Magnetically-Controlled Shunt Reactors: Historical Overview, Operating Principles, Computer Simulation and Return of Experience 3031259564, 9783031259562

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Lecture Notes in Electrical Engineering 1000

1000th Volume of LNEE · 1000th Volume of LNEE · 1000th Volume of LNEE · 1000th Volume of LNEE · 1000th

G. A. Evdokunin · M. V. Dmitriev · A. S. Karpov · E. B. Sheskin · A. G. Dolgopolov · D. V. Kondratenko

MagneticallyControlled Shunt Reactors Historical Overview, Operating Principles, Computer Simulation and Return of Experience

Lecture Notes in Electrical Engineering Volume 1000

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 Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, München, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, 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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G. A. Evdokunin · M. V. Dmitriev · A. S. Karpov · E. B. Sheskin · A. G. Dolgopolov · D. V. Kondratenko

Magnetically-Controlled Shunt Reactors Historical Overview, Operating Principles, Computer Simulation and Return of Experience

G. A. Evdokunin Peter the Great St.Petersburg Polytechnic University Saint Petersburg, Russia

M. V. Dmitriev Peter the Great St.Petersburg Polytechnic University Saint Petersburg, Russia

A. S. Karpov JSC SO UPS Moscow, Russia

E. B. Sheskin Peter the Great St.Petersburg Polytechnic University Saint Petersburg, Russia

A. G. Dolgopolov LLC Energy Standard Moscow, Russia

D. V. Kondratenko PJSC LUKOIL Moscow, Russia

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-3-031-25956-2 ISBN 978-3-031-25957-9 (eBook) https://doi.org/10.1007/978-3-031-25957-9 Translation from the Russian language edition: “Upravl.emye podmagniqivaniem xuntiru wie reaktory” by G.A. Evdokunin, © Rodnaya Ladoga, Saint-Petersburg 2013. Published by Publishing House Rodnaya Ladoga, Saint-Petersburg. All Rights Reserved. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 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 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The book is based on the investigations which have been performed for many years at the Higher School of Electrical Power Systems of the Institute of Energy of Electrical Engineering of Peter the Great St.Petersburg Polytechnic University under the direction of Prof. G. A. Evdokunin. These studies concerned simulating and estimating the efficiency of the application of controlled shunt reactors (CSRs) with different operating principles and designs. The developed software allowed analysing the constructive features of reactors, studying the behaviour of controlled reactors under different steady states and transient electromagnetic and electromechanical processes, and estimating their effectiveness. The first software complex was created at Peter the Great St.Petersburg Polytechnic University by E. V. Korshunov in 1989. As a result of the investigations, the priority was given to developing CSR with magnetic biasing by direct current suggested by a group of the employees of Alma-Ata Power Institute, namely by E. N. Brodovaya, A. M. Bryantsev, S. A. Gordeev, S. E. Sokolov and others. The practical implementation of such a CSR was carried out under the guidance of A. M. Bryantsev. L. V. Leytes, A. I. Lurye (FGUP VEI—All-Union Electrotechnical Institute named after Lenin); M. A. Biki, S. V. Ukolov (the “Zaporozhtransformator” factory); A. G. Dolgopolov, A. I. Zaytsev (NTC VEI in Tolyatti—Scientific and Technical Centre of All-Union Electrotechnical Institute) took part in the development and realization of the CSR project at the stage of projecting and designing. Large contribution to the promotion of the expediency of CSR implementation in power systems of Russia and other countries was made by the scientists of Peter the Great St.Petersburg Polytechnic University: A. N. Belyaev, A. A. Ragozin and S. V. Smolovik. They also performed large volume of research on the analysis of the effectiveness of CSR use. The work on the modern software for CSR in the EMTP program carried out by M. V. Dmitriev (Peter the Great St.Petersburg Polytechnic University) and E. B. Sheskin (Peter the Great St.Petersburg Polytechnic University) as well as work of all the group of authors of Saint-Petersburg State University was performed in close collaboration with JSC “ELUR” (JSC “Electrical Controlled Reactors”), namely A. G. Dolgopolov, D. V. Kondratenko, K. V Aristov, O. A. Sidelev. v

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The chapters of the book were written by the authors: introduction by G. A. Evdokunin; Chap. 1 by G. A. Evdokunin, A. G. Dolgopolov; Chap. 2 by G. A. Evdokunin and A. S. Karpov; Chap. 3 by M. V. Dmitriev and E. B. Sheskin (with the participation of A. G. Dolgopolov and D. V. Kondratenko); Chap. 4 by M. V. Dmitriev and E. B. Sheskin; Chap. 5 by E. B. Sheskin; Chaps. 6–8 by M. V. Dmitriev and E. B. Sheskin (with the participation of A. G. Dolgopolov and D. V. Kondratenko in discussion on Chap. 7); Chaps. 9 and 10 by A. S. Karpov; Chap. 11 by A. G. Dolgopolov, D. V. Kondratenko and K. V. Aristov. The general editing of the book was carried out by G. A. Evdokunin (Peter the Great St.Petersburg Polytechnic University). The translation from the Russian Edition into English was performed by O. Gook. The authors express their great thanks to all who helped in editing this book (in particular, to O. A. Sidelev, the general director of JSC “ELUR”) and will be thankful to those who will make remarks and suggestions on the improvement of the content of the book. The book is intended for postgraduate students and engineers of the department of electric power systems and networks, workers of electric power system and networks as well as for the students of professional development faculties and institutes on this or related disciplines. Saint Petersburg, Russia Saint Petersburg, Russia Moscow, Russia Saint Petersburg, Russia Moscow, Russia Moscow, Russia

G. A. Evdokunin M. V. Dmitriev A. S. Karpov E. B. Sheskin A. G. Dolgopolov D. V. Kondratenko

Introduction

Shunt reactors (SRs) as elements of an electric power system are usually found at substations and transmission lines of 330 kV and higher voltage levels. In case of extremely long-distance lines, these can be used also at lower voltage levels of 110 and 220 kV. The main purpose of SR is reducing voltage at the open end of an overhead or cable line to the permissible level under the condition of open-end connection to the buses of the supply network (it can be either an electric power plant or a substation). Such a reactor installed at a line is referred to as a line reactor. The second aim of SR installation is limiting so-called drain of surplus reactive power from an overhead or cable line (at light loads over the line) into the adjacent grid. Such a reactor is installed at the buses of a substation (power station) and is referred to as a substation reactor. It should be mentioned that these are generators of an electric power plant which run the danger exposed by reactive power drain, so the producers of generators (turbogenerators, as a rule) limit severely the maximum permissible value of reactive power consumption for a generator. However, reactive power drain into an ordinary grid, in particular, into a grid of lower voltage level, can be also dangerous because of an impermissible voltage increase. The third purpose of SR is reducing the value of quasi-stationary (temporary) overvoltages and the energy of switching overvoltages to the levels permissible for surge arresters (SA) installed at the line, which sometimes do not have enough margins of sustained voltage and absorbed energy. First of all, line and substation (station) reactors are required under light load or no-load conditions of line operation. As the active power delivered by a line increases, the more and more reactive power generated by the capacitance of the line is consumed by its own longitudinal inductance and, therefore, the need for shunt reactors as additional reactive power consumers installed at the ends of the line or at the buses of adjacent substations (power stations) is decreased. The condition of active power transmission under which all the reactive power produced by the line capacitance is absorbed in the longitudinal inductance of the line is referred to as the surge impedance (natural) loading. Under this condition, there is no need for

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reactors at all, since the line is balanced in terms of reactive power; i.e. there is neither a reactive power source nor a reactive power consumer. If under a condition of power transmission close to the natural loading reactors remain connected to the line (or to the buses) and continue consuming reactive power (though it is already not required), this results in a voltage reduction on the line, a decrease in its transfer capability and an increase in losses. The most profound negative influence on the transfer capability is exerted by shunt reactors in the case of long-distance transmission lines, since the total reactive power of SRs installed in such lines is considerable, as a rule. To eliminate the considered negative influence, shunt reactors must be equipped with individual circuit breakers and be switched repeatedly during the day in accordance with daily variations of the power delivered over the lines. At the same time, it is known that switching operations with reactors are not desirable since they lead to voltage surges in the places of SR installation, to the rapid expenditure of circuit breakers life and to the appearance of switching overvoltages affecting the insulation of the reactor windings. Besides that, the disconnection of reactors is impermissible if it coincides with emergency switching operations in the electric power transmission system since the fast connection of SR required for limiting overvoltages is not possible in this case. Apart from the reduction in the power transfer limit discussed above, shunt reactors, the reactive power of which cannot be controlled smoothly decreases the smallsignal stability margin of an electric power transmission system. Thus, for example, at the first 1150 kV Ekibastuz-Kokchetav-Kustanay transmission system, the transfer capability of the line constituted only about 40% of its natural loading because of the use of uncontrolled shunt reactors as reactive power compensation devices. All the listed disadvantages of SR can be overcome by substituting them with controlled shunt reactors (CSRs). The creation of CSR expanded the conventional area of shunt reactor application. For example, in 35–220 kV networks in Russia and foreign countries, so-called reactive power compensation devices (RPCD) representing the parallel connection of CSR and a capacitor bank providing smooth control of reactive power from the mode of consumption to the mode of generation have found wide application. The use of controlled shunt reactors allows increasing the small-signal stability margin of power transmission system almost to the natural loading which is especially important for long-distance lines. The use of CSR has made it possible to create transnational AC electric power transmission system up to 2000–2500 km in length without the use of expensive DC transmission technology. The need for controlled reactive power compensation devices exists in networks of all voltage levels. However, these are the grids rated at voltage 500 kV and above, where there is the greatest number of important tasks solved with the help of CSR. First of all, 500–750 kV line have longer lengths and their phases are made of conductors splitted into several components (in order to limit the corona losses). For this reason, such lines are sources of increased reactive power which varies within a wide range depending on a condition of power transmission system resulting in impermissible voltage variations in the grid, an increase in losses (at a decrease in

Introduction

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voltage) and a risk of damage to the equipment (at an increase in voltage). Secondly, 500–750 kV electric power transmission systems, as a rule, perform the important function of backbone and intergovernmental interties, so these must be capable to deliver considerable power with appropriate stability margin. Taking into account the above-mentioned considerations, the authors have decided to focus on controlled shunt reactors intended for 500 kV electric power transmission systems.

Contents

Part I

Basic Principles

1

Brief History of Controlled Shunt Reactor Invention . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2

Controlled Shunt Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Reducing Active Power Losses in Electric Power Transmission Systems Equipped with Controlled Shunt Reactors (at Intermediate Substations and at the Buses of Power Stations) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Increasing the Limiting Values of Power Transmitted Over Electric Power Transmission Systems with Controlled Shunt Reactors Installed at Intermediate Substations . . . . . . . . . . . 2.3 Increasing the Limiting Value of Power Defined by the Aperiodic Stability Condition in Electric Power Transmission Systems Equipped with Controlled Shunt Reactors at Intermediate Substations . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Estimating the Effect of a Controlled Shunt Reactor Installed at the Buses of a Power Station on the Small-Signal Stability Performance of the Electric Power Transmission System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Equivalent Circuit and Its Parameters . . . . . . . . . . . . . . . . . 2.4.2 Comparative Evaluation of CSR/SR Influence on the Small-Signal Stability Indices with no Account Taken of the Stabilization Channels of the Generator AVR . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Comparative Evaluation of CSR/SR Influence on the Small-Signal Stability Indices with Account Taken of the Stabilization Channels of the Generator AER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.4.4 Determining the Requirements to the Expedient Combination of the Gain Factors of the Proportional Voltage Control Channels of the Generator AER and CSR Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Estimating the Effectiveness of CSR Installation at the Buses of an Electric Power Plant with Generators Equipped with Modern Microprocessor Excitation Regulators . . . . . . . . . . . . . . . . 2.4.6 Computation of Small-Signal Stability Limits for Circuits with CSR/SR . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

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Operating Principle and Design Features of a Magnetically Controlled Shunt Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Magnetic System of a Controlled Reactor . . . . . . . . . . . . . . . . . . . . 3.2 Windings of a Controlled Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Power Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Control Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Compensation Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Design Modifications and the Range of Manufactured CSRs . . . . 3.3.1 CSR with a Capacity Lower than 32 MVAr . . . . . . . . . . . . 3.3.2 CSR with a Capacity Above 32 MVAr . . . . . . . . . . . . . . . . 3.3.3 Technical Characteristics of the Most Widespread CSRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method of Controlled Shunt Reactor Computer Simulation . . . . . . . 4.1 Main Constructive Elements of the Reactor RTU-180000/500 and Its Simulation . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Magnetization Characteristic of Steel . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Modelling Reactors of Arbitrary Design . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating Conditions of CSR, Simulation and Operation of the Automatic Control System (ACS) . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 General Description of ACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Detailed Description of the Operation Algorithms of the ACS Channels and Its Operating Modes . . . . . . . . . . . . . . . . 5.2.1 Automatic Voltage Stabilization Mode . . . . . . . . . . . . . . . . 5.2.2 Mode of Forced Power Picking Up . . . . . . . . . . . . . . . . . . . 5.2.3 Mode of Forced Power Shedding . . . . . . . . . . . . . . . . . . . . . 5.2.4 Mode of Automatic Current Stabilization in the Power Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Examples of ACS Operation for the Reactor RTU-180000/500 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Example of ACS Operation in the Circuit “Line with SR and CSR” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5.3.2 Example of ACS Operation in the Circuit “Line with CSR and SCB” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.3.3 Example of ACS Operation in the Current Stabilization Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Part II 6

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Special Application Scenarios

Internal Overvoltages on Overhead Transmission Lines with Controlled Shunt Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 SA and Internal Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Temporary Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Open-End Closing of an Overhead Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Open-End Closing of an Overhead Transmission Line to a Single-Phase Short Circuit . . . . . . . . . . . . . . . . . . 6.2.3 Breaking of an Electric Power Transmission System . . . . 6.3 Switching Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Open-End Closing of an Overhead Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Open-End Closing of an Overhead Transmission Line to a Single-Phase Short Circuit . . . . . . . . . . . . . . . . . . 6.3.3 Breaking of the Electric Power Transmission System . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-phase Auto-reclosure of Overhead Transmission Lines with Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Electrostatic Component of the Fault Contribution Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Component of the Fault Contribution Current from CSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Component of the Fault Contribution Current from SR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.4 Electromagnetic Component of the Fault Contribution Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.5 Recommendations on the Reduction of the Fault Contribution Current in the SPAR Cycle . . . . . . . . . . . . . . 7.2 Recovery Voltage in the SPAR Cycle . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 The Case a Phase of CSR is Open . . . . . . . . . . . . . . . . . . . . 7.2.2 The Case the Delta-Connected Windings of CSR Are Shunted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Recommendations on the Recovery Voltage in the SPAR Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 118 120 120 123 125 126 127 128 132 134 137 138 139 141 146 147 149 150 151 153 155 156

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Contents

Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Aperiodic Currents at the Energization of Uncontrolled Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Aperiodic Currents at CSR Energization . . . . . . . . . . . . . . . . . . . . . 8.3 Limiting Aperiodic Currents with the Help of Pre-Insertion Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Limiting Aperiodic Currents with the Help of Controlled Switching Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Methods of Choosing Measures for Limiting Aperiodic Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Special Capabilities of CSR for Limiting Aperiodic Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage Stability Enhancement by Use of Reactive Power Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Equivalent Circuit and Its Main Characteristics . . . . . . . . . . . . . . . 9.2 Enhancement of the Load Bus Stability Under Short Circuits . . . 9.3 Improving the Conditions of the Start-Up of Large Induction Electric Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Analysis of the Overvoltage Affecting the Converter and the Insulation of the CSR Control Winding . . . . . . . . . . . . . . . . . . 10.1 Possible Causes of Dangerous Switching Overvoltages at the Terminals of the Control Winding . . . . . . . . . . . . . . . . . . . . . 10.2 Switching a Three-Phase Group of Single-Phase CSRs . . . . . . . . 10.3 Switching a Three-Phase CSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Estimating the Influence Which Non-simultaneous Switching of the Phases of the Reactor Circuit Breaker has on the Value of Overvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Switching Operation of CSR Energization Preceded by Its Disconnection Under the Condition of 50% Load Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Special Topics in Design and Commissioning of CSR Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Design Solutions and Equipment Arrangement . . . . . . . . . . . . . . . 11.2 Realization of the Control, Supervision and Self-Diagnostic Functions of a CSR Complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Specific Features of CSR Relay Protection . . . . . . . . . . . . . . . . . . . 11.4 Putting CSR in Commercial Operation, Field Testing . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157 158 163 165 169 170 176 180 181 183 183 186 190 197 199 200 203 205

208

211 211 215 215 219 222 236 240

Contents

xv

Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Abbreviations

AC ACS AER AR CB CCC CL CpW CS CSC CSR CSRT CtW EC EMF EMTP EPTS F MC MMF OPL PR PW RODU RPA RPCD RTDU SA SCB SIL SPAR

Auxiliary contacts Automatic control system Automatic excitation regulator Automatic reclosing Capacitor bank Common control channel Cable line Compensation winding Controlled switching Controlled static compensator Controlled shunt reactor Transformer-type controlled shunt reactor Control winding Efficiency coefficient Electromotive force Electromagnetic transients program Electric power transmission system Fault (short circuit) Main contacts Magnetomotive force Overhead line Pre-insertion resistor Power winding Single-phase electromagnetic part of the reactor Relay protection and automation Reactive power compensation device Three-phase electromagnetic part of the reactor Surge arrester Static capacitor bank Surge impedance loading Single-phase auto-reclosing xvii

xviii

SR SVC TPAR

Abbreviations

Shunt reactor Static VAR compensator Three-phase auto-reclosing

Part I

Basic Principles

Chapter 1

Brief History of Controlled Shunt Reactor Invention

The history of the creation of controlled shunt reactors (CSR) given below does not claim to be exhaustive; it only outlines specific features of the suggested CSR constructions and names the authors of these inventions along with the organizations in which they worked. The brevity is caused by the limited volume of the book and also by the reason that it is impossible to get all the authors, which took part in the work on the CSR creation, involved in the writing of a more comprehensive review, since, above all, their views on this history can be sufficiently different. Thus, we think it possible and reasonable that all who consider themselves concerned about such an important and necessary for the power industry of our country affair could write other more detailed publications on this theme. The short excursus in the history of CSR creation given here is written with the use of publication [1]. In the area of power engineering, the last century is characterized by the creation of flexible and controlled electrical grids with the use of new electric power equipment, information technologies, primary and secondary control means, and microprocessor protection and automation devices. A new rapidly developing area in voltage and reactive power regulation is the application of controlled shunt reactors in electric grids of all voltage levels, which is becoming more and more widespread. In the end of the second decade of the XX century, a problem of ac power transmission technique was outlined which consisted in the fact that the capacitance of overhead transmission lines assumes sufficient influence in the case of long-distance high voltage power transmission systems, which leads to an inadmissible voltage increase, for the reduction of which the installation of shunt reactors is required. In the beginning of the 40th years of the XX century, R. Rudenberg (Germany) was one of the first researchers who suggested to use the intensive magnetic saturation of electrotechnical steel to solve this and some other problems, pointing out at the same time that it is necessary to eliminate higher harmonic components in electrical power grids. The ideas of R. Rudenberg got further development and wide practical implementation in works of E. Friedlander (GEC, England). The magnetic system of such reactors is analogous to the magnetic conductor of power transformers. The working range of magnetic induction values of these reactors lay © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_1

3

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1 Brief History of Controlled Shunt Reactor Invention

beyond the bend of the magnetization curve of the magnetic conductor steel. These devices provided for the absorption (compensation) of capacitive reactive power and prevented a voltage increase on long-distance ac transmission lines rated at voltage above 200 kV. The GEC Company produced and installed in different countries of the world more than 50 ferromagnetic reactors (with installed capacity up to several hundred MVAr). However, these reactors have not become widespread because of unsatisfactory engineering-and-economical performance. In USSR, in order to solve this problem, the technology of regulating the reactive power consumed by power transformers through direct current magnetic biasing was suggested and realized in 1954–1956 years (the suggestion of I. S. Bruk). D. I. Azaryev performed the analysis of a long-distance power transmission system with magnetically controlled reactors-transformers and forced capacitor banks. The history of practical creation and application of controlled reactors originated in 50th years of the last century, when the development and construction of highvoltage and ultra-high-voltage transmission lines was started. In the same time period, requirements to such equipment were defined, the main of which were as follows: • • • • • •

sinusoidal form of the consumed current; large regulation coefficient; the possibility to be switched directly to high voltage grid; high response speed (regulated at the request of the customer); low consumption of active materials and low level of losses; simplicity of design and building, maintainability.

These requirements have not varied sufficiently by today and define the technical suitability of the device along with other requirements determined by a specific construction. In 1955, the BBC company produced a controlled reactor with capacity of 100 MVAr and rated voltage of 10 kV intended for testing high-capacity turbogenerators, which was named after its developer—Friedlander’s reactor (Fig. 1.1) [2]. The inductive reactance of the reactor was changed by means of direct current biasing of its magnetic system. The reactor consists of two flat-laminated six-leg magnetic conductors, on each of which the following components are installed: two identical three-phase windings connected in zigzag; two identical delta-connected windings, and two direct current windings, each of which embraces three legs of the magnetic conductor. Constant magnetic flux is locked within each magnetic conductor and produces uniform magnetic biasing of all the legs. Even harmonic components are closed in the control circuit, threefold harmonic components circulate in the delta-connected windings, and the 5th and the 7th harmonic components run in the circuit of parallel branches formed by the main windings connected in zigzag. The harmonic components produced to the grid are generally the 11th and the 13th harmonics and multiples of them (of higher degrees, but with smaller amplitudes), which provides practically sinusoidal input current under an induction value of about 1.0 T. The reactor had low engineering-and-economical characteristics and low response speed because of direct electromagnetic coupling between ac and dc windings. In

1 Brief History of Controlled Shunt Reactor Invention

5

Fig. 1.1 The electrical circuit of Friedlander’s reactor

the same year, the description of the reactor of Kramer [3] appeared which was constructed by an analogous scheme with each core splitted in four parts, so that the control and compensation windings were placed inside the operating one. The technique of winding and assembly of such a reactor is rather complicated. “Circuit-based” solutions of the compensation of higher harmonic components in current up to the 9th one had already found an application in these constructions, but these reactors did not get further development because of the mentioned disadvantages, and, possibly, for some other reasons. In 1951, Doctor of Science M. S. Libkind suggested a controlled reactor with a rotating magnetic field for transmission lines of high-voltage and ultra-high-voltage levels [4], which represented a laminated cylindrical magnetic conductor with slots, in which a distributed ac winding and a toroidal dc winding were placed embracing either the external, or the internal, or both the yokes and providing axial circular magnetic biasing of one or both the two yokes (Fig. 1.2). The distinctive feature of controlled reactors with a rotating magnetic field is that the sinusoidal form of consumption current is provided for by the use of a distributed ac winding in combination with 60° phase zone and circular magnetic symmetry (without additional measures). For a long time, the main attention had been paid on the development of this reactor. The main points of the concept of controlled reactors with a rotating magnetic field are published in numerous articles and monographs. In particular, at the same time the concept of self-biasing was suggested [5]. In whole, the performed investigations showed that it was hardly possible to create reactors with a rotating magnetic field with a capacity of hundreds MVAr for voltage levels of 110 kV and above with acceptable engineering-and-economical performance because of their disadvantages, such as the complexity of design, low voltage of the operating winding, high level of the leakage field, etc.

6

1 Brief History of Controlled Shunt Reactor Invention

Fig. 1.2 The construction scheme of M. S. Libkind’s reactor with a rotating magnetic field

Fig. 1.3 Possible modifications of controlled reactors with a spatial magnetic conductor

By the middle of 70th, a new tendency to develop reactors of the transformer-type design with a pulsating magnetic field and concentrated windings had been formed. These investigations were started in the power institute of Alma-Ata. As the result of them, constructions with a spatial magnetic conductor were suggested (Fig. 1.3) [6]. One of these constructions, which had capacity of 2.5 MVAr and rated voltage of 10 kV, with a six-leg spatial magnetic conductor was produced at the Yuzhkazenergoremont enterprise in the city of Alma-Ata and implemented at Chorga substation of the East electrical grids of Altayenergo [7]. Large volume of theoretical and model research was carried out in Tallinn Polytechnical University under the guidance of Y. Y. Yarvik, Candidate of Technical sciences [8, and other], where constructions of controlled and saturable reactors

1 Brief History of Controlled Shunt Reactor Invention

7

Fig. 1.4 Double symmetrical magnetization by even harmonic components

were suggested, the distinctive feature of which was the circuit-based compensation of higher harmonic components in the reactor current. The researchers of controlled reactors unreservedly accepted the concept of double symmetrical biasing by even harmonic components of current appearing when the constant field was imposed on the alternating one, which was used in all the constructions of transformer-type CSR with direct current biasing without exception. According to this concept, the magnetic system of the simplest single-phase reactor (saturating choke) with magnetic biasing is made of two identical magnetic conductors, at each of which the sections of the dc winding connected in aiding-series circuit and the sections of the ac winding connected inverse-parallel are placed. As a result of this, 1st harmonic emf at the terminals of the control winding is equal to zero, and even harmonic components are closed in the circuit formed by parallel branches of the alternating current winding (Fig. 1.4). Odd harmonics are not compensated, so the choke produces them to the grid. The compensation of odd harmonics was performed by using zigzag circuits and the parallel connections of delta- and star-circuits and required the duplication of the magnetic system (Fig. 1.5). The compensation of the 11th and 13th harmonics and harmonic components of higher orders was not carried out. In principle, the compensation of these harmonic components is possible as well, but it demands the

8

1 Brief History of Controlled Shunt Reactor Invention

Fig. 1.5 Circuit-based methods of the 5th and 7th current harmonics compensation

additional duplication of the magnetic system, which is obviously not reasonable. In fact, this meant a return to the initial position, i.e. to Friedlander’s reactor. Further investigations were aimed at the improvement of engineering-andeconomical performance: a decrease in active material consumption and losses, the simplification of design and circuit decision, an increase in the effectiveness of magnetic biasing, and the improvement of current waveform. In the beginning of the 60th, the method of improving the current waveform of single-phase chokes by the artificial shaping of the weber-ampere characteristic with the use of cores with variable section was suggested in the Polytechnical Institute of Odessa [9], as shown in Fig. 1.6. Of a large number of circuit decisions and constructions suggested for reactors with the magnetic biasing of the steel (with axial, transverse, circular, and rotating

1 Brief History of Controlled Shunt Reactor Invention

9

Fig. 1.6 Possible constructions of the magnetic conductor of controlled throttles for shaping the waveform of current

magnetic field, etc.), it was the transformer-type CSRs with the axial biasing of the cores on which the windings of the reactors are located which found practical application. In 1971, a work of G. Becker was published [10], in which the construction (a six-leg magnetic system) and operating principle of a magnetically controlled threephase three-wound reactor was described, the cores of which had parts with reduced sections operating in the extreme saturation mode, i.e. with a value of induction above 2.0 T, while the variation of inductive reactance was provided by a pulsating field created through regulating the firing angle of thyristors. For obscure reasons, the work of G. Becker had been left unnoticed. In 80th, this idea got further development in works of A. M. Bryantsev [11, 12], Doctor of science, graduated from the Power Institute of Alma-Ata, in the magnetic-valve type reactors in which self-biasing, which was performed through the intermittent short-circuiting of a number of turns of the secondary winding, was used along with the extreme saturation of parts of the magnetic circuit. With a piecewise-linear magnetization curve, the waveform of the reactor current is not sinusoidal only in the interval corresponding to the transition from the preextreme magnetization mode to the extreme one, i.e. in the area of the curve bend (Fig. 1.7). The further increase of the control current does not influence on the waveform of the operating current, since the characteristic of the reactor in this area is practically linear (at the expense of the saturation of parts with reduced sections). The content of harmonics in the consumed current is less than 5%, and this value can be made even lower with the use of filters. For CSRs of higher voltage levels, the authors use the concept of external magnetic biasing by a special direct current source. This reactor, which has become the most widespread in power utilities of Russia and CIS countries, is in the focus of attention in this book. The first commercial prototype of this CSR type (RTU-25000/110) was produced at Zaporozhskiy transformer-building factory in 1998 and, after being tested at the test site of NTC VEI in the city of Tolyatty, was put into operation at Kudymkar substation in the North electrical grids of Permenergo in September, 1999.

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1 Brief History of Controlled Shunt Reactor Invention

Fig. 1.7 The operating principle and design of a magnetic-valve controlled reactor

Now, the production of magnetically controlled shunt reactors with rated voltage of 35–500 kV and capacity of 25–180 MVA is concentrated at Zaporozhskiy transformer-building factory (PJSC “Zaporozhtransformator”, Ukraine). A controlled reactor with a similar operating principle started to be produced at Moscow electric factory [13]. The main distinction of this CSR from the production of PJSC “Zaporozhtransformator” is that the function of reactive power consumption is combined with the function of magnetic core biasing in the primary power winding. In this construction, the rectified voltage of thyristor converter is connected to the neutral terminals of the star-connections of the splitted power winding of the reactor, between the sections of which direct biasing current is flowing. The presence of the rectified biasing current and higher harmonic components in the splitted branches of the power winding of the reactor calls forth additional requirements to the design, the scheme of current transformer connections, control algorithms, and relay protection and automation. The second sufficient constructive distinction of CSRs produced by Moscow electrical factory is that the magnetic system is made not flat-laminated, as in power transformers and CSRs of Zaporozhtransformator, but of composite cores of variable section with non-magnetic gaps. It allows halving the content of odd higher

1 Brief History of Controlled Shunt Reactor Invention

11

harmonics, but makes the no-load current approximately three times greater, reduces the depth of regulation, and also complicates the manufacturing technique. The pilot model of such a reactor for the 500 kV voltage level was installed at 500 kV Nelym substation at the end of 2009. In 1970th, in Canada, the BBC company implemented a controlled reactor, the operating principle of which was based on the displacement of the primary magnetic flux to the air gap of the frame of the shell-type conductor, which is possible if the short-circuit voltage the between power and control windings is equal to 100%. Current control is performed through the variation of the firing angle of a thyristor group connected in-series in the control winding circuit. A delta-connected winding was used for the filtration of three-fold harmonics components. There was the whole spectrum of other odd harmonics in the operating current, and the level of losses was found to be inadmissibly high because of additional losses caused by the external field [14]. This idea found further development in works of Doctor of Science G. N. Aleksandrov, under whose leadership a transformer-type controlled shunt reactor (CSRT) was designed and implemented [15], which represented a power transformer with 100% short circuit voltage and inverse-parallel thyristor switches installed at the secondary winding and designed for the full capacity of the reactor. Similarly to the well-known circuit of a static var compensator (SVC), fully opened thyristors provide the maximum capacity of CSRT, while with closed thyristors the circuit corresponds to the no-load condition of a transformer. In intermediate operating conditions, the consumption power is smoothly adjusted through the variation of the control angle of the valves, which is accompanied by the appearance of higher harmonic components in the consumption current, for reduction of which filters are installed at the low voltage side. When the thyristors in the corresponding sections of the control winding are opened, the magnetic flux is displaced from the core, locked in the gap between the power (PW) and the (CtW) control windings and decreases in the core to a negligible value under the rated voltage. The magnetic flux is closed over the main and additional yokes covering the gap, the cross-sections of which are chosen so that induction in the steel corresponds to the part of the magnetization curve below the bending point. For this reason, the volt-ampere characteristic of the reactor is linear in the whole control range. A 50 MVAr, 420 kV controlled reactor of the CSRT type with magnetic flux switching was implemented in India, and two more such reactors were installed in Angola at 220 kV voltage level. These reactors have not found wide adoption in Russia so far, with the exception of two 25 MVAr, 110 kV reactors in IPG (interregional power grid) of East Siberia. To a large extent, this is caused by the presence of a thyristor group designed for the full capacity of the reactor, which increases the costs of CSRT and its operation. Controlled reactors can operate, if necessary, in parallel with static capacitor banks forming so-called controlled static compensators (CSC) providing both consumption and generation of reactive power in the amount equal to the capacity of the capacitor banks.

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1 Brief History of Controlled Shunt Reactor Invention

References 1. Sokolov SE, Dolgopolov AG (2012) Controlled reactors, the history of creation [Upravlyaemye reaktory, istoriya sozdaniya]. Novosti elektrotekhniki 3(75):18–30 2. Fisher F, Friedlander E (1955) D. C. controlled 100 MVA reactor. GEC J 22(2) 3. Kramer W (1959) Drehstromiransformator mit regelbaren Magnetisierungsirom // ETZ-A. 1959. Bd. 80, H. 4. S. 441–445 4. Libkind MS (1961) Controlled reactor for an alternating current transmission line [Upravlyaemy reaktor dlya linii peredachi peremennogo toka]. The Publishing House of USSR Academy of Science, Moscow, 204 p 5. Sokolov SE (1971) Investigation of supply circuits of the biasing winding of a controlled reactor with rotating magnetic field [Issledovaniye skhem pitaniya obmotki podmagnichivaniya upravlyaemogo reaktora s vrashchayushchimsya magnitnym polem]. Energetika i elektrifikatsiya, Alma-Ata: Kaz PTI 1:84–91 6. Sokolov SE, Bryantsev AM (1975) Three-phase controlled reactor with cylindrical windings [Trekhfazny upravlyaemy reaktor s tsilindricheskimi obmotkami]. Theses of reports at the 5th all-USSR inter-university conference on the theory and computational methods of non-linear elements of circuits and systems, Tashkent, vol 2 7. Bryantsev AM, Sokolov SE, Biktashev ShSh et al (1982) Core-type controlled reactor with a spatial magnetic conductor in 35–110 kV electrical grids [Sterzhnevoy upravlyaemy reaktor s prostranstvennym magnitoprovodom v elektricheskoy seti 35–110 kV]. Electricheskie stantsii 5:53–55 8. Tellinen YuYu, Yarvik YaYa (1991) Selection of an optimal design of 525 kV and 180 MVA controlled reactor [Vybor ratsionalnoy konstruktsii upravlyaemogo reaktora 525 kV, 180 MVA]. Electrotekhnika 2:35–37 9. Bobrikov SA, Somov VA (1963) A method of producing the magnetic conductor of a coil with a steel core having the specified dependence of the magnetizing current and the flux [Metod izgotovleniya magnitoprovoda katushki so stalnym serdechnikom, imeyushchego zadannuyu zavisimost mezhdu namagnichivayushchim tokom i potokom]. Izv. vuzov. Elektromekhanika 12:1332–1337 10. Becker H (1971) Ein statischer Phaseiischieber zur Kompensatior. Von Blind- laststosen / ETZ-B. 1971. Bd 23, H. 12 11. Bryantsev AM (1986) Magnetically controlled ferromagnetic devices with extremely saturated parts of the magnetic system [Podmagnichivayemye ferromagnitnye ustroystva s predelnym nasyshcheniyem uchastkov magnitnoy tsepi]. Elektrichestvo 2 12. Bryantsev AM (ed) (2004) Magnetically controlled electrical reactors. Collected articles [Upravlyaemye podmagnichivaniyem elektricheskiye reaktory. Sb. statey]. Znak, Moscow, 264 p 13. Chvanov VA (2008) Controlled shunt reactor as a control object [Upravlyaemy shuntiruyushchy reaktor — obyekt upravleniya]. Electro 2:38–43 14. Reichert KJ, Kauferle J, Glavitsh H (1974) Controllable reactor compensator for more extensive utilization of high voltage systems. In: Conferens Internationale des Grands Rezeaux Elektriques (CIGRE. 25 Session. Report 32-17. 1974) 15. Aleksandrov GN (2002) Fast-acting 420 kV, 50 MVAr transformer-type controlled reactor has been put in operation [Bystrodeystvuyushchy upravlyaemy reaktor transformatornogo tipa 420 kV 50 MVAr pushchen v ekspluatatsiyu]. Elektrichestvo 3

Chapter 2

Controlled Shunt Compensation

2.1 Reducing Active Power Losses in Electric Power Transmission Systems Equipped with Controlled Shunt Reactors (at Intermediate Substations and at the Buses of Power Stations) Electric power transmission over high voltage transmission lines encounters a number of serious technical problems. One of these problems is a decrease in the efficiency factor under light load conditions. Let us show that the efficiently factor can be increased sufficiently in schemes of long-distance power transmission systems with shunt reactors installed in intermediate points of the line under loads lower than the surge impedance (natural) loading. Let us consider the circuit of an electric power transmission system with one intermediate reactor (Fig. 2.1). Let us assume that the terminal voltages have equal magnitudes and the angular difference between them is equal to zero: U 1 = U 2 = U (zero-load operating condition). Let us determine the distribution of current and voltage along the line neglecting active power losses in it. Under the assumptions made above, the current and voltage distributions are symmetrical relative to the midpoint (MP), while the current in the middle of the line is equal to half of the reactor current I˙M P = − jU M P · b R /2 (see Fig. 2.1), so the scheme with two-end feed can be represented in the form of two circuits, each of which is loaded with a reactor of susceptance bR /2. Let us also assume that the power of the reactor is chosen in such a way that the voltage at the midpoint of the line is equal to the supplying voltage U MP = U. Formulas for voltage and current distribution in any point of the line were deduced in [1] for this case: ) ( / cos λ 4 − λx / Ux = U · ; cos(λ 4)

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_2

(2.1)

13

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2 Controlled Shunt Compensation

U1

Fig. 2.1 Electric power transmission system with one intermediate reactor

U2

U MP IMP

IMP BR

gR

) ( / sin λ 4 − λx U / · I˙x = j , ZSI cos(λ 4)

(2.2)

where λx , λ/4, λ are the wavelengths of the parts lx , l/4, l of the line; λx is counted off from the sending end of the line; Z SI is the surge impedance of the line with losses neglected. Active power losses in the two sections of the line under no-load conditions

Δ PR N L

∮l/2 ∮l/2 v c 2 · | I˙x |2 · dl x , = 2 · 3 · | I˙x | · R · dl x = 6 · R · ω 0

(2.3)

0

where R is the linear resistance of the phase. | | Let us substitute the expression for the magnitude of the current | I˙x | from (2.2) into (2.3). And get Δ PR N L

( / )/ ( / ) 1 − sin λ 2 λ 2 3 · U2 ( / ) = · R·l· , 2 ZSI 1 + cos λ 2

(2.4)

Under the natural load condition, the magnitudes of voltage and current are equal along the whole length of the line and constitute, respectively, U x = U, I x = U/Z SI , while the active power losses (with zero reactive power consumed by the reactor) are determined by the expression Δ PRnat = 3 · I 2 · R · l = 3 ·

U2 · R · l. Z S2 I

In such a way, at no-load, the relative power losses in a line containing a reactor (with respect to the heating losses at the natural load) are equal to ( / )/ ( / ) | 1 − sin λ 2 λ 2 ΔPR N L || ( / ) = , | ΔPRnat b R /=0 1 + cos λ 2

(2.5)

In the same way, the formula for the relative losses in a line without reactor can be got. As a result of this, we will have:

2.1 Reducing Active Power Losses in Electric Power Transmission Systems …

/ | 1 − sin(λ) λ Δ PR N L || = . Δ PRnat |b R =0 1 + cos(λ)

15

(2.6)

For example, from formula (2.6) we have for lengths of l = 600 and 1200 km (line without a reactor): | ΔPR N L || = 0.04 and 0.186, ΔPRnat |b R =0 While from formula (2.5) (line with a reactor): | ΔPR N L || = 0.008 and 0.016. ΔPRnat |b R /=0 Thus, the presence of an uncontrollable reactor results in a sufficient decrease in losses in the electric power transmission system under no-load conditions. In the case of a 1200 km long line with reactors installed in it, it was suggested that the line was composed of two sections like those presented in Fig. 2.1, 600 km long each. Thus, the no-load heating losses in the 1200 km line with no reactor constitute about 20% (18.6%) of losses at the natural load, while in the case of the line of the same length containing two reactors the losses are by an order lower (1.6%). Obviously, the presence of active power losses in reactors decreases the positive effect which they have on the reduction of power losses in a transmission line at light loads, but this influence is insignificant. On the contrary, the presence of the reactor increases losses as the power transferred through an overhead transmission line increases. For this reason, the need for the installation of a controlled reactor instead of an uncontrollable one becomes apparent. Example 1 Compare the values of active power losses in the electric power transmission system with reactors (SR and CSR) shown in Fig. 2.2 at the natural loading with the following parameters of the scheme: the length of a transmission line section is l = 250 km (λ = 15º), the voltage class of the line is 500 kV, the reactors are intended to absorb 50% of the charging power of both sections, the voltages at the terminals of the transmission line are equal to the rated value. The basic units: U base = U rated , Z base = Z SI —the surge impedance of the transmission line [2]. Here the circuit of the power transmission system contains a lumped shunt inductive reactance in addition to uniform line sections. To determine the influence of this Fig. 2.2 The computational diagram of an electric power transmission system with one intermediate reactor

16

2 Controlled Shunt Compensation

element on the value of maximum power that can be delivered over the line, we can use formulas given in [1, 3] for the generic coefficients of two-ports A˙ e , B˙ e , C˙ e , D˙ e , containing both the line and the reactor. The coefficients are obtained by multiplying the coefficient matrices of all the elements of the transmission line (two sections of the line and the reactor) connected in-series. If the transmission line is presented by the parameters of the equivalent two-port (the case the losses in the transmission system are neglected and the voltages at its ends are equal [1]), the expressions for active and reactive power have the following form: P= Q 1 = −Q 2 =

U2 · sin(δ); Be'' U2 De' 2 · U − · cos(δ), Be'' Be''

(2.7)

(2.8)

( ( ) ) where Be'' = Im B˙ e = j Be , De' = Re D˙ e = j De . The imaginary part of the coefficient B˙ e of the equivalent two-port equals to Be'' = Z S I sin 2λ + b R sin2 λ.

(2.9)

Let us determine the angle δ across the section of the line and the voltage in the point of reactor connection U R at the natural load P* = 1 p.u. (the natural power of the overhead transmission line is taken for the basic power). The imaginary part of the parameter B˙ e in per units ''

Be ∗ = sin 2λ + b∗R sin2 λ, where b∗R is the susceptance of the reactor in the per unit system b∗R = 2tg

λ = 2tg7.50 = 0.26, 2

''

Be ∗ = sin(2 · 15◦ ) + 0.26 · sin2 (15◦ ) = 0.52. Let us determine the angle δ over the section P ∗ = sin

2δ 2δ = sin = 1, from where δ = 15.7◦ . Be'' ∗ 0.52

Let us determine the voltage at the place of reactor installation U R∗ P∗ = 1 =

U R∗ U R∗ sin δ = sin 15.7◦ , sin λ sin 15◦

2.1 Reducing Active Power Losses in Electric Power Transmission Systems …

17

from where U R∗ = 0.955. Let us find the reactive power consumed by the reactor (from the power-angle characteristic) Q ∗R = 2

0.955 U R∗ (cos δ − U R∗ cos λ) = 2 (cos 15.7◦ − 0.955 · cos 15◦ ) = 0.29 sin λ sin 15◦ (Q R = 260 MVAr).

Active power losses per the line length λ ΔPS∗R =

P ∗2 + (Q ∗R /2)2 ∗ rl , U R∗2

1 250 250 = 0.033. where rl∗ = rn0 l Z1S I = 0.1 3 The number of conductors n in the phase is taken equal to 3, the linear resistance r 0 = 0.1 Ω/km, Z SI = 250 Ω. Then

ΔPS∗R =

12 + (0.145)2 0.033 = 0.037 (0.955)2

Substituting SR with CSR, we get ΔPC∗ S R =

12 + 02 0.033 = 0.033 12

The difference in losses in physical units (per a length of 2λ): ΔPS R − ΔPC S R = 2 · 900 · (0.037 − 0.033) = 7.2 MW. We can account for the active power losses in SR estimating them at 0.5 MW per three phases and neglect the losses in CSR under the natural load condition. So, the difference in power losses is ΔPS R − ΔPC S R = 7.2 + 0.5 = 7.7 MW. With the peak-load effective duration of τm = 6000 h, the difference in the power losses is as follows: ΔW = 7.7 · 6000 = 4.62 × 104 MWh In such a way, a voltage decrease at the place of reactor installation from 1.0 U rated to 0.955 U rated results in a sufficient increase of active power losses which can be eliminated by using a controlled reactor.

18

2 Controlled Shunt Compensation

Fig. 2.3 The computational diagram of a grid with a reactor installed at the buses of the electric power station

G

T

OPL

SR/SCR

Example 2 Compare the total losses in the generators of an electric power station with SR or CSR installed at the buses of the power station [2]—see the scheme of Fig. 2.3. Let us consider two load conditions of the generator: • the operating condition with cos ϕ = 1 (the generator outputs only active power to the grid); • the rated operating condition of the generator. For calculations we will choose the turbogenerator TVV-1000 with the following parameters: P = 1000 MW, cosϕ = 0.9, x q = 2.24 p.u., x d = 2.35 p.u., x ad = 2.03 p.u., the rotor resistance r f = 0.00132 p.u., the armature resistance r a = 0.005 p.u., the resistance of the transformer: r T = 0.0055 p.u. Let us determine active losses in the stator under the rated operating conditions (in the per unit system—p.u.) Pa = I 2 · ra = 12 · 0.005 = 0.005p.u. Let us determine active losses in the stator under the rated operating conditions (in physical units—ph.u.): Pa = Pa [p.u] · Sbase = 0.005 ·

1000 = 5.5555 MW 0.9

Let us determine active power losses in the rotor under the rated operating conditions (in p.u.): P f = I 2f · r f = 1.4422 · 0.00132 = 0.002745 p.u. Let us determine active power losses in the rotor under the rated operating conditions (in ph.u.): P f = P f [p.u] · Sbase = 0.002745 ·

1000 = 3.05 MW. 0.9

Active power losses in the stator under the operating condition with cos ϕ = 1 (in p.u.):

2.1 Reducing Active Power Losses in Electric Power Transmission Systems …

19

Pa = I 2 · ra = 0.92 · 0.005 = 0.00405 [p.u] Active power losses in the stator under the operating condition with cos ϕ = 1 (in ph.u.): Pa = Pa [p.u] · Sbase = 0.00405 ·

1000 = 4.5 MW. 0.9

Active power losses in the rotor under the operating condition with cos ϕ = 1 (in p.u.): P f = I f · r f = 1.1522 · 0.00132 = 0.001752 p.u Active power losses in the rotor under the operating condition with cos ϕ = 1 (in ph.u.): P f = P f [p.u] · Sbase = 0.001752 ·

1000 = 1.95 MW. 0.9

The difference in the stator losses (in ph.u.): ΔPa = 5.5555 − 4.5 = 1.0555 MW. The difference in the rotor losses (in ph.u.): ΔP f = 3.05 − 1.95 = 1.1 MW. With the peak-load effective duration of τm = 6000 h, the difference in the energy losses in the stator ΔW a and the rotor ΔW f constitute, under these two operating conditions: ΔWa = ΔPa · τm = 1.0555 · 6000 = 6.333 × 103 MWh ΔW f = ΔP f · τm = 1.1 · 6000 = 6.6 × 103 MWh Thus, the substitution of SR with CSR at the buses of the power station, which allows supporting the reactive power output of the generator at a minimum level, decreases sufficiently active power losses in the rotor and stator of the synchronous generator (as well as in the system of dc current rotor supply) and in the unit transformer of the station.

20

2 Controlled Shunt Compensation

2.2 Increasing the Limiting Values of Power Transmitted Over Electric Power Transmission Systems with Controlled Shunt Reactors Installed at Intermediate Substations The idea to increase the limiting value of power transmitted over a long-distance power transmission line by supporting voltage at intermediate points of the line by means of reactive power control has been known for a long time [4, 5] and others]. Nowadays, generators of intermediate electric power stations, synchronous compensators and static thyristor var compensators are used as reactive power regulation devices. Controlled shunt reactors also represent a means of increasing the power transmission limit since they support constant voltage (do not allow voltage to decrease) in the places of their installation under operating conditions up to the natural loading (if a source of reactive power is available, voltage can be maintained also at loads higher than the natural). Let imagine a transmission line with a length λ divided into n equal sections with a length λ/n, at the ends of each the installation of controlled reactive power compensation device (RPCD, Fig. 2.4) is suggested [6–11]. Let us assume that the control range within which the devices can vary the absolute value and the sign of reactive power output is enough to maintain the set voltage value U in all these points under the variations of the transferred active power P. Under these conditions, the expression for the active power transferred over the line, which is correct for any section λ/n of the line, has the form P=

ZSI

/ U2 / · sin(δ n) · sin(λ n)

or, in p.u. P∗ =

/ sin(δ n) / , sin(λ n)

(2.10)

where δ is the total angle across the electric power transmission system (between the voltages at the terminals of the line), δ/n is the angle between the voltage phasors at the ends of any section.

Fig. 2.4 The computational diagram of an electric power transmission system with several RPCDs

2.2 Increasing the Limiting Values of Power Transmitted Over Electric …

21

It follows from formula (2.10), that the maximum value of power is achieved when the angle δ/n = 90° (not δ = 90°), and it is equal to ∗ Pmax =

1 / . sin(λ n)

(2.11)

As follows from (2.11), the maximum of power transferred can be made as large as is wished irrespective of the line length by increasing the number of sections at which RPCD are connected. However, in order to provide the transmission of active power in accordance with (2.10) with set voltages U, the reactive power compensation devices must be controlled according to the formula / / cos(δ n) − cos(λ n) / Q =2· sin(λ n) ∗

(2.12)

The form of the characteristic Q * (δ/n) for δ/n < π /2 is given in Fig. 2.5 showing that transmitting active power in the range 0 < P* < 1 (from no-load to the natural loading) requires the installation of reactive power consumption devices of relatively low capacity Q* = 2tg(λ/(2n) (in each division point) regulated from the specified value to a zero value, i.e. CSRs. In order to transfer power above the natural loading, there is the need for controlled reactive power generation up to Q* ∗ ) in each division point of the line, i.e. devices of much = 2ctg(λ/n) (if P ∗ = Pmax higher capacity (with small λ/n), in addition to the means of controlled reactive power consumption described above. As a rule, such operating conditions are not reasonable in economical terms (mainly because of deteriorations in the engineeringand-economical performance of a power transmission line carrying loads greater than the natural power), and for this reason CSR becomes the main means of increasing the power transmission limit (especially for long-distance overhead transmission lines). The controllability of such devices (controlled reactors) is very important since uncontrollable shunt inductive compensation always reduces the equivalent value of the surge impedance loading of a line (see the expressions for P (2.7) and Be and (2.9)). Besides that, controlled reactors also solve another important problem of long-distance electric power transmission, namely, the problem of maintaining Fig. 2.5 Control of RPCD reactive power

22

2 Controlled Shunt Compensation

small-signal and transient stability under operating conditions close to the surge impedance loading.

2.3 Increasing the Limiting Value of Power Defined by the Aperiodic Stability Condition in Electric Power Transmission Systems Equipped with Controlled Shunt Reactors at Intermediate Substations Let us derive the expression for the simplest small-signal stability criterion considering, in a first approximation, that the controlled shunt inductive compensation is continuously distributed along the line (n → ∞). The issue of small-signal stability of lines with lumped controlled reactors is discussed below. The main aim of compensating the parameters of a line by shunt inductance is reducing its wavelength λe (λe < λ). In this case, the coefficients Ae , De (Ae < A, De < D) determining voltage mode along the line under no-load conditions change for the better. However, a decrease in the wavelength of the line λe < λ results in an increase in the coefficient Be > B, which reduces the limiting value of power transmitted (or increases the angle across the transmission line if the amount of transmitted power remains at the initial level). With shunt inductive compensation by distributed inductive susceptance bk = –bL , the equivalent wavelength λe will be defined from the expression: λe = l ·

√

x · (b + bk ) = l ·

√

x · (b − b L ) = l ·

√

√ x ·b·

1−

bL b

or λe = λ ·

√

1 − KL,

(2.13)

where K L = bL /b is a coefficient showing the degree to which the inductive susceptance bk = −bL compensates the shunt capacitive susceptance b of the line. The values x, b are the linear (specific) inductive reactance and the linear capacitive susceptance of the uncompensated line, respectively. It is evident from (2.13) that λe < λ with 0 < K L ≤ 1. Under any kind of compensation the equivalent wavelength λe changes with a change in the equivalent surge impedance Z S Ie . In the considered case √ Z S Ie = Z S I ·

1 − Kc , 1 − KL

(2.14)

Thus, shunt compensation with 0 < K L ≤ 1 reduces the wavelength, but increases the surge impedance Z S Ie . The equivalent natural power Pnate in this case can be

2.3 Increasing the Limiting Value of Power Defined by the Aperiodic …

23

expressed by the formulas: Pnate =

U2 U2 U2 =√ / . =√ / Z S Ie x (b + bk ) x be

(2.15)

The active power transferred over the line is equal to P=

Z S Ie

U2 · sin(δ), · sin(λe )

(2.16)

√ / √ where λe = λ · 1 − K L , Z S Ie = Z S I · 1 (1 − K L ). When a series of operating conditions is studied (for example, operating conditions associated with variations in the transferred power P), these parameters, in general case, should be considered variable as well as the compensation coefficient K L which changes due to variations in the reactor susceptance bL . The regulation of reactors aimed at supporting the set voltage U in all points of the line under variations of the power transferred in the range 0 < P < Pnat causes the equivalent shunt capacitive susceptance of the line to vary within the range b − b R = 0 ≤ be ≤ b. Since with any value of be the magnitude of voltage is maintained constant along the line, then any of these operating conditions is artificial surge impedance loading / with the line parameters Z S Ie , λe and the operating condition parameter Pnate = U 2 Z S Ie . Under the continuous control of reactors at the line associated with continuous variations in the transmitted active power we have the line passing through the infinite number of surge impedance loading conditions (continuous changes in the equivalent natural loading) in the range 0 ≤ Pnate ≤ Pnat . The left boundary of this inequality corresponds to the operating condition with zero load carried on the line P = 0 (the reactors are fully in operation and compensate the distributed capacitance of the line), the right one is achieved in the condition in which the artificial natural power Pnate is equal to its original value Pnat (the reactors are taken out of operation, bL = 0 and Pnate = Pnat ). Since under the natural loading the angle across the line is equal to its wavelength, we have: δ = λe .

(2.17)

Substituting (2.17) into (2.16), we will get P=

U2 . Z S Ie

(2.18)

The equivalent surge impedance Z S Ie can be expressed through the equivalent wavelength λe and the angle δ on basis of (2.17).

24

2 Controlled Shunt Compensation

Z S Ie = Z S I ·

√ / / / 1 (1 − K L ) = Z S I · λ λe = Z S I · λ δ.

Finally, instead of (2.18), we will have: P=

U2 · δ. ZSI · λ

(2.19)

It can be seen from formula (2.19) that in the case of the automatic voltage control at the line performed through the control of the reactors, the small-signal stability problem is eliminated, since, according to the simplest criterion, dP U2 = = const > 0. dδ ZSI · λ

(2.20)

i.e. the derivative of power with respect to angle is always positive, irrespective of the length of a line and its loading in the range of 0 < P < Pnat . It should be mentioned that expression (2.20) is correct if voltage deviations in any point of the line are equal to zero in the small (ΔU = 0). The latter condition can be met only with theoretically large gain factors of the reactor regulators. For instance, if the regulator performs proportional error-closing voltage control in the form of ΔbL = K R : ΔU, then ΔU will tend to zero with K R approaching infinity. The law for controlling the reactor susceptance as a function of the angle (or the value of power delivered) can be obtained in the following way. Since / / / K L = b L b = −(λe λ)2 + 1 = 1 − (δ λ)2 ,

(2.21)

( / ) b L = b · 1 − (δ λ)2 .

(2.22)

we will get

The next step to aperiodic small-signal stability analysis is considering the scheme of a power transmission system with two line sections and a controlled reactor in the middle of the line (Fig. 2.6).

Fig. 2.6 The scheme of a power transmission system with two line sections and CSR in the middle point

2.3 Increasing the Limiting Value of Power Defined by the Aperiodic …

25

The computational diagram of Fig. 2.6 contains the power plant G, two sections of the line with a wavelength of λ each, and the infinite bus system S. Let us assume that the magnitudes of voltage at the ends of the line are equal (U G = U S = U) and constant in the small (ΔU G = 0, ΔU C = 0), and the voltage in the middle point of the line is equal to U R . Active power losses in the line and reactor are neglected. Under these assumptions, the angle separations between the voltages at the ends of the line and the voltage in the middle of the line will be the equal and constitute δ. Some additional assumptions will be introduced below. A change in the sign of the determinant of the linearised steady state equations system occurring during the gradual loading of an initial stable operating condition is taken as the criterion of aperiodic small-signal stability loss (the value of the determinant is proportional to the free term of the characteristic equation of the system). The steady state equations of the power transmission system shown in Fig. 2.6 have the form. U · UR · sin(δ); Z S I · sin(λ) U · UR U R2 Q1 = · cos(δ) − · cos(λ) = Q 2 Z S I · sin(λ) Z S I · sin(λ) P=

where P, Q1 , Q2 are the active and reactive power flows at the end of the first line section and at the beginning of the second one, respectively. The reactive power balance equation. 2 · Q1 = Q R . Let us rewrite the equations in the per unit system with U base = U, Pbase = Pnat = U 2 /Z SI and get ⎫ K ⎪ P ∗ = sin(λ) · sin(δ); ⎬ K · (cos(δ) − K · cos(λ)); Q ∗1 = sin(λ) ⎪ ⎭ 2 · Q ∗1 = Q ∗R ,

(2.23)

where K = U R /U is the voltage step. On basis of (2.23), let us compose a system of linearised equations which is correct for small deviations near any steady state operating condition (the variables of this condition are identified with the subscript “0”). Using the formulas for total increments: ΔP ∗ = Then

∂ P∗ ∂ Q ∗R ∂ P∗ ∂ Q ∗R · ΔK + · Δδ; ΔQ ∗R = · ΔK + · Δδ. ∂K ∂δ ∂K ∂δ

26

2 Controlled Shunt Compensation

ΔP ∗ = ΔK · sin(δ0 ) + Δδ · K 0 · cos(δ0 ) = 0; 2·Δδ 2·ΔK · (cos(δ0 ) − 2 · K 0 · cos(λ)) − sin(λ) · K 0 · sin(δ0 ), ΔQ ∗R = sin(λ)

} (2.24)

where ΔP* , ΔQ ∗R , ΔK, Δδ are the small deviations of operating condition variables (P* , Q ∗R , K, δ) from their steady-state values (P* , Q ∗R , K, δ) in the operating condition studied for aperiodic stability. The equality ΔP* = 0 follows from the suggestions that the turbine output is constant PT = const and there is no motion of the rotor under state operation conditions. Then it follows from the equation of motion ( / steady ) T j ω0 · p 2 · (2 · δ) = PT∗ − P ∗ that the increment ΔP* = 0. The reactive power of a controlled reactor. Q R = U R2 · b R , where bR is the susceptance of the reactor. In the per unit system Q ∗R = K 2 · b∗R , where b∗R = b R · Z S I . The linearised equation of a controlled reactor ∂ Q ∗R ∂ Q ∗R · ΔK + · Δb R = 2 · K 0 · b∗R0 · ΔK + K 02 · Δb∗R . ∂K ∂b∗R

ΔQ ∗R =

Taking into account the equation of the proportional regulator of the reactor operating in response to the voltage deviation ΔK with the gain factor K R , Δb∗P = K R · ΔK we have, finally ) ( ΔQ ∗R = 2 · b∗R0 + K 0 · K R · K 0 · ΔK .

(2.25)

We have got three Eqs. (2.24) and (2.25) with the unknowns ΔQ ∗R , ΔK , Δδ. The determinant D of this system with account of the equality b∗R0 =

Q ∗R0 K 02

=

2 · (cos(δ0 ) − K 0 · cos(λ)) K 0 · sin(λ)

have the form D = 2 · K 0 · cos(2 · δ0 ) + K 03 · K R · sin(λ) · cos(δ0 ).

(2.26)

As is evident from (2.26), under an initially stable operating condition, for example, under no-load conditions (δ0 = 0) with no control of the reactor (K R = 0) and with the voltage on it supported equal to U R = U (K 0 = 1), the determinant

2.3 Increasing the Limiting Value of Power Defined by the Aperiodic …

27

D = 2 > 0. As the load increases (the angle δ0 increases), the determinant reduces and crosses a zero value at δ0 = 45°, i.e. when the line is loaded so that the angle δ0 = 45° (90° across the line) the aperiodic stability is violated. As is obvious from (2.26), it is possible to delay zero crossing by the determinant, i.e. to increase the permissible angle δ0 at least to values of δ0 < 90° across the section (180° across the line) by implementing automatic reactive power control at the reactor with K R > 0. Thus, in the considered scheme of compensation with a lumped reactor, aperiodic stability is maintained if the angle across the section of the line δ0 < 45° with K R = 0 (uncontrollable reactor) and δ < 90◦ with K R → ∞ (automatically controlled reactor). It can be shown that, with any number of sections equal / to n, aperiodic stability is maintained if the angle across the section δ < 90◦ n (K R = 0) and δ < 90◦ (K R → ∞). With a realizable value of the control coefficient / K R of the reactor, the angle across the section will remain within the range 90◦ n < δ < 90◦ depending on the value of K R . Example 3 Is it possible in terms of aperiodic stability to deliver power P* = 0.9 (90% of the natural load) over the transmission system of Fig. 2.6 with sections of λ = 60◦ under the following conditions: (a) there is an uncontrollable fixed reactor chosen to compensate 50% of the line capacity; (b) there is a controlled reactor controlled “manually” so as to support voltage U R = U (K 0 = 1) under all operating conditions up to P0∗max = 0.9; (c) there is a controlled reactor with an automatic voltage control system intended to maintain voltage at the level U R = U (K = 1) under all operating conditions 0 ≤ P ∗ ≤ 0.9. (a) The equivalent constant B* e ((2.9) and [1]) Be∗ = sin(2 · λ) + b∗R0 · sin2 (λ). It follows from the statement of the problem that if the reactor compensates 50% of the line capacitance the voltage at the midpoint of the line must be equal to 1 (K 0 = 1) under no-load conditions, from which, according to (2.23), the power of the reactor is equal to Q ∗R0 =

2 · (1 − cos(λ)) = 1.15. sin(λ)

Thus, b∗R0 = Q ∗R0 = 1.15. In such a way, we have Be∗ = 1.73, and the limiting value of power delivered is P∗ =

| sin(2 · δ) || = 0.58 < 0.9 Be∗ |δ=45◦

28

2 Controlled Shunt Compensation

(b) According to (2.26), to determine the value δ 0 corresponding to the aperiodic stability limit, it should be suggested that K R = 0 (and K 0 = 1 from the statement of the problem) for the scheme of reactor with no automatic control system. We have the equation for the operating conditions corresponding to the aperiodic stability limit 2 · cos(2 · δ0 ) = 0 from which the angle δ0lim across the section of the line must be equal to δ0lim < 45◦ in order to maintain stability. The reactive power of the reactor under this limiting condition Q ∗R0 = b∗R0 =

2 · (cos(45◦ ) − cos(λ)) = 0.48 sin(λ)

and the limiting value of power transmitted ∗ Plim =

sin(90◦ ) = 0.82 < 0.9 sin(2 · λ) + b∗R0 · sin2 (λ)

i.e. transferring the expected amount of power is impossible in this case as well. (c) If the voltages at the ends of the sections U = 1, the angle across the line with P* = 0.9 is equal to ( ) δ0 = arcsin P0∗ · sin(λ) = 51.2◦ . On basis of (2.26) we have the required value of the gain factor K R which turns the determinant D to zero KR = −

2 · cos(2 · 51.2◦ ) 2 · cos(2 · δ0 ) =− = 0.8. sin(λ) · cos(δ0 ) sin(60◦ ) · cos(51.2◦ )

In such a way, all the operating conditions of power transmission within the range 0 ≤ P ∗ ≤ 0.9 are aperiodically stable if the coefficient of the reactor regulator is not less than K R = 0.8.

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed at the Buses of a Power Station on the Small-Signal Stability Performance of the Electric Power Transmission System Controlled shunt reactors (CSR) have been already widely adopted in electric power systems of Russia, especially at intermediate 500 kV substations. However, only

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

29

uncontrollable and, in most cases, practically non-switched shunt reactors (SR) are still used at power plants. Such reactors are constantly loading generators with reactive power irrespective of an operation condition of the power transmission system from light loads to the expected and limiting loads. As shown in Example 2 of Sect. 2.1 and in [2], the surplus loading of generators causes sufficient losses in the armature and rotor circuits of electric machines, the excitation systems, and step-up transformers of the units. Heavy current loads of the rotor circuits of synchronous machines complicate their cooling systems, lead to a decrease in the estimated field forcing current of the machine under emergency conditions and to an overall reduction of the operating reliability of power station generators. The main reason adduced by the opponents of CSR installation at the buses of power stations is that in this case there is a reduction in the estimated value of the excitation emf of synchronous generators which is proportional to the field current decreasing, in its turn, as the reactive power consumed by the controlled reactor decreases. In order to provide a grounded objection to this widespread cofusion, the comparative analysis of stability performance for both the cases of using SR and CSR at the buses of an electrical power station is carried out in the present section.

2.4.1 Equivalent Circuit and Its Parameters In order to estimate the influence that a controlled shunt reactor installed at the buses of a power station exerts on the small-signal stability indices let us consider a power transmission system composed of a generator, transformer, line and an infinite bus system (see Fig. 2.3). The equivalent generator represents two synchronous generators TVV-500-2. The length of the 500 kV overhead transmission line has been chosen so that a 180 MVAr controlled or uncontrollable reactor installed at the buses of the power station absorbs exactly half of the charging power of the line (this condition is met by a 375 km long overhead line). The parameters of the transmission system elements are given in Attachment 1. The equivalent circuit of the power transmission system (with losses neglected, but with account of the line capacitance) is shown in Fig. 2.7. Using the equivalent circuit as an initial approximation, one can show easily the main distinction, for instance, between the expressions for the power transmission limit in the circuit with SR and CSR. Fig. 2.7 The equivalent circuit of a power transmission system with an uncontrollable/controlled shunt reactor (the scheme of Fig. 2.3)

30

2 Controlled Shunt Compensation

The equivalent circuit of Fig. 2.7 can be reduced to the simplest “emf behind a reactance” equivalent by multiplying the coefficient matrices of the two-ports representing the elements of the transmission system: the generator, transformer, reactor, and the line [1]. Thus, we can get the following expression for the equivalent reactance of the whole transmission system, which is equal to the imaginary part of the coefficient B˙ e of the equivalent two-port ''

Be S R = Z S I · sin λ + (X d + X T ),

(2.27)

where X T is the reactance of the transformer. If CSR is installed, the equivalent reactance of the whole transmission system (Be ) loaded above the natural (limiting) power can be expressed as follows (the reactive power of CSR is almost zero) ''

Be C S R = Z S I · sin λ + (X d + X T ) · cos λ.

(2.28)

In such a way, under operating conditions close to the limiting condition, the equivalent reactance is in principle lower in the case of CSR installation than this in the case of SR installation. '' '' Figure 2.8 shows the reactances Be S R and Be C S R varying as a function of the line length in the range (0−π/2). Then the peak values of the power-angle curves of the electric power transmission system with SR or CSR are equal, respectively, to PmS R =

Eq · U Eq · U PmC S R = '' C S R '' S R , Be Be

and, therefore, the peak value of the power-angle curve in the case of CSR installation is always higher than this in the case of SR installation provided that the value of the internal emf E q is the same in both the cases under limiting conditions. In the case of transmission lines of relatively small lengths (about 300 km and below) the expected difference in the limiting values of power transmitted is small, but the limiting value of power in the case of CSR is always principally higher (and the longer the line the higher the value, see (2.28)). The results of this simple analysis will be confirmed below by calculations made with more complicated mathematical description of the power transmission system. Generally, it is assumed in the calculations given below that the generators of the power station are equipped with automatic voltage (excitation) regulators of strong action (AVR-SA) (Fig. 2.9); the analysis of Sect. 2.4.4 concerns the cases of generators equipped with modern microprocessor automatic voltage regulator (AVR) with a proportional-plus-integral voltage control channel (PI-channel). A. Automatic Voltage (excitation) regulator (AVR) of a generator The mathematical description of AVR is based on the transfer functions of its components.

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

''

31

''

Fig. 2.8 Reactances Be S R and Be C S R as a function of line length in the wavelength range (0−π/2)

Fig. 2.9 The simplified structural diagram of ARV-SD

The proportional voltage control channel is presented by an aperiodic element with the transfer function W0u ( p) =

K 0u T0u p + 1

where K 0u is the gain factor of the proportional voltage control channel; T0u is the time constant of the channel.

32

2 Controlled Shunt Compensation

The proportional voltage derivative control channel is presented by a time-delay differentiating element. The transfer function of the channel has the form W1 p ( p) = K 1u · WΔ1u ( p) =

K 1u · p T1u p + 1

where K 1u is the gain factor of the channel; T1u is the time constant of the channel. voltage unit The maximum absolute value K 1u = 7.2 excitation , T1u = 0.039 s. stator voltage unit The frequency block (FB) is presented by a time-delay element W F B ( p) =

p , TF B p + 1

where TF B is the time constant of the frequency unit. For the frequency range (0−50) 1s , the constant TF B = 0.07 s. The proportional voltage frequency control channel is presented by the series connection of a passive differentiating and an instantaneous amplifying element W0ω ( p) = K 0ω · WΔ0ω ( p) = K 0ω ·

p T0ω p + 1

where K 0ω is the gain factor of the proportional frequency control channel; T0ω is the time constant of the channel. The maximum value of the gain factor K 0ω = voltage unit , T0ω = 1 s. 15 excitationrad/s The proportional frequency control channel is presented by the series connection of a passive differentiating and an instantaneous amplifying element: W1ω ( p) = K 1ω · WΔ1ω ( p) = K 1ω ·

p , T1ω p + 1

where K 1ω is the gain factor of the proportional frequency derivative control channel; T1ω is the time constant of the channel. The maximum value of the gain factor voltage unit K 1ω = 5.5 excitationrad/s , T1ω = 0.026 s. 2 The proportional field current derivative control channel is presented by the series connection of a time-delay amplifying element and a differentiating element with the transfer function W1i f ( p) =

K 1i f , T1i f p + 1

where K 1i f is the gain factor of the field current derivative control channel; T1i f is the time constant of the channel. The group of elements forming the main control channel (amplifier, filter, control system, thyristor rectifier, and field winding voltage feedback) is presented by an equivalent aperiodic element, which transfer function can be written as follows:

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

W MCC ( p) =

33

1 , TCCC p + 1

where TCCC is the time constant of the main (common) control channel. When processes associated with finite disturbances are concerned, the additional limitations of voltage at the field winding are taken into account: ⎧ ⎪ ⎨ Er , Er min ≤ Er ≤ Er max ; Er = Er max , Er > Er max ; ⎪ ⎩ Er min , Er < Er min . Below the proportional frequency control channel and the proportional frequency derivative control channel are referred to as stabilization channels. B. Automatic regulator of CSR Since in the present section we concern the influence of CSR on the stability and operating conditions of a power transmission system, then physical processes in structural elements of the reactor can be neglected, and it is convenient to present CSR as a variable susceptance. In the calculations below the automatic regulator of CSR is realized in the form of proportional regulator with an error-closing voltage control channel (b R − b R0 ) =

K 0u R (U R − U R0 ) (T0u R p + 1)(TCCC p + 1)

where b R0 is the susceptance of the CSR in the initial operating condition; U R0 is the voltage in the point of CSR connection; K 0u R is the gain factor of the proportional voltage control channel; T0u R is the time constant of the channel; TMCC is the time constant of the main control channel.

2.4.2 Comparative Evaluation of CSR/SR Influence on the Small-Signal Stability Indices with no Account Taken of the Stabilization Channels of the Generator AVR In order to make the grounded choice of the settings of the generator’s and CSR’s regulators in the compared alternatives and to analyse their effect they have on the stability indices of power system operation (in the main, the roots of the characteristic equation of the system under weakly disturbed operating conditions are considered as stability indices; more comprehensive interpretation of stability indices is given in Sect. 2.4.3), we will consider an operating condition in which about half of the estimated transmitted power is delivered by the line: P = 0.5 p.u. (in fractions of

34

2 Controlled Shunt Compensation

the natural loading of the overhead transmission line). As additional calculations showed, the settings chosen under such conditions provide satisfactory damping of electromechanical transients in the whole range of the values of power transmitted over the system. Let us select the typical values of settings for the automatic excitation regulator. Thus, in order to meet the requirement that the control droop must be δ = 5%, we will choose the gain factor of the proportional voltage control channel from the following voltage unit 1 = −20 excitation . condition: K 0u = − 1δ = − 0.05 stator voltage unit When choosing the gain factor of the voltage derivative control channel (this concerns any signal of this kind, e.g., the frequency or field current derivatives) it should be taken into account that setting large values of the gain factors, which sometimes is dictated by the equal damping curves (i.e. small-signal stability requirements), can contradict the transient stability requirements since sufficiently large input signals result in a huge value of the control signal which will be chopped in order to eliminate impermissible influence on the field winding, and for this reason the effect of the large gain factor will be relatively small. Taking into account that the derivative control signal can be several times greater than the proportional control signal, the gain factor of the derivative control channel is taken sufficiently lower. With the regard for the aforementioned considerations, we will assign this gain factor voltage unit [12]. a value of K 1u = −5 excitation stator voltage unit/s To begin with, let us determine the aperiodic and oscillation stability indices of a power transmission system with no reactor, with SR, and with CSR (with different response speeds), i.e. let us find the roots of the characteristic equation of a weakly disturbed operating condition. The calculations are performed with zero gain factors of the stabilization channels and the gain factors of the proportional and derivative voltage control channels equal to −20 and −5, respectively. The results of the calculations are given in Table 2.1. The gain factor of the proportional voltage control channel of CSR is taken equal to −20. It is evident from Table 2.1 that the installation of CSR instead of SR at the buses of an electric power plant (with a sufficiently large time constant τR = 1.0 s corresponding to the rate of power pick-up by the reactor equal to 3τP = 3.0 s) halves the main real root of the characteristic equation (i.e. reduces the damping rate of the aperiodic component of motion) and does not almost affect the oscillation stability (the damping of the oscillatory component of motion). The analysis of the data presented in Fig. 2.10 confirms the conclusion based on the data of Table 2.1 that the aperiodic root decreases in the case of CSR installation with any value of the coefficient K 0u R . Table 2.1 The main roots of a weakly disturbed operating condition with the power transmitted P = 0.55 Without SR/CSR

SR

CSR τ R = 1 s

CSR τ R = 0.1 s

− 0.1978 ± 7.4177i − 0.4092

− 0.2457 ± 7.5213i − 0.4491

− 0.2403 ± 7.5605i − 0.1991

− 0.3268 ± 7.5999i − 0.2084

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

35

Fig. 2.10 The aperiodic stability indices versus the gain factors of the proportional voltage control channels of AERs of the generator and CSR

Figure 2.11 shows the influence that the time constant and the gain factor of the proportional voltage control channel of CSR have on the oscillation stability indices. The data of Fig. 2.11 indicate that an increase in the value K 0u R enhances the damping of the oscillation component of motion, but the increase is small, so it should be admitted not effective to affect the coefficient K 0u R for this purpose. As is evident from the figure, increasing the response speed of CSR for the same purpose is not reasonable as well.

2.4.3 Comparative Evaluation of CSR/SR Influence on the Small-Signal Stability Indices with Account Taken of the Stabilization Channels of the Generator AER Since under real operating conditions the stabilization channels of the automatic excitation regulators of generators improve the damping of electromechanical transients rather efficiently, then we take their action into account when comparing the stability indices of a power transmission system with SR and CSR. Let us adjust the stabilization channels of the generators’ AERs for the following cases: • an uncontrollable SR is installed at the buses of the electric power plant; • a CSR with a response speed of τR = 1 s (the rate of power pick-up is 3τR = 3 s) is installed at the buses of an electric power plant;

36

2 Controlled Shunt Compensation

Fig. 2.11 The oscillatory stability indices versus the gain factor of the proportional voltage control channel and the time constant of CSR (with K 0u = −20)

• a CSR with a response speed of τR = 0.1 s (the rate of power pick-up is 3τR = 0.3 s) is installed at the buses of an electric power plant. The choice of stabilization coefficients at the automatic excitation regulator of the generator will be made on basis of D-decomposition curves plotted in the plane voltage unit (for SR) and of the parameters K 0ω and K 1ω with K 0u = −20 excitation stator votage unit voltage unit K 0u = −20 excitation , K 0u R = −20(for CSR). The stabilization coefficients stator voltage unit chosen with the help of these figures correspond to the maximum damping of the main oscillatory component of a transient, and they can be called optimal in this sense. It follows from Figs. 2.12, 2.13 and 2.14 that the damping of the main oscillatory component of motion decreases to some extent when SR is substituted with CSR, but with the typical adjustment of AER stabilization coefficients the damping is satisfactory in both the cases of SR and CSR installation (with approximately the same settings in both the cases). Let us consider in more detail the critical issue of a decrease in the absolute value of the characteristic equation real root (in the case of CSR installation at the buses of a power plant instead of SR) corresponding to the deceleration of damping of the aperiodic components of motion (nearly 2 times lower in the case of CSR installation compared with the case of SR). The behaviour of a transient under weakly disturbed operating conditions depends not only on the roots of the characteristic equation, but also on the initial and final values of motion components. Thus, Figs. 2.15, 2.16 and 2.17 present the results of calculations of transients occurring under small (but finite) disturbances in the power transmission system associated with an increase of 0.05 p.u. in the active power transferred over the line (under the initial operating conditions the power P0

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

37

Fig. 2.12 The lines of equal damping for determining the optimal damping coefficients of the proportional frequency and frequency derivative control channels (the case of SR)

Fig. 2.13 The lines of equal damping for determining the optimal damping coefficients of the frequency and frequency derivative control channels (the case of CSR with a time constant of τR = 1 s)

38

2 Controlled Shunt Compensation

Fig. 2.14 The lines of equal damping for determining the optimal damping coefficients of the frequency and frequency derivative control channels (the case of CSR with a time constant of τR = 0.1 s)

= 0.5 p.u.) with different gain factors of the proportional voltage control channels of the generator AER and CSR regulator. It is clearly shown in Fig. 2.15 (plotted for K 0u = −10 with variations of K 0u R ) that in spite of the faster damping of the aperiodic component of motion in the case of the SR installation the transient quality in this case (the solid curve) is worse than this in the case of CSR installation with a smaller absolute value of the aperiodic root (dashed curves). As is obvious from the figure, this is caused by the difference in the steady state values of operating condition variables (in particular, of the voltage at the buses of the station) which is caused by variations in the CSR susceptance. As the gain factor of the generator AER K 0u (Figs. 2.16 and 2.17) increases, the characteristics of transients in the cases of SR and CSR draw closer. It should be mentioned, after all, that a voltage deviation at the perturbation of an operating condition of a power transmission system (for example, at the power pick-up) is in principle lower in the case of CSR (voltage is closer to the reference) than in this the case of SR, which can be explained, physically, by the fact that the susceptance of CSR after the perturbation starts to reduce (which contributes to a voltage increase) while the susceptance of SR remains constant. With real values of the gain factor of the proportional voltage control channel at the generator this difference is quite small. The computations of transients associated with small load drops do not have any peculiarities in comparison with load pick-up and are not given here for this reason. The simulation of a single small active power surge on the power transmission system is realised by a stepwise change in the mechanical torque of the turbine, which

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

39

Circuit with SR Circuit with CSR K 0uR=-20 Circuit with CSR K 0uR=-50

Fig. 2.15 The transient of voltage variations at the buses of the electric power station under small (but finite) disturbances in the power transmission system associated with an increase in the active power delivered by the line. The generator AER has K 0u = −10

Circuit with SR Circuit with CSR K 0uR=-20 Circuit with CSR K 0uR=-50

Fig. 2.16 The transient of voltage variations at the buses of the power station under small (but finite) disturbances in the power transmission system associated with an increase in the active power delivered by the line. The generator AER has K 0u = −20

40

2 Controlled Shunt Compensation

Circuit with SR Circuit with CSR K 0uR=-20 Circuit with CSR K 0uR=-50

Fig. 2.17 The transient of voltage variations at the buses of the power station under small (but finite) disturbances in the power transmission system associated with an increase in the active power delivered by the line. The generator AER has K 0u = −50

may correspond, for example, to local load trip or to the unloading of a parallel intertie (load disconnection at this intertie). In such a way, the presented computations shows that a reduced absolute value of the main real root, which takes place when SR is substituted with CSR, does not result in the deterioration of transient quality under small perturbations of the power system operating conditions. On the contrary, under disturbances, voltage in a circuit with CSR always remains closer to the reference, i.e. is higher than in the case of SR, during the entire transient.

2.4.4 Determining the Requirements to the Expedient Combination of the Gain Factors of the Proportional Voltage Control Channels of the Generator AER and CSR Regulator The installation of CSR at the buses of an electric power station allows the reduction of losses in the armature and rotor circuits of electrical machines and their excitation systems as well as in step-up unit transformers provided by the possibility to control gradually reactive power consumption under all operating conditions in the range from light loads to loads close to the surge impedance loading. To estimate the amount of power which must be absorbed by CSR in order to provide the reactive power shedding of the generator as a function of the transmitted power P, we write

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

41

down the expressions for the power-angle characteristics for the active and reactive power delivered by a transmission line with account of losses P1 = U12 · g11 +

U1 · U2 · sin(δ12 − α12 ); Z 12

Q 1 = −U12 · b11 −

U1 · U2 · cos(δ12 − α12 ); Z 12

(2.29) (2.30)

With known terminal voltages U 1 and U 2 , the angle δ12 across the line can be determined from formula (2.29) for all predetermined values of the active power transferred over the line. Then, from expression (2.30) the current value of power consumed by CSR installed at the buses of the station can be determined, which allows maintaining the operating condition of the power station generators close to cosϕG = 1 (under all operating conditions of the power transmission system from no-load to the natural loading)—see Fig. 2.18. A change in the transferred power P causes, in particular, the transient of voltage variations at the buses of the station, which, in its turn, actuates the reactor’s regulator and the generator’s AER. Let us perform a series of computations of electromechanical transients changing active power generation within the range (0.5−0.8) p.u. and varying the gain factors of the proportional voltage control channels of the generators’ AER K 0u and the CSR regulator K 0uR : • for Fig. 2.19 it is assumed that K 0u = −20;

Fig. 2.18 The power of CSR required to provide the operation of generators with cosϕG = 1 depending on the active power transferred

42

2 Controlled Shunt Compensation

a

b

U, p.u. K0uR=-5 K0uR=-50

t,s

c

BR,p.u. K0uR=-5 K0uR=-50

t,s

Fig. 2.19 a Variations in active power. K 0u = –20. b Voltage variations at the point of CSR connection (at the buses of the power station). K 0u = − 20. c Variations of the CSR susceptance. K 0u = − 20. d Reactive power variations at the sending end of the line. K 0u = –20. 19 Variations of reactive power generation K 0u = − 20. f Variations of reactive power generation (with an enlarged time sweep for t = 50–70 s). K 0u = − 20

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

d

e

f

Fig. 2.19 (continued)

43

44

2 Controlled Shunt Compensation

• for Fig. 2.20 it is assumed that K 0u = −50. It is evident from Fig. 2.19a, b that with K 0uR = −5 a change in the transferred active power from 0.5 to 0.8 p.u. leads to a voltage decrease to 0.992 p.u. (Fig. 2.19b). This, in its turn, reduces the susceptance of CSR from 0.2 to 0.16 p.u. (see Fig. 2.19c). Meanwhile, as shown in Fig. 2.19d, e, almost all the reactive power at the sending end of the line is absorbed in CSR and only very small portion of it (0.02 p.u.) is consumed by the generator (Fig. 2.19d, e). It is also obvious from Fig. 2.19d that an increase in the response speed of CSR from τR = 1 to τR = 0.1 does not affect operating conditions of the system on the whole. In the main, the obtained results correspond to the dependence of Fig. 2.18 which is suitable for the analysis of steady states and was plotted under the assumption that the voltage at the buses of the power station is maintained perfectly equal to U = 1.0 p.u. On the one hand, an increase in the value of the gain factor of the CSR proportional voltage control channel to K 0uR = − 50 allowed improving the droop of control (a change in the transferred active power from 0.5 to 0.8 p.u. led to a voltage reduction to 0.997 p.u., see Fig. 2.19b), but, on the other hand, it resulted in overcontrol (the unnecessary unloading of CSR, see Fig. 2.19c) followed by unfavourable reactive power distribution between CSR and the generators for maintaining reactive power balance in the node (see Fig. 2.19d, e) under the same operating condition. It should be mentioned that an increase in the response speed of CSR from τR = 1 to τR = 0.1 affects only the behaviour of transient, but not the distribution of reactive power between the generators and CSR. Let us repeat the computations of Fig. 2.19 for the gain factor of the proportional voltage control channel of the generators AER equal to K 0u = −50. The results are presented in Fig. 2.20. It is evident from Fig. 2.20, c that with K 0uR = − 5 a change in the transferred active power from 0.5 to 0.8 p.u. leads to a small change in the CSR susceptance: from 0.2 to 0.183 p.u. However, as shown in Fig. 2.20e, f, such control is not enough to provide cosϕ = 1, and CSR causes the generator to give additional reactive power output. In this case, the role of CSR in voltage support and its influence on the system operation conditions reduce. An increase in the value of the coefficient of the CSR proportional voltage control channel from K 0uR = − 5 to K 0uR = − 50 also does not give a satisfactory result: it leads to the situation already discussed that CSR drops its power too abruptly due to overcontrol, which results in the unfavourable distribution of consumed reactive power for maintaining the balance of reactive power in the node. The examples show that in order to provide the desired reactive power distribution between the generator and CSR, certain coordination of the coefficients K 0u , K 0uR should be made. In Fig. 2.21, the operation areas of the generators in the plane of the coefficients K 0u –K 0uR are plotted (the underexcitation operating condition—ϕG < 0◦ , the overexcitation operating condition—ϕG > 0◦ , the operating condition with ϕG ≈ 0◦ ) with respect to the reciprocal combinations of the coefficients of the proportional

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed … Fig. 2.20 a The active power transferred over the overhead transmission line to the system K 0u = − 50. b Voltage variations at the point of CSR connection (at the buses of the power station). K 0u = − 50. c Variations of the CSR susceptance. K 0u = − 50. d Reactive power variations at the sending end of the line. K 0u = − 50. e Variations of reactive power generation. K 0u = − 50. f Variations of reactive power generation with an enlarged time sweep for t = 50–70 s. K 0u = − 50

a

45

P, p.u.

t,s

b

U, p.u. K0uR=-5 K0uR=-50

t,s

c

BR,p.u.

K0uR=-5 K0uR=-50

t,s

46 Fig. 2.20 (continued)

2 Controlled Shunt Compensation

d

Q1,p.u. K0uR=-5 K0uR=-50

t,s

e

f

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

47

Fig. 2.21 The coordination of the settings of the generator and CSR regulators K 0u and K 0uR providing the desired reactive power output of generators (areas of different colour) determined with the help of the equal damping curves of the main aperiodic component of motion

voltage control channels of the generator and CSR regulators: K 0u , K 0uR , respectively (the parameter of the curves is the constants of the aperiodic motion of the system) It is evident that the time constant of the damping of the aperiodic component of motion is nearly the same and equal to τ0 = 2.9−3.3 s for each pair of the coefficients providing the operation of the generators with ϕG ≈ 0◦ . Thus, in order to use effectively a CSR installed at the buses of a power station (i.e. to provide the operation of generators with the load angle close to cosϕ = 1), it is necessary to adjust correctly the gain factor of its proportional voltage control channel taking into account the preset coefficients of the generators’ AERs or to coordinate them simultaneously if it is possible to change the coefficients of the generators’ AERs selected earlier. For example, if the setting of the generator AER is K 0u = − 50, it is reasonable to choose the gain factor of the CSR proportional voltage regulator K 0uR from the range (10–15). As is clear from the computations presented in Fig. 2.19e, f, or in Fig. 2.20e, f, the intentional increase of the response speed of CSR, e.g., to a value of τR = 0.1 and below (the installation of a transformer-type CSR) can not be grounded, since it does not have any advantage. Thus, in the cases of static excitation control systems of synchronous generators, minimum reactive power output at the terminals of the generator is provided by the correct coordination of the settings of the generator AER and the CSR regulator.

48

2 Controlled Shunt Compensation

2.4.5 Estimating the Effectiveness of CSR Installation at the Buses of an Electric Power Plant with Generators Equipped with Modern Microprocessor Excitation Regulators The automatic excitation regulator ARV-SDP1 was the most widespread regulator in the XX century. Starting from 2004, digital excitation systems have been implemented intensively. In most cases, the static dependence of an output variable on external actions is not desirable and causes a control error, so the droop must be reduced. The static deviation decreases with an increase in the transfer ratio of the system, but in order to eliminate the static deviation fully the gain factor of the proportional voltage control channel K 0u must be increased sufficiently, which is not possible because of the considerable deterioration of the oscillation stability level. At early stages of excitation system development, analog automatic excitation regulators did not allow changing dynamically the value of the coefficient K 0u on the appearance of the electromechanical oscillations of the rotor. The problem of providing zero droop of various automatic control systems was solved in theory long ago using different methods, among which there was the creation of astatic control systems based on integrating elements. However, this method of providing zero droop of the automatic excitation regulators of synchronous generators became widespread only after the rapid development of microprocessor devices. Modern domestic and foreign microprocessor automatic excitation regulators are equipped with a proportional-integral voltage control channel (PI-channel) with the considerably reduced gain factor K 0u of the proportional voltage control channel. This leads to an increase in the oscillation stability levels and to a decrease in the required gain factors of the stabilization channels. As an example, the simplified structural scheme of a modern microprocessor automatic excitation regulator of the AVR-M type is presented in Fig. 2.22. The common control channel (CCC) of the automatic excitation regulator AVRM (Fig. 2.22) forms the proportional-integral control law and, in this way, provides astatic control. The aggregated output signal produced by control channels comes to the input of CCC, where the proportional-integral output signal of the excitation regulator output is formed. As earlier in Sect. 2.4.4, we will perform a series of computations associated with an increase in active power transferred over the line in the case the generators of the electric power plant are equipped with automatic excitation regulators of AVR-M type for two cases: • an uncontrollable SR is installed at the buses of the electric power plant; • CSR is installed at the buses of the electric power plant; As shown in Fig. 2.23b, the automatic voltage regulator of the power plant generators performs astatic control of the voltage at the buses with zero droop for both the cases of SR and CSR.

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

49

Fig. 2.22 The simplified structural scheme of AVR-M

Thus, due to zero droop of voltage control at the buses of the electric power plant, the effect that voltage deviations in the system with CSR is principally lower in comparison with the case of SR installation (see Figs. 2.16 and 2.17) is levelled. However, as is evident from Fig. 2.23c, the susceptance of CSR does not vary under the transition from one steady-state condition to another under such control. Therefore, if automatic excitation regulators with a PI control channel are used in generators, the use of CSR with a proportional voltage regulator is not permissible. Let us consider how to change the control law of CSR. Modern automatic control systems (ACS) of CSR can be controlled to change both voltage and current references, continuously as well (with a discrecity up to 1 s). With regard to CSR installed at the buses of an electric power plant or at the sending end of a transit line, this means that the reactor can operate in the mode of supporting the desired value of the power grid current (power), which changes every second and corresponds to a current value of the active power delivered by the line. In this connection, the ACS of CSR can be adjusted either to control the load angle of the generator and maintain, respectively, cosϕG = 1, or to control the active power transferred over the line with the subsequent recalculation of the required CSR reactive power by known expressions, for instance, by the simultaneous solving of (2.29) and (2.30). In this way, CSR is constantly maintaining the desired power corresponding to the line loading, i.e., automatically sheds power when the line is loaded by active power up to the natural loading and picks up its full capacity when the line is approaching to no-load condition. At that, there is no necessity to coordinate the settings of the control channels of the automatic excitation regulators of synchronous generators and CSR. As an example, let us consider the way to control the CSR power which allows maintaining the load angle of the power station generators close to cosϕG = 1 under operating conditions from no-load to the natural loading. Thus, with the same increase in the transferred active power (Fig. 2.24a) the voltage level is maintained with zero droop at the expense of voltage control at

50

2 Controlled Shunt Compensation

a

P, p.u.

t,s

b

U1, p.u. Circuit with SR Circuit with CSR

t,s

c

BR,p.u.

t,s

Fig. 2.23 a Variations of active power generation. b Voltage variations at the point of SR/CSR connection (at the buses of the power station). c Variations of the CSR susceptance

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

51

the buses of the electric power plant (Fig. 2.24b). Meanwhile, the required variations of CSR susceptance in dependence on the operation conditions of the power transmission system are provided (Fig. 2.24c). At the same time, as shown in Fig. 2.24d, the operation of the generator with minimum reactive power output is provided in all the considered operating conditions, i.e. the load angle of generators is supported cos ϕG ≈ 1. Thus, the astatic regulation of the CSR susceptance, which allows varying its power in accordance with a current operating condition of active power transmission over the line, is necessary to provide the effective use of CSR at the buses of a power station, the generators of which is equipped with proportional-integral automatic excitation regulators. In this case, the function of voltage control at the buses of the power station and at the point of CSR connection is assigned to the excitation regulators of synchronous generators, while the control of the CSR power in accordance with the operating condition of the power transmission system allows changing its susceptance under the transition from one operating state to another.

2.4.6 Computation of Small-Signal Stability Limits for Circuits with CSR/SR Let us perform the comparative computations of the small-signal stability limit for schemes with SR and CSR of equal capacity installed at the buses of an electric power plant. With the resistances of the armature and transformer windings neglected, the magnitude of the internal emf E Q in the per unit system in relation to the rated parameters of the generator is equal to: ┌( | ) )2 ( ) )2 ( ( | | | Prated · X q + X m · Xq + Xm Q | E Q | = √ U1 + rated + U1 U1 √( ) ) ( 0.527 · (2.56 + 0.126) 2 0.85 · (2.56 + 0.126) 2 1.0 + = + 1.0 1.0 = 3.32 p.u. For nonsalient pole synchronous generators with X d = X q , the internal emf E Q is equal to the emf E q , so E q = 3.32 p.u. The computations of the small-signal stability limit will be performed for schemes with SR and CSR installed at the buses of the power plant under the variations of the gain factor of the proportional voltage control channel of the generator AER. For each value of the coefficient K 0u , the gain factor of the proportional voltage control channel of the CSR regulator K 0uR is chosen in correspondence with Fig. 2.21 so that generators operate with cosϕG = 1. The results of the computations of the process of

52

2 Controlled Shunt Compensation

a

P, p.u.

t,с t,s

b

U1, p.u.

t,с t,s

c

BR,p.u.

t,с t,s

Fig. 2.24 a Variations of active power generation. b Voltage variations at the point of SR/CSR connection (at the buses of the power station). c Variations of the CSR susceptance. d Reactive power variations at the sending end of the line

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

d

53

QG,p.u.

t,с t,s

Fig. 2.24 (continued)

the gradual loading of the transmission system till the loss of stability are presented in Figs. 2.25 and 2.26: • in Fig. 2.25 the gain factor of the AER proportional voltage control channel is K 0u = − 20, the coefficient of the reactor is K 0uR = − 5; • in Fig. 2.26 the gain factor of the AER proportional voltage control channel is K 0u = − 50, the coefficient of the reactor is K 0uR = − 15; The aperiodic small-signal stability limits for schemes with SR/CSR: • for Fig. 2.25: PSR = 2.25 p.u. and PCSR = 2.3 p.u. • for Fig. 2.26: PSR = 2.4 p.u. and PCSR = 2.45 p.u. The limiting value of transmitted active power defined by the aperiodic stability condition is higher in the case of CSR installation than this in the case of SR installation, which is explained by a reduction in the reactive power consumed by CSR under the limiting operating conditions and an increase in the amplitude of the powerangle characteristics (in the limiting value of power defined by the aperiodic stability conditions). To some degree, the increase in the limit is caused by the fact that, under any operating condition, the voltage level in the circuit with CSR supported by the regulators of the generator and reactor is in principle higher that this in the circuit with SR, where the voltage level is maintained only by the regulator of the generator (see Figs. 2.25c and 2.26c). It can be seen from Figs. 2.25d and 2.26d that the emf of the generator (the field current or the voltage at the rotor rings) is lower in the case of CSR than this in the case of SR during the whole period of gradual loading till the loss of stability, while the internal angle is larger. Nevertheless, a reduction in the CSR susceptance to a zero value under limiting operating conditions and more effective voltage support in the case of CSR installation result in higher limiting values of

54 Fig. 2.25 A Active power transferred over the overhead transmission line to the system K 0u = − 20, K 0uR = − 5. b The absolute angle of the generator’s rotor. K 0u = − 20, K 0uR = − 5. c Voltage at the point of SR/CSR connection (at the buses of the power station). K 0u = − 20, K 0uR = − 5. d The field voltage of the generator. K 0u = − 20, K 0uR = − 5

2 Controlled Shunt Compensation

a

P, p.u. Circuit with SR Circuit with CSR

t,s t,с

b

δ,rad Circuit with SR Circuit with CSR

t,с t,s

c

U, p.u. Circuit with SR Circuit with CSR

t,с t,s

2.4 Estimating the Effect of a Controlled Shunt Reactor Installed …

d

55

Uf, p.u. Circuit with SR Circuit with CSR

t,с t,s

Fig. 2.25 (continued)

transmitted power defined by the aperiodic small-signal stability conditions, while under normal operating conditions, the current load of the armature and rotor circuits decreases sufficiently. It should be mentioned that, according to paragraph 5.1.23 of The Operational Regulations for Electric Power Plants and Networks of Russian Federation, shortterm current overloads of the armature and rotor of generators and synchronous compensators are permitted under emergency conditions in correspondence with instructions of the producer factory, technical conditions and State standards. Permissible field current overload of generators and synchronous compensators with the indirect cooling of the windings is determined by the permissible overload of the armature. For turbogenerators with direct or water cooling of the rotor winding, the permissible field current overload must be determined by the current ratio in relation to the rated rotor current—see Table 2.2. It should be mentioned that lower current load of the rotor under normal operating conditions in the case of CSR results, obviously, in higher value of the permissible short-term current overload of the rotor, but it must be confirmed by the producer factory.

56 Fig. 2.26 a Active power transferred over the overhead transmission line to the system K 0u = 50, K 0uR = − 15. b The absolute angle of the generator K 0u = 50, K 0uR = − 15. c Voltage at the point of SR/CSR connection (at the buses of the power station). K 0u = 50, K 0uR = − 15. d The field voltage of the generator. K 0u = 50, K 0uR = − 15

2 Controlled Shunt Compensation

a

P, p.u. Circuit with SR Circuit with CSR

t,с t,s

b

δ,rad Circuit with SR Circuit with CSR

t,с t,s

c

U, p.u. Circuit with SR Circuit with CSR

t,с t,s

References

57

d

Uf, p.u. Circuit with SR Circuit with CSR

t,с t,s

Fig. 2.26 (continued)

Table 2.2 Permissible field current overload of turbogenerators The duration of overload, minutes, no more than

Turbogenerators TVF, except for TVF-120-2

TGV, TVV (up to 500 MV inclusive), TVF-120-2

60

1.06

1.06

4

1.2

1.2

1

1.7

1.5

0.5

2.0

–

0.33

–

2.0

References 1. Evdokunin GA (2011) Electrical power systems and networks [Elektricheskiye sistemy i seti]. Sintez-Book, Saint-Petersburg, 284 p 2. Evdokunin GA, Smolovik SV (2008) Evaluating the effectiveness of reducing active power losses in elements of a power transmission system with the use of controlled shunt reactors [Otsenka effektivnosti snizheniya poter aktivnoy moshchnosti v elementakh elektroperedachi pri primenenii upravlyaemykh shuntiruyushchikh reaktorov]. Energoexpert 4:76–79 3. Demirchyan KS, Neyman LR, Korovkin NV et al (2003) Fundamentals of electrical engineering, vol 3. [Teoreticheskiye osnovy elektrotekhniki. T.3]. Piter, Saint-Petersburg, 377 p 4. Vulf AA (1941) Problems of electric power transmission over extra-long distances through compensated lines [Problema peredachi elektricheskoy energii na sverkhdalniye rasstoyaniya po kompensirovannym liniyam]. GEI, Moscow–Leningrad, 98 p 5. Kryukov AA, Libkind MS, Sorokin VM (1981) Controlled shunt compensation of ac power transmission system [Upravlyaemaya poperechnaya kompensatsiya elektroperedachi peremennogo toka], Libkind MS (ed). Energoatomizdat, Moscow, 184 p

58

2 Controlled Shunt Compensation

6. Ragozin AA, Seleznev YuG, Evdokunin GA (1994) New technical solution to the problems long-distance a.c. power transmission lines. In: 9th international power system conference, St. Petersburg 7. Belyaev AN, Smolovik SV (2003) An improvement of AC electrical energy transmission system with series compensation by implementation of controllable shunt reactors. In: Proceedings of IEEE power engineering society (PowerTech 2003), Bologna, Italy 8. Bryantsev AM, Dolgopolov AG, Evdokunin GA et al (2003) Magnetically controlled shunt reactors in 35–500 kV networks [Upravlyaemye podmagnichivaniyem shuntiruyushchiye reaktory dlya seti 35–500 kV]. Elektrotekhnika 1 9. Evdokunin GA, Ragozin AA (1996) The investigations of small-signal stability of longdistance power transmission systems with controlled shunt reactors [Issledovaniye staticheskoy ustoychivosti rezhimov dalnikh liny elektroperedachi s upravlyayushchim shuntiruyushchim reaktorom]. Elektrichestvo 8 10. Belyaev AN, Evdokunin GA, Smolovik SV, Chudny VS (2009) Grounding the necessity of using controlled shunt compensation devices for transit 500 kV power transmission systems [Obosnovaniye neobkhodimosti primeneniya ustroystv upravlyaemoy poperechnoy kompensatsii dlya tranzitnykh elektroperedach klassa 500 kV]. Elektrichestvo 2 11. Evdokunin GA (2009) Small-signal stability of power transmission systems with controlled shunt reactors [Staticheskaya ustoychivost rezhimov elektroperedachi s upravlyaemymi shuntiruyushchimi reaktorami]. Energoexpert 6:48–52 12. Yurganov AA, Kozhevnikov VA (1996) The control of synchronous generator excitation [Regulirovaniye vozbuzhdeniya sinkhronnykh generatorov]. Nauka, Saint-Petersburg, p 138

Chapter 3

Operating Principle and Design Features of a Magnetically Controlled Shunt Reactor

The main function of a magnetically controlled shunt reactor (CSR) is voltage and reactive power control. In CSR with magnetic biasing, the steel of the magnetic conductor is saturated by direct flux produced by rectified current flowing through a special control winding (CtW) in order to provide the smooth regulation of reactive power consumption and, consequently, smooth voltage control at the connection point. In fact, the operating principle used in the high-voltage transformer-type device is this of the magnetic amplifier, i.e. the inductive reactance of the power winding (PW) of the reactor reduces as the cores of the magnetic conductor get saturated. In real constructions of CSR, the range of smooth reactive power control with a ratio of more than 100 can be provided for by changing the state of the magnetic conductor steel from the unsaturated condition to a deep, close to the extreme saturation, condition under which the magnetic permeability of steel approaches the magnetic permeability of air. Constructively, CSR represents a device consisting of: • an electromagnetic part (the magnetic conductor, windings); • a semiconductor converter; • an automatic control system. Figure 3.1 presents the basic circuit of one phase of such a reactor with a shell-core magnetic conductor and two half-cores carrying the power windings PW connected to the system voltage E S and sections of the control winding CtW connected in opposition, to which the direct voltage source E CtW is connected. The direct magnetic biasing flux produced by the CtW current is locked between the central half-cores, while the alternating flux is closed through the upper and side yokes of the magnetic conductor and is added to the direct flux in the half-cores. In most constructions of high-capacity CSRs intended for voltage levels of 220 kV and above, a separate special winding (the compensation winding—CpW) is provided for, which is divided into two aiding-connected sections, each of which embraces a half-core. The terminals of the three phases are connected in delta. The windings are placed on the magnetic conductor of CSR in the following order: CpW–CtW–PW. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_3

59

60

3 Operating Principle and Design Features of a Magnetically Controlled …

Es

Fig. 3.1 The basic circuit of a CSR phase

* PW

*

*

CtW ICtW

ECtW ICtW

The arrangement of the windings on the magnetic system of a CSR phase, which consists of two half-cores (1), the upper (2) and the lower (3) horizontal yokes, and two side yokes (4), is shown in Fig. 3.2. Two sections of the control winding CtW are placed on the half-cores, connected in opposition, and switched to a controllable direct voltage source. The power winding PW embraces two adjacent half-cores carrying the control windings. The creation of separate paths for alternating and direct fluxes, which is provided for by the shell-core construction of the magnetic conductor with the splitted cores of the phases, and the opposite connection of PW and CtW sections ensure the independence of electromagnetic processes in the PW and CtW windings located at the same magnetic conductor. In order to interconnect separate single-phase devices into a three-phase one, the power windings are connected by the “Y/Y with the grounded neutral” scheme and each phase of the power winding is made of parallel branches with an input terminal to the middle (Fig. 3.3). In each phase, the sections of the control winding are connected in series-opposition, while the terminals of all the phases are connected in parallel and switched to the terminals of the converter.

3.1 Magnetic System of a Controlled Reactor In the main, the magnetic system of CSR is similar to this of a conventional three-winding transformer with a shell-core magnetic conductor, but with some constructive distinctions (Fig. 3.2):

3.1 Magnetic System of a Controlled Reactor 2

4

PW

CtW

CpW

61 1

CpW

CtW

1

CtW

CpW

CpW

CtW PW 4

3

Fig. 3.2 The cross-section of the CSR magnetic system

1. The magnetic conductor of CSR contains a splitted core (two half-cores) instead of one central core. The two half-cores embraced by the power winding along with the control winding, the sections of which are connected in opposition, realize the concept of the magnetic valve and are the most important element of CSR. 2. The sections of the yokes are larger than these of the half-cores. Under operating conditions of reactive power consumption, the half-cores of CSR are in the state of magnetic saturation by turns, at that, the duration of the saturated state within the period of the fundamental frequency depends on the power picked up by CSR. As the half-cores change from the saturated state to the unsaturated one and visa versa, the distortion of current curve by higher harmonic components takes place in the power winding. This results in the deterioration of electric energy quality in the point of CSR connection. Increasing the sections of the yokes is one of the design solutions which allow reducing current distortion in the power winding as well as decreasing the magnitude of current surges under switching operations (large cross-sections of the yokes prevent them from saturating even under extreme operating conditions of CSR). The power winding (PW) embraces both the half-cores without being divided into sections. 3. Ring or attached shunts. The use of such shunts made of electrotechnical steel allows redirecting the magnetic leakage flux to the magnetic conductor, increasing the efficiency factor of the device in such a way.

62

3 Operating Principle and Design Features of a Magnetically Controlled …

To 220-720 kV buses or line

*

*

*

PW

*

*

*

*

*

*

(+)

CtW (-)

*

*

*

CpW

*

*

* Main TMP

CT PT Settings

САУ ACS Redundant TMP

Fig. 3.3 The schematic electrical diagram of a three-phase three-winding CSR

3.2 Windings of a Controlled Reactor 3.2.1 Power Winding Let us assume that there is only one power winding PW, while the control winding and the compensation winding are absent or open. The power windings of a three-phase CSR are connected directly to the highvoltage buses and, by analogy with the high-voltage windings of transformers, are connected by the “Y/Y with the grounded neutral” scheme (Fig. 3.4). At that, the

3.2 Windings of a Controlled Reactor

UPWA

IPWA

63

UPWB UPWC

IPWB

IPWC UN

Fig. 3.4 The connection scheme of the CSR power windings B(t),T

2,0

2,0

Core #1

1,5

1,0

0,5

0,5

0,0

0,0

-0,5

-0,5

-1,0

-1,0

-1,5

-1,5

0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

Core #2

1,5

1,0

-2,0

B(t),T

t,s

-2,0

0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

t,s

Fig. 3.5 Magnetic induction in each of the half-cores (cores 1, 2) of a CSR phase under sinusoidal voltage applied to the power winding

current flowing in the winding produce equal magnetic fluxes (and inductions) in both the half-cores (Fig. 3.5) and the peak value of the magnetic induction is approximately equal to the saturation induction of the steel, which the CSR magnetic conductor is made of. This permits increasing the utilization factor of steel and getting a maximum control range of the device. The current flowing in the power winding under the condition of Fig. 3.6 is the magnetization, or no-load, current of CSR.

3.2.2 Control Winding Let us assume that the compensation winding is absent or open (there are only CtW and PW).

64

3 Operating Principle and Design Features of a Magnetically Controlled … i(t), А

1,5

1,0

0,5

0,0

-0,5

-1,0

-1,5

t,s 0

0,01

0,02

0,03

0,04

0,05

0,06

Fig. 3.6 No-load current of CSR

The control winding of CSR serves the function of biasing its magnetic conductor by direct current. The control windings of all the phases are connected in parallel and switched to a controllable direct voltage source (Fig. 3.7). Applying direct voltage to the control winding will cause a transient in it, during which the current in the winding will increase to the steady-state value determined by the expression I CtW = E CtW /RCtW , where ROU is direct current resistance of CtW, E CtW is the voltage of the source connected to CtW. The direct current flowing through the control winding produces direct magnetic flux and induction in the half-cores. Due to the opposite connection of the control winding sections, the fluxes in the half-cores have opposite directions, but equal values (the inductions will be also equal—see Fig. 3.8). The opposite connection of the CtW sections allows eliminating voltage transformation from the primary (power) winding to the secondary (control) winding. For this reason, there is no alternating voltage from the power winding at the terminals of the control winding at no-load, even if the winding is open. When both the windings are in operation, i.e. when the power winding is connected to the high voltage buses, and the control winding is connected to a direct voltage source, the magnetic fluxes produced by these windings in each of the half-cores are summed up (the inductions created by these fluxes are also summed up: Fig. 3.9 is the result of the superposition of Figs. 3.5 and 3.8) In Fig. 3.9, the first half of the period T: induction in half-core 1 is higher than the saturation induction of 2 T, and induction in half-core 2 is lower than the saturation induction. The second half: induction in half-core 2 is higher than the saturation induction, and induction in half-core 1 is lower than the saturation induction.

3.2 Windings of a Controlled Reactor

65

A

B

C

RShR ECtW

*

ICtWA*

ICtWB

*

*

*

*

ICtWC RShR

Fig. 3.7 The connection scheme of the control windings of CSR phases

3

B(t),T Core #1

2 1 0 -1

Core #2

-2 -3

t, s 0

1

2

3

4

5

Fig. 3.8 The growth of magnetic induction in each of the half-cores (cores 1, 2) of a CSR phase under the rated direct voltage applied to the control winding

It has been mentioned above that under no-load conditions the peak value of the alternating induction component produced in the central core by the power winding is approximately equal to the saturation induction. If the voltage applied to the control winding is such that the direct component of induction is also nearly equal to the saturation induction, then the resulting induction in each of the cores will be higher

66

3 Operating Principle and Design Features of a Magnetically Controlled … B(t), T

3

2

1

Core #1 0.5 T

0

0.5 T

-1

Core #2 -2

-3

t, sс 0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

0,040

Fig. 3.9 The addition of the magnetic fluxes (inductions) produced by the power and control windings in the half-cores (cores 1, 2) under the rated conditions

than the saturation induction for half of the period exactly. These operating conditions are referred to as the half-wave saturation mode. The magnetically controlled shunt reactor is designed so that its rated operating conditions are close to the half-wave saturation mode, because at this mode the halfcores are saturated by turns (during the half of the fundamental frequency period), and, consequently, the current consumed by CSR under the rated conditions will not contain harmonics. Figure 3.10 presents the current of the power winding and its harmonic composition for the half-wave mode of reactor operation. Let us consider intermediate operating conditions of reactive power consumption between no-load and the half-wave saturation condition. The power of the reactor is controlled through variying the direct component of magnetic induction in its half-cores by changing the current flowing through the control winding. Consequently, it is necessary to reduce current in the control winding in order to cause the reactor to absorb less than the rated power. As the magnitude of current in the control winding is reduced, the direct component of magnetic induction decreases. The decrease in the direct component of induction will result in a reduction of the part of the period for which each of the half-cores is in the saturated state. Correspondingly, the saturated states of each half-core will alternate with the periods within which they are both not saturated. At that, the current in the power winding of the reactor will decrease, and the waveform of the current will be distorted by higher harmonic components. In Fig. 3.11, the oscillogram of the power winding current and its harmonic composition are presented for the mode of 40% of rated power consumption. It

3.2 Windings of a Controlled Reactor 30 0

67

i(t), A

20 0

20 0

I, A

16 0

10 0

12 0

0

8 0

100

4 0

200 300

Harmonic #

1 0

0,00 5

0,01 0

0,01 5

0,02 0

0,02 5

0,03 0

0,03 5

t, s

0

3

5

7

9

15

11 13

17 19 21

23 25 27

29

Fig. 3.10 Current in the power winding of the reactor under the half-wave saturation condition

is evident from the oscillogram that the current curve is distorted to a considerable degree. According to Fig. 3.11, the odd harmonics from the 3rd to the 9th are the most pronounced. The total distortion current constitutes 42.3% of the peak value of the 1st harmonic current, but it makes up 12.8% or 0.13 p.u. with respect to the rated current. Figure 3.12 gives the dependences of higher harmonic components in the power winding current on the value of the PW current, i.e. on the power consumed by the reactor. The maximum of the 3rd harmonics corresponds to the power winding current of 80 A (about 40% of the rated power). At that, the effective value of the 3rd harmonic current totals about 25 A or 12.6% of the rated current of the reactor. It is obvious that the sufficient distortion in the waveform of the power winding current is caused mainly by the 3rd harmonic component. As a rule, in order to compensate the 3rd and other 3-fold harmonics, the design solution consisting in connecting a special (compensation) winding of the reactor in delta configuration is used. i(t), A

300

60

200

50

100

40

0

30

-100

20

-200

10

I, A

Harmonic # -300 0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

t, s

0

1

3

5

7

9

11

Fig. 3.11 Current in the power winding of the reactor under the condition of the consumption of 40% of the rated power

68

3 Operating Principle and Design Features of a Magnetically Controlled …

Fig. 3.12. The magnitudes of harmonic components versus the current in the power winding of the reactor (the rated current of the reactor is 200 A). The compensation winding is absent

3.2.3 Compensation Winding The compensation winding of CSR is delta-connected (Fig. 3.13) and serves two main functions: • compensates 3-fold harmonic components; • serves as the secondary winding of the supply transformer, to which semiconductor converters providing the magnetic biasing of the reactor’s magnetic conductor are connected along with filtering and compensating units (FCU), if they are required.

А

*

ICpWA

ICpWA

*

*

* В

*

ICpWB

ICpWB

С

*

ICpWC ICpWC

Fig. 3.13 The connection scheme of the compensation windings of CSR phases

3.2 Windings of a Controlled Reactor

69

The influence of the compensation winding on the harmonic composition of current in the power winding can be seen from comparison of Fig. 3.14a and b by example of the condition of 40% of rated power consumption, in which the 3rd harmonic component in the power winding current was maximum. We should remind that the resulting distortion current constituted 0.13 p.u. (12.8% with respect to the rated current of the reactor) under this condition in the case of the absence of the compensation winding, while the presence of the delta-connected winding causes this parameter to decrease to 0.04 p.u. at the expense of the full compensation of the 3rd and 9th harmonic components. It should be mentioned that the use of only two low-capacity FCUs adjusted to compensate the 5th and 7th harmonic components permits eliminating the distortion of the power winding current almost totally under any operating condition. It has been noted above that the rated conditions of CSR are close to the half-wave saturation condition, in which there is no distortion of the current running through the power winding. In the compensation winding only odd three-fold harmonic currents are locked. The most pronounced of them is the third harmonic. It is evident that under the rated conditions the current in the compensation winding will be low because of the absence of distortion, while the maximum of the compensation winding current will take place when the device carries about 50% of the rated load (see Fig. 3.15). i(t), A

300

60

200

50

100

40

0

30

-100

20

-200

10

I, A

a)

Harmonic # -300

300

0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

t, s

i(t), A

0

60

200

50

100

40

0

30

-100

20

-200

10

-300

0

0,005

0,010

0,015

0,020

0,025

0,030

0,035

t, s

1

3

5

7

9

11

I, A

b)

Harmonic #

0 1

3

5

7

9

11

Fig. 3.14 Currents in the power winding and their harmonic composition under the condition of 40% of the rated power consumption. a CpW is open; b CpW is closed

70

3 Operating Principle and Design Features of a Magnetically Controlled … i(t), A

2000

i(t), A

300

1500

200

1000 100

500

0

0 -500

-100

-1000 -200

-1500 -2000

0

0,05

0,10

0,15

0,20

0,25

t, s

-300

0,05

0

0,10

0,15

0,20

0,25

t, s

Fig. 3.15 Current variations in the compensation and power windings during the increase of the CSR power from the no-load to the rated value

It follows from the example of Fig. 3.15 that the maximum of current in the compensation winding is approached in 0.18 s after the application of direct or rectified voltage to the control winding. At this moment the amplitude of the power winding current is equal to about 150 A, which corresponds to 50% of the power consumed. It should be noted that the rate of power picking-up and shedding by CSR is determined by parameters of the reactor itself, the state of its magnetic system at the moment when power pick-up or shedding starts, and the voltage applied to the control winding. For accelerating the processes of power picking-up and shedding, additional semiconductor converters with increased voltage are used, which are connected to the control winding for a short time in accordance with the algorithms put in the automatic control system of the reactor. The example of power picking-up and shedding by CSR is presented in Fig. 3.16. It can be seen that the time of power picking-up (forcing) and shedding (unforcing) is about 0.3 s. For getting more details on the automatic control system (ACS), see Chap. 5. i(t), A

30 0

forcing

20 0

i(t), A

250 0

unforcing

forcing

unforcing

200 0

10 0

150 0

0 100 0

100

50 0

200 300

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

t, s

0

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

t, s

Fig. 3.16 Current in the power and control winding under the forcing and unforcing of CSR power: a current in the power winding of CSR; b current in the control winding of CSR

3.3 Design Modifications and the Range of Manufactured CSRs

71

3.3 Design Modifications and the Range of Manufactured CSRs Various circuit arrangements and design modifications of CSR have been developed and tested during the recent 12 years in the course of which magnetically controlled shunt reactors have been actively implemented by the producer factory PJSC “Zaporozhtransformator”. The construction of a magnetically controlled shunt reactor is based on the following principles: • the control of the reactor power is carried out through saturating the magnetic system of CSR by direct magnetic flux of controllable value; • direct magnetic flux in the cores of the reactor is produced by direct (rectified) current flowing in the control winding of the reactor; • the control of the reactor’s power in its power winding is carried out by a magnetic biasing source of relatively low capacity (the magnetic valve principle); • the reduction of higher harmonic components in the reactor current requires special measures. The above mentioned tasks were solved by splitting the core of each phase into two (two half-cores) and separating functions of the windings. In such a way, one of the winding (the power winding) must provide the direct connection of CSR to the grid of any voltage level, while the other (the control winding) must provide the saturation of the magnetic system at the expense of direct (rectified) current flowing in it. In order that a converter unit of low capacity can be connected to the control winding, there must be no alternating voltage at its terminals, which is achieved by the opposite connection of the control winding sections. Since the working point on the magnetization curve moves to the non-linear part as the reactor is loaded, the current of the power winding is distorted. Since the sufficient distortion of the CW current curve is caused mainly by the 3rd harmonic component, the most reasonable way to eliminate it is to use a delta-connected winding in CSR. Nowadays, several types of circuit design of 35–500 kV magnetically controlled shunt reactors are widely adopted. The choice of one or another embodiment depends on a plenty of factors: the overall dimensions, weight, and the cost characteristics of a CSR complex, repairability, the complexity of electromagnetic part production, the required capacity, etc. The main factors determining the embodiment of CSR is its installed capacity and voltage level: • as a rule, reactors with a capacity less than 32 MVAr do not have the compensation winding, i.e. only the power and control windings are available; reactors with a capacity above 32 MVAr have all the three windings;

72

3 Operating Principle and Design Features of a Magnetically Controlled …

• reactors designed for voltage levels up to 220, 330 kV have three-phase arrangement (with the electromagnetic part of the RTDU line); reactors intended for the voltage level of 500 kV and above represent three-phase groups of single-phase reactors (with the electromagnetic part of the RODU line).

3.3.1 CSR with a Capacity Lower than 32 MVAr The modification with two windings, namely, the power and the control windings, has been chosen (Fig. 3.17) as the main constructive decision for CSR with a relatively low capacity (32 MVAr and below). The arrangement of the electromagnetic part of this CSR modification is rather complicated, since it has three phases and, besides that, the connection scheme of the power winding, for example, must allow for the possibility that direct current can flow in it under transient conditions and prevent this current from entering into the grid, which presents some problems for the relay protection of CSR. The control winding of such CSR is also complex: the connection scheme of the control winding represents an open double-delta connection and combines several functions: • connecting a low-capacity (about 1% of the installed capacity of CSR) transformer-converter unit providing the circulation of direct current in the control winding to the +/− terminals; • compensating three-fold harmonic components at the expense of the deltaconnection of the control winding; • supplying transformer-converter units directly from the control winding by connecting them to the alternating voltage terminals of the control winding; • combining the functions of the control and compensation windings in one secondary winding, which allows not only the reduction of a number of windings, but also the reduction of active material consumption. Let us consider CSR of the RTU-25000/100-UHL1 type as the most widespread modification of a two-winding reactor. The reactor consists of: 1. An electromagnetic part consisting of a shell-type magnetic conductor with six half-cores (two half-cores per phase). The design of the phase of such a reactor is presented in Fig. 3.18. The magnetic system of a CSR phase is composed of two half-cores (1), the upper (2) and the lower (3) horizontal yokes and two side yokes (4). On each of the half-cores, sections of the control (CtW) and power (PW) windings are placed. In Fig. 3.18, as opposed to Fig. 3.2, the power winding has two sections, each of which is located on its own half-core. Since these sections are aiding-connected, the scheme of Fig. 3.18 uses the very magnetic valve concept that was discussed when introducing Fig. 3.2. 2. Two single-phase transformer-converter units of the OMPP-200/22/0.22 type connected via protectors to the ac terminals of the control winding and providing the full-range control of the reactor’s power.

3.3 Design Modifications and the Range of Manufactured CSRs

73

Fig. 3.17 The basic circuit of a two-winding CSR of the RTU-25000/110-UHL1 line: 1—RTDU100000/220 is the three-phase electromagnetic part of RTU-25000/110; 2—the three-phase semiconductor converter PPM-200/750; 3—ACS—the automatic control system of the reactor; 4— the converter transformer of the OM-200/22/0.22 type; 5—the preliminary biasing transformer TM0-2.5/0.4/0.012; 6—the protector of the PKT 110-10-31.5-12.5 type; 7—SP—surge protector; 8—DCS—direct current sensor; 9—DVS—direct voltage sensor; CT1-CT10—integrated current transformers

74

3 Operating Principle and Design Features of a Magnetically Controlled … 2

PW CtW

1

CtW PW

1

PW CtW

CtW PW

PW CtW

4

3

Fig. 3.18 The sectional view of the magnetic system of a phase of 25 MVAr 110 kV CSR (the last phase on the left of the three-phase magnetic conductor is shown). A separate compensation winding is absent

3. Two initial biasing transformers of the TMO-2.5/0.4/0.012 type connected to a 380 V three-phase electric grid. These transformers are connected to single-phase converters of the PPM-200/750 kV type at the low voltage sides and serve for the initial magnetic biasing of the reactor before its energization. The circuit of the converter unit is presented in Fig. 3.19. 4. A digital automatic control system in which algorithms for controlling the power of the reactor are realized. Two resistors are installed between the +/− terminals of the control winding inside the reactor’s tank, the point of their connection is grounded. The resistor is necessary in case the connection between the control winding and the poles of the converter is broken in order to dissipate the energy accumulated in the control winding. In the process of CSR operation, the information got from the direct current and voltage sensors (DCS and DVS, respectively) is used. On basis of this information, the limitations of the rectified current of the converters is set under different operating conditions of CSR including the case of the converter and transformer overload, the preliminary biasing condition, etc.

3.3 Design Modifications and the Range of Manufactured CSRs

Fig. 3.19 The circuit of the converter unit of the PPM-200/750 type

75

76

3 Operating Principle and Design Features of a Magnetically Controlled …

3.3.2 CSR with a Capacity Above 32 MVAr Reactors with a capacity above 32 MVAr have not only different arrangement of the electromagnetic part, but also a different set of equipment. Let us consider circuit design types of such reactors by the example of the reactor RTU-100000/220-UHL1 (Fig. 3.20). The magnetic conductor of the reactor, like this of RTU-25000/110-UHL1 shown in Fig. 3.18, represents a shell-type construction with six half-cores (two half-cores per phase). Along with different connection schemes of the control and power windings, the main distinction is that functions of the control winding are divided. There is a separate additional compensation winding in reactors with a capacity above 32 MVAr, which, as has been mentioned above, serves the function of compensating three-fold higher harmonic components in the power grid current and is used for the connection of low-capacity (about 1% of the installed capacity of the reactor) transformerconverter units providing the magnetic biasing of the reactor. If there are no additional connections, the current of TMP and the 3rd harmonic current do not exceed 20% of the rated current of the reactor, the compensation winding is made with a reduced cross-section. The absence of direct electromagnetic coupling between the power and the control windings, which is provided by implementing an additional compensation winding located between CtW and PW, allows refusing from the complicated connection scheme of the power winding, since the possibility that the rectified current will flow in it under transient conditions is eliminated. This circumstance allows providing for the set of current transformers necessary for the realization of fast-acting protection. Sections of the control winding of each phase are connected in opposition with respect to each other, so there is no alternating voltage at its terminals, which permits interconnecting the sections and switching them to the rectified voltage terminals of the converter unit intended for magnetic biasing. As opposite to RTU-25000/110-UHL1, there is full-value three-phase voltage at the terminals of RTU-100000/220-UHL1 compensation winding, so a three-phase transformer-converter unit of the TMP-1000-10/0.4 type can be connected to them, which provide the magnetic biasing of CSR. A 100 MVAr 220 kV CSR contains two such biasing units, the main and the redundant one. The redundant TMP is supplied from the 6–35 kV switchgear and, along with its main function of bias current control, server another no less important function of the preliminary magnetic biasing of the reactor before the power grid voltage is applied to it. The capacity of the TMP transformer of 1000 kVAr and its output low-side voltage of 400 V are determined by the necessity to provide the pick-up of reactor power from 5 to 100% or visa versa within not more than 1 s (the requirement of the Costumer). It should be mentioned that if the forced power picking-up and shedding is provided for not by TMP feeding from the compensation winding of the reactor, but by TMP

3.3 Design Modifications and the Range of Manufactured CSRs

77

Fig. 3.20 The basic circuit of a three-winding CSR of the RTU-100000/220-UHL1 line: 1— RTDU-100000/200—the three-phase electromagnetic part RTU-100000/220; 2—TMPm—the main 1000 kVA 10/0.4 kV transformer-converter unit; 3—TMPr—the redundant 1000 kVA 6– 35/0.4 kV transformer-converter unit; 4—PPm, PPr—three-phase controllable semiconductor converters; 5—ACS—automatic control system; 6—DCS—direct current sensor; 7—DVS—direct voltage sensor; 8—SP-2.5/1000—a surge protector; 9—CT1-CT11—integrated current transformers; 10—TV1, TV2—220 and 10 kV voltage transformers; 11—B220kV—the 220 kV circuit breaker of the reactor; 12—Bm, Br—the circuit breakers of the main and redundant TMP

connected directly to the 6–35 kV switchgear, the time of full power picking-up or shedding can be reduced sufficiently to 0.5–0.6 s.

78

3 Operating Principle and Design Features of a Magnetically Controlled …

A decrease in the time of CSR power picking-up and shedding depends on the value of the rectified voltage applied to the terminals of the control winding. Since the short-circuit voltage of the reactor is about 50%, then, as the reactor is loaded, the voltage at the compensation winding decreases and, consequently, the rectified voltage applied to the control winding also reduces. If TMP is connected to 6–35 kV grid, the power of which is sufficiently higher than the capacity of the transformer TMP-1000, the output rectified voltage remains almost invariable during all the period of reactor power picking-up. The functions of the resistors installed in the tank of CSR and connected in opposition to the aiding-connected sections of the control winding as well as functions of the direct current and voltage sensors are the same as these of RTU-25000/110UHL1. According to the requirements of JSC “FGC of UPS”, the time of a full change in CSR power must be not longer than 0.3 s in 500 kV power grids. For this reason the standard packaging of a 500 kV reactor (as opposed to 110–330 kV reactors) contains a semiconductor converter with increased rated rectified voltage (PPD — dynamic, see Fig. 3.21). It is used under the conditions of forced power picking-up and shedding and also performs the function of preliminary magnetization. CSR of all voltage levels include the main and the redundant converter units (TMPM and TMPR ). In the standard modifications of 220–330 kV CSR without TMPD , the functions of preliminary biasing are served by TMPR connected to the 6–35 kV auxiliary switchgear (see Fig. 3.20). The dynamic converter is supplied from the 1000 kVAr transformer TMP with the low side voltage of 1 kV (as opposed to the main and the redundant TMPs with the voltage of 400 V). For this reason, the increased rectified voltage of 1485 V (see Table 3.4) appears at the terminals of such a dynamic converter when the thyristors are fully open. By today, the adoption of 35–500 kV CSR production process has been finished and changed to the stage of serial production. By the moment the book was written (November, 2012), 76 magnetically controlled shunt reactors had been installed in Russia and CIS countries. The types and number of installed CSRs are given in Table 3.1.

3.3.3 Technical Characteristics of the Most Widespread CSRs As follows from Table 3.1, the most required are the following CSR types: RTU-25000/110, RTU-100000/220, and RTU-180000/500. The main technical characteristics of them are presented in Tables 3.2, 3.3 and 3.4.

3.3 Design Modifications and the Range of Manufactured CSRs

79

Fig. 3.21 The basic circuit of a three-winding CSR of the RTU-180000/500-UHL1 line: 1— RODU-60000/200—the single-phase electromagnetic part RTU-180000/500; 2—TMd—the main 1000 kVA 6(10)/1.1 kV transformer of dynamic modes; 3—TMm—the main 1000 kVA 10/0.4 kV transformer of static modes; 4—TMr—the redundant 1000 kVA 10/0.4 kV transformer of static modes; 5—PPm, PPr, PPd—three-phase controllable semiconductor converters of the main, redundant and dynamic TMPs, respectively; 6—ACS—automatic control system; 7—DCS—a direct current sensor; 8—DVS—a direct voltage sensor; 9—SP-2.5/100—a surge protector; 10—a surge arrester (only for line CSR); 11 CT1-CT9—integrated current transformers; 12—TV1, TV2—500 and 10 kV voltage transformers; 13—BA, BB, BC—the 500 kV circuit breakers of the reactor; Bm, Br, Bd—the circuit breakers of the main, redundant and dynamic TMP, respectively; BCpW—circuit breakers intended for CpW shunting (only for line CSR)

80

3 Operating Principle and Design Features of a Magnetically Controlled …

Table 3.1 The range and number of the CSRs produced and put into operation Type RTU-25000/35

Capacity, kVAr 25,000

Voltage, kV

Quantity

38.5

7 26

RTU-25000/110

25,000

121

RTU-63000/110

63,000

121

1

RTU-25000/220

25,000

242

1

RTU-63000/220

63,000

242

6

RTU-100000/220

100,000

242

15

RTU-180000/330

180,000

347

3

RTU-180000/500

180,000

525

17

Table 3.2 The main technical characteristics of RTU-25000/110 Technical characteristics (the name of the parameter)

The value of the parameter

The main characteristics of the reactor Factory model (brand)

RTU-25000/110

Rated capacity, MVAr

25

Number of phases

3

Rated voltage, kV

121

Maximum operating voltage, kV

126

Voltage level of the neutral, kV

35

Possible ways of neutral grounding: Dead grounding (yes/no)

Yes

Rated voltage of the power winding, A

119.3

Rated voltage at the control winding of one core at no-load and with the rated 11 voltage applied to the power winding, kV Rated biasing current of the control winding, A, not greater than

720

Rated frequency, Hz

50

No-load losses at no-load voltage, kW

25

Total losses under the rated voltage and rated frequency, kW

240

Losses tolerance, %

+15

Deviation of reactive current in each phase of the reactor from the arithmetic mean of currents of all the three phases, % of the rated current, not greater

±3

Minimum time of a power change from 5 to 100% or inversely, s, not longer than

5

Time of turning to the rated conditions with preliminary magnetic biasing, s, at the most

0.02

Permissible power overload (for not longer than 20 min), % of the rated capacity (with the maximum operating voltage of the grid)

30 (continued)

3.3 Design Modifications and the Range of Manufactured CSRs

81

Table 3.2 (continued) Technical characteristics (the name of the parameter)

The value of the parameter

20 Permissible current overload of the control winding (for not longer than 20 min), % of the rated current (with the system voltage not lower than the rated voltage) Amplitude of any high harmonic component of the power grid current under the rated sinusoidal voltage, % of the rated current, not higher than

3

Excess of the temperature of the reactor’s elements over the ambient temperature under the rated current in the power winding must be not greater, degrees • Of the winding (measured by the resistance)

65

• Of the oil in upper layers (measured with a thermometer)

60

• Of the surfaces of the magnetic system and elements (measured by a thermocouple)

75

Short-circuit voltage between the control and the compensation windings, %, 30 not less than Doubled amplitude of vibration on the wall of the tank, µm, at the most

150

Corrected level of the acoustic power, dBA, at the most

85

Delivery package The electromagnetic part of the reactor RTDU-25000/110

Yes

Magnetic biasing system

Yes

Automatic control system (ACS), which is to be installed at the control board Yes of the substation Surge protector (SP)

Yes

Monitoring system

At the request of the customer

Direct current sensor, pieces

1

Protector PKT 101-10-315-12.5, pieces

4

Automatic control system (ACS) Automatic control system with voltage and current control channels

Yes

The voltage reference range, kV

105–125

The current reference range, A

0–120

Life time, years, no less than

30

Warranty operation life, months

36

Biasing system Number of converter units OMPP-200/22/0.22

2

Rated capacity of the converter transformer, kVA

200

Rated voltage of the primary winding of the converter transformer, kV

22

Rated voltage of the secondary winding of the converter transformer, kV

0.22

Rated rectified voltage of the converter, V

200

Rated rectified current of the converter, A

750

82

3 Operating Principle and Design Features of a Magnetically Controlled …

Table 3.3 The main technical characteristics of RTU-100000/220 Technical characteristics (the name of the parameter)

The value of the parameter

The main characteristics of the reactor Factory model (brand)

RTU-100000/220

Rated capacity, MVAr

100

Rated voltage, kV

242

Maximum operating voltage, kV

252

Voltage level of the neutral, kV

35

Rated voltage of the power winding, A

238

Rated line voltage of the compensation winding under the no-load condition 11 of the reactor, kV Rated current of the control winding, A, not greater

2000

Rated frequency, Hz

50

Voltage level of the control winding, kV

35

Total losses under the rated voltage and rated power, kW

600

Losses tolerance, %

+15

Deviation of reactive current in each phase of the reactor from the arithmetic ±3 mean of currents of all three phases, % of the rated current, not greater Minimum time of a power change from 5 to 100% or inversely, s, not longer 1 than Time of turning to the rated conditions with preliminary biasing, s, at the most

0.02

Permissible power overload (for not longer than 20 min), % of the rated capacity (with the maximum operating voltage of the grid)

30

Permissible current overload of the control winding (for not longer than 20 20 min), % of the rated current (with the system voltage not lower than the rated voltage) The amplitude of any high harmonic component of the power grid current at 3 the rated sinusoidal voltage, % of the rated current, not higher than The excess of the temperature of the reactor’s elements over the ambient temperature under the rated current of the power winding must be not greater, degrees • Of the winding (measured by the resistance)

65

• Of the most heated point of the winding (confirmed by computations)

78

• Of the oil in upper layers (measured with a thermometer)

60

• Of the surfaces of the magnetic system and elements (measured by a thermocouple)

85

Short-circuit voltage between the control and compensation windings, %, not less than

50

Doubled amplitude of vibration at the wall of the tank, µm, at the most

200

Sound volume, dBA, at most

90 (continued)

3.3 Design Modifications and the Range of Manufactured CSRs

83

Table 3.3 (continued) Technical characteristics (the name of the parameter)

The value of the parameter

Delivery package The electromagnetic part of the reactor

Yes

Biasing system

Yes

Automatic control system (ACS), which is to be installed at the control board of the substation

Yes

Surge protector (SP)

Yes

Monitoring system

At the request of the customer

Automatic control system (ACS) Automatic control system with voltage and current control channels

Yes

Voltage droop of ACS, % of rated system voltage

1–5

The voltage reference range, kV

200–250

The current reference range, A

6–240

The accuracy of voltage reference setting, kV, at most

1

The accuracy of current reference setting , A, at most

1

Communication interface between ACS and automatic system of technological process control of the substation

The protocol IET 60870-5-101 (RS-232)

Climatic construction—UHL4 for installation in enclosed space with an ambient temperature of +5 to +35 °C

Yes

Biasing system The main converter unit TMP-1000/10/0.4(540/2000)

1

The redundant converter unit TMP-1000/10/0.4(540/2000)

1

Rated capacity, kVA

1000

The rated voltage of the primary winding of the transformer, kV

10

The rated line voltage of the secondary (valve) winding of the transformer, kV

0.4

Total losses (under the rated power), kW, at the most

28

No-load losses (with locked converter), kW, at most

3

Scheme and group of connection of the primary and secondary (valve) windings of the transformer

Yn/Δ-11

The rated line supply voltage of the converter, V

400

The rated frequency of the supply voltage of the converter, Hz

50

The maximum output voltage of the converter, V

540

The rated rectified current, A

2000

Permissible overload during a period of 20 min at most, A

2400

The rated power of heat losses in the converter, W, no greater than

13,800

84

3 Operating Principle and Design Features of a Magnetically Controlled …

Table 3.4 The main technical characteristics of RTU-180000/500 Technical characteristics (the name of the parameter)

The value of the parameter

The main characteristics of the reactor Factory model (brand)

RTU-180000/500

Electromagnetic part arrangement • Single-phase (yes, no)

Yes

• Three-phase (yes, no)

Yes

Rated voltage, kV

525

Maximum operating voltage, kV

550

Voltage level of the neutral, kV

35

Rated voltage of the power winding, A

198

Rated line voltage of the compensation winding under the no-load condition 11 of the reactor, kV Rated current of the control winding, A, not greater

2000

Rated frequency, Hz

50

Possible ways of neutral grounding: • Dead grounding (yes/no)

Yes

• Grounding though a compensating reactor with corresponding overvoltage Yes protection of surge arrester (yes, no) Total losses under the rated voltage and rated power • For single-phase arrangement (per three phases), kW

1080

• For three-phase arrangement, kW

900

Losses tolerance, %

+15

Deviation of reactive current in each phase of the reactor from the arithmetic ±3 mean of currents of all three phases, % of the rated current, not greater Minimum time of a power change from 5 to 100% or inversely, s, not longer 0.3 than Time of turning to the rated conditions with preliminary magnetic biasing, s, 0.02 at the most Permissible power overload (for not longer than 20 min), % of the rated capacity (under the maximum operating voltage of the grid)

30

Permissible current overload of the control winding (for not longer than 20 min), % of the rated current (with the system voltage not lower than the rated voltage)

20

The amplitude of any higher harmonic component of the power grid current 3 under the rated sinusoidal voltage, % of the rated current, not higher than Excess of the temperature of the reactor’s elements over the ambient temperature under the rated current of the power winding must be not greater, degrees • Of the winding (measured by the resistance)

65 (continued)

3.3 Design Modifications and the Range of Manufactured CSRs

85

Table 3.4 (continued) Technical characteristics (the name of the parameter)

The value of the parameter

• Of the most heated point of the winding (confirmed by computations)

78

• Of the oil in upper layers (measured with a thermometer)

60

• Of the surfaces of the magnetic system and elements (measured by a thermocouple)

85

Short-circuit voltage between the control and compensation windings, %, not less than

50

Doubled amplitude of vibration at the wall of the tank, µm, at the most

200

Sound volume, dBA, at most

90

Delivery package The electromagnetic part of the reactor • Three electromagnetic parts if the arrangement of the electromagnetic part Yes is single-phase • A redundant phase for single-phase arrangement

At the request

• One electromagnetic part if the arrangement of the electromagnetic part is Yes three-phase Biasing system

Yes

Automatic control system (ACS), which is to be installed at the control board of the substation

Yes

Surge protector (SP)

Yes

Monitoring system

At the request of the Customer

Automatic control system (ACS) Automatic control system with voltage and current control channels

Yes

Voltage droop of the ACS regulator, % of U C

1–5

The voltage reference range, kV

500–550

The current references range, A

0–200

The accuracy of voltage reference setting, kV, at most

1

The accuracy of current reference setting, A, at most

1

Communication interface between ACS and automatic system of technological process control of the substation

The protocol IET 60870-5-101 (RS-232)

Climatic construction—UHL4 for installation in enclosed space with an ambient temperature of +5 to +35 °C

Yes

Biasing system (the main and redundant converter units) The quantity of converter units TMP-1000/10/0.4 (540/2000)

2

Rated capacity, kVA

1000

Rated voltage of the primary winding of the transformer, kV

10

Rated line voltage of the secondary (valve) winding of the transformer, kV

0.4 (continued)

86

3 Operating Principle and Design Features of a Magnetically Controlled …

Table 3.4 (continued) Technical characteristics (the name of the parameter)

The value of the parameter

Total losses (at the rated power), kW, at the most

28

No-load losses (with locked converter), kW, at most

3

Scheme and group of connection of the primary and secondary (valve) windings of the transformer

Yn/Δ-11

Rated line supply voltage of the converter, V

400

Rated frequency of the supply voltage of the converter, Hz

50

Maximum output voltage of the converter, V

540

Rated rectified current, A

2000

Permissible overload during a period of 20 min at most, A

2400

Rated power of heat losses in the converter, W, no greater than

13,800

Biasing system (converter unit of dynamic modes) The number of converter units TMP-1000/(6)10/1.1 (1485/2000)

1

Rated capacity, kVA

1000

The rated voltage of the primary winding of the transformer, kV

6 (10)

The rated line voltage of the secondary (valve) winding of the transformer, kV

1.1

Total losses (at the rated power), kW, at the most

21

No-load losses (with closed converter), kW, at most

3

Scheme and group of connection of the primary and secondary (valve) windings of the transformer

Yn/Δ-11

The rated line supply voltage of the converter, V

1100

The rated frequency of the supply voltage of the converter, Hz

50

The maximum output voltage of the converter, V

1485

The rated rectified current, A

2000

Chapter 4

Method of Controlled Shunt Reactor Computer Simulation

Nowadays, theoretical and practical interest in the development of the detailed simulation of high-voltage power equipment with complicated design of the magnetic system has increased sufficiently [1, 2]. For example, the creation of the computer model of a controlled reactor [3] allows analysing its behaviour under balanced and unbalanced steady state and transient operating conditions, estimating its response speed, revealing the peculiarities of reactor switching together with power transmission lines (including switching operations under single-phase auto-reclosure), and finding the optimal algorithms of CSR power control already at the stage of development.

4.1 Main Constructive Elements of the Reactor RTU-180000/500 and Its Simulation The magnetic system of one phase of a controlled reactor is presented in Fig. 4.1. In the centre, there are two magnetic cores (two half-cores), on which the compensation winding, the control winding, and the power winding are placed. An elementary part of the magnetic conductor characterized by the section S and the length l, within which the magnetic flux F is equal along all the whole length and section of the magnetic core at the particular time moment, is referred to as a magnetic core. In Fig. 4.1, the fluxes closing through the magnetic conductor are denoted by digital indices, while the leakage fluxes are designated by a numeral and the letter S. Two central cores with the fluxes F1 and F2 are interconnected by the central yokes with the fluxes F3 and F4 . The central yokes are made thickened and do not become saturated, which leads to the enhancement of the harmonic composition of the current flowing through the power winding. There are also two side yokes F5 and F6 which represent paths for the magnetic flux produced by the alternating current of the power winding. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_4

87

88

4 Method of Controlled Shunt Reactor Computer Simulation ФS9 Ф3

0 1 CpW PW CtW

ФS7

Ф5

CpW CtW

CtW

0 2 CpW

CpW CtW PW

iCpW

iCpW

iCtW

iCtW

Ф6

ФS8

iPW

ФS5

ФS3

ФS1

Ф1 3 0

Ф2

Ф4

ФS2

ФS4

ФS6

4 0

ФS10

Fig. 4.1 The magnetic system of a CSR phase

In the circuit of Fig. 4.1, the following leakage paths are taken into account: • the paths between the compensation winding and the central cores (half-cores) Fs1 and Fs2 ; • the paths between the control winding and the compensation winding Fs3 and Fs4 ; • the paths between the power winding and the control winding Fs5 and Fs6 ; • the paths between the side yokes and the tank Fs7 and Fs8 ; • the paths between the central yokes and the tank Fs9 and Fs10 . The design of the considered CSR suggests that the power winding embraces both the half-cores, and there must be one leakage path between the power and the control windings. However, in order to get a symmetrical equivalent circuit and to reduce the volume of computation, the assumption has been made that this circuit is equivalent to the circuit with two leakage paths Fs5 and Fs6 , the sections of which are less by a half than the initial one. The magnetic paths of section S and length l shown in Fig. 4.1 can be associated with the magnetic reluctances R and the equivalent magnetic circuit presented in Fig. 4.2. The indices of the magnetic reluctances are the same as these of the corresponding fluxes. The circuit contains:

4.1 Main Constructive Elements of the Reactor RTU-180000/500 and Its … R3

1

89

2 9

5 6

RS7

1

R5

2

RS5

3

RS3

RS1

4

R1

R2

RS2

RS4

RS6

10

11

12

R6

RS8

RS9

FCpW

FCpW

13

7

RS10

FCtW

FCtW

8

FPW

FPW 3

R4

4

Fig. 4.2 The equivalent circuit of the CSR magnetic system

• magnetomotive forces F = iW, where i is the current of a winding, W is the number of its turns; • non-linear magnetic reluctances R (for which μ = f (B)) representing paths of magnetic fluxes in the elements of the steel magnetic conductor (in the cores, the central and side yokes); • linear magnetic reluctances R corresponding to leakage paths (for which μ = const). The accepted model of the magnetic system of the RTU reactor is based on the real design of its magnetic circuit with account taken of the winding locations. The equivalent circuit of the magnetic system is specified by nodes and the most important paths (branches) of magnetic flux distribution, which approximate, under certain assumptions, the magnetic field pattern. The number of considered branches and nodes is chosen so that they provide the satisfactory approximation of the field without the unnecessary complication of the magnetic circuit. The described concept of magnetic system modelling is based on field description by the scalar magnetic potential, the determination of which supposes that rotH = 0 in the considered area. Since the latter supposes that the field is concentrated exclusively outside the windings, the radial dimensions of the coils are not taken into account. Apart from introducing slim windings into the model, we neglect the frequency dependences of losses in the steel on eddy currents, and the hysteresis phenomenon. Real dimensions of the coils can be taken into account in various ways, one of which is mentioned in [1]. The steel losses are treated in the same way, for instance [2]. However, at the present stage of research, considering the dimensions of coils and steel losses [2] in the computer program have been found unreasonable.

90

4 Method of Controlled Shunt Reactor Computer Simulation

The circuit of Fig. 4.2 contains 4 nodes (q = 4) and 16 branches (p = 16). The number of equations describing the configuration of such a magnetic system in accordance with Kirchhoff laws: • the first Kirchhoff law: n = q − 1 = 3; • the second Kirchhoff law: m = p − q + 1 = 13. As a result, the following equations can be written for each of the three CSR phases: by the first Kirchhoff law (the sum of fluxes in the node is equal to zero); node 1: ϕs7 + ϕ5 + ϕs5 + ϕs3 + ϕs1 + ϕ1 − ϕs9 − ϕ3 = 0; node 2 : ϕs8 + ϕ6 + ϕs6 + ϕs4 + ϕs2 + ϕ2 + ϕs9 + ϕ3 = 0; node 3 : −ϕs7 − ϕ5 − ϕs5 − ϕs3 − ϕs1 − ϕ1 − ϕs10 − ϕ4 = 0.

(4.1)

by the second Kirchhoff law (the sum of magnetic voltage drops Hl is equal to the sum of the magnetomotive forces acting in the loop): loop 1: Hs7 ls7 − H5l5 = 0; loop 2: H5l5 − Hs5 ls5 = −FP W ; loop 3: Hs5 ls5 − Hs3ls3 = −FCt W ; loop 4: Hs3 ls3 − Hs1 ls1 = −FC pW ; loop 5: Hs1 ls1 − H1l1 = 0; loop 6: Hs9 ls9 − H3l3 = 0; loop 7: H1l1 + H3l3 − H2 l2 − H4 l4 = 2FCt W ; loop 8: H4 l4 − Hs10 ls10 = 0; loop 9: H2 l2 − Hs2 ls2 = 0; loop 10: Hs2 ls2 − Hs4 ls4 = FC pW ; loop 11: Hs4 ls4 − Hs6 ls6 = −FCt W ; loop 12: Hs6 ls6 − H6l6 = FP W ; loop 13: H6l6 − Hs8 ls8 = 0.

(4.2)

The equations of the magnetic system must be supplemented with the equations of reactor windings. The electrical connection of the windings of three reactor phases is presented in the scheme of Fig. 4.3. The power winding encompasses both the half-cores. In a three-phase group of single-phase reactors, the power windings of different phases are star-connected with the grounded neutral. The control winding has two parts, each of which embraces one of the halfcores. Two parts of the control winding are connected in opposition so that the magnetomotive forces (mmf) created by the current flowing through them are pointed

4.1 Main Constructive Elements of the Reactor RTU-180000/500 and Its …

91

UPWA UPWB UPWС

iPWA

iPWB

*

iPWC UN

*

*

А iCpWA iCpWA

iCtW

ECtW

*

*

*

iCtW

В

*

iCpWB iCpWB

С

*

iCpWC iCpWC

Fig. 4.3 The electrical scheme of connection of reactor’s windings

at different directions. The control winding is affected by the electromotive force (emf) E from the magnetic biasing source. The compensation winding has two parts, each of which embraces one of the half-cores. The two parts of the compensation winding are aiding-connected. In a three-phase group of single-phase reactors, the compensation windings of different phases are delta-connected. The equations of the electrical part of the circuit: PW, ph. A U P W A = i P W A · R P W + W P W · (ϕ's5 + ϕ's3 + ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 + ϕ's4 + ϕ's6 )| A ; PW, ph. B U P W B = i P W B · R P W + W P W · (ϕ's5 + ϕ's3 + ϕ's1 + ϕ'1 PW, ph. C U P W C CtW, ph. A UCt W A

+ ϕ'2 + ϕ's2 + ϕ's4 + ϕ's6 )| B ; = i P W C · R P W + W P W · (ϕ's5 + ϕ's3 + ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 + ϕ's4 + ϕ's6 )|C ; = i Ct W A · RCt W + WCt W · (ϕ's3 + ϕ's1 + ϕ'1 − ϕ'2 − ϕ's2 − ϕ's4 )| A

92

4 Method of Controlled Shunt Reactor Computer Simulation

CtW, ph. B UCt W B = i Ct W B · RCt W + WCt W · (ϕ's3 + ϕ's1 + ϕ'1 CtW, ph. C UCt W C CpW, ph. A UC pW A CpW, ph. B UC pW B CpW, ph. C UC pW C

− ϕ'2 − ϕ's2 − ϕ's4 )| B ; = i Ct W C · RCt W + WCt W · (ϕ's3 + ϕ's1 + ϕ'1 − ϕ'2 − ϕ's2 − ϕ's4 )|C ; ) ( = i C pW A · RC pW + WC pW · ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 | A ; ) ( = i C pW B · RC pW + WC pW · ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 | B ; ( ) = i C pW C · RC pW + WC pW · ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 |C (4.3)

In Eqs. (4.3): • voltages of the phases of the power winding U PW are determined by the external, with respect to the reactor, grid and are known for this reason; • voltages of the phases of the control winding U CtW are known and equal to the applied control emf E; • voltages of the phases of the compensation winding U CpW are unknown, since it does not carry load and is idle; additional equations for the delta-connection of the compensation windings are required: the second law: UC pW A + UC pW B + UC pW C = 0; the first law: i C pW A = i C pW B ; the first law: i C pW B = i C pW C .

(4.4)

The system of non-linear differential equations (4.1)–(4.4) determines the solution at each calculation time step (n + 1) with account for the values of variables found at the previous step (n). Let us transform the system into a form easy for solving. Let us differentiate equations (4.1) with respect to time. For instance, for the 1st node: ϕ's7

(n+1)

− ϕ's9

(n+1)

+ ϕ's5

− ϕ'3

(n+1)

+ ϕ'5 (n+1)

(n+1)

+ ϕ's3

(n+1)

+ ϕ's1

(n+1)

+ ϕ'1

(n+1)

=0

Let us linearize equations (4.2). The magnetic field intensity in the core can be calculated with the use of the integration formula of the implicit Euler method H (n+1) = H (n) + H '(n+1) · ΔT | | | where ΔT is the integration time step; H '(n+1) = ddtH |n+1 ≈ ∂∂ HB |n · ∂dtB |n+1 = | ∂ϕ | ∂H | · | · 1 is the derivative of the magnetic voltage of the core at the integration ∂ B n dt n+1 S step n + 1. Then it is convenient to perform linearization with the help of the expression

4.1 Main Constructive Elements of the Reactor RTU-180000/500 and Its …

93

H (n+1)l = H (n)l + H '(n+1)l · ΔT = H (n)l + ϕ'(n+1) · R (n+1) · ΔT | where R (n+1) = ∂∂ HB |n · Sl is the magnetic reluctance of the magnetic core, which can be assumed constant at the integration step (n + 1) and equal to its value calculated at step (n) by known values. B

(n)

H

(n)

(

= f B

(n)

| ) ∂H | | . , ∂ B |n

For example, the following expression can be obtained for loop 2 of system (4.2) ( ) (n+1) (n+1) ϕ'5 R5 (n+1) − ϕ's5 Rs5 (n+1) · ΔT + i P W (n+1) W P W = −H5 (n)l5 + Hs5 (n)ls5 , where the quantities unknown at step (n + 1) are placed to the left from the sign of equality, while the known quantities are in the right side. Let us rewrite Eqs. (4.3), (4.4) for step (n + 1). For example, the equation of system (4.3) for the compensation winding of phase C takes the form: UC pW C (n+1) = i C pW C (n+1) · RC pW + WC pW ) ( (n+1) (n+1) (n+1) (n+1) |C , · ϕ's1 + ϕ'1 + ϕ'2 + ϕ's2 and, e.g., the last equation of system (4.4) will be i C pW B (n+1) = i C pW C (n+1) . With regard for the performed transformations, system (4.1)–(4.4) should be solved in the following way. 1. The initial magnetic fluxes of the cores F(0) are specified, and the inductions of the cores H(0) = f (B(0) ), the cores B(0) = F(0) /S, the magnetic field intensity | in ∂H | l and the magnetic reluctances of the cores R = ∂ B 0 · S are calculated. Typically, it can be assumed that in all the cores F(0) = 0, then B(0) = 0, H (0) = 0, R = 0. 2. The transformed equations (4.1)–(4.4) are solved at each time step (n + 1) with known voltages U PW and U CtW = E applied to the power and compensation windings and with the values of field intensity H (n) and magnetic reluctances R defined at the previous step. Solving the equations gives the derivatives of the fluxes ϕ'(n+1) in the cores as well as currents in the phases of all the windings i P W (n+1) , i Ct W (n+1) , i C pW (n+1) . 3. On basis of already known fluxes F(n) and the derivatives ϕ'(n+1) , which have been just determined in item 2, a change to the next calculation step is carried out with the use of the integration formula of the implicit Euler method. ϕ(n+1) = ϕ(n) + ϕ'(n+1) · ΔT

94

4 Method of Controlled Shunt Reactor Computer Simulation

4. The induction of the cores B(n + 1) = F(n + 1) /S, intensity H(n + 1) = | the field l ∂H | (n + 1) ), and the magnetic reluctance R = ∂ B n+1 · S are computed. f (B 5. Then go to item 2 of the algorithm.

4.2 Magnetization Characteristic of Steel When solving the equation system of a reactor the dependences H = f (B) are required for each of the cores (magnetic or air). ⟨ For air cores H = B μ0 is correct, where μ0 = 4π ×10−7 H/m. When modelling reactors and transformers it is convenient to use for magnetic cores the magnetization curve of steel presented in Fig. 4.4, which is defined by the analytical expression. [ [ ]− 1 ] H = B · a − c · (d · B)n + 1 n where the coefficients from the table given below are entered into. Coefficient

Value

a

795,775

c

795,714

d

0.4996

n

42

Fig. 4.4 The magnetization characteristic of steel used when modelling CSR

4.3 Modelling Reactors of Arbitrary Design

95

The magnetization curve presented in Fig. 4.4 correlates very well with the experimental curve of electric steel, which the magnetic system of a reactor is made of.

4.3 Modelling Reactors of Arbitrary Design One of the first programs for detailed simulation of arbitrary electrical and magnetic circuits of transformers and controlled reactor has become the NRAST program [3] developed at the Department of Electrical Power System and Networks of Saint-Petersburg State Polytechnical University. Nowadays, NRAST is almost not used because of out-of-date interface and unsatisfactory compatibility with modern software. Another software package which allows calculating processes in the magnetic systems of transformers and reactors is EMTP. The EMTP (Electromagnetic Transients Program) software package is well known all over the world. Its second name is ATP (Alternative Transients Program). The EMTP package is a Canadian-American collaboration intended for calculating electromagnetic processes in circuits of different complexity. Low costs of the program and its apt modern interface have become the reason for which it has been widely distributed in different countries. It is EMTP in which a large number of electromagnetic transients computations, which the authors of the articles published in different journals produced by IEEE (Institute of Electrical and Electronics Engineers) are referred to, are performed. Working with EMTP includes three main stages: 1. Creating the scheme of the network in the ATPDRAW graphics editor, assigning parameters of the elements, choosing the time interval and calculation step. 2. Solving the equations describing the given circuit. 3. Viewing results, plotting oscillograms in the PLOTXY program. The most time-consuming is the first stage, i.e. the rational placement of elements (pictograms) on the screen and connecting them with junction lines. The possibility is provided for in EMTP to compose schemes either of a set of “typical” elements or of a set of the elements (“models”) developed and described by the particular user for their need and at their own discretion. For creating models of such non-typical devices, which will be inserted in the computation scheme in the form of pictograms and connected with already existing pictograms of typical elements, there is the integrated utility MODEL’S LANGUAGE in the ATPDRAW editor. This very utility is used for creating models of magnetically controlled shunt reactors. In the EMTP program, there are two types of models distinguished principally in terms of their interaction with the external circuit: the conventional models and TYPE 94.

96

4 Method of Controlled Shunt Reactor Computer Simulation

The conventional model is the model which gets all the variables of the INPUT list from the external circuit at the beginning of each integration time step and gives the results of its operation (variables of the OUTPUT list) only at the end of the step. For this reason, the result of the model operation can be used in the external circuit not at a current integration step, but only at the following one. In other words, in such models, some variables lag behind the rest of the scheme by one calculation step. TYPE 94 is the model working in synchronism with the rest of the scheme without any delay. The synchronism is achieved in one of two ways: • by organizing a series of iterations between the model and the external scheme at each integration time step (ITERATE); • by reducing the external scheme to the “emf behind resistance” equivalent (THEVELIN EQUIVALENT) at each integration time step and transmitting the values of emf and resistance into the model in order to provide accurate account (without iterations) of the external scheme when solving the equation system. At each integration step, the organization of iterations or the forming of the external scheme equivalent are performed automatically by the MODEL’s means depending on which type of models is chosen: ITERATE or THEVELIN. For the needs of magnetically controlled shunt reactors simulation the TYPE 94 models are not suitable for the following reasons: • iterations or forming the network equivalent with respect to the terminals of the model are possible only for models with the limited number of terminals (three single-phase and one three-phase terminal, at the most), while the reactor has three phases with three windings each; • iterations or forming the network equivalent are impossible if there are two models of TYPE 94 in the scheme, while the schemes are found in operation, in which not one, but several controlled reactors operate simultaneously; • iterations or forming the equivalent increase sufficiently the time of calculation. For the mentioned considerations, conventional models are used for controlled reactor simulation in EMTP, which allows taking into account the necessary number of reactor windings, performing calculations in circuits with several reactors, and reducing calculation time. At the modelling of CSR, voltages applied to its windings from the external scheme are measured at each integration step. Then these voltages are delivered inside the model as the INPUT variables. There, after solving the equation system of the reactor, currents in its windings are determined and then these currents, as the OUTPUT variables, become control actions for current sources, which inject them into the grid taking into account, in such a way, the response of the modelled device (controlled reactor) to the voltages applied to its windings from the side of the system. An important preparatory stage in working with the EMTP program and MODEL’S LANGUAGE is forming the equation system of the reactor and its linearisation. The equations are composed for magnetic and electrical circuits by the first and the second Kirchhoff laws. The most complicated task is writing expressions

4.3 Modelling Reactors of Arbitrary Design

97

for magnetic and electrical voltage drops, which are included in the equations of the second Kirchhoff law. For the magnetic core j, the magnetic voltage drop can be expressed in instantaneous values as follows: Hjl j = ∂H

∂ Hj ∂ Hj ϕj Bjl j = lj = ϕj · Rj ∂ Bj ∂ Bj Sj

l

where R j = ∂ B jj · Sjj is the magnetic reluctance of the core j; j; Fj is the magnetic flux of the core j; Bj = Fj /S j is the magnetic induction of the core j; S j is the section of the magnetic core j. Let N 1 be the number of windings and N 2 be the number of magnetic cores. Then, according to Kirchhoff laws for magnetic and electrical circuits, the following expression can be written in instantaneous values: • for the magnetic core j encompassed by the winding m: U j = −H j l j +

N1 ∑

i p · W jp

p=1

where H j = f (Bj ) is the intensity of the magnetic field of the core j; U j is the magnetic potential difference at the ends of the magnetized core j; lj is the length of the core j; ip is the value of current in the winding p; W jp is the number of turns of the winding p embracing the magnetic core j; ip · W jp = F p is the magnetomotive force of the winding p. • for the electrical winding k embracing the core m: Uk = i k R k +

N2 ∑

ϕ'm · Wmk − E k

m=1

where U k is the potential difference at the terminals of the winding k; ik is the value of current in the winding k; Rk is the resistance of the winding k; E k is the emf source of the winding k (in transformers E k = 0); F’m is the derivative of the magnetic flux of the core m with respect to time; W mk is the number of turns of the winding k encompassing the magnetic core m. The equation system of the reactor containing, among all, differential equations is linearzsed with the help of the integration formula of the implicit Euler method. H j (n+1)l j = H j (n)l j + H j'

(n+1)

l j · ΔT = H j (n)l j + ϕ'j

(n+1)

· R j (n+1) · ΔT

After linearization, the expressions for magnetic and electrical voltage drops will take the form

98

4 Method of Controlled Shunt Reactor Computer Simulation

U j (n+1) = −ϕ'j

(n+1)

· R j (n+1) · ΔT +

N1 ∑

i p · W j p − H j (n)l j

p=1

Uk (n+1) = i k (n+1) · Rk +

N2 ∑

ϕ'm

(n+1)

· Wmk − E k (n+1) .

m=1

These expressions fully coincide with those which have been written when simulating one of controlled reactors, namely, the reactor RTU-180000/500.

References 1. Evdokunin GA, Dmitriev MV (2009) Power transformer transients with its magnetic system detailed modelling [Modelirovaniye perekhodnykh protsessov v elektricheskoy seti, soderzhashchey transformatory pri uchete konfiguratsii ikh magnitnoy sistemy]. Izvestiya RAN. Energetika 2:37–48 2. Evdokunin GA, Nikovaev RN (2009) Modelling and analysing transients in transformers [Modelirovaniye i analiz perekhodnykh protsessov v transformatorakh]. Nauchnotekhnicheskiye vedomosti SPbGPU 4–1(89):207–215 3. Evdokunin GA, Korshunov EV, Sepping EA, Yarvik YaYa (1991) Method of the computer computations of electromagnetic transients in ferromagnetic devices with the arbitrary configuration of magnetic and electrical circuits [Metod rascheta na EVM elektromagnitnykh perekhodnykh protsessov v ferromagnitnykh ustroystvakh s proizvolnoy strukturoy magnitnoy i elektricheskoy tsepey]. Elektrotekhnika 2:56–59

Chapter 5

Operating Conditions of CSR, Simulation and Operation of the Automatic Control System (ACS)

5.1 General Description of ACS The automatic control system of CSR serves the function of producing direct magnetic flux in the half-cores of the magnetic system of the device necessary for creating and supporting the desired levels of reactive power absorption by the electromagnetic part of the reactor. Without this system, CSR loses almost all its advantages and changes to a conventional shunt reactor with a constant value of reactive power consumption. Actually, ACS sets the control (firing) angles of the thyristors of a semiconductor converter connected to the terminals of the control winding changing, in such a way, the rectified voltage applied to this winding and the current flowing in it. Controlling the current flowing through the winding causes variations of the magnetic flux in the cores embraced by this winding and results in an increase or reduction in the current running through the power winding. The basis of the automatic control system is a proportional regulator. This means that the control algorithm is as follows: 1. The operator sets the reference, i.e. the value of an operating condition variable (voltage at the buses, which the reactor is connected to, or current in the power winding), which the regulator is expected to support by varying current in the control winding. 2. In the point of reactor connection, the operating condition variable of the same name is measured (voltage or current). 3. The measured value is compared with the reference assigned by the operator, and their difference, i.e. the error signal, is calculated. 4. The firing angle of the converter thyristors is chosen in proportion to the error signal in order to achieve the level of reactive power consumption with which the error signal will fall in the normal control range. 5. Transition to the start of the cycle. Four basic operation modes of CSR ACS can be distinguished. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_5

99

100

5 Operating Conditions of CSR, Simulation and Operation …

1. The mode of automatic voltage stabilization. This mode is the main for ACS. It is intended for maintaining voltage at the point of reactor connection by the smooth adjustment of the reactive power being consumed, the value of which depends on the reference of the regulator. It is evident that this mode is mostly needed under the conditions of daily voltage variations corresponding to the load schedule. 2. The mode of the stabilization of the set current value in the power winding. In this mode current is fixed at the level assigned by the operator. 3. The mode of forced power picking up. This mode is short-term and realized only in the cases when the measured value of a condition variable is sufficiently higher than the reference value set by the operator. Physically, the forcing mode supposes applying voltage which is several times higher than the rated voltage to the control winding. This causes the current in the winding to increase more rapidly and, correspondingly, accelerates the process of power picking up. 4. The mode of forced power shedding. This mode is necessary for accelerated power shedding. The mode is realized by applying voltage of the opposite polarity with respect to the voltage in mode 3 to the control winding. To realize the four specified modes, CSR contains two converters. The main converter is in operation under normal conditions and is necessary to support a steadystate value of current in the control winding of CSR or to control current under small power variations, while the second one (dynamic) is intended for applying increased voltage to the control winding in order to make the reactor change from one mode into another in the forced manner. ACS is responsible for the changeover of the converters in accordance with the algorithms built into it or to requests of the operator. Let us consider the algorithms of each of the four modes in detail.

5.2 Detailed Description of the Operation Algorithms of the ACS Channels and Its Operating Modes 5.2.1 Automatic Voltage Stabilization Mode The automatic voltage stabilization mode is necessary, first of all, for supporting set voltage at the point of reactor connection. Let us consider the algorithm of ACS operation in this mode. 1. Once in a period of the system frequency, the system voltage U S is measured. 2. The measured voltage U S is compared with the reference value of voltage U ref set by the operator. 3. The error signal ΔU = U S − U ref is calculated and the control angle of the converter thyristors proportional to the error signal is chosen. As ΔU varies within the range (0–k)U ref the control angle changes proportionally from αNL (with ΔU = 0) to αrated (with ΔU = kU ref ). Here αNL , αrated are the values of the control

5.2 Detailed Description of the Operation Algorithms of the ACS Channels …

101

angles, with which the steady-state values of currents in the power winding are equal to I NL and I rated under the rated system voltage; k is the droop coefficient set by the operator within the limits (0.01–0.05)U ref with a discrecity of 0.01 (1%). With the value ΔU exceeding kU ref , ACS will operate in the mode of limiting the power winding current to the rated level. We should mention that the no-load current of the reactor I NL corresponds to the consumption of 3–5% of the rated power by the reactor. The quantity characterizing control accuracy is referred to as the droop coefficient: (5.1) where ΔεP is the deviation of the controlled value from the reference caused by is the deviation of the controlled any external action with the open control loop; value from the reference caused by the same action in the closed-loop control system. As is evident from item 3 of the ACS algorithm described above, the control device is rigidly associated with two angles of the converter, namely, the angle corresponding to the no-load condition of the reactor, and the angle corresponding to the rated condition. In other words, the no-load angle is the control angle of the converter thyristors with which the voltage applied by it to the control winding produces such current in it, with which the current in the power winding is equal to the no-load current of the reactor. Similarly, the rated angle is such a control angle of the converter thyristors with which the voltage applied by it to the control winding produces such current in it, with which the current in the power winding is equal to the rated current of the reactor. In many computations of the processes running in circuits with CSR it is acceptable to substitute the thyristor converter with the dc voltage source E 0 , the value of which is a function E 0 = f (ΔU) of voltage deviation from the reference set by the operator. Since ACS of RTU-180000/500 realizes the proportional control law, the regulation curve E 0 = f (ΔU) represents a straight line. The curve is determined by two points: no-load and rated operating conditions, corresponding to voltages E 0 N L = 0 V and E 0 rated = 146 V applied to the CtW, respectively. The point of the characteristic E 0 = f (ΔU) corresponding to no-load has the coordinates ΔU = 0, E 0 = 0. The point of rated conditions has the coordinates ΔU = kU ref and E 0 = E 0 rated , where U ref is the reference value set by the operator. Then the equation of a linear regulation curve is: E0 =

E 0 rated · ΔU. k · Ur e f

(5.2)

Expression (5.2) and Fig. 5.1 present the regulation curve of ACS of RTU180000/500 with the following values of the parameters: k = 0.02; E0 rated = 146 V; U ref = 500 kV.

102

160

5 Operating Conditions of CSR, Simulation and Operation …

E0 , V

140 120 100 80 60 40 20 0 -20

ΔU, kV -3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

Fig. 5.1 An example of the regulation curve

5.2.2 Mode of Forced Power Picking Up The channel of forced power picking up is necessary to provide accelerated power picking up by the reactor. The essence of the forcing mode is applying voltage to the control winding, which is several times higher than the rated value, for a short-term time period. Thus, it can be seen from Fig. 5.2 that when voltage of 1500 V is applied, the current in the control winding approaches the value which it will have in a steady state with applied voltage of 146 V much more rapidly. The forcing mode in ACS switches on under the following combination of conditions: • the error signal exceeds the value of droop ΔU > kU ref ; • current in the power winding of the reactor in less than the rated current by 70%. Under the combination of these conditions, ACS changes to the forced power picking up mode enabling the dynamic converter with control angles corresponding to the maximum response speed. The forcing mode will be maintained until the power grid current reaches the rated value or voltage at the buses returns to the normal regulation range 0 < ΔU < kU ref .

5.2 Detailed Description of the Operation Algorithms of the ACS Channels …

103

ICtW(t), A

1500 V

150 V

t,s Fig. 5.2 The transient of current rise in the control winding at the switching on of 150 V or 1500 V voltage source

5.2.3 Mode of Forced Power Shedding The mode of forced power shedding (the unforcing mode) is based on the same principle as the forcing mode, i.e. on the short-term application of increased voltage to the control winding. When the voltage of opposite polarity is applied, the magnetic flux produced in magnetic cores is directed in opposition with respect the direct magnetic flux in the previous mode. The unforcing mode in ACS switches on under the following combination of conditions: • the error signal is less than zero ΔU < 0 (the system voltage is lower than the reference); • current in the power winding of the reactor in higher than the rated current by 30%. Under the combination of these conditions, ACS changes to the forced power shedding mode enabling the dynamic converter in the inverter mode. The unforcing mode is maintained until the reactor changes to no-load conditions or voltage at the buses returns to the normal regulation range 0 < ΔU < kU ref .

104

5 Operating Conditions of CSR, Simulation and Operation …

5.2.4 Mode of Automatic Current Stabilization in the Power Winding This mode is intended for maintaining power consumption at the desired level. Changing the power consumed by the reactor can be carried out by varying the voltage applied to the power winding, which results in changes in the amplitude of the alternating magnetic flux and the time period, for which the cores of the reactor are saturated. It is obvious that when the system voltage at the point of reactor connection changes, the correction of current value in the control winding is necessary. Supporting current in the control winding at the level defined by the reference is performed by the use of three values of the converter control angles corresponding to the three voltage levels: • voltage of the control winding with which the reactor absorbs 120% of power under the rated system voltage; • voltage of the control winding with which the reactor absorbs 40–60% of its rated power; • voltage of the control winding with which the no-load current is flowing in the power winding. Each of these levels corresponds to its own range of the error signals defined for the current in the control winding (Table 5.1). Depending on the value of the error signal, which represents the deviation of the average effective value of currents in three phases from the reference, ACS chooses one of the three values of the thyristor control angle. Therefore, if it is required to support any intermediate consumption level, for example, 75% of the rated power, then the control system maintains current in the power winding by applying voltages of two levels by turns—one of them is higher than the required voltage, and another is less than it. At that, variations of the direct component in the current of the control winding will have the saw-tooth form. The algorithm of the operation of RTU-180000/500 ACS in the mode of current stabilization in the power winding: 1. Once in a period of the system frequency, the value of current in the power winding of the reactor I PW is measured. 2. The error signal ΔI = I PW – I ref is calculated, where I ref is the reference value of current set by the operator. 3. Depending on the value ΔI, the control angles of the semiconductor converter thyristors are set in accordance with Table 5.1. Table 5.1 Ranges of the error signal values corresponding to three values of the control angle

Value ΔI

The control angle

−0.1 · Irated ≤ ΔI < −0.01 · Irated

αadd

|ΔI | ≤ 0.01 · Irated

α0.5

0.01 · Irated < ΔI ≤ 0.1 · Irated

αNL

5.3 Examples of ACS Operation for the Reactor RTU-180000/500

105

5.3 Examples of ACS Operation for the Reactor RTU-180000/500 5.3.1 Example of ACS Operation in the Circuit “Line with SR and CSR” An example of operation of the regulator model with parameters k = 0.02, U ref = 525 kV in the test circuit is given in Fig. 5.3. The following components are included in the circuit: • a three-phase source of the system voltage E S with the peak-phase value E m = 428 kV; • the inductive reactance of the system X S = 15 Ω; • 500 kV, 300 km overhead transmission line; • CSR RTU-180000/500 with its control system; • 2 uncontrolled 180 MVAr shunt reactors; • 3 circuit breakers (B1 , B2 , B3 ) with the help of which the elements of the circuit are switched. In the circuit of Fig. 5.3, a series of the switching operations listed below is performed. The envelopes of currents and voltages of CSR windings have the form depicted in Figs. 5.4 and 5.5. In the circuit of Fig. 5.3, a series of the switching operations listed below is performed. The envelopes of currents and voltages of CSR windings have the form depicted in Figs. 5.4 and 5.5. 1. Before the operation of the ACS system is started to be illustrated, the line with CSR installed at its receiving end is open-end closed. In a steady state, voltage at the receiving end of the overhead transmission line is 460 kV, which is greater by 32 kV than the maximum operating voltage of 428 kV. 2. At the time moment t = 5 s the contacts of the circuit breaker B1 are closed, the ACS control loop is enabled, the forcing mode of power picking up is realized, ES

XS

OPL UA,UB,UC, IA,IB,IC

B2 B3 B1

SR1

SR2

СSR

Fig. 5.3 Test circuit for illustrating the operation of RTU-180000/500 ACS

ACS САУ СSR УШР

106

5 Operating Conditions of CSR, Simulation and Operation …

UPW(t), kV

600

460 kV

-400 -600

20

25

406 kV

427 kV

Disconnection Отлючение of reactor реактора ШР1 SR 1

-200

Disconnection Отлючение of reactor реактора ШР2 SR 2

0

410 kV

Connection Включение of reactors реакторов SR 1 and SRШР 2 1 и ШР2

200

427 kV

Включение Closing of theконтура control регулирования loop

Closing the line with CSR to no-load (NL)

400

t,s 0

400

5

10

15

30

35

40

IPW(t), A

300 200 100 0 -100 -200 -300 -400

t,s 0

5

10

15

20

25

30

35

40

Fig. 5.4 Voltage and current in the power winding of CSR in Fig. 5.3

and the regulator forms a control action proportional to the error between the effective value of the line voltage U AB and the reference U ref = 525 kV; voltage at the receiving end of the line reduces by 33 kV (to 427 kV). 3. At the time moment t = 20 s the contacts of the circuit breakers B2 and B3 are closed and additional reactors SR1 and SR2 are connected at the receiving end of the line. A sharp voltage drop in the control point occurs, the error signal falls out of the control range, and the forced power shedding takes place, which causes the voltage at the receiving end of the line to increase to 410 kV. 4. At the time moment t = 25 s, the contacts of the circuit breaker B3 are opened, and the reactor SR2 is disconnected. Voltage at the receiving end of the line increases, and the regulator gives the signal to pick up power. The current of the power winding increases and becomes settled at the value constituting about 40% of the rated current; the value of voltage at the receiving end of the line becomes equal to 406 kV.

5.3 Examples of ACS Operation for the Reactor RTU-180000/500 1500

107

UCtW(t), V

1000 500 0 -500 -1000 -1500

t,s 0

2500

5

10

15

20

25

30

35

40

ICtW(t), A

2000

1500

1000

500

0

t,s 0

4000

5

10

15

20

25

30

35

40

ICpW(t), A

3000 2000 1000 0 -1000 -2000 -3000 -4000

t,s 0

5

10

15

20

25

30

35

40

Fig. 5.5 Voltage applied to the control winding, currents in the control and compensation windings in the circuit of Fig. 5.3

108

5 Operating Conditions of CSR, Simulation and Operation …

5. At the time moment t = 35 s, the contacts of the circuit breaker B2 are opened, and the auxiliary reactor SR1 is disconnected. Voltage at the buses of the receiving substation restores and CSR again changes to the mode of reactive power consumption. It can be seen from Figs. 5.4 and 5.5 that in the case of a sudden change in the voltage of CSR PW, the control system enables the forcing and unforcing channels for a short time, which make CSR to turn rapidly to the required level of reactive power consumption or to shed power.

5.3.2 Example of ACS Operation in the Circuit “Line with CSR and SCB” Let us consider a circuit containing a 90 MVAr capacitor bank (CB) connected in parallel with a 180 MVAr CSR. Connecting such CB together with CSR provides smooth reactive power control in the connection point within the range from −90 to 90 MVAr only at the expense of the control system of the reactor without CB switching. An example of operation of the regulator model with parameters k = 0.02, U ref = 525 kV in the test circuit of Fig. 5.6, which differs from the scheme of Fig. 5.3 only by the fact that a line length of 500 km is reduced to 100 km and CB is installed instead of SR1, is given below. The sequence of switching operations is also slightly different. The envelopes of currents and voltages of CSR windings have the form depicted in Figs. 5.7 and 5.8. At the time moment t = 0 s, open-end closing of the line with CSR with no load at the receiving end takes place; voltage at the receiving end of the line becomes equal to 434 kV in a steady state, which is higher the maximum operating voltage by 6 kV. ES

XS

OPL UA,UB,UC, IA,IB,IC

B2 B3

CB

SR

B1

САУ ACS УШР СSR

СSR

Fig. 5.6 Test circuit for illustrating the operation of RTU-180000/500 together with a capacitor bank

5.3 Examples of ACS Operation for the Reactor RTU-180000/500

UPW(t), kV

600

437 kV

434 kV

421 kV

420 kV

Disconnection Отлючение reactor SR реактора ШР

Подключение Connection of reactor реактора ШР SR

of

-200

421 kV Включение Closing of контура the control регулирования loop

0

Включениеof КБCB Connection

200

Closing the line with Включение линии с УШР х.х. (NL) CSR to на no-load

400

109

-400

-600

t,s 0

400

5

10

15

20

25

30

35

5

10

15

20

25

30

35

40

IPW(t), A

300 200 100 0 -100 -200 -300 -400

t,s 0

40

Fig. 5.7 Voltage and current in the power winding of CSR in the circuit of Fig. 5.6

At the time moment t = 5 s, the circuit breaker B2 connects CB. At that, the reactive power generated by the capacitor bank causes an increase in voltage at the connection point to 437 kV. At the time moment t = 10 s, the circuit breaker B1 enables the control channel. The regulator reveals a voltage deviation from the reference and forms a control signal proportional to the error signal. CSR picks up power in the forced way and the voltage reduces to about 421 kV. At the time moment t = 20 s, the auxiliary reactor SR is connected by the circuit breaker B3 . A voltage decrease in the control point takes place, and CSR sheds its power, which allows levelling voltage at the receiving end of the line, which becomes equal to 420 kV. At the time moment t = 30 s, the auxiliary reactor is disconnected, voltage restores and the regulator forms the signal to increase current in the power winding.

110

5 Operating Conditions of CSR, Simulation and Operation …

1500

UCtW(t), V

1200

900

600

300

0

0

2500

5

10

15

20

25

30

35

10

15

20

25

30

35

10

15

20

25

30

35

t,sс t,

40

ICtW(t), A

2000

1500

1000

500

0

t,s 0

4000

5

40

ICpW(t), A

3000 2000 1000 0 -1000 -2000 -3000 -4000

t,s 0

5

40

Fig. 5.8 Voltage applied to the control winding, currents in the control and compensation windings in the scheme of Fig. 5.6

5.3 Examples of ACS Operation for the Reactor RTU-180000/500

111

5.3.3 Example of ACS Operation in the Current Stabilization Mode Let us consider the circuit of Fig. 5.6 with the same sequence of switching operations, but with the stabilization of current in the power winding of CSR. The current reference is I ref = 198 A. The envelopes of currents and voltages of CSR windings have the form depicted in Figs. 5.9 and 5.10. 1. At the time moment t = 0 s, open-end closing of the line with CSR under the no load condition at the receiving end takes place. 2. At the time moment t = 5 s, the circuit breaker B2 connects CB; the reactive power generated by the capacitor bank causes imbalance resulting in a voltage increase at the point of connection. UPW(t), kV

600

10

408 kV

423 kV

Disconnection of reactor SR

5

423 kV

Connection of reactor Подключение SRреактора ШР

-200

Включение контура Closing of the control loopрегулирования

0

437 kV

Включение КБ Connection of CB

200

434 kV

Closing the line линии with Включение CSRсtoУШР no-load (NL) на х.х.

400

-400

-600

t,s 0

400

15

20

25

30

35

40

IPW(t), A

300 200 100 0 -100 -200 -300 -400

t,s 0

5

10

15

20

25

30

35

40

Fig. 5.9 Voltage and current in the power winding of CSR in the circuit of Fig. 5.6 with the power winding current stabilization channel enabled

112

5 Operating Conditions of CSR, Simulation and Operation …

1500

UCtW(t), V

1200

900

600

300

0

0

3000

5

10

15

20

25

30

10

15

20

25

30

10

15

20

25

30

35

t,s

40

ICtW(t), A

2500

2000

1500

1000

500

0

t,s 0

4000

5

35

40

ICpW(t), A

3000 2000 1000 0 -1000 -2000 -3000 -4000

t,s 0

5

35

40

Fig. 5.10 Voltage applied to the control winding, currents in the control and compensation windings in the scheme of Fig. 5.6 with the power winding current stabilization channel enabled

5.3 Examples of ACS Operation for the Reactor RTU-180000/500 300

113

UCtW(t), V

a)

250

200

150

100

50

0 19,0

t,s 19,4

19,8

20,2

20,6

21,0

Fig. 5.11 Detailed representation of the voltage applied to the control winding presented in Fig. 5.10: a near the moment t = 20 s when the reactor SR was connected; b near the moment t = 30 s when the SR was disconnected 300

UCtW(t), V

b)

250

200

150

100

50

0 29,0

t,s 29,4

29,8

30,2

30,6

31,0

Fig. 5.11 (continued)

3. At the time moment t = 10 s the control loop is closed; the regulator reveals a current deviation from the reference and forms a control signal proportional to the error signal. CSR picks up power in the forced mode, and voltage reduces. When the amplitude value of current reaches 280 A, the regulator turns to the mode of current stabilization at the set level. 4. At the time moment t = 20 s, the auxiliary reactor SR is connected by the circuit breaker B3 . Voltage in the control point reduces, and the current of the power winding also decreases slightly. The regulator recovers the current value to the set level.

114

5 Operating Conditions of CSR, Simulation and Operation …

5. At the time moment t = 30 s, the auxiliary reactor SR is disconnected, voltage is restored, current increases, and the regulator change the control signal to zero for a short time in order to restore the value of current set by the reference. A closer picture of the voltage applied to the control winding is given in Fig. 5.11. It can be seen that the desired value of current is maintained not continuously, but at the expense of the alternate changing of the control angles, which cause the converter to apply voltages of three different levels to the control winding. In such a way, different desired current values correspond to the different duration of time intervals for which voltage of one or another level is applied.

Part II

Special Application Scenarios

Chapter 6

Internal Overvoltages on Overhead Transmission Lines with Controlled Shunt Reactors

Under normal operation conditions, voltage at the insulation of equipment must not exceed the maximum operating voltage. Any excess over the amplitude of the maximum operating voltage by the instantaneous value of voltage at the insulation is accepted to be referred to as overvoltage. In most cases overvoltages are short-term, since they appear under rapidly decaying transients or under emergency conditions, the duration of which is limited by the operation of relay protection and system automation. The duration of different types of overvoltages varies from units of microseconds to several hours. Even the most short-term overvoltages can lead to insulation fault or flashover associated with the necessity to disconnect the damaged element of the grid afterwards, i.e. to possible interruptions in power supply of consumers or to a reduction in electrical energy quality. Different types of overvoltages are distinguished by the place of appearance. Phase-to-ground overvoltages are of the most practical significance. These overvoltages affect the insulation separating current-carrying parts of equipment from the ground and grounded constructions. According to origins of appearance, two types of overvoltages are distinguished: internal and external. External overvoltages are caused by the impact of energy sources external with respect to the considered network (for example, by lightning strokes). Internal overvoltages develop because of the processes caused by the operation of the electrical grid, appear under unfavourable circuit configuration, and also may result from the operation of switching devices or insulation damages. In the computations of external (lightning) overvoltages affecting the insulation of power transformers and reactors (both controlled and uncontrolled), the matter of primary importance is the distance from the equipment [1, 2] to protective devices (surge arresters, SA), and the protective characteristics of SA. The configuration of the magnetic systems and the schemes of winding connection of transformers and reactors are the issues of secondary importance and almost do not influence on the level of lightning overvoltages. For this reason, in the calculations of lightning overvoltages, such equipment is presented only by its input capacitance, which depends on construction, but has rather narrow range of values within each voltage level. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_6

117

118

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

Therefore, the main problems of CSR insulation protection against external (lightning) overvoltages are solved just in the same way as the problem of protection of conventional uncontrolled reactors; CSR does not have any significant peculiarities here. Since the aim of the book is to investigate the specific features of CSR and its electromagnetic part, then the studies of external (lightning) overvoltages are not presented here, and all the attention is paid to internal overvoltages.

6.1 SA and Internal Overvoltages Internal overvoltages are divided into the temporary (quasi-stationary) and switching types depending on the time for which they affect insulation. Both the types of overvoltages represent a danger to the equipment of electrical grids, but with the most attention they are studied when the main characteristics of surge arresters (SA) are chosen [3]. Temporary overvoltages appear under temporary, from the viewpoint of operation, conditions and unfavourable combination of the network parameters and can last till the circuit or the operating mode changes. The duration of such overvoltages (from seconds to tens of minutes) is limited by the action of relay protection or the operating stuff. Switching overvoltages appear under all kinds of fast changes in the operating condition of the network associated with the operation of switching devices (energization and de-energization of grid elements), insulation faults as well as under sharp changes in the parameters of non-linear elements. Modern surge arresters are intended to protect the insulation of equipment against lightning and switching overvoltages. These kinds of overvoltages have impulse behaviour and relatively low energy, which can be absorbed by a surge arrester without any risk, if it has been chosen correctly. Temporary overvoltages, because of their possible long duration, may cause the multiple actuation of a surge arrester and sufficient energy release in it followed by the overheating and damage of SA. According to the commonly recognized opinion, modern surge arresters are not intended to suppress temporary overvoltages and protect equipment against them, since it would require unreasonable expenditures on parallel elements in the construction of a surge arrester. The main characteristics of a surge arrester defining its operation under overvoltages are [3, 4]: • the maximum continuous operating voltage U MCOV , kV; • the specific energy absorbtion capability W s (kJ/kV). The maximum operating voltage of a surge arrester is one of the points on its volt-ampere characteristic. With known U MCOV , one can easily find protective characteristics of a surge arrester, i.e. values of the residual voltage under various surge currents. The maximum operating voltage of a surge arrester determines directly:

6.1 SA and Internal Overvoltages

119

• the reliability of SA operation under the operating system voltage and under temporary overvoltages, which the device is not intended to suppress; • the immunity of equipment to lightning and switching overvoltages (the higher U MCOV the higher residual voltages and the worse protection). The specific energy absorbtion capability of SA defines its capability to let through surge currents and absorb their energy without damages in the construction. In 330–750 kV electrical networks, the most dangerous internal overvoltages appear, first of all, on long-distance overhead transmission lines. Surge arresters installed at such lines (at the input terminals of the switchgear or near line reactors SR and CSR) are always exposed to an increased danger from temporary overvoltages of sufficient magnitude and duration, and high-energy switching overvoltages. Let us discuss internal overvoltages by an example of a 500 kV electric power transmission system consisting of a 500 kV, 500 km overhead transmission line with a reactor, conventional uncontrolled SR or uncontrolled CSR, connected at its receiving end. The main estimated cases for the analysis of internal overvoltages are given in Figs. 6.1, 6.2 and 6.3 (the individual circuit breaker of the reactor is not shown): • open-end closing of an overhead transmission line; • open-end closing of an overhead transmission line to a single-phase short circuit at its end; • breaking of an electric power transmission system, for instance, as a result of out-of-step condition.

ES

R, L

UL

OPL

R, L

ES

R, L

ES

B2

B1 SA

SR (CSR)

Fig. 6.1 Closing an overhead transmission line

ES

R, L

UL

OPL B1

B2 F SA

SR (CSR)

Fig. 6.2 Closing an overhead transmission line to a single-phase short circuit at the receiving end

120

ES

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

R, L

R, L

UL

OPL

ES

B2

B1 SA

SR (CSR)

Fig. 6.3 Breaking an electric power transmission system

Another important estimated case of internal (temporary) overvoltages is so-called single-phase auto-reclosing (SPAR) considered in Chap. 7.

6.2 Temporary Overvoltages Temporary and switching overvoltages in the circuits of Figs. 6.1, 6.2 and 6.3 arise simultaneously, which complicates the individual analysis of each of the overvoltages. It order to estimate the possibility to limit the temporary overvoltages with the help of CSR, we will consider three operating conditions given below. In all the cases the supply grid voltage corresponds to the maximum operating voltage of a 500 kV network equal to 525 kV. It is assumed that the positive-sequence and zero-sequence inductive reactances of the grid at a frequency of 50 Hz are the same and equal to: • 50 Ω at the sending end of the line (a low-capacity system); • 5 Ω at the receiving end of the line (a very high-capacity system, a high-capacity station). The inductive reactance of the grid to which the line is connected (by the receiving end) is important only if the electric power transmission system is broken and it is intentionally taken very small (5 Ω only), since in this case, on the opening of the circuit breaker B2 , internal overvoltages at the receiving end of the line will be always the severest.

6.2.1 Open-End Closing of an Overhead Transmission Line In the scheme of Fig. 6.1, a line with a reactor, which is taken out of operation, is under the condition of single-end feeding. At the time moment t = 3 s counting from the start of computations, the command is given to put the reactor into operation because of an impermissible voltage increase at the receiving end of the line:

6.2 Temporary Overvoltages 500

121

U(t), kV

450

393 kV

400

388 kV

CSR

350

388 kV SR

300

250

2.8

2.9

3.0

3.1

3.2

3.3

3.4

t,s

3.5

Fig. 6.4 The effective value of phase voltage in the circuit of Fig. 6.1

• the conventional reactor is connected to the line by its own circuit breaker (which is not shown in Fig. 6.1); • the controlled shunt reactor has been already connected to the line and operated at no-load with E 0 = 0; at the the time moment t = 3 s the forced power picking up started with E 0 = 1500 V applied; starting from the instant t = 3.3 s the field voltage of the reactor changes from the forced value to the rated E 0 = 132 V. Figure 6.4 shows the results of calculations of the effective phase voltage value at the place of reactor installation at the receiving end of the line, which has been determined in the scheme of Fig. 6.1 under the aforementioned conditions. The phase √ value of the maximum operating voltage of a 500 kV grid is 525/ 3 = 303 kV. Before the reactor was put in operation, temporary overvoltages at the receiving end of the line had constituted 393 kV (in the case of SR) and 388 kV (in the case of CSR). After the reactor was brought into operation, the voltage at the receiving end of the line reduced to 338 kV. Let us estimate the danger which such overvoltages represent to the surge arresters installed at the receiving end of the line. Permissible overvoltage ratios for the typical surge arrester are given in Table 6.1. Permissible overvoltage ratios for surge arresters with standard operating voltages of 303, 318, and 333 kV are given in Table 6.2 (for the unfavourable case when SA has already dissipated the overvoltage energy, but has not get cold yet). The analysis of Table 6.2 shows that for the concrete single-end fed 500 kV, 500 km line without a reactor (voltage at the receiving end of the line constitutes about 388–393 kV):

122

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

Table 6.1 Permissible overvoltage ratio of the typical surge arrester. It is set in per units relative to the maximum operating voltage U MCOV of SA for two cases: without (*) and with (**) preliminary dissipation of overvoltage energy The duration T of increased voltage application Permissible overvoltage ratios on SA, not less 0.1 s

1.50*/1.40**

1s

1.43*/1.35**

10 s

1.37*/1.30**

100 s

1.31*/1.23**

1200 s (20 min)

1.23*/1.15**

3600 s (1 h)

1.19*/1.10**

Table 6.2 Permissible voltage increase on a 500 kV surge arrester as a function of its maximum operating voltage The duration T of increased voltage Maximum operating voltage of a surge arrester, kV application UMCOV = 303 kV UMCOV = 318 kV UMCOV = 333 kV 0.1 s

424

445

466

1s

409

429

450

10 s

394

413

433

100 s

373

391

410

1200 s (20 min)

348

366

383

3600 s (1 h)

333

350

366

• surge arrester with U MCOV = 303 kV can sustain operation without a reactor no longer than 10 s; • surge arrester with U MCOV = 318 kV can sustain operation without a reactor no longer than 100 s; • surge arrester with U MCOV = 333 kV can sustain operation without a reactor no longer than 5 min. Consequently, the response speed at which forced power picking up by CSR after the detection of a dangerous voltage increase at the receiving end of a 500 kV overhead transmission line and making the decision to put the reactor into operation takes 0.3 s is more than enough to eliminate the damage of a surge arrester with any U MCOV . After the reactor (SR or CSR) gains its rated capacity, voltage at SA will be equal to 338 kV which, according to Table 6.2, exposes danger to SA only if its duration is about 1 h (for U MCOV = 303 kV) and more than 1 h (for U MCOV = 318 kV, 333 kV). The difference between the initial voltage values at the receiving end of the line (388 kV and 393 kV, see Fig. 6.2) is caused by the fact that an unloaded CSR consumes the biasing current from the system, which has approached several tens of amperes due to the appearance of temporary overvoltages as shown in Fig. 6.5 (before t = 3 s).

6.2 Temporary Overvoltages 400

123

i(t),A SR

300 200 100 0 -100 -200 -300 -400 2.8 400

2.9

3.0

3.1

3.2

3.3

3.4

t,s

3.5

i(t),A CSR

300 200 100 0 -100 -200 -300 -400 2.8

2.9

3.0

3.1

3.2

3.3

3.4

t,s

3.5

Fig. 6.5 Oscillograms of currents in the power winding of phase A of the reactor in the scheme of Fig. 6.1

6.2.2 Open-End Closing of an Overhead Transmission Line to a Single-Phase Short Circuit In the scheme of Fig. 6.2, a line with a reactor, which has been taken out of operation, is under the condition of single-end feeding. At the time moment t = 2.9 s counting

124

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

from the start of the computation, a single-phase short circuit appears on phase C, but the line is not tripped (in practice, on contrary, the line will be rather soon tripped by the action of relay protection). At the time moment t = 3 s, the command to put the reactor into operation is given because of an impermissible voltage increase at the receiving end of the line: • the conventional reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.2); • the controlled shunt reactor has been already connected to the line and operated under the no-load condition with E 0 = 0; at the the time moment t = 3.0 s the forced power picking up started under E 0 = 1500 V; starting from the time moment t = 3.3 s the field voltage of the reactor changes from the forced value to the rated E 0 = 132 V. Figure 6.6 presents the results of calculations of the effective phase voltage value at the place of reactor installation at the receiving end of the line, which have been obtained in the scheme of Fig. 6.2 under the conditions described above. Before the reactor is put into operation, the voltage increase following the single-phase fault on the line has had different values: up to 430 (with SR disconnected) and 400 kV (with CSR is in operation, but not loaded). Let us explain that. Since the zero-sequence inductive reactance of an overhead transmission line is higher than the positive-sequence inductive reactance, then, under short circuits at the receiving end of the line, the current of a single-phase fault is always lower than this of three-phase fault, and voltage at the healthy phases of the line exceeds the value which it has been equal to before the short circuit. For CSR, on contrary, the 500

U(t), kV

450

400

430 kV

393 kV

CSR

400 kV

388 kV

365 kV SR

350

353 kV

300

250 2.8

2.9

3.0

3.1

3.2

3.3

Fig. 6.6 The effective value of phase voltage in the scheme of Fig. 6.2

3.4

t,s

3.5

6.2 Temporary Overvoltages

125

zero-sequence reactance is lower than the positive-sequence reactance because of the presence of delta-connected compensation windings. Thus, the presence of even unloaded CSR at the receiving end of the line results in that a voltage increase of 400 kV at the healthy phases is not so high as it would have been without CSR (430 kV) under a single-phase short circuit. Let us estimate the danger which such overvoltages represent to SA installed at the receiving end of the line. According to Table 6.2, with voltage of 430 kV: • surge arrester with U MCOV = 303 kV can withstand operation without a reactor no longer than 0.1 s; • surge arrester with U MCOV = 318 kV can sustain operation without a reactor no longer than 1 s; • surge arrester with U MCOV = 333 kV can stand operation without a reactor no longer than 10 s. The disconnection time of a line with a short circuit can be either less than 0.1 s (the operation of the main protection of the line) or about several seconds (the operation of the backup protection). In the latter case, under the condition of the example considered, there is a risk that a surge arrester with U MCOV = 333 kV, 318 kV will be damaged. According to Table 6.2, SA is capable to withstand voltage of 400 kV during several seconds (with U MCOV = 333 kV) and for longer time (with U MCOV = 318 kV, 333 kV), i.e. SA will not be damaged even in case the line is tripped by the backup protection instead of the main. As is evident, the presence of even unloaded CSR at the line reduces sufficiently an increase in voltage on the line under a single-phase fault eliminating the risk of SA damage.

6.2.3 Breaking of an Electric Power Transmission System In the scheme of Fig. 6.3, a line with a reactortaken out of operation is under the condition of two-end feeding, i.e. is closed into a transit and is operating under normal conditions in step with the system. At the time moment t = 2.9 s counting from the start of the computation, the command is given to break the normally operating transit. At the time moment t = 3.0 s, the command to put the reactor into operation is given because of an impermissible increase in voltage at the receiving the end of the line: • the conventional reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.3); • the controlled shunt reactor has been already connected to the line and operated under the no-load condition with E 0 = 0; at the time moment t = 3.0 s the forced power picking up started under E 0 = 1500 V; starting from the time moment t =

126 500

6 Internal Overvoltages on Overhead Transmission Lines with Controlled … U(t), kV

450

400 CSR 350

300

250 2.8

SR

338 kV

304 kV

2.9

3.0

3.1

3.2

3.3

3.4

t,s

3.5

Fig. 6.7 The effective value of phase voltage in the scheme of Fig. 6.3

3.3 s the field voltage of the reactor changes from the forced value to the rated E 0 = 132 V. Figure 6.7 shows the results of calculations of the effective phase voltage value at the place of reactor installation at the receiving end of the line, which have been obtained in the scheme of Fig. 6.3 under the conditions described above. Before the transit was open, voltage at the receiving end of the line had constituted 304 kV which corresponded to the maximum operating voltage of 500 kV grid (303 kV), which is natural, since the receiving system is a high-capacity one, with low internal impedance. After the transit was broken, the voltage increased to 400 kV and then, starting from the moment of 3 s, the reactors were brought into operation, and the voltage reduced to 338 kV (instantly for SR, and within a forcing time of 0.3 s for CSR). According to Table 6.2, voltage of 400 kV can be sustained by SA for several seconds (with U MCOV = 333 kV) and for longer time (with U MCOV = 318 kV, 333 kV). Thus, the response speed at which forced power picking up by CSR takes 0.3 s is more than enough to eliminate damages of surge arresters with any U MCOV .

6.3 Switching Overvoltages The calculations of the processes accompanying switching operations on an overhead transmission line will be carried out in two stages. At the first stage, switching overvoltages will be determined with no account taken of SA action, which will

6.3 Switching Overvoltages

127

allow analysing the influence of CSR on overvoltage levels. At the second stage, the calculation of the energy released in surge arresters will be performed in order to estimate the influence of CSR on the requirements to the specific energy absorbtion capability of installed SAs. As a rule, the availability of SA limits switching overvoltage to the safe level. For this reason, if SAs are available, overvoltages are not studied, and all the attention is concentrated on determining the requirements to the specific energy absorbtion capability of SA. In the calculations of the energy released, SA is presented by its volt-ampere characteristics, for which the residual voltage totals 800 kV with the surge current of 1 kA and 30/60 µs form (it is the typical 500 kV SA).

6.3.1 Open-End Closing of an Overhead Transmission Line In the scheme of Fig. 6.1, at the time moment t = 3.0 the circuit breaker B1 applies voltage to the line. Initially, the reactor has already been connected to the line: • the conventional reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.1); • the controlled reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.1) and is biased preliminarily [5] by the voltage E 0 = 30 V. Figure 6.8 presents the results of switching overvoltage calculation with the action of SA neglected. It is clear that the voltage oscillograms are very close to each other, i.e. SR and CSR (preliminarily biased) of the same capacity behave very similarly during the transient of symmetrical three-phase line closing. However, in the case of CSR, overvoltages are still slightly lower (973 kV as against 983 kV), but the difference is on the verge of the simulation error. The oscillograms of the energy released in SA are given in Fig. 6.9. In the considered case, the maximum energy has been emitted in the SA of phase A. In the case of CSR, the energy is slightly lower (640 kJ as against 720 kJ). With the maximum operating voltage of SA equal to U MCOV = 303 kV, such energy W corresponds to the energy absorbtion capability of about W s = 2.0–2.5 kJ/kV. The minimum energy absorbtion capability of SA produced nowadays for 110– 750 kV networks constitutes W s = 2.0–3.0 kJ/kV. The overwhelming majority of 500 kV SAs produced by the industry has the energy absorbtion capability of W s = 4.0–5.0 kJ/kV, very rarely this of 500 kV SA achieves 10 kJ/kV. It is evident that at the open-end closing of a line with CSR connected, requirements to the energy absorbtion capability of SAs are slightly reduced, but the reduction is not noticeable against the values of energy absorbtion capability of 4–5 kJ/kV permissible for 500 kV SAs.

128 1.2

6 Internal Overvoltages on Overhead Transmission Lines with Controlled … U(t), MV SR А В С

0.8

0.4

0.0

-0.4

-0.8 983 kV -1.2 2.98 1.2

3.00

3.02

3.04

3.06

t,s

3.08

U(t), MV CSR А В С

0.8

0.4

0.0

-0.4

-0.8 973 kV -1.2 2.98

3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.8 Overvoltages at the receiving end of the line of Fig. 6.1 not limited by the action of SA

6.3.2 Open-End Closing of an Overhead Transmission Line to a Single-Phase Short Circuit In the scheme of Fig. 6.2, at the time moment t = 3.0 s, the circuit breaker B1 applies voltage to the line, but a single-phase short circuit exists on phase B at the end of the line. Initially, the reactor has already been connected to the line:

6.3 Switching Overvoltages 1.0

129

W(t), MJ SR

0.8 720 kJ

А

0.6

0.4

0.2

В С

0.0 2.98 1.0

3.00

3.02

3.04

3.06

t,s

3.08

W(t), MJ CSR

0.8 640 kJ

А

0.6

0.4

0.2

В С

0.0 2.98

3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.9 The energy released in SAs in the scheme of Fig. 6.1

• the conventional reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.2); • the controlled reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.2) and is biased preliminarily by the voltage E 0 = 30 V. The results of switching overvoltage calculation with the action of SAs neglected are given in Fig. 6.10. It is evident that the voltage oscillograms are close to each

130

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

other. However, in the case of CSR overvoltages are lower by approximately 10% (1030 kV as against 1110 kV), which has been already explained by the fact that under unbalanced operating conditions CSR reduces an increase in voltage at the healthy phases because of the delta-connected compensation windings. Here, the operating condition is unbalanced due to a single-phase short circuit at the line.

1.2

U(t), MV SR

А

0.8

С

0.4 В

0.0

-0.4

-0.8

-1.2 2.98 1.2

1110 kV 3.00

3.02

3.04

3.06

3.08

t,s

U(t), MV

[MV]

CSR

А

0.8

С

0.4 В

0.0

-0.4

-0.8

-1.2 2.98

1030 kV 3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.10 Overvoltages at the receiving end of the line of Fig. 6.2 not limited by the action of SA

6.3 Switching Overvoltages 2.0

131

W(t), MJ SR А

1.6

1680 kJ

1.2

0.8

0.4 С

0.0 2.98 2.0

В

3.00

3.02

3.04

3.06

t,s

3.08

W(t), MJ CSR

1.6 1230 kJ

А

1.2

0.8

0.4 С

0.0 2.98

В

3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.11 The energy released in SAs in the scheme of Fig. 6.2

The oscillograms of the energy released in SAs are given in Fig. 6.11. Under the considered conditions, the maximum energy has been released in the surge arrester of phase A. In the case of CSR the energy is lower by 25% (1230 kJ as against 1680 kJ) because of reduced overvoltages. With the maximum operating voltage of a surge

132

6 Internal Overvoltages on Overhead Transmission Lines with Controlled …

arrester equal to 303 kV, such energy corresponds to the energy absorbtion capability of 4.0–5 kJ/kV, which is the most widespread value of the energy absorbtion capability of modern 500 kV SAs. It is evident that, when an overhead transmission line with CSR is closed with an open end to a short-circuit requirements to the energy absorbtion capability of SA are less strong.

6.3.3 Breaking of the Electric Power Transmission System In the circuit of Fig. 6.13 at the moment t = 3.0 s the circuit breaker B2 trips the electric power transmission system because of out-of-step operation (emfs to the right and to the left of the line are opposite in phase). Initially, the reactor has already been connected to the line: • the conventional reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.3); • the controlled reactor is switched to the line by its individual circuit breaker (which is not shown in Fig. 6.3) and is preliminarily biased by the voltage E 0 = 30 V. The results of the switching overvoltage calculation with SA action neglected are given in Fig. 6.12. It is evident that the voltage oscillograms are close to each other. However, in the case of CSR overvoltages are lower by approximately 10% (1290 kV as against 1390 kV), which has been already explained by the fact that under unbalanced operating conditions CSR reduces an increase in voltage at the healthy phases because of the delta-connected compensation windings. The unbalanced operating conditions are caused by the fact that the circuit breaker B2 in the circuit of Fig. 6.3 was opened at the zero-crossing of current which occurs not simultaneously in all the phases. The oscillograms of the energy released in SAs are given in Fig. 6.13. In the considered case, the maximum energy has been emitted in SA of phase A. In case of CSR, the energy is lower by 25% (1600 kJ as against 2150 kJ), since overvoltages are lower. With the maximum operating voltage of SA equal to 303 kV such energy corresponds to the energy absorbtion capability of about 5–7 kJ/kV. The second SA will be sufficiently more expensive than the first one. It is evident, that when an overhead transmission line with CSR is closed to a short circuit with an open-end, the requirements to the energy absorbtion capability of SA are sufficiently reduced.

6.3 Switching Overvoltages 1.5

133

U(t), MV 1390 kV

SR

1.0

0.5

А

В

С

0.0

-0.5

-1.0

-1.5 2.98 1.5

3.00

3.02

3.04

3.06

t,s

3.08

U(t), MV 1290 kV

СSR

1.0

0.5

А

В

С

0.0

-0.5

-1.0

-1.5 2.98

3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.12 Overvoltages at the receiving end of the line of Fig. 6.3 not limited by the action of SA

134 2.5

6 Internal Overvoltages on Overhead Transmission Lines with Controlled … W(t), MJ SR С

2150 kJ

2.0

1.5

В

1.0

0.5

А

0.0 2.98 2.5

3.00

3.02

3.04

3.06

t,s

3.08

W(t), MJ СSR

2.0 С

1.5

1600 kJ В

1.0 А

0.5

0.0 2.98

3.00

3.02

3.04

3.06

t,s

3.08

Fig. 6.13 The energy released in SA in the scheme of Fig. 6.3

References 1. Regulations of power units arrangement, 7th edn [Pravila ustroystva elektroustanovok. 7-e izd.]. Energoatomizdat, Moscow (2004) 2. Dmitriev MV (2010) Lightning overvoltages on the equipment of 35–750 kV switchgear and protection against them [Grozovye perenapryazheniya na oborudovanii RU 35–750 kV i zashchita ot nikh]. The Publishing House of State Polytechnical University, Saint-Petersburg, p 64

References

135

3. Dmitriev MV (2007) The application of surge arresters in 6–750 kV electrical grids [Primeneniye OPN v elektricheskikh setyakh 6–750 kV]. Izdatelstvo “ZEU”, Saint-Petersburg, 60 p 4. GOST R 52725-2007 (2008) Surge arresters (SA) for 3–750 kV alternating current power units. General technical requirements and testing methods [Ogranichiteli perenapryazheny nelineynye (OPN) dlya elektroustanovok peremennogo toka napryazheniyem ot 3 do 750 kV. Obshchiye tekhnicheskiye trebovaniya i metody ispytany]. Introduced on January 1, 2008 5. Evdokunin GA, Korshunov EV, Sepping EA, Yarvik YaYa (1991) Method of the computer computations of electromagnetic transients in ferromagnetic devices with the arbitrary configuration of magnetic and electrical circuits [Metod rascheta na EVM elektromagnitnykh perekhodnykh protsessov v ferromagnitnykh ustroystvakh s proizvolnoy strukturoy magnitnoy i elektricheskoy tsepey]. Elektrotekhnika 2:56–59

Chapter 7

Single-phase Auto-reclosure of Overhead Transmission Lines with Reactors

The auto-reclosing (AR) of overhead power transmission lines is an effective measure for increasing the reliability of power supply of consumers. Since the majority of short circuits on 330–750 kV overhead transmission lines are single-phase, singlephase auto-reclosing (SPAR) is used on these lines, while three-phase auto-reclosing (TPAR) is applied either in the case of SPAR failure or under multi-phase faults. In the SPAR cycle, after the faulted phase has been tripped at two ends, an electric arc can keep on burning at the place of fault getting current contribution from the healthy phases of the line; the reclosing of the phase must be performed after the starvation of the arc, otherwise, SPAR will fail and the full three-phase tripping of the line will be required. For this reason, when using SPAR, it is essential to provide such a value of contribution current that the arc could be self-extinguished during the dead time, i.e. during the time interval within which the faulted phase of the line is disconnected from the grid by the circuit breakers of the sending and receiving ends. The highest probability of successful SPAR is achieved: • when contribution currents are low; • when there is no repeated faults at the place of a short circuit after the starvation of arc, which depends on the recovery voltage level. The fault contribution current and the recovery voltage are determined by the construction of the line (its linear inductive and capacitive parameters), the length of the line and its transposition, the number of shunt reactors connected to the line, their design and the presence of so-called quadruple legs—zero reactors [1, 2] in their neutrals. Nowadays, controlled shunt reactors CSRs are applied in high-voltage electrical grids along with SRs of conventional design [3]. For this reason, specific aspects of SPAR on lines with CSRs represent a matter of great practical interest. Below, simple analytical expressions for calculating the contribution current and recovery voltage in the SPAR cycle on overhead lines with reactors of different types are given. If necessary, the expressions can be refined by the detailed computer simulation of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_7

137

138

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

processes in the EMTP/ATP program, for which detailed CSR models of different voltage levels and capacity [4] as well as the model of an open arc based on the solution of the arc column energy equation [5] have been developed recently.

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle The value of fault current contribution has statistical behaviour defined by such accidental factors as the phase of the line at which a short circuit appeared; the angular difference between the voltages at the terminals of the line depending on the amount of power delivered; the location of a fault place at the line; the number and the location (at the ends) of shunt reactors at the line; the operating voltage level; the length of arc space, and weather conditions. It should be taken into account that arc extinguishing also depends on the accidental value of the aperiodic component of fault contribution current. In Fig. 7.1 a line with connected SR and CSR is shown, on which a single-phase fault appears at phase A at the time moment “1” tripped at the moments “2” and “3” by the main circuit breakers of the line; after that, the short-circuit current stops flowing in the place of fault, and the resulting fault contribution current I RES starts running instead of it. Apart from the currents of SR and CSR, the total contribution current at the place of fault is determined by an electrostatic (capacitive) and electromagnetic components. The electrostatic component is caused by the presence of the system operating voltage at the healthy phases of the line, while the electromagnetic component is caused by currents in the healthy phases. In the designations of Fig. 7.1, the total contribution current I˙RES is determined as

A

S=P+

2

3

B C I SR

Q1

X X NSR

I CSR

SR 1

X 1CSR ,

I RES

X 0CSR

X NCSR

1

SR Fig. 7.1 SPAR on an overhead line with installed shunt reactors

СSR

Q2

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

139

( ) ( ) I˙RES = I˙ES + NCSR I˙CSR + NSR I˙SR + I˙EM ,

(7.1)

where I˙ES and I˙EM are the electrostatic and electromagnetic components, respectively; I˙CSR and I˙SR are the fault contribution currents from CSR and SR; N CSR and N SR are the numbers of CSRs and SRs at the line. The total fault contribution current I˙RES consists of two components, each of which in (7.1) is placed in round brackets: the first one is defined by the operating voltage at the healthy phases of the line (fault current contribution through the capacitances of the line SR and CSR), the second one is determined by current in the healthy phases of the line. As a rule, the angle between the components is close to 90°, which allows finding the value of the fault contribution current as IRES

| | /( )2 ( )2 |˙ I˙ES + NCSR I˙CSR + NSR I˙SR + I˙EM = IRES | =

7.1.1 Electrostatic Component of the Fault Contribution Current In Fig. 7.2 the capacitive equivalent circuit of an overhead line in the dead time of SPAR is shown, where the following designation are accepted: BM is the phaseto-phase capacitive susceptance of the line, B0 is the intrinsic phase-to-ground capacitance of the phase. For a multiple-transposed line, the considered capacitive susceptances do not depend on the phase of the line (A , B , C). Using the capacitive equivalent circuit of the line, i.e. assuming that the voltages at the sending and receiving ends are equal to each other in magnitude and angle, it is easy to write ( ) ) ( I˙ES = U˙ B − U˙ A · (jBM ) + U˙ C − U˙ A · (jBM ) EA EB EC

UA

BM BM

UB

BM B0

I ES

UC

B0

B0

Fig. 7.2 The capacitive equivalent circuit of an overhead line in the dead time of SPAR

140

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

√ ∗ where BM = BM lOPL , lOPL is the length of the line (km), j = −1 is the imaginary unit. Considering E˙ A + E˙ B + E˙ C = 0 and U˙ A = 0, U˙ B = E˙ B , U˙ C = E˙ C we will get ∗ I˙ES = −jBM lOPL · E˙ A ,

(7.2)

/ / | | where |E˙ A | = UMO 2 3 is the peak phase value of the maximum operating system voltage (here and below the formulas and calculation results are given for the peak values of the total fault contribution current components). Linear phase-to-phase capacitive susceptance can be found as )/ / / ( ∗ B1∗ = ωC1∗ = ω (υ1 ZB1 ), B0∗ = BS∗ = ωC0∗ = ω (υ0 ZB0 ), BM = B1∗ − B0∗ 3, where ZSI1 = 250 ÷ 400 Ω (according to [1]) and ZSI0 ≈ 2 · ZSI1 are the positive/ and zero-sequence values of line surge impedance, υ1 = 3 · 108 m/s and υ0 = υ1 1, 5 are the speeds of electromagnetic wave distribution along the line of positive and negative sequences, ω = 2π f = 314 rad/s. For example, for a 500 kV line of typical construction (with horizontal placement of phase conductors) ZSI1 = 270 Ω is correct and we get the electrostatic component of the fault contribution current of about 15 A per 100 km of the line length from formula (7.2), see Fig. 7.3. IES, A

0 -10 -20 -30 -40 -50 -60 -70 -80

0

100

200

300

400

lOPL, km 500

Fig. 7.3 The electrostatic component of the fault contribution current for the typical 500 kV overhead line

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

141

7.1.2 Component of the Fault Contribution Current from CSR A controlled shunt reactor has delta-connected windings. Depending on the type of CSR, either the control (CtW) or the compensation (CpW) windings can be connected in delta. For high-capacity reactors in 330–750 kV grids, the delta-connected windings are the compensation windings. The presence of delta-connected windings causes CSR to increase the total fault contribution current. There are several ways to reduce a negative influence of CSR on the fault contribution current in the dead time of SPAR including both opening the delta-connection and it’s shunting. Besides that, there is the conventional method to suppress fault contribution current in 330–750 kV high-voltage electric power transmission systems, namely, to install an additional compensation reactor in the neutrals of shunt reactors [1, 2]. From the side of the supply grid, CSR represents a device with three phase terminals and a neutral one, in which the sum of phase currents is flowing. So, neglecting the resistances of the windings, small in relation to the inductive reactances, we can write the equation system of CSR under steady-state or quasi steady-state conditions in the following way: U˙ A − U˙ N = jXS I˙A + jXm I˙B + jXm I˙C ; U˙ B − U˙ N = jXm I˙A + jXS I˙B + jXm I˙C ; U˙ C − U˙ N = jXm I˙A + jXm I˙B + jXS I˙C ; ( ) U˙ N = jXN I˙A + I˙B + I˙C , where U˙ A , U˙ B , U˙ C and I˙A , I˙B , I˙C are the voltages and currents of the phases of the CSR power winding; U˙ N is the voltage at the neutral in which a reactor with an inductive reactance of X N can be installed; X S and X M are the intrinsic inductive reactance of the reactor’s phase and the mutual phase-to-phase inductive reactance, respectively. The Positive Sequence Experiment The equation system of the reactor U˙ A − U˙ N = jX1 I˙A ; U˙ B − U˙ N = jX1 I˙B ; U˙ C − U˙ N = jX1 I˙C ; ( ) U˙ N = jXN I˙A + I˙B + I˙C = 0 , where X1 is the positive-sequence inductive reactance of CSR. If three voltages U˙ A , U˙ B , U˙ C applied to CSR from the side of the system are positive-sequence voltages, then the phase currents I˙A , I˙B , I˙C are also positivesequence: I˙B = a2 I˙A , I˙C = aI˙A . Then, simultaneous consideration of the general system and the system in the positive sequence experiment gives X 1 = X S − X M .

142

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

The Zero Sequence Experiment The equation system of the reactor U˙ A − U˙ N = jX0 I˙0 ; U˙ B − U˙ N = jX0 I˙0 ; U˙ C − U˙ N = jX0 I˙0 ; ( ) U˙ N = jXN 3I˙0 , where X 0 is the zero-sequence inductive reactance of CSR. If three voltages U˙ A , U˙ B , U˙ C applied to CSR from the side of the system are zerosequence voltages, then the phase currents I˙A , I˙B , I˙C are zero-sequence currents: I˙A = I˙B = I˙C = I˙0 . Then, simultaneous consideration of the general system and the system in the positive sequence experiment gives X 0 = X S + 2X M . Since X0 = XS + 2Xm and X1 = XS − Xm , then parameters of the reactor are 2X1 + X0 ; 3 X0 − X1 Xm = . 3 XS =

The general equation system of CSR can be reduced to the form U˙ A =j(XS + XN )I˙A + j(Xm + XN )I˙B + j(Xm + XN )I˙C ; U˙ B =j(Xm + XN )I˙A + j(XS + XN )I˙B + j(Xm + XN )I˙C ; U˙ C =j(Xm + XN )I˙A + j(Xm + XN )I˙B + j(XS + XN )I˙C . Let the phase emfs of the system make up E˙ A , E˙ B , E˙ C . Then under normal conditions U˙ A = E˙ A , U˙ C = E˙ C , U˙ A = 0, , while after a short circuit (on phase A) we will have U˙ B = E˙ B , U˙ B + U˙ C = E˙ B + E˙ C = −E˙ A . Then, from the latter system of equation, we will get current in phase A of the reactor in the presence of arc in the dead time of SPAR as follows I˙A = −jE˙ A

(Xm + XN ) (XS − Xm )(XS + 2Xm + 3XN )

or ] ˙ [ 1 ˙IA = −j EA 1 − 3 X1 X0 + 3XN The Delta-connection of the Reactor CpWs is Shunted If the delta-connection of the reactor’s CpWs is shunted, then the intrinsic reactance of a CSR phase is equal to the zero-sequence reactance X S = X 0 , from where, taking

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

143

into account that X S = (2X 1 + X 0 )/3, the equality X 1 = X 0 follows (the positivesequence reactance of CSR, like this of a short-circuited transformer, becomes equal to the zero-sequence reactance). Then, current in phase A of the reactor ] ˙ [ 1 ˙IA = −j EA 1 − 3 X0 X0 + 3XN The Delta-connection of the Reactor CpWs is Open If the delta-connection of the reactor’s CpWs is open, then the phases of the reactor do not affect each other, and the mutual reactance of CSR phases X M = 0, from where, taking into account that X M = (X 0 − X 1 )/3, the equality X 0 = X 1 follows (the zero-sequence reactance of CSR becomes equal to the positive-sequence reactance). Then, current in phase A of the reactor ] ˙ [ 1 ˙IA = −j EA 1 − 3 X1 X1 + 3XN According to the scheme of Fig. 7.1, the fault contribution current from the reactor will be of opposite sign with respect to the current in the phase of the reactor, i.e. I˙CSR = −I˙A (or I˙SR = −I˙A ). The overall expressions describing different ways to reduce a negative influence of CSR on the arc current in the dead time of SPAR are given below. No CSR switching, the installation of a forth CSR leg ] ˙ [ 1 1 ˙ICSR = j EA − CSR 3 X1CSR X0 + 3XNCSR

(7.3a)

Opening the delta-connection of the CSR windings, the installation of a forth CSR leg X CSR E˙ A I˙CSR = j CSR · CSR N X1 X1 + 3XNCSR

(7.3b)

Shunting the delta connection of the CSR windings, the installation of a forth CSR leg E˙ A X CSR I˙CSR = j CSR · CSR N X0 X0 + 3XNCSR

(7.3c)

Disconnecting the CSR phase of the same name with the faulted phase of the line (the forth CSR leg does not influence on current and is not used here for this reason) I˙CSR = 0.

(7.3d)

144

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

/ 2 The following designations are used in the formulas: X1CSR = UMO QCSR is the positive-sequence inductive reactance of CSR; QyIIIP is a current value of three-phase power of CSR during SPAR; X0CSR is the zero-sequence inductive reactance of CSR determined by its design; XNCSR is the forth ray’s inductive reactance. Comparing currents (7.2) and (7.3) one can see that the fault current contribution from CSR with a forth ray in the neutral has the opposite sign with respect to the capacitive component I˙ES and can compensate it partly or fully almost in all the cases, except for the first case, in which the current of CSR coincides with I˙ES in the sign, since it is typical for reactors that ( ) X1CSR > X0CSR + 3XNCSR In Figs. 7.4, 7.5, 7.6 the first, second and third methods of reducing fault current contribution are illustrated. All the computations have been performed for the typical 500 kV CSR produced by JSC “Zaporozhtransformator” [3] which has the control range of power consumption QCSR = 0 ÷ 180 MVAr (the overload up to 30% is permissible for a short time), X0CSR = 845 Ω. According to Fig. 7.4, the reduction of a negative influence of CSR on the total current can be achieved by forcing its power during SPAR together with the use of a forth ray with an inductive reactance of about 200 Ω. ICSR,A

40 20

300

0

200

-20

100

-40

50

-60

0

-80 -100 -120 -140 -160 0

20

40

60

80

100

120

140

160

180

220 Q200 CSR,MVAr

240

Fig. 7.4 Arc contribution from a 500 kV CSR (calculations performed by (7.3a)). The inductive reactance of the forth ray varies within a range from 0 to 300 Ω

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

80

145

ICSR,A

70 60 50

300

40

200

30 20

100

10

50

0

0

-10 -20 0

20

40

60

80

100

120

140

160

180

Q200 220 CSR,MVAr

240

Fig. 7.5 Arc contribution from a 500 kV CSR with open delta-connection (calculations performed by (7.3b)). The inductive reactance of the forth ray varies within a range from 0 to 300 Ω

ICSR,A

100 90 80 70 60 50 40 30 20 10 0 0

50

100

150

200

X

CSR 250 N

, Ohm

300

Fig. 7.6 Arc contribution from a 500 kV CSR with the shunted side of delta-connection (calculations performed by (7.3c)). The inductive reactance of the forth ray varies within the range from 0 to 300 Ω

146

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

7.1.3 Component of the Fault Contribution Current from SR In the circuit of Fig. 7.1, the fault current contribution from an uncontrolled SR in the dead time of SPAR, with the arc burning, can be found from formula (7.3b) derived for a CSR with open delta-connection EA X SR I˙SR = j SR · SR N SR X1 X1 + 3XN

(7.4)

/ 2 where X1SR = UMO QSR is the positive-sequence inductive reactance of the reactor’s phase at the fundamental frequency; XNIIIP is the reactance of the forth ray. Comparing currents (7.2) and (7.4) we can see that fault current contribution from SR with a forth ray in the neutral has the opposite sign with respect to the capacitive current component I˙ES and can compensate it partly or fully. As an example, Fig. 7.7 shows calculation results for a 500 kV SR with UMO = 525 kV and QSR = 180 MVAr, from which it is evident that the conventional shunt reactor without a forth ray does not influence on the fault contribution current in the dead time of SPAR.

40

ISR,A

35 30 25 20 15 10 5 0 0

50

100

150

200

Fig. 7.7 Arc contribution from a 500 kV SR in the dead time of SPAR

SR

, Ohm XXNNШР , Ом 250

300

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

147

7.1.4 Electromagnetic Component of the Fault Contribution Current In Fig. 7.8 the circuit for determining the electromagnetic component of the fault contribution current is given, where the following designation are accepted: XS∗ — the linear value of the intrinsic longitudinal inductive reactance of a phase of an overhead line; lF and (lOPL –l F ) are the distances between the place of fault and (S) ) and receiving (R) ends of the line, respectively; XCS = /( / the sending of a line section with a length of 1 /BCS = 2 B/0∗ lF is the / (capacitive reactance ) lF 2; XCR = 1 BCR = 2 /B0∗ (lOPL −lF ) is the capacitive reactance of a line section with a length of (lOPL −lF ) 2; XRS and XRR are the phase-to-ground reactances of reactors installed at the sending and receiving ends of the line, respectively. For a multiple-transposed line, the parameters of the circuit of Fig. 7.8 do not depend on which phase of the line (A, B, C) is affected by a short circuit. The electromagnetic component of the fault contribution current depends on the average current in the healthy phases among the trace of an overhead line. In simplified calculations it is acceptable to assume that currents at the sending end, middle point and receiving end of the line have equal magnitudes and phase angles. Then I˙EM =

jXS∗ lF

ΔE˙ 2 ΔE˙ 1 − ∗ , + (jXRS ∥(−jXCS ) ) jXS (lOPL − lF ) + (jXRR ∥(−jXCR ) )

(7.5)

where ΔE˙ 1 and ΔE˙ 2 are the longitudinal emfs induced in open phase A by currents in the healthy phases I˙B and I˙C in the circuit of Fig. 7.8: ) ( ΔE˙ 1 = jXM∗ lF · I˙B + I˙C = −jXM∗ lF · I˙A ; ) ( ΔE˙ 2 = jXM∗ (lOPL − lF ) · I˙B + I˙C = −jXM∗ (lOPL − lF ) · I˙A , where I˙A is the operating current of phase A which would have flown through it in the absence of SPAR. The inductive parameters of an overhead line included in (7.5) can be found as

Fig. 7.8 The equivalent circuit of a line in the dead time of SPAR

148

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

/ X1∗ = ωL∗1 = ω · ZSI1 υ1 , / X0∗ = ωL∗0 = ω · ZSI0 υ0 , )/ ( XS∗ = 2X1∗ + X0∗ 3, )/ ( XM∗ = X0∗ − X1∗ 3 Let consider some particular cases varying the number of reactors connected to the line. 1. Line without reactors The longitudinal inductive reactance of lines with a length of several hundreds kilometres and below is sufficiently lower than the transverse capacitive reactance, so we have, instead of (7.5) [ I˙EM =

XM∗ B0∗ lF2 X ∗ B∗ (lOPL − lF )2 − M 0 2 2

] · I˙A

It is evident that the electromagnetic component of the fault contribution current takes its maximum value if a short circuit occurs either at the sending or at the receiving end of the line and its value is equal to ∗

∗ 2

X B l I˙EM = ± M 0 OPL · I˙A 2

(7.6)

For instance, the factor of proportionality between I˙EM and I˙A determining the maximum possible electromagnetic component of fault contribution current for a 500 kV overhead line of typical design, which has been calculated by formula (7.6), is given in Table 7.1. If such a 500 kV line is delivering rather large amount of active power, say 1000 MW at voltage of 525 kV, then the amplitude of phase current constitutes 1550 A and causes fault contribution currents given in the last row of Table 7.1 (peak values). 2. Line with one reactor Let us assume that one reactor (SR or CSR), which is not disconnected for the time of SPAR, is installed at the line. For example, if the reactor is installed at the sending Table 7.1 Maximum electromagnetic component of fault contribution current for a typical 500 kV overhead line l OPL, km I EM /I A

0 100 0 2.7 ×

I EM , A with 0 4 IA = 1550 A

150 10−3

6.2 × 10

200 10−3

250

300

350

400

450

500

0.011 0.017 0.025 0.034 0.044 0.055 0.068 17

27

38

52

68

86

106

7.1 Fault Current Contribution in the Single-Phase Auto-reclosing Cycle

149

end of the line, then the reactance XRS ∥XCS in (7.5) increases in comparison with the case with no reactor, and, consequently, the electromagnetic component of fault contribution current reduces and becomes less than the values given in Table 7.1. The current I EM will approach the values given in Table 7.1 only if a fault is located on the line close to the reactor. 3. Line with two reactors If reactors (SR or CSR), which are not disconnectied for the time of SPAR, are installed at both the sending and the receiving ends of the line, then the reactances XRS ∥XCS and XRR ∥XCR will increase substantially with respect to the case with no reactor at the line, and the electromagnetic component of fault contribution current will reduce correspondingly and will be almost zero irrespective of fault location on the overhead line.

7.1.5 Recommendations on the Reduction of the Fault Contribution Current in the SPAR Cycle According to Table 7.1, the value I EM becomes considerable only in the case of a long heavy loaded overhead line without reactors. Since at long-distance transmission lines, as a rule, all the installed reactors are fixed (not switched off), it is acceptable to neglect the value I EM in (7.1) in comparison with the capacitive and other components of fault contribution current, assuming that I˙RES = I˙EM + NCSR I˙CSR + NSR I˙SR . To some degree, the time within which the arc of fault contribution current is extinguished is a random quantity. In [2], the approximation of the dependence of arc extinguishing time (with a probability of 0.9) on the amplitude of fault-contribution 2 is suggested. For example, if the amplitude of current text0,9 = 0.2 + 2.86 · 10−4 · IRES fault contribution current is I RES = 70A, we can find text0,9 = 1.6 s using the given dependence. For currents of higher values the time of arc extinguishing will be much greater, according to [2], though the cases are known from operational experience when fast arc extinguishing takes place with currents higher than 70 A. With the current IEM neglected, we will assume that the total fault contribution current IRES ≤ 70 A is still permissible (for lines not equipped with reactors this value is achieved at a length of 400–500 km). Then the following recommendations on performing SPAR on lines with CSR can be given: 1. CSR is not switched, the forth CSR ray is installed—this way is applicable for lines up to 200 km in length, but only if CSR power forcing is available; for longer lines, the forth ray is required in addition to power forcing; 2. opening the delta-connection of CSR windings, the installation of the forth CSR ray—opening only is applicable for lines up to 400–500 km in length; for longer lines, CSR power forcing and the forth ray are needed;

150

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

3. shunting the delta-connection of the CSR windings, the installation of the forth CSR ray—shunting only is applicable for lines up to 400–500 km in length; for longer lines, the forth ray is required; 4. the disconnection of the CSR phase of the same name with the faulted phase of an overhead line—is applicable for lines up to 400–500 km in length; the installation of the fourth ray is useless, because in this case it does not influence on fault contribution current. Taking into account the complexity of realization of one or another technical decision, we can formulate the following recommendations on performing SPAR on an overhead line with CSR: • for overhead lines shorter than 400–500 km (the majority of lines), it is necessary to disconnect a phase of CSR; • for overhead lines longer than 400–500 km it is necessary to shunt the deltaconnection and use the fourth ray. At overhead lines longer than 400–500 km, the fourth ray is required in case the electrostatic component of fault contribution current is high. Since lines of such long length are, as a rule, equipped with several reactors, the installation of the fourth ray can be provided for in the CSR neutral or/and in the SR neutral. The choice of the inductive reactance of the fourth ray depends on the neutral of which reactor it is installed in.

7.2 Recovery Voltage in the SPAR Cycle The case considered above, in which the controlled shunt reactor remains connected to an overhead line and no switching operation is performed in its circuit during SPAR, is sometimes permissible in terms of fault-contribution current, but often is not allowable in terms of the recovery voltage. Unfortunately, there are no simple and easy-to-use developed analytical expressions, so we limit ourselves to presenting two oscillograms of recovery voltage at an 500 kV, 150 km long overhead line drawn in the EMTP program (the fault contribution arc dies out at the time moment t = 4 s). It is obvious from Fig. 7.9 that the maximum value of voltage at the open phase of the overhead line with respect to the ground exceeds/the amplitude of the maximum √ √ 3 = 428 kV) and represents operating voltage in the 500 kV network ( 2 · 525 the risk of SPAR failure and expose danger to the equipment connected to the line.

7.2 Recovery Voltage in the SPAR Cycle

1.5

151

U(t),MV a)

1.0

0.5

0.0 -0.5

-1.0

-1.5 3.90

1.5

3.95

4.00

4.05

4.10

4.15

4.20

4.25

t,s

4.30

4.00

4.05

4.10

4.15

4.20

4.25

t,s

4.30

U(t),MV b)

1.0

0.5

0.0 - 0.5

-1.0

-1.5 3.90

3.95

Fig. 7.9 Voltage at the open phase of a 500 kV, 500 km long overhead line after arc starvation at the moment of 4 s. The capacity of CSR is QCSR = 60 MVAr (a) and 180 MVAr (b)

7.2.1 The Case a Phase of CSR is Open For reducing fault contribution current at an overhead line which is not longer than 400–500 km, it is recommended to open a phase of CSR.

152

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

If there is no SR at the line (only CSR is installed), the condition | substituting | / then, / X1SR = ∞ into condition (7.7), we always have |U˙ A E˙ A | = BM (B0 + 2BM ) ≈ 0, 1, i.e. the voltage is minimum and does not represent danger. If there is a SR at the line (along with CSR), then the ratio of a 50 Hz voltage increase sustained at the open phase of the overhead line can be got as follows ) ( XNSR 1 | | − BM SR SR · SR | U˙ A | X1 +3XN X | |= ( )1 SR SR | E˙ | X1 +2XN A · 1 − (B0 + 2BM ) X SR +3X SR X SR 1

(7.7)

1

N

∗ l, B0 = B0∗ lOL . where BM = BM Figure 7.10 represents 50 Hz voltage ratio as a function of the reactance of the fourth ray installed at the neutral of SR for the | typical / | 500 kV overhead line. It is evident that substantial increases in voltage |U˙ A E˙ A |>0.5 are probable on 150– 250 km long lines and depend sufficiently on the reactance of the fourth ray.

UA/EA

1

0,8

0,6

0 0,4

100 0,2

300 200

300 200

100

0 0

0

100

200

300

400

lOPL, km

Fig. 7.10 50 Hz voltage ratio at the open phase after arc starvation in the SPAR cycle for the typical 500 kV overhead line. In the time of SPAR, only one SR with a fourth ray of 0–300 Ω is connected to the overhead line

7.2 Recovery Voltage in the SPAR Cycle

153

7.2.2 The Case the Delta-Connected Windings of CSR Are Shunted For reducing fault contribution current in an overhead transmission line which is longer than 400–500 km it is recommended to shunt a phase (three phases) of the CSR delta-connection and to use a fourth ray in the CSR neutral at the same time. After the arc of fault contribution current is successfully extinguished, 50 Hz voltage restores in beating with the ratio of a steady-state value ( ) XNSR XNCSR 1 | | − BM · 1 + X SR +3X SR · SR | U˙ A | X0CSR +3XNCSR X0CSR X 1 1 N | |= ( ) | E˙ | X1SR +2XNSR X0CSR +2XNCSR 1 1 A − (B0 + 2BM ) CSR CSR · CSR + SR SR · SR X0

+3XN

X1 +3XN

X0

(7.8)

X1

If there is no SR at the line (only CSR is installed), then, substituting the condition X1SR = ∞ into (7.8), we get the 50 Hz voltage ratio at the open phase as presented in Fig. 7.11. It there is SR at the line (along with CSR), then for each particular overhead line of specified length and construction the calculations must be performed by (7.8) considering the capacity of SR and CSR, and the places of the fourth ray installation (at the neutral of SR and/or at this of CSR). Figures 7.12, 7.13, 7.14 shows 50 Hz voltage ratio at the open phase as a function of the installation place of the 0–300 Ω fourth ray: UA/EA

1

0,8

0

0,6

300 0,4

200 0

0,2

100

300 200

0 0

100

200

300

400

100 500

lOPL, km

Fig. 7.11 50 Hz voltage ratio at the open phase after arc starvation in the SPAR cycle for the typical 500 kV overhead line. During SPAR, only one CSR with a 0–300 Ω fourth ray and a shunted phase of the delta-connection is connected to the overhead line

154

1

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

UA/EA

0,8

0

0,6

0,4

0 100

0,2

300

0 200

100 200

200 300

300

400

500

600

700

lOPL, km 800

Fig. 7.12 50 Hz voltage ratio at the open phase after arc starvation in the SPAR cycle for the typical 500 kV overhead line. During SPAR, one CSR with a 0–300 Ω fourth ray and a shunted phase of the delta-connection along with one SR without fourth ray are connected to the overhead line 1

UA/EA

0,8

0 0,6

100 0,4

200

0 200

300

0 100 200 300

0,2

300

400

500

600

700

lOPL, km 800

Fig. 7.13 50 Hz voltage ratio at the open phase after arc starvation in the SPAR cycle for the typical 500 kV overhead line. During SPAR, one CSR with a shunted phase of the delta-connection and without a fourth ray and one SR with a 0–300 Ω fourth ray are connected to the overhead line

7.2 Recovery Voltage in the SPAR Cycle

1

155

UA/EA

0,8

0

0,6

0

0,4

300 0,2

0 200

200

100

300

400

200

500

100

300

600

700

lOPL, km 800

Fig. 7.14 50 Hz voltage ratio at the open phase after arc starvation in the SPAR cycle for the typical 500 kV overhead line. During SPAR, one CSR with a 0–300 Ω fourth ray and a shunted phase of the delta-connection along with one SR with the same 0–300 Ω fourth ray are connected to the overhead line

• the fourth ray is installed only at the neutral of CSR (Fig. 7.12); • the fourth ray is installed only at the neutral of SR (Fig. 7.13); • the fourth ray is installed at the neutral of CSR and the same one is placed at the neutral of SR(Fig. 7.14).

7.2.3 Recommendations on the Recovery Voltage in the SPAR Cycle In order to eliminate resonance overvoltages on the open phase after the starvation of fault-contribution arc (and also to reduce the probability of repeated faults of the air gap) | /it is|necessary to aim at the minimization of the recovery voltage value. Voltage |U˙ A E˙ A | < 0, 5 can be considered permissible (with some margin). Understanding that some errors can be made when specifying values included in (7.7) and (7.8), it is reasonable to perform calculation not only for a specific length of the line, but also for lengths close to the specified one, since the resonance overvoltages sometimes appear in the very narrow range of the circuit parameters (see Fig. 7.10 with XNSR = 200 and Fig. 7.11 with XNCSR = 100 Ω). For lines with several reactors it is important to include in calculations not only the situation when all reactors have been in operation by the moment of SPAR actuation, but also the case when one of the reactors has been switched off by this moment.

156

7 Single-phase Auto-reclosure of Overhead Transmission Lines …

If the recovery voltage is impermissible in any of the considered cases, then it is possible to act in one of the following way: 1. to change the place of the fourth ray installation and adjust its parameters maintaining fault contribution current at the permissible level; 2. for lines of borderline length (400–500 km for 500 kV overhead lines), to change the way of reducing the fault contribution current maintaining it at the permissible level (to use the disconnection of CSR phase instead of shunting the delta-connection of windings, and visa versa); 3. to use the possibility to disconnect the CSR phase of the same name with the faulted phase of the overhead line.

References 1. Evdokunin GA (2011) Electrical power systems and networks (Elektricheskiye sistemy i seti), Sintez-book, Saint-Petersburg, p 284 2. Belyakov NN, Kadomskaya KP, Levinshtein ML (eds) et al (1991) Processes under the singlephase auto-reclosing of high-voltage lines (Protsessy pri odnofaznom povtornom vklyuchenii liny vysokikh napryazheny), Energoatomizdat, Moscow 3. Kondratenko DV, Dolgopolov AG (2009) The operating experience of magnetically controlled shunt reactors produced by JSC “Zaporozhtransformator” in Lithuania and Kazakhstan (Opyt ekspluatatsii upravlyaemykh podmagnichivaniyem shuntiruyushchikh reaktorov proizvodstva OAO “Zaporozhtransformator” v Litve i Kazakhstane), Energo-Info, vol 10, issue 33 4. Evdokunin GA, Dmitriev MV, Karpov AS et al (2001) Computer simulation of controlled shunt reactors of various types and comparing their characteristics (Kompyuternoye modelirovaniye upravlyaemykh shuntiruyushchikh reaktorov razlichnykh tipov i sravneniye ikh tekhnicheskikh kharakteristik). Energetik 3:27–31 5. Dmitriev MV, Evdokunin GA, Gamilko VA (2005) EMTP simulation of the secondary arc extinction at overhead transmission lines under single phase automatic reclosing. In: 2005 IEEE St. Petersburg PowerTech Proceedings, Report № 15. ISBN 5-93208-034-0

Chapter 8

Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

The number of SF6 circuit breakers installed in grids rated at voltage of 110 kV and above is growing constantly. Such circuit breakers are used at both new and operational facilities (when substituting 110–220 kV oil and 110–750 kV air circuit breakers). In recent years, a series of damages of so-called line SF6 circuit breakers, i.e. circuit breakers which switch overhead transmission lines with shunt reactors connected, occurred at a number of substations [1]. All the faults took place in the “closing—fast opening” cycles when in a short time after the closing of an overhead line with reactors (at which an aperiodic component caused by the presence of reactors appeared in the current of the line circuit breaker) the command to trip the line was given. The increased portion of aperiodic component in small interrupted current flowing through asingle-end fed 500 kV overhead line resulted in the continuous absence of zero values in this current and turned out to be impermissible for a SF6 circuit breaker with the auto-puffer technique of arc quenching, in which the intensity of arc extinguishing is determined by the value of the interrupted current. The value of maximum possible aperiodic component of current in a reactor defines so-called current surge at its energization. In the linear statement of the task (with no account taken of the magnetic conductor), the current surge of a reactor does not exceed the doubled amplitude of the rated current of the reactor. With the magnetic system of the reactor considered, the expected current surge can take a different value. Since no data on the magnetic system of uncontrolled reactors were available (about the magnetic conductor and its non-magnetic air gap), current surges for these reactors were determined in the linear statement; for CSR all the necessary data were available and taken into account in calculations. Let us consider in more detail the causes of the appearance of aperiodic currents and the main ways to limit them in lines with uncontrolled reactors and in lines with CSRs.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_8

157

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

8.1 Aperiodic Currents at the Energization of Uncontrolled Reactors In the general case, when voltage is applied to inductive elements (for example, reactors, Fig. 8.1), two components appear in the current of the circuit breaker: the periodic component, which is equal to the current of a normal steady-state condition, and the aperiodic one caused by the impossibility to change the current of the reactor from zero to a steady-state value instantaneously. The aperiodic component is characterized by the initial value and the rate of decay. The initial value of the aperiodic component of current depends on the instant when the contacts of the circuit breaker are closed (for example, if the contacts are closed at the moment when the instantaneous value of the system voltage is close to zero, then the aperiodic component has the maximum value equal to the amplitude of the periodic component of current.) The time constant of aperiodic current decay is determined by the relationship between the resistance and inductive reactance in the circuit where it flows. The phase currents of a 500 kV, 180 MVAr reactor during its energization are shown in Fig. 8.2. In Fig. 8.2a, the periodic component of phase current has the peak value of 280 A under a normal steady-state condition (the voltage level in the 500 kV grid corresponds to the maximum operating voltage of 525 kV). In Fig. 8.2b, the maximum value of current in phase A under the transient of reactor energization is determined as the sum of the periodic (with an amplitude of 280 A) and aperiodic (just under 280 A accounting for decay) and is equal to 560 A at first moments. Let us consider now the process which takes place when the reactor is energized together with the overhead line to which it is connected (Fig. 8.3). The factor of charging power compensation for an overhead transmission line K is determined by the expression [1, 4] K = bReq v/b1 , where bReqv = N:bR is the inductive susceptance of N reactors connected to the overhead line; b1 is the positive-sequence capacitive susceptance of the overhead line. The current in the circuit breaker of the line has two components (see Fig. 8.4, initial high-frequency oscillations are neglected): Fig. 8.1 Reactor energization

8.1 Aperiodic Currents at the Energization of Uncontrolled Reactors

159

Fig. 8.2 Phase currents of 500 kV, 180 MVAr SR during its energization in the circuit of Fig. 8.1: a—under steady-state operating conditions; b—under the transient of reactor energization at the time moment when the instantaneous value of voltage at phase A takes a zero value

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Fig. 8.3 Closing a line with a reactor at no-load: a—the reactor is installed at the receiving end of the line; b—the reactor is installed at the sending end of the line

Fig. 8.4 Current in phase A of an overhead transmission line with one 180 MVAr shunt reactor installed at the receiving end of the line (the circuit of Fig. 8.3a) at line energization at the moment when the instantaneous value of voltage of phase A is equal to zero as a function of line length: 175 km (K ≈ 1); 220 km (K = 0.8); 290 km (K = 0.6)

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161

• the periodic component of line current in the line circuit breaker is equal to the algebraic sum of the capacitive current of the line and the inductive current of the reactor; it depends on K; • the value of the aperiodic component of current does not depend on the capacitive susceptance of the line (or on K) and is determined by the inductive susceptance of reactors in the line (their number and capacity) as well as by the instant at which the contacts of the line circuit breaker are closed (near a maximum or zero value). Figure 8.5 shows current in phase A of the circuit breaker of a 500 kV, 175 km long overhead line with one 180 MVAr reactor connected. The charging power of such a line is fully compensated (K ≈ 1), and the periodic component of the circuit breaker current under a steady-state condition is absent, so the current in phase A is determined only by the aperiodic component and achieves 280 A at first moments. The rate of decay of the aperiodic component depends on the relationship between the resistance and inductance of the circuit. This relationship of an overhead line is higher than this of the typical supply grid. For this reason, the aperiodic component of current in Fig. 8.5a decays more rapidly than this in Fig. 8.5b, in which the aperiodic current is running in the line circuit breaker, but is not flowing through the line itself. For a number of curves shown in Figs. 8.4 and 8.5 the time of aperiodic component decay achieves several seconds, during which the current of the line circuit breaker does not take zero values, which may cause difficulties with arc extinguishing in case the fast opening of the circuit breaker is required right after its closing. The examples of fast closing-opening cycles, in which the dangerous aperiodic component can appear in the interrupted current of the healthy phases, are as follows:

Fig. 8.5 The current of phase A of an 500 kV, 175 km overhead transmission line with one 180 MVAr shunt reactor at the closing of the line at the moment when the instantaneous value of voltage at phase A is equal to zero:

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

• primary line energization and its opening because of the misoperation of protection or because of a fault on the line (single-phase, double-line-to-ground, or phaseto-phase); • closing the line in the cycles of three-phase automatic reclosure and its opening due to a short circuit (single-phase, double-line-to-ground, or phase-to-phase) which has not been cleared in the dead time of AR. • a—the reactor is installed at the receiving end of the line (the circuit of Fig. 8.3a); • a—the reactor is installed at the sending end of the line (the circuit of Fig. 8.3b). Recently, the most widespread type of circuit breakers in 110–750 kV grids is the live-tank SF6 circuit breaker (in terms of design) with the auto-puffer technique of arc quenching. When the circuit breaker is in the closed position, the main portion of current flows through the main contacts. During the opening of the circuit breaker, the motion from the drive is transmitted to the moving contacts which are sliding out of the fixed contacts. At the moment when the moving contacts start to slide, the compression of gas mixture begins. After the main current-carrying contacts are open, current moves to the arcing current-carrying circuit, between the contacts of which the rupturing electric arc has arisen by the moment when these contacts are open. At the instant when the arcing contacts are open, the pressure of the SF6 gas or gas mixture in the blow cylinders has already reached the required level. The rupturing arc is blown, cooled and quenched by the gas flow passing through the gap between the insulation blast hole and moving arcing contact. After the arc is extinguished, the necessary insulation gap is created as a result of further sliding of the moving contacts. The total break time for a circuit breaker of the described design is about 40 ms. In the “closing–opening” cycles the danger represented by one or another aperiodic component of current must be checked in the process of testing circuit breakers at producer factories or in independent laboratories. Unfortunately, such tests are not performed nowadays. Thus, it can be assumed, for a rough approximation, that the aperiodic component of current is not dangerous for a circuit breaker only if current in the circuit breaker takes zero values not later than 80 ms after its closing. This time interval is obtained by adding up the time of misoperation or normal operation of relay protection devices (about 40 ms) and the total break time of the circuit breaker (about 40 ms). For example, using this criterion for the oscillograms of Fig. 8.4 (obtained for the case when the reactor is connected at the receiving end of the line), one can conclude that the aperiodic component is dangerous for the circuit breaker of an overhead line with K > 0.6. If the reactor is connected at the sending end of the line, the aperiodic component of current will be dangerous within enlarged range of the compensation factor K > 0.5. The same situation with switched currents is typical not only for 500 kV overhead transmission lines, but for all 330–750 kV overhead transmission lines with connected reactors.

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163

In order to reduce the danger exposed by aperiodic currents, the following methods can be used [2, 3]: • to take the reactor out of operation before the line is closed; the connection of the reactor must be performed after a time lag of several seconds; • to use pre-insertion resistors (PR); • to use controlled switching units (CS). It should be mentioned that requirements to the value of PR resistance and CS settings are notably different depending on the task for which they are intended, i.e. for limiting switching overvoltages or for limiting the maximum value of aperiodic currents.

8.2 Aperiodic Currents at CSR Energization Controlled reactors allow changing reactive power consumption in a wide range of values. For example, the range of the reactor RTU-500 from the minimum to the rated power is 180 MVAr; the typical controlled reactor considered above has the same rated capacity. As CSR changes the power consumed, it changes at the same time the degree (factor) of compensation of the line capacitance K. For this reason, it may seem that if CSR, which is energized simultaneously with the line, is adjusted to consume minimum reactive power, it will be equivalent in the essence to the absence of reactor at the line, i.e. to the absence of aperiodic current problem. Actually, CSR energization is accompanied by complex transients in its magnetic system, the behaviour and the development speed of which depend on the state of the magnetic system before energization as well as on the value of voltage applied to the control winding. Figure 8.6 shows the envelopes of sinusoidal current in phase A of the power winding of CSR under its energization at the instant t = 0 when the instantaneous value of voltage at phase A takes its maximum value. It is evident that the rate of power picking up in the case of rated excitation and in the case of short-term forcing is sufficiently different: in the first case it took the reactor several seconds to gain phase current with a peak value of 280 A (corresponding to three-phase power of 180 MVAr), while in the latter case it took fractions of a second. However, in most cases, CSR is energized not in the way shown in Fig. 8.6, but with the use of so-called preliminary magnetic biasing. The essence of the method is that by the moment of CSR power winding energization the magnetic system of CSR has been already prepared by some control voltage applied preliminarily to CtW. Figure 8.7 shows the envelopes of sinusoidal current in phase A of the CSR power winding, the magnetic system of which has been preliminarily biased by the moment t = 3 s by applying voltage of 30 V to the control winding during a long time period.

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Fig. 8.6 Current in phase A of the power winding of CSR under its energization at t = 0 when the instantaneous value of voltage at phase A takes its maximum value: 1—the rated voltage of 140 V is applied to CtW; 2—in the interval 0–0.3 s the forced voltage of 1500 V is applied, after that, the rated voltage is applied

Fig. 8.7 Current in phase A of the power winding of CSR under its energization at t = 3 when the instantaneous value of voltage at phase A takes its maximum value: 1—voltage of 30 V corresponding to preliminary magnetic biasing is applied to CtW; 2—at the moment t = 4 s the voltage of 30 V changes to the rated field voltage of 140 V; 3—the rated field voltage of 140 V is applied right after the energization of CtW, i.e. at t = 3 s

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165

As is clear, the preliminary magnetic biasing of CSR results in that current in the power winding has the same amplitude of 280 A as under the condition of rated power consumption in the first moments after CSR energization. The rated biasing voltage applied to CtW after that (curves 2, 3) gives very fast (even “instantaneous”) turning to the rated condition of consumption. The analysis of Fig. 8.7 shows that the performance of preliminarily biased CSR at first moments after its energization does not much differ from the performance of an uncontrolled reactor of the same capacity. For this reason, the aforementioned methods of reducing aperiodic currents in lines with conventional reactors are actual also for lines with CSR (K is calculated for the rated capacity of CSR).

8.3 Limiting Aperiodic Currents with the Help of Pre-Insertion Resistors Historically, pre-insertion resistors appeared long before the appearance of controlled switching devices and the mass implementation of surge arresters (SA) in networks. The main task assigned to the resistors was limiting switching overvoltages in ultrahigh-voltage grids, in which the safety margins of equipment insulation are low and are found to be comparable with switching overvoltage ratios. The implementation of modern surge arresters (along with controlled switching) has solved the problem of switching overvoltages without the use of pre-insertion resistors. Nowadays, some specialists suggest equipping line circuit breakers with preinsertion resistors again, not for limiting overvoltages, but for reducing the aperiodic component of current. Figure 8.8 shows the basic circuitof a breaker with a resistor. Such a circuit breaker has the main (MC) and auxiliary (AC) contacts. During the closing of the circuit breaker, the auxiliary contacts are closed first putting into operating the resistor which damps transients (or switching overvoltages, or aperiodic currents); after that, MCs are closed shunting the resistor. As a rule, resistors are not used during the opening of the circuit breaker. During the closing of a circuit breaker equipped with a resistor, transients appear twice: the first time is at the closing of AC and the second time is at the closing of Fig. 8.8 The basic circuit of a breaker with a pre-insertion resistor

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

MC. A large value of R gives good damping at the first stage of closing, but transients at the second stage of closing will be more intensive. Obviously, the choice of the resistance R must be grounded. Choosing the value of the resistance is made on basis of the following criteria: • good damping of transients during the closing of AC and MC must be provided; • the energy emitted in the resistor must be permissible. If the pre-insertion resistor is necessary for limiting switching overvoltages, then, according to the research [4], its value must be close to the surge impedance of the line, i.e. must constitute about 300–400 Ω. If the pre-insertion resistor is necessary for limiting the aperiodic component of current, then its value must be chosen such that the aperiodic component would decay during the time of resistor operation (from the moment of AC closing to the moment of MC closing). The aperiodic component is caused by the presence of N reactors at the line. The time constant of reactor current decay can be found as τR =

L Reqv R

/ / where L Reqv = xReqv /ω, xReqv = x R N , x R = U R2 Q R , N—is the number of reactors at the line. The full attenuation of the aperiodic component will take time 3τR . Let us calculate the value of the resistance R which will provide the full attenuation of the aperiodic component of current of one reactor within the time ΔT: 3τ R ≤ ΔT R≥

3 U2 · ωΔT N Q

In Fig. 8.9 the results of calculation of minimum resistance which will provide the attenuation of the aperiodic component of current in time smaller than ΔT are presented. For example, with ΔT = 0.02 s (the time interval between the operation of AC and MC is 20 ms) the resistance of not less than 700 Ω is required for an overhead line with one reactor, and the resistance of not less than 350–400 Ω is required for an overhead line with two reactors. For confirmation, Fig. 8.10 shows the oscillograms of current in a 500 kV overhead line obtained under the conditions of Fig. 8.3 (length of 175 km, one SR). With the operation time ΔT = 20 ms the resistor R = 400 Ω does not provide the full attenuation of the aperiodic current, while the resistor R = 800 Ω does. If there are two reactors at the line, then the choice of resistance must be performed with the help of Fig. 8.9 for the number of reactors with which the aperiodic current is the most dangerous. If a circuit breaker has several series breaks, each of which is

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167

Fig. 8.9 Requirements to the value of resistance providing the full decay of the aperiodic component of current of a 500 kV overhead line with N reactors in the time ΔT of its operation

Fig. 8.10 Current in phase A of a 500 kV, 175 km long overhead line with one 180 MVAr shunt reactor installed at the receiving end (the circuit of Fig. 8.3a) under the closing of the line at the time moment when the instantaneous value of voltage of phase A is equal to zero. The line circuit breaker is equipped with a resistor (AC are closed at 0.02 s, MC are closed at 0.04 s, the time of resistor operation is 0.02 s)

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

equipped with a resistor, then the requirements of Fig. 8.9 must be met by the total resistance of all the resistors connected in series. The resistor chosen by Fig. 8.9 must be checked for the capability to withstand energy loads during switching operations. The maximum amount of energy is released in the resistor if the circuit breaker is closed to a short circuit, when the full phase voltage of the grid is applied to the resistor.

P=

( / √ )2 UR 3 R

=

(U R )2 3R

The energy of losses in the resistor during the its operation time W = P · ΔT =

(U R )2 · ΔT 3R

Figure 8.11 presents the calculations of the required capability of the resistor to dissipate the energy during closing to a short circuit. If a circuit breaker has several series breaks, each of which is equipped with a resistor, then the requirements of Fig. 8.11 must be met by the total resistance of all the resistors. It should be taken in consideration that closing a circuit breaker to a short circuit can be repeated within a time period which is insufficient for the cooling down of the resistor. Therefore, real requirements must be 2–3 times greater than the values W obtained in Fig. 8.11. The producer-factories manufacturing 500 kV SF6 circuit breakers certified for use at the utilities of JSC “FGC of UPS” confirm that it is possible to produce 500 kV circuit breakers with resistors of R = 1000 ÷ 1600 Ω. The operation time of resistors

Fig. 8.11 Requirements to the capability of the resistor to dissipate energy as a function of its value (200, 400, 600, 800, 1200 Ω) and the time of its operation ΔT

8.4 Limiting Aperiodic Currents with the Help of Controlled Switching …

169

is ΔT = 10 ms. With this operation time, according to Fig. 8.9, a resistor of not less than 1400 Ω is required for a 500 kV overhead transmission line with one reactor, and a resistor of not less than 700 Ω is needed for a line with two reactors. Since shunting a resistor, the value of which is 2–3 times greater than the surge impedance of the line, may cause a transient accompanied by the appearance of a new aperiodic component in the current of the line, it is necessary to perform corresponding computer calculation of current. The calculations showed that the following resistors will be optimal for a 500 kV overhead line with 180 MVAr reactors: 1200 Ω for lines with one reactor; 600 Ω for lines with two reactors. It is evident that the values of resistors are several times greater than the “conventional values” recommended on the conditions of limiting switching overvoltages. The optimal values of resistors for 330 kV, 750 kV and other transmission lines can be grounded in the same way.

8.4 Limiting Aperiodic Currents with the Help of Controlled Switching Devices During the operation of circuit breakers, transients arise at both closing and opening. During the closing of circuit breakers: • switching overvoltages can be limited with the use of controlled switching unit adjusted to close the contacts near a zero value of the system voltage (“controlled closing”); • the aperiodic component can be minimized with the use of a controlled switching unit adjusted to close the contacts near a maximum value of the system voltage. During the opening of circuit breakers, if there is a risk of repeated breakdowns between the contacts, switching overvoltages also can be limited with the help of a controlled switching unit (“controlled opening”). The unit must be adjusted in such a way that the moment when the contacts are open is shifted far enough from a zero value of current, so that the distance between the contacts will be sufficient and correspond to a high dielectric strength of the gap between the contacts by the moment of current zero crossing and arc quenching. With the appearance of modern surge arresters in grids, the main purpose of controlled switching could be not limiting switching overvoltages, but limiting aperiodic currents. At that, the required accuracy of CS adjustment is highly dependent on the degree to which the charging power of the line is compensated: • if the compensation factor is close to unit, current in the circuit breaker almost does not contain the periodic component, therefore, on the appearance of the aperiodic component, the total current of the circuit breaker will not take zero values for a long time; in these cases, the accuracy of switching must be rather high;

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Fig. 8.12 Current in phase A of a 500 kV, 175 km line with one 180 MVAr SR at its energization:

• the more the compensation factor differs from unit, the more periodic component is contained in the current of the circuit breaker and the less danger the appearance of the aperiodic component represents, so the requirements to the accuracy of switching is less strong. In Fig. 8.12 the required accuracy of controlled switching device adjustment is analysed by an example of a 500 kV, 175 km long overhead line with one reactor (the compensation factor is 1.0). It is evident that if the moment of switching deviates only by 0.5 ms, the current of the circuit breaker contains an aperiodic component of about 50 A, which will result in the failure of arc quenching in the absence of the periodic component (current does not take a zero value for more than 80 ms). Presently, the accuracy of controlled switching is not better than ±1 ms, i.e. it is not enough high to solve the problems of aperiodic currents at lines with full charging power compensation. • exactly at a maximum of voltage of phase A; • with a deviation of 0.5 ms from a maximum of voltage of phase A.

8.5 Methods of Choosing Measures for Limiting Aperiodic Currents Let us consider an overhead transmission line with shunt reactors connected to it. Let the sine wave of system voltage be described by the expression e(t) = E m · cos(ωt + ψ)

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171

where E m —is the peak phase-to-ground value of the maximum operating voltage of the grid. Under a steady-state operating condition, currents of reactors and of the line have the inductive and capacitive nature, respectively, with respect to the system voltage: i R P (t) = −I R P sin(ωt + ψ); i O P L (t) = I O P L sin(ωt + ψ) In the general case, under the transient of energizing an overhead line with connected reactors the aperiodic component can appear in the current of the reactors (and in the current of the line circuit breaker), the initial value of which is I R A = I R P · sin ψ and its variation in time is described by the expression i R A (t) = I R P · exp(−t/τ ) = (I R P · sin ψ) · exp(−t/τ ) In such a way, the components of current in the line circuit breaker during the single-end closing of the line are presented in Fig. 8.13: • the periodic component of the reactor current with the amplitude I RP • the aperiodic component of the reactor current with the initial maximum value I RA and the time constant of decay τ; • the periodic component of current of the unloaded line (capacitive current) with the amplitude I OPL . The relationship between I RP and I OPL corresponds to K—the degree to which the capacitive susceptance of the line is compensated by the inductive susceptance

Fig. 8.13 The components of current in the circuit breaker of an overhead line with shunt reactors

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Fig. 8.14 The compensation factor versus the length of 500 kV line of typical design, and the capacity of connected reactors

of the reactors. K =

IR P IO P L

For the typical 500 kV overhead line, the dependence of K on the length of the line and the number of reactors of typical capacity is shown in Fig. 8.14. At the moment of line closing t = 0 the system voltage will be e(0) = E m :cosψ where ψ is the angle (rad) at which the closing is performed. With ψ = π/2 we have e(0) = 0, i.e. the closing of the line coincides with a zero value of the system voltage, and, consequently, the initial value of the aperiodic current of reactors will be maximum and equal to the peak value of the periodic component of current in the reactors I RA = I RP : sinψ = I RP . With ψ = 0 we have e(0) = E m , i.e. the closing of the line coincides with a maximum of the system voltage and, consequently, there is no aperiodic current I RA = 0. For limiting aperiodic currents, CS units are adjusted to close the line near a maximum of the system voltage: ψ = 0. Taking into account the possible inaccuracy of CS operation, the closing of the line actually takes place not with ψ = 0, but with some error ψ = ± Δψ. At that, the instantaneous value of the system voltage will be e(0) = E m · cos ψ = E m · cos(±Δψ) The initial value of the aperiodic current is equal, consequently

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173

I R A = I R P · sin(±Δψ) = ±I R P · sin Δψ and its variations in time are described by the formula i R A (t) = ±(I R P · sin Δψ) · exp(−t / τ ) Calculations of current with no account taken of the aperiodic component attenuation The extinction of current arc is most probable at the instants when the total current of the line circuit breaker takes minimum values; there can be two such instants, according to Fig. 8.13: Imin1 = I R A + I R P − I O P L ; Imin2 = I R A − I R P + I O P L It is desirable that the total current of the line circuit breaker would change a sign at these moments. Since the aperiodic components in Fig. 8.13 is assumed to have positive polarity, Imin1 ≤ 0 or Imin2 ≤ 0 can be considered as the conditions of successful circuit breaker operation, from where I R A + I R P − I O P L ≤ 0; IR A − IR P + IO P L ≤ 0 Let us consider, for example, the first condition: I R P · sin Δψ + I R P − K ≤

IR P ≤ 0; K

1 1 + sin Δψ

Similarly, from the second condition, we can find K ≥

1 1 − sin Δψ

Because 0 ≤ K < ∞, then finally we have the following conditions {

0 ≤ K ≤ 1+sin1 Δψ ; 1 ≤ K < ∞. 1−sin Δψ

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Calculations of current with account of aperiodic component attenuation If it is necessary to open an overhead line with reactors after its energization and the time interval between the closing of the line and the attempt of arc quenching is T B , then it is necessary to use not the initial value ( /of)the aperiodic component I RA , but the value with decay considered I R A · exp −T τ for determining conditions of arc extinction. Then, the conditions defined above can be modified to the form { 0 ≤ K ≤ 1+exp(−T1 τ )·sin Δψ ; / 1 ≤ K < ∞. 1−exp(−T / τ )·sin Δψ The resistance of the power winding of a 500 kV controlled or uncontrolled reactor is about R = 4 Ω, while the inductive reactance under the load constitutes X = / rated / 1530 Ω. The time constant can be estimated at τ R = L R = X (ω R) ≈ 1.2 s. The circuit in which the aperiodic current of the reactor is flowing includes not only the reactor, but also the overhead line (if the reactor is installed at the receiving end) as well as the equivalent of the supply grid. With account of these, the time constant τ of the aperiodic current decay will be smaller than this of the reactor τ < τR . Suggest τ = 0.8 s. The minimum time interval between the closing and the opening of the line (the termination of affecting the arc, i.e. the last possibility to extinguish it) constitutes about T B = 0.08 s, which has been explained above. Taking into account the above mentioned considerations, the attenuation of aperi( / ) odic current in 80 ms can be estimated at exp −T τ ≈ 0.9 (which corresponds to the most adverse case of reactor installation at the sending end of the line) and, therefore, the conditions found earlier will be { 1 ; 0 ≤ K ≤ 1+0.9·sin Δψ 1 ≤ K < ∞ . 1−0.9·sin Δψ If the reactor is installed at the receiving end of the line, the attenuation of aperiodic currents will be greater, so the area of dangerous values of K will be smaller. The specified conditions can be used for plotting the dependence Δψ = f(K) (see Fig. 8.15) of the required accuracy of controlled switching on the compensation factor of the charging power of the line. This dependence allows determining the area of application of controlled switching devices for an overhead line with account of the accuracy of their operation achieved by the present time, i.e. determining with which values of the coefficient K controlled switching solves the problem of aperiodic currents, and with which K the possibilities of controlled switching are not enough to limit aperiodic currents. As as rule, the accuracy of controlled switching is specified in milliseconds, not in radians. Then, before applying the conditions, it is necessary to translate milliseconds in radians by the following formula

8.5 Methods of Choosing Measures for Limiting Aperiodic Currents

175

Fig. 8.15 The area of application of different measures for limiting aperiodic currents

Δψ = Δψms ·

π 10 ms

Nowadays, the producers of controlled switching devices declare the accuracy Δψms = 2 ms and, much rarely, Δψms = 1 ms. For this reason, we will proceed from the accuracy of Δψms = 2 ms in the case of controlled switching use. The case of uncontrolled switching is characterized by the “accuracy” Δψms = 5 ms. Four characteristic zones can be distinguished in Fig. 8.15. Zone 1. With 0 ≤ K ≤ 0.53 aperiodic currents do not represent danger with any Δψmc , i.e. irrespective of the moment of line energization. Measures of aperiodic currents limiting are not required. Zone 2. With K > 0.53, the conditions determined earlier are not fulfilled, so there is a danger that the arc quenching could fail, and additional measures are required. If controlled switching is used as such measures, the effect of its using depends on the accuracy of its operation Δψms to a considerable degree: • with Δψms = 2 ms it is reasonable to use controlled switching within a very narrow range 0.53 ≤ K ≤ 0.65; with K > 0.65 this accuracy is not enough; • with Δψms = 1 ms the range is somewhat wider—0.53 ≤ K ≤ 0.78. Zone 3. The accuracy of controlled switching is obviously not enough, so its application is useless. Using pre-insertion resistors or switching the line without a dangerous number of reactors is required. Zone 4. The vast majority of overhead lines have K ≤ 0.8, values of K ≤ 1.5 are very rare, so it is the value K = 1.5 which has been chosen as the maximum for Fig. 8.15. It is evident that for 1 ≤ K ≤ 1.5 controlled switching with Δψms = 2 ms (and even with Δψmc = 1 ms) can not solve the problem of aperiodic currents.

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Thus, using the results of the analysis of Fig. 8.15, the following general recommendations on the problem of aperiodic currents can be given supposing that the accuracy is Δψms = 2 ms (the values with Δψms = 1 are given in the brackets): • with 0 ≤ K ≤ 0.53 limiting measures are not required; • with 0.53 ≤ K ≤ 0.65 (0.53 ≤ K ≤ 0.78) limiting measures are required; controlled switching is recommended as the simplest solution; • with K > 0.65 (K > 0,78) limiting measures are required; the only possible decision is using pre-insertion resistors or switching the line without a dangerous number of reactors. We should remind that Fig. 8.15 is drawn for the most unfavourable case when reactors are installed at the sending end of the line (at the side where the line is closed). If reactors are installed at the opposite end, the area of effective operation of controlled switching will be wider than to K < 0.65 (K < 0.78).

8.6 Special Capabilities of CSR for Limiting Aperiodic Currents A distinctive feature of CSR, in comparison with conventional reactors, is, first of all, that CSR has a compensation winding connected in delta. If special circuit breakers are available, CpW can be opened or shunted in the set time moment. Also, the possibility of forced power picking up or shedding is provided for in CSR. The forcing and unforcing modes allow the fast changing of the power consumed by CSR. The rate of power change depends on the value of the voltage (positive or negative) applied to CtW. For example, with the typical value of forcing voltage of 1500 V, it will take about 0.3 s to pick up full power. This response speed is not enough to change sufficiently the compensation factor K and to achieve a favourable level of the periodic current component against the aperiodic component found in the current of the circuit breaker, because the whole cycle of line closing and opening may take only 0.08 s. In order to provide sufficientresponse speed of CSR the forcing voltage should be several times greater than 1500 V. Opening CpW will change the harmonic composition of current in the power winding (it will become worse) and, in addition to that, the electromagnetic coupling between three phases of CSR, which has been provided for at the expense of closed deltaconnection and had sufficient influence on processes under open-phase operating conditions such as SPAR, will disappear. However, under three-phase supply, the listed consequences of CpW opening are not very notable, so they will not affect the aperiodic current and will not be considered here. Shunting CpW turns CSR to the short circuit operating condition. Since the short circuit voltage of CSR is close to 50%, then shunting CpW (short circuiting CpW) will result in a decrease in the inductive reactance of the reactor approximately by a

8.6 Special Capabilities of CSR for Limiting Aperiodic Currents

177

Fig. 8.16 The area of application of different measures for limiting aperiodic currents on an overhead line with CSR with account of the possibility to shunt the delta-connection of CpW windings

factor of two, so the power consumed by the reactor will be two times greater, and the compensation factor K will change, which, undoubtedly, will have effect on the effectiveness of the use of controlled switching devices. It should be mentioned that shunting CpW increases the power of CSR irrespective of the state of its magnetic system and the control voltage applied. Figure 8.16 shows the dependences Δψ = f (K), but, unlike Fig. 8.15, the range of values K is enlarged to 2.5. It is made in order to consider an increase in K due to the shunting of the compensation winding. The points K = 2.1 and K = 1.4 are shown on the curve separating zone 3 and zone 4. These points are shown because controlled switching becomes effective for limiting aperiodic currents with K ≥ 2.1 (the accuracy of CS Δψms = 2 ms) and with K ≥ 1.4 (the accuracy of CS Δψms = 1 ms). Let us assume that such high coefficients K have been obtained by shunting CpW. If, after the shunting of CpW, the coefficients became K = 2.1 and K = 1.4, then they had constituted, respectively, K = 1.05 (or K ≈ 1) and K = 0.7 before shunting. These points belong to the curve dividing zone 3 into zones 3A and 3B. Whereas earlier (in Fig. 8.15) controlled switching was useless in any point of zone 3, now the points belonging to zone 3B can be made safe at the expense of CpW shunting and transferring to zone 4. While earlier resistors or separate switching of line and reactors must be used everywhere in zone 3, now the area of application of these technical solutions is reduced to zone 3A with the use of CpW shunting.

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

It is obvious from Fig. 8.16 that with the accuracy of controlled switching Δψms = 1 ms zone 3A degenerates, i.e. the application of such a complex and expensive technical decision as pre-insertion resistors or the use of inconvenient in operation separate switching of a line and reactors will never be required on an overhead transmission line with CSR. Zone 1. With 0 ≤ K ≤ 0.53 aperiodic currents do not expose danger with any Δψms , i.e. irrespective of the moment of line energization. Measures for aperiodic currents limiting are not required. Zone 2. With K > 0.53 the conditions determined earlier are not fullfiled, so there is a danger that the arc quenching will fail, so the limiting measures are required. If controlled switching is considered as such measures, the effect of its use depends on the accuracy of its operation Δψms to a considerable degree: • with Δψms = 2 ms it is reasonable to use controlled switching within a very narrow range 0.53 ≤ K ≤ 0.65; with K > 0.65 this accuracy is not enough; • with Δψms = 1 ms the range is somewhat wider—0.53 ≤ K ≤ 0.78. Zone 3A. Using pre-insertion resistors or switching the line without a dangerous number of reactors is required. Zone 3B. For points of this zone it is recommended to use controlled switching and preliminary (before line energization) shunting of CSR CpW. The area of application of such a decision depends to a high degree on the accuracy Δψmc of controlled switching: • with Δψms = 2 ms the decision is effective with any K > 1; • with Δψms = 1 ms the decision is effective with any K > 0.7. Zone 4. The line comes in this zone of unusually high coefficients only for the time of CpW shunting. Thus, if the accuracy of controlled switching Δψms = 1 ms is provided on the line with CSR, the following recommendation on the problem of aperiodic current can be given on basis of the analysis of Fig. 8.16: • with 0 ≤ K ≤ 0.53 limiting measures are not required; • with 0.53 ≤ K ≤ 0.78 limiting measures are required, controlled switching is recommended as the simplest solution; • with K > 0.78 limiting measures are required, using controlled switching of the line circuit breaker along with shunting CpW is reasonable; • pre-insertion resistors or switching the line without a dangerous number of reactors are not required with any K. In practice, there are cases when not all the reactors installed at the line are controllable, for example, one of the reactors is controllable, and another is not (with equal rated capacities of both the reactors). It is evident that the coefficient K will increase not by the factor of two, but only by the factor of one and a half in the case of CpW shunting, i.e. the conventional reactor prevents CSR from revealing all the

8.6 Special Capabilities of CSR for Limiting Aperiodic Currents

179

advantages of CpW shunting. In Fig. 8.16 the thin line indicates the curve separating zone 3A and zone 3B in this case. Zone 3A has enlarged dimensions, and the problem of aperiodic currents can not be solved within the range 0.78 < K ≤ 0.92 even if the accuracy of controlled switching is high Δψms = 1 ms and shunting CpW is used; i.e. in the specified range of K it is necessary to use resistors or switch the line with one reactor (instead of two). In order to approve the performed considerations, we will give a number of oscillograms. In Fig. 8.17 the oscillogram of current in phase A of the circuit breaker of a 500 kV, 175 km long line with one 500 kV, 180 MVAr CSR connected at the sending end is shown. Line energization has occurred at the instant of zero voltage at phase A. It is evident that current does not almost contain the periodic component, since K ≈ 1. Moreover, the oscillogram of current almost totally coincides with the oscillograms for a conventional uncontrolled reactor: the same initial value of the aperiodic component I RA = I RP = 280 A, the same rate of decay. If controlled switching with an accuracy of 2 ms is applied on this line, then, in the worst case, the initial value of the aperiodic current will be (Fig. 8.17b) ( / ) I R A = I R P · sin Δψ = 280 · sin 2 ms · π 10 ms = 165 It is clear from Fig. 8.17 that controlled switching has not solved the problem of aperiodic currents, which agrees fully with the data of Fig. 8.16, where the point Δψms = 2 ms, K ≈ 1 belongs to dangerous zone 3. According to Fig. 8.16, shunting CpW will increase the coefficient to K ≈ 2 and move the line from the dangerous zone to safe zone 4.

Fig. 8.17 Current in phase A of the circuit breaker of a 500 kV, 175 km long overhead transmission line under its energization together with a preliminarily biased 500 kV, 180 MVAr CSR:

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8 Limiting Aperiodic Currents of Line Circuit Breakers with the Help of CSR

Fig. 8.18 Current in phase A of the circuit breaker of a 500 kV, 175 km long overhead transmission line under its energization together with a preliminarily biased 500 kV, 180 MVAr CSR. The switching operation is performed at a maximum of voltage of phase A with an error of 2 ms. Shunting CSR CpW is performed

For a check, in Fig. 8.18, shunting the CpW delta-connection shortly before line energization is used additionally for this 500 kV line, the circuit breaker of which is equipped with a controlled switching device with the accuracy Δψms = 2 ms. It is shown clearly that the current of the line circuit breaker has already started to take zero values by the moment of 80 ms, so possible opening of the line will not be accompanied by the failure of the line circuit breaker. • switching at a zero value of voltage of phase A (ψms = 5 ms); • switching at a maximum value of voltage of phase A with an error of 2 ms (ψms = 2 ms);

8.7 Conclusion 1. The grid companies using SF6 circuit breakers as line circuit breakers should send the producers of circuit breakers an urgent suggestion to perform constructive improvements of the circuit breaker which will allow switching unloaded lines with a high degree of capacitance compensation by shunt reactors (possibly, with improvements of the arc-quenching system). 2. In technical documents for circuit breakers the requirements to the content of aperiodic component in the total current must be specified: the permissible level,

References

3.

4.

5.

6.

181

the permissible decay time constant or the time interval within which the instantaneous value of the total current must take zero values. These requirements must be checked in the process of testing circuit breakers. When typical SF6 circuit breakers are installed (without the improvements mentioned in item 1), specific operating conditions of these circuit breakers in overhead lines with reactors, which are associated with aperiodic current extinguishing, must be considered in projects. Special attention should be paid to lines with a degree of charging power compensation K > 0.5. For limiting the aperiodic component of current in an overhead line with reactors the following measures can be suggested if grounding calculations are provided for: renunciation of switching a line with the undesirable number of reactors, or using circuit breakers with pre-insertion resistors, or using circuit breakers equipped with controlled switching units. As a rule, the simplest decision is controlled switching, but the area of its effective operation is limited to a relatively narrow area of the compensation factor K due to insufficient accuracy, outside which it it necessary to apply more complicated technical solutions, such as the renunciation of switching a line with the undesirable number of reactors or the use of resistors. The choice of resistors and the adjustment of a controlled switching unit are in principle different from the cases when these are used for limiting switching overvoltages. The installation of controlled shunt reactors instead of uncontrolled at overhead lines (with the possibility to shunt CpW for the time of primary line closing) along with equipping such lines with controlled switching devices (with an accuracy not worse than Δψms = 1 ms) could solve the problem of limiting values of aperiodic currents in lines to the level acceptable for SF6 circuit breakers.

References 1. Dmitriev MV, Evdokunin GA et al (2008) Switching high-voltage lines and impacts on circuit breakers [“Kommutatsii vysokovoltnykh VL i vozdeystviya na vyklyuchateli”]. Novosti elektrotekhniki, No. 3(51) 2. Dmitriev MV, Evdokunin GA, Grinev NV (2012) Aperiodic currents in overhead lines with reactors [“Aperiodicheskiye toki na VL s reaktorami”]. Novosti elektrotekhniki, No. 4(76) 3. Dmiriev MV (2012) The method of choosing measures for struggling with aperiodic currents [“Metodika vybora meropriyaty po borbe s aperiodicheskimi tokami”]. Novosti elektrotekhniki, No. 5(77) 4. Evdokunin GA (2011) Electrical power systems and networks [Elektricheskiye sistemy i seti], Sintez-book, Saint-Petersburg, 284 p

Chapter 9

Voltage Stability Enhancement by Use of Reactive Power Compensation

Synchronous and asynchronous electrical motors represent the prevalent and, as a rule, rather important portion of load in electrical grids. When a power supply system is designed, it is necessary to provide conditions for the run-up of the motors, the required voltage levels under the rated conditions providing the most efficient engineering-and-economical performance as well as permissible levels and duration of short-term voltage reductions which do not cause synchronous motors to fall out of step with the grid or asynchronous motors to breakdown. Interruptions of power supply, especially for crude oil production, are fraught with that the contingency results in the stoppage of the machinery literally in several seconds, and the further extraction of oil can be started not earlier than in hour and a half or two hours and, in some cases, in several days. For this reason, when the power system of a new oilfield (which in many cases is autonomous) is designed, the main priority is given to providing uninterrupted, reliable and high-quality power generation as well as power system survivability under different contingencies [1].

9.1 Equivalent Circuit and Its Main Characteristics The load composition in the autonomous power supply system of a producing oilfield can be often rather different from this of interconnected power systems. In particular, the total portion of motor load can achieve 95% (about 60% of asynchronous load and 35% of the synchronous load). Besides that, these power supply systems often include highly-manoeuvrable gas-turbine or gas-reciprocating units and are characterized by the radial structure with a remoteness of consumers of 10–20 km. The aim of the chapter is to estimate the effectiveness of the use of modern reactive power compensation devices based on CSR and static capacitor bank (SCB) in autonomous electric power systems with high percentage of motor load (synchronous and asynchronous) and to define the basic requirements for the response speed of the mentioned devices. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_9

183

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

Fig. 9.1 The simplified scheme of a power system supplying autonomous oilfields

In Fig. 9.1 an example of the simplified power supply circuit of an autonomous oilfield is given. The synchronous generator of a 25 MW gas-turbine power plant supplies consumers through a twin-circuit 35 kV, 20 km long overhead transmission line. The composition of the consumers’ load is as follows: 60% of asynchronous motor load, 35% of synchronous load, and 5% of static load. The dynamic performance of a gas turbine is taken into account correctly on basis of the investigations [2], according to which a gas-turbine unit can be presented as a control object (block diagram) [3]. In accordance with the block diagram presented in Fig. 9.2, the error signal equal to the deviation from the rated rotation speed E r = 1 – N, where N is the current relative speed of gas turbine rotation, is given to the input of the gas turbine speed controller. The output of the speed controller of a gas turbine is the value of power P0 necessary to maintain the specified rotation speed. The speed controller of a gasturbine itself can be presented as a first-order aperiodic unit, the typical parameters of which are equal to K d = 25, T g = 0.05 s. The obtained output signal of the gas turbine speed controller must be verified to correspond with the specified control range of equipment operating conditions, for which an additional limiting unit is introduced to the block diagram: • if P0 ≥ Pmax , than P = Pmax ; • if P0 ≤ Pmin , than P = Pmin . Then, the fact should be taken into account that a gas turbine requires rather large amount of fuel for operating at no load: 23% of the rated gas consumption. In such a way, the control range of a gas turbine is within not the limits from 0 to 100%, but from 23 to 100%. For this reason, the corresponding units are introduced to the block diagram of the gas turbine mathematical model. Changing the rotation speed of a gas turbine is performed by controlling gas feeding through affecting the gas valve. The response time of changing the gas valve

9.1 Equivalent Circuit and Its Main Characteristics

185

Fig. 9.2 The simplified mathematical model of a gas-turbine

position can be taken into account by introducing a first-order aperiodic unit with the time constant T V = 0.05 s. The regulation of the gas valve position, in its turn, leads to changes in gas consumption. The response time of gas consumption change is also accounted for by a first-order aperiodic unit with the time constant T f = 0.4 s. The resulting mechanical torque of a gas turbine is a function of temperature and pressure in the burner, counter-pressure, and the rotation frequency. Beside that, the mechanical torque of a gas turbine is defined by the characteristics of the automatic speed controller and, generally, depends on the speed of rotation. In accordance with the block diagram (Fig. 9.2), the mechanical torque of a gas turbine is defined by the transfer function f 2 which, in correspondence with [3], can be presented in the following way: f 2 = 1, 3 · (W F − 0, 23) + 0, 5 · (1 − N ), where W F is the output signal of the unit simulating the variations of gas consumption under speed control. The method of mathematical simulation of synchronous electrical motors is based on the use of the full equation system of transients by Park and Gorev with account taken of fast transients in the armature windings and is presented in numerous works, such as [4]. Synchronous electric motors are equipped with simple automatic systems of excitation control (voltage correctors) with a droop of excitation control below 10%, which is enough widespread in autonomous power systems [5]. The mathematical model of an asynchronous (induction) motor with a squirrelcage rotor is similar to this of a synchronous machine without the field winding and automatic excitation regulator. The mechanical torque M T developed at the shaft of an induction motor depends on the peculiarities of technological process, the electromechanical and kinematic

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

systems of the machinery, etc. The asynchronous drive of compressor plants, which has become mostly widespread in the autonomous power systems of oilfields, is characterized by the dependence of the developed torque on the slip M T = f(s) and, according to [6], can be presented in the following way:  M = K load · Pst + (1 − Pst ) ·



s − s0 1 − srated

2  · cos ϕ

where K load is the load factor of the induction motor; snom is the rated slip of the induction motor; Pst is the static resisting torque (the initial resisting torque). In further calculations, in order to simplify the mathematical model of a power supply system, groups of asynchronous and synchronous electric motors are presented by the corresponding equivalent electrical machines. Parameters of the equivalent asynchronous and synchronous electric motors are averaged and have been calculated on basis of the data on the most frequently used electric motors in the autonomous systems of oilfields.

9.2 Enhancement of the Load Bus Stability Under Short Circuits As one of possible contingencies, we will consider a three-phase short circuit on one of the lines near the buses of a gas-turbine electric power plant followed by the trip of one of the circuits which is cleared by the main protection. Modern 35–110 kV circuit breakers have an opening time of 0.02–0.025 s (according to the information given at the site www.abb.com for SF6 circuit breakers designed for rated voltage below 110 kV). The actuation time of modern microprocessor relay protection terminals constitutes 0.01–0.015 s. Therefore, we will assume in further calculations that the total time of three-phase short circuit clearing, which includes both the opening time of a circuit breaker and the actuation time of relay protection, is 0.04 s. In order to make the representation of results clear, here and in the computation below, we will assume that the braked state of induction motors corresponds to the slip s = 1.0 p.u. Figure 9.3 shows the result of computation of the transient variations in the relative angle between the rotors of the synchronous generator and the equivalent synchronous electric motor. As can be seen, the first oscillation of the relative angle between the rotors of the generator and synchronous electric motor is not critical, and the loss of parallel operation stability occurs at the second oscillation. At the same time, there is a decrease in voltage at the load bus of the consumer under post-fault conditions (Fig. 9.4). A sufficient increase in the load carried by the operating transmission line (after the disconnection of the parallel circuit by the main protection) results in further voltage decrease. Due to the voltage reduction under post-fault conditions, the characteristic

9.2 Enhancement of the Load Bus Stability Under Short Circuits

187

Fig. 9.3 Variations of the relative angle between the rotors of the power station generator and synchronous motor

Fig. 9.4 Voltage variations at the load bus of the consumer

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

Fig. 9.5 Variations of the electromagnetic and decelerating torques of an induction motor: 1—is the electromagnetic torque of the induction motor; 2—is the decelerating torque of the induction motor

of the electromagnetic torque of the induction motor connected to this bus becomes lower than its mechanical torque (Fig. 9.5). This causes a classical voltage cascade, when the induction motor starts to brake consuming more and more reactive power, which, in its turn, results in further voltage reduction and the stoppage of the motor (Fig. 9.6). Thus, the main cause of the development of heavy emergencies in such systems is the potentiality of voltage cascade development under post-fault conditions which can result in the long stoppage of technological equipment followed by the long restoration of technological processes. At that, as it has been shown above, the application of modern fast-acting switching equipment and protective relays in such systems does not ensure maintaining the transient stability of system operation. Let us consider the case of installing a reactive power compensation device (RPCD) based on a 25 MVAr controlled shunt reactor and a 25 MVAr static capacitor bank (SCB) at the buses of the consumer. Such device can smoothly control its reactive power output within the range from 0 to 25 MVAr which corresponds to the relative susceptance of RPCD Bp = 1 … 0 in the per unit system. Let us estimate the influence of RPCD on the stability of load under emergency conditions. The main characteristic of CSR included in RPCD affecting load stability is the response speed at which the reactive power of CSR reduces to the minimum value. It should be mentioned that what is concerned is the response speed corresponding not to

9.2 Enhancement of the Load Bus Stability Under Short Circuits

189

Fig. 9.6 Variations in the slip of the induction motor

Fig. 9.7 Variations of the relative angle between the rotor of the power station generator and the rotor of the synchronous motor with the installation of CSR + SCB

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

repeated changes in CSR power, but to a single event of CSR power shedding, i.e. to the unforcing mode. Let us define the required time of CSR power shedding for the considered power supply circuit of an autonomous oilfield. A change in the response speed (the unforcing time) of a magnetically controlled shunt reactor can be carried out by various relatively simple technical measures: • removing control impulses from the thyristors of the semiconductor converter; • shunting the control winding by a special shunt diode; • applying inverse voltage to the terminals of the control winding. The latter of the aforementioned measures allows CSR to shed power from the maximum to no-load value in about 0.3 s and is provided for by relatively simple technical measures in the control system of CSR. The results of transient calculations (Figs. 9.7, 9.8 and 9.9) show that the use of the CSR + SCB installation allows increasing the level of transient stability of electric motors at the load bus under contingencies due to supporting higher voltage levels under post-fault conditions. Thus, in Fig. 9.9, the equivalent capacitive susceptance (power in the per unit system) of the CSR + SCB installation is about 0.23 p.u. under the initial steady state (the mode of reactive power generation), which corresponds to the absorption of reactive power equal to 0.77 p.u. by CSR (the inductive susceptance of CSR is 0.77 p.u.). Due to a change (reduction) in the CSR susceptance in the CSR + SCB installation under the post-fault condition, the reactive power output of SCB increases rapidly approaching its rated capacity in a time of about 0.3 s (Fig. 9.9). In such a way, due to effective voltage support at the load buses (Fig. 9.8) the electric motor does not decelerate (with subsequent stoppage) and the danger of the loss of the electric motor transient stability is eliminated. The generalized dependencies of the electromagnetic and decelerating torques of an induction electric motor on slip with various response speeds (the time of CSR unforcing) of a controlled reactive power compensation device are shown in Fig. 9.10 (τ P is the unforcing time constant). It is clear that the unforcing of CSR in a time above τ R = 4.5 s no longer provides the effect of increasing the transient stability margin and does not eliminate voltage cascades under post-fault conditions. However, as has been shown above, the existing constructions of magnetically controlled CSR provide the full power shedding of the reactor in a time of 3τ R ≤ 0.3 s, i.e. solve the problem of load bus stability under typical contingencies.

9.3 Improving the Conditions of the Start-Up of Large Induction Electric Motors The processes of the start-up of large induction motors are accompanied by inrush currents of significant ratios (close to the values of short-circuit currents) and by a

9.3 Improving the Conditions of the Start-Up of Large Induction Electric …

191

Fig. 9.8 Voltage variations at the load bus of the consumer with the installation of CSR + SCB

Fig. 9.9 Variations of the CSR + SCB susceptance

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

Fig. 9.10 Variations of the electromagnetic and decelerating torques of the induction motor with different response speeds of CSR: 1—the electromagnetic torque of an induction motor with τR = 0.3 s; 2—the electromagnetic torque of an induction motor with τR = 3.0 s; 3—the electromagnetic torque of an induction motor with τR = 4.5 s; 4—the decelerating torque of the induction motor

reduction in voltage levels. The duration of such transients is sufficient and can total several tens of seconds. Let us consider the process of the group starting of induction motors forming about 65% of the total load after their complete stoppage. Figures 9.11 and 9.12 show the results of the calculations of variations in the relative angle between the rotors of the generator of a gas-turbine power plant and a synchronous electric motor as well as voltages at the load bus under the repeated startup of an induction motor after its complete stoppage without the use of controlled reactive power compensation devices. It is shown that the danger that the transient stability of the relative motion of the generator and synchronous electric motor rotors will be disturbed arises under such start-up in an autonomous power system. The voltage reduction associated with the starting of a tripped induction motor (Fig. 9.12) results in the out-of-step conditions of the generator’s and synchronous motor’s operation and, consequently, to the failure of asynchronous load starting. Let us consider the effectiveness of the use of controlled reactive power compensation devices based on CSR + SCB for improving the conditions of the start-up of large induction motors. Thus, it can be seen from Fig. 9.13 that the application of a controlled installation of reactive power compensation has provided the stability of the relative motion of power plant generators and equivalent synchronous electric motors. A higher

9.3 Improving the Conditions of the Start-Up of Large Induction Electric …

193

Fig. 9.11 Variations of the relative angle between the rotor of the power station generator and the rotor of the synchronous motor during the stopping t open and starting t close of the induction motor

Fig. 9.12 Voltage variations at the load buses during the stopping t open and starting t close of the induction motor

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9 Voltage Stability Enhancement by Use of Reactive Power Compensation

voltage level (Fig. 9.14) during the starting of a large induction motor is provided for by the intensive regulation of the CSR susceptance in the CSR + SCB installation (Fig. 9.15). According to Fig. 9.15, the stopping of induction motors takes place at the time moment t open . After the induction motors are tripped, the reactive power absorbed by CSR is increased to the rated value in order to limit an increase in voltage at the load bus; thus, the reactive power produced by the CSR + SCB installation turns to zero (the resulting susceptance of CSR + SCB becomes equal to zero (curve 1)). At the time moment t close , the group starting of induction motors is performed; at that, the reactive power consumed by CSR decreases to zero for the starting time (curve 1), while the reactive power generated by the CSR + SCB installation takes its maximum value at the expense of the capacitor bank (BCSR+SCB = 1 p.u.). After the end of the process of induction motors group starting, the susceptance of the CSR + SCB installation changes as a result of a change in the reactive power absorbed by CSR. The operating conditions of the CSR + SCB installation after the starting of induction motors is completed coincide with the initial condition. Another illustration of the successful group starting of induction motors provided by changes in the CSR susceptance is Fig. 9.16 showing that the electrical torque is always higher than the decelerating torque during the group starting of induction motors.

Fig. 9.13 Variations of the relative angle between the rotor of the power station generator and the rotor of synchronous motor during the stopping t open and starting t close of the induction motor with the operation of the CSR + SCB installation taken into account

9.3 Improving the Conditions of the Start-Up of Large Induction Electric …

195

Fig. 9.14 Voltage variations at the load buses at the stopping t open of a large induction motor with the operation of the CSR + SCB installation taken into account: 1—voltage variations at the load bus; 2—variations of the induction motor slip

As in the previous calculations, the response speed (the time of unforcing) of the controlled shunt reactor in the CSR + SCB installation is assumed to be equal to 0.3 s. The results of the computations of induction motors group starting with different values of the response speed of the controlled shunt reactor in the CSR + SCB installation are presented in Fig. 9.17. In such a way, the computations of Sects. 9.2 and 9.3 have showed that the problems of the transient stability of load buses in autonomous power systems containing large number of asynchronous and synchronous motors can be effectively solved by installing devices of controlled reactive power compensation based on CSR + SCB both under post-fault conditions and under the conditions associated with the starting of large induction motors (group starting). At that, modern constructions and control algorithms of magnetically controlled shunt reactors provide the required response speeds in all the cases considered. Higher speed of reactive power control provided for, e.g., by the use of more expensive transformer-type controlled shunt reactors or static thyristor compensators cannot be grounded in such cases.

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Fig. 9.15 Variations of the susceptance of the CSR + SCB installation at the starting t close of the induction motor: 1—variations of the susceptance of the CSR + SCB installation; 2—variations of the induction motor slip

Fig. 9.16 Variations of the electromagnetic and decelerating torques of the induction motor at the starting t close : 1—the electromagnetic torque of the induction motor; 2—the decelerating torque of the induction motor

References

197

Fig. 9.17 Variations of the electromagnetic and decelerating torques of the induction motor with various response speeds of the CSR + SCB installation: 1—the electromagnetic torque of an induction motor with τR = 0.3 s; 2—the electromagnetic torque of an induction motor with τR = 0.75 s; 3—the decelerating torque of an induction motor

References 1. Andrus ST, Belyaev AN (2008) “Controlled reactive power sources providing the stability of the load buses of oil producing complexes” [“Upravlyaemye istochniki reaktivnoy moshchnosti dlya obespecheniya ustoychivosti uzlov nagruzki neftegazodobyvayushchikh kompleksov”]. Nauchno-tekhnicheskiye vedomosti SPbGPU No 1, 92–97 2. Rowen WI (1983) Simplified mathematical representations of heavy-duty gas turbines. ASME J Eng Power 865–872 3. Sharma C (1998) Modeling of an island grid. IEEE Trans Power Syst 13(3):971–978 4. Belyaev AN, Smolovik SV, Okorokov RV Pershikov GA, Chydny VS (2006) Fundamentals of transients in power systems: summary of lectures. Part 1 [Osnovy perekhodnykh protsessov v elektroenergeticheskikh sistemakh: Konspekt lektsy. Chast 1], SPbGPU, Saint-Petersburg, 112 p 5. Belyaev AN (2008) “Increasing the transient stability of the autonomous power systems of oilproducing complexes based on electrical braking” [“Povysheniye dinamicheskoy ustoychivosti avtonomnykh energosistem neftegazodobyvayushchikh kompleksov na osnove elektricheskogo tormozheniya”]. Nauchno-tekhnicheskiye vedomosti SPbGPU, No 4(63), the main issue, 163– 169 6. Belyaev AN, Smolovik SV, Okorokov RV, Pershikov GA, Chydny VS (2006) Fundamentals of transients in power systems: summary of lectures. Part 2 [Osnovy perekhodnykh protsessov v elektroenergeticheskikh sistemakh: Konspekt lektsy. Chast 1], SPbGPU, Saint-Petersburg, 112 p

Chapter 10

Analysis of the Overvoltage Affecting the Converter and the Insulation of the CSR Control Winding

A number of cases have been registered when the power elements (the protective varistors and thyristors of semiconductor converters) of the biasing system have been damaged during the operation of CSR, at its energization in the absence of preliminary magnetic biasing. The major part of the damages to the elements of the biasing system is connected with the inadequate protection of semiconductor converters against switching overvoltages. The aim of this chapter is to reveal the causes of the overvoltages which affect the converter and the insulation of the control winding under different operating conditions of 500 kV CSR and to calculate the energy of switching impulses in order to define the requirements for the necessary energy capacity of protective devices. A three-phase group of single-phase reactors of the RODU-60000/500 type contains an integrated shunt resistor with an impedance of 21 Ω in each phase (Fig. 10.1); three-phase CSR of the RTDU-180000/500 type has one such shunt resistor at the terminals of the aggregated control winding (Fig. 10.2). The following designations are used in Figs. 10.1 and 10.2: RShR are shunt resistors; R1 –R6 , C1 –C6 are the resistances and capacitances of damping circuits providing the limitation of the amplitude and rate of rise of the recovery anode voltage at the thyristors; L1 –L6 are the saturation throttles limiting the rate of rise of the current flowing through the thyristors during their opening; VS1 –VS6 are power thyristors; CPB are blocks of cascade protection closing the circuits to let through signals to the control junction of the bridge thyristor; VD1.1–VD6.1 are symmetrical limiters of opposite sign voltage; VD1.2–VD6.2 are diodes intended to eliminate the charging of the capacitive damping circuits under inverse voltages at the thyristors; RU1, RU2 are varistors designed to protect the rectifiers against surge overvoltages appearing under the switching of the controlled shunt reactor or under the emergency conditions.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_10

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Fig. 10.1 The simplified circuit of electrical connections of the control winding and power semiconductor devices of a three-phase group of the single-phase reactors RODU-60000/500

10.1 Possible Causes of Dangerous Switching Overvoltages at the Terminals of the Control Winding Constructively, the sections of the control winding of a magnetically controlled shunt reactor located on the half-cores of each phase of the magnetic conductor are connected in opposition with respect to the main alternating flux of the power winding. Under the condition that the device is absolutely symmetrical (the halfwindings of the control (CtW) and compensation (CpW) windings have equal number of turns, the cross-sections of the half-cores are equal, and saturation inductions in the half-cores are equal), such a design ensures the absence of potential difference at the terminals of the control winding under both normal and transient operating conditions associated, for instance, with the switching of CSR with zero initial induction in the magnetic conductor.

10.1 Possible Causes of Dangerous Switching Overvoltages at the Terminals …

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Fig. 10.2 The simplified circuit of electrical connections of the control winding and power semiconductor devices of the three-phase reactor RTDU-180000/500-UHL1

Under these conditions, switching operations with CSR cannot cause overvoltages at the terminals of the control winding neither at the application of supply voltage from the side of the power winding at various instants nor at the not simultaneous closing of the contacts of the reactor circuit breaker, irrespective of the CSR circuit arrangement (a group of single-phase reactors or a three-phase one) and irrespective of the values of shunt resistors. The availability of a grounded electrostatic screen between the power and control windings eliminates the capacitive nature of overvoltages at the terminals of the control winding resulted from contingencies in the external system. In order to reveal possible causes of overvoltages at the terminals of the control winding, we will use Eq. (4.3) giving the relationship between the current iCtW and the voltage U CtW of the control half-windings and the corresponding magnetic fluxes in the equivalent scheme of CSR magnetic circuits (Fig. 4.2). ( ( ) ) UCt W = i Ct W · RCt W + WCt W · ϕ'1 + ϕ's1 + ϕ's3 − WCt W · ϕ'2 + ϕ's2 + ϕ's4

(10.1)

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In expression (10.1) the sum of flux derivatives in the first brackets applies to the first half-core and gives the resulting derivative of the flux coupled with the first half winding; the sum of flux derivatives in the second brackets applies to the seconds half-core and gives the derivative of the flux coupled with the second half-winding. As has been mentioned, the damages of the valves took place at the switching of CSR to no-load conditions; thus, the current of the control winding in the given expression is assumed to be equal to zero iCtW = 0. In this case the required voltage is this at the terminals of the control winding U CtW . Analysing (10.1) one can suggest the following causes of probable appearance of overvoltages at the terminals of the control winding U CtW : 1. A little constructive difference in the number of turns of the half windings of the control winding W CtW , 2. A difference in the values of flux derivatives (10.1) in the half-cores which, in its turn, can be caused by a number of reasons: • some constructive asymmetry of the device; • a difference in the saturation inductions of the half-cores; • a difference in the initial values of fluxes in the half-cores at the energization of the device. The constructive asymmetry of CSR (a difference in the number of turns of the half windings, a difference in the cross-sections of the half-cores, and a difference in saturation inductions) should be considered only as a theoretical reason for the appearance of increased voltage values at the terminals of the control winding. Thus, the performed tests of CSR of the RODU-60000/500-UHL1 type confirmed that the device is to a high degree symmetrical: the unbalance voltage of the control winding U nb U nb is about UCt W = 0.65 V; the unbalance current totals UCt W = 0.05 A. In such a way, it should be suggested that the main cause of the appearance of dangerous switching overvoltages at the terminals of the CSR control winding is the difference in the initial values of fluxes in the half-cores at the energization of the device. The disconnection of CSR under a previous load condition by interrupting current in the control winding through the removal of the control impulses from the thyristors of the semiconductor converter can result in the appearance of residual induction in the magnetic system of CSR, which persists for a long time till the following CSR energization. It should be mentioned that in this case the residual inductions of the half-cores have opposite signs, which is connected with the flowing of direct current through the opposite connected half windings of the control windings under the initial operating conditions of CSR (see Fig. 10.3). At the following CSR energization under no-load conditions without preliminary magnetic biasing, equal alternating magnetic fluxes (of the sinusoidal form and with the peak value of induction of 1.6–1.7 T, see Fig. 3.5) tend to appear in both the halfcores under the forced component of the system voltage. The sufficient difference between the initial and final states of the CSR magnetic system causes the intensive transient of balancing (changing) the magnetic fluxes of both the half-cores.

10.2 Switching a Three-Phase Group of Single-Phase CSRs

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Fig. 10.3 The disconnection of CSR under the rated load conditions with the interruption of current in the control winding

According to expression (10.1), the difference in the flux derivatives in the halfcores during the transient results in the appearance of potential difference between the terminals of the control winding. The estimation of the maximum value of the potential difference appearing at the terminals of the control winding as well as the estimation of the switching operation energy is presented in the following sections. In them, two different constructions of CSR are considered (see Figs. 10.1and 10.2).

10.2 Switching a Three-Phase Group of Single-Phase CSRs Let us consider the process of energization of a three-phase group of single-phase CSRs with integrated shunt resistors RShR = 21 Ω in each phase (see Fig. 10.1). Figure 10.4 shows the result of calculation of the transient associated with CSR energization with non-zero differently directed residual inductions of the magnetic system at the moment of voltage zero-crossing in phase A. CRS energization has been preceded by its disconnection under the condition of rated power consumption through the removal of the control impulses from the thyristors of the semiconductor converter. It is shown that the voltage at the terminals of the control winding achieves 20 kV under this switching operation, i.e. the failure of the semiconductor converter is inevitable, since the permissible inverse voltage for the thyristors is only 2.5 kV.

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Fig. 10.4 Voltage at the terminals of the control winding at CSR energization (a) and the voltage drop across the shunt resistors (b). c The derivatives of fluxes in the half-cores of different phases under CSR energization

10.3 Switching a Three-Phase CSR

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The energy released in the shunt resistors of CSR within a time period from 0.10 to 0.18 s (Fig. 10.4) will be equal: ∮0.18 W = i 2 Rdt = 637 kJ. 0.1

It is clear from Fig. 10.4 that the derivatives of the half-core fluxes under the transient of new operating condition setting are sufficiently different from each other, which, in accordance with (10.1), is the cause of overvoltages at the disconnected converter unit. Maximum values of the overvoltages at the terminals of the control winding (Fig. 10.4a) correspond to the maximum difference between the derivatives of the half-core fluxes (Fig. 10.4c). Thus, switching a three-phase group of single-phase CSR at the zero-crossing of voltage in phase A preceded by the disconnection of CSR under the condition of rated power consumption leads to the appearance of dangerous switching overvoltages at the terminals of the control winding; the energy released in the shunt resistors achieves W = 637 kJ.

10.3 Switching a Three-Phase CSR Let us consider the process of switching a three-phase CSR with an integrated shunt resistor RShR = 21 Ω at the terminals of the aggregated control winding (see Fig. 10.2). Figure 10.5 shows the calculation of the transient associated with CSR energization at the moment of voltage zero-crossing in phase A. CRS energization has been preceded by its disconnection under the condition of rated power consumption by removing the control impulses from the thyristors of the semiconductor converter. It is shown that the voltage at the terminals of the control winding achieves about 45 kV in this case, i.e. the failure of the semiconductor converter is inevitable and the damage of the control winding insulation is possible as well. The energy realised in the shunt resistors of CSR in the time period 0.10–0.12 s (Fig. 10.5, b) will be equal: ∮0.12 W = i 2 Rdt = 512 kJ 0.1

It is evident from Fig. 10.5 that the derivative of the resulting fluxes in both the half-cores (indices 1, 2) of all the phases are equal at the initial time moment, which corresponds to a steady state of the CSR magnetic system. However, the derivatives of the fluxes in the half-cores under the transient are sufficiently different, for example, for phase A, the maximum difference takes place at the time moment t 1 . At that, as

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Fig. 10.5 Voltage at the terminals of the control winding during CSR energization at the zero-crossing of voltage in phase A (a) and the voltage drop across the shunt resistors (b). c The derivatives of fluxes of the half-cores of different phases under CSR energization at the zero-crossing of voltage in phase A

10.3 Switching a Three-Phase CSR

207

shown in Fig. 10.5a, at the time moment t 1 the voltage at the terminals of the control winding takes its maximum value, which confirms the suggestions about the causes of overvoltages at the terminals of the control winding made above. In order to estimate the influence of the moment of switching on the value of voltage at the terminals of the control winding and on the energy emitted in the shunt resistors, we will consider the process of re-energization of a three-phase CSR at the moment when voltage in phase A cross a maximum value (Fig. 10.6). It is shown in Fig. 10.6 that voltage at the terminals of the control winding reaches 40 kV. Under such a switching operation, the failure of the semiconductor converter is also inevitable and the damage of the control winding insulation is possible. The energy realised in the shunt resistors of CSR within the time period 0.10–0.12 s (Fig. 10.6b) will be equal: Fig. 10.6 a Voltage at the terminals of the control winding at CSR energization at a maximum of voltage of phase A. b Voltage drop across the shunt resistors. CSR energization occurs at the moment when voltage in phase A takes its maximum value

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∮0.12 W = i 2 Rdt = 528 kJ 0.1

Thus, the moment of the energization of a three-phase CSR almost does not influence on the value of overvoltages and on the energy released in the shunt resistors under the switching impulse.

10.4 Estimating the Influence Which Non-simultaneous Switching of the Phases of the Reactor Circuit Breaker has on the Value of Overvoltage Let us estimate the influence of non-simultaneous switching of the phases of the reactor circuit breaker on the form of the impulse and its energy. CRS energization has been preceded by its disconnection under the condition of rated power consumption by removing the control impulses from the thyristors of the semiconductor converter. Figures 10.7 and 10.8 give the results of calculations of the transient associated with CSR energization with non-zero initial values of inductions in the half-cores and with account taken of the fact that the phases of the reactor circuit breaker are switched not simultaneously: • at the zero-crossing of voltages in phases A, B, C (Fig. 10.7); • when voltages in phases A, B, C cross their maximum values (Fig. 10.8). When CSR is energized at the zero-crossing of voltage, the energy realised in the shunt resistors of CSR within the time period 0.10–0.125 s (Fig. 10.7b) will be equal: 0.125 ∮

W =

i 2 Rdt = 561 kJ 0.1

When CSR is switched on at a maximum of voltage, the energy released in the shunt resistors of CSR in the time period 0.1–0.2 s (Fig. 10.8b) will be equal: ∮0.2 W = i 2 Rdt = 177 kJ 0.1

The comparison of Figs. 10.7 and 10.8 show that the non-simultaneous switching of the phases of the CSR circuit breaker has sufficient influence on the value of switching impulse and on the energy emitted in the shunt resistors: thus, when each phase is closed at the instant of voltage zero-crossing in this phase, the overvoltages observed at the terminals of the control winding are sufficiently higher (up to 50 kV,

10.4 Estimating the Influence Which Non-simultaneous Switching … Fig. 10.7 Voltage at the terminals of the control winding at the moments when voltages of the phases cross zero values (a) and the voltage drop across the shunt resistors (b). c The derivatives of the half-cores fluxes in different phases during CSR energization at the zero-crossing of voltages in phases A, B, C

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Fig. 10.8 Voltage at the terminals of the control winding during CSR energization at the moments when voltages of the phases take maximum values (a) and the voltage drop across the shunt resistors (b). c The derivatives of the half-cores fluxes in different phases during CSR energization at maximum of voltages in phases A, B, C

10.6 Conclusion

211

see Fig. 10.7) than when the switching operation is performed at maximums of voltages (up to 25 kV, see Fig. 10.8).

10.5 Switching Operation of CSR Energization Preceded by Its Disconnection Under the Condition of 50% Load Consumption Let us estimate the influence of the previous load conditions of CSR on the voltage value at the control winding. In Fig. 10.9 the results of the calculation of the transient associated with the energization of a three-phase CSR (at the zero-crossing of voltage in phase A) are presented. The energization of CSR has been preceded by its disconnection under the condition of consuming 50% of the rated power. The energy realised in the shunt resistors of CSR within the time period 0.10–0.12 s (Fig. 10.9b) will be equal: ∮0.12 W = i 2 Rdt = 80 kJ 0.1

It is obvious that the energy released in the shunt resistors is sufficiently lower in comparison with this in the case when the preceding mode of CSR has been the condition of the rated reactive power consumption.

10.6 Conclusion 1. The switching of a three-phase group of single-phase CSRs with 21 Ω shunt resistors integrated into each phase (the preceding operating conditions are the rated) at the zero-crossing of voltage in phase A causes switching overvoltages at the terminals of the control winding with a maximum value of the voltage impulse equal to about 20 kV. The reduction in the equivalent resistance of the shunt resistors (integrated into each phase) with respect to the case of a three-phase CSR results in an increase in the time constant of transient decay in the control winding. As a result of this, the energy released in the shunt resistors is maximum and totals W = 637 kJ. Thus, such a switching operation leads to the damage of the thyristors of the semiconductor converter, so the installation of additional protective varistors of sufficient energy capacity at the terminals of the control winding is needed to dissipate the energy released in the shunt resistors. One of the possible measures for reducing the duration of switching overvoltages under switching operations with a three-phase CSR group is increasing the resistance

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Fig. 10.9 Voltage at the terminals of the control winding under CSR energization (a) and the voltage drop across the shunt resistors (b). c. The derivatives of fluxes in the half-cores of different phases under CSR energization

10.6 Conclusion

2.

3.

4.

5.

6.

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of the shunt resistors; however, the amplitude of switching impulses will increase as the duration of overvoltages reduces. Switching a three-phase CSR (the preceding operating condition is the rated) with a common control winding and one 21 Ω shunt resistor (with a lead-out terminal in the middle) at the zero-crossing of phase voltage results in the appearance of switching overvoltage with a maximum value of the impulse of about 45 kV. Such overvoltages are dangerous not only for the thyristors of the semiconductor converter, but also for the insulation of the control winding. In this case the energy released in the shunt resistors achieves the value W = 512 kJ. Non-simultaneous switching of the phases of the reactor circuit breaker with non-zero values of inductions in the half-cores of CSR exerts influence on the overvoltage value. Thus, if CSR is energized at the instants when each of the phase voltages takes a zero or maximum value, overvoltages with maximum values of 50 kV and 25 kV, respectively, appear at the terminals of the control windings. The energy released in the shunt resistors in the first case is equal to 561 kJ, and in the second case it totals 177 kJ. In such a way, equipping the phases of the reactor circuit breakers with special devices, which make it possible to perform switching operations at specified time moments (controlled switching near a voltage maximum), allows reducing the requirements for the energy capacity of protective devices and decreasing switching overvoltage by the factor of two. The greatest impact on the value of overvoltages is exerted by non-zero initial values of induction in the magnetic system of CSR (which depend on the load condition of CSR preceding its disconnection). Thus, if the load of CSR constitutes 50% of the rated value, then even under unfavourable switching operation at the zero-crossing of system voltage in the phases, the maximum value of the overvoltage impulse totals 25 kV with the energy dissipated in the shunt resistors equal to 80 kJ. Safe energization of CSR with the open control winding can be realized either with the control of the load mode preceding the disconnection or with equipping the control winding with protective devices with sufficient energy capacity. One of the measures allowing the elimination of dangerous overvoltages is the preliminary magnetic biasing of CSR. Using preliminary magnetic biasing before CSR is connected to the grid allows eliminating the appearance of dangerous overvoltages at the terminals of the control winding. In this case, the control winding is closed to the operational converter, and the voltage at the control winding is defined by the characteristics of the connected rectified voltage source.

Chapter 11

Special Topics in Design and Commissioning of CSR Complexes

More than 12 years have passed since the development, commercial production and putting into operation of the first magnetically controlled shunt reactor. Nowadays, more than 70 controlled reactors of the RTU line are installed in Russia and CIS countries. In spite of the fact that this kind of equipment is of mass production at least in Russia, the designing, adjustment and field testing of CSR are frequently connected with certain difficulties. In the present chapter, some peculiarities of designing and installation of controlled shunt reactors resulted from their construction and physical processes appearing in them under transient, steady-state and switching conditions are considered.

11.1 Design Solutions and Equipment Arrangement The process of the implementation of power system equipment is always connected with a number of design tasks which are to be performed, and the controlled shunt reactor is not the exception. When grounding the choice of the required CSR capacity, it is necessary to solve such problems as providing required voltage quality in nodes of a power system, the optimization of reactive power flows, the minimization of power losses, increasing the transfer capability of power transmission lines, and smallsignal and transient stability enhancement. After these tasks are considered and the required capacity of compensation devices is determined, the designer encounters a problem of placing the equipment at the territory of the substation and connecting its individual units. Let us consider in more detail circuit and layout decisions applied when designing a CSR installation at the substation. A CSR complex of the RTU line consists of three main parts: • the electromagnetic part (EMP) of the reactor of the RTDU or RODU type (Fig. 11.1); © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9_11

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Fig. 11.1 The electromagnetic part of CSR of the RTDU-25000/220-UHL-1 type

• transformers with semiconductor converters (TMP) (Fig. 11.2); • the automatic control system (ACS) (Fig. 11.3). The EMP is similar to this of conventional power transformers and, for this reason, has similar requirements for placing, but it is necessary to account for some peculiarities associated with the special purpose of the reactor’s secondary windings. TMP of outdoor unit construction represents an installation consisting of a stepdown transformer and a semiconductor converter installed on a common frame and interconnected by a short, about 1 m long, rigid busbar bridge delivered in the package. TMPs are installed at an outdoor site in close proximity to the EMP.

Fig. 11.2 Transformer-converter unit (TMP)

11.1 Design Solutions and Equipment Arrangement

217

Fig. 11.3 General view of the ACS cabinet

ACS represents a microprocessor device enclosed in the standard cabinet installed in a heated building near the power part of the complex or in the building of the operational control desk (OCD). The specific features of the secondary windings of 220–500 kV three-winding reactors (see Figs. 3.20 and 3.21) are as follows: • the presence of predominant 3rd and threefold harmonic components in the current of the compensation winding under steady state conditions; • the absence of electromagnetic coupling between the control and power windings. The first of the aforementioned characteristics should be taken into account when designing a bus system for making a delta-connection in case the reactor consists of a group of three single-phase reactors (RODU). In order to save on space at the substation site, the bus system can be made of a cable which must be designed to withstand a sufficient value of 3rd harmonic current. Also, this feature must be taken into account when designing relay protection of CSR, which will be considered in detail below. The load current from TMP is rather small and does not exceed 80 A with regard for possible overload. The calculation of short circuit current in the delta connection of the compensation windings and the bus system supplying TMP does not differ from short circuit current calculations at the low voltage side of a conventional transformer with Yn/D-11 connected windings; there is no current contribution from the side of TMP.

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The second specific feature allows reducing the distance between the insulators of +/− poles in spite of the fact that formally the rated voltage of the control winding is 40 kV (for a 500 kV CSR). When choosing this distance it is necessary to take into account the rated voltage of the semiconductor converters supplying the control winding and the convenience of assembly. When choosing a bus system at the side of rectified voltage on the condition of heating it is necessary to base on the rated current of the semiconductor converters and their overload capability; as for the thermal-withstand capability under faults, the current contribution of a fault place is caused only by rectified current from the side of semiconductor converter. The specific feature of 110 kV two-winding reactors (see Fig. 3.17) is that the compensation and control winding are combined in one multiple-section winding representing an open double-delta connected circuit. The equipotential terminals of this delta connection are connected to the poles of full-wave semiconductor converters supplied through single-phase transformers from other intermediate terminals of the double-delta connection of the control winding, the voltage between these terminals totals 22 kV at no-load. The control winding of a two-winding reactor is supplied with rectified current from two (the main and redundant) single-phase converter units placed at a common frame (OMPP). Each unit consists of a single-phase transformer and a low capacity (200 kVA) semiconductor converter. The single-phase transformers are connected to the control winding via high-voltage protectors. The function of preliminary magnetic biasing is served by single-phase low-capacity transformers of the TMO-2.5/0.4/0.012 type supplied from the 0.4 kV grid. When choosing a bus system between the secondary winding of a two-winding CSR and single-phase transformers (OM) on the condition of short circuit thermalwithstand current, the reactor is presented as a two-winding transformer with Yn/D11 connected windings in the analytical model. Since the transformers of semiconductor converters are single-phase, the expected type of short circuit at the alternating current side of OMP is a single-phase short circuit; there is no current contribution from the converters. A bus system at the rectified voltage side is chosen in the same way as has been described above for a three-winding CSR modification. The CSR complex is equipped with external current and voltage sensors in order that the automatic control system can perform its algorithms of. The place where the sensors are installed is determined by the designer with regard for two major requirements: • it is necessary to place the sensors at any pole of the common bus system of all converters eliminating the possibility that these can be disconnected when the main or redundant TMP is put out of operation or when the faulted phase is taken out for repair and replaced with a redundant one; in other words, in order to control the total rectified current from any TMP, the sensors must be placed between TMP groups and a phase of the reactor; • it is necessary to eliminate the loading of the sensors caused by the tension of the bus system conductors.

11.2 Realization of the Control, Supervision and Self-Diagnostic Functions …

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All line CSRs are equipped with additional overvoltage suppressors connected between the ±poles (see Fig. 3.21). The requirements for their installation are analogous to the above mentioned requirements to current and voltage sensors. When arranging the main elements of a controlled shunt reactor complex, it is necessary to consider the issues of reliability and usability of the complex equipment along with physical characteristics of CSR. The reliability of the electromagnetic system and oil-immersed transformers is rather high as opposite to this of semiconductor converters, which is the reason for implementing a redundant TMP for the power standby of the control winding. In the case of the failure of the main converter, the redundant one performs its functions. In order to carry out repair of a semiconductor converter it is necessary to provide trucks with access to the tank so that the semiconductor converter can be removed and damaged semiconductor elements can be replaced. It is also necessary to have easy access to conjunctions cabinets (CC) placed on the frame of semiconductor converters in order to reveal failing equipment. If transformer-converter units are placed at a high height, the access to the conjunction cabinets can be provided for by constructing maintenance floors.

11.2 Realization of the Control, Supervision and Self-Diagnostic Functions of a CSR Complex The main system which not only performs the control of CSR, but also checks its primary parameters and the settings of a temperature condition of TMP, carries out the self-diagnostics of control circuits and gives fault signals to relay protection and automation devices is the automatic control system of a CSR complex (ACS). The main functions performed by ACS of CSR of the RTU line are as follows: • automatic control of the value of the CSR inductance within the set limits in order to support voltage at the point of connection; • providing the manual control of CSR current by the step-wise changing of the firing angle of semiconductor converter thyristors; • automatic support of a set current value in the power winding of the reactor; • turning CSR from the automatic mode to the manual control mode and visa versa; • displaying variables of an operating condition, the assigned control settings, and the state of the complex circuit; • warning of overloads and damages in the TMP converters; • the detection of current overloads in the power winding of CSR followed by the automatic limitation of power and generation of the corresponding signal; • the detection of overload and overheating of the converters followed by the automatic limitation of power and generation of the corresponding signal; • supervision over the control of converters’ thyristors; • the realization of control actions from external devices of protection and automation, including the possibility to perform remote control of operating conditions;

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• the realization of the preliminary magnetic biasing mode of CSR; • recording and archiving all the events registered by ACS. Constructively, ACS is made in the form of a two-side maintenance cabinet, where the following devices are placed: an electronic block of automatic control (ACB); the panel of measuring voltage and current transducers; the panels of output relay protection signals, indication and control; control devices and terminal blocks of external connections. In Fig. 11.3 a general view of the ACS cabinet is presented. ACS consists of the following units: ACB—the block of automatic control; ICP—the indication and control panel; MVT—the panel of measuring voltage transducers; MCT—the panel of measuring current transducers; ORSP—the panel of output relay protection signals. The block of automatic control includes: CIF—a cell forming control impulses; CIC—a cell controlling control impulses; CPU—an industrial computer with add-in modules. Signals from the potential transformers (PTs) of the high-voltage (HV) grid and PTs of the compensation winding buses (CpW PTs) of the reactor are transduced and then come to the panel of measuring voltage transducers (MVT). Voltages from MVT proportional to the voltages of the power and compensation windings come to the industrial computer of the ACB block where voltage in the high-voltage grid is measured, the synchronization signal (d0) is formed, and the presence of signals from PT and CpW PT is checked. If the signal from PTs of the HV grid disappears, the control system removes control impulses from the operational converter (the main or redundant) turning it to the shunting diode mode (the shunting branch remain closed). At the same time, the preliminary magnetic biasing mode is provided by TMP connected to the switchgear of the substation. Signals from the measuring current transformers of phases of the CSR power winding (I PW ) come to the panel of measuring current transducers MCT and, after current-to-voltage transformation, arrive to the ACB block where they are measured and the corresponding overload signals are formed. In case the reactor is overloaded by current in the power winding, the control system blocks the control impulses of converters and turns the converters to the mode of shunting diode. At the same time the Protection indicator on the operator panel turns on (the State screen) and the contact signal of Protection actuation is formed. After current in the control winding decreases below the overload threshold, the system unblocks the control impulses. At that, the Protection indication on the operator panel turns off, and the contact signal of Protection Enabling is removed.

11.2 Realization of the Control, Supervision and Self-Diagnostic Functions …

221

Transformed currents from the current transformers of phases of semiconductor converters come to the panels of measuring current transducers MCT and, after current-to-voltage transformation, arrive to the ACB block where overload signals are formed. If the overload of a converter by phase currents is detected, the control system blocks the control impulses of the operational converter and turns it to the mode of shunting diode. At the same time the Protection indicator on the operator panel turns on (the State screen), and the contact signal of Protection actuation is formed. After the current in phases of the converter decreases below the overload threshold, the system unblocks the control impulses. At that, the Protection indication on the operator panel turns off, and the contact signal of Protection actuation is removed. If the overload of a converter is more than 150%, the control of this converter is disabled and can be enabled only manually. The transformed current of the control winding comes from the direct current sensor to the ACB block to be measured in order to reveal the presence of preliminary magnetization current and the overload of the control winding. In case the direct current overload of the control winding is detected, the control system blocks the control impulses of converters and turns the converters to the mode of shunting diode. At the same time the Protection indicator on the operator panel turns on (the State screen), and the contact signal of Protection actuation is formed. After the current in the control winding decreases below the overload threshold, the system unblocks the control impulses. At that, the Protection indicator on the operator panel turns off, and the contact signal of Protection actuation is removed. In order that the above mentioned functions of control, protection and monitoring can be performed, the following signals from external sensors are received by ACS: Measuring: • voltage from HV PT; • voltage from CpW PT; • synchronization voltage from PT of 6, 10 or 35 kV auxiliary switchgear (only for line CSRs); • currents in the phases of the CSR power winding from the measuring windings of integrated current transformers; • currents in the phases of TMP transformers (the main, redundant, and dynamic) from the measuring windings of integrated current transformers; • the rectified current of the control winding from the direct current sensor. Contact signals transduced into logical signals: • • • • •

the state of the contacts of the power winding circuit breaker; the state of the contacts of the 10 kV circuit breaker of the main TMP; the state of the contacts of the 10 kV circuit breaker of the redundant TMP; the state of the contacts of the 6 (10, 35) kV circuit breaker of the dynamic TMP; the state of the contacts of the first stage of the main semiconductor converter’s thermal sensor; • the state of the contacts of the second stage of the main semiconductor converter’s thermal sensor;

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11 Special Topics in Design and Commissioning of CSR Complexes

• the state of the contacts of the first stage of the redundant semiconductor converter’s thermal sensor; • state of the contacts of the second stage of the redundant semiconductor converter’s thermal sensor; • OK signals from the conjunction cabinets (CC1, CC2, CC3); • the signal of the external blocking of converters. When the first stage of the thermal sensor of a semiconductor converter is actuated, the control system reduces the power of this converter. When the second stage of the thermal sensor of a semiconductor converter is actuated, the control system turns this converter to the no-load mode. The monitoring functions described in the present section can be additionally provided by individual monitoring systems controlling the state of high-voltage leadins insulation, the appearance of dangerous gas dissolved in the reactor’s oil, the moisture content and thermal conditions of the windings and the oil, and performing the statistic processing of current registrations of monitoring and measuring equipment and the monitoring signals of protective devices.

11.3 Specific Features of CSR Relay Protection Despite the similarity in appearance and construction of controlled reactors and conventional oil-immersed transformer devices, the formers have sufficient distinctions in terms of operating conditions, construction and circuit arrangement. For this reason, well-known methods and devices used in relay protection and automation, the existing microprocessor terminals of relay protection, and adopted design methods are not applicable to them. Moreover, there are no developed and approved guidelines or other methodology, or documents on relay protection of CSR yet. Therefore, the aim of the present section is to summarize the existing experience and to familiarize specialists of corresponding professions with the practice of designing and putting into operation CSR and their means of relay protection and automation. Here, the possibility to use electrical protection for controlled reactors and peculiarities of its application are considered, since gas protection, terminal insulation control (TIC), fire fighting, monitoring, sensors of temperature and oil level for the oil-immersed equipment of CSR do not differ from those of power transformers of the same capacity and voltage level in terms of arrangement, designing, assembly and operation. The main distinction between power transformers and controlled reactors is defined by the operating principle of the latter. Under normal operating conditions of power transformers, almost all the power from the supply side is transferred to the load side; reduced currents at the high-voltage and low-voltage sides are equal, and the magnetizing current can be neglected when choosing and designing protection (except for the surge of magnetizing current at energization).

11.3 Specific Features of CSR Relay Protection

223

For magnetically controlled reactors, the magnetizing current (or the current flowing through the magnetization shunt branch in the equivalent T-circuit) is the principal operating reactive load current of the power winding which depends on the biasing current running through the control winding and is not accompanied by the corresponding 1st harmonic current in the delta connection of the compensation windings. Under normal load conditions of CSR, its secondary compensation winding is loaded only by current of 3rd harmonic component, since currents of higher threefold harmonics and current in the transformer of the main TMP connected to it, the capacity of which is less than 1% of the rated CSR capacity, can be neglected. It is followed from what has been stated above that the main differential protection of CSR can not be designed in the same way as that of transformers, for which the operating zone of such protection includes all high-voltage and low-voltage windings. For this reason, the longitudinal differential protection is connected to current transformers at the supply side and the side of the PW neutral providing fastresponse protection against internal phase-to-phase and single-phase faults. Under the most probable turn-to-turn faults, the longitudinal protection of an individual power winding is idle, so it must be supplemented with the transverse differential current protection connected to CTs of parallel branches of the PW phases. The composition of protection of the primary power winding of CSR and its design are similar to a considerable degree to the relay protection of uncontrolled shunt reactors of the same voltage level, which have only one winding. As shown in [1–4], the behaviour of currents in the compensation and control windings also has some peculiarities which impede selecting for them the protection usually used in power transformers. In particular, it concerns the control winding, the sections of which are flowed round in parallel by the rectified current of the three-phase thyristor converter TMP. Choosing and designing protection for the compensation winding is complicated by the fact that in-phase currents of commensurable values, analogous to zerosequence currents and hardly distinguishable between each other, circulate in each phase of its delta connection under the conditions of switching on and automatic reclosure, load conditions, external single-phase short circuits and internal turn-toturn faults. Thus, under the condition of a single-phase short circuit, there are zerosequence currents in all the three phases of the compensation windings at the supply side, which values and phase angles correspond to the reduced PW phase currents I0 constituting about 60% of the rated value, and it is necessary to restrain protection from operating under these currents by assigning appropriate current or time settings. In-phase currents of similar values (with aperiodic components and higher harmonics) may appear in phases of the compensation winding under switching to the grid or automatic reclosure conditions. Against the background of the considered currents, which appearance must not cause the triggering of the CpW protection, it is desirable to provide the maximum sensitivity of the protection to turn-to-turn faults both in CpW and in adjacent windings of the reactor especially as because the control winding does not have its own protection against turn-to-turn short circuit. If a small number of turns of a winding are short circuited (a coil or an individual turn), the value of fault current in the

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11 Special Topics in Design and Commissioning of CSR Complexes

phase of the winding can be less than 10% of its reduced rated value (especially, at faults through a transient resistance), so the setting of the primary protection must be comparable to this value or at least to the primary setting of the transverse current protection of the power winding (0.15–0.2 p.u.). Another sufficient distinction is that the equipment of controlled reactors contains transformers with converters (TMPs) connected both to the compensation winding and to the substation switchgear by overhead or cable bus system through circuit breakers. The issues of choosing and approving the settings of overcurrent protection (OCP) for these feeder bays and providing its standby require considering the operating conditions of semiconductor converters in TMPs. Specific technical features of CSR affecting the choice and design of relay protection include the value of short circuit voltage between the windings, the level of currents of external faults associated with it, current surges in the windings of the reactor at its energization and automatic reclosure, and overload capacities. For 35 and 110 kV CSR of a relatively low capacity (10–25 MVAr) the arrangement of the electromagnetic part with two windings, namely, the power (PW) and the control winding (CtW) connected by the scheme of open double-delta connection is more desirable in terms of engineering-and-economical performance. Such a control winding combines the functions of magnetic biasing and compensation (locking in the delta-connection) of three-fold higher harmonics (see the circuit of Fig. 3.17). The power part of the biasing system is made of two single-phase converters of low capacity placed at the common frame with supplying transformers connected to the terminals of the control windings of the reactor through high-voltage protectors. Such CSRs often operate in parallel with a capacitor bank and may have the common automatic control system. 220 and 330 kV reactors with a capacity of 63–180 MVAr (like 110 kV CSRs of a capacity more than 50 MVAr) are designed with three separate windings, namely, the power, compensation, and control windings. The delivery package includes two identical three-phase transformers with thryristor converters (TMP); the main one is connected to the terminals of the compensation winding through a 10 kV circuit breaker, while the redundant one is connected to the 6 or 10 kV switchgear of the substation. The schematic diagram of these reactors is shown in Fig. 3.20. CSRs of 500 kV and above voltage levels installed at buses or in a line have stronger requirements to the response speed: the time of the full picking-up or shedding of power must be not greater than 0.3 s. For this reason, with the same circuit arrangement and the composition of windings in the electromagnetic part, the biasing system also contains an additional third “dynamic” TMP with an increased value of maximum rectified voltage (see Fig. 3.21). This TMP is connected to a 6 or 10 kV external supply source providing forcing modes of power picking-up or shedding as well as the preliminary magnetic biasing of the reactor under its energization. Besides that, the arrangement of the electromagnetic part of these reactors can be either three-phase or single-phase in order to reduce transport dimensions and the mass of the device.

11.3 Specific Features of CSR Relay Protection

225

Specific characteristics of operating conditions and design of protection for CSR with magnetic biasing have already been considered in a number of publications [1– 4], in which it is shown that the main distinction between the protection of CSR and transformer is the need for individual protection for each of the reactor’s windings, because alternating load current runs only in the power winding. For this reason, we will mention below only how to increase additionally the effectiveness of relay protection and enlarge its composition for various modifications of reactors. According to [1–4], the minimum required composition of the relay protection of a three-winding CSR includes the following protection system (along with TIC if it is required, gas protection, and overload alarm system of ACS): • for the power winding of a reactor—the longitudinal and transverse differential current protection; • for the compensation winding—two-step overcurrent protection (OCP); • for the control winding—OCP at CT of the grounded terminal of the middle point of the control winding; • for feeder bays of the compensation winding—OCP at integrated CTs of the compensation winding terminals (for a three-phase modification of CSR) and two-step overcurrent protection at CTs of the cells of TMP circuit breakers; • for protection against single-phase short circuits at the side of the compensation winding with low fault currents—zero sequence voltage protection. As has been shown in a number of publications, the most sensitive and universal protection of the reactor is OCP of the compensation winding if it is connected to measure full currents in the phases of the compensation winding delta connection and is restrained from operating under the conditions of energization, automatic reclosure, and external faults. Since currents in the compensation winding have the same behaviour and close values under the mentioned normal conditions and internal faults (turn-to-turn short circuits), it is necessary to use rather complicated algorithms including the filtration of input signals, protection blocking at external faults or automatic reclosure, and braking by 2nd harmonic current at energization, in order to provide minimum possible current and time settings (references) of this protection. Ways to restrain OCP of the compensation winding from operating under external short circuits and other contingencies are given in Table 11.1 and, if the protection is realized in the OCP terminal, the current setting of this protection of about 0.1 p.u. and the time setting of 0.5 s can be provided. The required functions of blocking by zero-sequence current and voltage along with the second harmonic current under switching on and automatic reclosure are available in most of produced relay protection terminals with freely programmable logic (ABB, Siemens, Areva, etc.). The considered OCP of the compensation winding connected to measure full currents in the phases was realized in the relay protection of a line 500 kV CSR at the open switchgear of Aksusskaya GRES in Kazachstan. During field testing its current setting was increased from 200 to 400 A (primary), which is less than 0.1 p.u. of the reduced rated value, in order to restrain the protection from operating under switching conditions. The time lag restraining the protection from operation

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11 Special Topics in Design and Commissioning of CSR Complexes

Table 11.1 Ways to restrain OCP of the compensation winding from operating under external short circuits and other contingencies No.

Parameter for restraining

Limiting value

Method of restraint

Value for restraining

From 0 to 100 A

1

Load (TMP)

By the current setting

Up to 100 A

2

The 3rd harmonic From 0 to 0.2 p.u

Filtration

To 1500 A of the peak value

3

Open-phase condition

By the time setting or To 1.5 s or 0 s U0 (3I 0 PW) blocking

4

Single-phase To 0.6 p.u short circuit at the supply side, SPAR cycles

By the time setting or To 1.5 s or 0 s 3I 0 PW (U 0 ) blocking

5

Switching-on currents and TPAR

To 0.8 p.u. of the peak value, to 0.3 p.u of the effective value

By the time setting or blocking (braking) the 2-d harmonic in the current of CpW (PW)

6

Currents of external through faults

2 p.u not greater than 2 By the time setting I nom

0.5 s

7

The duration of unbalanced grid voltage and load currents

To 5%

To 400 A

From 0 to 0.4 p.u. under rated biasing

By current in the delta of the compensation winding

To 5 s or 0 s

Note Conditions 1–4 are not the expected conditions for if protection is realised in OCP terminals with eliminated higher harmonics and blocking by U 0 or 3I 0

in cycles of automatic reclosure was taken equal to 3.5 s, since the blocking functions of protection which can be used under these conditions were not enabled. It should be emphasized that it is not permissible to connect the current circuits of the compensation winding OCP in delta, since in this case the protection, being restrained from interrupting three-fold harmonic currents and turn-on currents, will loose the ability to operate under turn-to-turn faults in windings of the reactor, under which currents in the phases of the compensation winding are in-phase and do not flow into the RP terminal through the delta-connection of the secondary circuits of CTs. For the same reason, differential current protection at the delta-connection of CTs of the compensation winding and at the star-connection of CTs of the TMP circuit breakers will be operable only at rare phase-to-phase short circuits, so, with the settings of CpW OCP of about 500 A and 0.5 s, the use of this protection is unreasonable. The absolute selectivity and the absence of a time lag necessary for protection of high-capacity transformers and reactors from the standpoint of fault current values and the influence on the power system stability are not required for protection of the secondary winding of a reactor with a short-circuit voltage of about

11.3 Specific Features of CSR Relay Protection

227

50%, since currents in the phases of the power winding under any fault at the side of the compensation or control winding are not greater than twice the rated value. The considered current protection has high sensitivity to turn-to-turn faults in the compensation winding and adjacent windings of the reactor as well as to other types of short circuits including external faults at the low voltage side. Thus, being the main protection for the compensation and control windings, this OCP is at the same time the backup for the rest of the reactor’s protective relays. There are modifications of CSR, for example, RTU-63000/220 (110), which power winding does not have parallel branches and corresponding groups of current transformers for the transverse differential current protection. In this case, the only electrical protection operating under turn-to-turn faults in the power winding of the reactor is the considered CpW OCP. Three-phase three-system (three-relay) implementation of the compensation winding OCP increases its sensitivity under single-phase short circuits in zones of its backup action, i.e. under turn-to-turn faults in adjacent windings and under singlephase ground short circuit of the compensation winding bus system and its feeder bays (TMP). At the same time, this implementation supplements the protection with the quality of self-redundancy, i.e. faults in the current circuits or failure of operation in one of the phases are duplicated by the possibility of operation of other OCP phases. For this reason, if no backup protection of the same or other modification is available for the compensation winding, it is possible to limit oneself to using the only group of CTs in the delta-connection of the compensation winding. According to [5], for transformers and reactors, a minimum value of current of full coil (for the power winding) or turn-to-turn (for the compensation and control windings) short circuit in the open part of the windings constitutes about 0.3 p.u. (for windings made of several parallel conductors). Then, if the said setting of 0.1 p.u. is provided, CpW OCP with a sensitivity index of not less than 2 protects a reactor against any type of full solid turn-to-turn (for the compensation and control winding, or one coil for the power winding) short circuit. Despite the high sensitivity and the effectiveness of CpW OCP and TMP OCP under single-phase short circuits at the low voltage side (with the grounded neutral of TMP), additional zero-sequence voltage protection operating to disconnect the reactor from the grid is also necessary, which requires explanations. As a rule, single-phase 500 kV reactors, especially if a redundant phase of jumper connection is available, have an air-insulated bus system of the compensation winding delta-connection with a total length of conductors up to several hundred meters. The most expectable type of fault is this case is a single-phase short circuit in the circuit of the mentioned air-insulated bus system. A particular case of such a fault is the destruction of a bus system phase associated with a fall of the conductor to the ground, i.e. the combination of a single-phase short circuit with the opening of the compensation winding delta-connection. At that, the single-phase short circuit can be either solid, if the conductor falls on a grounded construction, or through a transientresistance, in which case the single-phase short circuit current is not enough to cause the triggering of both the compensation winding OCP and OCP of the TMP circuit breaker.

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11 Special Topics in Design and Commissioning of CSR Complexes

In the first case, if the main and redundant TMP operate with the dead-grounded neutral, TMP (or two TMPs, if the redundant one was connected to the compensation winding and its circuit breaker was closed) will be tripped and the reactor will remain in operation with a single-phase fault at the low voltage side and the open delta-connection of compensation winding. As a rule, backup zero-sequence voltage protection at the terminals of the open delta-connected winding of 10 kV PT, if it is provided for in the project, only performs action to alarm. In this situation, the operating staff is exposed to the danger of electrocution in the area of the compensation winding bus system, while in the power winding of CSR, which remains in operation, a sufficient value of 3d harmonic current component appears (up to 20% of the rated current if the reactor carried about 50% of the rated load under the previous operation conditions). If TMPs are connected by the scheme with the isolated neutral or a single-phase short circuit is closed through a large transient resistance, none of the protective relays, except for zero-sequence voltage alarm at PT-10 kV, will operate, and the reactor will remain in operation carrying the same load as before the fault with corresponding level of 3d harmonic in the current consumed by the power winding. An example of the breaking of the bus system of the secondary winding and subsequent emergency trip by OCP at the low voltage side of the 500 kV line controlled reactor at Barabinskaya substation in July, 2011 is given in Fig. 11.4. In the mode of current variations in phases of the secondary winding delta-connection one can trace, at first, a reduction of the 3d harmonic to a zero value as the conductor is getting warm and falls out of the apparatus clamp, then this current remains equal to zero during the process of falling (or swinging) of the conductor till a short circuit to conductive constructions, and, at the last stage, single-phase short circuit currents followed by OCP action to disconnect the reactor are observable. It should be explained that in the considered case, in the CSR circuit of Barabinskaya substation, a transformer at the low voltage side does not have an individual circuit breaker, i.e. it is connected deadly to the bus system of the secondary winding delta connection of the reactor. For this reason, the transformer OCP at the low voltage side operates to open the 500 kV circuit breaker of the power winding. Nowadays, delivery packages and corresponding projects of 110–500 kV three-winding CSR provide for the availability of individual circuit breakers in the supply circuits of transformers of each TMP, so their OCP is designed to open a 10 kV circuit breaker and to open the mains switch by CBFP (circuit breaker failure protection) only in the case of its failure. With such a scheme of connections, the reactor would have remained in operation after OCP had disconnected a low-capacity transformer at the side of the compensation winding by its individual circuit breaker. It should be mentioned that similar situation is probable for three-phase 110– 330 kV CSRs as well, though their bus system at the low voltage side has shorter length and can be of either overhead or cable construction. In case relay protection does not open the circuit breaker of the power winding under single-phase short circuit and the disconnecion of the main TMP, the reactor can operate with the set load and magnetic biasing from the redundant TMP connected to 6 or 10 kV switchgear of

11.3 Specific Features of CSR Relay Protection

229

Fig. 11.4 The emergency trip of 500 kV CSR at Barabinskaya substation. Downward: voltage of phase A and zero-sequence voltage at PT-500 kV, voltage of phase B and zero-sequence voltage at the low voltage side, current in one phase of the converter transformer, currents in CTs of three phases of the secondary winding delta-connection, currents in three phases of the power winding, logic signals of OCP triggering and the opening of phases of 500 kV CSR circuit breaker

the substation for a long time. The same situation takes place if the reactor operates with the redundant TMP during the repair (maintenance) of the main one. It should be also mentioned here that in a number of substations, in particular in IDGC of the East, the main TMP connected to the compensation winding operates with the ungrounded neutral of the HV winding. In these cases, only the considered zero-sequence voltage protection is functional under single-phase short circuit at the low voltage side of the reactor (in the compensation winding and behind it). Moreover, the fall of any bus system stub not followed by the breaking of the compensation winding delta-connection and large short circuit current will remain invisible for the reactor and for overcurrent protective relays of the compensation winding, but will cause the phase voltage of the compensation winding to appear at neighbouring constructions which is connected with explicit danger to the operating stuff. For this reason, zero-sequence voltage protection with action to disconnect the reactor must be provided for in all three-winding 110–750 kV CSRs as backup protection against single-phase faults at the compensation winding side. Its time lag must be enough large in order that the main (and the redundant, for 500 kV CSR) TMP could be disconnected by actions of their OPs under single-phase short circuits behind the circuit breaker of TMP, i.e. under external faults outside the the bus system area of the compensation winding delta-connection.

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11 Special Topics in Design and Commissioning of CSR Complexes

Apart from eliminating lasting danger to the operating staff, and current and voltage distortions by 3d harmonic currents in the mains, this protection remains the only type of electrical protection for three-windings CSRs which operates under faults between the compensation winding of the reactor and the frame (magnetic conductor). After the main (redundant) TMP with the grounded neutral connected to the compensation winding is disconnected by its OCP, the low voltage grid of CSR at the side of the compensation windings remains in operation with the isolated neutral. Since the length of this grid and its capacitance to ground are rather small, both current and gas (till the fault changes to turn-to-turn short circuit) protections of the reactor are not sensitive to such phase-to-ground fault of the compensation winding. It should be taken into account that the compensation winding of CSR is the closest winding to the cores of the magnetic conductor, i.e. the probability of its fault to the frame is higher in comparison with this for the other windings of the reactor. The placement of the winding on the insulating bakelite cylinder with additional insulating gaps and channels for cooling almost eliminates the possibility of fault between the winding and cores of the magnetic conductor, but ground faults of its taps, lead-ins and external bus system are more probable. Comparing to three-windings CSRs with full set of the main and backup enough sensitive protection, the situation is quite different for two-winding 110 and, in particular, 35 kV reactors with the isolated neutral. Magnetically controlled reactors of relatively low capacity and voltage levels of 110 kV and below [2, 4, 6] are made with two windings, the power and the compensation one, in order to reduce the consumption of active materials. The basic circuit of such reactors is given in Fig. 3.17 and the constructive arrangement of one its phase is presented in Fig. 3.18. In these reactors the control winding combines functions of the compensation (locking threefold harmonics) and control windings (the magnetic biasing of the magnetic conductor cores) at the expense of its open double-delta connection scheme. The coaxial arrangement of sections of the power and control windings on the magnetic cores (Fig. 3.18) results in direct electromagnetic coupling between the windings (as opposed to three-winding CSRs, in which sections of the control winding are connected in opposition with respect to the power and compensation windings). This electromagnetic coupling causes direct current components in sections of the reactor windings under the transient conditions of power picking-up or shedding. To illustrate this, in Fig. 11.5 oscillograms of currents in the reactor windings under power picking-up from no-load to the rated value are presented. The 1st harmonic component of current is present only in the terminals of phases of the power winding. Under power picking up,the direct current component caused by an increase in the biasing current is predominant in individual sections and branches of the power and control windings. Besides that, the 2nd harmonic in half-branches of the power winding and the 3d harmonic in half-branches of the control winding delta-connection have considerable values.

11.3 Specific Features of CSR Relay Protection

231

Fig. 11.5 Currents in the branches of the reactor windings under power picking-up. Downward: in a half-branch of a power winding phase, in the phase of the power winding, in a half-branch of the control winding delta-connection, the rectified biasing current, in a half-neutral of the power winding

Under transients, in half-neutrals of the power winding, interconnecting the neutral terminals of the PW star-connections, the direct component (the lower phenomenon in Fig. 11.5) is locked, which causes the saturation of current transformers and a decrease in the response speed. For this reason, integrated current transformers at the side of the neutral encompass both the terminals of the power winding (Fig. 3.17) which allows the reciprocal subtraction of the direct component and the realization of the longitudinal differential zero-sequence current protection (only for 110 kV reactors with the deadly grounded neutral). Thus, in the reactor RTU-25000/110, the only possible composition of relay protection against all types of faults is defined by the existing set of integrated current transformers and includes gas protection, two-stage OCP at the 110 kV terminals, the longitudinal differential zero-sequence current protection for the power winding, OCP at the grounded terminal and at the supply terminals of power winding converters as well as protectors in the supply circuits of the converters [4, 6]. In 35 kV 10–25 MVAr controlled reactors the neutral of the power winding is not grounded, since these operate in networks with the isolated neutral. In this connection, zero-sequence protective relays are not applicable, and the composition of relay protection for these CSR can be accepted as follows: • • • •

two-stage overcurrent protection at the terminals of the power winding; gas protection with the control of oil level; OCP at CTs in the grounding circuit of the control winding; overcurrent protection at the terminals of the power winding supplying OMP;

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11 Special Topics in Design and Commissioning of CSR Complexes

• high-voltage protectors in the supply circuit of OMP; • the control and limitation of reactor overload in ACS with action to alarm. Principally, the arrangement of the power winding of such reactors in the form of parallel branches with a lead-in to the midpoint would allow, with additional CTs installed in the half-branches of the power winding, the application of singlephase longitudinal and transverse differential current protection like in three-winding reactors of higher voltage levels. However, apart from an increase in the number of terminals and the complication of the construction, it is necessary to take into account the above mentioned direct component, which does not appear in the grid, but causes the saturation of CTs in these branches at the side of the neutral. Thus, biasing currents circulating in branches of the windings of such two-winding CSRs and the absence of necessary CT groups associated with that make it not possible to use fast-acting differential current protection with absolute selectivity required by PUE (Regulations of power units arrangement) for transformer and reactor equipment of this voltage level and capacity. The possibility to install the longitudinal differential zero-sequence current protection in 110 kV reactors of this arrangement with the deadly grounded neutral does not solve the problem as this protection operates only under faults to the magnetic conductor, which are hardly probable for the power winding, and does not act under turn-to-turn and phase-to-phase faults. For reactors of 35 kV and lower voltage levels intended for using in grids with the isolated neutral, where ground fault currents are small, this protection does not work and becomes pointless. As a result of this, these CSRs are protected from internal faults only by slow-acting protective relays, namely, the gas protection and OCP at the supply side without any backup. Two different technical solutions can be applied in order to use fast-acting protective relays with absolute selectivity against internal faults in the power winding of controlled reactors of this modification. The first of them is the installation of current transformers in the branches of the power winding at the side of the neutral with the use of longitudinal and transverse differential current protection (similar to the protection of the power windings of three-winding reactors). For eliminating the saturation of current transformers under transient conditions it is necessary either to use modern current sensors not subject to saturation or to connect conventional current transformers to measure the difference between direct components in the branches of the power winding. This possibility is available because the power winding of each phase of the reactor is made with a lead-in to the midpoint on each half-core, i.e. has four sections which can be connected at the neutral side in different ways. One of the possible ways to place integrated CTs is given in Fig. 11.6, a for one phase of the power winding of the reactor. It supposes the placement of not less than 12 (taking into account redundant current circuits) integrated current transformers at the taps of the power winding neutrals with the corresponding number of the lead-outs to the lid of the reactor’s tank.

11.3 Specific Features of CSR Relay Protection ES

a)

233

b)

ТА1 ТА2

EА

ТА3

EВ

EС

ТА4 ТА5

*

* PW

*

* PW

*

* PW

CS

PW

*

* To the terminal

Fig. 11.6 Relay protection of the power winding: a—integrated CTs located at the taps of PW neutrals; b—the transverse current differential protection using a current sensor

Another less complicated solution is the application of one-system differential current protection used for synchronous generators and connected to measure the current flowing between the neutrals of two star-connections of the generator power winding [7, 8]. However, it is impossible to use the mentioned protection in CSR not applying additional solutions and technical means since there is no integrated CT in the branch between the neutrals of the power winding star-connections. Moreover, even if it had been installed, it would have not been operable under the conditions of saturation by direct current components for the above mentioned reasons. To eliminate conditions of CT saturation, a current sensor based on Hall sensor and installed in the circuit between the neutral terminals of the star-connections of the reactor power winding can be used as a source of information for protection instead of integrated electromagnetic current transformers. Then, the signal comes to a relay protection terminal; the first harmonic component is extracted and introduced to the measuring element of the protective relay to be compared with the set value. In case the neutral of the power winding is grounded, the operation of protection is blocked by the total fault contribution current through the grounded neutral of the reactor under external single-phase faults. The suggested solution is illustrated by Fig. 11.6b, where RTDU is the electromagnetic part of the reactor in the oil tank (only PW with half windings on the cores and CTs at the line terminals are shown schematically), CS—current sensor between the terminals of the neutrals of the power winding star-connections.

234

11 Special Topics in Design and Commissioning of CSR Complexes

Under normal conditions, including transients, there is no 1st harmonic current between the neutrals of the power winding of the reactor. At the appearance of a turn-to-turn fault in any section of the CSR winding, sufficient unbalance current starts to run between the half-neutrals of the power winding and through the current sensor. The signal of CS with the data on fault current is introduced to a RP terminal, where it is filtered with the extraction of the main harmonic component, compared with the reference value and, if the reference is exceeded, the command to trip the circuit breaker of the reactor is formed. In the existing modifications of 35–110 kV magnetically controlled shunt reactors, the neutrals of two star-connections of the power winding are led out to the lid of the tank of the electromagnetic part of the reactor (RTDU) for subsequent interconnection and, if necessary, grounding (for reactors of 110 kV and above voltage levels with the deadly grounded neutral). Integrated current transformers at the side of the power winding neutral of the reactor encompass both these lead-outs of the neutral (see the scheme of Fig. 11.6b), so only zero-sequence currents appearing under single-phase ground short circuits in the winding of CSR or in the external network flow through them. The current sensor is installed in the break between the terminals of the neutrals of the primary power winding star-connections; after that, one of the terminals can be grounded if necessary. Current sensors are series-produced devices with a wide range of rated currents which can measure both direct and alternating quantities not being saturated. The current sensor can either be built inside of the electromagnetic part of the reactor or be detachable, of outside installation. In the latter case, the reactors which have been already put in operation can be equipped additionally with such sensors, since these are produced also for out-of-door installation. This alternative is most required and can be implemented in the simplest way in CSRs working in a grid with the isolated neutral (6, 10, 35 kV), in which there is no other fast-acting protection against internal faults, because the typical differential current protection can not be realized. Blocking by zero-sequence current in the neutral is not required, since these grids operate with small ground short circuits currents. This alternative is also required for two-winding 110 kV CSRs, which longitudinal differential zero-sequence current protection does not act under turn-to-turn faults in the power winding. These turn-to-turn faults in the power winding are the most probable internal faults, as phase-to-phase short circuits inside the tank of a transformer are practically ruled out, and single-phase short circuits to the magnetic conductor are also hardly probable for the power winding located over the control winding. In grids with the isolated neutral, current in a protective relay can appear only under internal faults. For reactors of 110 kV and above voltage with the deadly grounded neutral of the power winding, the unnessesary operation of protection under external single-phase faults at the supply side can be eliminated by its blocking by the external fault contribution current flowing through the joint neutral of the power winding of a reactor (from integrated CTs).

11.3 Specific Features of CSR Relay Protection

235

Since under normal operating conditions of a reactor in a grid with isolated neutral there is no 1st harmonic component of current in the neutral of the reactor, and only small unbalance current can flow between the half-neutrals of the power winding, the primary setting of protection can be minimum and equal to 15–20 A which provides its high sensitivity to the most probable turn-to-turn faults of the winding. Under switching conditions of energization and automatic reclosure it is possible that currents of comparable value decaying in 0.1–0.2 s will appear, which requires introducing corresponding time delay of the mentioned protection or its blocking under switching on. It should be noted that, in order to increase the response speed of CSR, the halfneutrals of the power winding of two-winding 110 kV reactors can be grounded through a resistance, while in grids of 35 kV and below the neutrals can be not interconnected. In the first case the current flowing between the half-neutrals of the power winding under internal faults will be very small; in the second case it will be absent. However, internal faults will be accompanied by the appearance of corresponding alternating voltages between the half-neutrals of the power winding, which can be used in relay protection of these CSRs if current sensors at the terminals of the half-neutrals are substituted with voltage sensors (VS) at the same terminals. In this modification one-system differential protection is connected to measure the difference of voltages (not currents) between the neutrals of the power winding, which can achieve high values under emergency conditions, so VSs must be connected through appropriate dividers and surge suppressors (non-linear overvoltage suppressors). Thus, we can summarize the main principles of reactor protection. 1. The composition of relay protection of magnetically controlled reactors of different modifications applied in design practice is determined by specific features of their operation performance and the composition of integrated current transformers and can be extended, which is especially necessary to protect all the windings of CSR against the most probable turn-to-turn faults. 2. Overcurrent protection of the compensation winding, if it is connected correctly and restrained from operating under switching conditions, is the most sensitive and universal protection of three-winding CSRs against all types of internal and external short circuits. 3. In order to provide protection against long-term operation under a ground short circuit and eliminate a danger to the operating staff, it is necessary to provide additional zero-sequence voltage protection of the compensation winding and its bus system with action to disconnect the reactor after a time delay. 4. The most simple and effective way to protect the power winding of twowinding 35–110 kV CSRs is to use one-system transverse differential protection connected to a current or voltage sensor between the neutral terminals of the power winding led out to the lid of the reactor tank.

236

11 Special Topics in Design and Commissioning of CSR Complexes

11.4 Putting CSR in Commercial Operation, Field Testing As has been mentioned in the previous sections, the assembly of the electromagnetic part of a controlled shunt reactor does not differ from this of transformer equipment of the same voltage level in technological terms. The final stage of CSR installation project is performing field tests, the aims of which are as follows: • testing all the systems of the complex; • the synchronization of ACS with measuring transformers of the substation and CSR, the adjustment of the preliminary magnetic biasing mode; • the injection test of CSR, setting the required algorithms and blocking elements; • the injection test of the relay protection and automation systems of the reactor, testing the automation under different conditions; • confirming the reported parameters of a CSR complex under switching, dynamic and steady-state conditions; • teaching the staff and transferring the equipment to the operating organization. Testing the systems of a CSR complex includes a number of measures both at no voltage applied to the power winding of CSR,—i.e. the visual inspection of the correctness of equipment and secondary switching circuits assembly, checking the availability of necessary blocking elements of power circuit breakers automation,— and under applied voltage—controlling unbalance currents of the control winding sections, thermal testing, testing data transmission channels of ACS and the remote control of operating conditions of the reactor. At the same time with system testing, ACS and converters are syncronized with measuring potential transformers providing the reliable operation of CSR under steady-state conditions and conditions associated with temporary partial (SPAR) or full (TPAR) loss of voltage supply of the power winding for line CSRs. After ACS is synchronized with the potential transformer of 6–35 kV auxiliary switchgear, the preliminary magnetic biasing mode is being adjusted. It has been determined from experience that the assured biasing level at which CSR turns to the rated conditions without a time delay is provided if the rectified current of about 150–250 A, which corresponds to nearly 10% of the rated power of the control winding, runs through the converter. If under field testing a fixed firing angle of the converter providing the mentioned preliminary magnetic biasing current is found and programmed in ACS, then the time within which this current is gained in the control winding will be about 2 ÷ 3 s (see the experimental oscillogram for a 500 kV CSR in Fig. 11.7). When adjusting this mode for line CSRs, the dead time of TPAR cycle is taken into consideration which can total 0.5–5 s; at that, the assured time of reactor saturation under the preliminary magnetic biasing condition must not affect the time of automatic reclosure. In cases when the expected time of automatic reclosure is less than 3 s, the operation of the converter with two values of firing angles is provided, the first of which corresponds to higher output voltage of the converter, while the second one—to the voltage inducing a minimum necessary preliminary magnetic biasing current.

11.4 Putting CSR in Commercial Operation, Field Testing

237

ICtW(t), A 200 100 0 0,75

1,00

1,25

1,50

1,75

2,00

2,25

2,50

2,75

t,s

Fig. 11.7 Current variations in the power winding under the preliminary magnetic biasing mode

ICtW(t), A 150 100 50 0 4,30

4,40

4,50

4,60

4,70

4,80

4,90

t,s

Fig. 11.8 The accelerated (in comparison with the process of Fig. 11.7) increase of current within 0.6 s under the preliminary magnetic biasing mode

The operation of the converter with the first angle stops immediately when the required current value is achieved; in such a way the time of current gaining in the control winding can be reduced sufficiently, meeting the strongest requirements on the response speed of CSR in TPAR cycle (Fig. 11.8). The injection test of CSR is performed in order to set control laws for semiconductor converters and assign the limitations of power winding current and currents in the semiconductor converters. The limitations can be set either with account taken of possible CSR overload or without it. Also, in the process of the injection test, the harmonic composition of power grid current is controlled, and after that the operation of CSR with the assigned current and voltage references is tested. Simultaneously with the injection test of CSR, adjuster specialists of relay protection and automation systems check the correctness of current flow of the secondary circuits of relay protection and automation. Figure 11.9 shows the oscillograms of currents in the power and control windings of the line CSR RTU 180000/500-UHL1 under the imitation of a three-phase fault at a 500 kV overhead line. The dead time constituted about 0.45 s (see current in PW in Fig. 11.9), the reactor became ready to be energized approximately in three periods (see the current of the control winding in Fig. 11.9). There is an aperiodic component in currents of the power winding, since there is no synchronous switching device in the circuit breakers of the overhead line. To imitate a fault in the artificial way, the conditions for the disappearing of the signals of the potential transformer in RPA circuits have been created. Along with the considered way of testing the automation

238

11 Special Topics in Design and Commissioning of CSR Complexes

Fig. 11.9 Currents in the phases of the control and compensation windings under the imitation of TPAR cycle at a 500 kV line

operation algorithms, the experiences of real short circuits at overhead transmission lines take place. During field testing the following parameters are approved: the reactor gains its rated power without a delay if CSR is switched by the mains circuit breaker; at the same time, the value of power grid current surge is controlled; the time of power picking-up from no-load to rated conditions and the time of power shedding in opposite direction. In Figs. 11.10 and 11.11 oscillograms approving the above mentioned requirements for RTU-180000/500-UHL1 are presented. Under energization in Fig. 11.10, there is no aperiodic component in the phase currents of the power winding, since the circuit breaker of CSR is equipped with a synchronous switching device, and the peak value of the very first half-period of the power winding current corresponds to the rated value. The time of the rated current gaining (Fig. 11.11) from 5 to 100% is not more than 0.3 s. At the final stage of CSR field testing, thermal conditions of the EMP and TMP are checked; during the test CSR operates with load close to the rated value. Under the test, changes in the temperature of EMP windings and upper levels of oil are being registered during a long time period (not less than 10–12 h for 500 kV CSR) till the thermal condition is stabilized. After field testing has been completed and the equipment has been in operation for 72 h, within which the teaching of the staff is performed, the reactor is put into operation and Act on Works Executed is signed.

11.4 Putting CSR in Commercial Operation, Field Testing

239

UPWA(t), kV 500 0

t,s

-500 200 100 0 -100 -200 -300 2,0 1,5 1,0 0,5 0 1 0 -1 -2

0,925 IPWA(t), A

0,950

0,975

1,000

1,025

1,050

1,075

t,s 0,925 UCtW(t), kV

0,950

0,975

1,000

1,025

1,050

1,075

0,925 ICtW(t), A

0,950

0,975

1,000

1,025

1,050

1,075 t,s

t,s 0,925

0,950

0,975

1,000

1,025

1,050

1,075

Fig. 11.10 Delayless current gain at the energization of CSR of the RTU 180000/500-UHL1 type

UPWA(t), kV 500 0 -500 200 100 0 -100 -200 -300 1,5 1,0 0,5 0,0 1,5 1,0 0,5 0,0

t,s 1,60 IPWA(t), A

1,70

1,80

t,s 1,60 UCtW(t), kV

1,70

1,80

1,60 ICtW(t), kA

1,70

1,80

t,s

1,60

1,70

1,80

t,s

Fig. 11.11 Power picking up from 5 to 100% by CSR RTU 180000/500-UHL1

240

11 Special Topics in Design and Commissioning of CSR Complexes

References 1. Dolgopolov AG (2007) “Designing of the relay protection of magnetically controlled reactors” [“Proyektirovaniye releynoy zashchity upravlyaemykh podmagnichivaniyem reaktorov”]. Vestnik MEI, No 4 2. Dolgopolov AG (2009) “Specific features of the relay protection of magnetically controlled reactors of different modifications” [“Osobennosti releynoy zashchity upravlyaemykh shuntiruyushchikh reaktorov razlichnykh konstruktsy”]. Electricheskiye stantsii, No 4 3. Dolgopolov GA (2009) “Controlled shunt reactors. Choosing overcurrent protection settings” [“Upravlyaemye shuntiruyushchiye reaktory. Vybor parametrov maksimalnykh tokovykh zashchit”]. Novosti electrotechniki, No 6(60) 4. Dolgopolov GA (2010) “Controlled shunt reactors. Choosing overcurrent protection settings” [“Upravlyaemye shuntiruyushchiye reaktory. Vybor parametrov maksimalnykh tokovykh zashchit”]. Novosti electrotechniki, No. 1(61) 5. Dolgopolov AG (2011) Relay protection of controlled shunt reactors [Releynaya zashchita upravlyaemykh shuntiruyushchikh reaktorov], NTF Energoprogress, Moscow, 152 p [“Bibliotechka electrotechnika”, the appendix to the “Energetik” journal, vols 8–9, pp 152–153] 6. Zasypkin AS (1989) Relay protection of transformers [Releynaya zashchita transformatorov]. Energoatomizdat, Moscow 7. Dolgopolov AG (2011) “Relay protection of controlled shunt reactors for 35–110 kV power grids” [“Releynaya zashchita upravlyaemykh shuntiruyushchikh reaktorov dlya elektricheskikh setey 35–110 kV”]. Energetik, No 11 8. Fedoseev AM (1992) Relay protection of electric power systems [Releynaya zashchita elektroenergeticheskikh sistem]. Energoatomizdat, Moscow

Appendix A

Input data for the investigated synchronous generators Direct-axis synchronous reactance

X d , p.u.

2.56 2.56

Quadrature-axis synchronous reactance

X q , p.u.

Direct-axis transient reactance

X d , p.u. 0.36

Direct-axis subtransient reactance

X d , p.u





Quadrature-axis subtransient reactance



X q , p.u.

0.243 0.364

Leakage inductive reactance

Xs, p.u

0.24

Resistance of the field winding

r f , p.u.

8.44 × 10–3

Resistance of direct-axis damping circuit

rr d , p.u.

4.84 × 10–3

Resistance of quadrature-axis damping circuit

rrq , p.u.

3.319 × 10–3

Inertia time constant of the unit (with all rotating masses on the shaft T J , c considered T J = 2H J )

5.9

Let us take the natural power of a 500 kV overhead transmission line as the base power: S base = Pnat = 900 MW, the maximum operating voltage U base = 525 kV is chosen as the base voltage. Representing the parameters of the generator in the per unit system: • direct-axis synchronous reactance: p.u.b.

Xd

= Xd ·

900 Sbase = 3.92 p.u.; = 2.56 · Srated 588.2

• quadrature-axis synchronous reactance: X qp.u.b. = X q ·

Sbase 900 = 2.56 · = 3.92 p.u.; Srated 588.2

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9

241

242

Appendix A

• direct-axis transient reactance: p.u.b.

Xd



= Xd ·

Sbase 900 = 0.551 p.u.; = 0.36 · Srated 588.2

• direct-axis subtransient reactance p.u.b.

Xd

= X d ·

Sbase 900 = 0.372 p.u.; = 0.243 · Srated 588.2

• quadrature-axis subtransient reactance X qp.u.b. = X q ·

900 Sbase = 0.556 p.u.; = 0.3634 · Srated 588.2

• leakage inductive reactance p.u.b. base = 0.24 · Xs = X s · SSrated • resistance of the field winding p.u.b.

rf

= rf ·

900 588.2

= 0.367 p.u.;

Sbase 900 = 12.91 · 10−4 p.u.; = 8.44 · 10−4 · Srated 588.2

• resistance of direct-axis damping circuit p.u.b.

rr d

= rr d ·

900 Sbase = 7.41 · 10−3 p.u.; = 4.84 · 10−3 · Srated 588.2

• resistance of quadrature-axis damping circuit p.u.b. rrq = rrq ·

Sbase 900 = 5.08 · 10−3 p.u.; = 3.319 · 10−3 · Srated 588.2

• the inertia constant: p.u.b.

TJ

= TJ ·

900 Srated = 3.86 s. = 5.9 · Sbase 588.2

Representing the parameters of the transformer in the per unit system: X p.u.b. =

Usc Sbase 13.5 900 · · = 0.1928 p.u. = 100 Srated 100 630

Representing the parameters of the transmission line in the per unit system: p.u.b.

rl

= r0 · l ·

900 Sbase = 2.6 · 3.4735 · = 0.0295 p.u.; 2 5252 Ubase

Appendix A

243

p.u.b.

Xl

p.u.b.

bl

= x0 · l ·

= b0 · l ·

900 Sbase = 29.8 · 3.4735 · = 0.338 p.u.; 2 5252 Ubase

2 Ubase 5252 = 0.4 p.u. = 3.76 · 10−4 · 3.4735 · Sbase 900

Representing the parameters of SR/CSR in the per unit system: Q rated 180 · 106 −4 =  2 = 6.53 · 10 S; 2 Urated 525 · 103 2  2 525 · 103 Ubase −4 = 6.53 · 10 · = 0.2 p.u. = b0 · Sbase 900 · 106 b0 =

p.u.b.

bR

Appendix B

An example of the realization of the ACS model of RTU-180000/500 in the EMTP software package Assumptions for simulation In order to simplify the control system of the reactor and quicken the calculation of electromagnetic transients, the following assumptions can be made: • Not to simulate semiconductor converters. Processes in the converters do not affect directly CSR, in particular, because of the low capacity of the control system in comparison with the CSR capacity. This allows presenting a converter as a controllable source of constant emf. • Neglect the inertia of the regulator’s units, since a change in the operating condition of a reactor is characterized by its own time constant. Thus, while the units of the regulator have an inertia constant of about 20–40 ms, the individual time constant of the reactor is nearly 1–2 s. It should be mentioned that, for this reason, CSR designers have rejected using integral units in ACS in order to accelerate its operation. All the disadvantages of the proportional control of CSR do not deteriorate its controllability because of the natural large time constant of the control winding loop. The general view of the ACS model of RTU-180000/500 In the example considered, when the model of the regulator was under creation, both the standard units of the EMTP program (logical conversions, mathematical operations, units for the computation of effective signal value) and the units developed with the help of the MODELS language were used. It should be noted that there is the possibility to create a regulator using only the standard set of components, but the developed scheme can be found very cumbersome, less flexible and not convenient due to the limited number of units provided by the authors of the software package. Substituting a great number of interconnected typical components with simple units © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 G. A. Evdokunin et al., Magnetically-Controlled Shunt Reactors, Lecture Notes in Electrical Engineering 1000, https://doi.org/10.1007/978-3-031-25957-9

245

246

Fig. B.1 The general view of the regulator model

Appendix B

Appendix B

247

Table B.1 The main components of the ACS model for RTU-180000/500 1

Effective value measuring units (RMS). 6 such unit in all—one for each line voltage and one for each phase current

2

The model of the limiter. This unit limits voltage of the control winding at the set levels Emin, Emax

3

The model of the forcing channel created using the MODELS language. The unit contains algorithms of checking the parameters of an operating condition and, if the conditions of enabling the forcing mode are met, the unit starts to produce the forcing voltage set by the parameter Efors

4

The model of the unforcing channel created using the MODELS language. The unit contains algorithms of checking the parameters of an operating condition and, if the conditions of enabling the unforcing mode are met, the unit starts to produce the unforcing voltage set by the parameter -Efors

5

The model of the summarizer created using the MODELS language. This is an auxiliary unit which disables the main control channel at the enabling of the forcing channel

6

The voltage control unit created using the MODELS language. In this unit the control of line voltage values is performed. If one of the line voltages takes a zero value or reduces by 30%, then the control unit, in accordance with the value of the parameter Podm_Fors set by the user and equal either to 0 or to 1, changes the regulator to the forcing mode (0) or the preliminary magnetic biasing mode (1) (continued)

248

Appendix B

Table B.1 (continued) 7

The current control unit created using the MODELS language. The unit processes phase currents in accordance with the algorithm of the current stabilization channel

8

Sources. These blocks set the following parameters of the model: Ustab/Istab—the selection of the regulator’s channel (voltage/current stabilization) k—the droop of the regulator Inom—the rated current; Unom—the rated voltage; E0nom—the value of CtW voltage with which the rated current is flowing though PW; Ust_U—the voltage reference; Ust_I—the current reference

9

The time cutoff unit consisting of two elements: a source with the amplitude of signal defining the information on the instant of control circuit enabling, and the cutoff value. Thus, if the parameter T_start is equal, for instance, 1, then the feedback (the control loop) will start to operate in 1 s after the start of computations. Before this moment, i.e. with t ∈ [0; 1), the reactor operates at no-load

10

Auxiliary devices • controllable sources • signal type converters (from physical quantities to signals for the TACS units)

(continued)

created using the MODELS language allows making the scheme much more visual and simple to understand. In the EMTP program all the elements of control systems are the TACS units [EMTP User’s Guide], i.e. these exchange signals with each other, but not currents or voltages. The model of the regulator is presented in Fig. B.1, the description of its components is given in Table B.1.

Appendix B

249

Table B.1 (continued) 11

Auxiliary devices performing mathematical operations with signals – multiplication; – division; – addition; – subtraction; – multiplication by a number

12

Measuring devices used for getting signal oscillograms in different nodes of the control system

Automatic voltage stabilization channel The algorithm of the model is realized in accordance with the equipment certificate of ACS, and the model itself reflects the operation of the voltage stabilization channel at the control point with the use of the forcing and unforcing channels. Let us consider the operation of the voltage stabilization channel step by step: 1. Calculating the average effective value of line voltages (phase currents). As has been mentioned above, this procedure is performed with the help of the standard units of the EMTP program. Figure B.2 presents the fragment of the model

250

Appendix B

which performs such conversion (this unit is analogous to the unit calculating the average effective value of currents for the phases). This fragment of the model receives phase voltages from the external grid and then, with the use of signal-type transforming elements, the physical values are transformed into the TACS signal. The received values of the phase voltages are used for calculating the line voltages and, then, the effective values of these quantities, which come to the voltage control unit after that. This unit forms a signal corresponding to the line voltage U AB . 2. Calculating the signal of the error between the line voltage U AB and the reference. This procedure is performed with the help of the standard summarizer included in the set of standard units of the program. Figure B.3 shows the fragment of the scheme performing this operation. 3. The error signal ΔU obtained at the previous step comes into the chain of units shown in Fig. B.4, where the control signal is calculated in accordance with the analytical expression of the regulation curve given in Chap. 4.

Fig. B.2 Fragment of the model calculating the effective value of the line voltages

Fig. B.3 The fragment of the model calculating the error signal

Appendix B

251

Fig. B.4 The fragment of the model calculating the control signal

4. Then, the control voltage defined in accordance with the regulation curve comes to the limiter (unit 2 in Table B.1), where it is checked if the signal exceeds the set levels Emin, Emax. If the signal reaches the limit, the unit forms a special signal which is used then by the forcing and unforcing units (units 3, 4 in Table B.1) in their check algorithms. 5. The finally formed control signal from the stabilization channel comes to a special summarizer (unit 5 in Table B.1), where it is either blocked, if there is a signal from the forcing/unforcing units at the parallel input, or comes to the chain for checking the current in control winding without a change. 6. The value of current in the control winding comes to the checking chain, and its effective value is calculated, from which the limitation value Ioy_lim set by the source is subtracted afterwards; the result is multiplied by –1 and comes to the input of the logical addition unit, at the remaining input of which there is always 1. Thus, if current in the control winding exceeds the set limiting value, the result of logical addition will be zero and, therefore, the value of signal will also turn to zero (in such a way, the blocking of the converters is modelled). Otherwise, if current in the control winding is within permissible limits, the logical addition gives 1 and the value of the signal come to the time delay unit without a change (unit 9 in Table B.1).

252

Appendix B

Forcing and unforcing channels The algorithm of the operation of the forcing/unforcing channels is as follows: 1. Calculating the average effective values of currents for the phases. For this purpose, a unit analogous to that used in the voltages stabilization channels is used (see Chap. 5). 2. The measured value of the average effective value of currents comes to the forcing and unforcing units (units 3, 4 in Table B.1) where they are proceeded in accordance with the conditions described in the ACS equipment certificate. 3. At the same time with the average effective value, a signal from the limiter (unit 2 in Table B.1), which contains the information if the signal of the stabilization channel exceeds the set value (voltage is out of the control range), as well as signals from the voltage and current control units come to the forcing and unforcing units (units 6, 7 in Table B.1). The algorithm of the operation of the forcing and unforcing units suggests three cases of actuation: • voltage comes out of the control range and thr conditions for current in the power winding are met; • the signal from the voltage control unit is received; • the signal from the current control unit is received. 4. The obtained control signal comes to a special summarizer (unit 5 in Table B.1), where, if the signal is not equal to zero, it blocks the signal of the stabilization channel. The channel of the automatic stabilization of current in the power winding The algorithm of the operation of the channel for current stabilization in the power winding is as follows: 1. The same as item 1 in the previous section. 2. The obtained average effective value of power winding current for the phases comes to the unit of current control (unit 7 in Table B.1), where the algorithm described in Chap. 5 is realized. 3. Depending on the current value, the algorithm of the current control unit has two ways of operation: • a control signal corresponding to the range of effective current values determined in Chap. 5 is formed; • a special signal coming to the forcing/unforcing unit (units 3, 4 in Table B.1) which acts as described in item 3 of the previous section is formed. 4. The same as item 4 in the previous section. Parameters of the model assigned by the user For the convenience of presentation in calculation schemes, all the units of the model are grouped in one common block REG (Fig. B.5). The scheme of the grid and the

Appendix B

253

regulator presented in Fig. B.5 is composed specially for the illustration and check of the correctness of CSR regulator operation. The scheme contains a source of threephase emf with the peak phase voltage value of 428 kB (U), pre-insertion resistance (RS ), the model of a 200 km long line with distributed parameters (LCC), CSR500 with its control system (USHR and REG), an auxiliary reactor connected at the receiving end of the line (SR), a capacitor bank (CB), and a current measuring units with an output located behind CSR (I _probe). Changing the inductive reactance of the auxiliary reactor SR is used for reducing voltage (after its application) at the maximum speed in order to turn the regulator of CSR to the low limit Emin for demonstrating the operation of the unforcing channel. The unit I_probe is necessary for transmitting values of PW currents to the model of the CSR regulator. To operate correctly, the regulator must receive information on phase currents and voltages in the control point from the external grid (in theory, voltages at any node in the scheme can be used), by which it will calculate the effective values of the mentioned quantities. Thus, six conductors must be approached to the regulator as shown in Fig. B.5. The model of the regulator itself has the area of data input where the following parameters must be assigned (Table B.2); the purpose of these parameters is explained in Table B.3.

Fig. B.5 Test circuit with the model of RTU-180000/500 and the model of its ACS

254 Table B.2 Parameters of the model of ACS of RTU-180000/500 (the REG unit in the scheme of Fig. B.5)

Appendix B Data

Unit

Value

E0nom

V

146

Unom

kV

525

Inom

A

198

Ust_U

kV

500

Ust_I

A

198

Emax

V

146

Emm

V

0

T_start

s

1

k

–

0.02

Efors

V

1500

-Efors

V

−1500

Ixx

A

8

Reg_phase

–

1

Max drawdown

p.u

0.302

E_predjpodm

V

20

Podm_Fors

–

0

Ustab\Istab

–

1

Ioy_lim

A

2200

Appendix B

255

Table B.3 The description of the parameters of the ACS model for RTU-180000/500 E0nom

Voltage at the control winding producing such current in it with which current equal to the rated value is induced in the power winding

Unom

The effective value of the rated voltage

Inom

The effective value of the rated current in the given scheme

Ust_U = Uy

Voltage reference (line voltage in kV (!))

Ust_I = Iy

Current reference (phase current in amperes)

Emax

The upper limit of the regulator signal limiter

Emin

The low limit of the regulator signal limiter

T_start

Time of control circuit making

k

The droop coefficient

Efors

The forcing voltage

-Efors

The unforcing voltage

Ixx

The effective value of no-load current in the given scheme

Reg phase

Line voltage used by the regulator for forming the control signal (1—UAB , 2—UBC , 3—UCA )

Max_drawdown The level of line voltage reduction at which the regulator turns to the forcing/preliminary magnetic biasing mode E_pred_podm

The voltage of preliminary magnetic biasing of the control winding

Podm Fors

A parameter which determines the action of the regulator under the miss or set decrease of at least one of the line voltages (1—change to the preliminary magnetic biasing mode, 0—change to the forcing mode)

Ustab\Istab

A parameter setting the control law (1—voltage stabilization, 0—current stabilization)

Ioy_lim

The value of the maximum permissible current of the control winding in amperes