Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit: ICEERT 2022 (Lecture Notes in Electrical Engineering, 1084) 981996430X, 9789819964307

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Lecture Notes in Electrical Engineering 1084

Sanjay Yadav Rahul Kumar Hidayat Zainuddin Lvxiang Deng   Editors

Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit ICEERT 2022

Lecture Notes in Electrical Engineering Volume 1084

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

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Sanjay Yadav · Rahul Kumar · Hidayat Zainuddin · Lvxiang Deng Editors

Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit ICEERT 2022

Editors Sanjay Yadav Metrology Society of India New Delhi, India Hidayat Zainuddin Faculty of Electrical Engineering (FKE) Universiti Teknikal Malaysia Melaka (UTeM) Melaka, Malaysia

Rahul Kumar Control and Instrumentation Group Board of Radiation and Isotope Technology Navi Mumbai, India Lvxiang Deng Changsha, China

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-99-6430-7 ISBN 978-981-99-6431-4 (eBook) https://doi.org/10.1007/978-981-99-6431-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Committee Member

Conference Co-chairs Prof. Dr.-Ing. habil. Kerstin Thurow, Academician of German Academy of Engineering, Germany Prof. Dr.-Ing. habil. Hui Liu, Central South University, China

Technical Program Committee Chairs Prof. Yiming Zhang, Fuzhou University, China Assoc. Prof. Yi He, Wuhan University of Technology, China

Technical Program Committee Co-chairs Prof. Jie Zhang, Central South University, China Assoc. Prof. Syed Abdul Rehman Khan, Xuzhou University of Technology, China Prof. Yong Li, Hunan University, China

Organizing Committee Chairs Assoc. Prof. Yanfei Li, Hunan Agricultural University, China Prof. Zaigang Chen, Southwest Jiaotong University, China

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Committee Member

Organizing Committee Co-chair Prof. Shu Cheng, Central South University, China

Publication Chairs Prof. Dr. Sanjay Yadav, CSIR-National Physical Laboratory, India Assoc. Prof. Lvxiang Deng, Central South University, China Prof. Chengcheng Xu, Southeast University, China Assoc. Prof. Hidayat Zainuddin, Universiti Teknikal Malaysia Melaka, Malaysia Assoc. Prof. Lei Zhang, Central South University, China

Local Committee Prof. Jianqing Wu, Shandong University, China Prof. Xuelei Meng, Lanzhou Jiaotong University, China Prof. Li Shen, National University of Defense Technology, China Prof. Weixiang Xu, Beijing Jiaotong University, China Prof. Hrabrin Bachev, University of National and World Economy, Bulgaria Prof. Dragan Cisic, University of Rijeka, Croatia Prof. Li Guo, Hunan University, China Prof. Qiaokang Liang, Hunan University, China Assoc. Prof. Qiang Wang, Heilongjiang Institute of Technology, China Assoc. Prof. Ziji Ma, Hunan University, China Assoc. Prof. Yunfei Zhang, Changsha University of Science & Technology, China

Technical Program Committee Prof. Ratnesh Dwivedi, ESJ Paris - Ecole Supérieure de Journalisme de Paris, France Prof. Kosga Yagapparaj, Malaysia/Trine University, USA Prof. Edward H K Ng, Singapore Management University, Singapore Prof. Carlos Becker Westphall, Federal University of Santa Catarina, Brazil Prof. Francesco Musumeci, Politecnico di Milano, Italy Prof. Christos Bouras, University of Patras, Greece Prof. Guangjun Gao, Central South University, China Assoc. Prof. Yang Li, Dalian University of Technology, China Assoc. Prof. Qiang Yang, Northeastern University, China Assoc. Prof. Selim Ahmed, World University of Bangladesh, Bangladesh

Committee Member

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Assoc. Prof. Ng Choy Peng, Universiti Pertahanan Nasional Malaysia, Malaysia Asst. Prof. Chan Lee Kwun, Universiti Tunku Abdul Rahman, Malaysia Senior Lecturer Ribhan Zafira Abdul Rahman, Universiti Putra Malaysia, Malaysia Asst. Prof. Tham Mau Luen, Universiti Tunku Abdul Rahman, Malaysia Asst. Prof. Ramesh Kumar Ayyasamy, Universiti Tunku Abdul Rahman, Malaysia Asst. Prof. Mohamed Ramadan Gomaa Behiri, Benha University, Egypt Lecturer. Shuai Li, University of Electronic Science and Technology of China, Zhongshan Institute, China Dr. Chaoqun Xiang, Central South University, China

Youth Student Committee Chair Mr. Zhu Duan, Central South University, China

Youth Student Committee Co-chair Mr. Ye Li, Central South University, China

Youth Student Committee Mr. Rui Yang, Central South University, China Ms. Fang Cheng, Central South University, China Ms. Shi Yin, Central South University, China

Preface

This volume of Springer is dedicated to the 2nd International Conference on Information Control, Electrical Engineering and Rail Transit (ICEERT 2022) hosted by Central South University, China, held on 25th–27th November 2022 in Changsha, China (virtual conference). The Conference was exclusively focussed on recent trends in information control, electrical engineering and rail transit, which was well attended and attracted about 100 participants around the world. The ultimate plan of organizing the event was to make it a regular event. The response received was tremendous and extremely positive beyond our expectations. The immediate purpose of this Conference was to bring together experienced as well as young scientists who are interested in working actively on various aspects of information control, electrical engineering and rail transit. The keynote speeches addressed major theoretical issues, current and forthcoming observational data as well as upcoming ideas in both theoretical and observational sectors. Keeping in mind the “academic exchange first” approach, the lectures were arranged in such a way that the young researchers had ample scope to interact with the stalwarts who are internationally leading experts in their respective fields of research. Besides the invited lectures, a good proportion of the participants also presented their work through contributory talks and posters on this big platform. This was particularly encouraging and of benefit to the young participants, given that there were a good number of scientists of international repute among the participants, the feedback from whom could guide them in the right direction. All the contributions were refereed by experts. The major topics covered in the Conference are: Artificial Intelligence Applications, Information Control, Big Data Analysis and Processing, Computer Graphics and Image Processing, Traffic Information Engineering and Control, etc. We are indebted to Central South University, China for their preparation in hosting such a huge conference. We thank all the members of the Organizing Committee, Local Committee, Technical Program Committee who contributed their hard labour to make the Conference a great success. We gratefully acknowledge the editorial committee, experts and reviewers for their valuable suggestions on the review process of the papers submitted. ix

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We sincerely thank Springer and its staff for the publication of this issue. Last but not the least, we thank all the speakers and participants without whom the Program would not have been such as success. We hope we will have your active participation in the future ICEERT versions as well. Organizing Committee, ICEERT 2022 New Delhi, India Navi Mumbai, India Melaka, Malaysia Changsha, China

Sanjay Yadav Rahul Kumar Hidayat Zainuddin Lvxiang Deng

Contents

Photovoltaic Generation Scenario Reduction Method Based on Improved K-Means Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jianlin Li, Sijia Wang, Yaxin Li, and Haitao Liu Research on the Optimization of Fixed Value Boundary of Line Distance Protection Load Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhengxu Qian, Wenbin Cao, Xuanwei Qi, Song Wang, Wulue Pan, and Yudong Fang

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Fuzzy Adaptive Tuning PI Control Based MPPT Method for Variable Speed Wind Turbine System . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. S. Li, Y. G. Li, J. He, and Q. Y. Chen

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Research on Distribution of Grounding Current Based on Different Earth Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao Wei, Yong Ma, Bo Song, Qiang Fu, and Shengquan Wang

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Key Factors Identification for the Energy Efficiency of Metro System Based on DEMATEL-ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chen Chen Zhang, Xue Mei Xiao, and Yan Hui Wang

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A Design of Embedded Servo Measurement and Control System in High Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yunqi Guo, Yuanyin Wang, Yuchen Liang, Zikou Yu, and Yafei Zhang

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Calculation and Simulation Model of Three-Dimensional Electric Field Distribution of Porcelain Insulator String Deterioration Based on Passive Electro-optic Field Strength Sensing Technology . . . . . Xun Wang, Xinyang Guo, Feiran Wang, Zhenlong Ren, and Zilong Hou Numerical Simulation of Resistive Current Extraction of 10 kV MOA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. A. Huijun, Wenming Hong, Yuqiang Li, Genghao Cai, Guoxing Wu, Qibin Cai, and Qiongqi Chen

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Contents

Intelligent Scheduling of AGV Based on Adaptive Traffic Control System Theory in Automated Terminal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. N. Zhao and Y. Q. Liu

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Research on Automatic Generation and Verification of Test Sequence for New Train Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Yuanshan Zang, Kaicheng Li, Chenyue Li, Lei Yuan, and Yu Liu Occluded Vehicle Detection with Fusing Motion Information . . . . . . . . . . 117 Zhengtao Ke, Jiaqi Xiong, Xun Huang, and Yaowen Xiao Study of an Acitve/Reactive Power Coordinative Control Method in Capacitor Series Inverter-Based Microgrid . . . . . . . . . . . . . . . . . . . . . . . . 127 Da Li, Huaidong Yang, and Haixing Zheng Multi-AGV Cooperative Scheduling Model Based on Improved Time Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Yingqi Liu Research on CTCS-N Onboard Equipment Testing Method Based on Timed Automata Mutation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Zhuofan Gao and Tao He Research on Connection Mode Recognition Method for Medium Voltage Distribution Network Based on CIM File Resolution and Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Junhui Li, Yu Luo, Xinxiong Wu, Xigang Li, Yongqiu Liang, Jianpeng Ye, Minghuan Huang, and Ziyao Wang A Robust Control Approach for Virtually Coupled Train Set with Parameter Uncertainty Under External Perturbations . . . . . . . . . . . . 177 Yi Zheng, Yihui Wang, Peichang Gao, Songwei Zhu, Shukai Li, and Xiuming Yao Code-Based PSO-SVM Algorithm for Network Security Posture Warning of Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Kuan Tan, Youzhi Bao, Yuanlin Zhang, and Bangna Ding Connectivity Reliability of Compound Rail Transit Network: A Case Study of Beijing-Tianjin-Hebei Urban Agglomeration in China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Xuemei Xiao, Yanhui Wang, Zehong Zhou, and Chenchen Zhang Performance Analysis of Empirical Weighting Method and Helmet Variance Component Estimation Method in CPIII Data Processing of Long Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 Xiongwei Peng, Zhixiong Zhang, Yongchong Yang, and Wenzhuang Su

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Fault Self-healing Scheme of MMC-DC Distribution Line . . . . . . . . . . . . . 229 Zhong Liu, Kaixin Zhang, Junyan Zhang, Shenxing Shi, Chaowu Liu, and Xinzhou Dong Highly Reliable Warning Method for Tanker Rollover Based on Fuzzy Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 K. X. Pan and K. Wei Real-Time Train Rescheduling with Passenger Demand for Rolling Stock Rescue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Hangyu Wang, Yihui Wang, Kangqi Zhao, and Peichang Gao A DSC-Based Approach to Robust Adaptive Tracking Control for Strict-Feedback Nonlinear Systems with Dead-Zone Input . . . . . . . . . 271 Chengcheng Lu and Yunfeng Zheng Passenger Flow Estimation in Urban Rail Transit Transfer Station Based on Multi-Source Detection Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Yu Fei Peng and Xi Jiang Research on Maglev Track Irregularity Based on Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Qingqin Yang, Qi Zhang, Zhuo Zhang, Dixiang Chen, MengChun Pan, Wenwu Zhou, Kuan Su, Yuan Ren, Hao Ma, and Lihui Liu Research on Collection and Distribution Scheme of Railway Container Hub Based on Time Value–Space–Time Network . . . . . . . . . . . 303 Yuxuan Dong and Qi Li Thermal Simulation of I/O Subsystem of an All-Electronic Computer Interlocking Based on Finite Element Analysis . . . . . . . . . . . . . 317 Chao Sun, Zhiyu Xie, Biao Lv, and Yuxiang Kang Research and Optimisation of the Coupling Performance of Pantograph–Catenary System Based on Numerical Simulation and Experimental Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Wenzhi Xu, Tiehui Wu, Jingshen Wu, Decai Qin, and Yue Li Research and Application of Key Technologies for Intelligent Interpretation of Natural Resource Satellite Remote Sensing Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 Hai Xiao, Zhiqing Tang, Rui Qin, Weijun Qu, Le Cai, Jiangjiang He, and Huichao Wu Optimal Dispatch of Active Distribution Network with Electric Vehicles Based on Improved CROA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Haozhou Chen, Xun Li, Dazhong Zou, and Chunyan Wu

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Contents

Single-Track Railway Segment Passing Capability Calculation Study Based on Moving Block System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Fei Jiang and Qiang Li Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

About the Editors

Prof. Dr. Sanjay Yadav obtained his master’s degree in science (M.Sc.) in 1985 and his Ph.D. degree in Physics in 1990. Presently, he is Vice President of the Metrology Society of India. He was the Former Chief Scientist and Head of the Physico Mechanical Metrology Division of NPL. In addition, he was also holding the post of Professor at the Faculty of Physical Sciences, Academy of Scientific and Innovative Research (AcSIR), HRDG, Ghaziabad, teaching ‘Advanced Measurement Techniques & Metrology’ courses, taking practical classes and supervising graduate, master, and Ph.D. students since 2011. He is the Editor-in-Chief of MAPAN: The Journal of Metrology Society of India. He has more than 350 research publications to his credit, published in national and international journals of repute and conferences, besides contributing to several books as Editor and Author, published by Springer and MSI, as well as drafting several project, scientific, and technical reports, documents, and policy papers. Dr. Rahul Kumar obtained his B.Tech. degree in Electronics and Communication Engineering from Invertis University in 2015. He has completed his Doctoral degree from the Academy of Scientific and Innovative Research (AcSIR), CSIRNational Physical Laboratory under the guidance of Dr. Sanjay Yadav (Chief Scientist) and Dr. P. K. Dubey (Senior Principal Scientist). During his Ph.D. tenure, he has published 20 research publications in national and international journals of repute, book chapters, and conferences. He has also filed a patent on the testing, calibration, and type approval of multiple blood pressure measuring instruments. He has also attended various national and international conferences and seminars. Presently, he is working as Technical Officer (C) in the Control and Instrumentation Group of the Board of Radiation and Isotope Technology (BRIT), Department of Atomic Energy, Government of India.

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About the Editors

Prof. Hidayat Zainuddin received his bachelor’s degree in electrical engineering from Universiti Teknologi Malaysia in 2003. He then obtained his Master of Science degree in Electrical Power Engineering with Business from the University of Strathclyde, Glasgow, in 2005. He received his Ph.D. degree from The University of Southampton in 2013. He has received almost RM 500,000 in research grants as Principal Investigator and almost RM 1.5 million as Co-researcher. Most of his research is mainly geared toward the sustainability of electrical power systems, which are associated with green technology, condition monitoring, and failure analysis for high-voltage transformers. These include investigating the surface discharge behavior of pressboard impregnated in mineral and ester oils and the performance of a mineral-ester oil mixture for transformer applications and the design and development of an optical fiber sensor for online monitoring of transformer oil for a smart grid application. Prof. Lvxiang Deng is Deputy Editor-in-Chief and Editorial Director of the editorial department of Traffic Safety and Environment (English version) of Central South University Press, Supervisor of master students in the School of Literature and Journalism and Communication of Central South University, and Deputy SecretaryGeneral and Deputy Director of the youth committee of the Research Association of Science and Technology Journals of Chinese Universities. He has published more than 20 papers in SSCI and CSSCI-indexed journals. His papers have been awarded many times as excellent papers by the China Association of Scientific and Technological Journals, the Hunan Association of Scientific and Technological Journals Editors, and the Hunan Association of Scientific and Technological Journals. He has won the honors of being an Excellent Editor of Chinese university science and technology journals, winning the Chinese science and technology journal youth editor award (Junma Award), winning the silver pen award for an excellent thesis, and being an Excellent Young Editor of Hunan Province.

Photovoltaic Generation Scenario Reduction Method Based on Improved K-Means Clustering Jianlin Li, Sijia Wang, Yaxin Li, and Haitao Liu

Abstract The country strongly supports and develops renewable energy generation under the dual carbon target, but the inherent instability, intermittency, and antipeak regulation characteristics of renewable energy such as photovoltaics affect the safe and stable operation of the power grid. To address this problem, the photovoltaic generation scenario is reduced based on the improved K-Means clustering. Firstly, we analyze the influence of solar irradiation intensity and module surface temperature on photovoltaic output and select the most influential factor as the basis for subsequent analysis. Secondly, choose a suitable probability density function to construct the photovoltaic output model. Then improve the traditional K-Means clustering algorithm by combining density peak clustering, to solve the problem of difficulty in determining the initial clustering center and the number of clusters. Finally, the improved K-Means clustering algorithm is applied to form a typical operation scenario of photovoltaic output in a certain region. The results of the analysis verified the effectiveness of the algorithm. Compared with the traditional K-Means clustering algorithm, the improved clustering algorithm has stronger convergence and faster convergence speed. Keywords Photovoltaic power generation · Scene reduction · Density peak clustering · K-Means clustering algorithm · Environmental factors

J. Li (B) · S. Wang · Y. Li Energy Storage Technology Engineering Research Center, North China University of Technology, No. 5 Jinyuanzhuang Road, Beijing 100144, China e-mail: [email protected] H. Liu Institute of Smart Grid Industry Technology, Nanjing Institute of Engineering, Nanjing 211167, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_1

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1 Introduction To achieve the goal of “double carbon” as soon as possible, countries around the world encourage the development of wind power, photovoltaic and other renewable energy, and have issued renewable energy support plans, many large domestic wind farms, photovoltaic (PV) power plants have been built to complete. However, PV power output is unstable, and such a large-scale grid connection will cause problems such as voltage crossing limits and excessive network losses, which will lead to high abandonment rates and complicate the scenarios in the power grid. The scenario analysis method is the mainstream method to deal with uncertainty planning problems at present. The literature [1] adopts the time-series simulation method, considering the characteristics of wind power, and obtains the wind-load joint time-series data to simulate a typical scenario by the Monte Carlo method. Authors in reference [2] adopt the typical day method, considering the characteristics of wind power, load, unit, and grid, and selects the day with the largest peak-to-valley difference in annual load as a typical day for annual planning. Authors in reference [3] adopt the scenario clustering method, based on K-Means clustering is used to generate typical day scenarios based on historical data, which is used in a doublelayer model for optimizing distributed power access. The scenario clustering method is currently most commonly used for analysis due to its high computational efficiency and ability to accurately characterize scenarios. Among them, the K-means clustering algorithm is simple, efficient, and applicable, but the traditional K-means clustering algorithm needs to artificially specify the initial clustering center and the number of clustering centers, so the clustering results are unstable. Therefore, this paper adopts the K-Means clustering algorithm based on density peak clustering to deal with the uncertainties encountered in the planning process. In terms of scenario division, authors in reference [4] cluster time-series samples based on the morphological distance to extract wind power output scenarios for each season; authors in reference [5] consider the temporal and seasonal nature of light and load to generate seasonal daily scenario cuts; authors in reference [6] predict electric vehicle charging effects with different seasonal intra-day intervals. All the above pieces of literature use spring, summer, autumn, and winter seasons as the scenario division types, but PV power output is mainly governed by solar irradiance, and different types of weather conditions can occur within the same season, and there are large differences in solar irradiance under different weather, so the scenario division by seasons does not apply to PV power output. In this paper, the K-Means clustering algorithm is improved by combining density peak clustering, and the improved clustering algorithm is used to generate PV output operation scenarios, and the scenarios are reduced based on the generalized weather types to form typical daily scenarios.

Photovoltaic Generation Scenario Reduction Method Based …

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Fig. 1 I-V curves under different irradiance at 25 °C

2 Environmental Factors Affecting PV Output 2.1 Effect of Solar Irradiation Intensity on PV Output Light is the energy source of the PV system, solar irradiance is proportional to the photocurrent of the PV module, while it has almost no effect on the photovoltage, so the PV output power is proportional to solar irradiance [7]. The I-U curves corresponding to different irradiance levels of PV modules at a certain temperature (25 °C) are shown in Fig. 1, from which it can be seen that there is a large difference in the PV output power at different irradiance levels.

2.2 Effect of Module Surface Temperature on PV Output The efficiency of PV modules is inversely related to the module temperature, with the power decreasing by about 0.04% for every 1 °C increase in temperature. Therefore, the modules should be placed in a ventilated environment so that the air circulation above and below the modules can take the heat away from the cells and avoid the modules from decreasing the PV output power due to the temperature increase. The I-U curves corresponding to different temperature levels of PV modules under certain irradiance (1000 W/m2 ) are shown in Fig. 2, from which it can be seen that the difference in PV output power at different module temperatures is small. In summary, the solar irradiation intensity has the greatest influence on the PV output power, and the module surface temperature has a weak influence on the PV

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Fig. 2 I-V curves under different temperatures at 1000 W/m2

output power. Therefore, in the subsequent analysis of this paper, the influence of solar irradiation intensity on the PV output power will be mainly considered, and the influence brought by the module surface temperature will be ignored.

3 Photovoltaic Power Output Model For the mathematical way to quantitatively describe the solar irradiation intensity distribution, scholars at home and abroad have conducted a lot of research, and the widely used one is the Beta distribution model [8, 9], whose probability density function has the expression f (E) =

    E β−1 E α−1 (α + β) 1− (α)(β) E max E max

(1)

where E max is the maximum value of solar irradiance E for a given period of time; α and β are the two shape parameters of the Beta distribution; and  is the gamma function. Integrating Eq. (1) yields the expression for the probability cumulative distribution function of solar irradiance E as E

(α + β) F(E) = (α)(β)

Emax 0

t α−1 (1 − t)β−1 dt

(2)

Photovoltaic Generation Scenario Reduction Method Based …

5

With different values of the parameters α and β, the trends of the solar irradiance probability density function f (E) and the probability cumulative distribution function F(E) are shown in Figs. 3 and 4, respectively.

Fig. 3 The trend of the probability density function of solar irradiation intensity

Fig. 4 The trend of the probability cumulative distribution function of solar irradiation intensity

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Then the inverse calculation of Eq. (2) is performed using a computer simulation of the actual solar irradiation intensity E. The expression is E = E max F −1 (E)

(3)

After obtaining the solar irradiation intensity from Eq. (3), the expression for calculating the PV power output is P = E Sη

(4)

where S is the total area of PV panels; η is the photovoltaic conversion efficiency.

4 Density Peak-Based K-Means Clustering Algorithm 4.1 Traditional K-Means Clustering Algorithm Clustering is an exploratory classification process that classifies all data in a dataset into multiple categories based on the similarity between data in the dataset, with the higher similarity between data in the same category and lower similarity between data in different categories. K-Means clustering algorithm has the advantages of easy implementation and high computational efficiency, so it has been widely used [10]. The core idea is to randomly select k data from the data set as the initial clustering center, then calculate the Euclidean distance of the remaining data to the k initial clustering centers, and divide each data into the category where its nearest initial clustering center is located, and then recalculate the mean value of all data in the divided categories. The mean value of all data in each category is recalculated and the k clustering centers are updated, and the above process is iterated until the degree of change of each clustering center is less than the specified threshold [11].

4.2 Improved K-Means Clustering Algorithm The initial clustering centers and the number of clustering centers are important factors affecting the results of the clustering algorithm, and if these two parameters are not selected properly, the clustering results are likely to fall into local optimum solutions. The initial clustering centers of the traditional K-Means clustering algorithm are randomly generated, so the clustering results are unstable, which is also the biggest shortcoming of the algorithm. Therefore, this paper combines density peak clustering to improve the selection of clustering centers, which is based on the

Photovoltaic Generation Scenario Reduction Method Based …

7

principle of the high density of clustering centers and relatively distant from other clustering centers with high density [12]. The improved K-Means clustering algorithm can easily find the initial cluster centers and determine their number, effectively avoiding the defective problems of the traditional K-Means clustering algorithm. The basic idea of the improvement is: firstly, the data with the largest local density in the clustered data set is determined as the first initial clustering center, then the data with a larger relative distance and larger local density from the clustering center is determined as the second initial clustering center, and so on to determine all the initial clustering centers, and then the data is divided according to the Euclidean distance, which is the same as the traditional K-Means clustering algorithm. The flow chart of the improved K-Means clustering algorithm is shown in Fig. 5 [13]. The steps of the improved K-Means clustering algorithm are as follows [14]: (1) The clustered dataset S contains n samples, S = {x1 , x2 , ..., xn }, each sample contains two feature parameters: the local density ρi and the relative distance to the nearest higher local density sample δi . (2) Calculate the distance between each sample di j , the expression is di j =

 m 

xik

−

2 x kj

1/2 (5)

k=1

(3) Set the truncation distance dc and calculate the local density of each sample ρi , the expression is ρi =

   2 exp − di j dc



(6)

i= j,1≤ j≤n

(4) The local density ρi is arranged in descending order, and Q = {q1 , q2 , ..., qn } is defined as the set of subscript serial numbers in descending order, we have ρq1 ≥ ρq2 ≥ · · · ≥ ρqn

(7)

(5) Calculate the closest distance from the sample xi to the higher local density sample δi , the expression is   ⎧ dqi q j , i ≥ 2 ⎨ min j |Z L |, and Z mCA = − 3 j × Z 1 + Z L will be located near the bottom of the R axis. According to the analysis, the relative phase relationship of the measured impedance between phases AB, BC, and CA in the case of the AB phase short circuit can be obtained as shown in Fig. 4 (The red dashed box in the figure indicates the action zone). At this time, the measured impedance Z mCA is close to the R axis, and has the risk of falling into the action zone of the polygonal impedance element. Based on the comparison of Figs. 3 and 4, the distribution characteristics of the measured impedance are consistent with that measured on-site when the fault occurred. Through theoretical calculation for verification, the result is consistent with the condition of the actual recording waves.

Fig. 4 Phase-to-phase impedance distribution during AB phase short circuit

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In addition, to ensure a proper direction of the polygonal impedance element, the directional offset angle below the R axis is taken as 15°, which means that the bottom line of the quadrant IV of the action zone is at an angle of −15° with the R axis. Owing to this, the measured impedance Z mCA has a high possibility of falling into the action zone even if it is located near the bottom of the R axis. In summary, according to the fault analysis of action recording waves, during the AB phase-to-phase short circuit fault, the phase-to-phase impedance of the nonfaulty phase CA entered the action zone of distance I section, thus leading to the protection action of distance I section. Through the analysis of the action zone, we found that the action zone was in a relatively flat shape and extended a lot to the right, and the IV quadrant of the action zone was even larger than the I quadrant of the action zone, resulting in non-faulty phase impedance falling into the action zone of distance I section in the case of end faults.

3 Optimization Scheme of Fixed Values 3.1 Analysis of Action Zone of Polygonal Impedance Element As shown in Fig. 5, the action zone of distance I section of the polygonal impedance element consists of six action boundaries numbered 1–6. Among them, boundaries 1 and 2 ensure reliable selection of fault directionality, boundary 3 is determined by the load limiting resistance value, and boundary 6 is determined by the reactance value calculated according to the fixed values of distance I section. According to the characteristics of the faulty operation problem, the IV quadrant area of the action zone needs to be narrowed, and the relevant boundaries are 2 and 3, of which boundary 2 ensures a reliable selection of fault directions. The intersection of boundary 3 with the R axis (i.e., the “fixed value of load-limiting resistance”) is set according to the avoiding load, and the same fixed value is used by the distance sections I, II, and III. For the action zone of the distance I section, the load-limiting resistance value is set too large, resulting in more area of the action zone deviating into the fourth quadrant. Therefore, the protection software was designed to calculate the resistance component available only to the action zone of the distance I section, and the resistance component was not shared by the distance II section and III section, so as to realize the self-adaptive optimization of the action zone of the distance I section by the protection software and address the problem that the non-faulty phase impedance may fall into the action zone of the distance I section in the case of end faults. As shown in Fig. 6, the black dashed box is the action zone of the circular impedance, the blue box is the action zone of the polygonal impedance, and the red dashed box is the action zone of distance I section under a fixed resistance value Rset . Comparing the action zones of the circular impedance element and the polygonal impedance element, it can be known that the reactance component XDZ is the

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Fig. 5 Schematic diagram of the action zone of distance I section

value converted from the fixed impedance value ZDZ to the X direction. The resistance component RDZ is the fixed value of load-limiting resistance, which is set according to the avoiding load impedance and shared by the distance sections I, II, and III. Generally, RDZ is suitable for distance sections II and III. Since the low- and medium-voltage lines are short, the reactance component of the action zone of the distance I section is relatively small compared with the fixed value of load-limiting resistance, causing the polygonal action zone of distance I section to be in a too flat shape, resulting in the non-faulty phase impedance falling into the action zone in the case of end faults. Therefore, considering the logic of the occurrence of faulty operation, the load resistance limit value of the polygonal impedance element is a key parameter in the boundary settings of the action zone.

3.2 Logic Optimization of Action Zone According to the design principle, the action zone of the polygonal impedance element for distance protection is distributed in four quadrants based on the principle that the area occupied by quadrant I should be the largest. If the fixed value of the load-limiting resistance of the action zone is too large, so that the action zone of quadrant IV is larger than that of quadrant I, the action zone design principle is

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Fig. 6 Action zones of circular impedance element and polygonal impedance element

violated. When the area of quadrants I and IV are equal, it can be calculated that the corresponding resistance component is about five times the reactance component. Considering a certain margin, the value of the resistance component for the distance I section is taken as four times the value of the reactance component as the upper limit to ensure that the action zone of quadrant I is larger than that of quadrant IV. By taking the above factors and principles into consideration, the optimized resistance component RsetI used in the polygonal action zone of distance I section can be calculated internally by the device as

RsetI = min

⎧ ⎨ ⎩

Rr LZ

Rset , 2

⎫ ⎬

+ Z Z D ∗ cos(ϕlm ), ⎭ 4X setI

(9)

From Eq. (9), it can be seen that the value of RsetI is determined by the minimum value of the three values. In Eq. (9), Rset in the first value is the fixed resistance value of the polygonal action zone of distance sections II and III, which corresponds to the item of the fixed value of load-limiting resistance. Since a small load-limiting resistance shall be set separately for distance I section and a too-small value of Rset will cause the loss of load-limiting capability, one-half of the value of Rset is taken according to the project experience.

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In the second value, Rr /L Z is the allowable transition resistance value of distance I section converted to the value of the secondary side, Rr is the allowable transition resistance value of distance I section (10 Ω is generally taken), LZ is the conversion factor of the impedance at the primary and secondary sides (PT ratio/CT ratio), ZZD is the fixed value of distance I section, and ϕlm is the positive sequence sensitivity angle of the line. The second value is to consider the transition resistance in the case of a line grounding fault, so as to improve the reliability of the distance protection action. In the third value, the reason why 4X setI is set is that when the area of quadrants I and IV of the polygonal action zone is equal, the resistance component is five times X setI . Considering a certain margin, 4X setI is set as the upper limit of the resistance component. In addition, a means of avoiding the fixed value input error is added. The maximum value of RsetI and X setI /2 obtained above is taken, where X setI /2 is used as the lower limit of the resistance component of the polygonal action zone of distance I section, which is approximately equal to the resistance fixed value RDZmin of the minimum quadrilateral characteristic of the circular characteristic periphery of the ' is corresponding fixed value of distance I section. Therefore, the final value of RsetI taken as ⎧ ⎫ X setI ' RsetI = max RsetI , (10) 2 The optimized action zone is drawn according to the above logic criterion, as shown in the red dashed box in Fig. 7.

Fig. 7 Optimized action zone of distance I section

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As can be seen from the figure, since the fixed value of load-limiting resistance RsetI in the Rset value is reduced to one-half of the original value, while the fixed reactance value is reduced from 8X setI to 4X setI , and the action zone is changed accordingly, the optimized action zone of distance I section is no longer flattened, which can theoretically avoid the faulty operation problem that the non-faulty phase impedance may fall into the action zone of distance I section when the end fault occurs. Through the calculation using the modified formula inside the device, the action zone of quadrant IV is smaller than that of quadrant I, which theoretically conforms to the setting principle and meets the action requirements.

4 Device Testing The fault of each section on the line was simulated by using the distance module in the Omicron system to import voltage and current, and other digital quantities to output electrical quantities. The optimized action zone of CSD-212A-G (protection program version V1.07LS) produced by Beijing Sifang Automation Co., Ltd. was verified, and a fault replay test was conducted.

4.1 Action Zone Verification As shown in Fig. 5, the action zone boundary is divided into impedance boundary and angle boundary. Boundary 1 and 2 are the angle boundary with the checksum within ±2° of the boundary angle, and boundary 3 and 4 are the impedance boundary with the checksum 1.05 times and 0.95 times the fixed resistance value, respectively, and boundaries 5 and 6 are the impedance boundary with the checksum 1.05 times and 0.95 times the fixed reactance value respectively. For the change of line impedance under different working conditions, the logic verification of different values of RsetI is satisfied by modifying the relevant setting values. The analysis result shows that the action zone of the distance I section can be verified one by one in the following four conditions, each of which simulates AB, BC, and CA phase-to-phase and ABC three-phase short-circuit faults. (1) Condition 1: Table 1 shows the set value, and Table 2 shows the calculation process of the fixed resistance value. Through calculation, RsetI is set as 4.452 Ω. The testing results are shown in Fig. 8, and the green plus sign in the right graph shows the correct action returned by the testing point, which is summarized in Table 3. (2) Condition 2: The fixed value of load-limiting resistance Rset is modified to 6.0 Ω, and the rest of the fixed values are shown in Table 1. Through calculation, RsetI can be set as 3.0 Ω. The testing results are shown in Fig. 9. (3) Condition 3: The CT ratio is modified to 100/1 so that the primary and secondary conversion factor LZ of impedance is 3.5, and the rest of the fixed values

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Table 2 Calculation of fixed resistance value Rset 2 Rr LZ

6.0 Ω + Z Z D ∗ cos(ϕ1m )

4X setI Rx = min X setI 2

{

Rset 2 ,

{

(

RsetI = max Rx ,

Rr LZ

X setI 2

6.31 Ω

) { + Z Z D ∗ cos(ϕ1m ) , 4X setI

4.452 Ω 4.452 Ω 0.556 Ω

{

4.452 Ω

Fig. 8 Graphs of testing results of action zone of distance I section under working condition 1

Table 3 Testing results of action zone of distance I section under working condition 1 Boundary

In-zone fault

Out-of-zone fault

1

−2◦

action

+2◦ no action

2

+2◦

action

−2◦ no action

3

1.05 times RsetI value action

0.95 times RsetI value action

4

1.05 times RsetI value action

0.95 times RsetI value action

5

1.05 times RsetI value action

0.95 times RsetI value action

6

1.05 times RsetI value action

0.95 times RsetI value action

are shown in Table 1. Through calculation, RsetI can be set as 3.457 Ω. The testing results are shown in Fig. 10. (4) Condition 4: The fixed value of load-limiting resistance Rset is modified to 0.1 Ω, and the rest of the fixed values are shown in Table 1. Through calculation, RsetI can be set as 0.556 Ω. The testing results are shown in Fig. 11. In summary, the four working conditions correspond to the four action zones of the distance I section, and the protection testing of the distance I section was conducted

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Fig. 9 Graphs of testing results of action zone of distance I section under working condition 2

Fig. 10 Graphs of testing results of action zone of distance I section under working condition 3

Fig. 11 Graphs of testing results of action zone of distance I section under working condition 4

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to simulate the AB, BA, and CA phase-to-phase and three-phase short circuit faults. The results are in line with the requirements, ensuring reliable and correct action.

4.2 Fault Replay Test For the faulty operation problem of distance I section of the line protection device, an enhanced fault replay module was used, and the recording wave file of the protection action fault was imported for fault replay. The results show that the distance I section of the CSD-212A-G protection device after action zone optimization can avoid the fault, ensuring reliable protection without action. If the fixed values of phase-to-phase distance impedance of distance II section and III section are set the same as I section. Since the value of Rset of distance II section and III section can be set as Rset can be calculated to be 8.904 Ω, indicating protection action, so fault phase ABC is selected. Rset = min{Rset , 8X set }

(11)

The same method is used to import two other recording waves of faulty operations, and the phenomena are the same as this faulty recording wave playback test. The above test proves that the optimization scheme of the action zone of the distance I section is feasible.

5 Conclusions In this paper, a kind of faulty protection operation accident of distance I section was analyzed, and by analyzing the recording waves of the faulty operations, the mathematical principle was deduced, and the problems of action zone setting of polygonal impedance elements were pointed out. When the distance I, II, and III sections share the same fixed value of load-limiting resistance, the non-faulty phaseto-phase impedance cannot avoid the load-limiting boundary in the IV quadrant in the case of an out-of-zone fault and then falls into the action zone of distance I section. Therefore, an optimization scheme for the fixed values of polygonal impedance elements was proposed, and restriction conditions were set for the fixed values of load-limiting resistance of distance I section, realizing self-adaptive optimization of the action zone of distance I section by means of the protection software [14, 15]. Besides, the optimized action zone boundary was verified using the Omicron device, and the fault recording waves were imported to verify the feasibility of the scheme.

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The action zone optimization idea of polygonal impedance elements proposed in this paper applies to all polygonal impedance elements, which guarantees the reliability of distance protection against out-of-zone faults. Fund Project Science and Technology Project (2021ZK07) of State Grid Zhejiang Electric Power Co., Ltd.

References 1. J. Shen, H.X. Zhang, Z. Wang, Q.C. Zhao, C.H. Zhang, X.T. Zhu, Analysis and solution of a distance protection mal-operation case. Electr. Power Eng. Technol. 36(03), 100–104 (2017) 2. A.L. Zhang, Y.Y. Cheng, F.Q. Huang, X. Zeng, Z.J. Liu, A setting method of the second-zone grounding distance protection for 110 kV lines applicable to distributed wind power integration. Zhejiang Electr. Power 41(01), 125–130 (2022) 3. S. Wang, X.M. Huang, X.H. Xuan, Analysis of 500kV line distance protection maloperation. Zhejiang Electr. Power 02, 28–30 (2007) 4. G.L. Liu, Cause analysis on line distance zone I protection maloperation in transformer no-load operation and its countermeasures. Smart Power 41(08), 60–63 (2013) 5. Y.Q. Li, Z.C. Wang, W. Liu, D.H. Wan, B. Liang, Y.X. Wang, K. Liu, M.H. Wen, A method of wide-area backup protection based on interaction with adjacent substation for substation’s DC power loss. Zhejiang Electr. Power 38(06), 17–20 (2019) 6. H.H. Sheng, B.Q. Zhu, Peripheral power system of electric-railway: protection scheme and operation. Zhejiang Electr. Power 04, 29–31+39 (2006) 7. Q.W. Sun, W. Tian, X.H. Yang, Analysis and improvement for WXH-802 distance protection malfunction. Heilongjiang Electr. Power 03, 220–222 (2006) 8. J. Wang, M.J. Chen, Design of distance protection device based on DSP. Zhejiang Electr. Power 02, 9–11+18 (2006) 9. X. Gao, G.X. Xu, D.F. Guo, S.Q. Niu, The setting method of load limiting resistor for heavy power flow lines in North China power systems. Autom. Electr. Power Syst. 01, 50–52 (2006) 10. J.J. Hong, J.C. Wang, Analysis and treatment of operating incorrectly of D30 line distance relay when TV fuse failed. Zhejiang Electr. Power 01, 50–52 (2006) 11. J.W. Hou, T. Liu, L.G. Yue, H.Z. Tang, Influence of fixed cascade compensation device on UHV line protection and the solutions. Zhejiang Electr. Power 39(06), 15–20 (2020) 12. X.M. Zhao, Analysis of earth fault compensation factor in digital distance relay and its application for testing. Zhejiang Electr. Power 05, 19–22 (2005) 13. S.H. Jin, Investigation on the configuration of main protection for 35 kV power line. Zhejiang Electr. Power 01, 67–68 (2002) 14. J. Ma, W. Ma, X. Yan, C. Liu, Z.P. Wang, Impedance complex plane based adaptive distance protection scheme. Power Syst. Technol. 40(01), 290–296 (2016) 15. S. Yang, S.L. He, Improving method of action characteristics of distance protection and its application. Electr. Power Eng. Technol. 31(04), 39–42+47 (2012)

Fuzzy Adaptive Tuning PI Control Based MPPT Method for Variable Speed Wind Turbine System S. S. Li, Y. G. Li, J. He, and Q. Y. Chen

Abstract The wind turbine system is in a harsh natural environment, and the output power is not optimal due to the rapid change of wind speed. Therefore, it is of great significance for the development and utilization of wind energy to study the maximum power tracking control algorithm of wind turbine and improve the generation efficiency of wind turbine. This paper presents a fuzzy adaptive tuning PI control (FATPI) algorithm to achieve the maximum power output of wind turbine. The maximum power output can be achieved by tracking the optimal speed of the wind turbine and adjusting the torque of the squirrel cage induction generator (SCIG). In order to verify the effectiveness of the algorithm in MATLAB/Simulink simulation, compared with traditional PI control and FATPI control, the results show that FATPI algorithm has better robustness and adaptability in maximum power point tracking (MPPT) of wind turbine. Keywords Wind energy · Wind turbine · Fuzzy adaptive tuning PI control · MPPT · SCIG

1 Introduction Nowadays, wind turbines have become more popular with a growing interest in renewable energy resources. Wind energy is considered to be a relatively effective solution to environmental pollution and energy shortage. The development of wind energy has increased dramatically worldwide. From 2001 to 2021, global installed wind power capacity grew 12.8% annually [1]. Global wind power installed capacity S. S. Li (B) · Y. G. Li · J. He Department of Computer Science, Qinghai University, Xining, Qinghai, China e-mail: [email protected] Q. Y. Chen Qinghai Telecom, Xining, Qinghai, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_3

31

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1000 800 600 400 200

94 24 31 39 48 59 74

198 121 159

238 283

319 370

433

488 540

591

650

743

837

Total(GW)

0

Fig. 1 Wind power total capacity, 2001–2021

reached about 837 GW at the end of 2021, as shown in Fig. 1. Therefore, research on wind power generation is of great significance for wind resource utilization. At present, there are many types of wind turbines, variable speed wind turbines have many advantages, power generation system and grid decoupling, so that the control optimization becomes more flexible. In this paper, SCIG is embedded in a wind turbine to improve the output power quality. By adjusting the torque of the wind turbine generator, the rotor speed of the generator can be tracked quickly and accurately. The main task of the control system is to adjust the torque of SCIG to improve the power quality. The most important concern of large wind farms is the maximum power acquisition of wind turbines. In literature, a number of control methods have recommended for the speed control of wind turbines. These are control methods such as the adaptive active fault-tolerant control, the higher order sliding mode control and the artificial neural networks control [2–4]. Recently, due to the vigorous development of wind power generation, it is necessary to reconsider the design of wind turbine controller, the design of a controller with strong adaptability, robustness and anti-interference will become very important. In this paper, the speed error and error change rate of the wind turbine rotor are transformed into fuzzy control rules and stored in the computer as knowledge. Then, according to the wind turbine’s response to the actual wind speed, the computer automatically adjusts PI parameters through fuzzy reasoning to achieve the maximum power output of the wind turbine [5]. The remaining four parts of this paper are organized as follows. The aerodynamic model of the wind power system is presented in Sect. 2. The design of the proposed FSAPI controller is presented in Sect. 3. In Sect. 4, the simulation results of classical PI control and FATPI control are compared. Finally, the conclusion is given in Sect. 5.

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2 System Model 2.1 Wind Turbine Aerodynamic Model The wind energy conversion system includes an aerodynamic subsystem, transmission chain system, electromagnetic subsystem and power subsystem, among which the aerodynamic subsystem mainly includes blades, hubs and rotors. The aerodynamic power captured by the blade can be expressed as [6]: Pr = ρπ R 2 v 3 C p (λ, β)/2

(1)

where v, ρ, β, Pr , C p (λ, β), R and λ are the wind speed, the air density, the pitch angle, the wind turbine power, the power coefficient, the rotor radius and the tip speed ratio (TSR), respectively.

2.2 Drive Trains Model The transmission chain system consists of a wind turbine rotor, a gearbox and a generator rotor. The mathematical equation of the transport chain model is expressed as [6]: Jl · dΩl /dt = Twt − i/η · TG

(2)

where η is the transmission efficiency, i is the transmission ratio, Twt is the wind turbine torque, TG is the generator torque, Jl is the inertia of the wind turbine rotor.

2.3 Generator Model The electromagnetic torque of SCIG is expressed in the (d, q) coordinate system as ( ) TG = 3/2 pL m i Sq i Rd − i Rq i Sd

(3)

where p is the pole pairs number, i Sq , i Sd are the stator current components, L m is the mutual inductance, i Rd , i Rq are the rotor current components. The stator and rotor current equations of the generator can be expressed as [6]:

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Fig. 2 Configuration of a SCIG wind turbine

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩

di Rd dt di Rq dt

di Sd dt di Sq dt

= =

= = VRd LR VRq LR

VSd LS VSq LS

− −

− − RR LR RR LR

· i Sd − LLmS · didtRd + ω S · (i Sq + LLmS · i Rq ) di · i Sq − LLmS · dtRq − ω S · (i Sd + LLmS · i Rd ) · i Rd − LLmS · didtSd + (ω S − ω) · (i Rq + LL mR · i Sq ) di · i Rq − LL mR · dtSq − (ω S − ω) · (i Rq + LL mR · i Sd ) RS LS RS LS

(4)

where L S , L R are the stator and rotor inductances, Ωh is the generator rotational speed, ω S is the stator field frequency, R S , R R are stator and rotor the resistances. The wind turbine based on SCIG will provide several advantages, including simple structure, durability, reliable operation, high efficiency, convenient maintenance and low price. The control structure diagram of the wind power generation system is shown in Fig. 2, which describes the wind power generation control system including MPPT control and pitch control. This paper focuses on MPPT control.

3 Controller Design 3.1 FATPI Controller Design In the process of wind power system operation, the characteristic parameters or structure of the generator change with the influence of wind speed, load, and interference factors. In order to realize MPPT of wind turbine, fuzzy theory is an alternative method to solve this problem. The basic principle is to use the basic theory and

Fuzzy Adaptive Tuning PI Control Based MPPT Method for Variable …

35

Fig. 3 Fuzzy PI control approach

method of fuzzy mathematics to represent rules by fuzzy sets and store these fuzzy control rules as knowledge. Then, according to the actual response of the wind turbine control system, the optimal adjustment of PI parameters is realized automatically by using fuzzy inference. Therefore, this paper studies the controller design of FATPI, which consists of two parts: traditional PI controller and FATPI controller, as shown in Fig. 3. PI controller output adaptively changes when the external wind speed changes according to the fuzzy adaptive tuning algorithm [7]. The conventional PI control algorithm is ∫t u(t) = K p0 e(t) + K i0

e(t)dt

(5)

0

where u(t), e(t), K p0 , and K i0 are output of the controller, error in the control system, proportional and integral respectively. The input of FATPI controller is composed of wind turbine rotor speed error and error change rate, and the output is based on fuzzy rules ΔK p and ΔK i . In the PI controller, the steady-state error is affected by K p and K i can change the dynamic characteristics of the wind power system. In the proposed controller, the fuzzy set is {N, Z, P}, where N, Z and P represent negative, zero, positive. The inputs and outputs of fuzzy variables and fuzzy rules use trigonometric membership functions for ΔK p and ΔK i as shown in the Table 1. Fuzzy rules are created to implement the proposed FATPI controller, and ΔK p , ΔK i are obtained to control the torque of the generator. Under external conditions, ΔK p and ΔK i are adjusted by fuzzy rules. The advantages of the traditional PI controller and FATPI controller are used to build an incremental PI controller. As shown in Eqs. (6)–(7). ΔK p and ΔK i are obtained from the FATPI controller. K p = K p0 + ΔK p

(6)

K i = K i0 + ΔK i

(7)

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Table 1 Fuzzy rules for ΔK p \ΔK i Error(E) N Error change (EC)

P

N

N\Z

N\Z

N\Z

Z

N\P

P\P

P\P

P

P\Z

P\Z

P\Z

4 Simulation Results According to the FATPI control scheme shown in Fig. 2, the controller simulation model is constructed in MATLAB/Simulink [8]. The performance of the controller is verified in the turbulent wind environment. The wind speed variation of the turbulent wind is shown in Fig. 4, the changes of ΔK p and ΔK i parameters of the FATPI controller are shown in Figs. 5 and 6, and the dynamic response of the SCIG wind turbine under two different control strategies is shown in Fig. 7. As clearly shown in Fig. 7, SCIG achieves good tracking performance under the action of turbulent wind, and the MPPT control is satisfactory by comparing the simulation results.

Fig. 4 Wind speed profile

Fuzzy Adaptive Tuning PI Control Based MPPT Method for Variable …

Fig. 5 ΔK p parameter of FATPI control

Fig. 6 ΔK i parameter of FATPI control

Fig. 7 Wind turbine rotor speed in PI control and FATPI control

37

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5 Conclusion Without considering the external interference, two different control algorithms are simulated by Matlab/Simulink to achieve a good tracking of the speed of the wind turbine. The first control algorithm is the traditional PI control algorithm, and the controller parameters are unchanged after adjustment. The second control algorithm is FATPI. The traditional PI controller has a big overshoot problem. The combination of PI controller and FATPI controller can improve the speed of maximum power tracking in the wind power system. The proposed FATPI control strategy has strong robustness and adaptability to external disturbances and internal parameter uncertainties of wind turbines. Simulation results show the effectiveness of FATPI control algorithm in power extraction maximization. Acknowledgements This work was supported by the Youth Foundation Program of Qinghai University [grant number 2020-QGY-11].

Appendix A Parameters of system: R = 45 m, ρ = 1.25 kg m3 , C p_max = 0.47, J l = 990 kg m2 ,i = 100, p = 2, Rs = 4 mΩ, Rr = 4 mΩ, L m = 5.09 mH, L s = 5.25 mH, L r =5.25 mH, ωs = 100 πrad/s, V s = 690 V

References 1. L. Joyce, Z. Feng, Global wind report (2021). https://gwec.net/global-wind-report-2022/ 2. C. Jian, Y. Wei, L. Qun, X.R. Ya, Y.D. Wen, R.K. Jia, J. Lin, Adaptive active fault-tolerant MPPT control of variable-speed wind turbine considering generator actuator failure. Int. J. Electr. Power Energy Syst. 143, 142–149 (2022) 3. K. Murat, A new perturb and observe based higher order sliding mode MPPT control of wind turbines eliminating the rotor inertial effect. Renew. Energy 133, 807–827 (2019) 4. Z.L. Shan, P.W. Hao, T. Yang, K.L. Jin, A RBF neural network based MPPT method for variable speed wind turbine system. IFAC-PapersOnLine. 48, 244–250 (2015) 5. K.L. Jin, Intelligent Control Theoretical Basis, Algorithmic Design and Application (Chapter 3) (Tsinghua University Press, Beijing, 2019), pp. 49–52 6. M. Iulian, I. Antoneta, Optimal Control of Wind Energy System (Chapter 3) (Springer, London, 2010), pp. 38–45 7. Y.L. Guo, Neural, Fuzzy and Predictive Control and its MATLAB Implementation (Chapter 4) (Electronic Industry Press, Beijing, 2018), pp. 187–201 8. Y.Z. Zhi, Proficient in MATLAB R2011a (Chapter 8) (Beihang University Press, Beijing, 2011), pp. 502–510

Research on Distribution of Grounding Current Based on Different Earth Models Chao Wei, Yong Ma, Bo Song, Qiang Fu, and Shengquan Wang

Abstract Whether the geoelectric structure reflects the real distribution of various underground media determines the accuracy of neutral point potential calculation of AC station transformer near the grounding pole of ultra-high voltage direct current (UHVDC). The effects of layered geoelectric structure model, magnetotelluric sounding (MT) profile continuation model and three-dimensional Kriging geoelectric structure model on the calculation of ground potential, penetration depth of DC current and distribution law of DC current in the earth are studied. The results show that for different geoelectric structure models, about 3% of the ground current will enter the deep earth 300 km underground; Comparing the DC bias current (DCBC) calculated by the three models with the system commissioning data of BaihetanJiangsu ±800 kV ultra-high voltage DC transmission project, it can be seen that the ground potential calculated by the three-dimensional geoelectric structure model has higher accuracy, and the uneven lithology will lead to the change of the spatial distribution of the stable current field. Keywords Earth models · UHVDC · Grounding electrode · HVDC transmission

C. Wei · Y. Ma · S. Wang (B) Electric Power Research Institute of State Grid Jiangsu Electric Power Co., Ltd, Nanjing, China e-mail: [email protected] B. Song · Q. Fu Maintenance Branch of State Grid Jiangsu Electric Power Co., Ltd, Nanjing, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_4

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1 Introduction Ultra-high voltage direct current (UHVDC) was first built in China, with a maximum rated operating current of 6250 A [1]. It is compared with the early high voltage direct current (HVDC), due to the UHVDC rating. The working current is large, and the grounding current of the grounding pole is larger in a single maximum mode. The grounding current of the UHVDC grounding pole is large, causing an increase in the influence of the grounding pole ground current on the DC bias of the transformer around the pole site [2–4]. During the ±800 kV Shanghaimiao-Shandong UHVDC project during the 1000A ground current commissioning, the DC biasing current (DCBC) monitored by the 1000 kV Changle Station #2 main transformer neutral point is 5.2 A; according to calculation, 6250 A The neutral point current at the ground current is as high as 32.06 A. Therefore, the establishment of the accurate geoelectric structural model, and accurate calculation of the neutral point potential of each station near the ground is the key to assess the impact of grounding current into the surrounding AC grid [5–8]. Over the years, China has carried out a lot of research on the influence and prevention of grounding currents into the earth, but the earth’s electrical structure model is too simplified, which is not in line with the actual situation. The calculation of the neutral point potential of each station in the grounding near-area AC system is large, and then the problem that causes the DCBC calculated value to deviate from the measured value and the calculation cost is high and the efficiency is low that has not been solved. Therefore, it is still a difficult problem to establish a geoelectric structural model that is more in line with the actual situation and accurately calculate the neutral point potential of the transformer in the near-area AC system to evaluate the influence of the grounding current on the AC grid. In addition, for the grounding structure model needed to calculate the grounding potential, most studies have established a three-dimensional grounding structure model with very central grounding by extending the MT profile [9–11] of the grounding electrode. The calculated ground potential of the current is applied at the centre of the model [12–14], so establishing an accurate geoelectric structural model becomes the key to assessing the grounding effect. In [15], the MT data of the periphery of the Hami grounding pole is used to establish a geoelectric structural model with a very dense centre of Hami grounding, and the bias current is calculated by combining the grid structure and parameters of the surrounding pole. In [13], based on the MT data of North China, a three-dimensional geoelectric structural model is established to calculate the three-dimensional induced geoelectric field when a geomagnetic storm occurs. When the above-mentioned literature establishes the geoelectric structural model, there is an error in obtaining the earth resistivity data by manually identifying the MT section colour. In addition, some grounding poles near the region [15] have no array type measuring points [16, 17] measurement data, only part of the MT profile. However, the two-dimensional MT profile can only reflect the geoelectric structure near the line, and it does not reflect whether there is

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41

a catastrophic region in the unknown region. Directly extending the profile to establish a three-dimensional geoelectric structure model will reduce the accuracy of the model and cause grounding. Extreme impact assessment is not accurate. Using the earth resistivity data of the near grounding area of ±800 kV BaihetanJiangsu UHVDC Project as the original data, the Kriging method is used to predict the earth resistivity around the MT profile, and a three-dimensional Kriging earth resistivity model is established. Three models are used to study the influence of different geoelectric structure models on DCBC. By comparing with the measured values, it is proved that different earth resistivity models and deep layer earth resistivity will affect the calculation accuracy of DCBC.

2 Analysis of IGF Based on Multiple Geomagnetic Storm Events 2.1 Kriging Method The Kriging method determines the earth resistivity value of the estimate point by calculating the squared value of the reciprocal of the distance between the known MT profile point and the estimate point, as in (1): Z (x0 ) =

∑

λi Z (x1 )

(1)

; Z (x0 ) is where λi is the weight value of the known measuring point, λi = ∑LL0 −P 0 −D the earth resistivity value of the MT section measuring point, the unit is Ω · m; Z (x1 ) is the earth resistivity of the point of assessment, the unit is Ω · m; L 0 is the ith linear distance between the measuring point and the evaluation point, the unit is km; P is the IDW model estimation parameter, take 2. Assuming the earth resistivity Z(x) of each point on each layer of the earth, and the attribute value at the point xi ∈ A(i = 1, 2, · · ·, n) is the regionalized variable Z (xi ), the Kriging prediction result x0 ∈ A of the attribute value Z ∗ (x0 ) at the reference point Z (xi )(i = 1, 2, · · ·, n) is the known sample point attribute value F. Weighted sum, as shown in (2). Z ∗ (x0 ) =

n ∑

λi Z (xi )

i=1

where λi is the weight coefficient to be determined.

(2)

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For the Kriging method unbiased, the minimum variance condition can be obtained as the unbiased condition, and the obtained weight coefficient λi (i = 1, 2, · · ·, n) can satisfy the relation (3): n ∑

λi = 1

(3)

i=1

On the premise of unbiased, the Kriging variance is the smallest to obtain the equations for solving the weights to be determined, as shown in (4): ⎧ n ∑ ⎪ ⎪ ⎨ λi C(xi , x j ) + u = C(x0 , x j ) ( j = 1, 2, · · ·, n) ⎪ ⎪ ⎩

i=1

n ∑

λi = 1

(4)

i=1

where C(xi , x j ) is the covariance function of Z (xi ) and Z (x j ).

2.2 Grounding Potential Algorithm Compared with the geodetic model, the size of the grounding electrode is small, and its shape will not affect the change of the ground potential, so it is approximated as a point. According to the constant current field theory, the basic form of the differential equation of the current field is: − → ∇ × E =0

(5)

∂ρv − → ∇· J =− ∂t

(6)

− → − → J =σ E

(7)

− → E = −∇U

(8)

− → − → where E is the electric field intensity. J is the current density. ρv is the volume charge density. σ is the conductivity. U is the scalar potential. There are two forms of equations to describe the current field by using the field quantity U to be solved, namely, the Laplace equation without the current source (9) and the Poisson equation with the current source (10). ∇ 2U = 0

(9)

Research on Distribution of Grounding Current Based on Different …

∇ 2U = −

∂ρv ∂t

43

(10)

Because the electric field equation is unique, as long as the boundary conditions of the field are determined, the electric field can be determined, and the unique solution can be obtained. Therefore, the boundary condition of the electric field equation near the grounding electrode is found, and the potential distribution near the grounding electrode can be obtained by solving this equation. Figure 1 shows the profile diagram of the field near the grounding electrode. According to the derivation of Maxwell equation, the field equation of the area 1 where the grounding electrode is located meets Poisson equation (9), and the area without the grounding electrode meets Laplace equation (10). If the earth resistivity of field 1–8 is ρ1~ ρ7 , the field equation of field 2–8 is: ∇ 2 Ui = 0

(11)

where Ui is the potential in each area. The geoelectric structure model is divided into two regions: the region with source and the region without source. For the region with source, the unit point charge density in this field is defined as the impact function: ρ(x) = δ(x − x ' ) where δ(x) can be expressed as:

Fig. 1 Field distribution near the grounding electrode

(12)

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⎧∫ ⎪ ⎨ δ(x) = 0, x /= 0 U ∫ ⎪ ⎩ δ(x) = 1, x = 0

(13)

U

When the charge is distributed in an infinitely small area, that is, ΔU → 0, the charge density will tend to infinity, that is, ρ → ∞. It can be pushed out by (5) and (6) − → ∇ 2U = ∇ J

(14)

It can be seen that the field equation expressed by the scalar potential can be − → obtained by deducing ∇ J . When there is a constant current source in zone 1: ∮ I =

− → − J d→ s =

∫

− → ∇ J dΩ

(15)

Ω

s

The current field can also be expressed as: ∫ I =

I δ(x)dΩ

(16)

Ω

So there are: − → ∇ J = I δ(x)

(17)

It can be seen that the field expression of the area where the grounding electrode is located is: ∇ 2 U = I δ(x)

(18)

After establishing 3D geoelectric structure model in ANSYS, apply boundary conditions: (1) Four vertical planes and bottom boundary conditions of the model: U =0

(19)

(2) Boundary conditions of ground air interface: dU =0 dn

(20)

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(3) Boundary conditions near the soil layer: Ui = U j

(21)

1 dU j 1 dUi = ρi dn ρ j dn

(22)

where, n is the outer normal, pointing from the ground to the air, and ρ is the charge density. After the boundary conditions are applied, the grid is divided to calculate the potential distribution in the area.

3 Construction of Earth Resistivity Model The magnetotelluric sounding profiles near the grounding electrode are collected and divided by vertical grids. The Xiamen-Guidong section is taken as an example for grid division, as shown in Fig. 2. Extract the raw data of earth resistivity, as shown in Table 1. The 3D model is horizontally divided into 100 layers. The horizontal grid division is adopted for each layer. The nodes falling within the magnetotelluric sounding range are used as the original earth resistivity nodes, and the points outside the measuring area are used as the prediction points. Based on the structural analysis, the spherical and exponential variograms are used to solve the Kriging equation (18).

Fig. 2 Xiamen–Guidong section grid node

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Table 1 Resistivity data of grid nodes of Xiamen East Guangxi profile Column

Row 1

2

3

4

5

…

1

3

3

3

3

3

…

2

2

2

3

3

3

…

3

2

2

2

2

2

…

4

2

1

1

1

2

…

5

2

1

1

1

2

…

…

…

…

…

…

…

…

⎧ h = 0 ⎪ ⎨0 [ ( )3 ] h ≤ a Z (h) = c · 23 ah − 21 ah ⎪ ⎩ c h >a

(23)

where c is the base value; a is the range; h is the lag distance; Z is the earth resistivity spatial prediction. The longitude and latitude coordinates and earth resistivity data of all nodes (including the original data nodes of MT depth profile of each layer and the unknown resistivity nodes of horizontal profile) on the horizontal profile of layer 100 in Fig. 1 are extracted. The colour of each node represents the resistivity value. Using the multi seed regional growth method, select the appropriate “seed” and “growth radius” to decompose the scattered point geoelectric structure regionally to form a layered geoelectric structure model, as shown in Fig. 3a, superimpose and integrate the block resistivity structures of each layer, merge the layers with the same resistivity into blocks, and form a three-dimensional block geoelectric structure model, as shown in Fig. 3b. The layered model and MT profile continuation model are established for comparison by using the methods in [5, 6].

4 Example Analysis 4.1 Calculation Results of Bias Current By combining the three kinds of earth electrical structure model with the structural parameters of Jiangsu power grid, the DC current of the neutral point of the transformer near the grounding electrode is calculated when the grounding current is 5000 A. Because the Baihetan-Jiangsu HVDC transmission project has not been completed, there is no measurement data, in order to verify the accuracy various earth resistivity models. It is compared with the measured values of the DC bias current of the AC power station near the Nanjing converter station and the Taizhou converter station in the ‘Ximeng-Taizhou ±800 kV UHVDC transmission project

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(a) point-like zonal earth resistivity

(b) Kriging geoelectric structure model Fig. 3 3D earth resistivity model

system commissioning second stage Jiangsu power grid transformer DC bias test report’ and ‘Jinbei-Nanjing ±800 kV UHVDC transmission project system commissioning period Jiangsu power grid transformer DC bias test report’, as shown in Table 2.

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Table 2 DC current data of transformer neutral point (5000 A working condition) Converter station

Name of main transformer

DCBC measured value/A

Uniform model/A

Layered model/A

Kriging model/A

Taizhou

Yandu

0.72

1.729

1.401

1.384

Shanghe

2.648

0.206

1.093

3.658

Chenbao

0.384

1.932

0.119

0.301

Lubei

1.44

0.205

2.894

2.541

Nanjing

Wansheng

0.736

0.303

0.992

0.896

Anlan

1.733

0.021

2.704

2.698

Liangdu

0.41

1.025

0.958

0.945

Guantan

0.50

1.114

1.207

1.023

Shuangsi

4.067

1.983

3.086

3.564

Huaian

0.767

0.898

0.852

0.848

Yutai

0.621

1.302

1.297

1.284

Comparing the calculated value and measured value of the transformer neutral point, although there is still some error between the calculated DCBC and the measured value based on the three types of geoelectric structures, the analysis shows that the geoelectric structure in Jiangsu is complex, there are a lot of rivers and lakes, and it is necessary to further adjust the land model. However, comparing the three models, it can be seen that the Kriging model has the highest accuracy, and the calculation error is within the acceptable range, which can meet the requirements of HVDC engineering calculation.

4.2 Distribution Law of Magnetic Bias Current It is defined that the proportion of DC current flowing in the earth from a certain depth underground to the surface to the current flowing into the earth is defined as the proportion factor. The penetration depth of the grounding current is shown in Fig. 4. Figure 4 shows that the current flowing into the ground from the grounding electrode will flow about 300 km underground. With the increase of the depth, the proportion of the current flowing underground to the current flowing into the ground decreases. The current flowing from the surface to the ground within 20 km accounts for about 80% of the total current, and the current flowing into the ground within 300 km underground accounts for about 3%. Therefore, both shallow and deep earth resistivity will affect the distribution of grounding current.

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Fig. 4 Penetration depth of grounding current

In the two types of geoelectric structures, two vertical profiles are respectively made with the grounding electrode position as the centre, and the current density distribution and resistivity distribution of the profile are shown in Fig. 5. Three types of geoelectric structure models are used to study the distribution law of current density. Due to the complexity of the structure, two symmetrical lines (red dotted lines in Fig. 5) 50 km on both sides of the grounding electrode of the three types of models are used to describe the current density on the take-up line, as shown in Table 3. It can be seen from Fig. 5 and Table 3 that the current density around the block with higher resistivity decreases, while that around the block with higher resistivity increases. In the Kriging geoelectric structure model, the earth resistivity of the block where point n3 is located is higher than that of point n3' at the same depth, and the current density of point n3 is greater than that of point n3' . This is mainly because when the grounding electrode current flows between different resistivity blocks, in order to ensure the continuity of the current, the current density suddenly changes at the boundary of different resistivity blocks, and the greater the difference in resistivity between different blocks, the greater the sudden change in current density. It can be seen that the difference of block resistivity will affect the current dispersion of the grounding electrode. The electric field intensity curves corresponding to the three geoelectric structure models in the near area of Maibu grounding electrode are shown in Fig. 6.

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30

2762

m1

m1'

1586

m2

m2'

1395

m3

m3'

10

m4

m4' 1095

5675

m5

10

m6

m6'

9325

m7

m7'

10

m8

m8'

4128

2102 1095

2141

10

m5'

124

(a) Depth profile and current density distribution of Kriging geoelectric structure model Fig. 5 Depth profile current density

Research on Distribution of Grounding Current Based on Different …

2762

k1

2028

k2

1395

k3

1095

k4

5675

k5

10

k6

9325

k7

10

k8

(b) Depth profile and current density distribution of layered geoelectric structure model Fig. 5 (continued)

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Table 3 Current density based on three earth models Points

Uniform model (A/m2 ) m1 –m8

m1 ' –m8 '

Layered model (A/m2 )

Kriging model (A/m2 )

k1 –k8

n1 –n8

n1' – n8 '

1

1.65E-05

1.41E-05

4.31E-06

4.21E-06

5.11E-06

2

1.38E-05

1.19E-05

3.54E-06

3.96E-06

3.87E-06

3

1.21E-06

1.23E-06

2.51E-06

3.61E-06

2.25E-06

4

1.95E-08

3.18E-05

5.48E-07

2.15E-07

–

5

5.2E-09

1.23E-09

3.73E-07

1.14E-08

3.69E-07

6

3.52E-12

4.28E-11

3.53E-07

8.74E-11

6.59E-10

7

2.26E-16

2.21E-16

2.91E-07

3.21E-13

6.59E-12

8

1.02E-17

1.02E-17

2.81E-07

5.12E-14

5.12E-14

By observing the resistivity curves of the three types of geoelectric structure models and the corresponding electric field strength curves, the position where the resistivity curve breaks is basically consistent with the position where the electric field strength curve breaks. This is mainly because the current has the characteristics of avoiding the high resistance body. The current density inside the low resistance body increases, while the current density above it decreases, and the electric field intensity curve produces a minimum value. High resistance body is opposite to the low resistance body. With the increase of depth, the back section of the electric field intensity curve appears smooth, mainly because the current has completely penetrated into the deep layer of the earth, while the earth resistivity around 300 km has little change. It can be seen from the deep earth resistivity of the area near the grounding that even at a depth of about 200 km, there may still be sudden change areas. Therefore, only building an earth resistivity model with a depth of 20 km will have an impact on the distribution of DC current. In the study, attention should be paid to the earth resistivity data from the surface to about 300 km underground. At the same time, the double integral on the observation surface after the electric field strength is divided by the resistivity is the current distribution. The above results indirectly confirm the accuracy of calculating the current distribution of the profile.

Research on Distribution of Grounding Current Based on Different …

(a) Earth resistivity of three models

(b) Electric field intensity curves of three models Fig. 6 Relationship between electric field strength and resistivity

53

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5 Conclusion (1) By comparing the penetration depth of DC current in three types of geoelectric structure models, the simulation structure shows that different geoelectric structure models will not affect the penetration depth of DC current. More than 50% of the incoming current will enter the deep ground more than 100 km, and about 3% of the incoming current will enter the deep ground 300 km underground. Therefore, it is far from enough to measure the earth resistivity of 20 km deep underground in the preliminary design of grounding site selection. (2) As the current tends to flow to the area with smaller resistance, the current avoids the area with higher resistance, resulting in a repulsive effect. However, the current flows to the area with low resistance, producing an attractive effect, which ultimately leads to the difference of current density and uneven distribution of the geoelectric field. In view of this situation, special attention should be paid to avoiding areas with high resistance near the grounding electrode in the future. (3) Comparing the relative error between the magnetic bias current calculated by homogeneous geoelectric structure model, layered geoelectric structure model and Kriging geoelectric structure model and the measured value, it proves that the Kriging model is more accurate in calculating the magnetic bias current. Acknowledgements This paper is supported by the project “Evaluation on the control of ground electrode and geomagnetic storm bias and the operation and maintenance strategy of the control device” (Grant: J2020030).

References 1. B. Zhang, L. Liu, Y. Liu et al., Effect of geomagnetically induced current on the loss of transformer tank. IET Electr. Power Appl. 4(5), 373–379 (2010) 2. Z. Wang, Risk assessment of power system oscillation instability based on geomagnetic storm events in the 24th solar cycle. IET Gener. Transm. Distri., IET Electr. Power Appl. 16, 137–148 (2022) 3. North American Electric Reliability Corporation (NERC), Effects of geomagnetic disturbances on the bulk power system (1994) 4. NERC,“2012 special reliability assessment interim report: effect of geomagnetic disturbances on the bulk power system (2012) 5. N. A. E. R. Corporation and the United States Department of Energy, High-impact, lowfrequency event risk to the north American bulk power system (2010) 6. K. Zheng et al., Effects of system characteristics on geomagnetically induced currents. IEEE Trans. Power Del. 29(2), 890–898 (2014) 7. Y. Liang, D.. He, H. Zhou, D. Chen, Optimal blocking device placement for geomagnetic disturbance mitigation. IEEE Trans. Power Deliv. 34(6), 2219–2231 (2019) 8. Benchmark geomagnetic disturbance event description. North Amer. Elect. Rel Corp., Atlanta, GA, USA, May 2016

Research on Distribution of Grounding Current Based on Different …

55

9. TPL-007-2 transmission system planned performance for geomagnetic disturbance events. North Amer. Elect. Rel Corp., Atlanta, GA, USA, May 2017 10. P. Yang, Y. Li, L. Liu., Optimal placement of grounding small resistance in neutral point for restraining voltage fluctuation in power grid caused by geomagnetic storm. IET Gener. Transm. Distrib. 13(8), 1456–1465 (2019) 11. J. Koen, T. Gaunt, Geomagnetically induced currents in the southern African electricity transmission network, in Proceeding of IEEE Bologna Technology Conference, Bologna, Italy (2003), pp. 1–7 12. J. Beland, K. Small, Space weather effects on power transmission systems: the cases of hydroquebec and transpower New ZealandLtd. Springer, Netherlands 176(8), 2550–2555 (2005) 13. T. J. Overbye, K. S. Shetye, T. R. Hutchins, Q. Qiu, J. D. Weber, Power grid sensitivity analysis of geomagnetically induced currents. IEEE Trans. Power Syst. 28(4), 4821–4828 (2013) 14. J. Chen, C. Liu, M. Wang et al., Power system responses to geomagnetic disturbances recognized using phasor measurement recordings. Int. J. Electr. Power Energy Syst. 113(10), 932–940 (2019) 15. S. Zhang, L. Liu, Research on the GIC governance scheme of the Xinjiang 750-kV power grid based on an equal allocation method. IEEE Access 8, 75419–75427 (2020) 16. M. Lu, H. Nagarajan, E. Yamangil et al., Optimal transmission line switching under geomagnetic disturbances. IEEE Trans. Power Syst. 33(3), 2539–2550 (2017) 17. M. Kazerooni, T.J. Overbye, Transformer protection in large-scale power systems during geomagnetic disturbances using line switching. IEEE Trans. Power Syst. 33(6), 5590–5999 (2018)

Key Factors Identification for the Energy Efficiency of Metro System Based on DEMATEL-ISM Chen Chen Zhang, Xue Mei Xiao, and Yan Hui Wang

Abstract A quantitative analysis method for identifying key factors influencing the energy efficiency of the metro system based on DEMATEL-ISM was proposed in response to the complex internal relationship of key factors. To be specific, a system of factors influencing the energy efficiency was established in terms of vehicles, operation organizations, and electromechanical equipment, with a focus on analysing the interactive relationship between the influencing factors. On this basis, a DEMATELISM model method system was put forward to analyse the importance of various factors using the centrality and cause degree of the influencing factors. Moreover, a multi-level hierarchical model for the factors influencing the energy efficiency was also built. Finally, the set composed of key factors of energy efficiency of the metro system was determined, providing theoretical support for the energy-saving optimization and system plan and design. Keywords Metro · Key factor identification · DEMATEL-ISM · Energy efficiency

1 Introduction The urban rail transit system has become an effective means of transportation to alleviate the increasingly intensive contradiction of supply and demand of transportation for its advantages of large capacity, safety and punctuality, energy saving and environmental protection. But energy consumption in system operation has soared with the growing scale of rail transit. For instance, the operating mileage of the urban rail transit system in Beijing reached 684.4 km, ranking the second in China, as of the end C. C. Zhang (B) · X. M. Xiao School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China e-mail: [email protected] Y. H. Wang State Key Laboratory of Rail Transit Control and Safety, Beijing Jiaotong University, Beijing 100044, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_5

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of December 2017. And the total annual energy consumption was about 1.4 × 109 kWh, its cost accounted for roughly 40% of the company’s total operating costs, leading to huge economic burden. Currently, scholars have achieved certain progress in the studies of energy consumption management and saving measures in the urban rail transit system. But most of the studies only partially probe into sub-systems [1–9]. Few studies have been conducted from a global perspective of the system analysis. This is because the analysis of factors influencing energy consumption is essential for energy conservation in the urban rail transit system, which has been performed by many scholars. But in most cases, only the association of a single element with energy consumption was analysed [10–14], with the lack of extensive discussions on the relevance and influence degree between various factors. Besides, there’s still no consensus on the definition of energy efficiency of the urban rail transit system and the relationship between energy consumption and energy efficiency. Furthermore, factors influencing the energy efficiency of the urban rail transit system have been rarely studied. The energy efficiency of the urban rail transit enterprise is to measure the energy utilization under the current technological level. From the perspective of output, it is the ability to acquire more outputs (passenger capacity) when the energy input of the urban rail transit operating company is certain. Besides, for input, it is the ability to minimize the input through fully utilizing current technologies when the output demands (passenger demands) are certain. On this basis, the efficiency of the urban rail transit system can be defined as: Definition 1 Energy efficiency of the urban rail transit system It is the ability to reduce energy consumption as much as possible through taking full advantage of present technologies when the demands for passenger flow of the urban rail transit system and the service level are constant, reflecting the efficiency of energy utilization. In this paper, a model for identifying key factors of influencing energy efficiency of the metro system was constructed using the DEMATEL-ISM method upon proposing the system of factors influencing the energy efficiency of the metro system. On this basis, key factors influencing energy efficiency of the metro system can be determined upon quantitatively analysing the comprehensive influence relationship and acting path between various factors, so as to provide a theoretical support and practical guidance for providing theoretical support for the energy-saving optimization and system plan and design.

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2 Analysis of Factors Influencing Energy Efficiency of the Metro System Metro is the main mode of urban rail transit. Based on literature research and field survey of the metro system in Beijing, this paper summarized 19 factors influencing energy consumption of the metro system from aspects of vehicle, operating organization, electromechanical equipment and seasons, and built a system for factors influencing energy efficiency of the metro system, as shown in Fig. 1. Influencing factors shown in Fig. 1 affect the energy efficiency of the metro system from a variety of aspects directly or indirectly, which are mutually influenced and restricted. According to the requirements of system modelling, an expert team consisting of 15 enterprise experts and university experts in related fields was formed to analyse the interactive relationship and degree of factors influencing energy efficiency of the metro system, as shown in Fig. 2.

Fig. 1 Factors influencing energy efficiency of the metro system

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Fig. 2 Interactive relationship of key factors influencing energy efficiency of the metro system

3 Analysis of Factors Influencing Energy Efficiency of the Metro System 3.1 DEMATEL-ISM Model Method The integration of the DEMANTEL (Decision Making Trial and Evaluation Laboratory)-ISM (Interpretive Structural Modelling) model can not only obtain the influence relationship between factors, but also reflect the influence degree between factors, effectively determine the casual relationship between factors and obtain the most profound key influencing factors [15, 16]. To identify the structural relationship and key factors of energy efficiency of the metro system, this paper derived the comprehensive influence matrix between various factors with DEMATEL as an auxiliary model and converted the comprehensive influence matrix into a reachable matrix input by the ISM model through threshold setting. On this basis, a multi-level hierarchical structure of factors influencing energy efficiency of the metro system was divided with ISM as the central model. Modelling steps of the identification model of key factors influencing energy efficiency of the metro system based on DEMATEL-ISM are presented in Fig. 3.

3.2 Analysis of the Importance of Influencing Factors Determination of the direct influence matrix. Factors of energy efficiency of the metro system are composed of vehicles, electromechanical equipment, operation

Key Factors Identification for the Energy Efficiency of Metro System …

Expert group

61

Determination of influnecing elements

Establish the direct influence matrix

Judgment of interactive relationship and degree between influencing elements, Threshold selection

Normalize the direct influence matrix Generate the comprehensive influence matrix Threshold selection Establish the reachable matrix

Non-conformance

Calculate the importance of the influencing element Problem setting Hierarchical division of the reachable matrix

Extract the skeleton matrix

Conformance

Explanation

End

Generate the multi-level hierarchical directed graph

Fig. 3 DEMATEL-ISM model method system

organization and others, which can be further divided into 19 sub-items of the influencing factor, marked as S1 , S2 , . . . , Sn (n = 1, 2, . . . , 19), respectively. A direct influencing matrix B is obtained between factors of energy efficiency of the metro system as per experts’ experience: ⎡

  B = B = bi j n×n

0 ⎢ b21 ⎢ =⎢ . ⎣ ..

b12 0 .. .

··· ··· .. .

⎤ b1n b2n ⎥ ⎥ .. ⎥ . ⎦

(1)

bn1 bn2 · · · 0

where, bi j is the direct influence degree of the influencing factor Si on S j , of which bi j = b ji , when i = j, bi j = 0. Value and meaning are shown in Table 1. Table 1 Values and meanings of bi j Influence degree

Strong

Relatively strong

General

Weak

No

Value

4

3

2

1

0

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Calculation of the comprehensive influence matrix. Factors in the direct influence matrix B were normalized using the linear proportion method to obtain the normalized direct influence matrix G = [gi j ]n×n . G=

max

1

n

1≤i≤n

j=1 bi j

Evidently, of which 0 ≤ gi j ≤ 1, and max

1≤i≤n

n

B

j=1 gi j

(2) = 1.

In the analysis, we discovered that the indirect influence relationship is also part of the relationship between influencing factors. Hence, a comprehensive influence matrix C = [ci j ]n×n was constructed to characterize the direct and indirect relationships between factors influencing the energy efficiency of the metro system. C = G + G2 + · · · + Gn =

n→∞

G(I − G n ) = G(I − G)−1 I −G

(3)

Calculations of influence degree and influenced degree of influencing factors. By adding the factors in each row of the comprehensive influence matrix C, the comprehensive influence of the influence factors corresponding to the row on other influencing factors can be obtained, which is the influence degree f i . It can be calculated in Eq. (4): fi =

n 

ci j , i = 1, 2, . . . , n

(4)

j=1

By adding the factors in each column of the comprehensive influence matrix C, the comprehensive influence of other influence factors on the influence factors corresponding to the column can be obtained and denoted as the influence degree ei . It can be calculated in Eq. (5): ei =

n 

c ji , i = 1, 2, . . . , n

(5)

j=1

Calculation of centrality and cause degree of influencing key factors. The centrality m i of the influencing factor Si reflects the comprehensive relationship between the influencing factor Si and other factors, which is calculated in Eq. (6). m i = f i + ei , i = 1, 2, . . . , n

(6)

where, f i represents the influencing degree of the factor Si ; ei represents the influenced degree of the factor Si ; the greater the value, the closer the relationship between

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the influencing factor and other influencing factors, and the higher the importance in the system. The cause degree n i characterizes the net impact of the influencing factor Si on other influencing factors, which can be calculated as shown in Eq. (7): n i = f i − ei , i = 1, 2, . . . , n

(7)

where, f i represents the influencing degree of the influencing factor; ei is the influenced degree of the influencing factor Si . If n i > 0, it indicates that the influence degree of the influencing factor Si on other factors is greater than that of other factors, which is considered as a cause factor with higher priority. If n i < 0, it means that the influence degree of other influencing factors on the influencing factors Si is greater than that on other factors, which is a result factor with lower priority.

3.3 Construction of Multi-level Hierarchical Model for Influencing Factors Calculation of the reachable matrix. By determining the appropriate threshold λ,  the reachable matrix K (K = ki j n×n ) can be calculated, specifically:

ki j = 1|ci j ≥ λ , (i, j = 1, 2, . . . , n)

(8)



ki j = 0|ci j < λ , (i, j = 1, 2, . . . , n)

(9)

Calculation of clustering coefficient of influencing factors. Clustering coefficients of the influencing factors can be employed to analyze the importance of influencing factors and further assisting in determining threshold selection, making the meaning expressed by the reachable matrix more abundant and reasonable. The clustering coefficient of the influencing factors Si in the reachable matrix refers to the ratio of the number of edges between Si and its neighboring nodes to the total number of possible edges. Hierarchical division of the reachable matrix. Hierarchical division of the reachable matrix can be expressed with π(K ) = {L 1 , L 2 , . . . , L l }, of which, L 1 , L 2 , . . . , L l represent the dividing hierarchy. Concrete steps are presented as follows: (i) List the reachable set R(Si ) and the leading set A(Si ) of the influencing factors Si according to the reachable matrix; (ii) Let L 1 = φ, j = 1;

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 (iii) L j = { Si ∈ K − L 1 − L 2 − · · · − L j  R j (Si ) ∩ A j (Si ) = R j (Si )}, of which R j (Si ) = { Si ∈ K − L 1 − L 2 − · · · − L j ki j = 0}, A j (Si ) = { Si ∈ K − L 1 − L 2 − · · · − L j k ji = 0}; (iv) When {K −L 1 −L 2 −· · ·−L j } = φ, the division is completed; when j = j +1, it will return to step (iii). Extraction of the skeleton matrix. In addition, a system skeleton matrix which is the most direct expression of the relationship of influencing factors in the system can be acquired through removing the strong connection factors, the cross-level binary relationship and the unit matrix (or its own influence on itself) from the reachable matrix. Influencing factors of the system were arranged hierarchically from top to bottom. At the same time, the reduced factors and its representative factors were supplemented at the same level. And the interactive relationship between both was identified. Specifically, the relationship between the factors of each level was expressed using directed arc from bottom to top with the supplementation of necessary cross-level relationship. On this basis, a multi-level hierarchical structure model was constructed.

4 Results Analysis The expert group illustrated the composition of factors influencing energy efficiency of the metro system as per their experience, defined the direct influencing factors for acquiring the direct influence matrix B. Moreover, the direct influence matrix was normalized and using the linear ratio method according Eqs. (2) and (3) together with relationship supplementing, so as to influence the matrix in a comprehensive manner.

Key Factors Identification for the Energy Efficiency of Metro System … S1 S1 S2 S3 S4 S5 S6 S7

B

S8 S9 S10 S11 S12 S13 S14 S15 S16

S2

S3

S4

S5

S6

S7

S8

S9

S10

S11

S12

S13

65 S14

S15

S16

0 4 0 3 0 0 0 0 0 2 0 0 0 0 2 0 0 2 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 1 0

0 0 0 0

0 0 0 0

0 0 2 0

0 0 0 0

2 2 0 1

0 0 0 0

0 0 0 0 0

0 2 0 0 0

0 0 4 0 0

0 0 0 0 0

0 2 0 0 0

0 0 0 0 0

0 0 0 0 0

0 4 0 0 0

0 0 3 0 0

0 3 3 0 0

0 0 0 0 0

0 0 0 0 0

3 0 0 0 0

0 0 4 3 0

0 0 4 0 4

0 0 0 0 0

0 0 0 0

0 0 2 0

0 0 0 0

0 0 0 0

0 0 0 0

0 3 0 0

0 4 0 0

0 4 0 0

0 3 0 0

0 3 0 0

0 2 0 0

0 0 0 0

0 0 0 0

0 0 0 0

2 2 2 3

0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

To clarify the importance of factors influencing energy efficiency of the metro system, the cause and result factors in the energy efficiency of the metro system are calculated, as shown in Fig. 4. According to the cause degree, passenger flow volume S12 , operation frequency S8 , load factor S7 , and train weight S1 are the top four key cause factors selected from cause factors. At the same time, load of EMCS S15 , classification plan S10 , efficiency of train traction motor S2 and running kilometrage S14 are the top four key result factors selected as per the influenced degree from the result factors. Besides, the intimacy (importance) of the interactive relationship between the influencing factors and other factors in the system can also be estimated as per the value of the centrality. The load of EMCS S15 has the maximum centrality, followed by passenger flow volume S12 , operation frequency S8 , and load factor S7 . These four factors were regarded as the main influencing factors. Moreover, load of EMCS S15 , passenger flow volume S12 , operation frequency S8 , load factor S7 , train weight S1 and efficiency of train traction motor S2 can be determined as key factors influencing energy efficiency of the metro system with comprehensive considerations in calculation results of centrality and cause degree. The set of optional values for the threshold λ is set in accordance with experts’ experience. And variations in the clustering coefficients of the influencing factors under different threshold conditions are shown in Fig. 5. As the fundamental purpose of threshold setting is to shield the relationship with small influencing factors for simplifying the system structure, contributing to the subsequent analysis. To ensure

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Fig. 4 Cause and result factors influencing energy efficiency of the metro system

the accuracy and rationality of the expression of system relationship, clustering coefficients with greater influencing factors under different thresholds were compared with the analyzed key factors. It can be found that the coincidence rate is high when λ = 0.0128. Key factors in coincidence include passenger flow volume S12 , operation frequency S8 , load factor S7 , train weight S1 , and efficiency of train traction motor S2 . Further, the expression of system relationship can be retained to the maximum extent. Hence, the reachable matrix K at λ = 0.0128 was selected as the input of the ISM model. S1 S1 S2 S3 S4 S5 S6 S7

K

S8 S9 S10 S11 S12 S13 S14 S15 S16

S2

S3

S4

S5

S6

S7

S8

S9

S10

S11

S12

S13

S14

S15

S16

0 1

0 1

0 0 0 0 0 1

0 0 0 0 1

0

0 1 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 1 0

0 0 0 0

0 0 0 0

0 0 1 0

0 0 0 0

1 1 0 1

0 0 0 0

0 0 0 0 0

0 1 0 0 0

0 1 1 0 0

0 0 0 0 0

0 1 0 0 0

0 0 0 0 0

0 0 0 0 0

0 1 0 0 0

0 1 1 0 0

0 1 1 0 0

0 0 0 0 0

0 0 0 0 0

1 0 0 0 0

0 1 1 1 0

0 1 1 1 1

0 0 0 0 0

0 0 0 0

0 1 1 0

0 1 0 0

0 0 0 0

0 0 0 0

0 1 0 0

0 1 0 0

0 1 0 0

0 1 0 0

0 1 0 0

0 1 0 0

0 0 0 0

0 1 0 0

0 1 0 0

1 0 1 1 1 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

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Fig. 5 Variations in the clustering coefficient under different thresholds

Factors influencing energy efficiency can be extracted from the skeleton matrix that is hierarchically divided as per the reachable matrix. And then, a multi-level hierarchical diagram of factors influencing the energy efficiency of the metro system is obtained, as shown in Fig. 6. Load of EMCS S15 at level 1 in Fig. 6 is the most intermediate factor that influences the energy efficiency of the metro system, which is in conformity with our experience. And the passenger flow volume S12 at level 9 is the most fundamental factor influencing energy consumption in the metro system. In other words, controlling passenger flow volume is the most effective way to control the energy efficiency of metro system. But it is impossible to control passenger flow volume for enhancing the energy efficiency due to the quasi-public characteristics of the metro system, which is inconsistent with the original intention of constructing the metro system. What’s more, the efficiency of energy utilization is improved through making the full use of existing technologies on the premise of safeguarding that both passenger demands and service levels are satisfied, according to the definition of the energy efficiency of the metro system. Upon tracking the upper level, it can be found that load factor S7 , operation frequency S8 , utilization rate of regenerative breaking S3 , and train weight S1 are fundamental factors that influence the energy efficiency of the system apart from passenger flow volume S12 . Then, combined key factors obtained from the centrality and cause degree, the set of key factors influencing energy efficiency of the metro system was determined as {load of EMCS S15 , passenger flow volume S12 , operation frequency S8 , load factor S7 , train weight S1 , efficiency of train traction motor S2 , and utilization rate of regenerative breaking S3 }.

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Fig. 6 Multi-level hierarchical structure of factors influencing energy efficiency of the metro system

5 Conclusion A quantitative analysis method for identifying key factors influencing the energy efficiency of the metro system based on DEMATEL-ISM was proposed in response to the complex internal relationship of key factors. In this paper, the following conclusions are obtained: (1) A system of factors influencing energy efficiency of the metro system from perspectives of vehicles, operation organizations, electromechanical equipment and others is established. (2) An identification model of key factors influencing the energy efficiency of the metro system based on DEMATEL-ISM is put forward in accordance with the expert group’s analysis on the interactive relationship between the factors.

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(3) The set of key factors influencing energy efficiency of the metro system is determined as {load of EMCS S15 , passenger flow volume S12 , operation frequency S8 , load factor S7 , train weight S1 , efficiency of train traction motor S2 , and utilization rate of regenerative breaking S3 }. Among them, the load of EMCS S15 is the most intermediate factor that influences the energy efficiency of the metro system, and the passenger flow volume S12 is the most fundamental factor influencing energy consumption in the metro system. Acknowledgements The paper was supported by the National Key Research and Development Program of China (Contract NO. 2017YFB1201105), Young and Middle-aged Teacher Education Research Project of Fujian Province (No. JAT200491), Young Teacher Research and Development Project of Xiamen University of Technology (Grant No. XPDKQ18004), and Natural Science Foundation of Fujian Province (Contract No. 2022J011248).

References 1. A. Nasri, M.F. Moghadam, H. Mokhtari, Timetable optimization for maximum usage of regenerative energy of braking in electrical railway systems, in Power Electronics Electrical Drives Automation and Motion (SPEEDAM), International Symposium on Power Electronics Electrical Drives Automation and Motion, Pisa, Italy (2010), pp. 1218–1221 2. R. Barrero, X. Tackoen, J.M. Van, Stationary or onboard energy storage systems for energy consumption reduction in a metro network. Proc. Inst. Mech. Eng. Part F: J. Rail Rapid Transit. 224, 207–225 (2010) 3. B. Guan, X. Liu, T. Zhang et al., Energy consumption of subway stations in China: data and influencing factors. Sustain. Cities Soc. 43, 451–461 (2018) 4. D. He, Y. Yang, Y. Chen et al., An integrated optimization model of metro energy consumption based on regenerative energy and passenger transfer. Appl. Energy 264, 114770 (2020) 5. M. Liu, C. Zhu, H. Zhang, W. Zheng et al., The environment and energy consumption of a subway tunnel by the influence of piston wind. Appl. Energy 246, 11–23 (2019) 6. F.M. Gomes, A.D.O.E. Aguiar, L. Vils, The influence of trains control system modernization on the energy consumption in the Sao Paulo subway. Energy Sustain. Dev. 47, 1–8 (2018) 7. S. Pan, H. Wang, F. Pei et al., An investigation on energy consumption of air conditioning system in Beijing subway stations. Energy Procedia 142, 2568–2573 (2017) 8. Z. Su, X. Li, Sub-system energy model based on actual operation data for subway stations. Sustain. Cities Soc. 52, 101835 (2020) 9. S. Yang, J. Wu, X. Yang et al., Analysis of energy consumption reduction in metro systems using rolling stop-skipping patterns. Comput. Ind. Eng. 127, 129–142 (2019) 10. A. González-gil, R. Palacin, P. Batty et al., A systems approach to reduce urban rail energy consumption. Energy Convers. Manag. 80, 509–524 (2014) 11. Y.M. Wang, Quantification Analysis on the Energy Factors of the Urban Rail Transit System (Beijing Jiaotong University, 2011) 12. W. Wang, Research of Energy Efficiency and Its Influence Factors of the Metro Based on Cointegration Analysis (Hebei University of Technology, 2012) 13. L. Shi, J. Zhang, X. Li, Importance analysis of influencing factors of traction energy consumption for urban rail transit based on grey correlation degree, in National Smart City and Rail Transit Academic Conference, Suzhou (2016), pp. 12–15 14. H.W. Yuan, L.Y. Kong, Study and calculation of influencing factors on urban rail transit energy consumption. Urban Rapid Rail Transit 25, 41–44+73 (2012)

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15. K.F. Xie, Z.M. Liu, Factors influencing escalator-related incidents in China: a systematic analysis using ISM-DEMATEL method. Int. J. Environ. Res. Public Health 16, 2478 (2019) 16. Y.M. He, J. Kang, Y.L. Pei et al., Research on influencing factors of fuel consumption on superhighway based on DEMATEL-ISM model. Energy Policy 158, 112545 (2021)

A Design of Embedded Servo Measurement and Control System in High Performance Yunqi Guo, Yuanyin Wang, Yuchen Liang, Zikou Yu, and Yafei Zhang

Abstract Using embedded technology and virtual instrument technology, an embedded measurement and control system is designed. The system combines control, test and analysis functions in one, in addition to a variety of bus communication capabilities. The hardware part of the system adopts dual FPGA structure of master–slave mode. At the same time, the peripheral devices are equipped with multiple bus communication modules. In order to realize the data interaction with the computer system, the 100 megabit Ethernet communication module is also used. The upper computer software of the system uses Labview development platform, which can realize the automation and intelligent design of the measurement and control software. After testing, the system has the characteristics of universality, portability, simple operation and stable operation, which can meet the measurement, control and analysis of most types of servo systems at present. Keywords Embedded system · Multiple bus communication · Servo system measurement and control · Portable

1 Introduction With the continuous development of servo technology and the expansion of modern production scale, the demand for servo system in various industries (industrial robots, rail transit, aerospace, etc.) is increasing day by day. At the same time, the requirements for its performance are increasing day by day, which requires higher performance and more functional servo measurement and control system to ensure the comprehensive and accurate servo system testing. Based on this, this paper designs and develops a universal comprehensive measurement and control system which is suitable for various types of servo systems. The system has the characteristics of multi-function, high performance, universal and portable, which can provide Y. Guo (B) · Y. Wang · Y. Liang · Z. Yu · Y. Zhang Beijing Institute of Precision Mechatronics and Controls, Beijing, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_6

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complete detection means and measurement control scheme for dynamic and static performance analysis of the servo system [1].

2 Overall Design of the Measurement and Control System The system must meet the following requirements: • Realizing the switch of the working mode. Considering the demand of servo system measurement and control in the external field, And in order to give full play to the portable characteristics of the measurement and control system, an embedded measurement and control box is designed, which is separated from the upper computer. When the external field testing, we’ll only need to carry a control system with a portable computer composed of embedded measurement and control box. • Realizing the function of typical signal generation. In order to obtain various key performance indicators of the servo system, the measurement and control system needs to generate a variety of typical signals to stimulate the servo system, so as to test its steady-state and dynamic response ability. • Realizing the function of data analysis. The ultimate purpose of this measurement and control system is to examine the performance of all aspects of the servo system through the analysis of the collected data, so the analysis ability of the collected data is a core function. • Realizing the function of friendly human-computer interaction. In order to better meet the operation needs of testers, the measurement and control system also needs to have a good human-computer interaction ability, that is, convenient parameter configuration way and friendly interface display ability. • Realizing the function of universality. This measurement and control system needs to be suitable for a variety of servo systems, so a variety of bus test interfaces are provided on the hardware, and corresponding test and analysis functions are reserved on the upper computer software. In order to meet the above requirements, this measurement and control system not only needs to have a variety of data communication methods and good human– computer interaction function, but also can automatically display, record, process and analyze data. Overall consideration, the system adopts the distributed structure design scheme of “upper computer—lower computer”, The portable industrial computer with powerful data processing ability is used as the upper computer, and the embedded system with high integration, diverse functions and high communication rate is used as the lower computer. The upper computer is used for signal generation, curve display, data analysis, human–computer interaction and automated testing. The lower computer realizes the transmission of instruction signals and the acquisition of measurement data [2]. The overall framework design of the system is shown in Fig. 1.

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Embedded measurement and control system Portable industrial computer and humancomputer interaction interface Ethernet

Embedded measurement and control box RS422 or CAN bus

Single machine servo system

1553B bus

Assembly machine servo system

AD collection

sensor

Fig. 1 The overall design diagram of the system

The measurement and control system will have the ability to test servo products in various modes. In the single machine mode, it connects with the single machine servo driver through CAN bus and 422 bus interface to test the performance of the single machine servo system. In the assembly mode, the servo system is connected through the 1553B bus and the analog signal acquisition interface [3]. After sending the control command, it receives the 1553B measurement signal and the analog signal of the angular displacement sensor. Then the data analysis and processing are carried out to test the various test characteristics of the servo products [4].

3 Hardware Design of the System The key of system design is the hardware of the lower computer, the lower computer uses the embedded system design. In the meanwhile, the embedded system design using a modular concept, and a variety of communication modules are integrated on a board: 1553B, CAN, 422, AD/DA analog acquisition and output. In order to reduce the volume of the board, the board adopts BGA package and eight layer PCB circuit board design. At the same time, the embedded system uses a dual FPGA chip structure of “master–slave mode” to ensure high speed data transmission, and the block diagram is shown Fig. 2.

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Main FPGA (XC7A75TFGG676)

SDRAM 16M*16bit

Ethernet interface

Parallel data bus 32 bit 16bit uplink, 16bit downlink 1553B interface

AD/DA interface

Deputy FPGA (XC7A75TFGG676)

RS422 interface

CAN interface Fig. 2 Design diagram of embedded board hardware

3.1 Design and Selection of the Main Control Part The main control part is responsible for data storage, processing, packaging and driving Ethernet communication interface module to communicate with the upper computer. At the same time, it also has the function of actively communicating with the slave chip and sending down the command. Xilinx ArtiX-7 series XC7A75TFGG676 is selected as the main FPGA, which adopts 28 nm process, low cost, low power consumption, internal integration of enhanced MicroBlaze soft processor. In order to achieve faster embedded processing, the chip uses more than 200,000 logic units, and the operating clock rate can be up to 200 MHz. In the speed and resources, can meet the requirements of the design [5]. In order to solve the problem of large amount of data communication between the embedded system and the upper computer, the Ethernet interface chip adopts W5300 network communication chip, which integrates 10/100 M Ethernet controller, MAC and TCP protocol stack. The hardware connection relationship between it and FPGA is shown Fig. 3.

clk rst

addr [9:0] data [15:0] cs_n FPGA rd_n

addr [9:0] data [15:0] cs_n W5300 rd_n

wr_n

wr_n

reset

reset

Fig. 3 Schematic diagram of the W5300 hardware interface

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3.2 Design and Selection of Deputy Control Part The slave control part is responsible for the command control, status acquisition and data management of each communication interface, including 1553B bus communication, CAN bus communication, RS422 serial communication, AD analog signal acquisition, etc. At the same time, the data received by each communication interface is packaged and uploaded to the main control part through the parallel bus. The deputy FPGA is responsible for IO port input and output control, data and instruction sending management, status and data receiving management [6]. The deputy FPGA chip is responsible for IO port input and output control, data and instruction sending management, status and data receiving management, etc. Its selection also uses the same chip as the main control part, the powerful processing power of the chip can meet the needs of the design. The CAN bus communication, RS422 serial communication and AD analog signal acquisition chip of the slave control part adopt the general control chip on the market, and the HI-1573 of HOLT Company is used as the 1553B bus transceiver, which can realize the signal conversion between the unipolar Manchester II code and the bipolar Manchester II code. The 1553B module adopts standard double redundancy design, which can automatically switch to another bus transmission mode in case of data transmission error in one bus. The following Fig. 4 is the interface design of 1553B digital bus communication in the embedded module [7].

4 Software Design of the System The software design of this system includes the software design of the lower computer and the software design of the upper computer. The software function of the lower computer is mainly the logic drive of the control chip to each functional interface. The main functions of the upper computer software are automatic testing, good human–computer interaction and automatic data processing.

Deputy FPGA

1553 B bus

Channel 1 Isolation transformer

Channel 2

HI-1573 transceiver

BC RT BM

Storage Control

RAM1

BC Isolation transformer

HI-1573 transceiver

BT BM

Fig. 4 The design diagram of the 1553B bus external interface

Storage Control

RAM2

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Main controller SDRAM data storage driver module

Network communication control driver module The data transmission module of parallel bus Parallel bus communication

Deputy controller

The data transmission module of parallel bus

RS422 Serial port control driver module

1553B bus protocol parsing module

CAN bus control driver module

AD collection control driver module

Fig. 5 Block diagram of embedded software system

4.1 The Software Design of the Lower Computer The software of the lower computer is divided into master control software and slave control software, and the two sets of software are respectively written into two FPGA control chips. The software system block diagram is as follows (Fig. 5). The master control software completes the driver functions of the W5300 network communication chip, SDRAM data storage chip and parallel bus communication, at the same time, the driver functions of each bus communication interface module and parallel bus communication are completed from the slave control software. This part of the design is based on the modular design idea, each module is independent and cooperates with each other, so as to reduce the difficulty of the design, and make the maintenance of the system becomes more simple. Xilinx ISE software and Verilog HDL language are used to carry out modular design for each communication bus, which includes code implementation, function simulation, logic synthesis, layout and wiring, board level debugging, and so on. Finally, the functions of each communication module are realized [8].

4.2 The Software Design of the Upper Computer The upper computer software needs to have good human–computer interaction function and automatic test function. The Labview development platform of NI company has the characteristics of strong human–computer interaction ability, convenient visualization and simple user interface, so the upper computer of the system uses Labview to develop the upper computer software.

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In order to realize the automation of the test software of the upper computer, a modular design method is adopted. After the test parameters are configured for the first time, each execution module executes in turn, and finally the test data required by the tester is displayed on the main interface. The main program of the test platform software mainly includes: initialization and self-test module, test item selection module, parameter configuration module, data acquisition, analysis, display, storage module, and the final data processing and report generation module.

5 System Test The embedded servo measurement and control system has carried out the communication performance test of 1553B bus, CAN bus and the servo system assembly test, as well as recorded the waveform on the communication line with oscilloscope.

5.1 The Performance Test of 1553B Bus and CAN Bus Communication In the 1553B bus communication mode, the measurement and control system is connected with an RT device and set as the 4 M/s data transmission rate. Each message sends 32 words of effective data with an interval of 140us. The waveform on the communication line is monitored by an oscilloscope. According to the calculation, the data transmission rate per second is 3.657 Mbit, plus the status words of the data head and tail, etc., meet the communication rate of 4 M per 1553B channel. In the CAN bus communication mode, the measurement and control system is connected to a CAN communication device with the USB interface. Through the parameter setting module, the message sending interval is set to 125us. The waveform on the communication line is monitored by the oscilloscope. As can be seen from the above figure, the data waveform display is good, with no large distortion. Through calculation, the data transmission rate per second is 512 Kbit, plus the information of frame head and frame tail, meeting the rate of 1 M for each CAN communication (Figs. 6, 7).

5.2 Servo System Assembly Test In order to carry out the system assembly test, the measurement and control system communicates with a servo system through the 1553B bus. The test equipment includes: embedded measurement and control system, servo control driver, servo actuator, test bench for simulating load, etc. The experiment simulates the working

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Fig. 6 The monitoring waveform of 1553B bus communication

1V per vertical grid

40us per horizontal grid

Fig. 7 The monitoring waveform of RS422 bus communication

1V per vertical grid

100us per horizontal grid

characteristics of the servo system under various load conditions. Through the measurement and control software of the upper computer, the control command is issued, the test data is collected, and the test data is automatically stored and analyzed. The test results are as follows in the Table 1. Table 1 Test results of servo position characteristics Data analysis of location characteristics The name of the data Positive maximum instruction (°) Negative maximum instruction (°) Positive maximum route (°) Negative maximum route (°) Maximum swing Angle in one direction (°) Ring width (°) Current zero offset (°) Nominal position gain (°/°)

The processing results The technical requirements 30.000 −29.996 30.003 −30.000 30.001

≥29.5 ≤−29.5 ≥29.5 ≤−29.5 ≥29.5

0.076

≤0.2

−0.013

≤0.1

1.000

≤1.05, ≥ 0.95

Linearity (%)

0.112

≤0.2

Position symmetry (%)

0.032

≤0.3

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The experimental results meet the performance indexes of the servo system, indicating that the embedded measurement and control equipment has the automatic test ability of the servo system.

6 Conclusions Using embedded technology and virtual instrument technology, a multi-function automatic servo measurement and control system is designed. The hardware and software design of the system are discussed in this paper. The performance of several kinds of bus communication is verified by experiments and the conclusion is drawn. The structure design of upper computer—lower computer used in this measurement and control system can flexibly adapt to a variety of test scenarios. The software and hardware adopt the modular design idea to realize the integration of multibus communication functions, and make up for the large volume and weight of the traditional PXI/PCI measurement and control equipment, so that this system becomes a multi-function comprehensive measurement and control system.

References 1. Y.L. Li, Design and implementation of embedded human-computer interaction interface based on FPGA (Beijing Institute of Technology, Beijing, 2016) 2. Y. Li, Dynamic reconfigurable design of general bus based on FPGA (Nanjing University of Aeronautics and Astronautics, Nanjing, 2016) 3. J.K. Zhang, Design and research of 1553B bus remote Terminal based on FPGA (Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, 2016) 4. J.J. Lei, Y.Y. Fan, Load measurement and control system of electric servo valve based on LabVIEW. Mach. Tool Hydraul. 47(2), 118–123 (2019) 5. S.L. Yang, C. Li, L. Yu, Design of core module of embedded communication system based on FPGA. Mod Electron Technol 41(22), 88–91 (2018) 6. H. Ren, Research on the application of 1553B bus interface in comprehensive measurement and control system (Harbin Institute of Technology, Harbin, 2016) 7. W.F. Shang, Design and implementation of data converter between 1553B bus and CAN bus based on FPGA (Xidian University, Hangzhou, 2015) 8. W. Li, Development of servo mechanism resonant frequency test system based on virtual instrument (Xidian University, Xi’an, 2014)

Calculation and Simulation Model of Three-Dimensional Electric Field Distribution of Porcelain Insulator String Deterioration Based on Passive Electro-optic Field Strength Sensing Technology Xun Wang, Xinyang Guo, Feiran Wang, Zhenlong Ren, and Zilong Hou

Abstract The three-dimensional electric field distribution calculation simulation model of the porcelain insulator string deterioration based on the borderless electrooptic field strength sensing technology is designed to effectively detect the deteriorated porcelain insulator string in the transmission line, prevent the porcelain insulator string falling off of the transmission line, and ensure the safe and stable operation of the power system. The three-dimensional electric field distribution simulation model of porcelain insulator string is constructed, and the sensor decoupling calibration method based on borderless electro-optic field strength sensing technology is used to accurately collect the three-dimensional electric field data of the porcelain insulator string; Judge whether the porcelain insulator string is deteriorated according to the three-dimensional electric field distribution of the output porcelain insulator. The experimental results show that this method can realize the three-dimensional electric field calculation of porcelain insulator string, effectively detect the deterioration of porcelain insulator string, and provide a reliable guarantee for the safe and stable operation of the power grid. Keywords Passive electro-optic field strength · Porcelain insulator string · Three dimensional electric field distribution · Decoupling calibration · Evidence theory · Data fusion

X. Wang · X. Guo (B) · F. Wang · Z. Ren · Z. Hou EHV Branch of State Grid Jibei Electric Power Co., Ltd., Beijing 102488, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_7

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1 Introduction In actual power work, the operating status of the transmission line is directly related to whether the power grid can operate safely and stably [1]. Insulator is an important part of the transmission line, where the degree of deterioration directly affects the safety and stability of the entire transmission line; once the insulator string deteriorates after the occurrence of the string drop phenomenon, not only the transmission line cannot work normally, the stability of the entire power system will also be threatened, but also increase the probability of power accidents, resulting in huge economic losses and casualties [2]. Among the methods for detecting these deteriorated porcelain insulator strings, the more significant achievements include the research of Fu Weiping et al. based on the calculation simulation model of the three-dimensional electric field distribution of porcelain insulator deterioration based on the decision tree [3], and the research of Wan Xun et al. on the calculation model of the three-dimensional electric field distribution of porcelain insulator deterioration based on the microwave transmission method [4]. The above models can effectively detect and identify the deteriorated porcelain insulators in the transmission line, but when collecting the data for the deterioration detection of the porcelain insulator, which reduces the detection accuracy of the deteriorated porcelain insulator to a certain extent [5]. This paper proposes a simulation model for calculating the three-dimensional electric field distribution of porcelain insulator string deterioration based on the passive electric field strong sensing technology, and provides a reliable basis for effectively avoiding and reducing the occurrence of power accidents by measuring the three-dimensional electric field data around the porcelain insulator string of the transmission line and using a finite element software to output the three-dimensional electric field distribution of the porcelain insulator string.

2 Ceramic Insulator String Deterioration Three-Dimensional Electric Field Distribution Calculation Simulation Model 2.1 Porcelain Insulator String Electric Field Data Acquisition of Passive Electric Field Strong Sensing Technology The specific process of accurate acquisition of electric field data of porcelain insulators based on the technology of unconditional electro-optical field strength can be summarized as follows: (1) Construct a three-dimensional unbounded electro-optical field strength sensor porcelain insulator string electric field theoretical value calculation model [6, 7]. R, R0 and E t are used to represent the matrix of real-time output of the

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three-dimensional unrelated electric light field strength sensor, the zero electric field output matrix and the theoretical value of the porcelain insulator string electric field. (2) Perform the coding method and chromosomal gene number determination operations. In the calibration method herein, the gene string is determined as a chromosomal individual, represented by x, and the number of genes in the string is satisfied as 3m. Chromosomal individuals can be expressed with formulas as: x = {x1 , x2 , ..., xi , ..., x3m }

(1)

(3) Perform the genetic algorithm parameter setting operation. The parameter setting operation of the genetic algorithm mainly includes the setting of parameters such as objective function and fitness function, population size, maximum genetic algebra, and selection probability. Among them, J (X ), f (X ) and M represent the objective function, fitness function and population size, respectively; G and ps represent the maximum genetic algebra and the probability of selection, respectively. (4) Perform a population initialization operation. Any individual with a number of M is selected as the initial population to perform population initialization, and g is used to represent the algebra, in which case g = 1 should be satisfied. (5) Using A to represent the fitness value, the fitness calculation operation of each individual in the contemporary population is performed. (6) After calculating the value of the fitness degree, the value of each fitness is arranged from largest to smallest. (7) Perform a termination judgment operation. If g < G is satisfied, step (8) is performed, otherwise the calculation is terminated, and the individual with the largest fitness value is the optimal solution. (8) According to the selection, crossover, and variation operators, the population update operation is performed, and the epoch number g should satisfy g = g+1, and the relevant operation is performed in step (5).

2.2 Porcelain Insulator String Three-Dimensional Space Electric Field Data Fusion DS Evidence Theory The advantage of DS evidence theory in processing the electric field data information of porcelain insulator string is that it is possible to accurately collect the threedimensional electric field data of the porcelain insulator string based on the sensor decoupling calibration method of an unrelated electro-optical field strong sensing technology without mastering any prior information of the porcelain insulator string [8], which can improve the efficiency of data fusion [9, 10]. Its specific definition is as follows.

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The identification framework of the electric field data of the porcelain insulator string is defined by the formula as: θ = (δ1 , δ2 , δ3 , ..., δn )

(2)

The elements in formula (2) have the characteristics of two repulsions and discreteness. If 2θ is used to represent a porcelain insulator to cross-identify the various subsets within the framework of electric field data awareness, then correspondingly a map can be obtained, which can be expressed by a formula as: ⎧ m : 2θ → [0, 1] ⎪ ⎪ ⎪ ⎨ m(δ) = 0  ⎪ ⎪ m( A) = 1 ⎪ ⎩

(3)

A∈θ

In the above equation, m represents the mass function. Evidence theory Kalman filter porcelain insulator string electric field data fusion The electric field data information collected by multiple three-dimensional unrelated electro-optical field strength sensors for the deterioration detection of the porcelain insulator string, and the electric field filtering data information through the filter are used as evidence of the electric field data information of the porcelain insulator string. Performing the algorithm calculation operation of the evidence theory improvement algorithm for the electric field data information of the porcelain insulator string, using k to represent the time, the weight ratio of the electric field data information of the porcelain insulator string received by multiple three-dimensional unrelated electric light field strength sensors can be expressed by the formula as: ωk = [ω1k , ω2k , ..., ω N k ]

(4)

The new porcelain insulator string data information sequence obtained by performing data fusion operations on the electric field data information of the porcelain insulator string can be expressed by formula: Y =

N  i=1

Zˆ i ×

T 

ωkT

(5)

i=1

where T performs the transpose operation. Performing a Kalman filter operation on the new porcelain insulator string data information sequence can obtain the ideal effect of the porcelain insulator string data information [11].

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2.3 Porcelain Insulator String Degradation Detection Based on Finite Element Software The deterioration of the porcelain insulator string in the transmission line is often not directly caused by high voltage, but because the high voltage makes the field strength formed in the insulator string too strong, and the electric field distribution of the normal porcelain insulator string is relatively uniform, basically in line with the U-shaped distribution. Therefore, the deterioration state of the porcelain insulator strings can be detected by analyzing the field strength distribution of the insulator string [12, 13]. Compared with the current existing ceramic insulator string electric field analysis calculation method, the expression of the matrix makes the solution method more standardized and the processing method more flexible when solving complex problems [14, 15]. The electric field data information of the porcelain insulator string after fusion treatment is input into the finite element software, the electric field distribution map of the porcelain insulator string is obtained, and the distribution state is analyzed, which can realize the degradation detection of the porcelain insulator string.

3 Experimentation and Analysis Taking a transmission line as the experimental object, ANSYS software is used to simulate the erection environment of the transmission line, and the method applied to the porcelain insulator string degradation test of the porcelain absolute atomic string of the transmission line is applied to verify the performance of the proposed method in the degradation detection of the porcelain insulator string. In order to verify the advantages of this model in fusing electric field signals, the signal waveform graph obtained by applying this method and literature [3] is plotted and simulated by applying the method and literature [3] for the deterioration of porcelain insulators based on decision trees, and the signal waveform graph obtained by the 3D electric field distribution calculation model for porcelain insulator degradation based on the microwave transmission method as shown in Fig. 1. Analysis of Fig. 1 shows that although the three models can achieve electric field data fusion, the noise content of the fusion electric field data obtained by the application paper [3] and the literature [4] model is relatively large when the electric field data is fused, and the noise content of the fusion electric field data obtained when the electric field data fusion is applied to the model in this paper is small. Taking a certain porcelain insulator string on the transmission line as an example, the electric field distribution calculation operation of the porcelain insulator string is performed, and the performance of the model in this paper in the calculation of the electric field distribution of the porcelain insulator string is verified, and the calculation results obtained are as shown in Table 1.

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Fig. 1 Waveform plots of signals from different models

15

Ampli tude

10 5

0

-5 -10 0

30

60

90

120

150 180 Time/s

210

240

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(a) Waveform diagram of the model signal in the literature [3] 15

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Table 1 Calculation results of electric field distribution of porcelain insulator strings Porcelain insulator serial number

The maximum internal field strength (V/mm)

Maximum surface field strength (V/mm) 3916

1

37.84

2

13.39

636

3

9.67

492

4

4.36

193

5

6.39

300

6

9.31

603

7

13.63

646

8

17.12

924

9

6.78

253 1576

10

23.56

11

4.49

220

12

10.56

523

13

11.21

589

As can be seen from Table 1, the application of the method in this paper can realize the calculation of the internal field strength and surface field strength of the porcelain insulator string in the transmission line, and can provide reliable porcelain insulator string field strength data for the deterioration detection of the porcelain edge string.

4 Conclusion The application of this method can realize the calculation of the internal and surface field strength of the porcelain insulator of the transmission line, and the data can be applied to the deterioration detection of the porcelain insulator of the transmission line to better realize the detection of the degradation of the porcelain insulator of the transmission line. Although the method in this paper can realize the deterioration detection of the porcelain insulator string of the transmission line, the reasons affecting the deterioration of the porcelain insulator string of the transmission line are not deeply analyzed. In the next stage, in the research work on the porcelain insulators of transmission lines, the reasons for the deterioration of the porcelain insulators of the transmission lines will be analyzed in depth. Acknowledgements The study was supported by “Science and Technology Project of State Grid Jibei Maintenance Company (Grant No. SGJBJX00SJJS2100625)”.

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References 1. P. Wang, K. Li, J.H. Geng et al., Study on space electric field of 110 kV faulty porcelain suspension insulator. Electr. Meas. Instrum. 57(14), 93–98 (2020) 2. H.D. Yang, W.G. Li, W.G. Li et al., Circuit model of suspensive disc-type porcelain insulator string and simulation study on its power transmission characteristics. High Volt. Appar. 56(05), 79–85 (2020) 3. W.P. Fu, F.X. Shi, W. Wang et al., Discriminating threshold selection method and diagnosis of deteriorated porcelain insulator based on decision tree. High Volt. Appar. 55(04), 149–154 (2019) 4. X. Wan, Z.T. Liu, Z.X. Gong et al., Microwave transmission method for detecting deteriorated ceramic insulators. Insul. Surge Arresters 04, 207–214 (2020) 5. L.N. Wang, S.L. Jian, B. Song et al., Research on the detection of faulty insulator in transmission line based on electric field distribution measurement. Insul. Surge Arresters 34(04), 199– 205+212 (2019) 6. Y. Cheng, L.Z. Xia, Z.F. Li et al., Detection of faulty porcelain insulator based on infrared imaging method. Insul. Mater. 52(03), 74–79 (2019) 7. W.N. Qin, Y.Q. Fang, X.L. Lei et al., Electric field characteristics of 500 kV AC transmission line with defect composite insulators. Water Resour. Power 39(03), 176–179 (2021) 8. W.H. Wu, R. Zhang, J.C. Yuan et al., Distribution of electric field and optimization of antipollution flash coating parameters for factory-composited insulators. Electr. Power 52(01), 88–95 (2019) 9. Y.S. Li, X. Hua, X.R. Shen et al., Research and application of B-spline surface boundary element method for calculating ultra-high voltage insulator strings electric fields. Trans. China Electrotech. Soc. 33(02), 232–237 (2018) 10. C.J. Guo, H.W. Mei, Y. Ma et al., Influence of RTV coating on the electric field distribution of 220 kV insulator string. Yunnan Electr. Power 47(01), 32–35 (2019) 11. L.M. Wang, B.N. He, Y.D. Jie et al., Electric field distribution characteristics of insulator string under lightning overvoltage. Insul. Mater. 52(03), 63–68 (2019) 12. M. Jiang, L. Li, K. Hua et al., Influence of interface defect on the electric field distribution of composite insulator. Jiangsu Electr. Eng. 38(04), 138–144 (2019) 13. W. Cao, M.J. Luan, W. Shen et al., Effects of carbonization of insulator core rod on properties of electric field distribution. Electr. Mach. Control 22(11), 89–95 (2018) 14. K.K. Gu, L. Cheng, X.L. Xu et al., Moving mechanism design and simulation analysis of automatic detection device for the guide rail type deterioration insulator. Insul. Surge Arresters 34(01), 188–195 (2018) 15. L.B. Zhao, Y. Bi, L.X. Zhao, Simulation of electric field distribution in parallel gap of composite insulators for lightning protection lines. Comput. Simul. 36(07), 100–103 (2019)

Numerical Simulation of Resistive Current Extraction of 10 kV MOA M. A. Huijun, Wenming Hong, Yuqiang Li, Genghao Cai, Guoxing Wu, Qibin Cai, and Qiongqi Chen

Abstract Arresters can protect electrical equipment connected in parallel with them from the impact of voltage surges and ensure safety of the entire power system. Therefore, its normality is critical to the safe and effective operation of electrical equipment and power systems. A new method for measuring the resistive current of a zinc oxide lightning arrester based on the analysis of the current size when the grid voltage crosses zero is proposed. The theoretical derivation of the impedance current when the grid voltage contains harmonics is carried out, the leakage current characteristics of the lightning arrester are analysed, and the resistive leakage current is simulated and optimized. Keywords Numerical simulation · 10 kV · MOA · Resistive current

1 Introduction Arresters can protect electrical equipment connected in parallel with them from the impact of voltage surges and ensure safety of the entire power system. Therefore, its normal is critical to the safe and effective operation of electrical equipment and power systems. The arrester is often connected between the voltage bus and the earth and in parallel with the equipment to be protected. At present, metal oxide arresters (MOA) are the most popular [1, 2]. Early preventive tests on lightning arresters involved regular power cuts. There are two main methods used for such tests: one is to check the insulation resistance of zinc oxide lightning arresters to ascertain whether their internal insulation has been affected by water, porcelain cracks, or damage to the silicone rubber; the other was to measure the reference voltage U1mA and leakage current at 75% U1mA of zinc oxide M. A. Huijun (B) State Grid Quanzhou Power Supply Company, Quanzhou 362000, China e-mail: [email protected] W. Hong · Y. Li · G. Cai · G. Wu · Q. Cai · Q. Chen State Grid Anxi Power Supply Company, Anxi 362400, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_8

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arrester under DC, which can accurately and effectively find the insulation defects such as arrester penetration, deterioration by dirt, cracking of porcelain insulation and local loose fracture. However, both methods have shortcomings, making real-time measurements desirable [3]. Masume et al. proposed the time delay addition method (TDAM) to obtain resistive current components by shifting the total leakage current by 1/4f, adding, summing, constructing capacitive current, and subtracting the leakage current from the obtained capacitive current. This method is simple in principle, convenient for operation, and does not require the voltage at both ends of the arrester to be measured. However, in TDAM, the voltage at both ends of the arrester is assumed to be ideal, and the effect of harmonic voltage is not considered. When the voltage contains one harmonic, the resistive current calculated by this method shows obvious discrepancy. Duan et al. separated the active component of the leakage current through the orthogonal decomposition method to monitor the online status of the arrester. Goran et al. used a genetic algorithm to extract the resistive component of the leakage current based on the equivalent model of the arrester for online monitoring of the arrester [4, 5]. However, the algorithm requires a better understanding of the initial conditions, and so, it has certain limitations in practical application. Relevant research has broken the limitation that zinc oxide surge arresters are only tested on line under operating conditions, and more methods such as partial discharge test, infrared temperature measurement and insulation resistance are used to analyse the relationship between the aging degree of surge arresters and current, time, temperature and other parameters. Some experts also use the method of artificial neural network for comparative analysis to determine the remaining service life of MOA [6–8]. The test signals are usually obtained in the form of automatic test, local test and remote test. After the test signals are processed by the computer, they can form the basis for judging the operating state of zinc oxide arrester. In the process of live test of zinc oxide arrester, the interference effect of electromagnetic field in the environment is mainly considered, and varistor and microcontroller are used to resist its influence [9, 10]. In this paper, a new method of measuring the resistive current in zinc oxide arresters based on analysing the current when the grid voltage crosses zero is proposed, and the resistive leakage current is simulated and optimized.

2 Equivalent Circuit of Arrester The equivalent circuit diagram of the arrester is shown in Fig. 1. The current voltage vector diagram is shown in Fig. 2. In Fig. 1, C is the linear capacitance, R is the nonlinear resistance, ic is the capacitive current component, iR is the resistive current component, and I is the total leakage current of the arrester. The increase in the resistive current, which only accounts for 10–20% of the total leakage current, is the main factor that causes the deterioration of the MOA, and the

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Fig. 1 Equivalent circuit diagram of the arrester

Fig. 2 Arrester current voltage vector diagram

accurate extraction of its resistive current from the total leakage current is key to judging the operation status of the MOA. As the core component of the MOA, the zinc oxide resistor is a varistor with excellent nonlinear volt ampere characteristics. When the voltage is low, it presents a state of high resistance and low current flow, which not only reduces energy consumption but also prevents thermal collapse. When the voltage rises to the critical point, the current increases sharply and is released with high amplitude and large energy. Therefore, the overvoltage is limited to a reliable margin. The resistor is also called the valve piece, which functions as an automatic switch. The volt ampere characteristics of varistors can be expressed as:  I =

U C

a (1)

In the formula, U is the voltage on both sides of the varistor, I is the current passing through the varistor, and C is a constant related to the material. α is the nonlinear coefficient of the varistor, whose value is >1. The higher the value of α is, the better the pressure-sensitivity characteristic. The value of α can be obtained from the following equation by measuring the currents I 1 and I 2 flowing through the resistance and the corresponding voltages U 1 and U 2 :   lg II21 lg I1 − lg I2 α= =  . U1 lgU1 − lgU2 lg U 2

(2)

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3 Simulation of Resistive Current of the Arrester 3.1 Theoretical Derivation of Impedance Current When the Grid Voltage Contains Harmonics If the grid voltage contains the third harmonic, the voltage at both ends of the arrester can be expressed as: ⎧ ⎨

u a = U1m sinwt + U3m sin3wt ◦ u b = U1m sin(wt − 120 ) + U3m sin3wt ⎩ ◦ u c = U1m sin(wt + 120 ) + U3m sin3wt

(3)

where U 1m is the amplitude of the fundamental component of the grid voltage and U 3m is the amplitude of the third harmonic component of the grid voltage. Simultaneously, the total current of the A, B and C phases is: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

Ia (t) = Iar (t) + wC0 U1m cos(wt) + wC12 U1m cos(wt − 120◦ ) + 3w(C0 + C12 )U3m cos(3wt) Ib (t) = Ibr (t) + w(C0 − C12 )U1m cos(wt − 120◦ ) . + 3w(C0 + 2C12 )U3m cos(3wt) ◦ ◦ Ic (t) = Icr (t) + wC0 U1m cos(wt − 120 ) + wC12 U1m cos(wt − 120 ) + 3w(C0 + C12 )U3m cos(3wt)

(4)

By analysing the total current of the A, B, and C three-phase arresters when the instantaneous value of voltage at both ends is zero, it can be concluded that the total current of the A, B, and C three-phase arresters when the respective voltage is zero is:

|Ia0 | = |Ic0 | = w(C0 − 0.5C12 )U1m + 3w(C0 + C12 )U3m (5) |Ib0 | = w(C0 − C12 )U1m + 3w(C0 + 2C12 )U3m From the above formula, it can be deduced that C 0 and C 12 are:  2|Ia0 |−|Ib0 | C0 = wU 1m +3wU3m 2(|Ia0 |−|Ib0 |) C12 = wU1m −6wU3m

(6)

It can be concluded that the resistive current flowing through each phase arrester is ⎧ ⎪ ⎨

◦

3m Iar (t) = Ia (t) − mcos(wt) − ncos(wt − 120 ) − 3(m + n) U cos(3wt) U1m ◦ U3m Ibr (t) = Ib (t) − (m − n)cos(wt − 120 ) − 3(m + 2n) U1m cos(3wt) ⎪ ⎩ I (t) = I (t) − mcos(wt + 120◦ ) − ncos(wt − 120◦ ) − 3(m + n) U3m cos(3wt) cr c U1m (7)

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Therefore, if the full current value corresponding to the zero crossing of phase A, B, and C grid voltage is measured, the interference of the grid voltage harmonics and inter-phase coupling capacitance can be removed to accurately calculate the resistive current of the A, B, and C three-phase MOA. In addition, because the changes in the fundamental component and the third harmonic component of the resistive current indicate various MOA faults, in practical applications, the resistive current extracted by this method should be FFT decomposed to obtain the fundamental component and each harmonic component of the resistive current so that the judgment of MOA faults is more targeted.

3.2 Analysis of the Characteristics of Lightning Arrester Leakage Current The leakage current i x of the metal oxide arrester in the small current area is the sum of the resistive current i R associated with the nonlinear resistance and the capacitive current i c associated with the capacitor. i x = i R + ic

(8)

The resistive current in the arrester model in the low current area can be expressed as:  i R = I0

u U0

a (9)

In the model, the capacitive current i generated by grain boundary capacitance i c can be expressed as: ic = c

du dt

(10)

Therefore, the leakage current i of the metal oxide arrester i x can be expressed as:  i x = I0

u U0

a +c

du dt

(11)

Therefore, Eqs. (9) and (10) show that i R is in phase with U at both ends of the arrester, while i c is derived from the voltage derivative of the arrester, and so, is inversely related to voltage U at both ends of the arrester.

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It can be seen from the vector diagram that the leakage current i x can be decomposed into i R and i c . Meanwhile, i c is in phase with current I, while i R and U are in phase, and the relationship between them is orthogonal, which provides a theoretical basis for further research on the harmonic analysis and correction of metal oxide arresters.

3.3 Simulation The metal oxide valve is simulated and analysed, and the harmonic correction algorithm in the previous section is simulated and analysed through simulation platform toolbox. The equivalent model of the arrester in the small current area is used for simulation. When verifying the simulation, the nonlinear coefficient of the arrester α is 25. The operating voltage u is 10 kV, and the frequency is 50 Hz. The national standard stipulates that the amplitude of the harmonic voltage shall not exceed 5%, but there is no requirement for the initial phase. In the actual power grid operation process, voltage harmonics above three times are low. Therefore, this paper only considers the influence of the third harmonic voltage on the extraction result of the resistive current component and takes u of the third harmonic voltage value in simulation_ u 3 = 3%u. To clearly display the variation relationship of voltage, leakage current, and resistive current components under harmonic conditions, the three components are compared and analysed to obtain the waveform diagram of voltage, leakage current, and resistive current components with 3% third harmonic voltage, as shown in Figs. 3 and 4. Additionally, the waveform of the resistive current component extracted by the harmonic correction algorithm in the previous section is compared with the waveform of the actual resistive current component of the arrester measured during the arrester simulation, and the results are shown in Fig. 3. The comparison between the actual resistive current and the resistive current extracted by the harmonic correction algorithm is shown in Fig. 4. From Figs. 3 and 4, it can be concluded that the leakage current and resistive current of the metal oxide arrester are relatively stable, and the waveform has periodicity and symmetry, which conform to the actual operation of the arrester. The actual resistive current component in Fig. 4 is highly consistent with the waveform of the arrester resistive current component extracted by the harmonic correction algorithm in the previous section in most areas. At the moment when the resistive current amplitude crosses the zero point, the waveform of the resistive current component value extracted by the harmonic correction algorithm has a small jitter, which may be due to the influence of a small amount of high-order harmonics in the grid voltage and the internal harmonics generated by the metal oxide arrester’s own nonlinear components. In order to assess the feasibility of practical applications, the influence of a small number of high-order harmonics in the grid is ignored in the simplified calculation. However, for the resistive current amplitude curve extracted using the

Numerical Simulation of Resistive Current Extraction of 10 kV MOA

95

Fig. 3 Waveform of voltage, full current and resistive current when the voltage contains 3% third harmonic

Fig. 4 Comparison between the actual resistive current and resistive current extracted by the harmonic correction algorithm

harmonic correction algorithm, the total resistive current component curve is highly consistent with the actual value curve, which better meets the needs of the actual monitoring process.

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4 Conclusion This paper introduces the basic principle and equivalent circuit of the lightning arrester. Considering the principle and the method to measure the resistive current of a zinc oxide lightning arrester, a new method for measuring the resistive current of a zinc oxide lightning arrester based on the analysis of the current size when the grid voltage crosses zero is proposed. The theoretical derivation of the impedance current when the grid voltage contains harmonics is carried out, the leakage current characteristics of the lightning arrester are analysed, and the resistive leakage current is simulated and optimized. Acknowledgements This work was supported by State Grid Quanzhou Power Supply Company Jiebangguashuai project, under Grant B31335220001.

References 1. P. Zhang, X. Zhou, G. Sheng, D. Shen, Y. Shi, A novel MOA detection method based on GPS wireless synchronization. China Int. Conf. Electr. Distrib. 2012, 1–5 (2012) 2. Y. Han, Z. Li, H. Zheng, W. Guo, A decomposition method for the total leakage current of MOA based on multiple linear regression. IEEE Trans. Power Deliv. 31(4), 1422–1428 (2016) 3. J. Chen, L. Xu, Z. Wan, X. Hu, L. Zhang, Research on monitor technology of MOA state based on third harmonic principle. IEEE Int. Conf. High Voltage Eng. Appl. (ICHVE) 2016, 1–4 (2016) 4. Q. Wang, L. Zhou, W. Chen, Design of new MOA arrester tester, in 2015 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (DRPT) (2015), pp. 1545–1548 5. T. Zhao, Q. Li, J. Qian, Investigation on digital algorithm for on-line monitoring and diagnostics of metal oxide surge arrester based on an accurate model. IEEE Trans. Power Deliv. 20(2), 751–756 (2005) 6. Z. Abdul-Malek, A.H. Khavari, C.L. Wooi, et al., A review of modeling ageing behavior and condition monitoring of zinc oxide surge arrester, in Research and Development (IEEE, 2016), pp. 733–738 7. N.A. Abdul Latiff, H.A. Illias, A.H. Abu Bakar, Analysis of leakage current on 11 kV zinc oxide surge arrester using finite element method. Appl. Mech. Mater. 785, 348–352 (2015) 8. Novizon, Z. Abdul-Malek, Electrical and temperature correlation to monitor fault condition of ZnO surge arrester, in International Conference on Information Technology, Computer, and Electrical Engineering (IEEE, 2017) 9. S.M. Seyyedbarzegar, M. Mirzaie, Electro-thermal modeling of surge arrester based on adaptive power loss estimation using finite element method. Int. Trans. Electr. Energy Syst. 26(6), 1303–1317 (2016) 10. M. Hou, H. Gao, S. Zhang, et al., Simulation study on lightning protection of distribution transformer with zinc oxide arrester, in International Conference on Electric Utility Deregulation and Restructuring and Power Technologies (IEEE, 2015), pp. 1763–1767

Intelligent Scheduling of AGV Based on Adaptive Traffic Control System Theory in Automated Terminal Y. N. Zhao and Y. Q. Liu

Abstract To solve the conflict problem of Automated Guided Vehicle (AGV) in the process of operation, an intelligent scheduling method based on adaptive traffic control theory is proposed. Dijkstra algorithm is used to plan AGV paths, and conflict areas of AGV are regarded as road intersections. Coordinated phases are considered as conflicts and adaptive traffic control is used to release AGV with corresponding phases, so as to establish a model aiming at minimizing AGV total travelling time. By simulating and analyzing the AGV network of a port, the superiority of the model is verified by comparing the AGV control effect with or without considering the adaptive control scheduling. The results show that the intelligent scheduling of the AGV based on the adaptive traffic control theory can effectively improve the working efficiency of the AGV, and improve the operation efficiency of intelligent port. Keywords Automated container port · Adaptive traffic control · Intelligent scheduling · Automatic guidance vehicle (AGV) · Path conflict

1 Introduction Quay crane is located in the wharf front, mainly responsible for the loading and unloading of containers on ships; and yard crane is the equipment responsible for handling containers in the yard area. As a kind of horizontal transport equipment, AGV plays the role of connecting quay crane and yard crane [1]. It is of great practical significance to study how to better control AGV at conflict points, realize intelligent scheduling of AGV and improve port efficiency.

Y. N. Zhao (B) · Y. Q. Liu College of Transportation Engineering, Dalian Maritime University, Dalian, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_9

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For the AGV scheduling problem of automated container terminals, many researches have been carried out by domestic and foreign scholars. JIN [2] et al. proposed a dynamic scheduling method based on scheduling priority in order to solve the scheduling problem of AGV. Hu [3] et al. established a mixed integer linear programming model with the goal of minimizing the operating cost, and proposed a particle swarm optimization decomposition method based on greedy search. On the basis of capacity constraints, Miyamoto [4] et al. used local and random search algorithms to achieve conflict-free path planning of AGV. Qin [5] et al. established an integrated scheduling optimization model based on the theory of flexible flow-shop scheduling with limited buffers, and designed a genetic algorithm to generate initial solutions based on the NEH heuristic algorithm to solve the model. The effectiveness of the model and algorithm is verified by comparing the results of the genetic algorithm and particle swarm optimization algorithm. Qin Yingpeng [6] et al. proposed a dynamic path planning based on the time window model, which not only solved the collision conflict problem of multi-AGVs, but also optimized the scheduling sequence by dynamically changing the priority of AGVs. At the same time, the research on AGV conflict point control of automated container terminals has also attracted the attention of relevant scholars. Li [7] et al. designed guidance paths for the working space of AGV in container terminals, and proposed a traffic control strategy to select AGV paths and avoid collisions. Yang [8] et al. established a mixed integer programming model to solve conflicts and congestion problems, and proposed a double-layer genetic algorithm based on congestion prevention strategy for dynamic path planning. Suyun [9] et al. analyzed the possible path conflict problem of AGV during the operation of automated terminals, and solved the problem by using conflict detection and improving speed control strategy without changing driving path and task scheduling. Yajie [10] et al. established a mixed integer programming model and set the compatibility and conflict phases of intersections, with the goal of minimizing the maximum completion time of all tasks by considering task allocation and collision avoidance constraints of AGV. To solve the above problems, this paper proposes an AGV intelligent scheduling based on adaptive traffic control system theory. And a mathematical model is established to minimize the total travel time of AGV, so as to improve the transportation efficiency of AGV.

2 Basic Thought 2.1 Collision Regulation This paper simplifies the conflict area of AGV operation into the intersection in the road traffic network, and uses the control method of road intersection to solve the problem of AGV conflict. If the AGV is coming from direction 1, as shown in the figure, then the AGV coming from direction 6, 7, 9 and 12 can also pass

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Fig. 1 Phase diagram of AGV at intersection

simultaneously. In this paper, the idea of coordinated phase is fully considered when controlling AGV driving at conflicting intersections (Fig. 1).

2.2 Adaptive Traffic Control Steps The adaptive traffic control process can be described as the following steps: (1) According to the actual AGV flow at the intersection, specify the maximum release time tmax of phase in the control system. (2) Calculate the time ta of all waiting AGVs leaving the intersection at the corresponding phase i, then the release time of the phase is t ti = min{tmax ,ta }. (3) According to the number of AGV arriving at the intersection at the end of the phase release time, the queue length Li of AGV arriving at the end of the current release phase can be obtained. (4) If there is no AGV waiting in queue at the end of the current release phase, or the cumulative green time is equal to the maximum green time, then perform the next phase of green light, return to step 2, otherwise continue. (5) The control center determines the new green light extension time ti . If ti +ti ≥ tmax , then ti = tmax , otherwise ti +ti = ti , return to Step 3.

3 Model 3.1 Assumptions (1) AGV runs at a constant speed without considering acceleration, deceleration and distance changes caused by turns. (2) One AGV corresponds to multiple container yard cranes, and the initial positions of AGV and container yard cranes are known.

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(3) AGV receives containers in static state, and AGV has the condition of waiting for free time of quay cranes. And AGV will transport containers to the buffer area without considering the delay time of AGV waiting yard cranes.

3.2 Parameter Setting In order to facilitate mathematical modeling of AGV operation, the parameter symbols are introduced as follows: q is AGV path node q = 1,2, …,Q; K indicates the AGV number k = 1,2, …,K; n is the number of container tasks n = 1,2……N; U is the number of quay cranes u = 1,2, …,U; m is the AGV traveling path m = 1,2, …,M; Xi j indicates whether AGV goes from node i to node j, if so Xi j =1, otherwise Xi j =0; qm(q−1,q) is the q node in path m; la is the length of AGV equipment; ls is the minimum safe distance between (q−1,q) (q−1,q) is the time when AGV numbered k reaches node q; Tk is two AGVs; Tk the time when AGV numbered k leaves node q; tq is the time of AGV to pass through the node; ts is the safe driving time of an AGV that does not conflict with other AGVs; tw(q - 1,q) is the waiting time of AGV at node q; T(u,n) is the completion time of the task n for quay crane u; t (u) is the completion time of all tasks for quay crane u; tnu is the moment when the container task n is delivered to AGV for quay crane u. (q−1,q) (q−1,q) hk is the priority of AGV numbered k at node q; yk is the phase of AGV q q at node q; f(yk1 , yk2 ) indicates whether the phases of the two AGVs are compatible q q q q at node q, if so f(yk1 , yk2 ) = 1, otherwise f(yk1 , yk2 ) = 0.

3.3 Model Building In this paper, a mathematical model is established to minimize the AGV travel time. Firstly, each AGV is assigned to a fixed quay crane and yard crane to per from the corresponding number of container tasks by the random method. Then, the AGV path is planned by the Dijkstra method. After the AGV sends the container to the target yard crane, it needs to return to perform the next task until the last task is completed.

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Formula (1) indicates that there are no repeated sections in the planned AGV path, and each node is accessed only once.  i

Xi j = 1

(1)

j

Formula (2) represents the detection of AGV conflict nodes. Formula (3) represents the time when AGV passes through a node completely. Formula (4) represents the time when AGV will not conflict with other AGVs and pass through the node. Formula (5) represents the conflict detection. Q(m 1 ,m 2 ) = Q m1 ∧ Q m2 la V

(3)

la + ls V

(4)

tq = ts =

(2)

  T Q = Tqm1 − Tqm2  < ts

(5)

When AGV conflicts at node, the priority of the release phase should be determined by the time when AGV reaches the node. Formula (6) denotes the priority relationship. (q0 ,q)

Tk2

(q ,q)

→ h k1 0

(q ,q)

> h k2 0

(q ,q)

→ hk1 0

(q ,q)

> hk2 0

(6)

When AGV arrives at the node and conflicts occur, formula (7) represents the time of leaving the node when AGV phase is compatible. Formula (8) represents the time when AGV with high priority leaves the node when AGV is phase incompatible. Formula (9) represents the time when AGV with low priority leaves the node when AGV is phase incompatible. (q−1,q)

Tk (q−1,q)

Tk1 (q−1,q)

Tk2

(q−1,q)

= Tk2

(q−1,q)

= Tk1

 q q , f yk1 , yk2 = 1

(7)

 q q (q−1,q) (q−1,q) , f yk1 , yk2 = 0 < hk1 > hk1

(8)

(q−1,q)

= Tk

 q q (q−1,q) (q−1,q) + twk2 (q−1,q) , f yk1 , yk2 = 0 < hk1 > hk2

(9)

Formula (10) represents the time when AGV starts the task n0 +1 when it returns to the quay crane after completing the task n0 and the quay crane has finished loading and unloading containers; Formula (11) represents the time when AGV waits for the task n0 +1 to start after the completion of the quay crane operation when AGV

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completes the task n0 and returns to the quay crane. qm0 (u,n 0 +1)

Tk

q

= Tk m Q

q (u,n 0 +1)

Tk m0

(u,n)

q

, Tk m Q

q

= tnu , Tk m Q

(u,n)

(u,n)

> Tu(u,n)

(10)

> Tu(u,n)

(11)

Formula (12) represents the completion time of transporting the container n of the AGV n, and Formula (13) represents the completion time of all container tasks of quay crane u. T (u,n) = Tk m Q q

t(u) =

(u,n)

N 

qm Q (u,n)

− Tk

(12)

T (u,n)

(13)

n=1

Formula (14) represents the moment when AGV arrives at node q. For the node without conflict, formula (15) represents the moment when AGV leaves the q node at a uniform speed. For collision nodes, formula (16) represents the moment when AGV with the highest priority leaves the q node at a uniform speed. Formula (17) is the departure time of AGVs to be waited. Formula (18) represents the duration of a phase. α represents whether there is AGV arriving within time ti , if so α=1, otherwise α=0. Formula (19) represents the phase ending moment. β is the sequence of AGV arriving at the phase. Formula (20) represents the waiting time of AGV. q

Tk m(q−1,q)

(u,n)

qm(q−1,q) (u,n)

= Tk

qm(q−1,q) (u,n)

q

= Tk m(q−1,q)

Tk qm(q−1,q) (u,n)

Tk

qm(q−1,q) (u,n)

= Tk

qm(q−1,q) (u,n)

Tk y (q−1,q)

= min(ti

y (q−1,q)

= ti

ti Tk

y (q−1,q)

y (q−1,q)

twk(q−1,q) = Ti

y (q−1,q)

(14)

, ∀q ∈ (0, Q − 1)

(15)

m(q−1,q)

q

y (q−1,q)

+  ti

q

(u,n)

l(q,q+1) , ∀q ∈ (0, Q) v

, ∀q ∈ (0, Q − 1), 0 < h k1

= Tk m(q−1,q)

+ Tk1m(q−1,q)

+

(u,n)

(u,n)

m(q−1,q)

> h k1

+ twk(q−1,q) , ∀q ∈ (0, Q)

, tmax )= min(

 L i ts L (0) ts +α , tmax ) la + ls la + ls

, ∀q ∈ (0, Q − 1), 0 < h m(q−1,q) > h m(q−1,q) k1 k1 q

+ (β − 1)ts , Tk m(q−1,q)

(u,n)

(16) (17) (18) (19)

  (q−1,q) y y (q−1,q) y (q−1,q) ∈ Ti − ti , Ti (20)

Intelligent Scheduling of AGV Based on Adaptive Traffic Control …

B

A 10 20

1 2 10 21 22 10 41 42

3 23 43

20 10 10 10 20 4 5 6 7 2425 26 27 4445 46 47

C 20 10 10 10 20

8 28 48

103

9 10 11 12 2930 31 32 4950 51 52

13 33 53

D 20 10 10 10 20 1415 16 17 3435 36 37 5455 56 57

18 38 58

20 10 1920 3940 5960

QC 60 61 62

10 77 78 10 93

a

6364 65 66 7980 81 82 94 95

b

c

6768 69 70 8384 85 86 96 97

d

e

7172 73 74 8788 89 90 98 99

f

g

7576 9192 100

YC

h

Fig. 2 Layout plan of port

4 Example Analysis The AGV road network is established based on the port wharf layout as the model, where A—D is the position of quay crane, a—h is the container area of the yard, c and d are the export container areas, and a, b, e, f, g and h are import container areas. The distance between nodes is measured in meters (Fig. 2). In the calculation example, there are four quay crane operations, and the AGV starting from each quay crane can correspond to multi-areas, and the basic parameters are set as la = 6m, ls = 4m, V = 4m/s. Simulation experiment is conducted in Matlab2017. The AGV driving path planned by the Dijkstra algorithm is shown in Table 1. Time conflict is used to detect the conflict positions of AGV, and adaptive traffic control is implemented to release AGV at conflict nodes. The simulation results show that the AGV scheduling with adaptive traffic control and coordinated phase can improve the efficiency of AGV. By comparing with the adaptive traffic control and coordinated phase control mode and the traditional node waiting control model, according to the time delay of AGV from each quay crane to complete the container task, it can be seen that the adaptive traffic control and coordinated phase can reduce the delay time of AGV completion and improve the overall efficiency (Table 2).

18-38-58-59-75-91-90-99-90-74-57-37-17-18

K9 :D-g

Unload 30

13-33-53-54-71-87-86-97-86-70-52-32-12-13 18-38-58-59-75-91-100-91-75-74-57-37-17-18

K7 :C-e

K8 :D-h

Unload 40

13-14-15-16-17-37-57-58-59-75-91-100-91-75-74-57-37-17-16-15-14-13

K6 :C-h

Unload 40

Unload 50

Unload 50

Unload 50

3-23-43-44-63-79-94-79-78-62-42-22-2-3 8-7-6-5-4-24-44-63-79-94-79-63-64-65-46-26-6-7-8

K4 :A-b

Unload 60

Load 30 Unload 30

Load 50 Unload 50

Task

K5 :B-b

3-23-43-44-63-79-78-93-78-62-42-2-33

K3 :A-a

8-9-10-30-50-68-69-70-86-97-86-85-84-83-82-95-82-66-47-27-7-8 13-33-53-54-71-87-98-87-86-85-84-83-96-83-67-68-69-51-31-11-12-13

K1 :B-e-c

K2 :C-f-d

Loading and unloading

Just unloading

Nodes and Paths

Route

Type

Table 1 AGV operation path and task arrangement

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Table 2 Operation delay of AGV in different quay cranes Number of quay cranes

A

B

C

D

Conventional control scheme/s

2564

2896

3342

2667

Adaptive control scheme/s

1328

1217

1623

1562

5 Conclusion In this paper, aiming at the conflict problem of AGV in an automated container port terminal when carrying out transportation tasks, an adaptive traffic control method is proposed to release AGV in phase to control the conflict intersection, and the idea of the coordinated phase is added to the control scheme. The simulation experiment proves that the adaptive traffic control method can effectively control the AGV at the conflict intersection than the traditional intersection waiting method, which making the delay time of AGV completing the task smaller and the total travel time of AGV smaller. Future research should combine the dynamic planning of AGV path with the control mode of adaptive traffic.

References 1. S. Park, J. Hwang, H. Yang, S. Kim, Simulation modelling for automated guided vehicle introduction to the loading process of Ro-Ro ships. J. Mar. Sci. Eng. 9, 441 (2021) 2. J. Jin, X. Zhang, Multi AGV scheduling problem in automated container terminal. J. Marine Sci. Technol.-Taiwan 24(1), 32–38 (2016) 3. H.T. Hu, X.Z. Chen, T.S. Wang et al., A three-stage decomposition method for the joint vehicle dispatching and storage allocation problem in automated container terminals. Comput. Ind. Eng. 129 (2019), 90–101 4. T. Miyamoto, K. Inoue, Local and random searches for dispatch and conflict-free routing problem of capacitated AGV systems. Comput. Ind. Eng. 91, 1–9 (2016) 5. Q. Qin, L. Chengji, Optimization of equipment coordination scheduling with considering buffer space in automated container terminal. Comput. Eng. Appl. 56(06) (2020), 262–270 6. T. Yingpeng, X. Kexin, L. Yegui, Z. Wen ‘an. Research of path planning in multi-AGV system. Comput. Sci. 44(S2) (2017), 84–87 7. Q.Li, A.C.Adriaansen, J.T.Udding, et al. Design and control of automated guided vehicle systems: a case study[J].IFAC Proceedings Volumes, 2011,44(1): 13852–13857. 8. Y. Yang, M. Zhong, Y. Dessouky et al., An integrated scheduling method for AGV routing in automated container terminals. Comput. Ind. Eng. 126, 482–493 (2018) 9. Z. Suyun, Y. Yongsheng, L. Chengji et al. Optimal control of multiple AGV path conflict in automated terminals. J. Transport. Syst. Eng. Inform. Technol. 17(02) (2017), 83–8 10. Y. Yajie, C. D. Fang, Y. Fang, Multi-resource coordinated scheduling of automated terminals considering AGV collision avoidance. Comput. Eng. Appl. 56(06) (2020), 246–253

Research on Automatic Generation and Verification of Test Sequence for New Train Control System Yuanshan Zang, Kaicheng Li, Chenyue Li, Lei Yuan, and Yu Liu

Abstract Aiming at efficiency and correctness of test sequences generation, we propose a method to automatically generate test sequences and verify their correctness. First, we design an automatic test sequence generation method based on the BERT model, which is used to learn the context between test cases to automatically generate test sequences. Second, we design a method to judge the correctness of test sequences based on the rule engine. The Named Entity Recognition (NER) is used to extract information from domain documents. We design a rule extraction algorithm to realize the automatic construction of the Rule Base. Then, we complete the correctness verification of test sequences based on Drools rule engine. Experimental results show that this method can automatically generate high-quality test sequences, and effectively verify the correctness of test sequences. Keywords New train control system · Black box testing · Test sequences automatic generation · BERT model · Rule engine

1 Introduction Compared with the CTCS-3 train control system, the new train control system (NTCS) takes on-board equipment as the core to adapt to the poor railway operation environment in western China [1]. It integrates the ground equipment of the train to reduce the operating cost of equipment along the line. The change of system structure makes it necessary to test it before it is put into operation, and the preparation of test sequences is a key step in black box testing. Y. Zang · K. Li · L. Yuan (B) · Y. Liu Collaborative Innovation Center of Railway Traffic Safety, Beijing Jiaotong University, Beijing 100044, China e-mail: [email protected] C. Li China Railway Information Technology Center, Beijing 100044, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_10

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In black box testing, in order to verify whether the new train control system equipment meets the requirements specification, it is necessary to design a test case set covering all system requirements, and verify whether the equipment under test meets the requirements by executing all test cases. The test sequence, which consists of a series of the test cases, is the guideline for functional test of the train control system, and its quality directly influences the correctness and efficiency of test work. However, manual generation of the test sequence means heavy workload, and the correctness cannot be guaranteed, so automatic generation of high-quality test sequence has always been the goal of researchers. At present, the methods of test sequence automatic generation of train control system mainly include the model-based method and the intelligent algorithm-based method. The model-based method uses models to describe the behaviour of objects, and then apply graph search or model checking techniques in the model to generate test sequences. Barberio et al. proposed an interoperable test environment to support the system level test of the ERTMS/ETCS control system developed in CRYSTAL. The Rail Model module can automatically generate test sequences through model checking technology [2]. S. Song used timed automata to model and verify the Zone Controller of CBTC, extracts the state information and transition conditions of ZC by analysing the UPPAAL model file to generate test cases, and then the improved depth first search algorithm is used to concatenate test cases into test sequences [3]. The intelligent algorithm-based method uses intelligent algorithms to transform test sequence generation problem into multi-objective optimization problem. Li Zhi adopts the dynamic programming algorithm to solve the sequence of cases with the shortest distance between cases as the optimization objective [4]. Li and Gan use deep learning and genetic algorithm to solve the problem of test sequence generation and optimization. Neural network is used to assign test items to test sites, and then genetic algorithm is used to optimize the test sequence according to the optimization objectives such as redundancy, coverage, time and energy [5]. Based on the research status, there are not many studies on the generation of new train control system test cases, and there are not many analysis and connection methods of existing cases. In view of the above problems, this paper uses the BERT model to realize the serial connection of test cases, and judges the correctness of the generated test sequence based on the rule engine. The main work is as follows: (1) An automatic test sequence generation method based on the BERT model is proposed. We transform the connection problem of test cases into a context problem between cases, and use the BERT model to infer the next test case based on the previous one. (2) A method of test sequences correctness verification based on Drools is proposed. We design a method to automatically extract knowledge from domain documents to improve the efficiency of Rule Base construction, and then use the rule engine to output verification results.

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2 Automatic Generation and Verification of Test Sequences Our research aims at generating the new train control system test sequence automatically and verifying its correctness. There are two key issues: First, connect test cases correctly according to the system workflow. Second, establish the verification criteria of the test sequence, and then establish the rule base to verify the test sequence. At present, the test of NTCS still relies on manual work, and there are many repetitive work in this process, resulting in low test efficiency [6]. In order to improve the efficiency and accuracy of the NTCS test, this paper adopts the method of deep learning to realize the automatic generation of the test sequence, and then introduces the Drools to judge the correctness of the test sequence.

2.1 Automatic Generation of Test Sequence Based on BERT Model The Bert model achieves good results in dealing with text logic and contextual relations [7], which is similar to the connection between two test cases. We therefore use the BERT model to capture the contextual relationships between test cases and thus determine whether an input case can be connected to another. Model fine-tuning process. We fine-tune the BERT model using the test sequences that have been executed in laboratory tests and then the model with the best performance is saved to generate the test sequence. The pre-training and fine-tuning process of the BERT model is shown in Fig. 1. Dataset. Based on the laboratory test of the new train control system, our data set consists of 20 sequences, including 336 test cases, with a total of about 16,000 characters. The training set and the testing set are divided by 8:2. Mark the test cases according to the context and input them into the BERT model for fine-tuning. The input and output of the BERT model are shown in Table 1. Since the model needs to learn the sequence relationship between cases, we design the input as a sentence pair. Label “IsNext” indicates that the test case 2 is a sequential case of that the test

Fig. 1 The pre-training and fine-tuning process

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Table 1 Input and output of the BERT model Test case 2

Test case 1

Label

In the backup mode, the train does not pass through the In the TR mode, check the IsNext balise group in the desired direction, then enters TR mode integrity of the train In the backup mode, the train does not pass through the China train control system NotNext balise group in the desired direction, then enters TR mode is divided into five levels

case 1, and label “NotNext” indicates that that the test case 2 is not a sequential case of that the test case 1. Evaluation Metrics. Cross entropy function is a loss function commonly used in the classification problem. The formula of cross-entropy loss function used in this paper is shown in Eq. (1): L=−

M 1  · yic log( pic ) n i c=1

(1)

where, M—Types of classification; yic —indicator variable, if the class is the same as the sample class, then yic = 1, if not, then yic = 0; pic —probability of class c corresponding to model prediction The accuracy describes the ratio of the correct number of samples to the total number of samples. The formula of accuracy is shown in Eq. (2): Acc =

TP +TN T P + T N + FP + FN

(2)

where, T P—True Positive; F P—False Positive; T N —True Negative; F N —False Negative

2.2 Correctness Verification of Test Sequence Based on Drools Rule Engine Drools is a rule engine which can provide multiple rule implementation methods and it is suitable for verification of test sequences. The basic components of Drools include business rules and rule engines [8] and the structure of the rule engine includes three modules: Rule Base, Working Memory and Inference Engine [9]. The flow of correctness verification is shown in Fig. 2. We extract the knowledge related to the verification criterion from the domain documents to build the Rule Base, input the test sequences generated by the BERT model as facts into the rule engine, and then run the rule engine and output the correctness verification results.

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Fig. 2 Execution flow correctness verification

Verification criterion of test sequence correctness. According to the work flow and actual test experience of the NTCS, it is necessary to meet the following rules for the correctness of the test sequence 10: (1) (2) (3) (4)

The test sequence cannot be empty. Under the same scenario, the same test case is executed only once. The mode conversion of the test sequence shall be feasible. The execution conditions of actions in the test sequence cannot conflict with each other. The arrangement of test conditions shall conform to the system operation logic.

Establishment of Rule Base. The time cost of manually extracting structured rules from unstructured domain documents is high. To overcome that problem, we apply knowledge extraction techniques to obtain rules from NTCS domain documents to build the Rule Base. First, the rule matching model shown in Fig. 3 is established by analyzing the execution process of NTCS test sequences, aiming to encapsulate the semantic relationships between entities in NTCS. The Executor entity is the initiator and undertaker of actions, and we call those actions the Action entity. Mode, Location and Level are the entities that describe the state that the Executor entity has reached or will reach, we call them the State entity. The Message entity represents the information that interacts with the Executor entity during the test, such as RBC messages. All those entities are connected by the relationship between entities. Second, Named Entity Recognition (NER) is used to identify all specific entities in the ontology model and their corresponding locations from the text to be processed [11]. We use the BERT + Bi-LTSM-CRF model to perform the NER task, where BERT can obtain dynamic word embeddings and Bi-LTSM-CRF is used to classify the word embeddings. Third, the rule extraction algorithm shown in Fig. 4 is designed. We take the Executor entity as the core of the statement, and the algorithm will continue only when there is at least one Executor entity in the statement. Then traverse the text to be processed to obtain the position of other entities, and finally obtain the rule content based on the relative location between entities and the relationship between entities in the rule matching model. Verify the correctness of the test sequence. The correctness verification workflow of test sequence is as follows: Step 1: Input the test sequence as facts and match the target conditions with the facts.

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Fig. 3 Rule matching model

Fig. 4 Rule extraction algorithm

Step 2: Read the rules, match the rules with the facts, and add the successfully matched rules to the conflict set. Step 3: Repeat Step 2 until all rules are matched. Step 4: Solve the conflict rules according to the priority. Step 5: Execute the selected rule. Step 6: Output the correctness verification results.

3 Results and Discussion 3.1 Automatic Generation Results of Test Sequences Training results of BERT model. The convergence process and accuracy performance of the model in the training process are shown in Figs. 5 and 6 respectively. The results show that the model has good convergence and performance in the training

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data set. After 80–100 epochs, almost all parameter combinations of the model have reached nearly 90% accuracy. Results analysis. Taking the test sequence TS-224 with the best accuracy in the test set as an example, the comparison results are shown in Table 2. After comparison, it can be found that the sequence predicted by the model in [TC-30] is not consistent with [TC-36] in the reference sequence compared with the reference sequence, the

Fig. 5 The convergence process performance of the model

Fig. 6 The accuracy performance of the model

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Table 2 The comparison results Sequence number

Category

Sequence content

TS-224

Pre

TC-124, TC-18, TC-22, TC-28, TC-30, TC-125, TC-52, TC-146, TC-357, TC-373, TC-361

Ref

TC-124, TC-18, TC-22, TC-28, TC-36, TC-125, TC-52, TC-146, TC-357, TC-373, TC-361

Table 3 Examples of rule extraction results Rule name

Rule content

TR_Level_ 01

Main Level (Pre-State); Train (Executor); is manually switched by the driver (Action); Backup Level (Post-State)

TR_Mode_ 12

OS mode (Pre-State); Train (Executor); accept message (Action); Message 3 (Message); FS mode (Post-State)

TR_Mode_ 15

FS mode (Pre-State); Driver (Executor); choose OS mode manually (Action); OS mode (Post-State)

reason is that these two cases are more similar in the beginning and the end part of the text, that is, they have the same Post-State and Pre-State, while the description part in the middle of the text is different. Except for this case, the test sequences generated based on the BERT model are consistent with the manually compiled test sequences, and it can be considered that the model can effectively complete the test sequence automatic generation.

3.2 Results of Correctness Verification Based on Drools Results of establishment of Rule Base. Use the knowledge extraction techniques to automatically extract entities and relationships between entities from unstructured text, and then output the structured test rules. The examples of rule extraction results are shown in table 3.

3.3 Results of Test Sequence Correctness Verification Take the automatically generated test sequence as input and evaluate whether the test sequence meets the requirements of the rules. If it passes the rule verification, the correctness verification passes, and if the correctness verification does not pass, the reason for not passing is displayed. Some of the sequence verification results are shown in Table 4.

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Table 4 The sequence judgment results Sequence number

Number of cases

Result

Rules violated

TS-1

74

Pass

None

TS-15

24

Not pass

TR_Level_05

TS-220

15

Pass

None

TS-310

47

Pass

None

TS-421

21

Pass

None

TS-537

8

Pass

None

TS-710

19

Not pass

TR_Mode_07

4 Conclusions In this paper, we proposed a method to automatically generate the test sequence of the new train control system and verify its correctness. The BERT model outputted the test sequence with high accuracy by learning the relationship between cases. The knowledge extraction method is used to build the Rule Base, and then we used the rule engine to measure the correctness of the test sequence of the new train control system. We evaluated the model performance in the test dataset. The experimental results show that the method is effective for automatic generation and verification of test sequences, and it can reduce the workload of testers. In future work, we will expand the rule matching model to support knowledge extraction in more test scenarios, and enrich the content of the Rule Base to achieve better usability of automatic generation and verification of test sequences. Acknowledgements This work is supported by the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project 2022JBXT000) and China State Railway Group Co.,Ltd.Science and Technology Research and Development Program Project (P2021G053).

References 1. L. Chunhui, C. Xin, Application of SCADE-based requirement analysis and test case design in RMU subsystem of new train control system. Railw. Signal. Commun. Eng. 18(2), 27–50 (2021) 2. G. Barberio, B.D. Martino, N. Mazzocca, L. Velardi, V. Vittorini V, An interoperable testing environment for ERTMS/ETCS control systems in Int. Conf. on Computer Safety, Reliability, and Security (Florence) (2014), pp 147–56 3. S. Song, Y.D. Chen, A test sequence generation method of zone controller based on timed automata. J. Meas. Sci. Instrum. 10(3), 266–276 (2018) 4. Y. Zhang, Z. Li, X. Chen, Rationality analysis of test sequence for CTCS-1 train control system based on expert system. in Int. Conf. on Computer Technology, Electronics and Communication (Dalian) (2017), pp 1088–92

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5. K. Li, Q. Gan, L. Yuan, Q. Fu, Optimized generation of test sequences for high-speed train using deep learning and genetic algorithm. in 2016 IEEE 19th Int. Conf. on Intelligent Transportation Systems (Rio de Janeiro) (2016), pp 784–9 6. P. Ning , T. Tang, L. Zhu, A deep learning-based test sequence automatic generation method for automatic train operation in high-speed railway system. in 2021 IEEE Int. Intelligent Transportation Systems Conf.(Indianapolis) (2021), pp 1792–96 7. J. Devlin, M. Chang, K. Lee, Toutanova K, BERT: Pre-training of deep bidirectional transformers for language understanding. Preprint arXiv:1810.04805 (2018) 8. R. Liu, Y. Wang, J. Zou, T. Ni, Research on the transformation from financial accounting to management accounting based on drools rule. Engine Comput Intel Neurosc 2022, 9445776 (2022) 9. D. Liu, T. Gu, J. Xue J, Rule engine based on improvement rete algorithm. In The 2010 Int. Conf. on Apperceiving Computing and Intelligence Analysis Proc.(Chengdu) (2010), pp 346–9 10. X. Si, W. Kuang, Q. Li, A method of generating engineering test sequence for urban rail transit CBTC system based on formalization. in IOP Conference Series: Earth and Environmental Science (2020), p 12192 11. W. Yang W, F. Deng, S. Ma, L. Wu, Z. Sun, C. Hu, Test case reuse based on software testing knowledge graph and collaborative filtering recommendation algorithm. in 2021 IEEE 21st Int. Conf. on Software Quality, Reliability and Security Companion(Hainan) (2021), pp 67–76

Occluded Vehicle Detection with Fusing Motion Information Zhengtao Ke, Jiaqi Xiong, Xun Huang, and Yaowen Xiao

Abstract Vehicle detection is essential for autonomous driving and Intelligent Transportation System (ITS), but it remains the challenge of occlusion. Occlusion leads to incomplete vehicle feature, which affects feature extraction and recognition. In this paper, we propose a vehicle detection algorithm of fusing motion information and adding localization branch for occluded vehicle detection. Firstly, RGB images and corresponding optical flow are input into two branches of the dual-stream network to extract appearance features and motion features. Then, we improve attention mechanism so that the model has outstanding feature extraction capability with fewer parameters when the two features are fused. Finally, the location prediction branch is added to acquire the localization confidence to evaluate the localization accuracy of the bounding box. We multiply the classification confidence and localization confidence to compute the final detection confidence, solving the problem of low correlation between the classification score and the localization accuracy. A series of experiments demonstrate the effectiveness of the algorithm in dealing with occluded vehicle detection, with accuracy of 87.34% and speed of 35.7 FPS, meeting the requirements of practical applications. Keywords Vehicle detection · Occlusion · Motion information · Feature fusion · Localization confidence

1 Introduction In recent years, the fields of autonomous driving and Intelligent Transportation Systems have received extensive attention from researchers, and vehicle detection is an important module for data acquisition of them. It is important to design robust vehicle detection algorithms [1]. Z. Ke · J. Xiong (B) · X. Huang · Y. Xiao School of Electronic and Electrical Engineering, Wuhan Textile University, Wuhan, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_11

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Current vehicle detection algorithms can be divided into traditional based algorithms and deep learning based algorithms. Traditional methods typically extract hand-crafted features to train classifiers to detect vehicles [2], or use motion information [3]. These methods have poor robustness and low accuracy in situations such as lighting changes. In contrast, deep learning based algorithms are widely used in the field of vehicle detection due to their robustness. Commonly, there are two-stage detection algorithms like RCNN and Faster RCNN [4, 5], and single-stage detection algorithms like YOLO and SSD [6, 7]. Both of them have achieved excellent accuracy on many datasets. However, vehicle detection is still challenging because of occlusion. Occlusion makes it difficult to extract and recognize vehicle features accurately. How to detect the occluded vehicles using limited features is the key to improve the accuracy of the algorithms. Zhang et al. [8] divide the vehicle detection into four partial detection. Reddy et al. [9] input the key points detected in 2D images into the 3D graph convolutional neural network to reconstruct the 3D model of the vehicle to achieve occluded vehicle detection. These methods alleviate the impact brought by occlusion, but are computationally intensive for end devices. It is found that the human visual system (HSV) enables humans to infer an object’s properties from the continuation of contours when part of its information is absent [10]. The occluded vehicle can usually retain some contour information. The motion information based on optical flow happens to contain the position information and contour information of the moving target, and the moving target is more likely to be a vehicle target [11]. Therefore, we propose the fusion of appearance feature and motion information to guide the appearance feature to reinforce the learning of contour feature and other salient feature. This allows the model to focus on the occluded object. In addition, the damage caused by an inaccurate bounding box can be enormous when there is heavy overlap of vehicles. As shown in Fig. 1, if vehicle A gets the inaccurate bounding box A2, the box of vehicle B will be suppressed by NMS (Nonmaximum suppression) due to the high value of IoU (Intersection Over Union) with vehicle A. Therefore, the high classification score detection box with inaccurate localization may affect the correct detection of other vehicles. To address the problem of mismatch between classification score and localization accuracy, localization confidence of the bounding box is predicted by the localization branch added, and then it is combined with the classification score to get the final detection confidence.

2 Methods The whole network architecture is shown in Fig. 2. In this paper, MobileNet v2 [12] is used to extract the feature of RGB images and corresponding optical flow images. The first layer is a conv2d, and IR is Inverted Residual Block proposed by Mobilenet v2. MAF is the motion and appearance fusion module we proposed for motion and

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Fig. 1 Inaccurate positioning of the detection box causes other vehicles to be missed. The yellow box is vehicle A’s bounding box A1, the blue is A’s bounding box A2, and green box is vehicle B’ detected box

Fig. 2 The architecture of the whole network

appearance features fusing that is extracted at different stages. FPN (Feature Pyramid Networks) is used to fuse the multi-layer features so that it improved semantic information of shallow features. After the fully connected layer, a localization prediction branch is added to obtain the localization score and then fused with the classification score, and the final score is used for NMS to get the detection result.

2.1 Motion and Appearance Fusion Module The attention mechanism is widely used for feature fusion between different modalities [11]. However, its use of global receptive field adds a large number of parameters.

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To ensure a lightweight model, we use local instead of global to get the weight to guide appearance feature learning. Specifically, V a is the appearance feature and V m is the motion feature in each feature extraction stage. And the feature of local enhancement Ualocal can be calculated as: Ualocal = Va ∗ Flocal (Vm )

(1)

F local is a function that extracts local feature relation of motion information. Specifically, for each feature point I m in V m , a sliding window of K*K size is designed to calculate the similarity between it and the rest of points in the window, and then we normalize the similarity to obtain the weight matrix W. For feature points I a at the same position as I m in V a , we use the matrix W to multiply all points in K*K size window, and then sum up to obtain the enhanced feature points I˙m in Ualocal . By setting the size of the K properly, the model can have good feature extraction quality while significantly reducing the number of parameters and the computational effort. For the feature Uactr s of reinforcement contour learning, it can be formulated as: Uactr s = Va ∗ Fctr s (Vm )

(2)

F ctrs is function that extracts contour feature of motion information. Specifically, for each point in contour feature detected by the Canny algorithm, multiply it with points in the corresponding location in V a to obtain the feature Uactr s . And then Ualocal f inal and Uactr s are summed to obtain Ua : Uaf inal = Ualocal + Uactr s

(3)

In Fig. 3, the first column is the original image, the second is the optical flow image, the third is the heat map without feature fusion, and the fourth is the heat map after feature fusion. It can be found that the effect of feature extraction is much better after the fusion of motion information.

Fig. 3 Comparison of heat maps before and after fusion of motion features

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Fig. 4 The architecture of detector

2.2 Localization Prediction Branch In order to avoid the damage of detection accuracy caused by bounding boxes with high classification scores but low localization quality, some work was proposed adding branch in the detector to predict the IoU of each detection box as an evaluation of the location quality [13, 14]. To solve the problem of absent location quality during NMS, IoU-Net single used predicted IoU as a criterion for NMS. However, single classification confidence or location confidence cannot represent both classification quality and location quality of the detection box effectively at the same time. As shown in Fig. 4, influenced by their work, we add a branch to predict IoU of the bounding box to evaluate the location quality. In order to improve the low correlation between the classification score of the detection box and the positioning accuracy, the final confidence S final is obtained by weighted fusion of the classification confidence and localization confidence: Sfinal = α ∗ Scls + (1 − α) ∗ Sloc

(4)

where S cls is the classification confidence and S loc is the localization confidence. α is the weight to control the contribution of the classification confidence and localization confidence to the final confidence. In this paper, α is 0.6.

2.3 Loss Function Classification branch, regression branch and localization branch are trained simultaneously in the fully connected layer, and the loss of the three branches is summed up as the total loss of the network: L total = L cls + L r eg + L loc

(5)

L cls is the classification loss function, L reg is the regression loss function, and L loc is localization loss function. Specifically, the cross-entropy loss function is used for the classification branch as shown in formula (6). C is the number of category and

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P(x i ) is the probability of detecting a box category as x i. In this paper, C is 1 and x is the label of vehicle. L cls = −

C 

P(xi ) log(P(xi ))

(6)

i

Regression branch using Smooth L1 loss function and in the formula (7), bbox pred is the detected bounding box, box gt is the groundtruth bounding box: L r eg =

n 1 Smooth L1 (bbox pr ed − bbox gt ) n i

(7)

The localization prediction branch is trained using the binary cross-entropy loss function BCE, which is formulated as L loc =

n 1 pr ed BC E(I oUi , I oUi ) n i

(8)

pr ed

I oUi is the predicted IoU and IoU i is the groundtruth IoU of the detected bounding box and ground-truth bounding box.

3 Experimentation and Analysis 3.1 Experimental Platform In this paper, the experimental platform is based on Ubuntu 18.04, Python 3.7, Pytorch 1.17 and NVIDIA GTX 1080Ti GPU. The initial learning rate is set to 0.001, and the learning rate is adjusted using the step method and decay factor is 0.0001.

3.2 Dataset The dataset in this paper contains a total of 39 video sequences with a total of 8578 images, of which 13 video sequences with occlusion, with a total of 3256 images, are selected from the DETRA public dataset. Since there are not enough scenes with occlusion, 26 video sequences with vehicle occlusion were obtained from road video surveillance, with a total of 5322 images. The ratio of the training set to the testing set is 8:2.

Occluded Vehicle Detection with Fusing Motion Information Table 1 Ablation experimental results

MobileNet v2 √

MAF

√

√

Location branch

√

AP (%) 82.15

√

√ √

123

√

86.62 83.87 87.34

3.3 Result In this paper, we use Average Precision (AP) to evaluate the model quality, and it is calculated under the condition of IoU of 0.5. The motion information fusion module and the localization prediction branch are applied to the baseline method MobileNet v2 respectively, to conduct ablation experiments to verify the effectiveness of the method we proposed. The size K of sliding window in MAF is 5. The results are shown in Table 1. The feature fusion module and the localization prediction branch can bring significant improvements in accuracy on the baseline method, with the motion feature fusion module improving accuracy by 4.47% and the localization prediction branch by 1.72%, and the combination of the two modules further improves accuracy, demonstrating the effectiveness of the method proposed in this paper. And our method achieves a speed of 35.7 FPS during inference, which meets the real-time requirement. Figure 5 shows some detection results. The first column is the original image, the second column is the result of the baseline method, and the third is our method. In Fig. 5a, the vehicle in the lower left corner is missed due to being obscured by leaves. By fusing the motion information to enhance the learning of motion region features, the vehicle target is successfully detected. In Fig. 5b, the vehicle in the bottom left corner is obscured by environmental objects and the baseline model fails to detect the vehicle completely but we succeed by enhancing contour features. In Fig. 5c, the vehicles are heavily overlapped, and many inaccurately positioned detection boxes result in NMS removing detection boxes of other vehicles by mistake in the baseline model. After adding localization branch and confidence combination, the detection boxes of the occluded vehicles are basically retained.

4 Conclusions Aiming at the problem of occlusion in vehicle detection, we propose a vehicle detection algorithm based on fusion of motion information. The dual flow network model is used to extract the appearance feature of RGB images and the motion feature of the corresponding optical flow images. Then the attention mechanism is improved to fuse the complementary information of the two modes with fewer learning parameters. The localization confidence is obtained by the localization prediction branch

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(a)

(b)

(c) Fig. 5 Comparison of detected results

added to evaluate the positioning quality, and it is combined with the classification confidence as the final score for NMS, solving the problem of mismatch between classification confidence and localization accuracy. Finally, the model achieves the detection accuracy of 87.34% and the speed of 35.7 FPS, making it suitable for application in practice. Next, we will try to improve the NMS to reduce the error suppression in overlapping case, so as to further improve the detection accuracy.

References 1. A.A. Husain, T. Maity, R.K. Yadav, Vehicle detection in intelligent transport system under a hazy environment: a survey. IET Image Proc. 14(1), 1–10 (2020) 2. Y. Wei, Q. Tian, J. Guo et al., Multi-vehicle detection algorithm through combining Harr and HOG features[J]. Math. Comput. Simul. 155, 130–145 (2019) 3. Y. Chen, Q. Wu, Moving vehicle detection based on optical flow estimation of edge. In 2015 11th International Conference on Natural Computation (ICNC). IEEE (2015), pp. 754–8 4. X. Han, Modified cascade RCNN based on contextual information for vehicle detection. Sensing Imaging 22(1), 1–19 (2021) 5. H. Nguyen, Improving faster R-CNN framework for fast vehicle detection. Math. Probl. Eng. (2019) 6. Y. Zhang, Z. Guo, J. Wu et al., Real-time vehicle detection based on improved YOLO v5. Sustainability 14(19), 12274 (2022) 7. J. Cao, C. Song, S. Song et al., Front vehicle detection algorithm for smart car based on improved SSD model. Sensors 20(16), 4646 (2020) 8. W. Zhang, Y. Zheng, Q. Gao et al., Part-aware region proposal for vehicle detection in high occlusion environment. IEEE Access 7, 100383–100393 (2019)

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9. N.D. Reddy, M. Vo, S.G. Narasimhan, Occlusion-net: 2d/3d occluded keypoint localization using graph networks[C]. in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition(CVPR) (2019), pp. 7326–35 10. J.S. Johnson, B.A. Olshausen, The recognition of partially visible natural objects in the presence and absence of their occluders. Vision. Res. 45(25–26), 3262–3276 (2005) 11. Z.C. Zhao, K.H. Zhang, J.Q. Fan, Q.S. Liu, Learning motion guidance for efficient unsupervised video object segmentation. Acta Autom. Sin. 2021, 48(x):1001–9. 12. Sandler M, Howard A and Zhu M, et al. Mobilenetv2: Inverted residuals and linear bottlenecks[C]. in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition(CVPR) (2018), 4510–20 13. B. Jiang, R. Luo, J. Mao, et al, Acquisition of localization confidence for accurate object detection. In /Proceedings of the European conference on computer vision (ECCV). (2018), 784–99 14. S. Wu, X. Li, X. Wang, IoU-aware single-stage object detector for accurate localization. Image Vis. Comput. 97, 103911 (2020)

Study of an Acitve/Reactive Power Coordinative Control Method in Capacitor Series Inverter-Based Microgrid Da Li, Huaidong Yang, and Haixing Zheng

Abstract The low voltage phenomenon will not only affect the normal operation of load, but also increase the transmission loss of active power, resulting in energy waste in microgrids (MGs). To reduce the probability of low voltage problems and improve the reactive power compensation capability, a two-dimensional power flow multi-time scale optimization control method of active and reactive power in MG based on the capacitor series inverter (CSI) is proposed. Firstly, the power output characteristics and the power flow control model with the energy storage unit of CSI are analyzed. Secondly, a two-dimensional power flow optimization control method is proposed, to achieve the most economical and the least loss. On a short time scale, the two-dimensional power flow optimization control method uses the charged state margin reserved by the energy storage to dynamically meet the load demand studied. Simulation results proved the effectiveness of the proposed method. Keywords Microgrid · CSI · Multi-time scales · Two-dimensional power flow · Optimal control

1 Introduction Voltage stability is vital for the efficient transmission of active power in distribution networks [1, 2]. However, with the large-scale access of nonlinear loads, the reactive loads in the grid become more and more reactive, causing the low voltage D. Li · H. Zheng (B) China Southern Power Grid Energy Efficiency and Clean Energy Co., Ltd., Guangzhou, China e-mail: [email protected] D. Li e-mail: [email protected] H. Yang Emerging Business Department, China Southern Power Grid Co., Ltd, Guangzhou, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_12

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phenomenon to become more and more pronounced [3]. The low voltage problem leads to large active losses on the line when it transmits active power, making the generation side less economical [4]. To solve the problem of low voltage, it is common practice to install additional reactive power compensation equipment or replace on-load regulating transformers in the grid [5]. However, the economics of installing additional equipment is poor and due to the random and fluctuating nature of the output of new generation equipment, it will lead to frequent fluctuations in the grid voltage and the reactive power demand will fluctuate with it. However, it is more challenging to achieve accurate and fast voltage regulation for reactive power compensators that use capacitor throwing as the main means [6]. A capacitor series inverter (CSI) is connected to the AC bus through an LC series coupling structure and has a wider reactive power regulation range compared to conventional inverters; it has higher voltage regulation accuracy compared to reactive power compensators and is more adaptable to fast regulation requirements [7, 8]. It has been demonstrated in the literature that DG units with CSI will have stronger bus voltage regulation and reactive power output capability at a lower cost [9, 10]. To reduce the active power transmission losses due to low voltage problems, optimal control of reactive power is very important. Researchers have more related results. The literature [11] proposed a reactive power optimization model for a distribution network containing DG and solved it using a multi-intelligent immune algorithm, which effectively reduces the active power losses in the network. In [12], a reactive electric control model for a distribution network containing OLTC and capacitors is proposed to minimize the daily energy losses and solved by a nonlinear interior point method with embedded discrete penalty terms. In [13], a microgrid (MG) voltage control optimization model with nonlinear constraints is proposed to coordinate the control of OLTC, capacitor, DG output and upper grid exchange reactive power to achieve the objective of minimizing active network loss and reactive power output cost of each reactive source. In [14], a cooperative control model of centralized reactive power in MG containing OLTC, DG, capacitor and D-STATCOM is proposed to meet the basic reactive power demand of the system and adjust the feeder voltage to the qualified range. The literature [15, 16] analyzed the reactive power output characteristics of PV, wind and gas turbines and proposed an optimal reactive power dispatching method before the day of the source-containing distribution network considering DG and capacitor bank coordination. The literature [17] proposed a fuzzy dynamic reactive power optimal dispatching model for distribution networks with the objectives of loss reduction and voltage fluctuation suppression. In [18], a dynamic optimization model for integrated dispatch of DG and reactive power compensation equipment is proposed for the overvoltage problem that may be caused by DG access to the distribution network. However, the existing research results only optimize one dimension of active or reactive power; for the MG with CSI-based DG units, the global optimum may not be achieved by considering only a single variable [19]. Therefore, in this paper, we propose the idea of “active-reactive two-dimensional tidal power flow optimal

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control” and combine it with a multi-time scale control method to arrange the operation of PV power and energy storage from the perspective of active and reactive power two-dimensional tidal power flows according to the prediction curves of PV power and load in long time scale, with the objective of local consumption and economic optimization.

2 Distribution Network Equipment Model 2.1 Simplified Model of Capacitive Inverter Power The capacitive inverter is coupled to the bus through a second-order LC branch. This branch is designed based on the load reactive power compensation capacity and the LC resonant frequency. The equivalent impedance of the LC branch Z CSI is calculated as follows. Z CC I =

1 − ωL ωC

(1)

Then the active and reactive power output from the inverter can be expressed as ( PCC I = ( Q CC I =

E2 VCC I E PCC cos δ − PCC Z CC I Z CC I E2 VCC I E PCC cos δ − PCC Z CC I Z CC I

) cos θ +

VCC I E PCC sin δ sin θ Z CC I

(2)

sin θ −

VCC I E PCC sin δ cos θ Z CC I

(3)

)

where E PCC and V CSI are the parallel network voltage and inverter output voltage, respectively; Z CC I is the equivalent coupling impedance; θ is the phase angle of the inverter coupling impedance, which is equal to −π/2; δ is the power angle. Combining Eqs. (2) and (3), a unified expression for active and reactive power is obtained as shown in Eq. (4). )2 ( ) ( E 2PCC VCC I E PCC 2 2 PCC + Q − = CC I I ZC ZC

(4)

The ratio of the square of the parallel network voltage to the equivalent coupling impedance of the inverter is noted as the power reference value Sbase , as shown in Eq. (5). Sbase = E 2PCC /Z C

(5)

As shown in Figs. 1, 2, assuming Sbase = 1, the relationship between the power output range and the ratio of inverter output voltage to bus voltage can be obtained

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Fig. 1 Power control range of the CSI Fig. 2 Power output range of CSI

according to Eqs. (4) and (5). In the figure, the z-axis represents the ratio of the output voltage to the parallel line voltage, and the x and y axes represent the normalized active and reactive power output ranges, respectively. From Fig. 1, it can be seen that the capacitive inverter can still achieve the power output including reactive power compensation when the output voltage is less than the parallel network voltage. This means that the capacitive inverter, as an energy conversion unit for grid-connected PV and energy storage, is able to reduce the voltage demand on the DC side while enhancing the flexibility of the power supply. If we take Sbase as the center of the circle and VCC I E PCC /Z C as the radius, the physical power output range of the capacitively coupled inverter can be obtained as shown in the black circle in Fig. 2.

2.2 Energy Storage Model Energy storage has only two operating states, charging and discharging, and its operating condition is usually described by the charge state. The charge state is the

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ratio of the capacity of the energy storage to its total capacity at the current moment and is strongly coupled to the operating results of the previous time period. When charging the energy storage unit. S OC(t + 1) = (1 − δ)S OC(t) − Pess (t)ηcha · Δt

(6)

When the energy storage device is discharged. S OC(t + 1) = (1 − δ)S OC(t) −

Pess (t) · Δt ηdis

(7)

where SOC(t) is the state of charge of the energy storage device at moment t. δ is the charging and discharging efficiency per unit time. Δt is the unit time interval. Pess (t) is the charging and discharging power at moment t, which is negative at the moment of charging and positive at the moment of discharge. ηcha and ηdis are the charging efficiency and discharging efficiency per unit time, respectively.

3 Two-stage Optimization Model for Two-Dimensional Tidal Power Flows at Long Time Scales The reactive power regulation of the capacitive inverter has a wide range, but during the high PV generation time, the real-time active power fluctuates greatly, and there is a possibility that the voltage crosses the limit due to the insufficient reactive power regulation capacity of the inverter, so the control of the short time scale requires the energy storage to dynamically adjust the charging and discharging power for auxiliary regulation. In order to ensure that the energy storage has sufficient regulation capacity in the short time scale and meets the real-time operation constraints, the SOC upper and lower limits should be adjusted and a certain adjustable margin should be reserved when developing the optimization scheme for the long time scale. Based on this, this paper adopts a two-stage optimization method to solve the coordinated active-reactive power control model of the new energy distribution network on a long time scale.

3.1 First Stage Optimization Objective Function Since the regulation of energy storage has a strong time-series coupling characteristic, the coupling optimization of the active regulation of energy storage devices at each time of the cycle is considered, and the sum of the system network loss and the cost of energy storage regulation is minimized as the optimization objective, which is expressed as follows.

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(8)

C where Ploss is the total active network loss during the optimization cycle. Pess is the regulation cost of energy storage during the optimization cycle, which can be calcuC can be obtained from the regulation lated by the following analytical method. Pess cost of energy storage and the tariff, where the regulation cost of energy storage can be divided into the operating cost C E1 and the depreciation cost C E2 , which is calculated as follows.

CE1 =

T ∑

( ) Comb Pct + Pdt Δt

(9)

( ) Cdep Udt 1 − Udt−1

(10)

t=1

CE2 =

T ∑ t=1

where, C omb is the maintenance cost coefficient of energy storage device (unit: Yuan/ kWh); Pct , Pdt are the charging and discharging power of energy storage device at moment t, respectively; T is the dispatch cycle duration; Δt is the time interval in hours; Udt , Udt−1 are the discharging state at moment t, the previous moment (t-1), respectively; C dep is the depreciation cost of energy storage device (unit: Yuan), calculated as follows. Cdep =

) ηdep ( C p Pess N + C S Sess N N

(11)

where, ηdep is the depreciation cost factor; PessN and S essN are the rated power and rated capacity of the energy storage device; C p is the present value of the installed cost per unit power of the energy storage device (unit: $/kW); C S is the present value of the installed cost per unit capacity of the energy storage device (unit: $/kW); N(t) is the number of cycles of the energy storage device at the current moment t, which is related to the depth of discharge DOD(t) at the current moment t, and its calculation formula is as follows. D O D(t) = 1 −

t Sess Sess N

N (t) = b1 + b2 e−b3 D O D(t) + b4 e−b5 D O D(t)

(12) (13)

t where Sess is the remaining power of the energy storage device at the current moment t; b1 –b5 are the parameters provided by the manufacturer. To maintain consistency in the units of the variables in the objective function, the regulatory cost of energy storage is expressed in terms of the regulatory cost after discounting it in conjunction with the unit price of electricity, which is expressed as follows.

Study of an Acitve/Reactive Power Coordinative Control Method … C Pess =

n Ess 1 ∑ [C E1i + C E2i ] τ Δt i=1

133

(14)

where τ is the unit price of electricity (in Yuan/kWh); ness is the total number of energy storage in the distribution network.

3.2 Second Stage Optimization of the Objective Function Solving the first stage optimization model can determine the storage active control plan, then the storage regulation cost is a deterministic quantity, so the objective function of the second stage optimization model no longer considers the storage regulation cost, and only considers the minimum expected value of active network loss of the system during the optimization cycle, which is expressed as follows. min F2 = Ploss

(15)

3.3 Constraints 3.3.1 Tidal Equation Constraint ⎧ n [ ( ( ) ( ))] ∑ ⎪ ⎪ V j (t) · G i j cos θi j (t) + Bi j sin θi j (t) ⎨ PGi (t) − PDi (t) = Vi (t) j=1

n [ ( ( ) ( ))] (16) ∑ ⎪ ⎪ V j (t) · Bi j cos θi j (t) + G i j sin θi j (t) ⎩ Q Gi (t) − Q Di (t) = Vi (t) j=1

where PGi denotes the active power of the power supply at node i, PDi denotes the active power of the load at node i, QGi denotes the reactive power of the power supply at node i, QDi denotes the reactive power of the load at node i, V i denotes the voltage amplitude at node i, V j denotes the voltage amplitude at node j, Gij denotes the conductance between nodes i and j, Bij denotes the conductance between nodes i and j, and θ ij denotes the difference between the voltages at nodes i and j of the phase angle difference.

3.3.2

Control Variable Inequality Constraints

The control variables of the model include the capacitive inverter reactive power compensation quantity QCSI , the active power output of the storage device Pess and the optical storage parallel network voltage V pves , with the following inequality constraints.

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Q CCIi. min ≤ Q CCIi ≤ Q CCIi. max , i ∈ Ωpves

(17)

Vpvesi. min ≤ Vpvesi ≤ Vpvesi. max , i ∈ Ωpves

(18)

Pessi. min ≤ Pessi ≤ Pessi. max , i ∈ Ωpves

(19)

where Ωpves is the set of optical storage grid-connected nodes; QCSIi is the reactive power compensation amount of the ith capacitive inverter, QCSIi.max , QCSIi.min are the upper and lower limits of the reactive power compensation amount of the ith capacitive inverter, respectively; V pvesi is the voltage of the ith optical storage gridconnected point, V pvesi.max and V pvesi.min are the upper and lower limits of the voltage of the ith optical storage grid-connected point, respectively; Pessi is the active output of the ith energy storage, Pessi.max , Pessi.min are the upper and lower limits of the active output of the ith energy storage. (1) The upper and lower SOC constraints for the energy storage device can be expressed by the following equation. S OCi. min + εessi ≤ S OCi ≤ S OCi. max − εessi

(20)

where, SOC i.max and SOC i.min are the upper and lower limits of the charge state of the ith energy storage respectively; εess is the reserved capacity margin factor, i.e., the ratio factor of the reserved capacity to the rated capacity of the energy storage. Combined with the SOC constraint of energy storage the maximum charge/discharge power constraint of Eq. (19) can be further transformed into Eq. (21). ⎧

( t−1 [ ] ) t Pessi. max = min [Pessi. max' ( Sessi − Sess N i · (S OC i min + εessi ) ) · ηdi /Δt ] t−1 t ' Pessi. max = max Pessi. min Sessi − Sess N i · (S OC i max + εessi ) · ηci /Δt

(21)

t t where, Pessi. max , Pessi. min are the upper and lower limits of the active output power of t−1 denotes the remaining power of the ith energy the ith energy storage moment t; Sessi storage device at the previous moment (t-1); ηci , ηdi are the charging and discharging efficiency of the ith energy storage device, respectively. Wherein, the remaining power of the energy storage device at the current moment can be calculated from the remaining power at the previous moment and the charging and discharging power at the current moment, and the specific calculation formula is.

t−1 t Sessi = Sessi + (Pcit ηci −

Pdit )Δt − Slossi (1 − Ucit )(1 − Udit ) ηdi

(22)

where, Pci and Pdi are the charging and discharging power of the ith energy storage device respectively; Ucit , Udit denote the charging and discharging state of the ith energy storage device at moment t respectively; S lossi denotes the static energy loss of the ith energy storage device.

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(2) In addition, the operation of the energy storage device shall satisfy the charge/ discharge balance constraint, i.e., the remaining power at the beginning of the operating cycle shall be equal to the remaining power at the end of the cycle, as expressed below. | T | | S − S 0 | ≤ ΔSessi , i ∈ Ωpves essi essi

(23)

T where, Sessi is the remaining power at the end moment of the ith energy storage 0 is the remaining power at the beginning moment of device operating cycle; Sessi the ith energy storage device operating cycle; ΔSessi is the charge/discharge balance allowable deviation amount, the specific solution can be made the deviation amount is 0, and the charge/discharge balance deviation amount of energy storage is determined by the real-time control situation, then there exists ΔSessi ≤ SessNi ·εess , so the reserved capacity margin coefficient can be taken according to the charge/discharge balance allowable deviation amount.

3.4 State Variable Opportunity Constraints The state variables of the model include PV inverter reactive output QCSI and each node voltage V. Since the optimization model accounts for the uncertainty of load and PV output, both QCSI and V are random variables. To avoid problems such as the high probability of node voltage crossing the limit under short time scale control and difficulty in tracking the voltage control plan for PV inverter reactive output, the optimization model for long time scale uses chance constraints, which are expressed as follows. t t t Pr{Q CC I i. min ≤ Q CC I i ≤ Q CC I i. min } ≥ a Q , i ∈ Ω pv

(24)

Pr{Vi. min ≤ Vi ≤ Vi. max } ≥ aV , i ∈ Ω

(25)

t t where, Q CC I i. max and Q CC I i. min are the upper and lower limits of the reactive power output of the capacitive inverter at moment i, respectively; a Q is the reactive power confidence level; V i.max and V i.min are the upper and lower limits of the voltage at node i, respectively; α V is the voltage confidence level; Ωpv is the set of PV parallel networks; Ω is the set of all nodes in the distribution network; Pr{} denotes the probability that the event holds. Since the modeling of load and PV uncertainty uses a prediction error model that follows a normal distribution, the “3σ principle” is used to determine the upper and lower limits of PV reactive power output at each moment, and the specific calculation formula is as follows. √ t 2 − (μtPpvi +3σPpvi )2 (26) Q tpvi.max = SpvNi

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√ t 2 − (μtPpvi +3σPpvi )2 Q tpvi.min = − SpvNi

(27)

where, S pvNi is the rated capacity of the ith PV inverter; μtPpvi is the expected value of t is the standard deviation of active active power output at the ith PV moment t; σPpvi power output at the ith PV moment t.

4 Adaptive Convergent Control Strategies at Short Time Scales The control logic and the boundary conversion conditions for different node types for the real-time charging and discharging power adjustment method for energy storage based on boundary conversion of optical storage node types are specified as follows. Step 1: Control logic based on optical storage PV node type. The real-time power data of the load and PV are collected, the real-time reactive adjustable capacity of the inverter is calculated, and the reactive power output target value of the inverter is solved according to the ideal optimal control plan trend calculation. If the target value of the reactive power output of the inverter is not greater than the value of reactive adjustable capacity, the voltage control plan of the grid-connected node of optical storage can be tracked by its output reactive power only. At this time, the control plan of the voltage tracking optimization scheme of the light storage grid-connected node, the control plan of the active power output of the energy storage device tracking optimization scheme, and the PV real-time active power data can be measured, that is, the light storage node is a PV type node, in this type, the control of the short time scale is the tracking of the long time scale optimization scheme. Therefore, the boundary condition for PV node type control based on PV storage is that the target value of inverter reactive power output is not greater than the value of reactive adjustable capacity. Step 2: Control logic based on optical storage QV node type. When the target value of inverter reactive power output is greater than the value of reactive adjustable capacity, the inverter reactive power regulation method alone can no longer track the voltage control plan of the grid-connected network. In this regard, firstly, the inverter’s reactive power output is controlled to the reactive adjustable capacity value, and the energy storage reactive output value is 0. The control plan of the PV storage grid voltage tracking optimization scheme is maintained, and the active power output target value of the PV storage system is obtained by solving the tide calculation with the PV storage QV node, and then the active power output target value of the energy storage device is obtained by subtracting the PV real-time active power measurement value. Finally, it is judged whether the target value of the active power output of the storage device meets the real-time maximum charge/discharge

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power constraint. Which, since the real-time SOC upper and lower limits constraint no longer considers the influence of reserved capacity margin, the real-time charge and discharge power upper and lower limits of energy storage are changed to the following equation. ⎧

) [ ( t−1 ] t Pessi. max = min [ Pessi. max , ( Sessi − SessNi · S OC i min )· ηdis /Δt ] t−1 t Pessi. min = max Pessi. min , Sessi − SessNi · S OC i max ) /(ηcha Δt)

(28)

Therefore, the boundary conditions based on the optical storage QV node type control are that the target value of the inverter reactive power output is greater than the value of the reactive adjustable capacity and the target value of the storage active power output satisfies the real-time maximum charge and discharge power upper and lower limits constraints. Step 3: Control logic based on the type of optical storage PQ node. On the basis of the second logic step, if the target value of energy storage active power output cannot meet the upper and lower limits of real-time maximum charge and discharge power constraints, the active power output value of energy storage is controlled as the real-time maximum charge and discharge power value, and the charge and discharge states are kept consistent with the target value. That is, the active power output value of energy storage under charging state is controlled as t t Pessi. min , and under discharging state is Pessi. max , plus the measured PV active power data can determine the joint active power output value of the optical storage power system, and the inverter reactive power output is equal to the reactive adjustable capacity value, and the storage reactive power output value is 0. Then the equivalent injected active and reactive power of the optical storage node can be determined, that is, the optical storage parallel network is a PQ type node. Therefore, the boundary condition based on the light storage PQ node type control is that the inverter reactive power output target value is greater than the reactive adjustable capacity value, and the storage active power output target value cannot satisfy the real-time maximum charge and discharge power upper and lower limits constraint.

5 Simulation Example In this paper, the modified IEEE33 node system is selected as the base data, and the photovoltaic storage co-generation system is connected at node 17 with an installed capacity of 2.1 MW. The total active and reactive load prediction curves of the system are shown in Fig. 3, the PV output prediction curve is shown in Fig. 4, and the energy storage parameters and other simulation parameters are set in Table 1. Combining the prediction curves of PV and load, the comparative results before and after optimization are obtained according to the solution of the method proposed in this paper as shown in Table 2.

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Fig. 3 Day-ahead load power forecast curve

Fig. 4 Forecast curve of PV output before the day

Analysis of the above table shows that the optimized network losses are reduced by 28.48%, which significantly improves the economy of distribution network operation. The voltage control schedule, active power output schedule of storage, time series variation of storage SOC and PV reactive power output curve for some time periods are given in Figs. 5, 6, 7, and 8 for the parallel network of optical storage respectively. Analysis of the above graph shows that, due to the high PV output and small system load during 11 –14 h, there is a large mismatch between the source and load in the timing characteristics, and the energy storage reduces the voltage amplitude of the parallel network by absorbing a large amount of active power to ensure that the voltage of the whole network is in the qualified range and also reduces the excess

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Table 1 Related simulation parameter settings Parameters

Numerical value

Parameters

Numerical value

PessN /MW

0.75

S 1 ess /MWh

1.5

S essN /MWh

3

ηdep /%

0.1

SOC max

0.9

N/time

4500

SOC min

0.2

εESS

0.1

Pess. min/MW

−0.75

τ Yuan/kWh

0.7

Pess. max/MW

0.75

S pvN /MVA

2.1

ηcha

0.9

V min /p.u

0.93

ηdis

0.9

V max /p.u

1.07

S loss /kWh

2

Vpves. min/p.u

0.93

C omb /$·kWh−1

0.1

Vpves. max/p.u

1.07

CS

/$·kWh−1

C P /$·kW−1

1200

αV

0.99

667

αQ

0.99

Table 2 Comparison of optimization effects

F 1 /kW

Ploss /kW

Pre-optimization

1605.05

1590.65

Post-optimization

1145.08

1137.59

Fig. 5 Voltage control plan for optical storage parallel network

active power backwards to cause a large amount of line loss; during 20 –23 h, the PV active output is 0, but the system load is In order to improve the economy of the system operation, the energy storage sends out a large amount of active power to meet the load demand, while the inverter stabilizes the voltage through reactive power compensation; it is noted that the voltage at the parallel network of light storage decreases slightly after 18:00. voltage remains within a reasonable range.

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Fig. 6 Energy storage active output plan

Fig. 7 Energy storage SOC timing variation curve

Fig. 8 Node voltage without optimized

For the convenience of observation, the voltage curves of nodes 16, 17 (parallel network), and 18 throughout the day before and after real-time control are given in Figs. 8 and 9, respectively.

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Fig. 9 Optimized node voltage

6 Conclusion This paper discusses the active-reactive two-dimensional tidal control method based on capacitively coupled inverters with high reactive power capacity, constructs a twostage optimization method to solve the two-dimensional tidal optimization model in long time scale, and a real-time charging and discharging power adjustment of energy storage based on the boundary conversion of optical storage node types in short time scale method. Real-time energy storage charging and discharging power adjustment method based on the boundary conversion of optical storage node types under a short time scale is proposed. The method can effectively use the reserved capacity margin of energy storage for real-time dynamic compensation, which can still ensure the voltage stability of system operation in the case of insufficient inverter reactive adjustable capacity, and has high engineering practical value.

References 1. P. Liu, Z. Cai, P. Xie, X. Li, Y. Zhang, A decomposition-coordination planning method for flexible generation resources in isolated microgrids. IEEE Access 7, 76720–76730 (2019) 2. M.E. Akdogan, S. Ahmed, Novel compensation methods using energy storage system (ESS) in islanded unbalanced single-/three-phase multimicrogrids. IEEE Trans. Ind. Appl. 58(4), 5457–5468 (2022) 3. M.S. Golsorkhi, D.J. Hill, M. Baharizadeh, A secondary control method for voltage unbalance compensation and accurate load sharing in networked microgrids. IEEE Trans. Smart Grid 12(4), 2822–2833 (2021) 4. R. Dutta, S. Chakrabarti, A. Sharma, Topology tracking for microgrids. IEEE Trans. Power Syst. 36(4), 2855–2865 (2021) 5. P.G. Rullo, L. BraCSIa, D. Feroldi, D. Zumoffen, Multivariable control structure design for voltage regulation in microgrids. IEEE Lat. Am. Trans. 20(5), 839–847 (2022) 6. Y. Wang, N. Zhang, H. Li, J. Yang, C. Kang, Linear three-phase power flow for unbalanced microgrids with PV nodes. CSEE J. Power Energy Syst. 3(3), 321–324 (2017)

142

D. Li et al.

7. W. Deng, N. Dai, K. Lao et al., A virtual-impedance droop control for accurate active power control and reactive power-sharing using capacitive-coupling inverters. IEEE Trans. Ind. Appl. 56(6), 6722–6733 (2020) 8. W. Deng, Z. Liu, H. Qin, M. Chen, J. Zhang, Study of a virtual-impedance of the capacitor-series inverter for wider accurate power control range. Energy Rep. 8(6), 27–36 (2022) 9. W. Deng, N.Y. Dai, et al., An enhanced power decoupling control for grid-connected capacitivecoupling inverters, in 2019 IEEE Energy Conversion Congress and Exposition (ECCE) (Baltimore, MD, 2019) 10. W. Deng, Q. Li, Y. Zhang, Y. Yi, G. Huang, An unequal power sharing strategy for capacitiveand inductive-coupling inverters in microgrid. IEEE Energy Convers. Congr. Expo. (ECCE) 2021, 3444–3451 (2021) 11. Y. Luo, Q. Nie, D. Yang, B. Zhou, Robust optimal operation of microgrid based on minimum confidence interval of distributed energy beta distribution. J. Mod. Power Syst. Clean Energy 9(2), 423–430 (2021) 12. M.B. Liu, C.A. Canizares, W. Huang, Reactive power and voltage control in distribution systems with limited switching operations. IEEE Trans. Power Syst. 24(2), 889–899 (2009) 13. S. Conti, A.M. Greco, Voltage regulation through optimal reactive power dispatching in microgrids, in The 14th IEEE Mediterranean Electro-Technical Conference, May 5–7 (AjaCSIo, France, 2008), pp. 792–798 14. R. Majumder, Aspect of voltage stability and reactive power support in active distribution. IET Gener. Transm. Distrib. 08(03), 42–45 (2014) 15. Y.Z. Gerdroodbari, R. Razzaghi, F. Shahnia, Decentralized control strategy to improve fairness in active power curtailment of PV inverters in low- voltage distribution networks. IEEE Trans. Sustain. Energy 12(4), 2282–2292 (2021) 16. G. Mitrentsis, H. Lens, A dynamic microgrid equivalent for enhancing the generalization capability of the exponential recovery model in stability studies. IEEE Trans. Power Syst. 36(3), 2709–2712 (2021) 17. B. Wei, Z. Qiu, G. Deconinck, A mean-field voltage control approach for microgrids with uncertainties. IEEE Trans. Smart Grid 12(2), 1455–1466 (2021) 18. P. Kou, D. Liang, R. Gao, Y. Liu, L. Gao, Decentralized model predictive control of hybrid distribution transformers for voltage regulation in microgrids. IEEE Trans. Sustain. Energy 11(4), 2189–2200 (2020) 19. Y. Xiang, W. Han, J. Zhang, J. Liu, Y. Liu, Optimal sizing of energy storage system in microgrids using fourier- legendre series based state of energy function. IEEE Trans. Power Syst. 33(2), 2313–2315 (2018)

Multi-AGV Cooperative Scheduling Model Based on Improved Time Window Yingqi Liu

Abstract In the process of automated agv terminal use. In order to solve the conflict problem of automatic guided vehicles (AGVs) in intersections, the scheduling problem of multiple AGVs is studied and optimized by the time window model. Based on setting the compatibility stage and the conflict stage at the intersection, the AGVs in the compatibility stage can pass through the intersection at the same time, and the AGVs in the conflict stage can delay the time window, and establish the cooperative scheduling model of multiple AGVs to avoid conflicts. The experimental results show that the model can effectively improve the working efficiency of AGV by comparing the experimental group with the traditional time window method and the optimized time window method, and improve the operation efficiency of the intelligent port. Keywords Improved time window · Collision avoidance: coordination and scheduling · The conflict phase · Intelligent port

1 Introduction The application of AGV in automated terminals is gradually increasing, and the research on its path planning is mainly divided into two types: static path planning and dynamic path planning. Ghasemzadeh et al. [1] proposed a method to avoid road network congestion on the basis of static network diagrams. Multi-AGV route search method. Chiew [2] proposed a bi-tonal regression sorting multi-vehicle path method to avoid congestion and deadlock. However, the optimized path distance obtained by this method may be longer. Gawrilow [3] established a multi-AGV static path model with a time window with the goal of minimizing the maximum amount of tasks passed by each edge in the simulation graph. Dynamic path planning is more about constructing a multi-objective path planning model based on the uncertain factors Y. Liu (B) School of Transportation Engineering, Dalian Maritime University, Dalian, Liaoning, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_13

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of the environment, which can continuously adjust the optimal path of the AGV. Aiming at the collision and deadlock problems, Smolic-Rocak et al. [4] proposed a dynamic path planning method for multiple AGV operations. The path planning of the AGV depends on the current task volume and task priority of the running AGV. In order to solve the shortest dynamic path The problem is that a path planning method using time window constraints is proposed, but this method requires window overlap testing to achieve AGV collision avoidance. Nishi et al. [5] proposed to combine AGV task scheduling and conflict-free path planning to establish a mixed-integer bi-level programming model, and use genetic algorithms to implement dynamic conflictfree path planning for AGV. Tai Yingpeng et al. [6] proposed an AGV dynamic path planning method based on a time window model, which uses the A* heuristic algorithm and considers collision avoidance conflicts. Simulation experiments show the applicability and robustness of the algorithm. Most studies believe that as long as the time difference between AGVs arriving at the same intersection is within the safe time allowed to pass, there will be conflicts, but if you consider the coordinated phase of the intersection, you can find that there is the possibility of two AGVs crossing the same intersection at the same time.

2 Mathematical Model 2.1 Assumptions (1) The capacity of each path is fixed, and the upper limit traffic flow of the path shall not be exceeded. Vehicles can drive in both directions on each path; (2) In a certain state on the path, the vehicle runs at a constant speed; (3) There is a certain safe distance between vehicles traveling in the same direction on a certain path, and this safe distance is realized by the installation of obstacle avoidance equipment; (4) Vehicles occupy only one path at the same time, and each path can accommodate no less than one AGV vehicle; (5) The deceleration time when the vehicle reaches the intersection and the acceleration time after passing the intersection are not considered; (6) The time for the vehicle to return to the path from the waiting station is not considered; (7) The time of unloading and loading of cargo during the mission is not considered; (8) The administrator can set the priority of the task in advance, and the default priority setting sequence is the time sequence of the task.

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2.2 Parameter R is the turning radius on the turning path; Vt0 is the no-load running speed of the vehicle on the straight path; Vt is the load running speed of the vehicle on the straight path; Vc0 is the no-load running speed of the vehicle on the turning path; Lv0 is the vehicle’s no-load running speed on the turning path Load running speed; Lv is the length of the vehicle body when the vehicle is empty; Lab0 is the length of the vehicle body when the vehicle is loaded; is the straight-line distance of the path ab; tki is the time window of the path i to the AGV transport vehicle k; tin ki is the start time of the a Is the end time of the path time; p path time window; tout ki k is the phase of vehicle k at intersection a, and a and b are the serial numbers of the intersection.

2.3 Mathematical Model Based on the above assumptions, the time window model of the AGV system path planning is as follows: T =

   tki = tkiin , tkiout

(1)

The path node occupancy of multiple AGVs in the automated container terminal scenario can be accurately described by mathematical models. Assuming that there are k AGVs that need to perform transportation tasks in a certain period of time, Denoted by the set. K = {a1 , a2 , ..., ak } For each AGV trolley, the path of the trolley is represented by Pk = {Pi , P j , ..., Pk }; The time window of path Pi relative to AGV transport vehicle ak is tki = [tkiin , tkiout ]. The time window of the path point of the transport vehicle ak performing the current task can be represented by tk = in out {[tkiin , tkiout ], [tkinj , tkout j ], ..., [tkn , tkn ]}. ⎫ ⎡ j ⎧ ⎪ t11 T ( p1 ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎢tj ⎪ T (p ) ⎪ ⎪ ⎪ ⎢ ⎪ ⎪ 2 ⎪ ⎪ ⎢ 12 ⎪ . ⎪ ⎪ ⎬ ⎢ .. ⎨ . ⎪ . ⎢ . =⎢ T = ⎪ ⎢ t1kj ⎪ T ( pk ) ⎪ ⎪ ⎢ ⎪ ⎪ ⎪ .. ⎪ ⎢ .. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎣ . . ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ j T ( pm ) t1m

⎤ j tr 1 j tr 2 ⎥ ⎥ .. ⎥ ⎥ . ⎥ j j j ⎥ t2k · · · tck · · · tr k ⎥ ⎥ .. .. .. ⎥ . . . ⎦ j j j t2m · · · tam · · · tm j

t21 · · · j t22 · · · .. .

out in r un tkb = tka + tab

r un tkab =

L v0 + L ab0 Vt0

j

ta1 · · · j ta2 · · · .. .

(2)

(3) (4)

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L v + L ab0 Vt

(5)

r un tkb =

π R + 2L v0 2Vc0

(6)

r un tkb =

π R + 2L v 2Vc

(7)

r un tkab =

n 

min D = max{

ai (tti + tci )}

(8)

i=1 n 

ai ≤n

(9)

xtmk = 1

(10)

xtmk = 1

(11)

i=1 M  m=1 K  k=1

Ntab = yab

n 

z itabk

(12)

i=1 in out tab = [tab , tab ]

Ntab + Ntba ≤

L ab Lv

(13) (14)

t ja ∩ tka ϕ( paj , pka ) = 1

(15)

t ja ∩ tka ϕ( paj , pka ) = 0

(16)

ai ∈ {0, 1}, 0 < i ≤ n

(17)

Parameter range:



1, Vehicle i did received the task 0, Vehicle i did not receive the task

(18)

1, Vehicle k does task m within time window tk 0, Vehicle k does not do task m within time window tk

(19)

ai =  xm tk

=

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 yab =  z itabk =

147

1, The path from intersection a to b exists 0, The path from intersection a to b does not exist

(20)

1, Vehicle i is on path ab within time window tk 0, Vehicle i is not on path ab within time window tk

(21)

(8) is the minimization of the maximum completion time into the objective function. (9) means that the number of vehicles in the task is not greater than the total number of vehicles in the system; (10) means that each task can only be assigned to one AGV at any time. (11) Each AGV can only complete one mission at any given time.

2.4 Analysis of Calculation Examples This article uses MATLAB R2020a software to carry out dynamic path planning simulation verification under time window constraints. Part of the horizontal transportation area of an automated terminal is selected, 300 m long and 100 m wide, including 45 yard operation lanes and 40 quay crane buffer lanes. The AGV travel speed is set to 2 m/s. This paper designs two sets of comparative experiments. One is the path planning when the number of tasks is the same, and the other is the path planning when the number of tasks is gradually increasing. (1) The number of tasks is the same The experiment set a batch of tasks including 40 subtasks, that is, it is necessary to plan 40 AGVs to generate paths from different yard operation lanes to different quay crane buffer lanes. Randomly generate 5 million batches of tasks, and calculate the number of potential conflicts of the route according to the start and end positions of the 40 subtasks in each batch. 200 batches of tasks were sampled for each category, and the average completion time of 40 subtasks in each batch of tasks was calculated. The experimental results are shown in Figs. 1 and 2. (2) The number of tasks is different Each batch of tasks contains 10, 20, 30, and 40 subtasks for classification and analysis. 200 batches of tasks are sampled for each category, and the average completion time and average waiting times of each batch of tasks are calculated. The experimental results are shown in Figs. 3 and 4. Show.

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Fig. 1 Comparison of average completion time

Fig. 2 Comparison of average waiting times

3 Conclusion The simulation results can be analyzed, and the improved time window method can be used to enable AGV scheduling to improve AGV work efficiency. Through the normal time window and the improved time window method and the waiting control method at the node, according to the time delay of the AGV from each quay crane to complete the container task, it can be seen that the improved time window method can reduce the delay time of the AGV completion. Improve overall efficiency.

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Fig. 3 Comparison of the average completion time of different tasks

Fig. 4 Comparison of average waiting times for different tasks

References 1. H. Ghasemzadeh, E. Behrangi, M.A. Azgomi, Conflict-free scheduling and routing of automated guided vehicles in mesh topologies[J]. Robot. Auton. Syst. 57(6–7), 738–748 (2009) 2. Scheduling and Routing of AMOs in an Intelligent Transport System[J]. IEEE Trans. Intel. Transp. Syst. 10(3), 547–552 (2009) 3. E. Gawrilow, M. Klimm, R.H. Hring et al., Conflict-free vehicle routing[J]. Euro J. Transp. Log. 1(1–2), 87–111 (2012) 4. N. Smolic-Rocak, S. Bogdan, Z. Kovacic et al., Time windows based dynamic routing in multiAGV systems[J]. IEEE Trans. Autom. Sci. Eng. 7(1), 151–155 (2009)

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5. T. Nishi, Y. Hiranaka, I.E. Grossmann, A bilevel decomposition algorithm for simultaneous production scheduling and conflict-free routing for automated guided vehicles[J]. Comput. Oper. Res. 38(5), 876–888 (2011) 6. T. Yingpeng, X. Kexin, L. Yegui et al., Research on multi-AGV path planning method[J]. Comp. Sci. S2, 84–87 (2017)

Research on CTCS-N Onboard Equipment Testing Method Based on Timed Automata Mutation Model Zhuofan Gao and Tao He

Abstract The onboard equipment of the Chinese Train Control System-New undertakes more functions of ground equipment, and the correctness and reliability of its functions are directly related to the safety of the whole train control system. The previous test methods for the train control system can no longer meet the requirements of CTCS-N. This paper will propose a test method for the mutation model of timed automata suitable for the CTCS-N onboard equipment, a complex system. Firstly, this paper analyses the CTCS-N onboard equipment typical scenes, establishes its timed automata model based on timed automata theory and verifies it. Secondly, according to the safety function of the system, a mutation operator is designed and injected into the model to generate a mutation model, and the consistency between the normative model and the mutation model is checked to generate a test case. Finally, the feasibility and superiority of this method are proved by the consistency evaluation of test cases. Keywords CTCS-N · Timed automata · Mutation testing · Onboard equipment

1 Introduction China’s Qinghai Tibet Railway has problems such as low traffic density, poor geographical environment, and difficult equipment maintenance [1]. The signal system of Golmud Lhasa section adopts the Incremental Train Control System, which

Z. Gao (B) School of Lanzhou, Jiaotong University, Lan Zhou, China e-mail: [email protected] T. He Gansu Research Center of Automation Engineering Technology for Industry & Transportation, Lan Zhou, China Gansu Rail Transit Signal and Control Evaluation Industry Technology Center, Lan Zhou, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_14

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is incompatible with the existing Chinese Train Control System. The basic specifications for the new train control system will be formulated in 2020. Traditional test workload accounts for about 40% of the total workload of system development, so the research on test methods has become a hot topic in recent years. The new design mode of the new train control system makes the onboard equipment more complicated and the test for the complex system is usually timeconsuming and laborious. The previous test methods for the train control system can no longer meet the requirements of CTCS-N. Model-based testing mainly relies on a static exhaustive traverse of the entire space [2]. The onboard structure model of the new train control system is large, and the time consumed and memory required to exhaust all traverses will explode. If the test method based on model mutation is not selected and all mutation operators are applied, a large number of variants will be generated, which will increase the test cost and reduce the test efficiency. At present, the majority of testing methods are to reduce workload while ignoring the quality of test cases. The method of this paper can effectively alleviate the space explosion problem of test case generation, save test costs and evaluate the integrity of test cases. In recent years, there has been a number of research on model mutation test methods. Lorber [3] proposed a method combining MBMT method with Time Computation Tree Logic. Aichernig [4] proposed MBMT method based on TA and realized it on MoMuT::TA. Guo Haonan [5] designed a scene model for ATO system of urban rail transit and verified the security of the system by combining variation test technology. This paper intends to combine model testing technology with mutation testing technology to effectively detect system faults and generate test cases, and to evaluate the adequacy of test cases. It provides technical support for the safety protection of the existing new train control system and provides some theoretical reference for the application of the new train control system in Western China and remote areas.

2 Introduction to CTCS-N Onboard Equipment and Typical Operating Scenarios 2.1 CTCS-N Onboard Equipment The new train control system conforms to the overall structure of existing CTCS and mainly consists of onboard equipment and ground equipment. Onboard equipment mainly consists of ATP main control unit, ATO main control unit, drivermachine interface (DMI), balise transmission module (BTM), track circuit reader (TCR), judicial record unit (JRU), train interface unit, speed measuring and distance measuring unit, train integrity checking unit, wireless communication unit, communication station and antenna, etc. Its main functions include multi-source integrated positioning of trains, checking of train integrity and sending train position reports to RBC and TSRS. Train driving safety can be monitored according to target-distance

Research on CTCS-N Onboard Equipment Testing Method Based … Communication antenna

Train tail equipment Train tail communication antenna

Train integrity inspection train tail equipment

Train control onboard communication radio 1

Train control onboard communication radio 2

Satellite antenna Onboard ATP equipment Satellite receiving unit

Wireless communication unit

Multi function control unit

153

Train integrity inspection unit

Judicial record unit

Train interface unit

ATP main control unit DMI Digital map

Speed measurement and distance measurement unit

Speed measuring equipment

Balise information module

BTM antenna

Track circuit information reader

TCR antenna

Fig. 1 CTCS-N onboard equipment structure

mode curves according to train parameters and ground equipment provided permits, line data, and electronic maps. The structure of CTCS-N onboard equipment is shown in Fig. 1.

2.2 CTCS-N Operation Scenario The main operation scenarios of the new train control system include registration and start-up, cancellation, grade conversion, traffic permit, RBC switching, TSRS switching, automatic phase separation, temporary speed limit, fault handling, disaster protection, backup monitoring mode, etc. Among them, the level conversion scenario is that CTCS-N plays an important role in ensuring the conversion of onboard equipment, so this paper intends to adopt the level conversion scenario as the main research scenario. Example of CTCS-3 to CTCS-N conversion: First, C3-RBC sends advance notice information to CN RBC and applies for route information. After receiving the route information, C3 RBC sends CN driving permission to onboard equipment; After the train passes the TSRS call balise, the onboard equipment starts to call TSRS and completes registration and electronic map download; When the train approaches RBC switching balise, C3-RBC sends RBC switching command to onboard equipment; After the front end of the train passes the RBC switch balise, CN-RBC sends the takeover command to C3-RBC and sends the level conversion command and driving permission to onboard equipment; After the rear end of the train passes RBC to switch balise, the communication between onboard equipment and C3-RBC ends; After the front end of the train passes the level conversion balise, the onboard equipment will automatically switch to the CTCS-N level. The schematic diagram of its level conversion scenario is shown in Fig. 2.

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Z. Gao and T. He Request Route Information CN-TSRS

Route information and train takeover information

Digital map Movement authority-C3

TSRS call balise group

CN-RBC

C3-RBC

Movement authority-CN

Movement authority-CN

Grade conversion balise group

End point of movement authority

Fig. 2 Schematic diagram of CTCS-3 to CTCS-N level conversion scenario

3 Timed Automata Model and Mutation Testing Method 3.1 Construction of Timed Automata Model Because the communication between subsystems in the CTCS-N level conversion scene has strict continuous time constraints, it expresses complex interaction characteristics. The theory of timed automata can characterize the relationship between continuous time and temporal logic, and it has special model verification tools to verify the correctness of model functions and performance [6]. Therefore, this paper chooses timed automata theory to model. The establishment and verification framework of timed automata model is shown in Fig. 3. Firstly, according to the technical specifications of CTCS-N, the key information of the operation scenario is sorted out, the flow chart of information interaction is generated, and the time automaton model is established. Then collate the security and functional requirements of the scenario and describe them using BNF statements. Finally, verify that the model meets its security and functional requirements in the UPPAAL modelling tool.

Fig. 3 Timed automata model establishment and verification framework

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Train control systems have complex characteristics such as distribution and mixing. It is very difficult to build a model that completely restores the reality. Therefore, some principles can be used to constrain the model, so that the model can clearly and accurately describe the system behaviour. Train control system modelling should follow the following three rules.

3.2 Mutation Test Process The mutation testing process implemented in MoMuT::TA [7, 8] designs a mutation operator according to the safety function of the system, and injects it into the established timed automata model to generate a mutation model; Then checks the consistency between the normative model and the mutation model. If the equivalent model (indicating that the mutation operator of the model is not injected) is discarded, the non-equivalent model is used to generate a test case set based on the test case generation algorithm.

4 CTCS-N onboard Equipment Test Case Generation 4.1 Time Automata Model of System The main research objects of the new train control system level conversion scenario are onboard equipment, balise, C3-RBC, CN-RBC, and TSRS. The product of time automata models of each subsystem are used to describe the whole system [9]: TA = Onboard  Balice  RBC1  RBC2  TSRS. The constructed timed automata model is shown in Fig. 4. After establishing the timed automata model, it is necessary to sort out the security and functional requirements of the system. According to the system specification, there are 6 functional requirements and 2 performance requirements, which are converted into BNF statements and verified based on the UPPAAL verifier. There is a circle after the verification statement every day. The green circle indicates that the verification has passed, and the red circle indicates that the verification has failed. The verification result is shown in Fig. 5.

4.2 Mutation Generation At present, there are 12 kinds of mutation operators for the timed automata model: change the original position, change the target position, auto loop, change the Sink position, change the position invariant, change the behaviour to other behaviour,

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Fig. 4 Time automata model of system

Fig. 5 System model verification diagram

reverse the clock reset, change the variable update, change the clock constraint operator, change the clock constraint constant, change the variable constraint operator, change the variable constraint constant. The fault modes of vehicle ground information interaction are sorted out according to the scene of onboard equipment level conversion. The TA statement is used as a bridge to directly establish a mapping relationship between the fault mode and the corresponding mutation operator. After analysis, the mutation operator corresponding to the vehicle ground information interaction is finally obtained as shown in Table 1. These mutation operators not only reflect the fault characteristics of the system functions, but also conform to the principle of temporal automata model mutation. After entering the instruction, MoMuT::TA first parses the elements of the XML file of the timed automata model, and finally injects the mutation operator into the TA model to generate the variant, which is still saved in the XML file supported by

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Table 1 Mutation operator corresponding to failure mode Failure mode

Corresponding mutation operator

Wireless communication delay

Reverse time reset Change clock constraint operator

Wireless message loss

Self cycling

Wireless message consistency error

Behaviour changes to other behaviours

Wireless message duplication Unexpected wireless message

Table 2 Number of variants generated Mutant object

Mutation operator

Number of mutants

On board equipment

Reverse time reset

103

Change clock constraint operator

35

Self cycling

37

Behaviour changes to other behaviours

312

Total

487

UPPAAL. It can be exported to UPPAAL for viewing. The number of variants and the number of variants generated are shown in Table 2. It can be seen from the table that the number of mutation models generated by behaviour change to other behaviour mutation operators is the largest, because the transformation of the timed automata model must include two positions and one behaviour, while the behaviour of other mutation operators is not found in every transformation, which leads to more variants generated by mutation operators that change the behaviour of the model.

4.3 Test Case Set Generation After getting the timed automata model and mutants of the system, first, check the consistency between the original model and each mutation model to get the cost equivalent mutants that can be converted into test cases, and then substitute the nonequivalent variants into the test case generation algorithm to get the test cases. The test case generation instructions for the on-board model are shown in the following figure. When the generation conditions are met, MoMuT::TA will store the test case in the specified folder. In the test case generation process, if the inconsistency between the timed automata model and the mutant is not found, a prompt will be output, indicating that the equivalent mutant is detected and no corresponding test case will be generated.

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Table 3 Number of test cases generated Mutation operator

Number of mutants

Reverse time reset

103

Number of test cases 32

Change clock constraint operator

35

21

Self cycling

37

20

Behaviour changes to other behaviours

312

301

Total

487

374

A total of 374 test cases were generated (Table 3), and the remaining 113 variants were consistent with the specification model, so no test cases were generated. The generated test cases are stored in the specified folder in AUT format.

4.4 Evaluation of Test Cases This article refers to Conformance Relation Score(CRS), Average Conformance Relation Score(ACRS) and Weighted Conformance Relation Score(WCRS) to evaluate the test cases [10]. C RSi = Ti /Mi , 1 ≤ i ≤ n AC RS =

n 

Ti /

i=1

W C RS =

n 

n 

Ml

(2)

j=1

(Ti ∗ C Si )/

i=1

(1)

n 

Tj

(3)

j=1

where, Mn represents the number of mutants generated by each mutation operator, and Tn represents the number of test cases generated by each mutation operator. The following table is the consistency evaluation table of system variation test. Table 4 is the consistency evaluation table of system mutation test. Table 4 Consistency relationship evaluation table Mutation operator

CRS

ACRS

WCRS

Reverse time reset

0.31

0.77

0.86

Change clock constraint operator

0.60

Self cycling

0.54

Behaviour changes to other behaviours

0.96

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From the table, the consistency score of “Behaviour changes to other behaviours “ is the highest, with high fault coverage, strong fault detection ability and relatively low consistency score of the other three. A score of 0.31 for changing the clock position indicates that the test environment cannot effectively observe errors or failures in this failure mode and that additional observations are required for the failure. However, ACRS and WCRS reach 0.77 and 0.86 respectively. The four mutators in the surface paper have good fault coverage, which can effectively generate test cases covering system failure modes.

5 Conclusion Train control system is a safe and demanding system, which is the key to ensure driving safety. This paper presents a test method based on time automaton mutation model. Firstly, it combs the structure of onboard equipment and the functions of typical scenes based on new column control specifications. The time automaton model of the system is established based on the time automaton theory, and the validator in UPPAAL is used to verify the correctness of the model. Mutant operator is designed according to the safety requirements of column-controlled onboard equipment. Mutants are generated in MoMuT::TA injection specification model, and test case sets are generated by consistency check between mutants and specification model. Finally, test cases are evaluated by consistency relationship evaluation. The evaluation results show that the generated test cases have high fault coverage, strong error detection ability and are more complete. This paper provides technical support for the test of train control system in Western and remote areas of China, and provides ideas for the further improvement and development of new train control system. Acknowledgements Key Talent Project Fund of Gansu Province in 2022 2022RCXM014 Research on Digital Twin Application Platform for Railway Signal System. Gansu Provincial Science and Technology Program Project in 2022 22CX3GA059 Research, Development, Popularization and Application of Integrated Design Platform for Railway Signal System. Gansu Provincial Science and Technology Program Project in 2020 20CX9JA125 Research and Industrialization of Intelligence Evaluation System for Railway Traffic Operators. Talent Innovation and Entrepreneurship Project of Lanzhou City, Gansu Province in 2021 2021RC-85 Research and Industrialization of Logical Check Training System for Railway Intersection Occupancy.

References 1. W. Ziqi, Research on Digital Track Map Generation Methods Towards Train Control Applications (Beijing Jiaotong University, Beijing, 2021)

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2. W. Tuo, Search-Based Functional and Temporal Testing for the Onboard Interlocking Software of the New Train Control System (Beijing Jiaotong University, Beijing, 2020) 3. F. Lorber, K. Larsen, B. Nielsen, Model-based mutation testing of real-time systems via model checking, in 2018 IEEE International Conference on Software Testing, Verification and Validation Workshops (Sweden, 2018), pp. 59–68 4. BK Aichernig, F. Lorber, Time for mutants—model-based mutation testing with timed automata, in International Conference on Tests and Proofs (Berlin, 2013), pp. 20–38 5. G. Haonan, L. Jidong, C. Ming, L. Hongjie, Research on verification of CBTC Onboard ATO functions based on time conformance testing theory. J. China Railw. Soc. 93–103 (2020) 6. M. Junri, Z. Miaomiao, A. Jie, Learning deterministic one-clock timed automata based on timed classification tree. J. Softw. 2797–2814 (2022) 7. A. Fellner, W. Krenn, R. Schlick, Model-based, mutation-driven test-case generation via heuristic-guided branching search. ACM Trans. Embed. Comput. Syst. 4 (2019) 8. W. Krenn, R. Schlick, S. Tiran, Momut::UML model-based mutation testing for UML, in 2015 IEEE 8th International Conference on Software Testing (Austria, 2015), pp. 1–8 9. Z. Zhenhai, Y. Jie, Modeling and Simulation Verification of Mode Transition Function of C3+ATO System (Control Engineering of China) (2020), pp. 1851–1858 10. W. Baiquan, Mutation TAIO-Based Test and Evaluation of Safety Function for New Train Control System (Beijing Jiaotong University, Beijing, 2018)

Research on Connection Mode Recognition Method for Medium Voltage Distribution Network Based on CIM File Resolution and Theory Junhui Li, Yu Luo, Xinxiong Wu, Xigang Li, Yongqiu Liang, Jianpeng Ye, Minghuan Huang, and Ziyao Wang

Abstract The proposals of “One Graph of Power Grid” and “Digital Grid” put forward higher requirements for the intelligent planning of distribution network, and extracting typical connection modes in the distribution network frame is an important part of the distribution network planning and analysis. In order to realize automatic identification of typical connection modes in distribution network, this paper presents a connection mode identification method for medium voltage distribution network based on CIM file parsing and theory method. First, the CIM file data of the study area is collected, the CIM file data is parsed, and the consistency and integrity of the data are checked. Then the component model in the CIM file is transformed into a node-branch model. The feed tree is obtained by using the depth-first search algorithm in graph theory. The topological features consisting of the branch type, node type, connection and segmented connection relationship of the feed tree are combined to match the feature library of matching connection modes. Finally, the connection mode recognition of the study area is completed. Finally, the model and algorithm proposed in this paper are tested and analysed in two different examples to verify the validity and applicability of the proposed method. Keywords CIM file · Connection mode recognition · Depth-first search algorithm · Feeder tree

J. Li · Y. Luo · X. Wu · X. Li · Y. Liang · J. Ye Dongguan Power Supply Bureau, Guangdong Power Grid Co., Ltd., Dongguan, China M. Huang Guangzhou Shuimu Qinghua Technology Co., Ltd., Guangzhou, China Z. Wang (B) South China University of Technology, Guangzhou, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_15

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1 Introduction The fourth industrial revolution, represented by the new generation of digital technology, is penetrating into all fields of economy and society. For this reason, the concept of “digital grid” has been put forward and the White Paper on Digital Grid has been published [1]. On the other hand, in order to improve the ability of data sharing and the degree of visualization of power grid, power grid companies further propose the construction requirements of “one diagram of power grid”, to improve the visualization level of power grid work [2]. The standard rate of connection mode is an important basis to measure the normalization of distribution network structure. Standardized connection mode can provide reference and basis for the upgrade and evolution of distribution network frame [3], configuration of automated three-terminal [4], and adjustment of operation mode [5]. Many scholars at home and abroad have studied the connection mode of distribution network. In the evaluation of connection modes, literature [6, 7] takes typical distribution network connection modes in cities as the research object, and compares and analyzes their reliability, economy, applicability, power supply capacity and other indicators. Document [8] builds a reliability evaluation matrix of 10 kV distribution network connection mode based on grey correlation degree. In order to calculate the reliability of complex distribution network, the papers [9, 10] propose that complex distribution network is divided into several typical connection modes, on which the power supply reliability of the entire distribution network is calculated. In the planning and selection of connection modes, the paper [11, 12] builds a distribution network planning model considering power supply reliability and topological constraints of connection modes, and uses the improved ant colony algorithm to solve the problem efficiently. Document [13] constructs the connection modes of medium voltage distribution network under different boundary conditions using the principle of elementary connection. Document [14] establishes a three-level classification structure of family, family and structural elements suitable for connection mode classification and planning. Therefore, extracting typical connection modes for analysis is the key link in the evaluation and planning of medium voltage distribution network. In connection mode recognition, Xiao Jun and Wang Chengshan of Tianjin University proposed a connection mode recognition method for urban medium voltage distribution network [15] based on topological analysis and pattern recognition theory. On this basis, the connection mode recognition algorithm is improved. Combining graph theory and topological method, the feature library for connection mode recognition [16–18] is enriched, which lays a solid theoretical foundation for connection mode recognition. With the enlargement of power network scale, the network structure of medium voltage distribution network is becoming increasingly complex and changing rapidly. It is obviously not advisable to rely on manual analysis of drawings and connection mode recognition. How to combine CIM files (XML files) exported from GIS system to realize automatic wiring mode recognition of medium voltage distribution network

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is a key problem to be solved in the current engineering field. At present, some studies have combined CIM file to carry out distribution network reliability analysis and calculation [19], line loss calculation [20], etc. It shows that combining CIM file data to carry out power network calculation and analysis is one of the key steps to realize power network automation and intelligence [21]. In order to improve the automation and intellectualization level of medium voltage distribution network planning, this paper presents a typical connection mode recognition method for medium voltage distribution network, which combines CIM file analysis data with graph theory. This method is introduced from four aspects: data input, preprocessing, graph theory analysis and feature extraction. The validity of this method is verified by two typical examples.

2 A Fast Identification Algorithm for Connection Mode of Medium Voltage Distribution Network The grid structure of distribution network is a key part in the planning and transformation of urban distribution network. However, the network structure of urban medium voltage distribution network is diverse and involves a large amount of data. It is important for the development of the entire power industry to quickly and accurately identify the connection modes in the current stock grid by extracting the characteristics of the distribution network, classifying and describing them effectively. Distribution network topology is usually drawn by planning professionals through CAD. With the development and evolution of distribution network structure, distribution network presents a more complex and variable topology. It often takes a long time to analyze and draw by professionals. In order to better solve this problem and improve the interoperability of the system, the International Electrotechnical Commission (IEC) has formulated the common information model (CIM) in IEC61970 series standards, the parsing method of analytic XML file and the description of related device class attributes of power network physical model. Currently, data import and export based on CIM/XML are the main ways of data exchange and information sharing between different systems and software. It is an important assistant tool for distribution network planning.

2.1 Data Preprocessing From the perspective of graph theory, the files parsed by CIM/XML are analyzed to extract the topological features of different connection modes in distribution network. First, in order for the input format to meet the requirements, the following preprocessing is required:

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Data integrity and consistency checks The data in this study was extracted from Automated Drawing/Device Management/ Geographic Information System GIS, and data loss may occur during the extraction process, so integrity and consistency checks are required to ensure the correctness of subsequent work. Network topology analysis The data extracted by the computer (including the information of the grid structure) is a physical model (graph model). To identify and calculate, the physical model is transformed into a mathematical model, which is the basis of the connection mode recognition. Distribution network planning requires closed-loop design and open-loop operation of the distribution network. When the connection line is disconnected, the distribution network is composed of several radial feeders starting from the substation. Graph theory analysis This is described, analyzed and modeled by introducing the concept of graph theory. A connected undirected graph without loops is defined as a tree. Referring to the concept of graph theory, one feeder line can be abstracted into one feeder tree, each feeder tree takes a substation as its root node and the downstream components as its regular nodes. Based on this concept, the medium voltage distribution network can be divided into several feeder trees, each of which is considered as the basic unit in this study. Feature extraction of wiring mode In “Technical Guidelines for Distribution Network Planning of Guangdong Grid Limited Liability Company (Revised Edition 2019)”, the main connection modes in a 10 kV medium voltage distribution network are: single radiation connection, N − 1 single loop network, N for one device, N segment M-connection. By identifying the characteristics in each feeder tree and the connections between different feeder trees, the connection modes in the distribution network can be identified.

2.2 Research on Connection Mode Recognition of MV Distribution Network Based on CIM File Analysis Network topology is the basis for identifying the connection mode of medium voltage distribution network. First, analyze the CIM model, extract the topology features in the distribution network, and form the topology structure of the line. Through the analysis and processing of the extracted feature points, the connection mode of the medium voltage distribution network can be effectively identified. Through the analysis of typical connection modes of medium voltage distribution network, the characteristics of power nodes and conventional nodes of connection

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modes can be extracted as the characteristic points of each connection mode. The power node includes the substation, the head end node of 10 kV bus element, and the conventional node includes the head end node of switch element, line element, and distribution transformer. According to the connection relationship between the power node and the conventional node, find out the lines under each power point, that is, find all the feeder trees. Connect each line through the information of the interconnection switch in each line to form a connection tree containing the connection mode information. Finally, match according to the characteristics to realize the connection mode recognition of the medium voltage distribution network.

2.3 Wiring Mode Recognition Steps After the computer analyzes the CIM file to obtain the network structure of the medium voltage distribution network, according to the logical order of division first and identification later, the following steps of wiring mode recognition are proposed in this study. The first step is to define the nodes in the topology, which are divided into power nodes and regular nodes. According to the components analyzed in the CIM file, the power node mainly includes the substation, the head end node (upstream node) of the 10 kV bus element, and the other nodes (including switch elements, line elements, head end nodes of the distribution transformer, etc.) can be regarded as conventional nodes; The second step is to take each power node as the starting point (root node), find the components matching the nodes (the first node or the last node), use the depth-first algorithm to conduct recursive search, and cycle through all nodes until all feeder trees are found; The third step is to traverse all switching elements whose switching state is off. If the first node and the end node of the switching element exist in two feeder trees, it is judged that there is a connection relationship between the two feeder trees; The fourth step is to mark the feeder trees that cannot be contacted as single radial feeder trees (Fig. 1). For the feeder tree with a connection relationship, the following classification discussion is required: When there is only one contact node on two interconnected feeder trees: (1) If two interconnected feeder trees come from the same substation (power node), these two feeder trees form Single-Ring Network Connection Mode of Different Buses in the Same Station(SRN-SS); Single-Ring Network Connection Mode of Different Buses in Different Stations (SRN-DS). (2) If two interconnected feeder trees come from different substations (power nodes), these two feeder trees form Single-Ring Network Connection Mode of Different Buses in Different Stations (SRN-DS);

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START

Read CIM file

Resolve topology nodes

Power node

General node

Traversal station element

Switch element or not

N

Y

Matching component node

Whether it is disconnected

Output feeder tree node number

Switching element in closed state

N

Y

Whether there are Two feeder tree numbers matching the head and end nodes of the switch

N

Single radial feeder tree

Y Feeder tree with connection relationship Fig. 1 Connection mode recognition steps

When the same switching equipment is used as an interconnection switch by multiple feeder trees: (1) If the load of the N feeder trees connected by the switching equipment is greater than Pmin, then the N feeder trees constitute N − 1 single loop network connection mode (N − 1 SRN);

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Connection relationship between feeder numbers

Feeder tree with connection relationship

Feeder tree without connection

Single radio connection mode

Only one connection node on the feeder tree with connection relationship

A switch is connected by multiple feeder trees

M connection nodes on a feeder tree (M>=2)

Two feeder trees from the same substation

Two feeder trees from different substations

The load of N connected feeder trees is greater than Pmin

The load of N feeder trees and K feeder trees connected is less than Pmin

Record the L section switches on the feeder tree minus the existing switches

SRN-SS

SRN-DS

N-1 SRN

NS-KB

LS-MC

Fig. 2 Connection mode recognition logic

(2) If there are K feeder trees with load less than Pmin among the N feeder trees connected by the switching element, then the N feeder trees form N-supply K-backup connection mode (NS-KB). When there are M contact nodes on a feeder tree (M ≥ 2): Traverse the feeder tree and record the L-section switches on the feeder tree minus the outgoing line switches, then the feeder tree is in the L-section M-connection connection mode (LS-MC) (Fig. 2). So far, output the connection mode of all feeders in the study area, including the connection relationship between feeders, which substation they come from, and the nature of the line.

3 Example Analysis In order to verify the connection mode recognition algorithm proposed in this study, it is applied to the following example. There are 3 substations, 15 feeder trees and 83 nodes in the figure. S1 , S2 and S3 represent substations, and T1 –T15 represent 15 feeder trees found by depth-first search algorithm, as shown in Fig. 3. This program is implemented with Python 3.8. The computer CPU is configured as i7-7700, and the wiring mode algorithm is repeated for 100 times. The average time for each wiring mode recognition algorithm is 0.0065171 s. The identified feeder tree is as follows (Table 1). After the network topology analysis and connection analysis of the whole network, all feeder trees can be divided into 15 feeder trees according to the connection relationship, which are respectively led out from three substation nodes (node 1, node 11, node 83). The feeder tree and components with connection relationship are as follows:

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10

9

T4

11

S3

79

T1

7 6 12

13

T5

14

81

80

82

T2

T3

77

76

75

78

68

5 16

15

72

73

67

66

74

4

T7 18

17

3

19

T11

23

21 25

S1

35

T9

T6

63

24

22

1

T8

64

70

T10

2

65

69

20

71

26

27

28

62

50 49

37

61

29

51

36

44

33

38 46 47 48

32

42 39

60

52

30

45 31

53 55

34

54

T14

T12

56

57

58

59

40 41

43

T13

S2

T15

83

Fig. 3 Example network

After analyzing the feeder tree of the whole network, the number of connection node and the number of connection feeder tree can be obtained. Taking the two feeder trees with connection relationship in the example as an example, feeder tree 0 and feeder tree 7 form the connection relationship, which is connected through node 5 and node 6. The remaining feeders with connection relationship are shown in Table 2. After identifying the feeder tree relationship, the connection mode of the whole network can be further analyzed, as shown in Table 3. By quickly identifying the connection modes, it is easy for planners to carry out distribution network topology analysis, count the number of connection modes in a certain area and the defects in the current connection modes, carry out targeted transformation analysis, improve the efficiency of distribution network planning analysis, and to facilitate subsequent research on the evolution of connection modes and the analysis of connection modes adopted in different areas. There are both cables and overhead lines in the medium voltage distribution network. The following calculation example combines the overhead line cable connection mode recognition algorithm, as shown in Fig. 4. There are 3 substations, 14 feeder trees and 78 nodes in the figure. S1 , S2 , S3 represent substations,

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Table 1 Example feeder tree Feeder tree

Node number under feeder tree

Feeder tree S1_ 1

1, 2, 3, 4, 5, 15, 16

Feeder tree S1_ 2

1, 17, 18, 19, 20

Feeder tree S1_ 3

1, 21, 22, 23, 24

Feeder tree S1_ 4

1, 25, 26, 27, 28, 29, 49, 50

Feeder tree S1_ 5

1, 35, 36, 37, 38

Feeder tree S1_ 6

1, 44, 45, 46, 47, 48

Feeder tree S3_ 1

11, 10, 9, 8

Feeder tree S3_ 2

11, 14, 13, 12, 6, 7

Feeder tree S3_ 3

11, 68, 69, 67, 66, 65, 64, 63, 70, 71, 72, 73, 74

Feeder tree S3_ 4

11, 75, 76, 77, 78

Feeder tree S3_ 5

11, 79, 80, 81, 82

Feeder tree S2_ 1

83, 34, 33, 31, 30, 32

Feeder tree S2_ 2

83, 43, 41, 40, 39, 42

Feeder tree S2_ 3

83, 55, 54, 53, 52, 51, 60, 61, 62

Feeder tree S2_ 4

83, 56, 57, 58, 59

Table 2 Example feeder tree and connection relationship of components Feed tree index Connection switch node number 0, 7

5, 6

Number of feeder tree node with connection 1, 2, 3, 4, 5, 15, 16 11, 14, 13, 12, 6, 7

7, 6

7, 8

11, 14, 13, 12, 6, 7

1, 2

20, 24

1, 17, 18, 19, 20

3, 11

29, 30

1, 25, 26, 27, 28, 29, 49, 50

11, 10, 9, 8 1, 21, 22, 23, 24 83, 34, 33, 31, 30, 32 4, 12

38, 39

1, 35, 36, 37, 38

13, 3

51, 50

83, 55, 54, 53, 52, 51, 60, 61, 62

3, 8

79, 71

1, 25, 26, 27, 28, 29, 49, 50

83, 43, 41, 40, 39, 42 1, 25, 26, 27, 28, 29, 49, 50 11, 68, 69, 67, 66, 65, 64, 63, 70, 71, 72, 73, 74 8, 13

63, 62

11, 68, 69, 67, 66, 65, 64, 63, 70, 71, 72, 73, 74

10, 9

82, 78

11, 79, 80, 81, 82

83, 55, 54, 53, 52, 51, 60, 61, 62 11, 75, 76, 77, 78

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Table 3 Connection mode recognition results of 83-node system segment mode

Node No

Single radial feeder tree 5

1, 44, 45, 46, 47, 48

Single radial feeder tree 14

83, 56, 57, 58, 59

Single loop network for outgoing line of the 1, 17, 18, 19, 20 same substation 1, 21, 22, 23, 24 Single loop network for outgoing lines of different substations

1, 17, 18, 19, 20 1, 21, 22, 23, 24

Single loop network for outgoing line of the 11, 79, 80, 81, 82 same substation 11, 75, 76, 77, 78 2 section 2 liaison

11, 14, 13, 12, 6, 7

3 section 2 liaison

83, 55, 54, 53, 52, 51, 60, 61, 62

3 section 3 liaison

1, 25, 26, 27, 28, 29, 49, 50

2 section 2 Liaison

11, 68, 69, 67, 66, 65, 64, 63, 70, 71, 72, 73, 74

T1 –T14 represent feeder trees, wherein feeder trees T1 , T2 , T3 , T5 , T11 , T14 are cable wiring, feeder trees T4 , T6 , T7 , T8 , T9 , T10 , T12 , T13 are overhead wiring, substation S1 has two buses, with feeder trees T1 , T2 and T3 , T4 , T5 respectively, substation S2 has two buses, with feeder trees T6 , T8 and T7 respectively, substation S3 has two buses, with feeder trees T11 , T12 , T13 and feeder trees T9 , T10 , T14 . This program is implemented with Python 3.8. The computer CPU is configured as i7-7700, and the wiring mode algorithm is repeated for 100 times. The identified feeder tree is as follows (Table 4). After the network topology analysis and connection analysis of the whole network, all feeder trees can be divided into 14 feeder trees according to the connection relationship, which are respectively led out from three substation nodes (Node 1, Node 27, Node 43). The feeder tree and components with connection relationship are as follows: After analyzing the feeder tree of the whole network, the number of connection nodes and the feeder tree of connection can be obtained. Taking the feeder trees T2 and T3 in Fig. 4 as an example, through network topology analysis, it is known that the feeder trees T2 and T3 are cable connection, and the two feeder trees form a connection relationship. The connection nodes are node 10 and node 11. The feeder trees T1 and T2 are connected to form a single loop network connection (cable connection) of different buses in the same station, Other feeders with connection relationship are shown in Table 5. After the feeder tree relationship is identified, the connection mode of the whole network can be further analyzed, as shown in Table 6.

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Fig. 4 Example network for connection mode recognition

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Table 4 Example feeder tree recognition Feeder tree

Line category

Node number under feeder tree

Feeder tree S1_ T1

Cable

1, 2, 3, 4, 5, 6

Feeder tree S1_ T2

Cable

1, 7, 8, 9, 10

Feeder tree S1_ T3

Cable

1, 15, 14, 13, 12, 11

Feeder tree S1_ T4

Overhead line

1, 16, 17, 18, 19, 20, 59, 33, 32

Feeder tree S1_ T5

Cable

1, 58, 57, 56, 55, 54, 65, 64

Feeder tree S2_ T6

Overhead line

27, 26, 25, 23, 22, 21, 24

Feeder tree S2_ T7

Overhead line

27, 28, 29, 30, 31

Feeder tree S2_ T8

Overhead line

27, 34, 35, 36, 37, 38, 73, 72

Feeder tree S3_ T9

Overhead line

43, 42, 41, 40, 39

Feeder tree S3_ T10

Overhead line

43, 44, 45, 46, 47, 48

Feeder tree S3_ T11

Cable

43, 49, 50, 51, 52, 53

Feeder tree S3_ T12

Overhead line

43, 66, 61, 60, 62, 63

Feeder tree S3_ T13

Overhead line

43, 67, 68, 69, 70, 71, 74

Feeder tree S3_ T14

Cable

43, 75, 76, 77, 78

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Table 5 Connection relation of feeder tree Node number of connection Feeder tree switch 10, 11

Line category Node number of feeder tree with connection relationship

Feeder tree S1_ T2

Cable

1, 7, 8, 9, 10

Feeder tree S1_ T3

Cable

1, 15, 14, 13, 12, 11

20, 21

Feeder tree S1_ T4

Overhead line 1, 16, 17, 18, 19, 20, 59, 33, 32

Feeder tree S2_ T6

Overhead line 27, 26, 25, 23, 22, 21, 24

31, 32

Feeder tree S1_ T4

Overhead line 1, 16, 17, 18, 19, 20, 59, 33, 32

Feeder tree S2_ T7

Overhead line 27, 28, 29, 30, 31

59, 60

Feeder tree S1_ T4

Overhead line 1, 16, 17, 18, 19, 20, 59, 33, 32

53, 54

Feeder tree S1_ T5

71, 72

Feeder tree S2_ T8

38, 39

Feeder tree S2_ T8 Feeder tree S3_ T9

Overhead line 43, 42, 41, 40, 39

64, 78

Feeder tree S1_ T5

Cable

Feeder tree S3_ T12 Overhead line 43, 66, 61, 60, 62, 63 Cable

1, 58, 57, 56, 55, 54, 65, 64

Feeder tree S3_ T11 Cable

43, 49, 50, 51, 52, 53

Overhead line 27, 34, 35, 36, 37, 38, 73, 72

Feeder tree S3_ T13 Overhead line 43, 67, 68, 69, 70, 71, 74 Overhead line 27, 34, 35, 36, 37, 38, 73, 72 1, 58, 57, 56, 55, 54, 65, 64

Feeder tree S3_ T14 Cable

43, 75, 76, 77, 78

Table 6 Connection mode recognition results of 78-node system Segment mode

Line category

Node No

Single radial feeder tree S1_ T1

Cable

1, 2, 3, 4, 5, 6

Single radial feeder tree S3_ T10

Overhead line

43, 44, 45, 46, 47, 48

Different in the same substation Single loop network of bus outgoing line

Cable

1, 7, 8, 9, 10 1, 15, 14, 13, 12, 11

2 section 2 liaison

Cable

1, 58, 57, 56, 55, 54, 65, 64

3 section 2 liaison

Overhead line

27, 34, 35, 36, 37, 38, 73, 72

3 section 3 liaison

Overhead line

1, 16, 17, 18, 19, 20, 59, 33, 32

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4 Conclusion This chapter introduces the typical connection mode recognition of distribution network based on CIM file data. First, analyze the CIM file, extract the topology features of the distribution network, build a topology model, then analyze and study the topology of the distribution network, identify each feeder tree by depth-first search, then identify each type of connection mode in the medium voltage distribution network through the different characteristics of each connection mode, and identify the connection mode of two medium voltage distribution network grids on the python platform, The effectiveness and feasibility of the method are verified by an example.

References 1. Y. Tang, Z. Shao, C. Guo, Y. Cao, Q. Ruan, Research on the concept of digital power grid. China Power 42(04), 75–78 (2009) 2. G. Liu, J. Wang, Y. Li, H. Han, Y. Tang, T. Liu, R. Dai, J. Dai, “A map of the power grid” spacetime information management system. Power Inf. Commun. Technol. 18(01), 7–17 (2020) 3. Z. Wang, D. Lin, G. Zeng, T. Yu, A practical large-scale distribution network planning model based on elite Ant-Q. IEEE Access 8, 58912–58922 (2020). https://doi.org/10.1109/ACCESS. 2020.2981825 4. G. Zeng, T. Yu, Z. Wang, D. Lin, Analytical reliability assessment of cyber-physical distribution system with distributed feeder automation. Electr. Power Syst. Res. 208 (2022) 5. Y. Wang, Y. Xu, J. Li, J. He, X. Wang, On the radiality constraints for distribution system restoration and reconfiguration problems. IEEE Trans. Power Syst. 35(4), 3294–3296 (2020). https://doi.org/10.1109/TPWRS.2020.2991356 6. G. Wan, F. Deng, Y. Zhang, Comparative study on reliability of two typical high-voltage distribution networks in mega cities. Power Syst. Protect. Control 49(06), 174–180 (2021) 7. J. Xiao, B. She, Comprehensive efficiency evaluation of distribution network connection mode. Power Grid Technol. 43(10), 3769–3781 (2019) 8. W. Bu, Z. Pan, Research on reliability evaluation of 10 kV distribution network connection mode. Heilongjiang Electr. Power 43(05), 400–402+406 (2021). https://doi.org/10.13625/j. cnki.hljep.2021.05.005 9. S. Zhang, C. Wen, L. He, M. Chen, Y. Lv, L. Li, A reliability evaluation algorithm for urban complex medium voltage distribution network based on typical connection mode. Sichuan Electr. Power Technol. 43(04), 20–23+83 (2020) 10. J. Zhang, Research on power supply reliability of typical connection theory of medium voltage distribution network. Yunnan Electr. Power Technol. 47(05), 24–27 (2019) 11. Z. Wang, J. Chen, D. Lin, G. Zeng, T. Yu, Double Q planning model of medium voltage distribution network based on elite ant colony Q algorithm. Power Autom. Equip. 40(11), 32–42 (2020) 12. J. Tang, Z. Wang, J. Zhang, H. Cao, C. Gao, T. Yu, A highly reliable multi power distribution network planning model based on cultural ant colony algorithm. Power Syst. Protect. Control 48(07), 99–107 (2020) 13. X. Liu, S. Ma, G. Xu, Typical connection mode of distribution network constructed by elementary connection model. Power Grid Technol. 36(02), 58–63 (2012) 14. W. Wang, Z. Zhang, X. Ma, Connection mode of medium voltage distribution network based on structural element theory. Power Syst. Autom. (11), 35–40 (2006)

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15. J. Xiao, Y. Wang, C. Wang, Connection mode recognition of urban medium voltage distribution network. Power Grid Technol. (10), 92–95 (2003) 16. Z. Wang, Research and Implementation of Distribution System Wiring Mode Model and Pattern Recognition (Tianjin University, 2009) 17. B. Xu, Improvement and Realization of Connection Pattern Recognition Algorithm for Medium Voltage Distribution Network (Tianjin University, 2012) 18. S. Jin, Optimization and Acceleration of Distribution Network Wiring Pattern Recognition (Tianjin University, 2010) 19. S. Zheng, Z. Lin, Y. Huang, W. Li, X. Peng, Reliability assessment of distribution network based on graphic modeling integration technology. J. Guangdong Univ. Technol. 39(03), 63–69 (2022) 20. B. Wei, M. Tang, H. Peng, M. Ma, Theoretical calculation of line loss of distribution network based on graphic analog conversion of GIS system. Appl. Energy Technol. (04), 12–15 (2021) 21. H. Bai, C. Zhou, Z. Yuan, J. Lei, Digital grid outlook and thinking based on digital twin. China South. Power Grid Technol. 14(08), 18–24+40 (2020). https://doi.org/10.13648/j.cnki. issn1674-0629.2020.08.003

A Robust Control Approach for Virtually Coupled Train Set with Parameter Uncertainty Under External Perturbations Yi Zheng, Yihui Wang, Peichang Gao, Songwei Zhu, Shukai Li, and Xiuming Yao

Abstract Virtual coupling has been widely studied in recent years as the nextgeneration signalling system, which separates trains by relative braking distance to increase railway line capacity. This paper investigates the robust H∞ control problem for virtually coupled train set (VCTS) to reduce the influence of disturbances on train operations. By capturing the dynamic evolution of VCTS, an error state-space model is established considering uncertain parameters, input constraints, and disturbances. Based on the robust H∞ optimal control theory, the H∞ state feedback control law is obtained, where the robust state feedback control gain is solved by linear matrix inequalities (LMIs) based on the condition for the existence of the robust H∞ state feedback control law. Finally, the model accuracy and control performance are verified via numerical simulations, which illustrate errors are controlled within a small range and converge to zero quickly, further the robustness of VCTS is guaranteed. Keywords Virtual coupling · Multi-train cooperative control · Robust H∞ control · Parameter uncertainty

Y. Zheng · Y. Wang (B) · S. Zhu · S. Li State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China e-mail: [email protected] P. Gao Department of Railway Communication and Signalling, Baotou Railway Vocational and Technical College, Baotou, China X. Yao School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_16

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1 Introduction In recent years, with the growth of rail passenger demand, the railway industry urges to increase transport capacity of existing networks. To meet the need of increasing transport capacity, it is an effective method by reducing the safe train separation distances. The concept of virtual coupling was proposed by European scholars around 2000 [1], which calculates movement authority based on relative braking distance between trains. This characteristic greatly reduces the distance between adjacent trains. The difference between absolute braking distance and relative braking distance is shown in Fig. 1. In addition, virtual coupling adopts the Vehicle-to-Vehicle (V2V) communication instead of the traditional Vehicle-to-Ground communication (V2G). Through V2V communication, the operational information, e.g., positions, velocities, and accelerations, can be exchanged directly among neighbouring trains. Due to the shorter distance between adjacent trains, the multi-train cooperative control method is particularly important to ensure the safe separation between trains. The operational scenarios of trains in virtual coupling signalling system involve coupling, coupled running, unintentional decoupling, intentional decoupling [2].

Fig. 1 The difference between absolute braking distance and relative braking distance

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Many scholars have investigated multi-train cooperative control under virtual coupling by using various models and algorithms in various scenarios. Liu et al. [3] proposed a coordinated control method based on multi-agent system, which achieves real-time dynamic adjustment and efficient operation of trains. Jaegeun et al. [4] introduced a gap reference generation scheme to ensure that trains could be coupled or decoupled successfully before a given location. The proposed robust gap controller is based on sliding mode control, and the mathematical analysis results verified its robustness. With the increasing safety analysis in virtual coupling, some researchers investigated on the multi-train cooperative control methods considering different unstable scenarios and interference factors. For an emergency braking scenario, Chen et al. [5] proposed a coordinated collision mitigation approach by using model predictive control (MPC) and minimized the total relative kinetic energy, where the simulation results showed that this method can avoid collisions effectively. Ma et al. [6] proposed an event-triggered control method with consideration of communication disturbances, which can effectively reduce disturbance by designing a stable range form of virtually coupled train set (VCTS). She et al. [7] proposed a MPC approach considering the disturbances during VCTS cruising phase, where optimization objectives and constraints are proposed to make the distance between trains maintained at a small value under the premise of safety. However, most of the above literatures measure control performance based on distance between trains, without adopting standard anti-interference indicators. During the actual running, trains will be inevitably affected by external perturbations such as weather conditions, line conditions, and actuator faults. To the best of our knowledge, up to now, little research has been done for the multi-train cooperative control of VCTS based on the robust H∞ theory, which shows an effective anti-interference ability in motor, aerospace, automobile formation, and other fields. Therefore, this paper presents a robust H∞ control approach for the VCTS, which considers the disturbance at the modelling level with parameter uncertainty. The train dynamic model considering disturbance and uncertain parameters is first established, and the error state space equations are then obtained. A robust H∞ controller is designed via solving the linear matrix inequalities (LMIs) based on the existing condition of controller stability with input constraints. A numerical study is carried out, where the case with uncertain parameters is compared with the case of fixed parameters. The computational results show the applicability and effectiveness of the proposed model and controller.

2 Dynamic Model for Virtually Coupled Train Set The formation structures and communication schemes of VCTS could be varied in different control strategies. In existing literatures, the formation structures mainly include leader–follower structure and local leader–follower structure [8]. In the leader–follower structure, there is only one leading train and several following trains in a VCTS, while each train is the leader of its successive train or a few successive trains in the local leader–follower structure. Due to the inadequacy of the existing

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research on local leader–follower structure, its advantages cannot be fully demonstrated. Communication scheme mainly includes communication between each train, communication between the leading train and following trains, and communication between the neighbouring trains. Each train in VCTS communicates only with the leading train. The centralized controller in the leading train receives position, velocity, and acceleration information from the following trains. After data processing and calculation by controller, control commands are sent to the following trains. Research [9] shows that 5G is the most effective technology to realize V2V in virtual coupling, and the information transfer rate is much higher than that of V2G communication. To formulate the dynamic model of VCTS, we make the following assumptions: A1. The formation structure of the VCTS is considered as the leader–follower structure. A2. Each train in VCTS communicates only with the leading train and the communication delay is not considered. A3. The centralized control scheme is adopted, where the leading train receives the operational information (e.g., position, velocity, and acceleration) of the following trains and sends back the control commands. A4. This paper only considers the coupled driving operational scenario where all trains have the same velocity and the distance between adjacent trains remains the same. The formation structure and communication scheme diagram are shown in Fig. 2. The mathematical formulation is presented to describe the trains’ operation of VCTS. Table 1 lists the parameters and variables used in the model formulation. The minimum safe distance could be minimized depending on the difference of velocity, braking rate between two adjacent trains and the safety margin. This paper considers the situation that the front train adopts emergency braking, and the latter train adopts maximum service braking. The minimum safe distance between train i and train i − 1 can be formulated as follows: di = dsb,i − deb,i−1 + sf

Fig. 2 The formation structure and communication scheme for the considered VCTS

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Table 1 Parameters and variables for the model formulation Symbol

Description

n

Number of the following trains

asb

Maximal service braking rate Emergency braking rate

aeb Δ

Δ

Δ

c1 , c2 , c3

Practical coefficients of the basic resistance

c1 , c2 , c3

Nominal values of the basic resistance coefficients

µ1 , µ2 , µ3

Half-length variation of the uncertain part of the basic resistance coefficients

ϖ1 , ϖ2 , ϖ3

Time-varying part in the basic resistance coefficients

sf

Safety margin

di

Minimum safe distance between train i and train i − 1

dsb,i

Maximum service braking distance of train i

deb,i

Emergency braking distance of train i

si

Position of train i

vi

Velocity of train i

ai

Acceleration of train i

xi

Distance deviation of train i

yi

Velocity deviation of train i

li

Length of train i

f

Force caused by external perturbation

mi

Mass of train i

=

v2 vi2 − i−1 + sf . 2asb 2aeb

(1)

As stated in assumption A2, we only consider the scenario of coupled driving scenario. The distance deviation and velocity deviation expressions are as follows: xi = si−1 − si − di − li−1 , yi = vi − vi−1 ,

(2)

where si is the position of train i, li−1 is the length of train i − 1, vi is the velocity of train i. The derivative of Eq. (2) is given as: x˙i = vi−1 − vi −

vi−1 ai−1 vi ai + , asb aeb

(3)

y˙i = ai − ai−1 . The train acceleration can be formulated as follows: ) ( f , ai = u i − cˆ1 vi2 + cˆ2 vi + cˆ3 + mi

(4)

182

Y. Zheng et al. Δ

Δ

Δ

where u i is the control input from the robust controller in the leading train. c1 , c2 , c3 are Davis coefficients with time-varying uncertainty around the known nominal values c j with half-length µ j . The practical resistance coefficients are described as c1 = c j + ϖ j (t)µ j , j = 1, 2, 3, where −1 ≤ ϖ j (t) ≤ 1 is the time varying part [10]. f represents the force exerted on VCTS by external perturbations, such as gust force, road irregularities, and the wear of actuators. The force produced by disturbance is unknown, and it can be calculated as the following equation referring to [11]: Δ

ω˙ = N ω,

(5)

f = V ω + V0 .

The force produced by disturbance can be calculated by ω, V and V0 . ω is a 0 c ]. V and variable related to the frequency, i.e., c. N can be described as N = [ −c 0 V0 are parameters associated with the amplitude of the force. By substituting the acceleration expression into Eq. (3), we then have: ) ) ( ( cˆ3 cˆ2 2 cˆ2 2 cˆ1 3 cˆ3 vi + 1 − vi−1 + vi − vi−1 + v x˙i = −1 + asb aeb asb aeb asb i ) ( cˆ1 3 vi vi−1 vi−1 vi f, − vi−1 − ui + u i−1 + − aeb asb aeb aeb mi−1 asb mi mi−1 − mi 2 y˙i = − cˆ1 vi2 + cˆ1 vi−1 f. − cˆ2 vi + cˆ2 vi−1 + u i − u i−1 + mi−1 mi

(6)

Since there exist higher order terms of velocity vi in Eq. (6), it is necessary to apply the linearization method for them [12]. The ideal velocity of the following train is the same as that of the leading train, the first-order Taylor approximation of the higher order term of vi at v0 is used, where v0 is the velocity of the leading train. The application is given as follows: f (vi ) ≈ f (v0 ) +

d f (v0 ) (vi − v0 ). dv0

(7)

By applying the above linearization method to Eq. (6), we obtain the following expressions: ˆ x˙i = Mˆ 1 vi + Mˆ 2 vi−1 + M3 u i + M4 u i−1 + M5 f + C, y˙i = u i − u i−1 + Nˆ 1 (vi − vi−1 ) + N2 f, Δ

Δ

Δ

3v 2 c 2v0 c2 + a0sb 1 , asb v 2 cˆ asb m i −aeb m i−1 , C = a0eb2 asb aeb mi−1 mi

Δ

M2 = 1 − aceb3 −

M4 = aveb0 , M5 = −mi N2 = mmi−1 . i−1 mi

−

+

Δ

3v 2 c 2v0 c2 − a0eb 1 , M3 = − avsb0 , aeb 2v03 cˆ1 2v 3 cˆ − a0sb 1 , N1 = −cˆ1 − 2cˆ2 v0 , aeb

where M1 = −1 + acsb3 +

v02 cˆ2 asb

Δ

(8)

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To establish state space equations, we define state variables as the distance error and velocity error between neighbouring trains. Errors refer to the difference between the actual deviation between trains and deviation in the equilibrium state, and they can be described as: δu i = u i − u ie , δxi = xi − xie , δyi = yi − yie ,

(9)

where u ie , xie , yie represent the control input force and deviation in equilibrium, i.e., converge to zero. To construct a typical robust H∞ optimal control problem, this paper defines the measured output as Y , which denotes the velocity of each train. It can be measured directly by velocity sensors installed in each train of VCTS. The performance output Z reflecting system performance is required to track the speed command and maintain the stability of VCTS. That means Z is related to the position and velocity of each train, ensuring position error and velocity error of VCTS are as small as possible under disturbance. Finally, based on the analysis and derivation above, the state space equations for VCTS under virtual coupled driving scenario are obtained as follows: ξ˙ (t) = (A + ΔA)ξ (t) + B1 f (t) + B2 u(t), Z (t) = C1 ξ (t) + D12 u(t),

(10)

Y (t) = C2 ξ (t), where

A

=

ξT

]T [ = δx1 · · · δx N δy1 · · · δy N , u T ⎡ ⎤ 0 M1 0 0 0 ⎢0 M1 0 0 ⎥ ⎢ n×n M1 + M2 ⎥ ⎢ ⎥ .. .. .. ⎢ 0 . . 0 ⎥ . ⎢ ⎥ ⎢ ⎥ ⎢ 0 M1 + M2 M1 + M2 . . . M1 ⎥ ⎢ ⎥, B1 ⎢ 0 N1 0 0 0 ⎥ ⎢ ⎥ ⎢ 0n×n 0 N1 0 0 ⎥ ⎢ ⎥ ⎢ ⎥ .. .. .. ⎣ 0 . . 0 ⎦ . 0 0 ... 0 N1

=

=

]T [ δu 1 . . . δu N , ⎡ ⎤ M5 ⎢M ⎥ ⎢ 5⎥ ⎢ . ⎥ ⎢ .. ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ M5 ⎥ = ⎢ ⎥, B2 ⎢ N2 ⎥ ⎢ ⎥ ⎢ N2 ⎥ ⎢ ⎥ ⎢ .. ⎥ ⎣ . ⎦ N2

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⎡ ⎤ ⎤ 0 M3 0 0 0 ⎢0⎥ ⎢M M 0 0 ⎥ ⎢ ⎥ ⎢ 4 3 ⎥ ⎢.⎥ ⎢ . . . ⎥ ⎢ .. ⎥ ⎢ .. . . . . 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢0⎥ ⎢ 0 . . . M4 M3 ⎥ = H Δ(t)E, H = = ⎢ ⎥, ΔA ⎢ ⎥, C2 ⎢1⎥ ⎢ 1 0 0 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢1⎥ ⎢ −1 1 0 0 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ .. ⎥ ⎢ .. . . . . ⎥ ⎣.⎦ ⎣ . . . 0 ⎦ 1 0 . . . −1 1 ⎡ ⎡ ⎤ ⎤ 0 ΔC1 0 0 0 0 ΔE 0 0 0 ⎢0 ⎢0 ⎥ ⎥ ⎢ n×n ΔC2 ΔC1 0 0 ⎥ ⎢ n×n ΔE ΔE 0 0 ⎥ ⎢ ⎢ ⎥ ⎥ .. .. . . . . .. .. ⎢ 0 ⎢ 0 . . 0 ⎥ . . 0 ⎥ . . ⎢ ⎢ ⎥ ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ 0 ΔC2 ΔC2 . . . ΔC1 ⎥ ⎢ 0 ΔE ΔE . . . ΔE ⎥ = ⎢ ⎢ ⎥, E ⎥, Δ(t) = ⎢ 0 ΔC3 0 0 0 ⎥ ⎢ 0 ΔE 0 0 0 ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ 0n×n 0 ΔC3 0 0 ⎥ ⎢ 0n×n 0 ΔE 0 0 ⎥ ⎢ ⎢ ⎥ ⎥ ⎢ ⎢ ⎥ ⎥ .. .. . . . . .. .. ⎣ 0 ⎣ 0 . . 0 ⎦ . . 0 ⎦ . . 0 0 . . . 0 ΔC3 0 0 . . . 0 ΔE diag{ϖ ΔC1] = · · · ϖ ϖ · · · , ϖ ϖ · · · , ϖ3 (t)}, (t), (t), (t), (t), (t), 1 2 2 3] ] 1 [ [ [ C12 C22 C32 , ΔC 3 = C13 C23 0 , ΔE = C11 C21 ΔC31 , ΔC2 = ]T [ 2 2 2 0 0 0 , C31 = a1sb , C12 = 3vasb0 − 3vaeb0 , C22 = 2v − 2v , µ1 µ2 µ3 , C11 = 3vasb0 , C21 = 2v asb asb aeb 1 1 C32 = asb − aeb , C13 = −1, C23 = −2v0 ⎡

Δ

Δ

Δ

where M1 , M2 , and N1 represent Davis coefficients, M 1 , M 2 , and N 1 take the nominal values of the basic resistance coefficients, C1 and D12 are composed of scalar weights, where the tuning parameters are chosen by the designer to achieve the desired performance [13]. For the control input, its upper and lower limits should be set according to the actual trains, i.e., −u i,min ≤ u i (t) ≤ u i,max , i = 1, 2, . . . , n.

(11)

where u i,max and u i,min represent the magnitudes of the maximum and minimum allowable values for the control input.

3 Robust H ∞ Controller Design and Linear Matrix Inequality Method A composite state feedback controller is designed, and the control law is given as: u(t) = K ξ (t),

(12)

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where the state feedback gain K can be obtained by the following LMIs approach. By substituting the control law (12) into state space Eq. (10), we obtain the controlled state space equations of VCTS as followed: ξ˙ = (A + ΔA + B2 K )ξ + B1 f, Z = (C1 + D12 K )ξ.

(13)

based on robust H∞ optimal control, when the variable γ takes the minimum value, the infinite norm of the transfer function from disturbance f to performance output Z needs to satisfy: T f z (s)∞ = (C1 + D12 K )[s I − ( A + ΔA + B2 K )]−1 B1∞ < γ ,

(14)

under this condition, the controller could achieve the ability to resist disturbance. To derive the existing condition of controller stability and solve the state feedback gain, we first introduce the following lemmas [14]: Lemma 3.1 For an algebraic Riccati inequality A T P + P A + γ −2 P B B T P + C T C < 0, if there exists a positive definite solution P, then A is stable and ||C(s I − A)−1 B||∞ ≤ γ holds. Lemma 3.2 Given proper dimensional matrices Y , Q and E, where Y is symmetric, then Y + D E F + E T F T D T < 0 holds for all matrices F with F T F ≤ I if and only if there exists a constant β < 0 such that Y + β −1 D D T + β E T E < 0. According to Lemma 3.1 and Eq. (14), when the system stability and H∞ performance requirements are satisfied, the following LMI expression can be obtained: ⎡ ⎤ P( A + ΔA + B2 K ) + (A + ΔA + B2 K )T P P B1 (C1 + D12 K )T ⎣ ⎦ < 0, B1T P −γ 2 I 0 0 −I C1 + D12 K (15) by substituting the parameter uncertainty into Eq. (15), the following LMIs are obtained:: ⎤ ⎡ P(A + B2 K ) + (A + B2 K )T P P B1 (C1 + D12 K )T ⎦+ ⎣ B1T P −γ 2 I 0 0 −I C + D12 K ⎡ 1 ⎤ (16) P H Δ(t)E + [H Δ(t)E]T P 0 0 ⎣ 0 0 0 ⎦ < 0, 0 00

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Y. Zheng et al. ⎡ ⎢ ⎣

⎤ ⎡ ⎤ P(A + B2 K ) + ( A + B2 K )T P P B1 (C1 + D12 K )T PH [ ] ⎥ ⎢ ⎥ B1T P −γ 2 I 0 ⎦ + ⎣ 0 ⎦Δ(t) E 0 0 + 0 −I C1 + D12 K ⎡ ⎤ 0 ET ] [ ⎥ ⎢ ⎣ 0 ⎦Δ(t)T H T P 0 0 < 0, 0

(17)

since Δ(t)T Δ(t) ≤ I , according to Lemma 3.2, Eq. (17) can be described as: ⎤ ⎡ ⎤ P(A + B2 K ) + (A + B2 K )T P P B1 (C1 + D12 K )T PH [ ] ⎥ ⎢ ⎢ ⎥ B1T P −γ 2 I 0 ⎦ + ε⎣ 0 ⎦ H T P 0 0 + ⎣ 0 −I C1 + D12 K ⎡0 ⎤ ET [ ] ⎢ ⎥ ε −1 ⎣ 0 ⎦ E 0 0 < 0. 0 ⎡

(18)

The following LMIs can then be obtained based on the Schur complement: ⎤ P( A + B2 K ) + (A + B2 K )T P P B1 (C1 + D12 K )T E T P H ⎢ −γ 2 I 0 0 0 ⎥ B1T P ⎥ ⎢ ⎥ ⎢ 0 −I 0 0 ⎥ < 0. C1 + D12 K ⎢ ⎥ ⎢ ⎣ E 0 0 −ε I 0 ⎦ 0 0 0 −ε−1 I HT P (19) ⎡

By multiplying diag{P −1 , I, I, I, I } on both sides of Eq. (19), the updated LMIs are obtained as follows: ⎡

( )T ( )T ( )T −1 + B K P −1 + A P −1 + B K P −1 B1 H C1 P −1 + D12 K P −1 E P −1 2 2 ⎢ AP ⎢ ⎢ −γ 2 I 0 0 0 B1T ⎢ ⎢ C1 P −1 + D12 K P −1 0 −I 0 0 ⎢ ⎢ E P −1 0 0 −ε I 0 ⎣ HT 0 0 0 −ε −1 I

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ < 0, ⎥ ⎥ ⎦

(20) Finally, the sufficient condition of controller stability under control constraint is obtained, i.e.,:

A Robust Control Approach for Virtually Coupled Train Set …

min ρ, ⎡ AX + B2 Y + (AX + B2 Y )T B1 (C1 X ⎢ −ρ I B1T ⎢ ⎢ 0 C1 X + D12 Y ⎢ ⎢ ⎣ EX 0 0 HT [ ] −Q ∗ ≤ 0, Y T −X

187

⎤ + D12 Y )T (E X )T H 0 0 0 ⎥ ⎥ ⎥ −I 0 0 ⎥ < 0, ⎥ 0 −ε I 0 ⎦ 0 0 −ε−1 I

qiT Qqi ≤ uˆ i2 , Q > 0. X > 0. (21) | u i,min −u i,max | i,max | |, qi is the − where X = P −1 , Y = K X , ρ = γ 2 , u i = u i,min +u 2 2 eigenvalue of the acceleration constraint inequality. The robust H∞ controller gain K = YX −1 is obtained such that the VCTS is stable with a attenuation level less than γ , i.e., each train could track the desired movement near the equilibrium state. Δ

4 Case Study 4.1 Setup In this section, a numerical study is designed, where the considered VCTS consists of a leading train and three following trains. Train 0 represents the leading train, while train 1, train 2, and train 3 represent the following trains. This VCTS is running in the virtually coupled scenario, where the leading train collects the position, velocity, and acceleration information of all following trains by V2V communication. In addition, the leading train sends control commands back to the following trains after the computation of the centralized controller. The simulation parameters are given in Table 2, which is chosen according to the experimental setting of [11] based on the Japan Shinkansen high-speed train. Each train is subjected to a force caused by external perturbations, i.e., f . The parameters related ] frequency of [ to amplitude and disturbing force are set as V0 = 4 × 104 N , V = 2 × 104 2 × 104 N , c = 0.2H z. The initial value of variable is given as ω(0) = [ 1 1 ]. The initial distance error and speed error of VCTS are given as 1.5 m and 0 m/s, respectively, i.e., ξ(0) = T [ 1.5 1.5 1.5 0 0 0 ] . Since −1 ≤ ϖj (t) ≤ 1, time-varying parameters in the train dynamic model are selected as ϖj (t) = sin(t). The temporary speed restriction of VCTS is set as 225km/ h, and the control constraints are set as u i,min = u i,max =

188 Table 2 Parameters of the high-speed train

Y. Zheng et al.

Parameter

Value

Unit

asb

0.8

m/s 2

aeb

1

m/s 2

c1

1.176 × 10−2

N /kg

c2

7.7616 × 10−4

N s/mkg

c3

6 × 10−3

N s 2 /m 2 kg

µ1

1.6 × 10−5

N /kg

µ2

2.6 × 10−4

N s/mkg

µ3

8.8 × 10−6

N s 2 /m 2 kg

sf

21

m

li

50

m

m0 , m2

3.19224002 × 108

kg

m1 , m3

3.19224 × 108

kg

1N /kg. Based on the parameters and assumptions, a few numerical simulations are conducted via the Simulink of Matlab. In addition, the control performance of the cases with uncertain parameters is compared with that of the case with fixed parameters.

4.2 Numerical Results By solving the LMIs given in (20) with the help of Matlab LMI toolbox, K = YX −1 and γ = 3.63 are obtained as the robust state feedback control gain and the attenuation level, respectively. As the dimension of K is large, it is not listed here. The distance error and velocity error of VCTS with parameters uncertainty are given in Fig. 3. By applying the robust control scheme to VCTS under external perturbations, each following train quickly tracks the reference speed of the leading train. In particular, the distance error and velocity error peak at the beginning of simulation, and then converge to zero, i.e., each train could be stable in the equilibrium condition of virtually coupled driving scenario. The simulation results reveal the effectiveness of the proposed robust H∞ control approach to deal with the disturbances. The controller is also applicable in the case of fixed parameters, as shown in Fig. 4. In the model with fixed parameters, Davis coefficients take the nominal values of the basic resistance coefficients. The accuracy of the model with fixed parameters is lower than that of the model with uncertain parameters, resulting in different control effects. The concrete numerical results of distance error reflecting controller performance are shown in Table 3. Specifically, in the case of fixed parameters, although the adjustment speed of the controller is faster, the peak value and overshoot of the controller increase. The increase in errors will lead to unstable train operations and safety risks.

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Fig. 3 The distance error and velocity error with uncertain parameters

In addition, Fig. 5 shows the control input of robust H∞ controller for VCTS with parameters uncertainty, where maximum amplitude does not exceed the limited value 1N /kg. Thus, the above simulation results can well verify that the designed robust H∞ control approach plays a good anti-interference role while satisfying the constraints.

5 Conclusions This paper has proposed a multi-train cooperative control method based on robust H∞ control theory, where the parameter uncertainty and external perturbations are considered for the VCTS. The train dynamic model of VCTS is established, where the distance error and velocity error are taken as state variables. Under the premise of satisfying input control constraint, a robust H∞ controller is designed, where the existence condition of controller stability and controller gain is given by constructing linear matrix inequalities. The simulation results show that for the disturbed VCTS with uncertain parameters, the designed robust H∞ control method can effectively make errors converge to zero, further, to ensure the robustness of VCTS.

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Fig. 4 The distance error and velocity error with fixed parameters Table 3 Performance comparison for uncertain and certain parameters Parameter

Peak time (s)

Peak value (m)

Setting time (s)

Overshoot (%)

Uncertain

0.24

1.99

3.03

1.99

Fixed

0.03

3.79

1.63

3.79

Fig. 5 Control input of robust H∞ controller for VCTS with parameter uncertainty

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In future research, the application scenarios of the controller could be expanded, such as coupling, unintentional decoupling, and intentional decoupling scenarios. The accuracy of the model can be further improved by considering the difference of train barking performance and the combination with other control methods such as event-trigger control, fuzzy control to improve the performance of the robust controller. Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC) (72071016).

References 1. U. Bock, G. Bikker, Design and development of a future freight train concept–“virtually coupled train formations.” IFAC Proc. Vol. 33, 395–400 (2000) 2. E. Quaglietta, M. Wang, R.M. Goverde, A multi-state train-following model for the analysis of virtual coupling railway operations. J. Rail Transp. Plan. & Manag. 15, 100195 (2020) 3. L. Liu, P. Wang, B. Zhang, W. Wei, Coordinated control method of virtually coupled train formation based on multi agent system, in International Conference on Smart Vehicular Technology, Transportation, Communication and Applications (Springer, 2018), pp. 225–233 4. J. Park, B.H. Lee, Y. Eun, Virtual coupling of railway vehicles: gap reference for merge and separation, robust control, and position measurement. IEEE Trans. Intell. Transp. Syst. (2020) 5. M. Chen, J. Xun, Y. Liu, A coordinated collision mitigation approach for virtual coupling trains by using model predictive control, in 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC) (2020), pp. 1–6 6. S. Ma, B. Bu, H. Wang, A virtual coupling approach based on event-triggering control for CBTC systems under jamming attacks, in 2020 IEEE 92nd Vehicular Technology Conference (VTC2020-Fall) (2020), pp. 1–6 7. J. She, K. Li, L. Yuan, Y. Zhou, S. Su, Cruising control approach for virtually coupled train set based on model predictive control, in 2020 IEEE 23rd International Conference on Intelligent Transportation Systems (ITSC) (2020), pp. 1–6 8. Y. Cao, J. Wen, L. Ma, Tracking and collision avoidance of virtual coupling train control system. Futur. Gener. Comput. Syst. 120, 76–90 (2021) 9. J. Lianghai, M. Liu, A. Weinand, H.D. Schotten, Direct vehicle-to-vehicle communication with infrastructure assistance in 5G network, in 2017 16th Annual Mediterranean Ad Hoc Networking Workshop (Med-Hoc-Net) (2017), pp. 1–5 10. S. Li, X. Wang, L. Yang, T. Tang, Robust efficient cruise control for high-speed train movement based on the self-triggered mechanism. Transp. Res. Part C: Emerg. Technol. 128, 103141 (2021) 11. X. Yao, L. Wu, L. Guo, Disturbance-observer-based fault tolerant control of high-speed trains: A Markovian jump system model approach. IEEE Trans. Syst. Man Cybern.: Syst. 50, 1476–1485 (2018) 12. J. Xun, J. Yin, R. Liu, F. Liu, Y. Zhou, T. Tang, Cooperative control of high-speed trains for headway regulation: a self-triggered model predictive control based approach. Transp. Res. Part C: Emerg. Technol. 102, 106–120 (2019) 13. C.D. Yang, Y.P. Sun, Mixed H2/H cruise controller design for high speed train. Int. J. Control. 74, 905–920 (2001) 14. L. Xie, M. Fu, C.E. de Souza, H∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback. IEEE Trans. Autom. Control 37, 1253–1256 (1992)

Code-Based PSO-SVM Algorithm for Network Security Posture Warning of Power System Kuan Tan, Youzhi Bao, Yuanlin Zhang, and Bangna Ding

Abstract The current power system online early warning technology achieves dynamic security assessment of the power system by analyzing the offline data of the power grid, which leads to low early warning accuracy due to the broad formulation of early warning indicators. In this regard, the power system network security posture early warning technology based on PSO-SVM algorithm is proposed. The PSO-SVM algorithm is optimized by adding nonlinear decreasing inertia weights to process the broad frequency vectors of the power system and reduce the broad frequency oscillation amplitude. A comprehensive early warning index based on the energy weight factor is established to achieve accurate early warning of the network security posture of the power system. In the experiment, the early warning accuracy of the proposed early warning technique is verified. The analysis of the experimental results shows that the early warning of power system network security posture constructed by using the proposed method has high early warning accuracy. Keywords Particle swarm algorithm · Support vector machine · Power system · Cybersecurity posture warning

1 Introduction The current traditional power system network security posture warning technology gives multiple indicators of the power system voltage posture level assessment of relevant research results, establishes a two-level fuzzy comprehensive evaluation method based on three groups of characteristic indicator subsets of voltage posture warning level, and conducts a guiding research on the development of voltage posture warning system, which is of great significance. One of the research difficulties of K. Tan · Y. Bao (B) · Y. Zhang Honghe Power Supply Bureau of Yunnan Power Grid Co., Ltd, Mengzi 661100, China e-mail: [email protected] B. Ding Guangdong Technology College, Zhaoqing 526000, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_17

193

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the current fuzzy comprehensive evaluation is how to scientifically and objectively synthesize a multi-indicator problem into the form of a single indicator in order to achieve comprehensive evaluation in a one-dimensional space, which is in essence how to reasonably determine the weights of these indicators [1]. However, the traditional power system network security posture warning technology does not explain how to determine the weights of each indicator, which to a certain extent affects the accuracy and objectivity of the assessment. The operation of the power system is affected by a variety of factors, and its operation state is in dynamic development and change, so it is necessary to establish an online monitoring and security early warning system for the power system. The so-called safety early warning of power system is to take the regular characteristics presented by the operation of power system as the starting point, through monitoring and analysis of various factors affecting the operation of power system, focusing on dynamic monitoring and alarm forecasting of the operation of power system. By using the tide calculation and static safety analysis modules, the branch tide information and node voltage information of the system can be obtained [2]. By drawing the tide animation and voltage isochronism diagram, the tide distribution and voltage distribution of the power grid can be vividly and graphically displayed, and the overrun information of the branch tide and node voltage can be visually displayed. In addition, other analysis modules such as low-frequency oscillation and interlocking fault can highlight the components of the system prone to low-frequency oscillation or interlocking fault on the screen, which makes it easy for staff to find out the weakness of the system in time and quickly deal with the overrun and heavy load problems to prevent serious accidents. The heavy research tasks such as transient stability assessment, voltage stability assessment, and relay protection calibration are mainly done through off-line analysis. Due to the large scale of modern power grids and the combinatorial explosion problem, manually specified operation modes and expected accident sets cannot be complete, so there may be serious safety hazards in some special operation modes, or in abnormal fault modes [3]. The safety sides of large-scale complex power grids are more numerous, and the limited computational capability of EMS in the traditional design mode cannot implement comprehensive and integrated online warning for the safety of power grids. Therefore, a new type of network security posture early warning technology for power system needs to be developed to provide a guarantee for the safe operation of the power system.

2 PSO-SVM Algorithm Optimization and Analysis There are two parameters in the PSO-SVM model that need to be determined: the penalty parameter C, and the wavelet kernel function parameter a. Their values have a great relationship with the prediction accuracy, and suitable parameters can improve the generalization ability of the model; therefore, it is necessary to select an optimization algorithm to optimize the parameters for early warning of the power system network security posture [4].

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The particle swarm algorithm (PSO) has outstanding performance in combinatorial optimization problems and is an intelligent optimization algorithm based on velocity a position search [5]. In each iteration, the particles not only consider the historical optimal point Pbest of their own search but also consider the historical optimal points Gbest of other particles within the population in order to find the optimal solution to the problem. In the standard PSO algorithm, the iterative formulas for velocity and position updates of the particles are Vi (k + 1) = W Vi (k) + cr (Pbest (k) + G best (k))

(1)

where Vi (k) and Vi (k + 1) represent the particle operation speed at moment k and moment k + 1, respectively; W represents the inertia weight, c represents the learning factor, and r represents the random number distributed on the interval [0,1]. The size of the inertia weight W determines how much the particle inherits the current velocity. A larger inertia weight, where the particle has a larger velocity in the original direction, flies further in the original direction and has a better exploration capability; a smaller inertia weight, where the particle has a smaller velocity in the original direction, flies closer in the original direction and has a better exploitation capability to extend the search space [6]. As the number of iterations increases, better exploitation ability is desired to make the particle perform local search in the optimal region of the search to find the optimal solution. In order to balance the global and local search ability, the inertia weights are usually adjusted by using linear time-varying weights, i.e., the inertia weights at the kth iteration. W (k) = Wmax −

Wmax − Wmin Imax

(2)

where Wmax and Wmin represent the maximum and minimum inertia weights respectively, and Imax represents the maximum number of iterations. The linear timevarying weights with linearly decreasing weights and improperly selected maximum iterations are prone to make the inertia weights decrease too fast and fall into the local extreme-optimal solution, to avoid this situation, this paper proposes nonlinear decreasing inertia weights with the following expressions. W (k) = Wmax −

ek − 1 e Imax − 1

(3)

According to the above steps, the PSO-SVM algorithm can be improved to provide algorithmic support for the subsequent power system warning technology.

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3 Power System Network Wideband Vector Processing The master station places the phase volume data sent from each sub-station in the real-time database and historical database according to the data time-scale information, so as to obtain the broadband phase volume information of each time section. However, the oscillation frequencies monitored by monitoring nodes at different locations for the same oscillation mode may differ to a certain extent, and there may be multiple oscillation modes for broadband oscillations [7]. Therefore, it is necessary to “unify” the same oscillation mode distributed in different locations, i.e., use the same oscillation frequency to describe the same oscillation mode distributed in different locations of the grid. Firstly, the phase quantities of all monitored lines in the same time section are clustered by frequency using cluster analysis, and divided into clusters, and each cluster is “unified” by frequency to obtain the oscillation frequencies of different oscillation modes. In the process of frequency “unification”, the measurement accuracy of the oscillation frequency is strongly correlated with the mode current amplitude, i.e., the larger the mode amplitude is, the more accurate the corresponding oscillation frequency is measured. Therefore, for a given oscillation mode frequency, the modal current amplitude and the modal frequency measured at different locations can be approximated as follows. fs =

m 

Is

(4)

i=1

where s represents the cluster serial number, m represents the number of monitoring points contained in cluster s, f s and Is represent the modal frequency and modal current amplitude collected at the i-th monitoring point in cluster s, respectively. Wide-frequency state estimation is an extension of traditional state estimation for voltage and current phase quantities in the same oscillation mode to obtain the real-time state of the power system. Wide-frequency state estimation can correct or reject bad data to improve the accuracy and precision of monitoring data, which is the prerequisite and basis for the implementation of each advanced application of the master station. For any mode with an oscillation frequency of f s , the line current and node voltage relationships for all measured branches can be expressed as I = [Y ( f s )A + Y S ( f s )]U + e

(5)

where I denotes the measured value of the current phase quantity; U is the state vector of the node voltage phase quantity; Y ( f s ) is a diagonal matrix composed of the series conductance of the measurement branch; Y S ( f s ) is a matrix composed of the parallel conductance at the end of the measurement branch; A is the voltage coefficient matrix; and e represents the measurement noise of the current. According to the observability principle, monitoring nodes are deployed at appropriate locations in the grid, and the

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measured node voltage and line current phase data (measured values) are used as inputs for state estimation, and the relationship between the measured values and the state vector can be expressed as Z = BU + e

(6)

where B represents the current coefficient matrix, Z represents the measured value, and U represents the measured voltage matrix. From the above method, the phase volume data of each oscillation mode can be estimated, and further the phase volume data are used to perform oscillation source identification and oscillation risk assessment.

4 Early Warning Indicator Selection At present, the main index used for the safety warning analysis of the broadband oscillation process is the damping ratio of the oscillation mode. To a certain extent, the damping ratio can reflect the decay characteristics of the mode, which provides a partial basis for the scheduling and operation personnel to take control measures. However, the damping ratio indicator alone cannot fully reflect the current system condition, especially when the system safety and stability margin is small, a small external disturbance can cause significant system oscillation or even instability. Therefore, this paper will study a comprehensive early warning index that takes into account the system safety and stability margin, system risk, and mode signal energy weighting factor [8]. The commonly used safety warning indexes for power networks are shown in Table 1. Table 1 Common indicators for safe operation of power systems Indicators

Features

Branch potential energy indicator

Reflects whether the peak is within the stability limit after the disturbance

Energy margin indicator

Stability is judged by the difference between the transient energy and the critical energy

Frequency indicator

Defined by the range of low-frequency oscillations

Dominant mode weakest damping ratio

Directly related to the characteristic value of the grid structure

Indicator

Reflects system stability

Amplitude indicator

Reflects the degree of harm to the grid

Peak-to-peak duration number of cycles

Reflects the trend of power fluctuation

Dynamic damping ratio

Reflects power oscillation under disturbance

First swing peak indicator

Reflects the security performance of the grid

198 Table 2 Peak indicator warning levels

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Number of continuous cycles

Early warning level

1

A (Security)

2

A (Security)

3

B (Dangers)

4

B (Dangers)

≥5

C (Highly hazardous)

The table shows that, since the amplitude indicator and the first swing peak indicator can reflect the power fluctuation of low-frequency oscillation, the nature is the same, so it is enough to take one of them for the study: The branch potential indicator and the energy margin indicator involve a more complex grid model, which is relatively huge and difficult to calculate, and the selection of these two indicators is not reasonable. According to the information of the state of the actual grid safe operation, combined with the system simulation signal and PMU actual measurement signal, especially when the active power change of the generator reaches the warning gaps value, it can be used as a basis to judge whether there is a suspicion of oscillation. Considering the frequency range of low-frequency oscillation, the change trend of active power and the danger of oscillation duration to the power grid, this paper selects four indicators, namely, frequency, weakest damping ratio of dominant mode, peak of first swing, and the number of continuous cycles of peak-to-peak, together to form an index system [9]. For an intricate power system, when the system is subjected to various disturbances, up and down fluctuations in power occur accordingly. According to the fluctuation interval, the peak value of power oscillation is recorded as Pmax ; and the trough value as Pmin . If Pmax − Pmin ≥ 100 MW, a weekly wave is considered to exist. Let the number of periods that the peak-to-peak value lasts be N, and the corresponding warning level is shown in Table 2. According to the above steps, the power system early warning indicators can be constructed to provide reliable and specific early warning criteria for the subsequent power system early warning technology [10].

5 PSO-SVM Algorithm-Based Network Security Posture Warning Scheme for Power Systems In conjunction with the improved PSO-SVM algorithm above, in order to quantitatively describe the energy margin, the minimum function value along the set of all tidal wave boundaries is first defined as Vcritical = min V (x)

(7)

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where, Vcritical represents the critical energy, if the value of the critical energy can be obtained, the power system transient stability margin can be expressed by the relative distance between the system energy at the moment of fault removal and the stability boundary after the fault can be expressed as F(X F ) = V (X F ) − Vcritical

(8)

where, V (X F ) represents the value of the selected Lyapunov function at the time of fault excision, and the indicator F(X F ) quantitatively describes the relative distance between the energy margin and the energy boundary at the time of fault excision, when the value is less than zero, it indicates that the fault trajectory does not cross the stability boundary and the system remains stable after fault excision. And the smaller the value, the further the system state is from the stability boundary at the time of fault excision, and the more stable the system is in this state. At this point, the design of the PSO-SVM algorithm-based network security posture warning method for power systems is completed.

6 Testing and Analysis 6.1 Test Preparation In order to be able to derive accurate test results, the power system network security posture warning method in the paper is tested. The traditional distributed power system network security posture warning technology is used as the comparison object, including the power system security warning technology based on OPC technology and the power system warning technology based on model relaxation. By setting a typical line fault, the relative distance between the system energy and the stability boundary under different fault durations is calculated, and the energy boundary factor is calculated as shown in Table 3. Table 3 Energy boundary factors under different power system line faults Time

Line failure

t = 0.06 s

t = 0.08 s

t = 0.10 s

2:00

Line 1

−0.795

−0.127

−0.657

4:00

Line 2

−0.795

−0.647

−0.478

6:00

Line 3

−0.954

−0.761

−0.975

8:00

Line 4

−0.364

−0.479

−0.581

10:00

Line 5

−0.468

−0.649

−0.617

12:00

Line 6

−0.654

−0.798

−0.168

14:00

Line 7

−0.648

−0.168

−0.368

16:00

Line 8

−0.491

−0.641

−0.659

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In this experiment, an extended IEEE RBTS-bus4 power system is used and a certain number of DGs are connected. This power system has three 110 kV substations, six main transformers, 17 l OkV feeders and 69 load points. The total capacity of the system is 84 MVA, and the total capacity of the feeders is 131.72 MVA. The maximum capacity allowed to pass through the contact switches is divided into two categories: 5.83 and 4.11 MVA. By using three early warning techniques for this power system, the early warning accuracy of the techniques is compared.

6.2 Analysis of Test Results The evaluation index of this test is the early warning accuracy of the early warning technology. The actual value of the early warning is determined by the fault line of the power system under control, and three early warning techniques are used to warn the power system and derive the early warning value of the early warning. Among them, the time period 8:00–14:00 is the actual warning value of the larger moment, when the security situation of the power system is in the danger level, by comparing the warning value of the three early warning techniques whether to achieve the actual warning range, compare its warning accuracy. The specific experimental results are shown in the following table. Among them, traditional technique 1 represents the power system security early warning technique based on OPC technology, and traditional technique 2 represents the power system early warning technique based on model relaxation (Fig. 1). According to the above experimental results, it can be seen that when the power system network security posture reaches the dangerous time, i.e., the time period of 8:00–14:00, only the early warning value of the early warning technique proposed in this paper, which achieves the accurate early warning of the power system, while the early warning value of the traditional early warning technique does not reach the early warning standard, indicating that the power system network security posture based on PSO-SVM algorithm proposed in this paper. Early warning has high warning accuracy and can meet the demand of early warning for power system.

7 Conclusion The power system early warning technology proposed in the article adopts a distributed structure and parallel processing of computing tasks, which significantly increases the computational speed and greatly improves the speed of early warning analysis and calculation, and can effectively reveal the trend of grid changes and assist in analyzing potential risks. It can dynamically display the power grid operation status and provide online information reference, which provides a new perspective for dispatching operation work.

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1.4

1.2

Early warning value

1.0

0.8 Early warning methods in this paper

0.6

Traditional warning methods1 0.4 Traditional warning methods2 0

2:00

4:00

6:00

8:00

10:00

12:00

14:00

16:00

Time

Fig. 1 Warning values at different moments

References 1. Y. Wang, D. Wang, Y. Tang, Clustered hybrid wind power prediction model based on ARMA, PSO-SVM, and clustering methods. IEEE Access 8, 17071–17079 (2020) 2. M. Barman, N.B.D. Choudhury, A similarity based hybrid GWO-SVM method of power system load forecasting for regional special event days in anomalous load situations in Assam, India. Sustain. Cities Soc. 61(3), 102311 (2020) 3. D.A. Putri, D.A. Kristiyanti, E. Indrayuni, A. Nurhadi, D.R. Hadinata, Comparison of naive bayes algorithm and support vector machine using PSO feature selection for sentiment analysis on e-wallet review. J. Phys. Conf. Ser. 1641(1), 012085 (2020) 4. Y. Sun, J. Zhu, X. Yu, C. Ye, G. Fan, Research on early warning of power grid construction safety based on PSO-SVM model. J. Phys. Conf. Ser. 1449(1), 22–24 (2020) 5. S. Shojaeian, S.H. Rizi, A simple PSO-based method for power distribution system components reliability parameters calibration. Acta Marisiensis Ser. Technol. 18(1), 40–46 (2021) 6. D.D. Wang, J. Jiang, J.Q. Mo, J. Tang, X.Y. Lv, Rapid screening of thyroid dysfunction using Raman spectroscopy combined with an improved support vector machine. Appl. Spectrosc. 74(6), 674–683 (2020) 7. S. Emamgholizadeh, B. Mohammadi, New hybrid nature-based algorithm to integration support vector machine for prediction of soil cation exchange capacity. Soft. Comput. 25(21), 13451– 13464 (2021) 8. R. Duo, X. Nie, N. Yang, C. Yue, Y. Wang, Anomaly detection and attack classification for train real-time ethernet. IEEE Access 9, 22528–22541 (2021) 9. Q. Ge, C. Guo, H. Jiang, Z. Lu, Q. Hua, Industrial power load forecasting method based on reinforcement learning and PSO-LSSVM. IEEE Trans. Cybern. 52(2), 1112–1124 (2022) 10. K. Zhou, Z. Liu, M. Cong, S. Man, Detection of chemical oxygen demand in water based on UV absorption spectroscopy and PSO-LSSVM algorithm. Optoelectron. Lett. 18(4), 0251–0256 (2022)

Connectivity Reliability of Compound Rail Transit Network: A Case Study of Beijing-Tianjin-Hebei Urban Agglomeration in China Xuemei Xiao, Yanhui Wang, Zehong Zhou, and Chenchen Zhang

Abstract Based on the complex network theory, the multi-layer network composed of metro networks and inter-city railway networks in city agglomeration is built, and the relative size of maximal connected subgraph, global efficiency and local efficiency are proposed to evaluate the connectivity reliability of the compound rail transit network. Taking the compound rail transit network of Beijing-Tianjin-Hebei urban agglomeration (CRTN-BTH) as an example, this paper will conduct an empirical study, that is, the nodes of the compound network are attacked randomly and selectively to analyze the changes of its connectivity reliability, and to identify the key hub nodes of the network. The simulation results indicate that the CRTN-BTH is not a scale-free network. The connectivity reliability of the compound network is better than that of the selective attack under the random attack, and the key hubs are identified. This study has important practical significance to guide the planning and development of regional rail transit. Keywords Urban agglomeration · Compound rail transit network · Complex network · Connectivity reliability

1 Introduction Integrated rail transit network plays an important role in strengthening the social and economic connection of urban agglomerations, realizing the regional spatial layout and industrial optimization. According to system theory, a well-designed network structure is the foundation and premise of a well-run network. The existing research X. Xiao · Z. Zhou · C. Zhang School of Mechanical and Automotive Engineering, Xiamen University of Technology, Xiamen 361024, China Y. Wang (B) State Key Laboratory of Railway Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_18

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on the characteristics of rail transit network mainly focus on the single mode of rail transit-subway network, railway network and high-speed railway network from the perspectives of the specific country and city [1–7]. Some research on the characteristics of the compound traffic network mainly focused on the bus-subway network and air-rail network. Zhu Zhenran [8] proposed a dynamic weighted model to measure the connectivity of intercity passenger transportation in China. Sun XiaoXuan [9] analyzed the topological properties of higher-speed railway network, lower-speed railway network and multi-layer railway network. Xu Feng [10] analyzed the topological characteristics and robustness of Chinese high-speed railway and civil aviation compound network. Mouronte Mary Luz [11] estimated different parameters in the urban bus and the subway networks of Madrid. The connection of rail transit network is the key to ensure the reliable operation of rail transit system. Therefore, this paper studies the connectivity reliability of the compound rail transit network. The rest of this article is organized as follows: in Sect. 2, a multi-layer network consisting of subway network and intercity railway network among urban agglomerations is constructed; in Sect. 3, the relative size of maximal connected subgraph, global efficiency and local efficiency are proposed to evaluate the connectivity reliability of the compound rail transit network; in Sect. 4, the feasibility and rationality of the methods described above are verified through the Beijing-Tianjin-Hebei city cluster, where the reliability analysis under random and selective attack is carried out, and the key hub nodes of network are identified; finally, the conclusion is drawn in Sect. 5.

2 Modeling of Compound Rail Transit Network 2.1 Modeling Define 1: Rail transit subnet: A subnetwork composed of urban rail transit, intercity railway and other transit networks in urban agglomerations. Based on the Space L method, the station of a certain rail transit network is taken as a node, and the operating line connecting two stations is taken as a connecting edge, a rail transit n mn (i ) , in which node vi/I represents the subnet model is abstracted as Bi = n mn m,n∈V

station vi belongs  tothe subnet G I , n represents the total number of stations in the subnet. E I = ei j/I , i, j = 1, 2, · · · , n, i = j, in which edge ei j/I represents the node pair composed of adjacent nodes vi and v j belonging to the subnet G I . Define 2: Compound rail transit network: The rail network model G consists of two or more rail transit subnets connected by hub stations.G = (G 1 , G 2 , · · · , G I ) = (V , E),V = (V1 , V2 , · · · , VI ), in which V is the set of nodes in network.V1 ∈ G1 , V2 ∈ G2 , · · · , VI ∈ GI .V1 ∩ V2 ∩ · · · ∩ VI = ∅.E = (E1 , E2 , · · · , EI ), in which E is the set of edges in network,E1 ∈ G1 , E2 ∈ E2 , · · · , EI ∈ GI .

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2.2 Metrics (1) Degree and degree distribution Degree is the most basic parameter to describe the statistical characteristics of nodes in a network. For the compound rail network, degree ki/I of node vi/I refers to the number of edges connected to node vi , and node vi belongs to the subnet G I . It is obvious that the greater the node degree is, the more nodes are connected to it, and the greater the importance of nodes in the network is. The degree distribution of all nodes in the network can be described by the distribution function p(k), which is equivalent to the probability of randomly selecting a node with degree k. For the rail transit network, the greater the node degree is, the more nodes are connected to it, which is usually the core interchange hub station in the rail transit network. The analysis of degree and degree distribution has practical significance for the research of rail transit system. (2) Betweenness Betweenness can be divided into node betweenness and edge betweenness. Betweenness refers to the proportion of the shortest path between any two nodes that passes a certain node or edge in the entire network. Only node betweenness is considered in this paper. For the network G = (V , E), the node betweenness Bi of node vi is expressed as follow: Bi =

 n mn (i) n mn m,n∈V

(1)

where n mn (i ) is the number of the shortest path between node vm and node vn which passes node vi , n mn is the number of the shortest path between node vm and node vn . Betweenness reflects the role of a node or edge in the whole network. The higher the betweenness, the higher the frequency of the shortest path through the node or edge between any two nodes in the entire network. In a rail transit network, it represents the frequency with which a station or line passes through the shortest path from one location to another, thereby identifying important stations or lines in the network. (3) Clustering coefficient The clustering coefficient is used to describe the degree of clustering between the vertices of a graph. Specifically, it is the degree to which the adjacent points of a point are connected to each other. Assuming that node i has ki nodes connected to it, there are actually E i edges between these ki nodes, and there may be a sum of Ck2i edges between these ki nodes, the clustering coefficient Ci of node vi is: Ci =

2E i ki (ki − 1)

(2)

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The clustering coefficient C of the entire network is as follows: C=

1  Ci N i

(3)

When C = 0, it means that any two nodes are not connected in the network and all nodes are isolated; when C = 1, it means that any two nodes are directly connected and the network is globally coupled. The clustering coefficient can reflect the degree of local density in the network and can be used to determine which nodes have the highest aggregation degree. (4) Average shortest path length The shortest path length refers to the minimum number of edges between two nodes in the entire network. The average shortest path length of the network is the average of the minimum number of edges between any two nodes. L=

 2 di j N (N − 1) i≥ j

(4)

where di j is the shortest path length between node vi and node v j , N is the total number of nodes in network. In the rail transit system, the average shortest path length can reflect the shortest path from one place to another, and it is an important indicator for analyzing the quality of rail network transportation services from the level of topology. (5) Network Diameter The network diameter refers to the maximum distance between two nodes in the entire network, which can reflect the maximum number of paths to be passed from one node to another in the entire network.

3 Connectivity Reliability of Compound Rail Transit Network This paper defines the connectivity reliability of compound rail transit network as the ability to maintain connectivity between subnets after being attacked by the whole network. There are two evaluation indicators that are included, the relative size of the largest connected subgraph and the global network efficiency.

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3.1 Relative Size of Maximal Connected Subgraph For an undirected connected graph, the maximal connected subgraph refers to the subgraph with the least number of edges connecting all nodes in the connected graph. The relative size of the maximal connected subgraph means, in a non-fully connected graph, the ratio of the number of nodes in the largest connected subgraph to the number of all nodes in network. After deleting two nodes, the original network is split into two connected subgraphs, as shown in Fig. 1. For a single rail network G, the relative size of the largest connected subgraph SG is expressed as follows: SG =

N G NG

(5)



where NG is the number of nodes of the largest connected subgraph after node deletion, NG is the total number of nodes in the initial network, SG ∈ [0, 1]. When SG = 1, the rail network is a fully connected network without removing nodes. When SG = 0, the last node is removed and there is no connected subgraph in network. The rail network G is a compound network, with the purpose of determining the maximum connected subgraph after removing nodes from the level of the entire rail network topology, the relative size of the largest connected subgraph SGi of the subgraph Gi is expressed as follows: 

SGi =

NGi

(6)

NGi 

In this formula, subnet Gi belongs to network G, NGi is the number of nodes belonging to the subnet Gi from the largest connected subgraph of the entire network after removing nodes. NGi is the number of nodes in the subgraph Gi of initial

Fig. 1 Topology change of network after removing nodes

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Fig. 2 Topology change of network after removing nodes

network, SGi ∈ [0, 1]. When SGi = 1, the largest connected subgraph in network includes the entire subnet Gi , and there is no node failure in Gi . When SGi = 0, there are two situations: one is that the largest connected subgraph in network does not contain any nodes of subnet Gi ; the other is that all nodes of subnet Gi failed. It can be seen that SGi may become larger in the process of removing nodes, while SG cannot become larger, and only remains unchanged. When SG is constant, it means that the removed node is outside the largest connected subgraph. When SGi is unchanged, it means that the removed nodes are outside the subnet, or the removed nodes are in the subnet while do not belong to the largest connected subgraph. For example, in the fully connected graph in Fig. 2, SGi is equal to 6/6, 2/6, 3/6, respectively. When a node belongs to the largest connected subgraph, it can be observed that the node has a greater probability of connecting to other nodes (or connecting to more nodes). SGi is the proportion of the number of these nodes in the subnet, which, to a certain extent, reflects the impact on the connectivity of the subnet after the failure of the entire railway network.

3.2 Global Efficiency Network efficiency is an important indicator for judging the changes of network connectivity after attacks. With regard to the network G, the global efficiency Eglob (G) is the average value of the network efficiency of all node pairs. The efficiency of the network between nodes is equivalent to the reciprocal of the shortest path length between nodes, which can be expressed by the following formula: Eglob (G) =

  1 1 1 εij = N(N − 1) i=j∈G N(N − 1) i=j∈G dij

(7)

In formula (7), N refers to the total number of nodes in the total network G; dij refers to the shortest path length between node vi and vj ; εij refers to the inverse of the shortest path length between node vi and vj . When there is no connecting path between node vi and vj , dij is regarded as infinity, and εij is equal to 0. When Eglob (G) = 0, all nodes in the network were isolated; When Eglob (G) = 1, any two nodes in the network were directly connected.

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In order to describe the changes in the network efficiency of the network composed of subnets after the node is removed, assuming that the subnet Gmn is a collection of subnet Gm and Gn , the network local efficiency Elocal (Gmn ) between the subnet Gmn is expressed as follows: ⎛ ⎞  1 ⎝ Elocal (Gmn ) = εmn ⎠ Nm Nn − Pmn i∈G ,j∈G m

(8)

n

In formula (8), Nm is the total number of nodes in the subnet Gm ; Nn means the total number of nodes in the subnet Gn ; Pmn means the number of node pairs that are repeated between the subnet Gm and Gn (Gm ∩ Gn = ); εmn means the node vm and vn that belong to the subnet Gm and Gn . εmn is equivalent to 1/dmn .

4 A Case Study 4.1 Rail Network Topology Properties This paper selects the compound rail transit network of the Beijing-TianjinHebei (CRTN-BTH) for empirical research. It is abstracted as a non-weighted and undirected network, which contains 517 nodes and 1685 edges. The topology of CRTN-BTH is simplified as shown in Fig. 3. The three metro networks G 1 (BeijingMetro), G 2 (T ian jinMetro), G 3 (Shi jiazhuangMetro) are connected by the intercity railway network G 4 , forming a compound rail transit network G. The nodes with degree 2 of CRTN-BTH account for more than 75% (Fig. 4). The power law distribution function p(k) = 0.4283k −2.302 is obtained by least squares

Fig. 3 Simplified diagram of Beijing-Tianjin-Hebei regional rail

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Fig. 4 Distribution of node degree

linear fitting, and the fitting square value R2 = 0.515. It can be concluded that the CRTN-BTH is not scale-free network. In addition, the network diameter is 44, and an average path length L = 15.76, global efficiency Eglob = 0.0858. The nodes with Ci = 0 account for 98%, only a few nodes’ clustering coefficient is greater than zero, which suggests that aggregation of CRTN-BTH is very poor.

4.2 Connectivity Reliability Analysis This paper analyzes the connectivity reliability of CRTN-BTH based on random attack and selective attack. The selective attack is divided into node degree attack and node betweenness attack. Connectivity Reliability Analysis of Whole Network Simulation attacks on the CRTN-BTH are shown in Figs. 5 and 6, where f represents the proportion of removed nodes. In summary, CRTN-BTH has strong fault tolerance and high connectivity reliability in the aspect of random attack. In the terms of selective attacks, the rail network exhibits low connectivity reliability, whether it is node degree attack or a node betweenness attack. The Beijing City Vice Center Station, Tianjin Railway Station, GUOMAO Station and others are important nodes in the rail network. When these stations are removed, the efficiency of the rail network has declined by more than 10%. Disaster prevention should be strengthened in these stations in daily operations.

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Fig. 5 Relative size of maximal

Fig. 6 Global efficiency connected subgraph

Connectivity Reliability Analysis of Subnets In order to analyze the changes in the connectivity reliability of the subnets under the attacks, by combining the subnets as shown in Fig. 7, the changes of the indicators after the attack are calculated.

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Fig. 7 Schematic diagram of combined subnets

The subnet G1 , G2 , G3 and G4 are compound, respectively, to subnets G14 , G24 , G34 , in which G14 = (G1 , G4 ), G24 = (G2 , G4 ), G34 = (G3 , G4 ); The subnet G1 , G2 , G3 and G4 are compound into subnets G124 , G134 , G234 , in which G124 = (G1 , G2 , G4 ), G134 = (G1 , G3 , G4 ), G234 = (G2 , G3 , G4 ). The calculation results of the network attacks are outlined below. (1) The relative size change of the largest connected subgraph After removing the nodes one by one, it can be found from Figs. 8, 9, 10 that the change of the relative size S of the largest connected subgraph of each subnet. It can be seen that the S of each subnet drops slowly under a random attack, while the S of each subnet drops rapidly under a selective attack. Some of these subnets, such as subnets G 24 and G 234 , experienced a huge decline after the removal of 1% of the nodes. This indicates that the important nodes in these subnets play a greater role in connecting their own subnets. In addition, through comparison, it can be found that the decline of S under node betweenness attacks is greater than that under node degree attacks, and the connectivity reliability is ranked as G134 > G124 > G234 in terms of S. (2) Changes in Network Efficiency After removing the nodes one by one, the changes in the network efficiency Elocal of each subnet are as demonstrated in Figs. 11, 12, 13. It can be seen that, compared with random attacks, only 1% of nodes fail under selective attacks, the network efficiency Elocal of each subnet declines significantly, of which, the subnets G 24 , G 124 and G 234 have fallen by as much as 80%. By comparison, the connectivity reliability is ranked as G134 > G124 > G234 according to local efficiency. It shows that in these subnets, the influence of key nodes on network connectivity is greater than that of other subnets, and the connectivity reliability is poor in the aspect of selective attack. After the failure of 10% nodes, the network efficiency Elocal of each subnet declines by 90% under the betweenness attack, and the degree of connectivity within the subnet has been extremely low. The key stations in the network mainly include Tianjin Railway Station, Beijing City Vice Center Station, GUOMAO Station, Xinbai Square Station, Shijiazhuangdong Railway Station, JIAOMEN West Station, XIZHIMEN Station, etc. After the failure of these sites, the efficiency of the subnet network will be greatly reduced, or even a cliff-like decline. In daily operations, it is necessary to strengthen protective measures to enhance anti-attack capabilities.

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Fig. 13 Attack based on node degree

5 Conclusion Based on complex network theory, this paper constructs a compound rail transit model and defines the connectivity reliability of the compound rail transit network. Then the relative size of the largest connected subgraph and the efficiency of the rail

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network are selected as the evaluation index of connectivity reliability. Through the empirical analysis of the compound rail transit network of Beijing-Tianjin-Hebei, the following conclusions are drawn: (1) Large-scale compound subnets are subject to selective attacks based on the entire network, and the efficiency of the subnets decreases greatly and the connectivity reliability is poor. The connectivity reliability of subnets is sorted as G134 > G124 > G234. (2) The key nodes in the rail network, such as Tianjin Railway Station, Beijing City Vice Center Station, GUOMAO Station, Xinbai Square Station, Shijiazhuangdong Railway Station, JIAOMEN West Station, XIZHIMEN Station play a vital role in the connectivity of the network. Acknowledgements This work was supported by the Youth Innovation Foundation of Xiamen, China (Number 3502Z20206065); the State Key Laboratory of Rail Traffic Control and Safety(Number RCS2021K003) , Beijing Jiaotong University; and the Natural Science Foundation of Fujian Province, China (Number 2021J011198).

References 1. Y.X. He, Xu ZH ZH, Y. Zhao, et al., Dynamic evolution analysis of metro network connectivity and bottleneck identification: from the perspective of individual cognition. IEEE Access. 7:2042-2052 (2019) 2. J.H. Zhang, S.L. Wang, X.Y. Wang, Comparison analysis on vulnerability of metro networks based on complex network. Physica A. 49672–78 (2018) 3. Y. Deng, Q. Li, Y. Lu, J. Yuan, Topology vulnerability analysis and measure of urban metro network: The case of Nanjing. J. Networks 8(6), 1350–1356 (2013) 4. Y.Y. Xing, J. Lu, S.H.D. Chen, Vulnerability analysis of urban rail transit based on complex network theory: a case study of Shanghai Metro. Public. Transport. 9(3), 501–525 (2017) 5. D. Sun, J, Guan SH T., Measuring vulnerability of urban metro network from line operation perspective [J]. Transport. Res. A-Pol 94, 348–359 (2016) 6. X.R. Wang, Y. Koç, S., Derrible Multi-criteria robustness analysis of metro networks. Physica. A. 474:19-31 (2017) 7. J.H. Zhang, F. Hu, S.H.L. Wang et al., Structural vulnerability and intervention of high speed railway networks. Physica. A A 462, 743–751 (2016) 8. Z.H.R. Zhu, A.M. Zhang, Y.H. Zhang, Connectivity of intercity passenger transportation in China: A multi-modal and network approach. J. Transp. Geogr.Geogr. 71, 263–276 (2018) 9. X.X. Sun, Y. Wu, X. Feng et al., Structure Characteristics and Robustness Analysis of MultiLayer Network of High Speed Railway and Ordinary Railway. J. Univ. Electron. Sci. Technol. China 48(2), 315–320 (2019) 10. F. Xu, J.F. Zhu, J.J. Miao, The robustness of high-speed railway and civil aviation compound network based on the complex network theory. Complex Syst. Complex. Sci. 12(1), 40–45 (2015) 11. M.L. Li, X.F. Wang, Q.X. Sun, Hub location model and algorithm for road-rail intermodal transportation network. J. China Railw. Soc. 38(12), 1–7 (2016)

Performance Analysis of Empirical Weighting Method and Helmet Variance Component Estimation Method in CPIII Data Processing of Long Line Xiongwei Peng, Zhixiong Zhang, Yongchong Yang, and Wenzhuang Su

Abstract Construction, operation and maintenance of high-speed railway must rely on a complete, efficient and accurate measurement system. Professional data processing methods must be used to ensure the coordinate accuracy of the track control network. Aiming at the accuracy problem of the track control network (CPIII) in the adjustment data processing of the long line restraint network, the data of the CPIII plane control network are preprocessed, and the experience weight is determined based on the CPIII observation data of different line lengths. The method and the Helmet variance component estimation method are used in free network adjustment and constrained adjustment, and the impact of the two weighting methods on the accuracy of different line lengths is analyzed. The results show that the Helmet variance component estimation weighting method is more suitable for adjustment calculations that require high accuracy and more redundant observations than the empirical weighting method; in the case of sufficient line length and known point position, the Helmet variance component estimation weighting method can reduce the point position error by 8–13% compared with the empirical weighting method. Keywords CPIII · Constrained network adjustment · Helmet variance component estimation

X. Peng · Z. Zhang · Y. Yang (B) · W. Su College of Surveying and Mapping Science and Technology, Xi’an University of Science and Technology, Xi’an 710054, Shaanxi, China e-mail: [email protected] X. Peng e-mail: [email protected] Z. Zhang e-mail: [email protected] W. Su e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_19

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1 Introduction With the continuous construction of high-speed railway, the increasing passenger mileage of high-speed railway puts forward higher requirements for the stability, continuity and smoothness of high-speed railway track. The construction, operation and maintenance of high-speed railway must rely on a complete, efficient and accurate measurement system and must use professional data processing methods to ensure the coordinate accuracy of CPIII points [1]. Li Jianping proposed an observation network with a distance of 120 m between two stations, which shortens the operation time [2]. Ouyang xin classical free network adjustment using different benchmarks, from the starting point of the line 1/4 line length point as a fixed point, the best accuracy [3]. Sun Lishuang et al. unified the observation points of adjacent stations into the coordinate system and obtained the highest approximate coordinate accuracy of CPIII control points by indirect adjustment [4]. Jiang Hao et al. installed hoops on both sides of the line to make up for the disadvantage of the existing CPIII traverse network lateral deviation [5]. In this paper, empirical weighting method and Helmet variance component estimation method are applied to CPIII data processing with different line lengths. By comparing the accuracy indicators such as the error in the point position, the error in the direction and the error in the side length after the adjustment, the influence of different weighting methods on the measurement accuracy is obtained.

2 CPIII Constraint Network Adjustment Method and Mathematical Model 2.1 Empirical Weighting Method CPIII plane network has only two kinds of observation values of distance and angle, for different types of observations, the general use of the prescribed weight method, each observation error m α , m s . Assume that the direction error is the unit weight error, the weights of direction and distance can be obtained [6, 7] as follows. ⎧ σ02 ⎪ ⎪ ⎪ ⎨ Pα = m 2 = 1 a 2 ⎪ σ ⎪ ⎪ ⎩ ps = 02 ms

(1)

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2.2 Helmet Variance Component Estimation Method In the precise measurement of control network, the reasonable random model can correctly reflect the accuracy of observation values and obtain accurate adjustment results. The Helmet estimation formula in indirect adjustment is: 

n α − 2tr (N −1 Nα ) + tr (N −1 Nα )2 tr (N −1 Nα N −1 Ns )

 tr (N −1 Nα N −1 Ns ) × n s − 2tr (N −1 Ns ) + tr (N −1 Ns )2  2 T T   2 = VαT Pα Vα VST PS VS σ 0α σ 0s

(2)

2.3 CPIII Constrained Network Adjustment Mathematical Model Since the necessary initial condition number of CPIII network is 3, when the CPI or CPII points measured by CPIII network are more than 2, the redundant constraint condition is formed. Assume that there are n observations (direction and distance)αi and S j in CPIII plane control network. A total of t are necessary observations, then select ∧

t independent quantity as the adjustment parameter X , by the indirect adjustment model. ⎧ ∧ ∧ ⎪ ⎨ α = B X + d i×1 i× p p×1 i×1 (i + 1 = n, p + q = t) (3) ∧ ∧ ⎪ ⎩ S = B X + d j×q q×1

j×1

j×1

∧

Take the approximate value X 0 for adjustment parameter x, error equation: ⎧ ∧ ⎪ ⎨ Vα = B1 x − lα 1

∧ ⎪ ⎩ Vs = B2 x − ls

(4)

2

According to the principle of least squares, the solution of unknown parameters can be obtained after indirect adjustment:

∧

x1 ∧

x2



 =

B1 B2

T   −1  T   B1 B1 l P × × P α = N B−1B W B2 B2 ls

(5)

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3 Engineering Instance Data Processing The experimental data in this paper are from the field measured data of CPIII plane control network of a high-speed railway in China. The total length of the line is about 13 km, 22 known points, 576 unknown points, 122 observation stations, 1506 directional observations and 1506 side length observations.

3.1 Processing Flow The data acquisition of high-speed railway CPIII control network is based on free station corner intersection method. Measurement data have horizontal value, slant distance, zenith distance, etc. The main contents of plane control network data processing are [8]. (1) Before data processing to field data acquisition, acquisition process should strictly comply with the specification. (2) Import the original data into reliability analysis, then carry out probability coordinate calculation, free network adjustment, constraint network adjustment.

3.2 Free Network Adjustment Processing In the process of CPIII adjustment, the observation data are first tested for slant distance, horizontal angle, vertical angle and ring closure difference, and the approximate coordinates of each point are obtained by calculation. The maximum value of the adjusted direction and distance corrections cannot exceed 3” and 2 mm [9]. Error Processing Results in Direction After the data used in the experiment is completed free network adjustment, the direction error results under different line lengths are obtained, respectively. From the analysis of Fig. 1, (1) The error in the direction of the empirical weighting method is stable at about 0.2 ~ 0.5 mm; the error in direction is about 0.4 ~ 0.7 mm when using Helmet weighting method. Error Processing Result in Side Length After the data used in the experiment is completed free network adjustment, the side length mean square error results under different line lengths are obtained, respectively. It can be seen from Fig. 2, when the mean square error of side length is obtained by using the Helmet-specific weight method. The mean square error of side length is stable at about 0.4 ~ 0.5 mm under the line length of 1 km, 5 km, 10 km and 13 km. The direction error is about 0.5 ~ 0.6 mm when using the empirical weighting method.

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Fig. 1 Error in direction

Fig. 2 Error in side length

The side length error will decrease with the increase of line length when using empirical weighting method. The side length mean square error using Helmet specific weight method remains stable under different line lengths.

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Fig. 3 Error in point position

3.3 Constraint Network Adjustment Results After the adjustment of rank deficit-free network, the known CPI or CPII encryption points are selected as the starting point, and all CPIII points are constrained adjustment. According to the ‘Specifications for High-Speed Railway Engineering Survey’, the maximum value of the direction and distance corrections after adjustment cannot exceed 3" and 2 mm. At the same time, the relative mean square error of adjacent CPIII points should be less than 1 mm. The maximum values of direction and distance corrections measured with CPI or CPII cannot exceed 4" and 4 mm. After the constraint network adjustment, the accuracy of the error in each point is obtained, as shown in Fig. 3. It can be seen from Fig. 3, under different line lengths, the mean square error of points obtained by Helmet-specific weight method is smaller than that by empirical weight method. When the line length is 1 km, the mean square error is between 0.6 and 0.8 mm. With the increase of the length of the line, when the length of the line is 13km, the error of the point is between 0.4mm and 0.7mm.

4 Conclusion There are currently few studies on accuracy stability over long distances. This paper mainly studies the free network adjustment and constraint network adjustment of CPIII plane control network and compares different weighting methods under long

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lines. The conditions for the use of different weighting methods are clarified to provide clear recommendations for future actual engineering data processing. The following conclusions are drawn: (1) Constrained network adjustment using different weighting methods can meet the requirements of measurement specification, but Helmet variance component weighting method is slightly better than empirical weighting method. In the case of long line and sufficient known points, Helmet variance component estimation method can reduce the mean square error of points by 8 ~ 10% compared with empirical weighting method. (2) The Helmet variance component estimation method is suitable for the adjustment calculation with high accuracy requirements, large adjustment network and more redundant observations. The empirical weighting method is suitable for the adjustment calculation of the traverse with less observations. (3) Helmet variance component estimation method is superior to empirical weighting method in processing side length mean square error. Empirical weighting method is more accurate than Helmet variance component estimation method in processing directional mean square error. (4) In future research, how to optimize the weighting method can ensure the quality and accuracy of measurement data processing when the known points are insufficient.

References 1. J.Z. Li, Study on data processing method of precision triangulation in CPIII vertical control network[D]. Lanzhou Jiaotong Univ. (2020) 2. J. Li, Research on precision control and data processing methods of CPIII control network[D]. China Univ. Geosci. (2013) 3. X. Ouyang, Research and program design of adjustment method for CPIII plane control network of high speed railway[D]. Cent.L South Univ. (2014) 4. L.S. Sun etc. Research on data processing method of CPIII plane control network[J]. J. Shenyang Jianzhu Univ. (Nat. Sci. Ed.), 33(02):323–329 (2017) 5. J H, Li Z L. Reconstruction project of precision survey control network of Jiaozhouwan Jinan passenger dedicated Line[J]. Beijing Surv. Mapp. 34(10):1348–1352 (2020) 6. S.L. Li, C.L. Liu, etc. Research on survey method of high speed railway CPIII vertical control network[J]. Sci. Surv. Mapp. 2011:45–47 7. X.Z. Cui, Z.L. Yu etc. Generalized surveying adjustment (new edition)[M]. Wuhan Univ. Surv. Mapp. Press. (2001) 8. Z.G. Li, Analysis of precision control survey technology for high-speed railway[J]. Low carbon world 19, 252–253 (2015) 9. China railway eryuan engineering group Co. Ltd. Code for engineering survey of high speed railway. China Railw. Publ. House (2010)

Fault Self-healing Scheme of MMC-DC Distribution Line Zhong Liu, Kaixin Zhang, Junyan Zhang, Shenxing Shi, Chaowu Liu, and Xinzhou Dong

Abstract After the short-circuit fault of DC distribution line, the fault develops very fast and the tolerance of power electronic devices is limited. It is necessary to quickly and selectively cut off the fault line from DC distribution network in order to realize the fault isolation and recovery of DC distribution line. In this paper, a selfhealing scheme for DC distribution line fault is proposed: when the DC distribution line fails, the fault in the line area is correctly detected. After the fault detection is completed, the blocking converter is locked, the whole line is powered off, the fault information of each line measurement point is used for fault location, and the fault section is identified and the fault location is obtained according to the location results; After the DC line fault is detected at the measuring point, the protection sends the disconnection command to the load switch, the load switch receives the command, and the DC load switch on both sides of the fault section is disconnected. After DC line fault isolation, put the load behind the fault point into the standby power supply to restore the power supply to the load at the fault point. The standby power supply is generally a distributed power supply; According to the fault location results, send power maintenance personnel to the site to fix the fault. After the fault is cleared, conduct manual switching operation to restore the DC distribution line to the normal operation mode. Keywords DC distribution network · Blocking converter · Fault self-healing

Z. Liu · J. Zhang · C. Liu Yangzhou Power Supply Company, State Grid, Yangzhou 225000, Jiangsu, China K. Zhang (B) · S. Shi · X. Dong DEE, Tsinghua University, Beijing 100084, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_20

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1 Introduction With the development of power electronics technology, flexible DC distribution network is becoming an important choice for future distribution network. It has the advantages of good power quality, low line loss, easy control, easy access to photovoltaic, wind turbine, energy storage and other distributed power sources [1]. According to the new characteristics of DC power grid, many scholars have proposed various DC distribution network topologies, including: single source radiation structure, double-ended power supply structure and multi-segment multi-connection structure [2]. Different topology determines the reliability of power supply and the current in case of failure. In order to ensure high power supply reliability and avoid multi-directional feeding of fault current, the flexible DC distribution network should adopt the topology structure of multi-section and multi-connection. Multi-segment and multi-connected DC distribution network has the characteristics of closed-loop structure and open-loop operation. During normal operation, each line operates independently without mutual interference; in case of fault, adjacent lines are standby for each other, which can theoretically ensure that each line can operate without power failure. Therefore, based on this topology, how to realize line fault identification, processing and power supply recovery is the focus of research [2–5]. First, at the level of fault identification, the existing protection includes sudden change protection and current–voltage change rate protection [3]. Some scholars also suggested that the travelling wave protection with ultra-high-speed action be applied to the distribution network [6]. These methods have high reliability, but poor selectivity. It is impossible to determine the fault section, which is not conducive to power supply recovery in the later period. With the development of communication, literature [7] introduced differential protection into DC distribution network to improve selectivity, and literature [8] proposed an algorithm based on transient highfrequency impedance comparison. This algorithm identifies fault lines by comparing high-frequency impedance measurement differences, which improves selectivity. However, because of the high sampling rate required by using transient information, and the large amount of information calculated and transmitted, it has high requirements for channels. Therefore, it is necessary to study a protection algorithm with low sampling rate, less transmission information, high reliability and good selectivity. Second, for fault handling, the disconnection of DC fault current can be completed through high-voltage DC circuit breakers [9], but compared with AC circuit breakers, it is extremely expensive and cannot be used in distribution networks on a large scale. Another method is to turn off the fault current through the MMC converter with fault-clearing capability [10–12]. Quickly turn off the fault current is conducive to prolonging the life of power electronic devices and reducing the outage time. On the basis that the fault current has been turned off, the load switch is used to disconnect the line without using the DC circuit breaker. For the second method, it is necessary to use the information before MMC locking to accurately determine the fault section. Therefore, in order to protect power electronic devices and reduce

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expensive investment, it is necessary to study the scheme of active control of fault current MMC and load switch for fault isolation. In this paper, a self-healing scheme of DC distribution line fault is proposed from the aspects of fault identification, fault treatment and power supply restoration; Then, the MMC converter is locked, the fault current is controlled to 0, and the fault section is identified according to the comprehensive criteria of current polarity on both sides of the fault point; After identifying the fault section, switch off the corresponding DC load switch to isolate the fault; After isolating the DC line fault, put the load behind the fault point into the standby power supply, restore the load power supply at the fault point, and finally restart MMC to restore the line power supply before the fault point. Dispatch power maintenance personnel to the site to repair the fault according to the fault location results; after troubleshooting, carry out manual switching operation to restore the DC distribution line to normal operation mode.

2 Structure of the System Single power supply multi-energy storage DC distribution network combines the advantages of radiation structure and ring structure to improve the reliability of power supply and keep each DC line running independently as much as possible. Therefore, the topology of DC distribution network without DC circuit breaker should adopt single power supply and multi-energy storage structure. The working mode of single power supply multi-energy storage DC distribution network is mainly divided into normal working mode, fault working mode and maintenance working mode. These three working modes are introduced below. Under normal working mode, the single power radiation DC line is shown in Fig. 1. For DC distribution line fault, take the short circuit fault of section NO as an example. After the short-circuit fault occurs in section NO, the measuring point detects the fault and then identifies the fault section and locates the fault location. It is shown in Fig. 2. After it is determined that the fault occurs, the protection sends a shutdown command to the converter, which acts to block the AC system from feeding fault current to the fault point and inhibit the development of the fault. After the fault

Converter AC Breaker

M

O

N

ES

ES

ES

P Interconnection switch

AC system

Fig. 1 Normal operating mode

DC load swtich

Dc load

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Converter AC Breaker

M

O

N

ES

ES

ES

P Interconnection switch

DC load swtich

AC system

Dc load

Fig. 2 DC distribution line failure

Converter AC Breaker

M

O

N

ES

ES

ES

P Interconnection switch

AC system

DC load swtich

Dc load

Fig. 3 DC distribution line fault isolation

current attenuates to less than the DC load current, disconnect the DC load switches on both sides of section NO, at this time, in order to reduce transmission loss. At this time, bus O and bus P lose power, and the branch load hanging on the bus also loses power accordingly, as shown in the Figs. 2 and 3. After the load switch is disconnected, the fault isolation is completed.

3 Process of Handling Faults The sequence of DC line fault isolation is as follows: a fault occurs somewhere on the DC distribution line—the system detects the DC line fault—the protection sends a shutdown command to the converter—the converter receives the command, and the shutdown—the protection judges the fault section according to the information of each section of line, and sends a shutdown command to the corresponding load switch—the fault current decreases, The load switch receives the command and turns off. After the line NO is cut off, using energy storage to supply power to the load of the line on this side can reduce the power failure range of DC distribution line and improve the reliability of power supply. The fault operation mode of DC distribution line is as follows. According to the fault location results, arrange power maintenance personnel to go to the site to fix the fault. After the fault is cleared, conduct manual switching operation to return the DC distribution line to the normal operation mode. The sequence of DC line fault recovery is as follows: once DC fault occurs, the load required for high power supply reliability will be disconnected, the power supply

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Converter AC Breaker

M

O

N

ES

ES

ES

P Interconnection switch

AC system

DC load swtich

Dc load

Fig. 4 Standby power supply input of DC distribution line

of the power grid will be seamlessly switched to the power supply of energy storage equipment, and other loads will lose power for a short time. After DC fault isolation, the tie switch is closed, and the load behind the fault point is powered by the adjacent converter line. When the load before the fault point loses power for a short time, the converter uses the energy storage equipment to restart quickly to restore the power supply to the load at the fault point. After the inverter with fault blocking is operated again, when the fault section returns to normal, it will close the loop with the adjacent inverter line for load switching and return to the normal operation mode. The maintenance working mode is similar to the fault working mode. Both of them isolate the maintenance line or fault line through the DC load switch and then connect the sound part of the power lost system to the power supply on the other side, so as to restore its power supply and ensure the complete and continuous operation of the sound part of the system. Taking no maintenance of DC line as an example, its switching operation is as follows. Firstly, the DC line is in the normal working mode and the tie switch is in the off position. At this time, the DC load switch can disconnect the normal load current and disconnect the DC load switches on both sides of the line NO. There is no need to lock the converter for maintenance. After the line NO is cut off, the line OP loses power at this time. Next, close the contact switches of AC system 1 and AC system 2, and AC system 2 supplies power to the DC load originally belonging to AC system 1. The power flow direction of line OP will also change under the maintenance state. Therefore, in the maintenance state of DC line, in order to reduce the scope of power failure, the corresponding tie switch also needs to be put into the closed position (Fig. 4).

4 Programme The following Fig. 5 shows the flowchart of fault isolation and recovery of DC distribution line, and the specific flow is as follows: (1) The current transformer at each measuring point of DC distribution system can effectively transmit and transform current signal. In this paper, 1 MHz sampling rate and 1 ms time window are selected to collect and store the current at each measuring point of DC distribution line in real time;

234 Fig. 5 Standby power supply input of DC distribution line

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Start Acquisition current sudden change N Check existence Y Fault section identification Converter blocking Fault current attenuation Fault isolation Energy storage access

(2) Calculate the current sudden change at the measuring point; (3) Calculate the current sudden variable at the measuring point and check the falling sudden variable. If it exceeds the setting value, it is judged that there is a fault and the protection is started; (4) The converter is locked and the current drops; (5) Compare the polarity of the current sudden change at adjacent measuring points. If the sudden drop exceeds the setting value, disconnect the load switch if the polarity is opposite, and also disconnect the load switch if the polarity is opposite, and the fault isolation is completed; (6) After DC line fault isolation, close the interconnection switch, put the load behind the fault point into standby power supply, and supply power from adjacent converter lines. At the same time, the energy storage equipment is used to quickly restart the converter to restore the load power supply to the fault point.

5 Simulation In PSCAD, a simulation model is built, and the parameters are shown in Table 1.

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Project

Value

AC system

35 kV

Converter transformer

35 kV/10 kV Y/D

Rated DC voltage

20 kV(±10 kV)

MMC converter

/

Number of submodules Submodule capacitance Cliff inductance

76 10 mF 50 mH

Length of lines: Line MN/NO/OP

/ 9/5/7 km

Capacity of loads/ES DC Load1/2/3 ES

/ 500.0/619.2/900.9 kW 1000 W

A total of six current measuring points are set in the simulation, which are, respectively, located at the two ends of the trunk line MN, NO and OP, to measure the current of the positive and negative poles. When t = 1 s, double pole short circuit fault occurs at the middle point of Line NO. The current waveform of each measuring point is shown in Fig. 6. It can be seen from Fig. 6 that in the steady state, the absolute value of the current measured at each point is different because the connected load branch line is shunted. The steady-state current at point M closest to the inverter outlet is the maximum, 0.18 kA, and the steady-state current at point P farthest away is the minimum, 0.08 kA. When t = 1 s, the current at each measuring point before the fault point increases rapidly, and the sudden change is positive. However, the current at the measuring point

Fig. 6 Fault currents of all points

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18 16 DC Voltage/ kV

14 12 10 8 6 4 2 0 0.0

0.2

0.4

0.6 Time/s

0.8

1.0

1.2

Fig. 7 MMC restart process

after the fault point drops rapidly, and the abrupt change is negative. Therefore, the fault section can be determined according to the polarity of the sudden variable at each current measuring point after the fault occurs. About 1.5 ms after the fault occurs, the inverter is locked and the fault current decreases accordingly. After the fault current drops to 0, the DC load switch will switch off the corresponding section according to the sudden variable information during the fault to complete fault isolation. After fault isolation, it is necessary to re-supply power to the load. The process of voltage recovery is essentially the restart process of MMC, that is, the whole process of capacitor charging of all submodules. The time consumed from restart to steady state establishment depends on the initial value of the capacitor voltage of the submodule and is related to the resistance and inductance of the charging circuit. Here is an example of the most extreme case, that is, the initial voltage of the submodule is 0, which is used to evaluate the voltage recovery time after fault isolation (Fig. 7). In the most serious case, it takes about 1.2 s to establish the voltage. It usually does not take such a long time, because when the locking starts, the energy on the capacitance of the submodule cannot be released completely, and some energy will remain. On the other hand, the oscillation process during startup is caused by the setting of system control parameters. In comprehensive consideration, the voltage recovery time of the trunk line after fault isolation is about 1 s, while the load node equipped with ES can recover immediately.

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6 Conclusion In this paper, a self-recovery scheme of DC distribution line fault is proposed: after the fault is detected, the locking converter is locked, and the whole line is powered off, and then the fault section is identified using the fault information of each line measurement point. After that, the protection sends the disconnection command to the load switch. After the DC line fault is isolated, the post-fault load is put into the standby power supply to restore the load power supply at the fault point. After the fault is completely cleared, restart MMC and restore the power supply of the whole line. Acknowledgements The research work of this paper is funded by the Science and Technology Project of State Grid Jiangsu Electric Power Co., Ltd. (Research on Fault Analysis and Protection Test Technology of Flexible DC Distribution Network) (J2021035).

References 1. J. Daozhuo, Z. Huan, Research status and prospect of DC distribution network. Power Syst. Autom. 36(8), 98–104 (2012) 2. Z. Huan, Research on several problems of flexible DC distribution network. Master, Zhejiang University (2014) 3. X. Shimin et al., Overview of research on DC distribution system protection technology. Chin. J. Electr. Eng. 34(19), 3114–3122 (2014) 4. W. Shouxiang, L. Qi, X. Shimin, Y. Dong, W. Chenqing, Y. Jinggang, Key technologies and prospects of DC distribution system control and protection coordination. Power Syst. Autom. 43(23), 23–30 (2019) 5. L. Yan, Research on line fault analysis and protection of multi terminal flexible DC power grid. Doctor, North China Electric Power University, Beijing (2019) 6. C. Fufeng et al., Analysis on the adaptability of single terminal traveling wave protection in medium voltage flexible DC distribution network. Power Syst. Prot. Control 44(22), 50–55 (2016) 7. S.D.A. Fletcher, P.J. Norman, K. Fong, S.J. Galloway, G.M. Burt, High-speed differential protection for smart DC distribution systems. IEEE Trans. Smart Grid 5(5), 2610–2617 (2014) 8. K. Jia, Z. Xuan, T. Feng, C. Wang, T. Bi, D.W.P. Thomas, Transient high-frequency impedance comparison-based protection for flexible DC distribution systems. IEEE Trans. Smart Grid 11(1), 11 (2020) 9. L. Wei, et al., Research and development of all solid state hybrid DC circuit breaker for distribution network. China Southern Power Grid Technol. 10(4), 37–42 (2016) 10. S. Gang, S. Bonian, Z. Yuming, L. Shupeng, Research on fault location and protection configuration of flexible DC distribution network based on MMC. Power Syst. Prot. Control 43(22), 127–133 (2015) 11. W. Sihua, Z. Lei, W. Junjun, C. Long, Research on the protection strategy of DC transmission system bipolar short circuit fault based on MMC. Power Syst. Prot. Control 49(11), 9–17 (2021) 12. Z. Chengyong, S. Bingqian, X. Jianzhong, Overview of typical schemes for active fault current control in flexible DC power grid. Power Syst. Autom. 44(5), 3–13 (2020)

Highly Reliable Warning Method for Tanker Rollover Based on Fuzzy Logic K. X. Pan and K. Wei

Abstract In view of the unreliability of tanker rollover warning method, a highly reliable warning method for tanker rollover based on fuzzy logic is studied. Firstly, the change of rollover state is analyzed when the tanker is driving, and three rollover characterization parameters are defined. Then, the probability function of tanker rollover risk is designed, and three rollover characterization parameters are used to estimate the probability of tanker rollover, respectively. Next, the probability fusion model is established based on fuzzy logic to obtain the optimal probability of predicting the rollover occurrence. Finally, the hierarchical warning is carried out according to the optimal probability. The tanker rollover warning system is built, and real vehicle experiments are carried out respectively in the open actual road and closed test site. The experimental results show that the proposed method can accurately identify the rollover risk and conduct the effective warning. To better illustrate the warning performance, the numerical calculation shows that the proposed method can accurately quantify the rollover risk, reduce the interference of sensor error information, overcome the problems of false alarm when the tanker is driving safely and missing alarm when the tanker is in rollover risk, and improve the reliability of tanker rollover warning. Keywords Rollover warning · Tanker · Fuzzy logic · Active prevention · Control of vehicle safety

K. X. Pan (B) School of Mechanical Electrical and Information Engineering, Xiamen Institute of Technology, Xiamen 361021, Fujian, China e-mail: [email protected] K. Wei School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_21

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1 Introduction With the rapid development of economy and industry, the demand for dangerous goods is increasing [1], transportation demand of them also increases sharply. Due to uneven distribution of production areas, most dangerous goods need to be transported from other places, in which road transport is the main mode of transport. Tank car is the transport vehicle with a tank body, which is used to transport various liquids, liquefied gases, powder goods, etc. Due to the large capacity, high efficiency and low cost, tank cars have become the main road vehicles of dangerous goods [2, 3]. However, because of the high center of mass and being easily disturbed by liquid [4], tank cars have frequent traffic accidents on the highway and affect traffic safety seriously. In the article 5, the causes of 708 dangerous cargo tank car traffic accidents are summarized. Among them, unilateral rollover accounts for the largest proportion, 29.10% [5]. Tank car rollover occurs quickly and only lasts for a very short time, so it is difficult for drivers to sense specific signs and take effective measures, which makes it difficult to avoid tank car rollover accidents [6, 7]. When the tank car loaded with dangerous goods overturns, it will cause damage to its own vehicle and other vehicles on the road, as well as environmental pollution, ecological damage, casualties and other adverse effects. On April 2, 2020, in Wen’an County, Langfang City, Hebei Province, a tank car loaded with aromatic hydrocarbons turned right, causing a rollover fire and igniting a nearby store due to excessive speed. Therefore, how to alert the rollover danger of tank cars has become a research hotspot in the field of road traffic safety. The traditional rollover warning methods for tank cars are as follows: first, define the single rollover characterization parameters and rollover threshold; Then the actual values of the characterization parameters are obtained through sensor measurement or dynamic model estimation. Finally, the actual values of the characterization parameters are compared with the corresponding thresholds to determine whether there is a rollover risk. In rollover warning methods, rollover characterization parameter is a key element, which is used to quantify and predict rollover risk. Common rollover characterization parameters include roll angle [8, 9], lateral acceleration [10, 11], static stability coefficient [12], lateral load transfer rate [13, 14] and rollover time [15]. In general, the traditional tank car rollover warning method realizes rollover hazard perception through a single rollover characterization parameter. However, when the tank car is running, its quickly changing posture, low stability and many other factors will cause rollover, so the rollover warning method based on a single parameter is less reliable. To solve the above problems, this paper proposes a reliable warning method for tank car rollover based on fuzzy logic. The method uses fuzzy logic to fuse multiple rollover characterization parameters, quantizes rollover risk in the form of probability, and realizes rollover warning under the condition of information redundancy.

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2 Reliable Rollover Warning Method 2.1 Rollover Characterization Parameters When the tank car turns or changes lanes, due to the fluidity of the liquid, the liquid in the tank will generate additional forces and moments on the side wall, thus affecting the roll stability of the tank car and increasing the roll risk of the tank car. Roll angle, lateral acceleration, and lateral load transfer rate are commonly used rollover characterization parameters, which can intuitively reflect the rollover risk of tank cars. However, it is difficult to measure the load of tank car wheels at high speed, resulting in inaccurate calculation of lateral load transfer rate. When the tank car rollover risk increases, the roll angle, lateral acceleration, and yaw rate at the center of mass will respond quickly and have similar change trends, which can jointly reflect the change of tank car rollover risk. For example, when the tank car is turning continuously, the changes of tank car roll angle, lateral acceleration, and yaw rate are shown in Fig. 1. Therefore, roll angle, lateral acceleration, and yaw rate are selected as the roll characterization parameters. At the same time, these three parameters can be obtained directly from the inertial sensor in a simple way, reducing the cost of rollover warning and facilitating its popularization.

Fig. 1 Change trend of roll angle, lateral acceleration, and yaw rate

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2.2 Probability Function of Rollover Hazard This paper estimates the rollover risk of tank cars in the form of probability. In order to convert the rollover characterization parameters and preset rollover threshold into the probability of rollover occurrence, a probability function of rollover risk needs to be designed. When the rollover characterization parameter is less than the rollover threshold, the estimated probability of rollover occurrence is less than 1. When the rollover characterization parameter is greater than or equal to the rollover threshold, the estimated probability of rollover occurrence is equal to 1. In addition, when the rollover characterization parameters are far less than or close to the rollover threshold, the change rate of the estimated rollover probability is small. Considering the above characteristics of the change in the probability of predicted rollover occurrence and the complexity of calculation, the probability function of rollover risk is established with sin function. Define the probability of tank car rollover based on roll angle estimation as Pα , the calculation formula is shown in Eq. (1):  Pα =

1 2

 sin − π2 +

α αT



+

1 2

|α| < αT |α| ≥ αT

1

(1)

where, αT is the preset roll angle threshold. Define the probability of tank car rollover based on lateral acceleration as Pβ . The calculation formula is shown in Eq. (2):  Pβ =

1 2

 sin − π2 +

β βT



+

1 2

|β| < βT |β| ≥ βT

1

(2)

where, βT is the preset lateral acceleration threshold. Define the probability of tank car rollover based on yaw rate as Pθ , the calculation formula is shown in Eq. (3):  Pθ =

1 2

 sin − π2 +

1

θ θT



+

1 2

|θ | < θT |θ | ≥ θT

(3)

where, θT is the preset yaw rate threshold.

2.3 Probability Fusion Model Pα , Pβ , and Pθ are the three predicted probabilities of rollover, which are obtained through inertial sensors and rollover hazard probability function. Due to various

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interferences in the working environment of the sensor, there may be some errors in the output value of the sensor, leading to uncertainty in a single probability [16, 17]. Therefore, it is necessary to fuse the three probabilities to obtain the optimal probability P for predicting rollover. In this paper, a probability fusion model is established by using fuzzy logic. The inputs are Pα , Pα , Pβ , and the outputs are P. The probabilistic fusion model is divided into three parts: fuzzification, fuzzy reasoning, and defuzzification. Fuzzification When more fuzzy sets are used to describe each input variable, the accuracy of the probability fusion model can be improved. However, it is cumbersome to formulate fuzzy rules, so both simplicity and flexibility need to be considered when selecting fuzzy sets. The inputs of probability fusion model are all probability, so three fuzzy sets are selected, namely, small (S), medium (M), and large (L). The membership function is used to convert the input Pα , Pβ , and Pθ into the membership of each set. The steeper the shape of the membership function, the higher the resolution, and the higher the output sensitivity; The slower the membership function changes, the lower the sensitivity. The membership functions of the three fuzzy sets are defined in Eqs. (4)–(6): ⎧ 0 ≤ x < 0.25 ⎨1 f S (x) = −4x + 2 0.25 ≤ x < 0.5 ⎩ 0 0.5 ≤ x ≤ 1 ⎧ 0 0 ≤ x < 0.25 ⎪ ⎪ ⎨ 4x − 1 0.25 ≤ x < 0.5 f M (x) = ⎪ −4x + 3 0.5 ≤ x < 0.75 ⎪ ⎩ 0 0.75 ≤ x ≤ 1 ⎧ 0 ≤ x < 0.5 ⎨0 f H (x) = 4x − 2 0.5 ≤ x < 0.75 ⎩ 1 0.75 ≤ x ≤ 1

(4)

(5)

(6)

where, f S (x) is the membership function of set S, f M (x) is the membership function of set M, and f H (x) is the membership function of set H, as shown in Fig. 2. For the three inputs Pα , Pβ , and Pθ , according to the membership function, we can get: f S (Pα ), f M (Pα ), f H (Pα ), f S (Pβ ), f M (Pβ ), f H (Pβ ), f S (Pθ ), f M (Pθ ), f H (Pθ ). Fuzzy reasoning Fuzzy reasoning is usually based on actual experience to write fuzzy conditional statements into a fuzzy rule table [18, 19], and the fuzzy rules formulated are shown in Table 1.

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Fig. 2 Membership function

Table 1 Fuzzy rules Pα

Pβ

Pθ S

S

M

H

M

H

S

S

S

M

M

S

M

M

H

M

M

H

S

S

M

M

M

M

M

H

H

M

H

H

S

M

M

H

M

M

H

H

H

H

H

H

When two or more of the three input probabilities are in the H set, it is considered that the optimal probability of predicted rollover is in the H set; When two probabilities are in the M set and one probability is in the H set, it is considered that the optimal probability of predicted rollover is in the H set. When the three probabilities are all in the M set, it is considered that the optimal probability of predicting rollover is in the M set; When two probabilities are in the S set and one probability is in the H set, it is considered that the optimal probability of predicted rollover is in the M set; when two probabilities are in the M set and one probability is in the S set, it is considered that the optimal probability of predicted rollover is in the M set; one probability is in the H set, one probability is in the M set, and one probability is in the S set. It is considered that the optimal probability of predicting rollover is in the M set. When two probabilities are in the S set and one probability is in the M or S set, it is considered that the optimal probability for predicting rollover is in the S set. 27 rules are determined in the fuzzy rule table, in which the fuzzy conditional statements are combined by using and operation, and the membership function of each rule output result is calculated by min function. For example, rule 1: if Pα is in the S set, Pβ is in the S set, and Pθ is in the S set, then the optimal probability of predicted rollover is in the S set. The membership

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degree of Pα in S set is f S (Pα ), Pβ in S set is f S (Pβ ), and Pθ in S set is f S (Pθ ), so the optimal probability of rollover is min f S (Pα ), f S (Pβ ), f S (Pθ ) . Other rules can be deduced in this way. Defuzzification The output of fuzzy reasoning is a fuzzy set, while the output of probability fusion model is a certain value. Taking a single value that best represents the fuzzy set from the reasoning fuzzy set is called defuzzification. The commonly used defuzzification methods are maximum membership method and barycenter method. The maximum membership method takes the value with the largest membership degree in all fuzzy sets as the output. This method is simple to implement, but it does not take into account the influence of other values with smaller membership degrees, which is not representative. The output result of barycenter method is more reasonable, and it is easy to produce a smooth output surface, which is conducive to improving the robustness of the model. In this paper, the center of gravity method is used to solve the ambiguity, and the calculation formula is shown in Eq. (7): 27 i=1 P=  27

f i wi

i=1

fi

(7)

where, P is the output of the probability fusion model, that is, the optimal probability to predict the occurrence of rollover, f i is the membership of the output result of the ith rule in the fuzzy rule table, and wi is the weight of the fuzzy set in the output result of the ith rule in the fuzzy rule table. The weight is usually taken as the middle value of each set, that is: w(S) = 0.25, w(M) = 0.5, w(H ) = 0.75.

2.4 Hierarchical Warning After obtaining the optimal probability P for predicting the occurrence of rollover, the rollover status of the tank car is divided into safety, low risk and high risk according to the value of P. The rules are as follows in Eq. (8): ⎧ Safety ⎨ P ≤ 0.5 0.5 < P ≤ 0.8 Low risk ⎩ 0.8 < P ≤ 1 High risk

(8)

The warning device includes signal lamp and voice unit. When the tank car is in a safe state, the signal light is green, and the voice unit does not work; When the tanker is at low risk, the signal light will turn yellow, and the voice unit will play: “Please drive safely”; when the tanker is at high risk, the signal light will be red, and the voice unit will play: “Danger, rollover is imminent”.

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Fig. 3 Rollover warning system

3 Rollover Warning System The tank car rollover warning system includes embedded processing unit, inertial measurement unit and alarm device, as shown in Fig. 3. The embedded processing unit is responsible for sensor information acquisition and processing, rollover risk analysis and communication with the alarm device, which is placed in the cab. The inertial measurement unit is used to measure the roll angle, lateral acceleration and yaw rate of the tank car and is fixed at the center of mass of the tank car’s territory. The warning device includes signal lamps and a voice unit. The signal lamps are fixed at the rear of the vehicle to remind surrounding vehicles. The voice unit is placed in the cab to remind the driver.

4 Experiment and Demonstration 4.1 Open Actual Road Experiment The open actual road test includes U-turn and lane change. The filling ratio of water in the tank car is 0.5. Since no anti-roll frame is installed, the rollover warning test under extreme working conditions cannot be carried out. By setting a reasonable rollover threshold, the reliability of the proposed rollover warning method is verified while ensuring the safety of the experiment. Experiment of U-turn The tank car first makes a U-turn at a constant speed of 15 km/h, taking the maximum values of roll angle, lateral acceleration, and yaw rate (2.3°, 1.3 m/s2 , 0.3 rad/s) as the corresponding preset rollover threshold. The experimental site is shown in Fig. 4. After the three rollover thresholds are determined, the tank car follows the same track, turns U-shaped turn at a constant speed of 20 km/h, and repeats the experiment for many times. Each experiment achieves the expected early warning results, as shown in Fig. 5, and the early warning success rate is 100%. The roll angle, lateral acceleration, and yaw rate of the tank car change little at the straight section of the starting point and the ending point and are less than

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Fig. 4 Experiment of U-turn

the corresponding rollover threshold. It is estimated that the optimal probability of rollover P ≤ 0.5, the tanker is in a safe state, the signal light is green, and the voice unit does not work. When the tank car starts to turn, the roll angle, lateral acceleration, and yaw rate increase rapidly, 0.5 < P ≤ 0.8. The tank car is in a low-risk state, the signal light turns yellow, and the voice unit plays: “Please drive safely”. When the tank car continues to drive in the U-bend, the roll angle, lateral acceleration, and yaw rate will approach and be greater than the corresponding rollover threshold, 0.8 < P ≤ 1. The tank car is at high risk, the signal light is red, and the voice unit plays: “Danger, rollover is imminent”. By comparing the roll angle, lateral acceleration, and yaw rate of the starting and ending straight sections, it can be seen that the cross-slope angle of the road will affect the roll angle of the tank car, but the impact on the lateral acceleration and yaw rate is small. Therefore, it is impossible to reliably predict the rollover risk of tank cars only depending on the lateral acceleration. Lane change experiment The tank car first changes lanes at a speed of 30 km/h in a straight section of three lanes, taking the maximum values of roll angle, lateral acceleration, and yaw rate (2.18°, 1.02 m/s2 , 0.25 rad/s) as the corresponding preset rollover threshold. The experimental site is shown in Fig. 6. After the three rollover thresholds are determined, the tank car changes lanes along the same track at a speed of 40 km/h and repeats the experiment for many times. Each experiment achieves the expected early warning results, as shown in Fig. 7, and the early warning success rate is 100%. At 21 s in Fig. 7a, the tanker starts to change lanes, the rollover risk of the tanker increases, and the tanker is in a low-risk and high-risk state successively. At 30 s in Fig. 7a, the tanker runs in a straight line, the rollover risk is reduced, and the tanker is in a safe state.

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(a)

(b) Fig. 5 Rollover warning result of U-turn

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Fig. 6 Experiment of changing lane

At 36 s in Fig. 7a, the direction of the tank car returns to the right, and the rollover risk of the tank car increases. The tank car is in a low-risk and high-risk state successively. It can be seen from Fig. 7b that the tanker has completed a lane change, and the rollover hazard occurs twice.

4.2 Closed Test Site Experiment After completing the rollover warning experiment under normal driving conditions in the open actual road, the experiment was carried out in the closed test site for extreme dangerous conditions, as shown in Fig. 8. In order to ensure the safety of the experiment, the tank car is in the no-load state, and anti-rollover frames are installed on both sides of the tank body. First of all, the tank car carries out steady rotation operation and gradually increases the speed. When one side of the anti-roll frame is close to the ground, it ends. The maximum values of roll angle, lateral acceleration, and yaw rate (1.28°, 3.98 m/s2 , 0.39 rad/s) are taken as the corresponding preset rollover threshold. At this time, the speed is 32 km/h. Then, the tank car performs steady-state turning operation on the same track, the speed increases to 40 km/h, and the experiment is repeated many times. Each experiment achieves the expected early warning results, as shown in Fig. 9, and the early warning success rate is 100%. Compared with Fig. 5a and Fig. 9a, the rollover risk of the tank car in Fig. 5a is less than that in Fig. 9a. However, due to the influence of liquid sloshing in the tank, the roll angle of the tank car in Fig. 5a is greater than that in Fig. 9a. Therefore, it is impossible to reliably predict the rollover risk of tank cars only depending on the roll angle.

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(a)

(b) Fig. 7 Rollover warning result of changing lane

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Fig. 8 Closed test experiment

4.3 Numerical Demonstration The reliability of this rollover warning method is verified by the results of real vehicle experiments on open real roads and closed test sites. In order to better illustrate the rollover warning performance of this method, the following numerical demonstrations are conducted, respectively, for the problems of false alarm and missing alarm. False alarm Assuming that the tank car is running safely, due to the failure of the inertial measurement unit, the lateral acceleration is large (the roll angle and yaw rate are normal), which is close to its corresponding rollover threshold. Assume that the probability of rollover based on roll angle is 0.3, the probability of rollover based on lateral acceleration is 0.7, and the probability of rollover based on yaw rate is 0.2, as shown in Table 2. Judging only by the lateral acceleration, the tank car is in a low-risk state of rollover, which is inconsistent with the actual situation, and there is a problem of false alarm. The optimal probability of rollover predicted by this method is 0.46, and the tank car is in a safe state, effectively overcoming the problem of false alarm when the tank car is running safely. Missing alarm It is assumed that the tank car is in danger of rollover, but the yaw rate is abnormal, which is far less than its corresponding rollover threshold. Assume that the probability of rollover based on roll angle is 0.7, the probability of rollover based on lateral acceleration is 0.8, and the probability of rollover based on yaw rate is 0.2, as shown in Table 3. Judging only by yaw rate, the tank car is in a safe state, which is inconsistent with the actual situation, and there is a problem of missing alarm. The optimal probability

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(a)

(b) Fig. 9 Rollover warning result of extreme dangerous condition

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Table 2 Rollover probability in case of false alarm Roll angle

Lateral acceleration

Yaw rate

Probability of rollover

0.3

0.7

0.2

Optimal probability of rollover

0.46

Roll angle

Lateral acceleration

Yaw rate

Probability of rollover

0.7

0.8

0.2

Optimal probability of rollover

0.7

Table 3 Rollover probability in case of missing alarm

of rollover occurrence estimated by this method is 0.7, and the tank car is in a lowrisk state of rollover, effectively overcoming the problem of missing alarm when the tank car is in danger of rollover.

5 Conclusion This paper proposes a reliable early warning method for tank car rollover height based on fuzzy logic. This method uses fuzzy logic to fuse roll angle, lateral acceleration, and yaw rate to obtain the optimal probability of predicting rollover occurrence and accurately quantify rollover risk. In the real vehicle experiment, the method can realize rollover warning under both normal driving conditions and extreme dangerous conditions of tank cars; In the numerical demonstration, this method can effectively solve the problems of false alarm when the tank car is running safely and missing alarm when the tank car is in danger of rollover. Since, the rollover threshold of tank cars varies dynamically under different working conditions, the research on dynamic estimation of rollover threshold of tank cars will be carried out next to improve the accuracy of rollover warning. Acknowledgements National Key R&D Program (2017YFC0804804), Xiamen Institute of Technology 2021 Production Teaching Integration Practice Training Base Construction Project (XJCJRH20003).

References 1. X. Zheng, B. Wang, Y. Zhao, A knowledge graph method for hazardous chemical management: ontology design and entity identification. Neurocomputing 430, 104–111 (2021) 2. M. Yu, S. Li, X. Xie, Analysis of supervising process of road hazardous freight transport and countermeasures. Highw. Transp. Technol. 27, 155–158 (2010)

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3. J. Vrabel, T. Skrucany, L. Bartuska et al., Movement analysis of the semitrailer with the tankcontainer at hard braking-the case study. IOP Conf. Ser.: Mater. Sci. Eng. 710, 12–25 (2019) 4. J. Ou, Y. Wang, E. Yang, TTR warning and anti-rollover control for semi-trailer. J. Chongqing Univ. 40, 67–76 (2017) 5. L. Shi, Statistical Analysis of Dangerous Goods Road Transportation Accidents and the Establishment of Integrated Management System (Chang’ An University, Xi an, 2014) 6. B. Zhang, C. Zong, D. Wang, Status of research and key technology of vehicle rollover warning system. Autom. Technol. 2010, 27–31 (2010) 7. I. Han, K. Rho, Characteristic analysis of vehicle rollover accidents: rollover scenarios and prediction warning. Int. J. Autom. Technol. 18, 451–461 (2017) 8. L. Fan, J. Hu, H. Liang, Research on bus anti-rollover model in extreme-turn conditions and active control method based on computer simulation, in 11th International Conference on Computer Science & Education (IEEE, Nagoya, 2016) 9. M. Jalali, E. Hashemi, A. Khajepour, Model predictive control of vehicle rollover with experimental verification. Control Eng. Pract. 77, 95–108 (2018) 10. P. Cruz, T. Echaveguren, P. Gonzalez, Estimation of heavy vehicle rollover potential using reliability principles. Revista Ingenieria de Construccion 32, 5–14 (2017) 11. K. Yamamoto, A. Ejiri, M. Oya, Rollover prevention control of vehicles with crosswind disturbance. Artif. Life Robot. 12, 250–258 (2021) 12. C. Winkler, D. Ervin, Rollover of heavy commercial vehicles. UMTRI Res. Rev. 31, 1–17 (2000) 13. H. Li, Y. Zhao, H. Wang, Design of an improved predictive LTR for rollover warning systems. J. Braz. Soc. Mech. Sci. Eng. 39, 3779–3791 (2017) 14. D. Chu, Z. Li, J. Wang, Rollover speed prediction on curves for heavy vehicles using mobile smartphone. Measurement 129, 375–380 (2018) 15. D. Chu, J. Cui, Z. Deng, Research on vehicular rollover warning based on improved TTR algorithm. China Mech. Eng. 27, 1557–1561 (2016) 16. X. Song, Research on Key Technologies of Vehicle Active Safety Based on Multi-source Information Fusion (Southeast University, Nanjing, 2014) 17. Q. Xu, X. Li, C. Chan, Enhancing localization accuracy of MEMS-INS/GPS/In-vehicle sensors integration during GPS outages. IEEE Trans. Instrum. Meas. 67, 1966–1978 (2018) 18. R. Jiang, Research on Vehicle Fusion Location Technology in Urban Canyon Environment (Southeast University, Nanjing, 2018) 19. R. Wang, Z. Chen, X. Ming, Energy management of parallel marine power system based on improved fuzzy logic control. J. Shanghai Jiaotong Univ. 55, 1188–1196 (2021)

Real-Time Train Rescheduling with Passenger Demand for Rolling Stock Rescue Hangyu Wang, Yihui Wang, Kangqi Zhao, and Peichang Gao

Abstract With the expansion of urban rail transit systems, there are more and more equipment failures, especially train failures, which could result in serious disruptions on the operation of trains. Hence, the effective, accurate and comprehensive rolling stock rescue planning and the real-time delay management are crucial for the resilient operation of urban rail transit system. A mixed integer linear programming formulation is proposed for the integrated rolling stock rescue planning and train rescheduling problem for an urban rail transit line, where the detailed passenger characteristic is also considered. Several numerical experiments based on real-world data of Beijing Subway Line 7 are carried out to demonstrate the effectiveness of the presented integrated approach. Keywords Urban rail transit · Train rescheduling · Rolling stock rescue · Passenger flow · MILP

1 Introduction As a large-capacity, punctual, convenient and low-carbon public transportation mode, urban rail transit plays an important role to relieve urban traffic congestion and environmental pollution. Frequent occurrence of failures results in operation disruptions and passenger stranded, etc. According to the statistics of Beijing subway, a total of 405 emergency events occurred in the 5 years, among which train failures reached 114 and ranked second [1]. Especially, when the failure cannot be eliminated in a specified time duration, it is necessary to rescue the disabled train from the fault H. Wang · Y. Wang (B) · K. Zhao State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China e-mail: [email protected] P. Gao Department of Railway Communication and Signalling, Baotou Railway Vocational & Technical College, Baotou, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_22

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location to the storage track or to the depot. Some train services may need to be cancelled or short-turned before the blocked area that is used for the train rescue. Many researchers have investigated the train rescheduling problem. Cacchiani et al. [2] and Zhang et al. [3] reviewed the models and algorithms of train rescheduling problem. Zhu and Goverde [4] proposed a train rescheduling model that could flexibly change train stops and turnaround positions according to the interruption events of railways. Wang et al. [5] proposed a mixed integer nonlinear programming model for the integrated train rescheduling and rolling stock circulation planning problem. Bešinovi´c et al. [6] proposed an integrated disruption management model, which involves both the train rescheduling and the passenger flow control, where the numbers of passengers arriving at stations were calculated using the origin–destination matrices. Yin et al. [7–9] proposed an integrated approach for the train scheduling problem considering the dynamic passenger demands at each station for the calculation of total passenger waiting time. The previous literature mainly focuses on the research of train rescheduling with initial delays and track blockages, but there are only a few researchers addressing the train rescheduling problem with rolling stock rescue. Zhu et al. [10] proposed a mixed-integer programming (MILP) model for metro train timetable adjustment in case of train rescue, where the operating time of trains, the location of backup trains, the rescue direction and passenger flow are considered. However, the passenger characteristics were not considered in detail when it is necessary for all passengers to get off the trains. And the specific dwell time and routes for the rescue train and the disabled train were not described either. In this paper, we propose a new MILP model for the train rescheduling in case of train rescue by extending the integrated train rescheduling and rolling stock circulation model in [5]. The selection of rescue trains, the operation direction of the rescue train and the coupled train (consisting of the rescue train and the disable train), and the passenger characteristics (e.g., the number of passengers on-board and waiting at platforms) are formulated in our MILP formulation.

2 The Handling Process of Rolling Stock Rescue When a rolling stock cannot rely on its own power to perform services due to the malfunction of traction or braking system, the fault rolling stock (i.e., the disabled train) needs to be rescued, i.e., be coupled with another well-functioned train (i.e., the rescue train). The newly coupled train then runs off the main track by using the power of the rescue train. The handling process of train rescue could be divided into five phases, namely, the fault handling phase, the rescue preparation phase, the rescue coupling phase, the exiting main track phase and the operation recovery phase, as shown in Fig. 1. In the fault handling phase, if the disabled train cannot operate normally by itself within the specified time, the driver of the disabled train should submit an application for rolling stock rescue. In the rescue preparation phase, a nearby well-functioned rolling stock is selected as the rescue train, and then it runs

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Fig. 1 A schematic diagram for different phases of the rolling stock rescue process

to the disabled train after the on-board passenger clearing process. In the rescue coupling phase, the rescue train is coupled with the disabled train, and the coupled train should be checked carefully. In the exiting main track phase, the rescue train pushes/pulls the disabled train to the storage track or the depot under a pre-specified speed limit. In the operation recovery phase, the rescue mission terminates and the train services are gradually rescheduled to the planned timetable. As mentioned above, when a rolling stock is malfunctioned and needs to be rescued, a rescue plan should be determined. Figure 2 gives two possible rescue routes, i.e., pushing directly to the depot and pushing to the next storage track. For route 1, the rescue train pushes the disabled train to the depot, then it is decoupled with the disabled train and put into operation again. For route 2, the rescue train pushes the disabled train to the nearby storage track, and then it is decoupled with the disabled train and continues its operation.

3 Mathematical Formulation for Train Rescheduling with Rolling Stock Rescue A mathematical model is presented for the integrated train rescheduling and rolling stock planning problem in case of rolling stock rescue, where the passenger characteristics are also considered. In this paper, we consider a metro line with two parallel tracks and one depot, which has three types of stations, i.e., normal stations, turnaround stations not connecting with depot and turnaround stations connecting with depot. The following assumptions are made in our paper: A1. Each station has two platforms where each platform can only allow one train to dwell at a time. A2. The stop-skipping strategy is not included in the rescheduling process except the rescue train and the disabled train. A3. Passengers in the rescue train and disabled train are evacuated at the stations nearby the fault location. Assumption A1 generally holds for most urban rail transit line, where the operation of trains follows the first-in first-out principle. The overtaking of trains is not

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Fig. 2 Illustration of two possible rescue routes for a disabled train

possible in general. In Assumption A2, the rescue train and the disable train skip the intermediate stations to reduce the delay of trains. For assumption A3, passengers in the malfunctioned train and the rescue train need to be evacuated for their safety. These passengers can be transported by the following trains. The parameters and decision variables are listed in Tables 1 and 2, respectively. For brevity, we only give the constraints for the up direction, however, the constraints for the down direction can be formulated similarly.

3.1 Operational Constraints for Train Rescheduling with Rolling Stock Rescue Arrival and departure constraints The train rescheduling model in this paper is extended based on Wang et al. [5]. The arrival time of service f at station i in the up direction can be calculated by     dn  up up up up dn turn a f,i = o f,i−1 d f,i−1 + r f,i−1 + eg, f,i dg,i + tg,i g∈G up depot,up

+ σ f,i ai

, ∀ f ∈ F, ∀i ∈ I.

(1)

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Table 1 Parameters and subscripts for the mathematical formulation Symbol

Description

I

Set of stations, I is the terminal station in the line

Inorm

Set of normal stations, Inorm ⊂ I

Iturn

Set of turnaround stations, Iturn ⊂ I

Idepot

Set of turnaround stations connected with depot, Idepot ⊂ I

F/G

Set of train services in the up/down direction

f /g

Train service index in the up/down direction, f /g ∈ F/G

i

Station index, i s is the index of the first station that has a storage track in front of the disabled train, i 0 is the index of the station closest to the fault location

n

The number of possible routes

r

Rescue route index dep

arr tmin /tmin

Minimum headway between two consecutive departure/arrival trains

ϕ

ϕ = 0 if the disabled train breaks down at station i 0 , and ϕ = 1 If the disabled train breaks down in the open track area between Station i 0 and station i 0 − 1

tstart

Start time of the malfunction of a train

tjudge

Time for fault judgement

tcoupling

Time for coupling operation of the rescue train and the disabled train

tpush

Time for the disabled train pushed to station i 0 when it breaks down in the open track area

tr

fixed dwell time for decoupling operation of the rescue train when route r is chosen

tclear

Time for passenger clearing process

coupling,up

ri

up

λi /λidn

coupling,dn

/ri

Running time of the coupling trains between station i and station i + 1/i − 1 in the up/down direction Passenger arriving rate of the station i

up μ f,i /μdn g,i

Passenger alighting ratio of the station i for train service f /g

C

Train capacity A big positive number

M up

up

a f,i /d f,i dn

a dn g,i /d g,i

Planned arrival/departure time of service f at station i in the up direction in the timetable Planned arrival/departure time of service g at station i in the down direction in the timetable

It is worth to note that, if train service f arrives at the normal station i, the rolling stock can only arrive, stop, and depart at station i, i.e., it cannot be connected with service g from the down direction or comes from the depot, so we have  g∈G

up

dn eg, f,i + σ f,i = 0, ∀ f ∈ F, ∀i ∈ Inorm .

(2)

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Table 2 Decision variables for the mathematical formulation Symbol

Description

Rr

Binary variable, Rr = 1 if the rescue route r is chosen

up dn a f,i /ag,i up dn d f,i /dg,i turn turn t f,i /tg,i dwell,up dwell,dn t f,i /tg,i up dn r f,i /r g,i

Arrival time of service f /g at station i in the up/down direction Departure time of service f /g at station i in the up/down direction Turnaround time of service f /g at station i in the up/down direction Dwell time of service f /g at station i in the up/down direction Running time of service f /g between stations i and station i + 1/i − 1 in the up/down direction

up

Binary variable, o f,i = 1/odn g,i = 1 if service f /g in the up/down

up

dn = 1 if service f /g is not canceled at Binary variable, x f,i = 1/x g,i

up

dn Binary variable, e f,g,i = 1/eg, f,i = 1 if service f /g in the up/down

up

o f,i /odn g,i

direction operates between stations i and i + 1/i − 1 up

dn x f,i /x g,i

the turnaround station i dn e f,g,i /eg, f,i

up

direction is connected with service g/ f in the down/up direction at turnaround station i, i.e., the rolling stock turns around at station i up

up

dn δ f,i /δg,i

dn = 1 if the rolling stock performing Binary variable, δ f,i = 1/δg,i

service f /g in the up/down direction goes back to the depot at turnaround station i up

up

dn σ f,i /σg,i

dn = 1 if the rolling stock performing Binary variable, σ f,i = 1/σg,i

service f /g in the up/down direction comes out from the depot at turnaround station i depot,up

ai

depot,dn

/ai

arr,up

arr,dn p f,i / pg,i off,up

p f,i

off,dn / pg,i

up dn κ f,i /κg,i

Arrival time of the trains from the depot to the station i in the up/down direction Number of arriving passengers from departure time of the train f − 1/g − 1 to departure time of the train f /g at station i Number of passengers getting off train f /g at station i up

dn = 0 if passengers get off according to the alighting ratio, κ f,i /κg,i up

dn = 1 if all passengers get off κ f,i /κg,i on,up

on,dn p f,i / pg,i

Number of passengers getting on train f /g at station i

onboard,up onboard,dn p f,i / pg,i

Number of passengers on-board when train f /g departing from station i

wait,up

p f,i i in

wait,dn / pg,i

Number of stranded passengers after train f /g departing from station i Index of the station where the storage track for the disabled train is located in

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If train service f arrives at the turnaround station i that is not connecting with depot, the rolling stock can also be connected with service g from the down direction, but cannot come from the depot, i.e., up

σ f,i = 0, ∀ f ∈ F, ∀i ∈ Iturn /Idepot .

(3)

Moreover, if station i is the turnaround station connecting with the depot, the arrival time of train service f involves three possible cases as described in constraint (1). The departure time of service f at station i in the up direction can be calculated by      up up up dwell,up up up dwell,up + d f,i = o f,i,i+1 a f,i + t f,i e f,g,i a f,i + t f,i + tclear g∈G   up up dwell,up +δ f,i a f,i + t f,i + tclear , ∀ f ∈ F, ∀i ∈ I.

(4)

It is worth to note that, if train service f departs from the normal station i, the rolling stock cannot be connected with service g to the down direction or goes back to the depot, so we have 

up

g∈G

up

e f,g,i + δ f,i = 0, ∀ f ∈ F, ∀i ∈ Inorm .

(5)

If train service f departs from the turnaround station i that is not connecting with depot, the rolling stock can also be connected with service g to the down direction, but cannot go back to the depot, i.e., up

δ f,i = 0, ∀ f ∈ F, ∀i ∈ Iturn /Idepot .

(6)

Moreover, if station i is the turnaround station connecting with the depot, the departure time of train service f involves three possible cases as described in constraint (4). In order to ensure the safety, the departure time and arrival time between two consecutive trains should be not less than the minimum headway, i.e.,   up up up up up up dep x f −u,i x f,i d f,i − d f −u,i ≥ x f −u,i x f,i tmin , ∀ f ∈ F, i ∈ I, u ∈ {1, 2, . . . , f − 1}, (7)   up up up up up up arr x f −u,i x f,i a f,i − a f −u,i ≥ x f −u,i x f,i tmin , ∀ f ∈ F, i ∈ I, u ∈ {1, 2, . . . , f − 1}. (8)

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Rolling stock circulation constraints When the service f is about to arrive at the station, the rolling stock used for it could come from the previous station in the same direction, turn around from the station in the opposite direction, or come out from the depot, i.e., up

up

x f,i = o f,i−1 +

 g∈G

up

dn eg, f,i + σ f,i , ∀ f ∈ F, i ∈ I.

(9)

In addition, service f in the up direction could be connected with at most one predecessor service in the down direction, i.e., 

dn eg, f,i ≤ 1, ∀ f ∈ F, i ∈ I.

(10)

g∈G

When the service f is about to leave the station, its rolling stock could continue to go to the next station in the same direction, turn around to the opposite direction at the station, or go back to the depot, i.e., up

up

x f,i = o f,i +



up

up

e f,g,i + δ f,i , ∀ f ∈ F, i ∈ I.

(11)

g∈G

Moreover, service f has to be connected with at most one successor service in the down direction,  up e f,g,i ≤ 1, ∀ f ∈ F, i ∈ I. (12) g∈G

Passenger demand constraints In order to calculate the number of stranded passengers, passengers are divided into arr,up off,up five categories (i.e., newly arriving passengers p f,i , alighting passengers p f,i , on,up

onboard,up

boarding passengers p f,i , on-board passengers p f,i

and stranded passengers

wait,up p f,i ),

the relationship among which is illustrated in Fig. 3. The number of newly arriving passengers can be calculated by arr,up

p f,i

up

= λi

  up up d f,i − d f −1,i , ∀ f ∈ F, i ∈ I.

(13)

The number of alighting passengers of train service f at station i can be calculated by off,up

p f,i

up

up

up

onboard,up

= ((1 − μ f,i )κ f,i + μ f,i ) p f,i−1

, ∀ f ∈ F, i ∈ I,

(14)

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Fig. 3 Schematic diagram of passenger flow calculation

which means that all the passengers on the rescue train and disabled train must get off at the corresponding stations, and the same when trains arrive at the terminal stations or turn around at turnaround stations. Otherwise for other normal stations, up alighting passengers are calculated by passenger alighting ratio μ f,i . We introduce up dn the variable κ f,i /κg,i to represent this logic, i.e.,

up

κ f,i

⎧ ⎪ 1, ∀ f ∈ F, i = I ⎪ ⎪ ⎪ ⎨ 1, f = f rescue , i = i 0 − 1 = 1, f = f fault , i = i 0 ⎪  up ⎪ ⎪ ⎪ e f,g,i , else ⎩

(15)

g∈G

The number of boarding passengers is calculated by on,up

p f,i

arr,up wait,up = min C, p f,i + p f −1,i , ∀ f ∈ F, i ∈ I,

(16)

which means that the passengers getting on train f depend on the capacity of train f and the sum of the newly arriving passengers and the stranded passengers. The number of on-board passengers is calculated by  onboard,up p f,i

=

onboard,up

p f,i−1

off,up

on,up

− p f,i + p f,i , ∀ f ∈ F, i ∈ I/{1} on,up p f,i , ∀ f ∈ F, i = 1

(17)

The number of stranded passengers can then be calculated by wait,up

p f,i

arr,up

= p f,i

wait,up

on,up

+ p f −1,i − p f,i , ∀ f ∈ F, i ∈ I.

(18)

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Train rescue constraints When a rolling stock is broken down at station i 0 or the open track area between station i 0 and station i 0 −1, the possible rescue routes are illustrated in Fig. 2 according to the experience of dispatchers. The number of possible routes is denoted by n. If a suitable rescue route is selected, we introduce a binary variable Rr to indicate that, i.e., n 

Rr = 1.

(19)

r =1

If route 1 is chosen, we define that the disabled train is stored at depot; if route 2 is chosen, we define that the disabled train is stored at the storage track of station i s , i.e., i in = R1 ∗ i + R2 ∗ i s , ∀i ∈ Idepot

(20)

After the fault occurs, the disabled train f fault needs to dwell for time tjudge , tcoupling to wait for judgement and coupling, and tpush could be obtained according to the distance from the fault location to station i 0 , i.e., dwell,up

t ffault ,i0 ≥ tstart + tcoupling + tjudge + ϕ ∗ tpush

(21)

The rescue train f rescue needs to clear passengers at the previous station, i.e., station i 0 − 1, the dwell time should be described by dwell,up

t frescue ,i0 −1 ≥ tclear .

(22)

After coupling, the rescue train and disabled train should skip all the stations between station i 0 and the station to store the disabled train, i.e., dwell,up

t ffault ,i

dwell,up

= t frescue ,i ≤ 0, i 0 < i < i in ,

(23)

and the coupled train has lower speed than normal operation, so we have up

up

coupling,up

r ffault,i = r frescue ,i ≥ ri

, i 0 ≤ i < i in .

(24)

After the coupled train arrives at the storage track or the station connected with the depot, it needs to dwell for uncoupling and other operations. The dwell time is different due to the difference of rescue routes. Thus, we introduce tr to represent it when the route r is chosen. dwell,up

t frescue,i ≥ in

n  r =1

Rr tr .

(25)

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3.2 Objective Function for Train Rescheduling with Rolling Stock Rescue The objective function of rescheduling and rolling stock rescue problem involves four parts: • minimize the deviations between the planned time and the actual time of all train services, • minimize the total number of cancellations of train services at stations, • minimize the time it takes to put the rescue train back into operation, • minimize the number of stranded passengers. The departure and arrival deviations with respect to the timetable are computed as follows:        up  up up  dn   dn odn Z deviation = o f,i−1 d f,i − d f,i  + g,i+1 dg,i − d g,i  i∈I,i= I f ∈F i∈I,i=1   g∈G  (26)   up  up  dn  dn  up  + o f,i−1 a f,i − a f,i  + og,i+1 ag,i − a dn g,i . g∈G i∈I,i= I

f ∈F i∈I,i=1

The objective function component related to train service cancellations can be computed by Z cancellation =

 f ∈F i∈I

up

(1 − x f,i ) +

 g∈G i∈I

dn (1 − x g,i ).

(27)

The time it takes to put the rescue train back into operation is calculated by up

Z back = d frescue ,iin .

(28)

The number of stranded passengers is computed as Z passengers =

 f ∈F i∈I

wait,up

p f,i

+

 g∈G i∈I

wait,dn pg,i .

(29)

To take the multiple performance indicators at the same time, we adopt the weighted sum method to deal with these multiple objective components. The objective function can be written as follows: min Z = w1 ·

Z deviation Z deviation,nom

+ w2 ·

Z cancellation Z cancellation,nom

+ w3 ·

Z back Z back,nom

+ w4 ·

Z passengers , Z passengers,nom

(30) where Z deviation,nom , Z cancellation,nom , Z back,nom and Z passengers,nom are normalization factor, which are calculated by solving the optimization problem related to each objective function component; w1 , w2 , w3 , and w4 are positive weights to denote the relative importance of each objective function component.

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Fig. 4 The layout of the Beijing Subway Line 7

4 Case Study The mixed-integer nonlinear programming (MINLP) model which we formulated in Sect. 3 can be transformed into a mixed integer linear programming (MILP) model via the transformation properties given in [11]. In this section, a numerical experiment is carried out for the presented integrated train rescheduling and rolling stock rescue planning model based on real-world data of Beijing Subway Line 7.

4.1 Set-Up Beijing Subway Line 7 was put into operation on December 28, 2014 and has 21 stations, as shown in Fig. 4. For the test case, the train rescheduling period is from 11:00 to 13:00, which is during off-peak hours. The number of involved train services in each travelling direction for the considered time period is 10. In the studied test dep case, the minimum headway tmin between consecutive train services is around 240 s. The parameters tjudge , tpush , tcoupling , t1 , t2 , tclear are set as 300, 60, 180, 540, 390 and 180 s, respectively. To demonstrate the effectiveness of the proposed model, a case of two rescue routes is considered, i.e., the train 6 is broken down between station HLG and DT in the up direction.

4.2 Numerical results The performance comparison of the integrated optimization for the two rescue routes is given in Table 3, where each objective function component value and the computation time are reported. It can be observed that each objective function component value of route 2 is better than route 1. Because in route 2, the disabled train is pushed out of the mainline so that the influence on other train services is reduced. The rescheduled timetable and the rolling stock rescue plan for route 1 and route 2 are given in Figs. 5 and 6. The black dashed lines are the planned train services and the coloured solid lines are the scheduled ones. The black solid lines at the start

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Table 3 Performance comparison for route 1 and 2 Route

Z obj (s)

Z deviation (s)

Z back (s)

Z cancellation

Z passengers

CPU time (s)

1

25.568

154,250

5613

21

2188

13

2

9.399

112,280

3859

6

671

7

Fig. 5 The computational result obtained by the integrated optimization model for route 1

and terminal stations represent the rolling stock circulation. The five vertical dotted red lines represent the start time of five phases of rolling stock rescue. The overlapping blue-green line represents the coupled train. Red stations represent turnaround stations and blue ones represent turnaround stations with storage tracks. The red squares represent stranded passengers and blue triangles represent on-board passengers. It can be observed that some passengers are stranded on the platform because the disabled train and the rescue train are cleared and cannot continue to carry passengers. These passengers are taken away by the following trains. If the route 2 is chosen, it can be seen that the rescue train will continue to carry passengers after moving back to the mainline operation and there will be no stranded passengers at the next station.

5 Conclusions In this paper, we have proposed a mixed integer linear programming formulation to generate rolling stock rescue plan and train reschedule with consideration of passenger flow for a metro line, where the arrival/departure time constraints, headway constraints, rolling stock circulation constraints, passenger demand constraints and

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Fig. 6 The computational result obtained by the integrated optimization model for route 2

rescue plan constraints are considered. The numerical experiment based on the data of Beijing Subway Line 7 demonstrates the effectiveness of the proposed integrated model of two rescue routes for a metro line. The experiment illustrates the difference between different rescue routes and can be solved in a short time. In this paper, the considered rescue routes only involve several forward possible choices. As a future work, we will consider more rescue routes under special circumstances, which may allow the train to run in reverse direction. Acknowledgements This work is supported by the Beijing Natural Science Foundation (L201014) and the National Natural Science Foundation of China (72071016).

References 1. Y. Chang, Train Rescheduling under the Failures of the Train Control System for Urban Rail Transit Systems (Beijing Jiaotong University, 2020) (in Chinese) 2. V. Cacchiani, D. Huisman, M. Kidd, L. Kroon, P. Toth, L. Veelenturf, J. Wagenaar, An overview of recovery models and algorithms for real-time railway rescheduling. Transp. Res. Part B: Methodol. 63, 15–37 (2014) 3. Y. Zhang, A. D’Ariano, B. He, Q. Peng, Microscopic optimization model and algorithm for integrating train timetabling and track maintenance task scheduling. Transp. Res. Part B: Methodol. 127, 237–278 (2019) 4. Y. Zhu, R.M. Goverde, Railway timetable rescheduling with flexible stopping and flexible short-turning during disruptions. Transp. Res. Part B: Methodol. 123, 149–181 (2019) 5. Y. Wang, K. Zhao, A. D’Ariano, R. Niu, S. Li, X. Luan, Real-time integrated train rescheduling and rolling stock circulation planning for a metro line under disruptions. Transp. Res. Part B: Methodol. 152, 87–117 (2021)

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6. N. Bešinovi´c, Y. Wang, S. Zhu, E. Quaglietta, T. Tang, R.M. Goverde, A matheuristic for the integrated disruption management of traffic, passengers and stations in urban railway lines. IEEE Trans. Intell. Transp. Syst. (2021) 7. J. Yin, T. Tang, L. Yang, Z. Gao, B. Ran, Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: an approximate dynamic programming approach. Transp. Res. Part B: Methodol. 91, 178–210 (2016) 8. J. Yin, L. Yang, T. Tang, Z. Gao, B. Ran, Dynamic passenger demand oriented metro train scheduling with energy-efficiency and waiting time minimization: mixed-integer linear programming approaches. Transp. Res. Part B: Methodol. 97, 182–213 (2017) 9. J. Yin, A. D’Ariano, Y. Wang, L. Yang, T. Tang, Timetable coordination in a rail transit network with time-dependent passenger demand. Eur. J. Oper. Res. 295(1), 183–202 (2021) 10. Q. Zhu, Y. Bai, D. Yin et al., Metro train scheduling adjustment model in the case of failure rescue. China Railway Sci. 166–174 (2021) (in Chinese) 11. A. Bemporad, M. Morari, Control of systems integrating logic, dynamics, and constraints. Automatica 35(3), 407–427 (1999)

A DSC-Based Approach to Robust Adaptive Tracking Control for Strict-Feedback Nonlinear Systems with Dead-Zone Input Chengcheng Lu and Yunfeng Zheng

Abstract A robust adaptive tracking control method based on DSC is presented for a class of uncertain nonlinear strict-feedback systems with dead-zone input. In order to deal with the “explosion of complexity” problem in the traditional backstepping method, the first-order low-pass filter is employed to process the virtual control signal, so the structure of controller is simplified. The main characteristic of this algorithm is to eliminate the influence of dead zone nonlinearity. Theoretical analysis proves that all signals of the closed-loop system are semi-globally uniformly and ultimately bounded. Finally, considering the simulation result of a single-link manipulator, by choosing parameters appropriately and adjusting the design parameters, can accomplish asymptotic convergence of the tracking error, and enhance transient performance. Via the result of simulation example, its efficacy of the approach is illustrated. Keywords Backstepping · Nonlinear system · Dynamic surface control · Adaptive control · Dead-zone input

1 Introduction In the actual industrial control system, the dead-zone nonlinearity widely existing, which will worsen control performance and even cause instability of the system. Controller design should take into account its existence, also the control system should be designed to reduce and remove the influence of dead-zone and promise the control performance of the system. Many scholars have carried out research. Zuo et al. [1] studied the nonlinear problem of unknown dead-zone, an adaptive control C. Lu · Y. Zheng (B) Dalian Maritime University, Dalian 116000, China e-mail: [email protected] C. Lu e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_23

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technology combined with dead-zone inverse [2] function was presented [4]. He et al. [3] designed an adaptive control scheme based on neural network to deal with the uncertainties and trajectory tracking problems caused by the unknown dead zone. In [4], an adaptive robust dynamic, dynamic surface control strategy is designed for dead-zone input dynamic nonlinear systems. The dead-zone model is approximately transformed into the sum of a linear part and a bounded part, and the bounded part is treated with time-varying disturbance terms by using robust adaptive control to solve the dead-zone problem [5]. On the basis of this, Ref. [7] proposed adaptive robust control method to compensate the dead zone by approximation capability of neural network and fuzzy control to unknown functions, respectively. In the case of uncertain nonlinear dead zone, a backstepping controller with adaptive specified performance is proposed in [8], which guarantees specified transient and steadystate performance. But it is affected by “complexity explosion”, which increases the complexity of design calculation and controller. To avoid the shortcomings of traditional backstepping control, Swaroop [9] proposed dynamic surface technology for a class of strictly feedback systems, using first-order linear filter to deal with virtual control law, which greatly relaxed the requirements of system equations and reference signals, and reduced the computational burden in the design process. Reference [10] proposed an inversion adaptive control method bottomed on neural network for a class of time-varying uncertain strict-feedback nonlinear systems. The above achievements widely use the adaptive neural network approximation method to settle the control issue of unknown nonlinear systems. However, Li [11] used neural network to approximate the dead zone model and the uncertainties in the system for the strict-feedback chaotic systems with dead-zone input, and also applied dynamic surface for the synchronization control design, ensuring that the synchronization error is arbitrarily small. However, the above methods have many adjustment parameters, which influence each other, and most of them can only make the tracking error converge to any small by adjusting parameters. This kind of method needs to spend a lot of time adjusting parameters to achieve the desired effect. In Ref. [12], the introduction of the first-order filter in the dynamic surface will lead to larger tracking error and lower control performance. Therefore, it is very important to improve the linear first-order filter. In [13], when establishing the dynamic surface of each step, the expanded state observer is applied to compensate and observe system disturbance, also the tracking differentiator is used to filter the pseudo-intermediate signal and obtain the differential signal. The use of tracking differentiator not only eliminates the calculation complexity but also improves the control effect. Because the first observer introduces the control output signal, the double feedback control of the dynamic surface is realized. In this paper, we devise a continuous feedback controller for a class of parameter strictly feedback systems with uncertain asymmetric dead-zone input. Through the use of dynamic surface technology, the error of the dynamic surface can be compensated via introducing a filter, and the computational expansion caused by the virtual control differential can be solved. Meantime, adaptive control is used to estimate the dead-zone characteristics and unknown parameters of the system online. Finally, the control algorithm designed effectively deals with the influence of the

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dead zone, which speeds up the convergence speed and improves the closed-loop system’s performance, ensures stability of the closed-loop system, and realizes the gradual convergence of tracking error.

2 Problem Description Consider a class of strictly feedback nonlinear systems with dead-zone input, ⎧ ⎪ ⎨ x˙1 = xi+1 + f i (x), i = 1, 2, ...n x˙n = gn (x)D(u(t)) + f n (x) ⎪ ⎩ y = x1

(1)

where xi = [x1 , x2 , ...xi ]T ∈ R, i = 1, 2, ..., n is the system state vector, f i (x) is a known smooth nonlinear system function, gi (x) denotes a known smooth continuous function, D(u(t)) ∈ R is the control input signal, and u(t) is the control output signal of the unknown nonlinear dead-zone model. ⎧ ⎪ ⎨ m r (u(t) − br ), u(t) ≥ br D(u(t)) = 0, −bl ≤ u(t) ≤ br (2) ⎪ ⎩ m l (u(t) − bl ), u(t) ≤ −bl br and bl are unknown positive constants, m r and m l are the mapping relations in the corresponding interval, also both unknown smooth continuous functions. The dead-zone input function is simplified as follows by using the mid-value theorem: D(u(t)) = m(u)u(t) + d(u(t))

(3)

⎧ ⎪ ⎨ −m r (u(t))br , u(t) ≥ br d(u(t)) = −m(u)u(t), −bl ≤ u(t) ≤ br ⎪ ⎩ m l (u(t))bl , u(t) ≤ −bl By substituting Eq. (3) into (1), one gets ⎧ ⎪ ⎨ x˙i = xi+1 + f i (x), i = 1, . . . , n x˙n = gn (x)m(u)u(t) + gn (x)d(u(t)) + f n (x) ⎪ ⎩ y = x1

(4)

For a strictly nonlinear system (1) with an input dead-zone model, this paper puts forward the control goal will be to devise a DSC-based approach to adaptive tracking controller u, which makes the tracking error x1 − yr convergent to zero and ensures

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that all signals should be semi-globally uniform and finally bounded for the closedloop control system.

3 Backstepping-Based Adaptive Dynamic Surface Controller Design In Sect. 3, we will devise a backstepping-based DSC to robust adaptive tracking control design algorithm for strict-feedback nonlinear systems with dead-zone input, and for such a system (1), come up with an appropriate method to solve it. Compared with the traditional backstepping method, there are n steps in the recursive design. For each step of the recursive design, we adopt a virtual control law αi , i = 1, 2, ..., n −1 to stabilize the ith subsystem of each step. The actual control law u is created at the final step to stabilize the nth subsystem. Then, the detailed procedure of the adaptive dynamic surface control scheme design is given as follows: Step 1: Defining the system tracking error s1 = x1 − yr (the first error surface), its derivative is s˙1 = x˙1 − y˙r = x2 + f 1 (x1 ) − y˙r

(5)

In order to satisfy the recursive design negative condition, the design virtual control law α2 for the above subsystem (5) is α2 = −k1 s1 − f 1 (x1 ) − y˙r

(6)

where k1 > 0 is a positive design constant. For the first time, the professor put forward DSC algorithm technology [9] to deal with the virtual control signal generated in the system, which has conveniently solved the problem of “explosion of complexity,” in the system control. We give a first-order low-pass filter as follows: τ2 z˙ 2 + z 2 = α2 z 2 (0) = α2 (0)

(7)

where τ2 is the filtering parameter and z 2 (·) is a continuous function of the filter, Step i: i(2, ..., n − 1). The derivative of si can be obtained as s˙i = x˙i − z˙ i = xi+1 + f i (x1 , x2 , . . . , xi ) − z˙ i

(8)

Choose the virtual controller αi+1 for xi+1 in (8) αi+1 = −ki si − f i (x1 , x2 , ..., xi ) + z˙ i

(9)

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where ki > 0 is a positive control parameter. Let αi+1 pass the first-order low-pass filter below. τi+1 z˙ i+1 + z i+1 = αi+1

(10)

Step n: In the n step, the nth dynamic surface sn = xn − z n is defined, and the derivative to (t) is s˙n = x˙n − z˙ n = gn (x)m(u)u(t) + gn (x)d(u(t)) + f n (x1 , x2 , ..., xn ) − z˙ n

(11)

For this last actual control law: u(t) u(t) = −

1 (−kn sn + f n (x1 , x2 , . . . , xn ) − z˙ n ) gn (x)m(u)

(12)

where kn > 0 is a control constant.

4 Stability Analysis The stability of the control system will be given by the following theorem statement. Theorem: Consider a class of strict-feedback nonlinear system (1) with unknown dead-zone input equation (2), virtual control laws (6), (9), and actual control law (12). For the bounded initial condition of the system, the Lyapunov function V (0) ≤ ε (ε is a positive design constant) is satisfied. By adjusting the design parameters ki (i = 1, 2, ..., n), τi+1 , ai , λ, the signal of the closed-loop system is semi-globally known to be finally bounded, and the output tracking signal gradually converges to zero. Owing to the limitations in this paper, it is no longer proved that the Lyapunov function is negative definite.

5 Simulation Through simulation, we cite our proposed control scheme to demonstrate and clarify its effectiveness. We will quote Ref. [14] to introduce a benchmark application example of a single-link manipulator driven by a brush DC motor. Consider the dynamics system of the single-link robotic manipulator, with q angular position, q˙ velocity, and q¨ acceleration, which can be expressed as follows:

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M q¨ + B q˙ + N sin(q) = w I L I˙ = −H I − K q˙ + V

(13)

where I is the motor’s armature current, q is the system output, and u is the control input voltage. The system parameter values are given to be considered with M = 1, B = 1, N = 10, w = 1, L = 0.05, H = 0.5, K = 10, V = D(u(t)). Then, we present this simple nonlinear dead-zone model: ⎧ ⎪ ⎨ 0.3(u − 1.2), u ≥ 1.2 D(u) = 0, −0.8 ≤ u ≤ 1.2 ⎪ ⎩ −0.2 (u + 0.8), u ≤ −0.8

(14)

The above formula can express the strict-feedback form of the system (4) discussed in the following text: ⎧ ⎪ ⎨ x˙1 = x2 + f 1 (x1 ) x˙2 = f 2 (x1, x2 ) + g2 x3 ⎪ ⎩ x˙3 = f 2 (x1, x2 , x3 ) + g3 D(u)

(15)

Setting the state variable,   x1 = q, x2 = q, ˙ x3 = I, g2 = 1 M, g3 = 1 L,  f 2 (x1, x2 ) = −N sin(x1 ) − Bx2 M,  f 2 (x1, x2 , x3 ) = −K x2 − H M x3 L, Control objective: The adaptive dynamic surface controller u is designed, so to force the output signal y(t) can gradually track the desired signal yr , and the closedloop system is guaranteed to be semi-globally ultimately bounded (SGUB). The control parameters chosen for simulation are k1 = 2, k2 = 2, k3 = 2. The control ˙ = 0, I (0) = 0. The filter initial initial value of system state are q(0) = 1, q(0) values are z 2 (0) = 0, z 3 (0) = 0. Through the running results of the program, the following three simulation results are drawn. Figure 1 of the simulation results shows that compared with the traditional dynamic surface control method, this control scheme has better path tracking performance, and we can see that the tracking error is gradually converging to be small enough to zero. As can be seen from Fig. 2, the control input signal is bounded, and in this text, the amplitude change of the input signal of control strategy method proposed is much smaller than the traditional dynamic surface control scheme. The simulation results shown in Fig. 3 directly verify the effectiveness of the parameter estimation of the proposed method.

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Fig. 1 Tracking performance

Fig. 2 Control input and output signals

Fig. 3 Parameter estimation

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6 Conclusion In this paper, we put forward a DSC method based on backstepping, which could be used to better control a class of nonlinear strict-feedback system with uncertain dead-zone input. By introducing a filter to eliminate the “explosion of complexity” and intermediate virtual control problem, a robust adaptive tracking control method based on dynamic surface technology is presented. The results of stability and theoretical analysis prove that this method can make all signals of the closed-loop control system stable and uniformly ultimately bounded and tracking error can converge to small enough and approach zero and eliminate the influence of dead-zone. The simulation results directly demonstrate the effectiveness, reliability, and correctness of the algorithm. Acknowledgements This work was financially supported by the Natural Science Foundation of Liaoning Province (20180520039).

References 1. Z.Y. Zuo, X. Li, Z.G. Shi, Adaptive control of uncertain gear transmission servo systems with dead zone nonlinearity. ISA Trans. 58, 67–75 (2015) 2. G. Tao, P.V. Kokotovi´c, Adaptive control of plants with unknown output dead-zones. IFAC Proc. Vol. 26(2), 73–76 (1993) 3. W. He, B. Huang, Y.T. Dong et al., Adaptive neural network control for robotic manipulators with unknown dead zone. IEEE Trans. Cybern. 48(9), 2670–2682 (2017) 4. C.L. Wang, L. Yan, Robust adaptive dynamic surface control fora class of MIMO nonlinear systems with unknown non-symmetric dead-zone. Asian J. Control 16(2), 478–488 (2014) 5. J.H. Yang, J. Wu, Y.M. Hu, Backstepping method and its applications to nonlinear robust control. Control Decis. 17(S1), 641–647 (2002) 6. J. Wang, J. Hu, Robust adaptive neural control for a class of uncertain non-linear time-delay systems with unknown dead-zone nonlinearity. Control Theory Appl. 5(15), 1782–1790 (2011) 7. T.S. Wu, M. Kar, H. Wang, H.S. Chen, Robust tracking control of MIMO underactuated nonlinear systems with dead-zone band and delayed uncertainty using an adaptive fuzzy control. IEEE Trans. Fuzzy Syst. 25(4), 905–918 (2017) 8. J. Na, Adaptive prescribed performance control of nonlinear systems with unknown dead zone. Adapt. Control Signal Process. 27(5), 426–446 (2013) 9. D. Swaroop, J.K. Hedrick, P.P. Yip, Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000) 10. Y. Li, S. Qiang, X. Zhuang et al., Robust and adaptive back stepping control for nonlinear systems using RBF neural networks. IEEE Trans. Neural Netw. 15(3), 693–701 (2004) 11. G. Li, Adaptive neural network synchronization for uncertain strict-feedback chaotic systems subject to dead-zone input. Adv. Differ. Equ. 2018(1), 188–203 (2018) 12. Y. Pan, H. Yu, Dynamic Surface Control via Singular Perturbation Analysis (Pergamon Press, Singapore, 2015) 13. G. Sun, L. Heng, Active disturbance rejection dynamic surface control of high-order nonlinear system with dead-zone. Control Theory Appl. 36(8), 1336–1344 (2019) 14. A.K. Kostarigka, G.A. Rovithakis, Prescribed performance output feedback adaptive control of uncertain strict feedback nonlinear systems, in Proc. 18th IFAC World Congress (2011), pp. 2650–2655.

Passenger Flow Estimation in Urban Rail Transit Transfer Station Based on Multi-Source Detection Data Yu Fei Peng and Xi Jiang

Abstract In the urban rail transit transfer station, multi-source detection data from AFC systems, train weighing systems, and intelligent video devices can be applied to estimate the more detailed distribution of passenger flow within the station. This paper first proposes a model for estimating passenger flow in different directions within the station based on the relationships between passenger flows. Further, this paper abstracts the model into a multi-layer hierarchical flow network and introduces the forward-passing and backward-propagation techniques to solve the proposed model. Finally, taking a typical transfer station as an example, the passenger flow in different directions within this station was estimated, and transfer passenger flow was further extracted. Keywords Urban rail transit transfer station · Passenger flow estimation · Multi-source detection data · Forward-passing · Backward-propagation

1 Introduction The detailed passenger flows within the transfer station include the inbound flow to different line directions, the outbound flow from different line directions, and the transfer flow between different line directions, which are important components of the operational status of the urban rail system. The passenger flow estimation within the station has been a hot but difficult research area, and many scholars have mainly focused on two research perspectives, the first perspective is to estimate the passenger flow within the stations from a network-wide aspect. These studies mainly consider route selection behavior [1], train capacity constraint [2], dynamic interaction of train and passenger [3], and other factors to obtain interval and transfer flow based on the methods of passenger flow assignment. However, it’s very challenging to Y. F. Peng · X. Jiang (B) School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_24

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accurately estimate the passenger flows because of the many factors considered and the complexity of the modeling process. The second perspective is to directly detect the passenger flow within the station. Some of these studies are based on positioning technologies such as mobile communications [4] and WIFI [5] to obtain passenger tracks which can be further integrated into the passenger flow in different directions within the station, but the large-scale application of these positioning technologies faces challenges due to policy, implementation conditions, costs, etc. Other studies directly detect the passenger flow or density of a particular zone within the station by using people counting technologies such as laser scanning [6] and intelligent video [7]. However, the direction (i.e., origin and destination) of passenger flow within the station cannot be distinguished by detection data which cannot be divided into passenger flows in different directions directly. In fact, the mixed passenger flow of the zone is the accumulation result of passenger flow in different directions, and there is relationship between these flows certainly. Therefore, based on the detection data of passenger flow and the relationship between different types of flows within the station, this paper studies the passenger flow estimation method to obtain more detailed passenger flow within the transfer station, which is helpful to meet the demand of actual operation decision-making for passenger flow control.

2 Problem Statement In a transfer station, the process of passenger movement is that passengers generate at the generation points (i.e., the entrance gates and the arriving trains) and disappear at the disappearance points (i.e., the exit gates and the departing trains) after passing through some facilities such as station halls, escalators, channels, and platforms. Figure 1 shows the passenger flows in different directions have different generation points (origin in the station) and disappearance points (destination in the station), including five types: train running direction departing train

arriving train pla platform

station hall entrance gate

departing train

arr r iving train t ain tr arriving t ai tr a n ru rrunning nning di d recti c on n train direction

de d parti t ng tr ttrain an ai departing

arriving train pla platform

exit gate

Inbound flow transfer flow between same platform

transfer flow between different platforms through-station flow intersection point generation point

departing train

arriving train

outbound flow

disappearance point

train running direction

Fig. 1 The passenger flow in different directions within a transfer station

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(i) outbound flow is the passenger flow which is from an arriving train to an exit gate; (ii) inbound flow is the passenger flow which is from an entrance gate to a departing train; (iii) transfer flow between different platforms is the passenger flow which is from an arriving train to the departing in another platform. (iv) transfer flow between the same platform is the passenger flow which is from an arriving train to the departing in the same platform. (v) through-station flow is the passenger flow which moves with a train. The intersection of passenger flows in different directions within the station can be described by constructing a passenger traveling network G = (V , E, P), as shown in Fig. 2, the element of node set V can be divided into three categories: (i) passenger generation vertexes, containing the entrance gate vertex oi (i ∈ [1, O]) and the arriving train vertex bi (i ∈ [1, B]); (ii) passenger disappearance vertexes, containing the exit gate vertex ci (i ∈ [1, C]) and the departing train vertex ai (i ∈ [1, A]); (iii) flow intersection vertex ri (i ∈ [1, R]) refers to the escalator or the channel. E is defined as the link set, comprising of passenger flow direction between nodes. The set P consists of all paths between any generation vertex and disappearance vertex. On the above network, an arriving passenger will select a path after determining a flow direction, and then start from the generation vertex (origin of the flow direction) and sequentially pass through some intersection vertexes and links on this path, and finally arrive at a disappearance vertex (destination of the flow direction). In a period of time, based on the spatial correlation between vertexes and links on the network, the passenger flow at each generation vertex is distributed in different directions and then onto the candidate paths, the path flows are aggregated at the intersection and disappearance vertexes eventually. At present, the passenger flow at some vertexes can be detected by some technologies. For example, the passenger flow data at the entrance and exit gates can be obtained through the AFC system, the load of arriving and departing trains can be obtained through train weighing technology, and the passenger flow data at escalators

Passenger leaves the station

the direction of inbound flow station

the direction of outbound flow

the direction of inbound transfer flow between different platforms the direction of through-station flow the direction of inbound transfer flow between same platform generation vertexes

disappearance vertexes

flow direction of a passenger

Fig. 2 The passenger traveling network within the station

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or channels can be obtained through smart video technology. With these detection data, this paper will build a model for estimating passenger flow in different directions within the transfer station, based on the above correlation between passenger flows of different vertexes in the passenger traveling network.

3 Modeling For a transfer station, the detection data used in this study are the passenger flow data at all gates, all arriving and departing trains, some escalators, and channels within a certain interval (e.g., 30-min interval). The constraints of the model are constructed based on the relationship between the passenger flow at generation vertexes S, the flow direction D, the selected path P, and the passenger flow at other detection vertexes M (containing intersection and disappearance vertexes which are detected) in the passenger traveling network. The objective of this model is to make the model estimation result as close as possible to the actual detection data. The relevant model notations and definitions are shown in Table 1. The objective function and constraints of the model are as follows: (1) Objective function ◠

The objective function C(wm , w m ) is to reduce the deviation between the detection ◠ data w m and the estimated passenger flow wm of the detection vertex m[8]. ◠

minC(wm , wm ) =

◠ 2 ∑ (wm , w m) 2 m∈M

(1)

(2) Constraints to describe the process of mapping the flow from the generation vertexes xs to the directions d according to the proportion αs,d . yd =

∑

xs × αs,d , d ∈ D

(2)

s∈Sd

(3) Passenger flow equilibrium constraints to ensure that the sum of the distribution proportion of passenger flow from the same generation vertex s is 1. ∑

αs,d = 1, s ∈ S

(3)

d∈Ds

(4) Constraints to describe the process of mapping the flow yd from the directions d to the path p according to the proportion βd, p . zp =

∑ d∈D p

yd × βd, p , p ∈ P

(4)

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Table 1 Symbol definition for the model formulation Notations Definitions S

Set of index of the generation vertex s, s ∈ S

Sd

Set of index of the generation vertex s which is related to the direction d

D

Set of index of the direction of passenger flow d, d ∈ D

Dp

Set of index of the direction of passenger flow d which is related to the path p

Ds

Set of index of the direction of passenger flow d which is related to the generation vertex s

P

Set of index of the path p, p ∈ P

Pd

Set of index of the path p which is related to the direction d

Pm

Set of index of the path p which is related to the detection vertex m

M

Set of index of the detection vertex m, m ∈ M

Mp

Set of index of the detection vertex m which is related to the path p

xs

The detection data of the generation vertex s

yd

The estimated passenger flow of the direction d

zp

The estimated passenger flow of the path p

wm

The estimated passenger flow of the detection vertex m

◠

wm

The detection data of the detection vertex m

αs,d

The estimated distribution proportion of passenger flow from the generation vertex s to the direction d

βd, p

The selection proportion of path p

γ p,m

Linking index, γ p,m = 1 if the detection vertex m belongs to the path p otherwise γ p,m = 0

(5) Passenger flow equilibrium constraints to ensure that the sum of the selection proportion of the candidate path p is 1. ∑

βd, p = 1, d ∈ D

(5)

p∈Pd

(6) Constraints to describe the process of aggregating path flows z p to the detection vertex m according to the linking index γ p,m . wm =

∑ p∈Pm

z p × γ p,m , m ∈ M

(6)

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4 Solution Algorithm The proposed model in Sect. 3 is a complicated nonlinear programming model with linear mathematical programming model constraints, which is difficult to solve directly by the standard solvers. Therefore, we introduce the forward-passing and backward-propagation algorithms to solve the proposed model [9, 10]. Based on the relationship of the four types of traffic flow (i.e.,xs ,yd , z p ,wm ) in the model, the model can be abstracted into a multi-layer hierarchical flow network based on the computational graph structure, which consists of four layers, namely, generation flow layer, direction flow layer, path flow layer, and detection flow layer, as shown in Fig. 3. The model-solving process in the above multi-layer network is shown in Fig. 4. Based on the initial proportion αs,d and βd, p , it is iteratively updated by forward and backward propagation to approximate the optimal solution, until the relatively optimal proportion αs,d and the passenger flow yd in different directions are obtained within a certain interval. In addition, considering that the route choice behavior within a small interval is almost constant, the path selection proportion βd, p is assumed to be constant in this paper. The solution algorithm is as follows: Step 1: Network initialization Step 1.1: Make iteration t = 1. t . Step 1.2: Initialize αs,d

Step 1.3: According to the maximum utility theory, and taking the walking distance d p and the walking time t p as major influencing factors, construct a multi-logit model for the selection proportion βd, p of path p, as shown in Eqs. (8) and (9):

Fig. 3 The multi-layer hierarchical flow network for the proposed model

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Fig. 4 The model-solving process based on the forward-passing and backward-propagation techniques

V( p) = σ × t p + τ × d p + ε βd, p = ∑

exp(V( p)) p∈Pd exp(V( p))

(8) (9)

where V( p) is the utility function of the path p, σ, τ are given parameters, and ε is random term. Step 2: Forward passing and backward propagation Step 2.1: Perform forward passing step Input data xs and sequentially implement Eqs. (2), (4), and (6) to calculate yd , z p ,wm . Step 2.2: Backward propagate the deviations and partial gradients. ◠

Step 2.2.1: Implement Eq. (1) to calculate C(wm , wm ) and sequentially implement Eqs. (10), (11), and (12) to obtain δ(m), δ( p), δ(d) which are the gradients of ◠ C(wm , w m ) about yd , z p ,wm . ◠

∂C(wm , w m ) ◠ = wm − w m , m ∈ M ∂wm

(10)

∂C(wm , w m ) ∑ = γ p,m × δ(m), p ∈ P m∈M p ∂z p

(11)

∂C(wm , w m ) ∑ = βd, p × δ( p), d ∈ D δ(d) = p∈Pd ∂ yd

(12)

δ(m) =

◠

δ( p) =

◠

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Step 2.2.2: Implement Eq. (13) to calculate ϕ(α) which is the gradient of C(wm , w m ) t about αs,d . ◠

◠

ϕ(α) =

∂C(wm , w m ) ∂C(wm , wm ) ∂ yd = × t = δ(d) × xs , d ∈ D, s ∈ Sd (13) t ∂αs,d ∂ yd ∂αs,d

t Step 2.3: Updating values of variables αs,d using gradient descent (GD), as shown in Eq. (14).

t+1 t αs,d = αs,d − θ × ϕ(α), d ∈ D, s ∈ S D

(14)

where θ is the learning rate. Step 3: If the following conditions are not satisfied simultaneously, then t = t + 1, t and yd at the current return to Step 2; otherwise, end the iteration and output αs,d iteration. (i) The iterative curve of the objective function converges; ◠ (ii) C(wm , w m ) < Cthr e , Cthr e is a tolerance threshold.

5 Case Study This paper takes a typical station as the case, which is a three-line transfer station for Line A, Line B, and Line C. It is also the terminal station for Line A and Line C. The structure of this station is divided into an at-grade hall level, an underground hall level, and an underground platform level. The platform level is a double-island platform level, where the outer side of the double-island is the Line B platform and the inner side is the Line A platform. Line A and Line B transfer through the south of the at-grade hall level and interchange with Line C at the north of the at-grade hall level. The station layout, detection points, and direction of passenger movement are shown in Fig. 5. This paper selects the period from 8:30 am to 9:00 am as the study period and uses the detection data (i.e., flow of all gates, all arriving and departing trains, some escalators and channels) as the input data to build the model. And then a multi-layer hierarchical flow network is constructed using Python 3.8.2. The network structure includes generation flow layer (13 nodes), direction flow layer (73 nodes), path flow layer (337 nodes), and detection flow layer (35 nodes). The model hyperparameter t is 1000 and θ is 0.00001. The iterative curve of the objective function is shown in Fig. 6. It can be seen that after 100 iterations the value of the deviation (i.e., the objective of the proposed model) is stable at around 7.7.

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Fig. 5 The layout, detection points, and passenger movement in the station

Fig. 6 The iterative process of the objective function

Figure 7 shows the passenger flow in different directions and its ratio within the station during the study period. It can be seen that (i) there are more passengers arriving at the train (i.e.,b1 –b4 ) than the gates (i.e., o1 –o9 ); (ii) the passengers entering the gates have four destinations (i.e.,a1 –a4 ), of which the passenger flow going to train a3 accounts for the largest proportion; (iii) the passengers alighting from the train may transfer to another line or leave the station through the gates. For example, the passengers alighting from the train b1 have ten destinations (i.e., c1 –c7 and a2 –a4 ), of which the passenger flow going to exit gate c1 accounts for the largest proportion. From the above results, this paper extracts the transfer flow in different directions and its ratio during the study period in Fig. 8. It can be seen that the transfer flow which is from trains (i.e., b1 –b4 ) to the downward direction of Line A (i.e., train a3 ) has the largest proportion, followed by the transfer flow which is from train (i.e., train b1 –b4 ) to the upward direction of Line B (i.e., train a2 ). Therefore, the operations department

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generation vertex

b4

5.4%

11.9%

9.1%

6.4%

12.0%

11.6%

4.5%

26.0% 4.9%

9.9%

8.0%

23.9%

7.3%

1.5%

5.1%

21.4%

11.3%

5.8%

26.0%

7.2%

7.0%

7.2%

5.8%

20.1%

14.7%

3.7%

b1 o9

7.0%

4.5%

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7.7%

9.2%

7.7%

4.9%

5.0%

16.8%

11.9%

4.7%

b2

16.8%

11.9%

4.7%

b3

100.0%

o8

12.7%

19.0%

39.8%

28.5%

o7 18.4% 29.7% 39.5%12.4% o69.4% 21.6% 40.9% 28.1% o59.7% 22.4% 39.0% 28.9% o48.7% 21.7% 41.2% 28.3% o3 15.3% 27.8% 42.1%14.9% o29.7% 22.4% 39.0% 28.9% o1 15.9% 28.4%39.2% 16.6% 0

200

400

600

800

1000

1200

1400

1600

disappearance vertex a1

a2

a3

a4

c1

c2

c3

c4

c5

c6

c7

Fig. 7 The passenger flow in different directions and its ratio within the station

400 300 200

45.1% 34.3%

45.4% 33.2%

20.6%

100

8.3%

13.1%

43.8% 31.1% 12.2%

12.9%

43.9% 31.1% 12.2%

0

transfer volume

50% 40% 30% 12.9% 20% 10% 0%

transfer ratio

Fig. 8 The transfer flow in different directions and its ratio within the station

needs to consider the convenience of transferring to the downward direction of Line A and upward direction of Line B during this period and shorten the transfer time as much as possible to improve the operational efficiency of the urban rail transit.

6 Conclusions This paper proposed a method for estimating detailed passenger flow within the transfer station using the multi-source detection data. Firstly, the relationship of passenger flows within the station was portrayed by constructing the passenger traveling network. Secondly, a mathematical planning model was proposed for estimating passenger flow in different directions within the station based on the relationship of generation flow, direction flow, path flow, and other detection flows. Then, the proposed model was abstracted into a multi-layer hierarchical flow network, and the forward-passing and backward-propagation techniques were introduced to solve it. The case indicates that the proposed model can estimate the passenger flows (including transfer flow) in different directions within a time interval, which can

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provide important data support for the operational decisions of metro system. In future study, aiming to improve the accuracy of the model estimation, it is necessary to explore the influence of detection error on estimated results. Acknowledgements This study is supported by a grant from the National Key R&D Program of China Project (No. 2022YFC3005204)

References 1. Y.S. Zhang, E.J. Yao, H.N. Dai, Transfer volume forecasting method for the metro in networking conditions[J]. J. China Railway Soc. 35(11), 1–6 (2013) 2. Y.T. Zhu, B.H. Mao, M.G. Li et al., Railway assignment model with vehicle capacity constraints [J]. J. Transp. Syst. Eng. Inf. Technol. 13(6), 134–139 (2013) 3. J. Jin, Passenger mode evolution mechanism of urban rail transit network operation [D]. Beijing Jiaotong University (2015) 4. Y. Tao, Y. Chen, Y. Lei, Research on a method of mining metro transfer passenger flow based on big data of mobile [J]. Sci. Technol. Vision 18, 1–2 (2018) 5. H.Y. Liu, The research of the subway clearing algorithm using big traffic[D]. Guilin University of ElectronicTechnology (2018) 6. Y.X. Sun, W. Guan, Y. Zou et al., Passenger surveillance information and management system at umt transfer station of Beijing[J]. J. Transp. Syst. Eng. Inf. Technol. 12(2), 187–193 (2012) 7. Y.J. Li, Z.Y. Pei, Q. Li et al., Application of intelligent video analysis technology in passenger flow monitoring of metro station [J]. Modern Urban Transit 3, 86–92 (2022) 8. Y.D. Yang, Research on optimization of passenger flow collaborative control in Urban rail transit network [D]. Beijing Jiaotong University (2021) 9. X. Wu, J.F. Guo, K. Xian et al., Hierarchical travel demand estimation using multiple data sources: a forward and backward propagation algorithmic framework on a layered computational graph[J]. Transp. Res. Part C. Emerg. Technol. 96(Nov.), 321–346 (2018) 10. Z.P. Tao, Research on theory and method for multi-state short-term prediction of passenger flow in urban rail transit using multi-source data [D]. Beijing Jiaotong University (2020)

Research on Maglev Track Irregularity Based on Power Spectral Density Qingqin Yang, Qi Zhang, Zhuo Zhang, Dixiang Chen, MengChun Pan, Wenwu Zhou, Kuan Su, Yuan Ren, Hao Ma, and Lihui Liu

Abstract The important characteristics and vibration characteristics of the track structure analysis can be reflected on track power spectrum, which has an important relationship with the stability of the train operation. In this paper, real-time detection data of maglev track is analyzed by the power spectrum, and based on the irregularity of height and track direction are deeply studied. The spatial spectrum features are analyzed from different window functions of the periodic graph. Then the characteristic distribution of spatial wavelength is obtained from the spectrum estimation image. It can be concluded that the characteristic points of the power spectrum are caused by the track structure (such as track row and track row spacing, etc.), so important information of track structure can be inverted through the analysis of the track wavelength characteristics. The power spectral density has certain guiding for track construction. Keywords Power spectrum · Maglev orbit · Periodogram · Correlation

1 Introduction In China, the construction of maglev trains is advancing and the addition of multiple lines is keeping pace, but the track irregularity detection has failed to keep up with the Maglev train’s multidimensional development. Track irregularity is the comprehensive characteristic of the basic construction track structure and is an important factor to affect a series of problems such as maglev force, random vibration, and line maintenance. In addition, the track geometric irregularity will directly affect the safety of the driving process, which can not be ignored. Q. Yang · Q. Zhang · Z. Zhang · D. Chen · M. Pan · Y. Ren · H. Ma · L. Liu (B) College of Intelligence Sicence, National University of Defense Technology, Changsha 410073, China e-mail: [email protected] W. Zhou · K. Su Hunan Lingxiang Maglev Technology Co, Ltd., Changsha 410000, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_25

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Since the construction of maglev track has been developed rapidly in this century, there are no unified standards for power spectrum analysis of maglev track irregularity domestic and overseas at present, and some new breakthroughs have been made in the research until recent years. For example, the United States, Germany, and other countries with relatively mature orbital systems set up corresponding orbital power spectrum function expressions according to the basic situation of their own orbits [1, 2]. In recent years, research has mainly focused on the stationary random noise fluctuations of train in running. The study of Carbone A and Palma F introduced a simplified PDS calculation method, and the results showed that there was a correlation between orbital deviation in PDS [3]. However, the stationary fluctuation could only be used as one of its detection indicators, which was not convincing for the structural characteristics of the whole track line. Shubin Z et al. used the inertial reference method to detect long-wave irregularity information of magnetic levitation orbit [4], but they failed to provide a detailed analytical formula for power spectrum and parameter data related to orbit. According to the comparison between the classical power spectrum and the modern power spectrum, Zhou Z et al. summarized the application range of the modern power spectrum, which is not applicable to the analysis of long-line data [5]. Geng Z et al. focus on the measured data of Tangshan low-speed maglev test line, analyzed the spatial distribution of various wavelengths of orbital geometric irregularity based on the period-graph method [6], and concluded that period-graph analysis has high similarity with German orbit high-interference spectrum. The German spectrum is also used for comparative analysis in this paper. At present, researches on track irregularity detection in railway are mainly carried out from power spectral density method and time–frequency analysis method, etc. These methods have been relatively mature and widely used in railway [7, 8]. Moreover, the discrete Fourier transform method is used in the power spectrum analysis of various orbits [9, 10]. This method has the advantages of high-precision calculation and strong versatility. Compared with traditional railway track, the maglev track is a non-contact track guided and supported by maglev force, which makes the structure of the traditional railway track has a fundamental difference. At the same time, the detection scheme also needs to make corresponding changes. In this paper, for a maglev express line that has been put into operation, a track irregularity detection is carried out on the upper and lower lines in September 2021. The track power spectral density analysis is conducted on the detected data, and the obtained results are compared with the track construction characteristics of maglev line. Based on the influence function of maglev track detection, Luo L obtained that the main irregularity detection was derived from the left–right altitude and left–right data of rail direction [11]. This paper analyzed the two major irregularities about their maglev track power spectral density and compared the wavelength information of feature points with the orbit parameters. Using the basic law of the German orbital spectrum formula to compare and observe the difference between the two routes of irregularity detection, analyze the causes of the phenomenon of orbit irregularity.

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2 Overview of Orbit Irregularity and Power Spectral Density 2.1 Detection of Track Irregularity For the detection of short-distance track irregularity, the fluctuation is affected by multiple random external factors. Even though the detection of long track can reflect a certain periodicity of the track, track irregularity should still be regarded as an actually random process. Because track irregularities with random characteristics, it is difficult to describe by mathematical formula. In the process of its random characteristics often adopts random statistical model, autocorrelation, and power spectrum density to represent. In addition, the amplitude, wavelength, or frequency space domain to achieve a comprehensive description of track structure [12, 13]. From the view of orbit measurement, altitude and orbit orientation both are divided into left and right parts and used chord measurement method. The main work of this study is to explore the distribution law of characteristic wavelengths in the power spectrum of altitude and orbit irregularity. This way can verify the correctness of analysis about the fundamental data of orbit construction. To summarize the types of irregular digital features, this paper analyzes the peak value, mean value, mean square value, and spectral density function of data features as follows.

2.2 Analysis of Orbit Power Spectral Density Power spectral density is a function used to describe the relationship between spectral amplitude density and spatial frequency or wavelength. It reflects the distribution law and characteristics of geometric irregularity about orbit spatial frequency or wavelength. That means orbit multi-information can be obtained by the orbit power spectral spectrum curve. Some common situations of power spectral density analysis are listed as follows. First, the meaning of area characterization in a fixed wavelength range is the mean square value of the orbital power spectrum of the wavelength component. The smaller the area of this section is, the less energy the spectral density contains, which means that the smoothness of this section is better. Secondly, the peak features in the figure can be regarded as the periodic prominent performance of the orbit. There are periodic spatial frequency components in the irregularity data of the original orbit. Maglev track power spectrum analysis includes bridges, tunnels, and roadbeds, and certain in-sample data are taken for analysis. The research ideas of this paper are shown in Fig. 1.

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Fig. 1 Technical route of orbital spectrum analysis

3 Sample Sources The track irregularity data detection sample in this study comes from the maglev express line data measured by a maglev track detection vehicle in September 2021, and the detection process is divided into the up-line and down-line. For the irregularity of maglev rail transit on this line, the data of left and right height and track direction are mainly studied. The track detection process is shown in Fig. 2. In sample selection, the longer the sample length, the more representative the analysis results, but the corresponding higher requirements for data, data processing time is also longer. Power spectrum analysis was performed on the data of the whole line. The upper line was 17.6 km long, and the lower line was 18 m long. Every 400 m was used as a sample for power spectrum analysis, with 16,000 sampling points in each sample, 44 and 45 samples in the upper and lower lines, respectively. The power spectral density values of the sub-samples of each line were averaged to analyze the occurrence of valid feature points in the map. Simple data processing research on the obtained data shows that the power spectrum of each sub-sample with orbit irregularity gradually decreases to stable, with a certain degree of weak stability. Combined with the above random analysis, maglev orbit can indeed be approximated as a random stationary process. The structure of maglev train is special, that is, the low-speed maglev track has three layers: rail, sleeper, and support beam. The construction of track is similar to the ballastless track of the wheel-rail railway. In view of the maglev line construction, summed up some data information: as shown in c [12] (Table 1). Sleeper spacing: priority:1. 2 m, 1.4 m for warehouse line section. It can be seen that the orbit spectrum data with a wavelength less than 0.8 m has little influence on

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Fig. 2 Track inspection and maintenance field map

Table 1 Test maglev express line infrastructure construction Construction of track

Bridge

Track

Spacing sleeper

Steel column

Length/m

25

12.5

1.2 or 1.4

0.8

the periodicity of orbit construction. Therefore, only the image feature points with wavelength greater than 0.8 m (i.e., spatial frequency less than 1.25) are analyzed in this paper.

4 Analysis and Comparison of Orbital Power Spectrum The orbital spectrum feature recognition method based on the periodic graph method used in this report introduces the orbital power spectrum analysis, which is compared with the German spectrum (red line). Period graph method is named direct method, which is a track spectrum feature recognition method for different foundations. It is mainly used in the field of railway track to analyze the track-related characteristics of different foundations. The periodic graph method can select a variety of different window functions, the boundary conditions, and transformation details of different window functions are different, respectively, in the orbital power spectrum transformation and comparison. The detection of irregularity data is to carry out spatial sampling of the orbit, so the spatial sampling frequency is 0.025 m. The orbit spectrum is carried out by discrete spatial Fourier change. The periodic characteristics of the orbit in the spatial distribution can be obtained by spectral analysis of the spatial frequency by the window functions. According to the characteristics of maglev route in this study, the most suitable method of orbit spectrum analysis is selected to extract orbit features so that it can analyze the characteristics of orbit data.

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4.1 Longitudinal Level of Rail The orbit longitudinal level of rail data represents the level of the orbit vertically in space. The height difference of the top surface of the same rail is detected along the line direction (Figs. 3, 4). By comprehensive analysis of the two data of upper and lower lines. The average of left and right longitudinal levels of rail can be obtained that there are obvious fluctuations when the spatial frequencies are 0.08, 0.81, and 1.25 (i.e., wavelength is 12.5 m, 1.23 m, and 0.80 m). According to the construction parameters of maglev track, the track features are obvious. Comparative analysis of left and right longitudinal levels of rail power spectrum shows that the left power spectrum is more accurate in identifying the track structure, and the amplitude fluctuation is larger. Compared with the German spectrum, it can be seen that the random signal with longitudinal level of rail power at the wavelength of 0.7–15 m has better stationarity. The waveform end appears upwarp.

4.2 Track Cross-Level Track cross-level refers to the top surface of the two rails, which should be kept in the same horizontal plane in the straight section, and should satisfy the requirements of ultra-high uniformity and smoothness of the outer rail in the curved section. The purpose of track cross-level measurement is to make the two rails force evenly and ensure the smooth running of vehicles (Figs. 5, 6). By comprehensive analysis of the two data of upper and lower lines. The averaging the left and right track cross-level directions, obvious fluctuations can be obtained when the spatial frequencies are 0.80 and 1.23 (i.e., wavelength is 1.25 m and 0.81 m). From the construction parameters of maglev track, it can be seen that the track spacing features are obvious. By comparing the power spectrum of left and right orbitals, the obvious wavelength distribution of left and right orbitals are similar. The wavelength of 0.7-10 m has better stationarity, and both show a trend of continuous decline to stable fluctuation. The end shows a slight upward trend. To sum up, the three window functions of the periodic graph method can realize the feature analysis of maglev orbit. There is no difference in the overall trend of the three window functions, and all of them can effectively identify the feature points. Indirect power spectrum analysis is also attempted but this way may not be effective for the analysis of single time data due to its own random jitter. It needs multiple running data to achieve a better track feature extraction effect. The image shows that when the spatial wavelength is less than 0.5 m. The “upwarping” phenomenon exists in both the irregularity of the longitudinal level of rail and track cross-level, and the phenomenon of the longitudinal level of rail is more obvious. Structural data such as track (12.5 m) and track spacing (1.2 m and 0.8 m) are accurately identified. The bridge structure can not be well identified, because the

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(1) Up line data

Fig. 3 Irregular longitudinal level of rail-based on Rectangular, Hamming, and Blackman Windows for up-line

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(2) Down line data

Fig. 4 Irregular longitudinal level of rail-based on Rectangular, Hamming, and Blackman Windows for down-line

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(1) Up line data

Fig. 5 Irregular track cross-level based on Rectangular, Hamming, and Blackman Windows for up-line

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(2) Down line data

Fig. 6 Irregular track cross-level based on Rectangular, Hamming, and Blackman Windows for down-line

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maximum roughness wavelength that the maglev rail detection system can detect is only 20 m. When the spatial wavelength reaches a region greater than 20 m, there will be a large error in the detected data, so the power spectrum function of the fitting calculation will inevitably have errors.

5 Conclusion The spectral estimation method of periodic graph can not only reflect the amplitude related to orbit irregularity but also reflect the information related to orbital spatial frequency or wavelength. The power spectrum of maglev track is used to analyze the wavelength characteristics of checking the parameters of different infrastructural structures under certain irregularity indexes in a certain sample, such as bridges, tunnels, and roadbeds. We explore the reasons for the appearance of feature points and verify the correctness of the variation results through the track structure. The main conclusions are as follows: (1) The characteristic wavelength of power spectrum of longitudinal irregularity track is affected by track structure. The distribution of spatial wavelength is affected by periodic irregularity of track (12.5 m) and spacing of track (1.2 m or 0.8 m) contained in track irregularity feature. (2) The characteristic wavelength in the power spectrum of cross-level irregularity is also affected by the track structure. The distribution of spatial wavelength is affected by periodic irregularity of spacing of track (1.2 m or 0.8 m) contained in the track irregularity feature. (3) It can be seen from the spectrum that the fluctuation of longitudinal spectrum is larger than that of the cross-level spectrum, which reflects that the periodical fluctuation interference of longitudinal disharmony is more in the running process. The reason for this phenomenon may be that the vertical force exerted by maglev train on the track is greater than the lateral force. (4) The long-wave smoothness of the track is obviously better than that of the short-wave smoothness. According to the image, the spectrum of the high-low and low-direction irregularity appears “upwarping” in the band less than 0.5 m, which may be caused by the uneven track surface. This paper analyzes the data obtained from the maglev express track of a certain line in September 2021, and the conclusion has a certain guiding role in the analysis of maglev express track route. However, with the continuous operation of the orbit, the orbit power spectrum is constantly evolving, and the evolution process of the orbit power spectrum is affected by seasonal and maintenance work, which can be carried out as the next research work of the maglev express rail power spectrum.

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References 1. W.O. Schiehlen, Dynamics of high-speed vehicles[M] (Springer-Verlag, Wien, New York, 1982) 2. A. Hamid, K. Rasmussen, M. Baluja, et al., Analytical descriptions of track geometry variations: Volume I—Main Text and Volume II—Appendices. USA: ENSCO Inc. (1983) 3. A. Carbone, F. Palma, Considering noise orbital deviations on the evaluation of power density spectrum of oscillators. In IEEE Trans. Circuits Syst. II: Express Briefs 53(6), 438–442 (2006) 4. Z. Shubin, L. Jianhui, L. Guobin, Long-wave irregularity detection of High-speed maglev track. J. Electron. Meas. Instrum. [J] 21(01), 61–65 (2007) 5. Z. Zhouhua, Experimental design of power spectrum estimation in modern signal processing course[J]. Exp. Technol. Manag. (2016) 6. Z. Geng, L. Jie, Y. Zijing, Estimation of power spectrum density track irregularities of low-speed maglev railway lines[J]. J. Railw. 33(10), 73–78 (2011) 7. K. Xiong, L. Xiubo, L. Hongyan et al., PSD of Bal-lastless T rack irregularities of High-speed railway [J]. Sci. Sin.: Technol. 44(7), 687–696 (2014) 8. X. Lei, C. Xianmai, X. Weichang et al., Analysis on track characteristic irregularity based on wavelet and Wigner-Hough transform[J]. Tiedao Xuebao/J. China Railw. Soc. 36(5), 88–95 (2014) 9. G. Fracastoro, E. Magli, Steerable discrete fourier transform[J]. IEEE Signal Processing Letters, Signal Processing Letters, IEEE, IEEE Signal Process. Lett, 3:319 (2017) 10. C.P. Chioncel, N. Gillich, G.O. Tirian et al., Limits of the discrete fourier transform in exact identifying of the vibrations frequency[J]. Rom.Ian J. Acoust. & Vib. 12(1), 16–19 (2015) 11. L. Lin, Track random excitati on functions [J]. China Railw. Sience 1, 74–11 (1982) 12. Z. Liwen, Line quality analysis and evaluation method based on track smoothness [D].Shanghai Univ. Eng. Sci. (2020) 13. L. Shuai. Typical feature identification and evolution analysis of high-speed railway track spectrum [D].Southwest Jiaotong Univ. (2018) 14. X. Hailin, Medium and low speed maglev transportation system engineering application of maglev express line [M] (China Railw. Publ. House, Beijing, 2018)

Research on Collection and Distribution Scheme of Railway Container Hub Based on Time Value–Space–Time Network Yuxuan Dong and Qi Li

Abstract Under the condition of railway container passengerized transport, the time value factor is taken into account to optimize the container collection and distribution scheme. Based on the space–time network, the time value–space–time network is constructed. Considering the constraints of arrival period, cargo and train arrival and departure time matching, and train carrying capacity, the optimization model of container hub node collection and distribution scheme is established with the objective of minimizing the generalized cost including transportation cost and time value consumption. Longhai Line and the hubs along the line are studied as an example, and the results based on the Whale Optimization Algorithm show that the collection and distribution scheme designed in this paper can reduce the total cost by 3.02% and improve the frequency of container train operation. In addition, the time value has a significant impact on the dwell time and ridership of cargoes. Keywords Collection and distribution · Container passengerized transport · Time-value-space–time network · Whale optimization algorithm

1 Introduction In the process of railway container transportation, hub nodes play an important role in transit, and it is of great practical significance to study the optimization of the hub node’s transportation plan to improve the network transportation capacity and enhance the quality of transportation services. In the research area of the optimization of the collection and distribution scheme, Liu [1] optimized the system of the China Railway Express (Chengdu), constructed a model with the minimum cost of the collection and distribution scheme, and Y. Dong School of Traffic and Transportation, Beijing Jiaotong University, Beijing, China Q. Li (B) China Railway Design Co., Ltd., Tianjing, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_26

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conducted simulation experiments under different transportation time constraints. Hao [2] constructed an inland container collection and distribution optimization model with the objective of the minimum total cost and designed a dynamic programming algorithm to solve it. Space–time network is an important method to deal with time-optimized objectives or time constraints, and many scholars now combine the space–time network with other dimensions to construct a multidimensional network to enhance its applicability. SteadieSeif [3] established a transport mode–time–space three-dimensional network for the transportation planning problem of perishable products under multiple transport modes. Xia [4] studied the high-speed railway fare optimization problem and constructed a price–time–space network to transform it into a multicommodity flow problem with space–time resource constraints. Gao [5] constructed a time–station–track expansion network for the adjustment of the high-speed railway train operating diagram under the condition of running extra trains. Many achievements have been made to study container transport with the time value of goods. Zhang [6] established a China Railway Express service network model with the lowest comprehensive cost based on the time value of goods and obtained the service network of different time value cargoes under different transportation situations by genetic algorithm. As a new transport organization mode, container passengerized transport is regarded as the future development direction of railway container transport [7]. Therefore, this study is carried out under the condition of container passengerized transport. Due to the differences in cargo categories and transportation demands, the key to the collection and distribution scheme is to consider the impact of the time value of cargoes on its transportation plan. Therefore, the optimization of the collection and distribution scheme in this paper can be considered as the sequential occupation of the space and time resources of the train by containers.

2 Time Value–Time–Space Network 2.1 Network Description The physical network can only describe the displacement of cargoes in space, while the space–time network reflects the spatial displacement and time consumption in the transportation process. The time value of cargoes can be regarded as the value lost due to the time spent in the transportation process [8], so the change in time value is related to the consumption of time. In order to reflect the influence of economic characteristics of cargo on the choice of transportation scheme, a time value–space– time is constructed.

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Table 1 Sets and parameters of the network Serial number

Sets and parameters

Meaning

1

Q

Container cargo, q ∈ Q

2

K

Passengerized train, k ∈ K

3

Station, i ∈ I

4

I   0, T

  Decision cycle, t ∈ 0, T

5

C

Time value

6

A

Network arc, a ∈ A

7

i O /i D

Virtual origin/destination point

8

i qO /i qD

Cargo origin/destination point

9

wq

Number of containers of cargo q, FEU

10

tqi,ar /tqi,de

Arrival/departure moment of cargo q at station i

11

tki,ar /tki,de

Arrival/departure moment of passengerized train k at station i

12

cq

Time value of cargo q, yuan/(FEU*h)

13

tl

Container loading and unloading time, h/FEU

2.2 Sets and Parameters The sets and parameters associated with the construction of the multidimensional network are shown in Table 1.

2.3 Network Structure The construction process of the time value–time–space network is as follows: ➀ The cargo q is located at the virtual origination point, whose initial state is i 0 = i O , t0 = 0, c0 = 0. i O ,ar

➁ Add virtual departure arc (i O , i qO , 0, tqq , 0, 0) ∈ Avd . The virtual origin arc is the arc that connects the virtual origin point to the real origin station. ➂ Add transport arc (i 1 , i 2 , t1 , t2 , c1 , c2 ) ∈ At . The transport arc describes the change in the space–time–time value of cargoes as they are transported between two nodes. The parameters are as follows:     i O ,ar i O ,ar , c2 = cq t2 − tqq t1 = tki1 ,de , t2 = tki2 ,ar , c1 = cq t1 − tqq

(1)

➃ Add loading/unloading arc (i 1 , i 1 , t1 , t2 , c1 , c2 ) ∈ Al . The loading and unloading arcs describe the change of the space–time–time value of cargoes during loading and unloading operations. The parameters are as follows:

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For unloading operations:     i O ,ar i O ,ar , c2 = cq t2 − tqq (2) t1 = tki1 ,ar , t2 = tki1 ,ar + wq tl , c1 = cq t1 − tqq For loading operations:     i O ,ar i O ,ar , c2 = cq t2 − tqq (3) t1 = tki1 ,de − wq tl , t2 = tki1 ,de , c1 = cq t1 − tqq ➄ Add waiting arc (i 1 , i 1 , t1 , t2 , c1 , c2 ) ∈ Aw . The waiting arc describes the change in the space–time–time value of cargoes as they wait to be transported. The parameters are as follows:  t1 =

i O ,ar tqq ,

t1 = i1 = tki1 ,ar + wq · tl , i 1 =

i qO i qO

,

  i O ,ar t2 = tki1 ,de − wq tl , c1 = cq t1 − tqq ,   i qO ,ar c2 = cq t2 − tq (4)

i D ,de

➅ Add virtual arrival arc (i qD , i D , tkq , T , c1 , c1 ) ∈ Ava . The virtual arrival arc is the arc that connects the actual destination point to the virtual destination point. The time value–time–space network is shown in Fig. 1, which reflects the transportation process of two batches of container cargo under multidimensional network conditions.

Fig. 1 Time value–time–space network

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3 Optimization Model of Railway Container Hub Collection and Distribution Scheme 3.1 Model Assumptions The assumptions of optimization model are as follows: ➀ It is assumed that the containers transported are all 40 ft standard containers. ➁ Loading and unloading capacity of container stations is sufficient. ➂ Railway container passengerized transport runs in strict accordance with the schedule. ➃ The container flow follows the principle of indivisibility.

3.2 Sets, Parameters, and Variables The parameters related to the construction of the network are not repeated here, and the remaining sets, parameters, and variables are shown in Table 2. Table 2 Sets, parameters, and variables of the optimization model Serial number

Sets, parameters, and variables

1

Ai+ / Ai−

Network arc with station i as origin/destination point

2

M

Train types, m ∈ M, m = 1 stands for first-level train; m = 2 stands for second-level train; m = 3 stands for general rail delivery

3

ckt m

Transportation cost of a container through train km on the transport arc, yuan/FEU

4

cl

Loading and unloading cost of a container, yuan/FEU

5

cw

Storage cost of a container at station, yuan/(FEU*h)

Meaning

6

vkm

Average speed of the train km , km/h

7

ψki m

Capacity of train km at the station i, FEU

8

τqmax

Maximum dwell time of cargo q, h

9

dq

Cargo destination

10

dkm

Train destination

11

Tqmax

Arrival period of the cargo, h

12

xqa yqi,km

Binary variable denotes whether the cargo q passes through the arc a

13

Binary variable denotes whether the cargo q pass takes the train km at the station i

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3.3 Model Construction The objective function (5) is to minimize the total economic cost of containers, including transport costs, transit costs, and storage costs: min F1 =

   q∈Q

ckt m

·

a∈At

xqa

+



c · l

xqa

+



w

c · (t2 − t1 ) ·

xqa

· wq

(5)

a∈Aw

a∈Al

The objective function (6) is to minimize the change in the time value of the containers: ⎞ ⎛ i D ,de   tkqm ⎝ O cqt dt ⎠ xqa wq min F2 = (6) i ,ar q

q∈Q a∈A

tq

To improve the solving efficiency of the model, this paper transforms the dualobjective function with linear weighting into a single-objective, denote {α, β} as the weight coefficients of function (5) and function (6), thus the formula for the generalized cost is as follows: min F =



(α · F1 + β · F2 )

(7)

q∈Q

s.t. ⎧ ⎪ ⎨ 1 i is the origin point a a xq − xq = 0 else ⎪ ⎩ a∈Ai+ a∈Ai− −1 i is the destination point  wq yqkm ≤ ψki m ∀i ∈ I, km ∈ K 



∀q ∈ Q

(8)

(9)

q∈Q

  wq tl xqa ≤ tki,de − tqi,ar yqkm m dq yqi,km = dkm 

∀q ∈ Q, ∀km ∈ K M , ∀a ∈ Al ∀q ∈ Q, ∀km ∈ K M

(t2 − t1 )xqa ≤ τqmax

∀q ∈ Q, i ∈ I

(10) (11) (12)

a∈Al ∪a w



(t2 − t1 ) xqa ≤ Tqmax

∀q ∈ Q

(13)

a∈A

xqa ∈ {0, 1}

∀q ∈ Q, ∀a ∈ A

(14)

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yqi,km ∈ {0, 1}

∀q ∈ Q, ∀km ∈ K M

309

(15)

Constraint (8) ensures flow balance on every vertex in multidimensional network. Constraint (9) ensures cargoes do not exceed the available capacity when selecting a train. Constraint (10) means that the loading and unloading time of cargoes shall not exceed the waiting time. Constraint (11) means the cargoes should travel in the same direction. Constraint (12) ensures the dwell time of the cargoes at the station shall not exceed the maximum dwell time. Constraint (13) ensures the whole transportation time of the cargoes shall not exceed the arrival period. Constraints (14) and (15) define that the decision variables are binary.

4 Whale Optimization Algorithm Through the introduction of virtual origin and virtual destination, different container flows have the same multidimensional network size, so the dimensions of the solution space are consistent, to take advantage of this feature, this paper uses the whale optimization algorithm (WOA) to solve. In this algorithm, a solution can be represented by a whale individual, so the process of using WOA to search for the solution to the problem can be seen as that several whale individuals constantly update their positions until a satisfactory solution is found, which includes three stages: surrounding prey, foaming net attack, and searching target. The following are the WOA steps: (1) Initialize parameters and position values of each dimension, and record their current positions as initial solutions. (2) Calculate the objective value (individual fitness value) of each individual in the population, the objective function of this paper is to minimize the generalized cost, if there is an individual better than the current optimal solution, then it will be set as the optimal solution. (3) The individual positions are updated and the fitness value of the solved objective function is calculated for each individual, and compared with the current optimal solution. (4) If the termination condition is reached, the iteration is stopped and the current optimal solution is output; otherwise, the iteration continues.

5 Case Study In order to verify the validity of the network and the optimization model, this section designs the road network structure as shown in Fig. 2 with the background of Longhai Line, and chooses Lanzhou, Xi’an, Zhengzhou, and Lianyungang as the hub nodes for the case study.

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Lanzhou Zhengzhou Xi'an Baoji

Shangqiu Luoyang

Lianyungang Xuzhou

Fig. 2 The road network used in the example

5.1 Example Analysis It is assumed that since 0:00, 28 batches of cargoes with different time values have arrived at each station in succession. High-value time-sensitive cargoes are recorded as Category 1, high-value time-insensitive cargoes are recorded as Category 2, low-value time-sensitive cargoes are recorded as Category 3, and low-value time-insensitive goods are recorded as Category 4. The category, volume, origin and destination points, and arrival time are shown in Table 3. Referring to the data in the Literature 8, the attribute information of cargoes with different categories can be obtained as shown in Table 4. In order to improve the service quality of container transportation, two different levels of container passenger trains and general rail delivery are designed to operate on the Longhai Line. The stop plan, average speed, and transportation cost of different levels of trains are shown in Table 5. The operation of container passengerized trains along the Longhai Line is shown in Table 6. The direction of upward is recorded as 1, and the direction of downward is recorded as 2. Other relevant parameters are shown in Table 7.

5.2 Example Solution The example data and parameters are substituted into the model, and the WOA is run in Python on a laptop with Windows 10 and Intel Core i7-10750H @2.60 GHz, and the number of iterations is taken as 200 after several pre-experiments. The collection and distribution scheme for each batch of cargoes is shown in Table 8, and the graph of the fitness function is shown in Fig. 3. The total time of this collection and distribution scheme is 445.34 h, and the generalized cost is 1.5618 million yuan, which can reduce the generalized cost by 3.02% compared with the scheme of transportation according to the order of arrival.

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Table 3 Cargoes information Batch

Category

Volume/FEU

Origin point

Destination point

Arrival time

1

4

18

Lianyungang

Lanzhou

0:17

2

3

32

Xi’an

Lianyungang

2:25

3

4

18

Lanzhou

Xi’an

4:18

4

2

31

Lianyungang

Baoji

5:05

5

1

27

Lanzhou

Lianyungang

7:15

6

2

36

Lianyungang

Zhengzhou

8:10

7

2

23

Zhengzhou

Lianyungang

9:21

8

3

20

Zhengzhou

Lanzhou

9:30

9

4

20

Baoji

Lianyungang

10:00

10

4

22

Lianyungang

Lanzhou

10:25

11

1

35

Xi’an

Zhengzhou

10:42

12

3

38

Lanzhou

Xuzhou

11:25

13

1

25

Shangqiu

Lanzhou

12:20

14

4

29

Zhengzhou

Xuzhou

13:06

15

2

16

Luoyang

Xuzhou

13:23

16

3

29

Xi’an

Baoji

13:58

17

2

30

Xi’an

Shangqiu

14:40

18

3

35

Lanzhou

Luoyang

15:18

19

1

14

Zhengzhou

Lianyungang

15:36

20

1

16

Zhengzhou

Xi’an

15:50

21

2

21

Zhengzhou

Baoji

16:40

22

3

12

Xi’an

Lanzhou

17:22

23

4

19

Lianyungang

Lanzhou

17:51

24

1

28

Lianyungang

Xi’an

18:27

25

2

27

Luoyang

Lanzhou

19:10

26

1

43

Zhengzhou

Baoji

20:21

27

3

27

Xi’an

Lianyungang

21:08

28

1

21

Lanzhou

Zhengzhou

22:40

Table 4 Attribute information of cargoes with different categories Category

Category 1

Category 2

Category 3

Category 4

Time value (yuan/(FEU*h))

346.46

143.21

41.17

7.38

Arrival period (h)

24

42

36

48

Maximum dwell time (h)

8

16

12

24

Weight coefficients

{0.2, 0.8}

{0.6, 0.4}

{0.4, 0.6}

{0.8, 0.2}

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Table 5 Attribute information of trains with different levels Train level

Stop plan

Average speed (km/h) Transportation cost (yuan/ FEU)

First level train

Stop at hubs

100

2000

Second level train

Stop at every station

75

1500

General rail delivery Operation on demand 50

1000

Table 6 The operation of container passengerized trains Number

Train level

Origin point

Origin time

Direction

1

First level

Lanzhou

8:30

1

2

First level

Xi’an

12:00

1

3

First level

Lanzhou

23:30

1

4

First level

Lianyungang

9:30

2

5

First level

Lianyungang

11:15

2

6

First level

Lianyungang

19:30

2

7

Second level

Xi’an

7:30

1

8

Second level

Lanzhou

12:45

1

9

Second level

Xi’an

16:00

1

10

Second level

Lanzhou

16:30

1

11

Second level

Lianyungang

6:15

2

12

Second level

Zhengzhou

10:15

2

13

Second level

Zhengzhou

17:30

2

14

Second level

Zhengzhou

22:00

2

Table 7 Parameters value table Parameters

Value

Stopping time with loading and unloading operations (h)

1.5

Stopping time without loading and unloading operations (h)

1/6

Container loading and unloading time (h/FEU)

1/30

Loading and unloading cost (yuan/FEU)

100

Storage cost (yuan/FEU*h)

20

Maximum train capacity (FEU)

50

5.3 Analysis of Collection and Distribution Scheme Due to the influence of cargo time value, train capacity, train and cargo arrival, and departure time matching, the collection and distribution scheme does not follow the principle of “first come, first served”, but gives priority to cargoes with higher time

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Table 8 The collection and distribution scheme Number

Generalized cost (yuan)

Train selection

Number

Generalized cost (yuan)

Train selection

1

23,871.58

11

15

22,160.76

7

2

42,018.94

7

16

24,784.65

12

3

23,528.05

10

17

44,472.90

9

4

62,257.21

11

18

33,380.04

10

5

165,500.80

1

19

38,474.96

2

6

59,218.15

4

20

31,864.68

4

7

54,566.47

1

21

34,138.44

13

8

22,853.37

12

22

13,755.66

4

9

43,790.40

General rail delivery + 9

23

32,497.15

6

10

66,036.68

5 + 14

24

102,715.50

6

11

76,979.65

2

25

51,161.62

13

12

42,746.21

8

26

146,052.30

14

General rail delivery + 5

27

37,773.17

3

10

28

91,587.91

3

13 14

139,186.2 38,249.17

Fig. 3 Whale optimization algorithm fitness function diagram

value and stronger time sensitivity. For example, for Cargo 3 and Cargo 5 with the same destination, Cargo 5 arrives later than Cargo 3, but because it is a high-value time-sensitive cargo, it is transported on Train 1 before Cargo 3. If the current mode of transportation is used, high-value time-sensitive goods such as Cargos 11 and 24 cannot be transported on the same day. Through this

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Table 9 The average dwell time and ridership of cargoes Category Average dwell time (h) First level train (%)

Category 1

Category 2

Category 3

Category 4

1.41

2.87

4.05

7.59

87.50

28.57

28.57

16.67

collection and distribution scheme, all cargoes are transported on the same day, which guarantees the arrival period of the cargoes. Due to the influence of time value, cargoes with different categories have different space–time distributions, the average dwell time and ridership of cargoes are shown in Table 9. The average dwell time increases with the decrease in time value, the proportion of Category 1 cargoes taking first-level trains is significantly higher than that of other categories. The results indicate that high-time value cargoes reduce the generalized cost by reducing the dwell time and taking high-level trains, and low-time value cargoes tend to reduce generalized costs by taking low-level trains and creating transportation conditions for other cargoes by extending the dwell time.

6 Conclusion Based on the construction of a time value–space–time network, considering the constraints of carrying capacity, operation time, transportation direction, and arrival period, the optimization model of container hub collection and distribution scheme with the goal of minimizing the generalized cost is constructed and solved by the whale optimization algorithm. The container collection and distribution scheme designed in this paper reduces the generalized cost and ensures that each batch of cargo can be delivered to the destination station within the arrival period, which improves the economy and timeliness of container transportation. In future studies, the collection and distribution scheme in case of uncertainty of cargo arrival time or train delay will be studied.

References 1. L.L. Liu, Y.Y. Tang, S. Chen, Optimization and simulation of container collection and distribution system of rongou+ in China. J. Transp. Eng. Inf. 18(03), 19–31 (2020) 2. C.L. Hao, Y.X. Yue, Optimization on combination of transport routes and modes on dynamic programming for a container multimodal transport system. Procedia Eng. 137, 382–390 (2016) 3. M. Steadieseifi, N.P. Dellaert, W. Nuijten, V.T. Woensel, A metaheuristic for the multimodal network flow problem with product quality preservation and empty repositioning. Transp. Res. Part B 106, 321–344 (2017) 4. Y. Xia, H.X. Wang, Y. Zhou, Z.W. An, Y.G. Wei, Optimization of ticket pricing for high-speed railway based on price-space-time network. J. China Railway Soc. 44(07), 11–20 (2022)

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5. R.H. Gao, H.M. Niu, Y.X. Jiang, Train timetable rescheduling based on a time-station-track multi-dimensional network under condition of running extra trains for high-speed railway. J. China Railway Soc. 42(05), 1–8 (2020) 6. Q. Zhang, H. Jiang, Y.G. Wei, M.J. Ling, H. Yang, Service network design of CHINA RAILWAY express based on time values of goods. J. China Railway Soc. 42(06), 12–17 (2020) 7. Y.G. Wei, Y. Su, C. Zhang, H. Yang, Q. Zhang, Innovation of rapid railway container passenger transportation system in China. China Railway 04, 1–7 (2016) 8. M.J. Ling, Integrated Optimization of International Container Transport Organization Based on CR Express (Beijing Jiaotong University, Beijing, 2020)

Thermal Simulation of I/O Subsystem of an All-Electronic Computer Interlocking Based on Finite Element Analysis Chao Sun, Zhiyu Xie, Biao Lv, and Yuxiang Kang

Abstract In this paper, the thermal simulation analysis of the I/O subsystem of an all-electronic computer interlocking (AECI) is carried out, and the finite element analysis software ANSYS Icepak is used to simulate and verify the temperature of the case in natural convection. The thermal simulation model was constructed by building the 3D structural model of each part, setting the parameters of key components, PCB board wiring, and hole passing information. According to the operating conditions of the case, set the corresponding solution parameters to build a natural convection model. The simulation results show that, first, the high-temperature area is mainly concentrated above the case, where a large number of chips with high heat consumption are concentrated, adjusting PCB layout can be a reasonable way to disperse the devices to solve the concentrating heat. Secondly, the temperature of the main heating area in the case is about 70 °C, which meets the normal working requirements of the device, for those individual components with too high temperature (>120 °C), the radiator or cooling fan can be considered. Keywords Rail traffic · Thermal simulation · I/O subsystem · All-electronic computer interlocking

1 Introduction Computer interlocking system is the core component of rail signal control system. The AECI is a new generation of interlocking equipment for railway signal control, which replaces the traditional electrical centralized interlocking system. China’s

C. Sun CRSC Research & Design Institute Group Co., Ltd, Beijing, China Z. Xie · B. Lv (B) · Y. Kang School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_27

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mainstream computer interlocking system research and development units are vigorously developing AECI. Reliability is the core index to measure the stability of computer interlocking system [1, 2]. Reliability simulation [3] is an important link in the research and development of computer interlocking system. In this paper, through the thermal simulation analysis [4] of an I/O case of AECI, the weak links of each board are located, and the devices with high temperature are found, which provides the basis for the subsequent reasonable distribution of the power and device layout of each board. In addition, the thermal simulation output is used as the input of the product performance margin model. Then based on the performance margin model, it can lay a foundation for subsequent reliability design, analysis, growth, management, and other work.

2 Simulation Model 2.1 CAD Import The import of CAD model can accurately reflect the structure and components of the case. The connection and fixing method of various components and the distribution of heat dissipation holes in the chassis shell will have an impact on the experimental results. The research prototype is an I/O case, whose overall dimension is 430 mm × 322 mm × 260 mm, which is mainly composed of chassis, cover plate, circuit board, and various components including heat source. Use SC (Space Claim) to model the whole case, and 3D model is shown in Fig. 1. The material of the chassis is aluminum alloy. In thermal simulation software, the material is set as “Aluminum6061-T651”, of which the thermal conductivity is 167 W/(m °C). For the overall connection method and fixing method of the case, without changing the precursor of the constraint fixing method and position, a reasonable simplification is required to simplify the model, reduce the difficulty of mesh division, and speed upper cover plate

Fig. 1 CAD model of I/O case

circuit board fixed buckle

chassis

side cover plate

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319

up the solution. Based on this, the simplification of the model mainly involves the heat dissipation holes, small bolts and fixing methods of the chassis, the detailed structure of connectors and fixed buckles, structures such as grooves and gaps, and the chamfering of the chassis and PCB board. The CAD body is transformed by using Level 0, Level 1, Level 2, and Level 3, four different transformation levels [5]. The simplified model is then imported into ANSYS Icepak.

2.2 ECAD Import The main purpose of importing the ECAD model is to calculate the power of each heat source in the case and the thermal conductivity of each part on the PCB board. Import the IDF file of the PCB output by the ECAD software (including the size, material, power dissipation, and other information of each device on the PCB) into ANSYS Icepak. Because the IDF file contains many models, such as resistors, capacitors, and other devices, for the sake of simulation speed, delete the devices with small size and low power dissipation, and keep only the devices with high power dissipation. The material of components on PCB should be determined according to the component manual. The material types of components in this experiment mainly include copper, polyimide, and porcelain, and the thermal conductivities of the three are 400, 0.35 and 5 W/(m °C). PCBs are complex structures primarily made of layers of copper and a dielectric material, depending on the location of the copper layer and the layout of the vias, the entire PCB will exhibit anisotropic thermal conductivity in a local area. Import the PCB wiring via information designed by ECAD to correctly reflect the thermal conductivity.

2.3 Combining CAD and ECAD Based on the case model imported from CAD, combined with the PCB model imported from ECAD. Because the coordinate system and coordinate origin of CAD software and ECAD software are inconsistent. Therefore, it is necessary to use the CAD-imported circuit board as the benchmark, use the move (rotation), and surface (line, point) alignment tools to align and adjust the ECAD-imported PCB, and then delete the circuit board model created by the CAD import. The thermal simulation model of the I/O case is established, as shown in Fig. 2 (Figs. 3, 4 and 5).

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Fig. 2 Thermal simulation model

Fig. 3 Original upper cover plate

3 Thermal Simulation Parameters According to the design manual of the product and the analysis of the operating environment, the operating environment temperature of the I/O case is 20 °C. During the thermal steady-state simulation process, the product is simulated at room temperature. The main heat sources inside the case are two IC-PCBs, eight IN-PCBs, and eight OUT-PCBs. Each PCB board contains different components, and the main heating devices are FPGA, DSP, DC-DC [6], etc. According to Table 1, the total power of the case can be calculated as P = 220 W.

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Fig. 4 Simplified upper cover plate

Fig. 5 PCB model

Table 1 PCB parameters

PCB

Power (W)

Volume (mm3 )

Number

IC-PCB

22

220 × 233 × 14

2

IN-PCB

11

220 × 233 × 16

8

OUT-PCB

11

220 × 233 × 15

8

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The case should be placed in the cabinet in actual use, and the heat dissipation method adopts natural convection and radiation heat dissipation [7, 8], and there is no boundary condition of forced convection in the model. In this way, the heat dissipation area of the case is the area of the upper and lower cover plates. Heat dissipation area: S = 2 × (430 × 322) = 2769.2 cm2 Surface heat flux: ϕ = P/S = 220/2769.2 = 7.94 × 102 W/cm2 The maximum temperature for the normal operation of the case is 75 °C. Combined with the operating ambient temperature, the increase in the internal temperature of the case should be controlled below 55 °C. According to the allowable temperature rise and heat flux of the equipment, the case can adopt natural convection or forced convection. When calculating natural convection in ANSYS Icepak, it is necessary to set the corresponding calculation area. It must be specified large enough to make the gradients of various variables in the far field small enough to ensure the accuracy of natural convection simulation calculations. The volume of the calculation area in this experiment is 1 m × 0.9 m × 1.8 m. The detailed steps for setting thermal simulation parameters are as follows: (1) Set the material of each component in the case and PCB board, and determine the thermal conductivity of each part. (2) According to the circuit diagram and each component manual, set the power of each component on the PCB. (3) Specify settings for radiation heat transfer, choose a reasonable flow regime (Turbulent), use the zero equation model to ensure the accuracy of the electron heat dissipation calculation, and consider a reasonable gravity direction. (4) Set the ambient temperature to 20 °C, and the radiation heat transfer temperature (usually the same as the ambient temperature). (5) Mesh the model, check the integrity of the mesh, and solve it.

4 Thermal Simulation Results 4.1 Case Simulation Results According to the initial conditions, the temperature distribution when the case reaches a thermal steady state at an ambient temperature of 20 °C is obtained, as shown in Fig. 6; the velocity vector is shown in Fig. 7; the particle trace diagram is shown in Fig. 8. Figure 6 shows that the maximum temperature of the case is 184 °C and the minimum temperature is 20 °C. From the overall temperature map of the case, it can be concluded that the main heating area of the case is concentrated in the upper front area because this area concentrates the chips with high heat consumption, which is the main heating area of the case. In the lower part of the machine case, the PCB board is mainly welded with capacitor, inductor, voltage regulator diode, and other

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Fig. 6 Case temperature distribution

Fig. 7 Velocity vector diagram

devices with low heat consumption, so the temperature is low. The outer chassis structure itself does not generate heat, and it is exposed to the air environment for a long time, so the lowest temperature appears in the case shell, which also confirms the correctness of the simulation from the side.

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Fig. 8 Case temperature distribution

As can be seen from Figs. 7 and 8, due to the large number of heat dissipation holes in the upper and lower cover of the case, cold air (20 °C) enters the lower cover plate through the air duct between PCB boards and flows out of the upper cover plate (37 °C). When passing through the air duct, heat is taken away to achieve the purpose of heat dissipation.

4.2 PCB Simulation Results As shown in Fig. 9, the device with the highest temperature in IN-PCB is the synchronous step-down converter (U2, U5), the temperature of both is between 100 and 130 °C, and the heat generation is more serious. The area where the temperature is concentrated is the fast recovery rectifier (D2, D3) side by side in the upper right corner. The temperature of the FPGA (U13, U17) is about 55 °C, which has a large design margin. As shown in Fig. 10, the devices with the highest temperature in OUT-PCB are still the synchronous step-down converter (U2, U5) and the fast recovery rectifier (D2, D3). The main heating source of OUT-PCB is FPGA and DC-DC. The temperature of FPGA (U15, U19) is about 60°C, which has a large design margin. As shown in Fig. 11, the fast recovery rectifier (D47, D48), FPGA (U120), and a large number of digital isolators are concentrated at the top right of IC-PCB, resulting in serious heating at the top right of IC-PCB. The device with the highest temperature in IC-PCB is the synchronous step-down converter (U114, U116), and the temperature is about 180 °C. Compared with IN-PCB and OUT-PCB, IC-PCB

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Fig. 9 IN-PCB temperature distribution

Fig. 10 OUT-PCB temperature distribution

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U120 D47 D48

U114

digital isolators U116

Fig. 11 IC-PCB temperature distribution

contains four FPGAs and three DC-DCs, as well as Ethernet transceiver chips and microcontroller chips with high heat consumption, so the overall temperature of IC-PCB is the highest.

5 Conclusions and Improvements According to the above thermal simulation experiments, the following conclusions can be drawn: (1) For the development and design of AECI, Icepak can be used to analyze the heat generation of various components in the case at low cost and visually. In response to the problems exposed by the simulation, the research department can improve the design, thereby reducing the cost and improving the reliability and get-right-first-time rate of product. The simulation results show that the high-temperature area is mainly concentrated on the top of the case because the chips with high heat consumption are concentrated in this area. The upper and lower cover plates of the case are designed with heat dissipation holes, so the heat dissipation performance is good, but the performance at the side position is poor.

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(2) In this thermal simulation experiment, the thermal model was constructed in detail. The CAD model retained the original connection mode and structure of the case. The ECAD model calculated the power consumption of each component. The PCB introduces the copper layer and the position of the via hole to accurately reflect its thermal conductivity. Based on the above conditions, the temperature distribution of each component can be calculated more accurately. In the area where the heat-generating components are dense, the temperature of the PCB board is mostly about 70 °C. For core main devices such as FPGA, microcontroller chips, etc., the temperature is 60–80 °C, which meets the normal working requirements of the device. However, there are some components with high temperature, the main reason is that such components (synchronous stepdown converter, fast recovery rectifier) are located on the main circuit, the input current is too large, and the volume is small, and the heat dissipation capacity is poor. Based on the above results and conclusions, the following improvement measures are proposed: (1) Reasonably arrange the location of components. The devices with higher heat generation can be distributed in a dispersive manner if the conditions permit. (2) Configure the case heat dissipation holes properly. The heat dissipation hole can be appropriately added to the side cover plate. (3) Heat sinks can be added if conditions permit. The installation of the radiator is low in difficulty, low in cost, and does not need to change the original arrangement.

References 1. X.L. Wang, Research on running model of simulation train in CTC system. Railway Signal. Commun. Eng. 10, 24–27 (2020) 2. F. Ye, Design of multi-dimensional reliability simulation of hardware products. Railway Signal. Commun. Eng. 11, 24–29 (2021) 3. Y.Q. Tang, D.J. Liu, H.Y. Yang, P. Yang, Thermal effects on LED lamp with different thermal interface materials. IEEE Trans. Electron Dev. 63, 4819–4824 (2016) 4. Y.J. Zhao, L.A. Chen, R. Qiao, Temperature field simulation and structure improvement of 12kV switchgear. J. Phys.: Conf. Ser. 2179, 012010 (2022) 5. M.H. Chen, Y. Zhou, S.J. Ma, N. Ma, Analysis of heat dissipation of electronic chassis based on Icepak. Video Eng. 45, 132–135 (2021) 6. Y.S. Fan, D.J. Liu, X.Y. Wang, H.J. Wang, Y.C. Wu, D.G. Yang, Thermal performance analysis for multiple heat source power devices, in 2019 20th International Conference on Electronic Packaging Technology (ICEPT) (Hong Kong, 2019), pp. 1–5 7. H.Z. Yu, M.X. Xu, H.X. Liu, Design and research on environmental heat control of pod based on Icepak. Laser & Infrared 52, 1017–1021 (2022) 8. L.N. Li, J. Lin, Simulation analysis of thermal runaway of sealed chassis based on ANSYS icepak. Electro-Optic Technol. Appl. 27, 75–79 (2012)

Research and Optimisation of the Coupling Performance of Pantograph–Catenary System Based on Numerical Simulation and Experimental Tests Wenzhi Xu, Tiehui Wu, Jingshen Wu, Decai Qin, and Yue Li

Abstract In this paper, the coupling performance of the rigid pantograph-catenary system is studied and optimised by means of numerical simulations and experimental tests in parallel, taking the rigid pantograph–catenary system of Tianjin Metro Line 6 as an example. The performance of the pantograph–catenary coupling is evaluated quantitatively in the time and frequency domains using the approximate entropy and EMD-HHT methods. The research process starts with the establishment of pantograph lumped mass model, pantograph physical model and rigid catenary physical model. The collision function algorithm in ADMAS software is used to establish the pantograph–catenary coupling relationship, and the dynamic contact force values of the pantograph––catenary are simulated. Combined with the numerical simulation and experimental test data, the performance of the pantograph–catenary coupling under different pantograph head stiffness, pantograph head mass, pantograph static contact force and train operating conditions is analysed. By adjusting the train operating conditions and pantograph parameters, the objective of optimising the pantograph–catenary coupling performance can be achieved, and the wear rate of carbon-based contact strips can be reduced by more than 25%. Keywords Urban rail transit · Pantograph–catenary system · Approximate entropy · EMD-HHT

1 Introduction In urban rail systems, trains obtain electrical energy through the pantograph–catenary system to make their traction and auxiliary power supply systems work. The coupling performance of the pantograph–catenary system directly affects the quality of power W. Xu (B) · T. Wu · J. Wu · D. Qin · Y. Li Tianjin Rail Transit Operation Group Co., Ltd., Tianjin, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 S. Yadav et al. (eds.), Proceedings of the International Conference on Information Control, Electrical Engineering and Rail Transit, Lecture Notes in Electrical Engineering 1084, https://doi.org/10.1007/978-981-99-6431-4_28

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supply to the trains [1]. Due to the limitation of installation space in the tunnels of urban rail transit systems and the shortcomings of flexible catenary which are prone to breakage accidents, the number of applications for rigid catenary in urban rail transit systems has proliferated in recent years, while relatively little research has been carried out on the coupling performance of pantograph–catenary under rigid contact networks. The stiff structure of the rigid catenary causes a dramatic deterioration of the pantograph–catenary coupling performance under conditions such as unsmooth contact lines, hard points and deteriorating wheel–rail relationships, which can extremely easily lead to abnormal wear events and fracture of components, seriously threatening the safe operation of urban rail transit systems. Simulation of the pantograph system provides technical support for the research of the pantograph–catenary coupling performance and the application of this method can quickly investigate the connection between the variation of the parameters of the pantograph–catenary system and the pantograph–catenary coupling performance from a theoretical perspective. For pantograph system modelling, a lumped mass model [2] is generally used, which can effectively reflect the pantograph vertical dynamics. As research develops, pantograph rigid body models and pantograph rigid–flexible coupled models [3] have also been used to reflect pantograph dynamics more realistically, but they may also decrease simulation efficiency to a certain extent. The dynamic contact response between the pantograph–catenary systems is a direct reflection of the pantograph–catenary coupling performance. In order to understand the dynamic variation of the pantograph–catenary contact forces over time, MATLAB [4] software and a combination of algorithms such as Dirac functions [5] and penalty functions [6] can be used to solve the dynamic pantograph–catenary contact forces. On the other hand, with the advancement of experimental testing techniques for the operational status of the pantograph–catenary system, how to effectively process a large amount of pantograph–catenary system data and systematically evaluate the coupling status of the pantograph–catenary system has become a new subject of pantograph–catenary system research. Wu et al. [7] investigated the maximum operating speed limiting pantograph–catenary systems by normalising the data and observing the maximum and minimum pantograph–catenary contact forces. Van et al. [8] investigated the influence of train speed on pantograph–catenary coupling performance by means of numerical statistics, difference spectra, band analysis and frequency coherence functions. In addition to this, machine learning [9] and deep neural network techniques are also used to process the pantograph–catenary contact response signal for the purpose of detecting defects in the pantograph–catenary system. This study is based on the abnormal wear problem of the pantograph– catenary of Tianjin Metro Line 6. The pantograph–catenary experimental data is measured by force sensors installed at the four pivot points of the carbon-based contact strips at the front and rear of the TSG18 pantograph. In order to minimise the influence of strong electromagnetic interference from the vicinity of the contact wire, a fibre optic sensor with a strong immunity to electromagnetic interference was selected to obtain the data with a sampling period of 2500 Hz.

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Fig. 1 Modelling of the TSG18-G pantograph

2 Pantograph–Catenary Modelling 2.1 Pantograph Modelling This research takes the TSG18-G pantograph as an example. This model pantograph is an articulated mechanical member that controls the raising and lowering of the bow action through the air circuit. In this study, a 1:1 solid modelling and assembly of the pantograph is carried out using SOLIDWORKS software. At the same time, in order to improve the simulation efficiency, this paper completes the modelling and parameter determination of the pantograph mass point system through the shaker vibration test method, the model is shown in Fig. 1. The equation of motion of the pantograph lumped model can be expressed as m 1 y¨1 + c1 ( y˙1 − y˙2 ) + k1 (y1 − y2 ) = −Fc

(1)

m 2 y¨2 + c1 ( y˙2 − y˙1 ) + c2 ( y˙2 − y˙3 ) + k1 (y2 − y1 ) + k2 (y2 − y3 ) = 0

(2)

m 3 y¨3 (t) + c2 ( y˙3 (t) − y˙2 (t)) + c3 y˙3 (t) + k2 (y3 (t) − y2 (t)) + k3 y3 (t) = F0

(3)

where Fc represents the dynamic contact force of the pantograph–catenary and F0 represents the static lifting force of the pantograph.

2.2 Catenary Modelling The suspension structure of the catenary should first be simplified. The catenary currently used in urban rail transit systems mainly uses gantry suspension, consisting of the main parts such as the nationalisation, contact wire, suspension structure, wire clips and insulation components, as shown in Fig. 2a. In practice, the bolt at the

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Fig. 2 Catenary suspension structures

connection between the suspension structure and the tunnel has a significant modulus of elasticity and little longitudinal deformation, so it can be considered as a fixed connection to the tunnel. The left and right bolts of the suspension structure can be equated to a vertical spring structure. The mass of the bolts and the suspension structure is relatively light compared to the insulation components and wire clips and is therefore negligible. Due to the symmetrical nature of the gantry suspension rigid catenary, the insulation components and wire clips can be equated to a mass block in the middle of the crossbeam of the suspension structure, simplifying the overall rigid contact network gantry suspension structure to a spring-crossbeam structure influenced by the gravity of mass in the middle of the crossbeam. Taking into account the deformation of the components as well as the parameters, it is further simplified as shown in Fig. 2b. In addition, solid modelling of the catenary can be completed using SOLIDWORKS software.

3 Pantograph–Catenary Modelling This research uses a solid model of the catenary combined with a simplified massspring-damping model of the pantograph for the pantograph–catenary coupling simulation. From the modelling of the catenary and pantograph above, they were imported into ADMAS software and a mass-spring equivalent model of the suspension system was added at 8 m intervals above the catenary, as shown in Fig. 3. The crucial aspect in establishing the pantograph–catenary coupling is to establish the contact between the pantograph head and the contact wire. The main methods for calculating the contact force between entities are the regression-based contact algorithm and the collision function-based contact algorithm. In this paper, the contact algorithm based on collision function is used and the calculation formula is Fc = kδ n + D δ˙

(4)

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(a)

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(b)

Fig. 3 Pantograph–catenary coupling model and simulation results

where Fc represents the pantograph–catenary contact force, δ represents the squeeze deformation of the pantograph–catenary collision and k and D represent the equivalent contact stiffness and equivalent damping, respectively. Using the measurement function of the ADAMS software, the simulation results of the dynamic contact forces of the pantograph–catenary can be obtained as shown in Fig. 3b.

4 Method for Analysis of Pantograph–Catenary Contact Response Signals The evaluation of the pantograph–catenary coupling performance is mainly concerned with the smoothness of the contact response signal. The current analysis method for the pantograph–catenary contact response signal is mainly to calculate the signal partial maximum, minimum, mean and standard deviation, so as to characterise the smoothness of the pantograph–catenary operation process. However, urban rail vehicles undergo three basic processes during operation: traction acceleration, smooth operations and braking deceleration, and these processes are usually completed within 3 min. The pantograph–catenary contact response signal is related to the speed of the vehicle on the one hand, and the wheel–rail condition, the smoothness of the contact wire and the attitude of the vehicle on the other. Therefore, the traditional method of evaluating the pantograph–catenary contact response signal is susceptible to the influence of individual anomalous data and the evaluation results are very unstable. On the other hand, as urban rail systems are characterised by frequent train starts and stops, it is difficult for trains to move at constant speed for long periods of time, and therefore the choice of data windows can substantially affect the research findings. This makes the traditional pantograph–catenary contact response signal evaluation method meaningless in the application of urban rail transit system. Therefore, it is particularly important to propose a non-stationary signal analysis and processing method applicable to pantograph–catenary systems.

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4.1 Signal Time Domain Analysis Method Based on Approximate Entropy There are mainly statistical and dynamical model-based measures of smoothness for the time domain of signals. In engineering practice, variance, peak factor, cliff factor and other indicators are often used to evaluate the signal time domain smoothness. However, for urban rail systems, the pantograph–catenary contact response signal is prone to short-term strong fluctuations due to unstable train speeds during operation and when disturbed by contact wire hard points or sensor signals. In order to avoid these factors from interfering with the overall evaluation results, this research introduces the concept of approximate entropy in the analysis of the signal time domain, which was originally introduced for the evaluation of foetal heart rate in 1991 by Pincus [10] and is now widely used in EEG signal processing problems to characterise the signal irregularity and smoothness, and has good anti-interference and anti-wild-point capabilities. It is suitable for processing non-smooth, non-linear signals generated by urban rail transit pantograph–catenary systems under complex operating conditions. For a non-smooth random sequence of length N as X = [x(1), x(2), ......, x(N )], transform x(i) into a subsequence of the original non-smooth sequence x(i ) = [x(i ), x(i + 1), x(i + 2), ......, x(i + m − 1)], 1 ≤ i ≤ N − m

(5)

In this case, the standard deviation S D of the original non-stationary series is obtained, and the pattern dimension m and similarity tolerance r are set. For each i value, the distance d between the vector and the residual vector is calculated d[x(i ), x( j)] = max|x(i − k) − x( j − k)|, 0 ≤ k