascade system of the bidirectional converter. Beijing Jiao tong University and Nanjing University of Aeronautics and Astronautics have respectively improved the stability of UC energy storage system and cascade system in different ways [3, 4]. Chinese Academy of Sciences and East China Jiao tong University respectively proposed a differential input voltage equalizing control strategy and a passive ripple compensation circuit to verify the feasibility of the model [5, 6]. Aiming at the problems of low inertia and poor bus voltage quality in DC microgrid. Xi’an University of Technology proposed an improved virtual capacitor control strategy for multi-port isolated DC-DC converter [7], aiming to improve the efficiency of the converter. Researchers in Spain, Finland and France have © Beijing Paike Culture Commu. Co., Ltd. 2024 C. Cai et al. (Eds.): ICWPT 2023, LNEE 1159, pp. 589–596, 2024. https://doi.org/10.1007/978-981-97-0877-2_61

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also proposed stability solutions for cascading systems [8. 9]. At the same time, some scholars have proposed a new type of DC-DC converter, which avoids a certain dead zone and improves the response time [10]. The impedance characteristics of UC converter under Buck and Boost conditions are given. The influence of main circuit filter parameters and control parameters on the supercapacitor DC-DC converter is analyzed and the design rules are given. Considering the change of inductance value caused by the saturation characteristics of the magnetic core, the control parameters are dynamically adjusted to improve the stability of the system and realize the cascade stability of bidirectional operation.

2 Impedance Analysis 2.1 Main Circuit The UC converter has the ability to function in both directions and features a half-bridge bidirectional Buck-Boost circuit. The main circuit for this component is depicted in Fig. 1. As the motor operates, it is supplied with the necessary energy in a sensible manner, with the UC converter operating in Buck mode. When the motor is slowing down or braking, a portion of the energy is recuperated and the UC converter switches to Boost mode.

Fig. 1. Main circuit of UC converter

2.2 Impedance Characteristics of UC Converter on Buck Condition The UC converter works in Buck mode – the output energy simplifies the main circuit as shown in Fig. 2. When Q2 is in the off state. After taking into account the series equivalent internal resistance of UC, the openloop output impedance of the UC converter in Buck condition can be determined using the following formula. 2 ( ZOO_ UC (S) = [DUC1

1 + SCUC rUC 1 + SCUC1 rCUC 1 + SCUC2 rUC2 || ) + +(SLUC + rLUC )]|| ||RUC SCUC SCUC1 SCUC2

(1)

The open loop output impedance of the UC converter under Buck condition is affected by adjusting the value of inductance LUC . The graph shows different values for LUC : 400 µH (solid line), 800 µH (dashed line), 1200 µH (short dashed line), and 2000 µH

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Fig. 2. Main circuit of UC converter on Buck condition

Fig. 3. UC converter’s output impedance on Buck condition (CUC2 = 4000 µF, variable LUC ) and (LUC = 400 µH, variable CUC2 )

(dotted line). Additionally, the impact of capacitance size CUC2 on the open loop output impedance was investigated. The Bode diagram in Fig. 3 illustrates this relationship. It is evident from the diagram that the open-loop output impedance of the UC converter exhibits a prominent peak near the resonant frequency of the LC filter when operating in Buck mode. Subsequently, as the frequency increases in the high-frequency range, there is a decrease in impedance. By increasing both inductance and capacitance, we observe that the inflection point of phase angle occurs at a lower level when reaching maximum impedance. The converter demonstrates only a specific level of impedance within the intermediate frequency range. Establish a small signal model for Buck working condition control of UC converter, and the transfer function from control to output is as follows:   Uin SC1UC + rCUC ||rUC uˆ 0   (2) Gvd = |uˆ in =0,ˆio =0 = dˆ SLUC + rLUC + SC1UC + rCUC ||rUC UC converter Buck condition closed-loop impedance: ZOO_ UC (S) =

uˆ O (S) ZOO_ UC (S) = ˆiO (S) 1+TUC (S)

(3)

The analysis focuses on the output impedance of the UC converter. The open-loop output impedance is represented by a dotted line, while the PI parameter P = 6, I = 0.05

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is also depicted by a dotted line. Additionally, the PI control parameter P = 2, I = 1 is represented by another dotted line. On the other hand, the solid line represents the PI control parameter P = 2, I = 0.05, and it represents the closed-loop output impedance of the control parameter. This information is illustrated in Fig. 4.

Fig. 4. Close-loop output impedance of UC converter on Buck condition

The closed-loop control has the ability to reduce the output impedance of the UC converter operating in Buck condition, resulting in improved output impedance characteristics in the middle frequency range. A higher value of parameter P in the PI controller leads to a decrease in the output impedance of the closed-loop band. On the other hand, the control parameter I has minimal impact. 2.3 Impedance Characteristics of UC Converter on Boost Condition When the UC converter works in Boost mode, it works as a post-stage converter in the double-cascade system, and its simplified main circuit is shown in Fig. 5. Currently, Q1 is in the off state.

Fig. 5. Main circuit of UC converter on Boost condition

UC converter open loop input impedance when operating in Boost mode: Zin0_UC (S) = D2 UC1 ZCUC + (SLUC + rLUC ) where, D’UC1 is the duty cycle under Boost condition.

(4)

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To investigate the impact of varying inductor LUC size on the input impedance of the UC converter operating in Boost mode, modifications were made. The Bode diagram depicted in Fig. 6 illustrates these changes. Specifically, the solid line represents LUC = 400 µH, while the dashed line corresponds to LUC = 800 µH and the short-dashed line corresponds to LUC = 1200 µH. Additionally, a dotted line indicates an open-loop input impedance with LUC set at 2000 µH.

Fig. 6. UC converter’s input impedance on Boost condition (CUC2 = 4000 µF, variable LUC )

It can be seen from the figure that the open loop input impedance of UC converter in Boost condition increases with the increase of inductor LUC , and increases with the increase of frequency, and there is no sag area. Increasing inductor LUC is conducive to the system stability when it works as a post-stage converter. Due to the Boost condition of the UC converter, the output filter capacitor CUC1 is in parallel with UC, CUC1 is mF level, CUC1 is far less than CUC , so the change of CUC1 size has little effect on the input impedance of cascade system II, and its influence is no longer analyzed. The small signal model of Boost condition control of UC converter is established. The closed-loop input impedance of Boost condition of UC converter is as follows: (S) = UO Ti + LUC + rLUC + ZCUC (D Ti−UC Iin + D2 )

(5)

where, Ti (S) is the UC converter current gain function. Transfer function of current to control: Gid =

ˆiin |uˆ =0,ˆi =0 = Io dˆ in 0

(6)

The analysis focuses on the input impedance of the UC converter in Boost condition. The open-loop input impedance is represented by a dot line, while different PI control parameters are depicted using dotted and solid lines in Fig. 7. When PI control is used in Buck condition of UC converter, the control parameter P is improved, which is beneficial to the stability of cascade system. The UC converter works in Boost condition, when P in PI parameter is large, it is beneficial to the stability

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Fig. 7. Bode diagram of closed-loop input impedance of UC converter under Boost condition

of the cascade system, but the change of I value has little influence on it. Therefore, the value of the control parameter P can be appropriately increased, which is conducive to the stability of the cascade system. Therefore, the selection rule of filter circuit parameters is as follows: inductance LUC needs to consider the two types of working conditions comprehensively, and carry out comprehensive selection; the filter capacitor CUC1 is beneficial to the stability of the cascade system and can be appropriately increased. The selection rules of the control parameters are as follows: increasing the value of the control parameter P is conducive to the stability of the cascade system and can be appropriately increased; Control parameter I has little effect. 2.4 Variable Inductance Parameter Due to the saturation characteristics of the inductance core, when the inductance current increases, the inductance saturation degree is deepened, and the inductance value will become smaller, and the inductance can be regarded as a controlled inductance, and the control quantity is the inductance current, that is L = f (iL )

(7)

As the inductor current iL increases and the inductor LUC decreases, when the UC converter works under Buck condition as the front stage, the open-loop output impedance decreases, which is conducive to the stability of the cascade system. When working under Boost condition, the open-loop input impedance decreases, which is not conducive to the stability of the cascade system. The cascade stability of UC converter under different loads can be improved by setting the control parameters. (P, I ) = f (iL )

(8)

When the UC converter works under Buck or Boost conditions, the control parameters are similar and no classification is required. The control parameters are selected by piecewise hysteresis control. When no load and light load, PI control parameters select a set of values P0 and I0, when the load increases, select another set of values P1 and I1, heavy load and full load P2 and I2.

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⎧ ⎨ if 0 < iL < I2 , then(P,I) = (P0 ,I0 ) if I