Flexible AC Transmission Systems [1st ed.] 9783030353858, 9783030353865

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CIGRE Green Books

CIGRE Study Committee B4: DC Systems and Power Electronics

Flexible AC Transmission Systems FACTS

CIGRE Green Books Series Editor CIGRE International Council on Large Electric Systems (CIGRE) Paris, France

CIGRE presents their expertise in unique reference books on electrical power networks. These books are of a self-contained handbook character covering the entire knowledge of the subject within power engineering. The books are created by CIGRE experts within their study committees and are recognized by the engineering community as the top reference books in their fields. More information about this series at http://www.springer.com/series/15209

Bjarne R. Andersen • Stig L. Nilsson Editors

Flexible AC Transmission Systems FACTS

With 632 Figures and 71 Tables

Editors Bjarne R. Andersen Andersen Power Electronic Solutions Ltd Bexhill-on-Sea, East Sussex, UK

Stig L. Nilsson Electrical Engineering Practice Exponent Sedona, AZ, USA

ISBN 978-3-030-35385-8 ISBN 978-3-030-35386-5 (eBook) ISBN 978-3-030-35387-2 (print and electronic bundle) https://doi.org/10.1007/978-3-030-35386-5 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Message from the President

CIGRE is the global expert community for electric power systems. It is a nonprofit organization based in Paris. It consists of members from over 100 countries representing 60 national committees. It functions as a virtual organization with members who are experts in their technical field, forming working groups dealing with issues facing the power delivery industry. In 2019, 230 working groups including more than 3000 experts were working together to resolve the identified issues. The output of the working groups is technical brochures. There are over 700 technical brochures, which contain the combined knowledge and practice of engineering experts from all over the world. The brochures are practical in nature enabling the engineer to plan, design, construct, operate, and maintain the power delivery systems as required. CIGRE has over 10,000 reference papers and other documents supporting the brochures and dealing with other relevant technical matters. This Green Book on Flexible AC Transmission Systems (FACTS) controllers, compiled by Study Committee (SC) B4, DC Systems and Power Electronics, provides state-of-the-art information on power electronic systems that can be used to support the changing needs of AC transmission systems. FACTS controllers can be used to enable higher power transfers and to maintain the power quality. The book comprises material from published technical peer-reviewed publications and technical experts in the field. CIGRE is a source of unbiased technical information. Engineers can refer this book without fear of favoring one supplier or country. It is a compilation of the combined expertise of many international experts providing an unbiased objective textbook in FACTS design. Like other CIGRE Green Books, this book contains input from many experts, not only one or two. These international experts have provided technical information relevant to readers irrespective of where the readers reside. The views expressed and suggestions made are unbiased objective statements. These can be used as references for engineers to develop standards and guidelines within their organizations. This book is a reference book for academia, power transmission engineers, consultants, and users. I would like to congratulate those involved from SC B4 who have compiled this book. Many of them have had to work in their spare time for hours to complete this

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task, for which they worked as volunteers. I would recommend this book in forming the basis for transmission and distribution system design activities now and in the future. October 2019

Dr. Rob Stephen Dr. Rob Stephen was born in Johannesburg, South Africa. He graduated from the University of the Witwatersrand in 1979 with a B.Sc. in Electrical Engineering. He joined the Eskom electricity utility in 1980. He holds M.Sc. and M.B.A. degrees, as well as a Ph.D. in Overhead Line Design. At Eskom he was Master Specialist in the Technology Group responsible for distribution and transmission technologies of all voltages covering both AC and DC and was responsible for the smart grid strategy for Eskom. He is past Chairman of CIGRE SC B2 on overhead lines and has held positions in CIGRE as Special Reporter and Working Group Chairman and has authored over 100 technical papers. He was elected International President of CIGRE in 2016. He is also a Fellow of the South African Institute of Electrical Engineers (SAIEE).

Message from the Chairman of the Technical Council

This Green Book on Flexible AC Transmission Systems (FACTS) aims at describing the remarkable progress in the electrical transmission technology derived from the increased application of power electronic devices and apparatus. The FACTS concept was conceived in the 1980s with the objective of providing the transmission systems with additional facilities to control power system operation, including voltage control using parallel connected devices and active power flow using series connected devices. As transmission systems are expanded to meet a growing demand of electricity, the need to use efficient and fast system control mechanisms to ensure stable and reliable electricity service of high quality for the consumers, who are becoming increasingly dependent on electrical power. At the same time, there may be objections from the public against the building of new transmission facilities. FACTS controllers can provide solutions to some of these issues, by enabling higher power transfers on existing and new lines. Although the technology name, FACTS, implies that the scope of applications would be only for transmission systems, distribution systems (medium and low voltage systems) will also benefit from many of those successful experiences gained during decades in the transmission segment of power systems. This Green Book has been authored by leading industry, research, and academic professionals as its intent is to provide a comprehensive view of the FACTS technology including the basic means of control in AC networks and the characteristics of available FACTS controllers. The book includes information on emerging controllers, technical description of FACTS controllers, application examples of all types of controllers, and economic, technical, and environmental studies considerations. Relevant technical issues of FACTS controllers have been considered, including electromagnetic compatibility, specification, testing, commissioning, life management – including reliability and availability – and operation, in order to serve as a truly useful guideline for utilities, regulators, project developers, investors, as well as for future research activities in terms of new ideas and applications. This Green Book on FACTS technology becomes available when CIGRE is celebrating its first Centennial Session, during the 4.0 Industry Thinking era, in which the distinctions between transmission and distribution and between end user and electricity provider are eroding and as the entire electric power system is becoming more interactive and reliant upon intelligent systems. vii

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Message from the Chairman of the Technical Council

CIGRE’s focus has, of course, widened to address the entire electric power system – the end-to-end approach (E2E). Generation, transmission, distribution, and end use of electric energy are all addressed across the entire spectrum from 1200 kV transmission grids to local micro-grids, employing AC or DC, and providing unbiased information willingly shared with other organizations. I take the opportunity to acknowledge the two Editors of this Green Book, Stig Nilsson and Bjarne Andersen, as well as all chapter authors and contributors for the excellent and timely contribution from which the entire global power systems community will benefit. Yours faithful,

Marcio Szechtman CIGRE Technical Committee Chair

Message from the Secretary General

In 2014, I had the pleasure to comment on the launch of a new CIGRE publication collection in an introductory message about the first CIGRE Green Book, the one on Overhead Lines. The idea to valorize the collective work of the study committees accumulated over many decades, by putting together all the technical brochures of a given field in a single book, was first proposed by Dr. Konstantin Papailiou to the Technical Committee (now Council) in 2011. In 2015, cooperation with Springer allowed CIGRE to publish the Green Book on Overhead Lines again as a “Major Reference Work” distributed through the vast network of this well-known international publisher. In 2016, the collection was enriched with a new category of Green Books, the CIGRE “Compact Series,” to satisfy the needs of the study committees when they want to publish shorter, concise volumes. The first CIGRE Compact Book was prepared by Study Committee D2, under the title Utility Communication Networks and Services. The concept of the CIGRE Green Books series has continued to evolve, with the introduction of a third subcategory of the series, the “CIGRE Green Book Technical Brochures” (GBTB). CIGRE has published more than 720 technical brochures since 1969, and it is interesting to note that in the first one, on tele-protection, the first reference was a Springer publication of 1963. A CIGRE Technical Brochure produced by a CIGRE working group, following specific Terms of Reference, is published by the CIGRE Central Office and is available from the CIGRE online library, e-cigre, one of the most comprehensive, accessible databases of relevant technical literature on power engineering. Between 40 and 50 new technical brochures are published yearly, and these brochures are announced in Electra, CIGRE’s bimonthly journal, and are available for download from e-cigre. In the future, the Technical Council of CIGRE may decide to publish a technical brochure as a Green Book in addition to the traditional CIGRE Technical Brochure. The motivation of the Technical Council to make such a decision is to disseminate the related information beyond the CIGRE community, through the Springer network. Like the other publications of the CIGRE Green Books series, the GB TB will be available on e-cigre in electronic format free of charge for the co-authors of the book. CIGRE plans to copublish new Green Books edited by the different study committees, and the series will grow progressively at a pace of about one or two volumes per ix

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year. This new Green Book, a Major Reference Work prepared by Study Committee B4 on Flexible AC Transmission Systems (FACTS), is the fourth of this subcategory. I want to congratulate all the authors, contributors, and reviewers of this book who give the reader a clear and comprehensive vision of the past, current, and future developments of FACTS. Secretary General

Philippe Adam Graduate of the École Centrale de Paris, Philippe Adam began his career in EDF in 1980 as a research engineer in the field of HVDC and was involved in the studies and tests of outstanding projects like the Cross Channel 2000 MW link and the first multiterminal DC link between Sardinia, Italy, and Corsica, France. After this pioneering period, he managed the team of engineers in charge of HVDC and FACTS studies of the R&D division of EDF. In this period, his CIGRE membership as a working group expert and then as a working group convener in Study Committee 14 was a genuine support to his professional activities. Then, he held several management positions in the EDF Generation and Transmission division in the fields of substation engineering, network planning, transmission asset management, and international consulting until 2000. When RTE, the French TSO, was created in 2000, he was appointed manager of the Financial and Management Control Department, in order to install this corporate function and the necessary tools. In 2004, he contributed to the creation of RTE international activities as Project Director first and then Deputy Head of the International Relations Department. From 2011 to 2014, he has been the Strategy Director of Infrastructures and Technologies of the Medgrid industrial initiative. In the meantime, between 2002 and 2012, he has served CIGRE as the Technical Committee Secretary and as the Secretary and Treasurer of the French National Committee from 2009 to 2014. He was appointed Secretary General of CIGRE in March 2014.

Preface

The global environment of electric power systems is changing due to various technical requirements. For instance, needs of long-distance, large-capacity EHV and UHV, DC and AC transmission, introduction of renewable energy, developments in dc grids, active distribution networks, massive exchange of information, integration of HVDC networks with power electronics, massive installations of energy storage, and awareness of environmental sustainability are defined and investigated in various activities. Further, with aging equipment, replacement and refurbishment options become important. Therefore, FACTS and DC equipment life cycle management and life extension become very important issues in view of the costs involved, efficiency, and reliability requirements. The developments of new technologies as well as new techniques are at the heart of our activities. The objectives of CIGRE are to disseminate and promote the interchange of technical knowledge and field experience in the field of electricity generation, transmission, and distribution. Being the largest global association in these areas, CIGRE provides a unique platform to combine the expertise of universities, research centers, laboratories, manufacturers, TSOs, developers, and utilities. Numerous international working groups develop solutions for emerging problems in an international context, which are often related to the scope of different CIGRE study committees. Within CIGRE, Study Committee (SC) B4 “DC Systems and Power Electronics” deals with all aspects of DC transmission systems and equipment, power electronic equipment, and the DC equipment for distribution systems. At all stages, technical, safety, economic, environmental, and social aspects are addressed as well as interactions with, and integration into, the evolving power system and the environment. All aspects of performance, specification, testing innovative technologies, operational experience, and the application of testing techniques are within scope, with a specific focus on the impact of changing interactions and demands due to evolution of the power system. Life cycle assessment techniques, risk management techniques, education, and training are also important.

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Dr. Rashwan graduated with B.Sc. in Electrical Engineering from Alexandria University, Egypt, and with a Ph.D. in Electrical Engineering from the University of Manitoba in Winnipeg, Canada. Dr. Rashwan started his career with Manitoba Hydro in 1974 as a plant engineer at Dorsey converter station. In 1993, he was appointed the Manager of HVDC Engineering. In 2002, Dr. Rashwan was appointed the President of Transgrid Solutions (TGS), an engineering power systems consulting firm located in Winnipeg. Dr. Rashwan has been involved in many HVDC and FACTS projects worldwide. He has worked with utilities, suppliers, and developers worldwide. He has authored and coauthored over 80 papers and reports in the area of HVDC and FACTS. Dr. Rashwan has been involved in CIGRE since 1982 mainly with Study Committee 14 which is currently Study Committee B4. Dr. Rashwan is a Life Fellow of IEEE, and a distinguished member of CIGRE. Dr. Rashwan was awarded in 2010 the prestigious IEEE HVDC Uno Lamm Award for his contributions to the field. Dr. Rashwan is the current chair of SC B4 and member of the Steering Committee.

Contents

Volume 1 Part I 1

.......................................

Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Willis Long and Stig L. Nilsson 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Electric Power Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Early Developments of Power Transmission Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Reactive Power and Voltage Control in AC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Long-Distance Power Transmission . . . . . . . . . . . . . . . 2.4 Special Industrial Voltage Control Issues . . . . . . . . . . . . 2.5 Power Transfers from Distant Generators to Load Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 FACTS Green Book’s Scope . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part II 2

Introduction

1

3 4 4 5 6 7 8 8 9 10

AC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

AC System Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stig L. Nilsson, Manfredo Lima, and David J. Young 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Early Developments of Electric Theory . . . . . . . . . . . . 1.2 Electric System Analysis Fundamentals . . . . . . . . . . . 2 AC Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Early Developments of Electric Power Systems . . . . . 2.2 AC Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Power System Frequency Domain Analysis . . . . . . . . . . . . . . . 3.1 Transmission Line Equations . . . . . . . . . . . . . . . . . . . 3.2 Simplified Power Flow Equations . . . . . . . . . . . . . . . .

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3.3 3.4

Analysis of Three-Phase Circuits . . . . . . . . . . . . . . . . Harmonic Network Analysis and Other Special Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Power System Time Domain Analysis . . . . . . . . . . . . . . . . . . . 5 Maximum Stable Power Transfer . . . . . . . . . . . . . . . . . . . . . . . 5.1 Power Transfer into a Resistive Load . . . . . . . . . . . . . 5.2 The Per-Unit System . . . . . . . . . . . . . . . . . . . . . . . . . 6 Power Transfer Through Long Overhead Lines . . . . . . . . . . . . 6.1 Load Limit for Uncompensated Long Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Transient Stability of Power Systems . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

AC Network Control Using Conventional Means . . . . . . . . . . . . . Stig L. Nilsson, Manfredo Lima, and David J. Young 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 AC Power System Control Objectives . . . . . . . . . . . . . . . . . . . 3 Overhead Transmission Lines and Underground Cables . . . . . . 3.1 Characteristics of Transmission Lines and Cables . . . . . 3.2 Reactive Power Compensation Needs for Lines . . . . . 3.3 The Ferranti Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Methods of Reducing Transmission Line Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Power System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Switchgear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Shunt Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Synchronous Machines . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Surge Arresters and the Control of Network Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Var Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Tools Available to Control Reactive Power Flow . . . . . . . . . . . 6.1 Passive Shunt Compensation . . . . . . . . . . . . . . . . . . . 6.2 Passive Series Compensation . . . . . . . . . . . . . . . . . . . 6.3 Active Reactive Power Compensation and Voltage Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Load Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Dealing with Disturbing Loads . . . . . . . . . . . . . . . . . . . . . . . . 9 Phase Unbalance Due to Single-Phase Loads . . . . . . . . . . . . . . 10 Increasing Stability for Very Long Lines . . . . . . . . . . . . . . . . . 11 Power Production Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Transmission System Control . . . . . . . . . . . . . . . . . . . . . . . . . 13 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contents

4

AC Network Control Using FACTS (Flexible AC Transmission Systems) Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antonio Ricardo de Mattos Tenório 1 AC Network Needs and FACTS Controllers . . . . . . . . . . . . . . 1.1 Active Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Reactive Power Transfer . . . . . . . . . . . . . . . . . . . . . . . 2 Topology of FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . 3 Description and Functions of SVCs . . . . . . . . . . . . . . . . . . . . . 3.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Application of SVCs . . . . . . . . . . . . . . . . . . . . . . . . . 4 Description and Functions of STATCOMs . . . . . . . . . . . . . . . . 5 Description and Functions of TCSCs . . . . . . . . . . . . . . . . . . . . 5.1 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . 6 Description and Functions of SSSCs . . . . . . . . . . . . . . . . . . . . 7 Description and Functions of UPFCs . . . . . . . . . . . . . . . . . . . . 8 Power Losses in FACTS Controllers . . . . . . . . . . . . . . . . . . . . 9 System Security and Reliability . . . . . . . . . . . . . . . . . . . . . . . . 10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part III 5

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Technical Description of FACTS Controllers . . . . . . . . . . . .

Power Electronic Topologies for FACTS . . . . . . . . . . . . . . . . . . . . Colin Davidson 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Semiconductor Switching Devices . . . . . . . . . . . . . . . . . . . . . . 2.1 Semiconductor Materials . . . . . . . . . . . . . . . . . . . . . . 2.2 Devices of the Thyristor Family . . . . . . . . . . . . . . . . . 2.3 Devices of the Transistor Family . . . . . . . . . . . . . . . . 3 Line-Commutated Thyristor Switches . . . . . . . . . . . . . . . . . . . 3.1 Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Self-Commutated Converters . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Current-Sourced Converter . . . . . . . . . . . . . . . . . . . . . 4.2 Voltage-Sourced Converter . . . . . . . . . . . . . . . . . . . . . 4.3 Self-Commutated Converter Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technical Description of Static Var Compensators (SVC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manfredo Lima and Stig L. Nilsson 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main Circuit Components of an SVC . . . . . . . . . . . . . . . . . . . 2.1 Thyristor Controlled Reactor (TCR) . . . . . . . . . . . . . . 2.2 Thyristor Switched Capacitors (TSC) . . . . . . . . . . . . .

91 92 93 94 95 95 97 100 102 107 107 120 121 123 123 124 125 127 129 130 131 131 131 134 136 136 139 140 140 141 152 153 155 156 157 157 159

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2.3 Thyristor Switched Reactors (TSRs) . . . . . . . . . . . . . . 2.4 AC Harmonic Filters . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 SVC Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 SVC Voltage Versus Current Characteristic . . . . . . . . . . . . . . . 4 Combinations of SVC Components . . . . . . . . . . . . . . . . . . . . . 5 First Brazilian SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Later Brazilian SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 TCR Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 TSC Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 SVCs Gate Power Drive Issues . . . . . . . . . . . . . . . . . . 7.4 Thyristor Valve Cooling System . . . . . . . . . . . . . . . . . 7.5 Thyristor Valve Control and Protection Systems . . . . . 8 SVC Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Early SVC Analog Control . . . . . . . . . . . . . . . . . . . . . 8.2 Digital Control Systems . . . . . . . . . . . . . . . . . . . . . . . 8.3 Additional Control Loops . . . . . . . . . . . . . . . . . . . . . . 8.4 The Use of Series Reactor to Reduce Harmonics and Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Coordinated Operation of SVCs Operating Electrically Close . . . . . 10 SVC Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 SVC Transformers Losses . . . . . . . . . . . . . . . . . . . . . 10.2 SVC Thyristor Controlled Reactor (TCR) Losses . . . . . . 10.3 SVC Thyristor Switched Capacitor Losses . . . . . . . . . 10.4 SVC Harmonic Filter Losses . . . . . . . . . . . . . . . . . . . 10.5 Control, Protection and Auxiliary Equipment Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Technical Description of Static Compensators (STATCOM) . . . . . Colin Davidson and Marcio M. de Oliveira 1 STATCOM Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 V-I Characteristics of a STATCOM . . . . . . . . . . . . . . . 1.4 Voltage-Sourced Converters . . . . . . . . . . . . . . . . . . . . 1.5 Limitations and Challenges . . . . . . . . . . . . . . . . . . . . . 2 Multi-pulse Circuits with Magnetic Coupling . . . . . . . . . . . . . . 3 Modular Multilevel Converter (MMC)-Based STATCOM . . . . 3.1 The Chain Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Half-Bridge MMC . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Other Primary Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 STATCOM Transformer . . . . . . . . . . . . . . . . . . . . . . . 4.2 STATCOM Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 DC Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

162 162 163 164 166 167 169 172 174 179 179 181 182 183 183 184 186 187 189 190 191 196 201 203 204 204 207 208 208 211 212 214 216 217 221 221 223 224 225 226 227

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4.4 AC Harmonic Filters . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 High-Precision Current Transducers . . . . . . . . . . . . . . 5 Layout Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Control Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Space Vector Control Concepts . . . . . . . . . . . . . . . . . . 6.3 Application Control . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Converter Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Special Control Considerations for Electric Arc Furnace Applications . . . . . . . . . . . . . . . . . . . . . . . . . 7 Losses and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Hybrid STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Technical Description of Thyristor Controlled Series Capacitors (TCSC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stig L. Nilsson and Marcio M. de Oliveira 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 TCSC Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . 3 Operating Range of TCSC Systems . . . . . . . . . . . . . . . . . . . . . 4 Power-Transmission Characteristic Controlled by TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cost Benefit of TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . 6 TCSC Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 TCSC Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 TCSC Dynamic Models . . . . . . . . . . . . . . . . . . . . . . . 6.3 TCSC Modeling Considerations for Long-Term Planning Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 TCSC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 TCSC Platform Equipment . . . . . . . . . . . . . . . . . . . . . 7.2 TCSC Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Valve Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Insulation Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 TCSC Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 No-Load Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Load Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Harmonic Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Torsional Interactions Between Turbo-Generators and TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Series Capacitor Bank Interactions with Turbo-Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Subsynchronous Damping Performance of TCSC Compensated Lines . . . . . . . . . . . . . . . . . . . . .

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228 229 229 232 232 233 237 240 243 245 248 249 253 254 256 260 264 265 266 267 268 275 276 276 276 277 279 280 281 281 282 288 288 288 289

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12

Stability Improvement and Power Oscillation Damping with TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Transient Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 System Damping Improvement . . . . . . . . . . . . . . . . . . 13 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Technical Description of the Unified Power Flow Controller (UPFC) and Its Potential Variations . . . . . . . . . . . . . . . . . . . . . . . . Ram Adapa, Stig L. Nilsson, Bjarne R. Andersen, and Yi Yang 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 UPFC Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 AC Power Flow Theories . . . . . . . . . . . . . . . . . . . . . . 2.2 UPFC Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Power Flows with an UPFC Installed in a Line . . . . . . 2.4 Operating Principles (Functions) . . . . . . . . . . . . . . . . . 3 UPFC Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 UPFC Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Overvoltage Protection and System Starts . . . . . . . . . . 4.2 VSC System Faults . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Converter Valve Protection Consideration . . . . . . . . . . 4.4 UPFC Impact on the Protective Relays . . . . . . . . . . . . 5 UPFC Converter System Control . . . . . . . . . . . . . . . . . . . . . . . 5.1 VSC Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 STATCOM Control Systems . . . . . . . . . . . . . . . . . . . . 5.3 SSSC Control Systems . . . . . . . . . . . . . . . . . . . . . . . . 5.4 UPFC Control Systems . . . . . . . . . . . . . . . . . . . . . . . . 6 Static Synchronous Series Compensator (SSSC) . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Possible Applications . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The SSSC Components . . . . . . . . . . . . . . . . . . . . . . . 7 Interline Power Flow Controller . . . . . . . . . . . . . . . . . . . . . . . 7.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Part IV 10

Applications of FACTS Controllers

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Controllers Using the Saturation of Iron for AC Network Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David J. Young 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Saturation Characteristic of Iron . . . . . . . . . . . . . . . . . . . . . 2.1 The Basic Static Var Compensator . . . . . . . . . . . . . . . . . 2.2 The Magnetic Constant Voltage Transformer . . . . . . . . .

292 292 292 294 294 299 300 302 302 303 306 307 311 311 329 329 330 332 333 334 334 335 337 339 343 343 345 346 346 346 348 353

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3

Harmonics in Saturated Reactors . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Harmonics in a Single-Phase Self-Saturated Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Harmonics in Three-Phase Self-Saturated Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Reduction of Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic Frequency Multipliers . . . . . . . . . . . . . . . . . . . 4 The Magnetic Amplifier or Transductor . . . . . . . . . . . . . . . . . . . 4.1 100 MVA Transductor for Alternator Testing . . . . . . . . . . 4.2 Tertiary-Connected Transductor for Dynamic Var Balancing in a 132/275/400 kV Network . . . . . . . . . 4.3 Magnetically Controlled Shunt Reactors (MCSR) . . . . . . . . 5 Development of Effective Compensation for Arc Furnaces . . . . . 5.1 Characteristic Features of Arc Furnaces . . . . . . . . . . . . . 5.2 Experimental Arc Furnace Compensation by Transductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Experimental Arc Furnace Compensation by Self-Saturated Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Commercial Applications of Saturated Reactors for Arc Furnace Compensation . . . . . . . . . . . . . . . . . . . . . . 5.5 Compensation by Decoupling Transformer-Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Three-Phase Self-Saturated Reactors with Harmonic Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 The Twin Tripler Saturated Reactor . . . . . . . . . . . . . . . . 6.2 The Treble Tripler Saturated Reactor . . . . . . . . . . . . . . . 6.3 Slope Correction for Saturated Reactors . . . . . . . . . . . . . 7 Applications of Self-Saturated Reactors . . . . . . . . . . . . . . . . . . . 7.1 Disturbances Caused by Industrial Loads . . . . . . . . . . . . 7.2 Compensation for Long Transmission Lines . . . . . . . . . . 7.3 Commercial Applications . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Static Var Compensation for the 2000 MW HVDC Cross-Channel Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Development of Magnetically Controlled Shunt Reactors in Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sergey V. Smolovik and Alexander M. Bryantsev 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Need for Reactive Power Control . . . . . . . . . . . . . . . . . . . . 3 Development of Magnetically Controlled Shunt Reactors in Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 MCSR Operation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Higher Harmonics Suppression . . . . . . . . . . . . . . . . . . . .

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362 362 363 366 368 369 371 374 375 376 376 376 378 381 382 383 383 385 387 388 388 388 390 392 398 401 402 402 404 404 406 408

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4.3 A Model for Stability Study . . . . . . . . . . . . . . . . . . . . . . Magnetically Controlled Shunt Reactor Operation Experience in 110–500 kV Power Grids . . . . . . . . . . . . . . . . . . 5.1 Overview of the MCSRs in Operation . . . . . . . . . . . . . . 5.2 Benefits of the MCSRs . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Voltage Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Power System Damping . . . . . . . . . . . . . . . . . . . . . . . . . 6 Tavricheskaya MCSR, Siberia . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12

Application Examples of SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hong Rao, Shi He, Xiaodan Wu, Marcio M. de Oliveira, Guillaume de Préville, Colin Davidson, Zhanfeng Deng, Tuomas Rauhala, Georg Pilz, Bjarne R. Andersen, and Shukai Xu 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Brief Introduction of SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 SVC in Wuzhou, Guangxi, China . . . . . . . . . . . . . . . . . . . . . . . 3.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 System Structure and Operating Parameters . . . . . . . . . . 3.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 SVC in Dong Anshan, Liaoning, China . . . . . . . . . . . . . . . . . . . 4.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 System Structure and Operating Parameters . . . . . . . . . . 4.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 SVCs in Gansu, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 SVC System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 SVCs in Holeta Substation, Ethiopia . . . . . . . . . . . . . . . . . . . . . 6.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 SVC Merlatière and Domloup in West France . . . . . . . . . . . . . . 7.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 System Structure and Operating Parameters . . . . . . . . . . 7.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 SVC in Kangasala Substation Finland . . . . . . . . . . . . . . . . . . . . 8.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 System Structure and Operating Parameters . . . . . . . . . . 8.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Taoxiang Substation SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Project Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Introduction of the Taoxiang SVC System . . . . . . . . . . .

412 412 413 415 418 419 420 423

425 427 428 428 428 432 432 432 433 436 436 437 437 439 442 443 443 443 444 444 445 451 452 453 453 454 457 459 460 460 460

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9.3 Main Parameters of the Taoxiang SVC . . . . . . . . . . . . . . 9.4 Technical Characteristics of the Taoxiang SVC . . . . . . . . 9.5 General Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Relocatable SVCs for National Grid, UK . . . . . . . . . . . . . . . . . . 10.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 System Structure and Operation Parameters . . . . . . . . . . 10.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Nemiscau SVCs in Quebec, Canada . . . . . . . . . . . . . . . . . . . . . 11.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 System Structure and Operation Parameters . . . . . . . . . . 11.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Viklandet and Tunnsjødal SVCs in Norway . . . . . . . . . . . . . . . . 12.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 System Structure and Operation Parameters . . . . . . . . . . 12.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Haramain High-Speed Railway (HHR) SVCs in Saudi Arabia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 System Structure and Operation Parameters . . . . . . . . . . 13.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Directly Connected SVCs in Texas, USA . . . . . . . . . . . . . . . . . 14.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 System Structure and Operation Parameters . . . . . . . . . . 14.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 SVCs at Bout De L’Ile (BDI) on the Island of Montreal, Hydro-Quebec, Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 System Structure and Operating Parameters . . . . . . . . . . 15.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Application Examples of STATCOM . . . . . . . . . . . . . . . . . . . . . . . Shukai Xu, Shaobo Wang, Guangjie Zuo, Colin Davidson, Marcio M. de Oliveira, Rizah Memisevic, Georg Pilz, Bilgehan Donmez, and Bjarne R. Andersen 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Brief Introduction of the STATCOM . . . . . . . . . . . . . . . . . . . . .

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513 515

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3

STATCOM in East Claydon, UK . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 System Structure and Operating Parameters . . . . . . . . . . 3.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 MMC STATCOM in Shanghai, China . . . . . . . . . . . . . . . . . . . . 4.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 System Structure and Operating Parameters . . . . . . . . . . 4.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 STATCOM in Cerro Navia, Chile . . . . . . . . . . . . . . . . . . . . . . . 5.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 System Structure and Operation Parameters . . . . . . . . . . 5.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Multiple STATCOMs in Guangdong, China . . . . . . . . . . . . . . . 6.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 System Structure and Operating Parameters . . . . . . . . . . 6.3 Control Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 STATCOM in Inner Mongolia, China . . . . . . . . . . . . . . . . . . . . 7.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 System Structure and Operation Parameters . . . . . . . . . . 7.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 STATCOMs in HVDC Converter Station in Yunnan, China . . . . . . 8.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 System Structure and Operation Parameters . . . . . . . . . . 8.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Performance Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 STATCOMs in Aurangabad, India . . . . . . . . . . . . . . . . . . . . . . . 9.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 System Structure and Operation Parameters . . . . . . . . . . 9.3 Main Operation Modes (or Control Function) and Protection System . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 STATCOM in Alabama, USA . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 System Structure and Operation Parameters . . . . . . . . . . 10.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Four STATCOMs in Queensland, Australia . . . . . . . . . . . . . . . . 11.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 System Structure and Operating Parameters . . . . . . . . . . 11.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . .

515 515 516 518 519 519 519 520 523 524 525 525 525 529 529 532 532 532 535 536 537 537 539 541 542 543 543 543 548 548 551 551 551 554 554 555 555 555 558 559 561 561 562 565

Contents

11.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hybrid STATCOM in Rourkela, India . . . . . . . . . . . . . . . . . . . . 12.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 System Structure and Operating Parameters . . . . . . . . . . 12.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 STATCOM System in South Australia . . . . . . . . . . . . . . . . . . . . 13.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 System Structure and Operating Parameters . . . . . . . . . . 13.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Mobile STATCOM, USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 System Structure and Operating Parameters . . . . . . . . . . 14.3 Major Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.5 Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

14

15

Application Examples of the Thyristor Controlled Series Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stig L. Nilsson, Antonio Ricardo de Mattos Tenório, Subir Sen, Andrew Taylor, Shukai Xu, Gang Zhao, Qiang Song, and Bo Lei 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Loading of AC Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 AC Systems with TCSC Installations . . . . . . . . . . . . . . . 2 Installed TCSC Base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 TCSC Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Brazil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Sweden: Stöde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 United Kingdom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Performance Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application Examples of UPFC and Its Variants . . . . . . . . . . . . . . Stig L. Nilsson, Shukai Xu, Bo Lei, Zhanfeng Deng, and Bjarne R. Andersen 1 Brief Introduction of UPFCs . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 UPFC Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xxiii

566 566 566 566 569 569 570 570 572 574 574 576 576 576 579 579 580 581 581 585

586 588 589 591 593 593 600 607 611 629 634 637 638 645

647 647

xxiv

Contents

1.2 Installed UPFC Systems . . . . . . . . . . . . . . . . . . . . . . . . . UPFC in Inez, USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 System Structure and Operation Parameters . . . . . . . . . . 2.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 UPFC in Kangjin, Korea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 System Structure and Operation Parameters . . . . . . . . . . 3.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Current Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 UPFC/Convertible Static Compensator (CSC) in Marcy, USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 System Structure and Operating Parameters . . . . . . . . . . 4.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 UPFC System Status . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 UPFC in Nanjing, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 System Structure and Operation Parameters . . . . . . . . . . 5.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 UPFC in Suzhou, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 System Structure and Operation Parameters . . . . . . . . . . 6.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 UPFC in Shanghai, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 System Structure and Operation Parameters . . . . . . . . . . 7.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Project Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

648 649 649 651 657 657 657 657 659 661 662 664 665 665 668 672 679 679 679 680 684 686 686 686 688 692 693 696 696 696 699 700 701 703 703

Volume 2 Part V 16

FACTS Controller Planning and Procurement . . . . . . . . . . .

Economic Appraisal and Cost-Benefit Analysis . . . . . . . . . . . . . . . Mário Duarte 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

707 709 710 712

Contents

3 4 5

General Approach to Economic Appraisal . . . . . . . . . . . . . . . . . Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identification of Alternatives and Assessing Relative Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Bespoke Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Performance Characteristics for Planning Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Functional Specification . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Measurement of Incremental Impact . . . . . . . . . . . . . . . . 6 Cost-Benefit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Initial Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Results Summarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Investment Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

FACTS Planning Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bjarne R. Andersen, Dennis Woodford, and Geoff Love 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Planning Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Specification Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Models for Planning and Specification Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Further Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Planning Studies for FACTS Controllers . . . . . . . . . . . . . . . . . . 2.1 Timeline for Undertaking Planning Studies . . . . . . . . . . . 2.2 Power System Studies Undertaken During Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 The Need for FACTS Controllers . . . . . . . . . . . . . . . . . . 3 Studies for Preparation of Technical Specification of a FACTS Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Development of Appropriate AC Network Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 FACTS Controller Rating . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Short Circuit Calculation . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Transient Stability and EMT Studies . . . . . . . . . . . . . . . . 3.5 Harmonic Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Modelling of FACTS Controllers . . . . . . . . . . . . . . . . . . 4.2 Steady-State Power Flow . . . . . . . . . . . . . . . . . . . . . . . . 4.3 AC Short Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Harmonic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Transient Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xxv

713 715 716 716 717 719 722 723 723 725 733 748 748 749 753 754 755 756 756 756 756 757 758 759 761 761 762 763 763 763 764 764 765 768 769 775

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Contents

4.6 Electromagnetic Transients (EMT) . . . . . . . . . . . . . . . . . 4.7 Real-Time Simulation (RTS) . . . . . . . . . . . . . . . . . . . . . 4.8 Models to Be Provided by the Vendor . . . . . . . . . . . . . . 4.9 Other Models and Tools . . . . . . . . . . . . . . . . . . . . . . . . . 5 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

778 782 783 783 783 783

Environmental Considerations for FACTS Projects . . . . . . . . . . . Bjarne R. Andersen, Bruno Bisewski, Narinder Dhaliwal, and Mark Reynolds 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Management of Environmental Issues and Stakeholder Engagement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Management of Environmental Issues . . . . . . . . . . . . . . . 2.2 Project Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Stakeholder Engagement . . . . . . . . . . . . . . . . . . . . . . . . 3 Impact of FACTS Controllers on the AC Network . . . . . . . . . . . 3.1 Impact of Changed Power Flows . . . . . . . . . . . . . . . . . . 4 Environmental Impact of a FACTS Station . . . . . . . . . . . . . . . . 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Environmental Aspects Related to Site Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Environmental Impact of the FACTS Station Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Decommissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Audible Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Relationship of Performance Limits to Time Duration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Audible Sound from FACTS Controllers . . . . . . . . . . . . 5.3 Environmental Influences on Audible Noise . . . . . . . . . . 5.4 Audible Noise Level Limits . . . . . . . . . . . . . . . . . . . . . . 5.5 Sound-Emitting Sources . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Sound Reduction Measures . . . . . . . . . . . . . . . . . . . . . . 5.7 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Sound Level Prediction . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Verification of Component Sound Power Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.10 Verification of Sound Levels from the FACTS Station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 Specification of Audible Noise Limits . . . . . . . . . . . . . . .

787

788 789 789 790 791 793 795 796 796 797 799 806 806 807 807 808 808 809 811 813 817 820 821 822 823 825

Contents

6 7

Electric and Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . Electromagnetic Emissions and Compatibility Limits . . . . . . . . . 7.1 Electromagnetic Interference (EMI) . . . . . . . . . . . . . . . . 7.2 Electromagnetic (EMC) Compatibility . . . . . . . . . . . . . . 7.3 Harmonics and Interharmonics . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

Procurement and Functional Specifications for FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ben Mehraban, Hubert Bilodeau, Bruno Bisewski, and Thomas Magg 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Selection of Bidding and Contracting Strategies . . . . . . . . . . . . . 2.1 Form of Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Bidding Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Contracting Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Bidding Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Invitation to Tender: Cover Letter . . . . . . . . . . . . . . . . . . 3.2 Instructions to Tenderers . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Information to Be Submitted by the Tenderers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Commercial Conditions and Payment Terms . . . . . . . . . . 4 Bid Evaluation and Comparison of Options . . . . . . . . . . . . . . . . 4.1 Evaluation of Proposals . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Technical Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Non-technical and Commercial Evaluation: Life Cycle Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Evaluation Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Preparation of a Functional Technical Specification . . . . . . . . . . 5.1 Objective of Functional Specifications . . . . . . . . . . . . . . 5.2 Project Background and Objectives . . . . . . . . . . . . . . . . 5.3 Standards and References . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Definitions/Acronyms/Abbreviations . . . . . . . . . . . . . . . 5.5 Scope of Project and Interfaces . . . . . . . . . . . . . . . . . . . . 5.6 Site, Environmental, and Network Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Performance Requirements . . . . . . . . . . . . . . . . . . . . . . . 5.8 Equipment Requirements . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Civil and Building Works Requirements . . . . . . . . . . . . . 5.10 System Studies and Design to Be Performed by the Contractor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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827 829 831 834 840 842 842 847 848 848 848 849 850 851 852 852 852 853 854 855 855 856 857 857 857 858 858 858 859 860 862 867 869 870 871

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5.12 5.13 5.14 5.15 References Part VI 20

Maintenance Requirements . . . . . . . . . . . . . . . . . . . . . . . Spare Parts and Special Tools . . . . . . . . . . . . . . . . . . . . . Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................

Implementation of FACTS Controllers

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FACTS Controller Integration and Design Studies . . . . . . . . . . . . Bjarne R. Andersen, Dennis Woodford, and Geoff Love 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Modelling Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Studies Performed During the Bidding Process . . . . . . . . . . . . . 3.1 Rating Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Dynamic Performance Studies . . . . . . . . . . . . . . . . . . . . 4 Post-award Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Equipment Design and Rating Studies . . . . . . . . . . . . . . 4.3 Interaction Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Studies at the Commissioning Stage of a FACTS Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Studies Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Switching AC Side Filters and Transformers . . . . . . . . . . 5.3 Performance of the Controls Applied for Damping Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 AC System Fault Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Studies Over the Operational Life of the FACTS Controller . . . . . . 6.1 Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Transmission Network Planning and Operational Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Post-disturbance Analysis (Model Validation Studies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Pre-specification Studies of New Transmission and Generation Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Model Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Challenges to Model Maintainability . . . . . . . . . . . . . . . 7.3 Approaches to Model Maintainability . . . . . . . . . . . . . . . 7.4 Future Prospects in Modelling and Model Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

872 872 873 874 876 879 881 882 884 884 887 889 890 890 892 895 900 901 903 904 906 907 907 907 908 909 910 911 911 911 913 918 918 919

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FACTS Equipment Design and Testing . . . . . . . . . . . . . . . . . . . . . Hubert Bilodeau, Bruno Bisewski, Manfredo Lima, Shukai Xu, Bo Lei, and Ben Mehraban 1 Project Management During Planning and Design Phases . . . . . 1.1 Duties of the Owner’s Implementation Team . . . . . . . . . 1.2 Vendor’s Project Management Structure . . . . . . . . . . . . . 1.3 Contracting Strategies and Contract Packaging . . . . . . . . 1.4 Contract Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Project Implementation Phase . . . . . . . . . . . . . . . . . . . . . 2 FACTS Equipment Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 General Testing Requirements . . . . . . . . . . . . . . . . . . . . 2.2 Primary Equipment Factory Testing . . . . . . . . . . . . . . . . 2.3 Control and Protection Equipment Factory Testing . . . . . . . 2.4 Discrete Protection System Tests (Not Embedded in Control System) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Cooling System Factory Tests . . . . . . . . . . . . . . . . . . . . . 2.6 Site Testing and Commissioning . . . . . . . . . . . . . . . . . . . 2.7 Performance Monitoring Period: Reliability and Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Example of FST/FAT Tests for the Ceará Mirim SVC in Brazil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Ceará Mirim SVC Main Circuit Component Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Ceará Mirim SVC Closed-Loop Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Ceará Mirim SVC Additional Control Loops . . . . . . . . . 3.4 Degraded Modes of Operation . . . . . . . . . . . . . . . . . . . . 3.5 Coordination Between Electrically Close SVCs to Avoid Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Real-Time Hardware-In-The-Loop (HIL) Tests . . . . . . . . 3.7 Step Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Performance Under Strong Disturbance Conditions . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commissioning of FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . Babak Badrzadeh, Andrew Van Eyk, Peeter Muttik, Bryan Lieblick, Bo Lei, Thomas Magg, Shukai Xu, and Marcio M. de Oliveira 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 General Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Role of Power System Modelling and Simulation . . . . . . . .

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922 923 927 927 929 930 934 934 936 941 956 956 956 956 957 957 957 959 960 960 962 963 964 966 971

973 973 973 974 975 977

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Four-Stage Commissioning Tests for FACTS Controllers . . . . . . 3.1 Checks on Equipment Prior to Commencement of Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 On-Site Equipment Tests . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Sub-system Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 System Commissioning Tests . . . . . . . . . . . . . . . . . . . . . 3.5 Grid Compliance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Typical Commissioning Tests for SVCs . . . . . . . . . . . . . . . . . . . 4.1 System Commissioning Tests . . . . . . . . . . . . . . . . . . . . . 4.2 Grid Compliance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Typical Commissioning Tests for STATCOMS . . . . . . . . . . . . . 5.1 System Commissioning Tests . . . . . . . . . . . . . . . . . . . . . 5.2 Grid Compliance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Practical Experience . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Typical Commissioning Tests for UPFCs . . . . . . . . . . . . . . . . . . 6.1 System Commissioning Tests . . . . . . . . . . . . . . . . . . . . . 6.2 Grid Compliance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Commissioning of TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . 7.1 Pre-commissioning Tests . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Sub-system Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 System Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Grid Compliance Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 System Interaction Tests . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Special Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Power Oscillation Damping . . . . . . . . . . . . . . . . . . . . . . 8 Model Validation Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 STATCOMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part VII 23

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FACTS Operation and Lifetime Management . . . . . . . . . .

Operation of FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . Vinay N. Sewdien 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Survey Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Role of FACTS in System Operation . . . . . . . . . . . . . . . . . . . . . 4 FACTS Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 FACTS Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Upgrade and Retirement of FACTS Controllers . . . . . . . . . . . . .

978 979 980 983 988 999 1015 1015 1017 1031 1031 1032 1035 1038 1038 1038 1040 1040 1041 1042 1043 1044 1044 1045 1048 1048 1054 1056 1061 1063 1063 1064 1065 1066 1068 1069

Lifetime Management of FACTS Controllers . . . . . . . . . . . . . . . . . 1071 Narinder Dhaliwal and Thomas Magg 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072 1.1 FACTS Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1073

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Maintenance of Facts Controllers . . . . . . . . . . . . . . . . . . . . . . . 2.1 Maintenance Management . . . . . . . . . . . . . . . . . . . . . . . 2.2 Scheduled Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Maintenance Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . 3 Maintenance Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Capacitor Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Control and Protection . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Interface Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Semiconductor Devices . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Station Auxiliary Supplies . . . . . . . . . . . . . . . . . . . . . . . 3.7 Surge Arresters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Valve Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Documentation and Staff Training . . . . . . . . . . . . . . . . . . . . . . . 4.1 Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Staff Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Spare Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Types of Components Used Within Controllers . . . . . . . . 5.2 Replacement and Management of Obsolescence . . . . . . . 6 Management of System Performance and Faults . . . . . . . . . . . . 6.1 FACTS Controller Faults . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Performance of the FACTS Controller in the AC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Life Assessment Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Life Assessment Timetable . . . . . . . . . . . . . . . . . . . . . . . 7.2 Alternatives and Justification . . . . . . . . . . . . . . . . . . . . . 7.3 Basis for Replacement/Refurbishment of Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Decommissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Control Cabinets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Cooling System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Site Clean-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7 Structures and Building . . . . . . . . . . . . . . . . . . . . . . . . . 8.8 Switchgear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9 Thyristors, IGBTs, and Electronic Circuit Boards . . . . . . . 8.10 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculation of FACTS Controller Performance . . . . . . . . . . . . . Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1075 1075 1076 1076 1078 1078 1078 1081 1083 1084 1085 1086 1087 1089 1089 1091 1093 1093 1094 1096 1096 1097 1097 1098 1100 1101 1102 1102 1102 1102 1103 1103 1103 1103 1103 1103 1103 1104 1104 1104 1110

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113

Contributors

Ram Adapa Electric Power Research Institute, Palo Alto, CA, USA Bjarne R. Andersen Andersen Power Electronic Solutions Ltd, Bexhill-on-Sea, East Sussex, UK Babak Badrzadeh Australian Energy Market Operator, Melbourne, VIC, Australia Hubert Bilodeau Retired from Hydro-Québec, Montreal, QC, Canada Bruno Bisewski RBJ Engineering Corporation, Winnipeg, MB, Canada Alexander M. Bryantsev JSV “ESCO”, Moscow, Russia Colin Davidson GE Grid Solutions – Grid Integration, Stafford, UK Antonio Ricardo de Mattos Tenório Operador Nacional do Sistema Elétrico – ONS, Rio de Janeiro, RJ, Brazil Guillaume de Préville GE’s Grid Solutions Business, Massy, France Zhanfeng Deng Global Energy Interconnection Research Institute (GEIRI), Beijing, China Narinder Dhaliwal TransGrid Solutions, Winnipeg, MB, Canada Bilgehan Donmez AMSC, Ayer, USA Mário Duarte EirGrid Plc, Dublin, Ireland Shi He Rongxin Huiko (RXHK) Electric Technology Co., Ltd., Anshan, China Bo Lei Energy Storage and Power Electronics, HVDC and Power Electronics Department, EPRI of China Southern Power Grid, Guangzhou, China Bryan Lieblick AMSC, Devens, MA, USA Manfredo Lima Transmission Planning and Studies Department, Chesf, Recife, Brazil Pernambuco University, Recife, Brazil Willis Long University of Wisconsin, Madison, WI, USA xxxiii

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Contributors

Geoff Love PSC Consulting, Dublin, Ireland Thomas Magg Serala Power Consulting, Johannesburg, South Africa Ben Mehraban American Electric Power, Columbus, OH, USA Rizah Memisevic System Perfomance and Connections, Power Link, Virginia, QLD, Australia Peeter Muttik GE Grid Solutions, Sydney, NSW, Australia Stig L. Nilsson Electrical Engineering Practice, Exponent, Sedona, AZ, USA Marcio M. de Oliveira ABB FACTS, Västerås, Sweden Georg Pilz System Engineering and Network Studies for FACTS Installations Worldwide, Siemens, Erlangen, Germany Hong Rao Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), Guangzhou, China Tuomas Rauhala Fingrid Oyj, Helsinki, Finland Mark Reynolds POWER ENGINEERs Inc., New York, NY, USA Subir Sen Central Transmission Utility-Planning & Smart Grid, Power Grid Corporation of India Ltd., New Delhi, India Vinay N. Sewdien TenneT TSO B.V., Arnhem, The Netherlands Sergey V. Smolovik JSV “STC UPS”, Saint-Petersburg, Russia Qiang Song Tsinghua University, Tsinghua, China Andrew Taylor Electricity Transmission, National Grid, London, UK Andrew Van Eyk ElectraNet, Adelaide, SA, Australia Shaobo Wang Rongxin Huiko (RXHK) Electric Technology Co., Ltd., Anshang, People’s Republic of China Dennis Woodford Electranix Corporation, Winnipeg, MB, Canada Xiaodan Wu NR Electric Co., Ltd., Nanjing, China Shukai Xu HVDC and Power Electronics Department, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), Guangzhou, China Yi Yang State Grid Jiangsu Electric Power Research Institute, Nanjing, China David J. Young Stafford, UK Gang Zhao NARI Group Corporation of Sate Grid Corporation of China (SGCC), Beijing, China Guangjie Zuo XJ Group Co., Ltd., Xuchang, China

Part I Introduction

1

Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology Willis Long and Stig L. Nilsson

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Electric Power Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Early Developments of Power Transmission Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Reactive Power and Voltage Control in AC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Long-Distance Power Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Special Industrial Voltage Control Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Power Transfers from Distant Generators to Load Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 FACTS Green Book’s Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Abstract

This Green Book on Flexible AC Transmission System (FACTS) controllers is intended to assist electrical engineers and power system planners in understanding how to select, apply, and manage power electronic systems used for the control of voltage, reactive power, and active power in AC systems. This introductory chapter provides some background and historical perspective on how AC power transmission systems function and how they evolved to become an indispensable infrastructure all over the world.

W. Long University of Wisconsin, Madison, WI, USA e-mail: [email protected] S. L. Nilsson (*) Electrical Engineering Practice, Exponent, Sedona, AZ, USA e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_1

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W. Long and S. L. Nilsson

Introduction

FACTS is an abbreviation of Flexible AC Transmission System used by the Electric Power Research Institute (EPRI) in the United States in its research documents developed beginning in 1987. The FACTS controllers are intended to assist electrical engineers and power system planners, who are faced with the problems on how to control the voltages in an Alternating Current (AC) power system as well as also controlling the power flows in the systems. EPRI prepared budget documents for the FACTS program that were circulated to the EPRI Advisory Committees for review and approval. The term was publicly introduced by Dr. Nari Hingorani at the American Power Conference 50th Annual Meeting in Chicago, Illinois (Hingorani 1988). CIGRE defines FACTS as follows: Power Electronic Devices used in Transmission and Distribution networks include controlled shunt and series reactive power, such as Static Var Compensator (SVC), Static Compensators (STATCOM) Thyristor Controlled Series Compensation Systems (TCSC), as well as devices capable of transferring active power between its terminals and provide shunt and series reactive power control, as well as devices with energy storage capability. Other types of devices may be developed as it becomes necessary to have more control over AC networks because of the need for increased power flows on the existing power lines in the AC networks (What is FACTS). The concise definition by IEEE for FACTS is: “Alternating current transmission systems incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability” (Larsen and Weaver 1995; Larsen and Sener 1996). The core technologies in FACTS controllers utilize power semiconductors, which enable faster response than what is achievable with electromechanically switched systems. FACTS controllers can be used to modulate injection of reactive power that can be used to stabilize the power system after a significant disturbance.1 Some FACTS controllers can also inject active power for system damping. That is, FACTS controllers are beneficial primarily where the AC system exhibits transient or dynamic stability limitations or where the duty cycle imposed on mechanically reactive power control systems or active power flow control systems are limited. This Green Book contains information about application issues, benefits of various controllers and trade-offs between conventional and FACTS controllers.

2

Electric Power Fundamentals

It is a fact of life of electric power flows that power flowing through an electric circuit also leads to power flowing into inductances in the circuits and capacitances surrounding the circuits. The energy stored in inductances and capacitances is not Reactive power is used to describe electromagnetic energy flows that do not perform any work.

1

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Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A. . .

5

associated with any work as contrasted with the active power flows. The stored energy is referred to as reactive power, which is basically a mathematical concept arising from the use of single frequency phasor mathematics. Energy stored in inductances and capacitances occurs in Direct Current (DC) as well as AC circuits although in a DC circuit, the energy stored in inductances and capacitances only flows when there is a change in the voltage or current flows. In an AC system, this occurs continuously because of the change in voltage and current polarities during each AC cycle. In fact, excessive amount of reactive power poses limitations on the length of overhead transmission lines as well as underground transmission cables when used for AC power transmission. That is, the amount of reactive power flowing in an AC system must be controlled in order for power to be delivered through an AC circuit. The issues with reactive power were well addressed by Charles Concordia as follows: “But why should we want to transmit reactive power anyway? Is it not just a troublesome concept, invented by the theoreticians, that is best disregarded? The answer is that reactive power is consumed not only by most of the network elements, but also by most of the consumer loads, so it must be supplied somewhere. If we cannot transmit it very easily, then it ought to be generated where it is needed. ——— There is a fundamental and important interrelation between active and reactive power transmission. We have said that the transmission of active power requires a phase displacement of voltages. But the magnitudes of these voltages are equally important. Not only are they necessary for power transmission but they must be high enough to support the loads and low enough to avoid equipment breakdown. Thus we have to control and, if necessary, to support or constrain, the voltages at all the key points in the network. This control may be accomplished in large part by the supply of consumption of reactive power at these points” (Concordia 1982). A special problem is associated with some industrial processes such as arc furnaces. Their operation can create large fluctuations of the active power, which translates into large, rapid voltage variations that lead to flicker in electric lights and can cause electric equipment to malfunction.

2.1

Early Developments of Power Transmission Theories

The theory for how long transmission lines behave was actually developed by telecommunications engineers after Samuel Morse in the 1830s and 1840s developed a practical method for message transmission using DC signaling combined with a code based on short and long pulses (Library of Congress). However, the square pulses used for the message transfer at the transmission end arrived at the receiving end as pulses with rounded edges because the higher frequencies contained in the pulsed signals were attenuated faster than the lower frequencies. Therefore, after a certain length of the telegraph line, the received pulses had been rounded off to the degree that the received signals were not possible to decipher. This lead to research about how to deal with the distortion of the coded signals as a function of distance.

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In 1855, Lord Kelvin proposed a law for prediction of the maximum operating speed for telegraph lines with negligible inductance and capacitive leakage (Martin 1969). This was followed by Heaviside, who in 1887 published a fundamental theory for how distortion-free transmission over a pair of wires would be possible if the ratio of the series resistance and the line inductance was equal to the ratio of the shunt conductance and the capacitance between the wires (Heaviside 1894). Heaviside’s analysis provided a foundation for how transmission lines behave although for long-distance power transmission reducing the shunt conductance around the conductors is not an option since minimization of the line losses is an important objective for efficient transfer of power. As is well known to electrical engineers, in a low loss overhead transmission line the capacitive charging current flowing into an open-ended long-transmission line will cause the voltage at the end of the line to increase. This is referred to as the Ferranti effect (Steinmetz 1971). Using antenna theory, if the line has the length a quarter wave at the applied power frequency voltage (1,500 km for 50 Hz and 1,250 km for 60 Hz), the voltage will be infinite and the current goes to zero, which of course does not represent a practical electric power transmission line. Fundamental frequency resonance at the quarter wavelength is also relevant for long High Voltage Direct Current (HVDC) lines since commutation failures in the HVDC converters will inject primarily large fundamental or second harmonic frequencies, which can be amplified along the line. (Harmonic frequency injection into a long AC or DC line can also lead to standing waves that might lead to interference with communication equipment.) If a long AC line is loaded up such that the load level is equal to the surge impedance of the line (for a lossless line this is equal to the square root of the ratio between the line capacitance and the inductance), the voltage and current will be the same as those at the sending end (CIGRE Green Book on Overhead Lines 2014).

2.2

Reactive Power and Voltage Control in AC Systems

Power engineers have long understood how to change the impedance of long lines such that the voltage along the line can be maintained over a range of loads from zero to some desired level (Miller 1982a). Theoretically, this can be achieved by installing synchronous condensers at multiple points along the line since these machines can be controlled to keep the line voltage constant for large variations in the line loading (Baum 1921). Compensating by inserting capacitors in series with the line conductors make the line appear to be shorter than it physically is. Compensation by inserting reactors in between the conductors and ground lowers the capacitive currents and thus reduces the Ferranti effect under low load conditions (Das 2002). Also, shunt capacitors reduce the inductive reactive power generated in the line at high loads, which keeps the receiving end voltages within a desirable boundary but can lead to high overvoltages from line to ground if the load is suddenly interrupted and the capacitor banks remain connected to the line (Miller 1982b).

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7

Reactive power compensation of lines by inserting capacitors in series was also recognized as a means to enable power to be transferred over long distances. This would be attractive for transfer of power from hydrogenation facilities often located far from the load centers. An early demonstration of such a system was the installation of a series capacitor bank in New York State (Shelton 1928). The need for electric power in Sweden after the Second World War combined with the availability of hydropower in northern Sweden led to application of series capacitors in the late 1940s in a newly developed 400 kV system (Jancke and Åkerström 1951). This was followed by installations of series capacitor banks in among other places the West Coast of the USA and Canada. However, as was predicted by Concordia, capacitive series compensation of AC lines could lead to subsynchronous resonance (SSR) when steam turbine generators were connected to such lines (Concordia and Carter 1941; Bodine et al. 1943). In fact, turbine shaft damage occurred in the Mohave generating station in the USA, as a result of SSR between the generator and series compensated lines connected to the generating station (Hall and Hodge 1976). It was determined that series compensation of lines connected to large turbo-generators could be an issue. However, SSR has not been an issue for hydro-generator plants and systems. In sparse, integrated power systems the power does not always flow through the desired path and in such systems so-called loop flows are often a critical issue. In situations where series compensation is not a viable approach, phase-shifting transformers are the preferred solution. Such phase shifters can be used to adjust the power flows by means of load tap changers that will adjust the phase angle between the two sides of the phase shifter but the insertion of the phase shifter in the circuit will lead to increased reactive power generation because the phase shifter inserted in the circuit will increase the series inductance in the circuit. This is an inherent part of the electric power system that needs to be controlled.

2.3

Long-Distance Power Transmission

Further to the topic of long-distance power transmission, we have in the USA the Oak Ridge National Laboratory report (ORNL) “Comparison of Costs and Benefits for DC and AC Transmission” (Diemond et al. 1987). This report is of considerable historical interest. Published in February 1987, it was led by Cliff Diemond and Gene Starr (Bonneville Power Administration) and edited by Willis Long (University of Wisconsin). This report presents information intended to assist electric utility system planners in making economic comparisons between equivalent AC and DC transmission systems. In doing so, it sets forth operational characteristics of the two systems, including: • • • •

Controllability of AC and DC systems Asynchronous interconnection using DC Power flow modulation by DC and AC systems AC voltage control by AC and DC systems

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• • • • •

W. Long and S. L. Nilsson

Power routing by AC and DC controls Increased power density over a transmission corridor by using DC Unchanged AC power flows and short circuit levels by using DC Control of short circuit impact by using AC techniques Reduced environmental impact in a DC line as compared with an AC line

For AC systems, information is provided on the use of series and shunt compensation to increase power transmission while maintaining stability and acceptable voltage profiles. Examples of sample calculations are provided, together with curves for comparing alternatives. The cost data for AC substations, DC and AC transmission lines, and DC underground cables are also presented, but these data points are dated and might not be representing the technology options available at present. However, the included techniques for calculating total costs (including the capitalized cost of losses) might still be useful.

2.4

Special Industrial Voltage Control Issues

Power electronic–based systems referred to as Static Var Compensators (SVCs) were developed in the 1970s to address these issues. The first experimental application of an SVC system for transmission line damping was the EPRI-Minnesota Power & Light and Westinghouse project commissioned in 1978. The system installed by MP&L at the Shannon substation would enable an 80 MW increase (from 320 to 400 MW) in the power from Manitoba to Minnesota.

2.5

Power Transfers from Distant Generators to Load Areas

The tools available to the power system planners and operators for management of the power flows and the reactive power generated as a part of the power flows were systems comprised of generators, synchronous compensators, shunt reactors and capacitors, and series capacitor banks. The power electronic alternative was limited to SVC systems, which were mostly used for voltage control at industrial sites. The oil embargoes of 1974 and 1979 dramatically changed the situation because the high cost of oil impacted the cost of electric energy in areas that relied on oil-fired power plants. The much higher energy cost also caused the cost of steel produced by older, energy-inefficient steel processes used in the USA to become noncompetitive in comparison to the more energy-efficient steel plants in other countries. The result was the steel production in the USA was shut down. Since these plants were in areas primarily served by electric power plants using coal, there was a surplus of power from coal plants in the mid-West in the USA but the oil-powered power plants produced high-cost electricity. The idea was put forth

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that if the high voltage transmission system between the mid-West and the southern states in the USA could be used to bring low-cost coal-based power to the oil using regions, some of the economic dislocations could be alleviated (Tice et al. 1984). This would require massive amounts of reactive power compensation equipment and also addition of systems that could be used to boost the power flows through the high power circuits. It would also require means to handle outages or disturbances in the system if some high power link would be interrupted. That is, system emergencies would not be allowed to cause a collapse of the power systems. This led to EPRI’s development of an ambitious plan to develop technologies that can be used to manage the active power flows in an AC system as well as manage the reactive power generated from high power flows on existing AC lines. The idea was to enable the use of any existing thermal capacity available in the existing power transmission lines for power flows from regions with surplus power to regions with a demand for lower cost power. A caveat was to do this without jeopardizing the reliability of the existing power system. This is how EPRI’s Flexible AC Transmission System (FACTS) development project arose (Larsen et al. 1992). The emphasis of the EPRI project was to develop thyristor controlled series capacitor (TCSC) systems for power flow control and Static Compensators (STACOM) systems for voltage control (Damsky 1992; Nilsson 1998).

3

FACTS Green Book’s Scope

This CIGRE Green Book is a collection of information intended to help power system planners, engineers, and operators navigate the increasingly complex FACTS options for how to manage the active and reactive power control technology options. The information is contained in the following: AC Systems • ▶ AC System Characteristics • ▶ AC Network Control Using Conventional Means • ▶ AC Network Control Using FACTS (Flexible AC Transmission Systems) Controllers Technical Description of FACTS Controllers • • • • •

▶ Power Electronic Topologies for FACTS ▶ Technical Description of Static Var Compensators (SVC) ▶ Technical Description of Static Compensators (STATCOM) ▶ Technical Description of Thyristor Controlled Series Capacitors (TCSC) ▶ Technical Description of the Unified Power Flow Controller (UPFC) and Its Potential Variations

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Applications of FACTS Controllers • • • • • •

▶ Controllers Using the Saturation of Iron for AC Network Control ▶ Development of Magnetically Controlled Shunt Reactors in Russia ▶ Application Examples of SVC ▶ Application Examples of STATCOM ▶ Application Examples of the Thyristor Controlled Series Capacitor ▶ Application Examples of UPFC and Its Variants FACTS Controller Planning and Procurement

• • • •

▶ Economic Appraisal and Cost-Benefit Analysis ▶ FACTS Planning Studies ▶ Environmental Considerations for FACTS Projects ▶ Procurement and Functional Specifications for FACTS Controllers Implementation of FACTS Controllers

• ▶ FACTS Controller Integration and Design Studies • ▶ FACTS Equipment Design and Testing • ▶ Commissioning of FACTS Controllers FACTS Operation and Lifetime Management • ▶ Operation of FACTS Controllers • ▶ Lifetime Management of FACTS Controllers

References Baum, F.G.: Voltage regulation and insulation for large power long distance transmission systems. J. AIEE. 40, 1017–1032 (1921) Bodine, B., Concordia, C., Kron, G.: Self-excited oscillations for capacitor compensated longdistance transmission systems. Presented at the AIEE National Technical Meeting, New York, 25–29 Jan 1943 CIGRE Green Book on Overhead Lines, Section 1, Chapter 4.2, CIGRE, Paris (2014) Concordia, C.: Foreword. In: Miller, T.J.E. (ed.) Reactive Power Control in Electric Systems. John Wiley & Sons, Inc., New York, NY, USA (1982) Concordia, C., Carter, K.: Negative damping of electrical machinery. Presented at the AIEE winter convention, Philadelphia, 27–31 Jan 1941 Damsky, B. (ed).: Proceedings: FACTS Conference 2, EPRI report TR-101784, December 1992, Electric Power Research Institute, Palo Alto Das, J.C.: Load Flow over Power Transmission Lines, Chapter 10. In: Power Systems Analysis: Short-Circuit Load Flow and Harmonics. CRC Press (2002) Diemond, C.C., Starr, G.: Comparison of costs and benefits for DC and AC transmission. In: Long, W.F. (ed.): Oak Ridge National Laboratory Report ORNL-6204, Oak Ridge (1987)

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Hall, M.C., Hodge, D.A.: Experience with 500-kV subsynchronous resonance and resulting turbine generator shat damage at Mohave generating station. Analysis and control of subsynchronous resonance, IEEE PES Special Publication 76 CH 1066-0-PWR, pp. 22–29 (1976) Heaviside, O.: Electrical papers (1894). https://archive.org/details/electricalpapers02heavrich. Accessed 28 Jan 2018 Hingorani, N.G.: High power electronics and flexible AC transmission systems. IEEE Power Eng. Rev. 8(7), 3–4 (1988) Jancke, G., Åkerström, K.F.: The series capacitor in Sweden. Presented at the AIEE Pacific general meeting, Portland, 20–23 Aug (1951) Larsen, E., Sener, F.: FACTS applications, IEEE FACTS Working Group and IEEE FACTS Application Task Force (1996) Larsen, E., Weaver, T.: FACTS overview, IEEE FACTS Working Group and CIGRE FACTS Working Group (1995) Larsen, E.V., Miller, N.W., Nilsson, S.L., Lindgren, S.R.: Benefits of GTO-based compensation systems for electric utility applications. IEEE Trans. Power Deliv. 7(4), 2056–2064 (1992) Library of Congress, 1793 to 1919: https://www.loc.gov/collections/samuel-morse-papers/articlesand-essays/invention-of-the-telegraph/. Accessed 28 Jan 2018 Martin, J.: DC signaling. In: Martin, J. (ed.) Telecommunications and the Computer, pp. 126–136. Prentice Hall (1969). Library of congress # 78-76038 Miller, T.J.E.: 1.5.2 voltage regulation. In: Miller, T.J.E. (ed.) Reactive Power Control in Electric Systems, pp. 13–18. Wiley (1982a) Miller, T.J.E.: Passive shunt compensation. In: Miller, T.J.E. (ed.) Reactive Power Control in Electric Systems, p. 108. Wiley (1982b) Nilsson, S.L.: Experience and use of FACTS. EPSOM ’98, Zürich, Sept 1998 Shelton, E.K.: The series-capacitor installation at Ballston., New York. Gen. Electr. Rev. 31, 432–434 (1928) Steinmetz, C.P.: Lectures on electrical engineering, vol. III. Dover Publications, New York (1971) Tice, J.B. et al.: New Transmission Concepts for Long Distance Energy Transfer for Oil and Gas Displacement, Proceedings, American Power Conference, vol. 46, pp 476–483 (1984) What is FACTS? http://b4.cigre.org/What-is-SC-B4. Accessed 28 Jan 2018

Willis F. Long, Professor Emeritus, Electric Power Systems, University of Wisconsin-Madison, USA. Willis F. (Bill) Long has been with the Departments of Engineering Professional Development and Electrical and Computer Engineering, University of Wisconsin-Madison) since 1973, serving as EPD’s Program Director, Electric Power Systems. Dr. Long’s principal research interests are in power electronic applications in electric utility systems. He is a Life Fellow of IEEE and has chaired several Power and Energy Society Committees and Working Groups. He is the recipient of the 2008 Uno Lamm HVDC Medal for Leadership and Relevant Contributions to the Spread of Knowledge and Promotion of HVDC Technology Among Power System Engineers and Scientists. He is a Distinguished Member of CIGRE, recipient of the 2009 Technical Committee Award, and immediate past Secretary of Study Committee B4, HVDC Links and AC Power Electronic Equipment. In 2012 he received the Philip Sporn Award from the US National Committee of CIGRE for Cumulative Career Contributions to the Advancement of the Concept of System Integration in the Theory, Design, and/or Operation of Large High-Voltage Electric Systems in the United States. Bill is a registered Professional Engineer in Wisconsin, USA. He is an active outdoorsperson and teaches special topics in mathematics to students at Marquette Elementary School.

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Stig L. Nilsson, Principal Engineer, Exponent, Inc., USA. Stig Nilsson started out working for the Swedish State Telephone Board with carrier communication systems. Following this, he worked for ASEA (now ABB) with HVDC systems and for Boeing with computer system developments. During his 20 years with EPRI in USA he initiated in 1979 the development of digital protective relaying system developments and in 1986 EPRI’s FACTS initiative. In 1991 he was awarded a patent on Apparatus for Controlling the Reactive Impedance of a Transmission Line. Stig Nilsson is a Life Fellow of IEEE. He has chaired the IEEE PES T&D Committee, the IEEE Herman Halperin Electric Transmission and Distribution Award Committee, the IEEE PES Nari Hingorani Facts and Custom Power Awards Committee, several IEEE Fellow nomination review committees, been a member of the IEEE Standards Board, IEEE PES subcommittees and working groups. Stig Nilsson has been the US Representative and Secretary of CIGRE Study Committee B4 on HVDC and Power Electronics. He is the recipient of the 2012 I.E. PES Nari Hingorani Facts and Custom Power Awards. He received the CIGRE U.S. National Committee Philip Sporn Award and the CIGRE Technical Committee Award in 2012. He has also received the CIGRE Distinguished Member Award for active participation in CIGRE Study Committees and the USNC of CIGRE (2006); and the CIGRE USNC Attwood Associate Award in 2003. Stig Nilsson is a registered Professional Engineer in the state of California, USA.

Part II AC Systems

2

AC System Characteristics Stig L. Nilsson, Manfredo Lima, and David J. Young

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Early Developments of Electric Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Electric System Analysis Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 AC Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Early Developments of Electric Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 AC Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Power System Frequency Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Transmission Line Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Simplified Power Flow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Analysis of Three-Phase Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Harmonic Network Analysis and Other Special Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Power System Time Domain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Maximum Stable Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Power Transfer into a Resistive Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Per-Unit System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Power Transfer Through Long Overhead Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Load Limit for Uncompensated Long Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Transient Stability of Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16 16 17 26 26 28 30 30 33 35 37 38 40 40 43 44 44 46 48

S. L. Nilsson (*) Electrical Engineering Practice, Exponent, Sedona, AZ, USA e-mail: [email protected]; [email protected] M. Lima Transmission Planning and Studies Department, Chesf, Recife, Brazil Pernambuco University, Recife, Brazil e-mail: [email protected] D. J. Young Stafford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_2

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Abstract

Electric power has become indispensable to most people in the world. It is transmitted either as direct current (DC) or as alternating current (AC). DC power is used to transfer large blocks of electric power at high voltage levels over long overhead lines or through underground or undersea cables. A significant amount of the AC power delivered to consumers is converted to DC before it is used to operate power electronic devices and various industrial processes, but DC power cannot be transformed to a higher or lower DC voltage level without first being converted to AC in an intermediate step. Consequently, AC power has become the dominating technology for transmitting and distributing the generated electric power to the end users. This chapter discusses the basic characteristics of AC electric power generation, transmission, and utilization. In order to do this, the fundamental scientific discoveries and concepts are presented, and some of the engineers and scientists and their contributions to the development of electric power systems are also discussed.

1

Introduction

1.1

Early Developments of Electric Theory

Electric power is now an indispensable commodity to most people in the world. Most power is generated by alternating current machines and transmitted either by direct current (DC) systems in which the polarity of the voltage and direction of the current flows are unchanging or by alternating current (AC) systems in which the polarity of the voltage and current changes periodically with a frequency defined by standards. DC power is primarily used to transfer large blocks of electric power over long, high-voltage overhead lines or through underground and undersea cables. It is both interesting and ironic that a significant amount of the AC power delivered to consumers is then converted to DC before it is used to operate power electronic devices and many industrial processes. The reason for this is that DC power cannot be transformed to a higher or lower DC voltage level without first being converted to AC in an intermediate step. AC power is therefore the dominating technology for transmitting the generated electric power to the users. This was not the case in the early days of electric power system developments. In the earliest days of the use of electricity, after Swan and Edison had independently developed satisfactorily operating incandescent lamps, local DC distribution networks sprang up to supply electric power to users from a nearby generator, driven by steam or water power.1 Although light provided by arc lamps was already being 1

Many scientists worked on making incandescent light sources beginning with Sir Humphry Davy in England in 1802. Sir Joseph Swan and Thomas Edison both made major breakthroughs on the design of electric light bulbs in 1877–1879, but the Edison vacuum light bulb with a carbon filament was the first practical, relatively reliable light bulb that made it into the market. http:// edisontechcenter.org/incandescent.html#inventors

2

AC System Characteristics

17

used, the incandescent lamp had the potential to provide small, long-lasting, and reliable light bulbs in domestic and commercial premises.2 Thus, the initial commercial driving force behind the development and growth of electric power distribution systems was to provide electric light. However, prior to the development of an electric light, means to generate electric power had to be developed. A British scientist, Michael Faraday, had discovered in 1831 that if electric current flowed in a conductor, it was possible to induce a current flow in a second, nearby, conductor by moving the first conductor and also by creating a changing current flow in the first conductor to induce a current in the second conductor (Chisholm 1911). This is the so-called induction effect, which was crucial in allowing electricity to be transformed from a curiosity into a powerful new technology. Several years after his first experiments, Faraday returned to the study of electricity and magnetism. He formed two separate windings, one on each side of an iron ring. When he energized one winding from a battery, he observed a transient current in the other winding; when he disconnected the battery, the second winding experienced another brief current but in the reverse direction. Faraday recognized this as electromagnetic induction – a current in one winding had magnetized iron, which in turn had induced a current in another winding. This was the prototype of a transformer. Another experiment involved a multi-turn spiral winding on a paper cylinder; moving one end of a long bar magnet rapidly into and out of the cylinder caused an alternating current to flow in the winding. He mounted a copper disc on an axle between the poles of a horseshoe magnet. When the disc was made to spin, he collected a constant current from sliding terminals on the axle and the rim of the disc. These are the fundamental discoveries that describe the functioning of generators, motors, and transformers needed for generation, transmission, and utilization of electric power.3

1.2

Electric System Analysis Fundamentals

1.2.1 Ohm’s Law for DC and AC Circuits Electric circuit theory had to be developed for design and analysis of electric power systems. It began with some very basic discoveries about the relationships between voltage and current flows.

Sir Humphry Davy constructed the first arc lamp (1807), using a battery of 2,000 cells to create a 100-millimeter (4-inch) arc between two charcoal sticks. When suitable electric generators became available in the late 1870s, the practical use of arc lamps began. The Yablochkov candle, an arc lamp invented by the Russian engineer Paul Yablochkov, was used for street lighting in Paris and other European cities from 1878. https://www.britannica.com/technology/arc-lamp 3 Faraday also determined the speed of light. 2

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The German (Bavarian) scientist, Georg Ohm, had discovered that the current flow from a direct current (DC) voltage source was inversely proportional to the resistance to current flow in the circuit.4 That is: I DC ¼

V DC R

(1)

where: IDC is the direct current in amperes. VDC is the DC voltage from the source in volts. R is the resistance in the circuit in ohms (named in honor of the inventor). The term for the inverse of resistance is conductance (1/R) with a unit called Siemens. The electric power (P) dissipated in the circuit described by Eq. 1 is the product of the voltage and the current, i.e.: P ¼ V DC I DC ¼

V 2DC ¼ RI 2DC R

(2)

A magnetic field surrounds a current flow whether through space, as during a lightning strike, or through a conductor. It takes energy to establish the magnetic field, which delays the current rise though the conductor. The energization transient current rise of a circuit when connected to a DC voltage source is described by the following simple differential equation: V DC ¼ iR þ L

di dt

(3)

where: L measured in Henry (H) is the so-called inductance of the circuit. Equation 3 shows that at time zero, when the current is zero, the rate of change in the current is inversely proportional to the magnitude of the inductance L. When the time goes to infinity, the rate of change of the current is zero, and the equation reverts to Ohm’s law as shown in Eq. 1.

4

These equations should be well known to all who have taken elementary physics and mathematical courses. The equations are valid for quasi-stationary electrical systems only (no radiation). They are just repeated here as an introduction to the development of the requirements for power system design and operation.

2

AC System Characteristics

Fig. 1 Step response of a first-order linear system

19 1.00 0.90 0.80 0.70 0.60

63% = time constant τ=L/R

0.50 0.40 0.30 0.20 0.10

α

0.00 -0.10

Assuming that the current at time zero is zero, then the solution to the differential equation (Eq. 3) is the well-known equation: i¼

 t V DC
1  e L = R R

(4)

where: e is the natural logarithm, approximately equal to 2.718281828459. t is the time in seconds. The ratio of L/R is the time constant, τ, for this simple circuit. It is the time at which about 2/3rds (63%) of the total change of the current flow has taken place. It can be expressed as the tangent of an angle α, where α is the slope of the response at time zero (Fig. 1). In this simple first-order linear system represented by Eq. 4, 95% of the response is reached when the exponential part of the equation is approximately 1/e3 (i.e., three time constants). After five time constants, the change is more than 99% complete. By using the Laplace transformation where p is the Laplace operator, Eq. 3 can be written as follows, assuming that the current i is zero prior to time zero:5 V DC ¼ iðR þ pLÞ p

(5)

Note that the Laplace transform of a constant is 1/p. This format enables algebraic manipulations of the equation and simplifies the solving of differential equations.

5

The Laplace transform was invented by the French mathematician Pierre-Simon Laplace (1749–1827), and systematically developed by the British physicist Oliver Heaviside (1850–1925), to simplify the solution of many differential equations. https://www.britannica.com/ science/Laplace-transform

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Solving Eq. 5 for i gives the following: i¼

V DC pðR þ pLÞ

(6)

The time domain solution of Eq. 6, which is typically found in lookup tables, is identical to Eq. 4. In the circuit described by Eq. 3, the DC voltage source may be replaced by an AC voltage source with the frequency ω in radians per second (ω is equal to 2πf where f is the frequency in Hz). If the resultant AC current has an amplitude I varying in time as sin(ωt), then, since the rate of change of sin(ωt), is ωcos(ωt), for steadystate conditions, Eq. 3 can be written as vðt Þ ¼ I ðR sin ωt þ ωL cos ωt Þ ¼ I ðR sin ωt þ X L cos ωt Þ

(7)

where ωL is substituted by XL, which is the inductive reactance for frequency f in ohms. Equation 7 shows that there are two orthogonal voltage components: one that is in phase with the current and one that leads the current by 90 . These two components form a right-angle triangle in which the hypotenuse is the square root of the sum of the squares of the two right angle components. This defines an AC impedance with an absolute value [Z], in ohms, equal to ½Z  ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 þ X 2L

(8)

The ratio of these two components is XL sin ϕ ¼ tan ϕ ¼ cos ϕ R

(9)

where ϕ is the angle between R and [Z], so that: R ¼ ½Z  cos ϕ or

R ¼ cos ϕ ½Z 

(10)

X L ¼ ½Z  sin ϕ or

XL ¼ sin ϕ ½Z 

(11)

and

By substituting the expressions for R and XL from Eqs. 10 and 11 into the right side of Eq. 7, the following equation is obtained: vðt Þ ¼ I ½Z ð cos ϕ sin ωt þ sin ϕ cos ωt Þ ¼ I ½Z  sin ðωt þ ϕÞ ¼ V sin ðωt þ ϕÞ

(12)

2

AC System Characteristics

21

That is, the voltage V is leading the current by ϕ radians and the magnitude V of the voltage is equal to V ¼ I ½Z 

(13)

This is the equivalent of Ohm’s Law (Eq. 1) for AC circuits. The admittance [Y] with the units of Siemens (S) is defined as the inverse of the impedance [Z]. Using admittance formulation, Eq. 13 can then be written as V ¼

I ½Y 

(14)

In Eqs. 13 and 14, the absolute values of the impedance and admittance are used. This provides the magnitude of the current but not the phase angle between the voltage and current. Normally the impedance Z is given as a complex number, R  jX, where R is the real component and X is the “imaginary” (quadrature) component. Similarly, the admittance Y has a real component (G) and a quadrature component (B) and can be written as Y = G  jB. The real component of the admittance is called the conductance and the quadrature component is the susceptance. If the absolute values of the impedance or admittance are replaced by the complex impedance or admittance, then Eqs. 13 and 14 will contain both the magnitude and phase angle information as shown in Eq. 12. In the analyses up to Eq. 14 only an inductive reactance has been considered. However, most electrical analysis problems also include a capacitive reactance. Capacitive currents arise when a voltage is applied to an insulator such as vacuum, air, an insulating fluid, or a solid insulating material, because of the electric field that surrounds any energized part in an electric circuit. This field originates from electric charges located at the surfaces of the conducting components. It can be measured in the insulating materials (dielectric) surrounding the charges. The relationship between the charge and, in this example, a steady-state DC voltage is as follows: Q ¼ CV DC

(15)

where Q is the charge in ampere-seconds (As). C is the capacitance of the dielectric system surrounding the charge, measured in farads (F). VDC is the voltage as measured between the point with the charge and some other point in space to which the electric field is referred. If it is assumed that a voltage, v, is increased from zero (i.e., there is no stored energy in the system prior to time zero) to some value V, then a displacement current will flow in the dielectric system, which will then be charged to a voltage V as follows: ð i dt ¼ Q ¼ CV

(16)

22

S. L. Nilsson et al.

Equation 16 describes a system in which a voltage v(t) develops as soon as the current is injected at time zero. If Eq. 16 is rewritten using the Laplace transformation assuming that no charge exists in the system prior to time zero, it will be: i ¼ CF p ðvðt ÞÞ p

(17)

Under this assumption, for steady-state conditions the Laplace operator p can be replaced by the complex operator jω (Gille et al. 1959). Furthermore, using the fact that j2 is defined as (1) and applying an AC voltage v( f( jωt)), the following expressions are obtained: vð f ðjωÞÞ ¼

ið f ðωt ÞÞ ið f ðωt ÞÞ ¼ j ¼ jX C ið f ðωt ÞÞ jωC ωC

(18)

Equation 18 shows how capacitive reactance XC is defined. When the capacitive reactance is compared to the inductive reactance as defined by Eq. 7, it is evident that the inductive reactance and capacitive reactance have different signs. This difference represents a phase shift of 180 between the currents through an inductance and a capacitance. The current lags the voltage in an inductance but leads the voltage in a capacitance. The differential equations used to describe an AC system are often solved directly by means of powerful computer programs based on numerical analysis methods or by means of Laplace equation methods. However, AC circuit analysis is often also performed in the frequency domain in which phasors are described by amplitudes and angles using complex number arithmetic. In the frequency domain Eq. 5 can be re-written by replacing the Laplace operator p with the complex operator jω as follows: F ðvð jωt ÞÞ ¼ iðR þ jX L Þ

(19)

If it is assumed that a complex voltage F(v( jωt)) equal to Ve jωt = V(cosωt + j sin ωt) is applied to a circuit with a complex impedance valid for the frequency ω radians per second of [Z]e jϕ = [Z](cos ϕ + jsin ϕ), then the steady-state current i(t) is as follows: i ðt Þ ¼

V e jωt V e jðωtϕÞ ¼ ½Z e jϕ ½Z 

(20)

The actual instantaneous current as a function of time t is then the real component of Eq. 20.  i ¼ Re

  V j ωtϕ V e cos ðωt  ϕÞ ¼ ½Z  ½Z 

(21)

2

AC System Characteristics

23

Equation 21 is an alternative derivation of Ohm’s law for AC. It shows that the voltage is leading the current by the angle ϕ as is described by Eq. 12 and the magnitude of the current is equal to the magnitude of the applied voltage divided by the absolute value of the impedance as described by Eq. 13. The angle function difference between Eqs. 12 and 21 arises because in Eq. 12 the current is the phase reference, whereas in Eq. 21, the voltage was chosen as the phase reference. If the reactance jXL in Eq. 19 is replaced by a capacitive reactance jXC, then the angle ϕ in Eq. 21 will be positive, which means that the current will lead the voltage by the angle ϕ. If a capacitor is added to the circuit described by Eq. 3, the capacitor current (i) is described by Eq. 17, and the system is then described by a second-order linear equation as follows: d 2 v R dv v þ ¼0 þ 2 L dt LC dt

(22)

If the rate of change of voltage is replaced by the Laplace operator p, the equation becomes as follows: R 1 p2 þ p þ ¼0 L LC

(23)

The general expression for the roots ( p) of this equation is: R p¼  2L

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

R 2 1  2L LC

(24)

It is convenient to simplify the appearance of this equation by substituting the pffiffiffiffiffiffiffi symbols α for R/2L, which is known as the damping factor, and ω0 for 1/ LC, which represents the undamped natural frequency of the capacitor and the inductor. Then, Eq. 23 can be written as p ¼ α 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α2  ω20

(25)

p1 ¼ α þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α2  ω20

(26)

p2 ¼ α 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi α2  ω20

(27)

The two roots of Eq. 25 are

and

24

S. L. Nilsson et al.

The general solution is of the form (Gille et al. 1959): V ¼ Aep1 t þ Bep2 t

(28)

The detailed solutions depend on the relative values of α and ω0. When α is greater than ω0, the transient is overdamped without any transient overshoot in response to a step in the voltage. When the damping factor is reduced so that α < ω0, the circuit is underdamped, and the solution is expressed in complex numbers and has a damped oscillatory response. This is typical for power systems since it is desirable to keep the losses as low as possible and still be able to operate the power system. These equations correspond to those used to describe mechanical systems; voltage can be considered as equivalent to force, and current is equivalent to velocity. In this equivalent model, a mass becomes an inductance, mechanical resistance is the electric resistance, and the mechanical stiffness is the capacitance.

1.2.2 Kirchhoff’s Laws The German (Prussian) scientist, Gustav Robert Kirchhoff, in 1845 announced his mathematical laws that allowed currents, voltages and resistances to be calculated for electric networks. These were extensions of Ohm’s law. One of these laws is the Kirchhoff’s current law that states that the sum of the currents entering a junction or electric node is zero, i.e., the total sum of all the currents entering a node must equal the total sum of the currents leaving the node. This is written as follows: k ¼N X

Ik ¼ 0

(29)

1

where Ik are the individual branch currents as illustrated in Fig. 2. Kirchhoff’s second law states that the sum of all potential differences in a loop of a network with N nodes is also zero. That is: Fig. 2 Node currents sum to zero

I1

I2

I4

I3

2

AC System Characteristics

25

Fig. 3 Branch voltages sum to zero

V12

1

V10

V20

0

k ¼N X

V23

2

V40

ðV kþ1  V k Þ ¼ 0

3

V34

V24

4

(30)

0

where: Vk+1 – Vk is the voltage drop in the branch between nodes k and k+1. Figure 3 illustrates this for the four branch networks marked with red arrows.

1.2.3 Electric Material Properties There are two fundamental material constants used to calculate the inductive and capacitive reactances. For inductance calculations, the material constant is referred to as the permeability, which for vacuum is denoted μ0 with units of Henry/unit length. The permeability of other materials is normally given as a multiplier of μ0 and written as μμ0. A similar material constant for dielectric material is the permittivity denoted by e0 for vacuum with units of Farad/unit length; a multiplier e is applied for other materials and is typically written as ee0 in electrical equations. The two constants μ0 and e0 are particularly significant because they relate to the speed of light (c) in a vacuum, as follows: 1 c ¼ pffiffiffiffiffiffiffiffiffi μ0 e0

(31)

c is almost exactly equal to 300,000 km/s. Furthermore, the wave impedance of free space is Z0 ¼

rffiffiffiffiffi μ0 e0

(32)

Z0 is about 377 ohms in the metric system and is a real impedance (resistance). It is also called the surge impedance which, for transmission lines, is calculated as (CIGRE 2014):

26

S. L. Nilsson et al.

rffiffiffiffi L pffiffiffiffiffiffiffiffiffiffiffiffi ¼ X LX C Z0 ¼ C

(33)

where L, C, XL, and XC are the circuit parameters for the lines and cables. It should be noted that for cables, the dielectric constant for the insulation material in the cable has a dielectric constant that is more than twice the dielectric constant of vacuum, which slows the wave propagation rate to less than half of the speed of light. Furthermore, since C is large (XC small), the surge impedance for a cable is very low. The 33 equations shown above provide the fundamental understanding needed to analyze power transmission systems.

2

AC Power Systems

2.1

Early Developments of Electric Power Systems

Toward the end of the nineteenth century, power system developments were pursued at a rapid pace in Europe and the United States. Lucien Gaulard of France and John Gibbs, a British engineer, demonstrated an AC power transmission and distribution system in London in 1881 (CIGRE 2014). At about the same time, Edison was one of the pioneers developing DC power distribution systems for commercial purposes. In 1882, he set up a DC distribution system of about 90 kilowatts in London (enough to supply about 1000 lamps) and a larger system with a generating capacity of 600 kilowatts, at Pearl Street in Manhattan, New York, in 1882–1883 (Sulzberger 2003a). Edison’s incandescent lamps were designed to operate at 100 volts. To allow for losses in the supply conductors, the dynamos (generators) were designed for 110 volts. Initially Edison used a two-wire system, but later devised a three-wire DC distribution system operating at, respectively, plus and minus 110 volts, with the third conductor at 0 volts. This improved the efficiency of the system, because the third conductor only carried the difference between the currents in the high-voltage conductors. Edison installed many more DC distribution systems, which were successful – up to a point, as they could only cover a very limited area around the generating station. George Westinghouse knew about the AC power distribution system that had been built by Gaulard and Gibbs. This system used “secondary generators” or transformers to step voltages up and down.6 Westinghouse acquired several of the Gaulard and Gibbs transformers in 1885 and the American rights to them in February 1886. Some voltage variation problems of the Gaulard-Gibbs system were solved by William Stanley, who worked for George Westinghouse in 6

The transformer makes use of the induction effect discovered and demonstrated in 1821 by Michael Faraday.

2

AC System Characteristics

27

Pittsburgh, Pennsylvania, USA. By September 1886, the Westinghouse Electric Company had designed the equipment needed to commercialize an AC distribution system. The first trial system was installed in Lawrenceville, Pennsylvania, several miles from the Westinghouse plant and served some 400 lamps for 2 weeks. This same equipment was then moved to Buffalo, New York, where, in November 1886, it became part of the first commercial AC electric power system in North America. By October 1887, more than 30 Westinghouse AC systems were in operation. George Westinghouse also heard about another inventor, Nikola Tesla and his accomplishments. Tesla developed the principal components needed for a system of AC electric power generation and transmission that are universally utilized throughout the world today. He had in November and December 1887 filed for seven US patents in the field of polyphase AC motors, power transmission, generators, transformers, and lighting. Westinghouse realized the importance of Tesla’s inventions, purchased Tesla’s AC patents, and employed Tesla to work on the full-scale development of AC systems. It was recognized early in this development that electric generators and motors would operate best if the electrical driving force could be made constant. In a singlephase AC system with a generator connected to a load through two conductors, a pulsating torque arises as described in Sect. 2.2 and causes undesirable shaft vibrations in the generators and motors installed in the system. The development of polyphase systems eliminated the pulsating torque. Tesla was a proponent of a two-phase, four-wire system in the late 1880s, in which a steady torque was produced when the two-phase voltages were equal and spaced apart by 90 electrical degrees (Tesla 1888). Two-phase systems of this type remained in operation for many decades. A more efficient solution is the three-phase system, described in more detail in Sect. 3.3, in which three equal voltages are spaced 120 electrical degrees apart. In such a system, which only needs three conductors, the torque used to drive the shaft of a generator is constant providing a vibration-free rotating force; when connected to a motor, this will deliver a vibration-free torque to the motor shaft. The first threephase power transmission system was built in Germany in 1891. This was a 100-mile-long AC line operated at 30 kilovolts (kV), supplying power from a hydro-generator at Lauffen to Frankfurt (CIGRE 2014). The line was installed by the Oerlikon Company (Sulzberger 2003b). Special designs of transformer (e.g., using the Scott connection) enable two-phase and three-phase systems to be linked together (Heathcote 2007). Early power stations were primarily coal-fired steam-generating stations, which required a reliable supply of water, access to a good transport system, and a sizeable area of land for stockpiling coal and for storage and disposal of waste products. Residents living close to the plants disliked the smoke pollution and, as urban land prices increased, there was pressure to locate generating stations remotely from residential areas. This was possible after Tesla’s improvements to transformer design facilitated this remote location of generating stations. Transformers convert low-voltage, high-current AC electric power sources to high voltages and low currents for efficient power transmission across high-voltage lines to load centers.

28

S. L. Nilsson et al.

The input power to a transformer equals the output power (minus a small amount of losses). At the end of the transmission line, the power is converted back to low voltage and distributed to loads. The availability of efficient transformers also enabled power from hydroturbines to be harnessed. Hydropower plants could only rarely be located close to population centers and therefore required long transmission lines to deliver power to the users. This was also a strong driving force behind the development of high-voltage transmission systems. The inherent difficulties with these developments are discussed in ▶ Chap. 1, “Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology.”

2.2

AC Power

AC power systems of today are operated with almost constant frequencies, but the world is split between two base system frequencies. One is 50 cycles per second (Hertz abbreviated Hz) and the other is 60 Hz. Systems using 50 Hz cannot be directly interconnected to systems using 60 Hz and vice versa. Some countries, for example, Japan, are split between 50 and 60 Hz regions. There are also other system frequencies in use for special applications. One of these is 400 Hz, which leads to lighter weight of generators and motors and therefore is used for marine and aeronautical power systems where transmission and distribution distances are short. In contrast, some single-phase traction (train) systems are operated at lower frequencies such as 162/3 Hz (50 Hz divided by 3); the inductive voltage drop, as described by Eq. 6, is smaller for low frequencies, and therefore the distance between traction feeder substations can be greater than if a 50 Hz supply were to be used. Figure 4 illustrates a single-phase alternating current system supplied by a generator whose voltage varies sinusoidally with time. If the frequency of this wave is f Hz with the angular frequency, ω = 2πf, then the magnitude of the voltage varies between plus and minus a maximum value, Vmax, which is the amplitude or crest value of the applied voltage. The instantaneous voltage v(t) (shown in Fig. 4 with arbitrary scales for illustration) is then vðt Þ ¼ V max sin ωt

(34)

If the generator is connected to a resistor (without any inductance), then in accordance with Eq. 12, Fig. 4 shows that the current will also vary sinusoidally with time and in-phase with the voltage: i ðt Þ ¼

V max sin ωt ¼ I max sin ωt R

(35)

The instantaneous power dissipated in the resistance is the product of the voltage and the current, similar to Eq. 2 for DC. Thus the instantaneous power for AC, with the unit of watts (W), is described as

2

AC System Characteristics

29

Fig. 4 Single-phase AC voltage, current, and power waveforms

p ¼ vi ¼ i2 R ¼ RðI max sin ωt Þ2 ¼ 0:5RðI max Þ2 ð1  cos 2ωt Þ

(36)

As is shown in Fig. 4, the AC power is only produced when the voltage and current are non-zero and have the same frequency. Furthermore, in a single-phase system, the power varies with twice the power frequency, and its average value is half of its crest value. In AC systems, the effective values of sinusoidally varying voltage and current are equal to the square root of their crest (or amplitude) values; this is the root-meansquare (RMS) value, which is calculated for the current as follows:

I rms

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð 1 T 2 ¼ i dt T 0

(37)

In Eq. 37, the time, T, over which the integration should take place is one full cycle equal to 1/f. The same form of equation applied to the voltage produces an RMS value for the voltage. Equation 37 is valid for any periodic current shape, but for the special case that the current is sinusoidal (without distortions), the RMS value is equal to the square root of the crest value. The equation for the average power can then be written as follows, assuming that reactance is present and causes a phase shift with an angle ϕ between the voltage and current: P ¼ V rms I rms cos ϕ

(38)

The term cosϕ is called the power factor. It arises as a result of the presence of inductances and capacitances in the circuit. These components just store energy for a portion of the cycle and then release the stored energy for an equal portion of each cycle. Consequently, they do not produce any active power, and the energy circulation is therefore termed reactive power, abbreviated as vars and denoted by the symbol Q, with the unit volt-ampere reactive or var which is calculated as

30

S. L. Nilsson et al.

Q ¼ V rms I rms sin ϕ

(39)

When the angle ϕ is non-zero, the simple product of voltage and current (VrmsIrms) is called the apparent power, denoted by S, with the unit volt-ampere (VA). The relationship between the three different power expressions is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ P2 þ Q2

(40)

An alternative way to express voltage and current is to use the complex formulations V=Vrmse jα and I = Irmse j(αϕ). The complex power can then be calculated using the conjugate of the current equal to I = Irmse-j(αϕ): S ¼ V I  ¼ V rms ejα I rms ejðαϕÞ

(41)

The voltage and current used in Eq. 41 are the RMS values of the voltage and current calculated using Eq. 37. If the voltage and current waveforms are distorted by frequency components different from the nominal power system frequency, the apparent power will not have the pure sinusoidal waveforms which are required for accurate calculation of P, the active power component.

3

Power System Frequency Domain Analysis

As described in ▶ Chap. 1, “Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology,” the transmission of electric power on overhead lines was investigated by Heaviside, who studied the behavior of telegraph lines that were being built beginning in the mid-1800s. In 1887 he published a fundamental theory for how distortion-free transmission over a pair of wires would be possible if the ratio of the series resistance and the line inductance was equal to the ratio of the shunt conductance and the capacitance between the wires. Many of the equations that are still in use for analysis and design of electric transmission lines were originally developed by Heaviside (1894). The equations he developed for telegraph lines are also valid for electric power circuits, although power transmission is at a single frequency, typically 50 or 60 Hz. Also, for electric power transmission, losses have to be minimized to achieve high system efficiency.

3.1

Transmission Line Equations

Figure 5 shows a simplified illustration for a long transmission line illustrated by using short segments of lumped inductance and capacitance models where each element represents a series inductance equal to ΔL and a shunt capacitance of ΔC. The surge impedance as calculated by Eq. 33 is then the square root of the ratio of ΔL and ΔC.

2

AC System Characteristics

31 Receiving end

Sending end

Ix

Is

Vs

Line inductance

Vx

x

Ir

Vr

Line capacitance

a

Fig. 5 Lumped element model of a long transmission line

Equations 42 and 43 are the equations governing the voltage and current distribution for transmission of power through a lossless transmission line and provide a reasonable approximation for the long distance electric power transmission illustrated by Fig. 5. Disregarding the line resistance is a reasonable approximation for long-distance electric power transmission unless the power losses have to be calculated. Equations 42 and 43 are so-called frequency domain equations valid for a single wavelength λ, which is calculated as the speed of light divided by the frequency. The speed of light is inversely proportional to the square root of the dielectric constant multiplied by the permeability as shown in Eq. 22 for vacuum. This equation is also applicable to air environments. Specifically, the equations describe the standing waves on a lossless transmission line of length a (Miller 1982): V ðxÞ ¼ V r cos βða  xÞ þ jI r Z 0 sin βða  xÞ

(42)

and for currents 

 Vr I ð xÞ ¼ j sin βða  xÞ þ I r cos βða  xÞ Z0

(43)

where V is a voltage phasor with a specific frequency, amplitude, and phase angle. I is a current phasor with a specific frequency, amplitude, and phase angle. x is the distance from the sending end to the point on the line where the voltage and current are to be calculated. The load at x = a (the end of the line) is Vr /Ir. Z0 is the surge impedance of the line as defined by Eq. 33. Z0 is a real impedance; that is resistive. L is the line inductance per unit length. C is the line shunt capacitance per unit length.

32

S. L. Nilsson et al.

pffiffiffiffiffiffiffi β is equal to ω LC . pffiffiffiffiffiffiffi Since 1= LC is the propagation velocity (u) along the line. 2π β ¼ 2πf u ¼ λ where λ is the wavelength of the applied AC voltage. These equations lead to the following conclusions: • The voltage profile along a line depends on the power factor of the load. • If the termination impedance is equal to Z0 which means Vr/Ir = Z0, then the voltages and currents are uniform along the entire line (Zx = Z0). • If the line is open (the termination impedance is infinite), the current Ir at the end of the line is zero, but the voltage at the end of the line is higher than at the sending end. It is amplified along the line from x = 0 to x = a by a factor as shown in Eq. 44. This voltage rise is the so-called Ferranti effect as described in ▶ Chap. 3, “AC Network Control Using Conventional Means”: Vx ¼ Vs

cos βða  xÞ cos ðβaÞ

(44)

Equation 45 is the result of setting x = 0 in Eq. 44: V 0 ¼ V s ¼ V r cos βða  0Þ ¼ V r cos θ

(45)

where θ is the electrical length of the line expressed in radians or wavelengths. Since there is no active power transfer into the line when the receiving end is open, Vs and Vr must be in phase: • If a line is opened to disconnect load at the receiving end, the voltage at the end of the line will revert to the open-circuit level, but in addition, a transient overvoltage equal to the step change in the current (Δi) divided by the surge impedance (Z0) will travel toward the closed line end. This adds to the overvoltage at the open end. Continuously connected shunt reactors can be used to limit the overvoltage at the open line ends as discussed in ▶ Chap. 3, “AC Network Control Using Conventional Means.” Equations 42 through 45 are valid for both overhead lines and underground cables. For overhead lines, the surge impedance, Z0, is between about 300 and 400 Ω, but for cables it can be between 25 and 40 Ω. This large difference is because the capacitance between the conductors and ground for overhead lines is quite low, but for cables it is very much larger, and this has a big impact for the capacitance C in Eq. 33. In cables this capacitance causes a high charging current to flow, in quadrature with the real (active power) current; this increases the thermal loading of the cable and limits the distance over which AC power can be transmitted through uncompensated cables. For example, a solid dielectric cable at 150 kV has a real

2

AC System Characteristics

33

power transfer capability of only 80% of its thermal capacity at a distance of 70 km, while a fluid-filled cable, which has a higher charging current, is limited to between 20 and 25 km (CIGRE TB 110 1996). A 400-kV solid dielectric cable can be used for up to 50 km, while a fluid-filled cable could not exceed a length of between 10 and 20 km (CIGRE TB 504 2012). In all AC power transmission systems, reactive power compensation is needed for satisfactory control of AC voltages. As described by Miller, reactive power compensation is a complex issue that requires careful analysis (Miller 1982). Lines can, and often must, be compensated to maintain a relatively flat voltage profile along their length, to avoid line overvoltages and undervoltages, and thereby to increase their power handling capacity, as described in ▶ Chap. 3, “AC Network Control Using Conventional Means.”

3.2

Simplified Power Flow Equations

The resistance, series inductance and shunt capacitance of transmission lines and cables are distributed relatively uniformly along the length of the line and cable. An accurate analysis of line behavior requires the use of second-order partial differential equations, but hyperbolic functions are typically used for such analysis (Nolasco et al. 2014). Nevertheless, for simple analytical purposes, it is satisfactory and convenient to represent the impedances as the total, “lumped” quantities of resistance R, series inductive reactance jXL, and shunt capacitive reactance – jXC, and it is often appropriate to analyze electric transmission lines using simple two-port network models as shown in Fig. 6. If such a network contains only linear components, it can be described by means of three equations (Gille et al. 1959; Fink and Beaty 1978; Anderson and Farmer 1996): V s ¼ AV R þ BI R

(46)

I S ¼ CV R þ DI R

(47)

AD  BC ¼ 1

(48)

In these equations A, B, C, and D are factors, which depend on the series and shunt impedances inside the two-port model. A and D are constants, B has the unit of ohms, and C is an admittance with the unit of Siemens. The network can be conveniently described in matrix format as follows: IS

Fig. 6 Two-port network model

VS

IR

Network

VR

34

S. L. Nilsson et al.



VS IS





A ¼ C

B D



VR IR

 (49)

There are two commonly used two-port models. One is a T-link as shown in Fig. 7, and the other is a Pi- link (so called because of its resemblance to the Greek letter Pi, Π) as shown in Fig. 8. The A, B, C, and D constants for the T-link are 

ð1 þ Y Z 1 Þ ðZ 1 þ Z 2 þ Y Z 1 Z 2 Þ ðY Þ ð1 þ Y Z 2 Þ

 (50)

and for the Pi-link are 

ð1 þ Y 2 Z Þ ðY 1 þ Y 2 þ Y 1 Y 2 Z Þ

ðZ Þ ð1 þ Y 1 Z Þ

 (51)

Note that an impedance is only defined for a specific, single frequency. The impedance Z in the Pi-link is equal to Z1 plus Z2 in the T-link, and Y in the T-link is equal to Y1 plus Y2 in the Pi-link. In simple load flow calculations for short lines (up to about 80 km or 50 miles), Y is set to zero, and Z is set to XL or jωL with the resistance in the line assumed to be zero. For longer lines, to improve the accuracy of the models, two or more two-port networks can be connected in series as shown in Eq. 43 for connection between two two-port networks. 

A1 C1

B1 D1



A2 C2

B2 D2



 ¼

ðA1 A2 þ B1 C 2 Þ ðC 1 A2 þ D1 C 2 Þ

ðA1 B2 þ B1 D2 Þ ðC 1 B2 þ D1 D2 Þ

 (52)

Physical line models for high-frequency study purposes are built using multiple T or Pi sections connected in series. This has been used in older transient network analysis (TNA) models built using lumped circuit parameters. These types of system have been replaced by real-time computer models, using the differential equations for transmission lines. For high-frequency transmission line studies such as those used for analysis of switching and lightning surges, the model of the earth’s impedance might have to be included, using Carson’s equations (Olsen and Pankaskie 1983). However, this Green Book will not elaborate further on this topic. IS

Fig. 7 T-link

IR Z1

VS

Y

Z2

IR

IS

Fig. 8 Pi-link

VS

VR

Y1

Z

Y2

VR

2

AC System Characteristics

3.3

35

Analysis of Three-Phase Circuits

All bulk power AC transmission lines are three-phase lines with the three-phase voltages operating at 120 electrical degrees apart, as illustrated in Fig. 9 by the representation of the vertical positions of the tips of the blades in a three-bladed propeller. In a three-phase system, the three individual-phase voltages have equal amplitudes with reference to ground. However, by convention, the voltage V used to describe the system voltage is the phase-to-phase voltage amplitude; that is, the distance between the tips of the propeller blades. Thus, the amplitude of the voltage to ground is the system voltage V divided by √3. The vector sum of the three symmetrical phase voltages is zero. The detailed analysis of an extensive three-phase power system requires equations to be formulated for each of the three phases throughout system; this analysis was, and still is, mathematically demanding even with the use of powerful computers. Charles LeGeyt Fortescue, a Canadian electrical engineer working for Westinghouse, developed a theory for how any set of N unbalanced phasors could be expressed as the sum of N symmetrical sets of balanced phasors known as symmetrical components (Fortescue 1918). For a three-phase system, these are called positive, negative, and zero sequence components. The positive sequence system is the dominant component, rotating in the positive direction from phase A to B to C (or RST, YBG or similar phase notations). The negative sequence rotates A to C to B, and the zero sequence components are all unidirectional. Other similar mathematical theories such as those proposed by Edith Clarke and R.H. Park are typically applied to rotating machine systems (Park 1929; Clarke 1943). However, the symmetrical component theory developed by Fortescue is commonly used to solve asymmetrical power system problems and especially for the analysis of unbalanced system short-circuit faults. The symmetrical component calculations make use of an operator a, which creates a phase shift of 120 and is defined as a ¼ ej120

Fig. 9 An illustration of a three-phase power system



(53)

36

S. L. Nilsson et al.

The square of a (a2) creates a phase shift of 240 , and the cube of a (a3) becomes a phase shift of 360 . The transformation of three voltages in a three-phase system can be calculated using for simplicity matrix formulations as follows: 2

3 2 1 V0 1 4 V1 5 ¼ 4 1 3 V2 1

1 a a2

32 3 1 Vа a2 54 V b 5 a Vc

(54)

where Va, Vb, and Vc, the inputs to the matrix, are the actual three AC system voltages provided with amplitudes and phase angles. The outputs from the matrix calculation are Vа0, the zero sequence voltage Vа1, the positive sequence voltage Vа2, the negative sequence voltage This is illustrated in Fig. 10 which shows the three fictitious measured voltages Va, Vb, and Vc with a graphical representation of the three sequential components. This might depict the AC system voltages during faults but not during steady-state operation of the AC system. The three zero sequence components are marked A0, B0, and C0; the positive sequence voltages are marked A1, B1, C1; and the three negative sequence voltages are marked A2, B2, and C2. The positive sequence system rotates from A to B to C, whereas the phase rotation for the negative sequence system is from A to C to B. The original voltages can be calculated by using the inverse matrix as follows: 2

3 2 Vа 1 4 Vb 5 ¼ 4 1 1 Vc

1 a2 a

32 3 1 V0 a 54 V 1 5 ¼ T 012 V 012 a2 V2

(55)

where T012 is the symmetrical 3  3 matrix. V012 is the 3  1 voltage column vector. Fig. 10 Illustration of the symmetrical component concept

B2

C1 VCA Vc

A1

VBC

Va

Vb B1 C2

VAB

A0 , B0 , and C0

A2

2

AC System Characteristics

37

The currents can also be transformed into symmetrical components. The sum of the three calculated zero sequence currents is then equal to the neutral current In. That is, In equals 3Ia0. For most electric power load flow calculations, only the positive sequence system is used, and the three-phase system is treated like a single-phase system. This is valid for most calculations since the zero sequence and negative sequence voltage and current components of a three-phase power system are normally small. However, for many three-phase high-voltage transmission lines, the impedances (primarily the inductive reactance) for each of the three phases are not precisely equal because the coupling between the phases and to ground is not identical for all of the phases. This is obvious in the case of a flat line configuration where all of the phases are suspended at the same height above ground; the center phase is strongly coupled to the outer phases, but the outer phases are not so closely coupled to each other. This unbalance can usually be corrected by rotating (transposing) the relative positions of the conductors, at intervals along the length of the line, so that each of the three phases has an overall equal coupling to the other phases and to ground. The individual-phase impedances can be converted to sequence components using the following operations shown in matrix form: Z 012 ¼ T 012 1 Z abc T 012

(56)

The T matrix is defined in Eq. 55. The symmetrical impedance matrix Zabc will include the self-impedances on the diagonal and the mutual impedances between the phases of the diagonal (Kundur 1994).

3.4

Harmonic Network Analysis and Other Special Studies

There are numerous new types of generators and loads which incorporate power electronic systems and generate harmonics, such as high-voltage DC (HVDC) systems, wind turbines, and flexible AC transmission system (FACTS) controllers. Consequently, it has become necessary to develop tools to calculate the magnitudes of the harmonic current flows and to assess the effects of these current flows throughout the AC system. This is described in more detail in ▶ Chap. 17, “FACTS Planning Studies.” Accurate harmonic load flow models are not easy to develop (CIGRE TB 139 1999). Furthermore, the AC system harmonic impedances are constantly changing as a result of line switching and generators being switched in or out to match the load demand; in addition, the characteristics of the connected loads are constantly changing, so that it is difficult to create a meaningful impedance plot for a selected point in the AC network. One other issue is that line transpositions which are made in order to balance the power frequency impedances of a line will not balance the harmonic impedances for that same line. Consequently, for the purposes of harmonic filter design, it is usual to study the harmonic impedances

38

S. L. Nilsson et al.

for many circuit conditions and to evaluate, for each harmonic, a locus within which all possible harmonic impedances will lie. Another specialized load flow study requires a DC model of a network in order to calculate the distribution of geomagnetically induced current (GIC) flows that arise as a result of the earth’s magnetic field disturbances caused by solar storms. These very low-frequency currents cause transformer saturation, which can lead to large flows of odd and even harmonic currents. The effects of GIC can be severe (Liu et al. 2009). Modeling of the GIC distribution in the networks also requires an estimation of the DC resistances throughout the network which is being studied. Special studies are needed to scan AC networks to discover if there is any potential for sub-synchronous resonance (SSR) that can cause serious damage to turbogenerator plants. The resonance might be of the torsional interaction (TI) form between series compensated lines and generators, or it could be induction generator effects (IGE) or torque amplification (TA). IGE can occur if there is insufficient electrical and mechanical damping at critical torsional frequencies appearing in the armature circuits of synchronous generators. IGE appears as the side bands between the fundamental power system frequency and the mechanical resonance frequencies in the turbogenerators. TA is a specific stress associated with dumping energy from series capacitors into the generators upon recovery from an AC system short-circuit event. The first two of these SSR types can be studied using frequency scanning of the positive sequence impedance system as viewed from the generator’s bus to determine the damping at the critical turbogenerator frequencies. There are many ways to perform such an analysis by creating Bode, Nichols, or Nyquist plots to evaluate the real component at the critical torsional frequencies (Anderson and Farmer 1996; Gille et al. 1959). TA effects require time domain analysis; see the Sect. 4.

4

Power System Time Domain Analysis

Many power system problems require calculations where time is a variable. Time domain programs are used to study the stability of power systems in response to disturbances such as short circuits inside the power system, loss of loads, or loss of generators. This involves study of the swing behavior of generators and the behavior of the system during and after switching operations and faults. The study of the stability of power systems with multiple generators, many transmission paths, and different loads is complex but can be done if the following features are included in the power system model (Anderson and Fouad 1993): • • • • • •

The system configurations before and after a disturbance The connected loads and their characteristics The synchronous machines affected by the disturbance The excitation systems of the generators The governors of the turbines Other supplementary controls and components of the power system

2

AC System Characteristics

39

Modeling of high frequencies, detailed switching operations, and other similar transient events in a power system requires different computational tools, often including detailed models of individual phases and lines, as well as discrete components such as transformers, circuit breakers, etc. It is desirable to make use of digital computers for such analyses. Breakthroughs in the design of digital computational methods eventually led to the development of the so-called Electromagnetic Transients Program (EMTP) (Dommel 1969; Dommel and Mayer 1974). The developed computational methods can include frequency-dependent components and nonlinearities. For example, the impedance of the ground under the transmission lines is frequency dependent, and surge arresters are nonlinear. EMTP programs are, for example, used for studies of TA effects of turbogenerators, but studies of TA stresses are based on power system transmission line models valid for power system frequencies and therefore may not include all AC system susceptance. A frequent issue, when using EMTP-type programs for the study of power systems in time domains significantly shorter than one period of the nominal power system frequency, is that the circuit impedances have to be modeled in such detail that the model is valid for the upper frequency of interest to the study objective. Leakage inductances and stray capacitances have to be included in the models to produce valid results for the study of interest. It may even be necessary to consider that the capacitance of a wound capacitor is reduced as the frequency of the applied voltage is increased, because there is an inductance between the foil layers that limits the current flow toward the ends of the foil and there is also direct capacitive coupling between the foil layers in the capacitor roll. Similarly, a reactor will behave as a capacitor at some high frequencies because the capacitive coupling between the winding turns of the reactor coil bypasses the inductance of the coils. Transformers will have a complex impedance spectrum because of the complexity of their winding arrangements. The complicated impedance characteristics of bus structures and other equipment may also have to be considered to achieve valid results. As a rule of thumb, a conductor might have an inductance of 1 to 1.5 μH per meter, and the wave propagation time in air along a 1-m conductor would be about 3 ns. While this might not be significant for many studies, a 10-m service drop plus a grounding conductor in series with a 2-nF coupling capacitor might have a resonance point at about 1 MHz, which limits the use of a coupling capacitor for highfrequency transient measurements. If a simulation is conducted using EMTP-type programs, the effect of the time step between calculations also has to be considered. Fixed or variable time steps might be built-in features of some computer programs, in which case the longest time step will be the determining factor in regard to the upper frequency for which the results will be valid. Although smoothing routines might be used in presenting the results, the validity of the results if converted to the frequency domain is limited to a fraction of the “sampling” frequency represented by the time between calculations. For example, if the time step between calculations is 10 microseconds, this is equivalent to a “sampling” frequency of 100,000 Hz but,

40

S. L. Nilsson et al.

depending on what is being calculated, the valid frequency range of the simulation will not exceed 20 to 25 kHz. Therefore, the setting up of a transmission system problem for study in an EMTP program is not easy, and such studies are often performed by specialists.7 EMTP-type programs are still based on quasi-stationary power system models, and it is assumed that there is no electromagnetic radiation from lines or other power system components. This is not correct if time domain phenomena are studied where the coupling from a transient source to the surrounding media can reach the study object faster than the conducted transient. It should be well known that the near field around an antenna cannot be modeled using far-field assumptions, but such mistakes are often made. For example, the effect of a surge on a transformer bushing from closing or opening disconnect switches or breakers may be seen sooner at the bushing by electric field coupling through the air from the switch than the conducted transient traveling along the busbars.8 Also, a reflection of the transient wave from the ground, a nearby conducting objects or an impedance discontinuity in front of or closely behind the source for the transient, will change the temporal characteristics of the transient wave in this simple example assumed to be applied to a bushing. This should make it clear that conventional time domain simulation tools using lumped parameter circuit models should not be used for studies of transients with rise times in the nanosecond to hundreds of nanosecond range. This requires different computer simulation tools (EPRI 1993).

5

Maximum Stable Power Transfer

5.1

Power Transfer into a Resistive Load

A transmission line, as shown in Fig. 11, with a resistive load and a constant voltage at the source can be used to illustrate the power transfer limit for transmission lines. In this simple system, IS is equal to IR, VS = VSe jδ, where δ is the phase angle between VS and VR, and if X = ωL, then the apparent power received at the receiving end is9  SR ¼ V R

7

V S V R jX



¼ VR

  V S cos δ þ jV S sin δ  V R  jX

(57)

EMTP is the name for a commercial program, but an alternative transients program (ATP) and systems in which EMTP is embedded, such as PSCAD, are available. 8 An electromagnetic wave travels one third of a meter per nanosecond in vacuum and slightly less along a conductor. Also, a wave traveling between a conductor and ground travels slower than a wave traveling between two conductors. 9 The star denotes the conjugate of the terms within the bracket.

2

AC System Characteristics

41 IS

Fig. 11 Simple lossless transmission line with resistive load

IR jωL

VS

VR

R

Per Unit Voltage, Active and Reactive Power

1

Resistive Load

0.5

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 Current Receiving End Voltage

Received Power

Reactive Power in Line

Fig. 12 Active and reactive power against load current for Fig. 11 system

SR ¼

jV R V S cos δ þ V R V S sin δ  jV R 2 X

(58)

The active power sent through the line is the real component of Eq. 58: P¼

V RV S sin δ X

(59)

The reactive power component is the “imaginary” part of Eq. 58: QR ¼

V R V S cos δ  V R 2 X

(60)

Thus, the power flow through the line causes a reactive power demand to be developed in the line. The capability of this lossless transmission line to transfer power under various conditions is illustrated in Fig. 12, which shows the active power P and reactive power Q supplied by an infinite source,10 plotted against the load current I. The 10

An infinite source is a generator whose output voltage does not change irrespective of changes to the load.

42

S. L. Nilsson et al.

Receiving End Voltage

1

Resistive Load

0

0

0.1

0.2

0.3 0.4 Received Power

0.5

0.6

Fig. 13 Transmitted power versus receiving-end voltage with a resistive load

variation of receiving-end (load) voltage, VR, expressed in per unit of the supply voltage, VS, is also plotted. When the magnitude of load resistance, R, is reduced, the current and reactive power each increase at different rates, whereas VR decreases. The active power also increases initially as the current increases. For the particular case when R is equal to X = jωL, the active power P reaches its maximum value (given by Pmax = VR2 / R = VS2 / 2R). At this load point, the numerical value of the active power P is equal to the numerical value of the reactive power Q. For this condition the receiving-end voltage VR is equal to VS/√2, and the angle δ is 45 . For this specific value of load resistance, the power has reached its maximum value; any further reduction of load resistance is accompanied by a reduction of both P and VR, whereas Q continues to increase. Figure 13 is a plot of the relationship between the load voltage VR and the transmitted power P, which shows how important it is for the stable operation of a system that voltages at load points should not be allowed to drop very far below the nominal value. It can be seen in Fig. 13 that, as the load increases, the rate at which the load voltage decreases becomes more rapid, eventually leading to a complete collapse of the load voltage when it reaches the nose of the curve. The load characteristic is unstable beyond the nose, and consequently the transferred power drops to zero. This kind of voltage instability is more prone to occur in systems with large inductive impedances. It can be exacerbated by loads that tend to consume constant active and reactive power irrespective of the magnitude of their applied voltage. Loads of this kind include those that are supplied by transformers with on-load tap changers, when the tap changers have an automatic control that attempts to maintain a constant secondary voltage. Ohtsuki, Yokoyama, and Sekine described this effect with an induction motor load (Ohtsuki et al. 1991). A high-voltage DC line controlled to transmit a constant power through the line is another form of constant load. Constant power control can destabilize an AC system. Power transfer into non-ideal loads is

2

AC System Characteristics

43

1.2 A

Receiving End Voltage

1.0

A1

0.8 0.6 0.4

D1

0.2 0.0

D

0.0

0.1

0.2

PF 0.95 Leading

0.3 0.4 0.5 0.6 Received Power PF 0.9 Lagging PF 0.8 Lagging

0.7

0.8

PF 1.0

Fig. 14 Family of voltage-load curves for different power factor loads

illustrated in Fig. 14, which shows a family of voltage-load curves for different power factor loads, including the unity power factor case illustrated in Fig. 13. When the load current has a power factor less than one, it contains a lagging component. In that case, the maximum power capability will be smaller, and the voltage for a given load will be reduced compared with the unity power factor load shown in Fig. 13. For a particular power factor curve and for any power less than the maximum, there are two possible operating points; for example, points A and A1, shown in Fig. 14, are stable because dVR/dP is negative, which means that an increased load will reduce the operating voltage and vice versa for a reduced load. Only the upper, stable values represent possible system operating conditions. However, if the load is increased or the power factor is decreased, the operating point moves toward the “nose” of the curve with a progressive reduction of voltage, which then tends toward a complete collapse of the load transmission. That is, operating points D and D1, shown in Fig. 14, are not possible since, as soon as the nose of the curve is reached, dVR/dP becomes positive and the system will collapse. It is clear from the curves with reduced power factor that a transmission line has a very limited capacity to carry any lagging reactive component of load, but Fig. 14 also shows an interesting result for a load with a leading power factor. This has the double advantage of increasing both the load voltage and the maximum power that can be transferred.

5.2

The Per-Unit System

In power system analysis, it is usually convenient to use a per-unit system to normalize system variables, especially when a great number of transformers are

44

S. L. Nilsson et al.

present, as in an actual high-voltage power system. Compared to the use of the physical units amperes, volts, and ohms, the per-unit system produces computational simplicity by eliminating units and expressing power system quantities as dimensionless ratios. A quantity in per unit is calculated as the ratio of the actual quantity in physical units to a base value of this quantity that has previously been defined. The per-unit (pu) system is normally built on defining a base power and nominal system voltage; a per-unit value in dimensionless units or in percent is obtained as follows: pu value ¼

actual value base value

(61)

If the quantity in pu is multiplied by 100, then the value is in percent of the base value. If the base power S is defined as kVABase, then the voltage and impedance for the base values are as follows: S¼

pffiffiffi 3kV Base I Base

(62)

The base current is defined as kVABase I Base ¼ pffiffiffi 3kV Base

(63)

Since it is assumed that the voltage in this example is given in kilovolts, the base impedance is then Z Base ¼

kV 2Base kVABase

(64)

Using Eq. 61, any calculated quantity can now be converted to pu values. A well-defined per-unit system can minimize computational effort, simplify evaluation, and facilitate understanding of system characteristics. In practice, the base values may be chosen independently and quite arbitrarily, while the other values follow automatically, depending on the fundamental relationships between system variables. Normally, the base values are chosen so that the principal variables will be equal to 1 per unit under rated conditions.

6

Power Transfer Through Long Overhead Lines

6.1

Load Limit for Uncompensated Long Lines

As described above, the power that can be transmitted through a long overhead transmission line is limited by the series inductance of the line and its SIL. Figure 15 illustrates a long transmission line connecting a generator, with voltage VS, to a load

2

AC System Characteristics

45

Fig. 15 Simple long line model

P X/2

X/2 Vm

VS

VR

Fig. 16 Midpoint line voltage VS

Vm

VR

δ/2 δ/2

center which includes a combination of generators and loads and has a voltage VR. To simplify the illustration, the line is shown as a simple series inductive impedance, X (split into two equal parts), and the effects of line resistance and shunt capacitance are ignored. The voltages at the ends of the line, VS and VR, are assumed to be maintained constant and equal for all values of line current I. The voltage, Vm, at the midpoint of the line is equal to VS and VR when there is no load. As the current increases, so does the angle, δ, between the voltages, as described by Eq. 65 and illustrated in Fig. 16. The amplitude of the midpoint voltage begins to decrease and is given by Vm = VS cos δ/2. By symmetry, because VS = VR, Vm will be in phase with the line current, I, and the power flowing through the line will therefore be P ¼ V mI ¼

V SV R sin δ X

(65)

The amount of power transferred, as a function of the angle across the line, is shown in Fig. 17. The power reaches a maximum value, given by Pmax = VS2 / X, if the angle δ shown in Fig. 16 reaches 90 ; with maximum power transfer, the voltage Vm has fallen to 70.7% of VS. If δ increases beyond 90 , then, as shown in Fig. 17, the transmitted power decreases and falls to zero when δ reaches 180 ; the region of operation between 90 and 180 cannot be sustained in steady state and is unstable. When the maximum power in this case is compared with the maximum power transfer in the simple case of Fig. 12, it can be seen that control of the load voltage, VR, has enabled the power transfer to be doubled compared with the condition in which there was a “dead” load and VR was not controlled. It is not practicable to operate near the maximum power condition with a steady-state power angle close to 90 , because a small disturbance could take the angle beyond 90 and, as was discussed in Sect. 4, cause the power transmission to fail.

46

S. L. Nilsson et al. P/Pmax 1

V1,δ1

jX12

V2,δ2

P1

0

90 δ1 - δ2 = δ [deg]

180

Fig. 17 Power angle curve

6.2

Transient Stability of Power Systems

An elementary view of system stability can be arrived as if it is assumed that, as in Fig. 17, there is one turbogenerator connected to a strong power system which is almost an infinite bus (not affected by any disturbance). The generator will be stable as long as the steady-state power angle δ does not exceed 90 . If the steady-state condition is disrupted by a fault or other disturbances, the generator will start to accelerate or decelerate. The mechanical swing equation for this condition is (Kundur 1994) 2H d 2 δ ¼ Pm  Pmax sin δ ω0 dt 2

(66)

where: • H is the inertia constant defined as the kinetic energy in watt-seconds at rated speed divided by the machine’s VA base rating. • ω0 is the nominal power system frequency in mechanical radians per second. • Pm is the mechanical input power to the machine. • Pmax is the maximum output power at δ equal to 90 . This can be rewritten as: d 2 δ ω0 ¼ ðP m  P e Þ dt 2 2H

(67)

where Pe is the electric power load. Equation 66 cannot be solved directly. The power system behavior is nonlinear. It includes saturation of magnetic circuits of generators, nonlinear loads, etc. Many system stability programs linearize the nonlinear components for small signal stability analysis, which is valid because for the system to be stable, it has to be small signal stable.

2

AC System Characteristics

47

A key concept to illustrate the stability of a single machine or a group of machines swinging together (modal equivalent) is the equal area criterion. This can be understood by multiplying both sides of Eq. 67 by 2dδ/dt which leads to Eq. 68 (Kundur 1994): 

dδ dt

2

ð ¼

ω0 ðPm  Pe Þdδ H

(68)

In order for a system to recover its normal operation after any disturbance, the mechanical power input and the electric power loads have to balance after some finite time. This is illustrated for a simple theoretical case shown in Fig. 18. This illustrates a power versus angle curve in which the steady-state power Pm is less than the maximum and the angle is δ1. If a fault occurs on the line and the power transfer falls to zero, the constant mechanical power input to the generator at the sending end will cause it to accelerate when its electrical load is lost; simultaneously, the loss of power into the receiving end will cause its generators to decelerate, but when the receiving-end system is very large, this effect will be small. However, the angle between the generator and the receiving system will begin to increase. Provided that the fault is cleared and the system is restored to normal within a few cycles, power flow will be able to resume, but the angle between the generator and the system will have increased to δ2, and the two systems will still be moving apart. At the angle δ2, the power transfer through the line will be P2; this load is greater than the mechanical input power, and because of the extra load, P2 – Pm, the machine at the sending end will start to slow down (and those at the receiving end will be speeding up), which slows the rate of separation. This recovery process can continue provided that (P – Pm) remains positive and the angle does not reach δcrit. In this simple example, the transfer energy lost during the fault is proportional to the area A1; when the area A2 between δ2 and δ3 (representing the surplus energy after the fault) is equal to A1, the machines at each end of the line will again be running at the same speed but will be separated by a larger angle than in the original steady state. At this point the excess transfer of energy will begin to reduce the transfer angle, leading to an oscillatory period before conditions settle back to steady-state transfer of Pm at angle δ1. The stability margin is indicated by the area Fig. 18 Equal area criterion Pmax A2 Amargin

Pm A1 0

0

δ1

δ2

90

δ3

δcrit

180

δ

48

S. L. Nilsson et al.

Amargin, between the angles δ2 and δcrit. Power system stabilizers are usually fitted on the generators to damp the oscillations to achieve faster return of the system to the post-fault steady-state condition. For the above example, a fault in the AC system brings the load to zero for a short time (which depends on the speed of operation of the protective relaying systems); the integral in Eq. 68 from the initial angle δ1 to the angle δ2 when the fault is cleared and power transfer is restored is ð δ2 δ1

ω0 Pm dδ ¼ A1 2H

(69)

After power restoration, the energy causing deceleration of the machine is equal to ð δ3 δ2

ω0 ðPm  Pe Þdδ ¼ A2 2H

(70)

To be stable, the area A2 + Amargin has to be at least equal to A1, i.e., δ2 must be less than δcrit.

References Anderson, P.M., Farmer, R.G.: Series Compensation of Power Systems. PBLSH! Inc., Encinitas (1996) Anderson, P.M., Fouad, A.A.: Power System Control and Stability. IEEE Press, Piscataway (1993) Chisholm, H. (ed.): “Faraday, Michael”. Encyclopedia Britannica, vol. 10, 11th edn, pp. 173–175. Cambridge University Press, Cambridge (1911). the 1911 Encyclopedia Britannica Cigre Green Book on Overhead lines, Cigre, Paris (2014) CIGRE TB 110: Comparison of High Voltage Overhead Lines and Underground. CIGRÉ, Paris (1996) CIGRE TB 139: Guide to the Specification and Design Evaluation of AC Filters for HVDC Systems. CIGRÉ, Paris (1999) CIGRE TB 504: Voltage and Var Support in System Operation. CIGRÉ, Paris (2012) Clarke, E.: Circuit Analysis of A-C Power Systems. John Wiley and Sons, New York, NY, USA (1943) Dommel, H.W.: Digital computer solution of Electromagnetic transients in single-and multiphase networks. IEEE Trans Power Syst. PAS-88(4), 388–399 (1969) Dommel, H.W., Meyer, W.S.: Computation of electromagnetic transients. Proc. IEEE. 62(7), 983–993 (1974) EPRI TR-102006: Electromagnetic Transients in Substations, Volume 2: Models, Validations and Simulations (1993). https://www.epri.com/#/search/Electromagnetic%20Transients%20in% 20Substations,%20Volume%202:%20Models,%20Validations,%20and%20Simulations/?to= 1533138725000&from=739318074000. Accessed 17 Jun 2019. Fink, D.G., Beaty, H.W.: Transmission systems, Chapter 14. In: Standard Handbook for Electrical Engineers, 11th edn. McGraw-Hill Book Company, New York (1978) Fortescue, C.L.: Method of symmetrical co-ordinates applied to the solution of polyphase networks. Trans. Am. Inst. Electr. Eng. XXXVII(2), 1027–1140 (1918) Gille, J.-C., Pelegrin, M.J., Decaulne, P.: Feedback Control Systems. McGraw Hill Book Company, New York (1959) Heathcote, J.M: J&P Transformer Handbook, 13th edn. Elevier Limited (2007). ISBN-13: 978-07506-8164-3

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Heaviside, O.: Electrical papers. https://archive.org/details/electricalpapers02heavrich (1894). Accessed 28 Jan 2018 Kundur, P.: Excitation systems, Chapter 8. In: Power System Stability and Control. McGraw Hill, New York (1994). ISBN 0-047-035958-X Liu, C.-M., Liu, L.-G., Pirjola, R.: Geomagnetically induced currents in the high-voltage power grid in China. IEEE Trans Power Delivery. 24(4), 2368–2374 (2009) Miller, T.J.E.: Reactive Power Control in Electric Systems. Wiley, ISBN 0-471-86933-3, New York (1982) Nolasco, J.F., Jardini, J.A., Ribeiro, E.: Electrical design, Chapter 4. In: Cigre Green Book on Overhead Lines. Cigre, Paris (2014) Ohtsuki, H., Yokoyama, A., Sekine, Y.: Reverse action of on-load tap changer in association with voltage collapse. IEEE Power Eng Rev. 11(2), 66 (1991) Olsen, R.G., Pankaskie, T.A.: On the exact, Carson and image theories for wires at or above the earth’s interface. IEEE Trans Power Syst. PAS-102(4), 769–778 (1983) Park, R.H.: Two reaction theory of synchronous machines. AIEE Transactions. 48, 716–730 (1929) Sulzberger, C.: Triumph of AC – from pearl street to Niagara. IEEE Power Energy Mag. 1(3), 64–67 (2003a) Sulzberger, C.: Triumph of AC. 2. The battle of the currents. IEEE Power Energy Mag. 1(4), 70–73 (2003b) Tesla, N.: System of electrical distribution. US Patent 381,970 1888. United States Patent Office. https://pdfpiw.uspto.gov/.piw?Docid=00381970&homeurl=http%3A%2F%2Fpatft.uspto.gov% 2Fnetacgi%2Fnph-Parser%3FSect1%3DPTO1%2526Sect2%3DHITOFF%2526d%3DPALL% 2526p%3D1%2526u%3D%25252Fnetahtml%25252FPTO%25252Fsrchnum.htm%2526r% 3D1%2526f%3DG%2526l%3D50%2526s1%3D0381,970.PN.%2526OS%3DPN%2F0381,970% 2526RS%3DPN%2F0381,970&PageNum=&Rtype=&SectionNum=&idkey=NONE&Input= View+first+page

Stig L. Nilsson started out working for the Swedish State Telephone Board with carrier communication systems. Following this, he worked for ASEA (now ABB) with HVDC systems and for Boeing with computer system developments. During his 20 years with EPRI in the USA, he initiated in 1979 the development of digital protective relaying system developments and in 1986 EPRI’s FACTS initiative. In 1991 he was awarded a patent on Apparatus for Controlling the Reactive Impedance of a Transmission Line. Stig Nilsson is a Life Fellow of the IEEE. He has chaired the IEEE PES T&D Committee, the IEEE Herman Halperin Electric Transmission and Distribution Award Committee, the IEEE PES Nari Hingorani Facts and Custom Power Awards Committee, and several IEEE Fellow nomination review committees and been a member of the IEEE Standards Board, IEEE PES subcommittees, and working groups. Stig Nilsson has been the US Representative and Secretary of CIGRE Study Committee B4 on HVDC and Power Electronics. He is the recipient of the 2012 IEEE PES Nari Hingorani Facts and Custom Power Awards. He received the CIGRE US National Committee Philip Sporn Award and the CIGRE Technical Committee Award in 2012. He has also received the CIGRE Distinguished Member Award for active participation in CIGRE Study Committees and the USNC of CIGRE (2006) and the CIGRE USNC Attwood Associate Award in 2003. Stig Nilsson is a registered Professional Engineer in the state of California, USA.

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Manfredo Lima was born in Recife, Brazil, in 1957, received the BSc degree in Electrical Engineering from Pernambuco Federal University (UFPE) in 1979, the MSc degree in Electrical Engineering from the same University in 1997, and the PhD degree in Mechanical Engineering with emphasis on automation systems from Paraíba Federal University (UFPB) in 2005. He joined Chesf in 1978, where he develops activities in the areas of power electronics, FACTS devices, power quality, control systems, electromagnetic transients, and HVDC transmission. In 1992 he joined Pernambuco University (UPE) where he develops research activities. Nowadays he is the Chesf representative on Cigré Brazil SC B4 (Power electronics and HVDC Links) and is a founding member of the Brazilian Electric Power Quality Society (SBQEE). David Young was educated at King Edward’s School, Birmingham, and read Mechanical Sciences at Cambridge University. After joining the General Electric Company (GEC), he was appointed as Assistant to the Company’s Consultant, Dr. Erich Friedlander, at Witton, Birmingham, where he was immediately involved in the early development of static var compensators (SVC) for flicker correction and then for their wider application in transmission and distribution systems. The first SVCs, using controllable saturated reactors, were quickly superseded by selfsaturated reactors. He became the chief engineer responsible for SVC and FACTS projects using saturated reactors and power electronic devices, initially at Trafford Park, Manchester, and then at Stafford where he was also responsible for harmonic filter design, including filters for HVDC projects. He was appointed as a consultant after the company became part of Alstom and worked as an independent consultant after retiring. He was a member of the Disturbances Study Committee of UIE (International Union for Electricity applications) which specified and produced the UIE/IEC Flickermeter and served on the IEE (Institution of Electrical Engineers) Panel P9. He was a member of several CIGRE Working Groups reporting on the application of SVCs and on reactive compensation and harmonic filtering for HVDC. In 1996 he was awarded GEC’s Nelson Gold Medal, and he received the IEEE PES FACTS Award in 2000.

3

AC Network Control Using Conventional Means Stig L. Nilsson, Manfredo Lima, and David J. Young

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 AC Power System Control Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Overhead Transmission Lines and Underground Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Characteristics of Transmission Lines and Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Reactive Power Compensation Needs for Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Ferranti Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Methods of Reducing Transmission Line Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Power System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Switchgear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Shunt Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Synchronous Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Surge Arresters and the Control of Network Overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Var Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Tools Available to Control Reactive Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Passive Shunt Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Passive Series Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Active Reactive Power Compensation and Voltage Control . . . . . . . . . . . . . . . . . . . . . . . . . 7 Load Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Dealing with Disturbing Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52 55 56 56 57 59 61 62 62 62 66 67 69 71 72 73 73 74 75 76 77

S. L. Nilsson (*) Electrical Engineering Practice, Exponent, Sedona, AZ, USA e-mail: [email protected]; [email protected] M. Lima Transmission Planning and Studies Department, Chesf, Recife, Brazil Pernambuco University, Recife, Brazil e-mail: [email protected] D. J. Young Stafford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_3

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9 Phase Unbalance Due to Single-Phase Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Increasing Stability for Very Long Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Power Production Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Transmission System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78 78 80 82 87 87

Abstract

Electricity has become a vital means of providing power for a very wide range of domestic and industrial applications. The networks of generators, transmission, and distribution circuits that have evolved to serve the needs of electric power users are highly complex and difficult for most to fully comprehend. In principle, however, the rules governing the design and operation of AC power systems are fairly simple. Briefly stated, in any electric power system, the control objectives are as follows: • The system frequency must be kept constant by closely matching the generation and the connected electric loads at all times. • The current flows have to be controlled so that no element of the power system is overloaded. • The voltages throughout the power system must be kept within a narrow range, usually between about 95% and 105% of the nominal voltage. • The power system must continue to supply the connected loads after the loss of the largest generating unit or any other transmission system element, even when the system is already being operated with one element out of service. This chapter discusses these common factors with emphasis on the power transmission elements of the networks; it describes the design of transmission networks and the control methods which were developed to enable electrical supply systems to operate with efficiency, reliability, robustness, and safety using conventional power system equipment. The power electronic controllers available for power system control are discussed in ▶ Chap. 4, “AC Network Control Using FACTS (Flexible AC Transmission Systems) Controllers.”

1

Introduction

As described in ▶ Chap. 2, “AC System Characteristics,” electric power transmission systems have evolved into extensive networks using high voltage, high power three-phase overhead transmission lines operating at voltages from about 100 kV up to 1000 kV and, to a lesser extent, underground cables that operate at up to 500 kV. Future line and cable designs will potentially operate at even higher voltages. Already in the 1970s, design information for AC systems operating up to 1500 kV was obtained through EPRI sponsored research in the USA (Comber et al. 1976).

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The need to transport very large amounts of electric power from remote areas in China has now led to the actual use of 1000 kV AC lines (Fairley 2019). AC systems have grown from small generation systems serving only local loads into extremely large interconnected systems. Major power generating stations, especially hydroelectric plants, are generally located far from the load centers. Power is delivered to these load centers through high capacity overhead transmission lines and underground cables. Many large highly concentrated loads such as steelworks draw most of their power from generating plants situated close by but are usually linked in to larger networks. The primary objective for an electrical network is to be able at all times to meet the load demands of all the power users connected to the system (who sometimes have different priorities and needs). The generated power has to be closely matched to the consumed power, because it is not feasible to store any significant amount of AC power for later use.1 If the demand for power is less than the generated power, the frequency of the power system, as discussed in ▶ Chap. 2, “AC System Characteristics” will tend to increase; the opposite happens if the generated power is less than the demand for power, so that the frequency will tend to decrease. In order to maintain the system frequency close to its target value, the total output of all the generators must be continuously adjusted to match the overall power demand on the network. Figure 1 illustrates features that are often present in an AC network. There will usually be a number of generating stations feeding into the network at different points to enable sufficient power to be supplied to the major load centers, such as cities and industrial plants, as well as to other adjacent systems. Networks will usually include some loads that can cause disturbance to other users and very often there will be sources of harmonics and potential unbalance. Figure 2 illustrates other aspects of the interconnections found in power systems. Transformers, as described in the Sect. 4.2 below, are used to step up the voltage from the generators feeding into the high voltage network and then to step it down at the load centers so that the power can be distributed to the various users. Because the process of network development typically takes decades, and technology changes over time, modern power systems typically include older subsystems operated at historically lower voltages, with higher voltage components overlaying the older systems. Thus, there is often more than one level of high voltage used in different parts of a network. All power system components are designed to have low losses so that the losses in the power system during normal operation can be kept to a minimum. Losses are basically just dissipated as heat that will be transferred to the environment, and they do not add any economic value. The costs of the transmission losses must initially be borne by the system operator but are eventually passed on to consumers via their

1

Electric power can be stored as mechanical or chemical power but normally not in any significant amount as electric power.

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Fig. 1 Typical power system AC network

Fig. 2 Typical interconnections to be found in power systems

tariffs. The inductive reactances in generators, transformers, transmission lines, and cables are normally much larger than the resistances. The reactances capture and release electric energy during each power cycle and there are some small but unavoidable losses caused by the currents flowing into and out of these reactances.

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It is therefore important that, as far as possible, the system reactances should not be greater than is necessary for the satisfactory operation of the network. The adverse effects of reactances on system voltages and system stability are described in ▶ Chap. 2, “AC System Characteristics.” In order to deal with these unavoidable effects on the system, transmission and distribution networks usually include reactive power balancing equipment such as shunt and series capacitor banks that counteract the effects of inductive reactance, and shunt reactors that counteract excessive capacitive reactive power. Series reactors must sometimes be installed to maintain satisfactory operating conditions for parts of the network. Synchronous compensators, as described in the Sect. 4.5.1, have often been used to provide a fast dynamic response to sudden changes of load or to other system conditions and disturbances. The special name for reactive power given by IEC is “var,” derived from volt-ampere reactive (IEC 60027-1 2005).

2

AC Power System Control Objectives

In any electric power system, the control objectives are as follows: • The generation and the connected loads have to be closely matched at all time to maintain a constant power system frequency. • The current flows in all parts of the system need to be monitored and controlled such that the integrity of the complete system is not threatened and that no element of the power system is thermally overloaded. • The voltages throughout the power system have to be maintained within a narrow range; this is typically between 95% and 105% of the nominal voltage but may under some abnormal or low load conditions be allowed to range between 90% and 110% of the nominal voltage. • A power system must be able to sustain the loss of any single generating unit or bulk power transmission system element without any serious effect on the connected loads. This is referred to as an N-1 contingency. This criterion must also be met if the system is already being operated with one significant element out of service, which is referred to as an N-1-1 contingency. For many large systems, two simultaneous events, an N-2 contingency, must be sustained without any serious effects. These requirements need to be satisfied taking into account outages for routine maintenance and the possibilities of the sudden loss of major loads or of generation and/or transmission capacity due to fault conditions. Therefore, networks need to be robust and reliable enough to ride through fault conditions with the minimum impact on users and then to resume continuous operation supplying the power demands of all users. Some large users may reach an agreement with their energy supplier that they will reduce their load demand under exceptional conditions of multiple contingencies in order that the interconnected network may remain in operation.

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3

Overhead Transmission Lines and Underground Cables

3.1

Characteristics of Transmission Lines and Cables

Our understanding of electric transmission line designs grew out of work performed by Heaviside when he studied telegraph lines in the late nineteenth century (Heaviside 1894). As described above and in more detail in ▶ Chap. 2, “AC System Characteristics,” conductors have both series inductance and shunt capacitance. Table 1 lists typical characteristics for 230 kV, 60 Hz, high power transmission lines and cables (Cigre TB 504 2012). In each case, the series inductive reactance, XL, is typically an order of magnitude larger than the resistance R (Cigre TB 110 1996). Although Table 1 shows circuit parameters for paper insulated lead covered (PILC) cables and high pressure pipe (PIPE) type cables, which are older technologies, this table illustrates the issues associated with cable systems. Modern crosslinked polyethylene (XLPE) cables have lower dielectric constant (ε = 2.2) and therefore lower shunt capacitances than older constructions but still have much higher capacitive charging currents than overhead line (OHL) systems. The shunt capacitance associated with the conductors of transmission lines and cables is dependent partly on the diameter of the conductor and partly on the spacing between the conductors. For convenience of analysis, the shunt capacitance in Table 1 is expressed as a capacitive susceptance (denoted by Bc). Its impact on the system is expressed as charging Mvar per km at the nominal system frequency and voltage. The capacitive susceptance between the conductors, including the ground, is very small for an OHL but much larger for cables. As described in ▶ Chap. 2, “AC System Characteristics,” this leads to a high surge impedance Z0 for an OHL and a much lower surge impedance for the cable alternatives. (For this reason, direct parallel connection of overhead lines and cables is not practicable because the cables would pick up the majority of the power flows if paralleled with a line.) The striking difference between cables and lines can be seen in the amount of capacitive charging power (Mvar/km) generated by the cables. Because most of the loads within large cities are typically fed by high voltage underground cables, an excess of capacitive vars is generated during light load periods. This is especially significant in cities during nights and weekends and can cause unacceptable Table 1 Typical OHL and cable parameters for nominal voltage 230 kV Nominal voltage, V0 OHL/cable R (ohm/km) XL (ohm/km) Bc (μS/km) Z0 (ohm) SIL (MW) Charging Mvar/km = V02 Bc

230 kV OHL 0.050 0.488 3.371 380 140 0.18

PILC cable 0.0277 0.3388 245.6 37.1 1426 13.0

PIPE cable 0.0434 0.2052 298.8 26.2 2019 15.8

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overvoltages, which might sometimes be reduced by switching out cable circuits and sometimes by switching in shunt reactors to bring the voltages down to within the acceptable range.

3.2

Reactive Power Compensation Needs for Lines

For short lengths of OHL, the shunt capacitive reactance is very much larger than the series inductive reactance and can usually be ignored in simple calculations. However, this simplification cannot be used for underground cables. Modeling of transmission line and cable circuits are described in detail in ▶ Chap. 2, “AC System Characteristics” from which Equation 56 is copied and included here as Equation 1 for convenience. This equation describes the power flows through a lossless, short transmission line. As is obvious from Equation 1, in order for active power (where the voltage and current are in phase) to flow through a transmission circuit there has to be a phase angle shift between the source and load sides of the circuit, because if the sending and receiving end voltages are in phase (δ = 0), there can be no active power flow through the circuit. Some reactive impedance is therefore essential for the transfer of power through an AC circuit. A consequence of this reactance is that the active power flow is accompanied by a reactive power flow. Equation 2 quantifies the reactive power which has to be provided from each end of the line to enable the active power flow. This equation describes the flows for a symmetrical circuit in which the voltage magnitude is the same at both ends of the circuit. j P1 j ¼ j P 2 j ¼

V1V2 V2 sin δ sin ðδ1  δ2 Þ ¼ X12 X

ð1Þ

V2 ð1  cos δÞ X

ð2Þ

jQ1 j ¼ jQ2 j ¼ where

V1 is the sending end voltage with an amplitude equal to V1 and an angle equal to δ1. V2 is the receiving end voltage with an amplitude equal to V2 and an angle equal to δ2. X12 = X is the line’s reactance. δ is the electric angle between the sending and receiving ends of the line (δ = δ1 – δ2). P1 is the active power sent from the sending end. Q1 is the reactive power supplied from the sending end. P2 is the active power received at the receiving end. Q2 is the reactive power supplied from the receiving end. A graphical representation of the active power flow equation, Equation 1, is provided on the right-hand side of Fig. 3 where V1 is the sending end voltage, V2

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P1, Q1

jX12

V2, d 2

P1

0

90

180

d 1 – d 2 = d [deg]

Fig. 3 Power transmission characteristic

is the receiving end voltage, and δ is the angle across the line. Figure 3 is the theoretical power angle curve that describes the power flow obtainable if the angle is changed slowly and held steady at a particular value. It does not show the power angle if the angle is rapidly changed and neither is it intended to show the thermal power flow limit. It just shows that, in steady state, the transmitted power reaches its  maximum value when the angle δ is 90 and begins to decrease when the angle δ  exceeds 90 . A practical steady-state power flow condition for a transmission line illustrated by  Fig. 3 is with an angle δ not exceeding about 30 , for which the power transfer would be up to about half of the maximum value. During normal (system intact) operation, the transmission lines and other network equipment are loaded typically to between about one-third and one-half of their thermal limits; the angle δ is on the left side of the 90 degree point shown in Fig. 3. If the loading of the circuit exceeds the 90 degree point, the system collapses. This can occur as a result of faults or severe outage conditions when some of the circuit elements in the system might be stressed beyond their thermal or short-time overload rating limits.  Normally, the load flow control needed to avoid exceeding the 90 or thermal limits need not be very fast acting as the thermal time constant of system elements is in the range of minutes, but the control must also take into account the protection settings (Cigre TB 051 1996). However, the reactive demands associated with an increased loading can lead to voltage collapse and an outage, unless the sending and receiving ends are able to supply the reactive power to support the voltages. Unintended reverse action of load tap changers, discussed in the Sect. 4.2, has also been implicated as a cause of a voltage collapse (Ohtsuki et al. 1991). In Fig. 4, it is assumed that the sending end is located in a strong system, with very small voltage variations for different power flow levels, but the receiving end is located in a weak system. In that case, the receiving end voltage can be described by the phasor Equation 3, where Iline is the current flowing in the line. V 2 ¼ V 1  ðX 12 I line Þ

ð3Þ

AC Network Control Using Conventional Means

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Receiving end voltage

3

Active power transfer

Pmax

Fig. 4 Voltage collapse example

Fig. 5 One phase of a long transmission line, represented as a Pi circuit

IS

VS

IR

Y1

X

Y2

VR

With: X = jωL and Y1 = Y2 = jωC/2

Figure 4 illustrates the situation where the power system at the receiving end of an overhead line does not provide enough reactive power to support the voltage. In this case, the receiving end voltage will be reduced to the point of collapse as the power transfer level increases. (This graph is referred to as the nose curve, because it has the appearance of a nose.)

3.3

The Ferranti Effect

As the length of line increases, the series reactance X becomes larger but the shunt reactance is reduced (susceptances Y1 and Y2, shown in Fig. 5, increased) and can no longer be ignored. This is especially significant for cables. Figure 5 uses a two-port network to illustrate the positive sequence impedance (or one of the three phases in a three-phase representation of a line) of a long transmission line or cable, as described in ▶ Chap. 2, “AC System Characteristics.” The network is modeled as a Pi-circuit fed by a constant voltage, VS, at the sending end, but it is assumed that the network has an open circuit at the remote end (the network resistance is not shown, because it is small compared with the reactance). With a total inductive reactance, XL, and a total shunt capacitive reactance, XC (represented by capacitive reactances of 2XC each end), the impedance of the line

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seen from the sending end is 2XC – XL. The voltage at the open circuit end of the line, VR, is VS  2XC/(2XC – XL). This voltage rise at the end of an unloaded line is called the Ferranti Effect (Steinmetz 1971). The practical significance of the Ferranti Effect can be illustrated by the example of an unloaded, 320 km (200 miles) long overhead transmission line operating at 60 Hz; for typical parameters of inductive reactance, 0.47 Ω per km (0.75 Ω per mile), and shunt capacitive reactance, 0.29 MΩ per km (0.18 MΩ per mile), the total series reactance is 150 Ω and the shunt capacitive reactance is 900 Ω, arranged as lumped components of 1800 Ω at each end. The net capacitive reactance seen from the sending end is 1650 Ω and the voltage at the remote end of the line is 1800/1650, i.e., about 1.09 times the sending end voltage, giving a Ferranti Effect voltage rise of about 9%. This representation of transmission lines by simple lumped components becomes increasingly inaccurate as line lengths increase; thus, using the same simple line model for a 640 km long (400 miles) overhead line, the overvoltage would be calculated to increase to about 50%. However, to obtain an accurate result for lines longer than 320 km, a more detailed model is needed and shows that a 50% increase would be obtained for a line with a length of about 670 km. Figure 6 is a detailed model of a long transmission line, represented by n short segments of lumped inductance and capacitance, where each segment represents a series inductance equal to L/n and a shunt capacitance of nC. As described in ▶ Chap. 2, “AC System Characteristics,” if the line is open (the termination impedance is infinite), the current Ir at the end of the line is zero but the voltage Vr at the end of the line is higher than at the sending end; this Ferranti voltage rise can be calculated as in Equation 4. V 0 ¼ V s ¼ V r cos βða  0Þ ¼ V r cos θ

ð4Þ

where θ is the electrical length of the line expressed in radians or wavelengths. Equation 4 illustrates how an overhead line can be compared to an antenna, in which the wavelength λ would be the speed of light divided by the frequency. The Receiving end

Sending end Is

Ix

Line inductance

Vr

Vx

Vs

x

Ir

Line capacitance

a

Fig. 6 Multi element model of a long transmission line

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AC Network Control Using Conventional Means

Fig. 7 Reactive compensation of long AC lines

61 IR

IS

VS

Y3

Y1 X

Y2

Y4

VR

With: X = jωL; Y1 = Y2 = jωC/2 and Y3=Y4=1/(2jωLS)

speed of light, as described in ▶ Chap. 2, “AC System Characteristics” is inversely proportional to the square root of the dielectric constant multiplied by the permeability. For air the speed of light is about 300,000 km/s. The wavelength is then for an overhead line about 6000 km for 50 Hz and 5000 km for 60 Hz. Thus, the quarter wavelength (which is where the impedance of an antenna is infinite, i.e., the voltage goes to infinity and the current goes to zero) for a typical AC line is just below 1250 km at 60 Hz (assuming a wave propagation speed equal to the speed of light). Therefore, very long lines have to be detuned in some way to avoid the quarter-wave resonance point. At 50 Hz, the Ferranti Effect is not so severe but is equally important. For the same typical conductor, the Ferranti Effect on a 320 km (200 miles) overhead line would be about 6%. The 50% overvoltage limit would be reached for a line about 800 km long (close to 500 miles). The quarter wavelength for a 50 Hz line is 1500 km (about 930 miles). A method commonly used to reduce the impact of the Ferranti Effect on long overhead lines is shown in Fig. 7, which again shows the line as a two-port network including the capacitive susceptances Y1 and Y2. It also includes shunt reactors (inductive susceptances Y3 and Y4) connected to the line at each end so that the effect of the line’s shunt capacitive reactance is significantly reduced (the net susceptance is Y1+Y3 at one end and Y2+Y4 at the other end of the line); hence the voltage rise for light loads is smaller.2 Shunt reactors are also used on cable circuits to extend the load limits of cables. However, for cables, assuming a dielectric constant of 2.2, the wave propagation speed is about 136,000 km (about 85,000 miles) per second, giving 340 km (about 212 miles) for a quarter wavelength. This is an unrealistic length for AC cable circuits but is fully acceptable and frequently used for HVDC cable links.

3.4

Methods of Reducing Transmission Line Inductance

The series inductance of transmission lines is clearly an important factor which limits the ability of a line to transmit power between its two ends. Several methods exist to reduce the intrinsic inductance of lines thereby improving their transmission capacity. The following methods are available to line designers for reduced surge impedance designs (Nolasco et al. 2014): 2

Parallel connected admittances (susceptances) can be added.

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Reducing the phase spacing of the line conductors by compaction of the line Increasing the number of conductors per phase bundle Increasing the conductor diameter Increasing the bundle conductor radius Introducing bundle expansion along the line span but keeping the conventional bundle spacing inside and near the towers

The possibility of reducing the effective inductance of the line by the insertion of series capacitors is discussed in the Sect. 6.2 of this chapter.

4

Power System Components

AC systems include a number of components used to control power flows and to enable transformation of the voltages up and down for different purposes. The following subsections provide information on some of the main components that have an impact on the power system.

4.1

Switchgear

Switchgear such as disconnect switches and circuit breakers are installed in the networks so that equipment and lines can be connected and disconnected as required for safe operation and maintenance of the network. There are many switching devices including load-break switches that cannot open fault currents but can interrupt load currents. Disconnect switches are intended to open and close circuits when loads are not connected; they must sometimes break a small amount of capacitive current when they are opened but not more than can be interrupted when the gap between the two ends of the disconnect switch is fully opened. These switches are opened to enable access to equipment and busbar segments for maintenance purposes. Earthing/grounding switches are usually also provided in substations to ensure that the equipment to be maintained cannot be made live. Circuit breakers are used to open a circuit when it is carrying load as well as when it is carrying fault currents, so that lines and equipment with faults can be quickly isolated from the power system; this enables the unfaulted parts of the AC system to resume operation.

4.2

Transformers

Transformers, as described in ▶ Chap. 2, “AC System Characteristics,” are the key components that make AC electric power distribution possible, by enabling power from generators operating at relatively low voltages but very high currents to be converted to high voltages and lower currents for transfer over long AC power lines

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Fig. 8 Simple single-phase transformer

63

Core N1 V1, I1

F11

F22 F12

F21

N2 V2, I2

or cables to a place close to the users. As shown in Fig. 2, the power then passes through other transformers and is eventually distributed at low voltage levels to feeders for use in industrial, commercial, and residential facilities. A basic singlephase transformer, illustrated in Fig. 8, consists of two coils, or windings, arranged around a continuous, closed, core made of a magnetic material (for power transformers, the material is a special form of steel) in such a way that they share a common magnetic flux; when one winding is energized by an alternating voltage, it generates an alternating magnetic flux most of which links directly into the second winding and produces an induced voltage between its terminals. A transformer is a practical application of Faraday’s law of induction. The simple winding arrangement in Fig. 8 illustrates the principle of a transformer, but in actual power transformers, the coils are typically arranged as cylindrical windings, placed one outside the other around the same limb of the core (Heathcote 2007). Mutual induction and mutual reactance are terms which describe the nature of the magnetic interaction between two windings. If it is assumed that a voltage, V1 is applied to one winding which is assumed to have N1 winding turns, this will produce a flux Φ1, with one component, Φ12, flowing in the core (and linking with the second winding with N2 turns), and a leakage flux, Φ11, flowing in the space between the winding and the core. The AC voltage applied to winding N1 generates a varying flux in the winding as follows V 1 ¼ N 1


 dΦ1 dΦ11 dΦ12 ¼ N 1 þ dt dt dt

ð5Þ

V 2 ¼ N 2


 dΦ2 dΦ22 dΦ21 ¼ N 2 þ dt dt dt

ð6Þ

and correspondingly

The magnetic field intensity, H, inside the winding is proportional to the current flow through the winding, the length, and the number of turns in the winding as follows:

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H¼

N I l

ð7Þ

where N is the number of turns in the winding. l is the length of the winding. The magnetic flux density, B is then B ¼ μμ0 H ¼ μμ0

N I l

ð8Þ

where μ0 is the permeability for vacuum. μ is the permeability multiplier for the magnetic material of the magnetic circuit. B is the flux density for each turn in the winding. The total flux through N turns in the winding is then Φ ¼ NBA ¼ μμ0

N2 A I l

ð9Þ

where A is the effective area of the flux path. The inductance of the winding, L, is derived from the geometry and material parameters of Equation 9. That is L ¼ μμ0

N2A l

ð10Þ

The resistance to the flow of a magnetic flux is called the reluctance and is defined as R¼

l Aμμ0

ð11Þ

The leakage flux in and around winding N1 is equal to the inductance L1 times current I1 through the winding; the flux that is routed through the core is equal to the mutual inductance M between the windings times I2, the current flowing in winding N2. Thus, if the circuit resistance is ignored V 1 ¼ L1

dI 1 dI þ M21 2 dt dt

ð12Þ

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The corollary for winding N2 is V 2 ¼ L2

dI 2 dI þ M12 1 dt dt

ð13Þ

If the leakage fluxes are insignificant, then from Equations 5 and 6 with Φ1 equal to Φ2, the following is found dΦ V 1 N 1 dt 1 N 1 ¼ ¼ V 2 N 2 dΦ2 N 2 dt

ð14Þ

I1 N 1 ¼ I2 N 2

ð15Þ

It then follows that

that is, the ampere-turns for the two windings must be the same. If the losses in the transformer are insignificant, then the power on both sides of the transformer must be the same. Therefore, if a load Z2 is connected to the N2 side of the transformer and using the fact that I2 Z2 is equal to V2 V 1 I 1 ¼ V 2 I 2 ¼ I 22 Z 2

ð16Þ

Using Equation 16 to transfer current I2 to the N1 side, the impedance Z2 transferred to the N1 side of the transformer is I 21 Z 1 ¼ I 22 Z2 ¼


2 N1 I 21 Z 2 N2

ð17Þ

or Z1 ¼


2 N1 Z2 N2

ð18Þ

Tap-changers are usually built into transformers to vary their turns ratio. These can be either no-load or on-load tap-changers. Tap-changers have a profound impact on managing the loading in the AC system; if a load has a constant impedance, changing the transformation ratio by means of an on-load tap-changer can be used to reduce the power consumed on the N2 side of the transformer. However, if the load on the N2 side has a constant power demand, then the power flow through the transformer will not change when the ratio of the transformer is changed (Ohtsuki et al. 1991). Special transformers have been developed for various applications. A phase angle regulator (PAR) is used to change the phase angle δ between the two sides of the transformer (Heathcote 2007). It can be used for load flow control but not for

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reactive power compensation. A quadrature boosting transformer (QBT) can also provide a solution for load sharing difficulties. A QBT is a shunt transformer provided with a secondary winding connected in series with a transmission line; it can be used to insert a voltage in quadrature with the voltage drop in a transmission line due to the flow of active power. This equipment can be used to increase or reduce the power flow in a line. When tap-changers are used in a PAR, they can be used to adjust the angular injection of voltage, and in a QBT, they can progressively reduce the load in a line when an overload condition is being approached.

4.3

Reactors

A reactor is basically a coil with only one winding. It works as an energy storage element because, as is shown in Fig. 9, it absorbs energy as the current increases in one quarter of the applied AC voltage cycle, and in the next quarter cycle, the absorbed energy is returned to the AC system. When a fundamental frequency voltage is applied to a pure reactor, the current  through it, as shown in Fig. 9, is delayed by 90 from its voltage. The reactive power Q that a three-phase reactor absorbs is Q¼

pffiffiffi V 2 3 jωL

ð19Þ

where 1.5

1

0.5

-0.5

Energy absorpon

-1

-1.5 AC voltage

Fig. 9 Reactor voltage and current

Reactor current

630

540

450

360

270

180

90

0

0

Energy return

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V is the system voltage (phase to phase voltage). L is the inductance per phase of the reactor. ω equals 2πf where f is the system frequency. The inductance of a long air-cored reactor is broadly described by Equation 10 with the permeability multiplier μ = 1 for air, so that the effective permeability is equal to μ0. The total leakage flux is only completely coupled to the turns at the middle of the coil. Towards the ends of the coil, some of the flux “seeps out” and is not coupled to those turns. This effect is particularly marked for short coils. “Fringing factors” are applied to the calculation of the coil reactance to take this into account. The leakage magnetic fields outside an air-cored reactor can cause significant circulating currents to flow in any conducting material which is near to it. Closed loops should be avoided in any earthing conductors in the vicinity of an air-cored reactor. Reactors of a given rating are much more compact if they include an iron core. In this case, the external leakage fields are much weaker and the fringing effects are less marked; the core is normally constructed to include short gaps, where the permeability is equal to μ0 (but the magnetic field is very strong because of the iron), in order to reduce the reactance compared with a continuous iron core. Iron-cored reactors are normally oil-insulated and mounted in a tank, like a power transformer. Whereas an air-cored reactor has a constant reactance, even for extreme overcurrents, the reactance of an iron-cored reactor will become increasingly nonlinear for strong overcurrents because of saturation in the iron core. Another approach to air-cored reactor design, which shortens the air path and minimizes the external magnetic field effects, is to surround the coil with an iron shroud, which captures virtually all of the leakage flux. Like gapped reactors, shrouded reactors are usually oil-immersed and oil-insulated. Shunt reactors must be connected to each phase of the three-phase system. To be effective, sufficient energy storage capacity must be connected to all phases (Cigre TB 051 1996).

4.4

Shunt Capacitors

A capacitor is similar to a reactor in that it also acts as an energy storage element. When energized from a fundamental frequency source, capacitors accumulate energy from the AC power system during a quarter of a cycle as the voltage increases and return the energy back to the power system during the following quarter cycle, as is shown in Fig. 10. Comparison with Fig. 9 shows that the reactor absorbs energy in the same quarter of the voltage cycle that the capacitor releases its energy and the reactor releases energy simultaneously as the capacitor absorbs it. The reactive power that a three-phase capacitor bank can generate is Q¼

pffiffiffi 2 3V jωC

ð20Þ

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S. L. Nilsson et al. 1.5

1

0.5

-0.5

630

540

450

360

270

180

90

0

0

Energy absorpon

Energy return

-1

-1.5 AC voltage

Capacitor current

Fig. 10 Capacitor voltage and current

where V is the system voltage (phase to phase voltage). C is the capacitance per phase of the capacitor. ω equals 2πf where f is the frequency. A fixed relationship exists between the maximum energy storage capability (Wmax) of these elements and their rating as expressed as follows: W max ¼

Qrated ωN

ð21Þ

where Qrated is the reactive power rating of the equipment. ωN is the rated angular power system frequency (2πf where f is the frequency). This way, it can be concluded that a capacitor’s energy storage capability corresponds to the rated power Qrated during 1/ωN seconds, i.e., 3.18 ms in a 50 Hz system or 2.65 ms in a 60 Hz system. There must be equal ratings of capacitors connected to each phase of a threephase system and, to be effective, sufficient total energy storage capacity must be connected (Cigre TB 051 1996). Capacitor banks for transmission applications are made up of a multiplicity of individual capacitor units, which are connected in series and parallel groups to provide the required total Mvar rating at the applied system voltage. Each capacitor unit is a container in which there are smaller individual capacitor elements, which are

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again arranged in series and parallel groups. To assist safe handling, the units also contain discharge resistors which dissipate any residual charge within a few minutes. In simple terms, each element consists of two sheets of aluminum foil, separated by a dielectric spacing material; the foils and spacers are wound into cylinders and then flattened before being interconnected and arranged inside the container of the capacitor unit. In early capacitors, the spacing material consisted of several layers of paper and the capacitor units were filled with mineral oil. The dielectric between the foils was the composite of paper and oil and the voltage rating of an element was a few hundred volts. Because mineral oil is flammable, capacitor faults sometimes led to fires. Although the losses in a capacitor are small, they are not negligible and, because of constraints on internal temperatures, the ratings of power capacitor units were originally limited to a few tens of kvar. Successive improvements in capacitor design and manufacturing techniques have included the use of fire-resistant chlorinated bi-phenyls (since abandoned on environmental grounds and replaced by other insulating fluids) as the fluid impregnant, and the introduction of polymer film for insulation between laser-cut aluminum foils. These changes resulted in higher rated voltages for the capacitor elements, lower losses, and reduced internal temperatures so that capacitor units can now have ratings of up to several hundred kvar and about 25 kV. Instantaneous overvoltage capability is limited by the puncture strength of the polymer films to a few times the crest value of the rated voltage. At lower levels of overvoltage, partial discharge conditions develop in the dielectric materials and will reduce the life of the capacitors. Even though modern capacitors have an extremely low failure rate, most power capacitors are protected by fuses as well as by protective relaying. In some capacitor designs, each individual element has its own fuse so that any faulty element will be disconnected without the need to take a complete unit or bank out of service. In a large bank, the change of capacitance will be insignificant; although the elements in parallel with a failed element will experience a slightly higher voltage, the affected capacitor unit is usually capable of continuing in service almost indefinitely without further failures. The most common type of external fuse is an expulsion fuse, which acts to disconnect a complete capacitor unit when internal elements fail and provides a visual indication of which unit has failed. The change in bank capacitance is more noticeable than for an internal fuse, and the failure is normally detected and alarmed by unbalance protection so that an outage can be planned to replace the faulty unit.

4.5

Synchronous Machines

4.5.1 Synchronous Generators Generators are machines used to produce electric power, i.e., they are used to convert mechanical energy into electrical energy. The source for the mechanical energy might be a dam with hydroturbines, steam generators that drive steam turbines, diesel generators, gas turbines, wind turbines, etc. Synchronous machines are

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complex and are best described in detailed text books (Kundur 1994; Anderson and Fouad 1993; Krause et al. 1995). Generators have a rotor with a DC magnetic field; the rotor is connected to the shaft of the turbine. A stationary set of windings, the stator, surrounds the rotor. The rotating field of the rotor interacts with the stator windings and a voltage is induced in the windings. The speed of the rotor and the arrangement of the stator windings are such that the output voltage is a three-phase voltage with a frequency equal to the nominal, fundamental power system frequency; typically 50 or 60 Hz. H. K. Park published the fundamental theory for analysis of synchronous machines (Park 1929). He used the d, q, 0 transformations where d is the direct axis, q is the quadrature axis, and 0 is the common mode quantity. This method is preferred over Fortescue’s positive, negative, and zero sequence networks for analysis of rotating machinery (Fortescue 1918). The terminal quantities of a synchronous machine can be described by the following two equations (Kundur 1994): ΔΨ d ðpÞ ¼ GðpÞΔefd ðpÞ  Ld ðpÞΔid ðpÞ

ð22Þ

ΔΨ q ðpÞ ¼ Lq ðpÞΔiq ðpÞ

ð23Þ

and

where Ψ is the instantaneous value of the flux linkage. p is the Laplace operator. G(p) is the stator to field transfer function. Ld is the d-axis operational inductance. Lq is the q axis operational inductance. The output voltage is controlled by an exciter, which acts on the field circuit to decrease or increase the flux as appropriate. A governor maintains the correct speed of the generator by controlling the input energy. The generator may be equipped with additional control systems, such as a power system stabilizer, to improve the recovery of the generator after system short circuits or other disturbances. When there is a sudden disturbance on the system, the effective reactance of a generator changes with time. This changing reactance is normally expressed in a simplified way and generators are characterized by their sub-transient, transient, and synchronous reactances. The sub-transient reactance is fairly small with a time constant of about 20 to 100 ms. The transient reactance is larger and might have a time constant from fraction of a second to a few of seconds. The synchronous reactance is substantially larger and is used for steady state calculations (Kundur 1994).

4.5.2 Synchronous Compensators Synchronous compensators are synchronous machines that do not generate power; they only draw a small amount of power from the system, sufficient to cover their

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operating losses and to enable them to rotate at synchronous speed when connected to the AC system. Since the energy required for their operation is small, their generated voltages are almost in phase with the AC system voltages. These machines are used to control the magnitude of the AC system voltage at their point of connection. By overexciting the compensator, it will generate reactive power, which increases the voltage at the point of connection, and by underexciting the machine, it will absorb reactive power and therefore reduce the voltage. A synchronous compensator has a rotating mass, the inertia of which will result in some output power being produced by the machine if the AC system starts to retard as a result of a system fault. Thus the machine inertia results in some power injection into (or absorption from) the AC system, which can be beneficial for system stability. A synchronous compensator is therefore used to provide fast voltage and reactive power control, appearing to the AC system as a voltage behind the impedance of the compensator. The voltage control system’s response would typically be about 500 ms, but it might be more or less if field forcing is applied (Kundur 1994). The internal “synchronous reactance” of a synchronous compensator is relatively high, and for steady-state conditions, the stable controllable range when absorbing reactive power is only about half of the continuous rating when generating reactive power. A synchronous compensator inherently responds much more quickly to rapid changes of its terminal voltage than to changes of its excitation. Its values of sub-transient and transient reactance are much lower than its synchronous reactance but, as their names imply, they are only effective for short periods immediately after a voltage change at the compensator terminals. The effective reactance increases from the transient reactance towards the synchronous reactance with a time constant of perhaps 1–2 s. If there is a change of phase angle of the applied voltage, this will apply a torque to the rotor. Because the compensator is not coupled to a power source, the rotor will start to change its speed, gaining or losing energy as it moves towards synchronism; there is then a decaying oscillation around the new equilibrium position. If there is an unfortunately timed sequence of phase angle changes (such as can be initiated by an arc furnace), it is possible for the compensator to lose synchronism with the system. On the one hand, whereas shunt capacitors and reactors are static devices (apart from the associated switchgear), synchronous compensators need the regular maintenance and refurbishment associated with rotating plant and they require a range of essential auxiliaries; they also require more substantial civil works and have higher losses than shunt capacitors and reactors. On the other hand, synchronous compensators allow the injection into the AC network of continuously variable reactive power, based on their ratings and the characteristics of their control systems.

4.6

Surge Arresters and the Control of Network Overvoltages

It is necessary for a network to be operated and controlled in such a way that all equipment is protected from excessive overvoltages. Surge arresters (sometimes

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called lightning arresters or surge diverters) are the devices normally used to prevent damage due to extreme short duration and transient overvoltages, including lightning strikes. For each nominal operating voltage used in different parts of the network, the equipment is tested to withstand impulse voltages greater than the protective voltage levels provided by the surge arresters. A continuous maximum operating voltage is also defined for each voltage level and the network needs to be equipped and operated so that the steady-state voltage never exceeds the permissible maximum operating voltage at any point in the network.

5

Var Compensation

Reactive power (var) compensation and voltage control are complex issues that require careful analysis (Miller 1982). Lines can and often must be compensated to maintain a relatively flat voltage profile along the line to avoid line overvoltages. Compensation is also used to increase the power flow through a line. Furthermore, compensation is used to reduce the reactive power flows in lines by minimizing the reactive current component flowing through the lines. Typical compensation strategies are as follows: • Capacitive compensation at the line ends is used to compensate the AC power system for the reactive power consumed by the line inductances when the line carries a heavy current. The conventional technology used for this is to install switched or fixed shunt capacitors. • Switched or fixed shunt reactors are used to prevent overvoltages during periods of low loads especially for networks including cable systems. Shunt reactors connected to a line increase the surge impedance of the line. • Switched shunt capacitors may be installed on long lines close to the line’s midpoint. Because this reduces the surge impedance of the line and provides voltage support at its midpoint, the transmission capacity of the line is increased. • Switched or fixed shunt reactors may be connected close to the midpoint of a line to reduce the voltage at its midpoint during light load conditions. Shunt reactors are also typically connected at both sides of a midpoint connected series capacitor bank. • Increasing the level of series compensation can be achieved by switching in additional series capacitors to improve the load carrying capability of a series compensated line in response to system disturbances, but this is only possible if the risk for subsynchronous resonance (SSR) is negligible. • For long cable circuit lengths, it may be necessary to place shunt compensation at some intermediate points along the cable to reduce the charging current flowing in the cable. If a long length of a high voltage underground cable trips at the load end, but remains connected at the source end, the resulting overvoltage on the cable due to the large amount of cable charging reactive power can be particularly severe (Cigre TB 504 2012).

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The optimum amount and location of fixed or switched shunt compensation in a power system must be determined by examining load flow cases for different load levels and taking into consideration future expansion.

6

Tools Available to Control Reactive Power Flow

6.1

Passive Shunt Compensation

As is shown in Fig. 9, in a purely inductive reactance, the current lags the voltage by  90 while, as is shown in Fig. 10, in a purely capacitive reactance the current leads  the voltage by 90 . Thus, if the reactive power demand in an AC system is lagging the voltage phasor, the addition of a capacitive shunt reactance can be used to reduce or cancel the inductive current flow and vice versa. Consequently, shunt reactors and capacitors are tools that can be, and are, used to compensate reactive power flows in AC systems. These reactive power components can be fixed (continuously connected to the power system) or switched. Switching of these elements enables the reactive power compensation to be controlled to be a close match to the active power flow requirements. Shunt reactors are often permanently connected at the ends of long transmission lines, but reactors may also be switched into service at selected locations to prevent the system voltage exceeding its upper voltage limits when the system load is light. Switched reactors are then disconnected when the load has risen sufficiently to give a satisfactory reactive power balance within the network. Shunt reactors for high voltages have normally been constructed with a gapped iron core or an iron shroud round an “air-core” coil and are oil-cooled, but air-cored, air-insulated reactors connected to a tertiary winding of a substation transformer are also used. When the load rises further and the inductive reactive power from the lines and transformers outweighs the line shunt capacitive reactive power, additional capacitive balancing can be provided by means of switched shunt capacitor banks made up of a series/parallel configuration of individual capacitor units, as described in the Sect. 4.4. Capacitor banks often include low impedance series reactors to limit the inrush current when they are energized, especially if more than one capacitor bank is installed at a substation; parallel switching of capacitor banks results in very high charging/discharging currents, which can lead to reduced capacitor life. When strong harmonic sources are present in a system, capacitor banks may be configured as harmonic filters which include larger series reactors to reduce harmonic distortion or to detune possible resonance conditions. Shunt capacitors are widely used in distribution systems to counteract the inductive component of system loads and raise the load power factor to a high value. Switched shunt reactors and capacitors can only be introduced into the network in a stepwise fashion and their controlled switching includes time delays to avoid unnecessary or frequent switching operations in response to a voltage disturbance of short duration. When an AC system needs faster or continuously variable reactive

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power compensation and voltage support, generators and synchronous compensators have traditionally been used, as discussed in the Sect. 4.5.2 above.

6.2

Passive Series Compensation

As is clear from Equation 1, long-distance power transmission, in which the series reactance X is large, involves large amounts of reactive power that is consumed by the line. By inserting a capacitor in series with the line, the effective series reactance is reduced as illustrated by Equation 24 (Anderson and Farmer 1996): Xeffective ¼ XL  XC

ð24Þ

where XL is the fundamental frequency series reactance of the uncompensated line. XC is the fundamental frequency capacitive reactance of the series capacitor. Although the effective reactance of the line is reduced by inserting a series capacitor, Equation 24 is oversimplified because the susceptance (shunt capacitance) of the line is ignored and other shunt connected voltage control equipment is ignored too. The amount of reactive power compensation inserted by means of a series capacitor is always proportional to the current flow through the line without any external control actions being needed (although the capacitor can be bypassed or additional series capacitors can be inserted through switching). Series compensation with fixed series capacitors has therefore been used for a long time to directly compensate the reactive power consumption in some transmission lines, thereby decreasing the angular difference between sending and receiving end voltages (Jancke and Åkerström 1951). Because series capacitors reduce the power frequency impedance of a compensated line, fault currents can be significantly increased to a multiple of the rated current. Special protective relaying systems are therefore needed to detect and clear faults on series compensated transmission lines (Wilkinson 2019). Immediately after a fault occurs on a line, the capacitors basically function as a short circuit, so that the fault current is initially limited by the line’s inductance. The delayed increase of the fault currents may not last very long but it might be sufficient for special, fast-acting protective relaying systems to initiate opening of the circuit breakers for the faulted line. Although capacitors are able to withstand the shorttime thermal effects of overcurrents, they must be protected against overvoltages by bypass devices, which need to operate before the overvoltage becomes high enough to cause capacitor failures. This means that the capacitors will not influence the fault currents in the line after they have been bypassed, but it also means that there will be a delay before the capacitors are reinserted in the line circuit after the fault has been cleared. This increases the impedance (reactance) of the line and, as a

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consequence, reduces the ability of the line to carry high loads straight away after clearing of the fault. Series capacitors always introduce natural frequencies below the power frequency. Series capacitors can resonate with the generator and line inductances at sub-synchronous frequencies; the subharmonic oscillations which follow any transient disturbances can lead to self-excitation of alternators, to rotor hunting, and to shaft oscillations. This phenomenon is known as sub-synchronous resonance (SSR) and has led to turbogenerator failures (Walker et al. 1975). However, there are now well-proven techniques to determine if a generator unit is at risk of SSR, and there are also protective relaying solutions to isolate a generator if SSR arises (Anderson and Farmer 1996). Another form of disturbance at subharmonic frequencies can occur when capacitors are in series with devices that have a nonlinear reactive characteristic because they use saturable iron in the magnetic path; these devices include transformers and gapped-core “linear” reactors. This kind of disturbance is known as ferroresonance (Engdahl 2017). It sometimes occurs as a result of transient conditions, such as the energization of a large transformer when there is a series capacitor in the supply circuit. Overvoltage protection across a series capacitor installation will sometimes operate to remove the resonance condition. Ferroresonance can be suppressed by means of suitable damping circuits included with a series capacitor installation. The grading capacitors across a multigap circuit breaker, when it is open, can be an unexpected source of series capacitance. Ferroresonance can also occur with voltage transformers but is typically associated more with distribution systems than with high power transmission lines. Series reactors are also used in some situations. One application for series reactors is when it is necessary to reduce short-circuit levels in a part of the network where the fault clearance capability of switchgear could otherwise be exceeded. Another situation occurs when one transmission line has such a low reactance compared with other available parallel paths that it accepts too much of the power flow and is in danger of being overloaded; a series reactor will increase its impedance and force other lines to take a greater share of the load. This generally increases the total reactive power absorption in the system and may require additional shunt capacitors to supply balancing reactive power. However, the active compensation provided by phase angle regulators (PAR) as described above is sometimes a preferred approach to reduction of circuit loading.

6.3

Active Reactive Power Compensation and Voltage Control

Synchronous generators, described in the Sect. 4.5, are the power plants from which power is injected into the system, but they are able to supply reactive power as well as active power. The exciter on a generator can be used to increase (overexcite) or reduce (underexcite) the excitation of a generator. When a generator is underexcited, the internal voltage behind its impedance is lower than the system voltage and the machine

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will draw reactive current from the bus to which it is connected. By absorbing reactive power from the AC system, the generator will act like a reactor and reduce the bus voltage but its RMS current will also increase.3 If the generator is overexcited, it will inject reactive power into the AC system and increase the bus voltage. Note that the generator’s excitation system includes underexcitation and overexcitation limits (Kundur 1994). Even though generators are capable of being used for AC voltage and reactive power control, these functions are now less readily utilized in deregulated power systems; there are significant costs associated with the flow of reactive currents, because they detract from the ability of the generators to produce active power. Synchronous compensators, described in the Sect. 4.5.2, have been widely used for voltage and reactive power control. They are synchronous machines that do not generate AC power and only draw power from the AC system to cover their operating losses. They provide a continuously variable source of reactive power. If they operate underexcited, they act like a variable shunt reactor, and if they are operated overexcited, they act like a variable shunt capacitor in the same way as synchronous generators do (Miller 1982). They also provide some inertia to the power system to which they are connected. The power electronic (FACTS) controllers available for power system control are described in ▶ Chap. 4, “AC Network Control Using FACTS (Flexible AC Transmission Systems) Controllers.”

7

Load Compensation

Very few loads operate with a power factor equal to one. Most loads draw currents that are not fully in phase with the voltage and therefore include a reactive component. If this reactive component of the current is allowed to be passed on from the load to the power source, it will cause additional losses in the power supply circuits but, more importantly, will cause severe voltage drops and will limit the power carrying capability of the network. It is therefore desirable to reduce the reactive component of the load current so that it is as close to zero as possible; since the power factor of loads is normally lagging, this reduction can be accomplished using shunt capacitors. These can be made up of switchable capacitor modules which approximately match the load, to minimize the amount of over- or undercompensation. Power factor correction components are normally located as close to the loads as possible and are typically switched automatically using local measurements and controls (Miller 1982). One example of this is the practice of installing switched shunt capacitor modules along medium voltage distribution lines. Many power electronic based loads also inject harmonics into the power system. Harmonic currents add losses to the power system and are therefore undesirable. Shunt capacitors will often act as a sink for higher order harmonics but sometimes harmonic filters are needed to prevent harmonics from entering the power system, as described in the Sect. 6.1. Capacitors inserted into the power system can also 3

Note that underexcitation will reduce the transient stability performance of the generator.

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magnify the effects of harmonics if their application results in harmonic frequency resonances (Cigre TB 553 2013). These applications of reactive power control equipment are effective in limiting reactive power demands from the load buses. However, the characteristics of the loads vary with the weather, time of day, day of the week, and seasons. The load characteristics are typically aggregated for use in load flow calculations.

8

Dealing with Disturbing Loads

The majority of disturbing loads, such as arc furnaces and rolling mills, are connected to sub-transmission or high voltage distribution systems. For such disturbing loads, necessary arrangements should as far as possible be made to alleviate the effects on other connected loads caused by these kinds of highly disturbing loads. Nevertheless, it can happen that the point of connection to the high voltage network is not strong enough to avoid interference effects and voltage disturbances on the wider network. Strengthening and reinforcing the network at the point of connection is usually costly, but appropriate strengthening might be the only way to accommodate these disturbing loads. Arc furnaces and rolling mills, etc., are just examples of the effects on power quality due to power electronic and other disturbing loads. Some loads can inject direct current into the network, usually at low distribution voltage levels, and this causes transformer saturation and generates even order harmonic currents. The transient effects of large motor starts and saturation of transformers when they are switched into service are also sources of temporary voltage dips and odd or even harmonic distortion. Under balanced system conditions, third and other triplen harmonic distortions in the line-to-line voltages are normally very low. However, when the system voltages or impedances become unbalanced, third harmonic voltages are able to develop in the line-to-line voltages and third harmonic currents will be able to flow. Due to the physical asymmetry of the conductors in a transmission line, the phase impedances are not quite equal, and this will result in unbalanced phase voltages. In order to even out these differences, it is usual to arrange for the conductors to be transposed in their relative positions at intervals along the route. Fifth and seventh (and higher) harmonic currents are commonly produced by industrial loads; harmonic filters are usually provided with the major distorting loads to reduce their impact on the system. However, these odd harmonics are also present in the magnetizing currents of all transformers; occasionally network capacitances and inductances can form a near-resonance condition which magnifies the harmonic voltage distortion at some locations on the high voltage network. These resonances can be particularly important for the lower order harmonic frequencies; significant voltage distortion at higher order harmonic frequencies is generally avoided because the transmission system shunt capacitance presents a low impedance to them. Harmonic studies are needed to determine appropriate means to remove or reduce any resonances, sometimes by avoiding certain circuit configurations or alternatively by adding tuned or damped filter circuits.

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Fig. 11 Load balancing circuit

9

Phase Unbalance Due to Single-Phase Loads

Strongly unbalanced loads are normally only encountered in distribution systems where single-phase traction loads could be fairly common. If there are several points from which such single-phase loads are supplied, the worst unbalance can usually be reduced by distributing the loads between the three phases of the system in order to approach a time-averaged balanced load. It is possible to convert a single-phase resistive load into a balanced three-phase load, without consuming extra power in the other phases, purely by means of reactive components, as shown in Fig. 11. If the single-phase load is variable between zero and a maximum value but the balancing components are fixed, their values can be chosen to compensate half the maximum load and thus halve the worst unbalance. Comprehensive balancing requires a dynamic balancer.

10

Increasing Stability for Very Long Lines

Figure 3 in the Sect. 3.2 illustrates the relationship between the power transferred through a transmission line and the angle between the voltages at the ends of the line. The underlying reason for the shape of this curve was identified in ▶ Chap. 2, “AC System Characteristics,” fig. 16, as the collapse of the voltage at the midpoint of the line, even when the terminal voltages are maintained at a constant value. In the early days of the development of long distance transmission, it appeared that this voltage instability would prevent AC power transmission over distances greater than about 200 miles. A basic solution to enable power to be transmitted over much longer distances was proposed by Baum (1921). He posited that if a very long line were to be subdivided into several sections, with a synchronous compensator installed to maintain a constant voltage at each point of connection, each section would have the same stability limit, and this would become the stability limit for the complete line – of any theoretical length. Figure 12 shows a basic example of this principle, with a synchronous compensator connected to the midpoint of a line, with one machine at the sending and an infinite bus

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Fig. 12 Midpoint shunt reactive power compensation by means of a synchronous compensator

79 P

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Fig. 13 Power/angle curves with synchronous compensator connected to the midpoint of a line

at the receiving end. The voltages at the ends of the line have the same magnitude and the compensator would be controlled to act as an “infinite busbar” and provide a constant voltage, Vm, nominally equal to the voltages at the line terminals. This midpoint “infinite busbar” is not required to supply active power and will not control the phase angle of Vm, but it supplies the reactive power necessary to control the voltage at the midpoint of the line. This additional voltage support effectively divides the line into two equal sections, each with a reactance X/2 and operating at an

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angle δ/2. Each section of line now has its own, independent, stability limit, which is reached when δ/2 = 90o. Thus the theoretical total angle between VS and VR can now   be 180 , i.e., double the conventional critical angle of 90 , with a resultant increase in power transfer capability of the long line. Figure 13 shows theoretical and practical power transfer curves with and without midpoint voltage control. This principle can be extended to use two or more synchronous compensators connected at several intermediate points in very long lines, as proposed by Baum, to permit the angles of the terminal machines to be more  than 180 apart.

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Power Production Control

Control of the generation plants in deregulated systems is isolated from the control of the rest of the power system, whereas in vertically integrated power systems, the control of the generation plants is closely integrated into the overall power system control. In general, system owners/operators have to perform the following functions: Long-term power adequacy planning: Long-term power adequacy planning requires analysis of the anticipated load growth over a time horizon longer than the time it takes to acquire or build new power plants and the associated transmission facilities. Short-term forecasting considering weather and season predictions: Short-term forecasting has a very wide time frame spanning day-ahead forecasts when considering weather predictions up to several years in the case of hydropower utilization. Scheduled outage planning: Outage planning requires analysis of the expected system loads for the duration of the outage. The outage analysis involves running contingency studies to ensure that no single (or sometimes double) contingency event can cause widespread system outages. Outages in adjacent power systems also need to be considered as a part of this analysis because an outage in one area might impair the security of another area. Day-ahead generation forecast and economic dispatch plan: Economic dispatch used to be an important part of system operation because it would lead to commitments to operate the power system with the most economically advantageous plants. It is still an important aspect of generation scheduling in many parts of the world. The economic dispatch function typically includes base power plants, such as nuclear power plants, that operate 24 h a day, 7 days a week, with minimum output power variations. Included in the generation mix are plants that supply power in hourly blocks throughout the day. Finally, there are some power plants designated as

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load-followers which make up for the unpredictable variations in the power demand. Variable, non-dispatchable power generation sources such as wind power generators and to some degree solar power plants also have to be considered in the generation dispatching function (Zia et al. 2013). In deregulated power systems, where the power comes from numerous independently owned and operated power plants, the power generation is supplied based on competitive bids from the available plants. The introduction of electricity markets and breakdown of the national monopolies has been seen as a means to increase efficiency of electrical energy generation and supply. It is assumed that competition will provide the strongest cost-minimizing incentives, more effectively than a typical cost based regulation would do, and it is also assumed that it has the ability to trigger innovation (Cigre TB 301 2006). If the demand for power is less than the available generating capacity, then competition should provide the lowest cost electric power to consumers. However, if the demand for power is higher than the generating capacity, the marginal cost of power theoretically goes to infinity and curtailment of loads will have to be implemented to avoid blackouts. However, the actual planning process to ensure reliable power generation plant commitments has become much more complex because of the emergence of renewable power plants, with less predictable performance attributes (Cigre TB 700 2017). Load shedding can also be a competitive function; consumers who have the lowest need for power are potentially able to offer to shed load for a price. Contingency analysis: The dispatching of power plants has to include considerations of transmission system constraints. Constraints are often the result of power congestion in the transmission system; for example, too much power might flow through lines that for some reasons are not capable of supporting the power flows. When the demand for transmission capacity exceeds the transmission network capabilities, it can lead to a violation of network security limits, which might be a thermal, transient, or voltage stability limit, or a (N-1) contingency condition (Cigre TB 301 2006). Sometimes the solution to avoid unacceptable transmission line loads is to operate power plants which are low in the merit order and do not produce the lowest cost power. These so called “must run” power plants might be necessary to ensure that the power system will operate securely. Furthermore, the power outputs from wind and solar power plants sometimes have to be curtailed because of power system congestion. Frequency control: Frequency control requires that at all times the generation has to match the loads, with the system losses counted as loads. This requires hourly and minute by minute commitment of generation facilities to achieve a stable operating frequency. This is typically managed by having load-following generating plants. For some systems, the operational target is to maintain the system frequency as closely as possible to the nominal frequency at all times. For other systems, the frequency may be allowed to vary within defined limits, such as a fraction of  1%, but over a 24-h period, the frequency is controlled such that the

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long-term average frequency returns to the nominal value.4 For short time and emergency conditions, the frequency may be allowed to deviate more widely, but some loads would be disconnected in stages to prevent the frequency falling to an unacceptably low value. During severe emergency conditions, many systems incorporate automatic load shedding in the case of generation deficiency, or generator dropping in the case that too much generation is connected to the system and is operating inefficiently. A consideration is also that many systems use the power frequency to keep time. Since it is not possible to achieve an absolutely constant balance between generation and loads, the clocks driven by the power system might run ahead or behind the standard real time. It then may become necessary to intentionally operate the power systems with generation deficiency to retard the clocks or to operate the system with power surplus to advance the clocks. Such control operations have to be run taking into account the entire system, since otherwise the phase angles between subsystems might exceed acceptable limits. In a worst case scenario after an extreme emergency that caused prolonged low frequency, the discrepancy of power system time against real time might not be recoverable and power system time would need to be reset.

12

Transmission System Control

The role of the transmission system operator is to manage the power flows determined by the generation dispatchers or energy managers. Transmission system operators typically perform the following functions: • • • • •

Load flow forecasting based on the generation schedule Congestion analysis Scheduled outage analysis Contingency analysis Voltage and reactive power control

The transmission system constraints considering load forecasts and scheduled outages are normally predetermined. The tool for this is a load flow program. Transmission system constraints or congestions might require adjustments to the power schedules discussed above (Cigre TB 301 2006). Also, transmission system operation requires 4

In the UK, where the frequency is allowed to vary within defined limits, it can be forecast that the frequency will fall when domestic power demand rises sharply at the end of some key sporting events. Before the forecast surge in demand, a pumped storage scheme is usually operated in its pumping mode; just before the surge, it is changed to generating mode. This additional power input helps to reduce the extent of the subsequent dip in frequency. Also in the UK, two high inertia waterwheel type generators are used to contribute to the energy demand of an intermittent pulsed load. As the load demand of the pulsed load increases, power is drawn from the generators, slowing them to half speed and releasing 75% of their stored kinetic energy; this energy contribution reduces the transient frequency disturbances and alleviates the stress on nearby generating sets.

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information about the state of adjoining power systems because the generation topology in one system can cause inadvertent power flows in other systems; the load flows across the key interfaces or through interconnected lines among different systems, and outages in the adjoining systems, might affect the system constraints. Therefore, these flows and outages have to be included in all contingency assessments. Contingency situations: The transmission system operator has to be prepared for unplanned losses of generation plants or transmission lines. Such events might occur in areas adjacent to the control area for which the specific operator is responsible. Contingency situations might require immediate actions by the operator to ensure continued stability of the power system or to contain any system overloads or other security issues. It will most likely require rerunning of contingency analysis programs and might lead to activation of system recovery procedures. The transient and other stability limits of dynamic nature might arise as a result of random, unplanned events. The load flow programs used by the operators are not suitable for modeling system stability issues, but these are considered by having predetermined load limits for each circuit or set of circuits. Unscheduled outages may arise because of line faults and equipment failures, which might lead to reduced security of the power system. Typically, in energy management computer systems, unforeseen events are simulated in a contingency analysis program in which random outages are constantly introduced to ascertain if the system is still stable and secure after an event (Xue et al. 1992). The result of this analysis can be used to preplan load shedding or generation dropping actions if a serious, unplanned disturbance were to occur. Accurate simulation results require that the state of the power system is fully known, but at times the actual state of the system might not be available because some system data is lacking. Holes in the measured data might then be plugged by the use of a state estimator that uses available data to estimate the missing data (Schweppe and Wildes 1970). Transmission system operator support tools: The transmission system operators have various tools available for management of their assigned control region. The primary means for controlling the voltage and hence the reactive power flows in the high voltage systems (primary control) were, prior to the introduction of FACTS controllers, as follows: • Automatic voltage regulators (AVR) systems used to control the output voltage from generators. • Synchronous compensators. • Shunt capacitors, fixed or switched. • Shunt reactors, fixed or switched. • Series capacitors, fixed or switched, which reduce the reactive power consumption of overhead transmission lines. • Transformer load tap changers (LTC), which are used to adjust the ratio of the transformer windings under load. • PARs can be used to control load flows by means of on-load tap changing but they introduce an inductive reactance in series with the line; the reactive power this absorbs needs to be considered since it increases the need for shunt compensation.

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• QBTs can be operated by controlling an on-load tap changer, which will compensate for some of the reactive power consumed by the line’s reactance but they can also be used to reduce the power flows through the line by inserting a voltage that increases the equivalent line voltage drop. Thus, they can act like a virtual line impedance that increases or reduces the line voltage drop between the source and load sides of the line. Network control: Network control, and specifically network voltage control (or regulation), is typically divided into three levels: primary control, secondary control, and tertiary control. These levels are temporally and spatially independent by nature. Temporal independence means that the three control mechanisms do not significantly interact with each other, operating in three adjacent time-scales or frequency bands and maintaining robust performance and stability, when facing system changes; if the control laws were more complex, there would always be the risk of oscillation and instability. These three levels, whose implementation and degree of automation vary among the various power systems, constitute the hierarchical structure of grid voltage control (Cigre TB 310 2007). • Primary control relates to automatic actions on individual equipment based on local measurements. The time scale ranges from 100 ms up to several seconds. This might include automatic regulation of the high-side voltage of power plant, possibly with line drop compensation; this partially increases grid voltage support but might introduce destabilizing interactions between primary voltage regulators. • The secondary voltage regulation (SVR) system as defined by Cigre performs the real time adjustment (manually or automatically) of the primary control reference points (voltage, reactive power) and handles control resources (by continuous controls as well as by switching on/off or up/down commands) as a function of system requirements (Cigre TB 310 2007). A special problem that might fit into the SVR regime is control of voltages in urban areas that have a high density of underground cable systems since the inherent shunt capacitance of cables leads to high system voltage under low load (night-time or holidays) conditions. • The tertiary voltage regulation (TVR) system, as defined by Cigre, is strongly related to economy and/or security optimization at the highest administrative authority level (utility, pool, or country). TVR operates in a relatively slow control mode (response time around 10 min when automatic), based on realtime measurements. The TVR response time depends on dispatcher reaction time (manual control) or the time required to compute new reference values (computer assisted manual control or automatic control). This response time must not be too long (to prevent the network from moving towards an insecure condition) or too short (to avoid any conflicting action with the primary and secondary controls). In case of an automatic closed-loop in the TVR system, its response time should not be lower than 5 min in order to preserve temporal independence from the SVR (Cigre TB 310 2007).

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Voltage and Var control: The most effective solutions for reactive power and voltage control involve some form of coordination between reactive power resources and system controllers. The control equipment requirements to achieve these benefits to system security are detailed below. • Voltage quality: Voltage levels must be maintained in accordance with the planned schedule, the supplier’s contract commitments, and the technical constraints. • Power system security: – Loss of one infeed or line must not endanger the network (i.e., a sufficient reactive power reserve should be made available). – Voltage values must remain within ranges compatible with equipment functional specifications (equipment overvoltage limits, minimum voltage for power station auxiliaries). – Voltage control efforts must be evenly distributed among available resources. – Excessive currents in equipment must be avoided. • Voltage control coordination contributes to network stability by increasing the system voltage stability margin or it may reduce the angle difference between generators). • Operating economy: The cost of production including losses (static optimization problem) and the cost of generation operated according to security constraints (essentially a dynamic problem) should be minimized. Voltage control is therefore a problem of dynamic optimization with security constraints (Guo et al. 2010). It involves a very wide range of time constants (from a few hundred milliseconds for the compensation of rapid fluctuations to several hours for load-following and the associated problem of generator start-up and shutdown). Voltage control actions must therefore be structured over several time scales. Furthermore, voltage control requires various forecast studies (daily, weekly, monthly), whose aim is to define the best equipment arrangement for real-time control and the optimized voltage plan to be implemented. Another major aspect is the local nature of the voltage/var control, as opposed to frequency/active power control. Reactive power control action (generator excitation, capacitor/reactor switching, etc.) has therefore mainly a local impact, making it possible to define many voltage control areas in an interconnected network. However, in a deregulated market scenario, owners of generating plants do not want to reduce the output of the plants to supply reactive power for network control. This requires the system operator to acquire ancillary services from the open market (Oren 2001). Furthermore, in the case of strongly interconnected networks, the voltage control areas may not be sufficiently decoupled and can develop significant adverse interactions. Geographical and temporal coordination of control actions are thus needed to meet the various functional requirements (quality, security, economy). This involves all the predictive studies and actions carried out to optimize voltage and reactive power controls, aiming at producing a satisfactory and coordinated

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behavior of its various components. The reactive power forecasts have to meet the following criteria: • Forecast studies must be carried out for various time horizons (day-ahead, weekahead, month-ahead). • Forecast studies are used to optimize the system voltages and reactive powers by defining the settings of the available controls, also including the choice of no load transformer tap settings. Network reliability is considered in these studies by checking the control margin for each forecast scenario. • Forecast studies attempt to establish a voltage profile, which is both economical and safe. Forecast studies have to be conservative in terms of reliability and therefore may not be optimum in terms of economy. Sufficient reactive reserve must be provided within each area to ensure that the system will be capable of riding through “normal” operating incidents; • Forecast studies aim at maintaining economy within reliability constraints for much longer time horizons than those dealt by primary, secondary, and tertiary control, which are meant for online operation. According to the real-time data needs, the Tertiary Voltage Regulation pursues the forecast reference values as closely as possible, while ensuring system security and reliability. Voltage control issues: The control of grid voltage and reactive power in large networks has become even more critical in the last decade, due to the higher utilization of transmission assets. Many issues contribute to this, including: the increased distance between production sites and the load centers; delays in building new transmission projects; larger interconnections and increased meshing; power interchanges over long distances; connection of large capacity units to higher voltage levels, etc. Suitable voltage and reactive power control solutions, which take into consideration higher loads and the associated transmission losses for multiple scenarios and contingencies are therefore needed. In many regions, there is a lack of real-time and closed-loop “automatic” coordination of reactive power resources and network voltage control, so that manual voltage/var control is still in use. Manual system control: Manual grid voltage control is still used by many system operators worldwide and typically involves: • • • •

Dispatching the generating units Forecasting reactive demand Scheduling the power plants’ high-side voltages Switching shunt capacitor or reactor banks for power factor correction and voltage regulation • Setting the voltage set points for LTCs When the voltage set points are controlled manually according to written operator instructions, or requested by the system operator when an urgent change is needed, untimely or inadequate control actions may occur during slow dynamic phenomena following unexpected events. Thus, this conventional approach to solving the

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network voltage control problem is nowadays unsatisfactory because the actual network operating conditions may quite often be different from their forecast values. In many regions, voltage and reactive power control is therefore being changed to take advantage of modern computer support systems.

13

Cross-References

▶ AC System Characteristics ▶ Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology

References Anderson, P.M., Farmer, R.G.: Series Compensation of Power Systems. Published by PBLSH! Inc., Encinitas, California, 92024-3749, USA (1996) Anderson, P.M., Fouad, A.A.: Power System Control and Stability. IEEE Press, New York (1993) Baum, F.G.: Voltage regulation and insulation for large power long distance transmission systems. IEEE Trans. Am. Inst. Electr. Eng. XL, 1017–1077 (1921) Cigre TB 051: Load Flow Control in High Voltage Power Systems. CIGRE, Paris (1996). https:// www.cigre.org/GB/publications/e_cigre Cigre TB 110: Comparison of High Voltage Overhead Lines and Underground. CIGRE, Paris (1996) Cigre TB 301: Congestion Management in Liberalized Market Environment. CIGRE, Paris (2006) Cigre TB 310: Coordinated Voltage Control in Transmission Networks. (2007) Cigre TB 504: Voltage and Var Support in System Operation. CIGRE, Paris (2012) Cigre TB 553: Special Aspects of AC Filter Design for HVDC Systems. CIGRE, Paris (2013) Cigre TB 700: Challenge in the Control Centre (EMS) Due to Distributed Generation and Renewables. CIGRE, Paris (2017) Comber, M.G., Doyle, J.R., Schneider, H.M., Zaffanella, L.E.: Three-phase testing facilities at EPRI’s project UHV. IEEE Trans. Power Syst. 95(5), 1590–1599 (1976) Engdahl, G.: Ferroresonance in Power Systems; Energiforsk Report, p. 457. (2017). https:// energiforskmedia.blob.core.windows.net/media/23470/ferroresonance-in-power-systems-energifor skrapport-2017-457.pdf. Accessed 19 Nov 2019 Fairley, P.: China’s Ambitious Plan to Build the World’s Biggest Supergrid, A massive expansion leads to the first ultrahigh-voltage AC-DC power grid. (2019). https://spectrum.ieee.org/energy/thesmarter-grid/chinas-ambitious-plan-to-build-the-worlds-biggest-supergrid. Accessed 24 April 2019 Fortescue, C.L.: Method of symmetrical co-ordinates applied to the solution of polyphase networks. Trans. Am. Inst. Electr. Eng. XXXVII(2), 1027–1140 (1918) Guo, Q., Sun, H., Tong, J., Zhang, M., Wang, B., Zhang, B.: Study of System-Wide Automatic Voltage Control on PJM System, pp. 1–6. IEEE PES General Meeting (2010). https://ieeexplore. ieee.org/document/5589635. Accessed 19 Nov 2019 Heathcote, J.M.: J&P Transformer Handbook, 13 edn. Elsevier Limited (2007). ISBN-13: 978-0-7506-8164-3. https://www.elsevier.com/books/j-and-p-transformer-book/heathcote/9780-7506-8164-3. Accessed 19 Nov 2019 Heaviside, O.: Electrical Papers. (1894). https://archive.org/details/electricalpapers02heavrich. Accessed 28 Jan 2018 IEC 60027-1: Letters Symbols to be Used in Electrical Technology – Part 1: General. (2005). https://webstore.iec.ch/searchform&q=60027-1. Accessed 19 Nov 2019 Jancke, G., Åkerström, K.F.: The series capacitor in Sweden. Presented at the AIEE Pacific general meeting, Portland, 20–23 Aug (1951)

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Krause, P.C., Wasynczuk, O., Sudhoff, S.D.: Analysis of Electric Machinery. IEEE Press, New York (1995) Kundur, P.: Excitation systems, chapter 8. In: Power System Stability and Control. McGraw Hill, New York (1994). ISBN 0-047-035958-X Miller, T.J.E.: Reactive Power Control in Electric Systems. Wiley, New York. ISBN 0-471-86933-3, USA (1982) Nolasco, J.F., Jardini, J.A., Ribeiro, E.: Electrical design, chapter 4. In: Cigré Green Book on Overhead Lines. Cigré, Paris (2014) Ohtsuki, H., Yokoyama, A., Sekine, Y.: Reverse action of on-load tap changer in association with voltage collapse. IEEE Power Eng. Rev. 11(2), 66 (1991) Oren, S.: Design of ancillary service markets. In: Proceedings of the 34th Hawaii International Conference on System Sciences. Maui, HI, USA (2001) Park, R.H.: Two reaction theory of synchronous machines AIEE. Transactions. 48, 716–730 (1929) Schweppe, F.C., Wildes, J.: Power system static-state estimation, part I: exact model. IEEE Trans. Power Syst. PAS-89(1), 120–125 (1970) Steinmetz, C.P.: Lectures on Electrical Engineering, vol. III. Dover Publications, New York (1971) Walker, D.E., Bowler, C., Jackson, R., Hodges, D.: Results of SSR tests at Mohave. IEEE Trans. PAS-94(5), 1878–1889 (1975) Wilkinson, S.: Series Compensated Line Protection Issues, GE Power Management, GER 3972. https://store.gegridsolutions.com/faq/Documents/LPS/GER-3972.pdf. Accessed 25 April 2019 Xue, Y., Wehenkel, L., Belhomme, R., Rousseaux, P., Pavella, M., Euxibie, E., Heilbronn, B., Lesigne, J.F.: Extended equal area criterion revisited (EHV power systems). IEEE Trans. Power Syst. 7(3), 1012–1022 (1992) Zia, F., Nasir, M., Bhatti, A.A.: Optimization methods for constrained stochastic wind power economic dispatch. In: IEEE 7th International Power Engineering and Optimization Conference (PEOCO), IEEE, Langkawi, Malaysia, pp. 129–133. (2013)

Stig L. Nilsson started out working for the Swedish State Telephone Board with carrier communication systems. Following this, he worked for ASEA (now ABB) with HVDC systems and for Boeing with computer system developments. During his 20 years with EPRI in USA he initiated in 1979 the development of digital protective relaying system developments and in 1986 EPRI’s FACTS initiative. In 1991 he was awarded a patent on Apparatus for Controlling the Reactive Impedance of a Transmission Line. Stig Nilsson is a Life Fellow of IEEE. He has chaired the IEEE PES T&D Committee, the IEEE Herman Halperin Electric Transmission and Distribution Award Committee, the IEEE PES Nari Hingorani Facts and Custom Power Awards Committee, several IEEE Fellow nomination review committees, been a member of the IEEE Standards Board, IEEE PES subcommittees and working groups. Stig Nilsson has been the US Representative and Secretary of Cigre Study Committee B4 on HVDC and Power Electronics. He is the recipient of the 2012 IEEE PES Nari Hingorani Facts and Custom Power Awards. He received the Cigre U.S. National Committee Philip Sporn Award and the Cigre Technical Committee Award in 2012. He has also received the Cigre Distinguished Member Award for active participation in Cigre Study Committees and the USNC of Cigre (2006); and the Cigre USNC Attwood Associate Award in 2003. Stig Nilsson is a registered Professional Engineer in the state of California, USA.

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Manfredo Lima was born in Recife, Brazil in 1957, received the BSc degree in Electrical Engineering from Pernambuco Federal University (UFPE) in 1979, the MSc degree in Electrical Engineering from the same University in 1997 and the PhD degree in Mechanical Engineering with emphasis on automation systems from Paraíba Federal University (UFPB) in 2005. He joined Chesf in 1978, where develops activities in the areas of power electronics, FACTS devices, power quality, control systems, electromagnetic transients and HVDC transmission. In 1992 he joined Pernambuco University (UPE) where develops research activities. Nowadays he is Chesf representative on Cigré Brazil SC B4 (Power electronics and HVDC Links) and is a founding member of the Brazilian Electric Power Quality Society (SBQEE).

David J. Young was educated at King Edward’s School, Birmingham, and read Mechanical Sciences at Cambridge University. After joining the General Electric Company (GEC), he was appointed as Assistant to the Company’s Consultant, Dr Erich Friedlander, at Witton, Birmingham, where he was immediately involved in the early development of static var compensators (SVC) for flicker correction and then for their wider application in transmission and distribution systems. He became the Chief Engineer responsible for SVC and FACTS projects using saturated reactors and power electronic devices, initially at Trafford Park, Manchester, and then at Stafford where he was also responsible for harmonic filter design, including filters for HVDC projects. He was appointed as a Consultant after the company became part of Alstom and worked as an independent consultant after retiring. He was a member of the Disturbances Study Committee of UIE (International Union for Electricity applications) which specified and produced the UIE/IEC Flickermeter and served on the IEE (Institution of Electrical Engineers) Panel P9. He was a member of several CIGRE Working Groups reporting on the application of SVCs and on reactive compensation and harmonic filtering for HVDC. In 1996 he was awarded GEC’s Nelson Gold Medal and he received the IEEE PES FACTS Award in 2000.

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AC Network Control Using FACTS (Flexible AC Transmission Systems) Controllers Antonio Ricardo de Mattos Tenório

Contents 1 AC Network Needs and FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Active Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Reactive Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Topology of FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Description and Functions of SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Application of SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Description and Functions of STATCOMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Description and Functions of TCSCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Principle of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Description and Functions of SSSCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Description and Functions of UPFCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Power Losses in FACTS Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 System Security and Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92 93 94 95 95 97 100 102 107 107 120 121 123 123 124 125

Abstract

This chapter describes the functional characteristics of proven FACTS controllers, their application in AC network, and the control and operating principles applicable to their use in power systems. FACTS controllers that have been proposed and prototyped or might be under development have not been included in this chapter. The AC network needs are clearly pointed out, and different

A. R. de Mattos Tenório (*) Operador Nacional do Sistema Elétrico – ONS, Rio de Janeiro, RJ, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_4

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applications are explored to provide for the reader a broad spectrum of functionalities of series, shunt, and series-shunt FACTS controllers. These FACTS controllers can improve the power systems’ performance and controllability.

1

AC Network Needs and FACTS Controllers

The functions of the power system transmission network are to deliver power generated from power plants to load centers and to provide interconnection between different power systems for economic power sharing and enhanced reliability. To achieve these functions, transmission networks should be able to handle power exchange (active and reactive power) in a flexible and efficient way. The ▶ Chap. 2, “AC System Characteristics” chapter provides an overview of AC system issues that need to be considered, and ▶ Chap. 3, “AC Network Control Using Conventional Means” chapter describes how these issues are managed without the use of FACTS controllers. FACTS controllers can improve the performance of the power system in the following ways: • Some provide continuous control of reactive power. • Some provide continuous control of AC line power flows. • Some controllers can simultaneously control both the active and reactive power flows in an AC system. • FACTS controllers can respond to changes in the AC power system in a cycle or less. • FACTS controllers can be inserted, disconnected, and reinserted without limitations. • FACTS controllers have built-in self-checking functions that will provide assurance to the system operators that the controller is able to perform its functions when required. The continuous control capability of the FACTS controllers can add damping to oscillatory, unstable, or lightly damped system oscillatory modes. Some FACTS controllers can be used to move power between AC transmission lines, which can enable power to be moved from higher loss and power-limited circuits to lower loss, higher power-carrying capacity circuits. This might reduce the transmission system losses, which would more than pay for the power losses in the FACTS systems themselves. The fast response and high duty cycle performance can also be used to improve the transient stability of the AC system and provide damping of the oscillatory modes arising after a system transient disturbance. These capabilities are beyond the capability of mechanically switched reactive power compensation equipment typically used in AC transmission systems. The FACTS controller’s self-checking capability is an improvement over mechanically switched reactive power compensation systems since it is not known

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if a switched compensation system will work or not until the time when the switching is initiated. However, FACTS controllers cost more than conventional mechanically switched reactive power control equipment. Nevertheless, in many actual applications, the installed FACTS controllers have enabled postponement of additional line construction, which could represent substantial capital cost savings. Therefore, the potential benefits from applying FACTS controllers needs to be clearly understood by the power system planners and operators in order to build the lowest cost and most efficient AC power system. More information about the cost-benefit analysis can be found in the ▶ Chap. 16, “Economic Appraisal and Cost-Benefit Analysis” of this book.

1.1

Active Power Transfer

Figure 1 shows a simplified transmission line. Let us assume that the active power flows from node s to node r. That means the phasor Vs is leading phasor Vr, as shown in Fig. 2. In order to understand the concept of active and reactive power, the equations below are defined. For a typical extra high-voltage transmission system, the reactance X is much larger than the resistance R, and it is possible to establish the following formula for active power transfer (lossless transmission line) (Elgerd 1983; Anderson and Farmer 1996). Psr ¼

V s :V r sin ðδsr Þ X

(1)

where δsr = δs  δr Fig. 1 Simplified short transmission line model

Zsr s

r

Vs

R

Vr

X

Psr Fig. 2 Phasor diagram of voltages

Prs Vs

δrs I j IX

Vr

w

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By examination of the power transfer of Eq. 1, it is possible to conclude that to change the flow on the line, it is necessary to vary the magnitude of the terminal voltages Vs and Vr, the phase angle δsr, or the system reactance X. As a practical matter, the magnitude of the terminal voltage cannot be varied significantly without a costly voltage upgrade, because the AC voltage has to be maintained in a narrow band, typically less than 5%. This leaves modification of the system reactance X or the relative phase angle δsr as feasible options for power flow control purposes. It is important to note that the direction of the active power flow is determined by the sine of the angle δsr. The terminal voltage magnitudes Vs and Vr do not have any influence on the direction. If Vs is leading Vr, the power direction is from s to r. On the other hand, if Vs is lagging Vr the power flow direction is from r to s.

1.2

Reactive Power Transfer

Regarding reactive power flow, it can be demonstrated that reactive power at each terminal can be expressed as follows (Elgerd 1983): Node

r Qr ¼

V s V r cos δsr  V 2r X

(2)

Node

s QS ¼

V 2s  V s V r cos δsr X

(3)

In the technical literature, an average reactive power flow Q is often defined as: Q¼

Qs þ Qr V 2s  V 2r ¼ 2 2X

(4)

Taking into account Eq. 4, the following conclusions can be drawn: • If Vs is greater than Vr, the direction of reactive power flow is from s to r. • If Vr is greater than Vs, the direction of reactive power flow is from r to s. • If Vs is equal to Vr, Eqs. 3 and 4 become the following equation: Qs ¼  Qr ¼

V 2s ð1  cos δsr Þ X

(5)

Therefore, in this particular case, the reactive power that flows into the line at both terminals is the same. The equations also show that reactive power cannot be transmitted from the sending end to the receiving end or vice versa. That is, it has to be provided locally at each end of the line.

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Topology of FACTS Controllers

When it comes to the way the FACTS controller is connected to a power system, i.e., shunt, series, or shunt-series, the connection depends on the type of issues the FACTS controller is supposed to resolve. On one hand, based on Eqs. 1 through 5, it is possible to conclude that issues associated with control of active power flow must be handled by series controllers. On the other hand, problems related to voltage/reactive power control are mainly resolved through shunt controllers. The use of series-shunt controllers, which are more complex in nature, is needed for applications that require universal controllability, such as controlling of voltage and active and reactive power depending on specific requirements. As an added complexity, for long AC lines, it is often necessary to distribute series and/or shunt controllers along the line in order to keep the voltage profile along the line as close to constant as economically feasible.

3

Description and Functions of SVCs

The most commonly applied FACTS shunt controller is the Static Var Compensator (SVC), usually known as an SVC. A detailed technical description of the SVC can be found in ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC).” The SVC is capable of absorbing or generating reactive power in order to control the magnitude of the system voltage to a preset level. The reactive power output of the SVC can be changed very rapidly and very often (no need to recover after a rapid excursion). This can be of great advantage to the AC system during and after faults in the network, assisting with decreasing any overvoltages and increasing the voltage during undervoltage condition. These actions help other essential equipment in the AC network stay connected during the transient and dynamic periods that follows recovery from faults in the network. If in the planning process of the SVC its location is carefully chosen, it can also dampen power oscillation through a control structure called POD (Power Oscillation Damping). However, it is worth mentioning that the shunt controller’s performance depends highly on where in the power system they are installed. The location has to be where the power flows are controllable and in addition, the power system states are observable. Therefore, damping of power oscillations requires a lot of dynamic studies, including small-signal linear analysis of the power system, to define the best placement of shunt FACTS controllers for this purpose. In-depth discussion on these issues is beyond this chapter. There are many different SVC configurations, but most of them use thyristorcontrolled reactors (TCR), thyristor-switched capacitors (TSC), harmonic filters, and/or breaker-switched or fixed capacitors as basic branches (CIGRE TB 78 1993). A generic SVC schematic diagram is shown in Fig. 3. An actual single line diagram for the Silves SVC in the Northern Brazil can be seen in Fig. 4 (Tenório et al. 2016).

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Fig. 3 Generic schematic diagram of an SVC using TCR and TSC

Fig. 4 Single line diagram for Silves SVC in the 500 kV network in Northern Brazil

The Silves SVC comprises two TCRs rated at 147.6 Mvar each, two TSCs rated at 129.4 Mvar each, and two single-tuned filters (5th harmonic) at 36.8 Mvar each, and the SVC is connected at 20 kV (secondary voltage). The rated output of the SVC is 200 to + 300 Mvar at 500 kV. The coupling transformer reactance is 15% and the transformer rating is 300 MVA.

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The TCRs are controlled continuously to provide inductive reactive power in order to keep the voltage at a preset value. When an overvoltage occurs, the TCRs decrease their firing angle to control the voltage within the operating voltage band, and the TSCs are switched off, if required. If the overvoltage is severe, the TCRs are put in full conduction in such a way as to help the system recover the voltage to a preset band. The harmonic filters are continuously in operation. Therefore, they should be considered when designing the inductive rating, which is reached with two TCRs and two single-tuned harmonic filters. When an undervoltage occurs, the TSCs are switched on, and TCRs increase their firing angle up to a point where they cease conducting if the voltage is severely depressed. The capacitive rating is reached with two TSCs and two single-tuned harmonic filters. More examples of SVC Applications can be found in ▶ Chap. 12, “Application Examples of SVC.”

3.1

Principles of Operation

The TCR is a nonlinear susceptance that can be controlled by the firing angle α of the antiparallel connected thyristor valves, with the firing angle always being delayed relative to its natural voltage zero-crossing. The TCR susceptance B as a function of the firing angle α is depicted in Fig. 5 and analytically can be expressed by Eq. 6. B¼

2ðπ  αÞ þ sin ð2αÞ pu π

(6)

By varying the firing angle α from 90 to 180 electrical degrees, it is possible to change the TCR susceptance from its rated susceptance (B=1/(ωL)) or 1 pu to Fig. 5 Voltage and currents at firing angles of α = 90 and 120 electrical degrees

I Vsys

Vsys I90 α = 90 deg α =120 deg

I120

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zero, i.e., an open circuit. Therefore, seen from the fundamental frequency points of view, a TCR susceptance can be continuously controllable from zero up to 1 pu. However, when operating at any point other than zero or 1 pu, it creates characteristic harmonic currents which have to be dealt with (see ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC)”). The TSC susceptance is not continuously controllable, as is the TCR, but it is switchable each time its current passes zero, i.e., when its voltage is at a peak or if the capacitor is already charged, when the voltage across the thyristor switch is zero or at a minimum. Operating this way, it generates no harmonic currents, since the TSC stops conducting at current zero-crossing, which means a firing angle of 90 electrical degrees, and again may resume conduction when the voltage across the thyristor switch is zero. In terms of control, the TSCs are simply inserted on and off in a binary logic in accordance with the SVC control system. Figure 6 illustrates the operation of a TSC with a binary control logic on/off. In normal operation, when voltages change relatively slowly, the TSC is typically switched on for a relatively long period of time and then off for a long period time, i.e., the TSC valve conducts continuously during the on-state creating a fully sinusoidal waveshape, and Fig. 6 only demonstrates the voltage and current waveshapes at turn on and turn off for one valve direction. However, the significance of the TSC switching performance is that it can be switched in and out in a rapid sequence, which enables the TSC to be used for damping control by using a bang-bang control function. This is an advantage over a mechanically switched capacitor, which can be inserted but not be quickly disconnected and reinserted to provide damping. The rated capacitive output is the sum of the harmonic filters plus all TSCs in operation. Conversely, the rated inductive output is the sum of the TCRs in operation minus the harmonic filters, which are always connected. The zero Mvar working point is usually reached when the reactive power absorbed by a TCR is equal to the reactive power generated by the harmonic filters at fundamental frequency. Due to the nonlinear characteristic of TCRs, it is necessary to apply a linearization curve to the firing control system in order to provide a constant gain for both the Fig. 6 Binary logic of switch-off and switch-on of a TSC

I V

Vsys

V

I

Vsys switch-off

switch-on

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U

Fig. 7 An SVC in closed loop control using an Automatic Voltage Regulator (AVR)

Ref

S

DV

AVR

BREF

SVC

Fig. 8 V-I characteristic of an SVC (seen from high-voltage side)

capacitive and the inductive range, i.e., the ratio between SVC susceptance and
ref , throughout the rated output voltage regulation error should be kept constant (ΔB ΔV range of the SVC, as shown in Fig. 7. As a variable susceptance source of reactive power, an SVC typically has the steady-state characteristic as shown in Fig. 8. The SVC has a straight line characteristic in the V-I plane, with its slope slightly increased to ensure that the two characteristics, i.e., the system load (blue trace) and the SVC output (red-green traces), always have an interception point in the output range. The added inclination to the SVC characteristic is commonly called the slope or current droop, and it is usually expressed in percentage of the rated power of the SVC. It can be expressed and seen from either the high-voltage side (system side) or the low-voltage side (SVC side). The interception of the two

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characteristics defines the operating point of the SVC as indicated by the coordinates (Io, Vo) in Fig. 8. The SVC response time depends on the strength of the system. However, typical response times specified for 60 Hz systems during a step response are as follows: (i) 33 ms for rise time (ii) 100 ms for settling time

3.2

Application of SVCs

SVCs can strongly improve the performance of AC grids by using its ability to inject or draw reactive power into or from the network. The following describes some features that may be specified for SVCs.

3.2.1 Control of Overvoltages in AC Grids One of the major sources of overvoltage in an AC grid is load rejection. Short circuits occur, and power components sometimes fail in an AC grid, and these events lead to the opening of circuit breakers, which may totally or partially disconnect load centers. The longer the transmission lines, the higher the overvoltage resulting from load rejections. This is mainly due to the Ferranti Effect, i.e., the charging of the transmission line (Anderson and Farmer 1996), and the reactive power surplus created by the load rejection. One important functionality of an SVC is its ability to control overvoltages by sending the SVC to its inductive rated output for an adequate period of time and in accordance with a specified overload/overvoltage inductive cycle. A typical overload inductive cycle is shown in Table 1 for an SVC connected to a 500 kV system. It shows the various voltages with time durations, which the thyristor valves have to be designed to withstand. These overvoltages are translated into overcurrents seen by the thyristor valves. Therefore, the overvoltages specified must be defined based on electromagnetic transient studies to express truly the power system needs as far as withstand capability of the equipment is concerned.

Table 1 Typical inductive overvoltage cycle for an SVC installed on a 500 kV network Typical overvoltagesa (SVC on 500 kV network) 1.80 pu 1.40 pu 1.30 pu 1.20 pu 1.10 pu a

1pu = 408.248 kVpeak

Time duration 33 ms 200 ms 1s 10 s Continuously

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3.2.2 Voltage Regulation and Reactive Power Supply for the AC Grid SVCs are designed to provide automatic voltage regulation within the specified operational voltage range. When a small disturbance occurs in a power system, the voltage and power are changed, and an SVC provides an excellent means of controlling the voltage to within a preset narrow band. Operational voltages lie between 0.95 and 1.05 pu in general. So if the SVC is operating close to zero Mvar, it is able to go either capacitive or inductive with full output to control the voltage at the set point. SVCs add a lot of operational flexibility and, therefore, can enhance the power system operation regarding voltage control. The number of operations of transformer on-load tap changers can be considerably reduced by using the SVCs to control the system voltage to a desired value. Most SVCs have a continuous control range, but some use stepwise control based on TSCs and TSRs (thyristor-switched reactors) only, which do not generate harmonics, and therefore harmonic filters are not required. The power system needs must be clearly specified by the customer to the bidder to avoid misunderstanding. To control in either a continuous mode (vernier) or stepwise is totally a matter dependent on the power system needs. In order to divide the reactive power demand between various SVCs in close proximity or even with nearby generators, a slope (current droop) is used in the controls to avoid overloading SVCs with smaller ratings, while the larger ones may be idle. The slope is determined in a steady-state study in which all load conditions and network topologies have to be carefully investigated to enable sharing of the reactive power needs between the SVCs. Ideally, sharing should be proportional to the SVC ratings and inversely proportional to their slopes after a disturbance. 3.2.3 Power Oscillation Damping of AC Grids In the planning of a new SVC, a question may arise about the possibility of the SVC helping to damp power oscillations that may occur in the grid after a contingency. The answer depends on the location of the new SVC in the network. The effectiveness of using a stabilizing signal such as a POD – power oscillation damping – is extremely dependent on the SVC location. However, if the planner is aware of this feature and explore the optimum location for system damping, the SVC might be able to damp power oscillations in addition to its other functions. By modulating the SVC reactive power, it is possible to damp oscillations in a range from 0.2 to 2 Hz, which is the range of typical electromechanical modes associated with a power system. SVC POD can play an important role in stabilizing the power system after a disturbance, and it can postpone some transmission reinforcements if the POD is well designed and the SVC location is optimized. The SVC POD has a simple structure comprising a gain, washout filter(s), low-pass filter(s), and lead-lag block(s) for dynamic compensation. Obviously, this POD can be more sophisticated in order to include additional functionalities depending upon the damping needs. Due to remote locations of SVCs, it usually uses as input a signal of frequency variation or the value of active power flow in a transmission line. Notice that depending on the power system characteristics, the

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sign of the POD gain needs to be changed if the power flow is reversed when the input signal used is the active power flow.

3.2.4 SVCs Operating in Close Proximity to Other SVCs SVCs are usually equipped with gain optimizers to ensure their stable operation under different levels of short circuit capacity at the point of connection. These gain optimizers acquire the short circuit capacity from the network, for instance, by means of injecting a pulse of current and measuring the voltage response. The short circuit power can be calculated from the measured information. Different manufactures may have different strategies. However, if there are two or more SVCs in close proximity, the signal treatment to estimate the short circuit may be impaired because the other SVC starts responding to the other, and consequently they disturb each other. In addition, the SVC may interact adversely and react among themselves due to relatively high controller gains during lower short circuit power conditions. This adverse behavior must be prevented to ensure proper and stable operation of the SVCs. These adverse interactions, called hunting, may have a severe impact on the SVCs stability. To mitigate these interactions, it is necessary to develop a gain reduction scheme that takes into account the number of SVCs in nearby operation and in voltage control. This controller gain reduction scheme can be a linear or nonlinear approach depending on the real-time studies developed in hardware in the loop (HIL) investigations during the Factory Acceptance Tests (FAT). Therefore, when several SVCs are operated in close proximity, it is necessary to provide communication between the SVCs in order to exchange their status information. This communication does not need to be fast, e.g., it may be sufficient to exchange information every 10 s (Tenório et al. 2016). A more detailed technical description of the Static VAR Compensator (SVC) can be found in ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC).” Application examples of the SVC can be found in ▶ Chap. 12, “Application Examples of SVC.”

4

Description and Functions of STATCOMs

A static synchronous compensator (STATCOM) is a reactive power-regulating device based on the voltage-sourced converter (VSC) technology. It can be used to maintain the AC system voltages and enhance the stability of the AC system (CIGRE TB 663 2016). That is, it basically performs the same functions as an SVC. Because of the smaller footprint required by STATCOM controllers, these controllers have become frequently used in applications from industry to electric power systems. The limitations of the gate turn-off thyristor (GTO) have been overcome by the development of the integrated gate commutated thyristor (IGCT), and the introduction and improvements of the insulated-gate bipolar transistor (IGBT) have made it possible to apply Pulse Width Modulation (PWM) techniques in the VSCs. This simple PWM technology has relatively high switching losses which, as described in ▶ Chap. 5, “Power Electronic Topologies for FACTS,” has led to the development of the lower loss modular multilevel converter (MMC)

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Fig. 9 Schematic diagram of a STATCOM

technology. The detailed technical description of the STATCOM can be found in the ▶ Chap. 7, “Technical Description of Static Compensators (STATCOM)”. The STATCOM is illustrated in Fig. 9. The core of the technology is an AC/DC voltage-sourced converter (VSC) that provides a compensation current (I), associated with a voltage (Vo) injected by the converter into the power system. The STATCOM current either lags or leads the system voltage (V1) by 90 electrical degrees. In this way, a STATCOM acts as a synchronous condenser/compensator with zero mechanical inertia. The relationship between the voltages, currents, and reactive power is easily derived from the schematic diagram shown in Fig. 9. Q¼

pffiffiffi pffiffiffi ðV 0  V 1 Þ 3:V 1 :I ¼ 3:V 1 : Xt

(7)

where V0 is the phase to phase fundamental frequency output voltage from the VSC, V1 is the phase to phase voltage at the connection point of the VSC, I is the fundamental frequency AC current flow through the transformer, and Xt is the fundamental frequency reactance of the transformer. Note that V0 is the synthesized fundamental frequency voltage component on the AC side of the STATCOM converter. Therefore, if V0 equals V1, the compensation current I equals zero, and no reactive power is generated or drawn from the network. If V0 is greater than V1, the current I is leading the AC system voltage (capacitive), and an amount of reactive power is injected into the point-of-common-coupling (PCC). Similarly, if V0 is less than V1, the current I is lagging the AC system voltage (inductive), and an amount of reactive power is drawn from the PCC. A comparison between an SVC and a STATCOM regarding their V-I characteristics is shown in Fig. 10, which illustrates the operating characteristics of a symmetrically rated SVC (equal inductive and capacitive reactive power generation at the nominal AC system voltage) and a STATCOM. The symbols used in the figure are:

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a

b

SVC

STATCOM

V D

Vov

Vov

Vmaxcont Vrefmax Vnom

A

D

Vmaxcont Vrefmax Vnom

A

B

Vrefmin

B

Vrefmin

Vmin

Vmin

C

C I

ICrated

Capacitive

Inductive

ILrated

I

ICrated

Capacitive

Inductive

ILrated

Fig. 10 Comparison of a STATCOM and an SVC – V-I Characteristics

Vnom: The nominal AC system voltage. Vmaxcont: The maximum voltage at which the system is able to operate continuously. Vrefmax: The maximum control system reference voltage. Vrefmin: The minimum control system reference voltage Vov: The maximum overvoltage at which the system is designed to operate. Vmin: The minimum voltage at which the semiconductor valves can be operated. IC: Capacitive output current IL: Inductive output current. As can be seen, a STATCOM can provide rated output reactive current even at very low voltages. This cannot be accomplished by an SVC, since its reactive current is dependent on the variations of the terminal voltage. However, for most transmission system applications, the performance of the shunt FACTS controllers below 80% of the nominal transmission system voltage is of limited value1. However, in some applications, the STATCOMs respond faster than the SVC, and its capability of boosting the low voltage can be important, e.g., for industrial and systems especially sensitive to short-term AC voltage perturbations. The low-voltage ride-through capability of the compensator should be specified by the purchaser or the system operator in published Grid Codes. The needs of a power system that can be provided by a STATCOM are listed below (CIGRE TB 144 1999). • • • •

1

Voltage regulation and control Increase of steady-state power transfer capacity Increase of transient stability margin Damping of power system oscillations

STATCOMs can provide assistance to industrial and commercial equipment subjected to very low voltages by boosting voltages faster than what is possible using capacitors.

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• • • • • •

Damping of subsynchronous power system oscillations Balanced loading of individual phases Reactive compensation of AC-DC converters and HVDC links Power quality improvement Flicker control Application involving energy storage

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Table 2 Comparison of SVCs and STATCOMs Attributes Semiconductor device

SVC Thyristor

V/I characteristic

Superior overvoltage performance Bulk transmission system and in the past in industrial applications Branches optimally designed for any range

Application

Reactive power range

Short circuit level requirement Valve reaction time –inherent switching frequency of the valves Low-frequency harmonics High-frequency harmonics (>30th) Power quality (flicker, voltage sags, load balancing, active filters) Availabilityb Footprint

Losses

Renewables and distributed generation Technology status

hrated/SCC > 3–4a (lower values require advanced control strategies) half-cycle

Higher content due to TCR harmonic generation Low content Good capability for voltage sags High (>99%) Larger depending on the rating and number of branches Lower total losses than STATCOM at full capacitive/ reactive operation More difficult to comply with some Grid Codes Mature with limited scope for valve improvements; wellknown among utilities

STATCOM IGBTs or any other high-power device with turn-off capability Superior undervoltage performance High/medium/low voltage (T&D)

Naturally symmetrical; asymmetrical ranges achieved with hybrid STATCOM/TSC/TSR (See Fig. 11) Virtually any Qrated/SCC

1–2 ms

Negligible content if properly controlled Very low content but still needs to be analyzed Superior performance at fast load variations; active filter capability (when properly dimensioned) High (>99%) Small; larger for hybrid STATCOMs Lower no load losses than SVC at 0 Mvar Easier integration for achieving Grid Code compliance Technology is mature but still improving; number of applications increasing particularly at lower voltages

Qrated = SVC or STATCOM rated reactive power; SCC = short circuit capacity Availability should be driven by the power system and customer requirements, not from the technology

a

b

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Except for the last bullet, all other features can also be provided by SVCs. It is important to highlight that if an energy source, such as a battery bank, is connected to the VSC, then the VSC is able to absorb energy and deliver this energy to the AC network. This concept is important because it helps to develop the theory behind a UPFC which is described in Sect. 7 (Larsen et al. 1992; Gyugyi et al. 1995). Table 2 shows a comprehensive comparison between STATCOM and SVC, providing the pros and cons of these FACTS controllers (Tenório 2014) It is worth mentioning that for overload inductive cycles such as the one described in Table 1, a STATCOM is not able to respond unless the semiconductor valve is designed for the maximum overvoltage, which may be costly. This is due to the high overvoltages demanded by power system with long lines and their respective switching transients. The use of thyristor-switched reactors (TSR) and/or thyristor-switched capacitors (TSC) combined with STATCOM has emerged for these transient overvoltage conditions. This is known as hybrid STATCOMs and brings out cost-effective design for applications that require the control of high transient overvoltages (TOV) or asymmetrical rating output. Combining the technologies of multilevel VSC (STATCOM) and the thyristor-based SVC results in an optimized FACTS controller regarding robustness, security and reliability, under- and overvoltage performance, TOV at fault clearing, speed of response, losses, etc. (Halonen and Bostrom 2015). A hybrid STATCOM schematic diagram is shown in Fig. 11. A more detailed technical description of the STATCOM can be found in ▶ Chap. 7, “Technical Description of Static Compensators (STATCOM).” Application examples of the STATCOM can be found in ▶ Chap. 13, “Application Examples of STATCOM.” Fig. 11 Hybrid STATCOM/ TSR/TSC

Vdc

VSC

Vdc

TSR

TSC

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Description and Functions of TCSCs

As described in ▶ Chap. 3, “AC Network Control Using Conventional Means,” series compensation is a proven technology that meets different needs of power systems. Series capacitors have been successfully used for many years in longdistance overhead transmission lines to improve the stability and power transfer capacity in transmission systems. Series capacitors have the effect of inserting a voltage in series with the transmission line whose polarity is opposite to the inductive voltage drop across the line. This results in a decrease of the apparent reactance of the transmission line. It is then possible to achieve high real power flows continuously through the line or by controlling the series reactance of the capacitor bank stepwise, high power flows for short time during emergency loading conditions. If control is added to a fixed capacitor, the inserted capacitor reactance can vary physically or virtually. Such control means may be based on mechanical switching equipment or power electronic devices. The insertion of a series capacitor element can be accomplished in two to five cycles depending on the type of switches that are used for the insertion operations. Once the additional series compensation is switched in, typically it will remain inserted until the operators have managed the situation that led to the need for the insertion before the inserted series capacitor element will be bypassed. This is in recognition of the fact that mechanical switching is relatively slow and has a limited duty cycle. When using power electronics, the effective capacitance inserted can be controlled very fast, and the constraints resulting from the use of conventional switches are removed, and the power flow can be controlled in accordance with preset strategies. The TCSC can provide the following benefits: • Compensation of long transmission lines to increase power flows • Control of power flow in lines, e.g., to prevent loop-flows of real power or prevent overloading of other lines • Improvement of transient stability and dynamic stability (power oscillation damping) More detailed technical description of the TCSC is provided in ▶ Chap. 8, “Technical Description of Thyristor Controlled Series Capacitors (TCSC).”

5.1

Principle of Operation

TCSC is equipment that belongs to what is generically called “Controllable Series Capacitor.” For controllable series capacitors, Eq. 1 becomes Eq. 8. Psr ¼

V sV r sin δsr X  Xc

(8)

where X is the line reactance and Xc is the net reactance of the controllable series capacitor. Therefore, the higher Xc, the higher the transmitted power.

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If Xc is controlled, the power flow can be adjusted to meet power system requirements. It is usual to define the factor λ=Xc/X as a compensation degree of the transmission line. Then the Eq. 8 may be written as: Psr ¼

V sV r sin δsr X ð1  λÞ

(9)

The TCSC is a conventional fixed series capacitor in parallel with a thyristorcontrolled reactor, similar to those used in SVCs except there is at least one reactor used for each of the three AC phases: that is, the controlled reactors are not connected to the high-voltage buses by means of a coupling transformer. Figure 12a shows a simplified schematic diagram of a TCSC and the main components of the TCSC. Figure 12b highlights the metal oxide varistors (MOV) typically used to protect the series capacitor when the current passing through the series capacitor bank increases due to short circuits. The TCSC is used for applications that require sophisticated, continuous, and fast control of the series impedance of a transmission line. Each thyristor valve is triggered twice per cycle. Since there is one valve per phase, the TCSC’s switching

Fig. 12 Generic schematic diagram of a TCSC

Compensated Transmission Line

a

TCSC

Local Signal Network Elements Ref

Main Control

Firing Control

Supplementary Control Remote Signals

b

MOV I line

C

L Thyristor Pair

Control System

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To Buckley

109 To Slatt

Bypass Disconnect

Isolation Disconnect

TCSC Module

Series Capacitor

Isolation Disconnect (with Resistor)

Varistor

Reactor Reactor

Thyristor Valve Bypass Breaker

Fig. 13 Single line diagram of Slatt TCSC – six-module TCSC commissioned in the USA

frequency in steady state is six times the power frequency. That is, the TCSC can begin to respond to a change in its operating point within just a few milliseconds. The capacitor is effectively bypassed if the thyristors are triggered such that the reactor carries continuous current. In this operating mode, the TCSC can be represented by a small series reactor. TCSCs can be a single module as shown in Fig. 12b or multi-module, i.e., with several modules in series, which allow the TCSC impedance to be controlled continuously and/or stepwise for each TCSC module. Figure 13 shows the single line diagram of a multi-module TCSC, which was commissioned in the USA, Slatt Substation, in the 1990s (CIGRE TB 554 2013; Piwko et al. 1994). The Slatt TCSC comprises six identical TCSC modules connected in series. Each module consists of a capacitor and a thyristor valve with its associated reactor and a varistor. The modules are independent and each one can operate either bypassed or inserted. When a module is bypassed, the thyristors are triggered for full conduction, and the effective reactance is slightly inductive due to the reactor in series with the valve. This design enables control of the power flows in the line over a wide range. However, other installed systems do not require this capability and therefore are typically designed to look like one module shown in the Slatt diagram. The impedance characteristic of a typical TCSC seen from fundamental frequency is shown in Fig. 14, which depicts a resonance point, around 143 electrical degrees, that has to be avoided by the control system. TCSCs usually work in a range from the resonant point, with some safety margin, up to 180 electrical degrees, when the TCR is blocked and the TCSC impedance is its natural series capacitor reactance. Close to the resonant point, the TCSC develops its maximum capacitive impedance. The inductive range is not usually used, except at the firing angle of 90 electrical degrees at which the inductive reactance is given by Eq. 10.

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Resonance

Fig. 14 Typical TCSC fundamental Impedance

X TCSC ¼ j

ðX C X L Þ ðX C  X L Þ

(10)

It is important to note that the reactance boost is due to the current through the capacitor and the inductor (when the TCR is conducting). This causes the non-sinusoidal voltage boost (jump) as seen in Fig. 15. Note that the line current continues to be almost sinusoidal, and the harmonic currents are primarily circulating through the capacitor and inductor only (Edris 1994). The natural resonant frequency of the TCSC circuit, k, is given by Eq. 11, expressed in per unit of the fundamental frequency (Tenório 1995). k¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X C =X L

pu

(11)

Furthermore, the firing angle α at which the TCSC develops a resonance can be expressed by Eq. 12. αr ¼ π  ð2n  1Þ:

π rd 2k

for n ¼ 1,2, . . .

(12)

The principle of operation of a TCSC depends on the function that the TCSC performs. The main functions and/or applications are: • Damping interarea power oscillations • Transient stability improvement • Damping subsynchronous resonance caused by torsional oscillations

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20 VC

15

Voltage Boost

VC/IC/IR/lline [V,A]

10 5

IC Iline

0 IR

-5 -10 -15 -50

0

50

100

150

200

250

wt (electrical degrees)

Fig. 15 Currents (capacitor & inductor) and voltage waveshapes of a TCSC – voltage boost when the TCR starts conducting

• Power flow control • Fault current limiter Using the TCSC it is evident from Eq. 9 that it would be possible to control the power flow through a transmission line by changing the control angle in the capacitive range by retarding the triggering point for the thyristor valves thereby boosting the degree of line compensation as shown in Fig. 14 without changing the angle δsr. That is, the line can be operated with a higher degree of compensation than, as discussed in ▶ Chap. 3, “AC Network Control Using Conventional Means,” is typically applied using fixed series compensation systems. The ability of the TCSC to provide damping of low damped oscillatory modes in the power system in addition to the ability of the TCSC to provide damping of large system swings after a system disturbance makes it possible to safely use a higher compensation degree with TCSC than for fixed compensation systems.

5.1.1 Damping Interarea Power Oscillations TCSCs are usually used as a part of the line compensation in such a way as to dynamically control the line reactance (CIGRE TB 554 2013). TCSCs are usually installed in addition to a fixed series capacitor, which provide the main part of the line compensation. The fixed series capacitor provides the increase of synchronizing torque; therefore, it increases the transient stability of the power system. The TCSC provides damping torque through its reactance modulation.

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MASTER CONTROL

Vref

.

V. TCSC Control

SYSTEM-1

TCSC

POD

P SYSTEM-2

Fig. 16 Schematic diagram of two power systems interconnected by a fixed series capacitor and a TCSC

Fig. 16 shows a schematic diagram of two power systems interconnected by a fixed series capacitor and a TCSC compensated transmission line (CIGRE TB 554 2013). When two power systems are interconnected by an AC link, a low frequency, interarea mode is established. The larger the two system inertias, the lower the interarea mode frequency. Furthermore, the weaker the AC link capacity, the lower the interarea mode frequency. The international experience with Power System Stabilizers (PSS) usage on generators for damping electromechanical frequencies is widespread (Kundur 1994). However, the range of electromechanical frequencies for PSS usage lies within 0.5–2.0 Hz. For lower frequencies (0). A controlled change of the TCSC reactance into TSR mode is very important to damp the power oscillations effectively and also avoids the operating region close to the parallel resonance shown in Fig. 15.

5.1.2 Fault Current Limiter The TCSC’s ability to rapidly vary its impedance continuously or stepwise can be used to limit fault currents. The TCSC can change from a capacitive range of operation to a fixed inductive impedance, expressed by Eq. 9, through the TSR mode. This functionality takes full advantage of the inherent speed of solid-state devices. Many TCSCs in operation use the TSR mode to protect itself against high short circuit currents and inherently limit the current due to the inductive reactance developed when the TCR is fired at 90 electrical degrees. Ideally, to perform as a fault current limiter, the TCSC should be designed to withstand the short circuit current and develop a high inductive impedance. Therefore, it is necessary to change some characteristics of the TCSC, such as equipment ratings and the natural resonance frequency of the LC (inductance-capacitance) circuit. To limit the fault current or power flow, one could just add a single reactance in series with the transmission line. Such a scheme is sometimes used for industrial applications. However, this has some disadvantages during steady-state operation including an increase of power losses and voltage drop as a result of the increased inductive line reactance. Although TCSCs also add losses to the power system, they may be located and controlled in such a way as to decrease the overall losses, by diverting the power flow to lines with lower power loss. The proper design of a TCSC for current limiting applications is outside the scope of this chapter. Simulation results are shown in Fig. 18, demonstrating the use of a TCSC as a fault current limiter (Tenório 1995). The strategy used for detecting the fault current was based on the rate of rise of the line current. The fault applied was a three-phase short circuit that remains up to the end of the simulation. The power system simulated consists of a 100 km, 230 kV transmission line that feeds three loads. The short circuit capacity from the generation is 10 GVA. The fault started at 30 ms, and it was located at the opposite end from the TCSC on the 230 kV transmission line.

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Fig. 18 Fault currents for phases a, b, and c fault current amplitude (dotted green: with TCSC/solid red: without TCSC)

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Figure 18 clearly demonstrate the current limitation resulting from using a TCSC in this power system

5.1.3 Damping Subsynchronous Torsional Oscillations According to the IEEE Subsynchronous Resonance (SSR) Working Group (IEEE 1980), subsynchronous oscillation (SSO) is “an electric power system condition where the electric network exchanges significant energy with a turbine-generator at one or more of the natural frequencies of the combined system below the synchronous frequency of the system following a disturbance from the equilibrium.” The term subsynchronous resonance is a particular case and describes the electromechanical subsynchronous oscillations associated with turbine-generator shafts and a series capacitor compensated power system when the oscillatory energy exchanged tends to grow. Figure 19 shows a simple power system that models the IEEE first benchmark system for SSR studies (IEEE 1977). For a simple power system such as that shown in Fig. 19, the natural electrical frequency is given by equation: 1 f e ¼ pffiffiffiffiffiffiffi ¼ f o 2π LC

rffiffiffiffiffiffiffi XC XL

(13)

where f0 is the electrical frequency corresponding to the synchronous frequency under ideal conditions), XC is the series capacitor reactance, and XL is the total reactance of the power system. However, complex power systems often have more than one resonant frequency and the analysis is more complex (Piwko et al. 1996). When the power system resonance is excited, it causes oscillating currents at electrical frequency fe in the stator, which give rise to rotor currents at subsynchronous ( fm=fofe) and supersynchronous ( fm=fo+fe) frequencies. If the subsynchronous frequency is near a torsional mode of oscillation, SSR problems may occur and could lead to the destruction of the generator shaft due to fatigue. There are different ways of identifying interactions between the turbine-generator shafts and power systems. These phenomena can be divided into self-excitation and transient torques. The self-excitation phenomena can be divided further into two types: induction generation effect and torsional interaction (Tenório 1995; Anderson et al. 1990). The TCSC can be designed to produce an inductive equivalent impedance at a range of subsynchronous frequencies. With this approach, the TCSC is neutral from an SSR standpoint within this range (Tenório 1995).

Fig. 19 Single line diagram of the IEEE first benchmark system

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In addition to the control system based on phase angle control, there is a control method used by some TCSCs called SVR (Synchronous Voltage Reversal) scheme. This control method has been proposed in (Ängquist et al. 1994). In this method the TCSC is controlled in terms of equivalent instantaneous voltage reversals. Instead of controlling directly the thyristor firing angle in order to set a determined TCSC reactance, this method controls the instant when the capacitor voltage reverses its polarity. At this instant the line current is at its maximum value. According to Ängquist, the capability of accomplishing controllable voltage reversals can be regarded as the main mechanism of interaction between the TCSC and the transmission system. Note that in this approach, it is assumed that the finite time in which capacitor voltage reverses its polarity (during thyristor conduction) can be approximated by an instantaneous voltage reversal (voltage boost) instead of a voltage ramp, as can be seen in Fig. 20 (Ängquist et al. 1996). To illustrate the capability of TCSCs of damping subsynchronous torsional oscillations, some simulation results are shown in Figs. 21 and 22. Both results were obtained by running a TCSC model developed in the ATP program (Tenório 1995 and Tenório et al. 1998). A simulation was carried out considering a 50 Ω series capacitor, which meant a compensation degree of approximately 35% in the power system shown in Fig. 19. According to Equation 13, the theoretical resonant frequency excited due to the short circuit is 27.7 Hz. The complementary frequency, i.e., 32.3 Hz (60–27.7), coincides with the fourth torsional mode of oscillation at 32.3 Hz. As a result there is a destabilization of this mode of oscillation that leads to a torsional interaction. Fig. 20 Instantaneous voltage reversal in steady state

LINE CURRENT

t

CAPACITOR VOLTAGE

BOOST t

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TORQUE3 (PU)

40.00

0.00

-40.00 0.00 60.00

TORQUE4 (PU)

5.00

10.00

TIME(S)

0.00

-60.00 0.00

5.00

10.00

TIME(S)

Fig. 21 IEEE first benchmark with Xc=50 Ω – buildup of torsional oscillations

TORQUE3 (PU)

1.00

0.00

-1.00 0.00 1.00

TORQUE4 (PU)

5.00

10.00

TIME(S)

0.00

-1.00 0.00

5.00

10.00

TIME(S)

Fig. 22 IEEE first benchmark with TCSC reactance order at 50 Ω – slightly damped torsional oscillations

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If a TCSC is inserted in the power system with a reactance order equal to 50 Ω, no SSR interaction is observed. Figure 22 shows torques 3 and 4 on the shaft which are slightly damped. Spectral analysis shows that no resonant frequency is found below 60 Hz (fundamental frequency). This demonstrates that from the network standpoint, at SSO frequencies, the TCSC does not behave as a capacitor; rather it develops inductive-resistive behavior. A properly designed TCSC will enhance power system stability and avoid the risk of SSR problems. In addition, the transient torques can be decreased by action of the TCSC, and this performance can be improved by using an SSDC (Subsynchronous Damping Control).

5.1.4 Power Flow Control Increasing the firing angle α toward the resonant point can only be used to dynamically control the TCSC impedance. It is worth remembering that the increase of TCSC impedance is a function of the current that passes through it. Figure 23 shows a typical impedance-current chart for a TCSC rated at 1500 A. As can be seen, the higher the TCSC current, the lower the TCSC impedance. For a single-module TCSC, it is possible to vary the TCSC impedance in accordance with its impedance-current characteristic, but at nominal current, the boost factor (XTCSC/XC) is typically about 1.20 pu. Therefore, running the TCSC at 3 pu of impedance is only possible for a limited period of time, depending on the operating line current (see Fig. 23). Controlling the active power flow using only a single TCSC module per phase seems not to be possible due to natural constraints of the capacitor bank and varistor rating. XTCSC XC 3,0

(pu)

Continuous 30 min. Overload 10 sec. Overload

Capacitive Xef Xc

1,2 1,0

Nominal Current Line Current (A)

0,0 X bypass –0,5

1500 1800

2700

Inductive

Fig. 23 Typical impedance-current capability characteristic (In = 1500 A)

3600

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Due to Eq. 1, it is not possible to change the sign of sine of δ; therefore, TCSCs are not capable of reversing the active power flow. To control the power flow in a transmission line, it would be necessary to install multi-module TCSCs and use them in a stepwise strategy, which may result in high costs of the TCSC but might still be a cost-effective approach if the power flow control capability can be used to schedule the power flows through desired transmission corridors. A more detailed technical description of the TCSC can be found in ▶ Chap. 8, “Technical Description of Thyristor Controlled Series Capacitors (TCSC).” Application examples of the TCSC can be found in ▶ Chap. 14, “Application Examples of the Thyristor Controlled Series Capacitor.”

6

Description and Functions of SSSCs

The Static Synchronous Series Compensator (SSSC) as described by CIGRE (CIGRE TB 371 2009) comprises a VSC connected in series with a transmission line, as shown in Fig. 24. It provides a voltage in series with the line that emulates either a capacitor or a reactor, thus defining a degree of series compensation. Unlike the TCSCs, because the SSSC injects a voltage in quadrature with the line current instead of modulating the line’s impedance, SSSCs can operate in a wide reactive power range. As a VSC it can provide a superior performance when compared to thyristorbased series controllers. For instance, being a voltage source, it can provide series compensation even at low but higher than zero line currents, i.e., the SSSC compensates the line independently of the line current, but if the line current is zero, it might need to have a source for charging of the DC side capacitor at startup. One issue related to the series connection of the converter, via a series transformer, is the occurrence of disturbances, e.g., line faults, leading to high line currents that cannot be handled by the semiconductor valve. Therefore, a fast bypass of the SSSC, resulting in zero inserted voltage, is always required for protection of the SSSC. The bypass function must operate with a very short delay requiring a solid-state bypass switch using high power thyristors. Mechanical, high-speed Fig. 24 Schematic diagram of an SSSC (CIGRE TB 371)

VC l

l

-

+ Vdo

Static Synchronous Series Compensator - SSSC -

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bypass switches are also needed to protect the solid-state bypass switches from being overloaded. Therefore, after a mechanical bypass operation, there will be some delay before the SSSC can be put back into operation. Also, the coupling transformer adds cost and introduces losses in the circuit. That is, there will be a cost and loss penalty in the evaluation of the SSSC-type system, compared with a TCSC. However, an SSSC does not require a platform, which reduces the visual impact. The main functions of the SSSCs are similar to those of TCSCs. According to CIGRE (CIGRE TB 371 2009), the main functions of SSSCs for a power system are in many ways similar to the functional requirements of a TCSC system: • Compensation of long transmission lines to increase power flows • Control of power flow in lines, e.g., to prevent loop flows of real power or prevent overloading of other lines • Receiving end voltage regulation of a radial line • Improvement of transient stability and dynamic stability (power oscillation damping) A more detailed technical description of the SSSC can be found in ▶ Chap. 9, “Technical Description of the Unified Power Flow Controller (UPFC) and Its Potential Variations.” Application examples of the SSSC can be found in ▶ Chap. 15, “Application Examples of UPFC and Its Variants.”

7

Description and Functions of UPFCs

Combined series-shunt compensation has the ability to decrease the apparent transmission line length by using series compensation and at the same time to control the line charging by using shunt compensation. In steady-state these compensations increase the surge impedance loading (SIL) of the transmission line permitting an increase in its transmission capacity, besides controlling the power flow (phase angle control). In addition, series-shunt compensation can enhance the power systems in different ways, e.g., by providing improvement of transient stability and damping of power oscillations, reactive power and voltage control/supply, dynamic load-flow control, etc. Traditionally AC power systems have been designed making use of mechanically switched series and shunt compensation in addition to voltage regulating equipment and phase-shifting transformers to control power flows (CIGRE TB 160 2000). Active and reactive power within an AC network are dependent on the voltages, phase angle, and impedance of the sending and receiving ends, as shown in Eqs. 1 through 4. If one can control these quantities, then it is possible to develop a universal controller for AC systems. These ideas have been pursued for a long time. The UPFC stands for unified power flow controller, and it provides controllability and flexibility for AC power systems. The UPFCs can act as STATCOMs and/or SSSCs in a joint control strategy and can inject active power into the line from the shunt connected VSC in the STATCOM into the series connected VSC. This can be used in both steady-state and dynamic

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Fig. 25 Schematic diagram of a UPFC

mode to improve power system performance. In addition to this primary goal, other functions can be added (CIGRE TB 160 2000): • Transient stability improvement • Power oscillation damping • Voltage stability improvement A schematic diagram of a UPFC can be seen in Fig. 25. The multi-compensating functions of a UPFC are achieved by means of two “back-to-back” VSCs coupled to a DC link capacitor, as indicated in Fig. 25. Converter 2 injects a power frequency voltage in series with the transmission line. The magnitude and phase angle of the injected positive sequence voltage are fully controllable. Depending on the phase angle of the voltage, converter 2 can control the level of series compensation or phase angle shifting. The series compensation level is defined by the component of the injected voltage in quadrature with the transmission line current. The component of injected voltage in quadrature with the transmission line voltage defines the phase angle control. The semiconductor switches used in converter 2 will be exposed to fault currents flowing through the AC line in which the UPFC is connected. The short circuit duty of these semiconductor switches might not be able to withstand the short circuit duties and may require fast-acting bypass switches to be installed that shunts the fault currents away from the converter (TB 160 2000). High power thyristor switches can be used for this, in which case the series converter can be put back into operation quickly after the cause of the short circuit currents have been eliminated (CIGRE TB 371 2009). Mechanical bypass switches might be used and will probably have to be installed to protect the thyristor switches. However, the restoration of the UPFC’s operation might then be delayed until the mechanical bypass switches have been opened again.

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Converter 1 has the basic function of supplying or absorbing the active power demanded by converter 2. In addition, converter 1 can act as a STATCOM, i.e., it can absorb or generate reactive power to the transmission system (Tenório 1995). The UPFC is the most complete and versatile of all FACTS controllers analyzed. It can use different control strategies, and it is able to control all quantities related to the power transfer and active and reactive power equations in a unified manner. That is, it can control the impedance of the line, the phase angles between the ends of the line, and the voltage at the point where the UPFC is connected. However, for long lines where distributed reactive compensation systems are needed and where shunt and series compensation systems might not be needed at the same points of the line, distributed UPFC systems might not be a practical, cost-effective approach. A more detailed technical description of the UPFC can be found in ▶ Chap. 9, “Technical Description of the Unified Power Flow Controller (UPFC) and Its Potential Variations.” Application examples of the UPFC can be found in ▶ Chap. 15, “Application Examples of UPFC and Its Variants.”

8

Power Losses in FACTS Controllers

The different FACTS controller options have different degrees of efficiency. Many FACTS controllers operate with outputs that vary with the operation of the power system. That is, there are daily, weekly, and seasonal duty cycles for these controllers. For these, both load and no load losses have to be considered. Some FACTS controllers are used only for specific contingencies. In that case, only the no load losses need to be considered. Most FACTS controllers include a power transformer for connection to the AC system. The no load and load losses in these transformers add to the losses in the power electronic subsystems in the FACTS controllers. The only FACTS controller that is not connected to the power system by means of a transformer is the TCSCs since they are placed on insulated platforms at power line potential.

9

System Security and Reliability

The introduction of FACTS technologies has raised concerns for the continued reliability of the power system. These questions are legitimate because FACTS does increase the stress level in the systems. However, FACTS technologies are not all new. Systems like HVDC behave in much the same way, and these systems have been successfully applied for decades. We also have experience from applications of SVCs since the late 1970s. Although there have been some unexpected problems resulting from installation of HVDC and static-var systems (an example is subsynchronous interactions between HVDC systems and nearby located turbo generators), all of these problems have been solved without many major problems. Thus, there is a significant experience base from which to build when FACTS is more widely introduced. The problems to consider are:

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• Will a failure of a FACTS controller (N-1 case) lead to security problems (N-2+ case)? That is, will the system become unstable for an outage of a FACTS controller itself or cause a cascading failure of the system? • Will a system disturbance with the loss of some part of the system (N-1 situation) also lead to an outage of the FACTS controllers (N-2+ situation)? • Will an outage of the auxiliary power systems lead to a situation that disables the entire FACTS controller and potentially cause equipment damage that prevents restoration of the operation? For example, redundant cooling pumps is not sufficient if the power to run the cooling pumps is lost or if a single source of raw water to the heat exchanges is lost. That is, single points of failures in the support systems must be considered when doing a system security study. • Will FACTS controllers interact destructively with other FACTS controllers, HVDC systems or PSSs, etc.? These aspects of FACTS controller installations need to be carefully studied to ensure that any potential system security issues are identified and that the operating domains and needs for redundancies within the FACTS controllers are properly included in the FACTS controller specifications. The reliability of the available FACTS controllers discussed in this chapter are proven from many years of use. Some of the controllers are modular and might then be able to operate in a degraded mode, which might provide higher availability. Also, FACTS controllers with lower complexity could also be an advantage. Based on comparisons with mature HVDC and SVC technologies, it can be assumed that the failure rate of the semiconductor components will be low. Semiconductor device redundancy is normally used to avoid forced outages for replacement of semiconductor devices. Too much redundancy is not desirable because it adds costs and losses. The coupling transformers used in FACTS controllers are similar to those used as generator step-up transformers or distribution stepdown transformers, which are based on proven technologies. The control equipment used in FACTS controllers is in many respects similar to the types of systems used in HVDC converter stations. The major issue is to have a maintainable life for the expected useful operating life of the FACTS controllers. This is an issue that affects all modern, digital control and protection systems because the design life of this type of equipment is typically short. In conclusion, the reliability of modern FACTS controllers can be expected to be good.

10

Conclusions

The main emphasis in this chapter has been to describe the proven FACTS concepts, their characteristics, and in principle their applications in power systems to meet ever-changing needs of system operators and planners. Therefore, in this chapter,

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other FACTS controllers that have been proposed or might be under development have not been included. In this chapter, the main performance characteristics of the proven FACTS controllers have been provided to guide the readers, who might consider procurement of FACTS controllers. However, it is not sufficient to consider only technical performance aspects of FACTS controllers. In addition to the performance requirements, costs (including cost of losses), reliability, complexity, and the need for distributed compensation in power systems must also be considered. When solutions to system issues can be resolved using breaker-switched equipment, e.g., capacitors or reactors, or by addition of power oscillation dampers in generators, then such solutions are likely to provide the cheapest option. However, when these measures cannot meet the required performance, then FACTS controllers should be considered and may be able to achieve the required performance without the need for construction of additional generators, overhead lines or cables, or at least to defer these investments.

References Anderson, P.M., Farmer, R.G.: Series Compensation of Power System, p. 49. PUBLSH! Inc., Encinitas (1996) Anderson, P.M., Agrawal, B.L., Van Ness, J.E.: Subsynchronous Resonance in Power Systems. IEEE Press, New York (1990) Ängquist, L.: Synchronous Voltage Reversal Control of Thyristor Controlled Series Capacitor, Ph.D. thesis. Royal Institute of Technology, Stockholm (2002) Ängquist, L., Gama, C.A.: Damping Algorithm Based on Phasor Estimation. IEEE WM, Columbus (2001) Ängquist, L., Ingeström, G., Othman, H.: Synchronous voltage reversal (SVR) scheme – a new control method for thyristor controlled series capacitors, Flexible AC Transmission System (FACTS 3): The Future in High-Voltage Transmission, 5–7 Oct. Baltimore (1994) Ängquist, L., Ingeström, G., Jönsson, H-Å.: Dynamical Performance of TCSC Schemes, paper 14-302, CIGRÉ Session (1996) CIGRE TB 144: Static Synchronous Compensator (STATCOM), WG 14.19, Cigre Technical Brochure TB 144, Paris (1999) CIGRE TB 160: Unified Power Flow Controller (UPFC), Cigre Technical Brochure 160. Paris (2000) CIGRE TB 371: Static Synchronous Series Compensator (SSSC), Cigre Technical Brochure 371, Paris (2009) CIGRE TB 554: Performance Evaluation and Applications Review of Existing Thyristor Control Series Capacitor Devices –TCSC; Technical Brochure 554. Cigre, Paris (2013) CIGRE TB 663: Guidelines for the procurement and testing of STATCOMS, Cigre Technical Brochure TB 663, Paris (2016) CIGRE TB 78: Voltage and Current Stresses on Thyristor Valves for Static Var Compensators, CIGRE Technical Brochure 78 (1993) Edris, A.A.: Flexible AC Transmission Systems – The State of the Art, IV SEPOPE, paper IP17, Foz do Iguaçu (1994) Elgerd, O.L.: Electric Energy Systems Theory – An Introduction, chapter 2, Second edition, International Student edition. McGraw-Hill International Company, Tokyo (1983)

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Gama, C.A., Leoni, R.L., Gribel, J., Eiras, M.J., Ping, W., Ricardo, A., Cavalcanti, J., Tenório, R.: Brazilian North-South Interconnection – Application Of Thyristor Controlled Series Compensation (TCSC) To Damp Inter-Area Oscillation Mode, paper 14-101. Cigre, Paris (1998) Gama, C., Ängquist, L., Ingeström, G., Noroozian, M.: Commissioning and Operative Experience of TCSC for Damping Power Oscillation in the Brazilian North-South Interconnection, paper 14-104, CIGRÉ Session (2000) Gyugyi, L., Schauder, C.D., Williams, S.L., Rietman, T.R., Torgerson, D.R., Edris, A.: The unified power flow controller: a new approach to power transmission controller. IEEE Trans. Power Delivery. 10(2), 1085–1097 (1995) Halonen, M., Bostrom, A.: Hybrid STATCOM Systems Based on Multilevel VSC and SVC Technology, HVDC and Power Electronics International Colloquium. Cigre, Agra (2015) IEEE Subsynchronous Resonance Task Force: First benchmark model for computer simulation of subsynchronous resonance. IEEE Trans. Power Syst. PAS-96(5), 1565–1572 (1977) IEEE Subsynchronous Resonance Working Group: Proposed terms and definitions for subsynchronous oscillations. IEEE Trans. Power Syst. PAS-99(2), 506–511 (1980) Kundur, P.: Power System Stability and Control. McGraw-Hill, Inc, New York (1994) Larsen, E.V., Miller, N.W., Nilsson, S.L., Lindgren, S.R.: Benefits of GTO-based compensation systems for electric utility applications. IEEE Trans. Power Delivery. 7(4), 2056 (1992) Piwko, R.J., Wegner, C.A., Damsky, B.L., Furumasu, B.C., Eden, J.D.: The Slatt thyristorcontrolled series capacitor project – design, installation, commissioning and system testing, CIGRE, paper 14-104, Paris (1994) Piwko, R.J., Wegner, C.A., Kinney, S.J., Eden, J.D.: Subsynchronous resonance performance tests of the slatt thyristor-controlled series capacitor. IEEE Trans. Power Delivery. 11(2), 1112 (1996) Tenório, A.R.M.: A Thyristor Controlled Series Capacitor Model for Electromagnetic Transient Studies, MSc thesis, University of Manchester, UK (1995) Tenório, A.R.M.: SVCs vs STATCOMs, Contribution to PS2/Q2.7, Cigre Session, Paris (2014) Tenório, A.R.M., Carvalho, A.R., Ping, W.W.: Thyristor Controlled Series Capacitor: A Means Of Improving Power Systems Stability Without Impacting SSR Interactions, V SEPOPE, Salvador, Brazil, 8–10 May (1998) Tenório, A.R.M.T., Nohara, A.A., Aquino, A.F.C.: Brazilian Experience Regarding Interactions between Series Capacitors and SVCs – Main Challenges of Tucuruí-Macapá-Manaus Interconnection Project, Cigré, paper B4-201. Paris (2016)

Antonio Ricardo De Mattos Tenório received his BSc degree with honors in Electrical Engineering from Federal University of Pernambuco, Brazil, in 1982, and his MSc in Electrical Power Engineering from University of Manchester, UK, in 1995. In 2010, he did an MBA at PUC-Rio (Pontifical Catholic University, Rio de Janeiro, Brazil) in Energy Business. Mr. Tenório joined CHESF (Brazil) in 1982 and in 2000 joined ABB Power Systems in Sweden, moving back to join ONS in Brazil in 2004, where he has been working since then. Mr. Tenório is an IEEE and CIGRE Member. He has been serving the CIGRE Brazilian National Committee as Secretary (2012–2016) and Charmain (since 2016) of the Brazilian Study Committee B4, being the Brazilian regular member of Study Committee B4 – DC systems and Power Electronics (since 2016). His area of interest includes HVDC links, FACTS controllers, Electrical and EMT studies, and Power Quality.

Part III Technical Description of FACTS Controllers

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Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Semiconductor Switching Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Semiconductor Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Devices of the Thyristor Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Devices of the Transistor Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Line-Commutated Thyristor Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Building Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Self-Commutated Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Current-Sourced Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Voltage-Sourced Converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Self-Commutated Converter Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

130 131 131 131 134 136 136 139 140 140 141 152 153

Abstract

Several types of semiconductor device can be used in FACTS applications. So-called line-commutated converter applications, such as SVCs, use inverseparallel-connected pairs of thyristors. The inability of such devices to turn off by control action limits their applicability. More sophisticated semiconductor devices can turn off by control action as well as turn on and allow selfcommutated converters, usually voltage-sourced converters (VSC), to be realized. VSCs most commonly use insulated gate bipolar transistors (IGBTs) as the switching devices. However, there are many ways of arranging switching devices to form a high-power VSC, the choice being a compromise between power ratings, harmonic performance, and complexity. For applications of relatively C. Davidson (*) GE Grid Solutions – Grid Integration, Stafford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_6

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low power, the well-known six-pulse Graetz bridge circuit, used with pulse width modulation to give acceptable harmonic performance, is widely used. At higher power levels, the modular multilevel converter (MMC) circuit using half- or fullbridge submodules connected in series gives excellent scalability and waveform quality.

1

Introduction

Since electric power transmission systems were developed, there has always been a need to convert direct current (DC) to alternating current (AC) or vice versa. Furthermore, the constant operating frequency of an AC system made it difficult to create variable speed motor drives for applications in industrial processes, electric locomotives, elevator drives, etc. This changed with the invention in the 1930s of the grid-controlled mercury arc rectifier and in the 1950s of the so-called siliconcontrolled rectifier (SCR) or thyristor. These innovations enabled an efficient means of converting AC to DC and vice versa at high power without using large rotating converters. A thyristor is a four-level semiconductor device with alternating p and n doping, that is, a p-n-p-n-type device (Bardeen 1967). This type of device is based on semiconductor technology that grew out of research at Bell Labs in the USA (Moll et al. 1956). The thyristor devices were commercialized by General Electric Co. (GE) at about the same time (semiconductors). The semiconductor-based technology that can be applied for power conversion in AC and DC systems has grown to include many different devices, which enable high-voltage DC (HVDC) power transmission as well as for FACTS systems used for reactive power compensation and for control of power flow in AC systems (CIGRÉ TB 337). The thyristor cannot be turned off by control action, and this limited its application to so-called line-commutated converters, where the AC system creates the conditions needed for the thyristor to turn off. More sophisticated types of semiconductor devices, capable of being turned off as well as on by control action, are needed to remove this dependence on the connected AC system for commutation. Such “self-commutated converters” can be voltagesourced or current-sourced. Switching devices used in voltage-sourced converter (VSC) applications need to be able to block voltage or pass controllable current only in the forward direction while passing uncontrolled current in the reverse direction. Such applications are therefore usually implemented with an asymmetric switching device (i.e., one whose reverse voltage withstand capability is significantly lower than its forward voltage withstand capability) and an inverse-parallel “freewheel” diode. Switching devices used in a current-sourced converter (CSC) need to be able to block voltage of either polarity but are only required to pass current in the forward direction. This chapter gives an overview of the main semiconductor and converter building blocks used to build FACTS controllers.

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Semiconductor Switching Devices

2.1

Semiconductor Materials

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Semiconductors are a class of materials with properties intermediate between those of conductors and insulators. In their pure state, semiconductors are very poor conductors of current, but their properties are dramatically altered by the addition of tiny but carefully controlled amounts of certain impurities, a process known as “doping.” Semiconductor materials are normally found in Group IV of the periodic table (silicon, germanium, etc.) or can be “compound semiconductors” consisting of a combination of elements from groups (4 n) and (4+n), for example, gallium nitride (gallium is in group III and nitrogen in group V) or silicon carbide (both silicon and carbon being in group IV). Suitable dopant materials normally come from groups III or V of the periodic table. Dopants from group V of the periodic table, such as phosphorus or arsenic, have more outer-shell electrons than the surrounding semiconductor material and thus are able to contribute surplus electrons to increase the conductivity of the semiconductor. Dopants based on group V elements are known as “donors” (because they donate additional electrons), and semiconductor materials made from them are known as “n-type” semiconductors. Dopants from group III, such as boron, aluminum, or gallium, have fewer outer-shell electrons than the surrounding semiconductor material and thus, in an analogous way, contribute “holes” to increase the conductivity of the semiconductor. Dopants based on group III elements are known as “acceptors,” and semiconductor materials made from these are known as “p-type” semiconductors. Some (unipolar) types of semiconductor device use only one type of material (p-type or n-type but not both), while others (bipolar) use alternating layers of both. The first transistors used germanium as the semiconductor material, but since the 1960s, silicon took over and has been the dominant semiconductor material for over half a century. While silicon is the preferred choice in most applications, it is starting to be challenged by two “wide-bandgap” materials: gallium nitride (GaN) for voltages of up to 1000 V and silicon carbide (SiC) for voltages above 1000 V. Silicon carbide might displace silicon in many high-power applications because of its potential to achieve much higher blocking voltages than is possible with silicon, although as of 2018 silicon carbide devices are still much more expensive than comparable silicon devices and are only used in certain niche applications.

2.2

Devices of the Thyristor Family

Devices of the “thyristor” family are robust, efficient, and capable of high-power handling capability. They are usually made from large-diameter single crystal silicon slices operated under a high clamping pressure and, in the event of a failure, always become a short circuit. They are latching devices, only being fully on or fully off and

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Fig. 1 The thyristor – standard (left) and gate turnoff (right)

Anode

Anode

Gate

Gate Cathode

Fig. 2 Symmetrical (reverseblocking) thyristor: vertical structure and equivalent circuit

Cathode

Anode

Anode

p n

Gate

p n

Gate

Cathode Cathode

without any stable intermediate state. Because of the latching behavior, thyristors have a comparatively low forward voltage drop and therefore low conduction losses and are able to sustain high-current surges lasting a relatively long time (cycles of power frequency) without exceeding the allowable junction temperature. That is, the thyristor can be used without damage where system short circuit currents are high, allowing time for the normal AC short circuit protective devices to clear faults. The same ruggedness in the face of surge currents also allows thyristors to be used as protective “crowbar” devices in a number of power electronic applications, usually to protect less rugged devices such as transistors from surge currents. The basic thyristor (as used in SVCs, TCSCs, and line-commutated HVDC converters) can only be turned on by gate action. Therefore, turning off the current flow requires an external circuit to force the current in the device to zero. The basic thyristor or silicon-controlled rectifier (Fig. 1) remains the most efficient high-power semiconductor switching device available. It is constructed from alternating layers of p-type and n-type semiconductor material (Fig. 2) and can be considered as the connection of a complementary pair of bipolar junction transistors (BJTs). It enabled the construction of current-sourced converters (CSC), in which the thyristors need to block voltage of either polarity but are only required to pass current in the forward direction. CSC converters used in HVDC converters and put into service in about 2015 utilize thyristor device rated up to 9000 V and 5000 A. Thyristors can be built with either symmetrical or asymmetrical voltage ratings. Symmetrical thyristors block (nearly) the same voltage in the positive and negative polarities, while asymmetric thyristors have a very low voltage rating (tens of volts) in the reverse direction.

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The thyristor remains in the blocking state (passing almost no current) until a pulse of current (typically a few amperes for a minimum of a few microseconds) is injected into the gate terminal. Thereafter the thyristor conducts current until an external circuit forces the current to zero. A certain minimum positive voltage is needed to allow the thyristor to latch safely into the conducting state and for the conduction area to spread over the entire device. However, since it has no capability to be turned off by gate action, a conventional thyristor cannot be used in applications where the conducted current must be forcibly turned off, unless a complex auxiliary circuit is provided that will force the current conducted through the device to zero. After the current reaches zero, a period of reverse voltage (hundreds of microseconds) across the thyristor is required for the charge carriers to recombine before the thyristor is once more capable of supporting positive voltage. However, thyristor devices that can be forced to turn off by means of gate control signals have been developed. These types of devices are referred to as gate turn-off thyristors (GTO). Applications in which GTOs have been used include motor drives (Williams 1993). The GTO, which first emerged with suitable power ratings in the 1980s, is a derivative of the thyristor with a different and more complex gate structure. The GTO is turned on in the same way as a thyristor but has the added feature that it can be turned off by injecting a negative current pulse into the gate terminal (i.e., extracting current from the gate). Complete turn-off takes some tens of microseconds, and the turn-off gate pulse has a large amplitude: typically one third of the anode current (i.e., the device has a turn-off gain of about 3). The gate drive circuit is thus a sizeable power electronic converter in its own right. GTOs also require snubber circuits (made up of diodes, inductors, resistors, and capacitor components) to limit the rate of rise of current at turn on and rate of rise of voltage at turn off, further adding to the complexity. A good treatment of thyristors and GTOs is given by Taylor (1987). Like conventional thyristors, GTOs can be either symmetrical, with blocking capability across the device for both positive and negative applied voltages (Fig. 2), or asymmetric (Fig. 3) in which case the device will only block current for voltages of one polarity applied between the anode and the cathode. Therefore, asymmetrical GTO devices cannot be used in CSC systems where symmetrical devices are needed. Asymmetric thyristors incorporate so-called anode shorts across the main reverse-blocking p-n junction. This measure reduces the reverse voltage withstand Fig. 3 Asymmetrical (anodeshorted) thyristor: vertical structure and equivalent circuit

Anode

Anode p p p p p p n

Gate

p n

Cathode

Gate

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capability in asymmetrical GTO devices to some tens of volts, but in voltage-sourced converter (VSC) applications where a so-called freewheel diode (which conducts if reverse voltage is applied across the thyristor) is always provided across the GTO, this is not an important limitation. In VSC applications where the low reverse voltage withstand capability can be accepted, anode shorts are highly beneficial because of the improved switching performance they bring. Voltage-sourced converters are an integral part of static synchronous compensators (STATCOM) and unified power flow controllers (UPFC) (CIGRÉ TB 144; CIGRÉ TB 160). A development of the GTO that appeared in the 1990s is the gate-commutated thyristor, or GCT. The GCT is very similar to the conventional GTO but with some modifications to the gate structure to allow operation with unity turn-off gain. Unity turn-off gain means that to turn off an anode current of 2000 A, a gate current of 2000 A is briefly extracted from the gate, giving rise to the concept that the anode current is “commutated” to the gate circuit. The motivation for making this change was the realization that a much faster and more efficient turn off can be achieved with unity turn-off gain than was possible with the higher turn-off gains typically used with GTOs. The main factor influencing the performance achievable with a GCT is the inductance of the connections between the device and its gate drive. That is, the designers must minimize this inductance to achieve good performance from the device. The final evolutionary step in the thyristor family is the “integrated gatecommutated thyristor” or IGCT. The IGCT addresses the problem mentioned above for the GCT by redesigning the packaging of the device so that the gate drive forms an inseparable part of the overall package and the gate connections completely surround the power semiconductor device. This allows the gate inductance to be extremely low, thus realizing the maximum benefits of the GCT. IGCTs with ratings of up to 6500 V and 5000 A (maximum turn-off current) have been produced. Because of the ruggedness of the IGCT, it has found an important niche in large industrial motor drives. However, in most mainstream power electronic applications, the insulated gate bipolar transistor (IGBT) discussed below has gradually replaced GTO-type devices.

2.3

Devices of the Transistor Family

There are many different semiconductor devices classified as transistors. Compared with devices of the thyristor family, transistors have lower voltage and current ratings and are comparatively “fragile.” They are usually made from quite small individual chips (connected in parallel where necessary to increase the current rating) with soldered wire-bond connections between the chips and external terminals. The normal failure mode of wire-bonded devices is an open circuit, which is not always desirable in high-voltage applications where transistors typically would be connected in series. In such applications, the total voltage across the whole stack is so high that an open circuit across an individual device would not be able to block the imposed voltage and would arc over, potentially leading to combustion of the

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failed device. Transistors can however be put into packages in which the emitter and collector surfaces are in contact with large plates. Where such packages are used, the transistor would normally fail in a short circuit mode. Transistors typically have a higher forward voltage drop than thyristors but have many advantages over thyristors, notably their much lower switching losses (leading to the ability to switch at faster rates) and the fact that they can be smoothly controlled from fully on to fully off and at all points in between. Although operation in these partly on regions must be limited to very short durations in order to avoid excessive power dissipation, this extra controllability allows the switching speed to be “tuned” in a way that is not possible with thyristors. Many types of transistors have been proposed since Bardeen, Brattain, and Shockley first demonstrated the idea in 1947 (Mohan et al. 1995). The most important types can be summarized as: • • • •

Bipolar junction transistor (BJT) Junction field effect transistor (JFET) Metal-oxide-semiconductor field effect transistor (MOSFET) Insulated gate bipolar transistor (IGBT)

One of the first types of transistor to find widespread use in high-power applications was the bipolar junction transistor, or BJT. BJTs are three-layer (p-n-p or n-p-n) transistor devices where one side of the device is an emitter and the other is a collector of charge carriers. The middle layer, called the “base”, is a control terminal used to modulate the impedance of the device. The term “bipolar” arises from the fact that carriers of both polarities participate in the conduction process. Today, the most commonly used devices in power applications (Fig. 4) are MOSFETs for lower voltages and powers (up to a few hundred volts) and IGBTs for higher voltages and powers. Since the early 2000s, silicon-based, high-current IGBT devices with voltage ratings as high as 6500 V have been applied in many high-power FACTS and HVDC systems. See Volke and Hornkamp for a comprehensive treatment of IGBTs (Volke and Hornkamp 2011). IGBTs are asymmetric devices; that is to say their reverse voltage rating is much less than their forward voltage rating. However, in applications such as for voltagesourced converters (VSC), this limitation is of no importance because in such applications, a “freewheel diode” is connected in inverse-parallel to the IGBT. Usually, the freewheel diode is integrated into the same package as the IGBT itself so as to minimize the inductance between the two devices. IGBTs are turned on by applying a positive voltage, typically +15 V, to the gate terminal. Returning the gate voltage to zero causes the device to turn off again, although many IGBT gate drives use a negative gate bias (e.g., 15 V), while the IGBT is intended to be off. This measure reduces the likelihood of unwanted turn on of the IGBT. The popularity of the IGBT is largely because it marries the relatively high-power handling capability of the bipolar transistor with the low gate power consumption of

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Fig. 4 Two important types of transistor: the IGBT (left) and MOSFET (right)

Drain Collector

Gate

Gate Emitter Source

the MOSFET. A variant of the IGBT, called the “injection-enhanced gate transistor” or IEGT, also exists (Okamura et al. 1998). MOSFETs are less important than IGBTs in high-power applications but, if built using silicon carbide material instead of silicon, have the potential to reach the power ratings currently obtained with silicon IGBTs. An important difference between a MOSFET and an IGBT is that a MOSFET inherently conducts current in both directions. Thus when a MOSFET is turned on, the “channel” between its source and drain terminals conducts current efficiently in either direction, and even when switched off, a parasitic “body diode” (shown in dotted on Fig. 4) provides an additional, less efficient, reverse current path. Some MOSFET applications are therefore realized without separate freewheel diodes.

3

Line-Commutated Thyristor Switches

Line-commutated converters (LCC) rely on the presence of an AC system that includes rotating synchronous machines (or other active AC voltage sources) to which the converter is connected. This allows such converters to use switching devices that can be turned on by control action but have no ability to turn off.

3.1

Building Blocks

Well before the IGBT made high-power self-commutated converters feasible for power system applications, thyristors had become established as a cost-effective and efficient power switching device and started to find applications in FACTS devices. Conventional thyristors (as distinct from gate turn-off thyristors and their derivatives, which came later) can be turned on by gate action but require an external circuit to force the current to zero (“line commutation”) and allow the thyristor to turn off again. In AC system applications, natural current zeroes occur twice every powerfrequency cycle, making thyristors an inherently suitable device for AC switches. Since thyristors conduct current only in one direction, the simplest building block for a line-commutated AC switch is an inverse-parallel-connected pair of thyristors, as illustrated on Fig. 5.

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Fig. 5 Basic AC linecommutated switch consisting of an antiparallel-connected pair of thyristors

Fig. 6 AC line-commutated thyristor valve consisting of series-connected antiparallelconnected pairs of thyristors

Although thyristors are available with voltage ratings of nearly 10 kV, this is still low compared with what is required to operate on most distribution grids, meaning that the simple thyristor switch of Fig. 5 is suitable only for the lowest grid voltages. To use a thyristor switch at higher voltages requires thyristor pairs to be connected in series as shown in Fig. 6. The resulting assembly of series-connected thyristor pairs is known as a thyristor valve. The series-connected thyristor pairs need additional voltage grading components, typically arranged as resistor-capacitor (RC) grading circuits as shown in Fig. 6. Bidirectional thyristor valves such as those shown in Fig. 5 and Fig. 6 can be used in one of two ways. In the first, the valve is used only as a fast switch (Fig. 7), regulating the current in the load only on a half cycle by half-cycle basis. The switch can be turned on at any time (although with an inductive load, it is best to limit the

138 Fig. 7 Bidirectional thyristor valve used as a fast switch in integral half-cycle control

C. Davidson Resistive Load Thyristor Gate V

I

Inductive Load Thyristor Gate V

I

Fig. 8 Bidirectional thyristor valve used as a fast switch in phase control

Resistive Load Thyristor Gate

V α

I

Inductive Load Thyristor Gate

V α

I

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turn on instant to certain regions of the cycle in order to avoid the creation of a highly offset current), but turn off can occur only at one of the natural current zeroes that occur twice every cycle. In this respect, the thyristor behaves rather like a circuit breaker except that the operation is considerably faster, with a turn-off delay of a maximum of half a cycle instead of typically 3–4 cycles. Because this mode of control gives entire half cycles of current in the load, it is sometimes referred to as integral half-cycle control. The second mode of operation is called phase control and allows the current in the load to be regulated continuously from a maximum value determined only by the impedance of the load down to a minimum approaching zero. In phase control (Fig. 8), the thyristor valve is turned on at a predetermined delay after the zero crossing of the AC supply voltage. The delay angle is usually termed α. For a resistive load, the permissible range of α is almost from zero to 180 ; for an inductive load however, values of α below 90 result in an offset current; therefore only the range from 90 to nearly 180 is used.

3.2

Applications

Bidirectional thyristor valves are an essential component of a static var compensator (SVC), where they are used to switch or control the current in shunt-connected reactors and capacitors (CIGRÉ TB 78; CIGRÉ TB 123). With shunt reactors, both integral half-cycle control and phase control are possible, such systems being referred to, respectively, as thyristor switched reactors (TSRs) and thyristor-controlled reactors (TCRs). TCRs are, however, more common because for relatively little additional cost, they give a continuously variable reactive power absorption capability. With shunt capacitors, only integral half-cycle control is used, the resulting system being referred to as a thyristor switched capacitor (TSC), because attempts to operate shunt capacitors in phase control result in very large transient currents every time the capacitor is switched. Nevertheless, a combination of a TCR and one or more TSCs can be very effective at providing smoothly controllable reactive power over a wide range. SVCs will be discussed in greater detail in ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC).” Another application is for control of power flows in high voltage, series compensated AC transmission lines. Series compensation usually takes the form of a large capacitor in series with the transmission line, but in some cases, a TCR is connected in parallel with the series capacitor so that the degree of series compensation can be varied. Such installations are known as thyristorcontrolled series capacitors (TCSC) and have been installed in transmission lines with 25 kA short circuit current capacity (CIGRÉ TB 554). TCSCs are discussed in detail in ▶ Chap. 8, “Technical Description of Thyristor Controlled Series Capacitors (TCSC)”. Thyristor switches are also used for solid-state transfer switch applications in distribution systems.

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Self-Commutated Converters

Self-commutated converters avoid the limitations inherent to line-commutated converters by using switching devices that can be both turned on and turned off by control action. This means that self-commutated converters can be used in applications where the connected AC grid contains no synchronous machines or other active sources. Self-commutated converters can be either current-sourced or voltage-sourced. In the first type, the direction and magnitude of DC current are held substantially constant by a large DC-side inductor, while in a voltage-sourced converter, the polarity and magnitude of DC voltage are maintained by a large DC capacitor. However, although current-sourced self-commutated converters are possible, they are uncommon compared with voltage-sourced converters.

4.1

Current-Sourced Converter

The basic current-sourced converter scheme is illustrated in Fig. 9 for a shuntconnected reactive compensation application (STATCOM). From a DC input current source, provided by inductor LS with current idc, the converter produces a set of three-phase output currents at the fundamental frequency of the AC power system. Theoretically, a 90 leading or lagging phase angle between the converter output currents and the AC system voltages can be established by the appropriate operation of the converter switches. A phase shift of 90 implies that only reactive power is exchanged with the AC grid, but the exchange of real power is also possible if the DC side of the converter contains a suitable source or sink of energy. The conceptual problem with the current-sourced converter is that the DC terminals of the converter are terminated by a current source (a charged inductor) and thus the AC terminals must be terminated by a voltage source otherwise the terminal voltages of the converter, and the voltage stress of the semiconductor switches, becomes undefined. The AC output of the converter is terminated by an inductive impedance resulting from the series connection of the source impedance of the AC system (including the generator, transmission line, and transformer impedances) and the leakage inductance of the coupling transformer used with the converter. Therefore, the AC outputs of the converter must be shunted by an appropriate capacitor or capacitive filter which can provide a voltage source-type termination to satisfy the fundamental operating requirement of switching converters. Coupling transformer V

iDC I

Solid-State DC-AC Converter

Fig. 9 Reactive power generation by a current-sourced converter

Ls

vDC

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ea eb ec

ia

Ta1

141

Tb1

i dc

Tc1

ib

vdc

Ls

ic Ta2

Tb2

Tc2

Fig. 10 Basic six-pulse current-sourced converter

The current-sourced converter produces a set of quasi-square wave output currents (instead of voltages), and, in order to satisfy the required equality of the instantaneous input and output powers, it must develop a balancing ripple voltage across the energy storage inductor carrying a DC current. Simple CSC-type converters using regular thyristor devices are used in most existing HVDC systems, but if used for reactive power control, they can only produce lagging reactive power because leading reactive power generation requires devices that can be turned off by control actions. The basic six-pulse, three-phase, current-sourced converter, shown in Fig. 10, uses six self-commutated semiconductor switches capable of conducting unidirectional current and blocking bi-directional voltage. A suitable high-power semiconductor switch for such a converter is a symmetrical GTO thyristor, which conducts current only from anode to cathode, but blocks both positive and negative anode to cathode voltages.

4.2

Voltage-Sourced Converter

A voltage-sourced converter (VSC), as the name implies, relies on a voltage source (normally in the form of a capacitor) connected on the DC side of the converter and is connected via inductances on the AC side to the AC network as shown in Fig. 11. Some VSC systems may not have readily identifiable AC and DC sides, but the basic principle still holds true. The voltage source on the DC side of the converter is used to synthesize a voltage at the AC terminals whose amplitude, phase, and wave shape can be controlled as desired. The aim is usually to create a sinusoidal voltage at the AC terminals, thereby minimizing the need for harmonic filtering. The amplitude and phase of the generated AC voltage, in relation to the voltage of the connected AC grid, govern the real and reactive power exchanged between the converter and the grid. For example, the STATCOM can be considered as a controllable voltage source connected to the AC system via a coupling inductance as illustrated in Fig. 11. The voltage-sourced converter (VSC) has almost completely replaced CSC systems in industrial applications as well as in applications for motor drives in electric propulsion applications. The major reason for this is the availability of

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Coupling transformer

V

i dc

Tie reactor

I

E

Solid-State DC-AC Converter

Cs

vdc

Fig. 11 Voltage-sourced converter scheme for reactive power generation

suitable high-power asymmetric semiconductor devices operating with relatively high switching frequencies that enables compact, relatively lightweight designs. There are a great many different arrangements of voltage-sourced converter (Arrillaga et al. 2007; Mohan et al. 1995). Some of the fundamental building blocks of VSC systems are described below.

4.2.1 Two-Level Phase Leg The simplest building block of any power electronic converter circuit is the so-called “two-level” phase leg shown in Fig. 12. The two-level phase leg is the simplest switching arrangement capable of producing AC output from a DC source in the form of a simple square wave and is so-called because the output voltage (with respect to the virtual neutral at the center of the capacitor) can be one of only two discrete values. If the upper of the two transistors is turned on, the output voltage is +1/2 Vdc, while if the lower of the two transistors is turned on, the output voltage is – 1/2 Vdc. The two transistors must never be turned on at the same time, as this would lead to an uncontrolled discharge of the capacitor, or “shoot-through,” and usually to an explosion of the transistors. The two-level phase leg has been the traditional building block of most common types of power converters, usually in the so-called Graetz bridge configuration shown for a voltage-sourced converter in Fig. 20 on page (148). Apart from the square wave output voltage waveform, the main disadvantage of the two-level phase leg is its inability to provide zero output to facilitate direct control of the

½ Vdc

T1

½ Vdc

D1

Virtual neutral

Vout ½ Vdc

T2

D2

-½ Vdc

Fig. 12 Two-level phase leg and output voltage waveform (Because turn off devices currently are so ubiquitous in high-power electronics, the symbol of a controllable switching semiconductor device is shown in the figures included here as that of an IGBT. This should not, however, be interpreted as a limitation since in principle, any of the following building blocks can be built with any type of self-commutated semiconductor switches)

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(a) Transfer from D1 to T2 T1

D1

T1

D1

T2

D2

T2

D2

T1

D1

T1

D1

T2

D2

T2

D2

(b) Transfer from D2 to T1

Fig. 13 Transfer from diode to IGBT conduction

amplitude of its fundamental output voltage without the application of pulse width modulation (PWM) or some indirect techniques, e.g., control of the DC voltage. PWM necessitates a considerable increase in the number of switch operations and was therefore not widely used with GTOs, although it has now become commonplace with IGBTs. In the two-level converter phase leg, current alternates between the upper and lower IGBT-diode pairs. The process of transferring conduction from upper to lower switches is known as commutation and is initiated either by turning on or turning off a transistor. Figure 13a shows what happens when the conduction is initially in diode D1 and current is transferred to the lower switch. In this case the commutation process is initiated by turning on T2. This temporarily creates a short circuit across the DC capacitor, resulting in a very fast-changing current around the loop formed by D1, T2, and the DC capacitor. This transient current drives the current in D1 to zero, and the diode ceases conduction a short time later. Figure 13b shows the converse case with the opposite direction of load current, where T1 turns on and forces D2 to turn off. In Fig. 14, the opposite process is illustrated, where current passes from an IGBT to the complementary diode. Figure 14a shows the transfer from T2 to D1, which is initiated by turning off T2. The current then has nowhere to go except through D1. Figure 14b shows the converse case where T1 turns off and transfers current to D2. For the commutation process between the upper and lower switches to be efficient and not excessively stressful for the semiconductor devices, it is important that the stray inductance around the loop formed by the two switches and the DC capacitor should be as small as possible.

4.2.2 Neutral Point Clamped (NPC) Multilevel Phase Leg A larger number of output voltages can be obtained from a phase leg by using a more complex circuit, such as the neutral point clamped or NPC circuit.

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(a) Transfer from T2 to D1 T1

D1

T1

D1

T2

D2

T2

D2

T1

D1

T1

D1

T2

D2

T2

D2

(b) Transfer from T1 to D2

Fig. 14 Transfer from IGBT to diode conduction

The three-level NPC phase leg, illustrated with its output voltage waveform in Fig. 15, has three input terminals to connect to a split or center-tapped DC source. As seen, there are twice as many transistors used as in the two-level phase leg, and additional clamp diodes Dc1 and Dc2 are also required to connect to the DC supply center tap which is the reference zero potential. However, with identical transistor rating, the total DC supply voltage can also be doubled so that the output VA per transistor remains the same. As illustrated in Fig. 15, the output voltage of the three-level phase leg can be positive, negative, or zero. Positive output is produced by gating on both upper transistors (T1 and T2) in the phase leg, and negative output is produced by gating on both lower transistors (T3 and T4). Zero output is produced when T2 and T3, connecting the center tap of the DC supply via the two clamp diodes to the output, are gated on. At zero output, positive current is conducted by T2 and Dc1 and negative current by T3 and Dc2. As indicated in the figure, the relative duration of the positive (and negative) output voltage with respect to the duration of the zero output is a function of control parameter α, which defines the conduction interval of the top upper and the bottom lower valves. Evidently, the magnitude of the fundamental component of the output voltage produced by the phase leg is a function of parameter α. When α equals 0 , it is maximum, while at α equals 90 , it is zero. Thus, one advantage of the three-level phase leg is that it has an inherent capability to control the magnitude of the output voltage without changing the number of valve switchings per cycle. The other advantage is that, with judicious choice of α, selected harmonic components of the output waveform can be eliminated. However, these advantages come at the price of greater complexity. In order to further reduce the harmonic content of the AC output voltage, the basic three-level neutral point clamped phase leg can be extended to a multilevel, 2n+1level (n = 1,2,3,. . .) configuration (Arrillaga 2007). In this case, 2n DC supplies,

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T1

145

D1

½ Vdc

½ Vdc Dc1

T2

D2

Dc2

T3

D3

T4

D4

Neutral α

½ Vdc -½ Vdc

Fig. 15 Three-level neutral point clamped phase leg and output voltage waveform

T1

D1

½Vdc

¼Vdc Dc1

T2

D2

Dc2

T3

D3

T4

D4

T5

D5

Dc5

T6

D6

Dc6

T7

D7

T8

D8

¼Vdc

¼Vdc Dc3

Vout

Neutral Dc4

α1 α2

¼Vdc

-¼Vdc

¼Vdc

-½Vdc

Fig. 16 Five-level neutral point clamped phase leg and output voltage waveform

provided by 2n DC storage capacitors (which are common to all three-phase legs of a complete three-phase converter), are connected in series, providing 2n+1 discrete voltage levels. 4n transistors and freewheel diodes are required, along with 2.(2n 1) clamp diode branches to selectively connect the 2n+1 voltage levels to the output. The total voltage rating of the clamp diode branches also increases with n. A five-level converter phase leg with the corresponding output voltage waveform, in which the 3rd, 5th, and 7th harmonics can be eliminated by suitable choice of α, is shown in Fig. 16. It is clear that the circuit complexity, control, and operational

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difficulties rapidly increase with the number of voltage levels. In addition to the technical difficulties, the uneven utilization of the valves and the escalating voltage ratings of the clamping diodes raise questions about economic viability.

4.2.3 Flying Capacitor Multilevel Phase Leg Another multilevel topology, the so-called “flying capacitor” (or sometimes “floating capacitor”) converter, is illustrated in Fig. 17 for its simplest (three-level) form. This topology employs a ladder structure of DC capacitors where the voltage on the capacitors is progressively increased from a selected lowest to a selected highest value. The size of the voltage increment between two capacitors defines the size of the voltage steps in the output voltage waveform. The simplest type of flying capacitor circuit, the three-level phase leg (Fig. 17), has some similarities with the three-level NPC phase leg in that there are four transistors connected between the positive and negative terminals of the main capacitor. As with the NPC phase leg, the positive voltage (+ ½ Vdc) is obtained by gating on T1 and T2, and negative voltage ( ½ Vdc) is obtained by gating on T3 and T4. However, the intermediate voltage is obtained not by gating on T2 and T3 (which would result in a shoot-through) but instead by gating either T1 and T3 or T2 and T4. Like the NPC converter, the flying capacitor converter can be extended to higher numbers of output levels, such as five, but also like the NPC converter, this is achieved at considerable expense in terms of greater complexity. For these reasons, few practical applications of either the neutral point clamped or flying capacitor topologies have been built with more than three levels. 4.2.4 The Half-Bridge Submodule The converter building blocks described in the preceding sections are not practical as stand-alone circuits because, to complete the electrical circuit, a connection would need to be made to the (virtual) neutral connection at the center of the capacitor.

T1

D1

½Vdc T2 Virtual Neutral

D2

Vout Vdc

½Vdc

T3

D3

T4

D4

α

-½Vdc

Fig. 17 Three-level “flying capacitor” phase leg

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T1

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D1

Vdc

Vdc T2

D2

Fig. 18 Half-bridge submodule (two-level)

One way to get round this problem is to make the return connection to one terminal of the capacitor instead, as illustrated for a two-level converter in Fig. 18, to form the “half-bridge submodule.” This circuit, first proposed by Marquardt, produces an asymmetric voltage waveform with values of either zero or Vdc (Lesnicar and Marquardt 2003). The half-bridge submodule has become very important in the modular multilevel converter (MMC) for HVDC applications – which can also be used in FACTS systems, although it may not be the most efficient building block for a purposebuilt STATCOM systems.

4.2.5 The H-Bridge By combining two, two-level phase legs sharing a common DC capacitor, the “Hbridge” or “full-bridge” circuit is obtained (Fig. 19). Although the line-to-neutral output voltage of each terminal (with respect to neutral) has only two possible voltage levels, the line-to-line output voltage of the H-bridge has three possible levels: Vdc and 0. The H-bridge concept can be extended to use three-level or five-level phase legs, and in such a case, the line-to-line output voltages have, respectively, five and nine output levels. In general, for an H-bridge based on n-level phase legs, the line-to-line output voltage has (2n 1) possible output levels. The H-bridge is widely used for low-power single-phase converter applications and is a fundamental building block of the “chain circuit” or “full-bridge MMC” topology that is now used in many high-power STATCOM applications.

Output voltage (line to line)

Vdc Ta1

Da1

Tb1

Db1 ea eb

Ta2

Da2

Tb2

Db2

α

-Vdc

Fig. 19 H-bridge or full-bridge (two-level)

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4.2.6 The Three-Phase (Graetz) Bridge With three phase legs connected to one common capacitor instead of two, the classic three-phase “Graetz” bridge is obtained (Fig. 20). This circuit is the most widely used power electronic converter circuit for three-phase applications at all but the highest power levels. In common with the H-bridge, a Graetz bridge based on n-level phase legs has a line-to-line output voltage with (2n 1) possible output levels. In its simplest form, a Graetz bridge converter consists of six selfcommutated semiconductor switches, each composed of an active semiconductor switch (here shown as an IGBT) in reverse parallel with a diode. This elementary arrangement is termed a two-level, six-pulse converter. This terminology simply states that: • Each of the three outputs can only be connected either to the positive or to the negative terminal of the DC source by the upper or lower element of the corresponding phase leg (hence, “two-level”). • The converter employs six functional semiconductor switches to form three phase legs. If the three switch phase legs are operated at the desired fundamental frequency, with 120 phase displacement, to connect the DC supply (capacitor) sequentially to the three output terminals via the appropriate converter switches, then a balanced set of three square waves (ea, eb, and ec) with respect to the hypothetical center of the DC supply (capacitor), as shown in Fig. 21a, is produced. This set will combine into a balanced set of quasi-square wave line-to-line voltage waveforms (eab, ebc, and eca) as illustrated in Fig. 21a. The currents through each semiconductor switch and diode forming a converter switch (e.g., Da1 and Ta1) are shown by the unshaded and shaded segments of the three output currents (ia, ib, and ic), together with the current through the DC storage capacitor, for reactive power generation in Fig. 21b, and for reactive power absorption in Fig. 21c. For clarity, the output currents of the converter are assumed to be free of harmonics. From these figures it can be observed that each semiconductor switch and its antiparallel diode carry alternately a 90 segment of the output current

Output voltage (line to line)

Vdc Ta1

Da1

Tb1

Db1

Tc1

Dc1

ia ib ic

Ta2

Da2

Tb2

Db2

Tc2

Dc2

ea eb ec α

-Vdc

Fig. 20 Three-phase or “Graetz” bridge (two-level)

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ea

VDC

eb

VDC

ec

VDC

eab

[a]

ebc

eca

ia

D a1 Ta1 1

ib ic

Ta2 D Tb2 D a2 b1 Tb1 D Db2 c1 Tc1

i dc D a1 ia ib ic i dc

Tc2

[b]

D c2

Ta2

Db1 Da2

T Tb2 a1 D T D b2 Tc2 b1 c1 D c2

[c] Tc1

Fig. 21 Converter phase leg (line-to-neutral) and output (line-to-line) voltage waveforms (a), converter switch (active switching device and diode) and DC capacitor currents during reactive power generation (b), and reactive power absorption (c)

in each cycle, that is, the current rating of the semiconductor switches and diodes is the same. It is also seen that the semiconductor switch has to be turned off (commutated) at the peak of the current when the output is capacitive (VAr generation), but it commutates naturally when the output current is inductive (VAr absorption). An ideal Graetz bridge converter will generate sinusoidal output voltages and will draw sinusoidal reactive currents from the AC system and zero average input current from the DC capacitor. In practice, due to system unbalance and other imperfections, as well as economic considerations, these ideal conditions are not achieved, but can be approximated quite satisfactorily by converter structures of sufficiently high pulse numbers (24 or higher).

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In a practical converter, the semiconductor switches are not lossless, and therefore the energy stored in the DC capacitor would be used up by the internal losses. However, these losses can be supplied from the AC system by making the output voltages of the converter lag the AC system voltages by a small angle. In this way the converter absorbs a small amount of real power from the AC system to replenish its internal losses and keep the capacitor voltage at the desired level. The amount of real power exchanged with the grid can also be varied temporarily to increase or decrease the capacitor voltage. In some converter topologies, this is the only way to adjust the amplitude of the output voltage produced by the converter and thereby the reactive power exchanged with the AC grid (as the amplitude difference between the converter output voltage and AC system voltage solely determines the magnitude and direction of the reactive current flow and thus the reactive power generation or absorption produced). The DC capacitor also has a vital function, even in the case of a perfect converter, in establishing the necessary energy balance between the input and output during the dynamic changes of the output power. It is, of course, also possible to use the converter with a DC source (e.g., a battery) or with an energy storage device of significant capacity (e.g., a large DC capacitor or a superconducting inductor). In this case the converter can control both reactive and real power exchange with the AC system. The capability of controlling real as well as reactive power exchange is a significant feature which can be used effectively in applications requiring power oscillation damping, leveling peak power demand, and providing uninterrupted power for critical loads. This feature clearly distinguishes a VSC system from the conventional thyristor-controlled SVC, to which no active power source can be connected.

4.2.7 Pulse Width Modulation of a Three-Phase (Graetz) Bridge The pulse width modulation (PWM) technique has been commonly employed for several decades to generate high-quality output waveforms by relatively low-power converters used in variable frequency AC motor drives and other applications. With this technique, the output of each converter phase leg is switched several times during a fundamental frequency cycle between the positive and negative terminals of the DC source, and the time intervals between consecutive switching operations are controlled so that the average of the positive and negative volt-second segments of the output waveform generated follows the desired sine wave (Holmes and Lipo 2003). Typical output voltage waveforms of two converter phase legs, generated by PWM, are shown in Fig. 22a, and the resulting line-to-line output voltage (i.e., the voltage between these two phase legs of the converter) is shown in Fig. 22b. For early power electronics applications, for which the only force-commutated devices available with suitable power ratings were thyristors or GTOs, the ability to use PWM was more limited because of the high switching losses of such devices. In such cases a more limited PWM technique can be used, requiring only modest switching frequencies and aiming at the elimination of specific harmonics (such as the 5th and 7th) from the output voltage waveform. Such a limited, so-called “programmed” PWM technique is illustrated in Fig. 23 by the converter output

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Fig. 22 Ideal PWM converter phase leg voltage: (a) and output voltage (b) waveforms

Fig. 23 Ideal PWM converter phase leg (a) and output (b) voltage waveforms with two “notches” to eliminate the fifth and seventh harmonics

voltage waveform in which the 5th and 7th harmonics are eliminated by two appropriate “notches.” (In general, an appropriately placed “notch” with a specific width is required for the elimination of a given harmonic.) It should be noted that harmonic elimination by the programmed PWM technique is not without penalty;

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the elimination of the selected (low order) harmonic(s) is associated with the significant amplitude increase of the remaining (higher order) harmonics. The advent of high-power IGBTs with much lower switching losses than GTOs has made such techniques less relevant, but the high overall switching losses of converters using PWM remain a significant disadvantage in grid-connected VSC applications, where the in-service lifetime is long and the lifetime cost of power losses can therefore be an important factor influencing the design. PWM-type converters are typically scaled up to higher power ratings by either connecting multiple IGBTs directly in series in each switch arm or by connecting multiple bridges in parallel (Aho et al. 2010).

4.3

Self-Commutated Converter Applications

The self-commutated converter building blocks described above can be used in several different types of FACTS application. In principle, either current-sourced or voltage-sourced converters can be used, although the widespread availability of IGBTs at high power ratings and the lower losses of a DC storage capacitor compared to a DC storage inductor have made voltage-sourced converters far more common, to the extent that “voltage-sourced converter” and “self-commutated converter” have become almost synonymous in normal usage. The most common self-commutated converter application in FACTS is the static synchronous compensator or STATCOM. The STATCOM is a shunt reactive compensation device that performs an analogous function to the Static Var Compensator (SVC). The STATCOM consists of a shunt-connected self-commutated (usually voltage-sourced) converter coupled to the AC grid via an inductance. The reactive power absorption or generation is varied by altering the magnitude of voltage produced by the converter. STATCOMs are described in greater detail in ▶ Chap. 7, “Technical Description of Static Compensators (STATCOM).” Another use of a self-commutated converter is the static synchronous series compensator or SSSC. The SSSC differs from the STATCOM in that the converter is inserted in series with a transmission line and is used as a rapidly variable series compensation device, primarily to regulate the impedance of the line and thus adjust the flow of real power. As of 2017, few SSSCs had been installed, but one such plant has been installed on a 220 kV AC line in Spain for Red Electrica de España (Chivite-Zabalza et al. 2014). The unified power flow controller (UPFC) combines the features of both STATCOM and SSSC, using two voltage-sourced converters – one in shunt and the other in series – coupled together in the DC side and via isolating transformers to the line to be compensated (CIGRÉ TB 160). Although first introduced in 1998 (Renz 1998), as of 2018, the UPFC is still relatively uncommon. It is described in greater detail in ▶ Chap. 9, “Technical Description of the Unified Power Flow Controller (UPFC) and Its Potential Variations.”

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In addition to these series and shunt compensation devices, self-commutated switches (in the form of GTOs) have been used in some solid-state breaker and fault current limiter demonstration systems where high current and device turn-off capability is needed (CIGRÉ TB 337).

References Aho, J. et al.: Description and evaluation of 3-level VSC topology based statcom for fast compensation applications. In: 9th IET International Conference on AC and DC Power Transmission, London (2010) Arrillaga, J., Liu, Y.H., Watson, N.R.: Flexible Power Transmission; The HVDC Options. Wiley (2007). John Wiley & Sons Bardeen, J.: Flow of Electrons and holes in semiconductors (physics of transistor effects), Chapter 4 in Part 8, The Solid State; In: Handbook of Physics, Mc Graw Hill Book Company, Second Edition (1967). ISBN: 07-012403-5 Chivite-Zabalza, F.J., Izurza, P., Calvo, G., Rodriguez, M.A.: Laboratory tests of the voltage sourced converter for a 47 MVAr series static synchronous compensator for the Spanish highvoltage transmission grid. In: 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), pp. 1–6. Manchester (2014) CIGRÉ TB 123.: Thyristor Controlled Series Compensation, (December 1997). CIGRÉ TB 144.: Static Synchronous Compensator (STATCOM), (August 2000). CIGRÉ TB 160.: Unified Power Flow Controller (UPFC), (August 2000). CIGRÉ TB 183.: FACTS Technology for Open Access, (April 2001). CIGRÉ TB 337.: Increased System Efficiency by the use of New Generations of Power Semiconductors, (December 2007). CIGRÉ TB 554.: Performance Evaluation and Applications Review of Existing Thyristor Control Series Capacitor Devices –TCSC, (October 2013). CIGRÉ TB 78.: Voltage and Current Stresses on Thyristor Valves for Static var Compensators, (October 1993). Holmes, D.G., Lipo, T.A.: Pulse Width Modulation for Power Converters. IEEE Press (2003). IEEE Press, 445 Hoes Lane, Piscataway, NJ 08854, USA Lesnicar, A., Marquardt, R.: An innovative modular multilevel converter topology suitable for a wide power range. In: Power Tech Conference Proceedings, vol. 3, p. 6 (2003) Mohan, N., Undeland, T.M., Robbins, W.P.: Part 2, Chapter 8, switch mode DC-AC inverters. In: Power Electronics, Converters, Applications and Design, 2nd edn. Wiley (1995). ISBN: 0-471-58408-8. Taylor: John Wiley & Sons Mohan, N., Undeland, T.M., Robbins, W.P.: Part 6, Semiconductor devices. In: Power Electronics, Converters, Applications and Design, 2nd edn. Wiley. ISBN: 0-471-58408-8 Moll, J.L., Tanenbaum, M., Goldey, J.M., Holonyak, N.: P-N-P-N Transistor Switches. In: Proceedings of the IRE (now IEEE), vol. 44(9), p. 1174–1182 (1956) Okamura, K., Nakajima, N., Souda, M., Endo, F., Matsuda, H., Kaneko, E.: Sub-microsecond pulse switching characteristics of a 4500-V IEGT. Conference Record of the Twenty-Third International Power Modulator Symposium (Cat. No. 98CH36133) (1998) Renz et al., Worlds First Unified Power Flow Controller on the AEP System, CIGRÉ paper 14–107, (1998) Semiconductors.: http://edisontechcenter.org/semiconductors.html. Accessed 21 Feb 2018 Taylor, P.D.: Thyristor Design and Realisation. Wiley (1987) Volke, A., Hornkamp, M.: IGBT Modules – Technologies, Drivers and Applications. Infineon Technologies AG, Munich (2011) Williams, B.W.: Power Electronics – Devices, Drivers, Applications and Passive Components. The Macmillan Press Ltd, Basingstoke & London (1993)

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C. Davidson Colin Davidson is Consulting Engineer, HVDC, at GE Grid Solutions, HVDC Activity, whose Center of Excellence is in Stafford, UK. He joined the company in January 1989, when it was part of GEC, and progressed through the positions of trainee Thyristor Valve Design engineer; manager, Thyristor Valves; engineering director and R&D Director, to his current role. He is a Chartered Engineer and a Fellow of the Institution of Engineering and Technology and has served on several IEC standardization committees for HVDC and FACTS. He has a degree in natural sciences, specializing in physics, from the University of Cambridge.

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Technical Description of Static Var Compensators (SVC) Manfredo Lima and Stig L. Nilsson

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Main Circuit Components of an SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Thyristor Controlled Reactor (TCR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Thyristor Switched Capacitors (TSC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Thyristor Switched Reactors (TSRs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 AC Harmonic Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 SVC Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 SVC Voltage Versus Current Characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Combinations of SVC Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 First Brazilian SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Later Brazilian SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 TCR Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 TSC Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 SVCs Gate Power Drive Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Thyristor Valve Cooling System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Thyristor Valve Control and Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Lima (*) Transmission Planning and Studies Department, Chesf, Recife, Brazil Pernambuco University, Recife, Brazil e-mail: [email protected] S. L. Nilsson Electrical Engineering Practice, Exponent, Sedona, AZ, USA e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_7

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8 SVC Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Early SVC Analog Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Digital Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Additional Control Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 The Use of Series Reactor to Reduce Harmonics and Losses . . . . . . . . . . . . . . . . . . . . . . 9 Coordinated Operation of SVCs Operating Electrically Close . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 SVC Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 SVC Transformers Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 SVC Thyristor Controlled Reactor (TCR) Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 SVC Thyristor Switched Capacitor Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 SVC Harmonic Filter Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Control, Protection and Auxiliary Equipment Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

This chapter provides a technical description of the Static Var Compensators (SVC) used in electrical power systems. It highlights the technological evolution from the 1980s, when the first SVCs were installed in Brazil, until the later SVCs installed in Brazil. Aspects of the control systems used in the two groups of SVCs are described, highlighting the advantages of the use of adaptive control systems in the later generation SVCs. The chapter also describes an innovative solution that uses a series reactor to reduce the harmonic filtering requirements and to avoid resonances with the power grid. This equipment is in operation in Brazilian Electric Power Grid since December 2016. The chapter also provides details of a control scheme used to coordinate the operation of two SVCs installed electrically close in the Brazilian Electric Power Grid.

1

Introduction

Static Var Compensators (SVCs) use thyristors for the control of reactive power (Hingorani and Gyugyi 2000). The SVC may consist of one or more of the following parts: • Thyristor Controlled Reactors (TCR), the thyristor is used to control the reactor output. • Thyristor Switched Capacitors (TSC), the thyristor is used to switch the capacitor in and out. • Thyristor Switched Reactors (TSR), the thyristor is used to switch the reactor in and out. • AC harmonic filters, which can be switched in and out by circuit breakers as necessary. These components are usually connected to the high voltage (HV) AC system by means of a SVC transformer. The connection point is typically called the point of common connection (PCC). The characteristics and the implementation of an SVC are described in the next sections of this chapter.

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Technical Description of Static Var Compensators (SVC)

2

Main Circuit Components of an SVC

2.1

Thyristor Controlled Reactor (TCR)

157

The TCR injects continuously varying inductive reactive power to the AC power network. TCRs are typically delta-connected air core reactors connected by bidirectional thyristor valves. The TCR reactors are typically divided in two, with the thyristor valve located between the two reactors. This arrangement limits the short circuit current values through the valves, in the event of a short circuit to ground, as well as providing some protection to the thyristor valve in the event of a lighting strike on the SVC busbar. The thyristor valves consist of thyristors connected in antiparallel, which allow current conduction in both AC voltage half-cycles. The TCR current is a function of the thyristor valve firing angle (Fig. 1). The angle is measured from the zero crossing of the AC voltage half-cycle at which the valves will be able to conduct. The TCR valve firing angle is determined by the SVC control system. The reactive power varies from its maximum value to zero, as the thyristor valve firing angle varies from the minimum to the maximum value, respectively close to 90
and 180
(Miller 1982; Cigré TB 25 1968; Cigré TB 78 1993). The SVC control system can be set to either control the AC system voltage or to give a reactive power output which depends on the AC voltage. The SVC control system is based on a signal representing the deviation between the voltage and the reactive power measured at the electric power system point of common connection (PCC) and the reference value set by the operator. See Sect. 3 of this chapter for more information about the operation and control of the SVC system. The delta connection of the TCR has as its main purpose the reduction of all thirdorder (triplen) harmonics when operating in balanced conditions. The maximum TCR root mean square (RMS) current is obtained for 90
firing angles, i.e., with the thyristor valves in continuous conduction. In this case, purely sinusoidal harmonic free AC current flows through the reactors and thyristors, as shown in green in Fig. 1.

Fig. 1 TCR current  firing angle (Provided by GE)

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For thyristor firing angles higher than 90
but smaller than 180
, AC periodic and nonsinusoidal currents circulate through the TCR. Only odd order harmonics are generated if the firing of the thyristors is symmetrical resulting in characteristic harmonic currents of order 6n  1 (n = 1, 2, 3. . .). The RMS value of the fundamental and the hth harmonic current components as a function of reactor current are given by the following equations (CIGRE TB 25 1986): I1 1 ¼  ½2  ðπ  αÞ þ sin 2α IL π

(1)

Ih 4  ½ cos α sin hα  h sin α cos hα ¼
I L hπ h2  1

(2)

where: I1 is the fundamental frequency component. Ih is the harmonic component of order h. IL is the reactor current at continuous conduction. α is the firing angle in radians varying between π/2 radians (90 degrees) for full conduction and π radians (180 degrees) for no conduction. h is the harmonic number equal to 6n  1 for six-pulse operation (three-phase connection). In 12-pulse connections the 5th, 7th, 17th, 19th, etc., harmonics are canceled in the high voltage winding of the transformer. The amplitudes of the harmonic currents depend on the TCR firing angle as shown in Fig. 2 for 5th, 7th, 11th, and 13th harmonics. In red one can see the fundamental frequency current RMS value in per unit as a function of the firing angle. The harmonic currents must be adequately filtered to ensure compliance with 1.0

0.06 0.05

0.8 0.7

0.04

0.6 0.5

0.03

0.4 0.02

0.3

fund 5th 7th 11th 13th

0.2

0.01

0.1

0.0 90

Harmonic current (pu)

Fundamental current (pu)

0.9

100

110

120

130

140

150

Firing angle (°) Fig. 2 TCR harmonic currents as a function of firing angle

160

170

0.00 180

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Control System

Harmonic Filter (FC)

Thyristor Controlled Reactor (TCR)

Fig. 3 Delta connected thyristor controlled reactor

the specification requirements for harmonic voltage distortions at the SVC PCC (Miller 1982; and Cigré TB 78 1993). As mentioned above, for three-phase systems, the preferred arrangement for the TCR is a delta connection (Fig. 3). In this case, when the power system is balanced, all the triplen harmonic currents circulate in the closed delta and are absent from the line currents. All the other harmonic currents previously mentioned are present in the line current and harmonic filters will typically be needed. It is important to ensure that the firing angles of the two antiparallel thyristors must be as equal as possible in steady-state operation. Unequal firing angles would produce even harmonic currents and DC components.

2.2

Thyristor Switched Capacitors (TSC)

The TSC injects a capacitive reactive power step change into the electric power system as the thyristor valves are either fully conducting or fully blocked. Each phase of the TSC consists of a capacitor, a bidirectional thyristor valve, and a small surge current limiting air-cored reactor (Fig. 4). In some designs, the surge current limiting reactors may be split in two, similarly to the TCR. The three phases are usually connected in delta to reduce the thyristor valve rated current (Cigré TB 25 1968; Cigré TB 78 1993). The reactor is needed primarily to:

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Fig. 4 Thyristor switched capacitor. (Photo by Permission of GE)

• Limit switching transients • Damp inrush currents • Filter harmonics coming from the power network or from any other SVC operating electrically close • Limit the surge currents in the thyristor valves under abnormal operating conditions such as control malfunction causing capacitor switching when transient-free conditions are not satisfied and to avoid resonances with transmission systems at particular frequencies (Hingorani and Gyugyi 2000) The TSC can be switched off at any current zero crossing by removal of the thyristor valve gate pulses. At the current zero crossing, the capacitor voltage is at its peak value and the switched-off capacitor stays charged temporarily at this voltage. Binary combinations of TSCs are sometimes used to reduce the steps when switching (e.g., 1, 2, 4. . .). If the voltage across the capacitor remains unchanged, the TSC could be switched in again without any transient at the appropriate peak of the applied AC voltage, as showed in Fig. 5 for a positively (a) and a negatively (b) charged capacitor. Figure 6 shows the switching transients obtained with a fully discharged (a) and a partially discharged (b) capacitor. The transients are caused by the nonzero dv/dt at the switching instant, which without the series reactor would produce a very large instantaneous current in the thyristor valve and the capacitor. The interaction between the capacitor and the series reactor produces the oscillatory transients present in the current waveforms. Based on that, the conditions for minimizing the switching transient in a TSC are:

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Fig. 5 Transient-free Switching by a TSC with (a) Positively Charged Capacitor and (b) Negatively Charged Capacitor

Fig. 6 Switching transients with the TSC capacitor fully (a) and partially discharged (b)

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• If the residual capacitor voltage is lower than the peak AC voltage, the correct switching instant is the one for which this voltage is equal to the capacitor voltage. • If the residual capacitor voltage is equal or higher than the peak AC voltage, the correct switching instant is at the peak of AC voltage, when the thyristor valve voltage is at its minimum. From the above, it can be concluded that, under normal conditions, the maximum possible delay in switching in a TSC is one full cycle of the applied AC voltage. If, however, the TSC modules have been disconnected as a result of severe overvoltage conditions, a longer delay might be needed before they can be switched back on again unless the equipment has been design for the resulting current stresses. This also means that firing angle control cannot be applied to a TSC, as a means of varying the output. The switching must take place at the specific instant at each cycle at which the abovementioned conditions for minimum transients are satisfied. For this reason, a TSC branch represents a single capacitive admittance that is either connected to or disconnected from the SVC medium voltage busbar. Therefore, on its own this device provides only a binary logic (ON/OFF) control for the reactive power injected into the power system (Padyar 2007). The TSC does not create harmonic currents, but it may magnify harmonics from other sources, e.g., an adjacent TCR or the AC system background harmonics. By using a coordinated operation strategy among TCRs and TSCs, a step free reactive power control can be achieved. A high degree of flexibility and low power loss operation can be achieved by the use of TSCs together with TCRs. Typically, the rating of the TCR is larger than the largest reactive power step that can be caused by the switching TSCs.

2.3

Thyristor Switched Reactors (TSRs)

If the TCR switching is restricted to fixed firing angles, usually 90
and 180
, then it operates as a thyristor switched reactor (TSR). The TSR represents a fixed inductive susceptance, and thus, when connected to the power system, it injects an inductive current proportional to the applied voltage. Several TSRs operating in parallel can provide an inductive equivalent susceptance variable in a step-like manner. If the TSR operates at 90
, its steady-state current will be purely sinusoidal and harmonics free. A combination of TSCs and TSRs can provide useful compensation with low power losses. Sometimes TCRs are also operated in some selected conditions as TSRs, e.g., if there are parallel TCRs, as described Sect. 7 of this chapter. This is a strategy to reduce the harmonic contribution of the overall SVC.

2.4

AC Harmonic Filters

AC harmonic filters are usually required for SVCs using TCRs but may not be required if only TSCs and TSRs are used, as in this case, only sinusoidal currents will flow.

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AC harmonic filters are designed using series and parallel combinations of inductors, capacitors, and resistors. They inject into the power grid capacitive reactive power the value of which depends on the filter design. They are typically connected at all times, but if redundant AC harmonic filters are used, they may be switched in and out by dedicated circuit breakers or by the main SVC circuit breaker, depending on the design used for these elements. The filter design depends on harmonic analysis studies carried out during the SVC design stage. For this, the harmonic impedance geometrical loci at the PCC are determined for the electrical network configurations defined in the specification, and in addition, the harmonic contributions from the SVC are calculated. Harmonic performance studies are performed to determine the effect of the harmonic currents generated by the SVC on the power network and to design the characteristics of the AC harmonic filters. Typically, this study must also consider the existing harmonic levels at the PCC. The filters are dimensioned so that the specified maximum harmonic distortion at the PCC is not exceeded and to achieve performance and ratings criteria (Pilz et al. 2013). Part of the capacitive reactive power supplied to the power grid by the SVC comes from the harmonic filters. Since harmonic voltage distortions in the power grid result from the interaction between it and the SVC, all system contingencies which may affect power system frequency response should be evaluated. Any tolerances in the power system parameters should be considered to assure that system parallel resonance points do not coincide with any of the SVC characteristic harmonics. As the harmonics generated by the SVC are strongly dependent on the operating point, a conservative approach is to consider the maximum values of the harmonics generated by the SVC equipment irrespective of its actual operation point. Thus, the objective of SVC harmonic performance studies can be summarized as the determination of: • The network harmonic characteristic impedance versus frequency required for filter design. • The effect of SVC harmonics on the power system. • The overall filter requirements and additional countermeasures to reduce harmonic distortions at the PCC to acceptable levels. • The contribution of the filters to the overall rating of the SVC.

2.5

SVC Transformer

Typically, the SVC thyristor controlled elements and filters operate at a different voltage to the voltage at the PCC, because the SVC design is optimized to provide the specified range of reactive power compensation at the lowest overall evaluated cost. Therefore, a SVC transformer is likely to be required. The typical SVC transformer impedance varies between 10% and 15% of the transformer’s rating. The impedance of the transformer, which is inductive at fundamental frequency, needs to be taken into account in the design of the overall

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SVC. When the SVC is in inductive output mode, the presence of the transformer reactance will decrease the SVC bus voltage so that the TCRs will generate less inductive reactive power than it would if the transformer had no reactance. Similarly, in capacitive mode, the presence of the transformer reactance will boost the SVC bus voltage meaning that TSCs and filters will generate more reactive capacitive power than it would if the transformer had no reactance. The transformer impedance also needs to be considered in the design of AC harmonic filters, if any. The secondary nominal voltage of the transformer is defined to optimize the TCR and TSC thyristor valve designs and varies according to the technology employed by each manufacturer. Some of the relevant requirements to be considered in the design of this equipment are the presence of harmonic currents produced by the TCRs and the power losses evaluation requirements specified for the SVC. Another consideration is whether to use single-phase or three-phase transformers. The decision may depend on the rating of the transformer, transport limits for the transformer, and the specified availability requirements, which may make a spare unit necessary or compulsory to achieve the specified reliability and availability requirements (Pilz et al. 2013).

3

SVC Voltage Versus Current Characteristic

The relationships between voltages, currents, impedances, and reactive power in a power system have been described in the ▶ Chap. 2, “AC System Characteristics” of this book. These relationships depend on several factors such as load condition and characteristic, network topology, and short-circuit levels at the studied point, and can be highly nonlinear for large changes. However, for small disturbance analysis at a steady-state operating point, it is possible to approximate the voltage versus current characteristic of a typical electric power system by a straight line with negative slope. Consider as an example an SVC consisting of a TCR and a fixed capacitive filter. The SVC steady-state operating point will then be given by the intersection between the characteristic curves of the electrical power system and the SVC, as shown in Fig. 7. The black line in Fig. 7 shows the SVC voltage versus current (V  I) operating characteristic. The control system will produce a current output which is dependent on the voltage at the PCC. The dependency is typically a slope or droop, which is expressed in percentage of the SVC rated power. This parameter can be set to different levels and is used to provide the desired steady-state load distribution when two or more SVCs or reactive power controlling devices with different ratings operate electrically close to each other. In Fig. 7, the SVC performance is analyzed considering three power system operating conditions, represented by the lines Load1, Load2, and Load3. The Load2 line intersects the SVC V  I characteristic at point A, where its terminal voltage VT is equal to the reference voltage set by the operator (VREF). In this condition, the SVC injects 0 Mvar in the electric power grid. If due to a load reduction, the electric power system operates along the Load1 line, the SVC

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Load 1

D Load 2

V1 V2

VT = Vref SVC OFF

Load 3

B SVC ON

A

V4 C

V3 E

Icmax

Ic2

0

IL.2

ILmax

Fig. 7 Operating voltage/current characteristic of an SVC

terminal voltage VT changes to V1, giving rise to an error signal ΔU = V1  VREF, which indicates to the SVC control system the existence of overvoltage in the electrical power system. The control system then acts by shifting the SVC operating point from point A to point B, where the SVC will inject the inductive current IL2 into the power system with a voltage error defined by the slope value used. Similarly, if due to a load increase, the electric power system starts operating along the Load3 line, the SVC terminal voltage VT moves to V3, giving rise to an error signal ΔU = V3  VREF, which indicates to the SVC control system the existence of undervoltage in the electric power system. The control system then moves the SVC operating point from point A to point C by switching in TSC modules, where this equipment injects into the power grid capacitive current IC2 with the voltage error defined by the slope value. Figure 7 shows in red the system voltage variation from Load1 to Load3 if the SVC had not changed its output (SVC OFF). Similarly the blue line shows the reduced voltage change with the SVC reactive power change. The SVC will control its terminal voltage according to the set slope for current values between its maximum capacitive limit ICMAX and its maximum inductive limit ILMAX. Once these limits are reached, the SVC will behave as a fixed, inductive, or capacitive shunt device, for which the reactive power injected into the electric power grid will vary with the square of its terminal voltage VT.

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Due to the capability of fast variations of its reactive power output, SVCs can respond very quickly to dynamic changes in the power grid, and other devices present in the network, such as generators and transformer tap changers may not react to the dynamic changes, as would have happened in a network without SVCs. Therefore, the SVC’s operating characteristics need to be coordinated with other existing reactive power sources through the slope, such that the other devices can react as required, allowing the SVC to gradually reduce its output as the other devices react. In this way, the SVC can regain the operating margins in readiness for any future event (Cigré TB 25 1968). If this coordination was not provided, the SVC would tend to operate at the extreme of its capability range due to its fast response. The consequence would be that the SVC would respond to normal network disturbances leaving little or no reserve for counteracting major system disturbances.

4

Combinations of SVC Components

As previously mentioned in this chapter, the active elements that can be integrated in an SVC are: • Thyristor controlled reactors (TCR), which provide continuously varying inductive reactive power according to the firing angle of the thyristors. • Thyristor switched capacitors (TSC), which provide capacitive reactive power changed in discrete mode (ON/OFF), when thyristor valves are fully conducting or totally blocking the current flow. • Thyristor switched reactors (TSR), which provide inductive reactive power changed in discrete mode (ON/OFF), when thyristor valves are fully conducting or totally blocking the current flow. AC single- or double-tuned filters are also used to provide part of the capacitive reactive power injected into the network by the SVC and to filter the TCR harmonic currents. As previously mentioned in this chapter, the connection of these elements to the high voltage bus is made through a SVC transformer, which may have two or three windings. The use of three-winding transformers produces the so-called 12-pulse configuration, where one of the secondary windings is star-connected and the other is deltaconnected. This configuration results in 12-pulse operation leaving harmonics of order (12n  1) and results in costs reduction of the SVC harmonic filters. However, this effect disappears if one SVC section is switched off, producing a six-pulse mode of operation that may not meet the specified harmonic requirements. The use of a two-winding transformer as described in Sect. 5 of this chapter, produces the so-called six-pulse configuration. This configuration might offer some operating flexibility but requires larger AC harmonic filters.

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Combinations of elements that integrate an SVC with inductive and capacitive fixed shunt elements produce the following possible configurations: • • • • • •

Single TCR – 6 pulse. Single TCR with AC harmonic filter – 6 pulse. Single TCR with AC harmonic filter and TSC – 6 pulse. Double TCR and 3-winding transformer – 12 pulse. Double TCR and 3-winding transformer with AC harmonic filters – 12 pulse. Double TCR and 3-winding transformer with AC harmonic filters and TSCs – 12 pulse. • Combinations of TCRs and binary switched TSCs with AC harmonic filters. • Combinations of binary switched TSRs and TSCs (no AC harmonic filter). • Addition of breaker switched capacitors and reactors for offsetting and extension of the operating range. Splitting the capacitive range of a SVC between TSCs and fixed or breaker switched capacitive elements (tuned or not tuned) allows loss reduction and increase of operative flexibility. Simpler configurations that have only TCRs are capable of supplying to the electrical power system only inductive reactive power. Configurations that do not use TCRs are able to provide step-wise changed reactive power values, producing more limited voltage control than those using TCRs. The choice of each of the configurations presented here depends on the performance requirements and associated costs, as each one has some advantages and disadvantages.

5

First Brazilian SVCs

Static Var Compensators (SVCs) have been successfully used for voltage control and to improve dynamic stability of electrical power systems since the 1980s. In the Brazilian power grid, the first equipment of this kind were installed in Fortaleza (140 to 200 Mvar/230 kV), Milagres (70 to 100 Mvar/230 kV) and Campina Grande (0 to 200 Mvar/230 kV) substations, all of them in Northeast region of Brazil (Lima 2013). Examples of SVC applications around the world that were put in service at that time are described by Lindström and Grainger (Lindström et al. 1984 and Grainger et al. 1986). These SVCs had two first-order single-tuned harmonic filters and two thyristor controlled reactors, which together with a three-winding SVC transformer, formed a 12-pulse system, dimensioned to supply continuously varied reactive power values between SVC nominal inductive and capacitive limits. As described in Cigré TB 25 (1968), elimination of harmonics can be achieved by using two TCRs of equal rating, fed from two secondary windings of a SVC transformer, one connected in star and the other one in delta, forming a 12-pulse system (Cigré TB 25 1968). In this case, both TCRs are controlled with equal firing angles. Since the applied voltages have a 30 degrees phase difference, the (6n  1, n being an odd number) order harmonic currents will be cancelled in the SVC

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Fig. 8 Campina Grande SVC 12-pulse configuration

transformer. In this case, the characteristic current harmonics injected in the power system are of the order (12n  1), i. e., 11, 13, 23, 25, . . . etc. Figure 8 shows a simplified single-line diagram of a 12-pulse SVC installed in Campina Grande substation. This arrangement is similar to the converters used in High Voltage DC (HVDC) transmission systems and has as its main purpose the elimination of some of the harmonics produced by the TCRs, especially the fifth and seventh order as mentioned before. Typically, such equipment has circuit breakers at the high- and medium-voltage transformer connections such that in case of unavailability of one section, the SVC is able to provide half of its nominal power to the power grid. However, in this mode of operation, there would be much higher harmonic distortion particularly at the fifth and seventh harmonic, as these would no longer be cancelled. The absence of TSCs results in high current values in the TCRs for SVC operation at values close to 0 Mvar at the PCC and results in higher power losses when compared to those SVCs using TSCs combined with fixed capacitive filters. The reactive power values calculated considering rated voltage (26 kV) at Campina Grande SVC medium voltage busbar are 114 Mvar inductive for each TCR branch and 97 Mvar capacitive for each filter branch. It should be noted that in most cases where the 12-pulse configuration is used, the harmonic distortion at the fifth and seventh harmonics would be unacceptable if one of the six-pulse sides is disconnected. If one of the AC harmonic filters is disconnected, the 11th and 13th harmonic distortion may be also unacceptable.

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In first Brazilian SVCs, the thyristor valves are ETT (electrically triggered thyristor) type. These thyristors require minimum off period in each half-cycle for powering the gate drive circuits, which can be provided in different ways as explained in Sect. 7.3. If the power for the gate unit is taken from the power circuit, there may be constraints on the minimum firing angle of the thyristors and therefore may not allow full utilization of the maximum TCR inductive capacity (Lima 2013). As fixed capacitor banks are used by first-generation SVCs, the equipment losses are not optimized, since a small output inductive reactive power results in high current values for the TCRs. A current limitation strategy is implemented in the first-generation SVCs as follows. In the event of thyristor valve overcurrent, a signal that reduces the SVC main control loop inductive limit is produced increasing the value of the minimum firing angle defined at valve design. Since the TCR maximum current is obtained when its firing angle reaches the minimum value, increasing this minimum angle will reduce the RMS current of the thyristor valves (Lima 2013). For the later generation SVCs described in Sect. 6, during an overcurrent condition, the TCRs should be forced to full condition or be blocked (nonconducting state) to protect the thyristors from damage.

6

Later Brazilian SVCs

In 2001, the next generation of SVC was installed in the Brazilian Electric Power System at Funil Substation, in the Brazil Northeast region. This equipment has two sequentially controlled thyristor controlled reactors (TCR), two thyristor switched capacitors (TSC), and two redundant double-tuned harmonic third- and fifth-order filters, which together with the 230/13.5 kV – 200MVA SVC transformer form a six-pulse system, able to supply to the electric power grid a continuously varying reactive power output from 100 Mvar inductive to 200 Mvar capacitive at PCC (Lima 2013). When using two six-pulse sequentially controlled TCR units of half-rated output to achieve the same overall reactive power output then the harmonic currents are reduced to 50% compared with a single TCR with the full rated capacity. Funil SVC has circuit breakers at its high and medium voltage busbars as shown in Fig. 9. This gives a high degree of flexibility and availability, due to the possibility of operation in the so-called degraded modes, when one or more of its elements are out of service. A valid degraded mode means an SVC configuration where, although the output power limits are reduced, it is possible to continuously vary its reactive power output within a reduced range, while keeping the harmonic distortion produced by the SVC within the specified limits. A valid degraded mode requires at least the presence of one TCR and one filter. The selection of valid degraded modes is performed automatically by the SVC control system. If an invalid degraded mode is produced, SVC auto reclosing is automatically blocked by the protection. The reactive power values calculated considering rated voltage (13.5 kV) at SVC medium voltage busbar are 86.4 Mvar inductive for each TCR branch, 72.4 Mvar

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M. Lima and S. L. Nilsson 230/13.5kV - 200MVA X = 15%

VCES

Y ICES

Δ

329μF

329μF

1.35mH

8.4mH

329μF

8.4mH

7620μF

329μF

0.96mH 0.096mH

8.4mH

0.96mH 7620μF

1.35mH 0.096mH

8.4mH

13.5kV

Fig. 9 Funil SVC (100 to +200 Mvar, 230 kV)

capacitive for each TSC branch, and 23.8 Mvar capacitive for each double-tuned filter branch. As the Brazilian electrical power system short circuit levels have increased substantially, the switching of large transformers is not a problem. Therefore, motorized circuit switches are used instead of circuit breakers at the medium voltage Silves SVC busbar as shown in Fig. 10. In the event of a fault in the SVC, the HV circuit breaker is tripped. Then the appropriate medium voltage interrupters open to enable continued operation with the optimum degraded mode. The control system checks if the resulting degraded mode is valid and if it is, the HV circuit breaker is reclosed and the SVC is connected to the network with a reduction in its range corresponding to the disconnected branch. The capacitive to inductive ranges excursion for the SVCs presented in Figs. 9 and 10 is described below and is shown in Fig. 11. • At the SVC capacitive limit (point I), the two TSCs are connected and the two TCRs operate at their maximum firing angles, close to 165
, with very small inductive current values. The two harmonic filters, as fixed shunt elements, are always connected. • When required by the electric power system, the excursion in the inductive direction starts with the use of TCR1 (TCR2 remains at its maximum firing angle). At point II, TCR1 firing angle is changed to αc,1 which represents the special condition where TCR1 has its inductive admittance value equal to the

αc is the TCR firing angle that produces TCR admittance equal in magnitude to the TSC value (B [TCR (αc)] = B(TSC).

1

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500 kV

Y Δ

300 MVA ek = 15%

Included in ABB’s scope of supply

20 kV

TCR 147.6 Mvar

TSC 129.4 Mvar

TSC 129.4 Mvar

TCR 147.6 Mvar

th

5 Harmonic Filter – 36.8 Mvar

5th Harmonic Filter – 36.8 Mvar

Fig. 10 Silves SVC (200 to +300 Mvar, 500 kV)

TSC2 capacitive admittance. At this point, the SVC control system is able to switch off TSC2, while simultaneously changing the TCR1 firing angle to provide a voltage variation free switching (60 Hz) for TSC2. • From this point, TCR1 returns to be the control element until point III, when TCR1 is fired at αc, so that its equivalent admittance equals TSC1 one. The point III condition is similar to that of point II when TSC1 is switched off and TCR1 is controlled to provide voltage variation free switching for TSC1. • From point III, TCR2 remains operating at its maximum firing angle and the SVC operating point control is performed by using TCR1. When TCR1, on the excursion into the inductive direction, reaches its minimum firing angle, it is fixed in this condition and operates as TSR1 (Thyristor Switched Reactor) continuously triggered at its minimum angle. • From this condition on, the SVC operating point control is accomplished by using TCR2 until it reaches its minimum firing angle, when the SVC operates at its inductive limit. SVC excursion in the capacitive range is done in a similar way to the inductive range described above but in the reverse order. In this case, TSC1 is inserted before TSC2. Suitable hysteresis values are used to avoid instability in the TSCs switching process. The strategy described here allows the electric power system to see the SVC operating in steady state as a continuously varying susceptance between its inductive

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Fig. 11 Capacitive to inductive limit excursion for the Funil and Silves SVCs

and capacitive nominal limits connected to PCC. The fixed capacitive filters, not mentioned in Fig. 11, are present in all operating points described here. In practice, most designs include a maximum firing angle limit for phase control, typically in the range of 165–170 degrees.

7

Thyristor Valves

Thyristor valves are used in SVCs to control the reactive power contribution from reactive power elements, such as reactors and capacitors. Thyristors used in some later Brazilian SVC valves were light triggered thyristors (LTT) where there is no need to convert optical signals into electrical signals at the thyristor valve potential as is required for the conventional strategy, which uses electrically triggered thyristors (ETT). Some LTT devices have integrated voltage

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break-over (VBO) protection that functions to turn on the devices if they are exposed to overvoltages (Schultz et al. 1996). VBO protection is also used for ETT devices (Lawatsch and Vitins 1988) but normally requires external circuitry. Light triggered thyristors (LTT) do not require gate power to be developed from circuits that are connected across the thyristor devices because the turn on signal is derived from photons injected from ground-based electronic systems directly into the gate area (Temple 1983). However, even LTT devices need to have some blocking voltage developed across the LTT devices prior to injecting the turn on pulse to achieve good current spreading in the thyristor wafers. If the conduction current is slow to develop, the thyristors might fail in case of a high current surge with a high current rate of change (di/dt). The use of LTT allows the operation at very small firing angles close to 90
for TCRs, and it is not necessary to supply power to the thyristor electronics during the firing process (Lima 2013). With ETTs, operation close to 90
is not possible if the thyristor electronics are supplied with power only from the snubber circuit. However, as discussed in Sect. 7.3, other solutions for supplying power to the thyristors electronics are possible and can allow continuous operation at a firing angle very close to 90
, one example provides power for the thyristor electronics from an independent external source. The overvoltage cycle specified for the SVCs is typically defined by the Grid Codes for the AC network. The requirements presented below are for the Brazilian AC network. The design of the SVC needs to consider the maximum voltage at the PCC and the most severe contingencies in the electric power system. The SVC has to ride through the overvoltage levels as specified, without tripping. The overvoltages are converted to overcurrents that are applied to the thyristor valves. • • • • • •

First step: 1.80 pu for 50 ms. Second step: 1.40 pu for 200 ms. Third step: 1.30 pu for 1 s. Fourth step: 1.20 pu for 10 s. Fifth step: 1.10 pu continuous (inductive). Sixth step: 1.05 pu continuous (capacitive).

For SVCs connected to the 500 kV Brazilian power system, 1.10 pu instead of 1.05 pu is used for the overvoltage cycle’s sixth step. Some relevant thyristor issues to be considered in the SVC valve design are discussed by Krishnayya (1984). These include: • Transient voltage withstand of devices when exposed to overvoltages causing reverse avalanche • On-state voltage and holding current device tolerances • Single cycle, multicycle, and subcycle surge current capabilities and recovery characteristics • Critical stresses on valves regarding their di/dt, dv/dt, surge current, and forward recovery capabilities

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A detailed description of TCR and TSC thyristor valves together with the most relevant stresses applied to these valves are provided in Cigré TB 78 (1993). The following information about TCR and TSC thyristor valves can be found in Cigré TB 78 (1993): • The use of reactors to reduce current stresses on TCR valves. • Details about firing and monitoring circuits of TCR and TSC valves. • Details about TCR and TSC valve overvoltage and overcurrent protection schemes. • Thermal models used for TCR and TSC thyristor valves. • Influence of the AC system and SVC main components such as fixed capacitors, TSCs, and filters. • Stresses on TCR and TSC valves resulting from switching and system faults as well as the ones associated with steady-state operation. • Stresses under system disturbance conditions as AC system faults, temporary overvoltages in the AC network, switching overvoltages, insulation failures within the SVC, and control malfunctioning.

7.1

TCR Thyristor Valves

A TCR thyristor valve can be defined as an electrical and mechanical assembly of series-connected thyristor levels used to control the current through a thyristor controlled reactor in an SVC. A thyristor level consists of two antiparallel thyristors and a parallel connected RC circuit, also known as a snubber circuit, used to damp switching transients and reduce the voltage stresses of the series-connected thyristors. Thyristor valves in SVCs normally comply with the requirements of IEC and IEEE standards, as for example IEC 61954:2011 (Static Var Compensators – Testing of Thyristor Valves) and IEEE Standard 1031–2011 (IEEE Guide for the Functional Specification of Static Var Compensators). See also ▶ Chap. 21, “FACTS Equipment Design and Testing” for more information. The TCR valve assembly has several series-connected thyristor levels, including redundant levels according to the design criteria for each project. Most high power thyristor valves are fluid cooled using deionized water mixed with an antifreeze liquid to prevent freezing of the cooling fluid, if required. In addition to thyristor heatsinks, the snubber circuit resistors also require liquid cooling. Thyristors used in SVCs are normally of the so-called press pack construction as shown in Fig. 12, where the two opposing sides of the package are cooper pole pieces used as current contacts. These thyristors need to be compressed in operation in order to obtain adequately low electrical and thermal resistance. Commonly a series-connected stack of thyristors shares a common clamping system. Thyristor valves can be assembled in steel or aluminum frames which react against the clamping force of the thyristor stack. Alternatively, the thyristor stack might be held together using insulating tensioning rods or bands. A compression spring assembly is used to compress the thyristor and heat sinks in a stack with a

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Fig. 12 Thyristor and heatsink series connections in a thyristor valve. (Photo by permission of GE)

specified force or the clamping force can be applied via insulating tension rods or bands such that there does not need to be a steel or aluminum frame. For example, the minimum clamping force for a 100 mm diameter thyristor would typically be close to 100 kilo Newtons. Thyristors are stacked alternately with liquid cooled heatsinks. Each thyristor is assembled between two heatsinks, and each heatsink cools two thyristors, except the outermost heatsinks, which only have thyristors on one side (Fig. 12). The connections from the valve in the valve hall to the outdoors SVC equipment are made using wall bushings located behind each valve. The connections between the valve electronics cards and the valve base electronics (VBE) are typically made by optical fibers that bring the firing commands to the valve and sends signals to the VBE concerning the status of the thyristors, reporting if the firing process was done successfully or not. The number of TCR thyristor levels depends on multiple factors, such as the secondary voltage value, the chosen overvoltage protection strategy, the valve extinction overshoot, the spread in recovery voltage, the voltage break-over protection level (VBO), and component tolerances. The extinction overshoot depends on operating conditions such as di/dt and thyristor junction temperature, but it also depends on the series arrangement of thyristor levels and the characteristics of the thyristors and snubber circuit components. A typical arrangement of a TCR thyristor valve used in SVCs for power systems application is shown in Fig. 13. Each thyristor valve consists of a number of thyristor modules. A brief description of the major parts of a typical thyristor module is summarized as follows. More details about the thyristor module are provided in Cao et al. (2010). Gate Electronics: Electronic cards that are responsible for supplying the gate pulse to the thyristor when required, in addition to the exchange of signals among the thyristors and the valve base electronics.

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Fig. 13 TCR thyristor valve for power systems application. (Photo by permission of GE)

Snubber Resistors (Water-Cooled) and Snubber Capacitors: Snubber circuit resistors connected in series with snubber capacitors, which are connected in parallel with the thyristors at each thyristor level, are used to damp switching transients and balance the recovery voltage stresses of the series-connected thyristors. Auxiliary Supply CT Stick: Current transformer used in some valve designs to feed electric power to the thyristor electronics from an external auxiliary source called ground level power supply (GLPS). Fast Grading Capacitors: Each thyristor along with its snubber circuit has a stray capacitance to ground. These capacitances are different for each location within the thyristor valve. The valve can be depicted as a capacitive ladder network, causing a potentially nonlinear voltage distribution for steep fronted surges. This effect can be mitigated by compensating the ground capacitances through suitably sized discrete capacitors connected in parallel to each thyristor level, known as fast grading capacitors. di/dt Reactors: Reactors connected in series with the valve in some valve designs are used to protect the thyristors against high di/dt arising from the discharge of stray capacitances, e.g., from wall bushings, at turn-on. Voltage Dividers: Thyristor devices exhibit leakage currents both in the forward and reverse applied voltage polarities. To ensure proper voltage sharing between devices in the blocked (nonconducting) state, resistive dividers may be needed across the antiparallel thyristors to equalize the voltage sharing between the seriesconnected thyristors to prevent overstressing the devices.

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During external faults on the SVC high voltage side, its current will be interrupted by high voltage breakers. If at the moment of the fault there is current in the TCR and the voltage applied to it is zero, the current continues to circulate. This is the so-called DC trapped current, whose amplitude and duration is a function of several factors, such as fault resistance and point of application at the voltage wave. This effect occurs because the current in the inductor is proportional to the integral of its terminal voltage and if the voltage during the fault is zero, a DC current appears in the TCR and only disappears at the first current zero crossing after the voltage recovery on fault clearing. In this condition, the thyristor valve will continue to conduct in only one direction, until the current reaches the zero crossing and extinguishes. The effect of the DC trapped current is to increase the junction temperature of the conducting thyristors. For valve design purposes, studies are performed during the design stages to calculate valve stresses associated to the worst condition for DC trapped currents and this condition corresponds to a symmetrical three phase fault on SVC high voltage busbar at the same time as the valve current reaches its peak value. As an example, the calculation of the DC trapped current values for Tauá SVC (45 to 90 Mvar, 230 kV) TCR thyristor valves, in operation in the Brazilian transmission system since 2016 (Aho et al. 2016) is presented in the next paragraphs. The calculation is based on continuous operation with worst case continuous current before a fault application at the SVC high voltage busbar. This will give high initial thyristor temperature for the DC trapped current calculation. The cooling system performance is calculated with a maximum ambient temperature of 40
C and with the redundant heat exchanger fans out of service. The calculated worst case initial thyristor junction mean temperature prior to the fault is about 80
C in the example case here presented (point A in Fig. 14). During the DC trapped current period, the TCR current decays but the thyristor junction temperature rises. The rate of decay of the TCR current depends on the L/R time constant of the equivalent circuit. The TCR reactor, thyristor valve resistances, and inductances are considered in the calculation. The transformer losses are not considered, which gives slightly slower decay for the DC trapped current and calculated stresses that are slightly higher than the actual ones. The fault is assumed to be cleared as soon as the worst case thyristor junction temperature during DC trapped current circulation reaches its maximum peak (Point B in Fig. 14) which is found to be 87
C for this project. Assuming that the fault is cleared at point B, the worst case thyristor junction temperature post fault clearing is dependent upon the assumed magnitude of the recovery voltage. In the presented case, a short-term overvoltage of 1.3 pu is used for the calculation, which gives the peak junction temperature of 91.1
C (point C in Fig. 14). This is much lower than the maximum allowed 125
C thyristor junction temperature. Furthermore, the DC trapped current scenario could only occur when there is a true short circuit fault on the SVC high voltage busbar with zero voltage at one TCR delta branch.

99.950

100.000

100.000

A

100.050

100.050

T (Secs)

T (Secs)

100.100

100.100

B

C

100.200

100.150

100.200

Thyristor current (A)

100.150

Thyristor temp. (degC)

Fig. 14 Thyristor junction temperature and DC trapped current for a TCR thyristor valve. (Provided by GE)

-1.000K 99.950

0.000K

2.000K

4.000K

6.000K

95.000

80.000

85.000

90.000

95.000

100.240

100.240

178 M. Lima and S. L. Nilsson

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The thyristor will turn off at the first current zero crossing and its temperature will then start to decrease. According to this analysis, the thyristor valve can withstand the worst possible current stresses associated with a DC trapped current due to a fault at the HV side of the SVC transformer.

7.2

TSC Thyristor Valves

In general, one can say that the thyristor valve for a TSC is very similar to that of a TCR, but for a given AC voltage, the TSC valve has more thyristors connected in series because of the need to withstand both the maximum AC voltage and the maximum trapped capacitor voltage after blocking. As the voltage is proportional to the integral of the current for a capacitor and as remarked in Sect. 2.2 of this chapter, TSCs are able only to perform an ON/OFF control of their current. The TSC valves are protected against overvoltages by metal oxide varistors (MOVs) connected directly between the main valve terminals to limit the voltage across the TSC valve. The MOV arresters are rated considering the most severe fault cases such as ground faults during overvoltages and misfiring, as well as normal operating conditions. During system overvoltage, the TSC valve may be blocked, and this may happen at higher than normal voltage, trapping high voltage on the capacitors. The valve protection may then prevent the reinsertion of the TSC when the voltage drops to normal, unless the TSC valve has been designed for the higher in-rush current that will result from the higher trapped voltage on the capacitor bank. TSC valves also need to be protected against capacitor overvoltages, which may cause high inrush currents in the valve. The capacitor overvoltage protection (COVP) is primarily a capacitor bank protection but also has an important part in controlling valve stresses. In one way of implementing this protection, the capacitor bank voltage is monitored and if the capacitor bank is charged to a voltage exceeding COVP level for the thyristor valves, triggering pulses will be generated to the valve for as long as the overvoltage condition persists. COVP will thus prevent the TSC valve from being switched out, reducing the voltage stresses over the valve. However, this might increase the duration and magnitude of the AC system overvoltage. An alternative is to allow the TSC to block during the overvoltage and then include an interlock system to prevent the valve from deblocking at a voltage that would be unsafe; however, this can lead to a delay in being able to resume operation after an overvoltage. The response of the TSC valves during system overvoltage events need to be studied and appropriate requirements should be included in the system specification to obtain the best solution.

7.3

SVCs Gate Power Drive Issues

RC snubber circuits are connected in parallel with each thyristor level to damp voltage transients and balance the voltage stresses between thyristor levels.

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For ETT (electrically triggered thyristor) valves, one strategy used to supply the energy necessary to the thyristors firing process is to use the energy stored in the snubber circuits when the valve is blocked as described below. In this case, the minimum TCR firing angle is typically not less than 93.0 degrees so that the snubber circuits can store enough energy to assure a safe firing process. At the thyristor level, there might, for example, be rectifiers or DC/DC converters to power the gate drive modules. This strategy is design dependent as there are several ways of converting energy to a suitable level for the thyristor electronics. These so-called energy stepdown (EC) units are fed by the snubber circuit current and they feed the thyristor valve electronics (TVE) that needs a DC supply to generate firing pulses and to handle the required monitoring functions. In case of total voltage collapse, the power supply is lost after a delay. The power supply snubber capacitors are recharged in half a cycle when the SVC is energized again. Another strategy to get energy for powering ETT thyristor gate driver units is to use an insulated current transformer called a CT Stick, mounted on the valve module frame. The CT Stick assembly is located in the same relative position for both TCR and TSC modules. This assembly receives power from a ground level power supply (GLPS) and provides the gate driver units power continuously. The GLPS unit is installed inside the valve room and its chassis is connected to ground potential. To enhance availability, the GLPS operates from a choice of AC supply and DC supply. Typically, the GLPS generates a high frequency current loop (for example, 800 Hz power source) that flows through the power supply loop, also known as CT loop which is effectively a single-turn primary winding that can power many thyristors. The main differences between LTTs (light triggered thyristors) and ETTs are the way of triggering and the LTT internal integrated protection functions. Some important protection functions can be integrated in the LTT such as BOD (break-over diode) and dv/dt protections (Temple 1983; Katoh et al. 2001). Therefore, the electronic components which are necessary for the external protection of ETTs might not be necessary for LTTs. For monitoring purposes, the LTT may require a simple circuit at the thyristor level to detect whether or not the thyristor blocks in the nonconductive state and trigger when ordered to do so. To use a LTT, it is only necessary to fix the optical fiber (Ruff et al. 1999) into the housing and connect this light pipe to a laser diode. The optical fiber performs the insulation between the main circuit (closed loop control and valve base electronics) and the thyristor firing circuit. This way, for LTTs, firing pulses are available independent of AC system voltage and no auxiliary energy is required within the valve except possibly for device monitoring purposes. Figure 15 shows a LTT and its optical fiber.

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Fig. 15 Direct light triggered thyristor

7.4

Thyristor Valve Cooling System

The thyristor valves’ cooling system is typically a closed single circuit deionized water cooling system. If the system can be exposed to freezing conditions, an antifreeze agent would be added to the water. In cold countries, some cooling systems have two circuits. The valve cooling circuit uses pure deionized water and the other uses water and glycol, with a heat exchanger between the two circuits. The valve heat sinks located on each side of the thyristors are cooled by a flow of deionized water that is also distributed to the TCR and TSC snubber circuits. Dry air coolers placed outdoors provide heat exchange between the cooling medium and the air. Fans are automatically started if the cooling medium temperature exceeds a certain level. One circulation pump with one redundant pump at standby maintains the cooling liquid circulation in the system. The valve losses, which are the sum of thyristor losses and the TCR and TSC snubber losses (and the losses in the di/dt reactors, if provided) during worst case operating conditions, determine the size of the cooling system. A typical cooling system used for a power system SVC is shown in Fig. 16. Redundant pumps, cooling radiators, and fans are typically provided to minimize the risk of the cooling system causing a shutdown of the SVC. A secure power source for the cooling system will be needed to avoid shutting down the SVC during temporary AC system disturbances since loss of power to the cooling system would be a common mode failure that would lead to a loss of the complete SVC.

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Fig. 16 Power system’s SVC cooling system. (Photo by permission of ABB)

7.5

Thyristor Valve Control and Protection Systems

The thyristor valve control consists of thyristor control units (TCU) and valve base electronics units (VBE) in which the thyristor monitoring system (TMS) is an integrated part. The VBE is located in the control cubicle and the TCUs are located on the valve itself. All communication between the control equipment and the valve equipment is carried out via fiber-optic light guides. Each ETT-based thyristor level requires gate drivers; this can be implemented in different ways, as follows: • Two separate gate drives per level. • One gate drive per level, driving both thyristors via an isolation circuit. • One gate drive per level, driving a common-cathode-connected pair of thyristors. In this case, one extra gate drive is needed at the end of the valve. There are several ways to design the TCUs for triggering and monitoring of the thyristors. The basic function of the TCU for ETT devices is to convert incoming light pulses to thyristor firing orders and to send back thyristor status to the TMS. When the TCU is energized and the voltage across the thyristor is forward, a signal is sent back to the VBE enabling the TCU to send a gate pulse to the thyristor. The TCR TCU contains a thyristor overvoltage protection providing protective firing if the voltage across the thyristor exceeds the protection level. Failure of individual thyristors generates an alarm. A failed thyristor is typically detected by sensing the voltage across the thyristor when the thyristor is in the off state. If there is no voltage, the thyristor is short circuited. This kind of information is easily communicated back to the control system by means of a laser diode and a

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Technical Description of Static Var Compensators (SVC)

183

fiber-optic link. The position of the failed thyristor will be indicated on the SVC Human Machine Interface (HMI) screen.

8

SVC Control System

8.1

Early SVC Analog Control

The first SVCs installed in the 1980s used purely analog and nonadaptive control systems as shown in Fig. 17. For these SVCs, the three-phase voltages and currents measured at the SVC high voltage side are used to calculate the UMED measured voltage which is compared with the reference voltage (set by the operator) to produce the error signal ΔU, which is the input to two control channels. The SVC control action is determined by either: • The normal channel, which is based on a proportional-integral controller (PI), that operates continuously and represents the main controller. • Or by a fast channel which acts based on a proportional-derivative controller (PD) and operates only during major disturbances due to the presence of a dead band. Because of its nonadaptive characteristics, a single gain value had to be used by the early SVC analog controls for all planned network operating conditions. The need to design for the lowest specified short circuit level determines the speed of response of the analogue controller, and the lower the level is the slower the response. In case of degraded network operation resulting in short-circuit levels lower than the minimum specified for the design at PCC, SVC operation could

Fig. 17 Analogue closed loop control

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become unstable. Therefore in such conditions, manual Var control mode might be required to avoid oscillatory or even unstable behavior. However, in manual mode of operation, the SVC is not able to control its terminal voltage, as it operates as a fixed susceptance whose value is defined by the operator. This problem is overcome through the use of adaptive control schemes in the newer SVCs as described in the next sections of this chapter.

8.2

Digital Control Systems

The closed loop control of a typical SVC that uses digital technology is based on the positive sequence voltage and the reactive current component measurements. Instantaneous voltage and current signals are filtered with a sequence of discrete infinite impulse response (IIR) filters tuned for 3rd, 5th,and seventh harmonics. According to Clarke (1943), these signals are then converted to alpha  beta domain from which the voltage signal is processed to positive and negative sequence components, and the SVC current signal (ISVC) is converted to D and Q components (rotating coordination), as defined by Park (1929). The positive sequence voltage vector length is passed through averaging and second harmonic filters as well as the SVC current. The current component is scaled with the slope and subtracted from the measured voltage along with the reference set-point. This forms the signal to be fed to the voltage controller. The function blocks and connections are shown in Fig. 18 (Aho et al. 2016). To avoid SVC control system instability or poor performance in terms of response times, and the associated system voltage control problems, an automatic gain controller can be included in the SVC closed loop control. The main purpose of this control feature is to adjust the SVCs main closed loop control gain over a wide range of power system operation conditions, such that the specified performance parameters for the step response test can be obtained (Belanger et al. 1984; Gutman et al. 1985).

ABC to αβ

Vsystem

αβ to v+/v-

T

x

+

T

Y=

6 Filtering 3H, 5H, 7H

∫ X ( Δt ) dt 0

-

6

N

Sliding average

Filtering 2H Reference

ABC to αβ

ISVC 6 Filtering 3H, 5H, 7H

αβ to DQ

T

x

X

T

Y=

∫ X ( Δt ) dt 0

N

Sliding average

6 Filtering 2H Slope

Fig. 18 Digital main controller input signal calculation

+

-

VERROR

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Technical Description of Static Var Compensators (SVC)

185

PI controller Valves

KP +

KGC

+

BSVC

1 sT

BSVC to BTCR BTSC

BTCR

BTSC

BTSC to FPTSC

αTCR

TSC ON/OFF

Under voltage strategy

Gain supervision

SCL

Gain optimization

VERROR

BTCR to αTCR

Fig. 19 Digital SVC closed loop control: adaptive loop

In its simplest form, the automatic gain control can be implemented as a gain switching control that applies to the SVC main control loop with a number of preset gain values, calculated, for example, according to the PCC short circuit level (SCL) measurement. In addition, an automatic device able to detect control system instability should be installed to assure stable behavior during, for example, operating conditions not considered during the design stages. Such features are implemented as shown in Fig. 19. The set of gains described below are applied to the signal VERROR. The SCL gain controller corrects the VERROR signal, shown in Fig. 18, based on the dynamic shortcircuit level measured at SVC PCC, as described below. Performance parameters related to SVC step response should be achieved as follows, in compliance with the definitions established by IEEE (IEEE Standard 1031 2011). • Maximum percent overshoot (MPO) of 30%. • Maximum rise time (Tr) of 33 ms. • Maximum settling time (Ts) of 100 ms. The gain optimization (GO) algorithm is based on the scheduled application of a small disturbance of the SVC output and the measurement of the relationship between the voltage change and the reactive power error corresponding to this disturbance, the so-called gain test. Based on the SVC output signal magnitude and polarity measured during the gain test application, the SCL gain value will be increased or reduced (Lima et al. 2017). The second control loop, called gain supervisor (GS), aims to preserve stable operation of the SVC if oscillations are detected in its output signal. This is done by reducing the KGC gain value from its present value until such oscillations are satisfactorily damped. The main control loop is based on a proportional-integral (PI) controller action, with parameters adjustable through the values of SCL and KGC gains. This controller is bypassed if the SVC terminal voltage at SVC PCC

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Fig. 20 Closed loop control: general block diagram

falls below a value defined by studies, forcing this equipment to operate with 0 Mvar output, constituting the so-called undervoltage blocking scheme. As shown in Fig. 19, the required SVC susceptance (BSVC) is distributed to the available controllable elements (TCRs and TSCs). The TSCs susceptances are determined based on the switching limits defined for these elements, which have a binary control strategy (ON/OFF). The TCRs currents are continuously controlled between their maximum and minimum limits, based on the thyristor firing angle defined by the SVC closed loop control system. These elements are responsible for the continuous control of the reactive power injected by the SVC into the power grid. This equipment control system consists of two fully redundant control units, producing a 100% redundancy level. Figure 20 shows a simplified block diagram of a typical SVC closed-loop control system. The adaptive control loop is inside the block “voltage control” (Lima et al. 2017). In Fig. 20, IO means input/output, POD means power oscillations damper, and Iorder is the current order defined for the TCRs.

8.3

Additional Control Loops

8.3.1 Undervoltage Blocking Scheme This control scheme is designed to avoid the SVC increasing the AC overvoltage after the recovery from a close up fault. It forces the SVC to operate at 0 Mvar if its terminal voltage drops below a preset value for a predetermined time. For example, in case of an SVC having two TCRs, two TSCs and filters (Fig. 10), this corresponds

6

Technical Description of Static Var Compensators (SVC)

187

to blocking two TSCs and one TCR, the remaining TCR being used to compensate the filters susceptance, resulting in 0 Mvar at PCC. This function aims to prevent the SVC operating at strongly capacitive points, generally associated with electrically close faults, when this operating mode could increase the overvoltage level on fault clearing. Detection of this scheme operating condition is based on the mean RMS values of the three phases of the PCC voltage for balanced three phase faults and the minimum RMS value of this voltage for unbalanced faults. The SVC is released to voltage control when this signal reaches a value higher than the blocking level plus a hysteresis defined during the system design. This undervoltage blocking scheme is able to operate for local and remote, balanced and unbalanced faults. The aforementioned blocking and unblocking levels can be modified based on the short circuit level (SCL) measured at PCC. This control loop could be activated or not depending on the power system voltage characteristics at PCC and on the level of overvoltages associated with faults clearing in the SVC influence area.

8.3.2 Degraded Mode Operation Some SVCs offer the possibility of automatic operation in degraded mode if components such as harmonic filters, TCRs or TSCs become unavailable. Enabling degraded operation provides a higher degree of flexibility and availability for the SVC equipment. To achieve the increasing SVC availability required by the Brazilian National Operator Grid Codes, Brazilian SVC specifications require valid degraded operating modes corresponding to configurations that, although the output reactive power compensation limits are reduced, provide continuously varying SVC output power while keeping SVC harmonic levels below the specified limits. Therefore, a valid degraded mode typically requires the presence of at least one TCR and filters as necessary or one TCR, one TSC and one filter for the configuration presented in Fig. 10, as an example. The selection of valid degraded modes is performed automatically by the SVC control system based on the status of the various elements, using medium voltage motorized switches. If an invalid degraded mode is produced, the SVC automatic reclosing function is blocked. This function can be activated or deactivated via the SVC human machine interface (HMI).

8.4

The Use of Series Reactor to Reduce Harmonics and Losses

Usually a utility SVC is connected to the selected point of a transmission grid using a SVC transformer. The transformer typically has a reactance value in the range of 12% to 20% and secondary (MV) voltage between 10 and 35 kV (Aho et al. 2016). As explained in Sect. 2 of this chapter, a TCR in operation produces harmonics due to the control of reactor current. The order of harmonics also depends on the firing angle of the thyristors. The harmonics generated by the TCR cannot be fully

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Fig. 21 Tauá SVC and the blocking series reactor

filtered, so a TCR increases harmonic levels at the SVC PCC. Furthermore, the network will include harmonic sources (background distortion) which may be magnified through resonance with the impedance of the SVC. One method to reduce the harmonics at PCC caused by the TCR is to increase the impedance between the SVC busbar and the PCC. The SVC transformer has built in impedance, so adding reactance in series with this transformer increases the overall impedance. The transformer reactance can be increased by increasing the distance between the windings around the same poles but the size of the transformer is smaller if an external additional reactor is used. This external reactor is called a blocking reactor (Aho et al. 2016). Figure 21 shows the configuration of the Tauá SVC, which has been in operation in the Brazilian power grid since 2016 and which uses this strategy. This concept was successfully implemented for the first time as reported in Aho et al. (2014). The abovementioned blocking reactor is connected between SVC BUS 1 and SVC BUS 2. Single-tuned filter banks FC1 and FC2 are tuned to filter fifth and seventh harmonic currents respectively generated by the TCR. TSC1 and TSC2 are not tuned and do not participate in filtering of TCR harmonics and therefore are connected to

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Technical Description of Static Var Compensators (SVC)

189

SVC BUS 1. In the presented case, the reactance of the blocking reactor is selected to be in the same range as the reactance of the SVC transformer (Aho et al. 2016). As detailed in Aho et al. (2016), the introduction of the series reactor produces the following advantages regarding the SVC main circuit design: • • • •

Reduction of the number of series-connected thyristors used in the TCR valves. Reduction of short-circuit requirements at SVC BUS 2. Reduction of total losses of the SVC. Avoidance of resonances among SVC filters and the power network in abnormal configurations.

For these reasons, the use of the series reactor allows the use of simple SVC technology in projects associated with high short circuit levels at PCC and where strict requirements for low power losses cannot be met by the use of equipment based on Voltage Source Converters (VSC) technology, as in the reported case of Tauá SVC.

9

Coordinated Operation of SVCs Operating Electrically Close

When there are two or more SVCs operating electrically close, the settings and gains of their closed loop control systems must be coordinated considering the dynamics of the power grid and the interactions among the SVCs. (These issues can also arise if an SVC system is close to another FACTS controller or an HVDC system.) Thus, studies and measurements of power grid voltage sensitivity at various reactive power operation levels should be made to define the appropriate gains. As mentioned in Sect. 8.2 of this chapter, the gain optimizer (GO) control loop depends on the measurement of the sensitivity of the electric power grid to the injection by the SVC of a susceptance pulse. However, if a second SVC operates electrically close to the one whose GO is active the apparent power network response will be masked by the response of the second SVC to the disturbance. As a result, the measurements made will be inaccurate, resulting in an incorrect gain adjustment. Lima and Lajoie discuss real cases related to SVCs operating electrically close in the Brazilian and the Hydro Quebec Power grids and proposed solutions to overcome the challenges that involve their coordinated operation (Lima et al. 2014 and Lajoie et al. 1990). The strategy to address this issue in the Brazilian case is based on the implementation of a control scheme and a fast telecommunication link between the electrically close SVCs. In general, the states of the different high gain, rapid response controllers need to be communicated to the other near-by controllers. Other communication technologies could be applied so the example given here is not the only viable solution. A signal inhibits the main control loop of the SVC that is not performing its gain test (the passive SVC) from reacting during the test period, i.e., the passive SVC is forced to operate with a constant output for a very short period. This scheme can be implemented as described as follows (Lima et al. 2017).

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• A signal is sent from the SVC that will perform the test (which will be referred to as the active SVC) to the passive one, indicating that the active SVC will apply the gain test. • Upon receiving the warning signal, the passive SVC applies a deadband to its control system and informs the active SVC that the gain test can be applied. • The active SVC receives this confirmation from the passive SVC and performs its gain test. • At the end of the gain test, the active SVC informs the passive one that the dead band can be removed. • The passive SVC removes the dead band and resumes its normal operation (automatic mode). If a major disturbance is applied in the electric power grid at this time, the dead band is deactivated and the passive SVC immediately resumes operation in voltage control mode, without waiting for the gain test performed by the active SVC to be completed. In that case, the gain test should be rescheduled. The main features of the abovementioned implemented scheme to provide the interchange of information between the electrically close SVCs are distributed algorithm, hardwired connection for the essential communication signals, and additional information transmitted via Distributed Network Protocol 3 (DNP3). This protocol is an open and public protocol being administered by the Distributed Network Protocol Users Group (DNP 2018). If the electric distance between the SVCs is small, it is possible to assume the same short-circuit levels for both equipment high voltage busbars. Then, the active SVC, when performing its gain test, informs the passive SVC of the short circuit level resulting from this test. The passive SVC then uses this value to determine its gain value. Even considering that both SVCs are supplied by different manufacturers, the approach described can be implemented without sharing any specific gain calculation strategies of each SVC, safeguarding the confidentiality and intellectual property aspects associated with each project.

10

SVC Losses

SVC total power losses are calculated at specified operation points, and SVCs will have been designed in order to optimize their total evaluated costs including equipment, engineering, and losses. The purpose of this section is to present the loss calculation principles. As sometimes it is difficult to measure the power losses at the site accurately, the loss evaluation is mainly based on the factory test results and theoretical calculations. The total SVC power loss is composed of different components considered in different ways. Therefore, it is necessary to analyze the loss calculation methods separately for each SVC component as described below. A power system SVC is composed of the following equipment:

6

Technical Description of Static Var Compensators (SVC)

• • • • • • • •

SVC transformer. Thyristor controlled reactors. Thyristor switched capacitors. Harmonic filters. Auxiliary services. Valves cooling systems. Control and protection systems. AC supply, cooling and heating systems for SVC cubicles and valve buildings.

10.1

191

SVC Transformers Losses

The SVC transformer is typically procured by the SVC contractor from another company, either within or external from the SVC contractor’s company. In this section, the SVC contractor will be referred to as the purchaser. The SVC contractor typically remains responsible for the SVC transformer, whether or not it is sourced from its own or another company. Transformers used for connecting SVCs to the AC grid dissipate energy in their conductor resistance, magnetic core flux heating, and heating as a result of induced currents in tank walls and other metallic components. The lost energy has a cost, because it requires power to be generated but not delivered to the ultimate users of the electric energy (Heathcote 2007). In order to be able to estimate the cost of this lost energy, the losses have to be known. Also, in order to compare the true cost of different transformer designs and of different manufacturers, the purchaser should, if possible, in the procurement documents state the capitalized value of losses to be used for the evaluation of proposals. The purchaser also has the responsibility of specifying the background harmonics and the harmonics from the SVC to which the transformer will be subjected, while the transformer manufacturer has the responsibility of designing the transformer, taking into account these specified harmonics (CIGRE TB 529 2013). This procedure is not unique to transformer losses but applies to all SVC losses. A small amount of DC current might also flow through the SVC side windings if the power semiconductor switching is not balanced between the positive and negative half cycles. The purchaser must also include the maximum value of DC current that the SVC transformer should be capable of handling without any component exceeding its specified temperature limits. DC currents will bias the transformer magnetizing characteristic causing the magnetizing current to be asymmetric and create noncharacteristic current harmonics as well as sending the core towards saturation. The potential for these aspects also have to be considered. Losses caused by harmonics may be highly localized eddy or circulating currents within parts of the windings. Also cores and tanks will contribute significant losses. Losses in service associated with harmonics, however, cannot be measured during the factory acceptance tests and therefore, must be calculated. The manufacturer should provide these calculations for the total service losses as per applicable standards and indicate these losses for different ratings. In addition to the total

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services losses (inclusive of harmonic effects) at various loads, the manufacturer should provide, prior to factory testing, the calculated value of eddy current losses at fundamental and harmonic frequency, which should be declared and with the client’s and the purchaser’s agreement, will be used to correct measured values. The fundamental frequency losses are normally covered in the guarantees subject to tolerance as specified in standards (IEEE C57.12 2015). The assessment may entail using calculating tools such as finite element methods (FEM). Manufacturers calculated and expected test values should be compared to the values derived from test measurements. The calculated losses and their distribution are used not only to assess if the transformer design will meet the requirements of the procurement specification but also for thermal modeling of the transformer to ensure that the hottest spot in the transformer does not violate the standard. There are, however, practical limits to the accuracy that can be obtained with models because transformer manufacturing involves not only an analytical design process but also tolerances in materials, manufacturing tolerances, dimensional creepages in cellulosic materials, etc. Consequently, even models that are based on the best mathematical descriptions of the underlying physical processes will always need to incorporate a certain degree of empiricism and tuning factors (CIGRE TB 659 2016). Calculation of the eddy current losses in windings, cores, and structural components is based on determining the amplitude and distribution of the magnetic stray flux. To simulate the loss distribution in the structural metal parts of a transformer requires first a nonlinear magnetic AC calculation using a FEM model with a very large number of mesh elements. The validity of the result will be highly dependent on the mesh size and placement and computer power to ensure numeric stability. The accuracy of loss calculations may depend on the level of details used in the modelling approach. To calculate the magnetic field distribution is, however, a straightforward mathematical procedure if the magnetic field due to eddy currents in all the conducting parts can be neglected. These conducting parts primarily consist of the copper (or aluminum) in the windings, the metallic frames that secure the core and winding assembly, the core material, and the tank including the magnetic shunts or aluminum/copper shields. It is, however, not possible to formally validate the simulation results using load-loss test data because eddy-current losses in the windings cannot be separated easily from stray losses in other metallic parts such as tank, core clamps, etc. (CIGRÉ TB 659 2016). There are, however, simplified mathematical methods usable for fundamental frequency domain calculations. These are published in standards and in some textbooks, which can be used to approximately estimate transformer losses (IEEE Standard C57.18.10; IEEE Standard C57.110– 1998; IEEE Standard 1158– 1991; Fitzgerald et al. 2003). For SVC transformer applications, it will be necessary to calculate the harmonic currents for each harmonic order and operating point to obtain an estimate for the annual cost of the losses dissipated in the transformer. Transformer losses are divided into no load losses and load losses. Both the no load and load losses for fundamental frequency currents and voltages are measured as part of the transformer tests prior to shipment from the factory. Essential inputs for transformer losses estimates are:

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Technical Description of Static Var Compensators (SVC)

• • • • • •

Transformer nominal MVA. Transformer actual load in MVA. Transformer rated primary voltage. Transformer rated secondary voltage. Actual primary voltage applying to the load condition considered. Transformer no load losses across the range of excitation (viz. system voltage divided by system frequency). Transformer load losses at fundamental frequency and standard reference temperature. Harmonic current spectra for transformer current at various loads to be considered. Primary and secondary resistances and temperature at which they apply. Ambient temperature – usually maximum daily average, average annual, maximum and minimum temperatures are sufficient. Winding temperature at Standard reference temperature. Fan and pump power requirements as applicable to the various loads considered.

• • • • • •

193

10.1.1 No Load Losses No load losses are mainly hysteresis and eddy current losses in the transformer core steel but will also include losses in the transformer’s dielectric system and a small component of winding losses. The core losses are the result of magnetic excitation and occur even when load current is not flowing through the transformer windings. The core losses are hysteresis losses, which are proportional to frequency, and eddy current losses, which are proportional to the square of the frequency. However, the core losses can vary significantly for different core designs and core material selection. Also, the design flux level in the cores will strongly affect the core losses. Harmonic currents have no effect on the no load losses, unless the excitation voltage is distorted, in which case the eddy current losses in the core will increase. The no load losses are measured during the factory tests by supplying rated voltage to the low voltage winding that is as distortion free as possible. The losses are temperature sensitive so it is preferred to have the no load test performed with the core as close to the specified operating temperature as possible. No correction for temperature need to be made if the top oil temperature is within 10
C of the reference temperature and if the temperature difference is not more than 5
C between the top and bottom temperature of the transformer (IEEE C57.12.90 2015). It should be noted that transformer standards make no prevision for temperature correction of no load losses, nor do they stipulate a range of temperatures for performance of the measurement. The hysteresis losses are a function of the chemical composition and manufacturing method of core steel production and should not be affected by temperature. Eddy losses, on the other hand, would theoretically reduce with increasing temperature, so measuring them as close as possible to the maximum daily average ambient temperature would appear to give the best optimization. In any case, it is uneconomical to raise the temperature of the core by raising the oil temperature to the reference temperature of 85
C, and it is impractical to raise the laboratory ambient temperature to that level.

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10.1.2 Load Losses The issue of interest for SVC transformers is how much the harmonic current flows will add to the measured fundamental frequency load losses. Therefore, the calculations need to consider the higher winding resistance and eddy current-related losses caused by the higher frequency harmonic currents as compared with the fundamental frequency losses measured as a part of the factory tests. The dominating component of the load losses are the DC resistance losses, since they consist of losses produced in the winding resistances by the load current. The second component is the stray flux losses, as discussed above, which are caused by the electromagnetic flux that originate from the transformer windings and induce losses in the core, core clamps, magnetic shields, tanks, and other transformer components. Stray losses can be further divided into winding stray losses and other stray losses. The winding stray losses are a combination of winding conductor strand eddy current losses and losses due to circulating currents between strands of parallel winding circuits. These losses may be considered as winding eddy current losses. Thus, the total fundamental frequency transformer load losses are given by: PLL ¼ PI 2 R þ PEC þ POSL

(3)

where: PLL is the total transformer load loss. PI2R is the summated winding DC resistance losses. PEC is the winding eddy current losses. POSL is the other stray losses. Transformer load losses are proportional to the square of load current, which as stated above, for an SVC normally contains a significant amount of harmonics. The RMS value of the current is given by: I RMS

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xh¼hmax ¼ I 2h h¼1

(4)

where: IRMS is the RMS current value at the actual operating point for the transformer. Ih is the harmonic current of order h with h = 1 equal to the fundamental frequency component. To calculate the load losses, the winding resistance measured at a uniform oil temperature during factory tests is used. The rated transformer current should then be used to estimate the IRMS2R losses at the resistance measurement temperature. The winding resistance used in this equation is the measured DC resistance. The additional losses at this temperature are obtained by subtracting this calculated value of I2R losses from the measured load losses appropriate to the measurement temperature. The power transformer total resistive winding losses under rated conditions at the measurement temperature can then be calculated for a two winding transformer as follows:

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Technical Description of Static Var Compensators (SVC)

h i PI 2 R ¼ k  ðI 1R Þ2  R1 þ ðI 2R Þ2  R2

195

(5)

where: k is 1.0 for single-phase transformers and 1.5 for three-phase transformers. I1-R is the high voltage fundamental frequency line current under rated conditions. I2-R is the low voltage fundamental frequency line current under rated conditions. R1 is the average DC resistance per phase of the high voltage winding(s). R2 is the average DC resistance per phase of each low voltage winding. Equation 5 is valid for a two-winding transformer but can be extended for threewinding transformers. These calculations assume fundamental frequency currents and voltages. Three-winding transformers for SVCs will have different harmonic current content in the windings since these transformers are used for 12-pulse SVC systems in which the 5th, 7th, 17th, 19th, etc. harmonic currents are cancelled out inside the transformer and only the (12n  1) harmonics flow in the high voltage winding. The IEEE and IEC standards for rectifier transformers cover the issues for more complex transformer configurations in detail (IEEE C57.18.10 1998; IEC 60076–57-129 2017). Proportioning of stray losses for ambient conditions for a regular AC transformer should be made separately for the eddy current and other stray losses. The winding eddy current losses are proportional to the square of load current and the square of the harmonic order and are given by: PEC ¼ PECO 

Ph¼hmax

I 2h h2 Ph¼1 h¼hmax 2 Ih h¼1

Xh¼hmax  I h 2 ¼ PECO  h2 h¼1 I RMS

(6)

where: PEC is the winding eddy current losses with nonsinusoidal load currents at the actual operating point. Because the losses were measured during the factory test of the transformer with continuous load current, the rated transformer current must be used in the loss equation. Ih is the harmonic component current. h is the harmonic number. PEC-O is the calculated winding eddy current losses calculated from the test data. The same calculation can be made for the other stray losses. If the two eddy current and other stray loss components are not possible to separate from each other, then the other stray loss component should be assumed to be 40% and the eddy current losses to be 60% of the stray loss component (IEEE C57.18.10 1998). Some manufacturers have found that the stray flux fields impinging on busbars and connections do not have the same effect on the losses as eddy current losses. Therefore, the IEEE standard for rectifier transformers uses an exponent of 0.8 when calculating the power losses for the other stray losses instead of 2 in the loss calculation in Eq. 6

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(IEEE C57.18.10 1998). That is, in that case, the eddy current loss component will be significantly larger than the other stray loss component.2 The eddy-current multiplier can be converted into a harmonic loss factor by dividing the numerator and the denominator of (6) by the fundamental current. This is the so-called harmonic loss factor for winding current losses (FHL) and is given by PEC/PEC-O. The other stray losses at the actual operating point are given by: POST ¼ ðPOST O Þ 

Ph¼hmax h¼1

I 2h h2

I RMSRated 2

¼ POSTO 

Xh¼hmax  h¼1

Ih

2

I RMSRated

h2

(7)

where: POST is the other stray loss at the actual operating point. POST-O is the other stray loss with rated current based on factory test.

10.1.3 Total Transformer Losses The total transformer losses can now be estimated as follows for any operating point: PTL ¼ PNLL þ PI 2 R þ PEC þ POSL þ PPF

(8)

where: PTL is the total transformer losses for the specific operating point. PNLL is the transformer no load losses. PI2R is the transformer I2R losses for the specific operating point. PEC is the winding eddy current losses for the specific operating point. POSL is the other stray losses for the specific operating point. PPF is the pumps and fans losses for the specific operating point.

10.2

SVC Thyristor Controlled Reactor (TCR) Losses

The TCRs inject harmonics into the electric power system due to their nonsinusoidal waveforms. The influence of these harmonic currents has an impact on the power loss calculation procedures of many other SVC components.

10.2.1 TCR Thyristor Valves Total TCR thyristor valve losses can be subdivided into four different loss categories. These are voltage divider losses, thyristor valve conduction losses, thyristor switching losses (ON/OFF), and reactor losses. When calculating thyristor valve losses, the most relevant factor is the TCR current. The current through the reactor when the thyristor valve is in continuous conduction mode is ITCR = V/ωL (Hingorani and Gyugyi 2000) where: 2

Note that in the IEEE standard C57.110 for regular power transformers, the eddy current and stray losses are given the same weight.

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Technical Description of Static Var Compensators (SVC)

197

V is the RMS value of the purely sinusoidal voltage applied to the TCR. L is the TCR reactor inductance. ω is the system angular frequency (2πf where f is the power system frequency). The average TCR thyristor current is then given by (IEEE standard 1031 2011): I TAV

pffiffiffi 2  ½ sin ðπ  αÞ  ðπ  αÞ cos ðπ  αÞ ¼ I TCR  π

(9)

where: ITAV is the average thyristor current. ITCR is the fundamental RMS current component for fully conducting thyristor valve. α is the thyristor firing angle in radians (from π/2 to π). This way, the true ITRMS thyristor current can be calculated by multiplying ITCR by a factor function of thyristor valve firing angle given by:

I TRMS

ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
 ðπ  αÞ  ½1 þ 2 cos2 π  α  1:5 sin ½2ðπ  αÞ ¼ I TCR  π

(10)

10.2.2 TCR Thyristor Valve Conduction Losses The most significant losses in a TCR thyristor valve are the thyristor valve conduction losses, which are due to the threshold voltage and the thyristor conduction resistance. Conduction losses for one single thyristor are given by: Pcthyristor ¼ U TH  I TAV þ rT  I 2TRMS

(11)

where: Pcthyristor are the conduction losses for one thyristor. UTH is the threshold thyristor voltage. rT is the thyristor conduction resistance. The TCR is a three-phase equipment where each phase has antiparallel connected thyristor pairs. The number of series-connected thyristor levels depends on the connection voltage and the number of redundant thyristors. Therefore, the losses calculated for one thyristor need to be multiplied by 3  2  number of seriesconnected thyristors to give the total thyristor valve conduction losses. In addition, there are some losses dissipated in busbars, etc. that might have to be considered.

10.2.3 Snubber Circuit Losses Snubber circuit capacitors are discharged at the time the thyristors are fired, which occurs twice per fundamental frequency cycle. Thus, the power loss calculated over 1 s is given by (IEEE standard 1031 2011):

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PSN ¼ 3 

i2 C sn U 2α C sn hpffiffiffi 2 ¼ 3fn   2  U 1  sin ðαÞ  2 n n

(12)

where: PSN are the snubber circuit losses. CSN is the snubber circuit capacitance per level. Uα is the instantaneous voltage across the snubber capacitors at the firing angle α. U1 is the fundamental valve connection voltage. n is the number of series-connected thyristors per phase of the valve. fn is the system fundamental frequency. α is the thyristor firing angle.

10.2.4 Thyristor Switching Losses Thyristors do not reach full conduction immediately upon the application of a turnon pulse to the gate. There is a finite time for the current to begin to flow around the gate area of the thyristor wafer. During the turn-on time, the voltage decays over a few microseconds (μs) as the current increases. The integral of the current times the voltage across the wafer represents energy dissipated in the wafer. This is the turnon loss. Similarly, when the gate pulse is removed from the device and the current is commutated from the device into circuits surrounding the device, the conduction current through the wafer does not instantaneously go to zero but reverses for a short period of time as the voltage transiently increases because the plasma that developed during the conduction interval needs to be removed before the wafer enters a nonconducting state. This is called the reverse recovery charge, Qrr. For the same reasons as there are losses dissipated in the wafer during turn on, there are losses dissipated in the device during the turn-off interval during this time interval. The time for devices to turn on and for the reverse recovery charge to be removed depends on the applied voltage, the current being switched, the diameter of the device, its gate structure, and a number of other device parameters. Therefore, the device and the specific application duties have to be known before an estimate of the turn on and turn off losses can be made. For large devices, these losses can be several joules per pulse.3 However, once the devices have been selected, the losses can be estimated as follows (IEEE standard 1031 2011): PTsoff ¼ 3  2  Qrr  √2  U 1  sin ðαÞ  f n

(13)

where: PTsoff are the turn-off losses for the TCR thyristor valve. Qrr is the thyristor recovery charge. n is the number of series-connected thyristors per phase of the valve. 3

See, for example, data sheet for a device 5STP 42 U6500. https://library.e.abb.com/public/ c92a9062c3392b1f83257c63004dbb1d/5STP%2042U6500_5SYA1043-07%20Mar%2014.pdf, accessed November 11, 2018.

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199

fn is the system fundamental frequency. α is the thyristor firing angle. U1 is the total fundamental valve voltage across the valve. A standard turn-on loss is assumed to be 0.2 Joule per pulse (IEEE standard 1031 2011). According to this, the turn-on losses are given by: PTswon ¼ 3  2  n  0:2  f n

(14)

10.2.5 Voltage Divider Losses Thyristors devices in the off-state (nonconducting) have a finite resistance. That is, if a voltage is applied across the device, when it is turned off, a small amount of current will flow through the device. The resistance of the thyristors in the off-state is temperature dependent and also varies from device to device. Thus, if a string of devices are connected in series, a leakage current will flow through the string but the voltage across each individual device will not be identical. Therefore, a resistor might be connected across each of the devices in the string forming a voltage divider to equalize the voltage division among the devices. This voltage divider will dissipate some power and should therefore be included in the overall loss estimate. The losses are present during the intervals when the devices are in the off-state. The voltage across the thyristors is:

U 1a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s  2 π sin 2α ¼ U1  α  π 2 2

(15)

where: U1 is the applied voltage. U1α is the RMS value of the thyristor blocking voltage. α is the thyristor firing angle in radians. The power dissipated in the voltage divider is then: Pvd ¼

3  U 21α n  Rvd

(16)

Where. Pvd is the voltage divider loss. n is the number of series-connected thyristor levels. Rvd is the voltage divider resistance per thyristor level.

10.2.6 Miscellaneous Other Loss Components Thyristor valves include fans and pumps for valve cooling. These auxiliary systems require power for their operation. The power demand of these systems should be categorized as either no-load or load losses, depending on the number of fans required to run at no load and at different load points.

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10.2.7 TCR Reactor Losses TCR reactor is one of the other major sources of power losses in an SVC. As the SVC secondary voltage is typically between 10 and 25 kV, the magnitude of the TCR current may be kilo amperes. The size and modularity of the TCR components of the SVC are determined through system studies and availability considerations. The resistance of the TCR modules can be estimated based on the quality factor of the manufactured reactors. This is defined as the ratio of reactance and resistance. That is the theoretical quality factor defined by QF = X/R. The resistance value that appears on the denominator of the quality factor formula defines the DC resistance of a specific reactor at a specific frequency. According to Mohan et al. (1995), the AC resistance is a combination of a constant DC resistance and a frequency related skin effect and eddy current resistance, given by RAC ¼ F R  RDC ¼

  REC 1þ  RDC RDC

(17)

where: RAC is the AC resistance. FR is the resistance factor. RDC is the DC resistance. REC is the skin effect and eddy current resistance. As established in this chapter, TCR current is AC, periodic, and nonsinusoidal for firing angle values different from 90
. According to Cigré, the TCR harmonic currents are given by Cigré TB 25 (1968) in per unit of the TCR current for 90 degrees firing angle: I h ðpuÞ ¼

4
 ½ cos α sin ðhαÞ  h sin α cos ðhαÞ πh h2  1

(18)

where: Ih is the harmonic current of hth order (h = 3, 5, 7, etc.). h is the harmonic order. α is the TCR firing angle. The TCR characteristic harmonics are those with h equal to 6n  1, n = 1, 2, 3. . . (Hingorani and Gyugyi 2000). The triplen harmonics (h = 3, 9, 15, 21, etc.) must also be considered in the loss calculations. Out of these, the third harmonic is probably the most significant. Fundamental and harmonic current values are taken into account in TCR reactor loss calculation. Total TCR reactor losses are given by: PTCreactor ¼ 3 

Xh¼49 I 2  X h  F Rh h h¼1 QF h

(19)

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where: PTC-reactor are the total losses for a three phase TCR reactor under rated conditions. Ih is the harmonic current of hth order. Xh is the TCR reactor inductive reactance of hth order. h is the harmonic order. QFh is the quality factor of hth order. FRh is the resistance factor.

10.3

SVC Thyristor Switched Capacitor Losses

TSC does not generate harmonic currents in steady state since its thyristor valves are either in fully conducting mode or in fully blocking mode if it is switched in with the capacitor voltage at its right level. The transients arising from switching of the TSC module occur infrequently, and therefore, these switching transients can be ignored when evaluating the TSC losses. This makes the loss calculation simple when compared to TCR losses.

10.3.1 TSC Thyristor Valve Losses When the TSC is in nonconducting mode, there will be losses dissipated in the snubber circuits and in voltage divider circuits as described in Sect. 7 with α equal to 180 degrees (π radians). When one TSC is switched in, the closed loop control changes TCR firing angle in a way that the total SVC reactive power changes slightly as described on Sect. 7 of this chapter. After that, actual SVC capacitive reactive power rise is accomplished by TCR firing angle increasing and decreasing its inductive reactive power. Thus TSC conduction losses are given by: Pcthyristor ¼ U TH  I TAV þ rT  I 2TRMS

(20)

where: UTH is the threshold thyristor voltage. rT is the thyristor conduction resistance. ITAV is the average thyristor current. The RMS TSC thyristor valve current is given by: I TRMS

pffiffiffi 2 U2  ¼ 2 Z TSC

where: U is the single phase RMS voltage applied to TSC. ZTSC is TSC impedance per phase.

(21)

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The average TSC thyristor valve current is given by: I TAV

pffiffiffi 2 U2  ¼ π Z TSC

(22)

where: U is the single phase RMS voltage applied to TSC. ZTSC is TSC impedance per phase. Other losses present in the TSC valve are small and can be neglected (IEEE Standard 1031 2011).

10.3.2 TSC Capacitor Losses In an ideal dielectric capacitor, the current should lead the applied voltage by 90 degrees. In the real world, every capacitor has impurity of dielectric materials. This causes a phenomenon where the capacitor current leads the applied voltage by less than 90 degrees as shown in Fig. 22. The dissipation factor or tan δ quantifies the ratio of equivalent series resistance to capacitive reactance and is given by: DF ¼ tan δ ¼

Rs ¼ 2πfCRS Xc

where: Xc is the capacitive reactance. RS is the equivalent series resistance.

Ideal current

d

Real current

Voltage Fig. 22 Current  voltage phase relationship of a dielectric capacitor

(23)

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203

f is the system frequency. C is the capacitor capacitance. Capacitor losses are proportional to the square of capacitor current and to the equivalent parallel resistance that can be solved by using Eq. 24. Thus total TSC capacitor losses are given by, where I is the RMS capacitor current: PC ¼ I 2 Rs ¼

I 2RMS  DF ¼ Q  DF 2πfC

(24)

where: IRMS is the capacitor current with due consideration of possible harmonic currents injected from the TCR.

10.3.3 TSC Damping Reactor Losses TSC damping reactor losses should be calculated using the same method as used for the TCR reactor losses. Harmonic frequency losses should be considered if the TCR injects harmonic current into the reactor otherwise only fundamental frequency losses are to be considered.

10.4

SVC Harmonic Filter Losses

The power loss calculation process for SVC harmonic filters is developed in a different way for each filter type (high pass, double tuned, single tuned, for instance). The main concern is the current division between the parallel connected elements, for example, in double-tuned filters. Every filter includes capacitors that are divided in two equal sized parts. This division is made for protection reasons. A current transformer is assembled between the capacitances which detects the fault current in case of a damaged capacitor. However, it does not affect the losses calculation since the equivalent capacitance of two parallel connected capacitors is the sum of the individual capacitances. Resistance of a single tuned filter is due to reactor and capacitor resistances. Actual resistors may also be used in the filter to provide broader harmonic filtering. Reactor resistances are calculated by multiplying its quality factor by the fundamental frequency inductive reactance. Equivalent series capacitor reactance is calculated by multiplying dissipation factor by capacitive reactance. The filter impedance varies as a function of frequency because of the frequency related reactances and apparent or actual resistances. Filter impedances must be calculated differently for each harmonic order. The real part of the filter impedance represents the filter resistance which causes filter losses. Fundamental filter current can be calculated by dividing SVC secondary voltage by the filter impedance. Filter losses can be calculated by multiplying filter resistances by the square of the RMS filter currents. These losses vary with the operating point of the SVC since the harmonic spectrum is different for each operating point.

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Control, Protection and Auxiliary Equipment Losses

According to IEEE (IEEE Standard 1031 2011), control and protection systems contribute only to a slight share of total SVC losses. SVC characteristic variation has only little impact on the control and protection system loss, so it is possible to use one fixed power loss for the SVC control and protection system. The power loss of the protection and control systems can be measured at site and can be assumed to be constant for the whole operating range. A typical power loss for the protection and control equipment is about 3.5 kW. The power loss for the control and protection system will be a no-load loss. Fans and pumps for the thyristor valve cooling system as well as heating and/or air conditioning systems of control and protection control rooms are the most intensive auxiliary power consumers. Heating and air conditioning power values are determined separately for each individual SVC. The thyristor valve cooling power is likely to be dependent on the SVC reactive output power.

References Aho, J., Thomson, N., Kähkönen, A., Kaasalainen, K.: Main reactor concept – a cost and performance efficient SVC configuration. The 16th European Conference on Power Electronics Application – EPE’14 ECCE Europe Procedures, Lappeenranta, 26–28 Aug 2014 Aho, J., Kuusinen, S., Nissinen, T., Kahkonen, A., Spinella, M., Campos, R., Lima, M., Salvador, H.: Blocking Reactor as Part of SVC System – A Novel Concept for Harmonics Reduction and Lowered Operational Losses, Cigré Paper B4–202, 46a. Cigré Session, Paris, 19–27 Aug 2016 Belanger, J., Scott, G., Anderson, T., Torseng, S.: Gain Supervision for Thyristor Controlled Shunt Compensators, CIGRÉ, Paper No. 38-01, Sept 1984 Cao, J.Z., Donogue, M., Horwill, C., Singh, A.: TCR and thyristor valves for Rowville SVC replacement project. In: 2010 International Conference on Power System Technology (POWERCON 2010), Hangzhow, Oct 2010 Cigré TB 25: Working Group 38–01, Task Force No. 2 on SVC, “Static Var Compensator”, p. 125, 1968 CIGRE TB 529: Guidelines for Conducting Design Reviews for Power Transformers, Apr 2013 CIGRE TB 659: Transformer Thermal Modelling, June 2016 CIGRÉ Technical Brochure 25, Static var compensators, 1986 Cigré TB 78: Task Force 01.02 “Valves for SVC” of Study Committee 14 “Voltage and Current Stresses on Thyristor Valves for Static VAR Compensators”, Oct 1993 Clarke, E.: Circuit Analysis of AC Power Systems, vol. I. Wiley, New York (1943) DNP Users Group.: https://www.dnp.org/AboutUs/DNP3%20Primer%20Rev%20A.pdf. Accessed 2 Nov 2018 Fitzgerald, A., Kingsley, C., Umans, S.: Electric Machinery, Sixty Edition. McGraw-Hill Higher Education, New York. ISBN 0-07-366009-4 – 0-07-112193-5 (2003) Grainger, W., Waite, G., Bolden, R., Gawler, R., Stewart, J., Craven, R.: Analytical Techniques for the Application of Static Var Compensators to Improve the Capability of Long Distance Transmission Systems to Remote Areas of Australia, 1986 Cigré Session, Paper 38–04 Gutman, R., Keane, J.J., Rahman, M.E., Veraas, O.: Application and operation of a static var system on a power system – American electric power experience, Part I: system studies. IEEE PES, Summer meeting, paper No. 84 SM 634-2, 1984 also IEEE, PAS, vol. PAS-104, No. 7, pp. 1868–1874, June 1985 Heathcote, M.J.: The J&P Transformer Book, 13th edn, pp. 812–821. Elsevier, Oxford (2007)

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Hingorani, N., Gyugyi, L.: Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems. IEEE Press, New York. ISBN 0-7803-3455-8 (2000) IEC 60076-57-129 Power transformers–Part 57-129: Transformers for HVDC applications (2017) IEC 61954:2011: Static var compensators (SVC) – testing of thyristor valves, Standard No 61954. International Electrotechnical Commission (IEC), Geneva (2011) IEEE Standard 1158–1991, Power Losses in HVDC Converter Stations IEEE Standard 1031–2011: IEEE Guide for the Functional Specification of Transmission Static Var Compensators, Standard No 1031. IEEE Standards Organisation (2011) IEEE Standard C57.110: Recommended Practice for Establishing Transformer Capability when Supplying Nonsinusoidal Load Currents (1998) IEEE Standard C57.18.10: Practices and Requirements for Semiconductor Power Rectifier Transformers (1998) IEEE C57.12.00-2015, IEEE Standard For General Requirements For Liquid-Immersed Distribution, Power, And Regulating Transformers (2015) IEEE C57.12, 90-2015, IEEE Standard Test Code For Liquid-Immersed Distribution, Power, And Regulating Transformers (2015) Katoh, S., Yamazumi, S., Watanabe, A., Amemiya, K.: Overvoltage self-protection structure of a light-triggered thyristor. IEEE Trans. Electron Devices. 48(4), 789–793 (2001) Krishnayya, P.C.S.: Important Characteristics of Thyristors of Valves of HVDC Transmission and Static Var Compensators, 1984 Cigé Session, Paper 14–10 Lajoie, E.G., Scott, G., Breault, S., Larsen, E.V., Baker, D.H., Imece, A.F.: Hydro-Quebec multiple SVC application control stability study. IEEE Trans. Power Deliv. 5(3), 1533–1550 (1990) Lawatsch, H.M., Vitins, J.: Protection of thyristors against overvoltage with breakover diodes. IEEE Trans. Ind. Appl. 24(3), 444–448 (1988) Lima, M.: A Thirty Years Technological Evolution Panel of Static VAr Compensation Application in a Brazilian Transmission Utility, Cigré Paper B4–12, HVDC and Power Electronics to Boost Network Performance Colloquium, Study Committee B4, Brasilia, 2–3 Oct 2013 Lima, M., Eliasson, P.E., Brisby, C.: Considerations regarding electrically close static var compensators with adaptive controllers joint operation and performance. In: XIII Symposium of Specialists in Electric Operational and Expansion Planning (SEPOPE), Foz do Iguaçu, 18–21 May 2014, SP077 Lima, M., Patricia Feingold, P., John Schwartzenberg, J.: Dynamic Performance Evaluation of Static VAr Compensators with Adaptive Control and Operating Electrically Close in Real Time Digital Simulator, Cigré Paper B4–117, Cigré Winnipeg 2017 Colloquium, Study Committees A3, B4 and D1, Winnipeg, 30 Sept–6 Oct 2017 Lindström, C.O., Walve, K., Waglund, G.: The 200 Mvar Static Compensator in Hagby, 1984 Gigré Session, Paper 38-02 Miller, T.J.E.: Reactive Power Control in Electric Systems. Wiley, New York. ISBN 0-471-86933-3 (1982) Mohan, N., Undeland, T., Robbins, W.: Power Electronics: Converters, Applications and Design, 2nd edn. Wiley, New York. ISBN 0-471-58408-8 (1995) Padyar, K.R.: FACTS Controllers in Power Transmission and Distribution. New Age International Publishers, New Delhi. ISBN 978-81-224-2541-3 (2007) Park, R.H.: Two reaction theory of synchronous machines. AIEE Trans. 48, 716–730 (1929) Pilz, G., Langner, D., Battermann, M., Schmitt, H.: Line – or Self Commutated Static VAr Compensators (SVc) – Comparison and Application with Respect to Changed System Conditions, Cigré Paper B4–03, HVDC and Power Electronics to Boost Network Performance Colloquium, Study Committee B4, Brasilia, 2–3 Oct 2013 Ruff, M., Schulze, H.J., Kellner, U.: Progress in the development of an 8-kV light-triggered thyristor with integrated protection functions. IEEE Electronic Devices (ED). 46(8), 1768–1774 (1999) Schultz, H.J., Ruff, M., Baur, B.: Light triggered 8 kV thyristor with a new integrated breakover diode. In: Proceedings from ISPSD, pp. 197–200 (1996) Temple, V.A.K.: Controlled turn-on thyristor. IEEE Trans. Electron Devices. ED-30, 816–824 (1983)

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M. Lima and S. L. Nilsson Manfredo Lima was born in Recife, Brazil in 1957, received the BsC degree in Electrical Engineering from Pernambuco Federal University (UFPE) in 1979, the MsC degree in Electrical Engineering from the same University in 1997 and the PhD degree in Mechanical Engineering with emphasis on automation systems from Paraíba Federal University (UFPB) in 2005. He joined Chesf in 1978, where develops activities in the areas of power electronics, FACTS devices, power quality, control systems, electromagnetic transients and HVDC transmission. In 1992 he joined Pernambuco University (UPE) where develops research activities. Nowadays he is Chesf representative on Cigré Brazil SC B4 (HVDC and Power Electronics) and is a founding member of the Brazilian Electric Power Quality Society (SBQEE).

Stig L. Nilsson started out working for the Swedish State Telephone Board with carrier communication systems. Following this, he worked for ASEA (now ABB) with HVDC systems and for Boeing with computer system developments. During his 20 years with EPRI in USA he initiated in 1979 the development of digital protective relaying system developments and in 1986 EPRI’s FACTS initiative. In 1991 he was awarded a patent on Apparatus for Controlling the Reactive Impedance of a Transmission Line. Stig Nilsson is a Life Fellow of IEEE. He has chaired the IEEE PES T&D Committee, the IEEE Herman Halperin Electric Transmission and Distribution Award Committee, the IEEE PES Nari Hingorani Facts and Custom Power Awards Committee, several IEEE Fellow nomination review committees, been a member of the IEEE Standards Board, IEEE PES subcommittees and working groups. Stig Nilsson has been the US Representative and Secretary of CIGRE Study Committee B4 on HVDC and Power Electronics. He is the recipient of the 2012 IEEE PES Nari Hingorani Facts and Custom Power Awards. He received the CIGRE U.S. National Committee Philip Sporn Award and the CIGRE Technical Committee Award in 2012. He has also received the CIGRE Distinguished Member Award for active participation in CIGRE Study Committees and the USNC of CIGRE (2006); and the CIGRE USNC Attwood Associate Award in 2003. Stig Nilsson is a registered Professional Engineer in the state of California, USA.

7

Technical Description of Static Compensators (STATCOM) Colin Davidson and Marcio M. de Oliveira

Contents 1 STATCOM Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 V-I Characteristics of a STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Voltage-Sourced Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Limitations and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Multi-pulse Circuits with Magnetic Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Modular Multilevel Converter (MMC)-Based STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Chain Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Half-Bridge MMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Other Primary Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 STATCOM Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 STATCOM Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 DC Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 AC Harmonic Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 High-Precision Current Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Layout Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Control Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Space Vector Control Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Application Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Converter Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Special Control Considerations for Electric Arc Furnace Applications . . . . . . . . . . . . . 7 Losses and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Hybrid STATCOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

208 208 211 212 214 216 217 221 221 223 224 225 226 227 228 229 229 232 232 233 237 240 243 245 248 249

C. Davidson (*) GE Grid Solutions – Grid Integration, Stafford, UK e-mail: [email protected] M. M. de Oliveira ABB FACTS, Västerås, Sweden e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_8

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Abstract

The static synchronous compensator (STATCOM) is a shunt-connected reactive power compensation device using a self-commutated converter, usually a voltage-sourced converter (VSC). Its name arose from its conceptual similarity to a traditional (rotating) synchronous compensator or condenser. A STATCOM can perform a similar function to an SVC but has better speed of response and better reactive power support capability during AC system voltage dips and is more compact. This chapter describes the main technological aspects of a STATCOM, including the topologies suitable for the converter and architecture of the controls. Two main converter topologies are considered – the type using magnetic combination of multiple six-pulse converter bridges (with thyristors or GTOs) and the modular multilevel converter type of STATCOM which is now becoming common. Descriptions of the other main items of primary equipment, along with layout and performance aspects, are also given.

1

STATCOM Fundamentals

1.1

Introduction

This chapter provides a brief overview of the technology of the static synchronous compensator (STATCOM). The performance characteristics which distinguish STATCOM from other shunt-connected reactive power compensation devices such as SVCs and rotating synchronous compensators are briefly discussed. Typical STATCOM applications are discussed later in the ▶ Chap. 13, “Application Examples of STATCOM” of this book. The static synchronous compensator (STATCOM), previously referred to as the static condenser (STATCON) or advanced static var compensator (ASVC) or selfcommutated static var compensator, is a shunt-connected reactive power compensation equipment which is capable of generating and/or absorbing reactive power whose output can be varied so as to maintain control of specific parameters of the electric power system to which it is connected (CIGRÉ TB144). The basic characteristic behavior of the STATCOM is equivalent to a voltage source whose magnitude can be controlled in a rapid manner, behind a reactance. This is inherently different from the characteristics of an SVC whose behavior is equivalent to a voltage-controlled shunt susceptance dependent upon the system voltage at the connection point. The SVC is described in detail in ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC)” of this book. The term “static” is used to indicate that it is based on solid-state power electronic switching devices with no moving or rotating components. The terms “synchronous” and “compensator” indicate that it is analogous to an ideal synchronous machine generating a balanced set of three sinusoidal phase voltages at fundamental frequency. Thus, the STATCOM typically consists of a voltagesourced power electronic converter (VSC) employing solid-state power electronic

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AC POWER SYSTEM

V CONVERTER SIGNALS

I

POWER SYSTEM SIGNALS

COUPLING TRANSFORMER

E SOLID STATE DC-AC CONVERTER

SWITCHING CONTROL SIGNALS

CONVERTER AND POWER SYSTEM CONTROLS

vdc

DC CAPACITOR

Fig. 1 Typical STATCOM overview

switching devices and a set of converter controls varying the STATCOM output voltage as shown in Fig. 1. The STATCOM provides operating characteristics similar to a rotating synchronous compensator (condenser) as illustrated on Fig. 2, but without the mechanical inertia since it has no rotating components. Furthermore, the power electronic character of the equipment provides rapid controllability of the three-phase voltages, both in magnitude and phase angle, in relation to the power system voltage at the point of connection. Whereas the output current of the STATCOM is substantially independent of the power system voltage and the equivalent impedance at the point of connection, the SVC output current is highly dependent upon the voltage and the equivalent impedance at the same point. This means that the SVC voltage regulator controlling the output needs to be designed to provide stable regulation under a wide range of power system equivalent impedance conditions representing system contingencies. This can only be achieved by reducing the response rate of the SVC. The independence of STATCOM output from equivalent system impedance means that the voltage regulator controlling the STATCOM output can be designed for a faster response rate than the SVC while providing stable regulation over the range of system contingencies.

210 Fig. 2 Reactive power generation by rotating synchronous compensator

C. Davidson and M. M. de Oliveira

V

System Busbar

Coupling Transformer

I Machine Transformer Synchronous + Leakage Reactance Reactance

X E

Exciter

The ability to deliver rated current over the full voltage range is the essential feature which makes the STATCOM resemble a rotating synchronous compensator in terms of performance. The rotating synchronous compensator will transiently deliver reactive current approximately in proportion to the change in voltage. Although the machine excitation system can rapidly respond to a change in power system voltage, the delivery of the reactive power output is relatively slow, when compared with SVC and STATCOM. However, due to the excitation voltage that can be applied and the energy stored in the rotor winding, the rotating synchronous compensator is capable of delivering higher short-term transient output compared with an SVC or STATCOM. The primary benefits of the STATCOM are the rapid response and strong output at reduced AC voltage which are paramount in terms of reducing the impact of a power system disturbance. In power system applications where reactive power can be varied slowly, STATCOMs are not intended to replace conventional solutions such as mechanically switched capacitors (MSCs) or reactors (MSRs). However, in applications where rapid controllable action, robust output, and utilization of short-term overload capability of the network are required, the STATCOM presents a unique solution which can be utilized either on its own or in combination with other equipment including conventional SVCs and rotating synchronous compensators. Typical applications of STATCOM are the same as those of the SVC, namely, to achieve: • • • •

Effective voltage regulation and control Reduction of temporary overvoltages Improvement of steady-state power transfer capacity Improvement of transient stability margin

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Technical Description of Static Compensators (STATCOM)

• • • • • • •

Damping of power system oscillations Damping of subsynchronous power system oscillations Balanced loading of individual phases Reactive power compensation of AC-DC converters and HVDC links Power quality improvement Reduction in rapid voltage fluctuations (flicker control) Distribution system applications

211

Throughout this chapter the STATCOM is treated like a load, with positive reactive power output (Q>0) indicating that the STATCOM is behaving like an inductor and negative reactive power output (Q10ms >10ms

Operating mode determination Coordination with other devices on network

~1ms-1s ~1ms-1s

Application Control

Over-riding control and measurements

Converter Control

Part of overall grid control

Control dedicated to STATCOM

~10μs-1ms ~10μs-1ms

PLL Synchronisation αβ-dq transformation id and iq current control

Switching/hardware Control

0: STATCOM absorbs reactive power from the power system • q(t) < 0: STATCOM generates reactive power to the power system Thus, pðtÞ þ j  qðtÞ ¼ V  ðIP  j  IQ Þ ¼ V  I where the * operator denotes the complex conjugate. Corresponding current and voltage vectors for STATCOM operating in capacitive and inductive modes are shown below in Fig. 22. In practice, three-phase voltages and current measurements are filtered prior to passing them to the control system. A phase-locked loop is employed in the control system in order to obtain the phase angle and frequency of the fundamental portion of the voltage space vector at the point of connection of STATCOM to the power system. A fast and stable PLL response is of utmost importance at large disturbances so that active power through the converter is transiently minimized thus avoiding large variations of the DC capacitor voltages. The values of IP and IQ can be derived directly from the terminal voltage space vector v and the current space vector i without coordinate transformation: I ¼ ðv  iÞ=V Q-axis

I

P-axis

V

Capacitive Operation (arg(E) = ξ)

jX.I E Q-axis

P-axis

V Inductive Operation (arg(E) = ξ)

E

jX.I

I Fig. 22 Vector diagram allowing for losses in the STATCOM converter

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Technical Description of Static Compensators (STATCOM)

6.3

237

Application Control

This section describes the part of the STATCOM control system which is specific to the requirements of the power transmission system and defines the purpose of the STATCOM in enhancing power system performance. Many of the application control features that need to be incorporated are well-known from conventional SVCs, but new possibilities such as active power exchange during system oscillations can be provided as long as they are coordinated with the DC voltage variations that the converter needs to be designed for. The main application control functions attainable through reactive power control of a STATCOM include: • • • •

Power system voltage control Power oscillation damping control System power factor control Reactive power control The “application control” also includes:

• Measurement functions which measure the actual power system quantities and provides appropriate signals to various control modules • Control parameter adjustment functions which provide for changes in control parameters under varying power system conditions • A start-up/shut-down function which provides control at the start-up and shutdown phases

6.3.1 Power System Voltage Control In STATCOM installations for transmission network applications, the most important control mode, similarly to the case of a transmission SVC, is usually power system voltage control. The voltage controller regulates the magnitude of the three-phase AC system voltages to minimize voltage swings, improve voltage stability, and assist voltage recovery after system faults, especially in the events of fault-induced delayed voltage recovery (FIDVR) (WECC 2012). The typical V-I and V-Q characteristics for such a control mode are illustrated on Figs. 3 and 4. The input to the voltage controller, which is usually a proportional plus integral (PI) type regulator, is an error signal (ΔV) calculated from the voltage reference VREF, the actual value V, and the STATCOM slope characteristic expressed as a voltage VSL as shown in Fig. 23. ΔV ¼ VREF  V  VSL The actual voltage value is derived from the measurement module. The slope voltage value VSL is proportional to the actual or demanded STATCOM current

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V ICmax limit

VREF +

_

DV

PI REGULATOR

QREF or IQ,REF

_ VSL -ILmax limit

SLOPE XSL

I, IQ,REF ,Q or QREF

Fig. 23 Power system voltage control

(IQ or IQ,REF) or to the reactive power output Q or QREF, which thus provides the required steady-state control characteristic. VSL ¼ XSL  I=Irated or XSL  Q=Qrated The value XSL is an operator-adjusted control parameter and defines the slope (droop) of the voltage control characteristic, i.e., the total p.u. voltage deviation per 1 p.u. generated/absorbed reactive power. The PI regulator output signal QREF represents the required STATCOM reactive power to correct the voltage error signal ΔV. The regulator gain and integrator time constant are normally adjusted to obtain stable operation with a fast response time at the highest possible equivalent system impedance (lowest system fault level). The regulator parameters can be calculated online to ensure a constant dynamic behavior independent of various system conditions.

6.3.2 Power Oscillation Damping Control This control, used on some transmission STATCOMs, is used for damping of power oscillations and for increasing the transmission capability of the power system. Power oscillations occur as an interaction between power generators, groups of generators or different areas of a synchronous AC system, typically with oscillation frequencies of 0.1–5 Hz, and may cause stability problems limiting the transmission capability of the power system. Grund et al. (1990) describes a study to design a similar damping controller for an HVDC link in the USA in order to damp an interarea oscillatory mode at 0.8 Hz, although it should be noted that HVDC links are more powerful than STATCOMs for damping such oscillatory modes because they can act on real power transmission. The power oscillation damping controller detects the occurrence of oscillations, enables the control circuit, and generates the modulation signal VPOD, which is added to

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239

the voltage reference value VREF and determines the STATCOM reactive power output. After sufficient damping of the power oscillations is achieved, the modulation signal returns to zero leaving the STATCOM output to be determined by the power system voltage control (Tiyono et al. 2017). This principle is similarly utilized in SVCs. If the particular STATCOM application includes appropriate energy storage capacity, more powerful oscillation damping can be achieved through the modulation of the active power (current) output, based on similar principles and control circuitry.

6.3.3 Reactive Power Reserve Control The reactive power reserve controller may be installed to achieve regulation of the reactive power output of the STATCOM slowly over a set time period to restore the var reserve. The measured reactive power output of the STATCOM is compared with the reference value QREG, and the error signal ΔQ is passed to an integral control circuit whose output shifts the voltage reference set point VREF by adding the signal ΔVQ: k ΔV Q ¼ ðQREG  QÞ s The var reference set point QREG is usually selected to maintain the steady-state operating point in the middle of the available STATCOM control range (i.e., at zero reactive power output) to ensure availability of sufficient dynamic reactive power compensation. This means that at all times the full range of STATCOM output is available to dynamically respond to any system contingency causing a voltage change. In this mode of operation, the system voltage can be controlled within a voltage range defined by the adjustable values Vmax and Vmin. If the voltage limits are exceeded, then limits are applied to the reactive power controller output to keep the actual system voltage within the defined range. This principle can be similarly utilized in SVCs.

6.3.4 Power Factor Control Power factor control is not usually applied to STATCOMs installed in HV transmission systems. However, this mode of control is more often utilized in STATCOM applications on distribution systems in the medium- and low-voltage range. The power factor controller regulates the power factor (cosφ) of the system at the point of connection of the STATCOM, with a slower response. Active and reactive power of the connected load (PL, QL) at the point of connection to the system are calculated from voltage and current measurements, and the required STATCOM output to achieve constant power factor at that point compensation is determined by: QREF ¼ PL tan φREF  QL where φREF is the required power factor angle. This principle can be similarly utilized in SVCs.

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6.3.5 Negative Phase Sequence Control Negative sequence components in the AC voltage at the point of STATCOM connection can result from unbalanced loads and unsymmetrical network impedances within the power system. They will also appear during power system fault conditions. The STATCOM can be controlled such that it reduces the negative sequence component in the AC voltages passively, actively, or such that the STATCOM draws only positive sequence currents from the power system. The priority between negative- and positive-sequence voltage control needs to be predefined for larger unsymmetrical disturbances when operation at full converter current is expected.

6.4

Converter Control

The converter control shown in Fig. 24 utilizes the reference values of reactive power (QREF) or reactive current (IREF), provided by the application control and the measured converter phase currents (I), system voltage (V), and DC capacitor voltage (vdc) to synthesize the required three-phase converter output voltage (E).

E

Network

Solid-state DC-AC Converter

+ vdc

switching signals (to gate units) measured quantities:

I V

vdc QREF or IREF

Fig. 24 Converter control for a two-level converter

Converter Control

Gate Gating Pulse Control Generator Signals

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241

6.4.1 Voltage Space Vector Control Adopting space vector notation, the output voltage space vector e of E may be expressed as: e ¼ M  vdc  e j  ψ ;

ω ¼ dψ=dt

where ω and ψ are the angular frequency and phase angle of the converter output voltage and M is the modulation index, defined as the ratio between the converter output voltage modulus E and the DC capacitor voltage vdc. Converting from a stationary reference frame to a rotating reference frame, e becomes E = EP + j∙EQ. Generally, two main control principles have been utilized with voltage space vector control, namely: • Control of modulation depth and phase angle of the converter voltage space vector E • Control of only the phase angle of the converter voltage space vector E Control of modulation depth and phase angle of the converter voltage space vector E enables independent control of real and reactive power (P and Q) and requires a converter which can vary the magnitude of the fundamental output voltage independently of the DC capacitor voltage, up to the limit of the DC capacitor voltage. Most converter architectures available as at 2018 can achieve this. However, with some early types of converter utilizing two-level converter architectures with GTOs as the semiconductor devices being switched at fundamental frequency, it was difficult to achieve the necessary control of fundamental output voltage independently of the DC capacitor voltage. Hence, an option for controlling such converters was to control only the phase angle of the converter voltage space vector E. This involves indirect control of the DC capacitor voltage and the modulus of E and permits only the independent control of reactive power Q. Since this control mode is generally not required with modern converters, it is not described in detail here; however, CIGRÉ TB144 provides a full explanation. Figure 25 depicts the top-level control structure for space vector control providing both modulation depth and phase angle based control. Schauder and Mehta (1993) provides details of possible basic structures for this type of control. The current space vector I is formed from measurements of the terminal voltage V and current I. Regulation of IP forms the basis of active power exchange, while regulation of IQ forms the basis of reactive power exchange. Thus, regulation of IP enables the STATCOM DC capacitor voltage to be controlled to a set point independent of the reactive power output of the STATCOM. In addition, auxiliary control signals, EP,aux and EQ,aux, for capacitor voltage balancing (in the case of a multilevel converter) and DC current control are generally added to the output of the space vector control as shown in Fig. 25.

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Vdc

EP_aux, EQ_aux

Vdc

Id_ref Vdc regulator

Vdc_ref

I

Formation of current space vector (IP and IQ)

V

+ EP

+ +

Current Space Vector Regulator

-

Phase locked loop

+ + EQ +

Calculation of 3-phase converter voltage reference

To converter gate pattern ψ logic

M

θ

Fig. 25 Modulation depth and phase angle control

6.4.2 Supplementary Control Functions Depending on the specific requirements of the STATCOM installation, certain other control functions may be required at the converter control level. These functions are not required in SVCs. Robustness of these functions for different system strengths and disturbances is essential for the proper and expected behavior of the converter; otherwise, converter block and STATCOM trip may occur. • Control of System Side DC Current (Transformer Saturation Control): Owing to nonideal characteristics of the STATCOM components, a DC current on the output (AC system side) of the converter may exist. This may lead to saturation of the STATCOM magnetics resulting in a high STATCOM current distortion. The DC components in the converter currents therefore may have to be detected and controlled to an acceptable minimum level. This detection requires other transducers than a conventional CT. • Voltage Balancing Control: In the case of a multilevel converter, care must be taken that the individual voltages of the capacitors on each individual H-bridge as well as the total energies in all three phases are balanced. Otherwise capacitor overvoltage and current distortion may result. If the voltages differ beyond a certain limit, the switching is modified such that the capacitors with the higher voltages inject energy to the network and capacitors with the lower voltages receive energy at the same time and an equalization is thus affected. • DC Capacitor Voltage Limit Control: In controlling the converter, it is important that the DC capacitor voltage limit is not exceeded in order to avoid damage to converter components and the DC capacitor. This is achieved through control of the reference value of vdc in cases where both modulation depth and phase angle of space vector is controlled, and through application of limits to the capacitive output of STATCOM in cases where only the phase angle of the space vector is controlled.

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243

• Converter Current Limit Control: The current limit of a converter is based on instantaneous and root-sum-of-squares currents and voltages or through utilizing a thermal model taking into account the semiconductor currents and ambient temperature. The maximum current of a converter is determined by the converter control through applying limits to the reactive power or current requirement assigned to the converter. The current protection of the converter should also take into account the safe operating area (SOA) of the semiconductor device. • Control of a STATCOM with Energy Storage: In cases where energy storage equipment is connected to the DC capacitors, the control of a STATCOM will be dependent on the characteristics of this equipment and would require control of both modulation depth and phase angle in order to obtain independent control of active and reactive power.

6.5

Special Control Considerations for Electric Arc Furnace Applications

Certain types of high-power industrial load can result in large fluctuations of the real and reactive power drawn by the load, leading to power quality problems affecting consumers connected to the same grid. Electric arc furnaces can cause particular problems in this respect because of the rapid and unpredictable fluctuations of real and reactive load current, which, if not adequately mitigated, can lead to problems of “flicker” in lighting equipment. STATCOMs can be a very effective way of mitigating flicker problems from arc furnaces (Fig. 26); however, they need to be controlled Fig. 26 Example of connection of arc furnace plant with compensation for the power system

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Fig. 27 Simplified circuit for modelling arc furnace compensation strategies

in a slightly different way (compared with transmission STATCOMs) in order to achieve their best performance (CIGRÉ TB237). There is a fundamental difference between a STATCOM (or SVC) designed to compensate for grid voltage disturbances and one designed to compensate for fluctuating loads. For grid voltage control applications, the control inherently has to be reactive (i.e., a feedback control is used, waiting for conditions to change, then acting) because the controller cannot know in advance what the source of a disturbance might be. However, for compensating industrial loads, it is possible to measure directly the current drawn by the load and use this as a feed-forward signal into the controls, thus achieving a faster response to disturbances. This is an important consideration because of the different operating duty of an arc furnace STATCOM compared with a transmission STATCOM. The transmission STATCOM exchanges mainly fundamental reactive current in quasi-periodic time dependency whereas the STATCOM for flicker mitigation mainly injects non-periodic currents. Figure 27 shows a simplified circuit for investigation of arc furnace compensation control strategies. The system impedance is modelled by the resistance R and reactance X. The impedance of the arc furnace transformer is modelled by the reactance XT. In principle there are two basic control approaches for mitigating the voltage fluctuation at the PCC: One basic control approach is to compensate the reactive power of the arc furnace and to smooth the fluctuations in active power consumption. This requires energy storage capability (higher DC capacitance) in the compensator. As a consequence of applying this approach in full, the arc furnace and the compensator appear as a purely ohmic load, which changes its resistance only very slowly. However, in order to achieve this, the compensator must be able to instantaneously provide energy when the power consumption of the arc furnace changes. This means that the compensator in the short term tries to maintain constant P and Q and only refines its calculation slowly to adjust its output in order to accommodate power balance between the network and the arc furnace.

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The alternative control approach is to let the compensator inject only reactive power such that the voltage fluctuations at the PCC are eliminated. The voltage fluctuation at the PCC resulting from changing active power consumption of the furnace is cancelled by reactive current injection of the compensator. The advantage of such a control scheme is that the compensator does not require large energy storage equipment, which may result in smaller overall investment cost. However, reduction on the flicker level is limited. In general, the arc furnace current will cause both amplitude and phase fluctuations of the PCC voltage. Since the flicker meters have a very low sensitivity to phase fluctuations, it is sufficient for the compensator to cancel only the amplitude fluctuations. In Larsson (1998) it is shown that these amplitude fluctuations of the voltage at the PCC can be compensated by injecting a purely reactive current which corresponds to the second control approach. Here the voltage deviations due to active power fluctuation are taken care of by overcompensation of the reactive current. The flicker control block creates the current reference signals for controlling the flicker. These signals are then passed on to the current controller which results in the STATCOM injecting the appropriate current into the network (power system), thereby resulting in the mitigation of the flicker. The first step in this process is to determine the fluctuations of the currents around their average fundamental component. This is best achieved by converting the current into the direct and quadrature axis equivalents. The direct or “d” component of the current can be described as that component which causes the flow of real power into the STATCOM (at the point of common coupling), and the quadrature or “q” component is the component that causes the flow of reactive power. The d and q components can be, respectively, determined by resolving the phase currents into their projections along the positive sequence voltage phasor and on an axis perpendicular to it. If the current waveform is smooth, balanced, and harmonic-free, then the resulting d and q quantities are thus transformed into non-time varying DC quantities. In reality, however, the d and q components would not be smooth. Subtracting the DC component of d and q from their instantaneous values is thus a convenient mechanism for determining the variation of current around its average value. The current controller could be a vector controller similar to that used in a transmission STATCOM. However, since the primary requirement of a controller for an arc furnace STATCOM is the ability to respond quickly to sudden changes of real or reactive power load with a current reference signal that may not be sinusoidal, other control concepts are sometimes used as an alternative. Often these involve a trade-off between speed of response (which is more important with an arc furnace STATCOM) and the switching losses of the converter (which are generally less important than in a transmission STATCOM).

7

Losses and Efficiency

The efficiency of high-power converters used in applications such as STATCOMs is very good (of the order of 98–99% at full current), but nevertheless such converters incur power losses when running, and the lifetime energy cost of these power losses is not negligible.

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Fig. 28 Power losses versus reactive power for a STATCOM versus an SVC

STATCOMs intended for utility (power transmission) applications are often designed for an operating life of 20–25 years or even longer, and the power losses in the STATCOM equate to lost revenue for the utility in question. The net present value (NPV) of the power losses over the lifetime of the equipment, brought forward to the time of purchasing the STATCOM, can be comparable to the capital expenditure (CAPEX) cost of the STATCOM equipment. No load losses are often much more important than load losses if the STATCOM normally operates in the middle of its operating range. Hence, great care needs to be taken in the design of the STATCOM to arrive not only at a design with adequately low CAPEX cost but also a design with low power losses. However, the subject is complex, depending on many factors including energy costs, local regulations, and accounting practices. There is little published data available on actual values of power losses for real STATCOM installations, but it is possible to indicate some general trends. Figure 28 shows qualitatively how the power losses in a STATCOM vary over its operating range in comparison with those of a typical SVC consisting of a TCR, TSC, and fixed filter. The most important point to note about Fig. 28 is its shape. The characteristic of a STATCOM is inherently (nearly) symmetrical, with the lowest losses occurring at 0 Mvar. For applications where the STATCOM is intended to be used for the majority of its life at 0 Mvar, this gives the STATCOM an advantage. By comparison, a typical SVC may result in comparable or slightly higher losses near 0 Mvar, but then when the TSC is switched in (and needs to be “backed off” by the TCR), the losses abruptly jump upward. However, at full capacitive output, an SVC may have lower power losses than a STATCOM. Hence, when the primary purpose is to provide capacitive var support for slow voltage variations in the power system, an SVC consisting of multiple TSCs may be more cost-effective than a STATCOM (but mechanically switched capacitor banks will be more cost-effective still). Hybrid installations

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including both TSCs and STATCOMs (Knight et al. 1998) may be a way of combining the best of both types of technology, as discussed in the next section. There are three major elements making up the power losses of a STATCOM: the STATCOM transformer, the STATCOM reactors, and the power electronic converter. The power consumption of auxiliary equipment (e.g., the cooling plant) may also be important, especially when losses are evaluated at high temperature and many cooling fans are in operation. However, losses in the DC capacitors of the converter are generally quite small when modern, polypropylene film capacitors are used. Because the power losses are relatively low in relation to the var output in STATCOMs and SVCs, direct measurement of the power losses is difficult with any useful level of accuracy. It is therefore common to evaluate power losses by a combination of calculation and measurement, using routine test data obtained under factory conditions and applying correction factors to reflect how the power losses would differ under service conditions. For STATCOM applications, there are currently no international standards governing how the power losses should be determined. However, for HVDC there are several IEC standards providing useful guidance that could be partly transferrable to STATCOM applications. For the STATCOM transformer and reactors, power losses can be determined similarly to the process described in IEC 61803 for HVDC installations. The main respect in which STATCOM (or HVDC) transformers and reactors differ from conventional AC equipment is that the winding currents generally contain a higher harmonic content. This needs to be allowed for by determining the winding resistance as a function of frequency and then extracting the frequency spectrum of the winding current. For the STATCOM converter, the situation is more complex and depends to a great extent on the type of converter technology used. IEC 62751 covers the method for determining power losses in the converter valves of a VSC-based HVDC system and is thus useful in providing general guidance for a STATCOM, but cannot be applied directly without some modification. The power losses in a voltage-sourced converter can be generally subdivided into two main categories: conduction losses and switching losses. Conduction losses occur as a result of the voltage drop occurring in a component caused by current flowing through it. This could include Joule losses (I2R) in elements such as busbars, but conduction losses in a STATCOM come primarily from the conducting voltage drop of the power semiconductor devices – which is current dependent but typically of the order of 2–3 V at rated current. The instantaneous conduction loss is simply the voltage drop multiplied by the instantaneous current, and the average power loss over a cycle is obtained by integration. The second category, switching losses, represents energy lost as heat each time one of the semiconductor devices makes a transition from conducting to nonconducting or vice versa. Switching losses can include the energy lost in the snubber components which were necessary with GTO-type devices; however, with IGBTs it is less common to use snubbers and with such devices, the switching losses are mainly those of the device itself. In general, each time an IGBT turns on or off, it incurs an energy loss of Eon or Eoff, respectively, and each time a diode turns off, it incurs a “recovery loss” Erec

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(the turn-on losses of diodes can be neglected). As shown earlier in ▶ Chap. 5, “Power Electronic Topologies for FACTS” of this book, every time an IGBT turns on, a diode turns off somewhere else, and vice versa: so each transition from IGBT conduction to diode conduction incurs an energy loss of Eoff, and each transition from diode conduction to IGBT conduction incurs an energy loss of (Eon + Erec). The total switching losses, in watts, are evaluated by summing all the switching energies that occur over a defined time period (such as 1 s). In PWM-type converters with (silicon) IGBTs, the switching losses were generally dominant as of 2018 because of the relatively high PWM carrier frequency – typically 1–2 kHz; however, in MMC-type converters the mean switching frequencies can be much lower, in the 100–200 Hz range, and as a result conduction losses tend to dominate with such converters. Looking into the future, with silicon carbide devices, we can expect to see the switching losses even of PWM-type converters becoming small compared with conduction losses.

8

Hybrid STATCOM

A STATCOM has improved characteristics compared to a SVC, especially for handling undervoltages. This is simply because it is capable of injecting full reactive power current independently of the voltage magnitude. On the other hand, SVCs, in contrast to STATCOMs, have a reactive power output proportional to the square of the voltage magnitude. This means a reduced reactive power support when the voltage drops, i.e., SVCs give less support to the network when they are needed most in applications to prevent system voltage collapse and motor stalling conditions. Conventional SVCs are however superior at suppressing temporary overvoltages since its reactive power absorption capability is higher without any major impact on the design. The hybrid STATCOM, based on combining both SVC and STATCOM technologies, is a favorable approach for utility applications when there is usually a need to incorporate some offset elements (capacitive and/or inductive) to achieve a larger required operating range, usually unsymmetrical (Knight et al. 1998; Halonen and Bostrom 2015). Using a STATCOM to cover the whole dynamic swing range would lead to an overdesign on either capacitive or inductive Mvar output sides. An example of a hybrid STATCOM solutions is shown in Fig. 29. It consists of a VSC (STATCOM), a thyristor switched capacitor (TSC), and a thyristor switched reactor (TSR). The V/I characteristics comprise a mixture of both the SVC and the STATCOM characteristics, where the VSC is responsible for the vernier reactive power control. One of the characteristics may dominate the other, i.e., either the STATCOM characteristics or the thyristor switched offset element characteristics, but the choice merely depends on the performance and the operational requirements. The hybrid STATCOM solution can be regarded as an upgraded SVC where the TCR is replaced by a VSC.

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Technical Description of Static Compensators (STATCOM)

Vdc

249

Vdc

VSC

TSR

TSC VSC VSC + TSR

Vov VSC

VSC + TSC

G

V

D

Vmaxcont Vrefmax Vnom

A

B

Vrefmin

Vmin

C

I Capacitive

Inductive

Fig. 29 Example of hybrid STATCOM topology and its VI characteristic

References Aho, J., et al: Description and evaluation of 3-level VSC topology based statcom for fast compensation applications. In: 9th IET International Conference on AC and DC Power Transmission, London (2010) Ainsworth, et al: Static VAr Compensator (STATCOM) Based on Single-Phase Chain Circuit Converters. IEE Proceedings: Generation, Transmission, and Distribution, Institution of Electrical Engineers. 145(4), 381–386 (1998) Betz, R.E., Summerst, T., Furneyt, T.: Symmetry compensation using a H-Bridge multilevel STATCOM with zero sequence injection. In: Conference Record of 2006 IEEE IAS Annual Meeting

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CIGRÉ Technical Brochure 144: Static Synchronous Compensator (STATCOM) CIGRÉ Technical Brochure 237: Static Synchronous Compensator (STATCOM) for arc furnace and flicker compensation. Working Group B4.19, Dec 2003 Edwards, C.W., et al.: Advanced static var generator employing GTO thyristors. IEEE Trans. Power Delivery. 3(4), 1622–1627 (1988) Erinmez, I.A. (ed.): Static Var Compensators. Report prepared by Working Group 38-01, Task Force No. 2 on SVC, CIGRÉ 1986 Grund, C.E., Hauer, J.F., Crane, L.P., Carlson, D.L., Wright, S.E.: Square Butte HVDC modulation system field tests. IEEE Trans. Power Delivery. 5(1), 351–357 (1990) Gyugyi, L.: Reactive power generation and control by thyristor circuits. IEEE Trans. Ind. Appl. IA-15(5), 521–532 (1979) Gyugyi, L., et al.: Advanced Static Var Compensator Using Gate Turn-off Thyristors for Utility Applications. CIGRÉ paper 23-203, 1990 Halonen, M., Bostrom, A.: Hybrid STATCOM systems based on multilevel VSC and SVC technology. In: CIGRÉ SC, vol. B4. HVDC and Power Electronics International Colloquium, Agra (2015) Hirakawa, M., Mino, Y., Murakami, S.: Application of self-commutated inverters to substation reactive power control. CIGRÉ, pp. 23–205 (1996) Ichikawa, F., et al.: Development of self-commutated SVC for power system. In: IEEE Conference Record of the Power Conversion Conference, Yokohama, 1993, pp. 609–614 (1993) IEC 61071: Capacitors for power electronics IEC 61803: Determination of power losses in high-voltage direct current (HVDC) converter stations with line-commutated converters IEC 62001 (all parts): High-voltage direct current (HVDC) systems—guidance to the specification and design evaluation of AC filters IEC 62751: Power losses in voltage-sourced converter (VSC) valves for high-voltage direct current (HVDC) systems IEEE 1676-2010: Guide for control architecture for high power electronics (1MW and greater) used in electric power transmission and distribution systems Knight, R.C., Young, D.J., Trainer, D.R.: Relocatable GTO-based static Var compensator for NGC substations. CIGRÉ Session 1998, Paper 14-102 Larsen E., et al: Benefits of GTO-Based Compensation Systems for Electric Utility Applications. IEEE, PES Summer Power Meeting, Paper No., 91 SM 397-0 TWRD, 1991 Larsson, T.: Voltage Source Converters for Mitigation of Flicker Caused by Arc Furnaces. Dissertation at School of Electrical Engineering and Information Technology (KTH) at University of Stockholm, ISBN 91-7170-274-1 (1998) Lesnicar, A., Marquardt, R.: An innovative modular multilevel converter topology suitable for a wide power range. In: Power Tech Conference Proceedings, vol. 3, p.6 (2003) Mori, S., et al.: Development of large static var generator using self-commutated inverters for improving power system stability. In: PES Winter Power Meeting., Paper No. 92WM165-1. IEEE (1992) Nakajima, T.: A new control method preventing transformer magnetisation for voltage source selfcommutated converters. IEEE Trans. Power Delivery. 11(3), 1522–1528 (1996) Park, R.H.: Two-reaction theory of synchronous machines: Generalised method of analysis – Part 1. Presented at the winter convention of the A.I.E.E. (1929) Povh, D., Weinhold, M.: Efficient computer simulation of STATCON. In: International Conference on Power System Transients, Lisbon, pp. 397–402 (1995) Scarfone, A.W.: A
150MVAr STATCOM for Northeast Utilities’ Glenbrook Substation. IEEE PES 2003 General Meeting, Toronto, pp.15-17 (2003) Schauder, C.D., Gyugyi, L.: STATCOM for Arc Furnace Compensation. EPRI Workshop, 13—14 July 1995, Chicago Schauder, C.D., Mehta, H.: Vector analysis and control of advanced static var compensators. IEE Proc-C. 140(4), 299–306 (1993) Schauder, C.D., et al.: Development of a
100 MVAR static condenser for voltage control of transmission systems. IEEE Trans. Power Delivery. 10(3), 1486–1496 (1995)

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Schauder, C.D., et al.: TVA STATCON Project: Design, Installation and Commissioning. CIGRÉ paper, pp.14-106 (1996) Sumi, Y., et al.: New static var control using force-commutated inverters. IEEE Trans. Power Apparatus Syst. PAS-100(9), 4216–4224 (1981) Suzuki, K., et al.: Minimum harmonics of PWM control for a self-commutated SVC. In: IEEE Conference Record of the Power Conversion Conference, Yokohama, pp. 615–620 (1993) Tiyono, A., Hariyanto, N., Grondona, A., Zhang, H., Srivastava, K., Reza, M.: Implementation of power oscillation damping function in STATCOM controller. In: 4th International Conference on Electrical and Electronic Engineering (ICEEE), Turkey (2017) Western Electricity Coordinating Council (WECC): Modeling and Validation Work Group Composite Load Model for Dynamic Simulations. Report 1.0 (2012)

Colin Davidson is Consulting Engineer (HVDC) at GE Grid Solutions, HVDC Activity, whose Centre of Excellence is in Stafford, UK. He joined the company in January 1989, when it was part of GEC, and progressed through the positions of Trainee Thyristor Valve Design Engineer; Manager, Thyristor Valves; Engineering Director; and R&D Director to his current role. He is a Chartered Engineer and a Fellow of the Institution of Engineering and Technology and has served on several IEC standardization committees for HVDC and FACTS, winning the IEC 1906 award in 2012. He has a degree in natural sciences, specializing in physics, from the University of Cambridge.

Marcio M. de Oliveira was born in Rio de Janeiro, Brazil, in 1967 and received the M.Sc. degree in electrical engineering from Federal University of Rio de Janeiro, Brazil, in 1992. He obtained the Technical Licentiate and Ph.D. degrees in 1996 and 2000, respectively, in the field of High Power Electronics from The Royal Institute of Technology in Sweden. He joined ABB FACTS in 2000, where he has worked in several technical areas such as power system design, real-time simulator studies, control system design and implementation, and R&D projects. Marcio currently holds a System Lead Engineer position, primarily driving technical marketing and sales activities of FACTS technology worldwide. He participated on CIGRÉ SC B4 WG53 “Guidelines for procurement and testing of STATCOMs,” and he is member of IEC TC22, being convenor of IEC 61954 maintenance team, related to testing of SVC thyristor valves. He received the 1906 IEC award in 2017.

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Technical Description of Thyristor Controlled Series Capacitors (TCSC) Stig L. Nilsson and Marcio M de Oliveira

Contents 1 2 3 4 5 6

7

8 9

10 11

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TCSC Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating Range of TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power-Transmission Characteristic Controlled by TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . Cost Benefit of TCSC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TCSC Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 TCSC Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 TCSC Dynamic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 TCSC Modeling Considerations for Long-Term Planning Studies . . . . . . . . . . . . . . . . . 6.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TCSC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 TCSC Platform Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 TCSC Thyristor Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Valve Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Insulation Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TCSC Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 No-Load Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Load Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harmonic Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Torsional Interactions Between Turbo-Generators and TCSC Systems . . . . . . . . . . . . . . . . . . 11.1 Series Capacitor Bank Interactions with Turbo-Generators . . . . . . . . . . . . . . . . . . . . . . . 11.2 Subsynchronous Damping Performance of TCSC Compensated Lines . . . . . . . . . .

254 256 260 264 265 266 267 268 275 276 276 276 277 279 280 281 281 282 288 288 288 289

S. L. Nilsson (*) Electrical Engineering Practice, Exponent, Sedona, AZ, USA e-mail: [email protected]; [email protected] M. M. de Oliveira ABB FACTS, Västerås, Sweden e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_26

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12

Stability Improvement and Power Oscillation Damping with TCSC Systems . . . . . . . . . . . 12.1 Transient Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 System Damping Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Thyristor-controlled series compensation (TCSC) systems and thyristor switched series compensation (TSSC) systems are power electronic systems developed in the late 1980s and early 1990s in response to the anticipated need for better utilization of existing high voltage overhead transmission lines because of the difficulties in getting approval for building new lines. The actual experience has been that TCSC systems are primarily being applied in areas with high growth rates where there is a need for long, high voltage AC transmission lines. However, even in areas with existing high power lines imbedded in the AC power system, the load carrying capacity of the lines can be improved by using fixed or switched series capacitor compensation systems. The inherent risks associated with increased loading of existing lines is that if the power system were to be subjected to severe disturbances, there might be a widespread blackout. TCSC systems represent a tool to manage disturbances and to avoid blackouts by quickly rerouting the power flows from the high stressed lines to lines with the ability to carry higher loads and thereby avoiding blackouts. TCSC systems have been applied to enable construction of long AC lines, which would be unstable if the TCSC systems were not installed. That is, TCSC systems have been proven to be a powerful tool to enhance the stability of the AC systems and even to provide damping of subsynchronous oscillations where the use of fixed series capacitor (FSC) installation could have caused subsynchronous resonance endangering the reliability of large steam turbine generators. The design requirements for the TCSC FACTS controller are discussed in this chapter. The fundamental operating principles of TCSC systems, the key TCSC design aspects, standards, and other documents, which would be useful to have by those who procure, maintain, or operate a TCSC system are also discussed in this chapter.

1

Introduction

When active power flows through a transmission line, a voltage drop between the sending and receiving ends of the line primarily because of the inductance in the line. If the resistance in the line and the capacitive shunt reactance between the conductors and ground are ignored, the active power sent is equal to the power received as described by Eq. 1. However, as described in the ▶ Chap. 1, “Introduction to Flexible AC Transmission Systems (FACTS) Controllers: A Chronology,” the active power flow also causes magnetic energy to be absorbed in the inductive reactance of an overhead transmission line. Assuming that the sending and receiving end voltages

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Technical Description of Thyristor Controlled Series Capacitors (TCSC)

255

are the same, then the reactive power required to be supplied from the sending and receiving ends of the line is described by Eq. 2. That is, the more active power that flows through the overhead line, the greater is the reactive power demand. jP S j ¼ jP r j ¼

V sV r V sV r sin ðδs  δr Þ ¼ sin ðδÞ X X

(1)

V2 ð1  cos δÞ X

(2)

jQS j ¼ jQr j ¼ where

Vs is the sending end voltage with an amplitude equal to Vs and an angle equal to δs. Vr is the receiving end voltage with an amplitude equal to Vr and an angle equal to δr. X is the line’s reactance. δ is the electric angle between the sending and receiving ends of the line (δ = δs  δr). Ps is the active power sent from the sending end. Qs is the reactive power demand at the sending end. Pr is active power received at the receiving end. Qr is the reactive power demand at the receiving end. If the sending end is located in a strong system, with small voltage variations for different power flow levels but the receiving end is a located in a weak system, then the receiving end voltage can be described by Eq. 3, where Iline is the current flowing in the line. V r ¼ V s  X I line

(3)

Voltage in p.u. of rated voltage

Figure 1 shows that if the power system at the receiving end of an overhead line is not able to provide reactive power, then the receiving end voltage will be reduced at 1.2 1 0.8 0.6 0.4 0.2 0 0

0.5 1 1.5 2 Actual power in p.u. of rated power

Fig. 1 Voltage collapse example

2.5

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high power transfer levels until it collapses. (This is referred to as the nose curve because the graph has the appearance of a nose). To avoid this, the voltage along the line has to be increased, which is accomplished by inserting equipment that provides capacitive reactive power as the load increases although the opposite can be needed under low load conditions. That is, when the line loading is very low, because of the Ferranti effect (Steinmetz 1971), reactive power might have to be absorbed along the line instead of added. Reactive power control can be accomplished by means of shunt compensation using capacitor banks/FACTS controllers or by means of series compensation by inserting capacitor in series with the line. For long overhead lines, series capacitors inserted into the overhead line is normally the preferred alternative. The compensation can be switched in or out depending on the line loading. FACTS controllers used for reactive power control enables continuous, often step-less control of the reactive power flows. This performance advantage can be used to optimize the reactive power compensation in the power system, to enable dynamic support to damp oscillatory modes and can be used to improve the transient stability of the power systems. One of the FACTS controller options used often in conjunction with fixed series capacitor (FSC) banks is the thyristor-controlled series compensation (TCSC) system (CIGRÉ TB 123 1997). TCSC systems are used to modulate the impedance of the series capacitors. These systems utilize large, high power thyristors as described in ▶ Chap. 5, “Power Electronic Topologies for FACTS.” The thyristor is the preferred semiconductor device for a controlled series compensation based on power electronics (TCSC and TSSC type systems) because of the short circuit performance of thyristor devices is superior to other semiconductors. Thyristor switched series capacitor (TSSC) type systems can also be applied since they enable rapid insertion or bypass of series capacitor banks. A prototype TSSC system was the AEP – ABB Kanawha River system installed into operation in 1991 (Keri et al. 1992). The Slatt multimodular TCSC system can also be used as a combination of switched and controlled series capacitor system (Larsen et al. 1992). Standards have been developed to assist power system planners and engineers about what is required when specifying a TCSC system and the IEEE has produced a recommended practice for specifying thyristor-controlled series capacitors (IEEE Standard 1534 2009). This standard provides information about design issues, information needed when procuring a TCSC system, as well as recommendations for factory and commissioning tests. IEC has also developed standards for series capacitor installations, which can be used in applicable portions for the specification of TCSC systems (IEC standard 60143-4 2010).

2

TCSC Principles of Operation

All of the installed TCSC systems were built using a reactor in series with a controllable thyristor valve and a metal oxide varistor (MOV) in parallel with a series capacitor as shown in Fig. 1 (CIGRÉ TB 554 2013). The MOV is used for

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overvoltage protection of the capacitors as well as the thyristors. The main reason for using thyristor devices is that when there are short circuits on the compensated line, the capacitors and the MOV bank are bypassed by switching the thyristors to full conduction mode. In that case, the thyristors will have to carry the full fault currents until the line breakers are opened or the TCSC system is bypassed by means of a spark gap (or any fast protective device) or mechanical bypass switches. Furthermore, during a power system disturbance, the TCSC systems are often required to operate by switching the TCSC system to the maximum compensation mode thereby providing synchronizing torque to stabilize the connected generators. The high current rating that can be achieved using large diameter, high voltage thyristors therefore make thyristors the device of choice for TCSC systems. Figure 2 illustrates that when the thyristors are not conducting, the system operates as a conventional series capacitor module. When the thyristors are conducting continuously as shown in Fig. 3, the module can be characterized as a small inductance in parallel with a capacitor (CIGRÉ TB 123). That is, in this operating mode, the impedance of the TCSC is primarily inductive. Figure 4 shows the state of the TCSC system when in the vernier control mode with the thyristors conducting for a fraction of a cycle. In that mode, in addition to the line current, currents are also circulating between the capacitor and reactor as shown in Fig. 5. In the capacitive modulation mode, shown in Fig. 5, the thyristor valve is turned on for a short period of time just prior to the voltage zero crossing at the 180 electrical degree point of the capacitor voltage (shortly before the maximum current through

Fig. 2 Thyristor-controlled series capacitor module with thyristors turned off

Fig. 3 Thyristor-controlled series capacitor module with thyristors conducting continuously

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Fig. 4 Thyristor-controlled series capacitor module with thyristors in the vernier conduction mode

TCSC Waveforms 1.5 1

Conduction angle (σ) Firing angle (α)

Amplitude

0.5 0 -0.5 -1

Angle

-1.5 Current

Capacitor Voltage w/o Thyristor Switching Capacitor Voltage with Thyristor Switching Thyristor Current

Fig. 5 Capacitor voltage and thyristor currents in the vernier control mode

the capacitor). The capacitor will then discharge through the thyristors and the reactor. The effect of this is that the capacitor will appear to be smaller, i.e., it will have a higher impedance. This increases the apparent degree of series compensation for the line thereby boosting the current flow through the line. When operating in this mode, the apparent impedance of the TCSC (X), the average thyristor current (ITAV) and root mean square (RMS) current (ITRMS) in steady state can be calculated as follows (IEEE 1534):

8

Technical Description of Thyristor Controlled Series Capacitors (TCSC)

X ðα Þ ¼

2

0

  B 2 2 j 6 61  k  σ þ sin ðσ Þ þ
4k   cos2 σ  B 4 2 2 2 ωC π 2 @ k 1 k 1

 k  tan

259

 σ 13 kσ  tan 7 2 2 C C7 A 5 π

(4)

I TAV ¼

   σ  I^L k2 1 σ kσ  cos  tan    sin k 2 2 2 k2  1 π

(5)

k2  I^L  A k2  1

(6)

I TRMS ¼ where A equals:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 9 u 8 σ  u > > > >  uσ < = cos sin σ 1 þ cos σ sin ðkσ Þ u 2  B A¼u 1þ þ 1þ 4 t4π > > kσ σ 1 þ cos ðkσ Þ kσ > > ; : cos 2 where B equals: 

2 6 B¼6 4

sin

  3 ðk þ 1Þσ ðk  1Þσ sin 7 2 2 7 þ 5 ðk þ 1Þσ ðk  1Þσ

where σ is 2 (π – α), the thyristor conduction angle. α is the control (firing) angle from capacitor voltage zero. k is λ/ω. ω is 2πf. f is the power frequency. λ ¼ p1ffiffiffiffiffi : LC

L is the inductance. C is the capacitance. I^L is the peak value of the power frequency component of the line current. As shown in Fig. 6, the degree of compensation using this so-called vernier control mode can be increased up to a maximum advance angle beyond which the firing would be too close to the resonance point for the module. If the firing of the

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Fig. 6 Control range for a single TCSC module assuming k = 2.5 in Eq. 4. The vertical axis uses the capacitor bank reactance amplitude as base, i.e., the impedance is equal to 1.0 when the thyristors are blocked

thyristors valve is delayed for some time when the thyristors are in the continuous conduction mode, the effect is similar. In this mode, as shown in Fig. 6, the thyristors are triggered at 90 with reference to the capacitor voltage zero. If in this mode, the triggering of the thyristors is delayed, the thyristor circuit will operate as a thyristorcontrolled reactor. That is, the inductive impedance can be modulated in a way that can be used to buck (oppose) the current flow through the line; a function typically reserved for phase angle regulators. Thus, the vernier control mode for the thyristors valve can be used to increase as well as decrease the current flow through the compensated line (CIGRÉ TB 123 1997).

3

Operating Range of TCSC Systems

The operating range for a single TCSC module is shown in Fig. 7. Typically, a series compensation system can be overloaded using the long-term and short-term overload capability of the capacitors. (IEEE Standard 824 2005; IEC 60143-1 to 2015), as shown in the figure. The short-term emergency rating is used during and after a short circuit event in the system where the TCSC is installed. This requires very powerful thyristor valves because the capacitors are assumed to be bypassed by the thyristors during the time it takes for the breakers to clear the fault. When the fault is cleared, the TCSC system must provide maximum reactive compensation to provide the needed synchronizing torque across the line where

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Technical Description of Thyristor Controlled Series Capacitors (TCSC)

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Fig. 7 TCSC capability for a single module controller

the TCSC system is installed. During this phase, the TCSC system could be operated and overloaded using its long-term overload rated current shown in Fig. 7. This requires the following: • The TCSC system should preferably not be bypassed during an AC system short circuit except on a line in which the TCSC system is installed but if bypassing is needed it must recover immediately after the short circuit is cleared. • The TCSC system must not fail or be permanently bypassed as a result of the AC system short circuit event. That is, failures requiring bypass of the TCSC system must be an independent event not associated with any system short circuit or other overload events for which the TCSC system is required to operate. For these reasons, as shown in Fig. 7, the TCSC system specifications would normally include a 30-min long-term overload rating and a 10 s emergency overload rating. The 30 min overload rating is typically specified for a 35–50% overcurrent and the 10 s rating is typically for 70–100% overcurrent, usually denoted “swing current” as shown in Fig. 8 (IEEE 1534 2009). The long-term overload rating is needed to redispatch the power flows after some major AC system disturbance, and the short-term overload rating is needed to manage the transient power swings during and immediately after an AC system fault. TCSC systems are typically combined with fixed or switched conventional series compensation systems (Gama et al. 1998). In some cases, a fully controllable TCSC, i.e., without any fixed series capacitor, is specified depending on planning studies. Impedance control of the high voltage lines using TCSC technologies can be used to

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Fig. 8 TCSC performance map

Fig. 9 Single line diagram of a six-module TCSC system

fine-tune the loading of parallel lines. Connecting several series connected TCSC modules together as shown in Fig. 9 is one way of achieving a large control range. The control range for a system consisting of four TCSC controllers is illustrated in Fig. 10. By using vernier control in combination with switching in and out of the series connected modules, a large and almost continuous control range can be obtained as shown in Fig. 11. The system illustrated in Fig. 11, can be considered as a combination of TSSC and TCSC systems. That is, it can offer a stepwise change in the overall transmission line impedance as well as impedance modulation control. This capability should make it possible to schedule the power flow on the TCSC compensated line; a capability which might be useful in a deregulated transmission

8

Technical Description of Thyristor Controlled Series Capacitors (TCSC)

Fig. 10 TCSC transient capability curves for a four module multimodule TCSC controller

263

Four Modules

2

Voltage (pu)

Three Modules Two Modules One Module

0

Modules Bypassed

–2 0

TCSC impedance

1 Line Current (pu)

2

CSC impedance - actual

4xTSSC + TCSC

3xTSSC + TCSC

capacitive operating area 3xTSSC π/2

Firing angle α

Compensation impedance - requested

2xTSSC

inductive operating area

1xTSSC

no compensation

CSC impedance - requested

Fig. 11 TCSC and TSSC impedance characteristics

system1. This capability is, however, associated with a higher cost since each TCSC module will have to include its own reactor and the bus work on the platform becomes more extensive. However, the benefit would be an increased power flow control range. The vernier control method can be applied on each phase independently of the other phases. Therefore, it could be used to balance the impedance between phases in an untransposed system (Nolasco et al. 2014). It could also be used to increase the power flow across two healthy phases in a system with a single phase to ground fault using single pole trip-reclose schemes. In this way, it could provide synchronizing 1

The stated objective of EPRI’s FACTS initiative was to provide utilities in the USA with methods for systems analysis, design, and operation that would enable better utilization of the existing transmission facilities and improve the operational flexibility (EPRI EL-6943 1991).

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torque even during a single-phase system short circuit event to improve the transient stability between sending and receiving ends connected by means of a single line. All TCSC systems can be controlled to add damping to the AC system. This has been the major reason for installing TCSC systems around the world (TB 554 2013). However, the modularity shown in Fig. 9 might not be needed where system damping is the major objective for the use of a TCSC system, which might be the case for a TCSC installation in a long radial line. In that case, a single TCSC system as shown in Fig. 7 would be the most economical solution. Other TCSC requirements are: • No DC component should be injected into the line by having asymmetrical firing between the two antiparallel connected thyristors. Therefore, in the system shown in Fig. 9, one module will normally have to be left with the thyristors in the nonconducting mode (capacitor module continuously inserted) to avoid passing small amounts of DC currents through the line. If, however, the line is also equipped with fixed series capacitors any DC component generated by the TCSC will be blocked by the fixed series capacitor. • Short circuit current through the TCSC system will be limited by the line impedance. However, if high short circuit currents are encountered that will overstress the capacitors or the overvoltage protection provided by MOV banks, then the thyristors of the TCSC system can be turned on and bypass the capacitors and the MOV bank. When the thermal limit of the thyristors is reached, a protective gap can be triggered or a mechanical bypass switch in parallel with the capacitors must be closed. • If the bypass breaker shown in Fig. 9 is closed at the peak of the through-fault current with a fully offset fault current and with the thyristors in the full conduction mode, the current through the thyristors will continue to circulate by freewheeling in the thyristor branch and the bypass switch (McDonald et al., 1994). Since the resistance in the circuit with the bypass breaker closed is very low and the inductance is relatively high, the time constant of this circuit (L/R) is long and therefore, the decay of the current will be slow. This scenario could well impose the highest thermal stress on the thyristors. The critical design issue for this high stress event is that the maximum junction temperature in the thyristors must be kept below the maximum allowable junction temperature or the thyristors might fail.

4

Power-Transmission Characteristic Controlled by TCSC Systems

As the TCSC device, as shown in Fig. 12, is a serially connected device and acts like a controlled reactance XTCSC, it affects the transmission line reactance directly. The extreme modes of operation for a TCSC module are with the thyristor path either blocked, in which case it is a conventional capacitor (net reactance of XC), or continuously gated where it appears as a small inductance (net reactance of Xbypass).

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U2 UC1∠δC1 U1∠δ

jX1

UC2∠δC2

jXTCSC

UC2 jX2

U2∠0

I P1

UC

δ

I1 = I2

US

P2 UC1

X1 + X2 = X12 U1

Fig. 12 Power system model including TCSC (left), the corresponding voltage-phasor diagram (right)

Between these two extremes, partial-conduction or “vernier” control can be used to increase the reactance in either the capacitive or inductive direction (Larsen et al. 1994). It is rather straightforward to write the equation for active power transmission, as the location of the TCSC along the transmission line does not have any effect on transmitted fundamental frequency power2. Therefore: P1 ¼ P 2 ¼ P ¼

U 1U 2 U 1U 2 sin δ sin δ ¼ X 12 þ X CSC X 12 ð1  K CSC Þ

(7)

where KCSC shown in Fig. 13 represents the so-called series-compensation rate or compensation degree (KCSC = XTCSC/X12). In the inductive regime of operation, device’s reactance XCSC in Eq. 7 exhibits positive reactance value, whereas in capacitive regime it is negative. The power transmission characteristics for several values of KCSC are depicted in Fig. 13. It is clear that only the characteristic amplitude of the power curve is modified by the series compensation.

5

Cost Benefit of TCSC Systems

As is shown in Fig. 13, the thyristor-controlled series compensation (TCSC) can provide improved stability for interconnected power systems, allowing higher power transfer levels and directing flows on desired transmission paths (EPRI EL-6943 1991; Larsen et al. 1992; Nyati et al. 1993; Christl et al. 1992). To ensure a reasonably accurate assessment of benefits and costs, it is important to have simulation models, which closely approximate the behavior of a TCSC. Such a In the same way as for a fixed series capacitor bank, the voltages on either side of the TCSC system will, however, need to be considered to avoid creating line voltages that will overstress the insulation of the line.

2

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Fig. 13 Power transmission characteristic modification imposed by TCSC

P/PMAX

KCSC = 0.4 KCSC = 0.2 KCSC = 0

1

KCSC = -0.2 KCSC = -0.4

0

90

180

δ [deg]

model must represent the physical constraints on operation of the TCSC, as they relate to voltage and current ratings of the equipment (CIGRÉ TB 145; Mittelstadt et al. 1992). Study results can then be used with confidence to specify the parameters of the TCSC, which most closely relate cost to the performance benefit seen in the system studies. For further information about the costs and benefits of TCSC systems, see ▶ Chap. 16, “Economic Appraisal and Cost-Benefit Analysis.”

6

TCSC Models

Many different mathematical models are used for study of electric power systems. Models are used by planners to study the effect of the power flows and voltage profiles in the power systems, for study of the stability of the system, and for engineering design of equipment under consideration. Numerous computer models have been developed also for TCSC controllers. CIGRÉ has published some theoretical application studies summarized below that illustrate various performance aspects of TCSC systems (CIGRÉ TB 145 1999)3. TCSC application studies and computer models are also described by IEEE (IEEE 1534 2009).

3

A comprehensive treatise specifically for the TCSC but also for some aspects of FACTS technology applications in general can be found in Ängquist 2002.

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6.1

267

TCSC Static Models

The reactance limits of the TCSC must be considered for static modeling as well as for dynamics (CIGRÉ TB 145 1999). These limits are relatively complex and time dependent. The characteristic limits are shown in Fig. 14, which shows the limits enforced in very short (one to tens of seconds) time frame. As implied by Fig. 14, these limits become progressively more restrictive in longer time frames. The TCSC controller’s operating limitations at very low line currents are not shown in Fig. 14 or any of the other figures shown in this section. That is, it is not possible for the TCSC to control the line impedance if the line current is below a certain threshold level. The main reasons for the low current operating limit are: • If the power for the thyristor gate drives is derived from the AC line current through the line, the power needed for the gate drives might also be insufficient to generate gate drive currents sufficient to turn on the thyristors. This might be one reason to transfer gate drive power from ground up to the energized platform or to use light triggered thyristors with built in self-protection. • The measuring systems used for the control system need to produce measurements with a sufficiently high signal to noise ratio and with a sufficient resolution to for example, enable synchronization of the thyristor valve firing, which relies on measurement of the capacitor voltages.

Fig. 14 Block diagram for the TCSC model for typical stability studies; line current is inferred on the horizontal axis in the figure

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• At low current levels, the voltage across the series capacitors is also very low and may not be high enough to cause current spreading across the entire thyristor surface area, which can cause current crowding on the thyristors’ surface area if the device is subjected to a high current rate of rise (di/dt) and lead to a device short circuit failure (Kinney et al. 1995). The low current operating limit could be at around 10% of the rated line current (IEEE 1534 2009). The minimum TCSC current limit needs to be considered in all of the model studies since it can affect the applicability and operation of the TCSC especially if SSR damping is one of the requirements.

6.2

TCSC Dynamic Models

Development of dynamic models is intrinsically related to the specific TCSC application. Power flow control, SSR mitigation, and power oscillation damping control have different model needs and representations.

6.2.1 Block Diagram Figure 14 shows a block diagram for a TCSC model for a typical stability study. The sign convention for this model is positive reactance in ohms for capacitive compensation and negative reactance in ohms for inductive compensation. The model has provisions for an open-loop auxiliary signal (Xauxiliary), which could be, for example, the input from an external power flow controller. The model also has provisions for a small-signal modulation input (Xmodulation). The reference (Xreference) is the initial operating point of the TCSC. These inputs sum to Xdesired, which is put through signal conditioning into a lag block. This lag is associated with the firing controls and the natural response of the TCSC and is represented by a single time constant (TTCSC). The time constant is application specific and may vary considerably. The output of the lag block is called XTCSC, which should have non-windup limits associated with the integration function. These limits are variable limits based on the TCSC reactance capability curve and equations as shown in Fig. 14. This value is added to the value of the fixed compensation (Xfixed), if used in a specific application, to obtain a total compensation value called Xtotal. For the network interface, care must be exercised to assure compatible signs and per-unit basis with the system equations used in the calculations. 6.2.2 Dynamic Reactance Limits Referring to the limits shown in Fig. 15, the TCSC model should permit operation anywhere within the enclosed region except for the area close to the zero line current where triggering of the thyristors is not possible. The boundaries are due to a number of constraints, as subsequently described. (All reactances are in per unit on XC except

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Fig. 15 Transient reactance limits; the horizontal axis is the line current

as noted, all voltages in per unit on ILrated*XC, and all currents are in, or converted to, amperes.) In the capacitive region, the constraints are due to: 1. Limit on firing angle, expressed as a constant reactance limit (Xmax0). 2. Limit on voltage across the TCSC which is a function of the current and the capacitive reactance. The maximum voltage limit is used during system transients when the maximum boos level is needed. 3. Limit on line current during short-term transient events at which point the TCSC will go into a protective bypass mode. Once the TCSC is bypassed on this overcurrent constraint, it is subject to a time delay on reinsertion after line current falls back below current limit. In a multimodule TCSC, it is possible that only some of the modules will bypass, since once one module bypasses the line current will drop, which in turn may allow the remaining modules to stay in capacitive mode. For simplicity in typical stability studies, it is suggested that this nuance be neglected. There is also a minimum current operating limit for both the capacitive and inductive operating range (not shown in Fig. 15). On the inductive side similar constraints apply: 1. Limit on firing angle, expressed as a constant reactance limit (Xmin0). 2. Limit on harmonic currents circulating between the thyristor branch and the capacitor, approximated as a constant voltage across the TCSC. (See 9.2.2.1 for calculation of the harmonic currents.)

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3. Limit on thyristor current. As an approximation, the fundamental frequency component of thyristor current is limited to that at which the TCSC can operate in thyristor bypass for the duration of the transient. See CIGRE TB 145 for a detailed description of these limits (CIGRÉ TB 145 1999).

6.2.3 TCSC Model Performance TCSC models used for system stability studies have been developed and tested in large-scale power system stability analysis programs (Price et al. 1992; SanchezGasca et al. 1993; Paserba et al. 1994). The simulation results described below show examples of the TCSC model performance (CIGRE TB 145 1999). The CIGRE TCSC stability model was tested on a 25-machine, 100 bus test system. This system included several interconnected areas, and therefore, several interarea modes of oscillation. In this study, the TCSC was located in a circuit between two of the areas which experience multiple swing modes for certain system disturbances. The TCSC for this system had a RMS line-to-line voltage rating of 500 kV, RMS line current rating of 2900 amperes, and a reactance rating (XC) of 8 Ω. Further demonstration of this stability model is included in Mittelstadt (Mittelstadt et al. 1992). 6.2.4 TCSC Model Alternatives The TCSC model defined above can be called a “voltage limited” model, because for most of the interesting performance scenarios, the limits on the TCSC reactance are determined from the maximum voltage capability of the TCSC equipment. Without having such a constraint included in the simulation model, the next best approximation is with fixed reactance limits. The following sections compare performance of a “fixed reactance limit” model with a “voltage-limited” model and demonstrate that the system performance is sufficiently different to warrant proper modeling. Three simulation cases are presented here for the CIGRE test system (CIGRE TB 145 1999): Case A – TCSC with 8 Ω XC nominal, voltage-limited model Case B – TCSC with +14/4 Ω fixed impedance limit model Case C – TCSC with +8/2 Ω, fixed impedance limit model For all three cases, the disturbance was a severe system fault between two areas, followed by line clearing. The remaining line between the areas, which includes the TCSC, picks up the additional current and the TCSC modulates its reactance to damp the power swings. The simulation results are presented in Figs. 16 and 17. In Fig. 16, the results of Cases A and B are plotted. The solid curve is the benchmark and shows performance with an 8 Ω TCSC represented with a voltage-limited model. The dashed curve shows performance with a 14 Ω TCSC represented with fixed reactance limits. On the first swing, the voltage-limited model is more reactance constrained due to the

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Fig. 16 Comparison of system dynamic performance with 8 Ω nominal voltage limited TCSC model (solid curves) and +14/4 Ω fixed reactance TCSC model (dashed curves)

large increase in line current. On subsequent swings, neither model is limited but performance differs due to the different behavior of the first swing. In Fig. 17, the solid curve shows the same benchmark case and the dashed curve shows performance with an 8 Ω TCSC represented with fixed reactance limits. On the first swing where line current is very high, the two models encounter roughly the same reactance limit, although the voltage-limited model allows the reactance to be over 8 Ω for a short time. In subsequent swings where line current is lower, however, the difference between the two models is more pronounced. The model with fixed

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Fig. 17 Comparison of system performance with voltage limited TCSC model (solid curves) and +8/2 Ω fixed reactance TCSC model (dashed curves)

reactance limits hits the 8 Ω maximum limit several times while the voltage-limited model shows that the TCSC reactance can exceed 8 Ω and provide greater modulation capability. In planning studies, the objective is to determine the TCSC rating required to satisfy specific system performance criteria. The examples illustrated in Figs. 16 and 17 show that the dynamic response of the system subject to voltage-limited modeling can be substantially different than those obtained with fixed reactance limits. Thus,

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by using a voltage-limited model, planning studies can more accurately determine the correct TCSC rating required to meet system performance requirements.

6.2.5 Operating Studies In operating studies, the objective is to accurately determine system performance with an existing TCSC. The voltage-limited TCSC model accurately represents the performance of the actual equipment while the model with fixed reactance limits does not. Consider again the simulations in Figs. 16 and 17 as examples, with the solid curves showing performance of the actual equipment. If constant reactance limit models (dashed curves) were used to represent the actual equipment, overall system performance is significantly different. Figure 16 shows that if the TCSC is represented by a 14 Ω fixed limit model, the big difference in the first swing performance of the TCSC causes all subsequent swings to be significantly different. Figure 17 shows that if the TCSC is represented by a 8 Ω fixed limit model, the TCSC’s modulation capability is incorrectly restricted. These cases illustrate the dilemma faced when using a simple fixed-reactancelimit model for the TCSC. It may not be possible to achieve simulation results which are a reasonable representation of the expected TCSC behavior, and even selecting the proper TCSC rating will be subject to some uncertainty. Regardless of the model used, the engineer should monitor the magnitude of terminal voltages to be certain that other system equipment is not subjected to unacceptable voltages during power swings and other operating considerations. 6.2.6 Modeling Exclusions The model described here is not suitable for analysis of harmonics, torsional interactions, high frequency transients, or unbalance problems. Each of these problems requires more detailed modeling of the TCSC and the host system. Electromagnetic transients programs are needed for study of high voltage transients imposed on the TCSC controller modules if a short circuit to ground occurs on the line at either side of the installed TCSC controller. Such transient events require a detailed high frequency model of the TCSC capacitor banks, reactors, thyristor valves, and bus structures. This need to take into account the facts that the capacitance of an AC power capacitor becomes inductive at high frequencies and that the winding capacitances of reactors dominate the high frequency impedance of the reactors. Also, the stray inductances of the bus work surrounding the thyristor structures of the TCSC controllers need to be included in a high frequency timedomain simulation model. Models for study of the TCSC systems during line short circuit events also need to include the non-linearity of metal oxide varistor (MOV) blocks. A simple model, which can be used if specific data about the nonlinear characteristics are not known, is as follows:

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I ¼ I0



V V0

/ (8)

where I is the current at voltage V. Io and Vo is typically chosen as the 1 mA knee point and the maximum continuous voltage rating of the material. α is an exponent, which varies with the composition and manufacturing of the MOV material and the applied current. The simplified model is useful for planning studies but not for TCSC design because the exponent α varies from the knee point to the maximum useful surge current through the MOV. It can be established through tests of MOV blocks (Sakshaug et al. 1988). A value for α equal to 33 has been used for simulation purposes (Anderson and Framer 1996a). Nowadays, electromagnetic transient simulation software allows for the direct representation of the MOV blocks by their voltage-current characteristics provided by the manufacturers. The trade-off when designing the MOV bank for overvoltage protection of series capacitors is between the knee point of the MOV material and the fundamental frequency overvoltage impressed on the capacitors at the maximum fault current in the transmission line in which the TCSC system is installed. CIGRÉ has developed basic information about the performance of MOV-based arresters for various applications including energy absorption capability of MOV arresters (TB 544 2013). The maximum allowable power frequency voltage across the capacitors is according to standards at least twice the rated capacitor voltage (IEEE Standard 1726 and IEC Standard, 143-1). The critical energy dissipation in the MOV material occurs during the 10 s swing current of the TCSC. After having been exposed to the energy injection during a power system external fault, and the corresponding temperature increase, the MOV shall be thermally stable against the swing voltage caused by the power system oscillation. Therefore, the MOV bank must not be bypassed during this interval. The swing voltage will appear as an overload voltage stress on the MOV for the specified duration (usually 10 s). In TCSC systems, the thyristor valves are typically used for thermal protection of the MOV banks. The compensated line might be reclosed into the fault adding energy dissipation in the MOV bank, which is made up of a number of parallel connected columns, unless the bank is bypassed. This makes it difficult to obtain uniform loss distribution among the MOV columns since with a nonlinearity index α of around 30, a very small difference between the nonlinearity of the several parallel columns will lead to large differences in energy dissipated in the different columns. Therefore, each of the parallel columns must be built to have close characteristics, which are verified during the current distribution test (IEC

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60099-4). That is, the MOV blocks in each of the parallel columns must be closely matched. Because aging of the MOV blocks will change the voltage versus current characteristics of the blocks, it is not possible to replace a failed MOV column with another new or spare column and to get even energy absorption. This requires that redundant MOV columns must be installed when the MOV bank is first built and installed (IEC 60143-2 2012).

6.3

TCSC Modeling Considerations for Long-Term Planning Studies

For long-term dynamic stability studies, the time limited overload capability must also be considered. Figures 10 and 11 illustrate the capability curves for a multimodule TCSC. Figure 18 shows typical capability curves for TCSC modules including the time-overload limits for both capacitive and inductive vernier operation.

Fig. 18 Reactance versus line current characteristics for multimodule TCSC including time overload capability

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Validation

Detailed digital and analog simulations, including those used in the design and commissioning of TCSC hardware must eventually be validated through system tests. The study results shown above have been used for positive sequence, fundamental frequency analysis of TCSC in electric power systems (Nyati et al. 1993; Mittelstadt et al. 1992; Urbanek et al. 1993). Validation of the study assumptions normally takes place during system acceptance testing typically including staged fault testing (Kinney et al. 1995), whenever staged fault tests are accepted by the transmission system operator.

7

TCSC Design

7.1

TCSC Platform Equipment

Platforms insulated from ground are used for series compensation systems on which the capacitors with their associated protection equipment are placed. One platform is used for each AC system phase. The platform for the controller and its equipment placed on the platform has to withstand wind, snow, ice, and seismic stresses (IEC Standard, 143-1; IEEE Standard 1726 2013). The protection systems used for a conventional series compensation system are typically comprised of bypass switches and MOV columns for overvoltage protection and a spark gap (or any Fast Protective Device) for protection of the MOV bank from overload. Information about the status of the series capacitors, switches, etc. is typically transmitted to ground level via fiber-optic data links. Bypass switches can be controlled from the ground level if the operating mechanism is placed at the ground level. Alternatively, the operating mechanisms can be placed on the platform level if power to operate the switches is brought up to the platform level. Most of these types of equipment are also used for TCSC systems (IEEE Standard 1534 2009). For TCSC controllers, thyristor valves with antiparallel connected thyristors as shown in Fig. 2 and their triggering system plus the reactors are added to the equipment on the platform. However, there exist possibilities for cost and size reductions of the capacitor protection systems since the thyristors can act to bypass the capacitors and the MOV columns during line short circuit events (CIGRÉ TB 123). The thyristor valves are placed outdoors on the capacitor platform and therefore, need to be housed in a weatherproof enclosure. This enclosure must also provide protection for electromagnetic interference (EMI) from outside of the enclosure as well as prevent the thyristor housing being an EMI source to external equipment (CIGRÉ TB 123 1997 and IEEE Standard 1534 2009). Some protection and control systems are also placed on the platform, depending on the manufacturer’s design philosophy. Typically, these systems will communicate through fiber-optic links with the control and protection systems located at ground levels. These systems need auxiliary power to operate. The thyristors also require power to turn on and for monitoring of the devices. If the thyristors are electrically

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gated, this power must be provided to the thyristors at the platform level or from the triggering circuit itself. Cooling fluids needs to be pumped up to and from the platform level from the ground level. The fluid is typically deionized water with glycol added to avoid freezing of the fluid. The electric field stress on the cooling fluid is a dielectric stress due to the AC applied voltage. The insulating pipes through which the fluid is pumped need to have sufficient creepage distance to avoid surface discharges. Also, these pipes will be exposed to solar radiation and pollutions, which have to be taken into account when selecting material for the cooling pipes and when the surface stresses on the pipes are considered. Furthermore, ethylene glycol might be considered as an environmentally hazardous fluid, which might require leak containment around the pipes. Fiber-optic links for control and protection systems can be similar to those already in use and proven for FSC banks.

7.2

TCSC Thyristor Valves

The thyristor valves are made up from several series connected antiparallel connected thyristors in order to achieve the voltage rating required for the valves (CIGRÉ TB 123 1997 and IEEE Standard 1534 2009). The valve design is similar to those used for SVC systems; see ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC)” for information about typical valve designs. However, the high surge current requirements for TCSC valves differ from those of SVC valves because the thyristors in TCSC systems must be able to ride through line short circuit events without being bypassed by a mechanical switch or a spark gap in order to be quickly returned to the vernier control mode to provide transient stability support of the AC system and to provide system damping to prevent unstable oscillations to arise. Thus, there is a trade-off to consider in the design of the valves between the electrical and thermal ratings of the thyristor devices. The design of the thyristor valves has to be verified through tests. IEC has issued a standard for the electrical testing of thyristor valves specifically for TCSC applications (IEC 62823 2015).

7.2.1 Thyristor Devices The voltage rating of thyristors can be increased by making the thyristor devices thicker but this causes higher bulk resistivity of the devices leading to higher losses and potentially higher junction temperatures in the devices, which is detrimental to short circuit current survivability. Larger diameter devices can be used, which reduces the current density in the thyristor devices leading to lower device losses. Therefore, TCSC valves typically used custom thyristor devices in order to meet the short circuit current duties. For example, the Slatt TCSC system uses 100 mm diameter thyristors rated at 3.3 kV (Urbanek et al. 1992). The forward voltage drop of these thyristors was typically less than 1.4 V when conducting for 8 ms and at a device temperature of 105  C. This design was required to meet the 20.3 kA short circuit current duty and 60 kA crest asymmetrical fault current duty. Larger

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diameter devices and lower short circuit current duties would enable the use of higher voltage devices. Thyristors have limitations on the rate of current rise (di/dt) upon turning on and also for the rate of voltage rise (dV/dt) when the thyristors are blocked (Mohan et al. 1995). In a TCSC system, the inductance in series with the thyristor valves normally limits the di/dt when the thyristors are turned on (Mohan et al. 1995). However, the di/dt which results from the transfer of current from one thyristor into the antiparallel device during the recovery phase after a high current transient event can be very large (McDonald et al. 1994). The di/dt stress in thyristors occurs along the turn-on line (the edge of the gate towards the bulk of the wafer) on the thyristor wafer. That is, the gate should have a long turn-on line to be able to sustain a high di/dt. One way to achieve a long gate line is to use an amplifying gate as shown in Fig. 19. The center of this wafer is the electrical gate contact. An electric current injected into the center of this wafer will induce larger current flows in the surrounding regions that turns on a second gate area, etc. Finally, the current is flowing through the conductors out to the six three-legged islands clearly visible in Fig. 19. The current flow from the edges of the long gate legs will then cause current flowing through the main thyristor. Because the gate length is substantial, this device can be subjected to a high di/dt without failing. If light were to be injected into the center of the thyristor wafer instead of an electric current, the electron flow resulting from injection of photons into the gate area will result in the turn on of the device in essentially the same way as the electron injection caused by an electric signal injected into the center gate. Thyristors can also be overstressed if the di/dt on turn on of the devices is too low because then the current will not spread over the entire thyristor wafer. This current spreading requires a defined voltage across the thyristor wafer when the turn on pulse is applied. A weak turn on of the thyristor device will also be the consequence of a weak turn on pulse to the gate of the thyristor device. This can be an issue when the TCSC controller is operating with low line currents and if the gate drivers for the thyristors are fed from current transformers (CTs) sensing the line current because then the voltage fed to the gate drivers is low. If power is fed to the gate drivers from a constant voltage source (requiring power from ground), then the risk for weak gate turn on pulses can be eliminated. The thyristors also have to conduct a sufficiently high current after the gate pulse is delivered to latch in the on-state. Fig. 19 Thyristor wafer design (courtesy of the Silicon Power Corporation)

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Thyristors also have dV/dt limits because a high capacitive current flow through the semiconductor wafers can cause an uncontrolled turn on of the thyristor devices. The current channels arising through the wafers for such a turn on will cause the device to fail. Therefore, emitter shorts are included in the wafer to limit the sensitivity for capacitive turn on and snubber circuits (resistor – capacitor network) are connected across each thyristor device to limit the dV/dt to which the thyristors can be exposed. The gate drivers typically also include a so-called voltage break-over (VBO) operation function, which will cause the thyristor device to be turned on even if a gate pulse is absent. This is used to turn on the device if a device is exposed to an excessive voltage, which can arise if the gate driver for one device in a string of devices fails and does not deliver a gate turn-on pulse. It can also retrigger the thyristors if the device current drops below zero temporarily. However, it will also turn on all the series connected thyristor devices if the valve is exposed to an excessive overvoltage. Thyristors can fail if the device is in the process of turning off and a forward voltage is applied across the valve. This forward voltage might be unevenly imposed on one device in a string of devices. Protective firing (turning on) of the devices is then required to avoid device failure during the recovery period, i.e., during the time from the zero crossing of the thyristor current at turn off until the thyristor can block full forward voltage again. This might be accomplished by the VBO function. The thyristor valve typically also incorporates various monitoring functions with information constantly transmitted via fiber-optic links to the station ground level. This includes the operational status of the thyristor devices so that failures of individual thyristors are known as soon as they occur.

7.2.2 Gate Driver Power Issues There are options to bring power via isolation transformers or capacitive dividers from ground up to the platform to power the platform control and protection systems. However, if the line to ground voltage is used to power the gate drivers, then this power source will be lost, if a line short circuit occurs that reduces the line to ground voltage, unless the gate drivers have built-in energy storage. Gate drivers can also be powered by using currents transformers (CTs) in series with the line current. The drawback with gate power derived from the CTs is that the power that can be pulled from the platform circuits varies with the load current flowing through the line. That is, when the line current is very low, it would not be possible to trigger the thyristors.

7.3

Valve Cooling

The thyristor devices need to be cooled to remove the switching and conduction power losses dissipated in the devices and their snubber circuits. Liquid cooling is the preferred cooling method. The objective of the cooling system is to keep the junction temperature in the thyristor devices as low as required for the application. That is, the temperature rise over the ambient temperature has to be controlled to prevent the junction temperature in the thyristor devices to rise to an unacceptable

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level during line short circuit events for which most of the thermal stresses will remain in the thyristor wafer and device package since the device heating will not be dissipated by the cooling media during such short-term events ( 0 or Uc Ic < 0), the transient process of the increase or decrease of power grid current IHV and control current Ic takes place (time intervals I – II, III – I). The average power of the control loop is about 5% of the rated capacity of the controllable reactor in order to achieve the transition from one stationary mode to another in about two periods of the system voltage frequency. However, this is necessary only during the transition. In any steady state mode, for instance, in the semiperiodic (nominal) mode or the full-period (maximum) one, the power consumed by the control loop reduces sharply, since it is necessary only to

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compensate the ohmic losses in the control winding and this power is less than 1% of the rated power. Advantages of the MCSR compared with an SVC using a coupling transformer: • Relatively low cost (approximately 150–200% of a conventional transformer of the same rated power). • Small footprint (105% of conventional transformer of the same rated power). • Grid connection without additional transformer when line connected. Drawbacks: A relatively large time constant (0.1 s) causing a slow response compared to an SVC.

4.1

Mathematical Model

Figure 2 shows the diagram of a magnetically controlled reactor and a possible electric equivalent. The diagram is explained below. • In the equivalent circuit, Lnet. and Lcon. are the inductances of the power and control windings, respectively, with the magnetic system completely saturated; • α is the firing angle of the thyristors corresponding to the time interval for which the core is saturated during the half-period of the system voltage, expressed in electrical degrees. • The complete range of possible operating modes corresponds to the range of α variations from 0 to π. For example,

Fig. 2 Diagram of a magnetically controlled reactor (left) and a possible electric equivalent (right)

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– The firing angle of thyristors of α = 0 corresponds to the no-load conditions of the reactor operation. – The angle of α = π/2 corresponds to the mode of semiperiodic saturation (nominal operating conditions). – The angle of α = π is the mode of maximum current consumption or fullperiod saturation. The equivalent functional scheme is not only a representation that allows the technical performance of a controllable electrical reactor in the power system to be described using the combination of well-known devices. It also reflects the economic potential of controllable reactors. The reactor is equivalent to a transformer which has double-wound windings of comparable capacity and voltage in terms of losses and material consumption. At the same time, the functionality of the reactor corresponds to the widely used thyristor controlled reactor (SVC) connected to the high-voltage grid through a coupling transformer. Thereby, rather than combining a coupling transformer with a reactor and a thyristor switch connected in-series (an SVC), we have only one transformer-type device, in which the inductances of the windings perform the function of a reactor and the controlled saturation of the core acts as the inverseparallel thyristor pair in the SVC. Thus, instead of three power elements there is one, the cost of which is comparable with the three aforementioned. The voltage and current of a MCSR is shown in Fig. 3. The plots presented in Fig. 3 have been obtained by calculations performed in accordance with the circuit diagram of Fig. 2 (left side) using computer software. These graphs can also be reproduced with high accuracy using the equivalent

Fig. 3 Typical plots of voltages and currents of a controllable reactor phase

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functional scheme in Fig. 2 (right), in which a phase of the controllable reactor is presented as an inverse-parallel thyristor pair with linear inductances connected in-series. In Fig. 3, Vnet is the voltage of power grid and Inet is the reactor current. Correspondingly Vcon and Icon are the voltage and current of the control winding.

4.2

Higher Harmonics Suppression

The design of the magnetic system of MCSR is performed so that the operation with the rated absorption of reactive power is close to so-called half-cycle saturation mode (when the resulting induction of each of the cores is more than the saturation induction of the steel during half of the period), as in this mode, half-cores will be alternately saturated (each for half of the period of the frequency) and hence the current of the MCSR in this operating mode does not contain harmonics (Bryantsev 2010; Dmitriev et al. 2013). Figure 4 presents the Fig. 4 Current in the power winding of the reactor in halfcycle mode (180 MVA, 500 kV reactor, rated current 207 A)

i(t), A 300 200 100 0 −100 −200 −300

0

0,005 0,010 0,015 0,020 0,025 0,030 0,035 t, sec

i, A 200

160

120

80

40

0 3

5

7

9 11 13 15 17 19 21 23 25 27 29 harmonic №

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Fig. 5 Current in the power winding of the reactor for the consumption of 40% of rated power

409

i(t), A 300 200 100 0 −100 −200 −300

0

0,005 0,010 0,015 0,020 0,025 0,030 0,035 t, sec

i, A 60 50 40 30 20 10 0 1

3

5

7

9

11

harmonic №

current of the power winding and its harmonic composition for the half-cycle mode of reactor operation. Intermediate operating conditions of reactive power consumption between no-load and the half-cycle saturation conditions are considered in Fig. 5. The power of the reactor is controlled by varying the direct component of magnetic induction in the half-cores by changing the current in 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. Therefore, the current in the power winding of the reactor will

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decrease, and the waveform of the current will be distorted by higher harmonic components. In Fig. 5, the plot of the power winding current and its harmonic composition are presented for the mode of 40% of rated power consumption. It is evident that the current curve is distorted to a considerable degree. According to Fig. 5, the odd harmonics from the third to the ninth are clearly represented. The total distortion current constitutes 42.3% of the peak value of the first harmonic current, but it makes up 12.8% or 0.13 p.u. with respect to the rated current. The maximum of the third harmonics corresponds to the power winding current of 80 A (about 40% of the rated power). At that current, the effective value of the third harmonic current totals about 25 A or 12.6% of the rated current of the reactor. It is obvious that the distortion in the waveform of the power winding current is caused mainly by the third harmonic component. As a rule, in order to compensate the third and other odd triplen harmonics, the design solution is to connect a special (compensation) winding of the reactor with delta connection. The compensation winding (CW) serves two main functions: • It reduces the triplen harmonic components; • It serves as a supply secondary winding of the reactor, to which converters providing the magnetic biasing of the reactor’s magnetic conductor are connected along with filtering and compensating units (FCU), if they are required. The influence of the compensation winding on the harmonic composition of current in the power winding can be seen from comparison of Fig. 6a and Fig. 6b, by example of the 40% of rated power consumption, in which the third harmonic component in the power winding current was maximum. Without the compensation winding, the resulting distortion current constituted 0.13 p.u. (12.8% with respect to the rated current of the reactor), while the presence of the delta-connected winding causes this parameter to decrease to 0.04 p.u. with full compensation of the third and ninth harmonic components. It should be mentioned that the use of only two low-capacity FCUs adjusted to compensate the fifth and seventh harmonic components permits eliminating the distortion of the power winding current almost completely in some operating condition. The MCSR rated mode is close to the half-cycle saturation condition, in which there is no distortion of the power winding current. In the compensation winding, only odd triplen harmonic currents are prevented. The largest 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 takes place when the device carries about 50% of the rated load.

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a i(t),A 300

i, A 60

200

50

100

40

0

30

−100

20

−200

10

−300

0 0

1

0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040

3

5

7

9

11

9

11

harmonic №

t, sec

b 300

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 0,040

0

t, sec

1

3

5

7

harmonic №

Fig. 6 Currents in the power winding and its harmonic composition in the condition of 40% of the rated power consumption. (a) CW is open; (b) CW is closed

4.3

A Model for Stability Study

The concept of defining a magnetically controlled reactor as a transformer-type device performing the equivalent functions of a semiconductor device was developed as the base of all the developments carried out during the last 10 years and allowed the existing developments both in the area of transformer-building industry and power electronics to be used. Generally, MCSR control law for power system stability investigations can be expressed as follows:  ð1 þ pT R ÞbR ¼ bR0 þ K 0u þ

 K 1u s ΔV R , 1 þ sT 1u

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Where: • bR, bR0 are actual and initial (in previous stable operation) MCSR conductivity, respectively. • K0u, K1u are the terminal voltage deviation ΔUp and its derivative control gains. • TR is the equivalent time constant of the MCSR control system. • T1u is the voltage derivative control loop’s time constant.

5

Magnetically Controlled Shunt Reactor Operation Experience in 110–500 kV Power Grids

Controllable shunt reactors have proved efficient in increasing the reliability of the Unified Power System (UPS) grid of Russia due to its capability to normalize the operating conditions for the transmission lines and power generators (Belyaev et al. 2016; Bryantsev 2010). Operation of long transmission lines of high and extra-high voltage classes showed that for the full utilization of the flow capacity, it is required to control the line reactor’s absorption of reactive power depending on the actual power transmission. The most vivid example was the reduction of the natural power capacity of the 1150 kV overhead line “Ekibastuz-Kokshetau-Kostanai-Chelyabinsk” by more than 50%, due to use of unregulated shunt reactors for reactive power compensation when putting the line in test operation in 1984. Today, a biascontrolled shunt reactor using the extreme saturation of the magnetic circuit sections has become the most widespread option (Bryantsev et al. 2006; Belyaev et al. 2016).

5.1

Overview of the MCSRs in Operation

MCSR implementation began in 1997, when a pilot MCSR prototype of RTU-25000/110-U1 version, as described below, was produced. In 1998, the reactor passed comprehensive tests and subsequently entered trial operation at the VEI STC test site in Togliatti. Afterwards, the reactor was sent to the Northern Electric Networks, Permenergo (Russian Federation), and was installed at the 110 kV substation “Kudymkar.” In September 1999, it was put into operation, together with the existing static shunt capacitors (SSC) which has a capacity of 52 Mvar. It was the first successful experience of the MCSR in commercial operation. The MCSR (110 kV 25,000 kVA) installed at substation “Kudymkar” Permenergo has been in operation for more than 19 years already (Bryantsev et al. 2006). In fact, a controllable reactive power source (RPS) was implemented, featuring a parallel connection of MCSR and the capacitor bank to provide a smooth regulation of reactive power both in the mode of absorption (within the rated power of the reactor) and in the mode of generation (within the rated power of the capacitors). To date in Russia and in some other countries (Kazakhstan, Belarus, Lithuania, and Angola), a large number of controlled shunt reactors with a total capacity of more than 8000 Mvar (Fig. 7 and Table 1) have been commissioned. The majority of the MCSR, with a total capacity of more than 6200 Mvar, are installed in Russia.

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Capacity, Mvar 9000

8374 MCSR capacity (as a part of RPS)

8000

MCSR capacity (separate units) 7000

6996

Total CSR capacity

6000 5143 4738

5000

6834

3903 4000

6161

3000

2478 2153 3473

2000 1183 1000

305

25

330

823 480

1898

2004

2005

255 2007

0 1998

2002

2003

2006

4308

4668

2123 355 2008

430 2009

430 2010

475 2011

835 2012

1540 2013

Fig. 7 Total Capacity of MCSR produced, January 2014

Table 1 MCSR characteristics of different voltage classes Voltage class, kV 10

Quantity 6  10

Power, Mvar 60

35

9  25 + 4  10

265

110

31  25 + 1  63

838

220

2  25 + 1  60 + 7  63 + 20  100

330

4  180

720

400 500

7  100 18  180

700 3240

Total

110

8374

2551

Country Russia Kazakhstan Russia Kazakhstan Russia Kazakhstan Russia, Kazakhstan, Angola Russia, Belarus, Lithuania Angola Russia Kazakhstan

At the time of writing (2019), none of the equipment listed in Fig. 7 had reported any failures, and the first MCSR has already been in service more than 19 years.

5.2

Benefits of the MCSRs

The 330 kV switch yard of the Ignalina nuclear power plant (NPP, Lithuania) is a major distribution node of the Lithuanian high-voltage power grid, which is part of

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Fig. 8 Electrical network 330 kV of Baltic republics

the Baltic Unified Power System (UPS). Six 330 kV overhead lines (one of which is dimensioned to 750 kV requirements) are connected to switchyard buses, to connect with the power systems of Lithuania, Latvia, and Belarus. The power network around Ignalina is shown in Fig. 8. The 750 kV power transmission line (thick black line in the figure) operates at a voltage of 330 kV. The capacitive charging capacity of the adjacent power lines connected to the Ignalina substation is about 280 Mvar Maintaining acceptable voltage and its stabilization in the nodal points of the power system are critical for ensuring the operational reliability of the equipment. Until 2008, voltage regulation in the 330-kV grid caused some difficulties because of the limited choice of control facilities. Excessive reactive power generated by power lines in the Ignalina area (up to 400 Mvar) made it necessary to limit the voltage levels during the summer and daily minimum. To control the reactive power and voltage at the Ignalina substation, two NPP turbine generators were operated in an under-excited mode consuming up to 280 Mvar. The absorption of reactive power by generators was limited to ensure acceptable power system stability conditions and usually did not exceed 150 Mvar. In accordance with international agreements, one of the conditions of entry of Lithuania into the European Community was to close the Ignalina NPP, followed by the possible construction of several new units on the site. Thus at least for 10–15 years, the 330 kV switch yard would be without control facilities for the reactive power generated by the above transmission lines at minimum loads, leading to unacceptable rise of operating voltages. Therefore, in accordance with research findings, it was recommended to install a MCSR at the 330 kV busbars at Ignalina substation. The MCSR was installed in August 2008.

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Voltage Control

The primary purpose of the MCSR and the MCSR-based reactive power sources (RPS) is voltage stabilization, reactive power distribution optimization, and reduction of losses in the high voltage grid. At the same time, the problem of potentially increasing power oscillations and decreasing dynamic stability of the power system can be solved. The accumulated operating experience and research-based recommendations show three feasible options for the installation of the MCSR and the MCSR-based RPS in power systems: • As part of extended intersystem transmission lines of 330, 500 kV; • At substation (power plant) busbars with a large number of outgoing power transmission lines or lines transmitting power through a very long overhead line • In autonomous power systems (or power systems located remotely from highcapacity sources) with a load requiring high voltage quality It should be noted that most of the MCSR-based RPS are installed in 110 kV grids of the oil and gas producing systems for voltage stabilization, facilitation of motor start operation, and removal of reactive power flows in the grids. To confirm the need for implementation of the MCSR in the extra-high voltages grids, the operating characteristics of several substations in the 500 kV Central Russia Intersystem Power Grid (IPG) were collected. These showed significant deviation of the voltage levels from the nominal value as shown in Table 2.

Table 2 Nodes in the 500 kV network IPG Center with deviating voltage levels

Substation Metallurgicheskaya Staryj Oskol Cherepoveckaya Vologodskaya Kaluzhskaya Novovoronezhskaya NPP Trubnaya Tambovskaya Volzhskaya HPP Borino Zvezda Volga Voronezhskaya

ΔU, kV QΣ, Mvar Wint. Wint. Sum. Sum. Wint. Wint. Max min max min Max min 23,24 12,46 2,7 5,1 87 95 21,15 10,4 4,61 3,8 296 302 0 0 18,66 9,22 0 0 0 0 8,46 2,18 0 0 7,9 6,67 0 0 98 74 7,01 11,97 7,55 2,7 45 21 5,33 4,54 2,37

3,14 5,38 0,37

1,32 0 1,06 0,73

6,03 0 3,61 8,4

0,83 2,92 163 4,78 15,2 160 2,1 0,5 395 0,12 1,09 4,14 0,56

8,76 2,8 2,36 7,86

164 0 198 130

Sum. max 50 198 147 153 0 167

Sum. min 18 131 153 160 0 112

161 166 466

163 166 399

161 173 466

168 0 207 83

164 163 199 122

169 165 207 89

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Table 2 provides information on the range of voltages and reactive power flow to the power facilities located in the territories served by the IPG Center, based on measurements performed in 2013. The ΔUnom column shows the deviation from the nominal operating voltage (in absolute units) at different load conditions. The QΣ column shows the total reactive power flowing to the node (or away from it) of all adjacent power lines in the considered nodes. This analysis provides important information enabling recommendations for installing MCSR (or MCSR-based RPS) to stabilize the voltage, to prevent excessive reactive power flows in the adjacent grids, and to reduce losses. Figure 9 shows the deviation of the operating voltage at the nodes from the nominal voltage. Each location marked on the x-axis provides information for four different operating modes, using four color columns, showing the variation of the voltage in different load conditions. The load conditions are winter-max, winter-min, summer-max, and summer-min, with the colors defined in the chart. The hollow bars indicate the absolute value of the reactive power that flows into the node in the corresponding load mode. This information highlights the relevance of extended implementation of controlled shunt compensation devices in the high-voltage grids of Russia and other countries with well-developed transmission system with a high content of long AC lines. Figure 10 shows an example of the successful application of a 180 Mvar MCSR on a 500 kV power transmission line installed at the Agadyr substation at the “NorthSouth” transit system of the Republic of Kazakhstan. Figure 11 shows the voltage 16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24

Q, Mvar 800

∆Unom, kV

600 400 200 0 -200 ∆U (winter, max) ∆U (winter, min) ∆U (summer, max) ∆U (summer, min) Q (corresponding to ∆U)

Fig. 9 Facilities in the 500 kV grid of IPG Center with deviating voltage levels

-400 -600 -800 -1000 -1200

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Fig. 10 North South 500 kV transmission system of the Republic of Kazakhstan

Fig. 11 The chart of voltage change at the 500 kV Agadyr substation before MCSR commissioning

Voltage, kV 550 540 530 520 510 500 490 480 470 01.01.2009

Date 03.01.2009

05.01.2009

07.01.2009

09.01.2009

change at the 500 kV busbar before the commissioning of MCSR. Figure 12 shows the voltage with the MCSR in operation, which demonstrates much smaller daily voltage variations. After the commissioning of the MCSR, the measurements of the voltage in the period of about 2 weeks, the voltage almost fits into the range of 510–520 kV.

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S. V. Smolovik and A. M. Bryantsev Voltage, kV 530

520

510

500

490 01.10.2010 03.10.2010 05.10.2010 07.10.2010 09.10.2010 11.10.2010 13.10.2010 15.10.2010

Fig. 12 The chart of voltage change at the 500 kV Agadyr substation after commissioning of the 500 kV, 180 Mvar, MCSR

5.4

Power System Damping

Based on the measurement of transients in the large 500 kV power system, and the impact the installed MCSR parameters and their settings discussed in detail in Belyaev et al. (2016), it has been shown that the damping properties of power systems depends mainly on the setting of automatic voltage (excitation) regulators (AVR) of physical and equivalent generators. As a rule, it appeared that the change of the time constant (Tcsr) of the MCSR (using continuous MCSR control law on voltage deviation) within a wide range has little effect on damping performance. Therefore, it was concluded that a fast response of the MCSR for system issues is not required. Table 3 shows the results of the eigenvalue calculations for the model of a simple transmission system with a long transmission line when a MCSR is installed on power plant high voltage buses. It was assumed that the power generators operate at two different power factors (cos (φ) = 0.992, mode 1, and cos (φ) = 0.9, mode 2). The real root shown in Table 3, in the second mode, is larger in absolute value, which illustrates the effect of the conditions of steady-state operation (large value of Table 3 Results of eigenvalue calculations № Mode Mode 1 Mode 2

Tcsr = 0.05 s 0.429  8.233i 0.270 0.373 + 8.566i 0.289

Tcsr = 0.1 s 0.413  8.20i 0.268 0.360 + 8.536i 0.2872

Tcsr = 0.5 s 0.456  8.016i 0.256 0.418 + 8.366i 0.273

Tcsr = 1 s 0.554  7.975i 0.242 0.514 + 8.337i 0.257

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EMF generator and a smaller transmission angle). A pair of complex roots shows that the parameters of MCSR insignificantly affect the dynamic stability performance – but by increasing the time constant of the reactor, the damping rate is improved. The determining factor is the availability of automatic excitation controls with stabilization of the generator (voltage frequency deviation and voltage frequency derivative). Dmitriev et al. (2013) shows that the losses in the rotor and stator circuits of power generators in case of power factor (cos (φ)) close to unity is much smaller compared to the operation at nominal power factor. According to Dmitriev et al. (2013), for an electric power plant of 2000 MW the potential savings amount to 30 million rubles ($ one million) per year.

6

Tavricheskaya MCSR, Siberia

Figure 13 shows the MCSR at the Tavricheskaya substation in Siberia. The general specifications of the controllable reactor RTU-180000/500 (put into operation in 2005 at the 500 kV substation “Tavricheskaya” in Siberia) as confirmed by factory and field tests is shown in Table 4.

Fig. 13 MCSR at Substation Tavricheskaya, 2005

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Table 4 The general specifications of the controllable reactor RTU-180000 Rated capacity (QR) Dynamic range Rated voltage UR Maximum operation voltage Power winding rated current IR Control winding rated voltage at the AC voltage terminals Rated biasing magnetization current of the control winding (biasing magnetization current) Minimum time of 5–100% QR power pick-up and 100–5% QR power decrease Summarized (total) losses at QR and UR Operational losses when daily load factor is within the range of 0.7 Amplitude of any higher harmonic of the current at the nominal sinusoidal voltage, % of the nominal current

Sound power level Double amplitude of tank wall vibration, average Top oil temperature rise above ambient Voltage controller droop, % of UR Permitted current overload of power winding (not more than 30 min) PW-CW short-circuit voltage Operating Modes

60 Mvar  3 = 180 Mvar 5–130% of QR 525 kV 550 kV 198 A 32 kV 2000 A 0.3 s Does not exceed 0.5% of QR 0.3% of QR UR control mode – not more than 3% of the rated current (IR) UR and QR control mode – not more than 1% of IR Not more than 108 dB Not more than 150 μm Not more than 60 С 1–5% of UR 120% of IR 50% Automatic voltage stabilization of 500 kV buses Automatic MCSR current control Manual control of reactive power and/or current

References Belyaev, A.N., Smolovik, S.V.: An improvement of AC electrical energy transmission system with series compensation by implementation of Controllable Shunt Reactors. In: Proceedings of IEEE PES PowerTech, Bologna (2003) Belyaev, A.N., Bryantsev, A.M., Smolovik, S.V.: Magnetically controlled shunt reactor operation experience in 110–500 kV power grids. Cigre Session paper B4-209 (2016) Bernard, S., Trudel, G., Scott, G.: A 735 kV shunt reactors automatic switching system for HydroQuebec network. IEEE Trans. Power Syst. 11(4), 2024–2030 (1996) Bryantsev, A.M., et al.: Magnetically controlled shunt power reactors. (Collection of articles. 2nd (expanded) edition. In: Bryantsev, A.M. (eds). Moscow. “Mark” (2010) (in Russian) Bryantsev, A., Dorofeev, V., Zilberman, M., Sminov, A., Smolovik, S.: Magnetically controlled shunt reactor application for AC HV and EHV transmission lines. Cigre session paper B4-307 (2006) Dmitriev M.V., Karpov A.S., Sheskin E.B. Dolgopolov A.G., Kondratenko D.V., Magnetically controlled shunt reactors, In: Evdokunin, G.A. (eds.) Saint-Petersburg, Publishing House

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“Native Ladoga”, 2013 (in Russian), 280 p. ISBN 978-5-905657-07-8. Publishing House “Native Ladoga” stopped working in 2017 (2013) Gama, C. Brazilian North-South Interconnection control-application and operating experience with a TCSC. In: IEEE Power Engineering Society Summer Meeting, vol. 2, pp. 1103–1108, 18–22 July 1999 Gerin-Lajoie, L., Scott, G., Breault, S., Larsen, E.V., Baker, D.H., Imece, A.F.: Hydro-Quebec multiple SVC application control stability study. IEEE Trans. Power Delivery. 5(3), 1543–1551 (1990)

Sergey V. Smolovik has been with the Department of Electrical Power Systems and Networks, Leningrad Polytechnic Institute (later on St.-Petersburg Polytechnical University) since 1966, serving as assistant professor, associated professor, professor, and head of the department (1990–2007). His research interests include power system stability problems as well as the issues of large energy pools operation, analysis and planning, modeling of transients in electric power systems. In 2007, he joined the Direct Current Research Institute (since 2013 Scientific and Technical Centre of the UPS of Russia, Saint-Petersburg). Professor, Doctor of technical science, academician of the Academy of Electrical Sciences of Russian Federation (1993), member of the IEEE and CIGRE, and honored power engineer of the Russian Federation (2001).

Alexander M. Bryantsev from 1973 to 1994 worked in the system of higher education of Kazakhstan in Almaty Energy Institute (Republic of Kazakhstan), including Head of the Department of Theoretical foundations of Electrical Engineering, Dean of the Faculty of Electrical Engineering, and Vice-rector for scientific work. From 1994 to 2000, he worked in the electrical industry of the Russian Federation at the Moscow electric plant “Energy” as deputy technical director, deputy general director for research. From 2000 to 2006, general director of JSC “Electric controllable reactors.” Since 2006, founder and chairman of the Supervisory Board of JSV “Electric grid compensators (‘ESCO’).” A well-known scientist in the field of development and application of controllable shunt reactors and reactive power compensation for high-voltage grid. Author of more than 200 patents. Professor, Doctor of technical Science, Laureate of the Government of the Russian Federation in the field of science and technology, Academician of the Academy of Electrical Sciences of the Russian Federation, member of the presidium of scientific council of public joint stock Сompany “Power Grid of Russia.”

Application Examples of SVC

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Hong Rao, Shi He, Xiaodan Wu, Marcio M. de Oliveira, Guillaume de Préville, Colin Davidson, Zhanfeng Deng, Tuomas Rauhala, Georg Pilz, Bjarne R. Andersen, and Shukai Xu

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Brief Introduction of SVCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 SVC in Wuzhou, Guangxi, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 System Structure and Operating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 SVC in Dong Anshan, Liaoning, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 System Structure and Operating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

425 427 428 428 428 432 432 432 433 436 436

H. Rao Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), Guangzhou, China e-mail: [email protected] S. He Rongxin Huiko (RXHK) Electric Technology Co., Ltd., Anshan, China e-mail: [email protected] X. Wu NR Electric Co., Ltd., Nanjing, China e-mail: [email protected] M. M. de Oliveira ABB FACTS, Västerås, Sweden e-mail: [email protected] G. de Préville GE’s Grid Solutions Business, Massy, France e-mail: [email protected] C. Davidson GE Grid Solutions – Grid Integration, Stafford, UK e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. R. Andersen, S. L. Nilsson (eds.), Flexible AC Transmission Systems, CIGRE Green Books, https://doi.org/10.1007/978-3-030-35386-5_12

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5 SVCs in Gansu, China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 SVC System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 SVCs in Holeta Substation, Ethiopia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 SVC Merlatière and Domloup in West France . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 System Structure and Operating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 SVC in Kangasala Substation Finland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 System Structure and Operating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Taoxiang Substation SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Project Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Introduction of the Taoxiang SVC System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Main Parameters of the Taoxiang SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Technical Characteristics of the Taoxiang SVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 General Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Relocatable SVCs for National Grid, UK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Nemiscau SVCs in Quebec, Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Z. Deng Global Energy Interconnection Research Institute (GEIRI), Beijing, China e-mail: [email protected] T. Rauhala Fingrid Oyj, Helsinki, Finland e-mail: tuomas.rauhala@fingrid.fi G. Pilz System Engineering and Network Studies for FACTS Installations Worldwide, Siemens, Erlangen, Germany e-mail: [email protected] B. R. Andersen (*) Andersen Power Electronic Solutions Ltd, Bexhill-on-Sea, East Sussex, UK e-mail: [email protected] S. Xu HVDC and Power Electronics Department, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), Guangzhou, China e-mail: [email protected]

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11.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Viklandet and Tunnsjødal SVCs in Norway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Haramain High-Speed Railway (HHR) SVCs in Saudi Arabia . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Main Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Directly Connected SVCs in Texas, USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 System Structure and Operation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 SVCs at Bout De L’Ile (BDI) on the Island of Montreal, Hydro-Quebec, Canada . . . . . . 15.1 Application Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 System Structure and Operating Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Main Operating Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.4 System Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The chapter starts with a brief introduction of the SVC technology and then provides a number of typical applications of the Static Var Compensator (SVC) from around the world. Some application examples are general transmission system applications, where the purpose of the SVC is to regulate and support the AC voltage and to minimize the over- and undervoltages that may occur during various faults and events in the network. Some examples demonstrate the ability to improve the power quality, e.g., due to disturbing loads such as arc furnaces, wind farms, traction loads, etc. Some SVC applications demonstrate the capability of the SVC to damp power system oscillations and to increase the power transmission capabilities of the AC system.

1

Introduction

This chapter starts with a brief overview of the design of the SVC. It then provides a number of examples from around the world of the application of SVCs. The following examples are included in this chapter: • An SVC in Wuzhou, Guangxi, China, to increase the transmission capacity of 500 kV transmission lines and to enhance system stability (contribution provided by Hong Rao, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), e-mail: [email protected], Shi He, Rongxin Huiko (RXHK)

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Electric Technology Co., Ltd., e-mail: [email protected] and Xiaodan Wu, NR Electric Co., Ltd., e-mail: [email protected]). An SVC in Dong Anshan, Liaoning, China, to stabilize the 66 kV AC voltage, which was impacted by load changes (contribution provided by Hong Rao, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), e-mail: [email protected], Shi He, Rongxin Huiko (RXHK) Electric Technology Co., Ltd., e-mail: [email protected] and Xiaodan Wu, NR Electric Co., Ltd., e-mail: [email protected]). Two SVCs in Gansu, China, to stabilize the voltage on the 750 kV transmission line which was impacted by a large wind farm (contribution provided by Hong Rao, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), e-mail: [email protected], Shi He, Rongxin Huiko (RXHK) Electric Technology Co., Ltd., e-mail: [email protected] and Xiaodan Wu, NR Electric Co., Ltd., e-mail: [email protected]). Two SVCs in Holeta substation, Ethiopia, to control the reactive power balance and voltage on four long 500 kV transmission lines (contribution provided by Hong Rao, Electric Power Research Institute of China Southern Power Grid (EPRI of CSG), e-mail: [email protected], Shi He, Rongxin Huiko (RXHK) Electric Technology Co., Ltd., e-mail: [email protected] and Xiaodan Wu, NR Electric Co., Ltd., e-mail: [email protected]). Two SVC at Merlatière and Domloup in West France to strengthen and enhance the network stability and quality (contribution provided by Guillaume de Préville, GE’s Grid Solutions Business; e-mail: [email protected]). An SVC in Kangasala Substation, Finland, which was designed to improve the damping of electromechanical interarea oscillations caused by network faults (contribution provided by Guillaume de Préville, GE’s Grid Solutions Business; e-mail: [email protected] and Tuomas Rauhala, Fingrid Oyj, Finland; e-mail: tuomas.rauhala@fingrid.fi). An SVC in the Taoxiang substation, China, which was designed to solve voltage instability issues of the Chengdu 500 kV ring network (Linxu Lei, Guangfu Tang, Zhanfeng Deng, Ting An, Global Energy Interconnection Research Institute (GEIRI), China; e-mail: – [email protected]). Relocatable SVCs for National Grid, UK, which were designed to be easily moved to another site in the UK. These SVCs use only TSCs, which are switched in small steps (contribution by Colin Davidson, GE’s Grid Solutions Business; e-mail: [email protected]). Two SVCs in Nemiscau, Quebec, Canada, which replaced two SVCs at the end of their useful life, supporting the long 735 kV transmission system during steady-state regulation and dynamic events and enhancing first swing stability by maintaining system voltages during large system disturbances (contribution by Marcio Oliveira, ABB, e-mail: [email protected]). Two SVCs at Viklandet and Tunnsjødal, Norway, which are designed to contribute to the reinforcement of the transmission grid and to secure the power supply to central Norway (contribution by Marcio Oliveira, ABB, e-mail: [email protected]).

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• Two SVCs for the Haramain High-Speed Railway (HHR) in Saudi Arabia, for traction load balancing of the 380 kV grid and to provide voltage support to the transmission system during and after contingencies in the surrounding network (contribution by Marcio Oliveira, ABB, e-mail: marcio.oliveira@se. abb.com). • Three directly connected SVCs, i.e., without dedicated transformer, in Texas, to improve and maintain system voltage stability in an area where the penetration of wind power production was expected to grow beyond 1 GW, including older generations of wind turbines (based on induction generators) (contribution by Marcio Oliveira, ABB, e-mail: [email protected]). • Two large SVCs at Bout De L’Ile (BDI) on the Island of Montreal, Canada. These SVCs are to support the long 765 kV transmission lines from the hydro generation in the North (contribution by Georg Pilz, Siemens; e-mail: [email protected]).

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Brief Introduction of SVCs

The Static Var Compensator (SVC) is a shunt compensation device, which can provide variable reactive power to maintain or control the voltage at its point of connection in the power system. Since the first type of SVC was put into operation in the 1960s, the SVC has become the most widely used FACTS controller in power systems. It is available in various configurations, such as saturated reactor (SR), thyristor-controlled reactor (TCR), thyristor-switched capacitor (TSC), etc. Today, SVCs typically consist of the TCR and TSC, filter capacitor (FC), and/or mechanically switched capacitor (MSC). ▶ Chap. 6, “Technical Description of Static Var Compensators (SVC)” in this book provides a technical description of the SVC. The SVC has a wide range of applications from low-voltage industrial applications to medium- and ultrahigh-voltage grids. In fact, thousands of SVCs have been put into operation worldwide. In utility applications, the SVC is used for voltage regulation through shunt reactive power compensation to prevent voltage instability, as well as to increase transient stability and dampen power oscillations. In industrial applications, such as steel mills and arc furnaces, the SVC is used to reduce flicker by compensating the randomly varying reactive power created by the loads. SVC devices have also been widely employed in China’s power transmission networks. In China, at the end of 2018, more than 30 substations had been equipped with SVC controllers. Most of these are installed in the 500 kV and 220 kV substations, where they are connected to the tertiary windings of the power transformers. The rated voltages of most of the SVCs in China are between 35 kVand 66 kV. The maximum capacity of the installed SVCs is 720 Mvar (4 sets of 180 Mvar). This chapter provides examples of the application of SVCs from around the world. Each example will generally provide:

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• The reasons for the application of the SVC • A description of the SVC • The system performance after the installation of the SVC The data provided in the application examples are clarified as follows: • The rating of the SVC is given at the minimum continuous voltage at the point of common coupling (PCC). • The power loss is given for the SVC valves when operating at maximum rating at nominal voltage. The power loss does not include the power loss in the other SVC components.

3

SVC in Wuzhou, Guangxi, China

3.1

Application Background

Wuzhou substation is located in the middle of the 500 kV AC transmission corridor from Guangxi power grid to Guangdong power grid in China Southern Power Grid (CSG). There are several HVDC schemes connected to the AC network in this area. System studies had shown that power flow would transfer to the AC corridor and would affect the voltage stability when an HVDC system is blocked. Installing dynamic reactive power control equipment at Wuzhou substation was an effective way to support the AC network voltage. It would increase the transmission capacity of the 500 kV transmission lines and would enhance system stability. Comparing SVC and STATCOM technology and cost at that time, a SVC with capacity around 200 Mvar was selected to be installed at 500 kV Wuzhou substation (Baorong et al. 2007). The SVC can operate in the following control modes: 1. 2. 3. 4.

Steady-state constant reactive power control mode Steady-state constant voltage control mode Dynamic reactive power support mode Remote control mode

3.2

System Structure and Operating Parameters

The SVC in this project is designed and owned by CSG, the manufacturer is Rongxin Power Electronic Co., Ltd. The SVC was completed and put into operation in May 2009. The single-line diagram (SLD) of the 35 kV/210 Mvar SVC is shown in Fig. 1. The main technical parameters of the SVC in the Wuzhou substation are shown in Table 1.

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Fig. 1 The SLD of the SVC system in the Wuzhou substation

Table 1 Technical parameters of the SVC equipment Parameter SVC rating

Step-down transformer

Semiconductor devices

Voltage (kV) SVC range (Mvar) TCR connection type TCR rating (Mvar) Connection type Ratio (kV) Capacity (MVA) Type Reverse blocking voltage(V) Average on-state current (A) Number of devices in series

Redundancy (%) Overload capability (current/time) Cooling method Full-load SVC valve losses (%) Estimated service life (year)

Value 35 0 /+210 (with all filters) Delta 210 YN d11 525/230  8 x 1.25%/35 750/750/240 Thyristor 7500 5600 12 10 1.2 pu/continuously Water cooling 0.25 25

The layout of the Wuzhou and Guangxi SVC is shown in Fig. 2. The land occupation is around 2400 m2. The control and protection system, thyristor valves, and valve cooling system are indoor. The water cooling radiators, TCR, circuit breakers, disconnectors and earthing switches, surge arrester, and filter banks are outdoor. The harmonic filters consist of capacitor banks and air-cored reactors, and some include resistors.

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Fig. 2 SVC layout

The SVC thyristor valves are arranged in a valve hall, and the valves are cooled by the valve cooling system. Because of space limitation in valve room, the three-phase thyristor valve was designed as a horizontal multilayer structure shown in Fig. 3. The control and protection system is shown in Fig. 4. The valve cooling system is shown in Fig. 5.

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thyristor valve for phase AB

thyristor valve for phase BC

thyristor valve for phase CA

Fig. 3 View of three-phase valve TCR valve

Fig. 4 SVC control and protection system

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Fig. 5 Valve cooling system

3.3

System Performance

After installing SVC, the normal voltage level of the 500 kV bus increased from 1.01pu to 1.022pu with the active power flow increasing from 1070 MW to 1100 MW. The recovery voltage after blocking a single HVDC pole increased from 0.972pu to 0.998pu. Furthermore, the reactive power flow between the Wuzhou and Luodong was reduced to about 20 Mvar after the SVC installation, compared to 130 Mvar before the installation of the SVC. The power angle stability margin and voltage stability margin were also improved, with the power angle stability margin increased to 46.9% from 46.2%, and the voltage stability margin was increased to 37% from 33% (Huifan et al. 2010).

4

SVC in Dong Anshan, Liaoning, China

4.1

Application Background

With the rapid development of the economy in the central region of the Liaoning Province, the power consumption experienced a rapid growth in 2000s, especially in the steel and metal production industry. After the implementation of the peak and off-peak pricing of electricity, the electricity consumption of some companies shifted to off-peak hours. This increased voltage fluctuations in the central Liaoning Power Grid due to insufficient dynamic reactive power support. As a consequence, some industrial users were seriously affected because of the impact of frequent overvoltage and undervoltage on equipment’s lifetime. Furthermore, tap change operation

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and capacitor switching were frequent. In response to the lack of controlled reactive power at the Dong Anshan substation of Anshan power supply company, the installation of a 66 kV SVC was proposed by Anshan power supply company and Rongxin Power Electronic Co., Ltd.

4.2

System Structure and Operating Parameters

The Dong Anshan SVC is designed and owned by State Grid Corporation of China (SGCC), and the manufacturer is Rongxin Power Electronic Co., Ltd. The SVC is connected directly to the 66 kV system where loads include a metal production load rated at 100 MVA. The SVC entered operation in January 2010. The SLD of the 66 kV/100 Mvar SVC is shown in Fig. 6. The 66 kV system is connected to the 220 kV network via a two-winding transformer. The direct connection of the SVC to the 66 kV network means that there is no transformer cost or power loss and the area occupied by the SVC is reduced (Yu Linlin et al. 2013). The main technical parameters of the Dong Anshan SVC are shown in Table 2. The layout of the Dong Anshan SVC is shown in Fig. 7. The land occupation is around 1400 m2. The control and protection system, thyristor valves, and valve cooling system are indoor. The water cooling radiators, TCR, circuit breakers, disconnectors and earthing switches, surge arrester, and filter banks are outdoor. The outdoor layout of the SVC TCR and the TCR valve room in the Dong Anshan substation are shown in Figs. 8 and 9. One of the AC harmonic filters can be seen in the foreground of Fig. 8. The TCR reactors are located close to the valve hall. The 66 kV light-triggered thyristor (LTT) valve group uses a double vertical structure. The left and right valve bodies constitute a single-phase valve group, and the left and right valve bodies are connected by a busbar. Fig. 6 Single-line diagram of Dong Anshan SVC

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Table 2 Technical parameters of SVC equipment Parameter SVC rating

Step-down transformer Semiconductor devices

Voltage (kV) SVC range (Mvar)

TCR connection type TCR rating (Mvar) Connection type Ratio (kV) Capacity (MVA) Type Reverse blocking voltage(V) Average on-state current (A) Number of devices in series

Redundancy (%) Overload capability (current/time) Cooling method Full-load SVC valve losses (%) Estimated service life (year)

Value 66 +30 Mvar to +100 Mvar (with all filters) 25 Mvar to +45 Mvar (with essential filters only) Delta 70 YNy0 220  2  2.5%/66 180/180 LTT (Nakagawa et al. 1995) 7000 1200 28 10 1.2 pu/Continuously Water cooling 0.25 25

Fig. 7 SVC layout

The Dong Anshan SVC cooling system and control and protection systems are similar in appearance to those at the Wuzhou SVC, but the control and protection of the TCR valves is fundamentally different because of the use of LTT. LTTs are directly turned on through a light pulse applied to the first stage of an amplifying gate structure. The only difference between an ETT and LTT is

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Fig. 8 The outdoor layout of the SVC system in Dong Anshan substation

Fig. 9 The Dong Anshan substation TCR valve

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the gate design of the two types of thyristors. In the case of an ETT, the thyristor is triggered by an electrical pulse applied to the gate. Driven by the HVDC application, a voltage breakover (VBO) protection has been designed into LTTs (also called Breakover Diode). The BoD triggers the LTT if the voltage is getting too high in the forward direction. In addition to the HVDC application, further applications of the LTT are FACTS, medium voltage drives, and pulsed power. Especially in applications requiring high valve voltages with many devices stacked in series connection, the LTTs offer essential advantages. By using LTTs with integrated protection functions, the number of external electronics assigned to the thyristors is reduced, and accordingly, the reliability of the converter can be increased (Cigre TB 337, 2007).

4.3

Main Operating Modes

The Main Operating modes are the same as those for the Wuzhou SVC. The SVC device normally operates in constant voltage control as follows: 1. The 3rd and 5th filter branches of the SVC system are kept in operation at all times to absorb the harmonics produced by TCR. 2. If there is a deviation between the voltage feedback and the reference signal, the output of TCR will be adjusted. The 7th and 11th harmonic filter branches will be switched according to the output of TCR. 3. If the reactive power output of TCR is reduced below 25 Mvar (adjustable) and the voltage is still too low, one of the filter branches is energized (7th first and 11th later). 4. If the reactive power output of TCR is increased to above 45 Mvar (adjustable) and the voltage is still high, one of the filter branches is de-energized (11th first and 7th later).

4.4

System Performance

After the SVC device was put into operation, the 66 kV bus voltage was stabilized within 67  0.5 kV, and the power quality was improved. The SVC also provides some support to the 220 kV system, reducing the voltage fluctuation range and improving the reactive power control of the 220 kV system. Figures 10 and 11 show typical daily 66 kV bus voltage before and after the installation of the SVC. The overall system operation is stable and reliable, and the SVC reduces the voltage fluctuation and flicker. Because the voltage is more stable, the transmission line and transformer loss are reduced.

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Fig. 10 Voltage measurement of 66 kV bus before commissioning the SVC

Fig. 11 Voltage measurement of 66 kV bus after commissioning – note the change in scale for the voltage changes

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SVCs in Gansu, China

5.1

Application Background

The second 750 kV transmission corridor, illustrated in Fig. 12, from Xinjiang grid to Northwest China, is one of the largest with 3600 MW transmission capacity. It comprises 6 substations and 12 lines over a transmission length of around 2160 km.

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Hami

70km

Hami converter station

420

South of Hami 300

360 300

285km

69km

166km 360 390

300 300

Shazhou SVC(-360MVar~360MVar)

Dunhuang

390

337km 390

Iqe

390

210

330 210

178km 210

210

Qaidam Fig. 12 The second 750 kV transmission corridor

The major problem of the Xinjiang AC power transmission system is an infeed of 1376 MW wind power at Jiuquan, near Shazhou station in Gansu Province. It caused voltage stability problems and a reactive power imbalance because of the dynamic reactive demands triggered by the active power fluctuation from the wind power turbines. The situation would become worse after the completion of the Jiuquan wind power farm. The large amplitude and fast fluctuation of the wind power would cause frequent load flow and voltage fluctuation in the transmission link from the Xinjiang grid to Northwest China. The Shazhou 750 kV substation is one of the six substations along the second transmission corridor. The maximum voltage fluctuation at the Shazhou substation reached 30 kV during heavy load periods in 2015. Therefore, a dynamic reactive compensation device (SVC) has been installed at the substation to reduce the voltage fluctuation and enhance the stability of the power grid. The SVC installed in the Shazhou 750 kV substation is able to operate in the following control modes: 1. Steady-state constant reactive power control mode 2. Steady-state constant voltage control mode 3. Remote control mode

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4. Local control mode 5. Coordinated control mode During normal operation, the SVC is operated in constant voltage control mode.

5.2

SVC System Structure and Operation Parameters

The SVC installed in the Shazhou 750 kV substation is owned by the SGCC and was provided by NR Electric Co., Ltd. The first stage with a rating of 360 Mvar SVC was put into operation in June 2013, and an additional SVC with a rating of 480 Mvar may be installed in the future. Two 66 kV/180 Mvar SVCs were installed in the first stage, both of which were made up of a 360 Mvar TCR and a 180 Mvar FC. The SLD of the two 66 kV/180 Mvar SVCs is shown in Fig. 13. The main technical parameters of each of the two SVCs are shown in Table 3. The layout of one SVC is shown in Fig. 14. The land occupation is around 1700 m2. The control and protection system, valve cooling system, and three-phase 750kV

66kV

66kV Bus I-2

66kV Bus I-1

TCR -360Mvar

FC3 FC5 63.5Mvar 59Mvar

FC7 TCR 57.5Mvar -360Mvar

FC3 FC5 FC7 63.5Mvar 59Mvar 57.5Mvar

Fig. 13 SLD of the two SVCs at the Shazhou 750 kV substation

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Table 3 Main technical parameters of each of the two SVCs Parameter SVC rating

Step-down transformer

Semiconductor devices

Voltage (kV) SVC capacity (Mvar) Connection type TCR rating (Mvar) Connection type Ratio (kV) Capacity (MVA) Type Reverse blocking voltage(V) Average on-state current (A)

Redundancy (%) Overload capability (current/time) Cooling method Full-load SVC valve losses (%) Estimated service life (year)

Water Cooling Radiators

Value 66 180/+180 Delta 360 Ia0i0(YNa0d11) 765√3/345/√3  2  2.5%/66 kV 700 Thyristor 6500 2800 10 None Water cooling 0.2 30

Water Cooling System

Valve Towers

Control Room

Filter Capacitors

Filter Reactors

TCR Reactors

Fig. 14 #1 SVC layout

valve towers are arranged indoors. The water cooling radiators, TCR, filter capacitors and reactors, earthing switch, arrester, and circuit breakers are arranged outdoors. The TCR valves are arranged in a valve hall, and the valves are cooled by a pumped water cooling system. The TCR valves in the 750 kV Shazhou substation are shown in Fig. 15.

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Fig. 15 TCR valve of #1 SVC of Shazhou substation

Fig. 16 Outdoor equipment of Shazhou substation SVCs

The outdoor equipment including all SVC branches and the valve buildings are shown in Fig. 16. The valve buildings are located in the center of Fig. 16.

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System Performance

During the engineering field test, the ability to output rated reactive power and the ability to control reactive power to an accuracy better than or equal to the technical requirement were proven. The step response of the SVC in Shazhou 750 kV substation is shown in Fig. 17. The step response time at the 750 kV busbar voltage is 48.8 ms, which is shorter than the required response time (less than 50 ms was specified). During the operation of the TCR, 3rd, 5th, and 7th filter, the maximum measured overvoltage is 75 kV, which is much lower than the rated insulation level of the SVC reactor. The SVC has played an important role by improving the stability of the power grid since its commissioning in 2013. The SVC can reduce the voltage fluctuation at the 750 kV busbar due to 1000 MW wind power fluctuation from 0.034pu to 0.007pu. The SVC also plays an important role in supporting the 750 kV Shazhou substation bus voltage and improving the power delivery capacity. According to simulation studies of the whole system, the SVC is able to increase the power delivery capacity by about 800 MW when one pole of the 800 kV/8000 MW Hami-Zhengzhou HVDC is blocked due to hardware failure or any other faults. The annual availability of the SVC in the Shazhou substation is higher than 99%. According to the PSD-BPA simulation (a software for power system simulation

Fig. 17 Step response curves.

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and analysis), the SVC is able to reduce the number of trips of wind power farm units (each 500 to 1000 MW) by 1 to 2 units after a serious fault. Therefore, the installation of SVC can help reduce the cost of system instability.

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SVCs in Holeta Substation, Ethiopia

6.1

Application Background

The Ethiopian Electric Power Corporation (EEP Co.) planned to build the Grand Ethiopian Renaissance Dam (GERD) hydropower station on the upper reaches of the Nile. The installed capacity of the hydropower station would be 6,000 MW, which would be one of Africa’s largest hydropower projects. The construction started in 2011 and was planned to be completed in 2016. The hydropower station would send power through four 500 kV transmission lines (GERD-Dedesa-Holeta) after the completion. Because the transmitted power is large and the transmission distance is long, reactive power balance and voltage control issues associated with the transmission system needed to be controlled. In order to provide stable operation of the power grid after the completion of the power plant and transmission system, EEP Co. installed a 900 Mvar SVC system in the Holeta substation. The SVCs installed in the Holeta substation was designed to operate in the following control modes: 1. 2. 3. 4. 5. 6.

Steady-state constant reactive power control mode Steady-state constant voltage control mode with reactive power reserve; Remote control mode Local control mode Coordinated control mode Independent control mode

6.2

System Performance

The engineering field tests verified that the SVC has the capability to stabilize the system voltage by providing fast reactive power support, thereby accelerating the recovery of the system voltage. The step response time of the SVC in Holeta substation satisfies the specified response time (less than 50 ms), as shown in Fig. 18 (Huang et al. 2016). The SVCs in Holeta substation have worked as expected since they entered commercial operation. The availability of the SVCs has reached 99.5%. As the GERD project has not been completed due to political reasons, the SVCs are currently used to provide voltage control for the Ethiopian grid. As the short circuit capacity of the Ethiopian power grid is very low, any fault such as single-phase-to-earth fault may cause large fluctuation of the power grid voltage, which may lead to power outages. According to the feedback from the EEP Co.,

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Fig. 18 Step response on the 400 kV side in the Holeta substation

the voltage of the power grid has been effectively controlled since the SVC was put into operation and the number of power outages has been reduced considerably.

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SVC Merlatière and Domloup in West France

7.1

Application Background

The Brittany and Vendée regions in West France boast breathtaking landscapes and beautiful coastlines. At times, however, these regions are susceptible to electric outages during peak demands. In 2011, the French Utility, Réseau de Transport d’Electricité (RTE), decided to address this issue by installing in these regions two large Static Var Compensators of +/ 250 Mvar each, the highest rated power ever installed in France. La Merlatière in Vendée and Domloup in Brittany were the two sites selected for the SVC installations. The main objective was to strengthen and enhance the French network stability and quality in case of large amplitude voltage variations. The first design criteria were that the SVCs would ensure a high level of availability and performance. Accordingly, the SVC would help to maintain the network voltage with regard to the electrical load variation by absorbing or supplying the necessary reactive power within tens of milliseconds.

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System Structure and Operating Parameters

Each SVC is composed of a star-delta step-down transformer, an MSE (mechanically switched equipment), a blocking reactor, a thyristor-controlled reactor (TCR), and a fifth harmonic filter. The single-line diagram (SLD) of the SVC is shown in Fig. 19. The blocking reactor results in an improvement of harmonic performance of the SVC, an optimization of SVC losses, and a reduction of SVC audible noise. One important constraint was the maximum noise level at the SVC boundary (