POWER SYETEM STABILITY AND CONTROL

Power System Stability and Control 00_Kundur_FM_i-xxii.indd 1 05/04/22 4:57 PM

00_Kundur_FM_i-xxii.indd 2 05/04/22 4:57 PM

Power System Stability and Control Prabha S. Kundur Om P. Malik Second Edition New York Chicago San Francisco Athens London Madrid Mexico City Milan New Delhi Singapore Sydney Toronto 00_Kundur_FM_i-xxii.indd 3 05/04/22 4:57 PM

Library of Congress Cataloging-in-Publication Data Names: Kundur, P. (Prabha) author. | Malik, Om P., author.  Title: Power system stability and control / Prabha S. Kundur, Om P. Malik.  Description: Second edition. | New York : McGraw Hill Education, 2022. | Includes bibliographical references and index. | Summary: “This is a comprehensive guide to power system stability and control, written as a professional and student reference”—Provided by publisher.  Identifiers: LCCN 2021062400 | ISBN 9781260473544 | ISBN 9781260473551 (ebook) Subjects: LCSH: Electric power system stability. | Electric power systems—Control. Classification: LCC TK1005 .K86 2022 | DDC 621.31—dc23/eng/20220207 LC record available at https://lccn.loc.gov/2021062400 Information contained in this work has been obtained by McGraw Hill from sources believed to be reliable. However, neither McGraw Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Sponsoring Editor Lara Zoble Editorial Supervisor Donna M. Martone Acquisitions Coordinator Elizabeth M. Houde Project Manager Radhika Jolly, KnowledgeWorks Global Ltd. Copy Editor Namita Panda Proofreader Upendra Prasad Indexer Alexandra Nickerson Production Supervisor Pamela A. Pelton Composition KnowledgeWorks Global Ltd. Art Director, Cover Jeff Weeks McGraw Hill books are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com. Power Systems Stability and Control, Second Edition Copyright ©2022, 2001 by McGraw Hill. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval system, without the prior written permission of the publisher. 1 2 3 4 5 6 7 8 9 LSC 25 24 23 22 21 ISBN 978-1-260-47354-4 MHID 1-260-47354-6 The pages within this book were printed on acid-free paper. 00_Kundur_FM_i-xxii.indd 4 05/04/22 4:57 PM

Contents Preface to the First Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Part I General Background 1 General Characteristics of Modern Power Systems . . . . . . . . . . . . . . . 3 1.1 Evolution of Electric Power Systems. . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Structure of the Power System. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Power System Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Operating States of a Power System and Control Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Design and Operating Criteria for Stability. . . . . . . . . . . . . . . . . 13 1.4.1 Normal Design Contingencies. . . . . . . . . . . . . . . . . . . . . 14 1.4.2 Extreme Contingency Assessment. . . . . . . . . . . . . . . . . 15 1.4.3 Renewable Energy Sources. . . . . . . . . . . . . . . . . . . . . . . 15 1.4.4 System Design for Stability. . . . . . . . . . . . . . . . . . . . . . . 16 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Introduction to the Power System Stability Problem . . . . . . . . . . . . 19 2.1 Basic Concepts and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.1 Rotor Angle Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1.2 Voltage Stability and Voltage Collapse. . . . . . . . . . . . . . 27 2.1.3 Mid-Term and Long-Term Stability. . . . . . . . . . . . . . . . 32 2.2 Classification of Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Historical Review of Stability Problems . . . . . . . . . . . . . . . . . . . . 34 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Part II Equipment Characteristics and Modeling 3 Synchronous Machine Theory and Modeling . . . . . . . . . . . . . . . . . . . 43 3.1 Physical Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.1 Armature and Field Structure. . . . . . . . . . . . . . . . . . . . . 43 3.1.2 Machines with Multiple Pole Pairs. . . . . . . . . . . . . . . . . 46 3.1.3 MMF Waveforms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.4 Direct and Quadrature Axes. . . . . . . . . . . . . . . . . . . . . . 49 3.2 Mathematical Description of a Synchronous Machine. . . . . . . . 49 3.2.1 Review of Magnetic Circuit Equations. . . . . . . . . . . . . . 50 3.2.2 Basic Equations of a Synchronous Machine. . . . . . . . . 53 3.3 The dq0 Transformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 v 00_Kundur_FM_i-xxii.indd 5 05/04/22 4:57 PM

vi Contents 3.4 Per Unit Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.1 Per Unit System for the Stator Quantities. . . . . . . . . . . 66 3.4.2 Per Unit Stator Voltage Equations. . . . . . . . . . . . . . . . . . 67 3.4.3 Per Unit Rotor Voltage Equations. . . . . . . . . . . . . . . . . . 68 3.4.4 Stator Flux Linkage Equations. . . . . . . . . . . . . . . . . . . . . 68 3.4.5 Rotor Flux Linkage Equations. . . . . . . . . . . . . . . . . . . . . 68 3.4.6 Per Unit System for the Rotor. . . . . . . . . . . . . . . . . . . . . 69 3.4.7 Per Unit Power and Torque. . . . . . . . . . . . . . . . . . . . . . . 71 3.4.8 Alternative per Unit Systems and Transformations . . . 72 3.4.9 Summary of per Unit Equations. . . . . . . . . . . . . . . . . . . 73 3.5 Equivalent Circuits for Direct and Quadrature Axes. . . . . . . . . . 75 3.6 Steady-State Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.6.1 Voltage, Current, and Flux Linkage Relationships. . . . 80 3.6.2 Phasor Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.6.3 Rotor Angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.6.4 Steady-State Equivalent Circuit. . . . . . . . . . . . . . . . . . . . 84 3.6.5 Procedure for Computing Steady-State Values. . . . . . . 85 3.7 Electrical Transient Performance Characteristics. . . . . . . . . . . . . 89 3.7.1 Short-Circuit Current in a Simple RL Circuit. . . . . . . . 89 3.7.2 Three-Phase Short-Circuit at the Terminals of a Synchronous Machine. . . . . . . . . . . . . . . . . . . . . . . . 90 3.7.3 Elimination of dc Offset in Short-Circuit Current. . . . . 91 3.8 Magnetic Saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.8.1 Open-Circuit and Short-Circuit Characteristics. . . . . . 92 3.8.2 Representation of Saturation in Stability Studies. . . . . 94 3.8.3 Improved Modeling of Saturation. . . . . . . . . . . . . . . . . 97 3.9 Equations of Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.9.1 Review of Mechanics of Motion. . . . . . . . . . . . . . . . . . . 105 3.9.2 Swing Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.9.3 Mechanical Starting Time. . . . . . . . . . . . . . . . . . . . . . . . . 108 3.9.4 Calculation of Inertia Constant. . . . . . . . . . . . . . . . . . . . 108 3.9.5 Representation in System Studies. . . . . . . . . . . . . . . . . . 110 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4 Synchronous Machine Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.1 Operational Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.2 Standard Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 4.2.1 Parameters Based on Classical Definitions. . . . . . . . . . 116 4.2.2 Accurate Expressions for Standard Parameters. . . . . . 119 4.2.3 Parameters Including Unequal Mutual Effects. . . . . . . 120 4.3 Frequency-Response Characteristics. . . . . . . . . . . . . . . . . . . . . . . 127 4.3.1 Armature Time Constant. . . . . . . . . . . . . . . . . . . . . . . . . 128 4.4 Determination of Synchronous Machine Parameters. . . . . . . . . 129 4.4.1 Enhanced Short-Circuit Tests. . . . . . . . . . . . . . . . . . . . . . 129 4.4.2 Decrement Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 00_Kundur_FM_i-xxii.indd 6 05/04/22 4:57 PM

Contents vii 4.4.3 Frequency-Response Tests. . . . . . . . . . . . . . . . . . . . . . . . 130 4.4.4 Calculation of Machine Parameters from Design Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5 Synchronous Machine Representation in Stability Studies . . . . . . . 135 5.1 Simplifications Essential for Large-Scale Studies. . . . . . . . . . . . . 135 5.1.1 Neglect of Stator pψ Terms. . . . . . . . . . . . . . . . . . . . . . . . 135 5.1.2 Neglecting the Effect of Speed Variations on Stator Voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.2 Simplified Model with Amortisseurs Neglected. . . . . . . . . . . . . 143 5.3 Constant Flux Linkage Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.3.1 Classical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 5.3.2 Constant Flux Linkage Model Including the Effects of Subtransient Circuits. . . . . . . . . . . . . . . . . . . . 150 5.3.3 Summary of Simple Models for Different Time Frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.4 Reactive Capability Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.4.1 Reactive Capability Curves. . . . . . . . . . . . . . . . . . . . . . . 152 5.4.2 V Curves and Compounding Curves. . . . . . . . . . . . . . . 157 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 6 AC Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.1 Transmission Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.1.1 Electrical Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . 159 6.1.2 Performance Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . 161 6.1.3 Natural or Surge Impedance Loading. . . . . . . . . . . . . . 163 6.1.4 Equivalent Circuit of a Transmission Line. . . . . . . . . . . 164 6.1.5 Typical Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6.1.6 Performance Requirements of Power Transmission Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 6.1.7 Voltage and Current Profile under No-Load. . . . . . . . . 169 6.1.8 Voltage-Power Characteristics. . . . . . . . . . . . . . . . . . . . . 173 6.1.9 Power Transfer and Stability Considerations. . . . . . . . 176 6.1.10 Effect of Line Loss on V-P and Q-P Characteristics. . . . 179 6.1.11 Thermal Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.1.12 Loadability Characteristics. . . . . . . . . . . . . . . . . . . . . . . . 182 6.2 Transformers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.2.1 Representation of Two-Winding Transformers. . . . . . . 185 6.2.2 Representation of Three-Winding Transformers. . . . . . 192 6.2.3 Phase-Shifting Transformers. . . . . . . . . . . . . . . . . . . . . . 197 6.3 Transfer of Power between Active Sources. . . . . . . . . . . . . . . . . . 200 6.4 Power-Flow Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 6.4.1 Network Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6.4.2 Gauss-Seidel Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 00_Kundur_FM_i-xxii.indd 7 05/04/22 4:57 PM

viii Contents 6.4.3 Newton-Raphson (N-R) Method. . . . . . . . . . . . . . . . . . . 209 6.4.4 Fast Decoupled Load-Flow (FDLF) Methods. . . . . . . . 212 6.4.5 Comparison of the Power-Flow Solution Methods. . . . 214 6.4.6 Sparsity-Oriented Triangular Factorization. . . . . . . . . . 215 6.4.7 Network Reduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 7 Power System Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.1 Basic Load-Modeling Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.1.1 Static Load Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.1.2 Dynamic Load Models. . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7.2 Modeling of Induction Motors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 7.2.1 Equations of an Induction Machine. . . . . . . . . . . . . . . . 225 7.2.2 Steady-State Characteristics. . . . . . . . . . . . . . . . . . . . . . . 232 7.2.3 Alternative Rotor Constructions. . . . . . . . . . . . . . . . . . . 236 7.2.4 Representation of Saturation. . . . . . . . . . . . . . . . . . . . . . 239 7.2.5 Per Unit Representation. . . . . . . . . . . . . . . . . . . . . . . . . . 240 7.2.6 Representation in Stability Studies. . . . . . . . . . . . . . . . . 242 7.3 Synchronous Motor Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 7.4 Acquisition of Load-Model Parameters. . . . . . . . . . . . . . . . . . . . . 246 7.4.1 Measurement-Based Approach. . . . . . . . . . . . . . . . . . . . 247 7.4.2 Component-Based Approach. . . . . . . . . . . . . . . . . . . . . . 249 7.4.3 Sample Load Characteristics. . . . . . . . . . . . . . . . . . . . . . 250 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 8 Excitation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8.1 Excitation System Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . 255 8.1.1 Generator Considerations. . . . . . . . . . . . . . . . . . . . . . . . 255 8.1.2 Power System Considerations. . . . . . . . . . . . . . . . . . . . . 256 8.2 Elements of an Excitation System. . . . . . . . . . . . . . . . . . . . . . . . . . 256 8.3 Types of Excitation Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 8.3.1 DC Excitation Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 258 8.3.2 AC Excitation Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 259 8.3.3 Static Excitation Systems. . . . . . . . . . . . . . . . . . . . . . . . . 261 8.3.4 Recent Developments and Future Trends. . . . . . . . . . . 264 8.4 Dynamic Performance Measures. . . . . . . . . . . . . . . . . . . . . . . . . . 265 8.4.1 Large-Signal Performance Measures. . . . . . . . . . . . . . . 265 8.4.2 Small-Signal Performance Measures. . . . . . . . . . . . . . . 267 8.5 Control and Protective Functions. . . . . . . . . . . . . . . . . . . . . . . . . . 270 8.5.1 AC and DC Regulators. . . . . . . . . . . . . . . . . . . . . . . . . . . 270 8.5.2 Excitation System Stabilizing Circuits. . . . . . . . . . . . . . 270 8.5.3 Power System Stabilizer. . . . . . . . . . . . . . . . . . . . . . . . . . 272 8.5.4 Load Compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 8.5.5 Underexcitation Limiter. . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.5.6 Overexcitation Limiter. . . . . . . . . . . . . . . . . . . . . . . . . . . 274 8.5.7 Volts-per-Hertz Limiter and Protection. . . . . . . . . . . . . 275 8.5.8 Field-Shorting Circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . 276 00_Kundur_FM_i-xxii.indd 8 05/04/22 4:57 PM

Contents ix 8.6 Modeling of Excitation Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8.6.1 Per Unit System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 8.6.2 Modeling of Excitation System Components. . . . . . . . 281 8.6.3 Modeling of Complete Excitation Systems. . . . . . . . . . 293 8.6.4 Field Testing for Model Development and Verification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 9 Prime Movers and Energy Supply Systems . . . . . . . . . . . . . . . . . . . . . 305 9.1 Hydraulic Turbines and Governing Systems. . . . . . . . . . . . . . . . 305 9.1.1 Hydraulic Turbine Transfer Function. . . . . . . . . . . . . . . 306 9.1.2 Nonlinear Turbine Model Assuming Inelastic Water Column. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 9.1.3 Governors for Hydraulic Turbines. . . . . . . . . . . . . . . . . 318 9.1.4 Detailed Hydraulic System Model. . . . . . . . . . . . . . . . . 326 9.1.5 Guidelines for Modeling Hydraulic Turbines. . . . . . . . 335 9.2 Steam Turbines and Governing Systems. . . . . . . . . . . . . . . . . . . . 336 9.2.1 Modeling of Steam Turbines. . . . . . . . . . . . . . . . . . . . . . 339 9.2.2 Steam Turbine Controls. . . . . . . . . . . . . . . . . . . . . . . . . . 348 9.2.3 Steam Turbine Off-Frequency Capability . . . . . . . . . . . 358 9.3 Thermal Energy Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 9.3.1 Fossil-Fuel Energy Systems. . . . . . . . . . . . . . . . . . . . . . . 362 9.3.2 Nuclear-Based Energy Systems. . . . . . . . . . . . . . . . . . . . 367 9.3.3 Modeling of Thermal Energy Systems. . . . . . . . . . . . . . 371 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 10 High-Voltage Direct-Current Transmission . . . . . . . . . . . . . . . . . . . . . 375 10.1 HVDC System Configurations and Components. . . . . . . . . . . . . 376 10.1.1 Classification of HVDC Links. . . . . . . . . . . . . . . . . . . . . 376 10.1.2 Components of HVDC Transmission System. . . . . . . . 378 10.2 Converter Theory and Performance Equations. . . . . . . . . . . . . . 379 10.2.1 Valve Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 10.2.2 Converter Circuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 10.2.3 Converter Transformer Rating. . . . . . . . . . . . . . . . . . . . . 399 10.2.4 Multiple-Bridge Converters. . . . . . . . . . . . . . . . . . . . . . . 399 10.3 Abnormal Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 10.3.1 Arc-Back (Backfire). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 10.3.2 Commutation Failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 10.4 Control of HVDC Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 10.4.1 Basic Principles of Control. . . . . . . . . . . . . . . . . . . . . . . . 406 10.4.2 Control Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . 417 10.4.3 Converter Firing Control Systems. . . . . . . . . . . . . . . . . . 418 10.4.4 Valve Blocking and Bypassing. . . . . . . . . . . . . . . . . . . . . 422 10.4.5 Starting, Stopping, and Power Flow Reversal. . . . . . . . 423 10.4.6 Controls for Enhancement of AC System Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 00_Kundur_FM_i-xxii.indd 9 05/04/22 4:57 PM

x Contents 10.5 Harmonics and Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 10.5.1 AC Side Harmonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 10.5.2 DC Side Harmonics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 10.6 Influence of AC System Strength on AC/DC System Interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 10.6.1 Short-Circuit Ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 10.6.2 Reactive Power and AC System Strength. . . . . . . . . . . 429 10.6.3 Problems with Low ESCR Systems. . . . . . . . . . . . . . . . . 430 10.6.4 Solutions to Problems Associated with Weak Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 10.6.5 Effective Inertia Constant. . . . . . . . . . . . . . . . . . . . . . . . . 431 10.6.6 Forced Commutation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 10.7 Responses to DC and AC System Faults. . . . . . . . . . . . . . . . . . . . 433 10.7.1 DC Line Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 10.7.2 Converter Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.7.3 AC System Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 10.8 Multiterminal HVDC Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 10.8.1 MTDC Network Configurations. . . . . . . . . . . . . . . . . . . 437 10.8.2 Control of MTDC Systems. . . . . . . . . . . . . . . . . . . . . . . . 439 10.9 Modeling of HVDC Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 10.9.1 Representation for Power Flow Solution. . . . . . . . . . . . 442 10.9.2 Per Unit System for DC Quantities. . . . . . . . . . . . . . . . . 457 10.9.3 Representation for Stability Studies. . . . . . . . . . . . . . . . 458 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 11 Control of Active Power and Reactive Power . . . . . . . . . . . . . . . . . . . 471 11.1 Active Power and Frequency Control . . . . . . . . . . . . . . . . . . . . . . 471 11.1.1 Fundamentals of Speed Governing. . . . . . . . . . . . . . . . . 472 11.1.2 Control of Generating Unit Power Output. . . . . . . . . . 479 11.1.3 Composite Regulating Characteristic of Power Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 11.1.4 Response Rates of Turbine-Governor Systems. . . . . . . 483 11.1.5 Fundamentals of Automatic Generation Control. . . . . 485 11.1.6 Implementation of AGC. . . . . . . . . . . . . . . . . . . . . . . . . . 499 11.1.7 Underfrequency Load Shedding. . . . . . . . . . . . . . . . . . . 503 11.2 Reactive Power and Voltage Control. . . . . . . . . . . . . . . . . . . . . . . 506 11.2.1 Production and Absorption of Reactive Power. . . . . . . 506 11.2.2 Methods of Voltage Control. . . . . . . . . . . . . . . . . . . . . . . 507 11.2.3 Shunt Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508 11.2.4 Shunt Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 11.2.5 Series Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 11.2.6 Synchronous Condensers. . . . . . . . . . . . . . . . . . . . . . . . . 515 11.2.7 Static Var Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 11.2.8 Principles of Transmission System Compensation. . . . 528 11.2.9 Modeling of Reactive Compensating Devices. . . . . . . . 541 11.2.10 Application of Tap-Changing Transformers to Transmission Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 00_Kundur_FM_i-xxii.indd 10 05/04/22 4:57 PM

Contents xi 11.2.11 Distribution System Voltage Regulation. . . . . . . . . . . . . 548 11.2.12 Modeling of Transformer ULTC Control Systems. . . . 551 11.3 Power Flow Analysis Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . 553 11.3.1 Prefault Power Flows. . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 11.3.2 Postfault Power Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 Part III System Stability: Physical Aspects, Analysis, and Improvement 12 Small-Signal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 12.1 Fundamental Concepts of Stability of Dynamic Systems. . . . . . 563 12.1.1 State-Space Representation. . . . . . . . . . . . . . . . . . . . . . . 563 12.1.2 Stability of a Dynamic System. . . . . . . . . . . . . . . . . . . . . 565 12.1.3 Linearization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 12.1.4 Analysis of Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 12.2 Eigenproperties of the State Matrix. . . . . . . . . . . . . . . . . . . . . . . . 569 12.2.1 Eigenvalues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569 12.2.2 Eigenvectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 12.2.3 Modal Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570 12.2.4 Free Motion of a Dynamic System. . . . . . . . . . . . . . . . . 571 12.2.5 Mode Shape, Sensitivity, and Participation Factor. . . . . 573 12.2.6 Controllability and Observability. . . . . . . . . . . . . . . . . . 576 12.2.7 The Concept of Complex Frequency . . . . . . . . . . . . . . . 577 12.2.8 Relationship between Eigenproperties and Transfer Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 12.2.9 Computation of Eigenvalues. . . . . . . . . . . . . . . . . . . . . . 584 12.3 Small-Signal Stability of a Single-Machine Infinite Bus System. . . . 584 12.3.1 Generator Represented by the Classical Model. . . . . . 585 12.3.2 Effects of Synchronous Machine Field Circuit Dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 12.4 Effects of Excitation System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 12.5 Power System Stabilizer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 12.6 System State Matrix with Amortisseurs. . . . . . . . . . . . . . . . . . . . . 626 12.7 Small-Signal Stability of Multimachine Systems. . . . . . . . . . . . . 634 12.8 Special Techniques for Analysis of Very Large Systems. . . . . . . 640 12.9 Characteristics of Small-Signal Stability Problems. . . . . . . . . . . . 654 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 13 Transient Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661 13.1 An Elementary View of Transient Stability. . . . . . . . . . . . . . . . . . 661 13.2 Numerical Integration Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . 668 13.2.1 Euler Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 13.2.2 Modified Euler Method. . . . . . . . . . . . . . . . . . . . . . . . . . 669 13.2.3 Runge-Kutta Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 13.2.4 Numerical Stability of Explicit Integration Methods. . . . 672 13.2.5 Implicit Integration Methods. . . . . . . . . . . . . . . . . . . . . . 672 00_Kundur_FM_i-xxii.indd 11 05/04/22 4:57 PM

xii Contents 13.3 Simulation of Power System Dynamic Response. . . . . . . . . . . . . 677 13.3.1 Structure of the Power System Model. . . . . . . . . . . . . . 677 13.3.2 Synchronous Machine Representation. . . . . . . . . . . . . . 678 13.3.3 Excitation System Representation. . . . . . . . . . . . . . . . . . 683 13.3.4 Transmission Network and Load Representation. . . . 685 13.3.5 Overall System Equations. . . . . . . . . . . . . . . . . . . . . . . . 686 13.3.6 Solution of Overall System Equations. . . . . . . . . . . . . . 687 13.4 Analysis of Unbalanced Faults. . . . . . . . . . . . . . . . . . . . . . . . . . . . 696 13.4.1 Introduction to Symmetrical Components. . . . . . . . . . 696 13.4.2 Sequence Impedances of Synchronous Machines. . . . . 700 13.4.3 Sequence Impedances of Transmission Lines. . . . . . . . 705 13.4.4 Sequence Impedances of Transformers. . . . . . . . . . . . . 706 13.4.5 Simulation of Different Types of Faults. . . . . . . . . . . . . 708 13.4.6 Representation of Open-Conductor Conditions. . . . . . 717 13.5 Performance of Protective Relaying. . . . . . . . . . . . . . . . . . . . . . . . 720 13.5.1 Transmission Line Protection. . . . . . . . . . . . . . . . . . . . . . 721 13.5.2 Fault-Clearing Times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 13.5.3 Relaying Quantities during Swings. . . . . . . . . . . . . . . . 729 13.5.4 Evaluation of Distance Relay Performance during Swings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733 13.5.5 Prevention of Tripping during Transient Conditions. . . . 734 13.5.6 Automatic Line Reclosing . . . . . . . . . . . . . . . . . . . . . . . . 736 13.5.7 Generator Out-of-Step Protection. . . . . . . . . . . . . . . . . . 737 13.5.8 Loss-of-Excitation Protection. . . . . . . . . . . . . . . . . . . . . . 740 13.6 Case Study of Transient Stability of a Large System. . . . . . . . . . 745 13.7 Direct Method of Transient Stability Analysis. . . . . . . . . . . . . . . 750 13.7.1 Description of the Transient Energy Function (TEF) Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 13.7.2 Analysis of Practical Power Systems. . . . . . . . . . . . . . . 754 13.7.3 Limitations of the Direct Methods. . . . . . . . . . . . . . . . . 760 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760 14 Voltage Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765 14.1 Basic Concepts Related to Voltage Stability. . . . . . . . . . . . . . . . . . 765 14.1.1 Transmission System Characteristics. . . . . . . . . . . . . . . 766 14.1.2 Generator Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . 770 14.1.3 Load Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 772 14.1.4 Characteristics of Reactive Compensating Devices. . . . 773 14.2 Voltage Collapse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776 14.2.1 Typical Scenario of Voltage Collapse. . . . . . . . . . . . . . . 777 14.2.2 General Characterization Based on Actual Incidents. . . . 778 14.2.3 Classification of Voltage Stability. . . . . . . . . . . . . . . . . . 779 14.3 Voltage Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779 14.3.1 Modeling Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . 780 14.3.2 Dynamic Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781 14.3.3 Static Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 00_Kundur_FM_i-xxii.indd 12 05/04/22 4:57 PM

Contents xiii 14.3.4 Determination of Shortest Distance to Instability. . . . . 804 14.3.5 The Continuation Power Flow Analysis. . . . . . . . . . . . 808 14.4 Prevention of Voltage Collapse. . . . . . . . . . . . . . . . . . . . . . . . . . . . 814 14.4.1 System Design Measures. . . . . . . . . . . . . . . . . . . . . . . . . 814 14.4.2 System-Operating Measures. . . . . . . . . . . . . . . . . . . . . . 815 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816 15 Subsynchronous Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819 15.1 Turbine Generator Torsional Characteristics. . . . . . . . . . . . . . . . . 819 15.1.1 Shaft System Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819 15.1.2 Torsional Natural Frequencies and Mode Shapes. . . . 826 15.2 Torsional Interaction with Power System Controls. . . . . . . . . . . 828 15.2.1 Interaction with Generator Excitation Controls. . . . . . 829 15.2.2 Interaction with Speed Governors. . . . . . . . . . . . . . . . . 835 15.2.3 Interaction with Nearby DC Converters. . . . . . . . . . . . 836 15.3 Subsynchronous Resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 838 15.3.1 Characteristics of Series Capacitor-Compensated Transmission Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . 838 15.3.2 Self-Excitation due to Induction Generator Effect. . . . 840 15.3.3 Torsional Interaction Resulting in SSR. . . . . . . . . . . . . . 840 15.3.4 Analytical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841 15.3.5 Countermeasures to SSR Problems. . . . . . . . . . . . . . . . . 846 15.4 Impact of Network-Switching Disturbances. . . . . . . . . . . . . . . . . 847 15.5 Torsional Interaction between Closely Coupled Units. . . . . . . . 850 15.6 Hydro Generator Torsional Characteristics. . . . . . . . . . . . . . . . . . 852 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852 16 Midterm and Long-Term Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 16.1 Nature of System Response to Severe Upsets. . . . . . . . . . . . . . . . 855 16.2 Distinction between Midterm and Long-Term Stability. . . . . . . 858 16.3 Power Plant Response during Severe Upsets. . . . . . . . . . . . . . . . 860 16.3.1 Thermal Power Plants. . . . . . . . . . . . . . . . . . . . . . . . . . . . 860 16.3.2 Hydro Power Plants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861 16.4 Simulation of Long-Term Dynamic Response . . . . . . . . . . . . . . . 865 16.4.1 Purpose of Long-Term Dynamic Simulations. . . . . . . . 865 16.4.2 Modeling Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . 865 16.4.3 Numerical Integration Techniques. . . . . . . . . . . . . . . . . 866 16.5 Case Studies of Severe System Upsets. . . . . . . . . . . . . . . . . . . . . . 867 16.5.1 Case Study Involving an Overgenerated Island. . . . . . 867 16.5.2 Case Study Involving an Undergenerated Island. . . . . 869 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 876 17 Methods of Improving Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 17.1 Transient Stability Enhancement. . . . . . . . . . . . . . . . . . . . . . . . . . . 879 17.1.1 High-Speed Fault Clearing. . . . . . . . . . . . . . . . . . . . . . . . 880 17.1.2 Reduction of Transmission System Reactance . . . . . . . 880 17.1.3 Regulated Shunt Compensation. . . . . . . . . . . . . . . . . . . 881 00_Kundur_FM_i-xxii.indd 13 05/04/22 4:57 PM

xiv Contents 17.1.4 Dynamic Braking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881 17.1.5 Reactor Switching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 882 17.1.6 Independent-Pole Operation of Circuit Breakers. . . . . 882 17.1.7 Single-Pole Switching. . . . . . . . . . . . . . . . . . . . . . . . . . . . 882 17.1.8 Steam Turbine Fast-Valving. . . . . . . . . . . . . . . . . . . . . . . 885 17.1.9 Generator Tripping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891 17.1.10 Controlled System Separation and Load Shedding. . . . 893 17.1.11 High-Speed Excitation Systems. . . . . . . . . . . . . . . . . . . . 894 17.1.12 Discontinuous Excitation Control. . . . . . . . . . . . . . . . . . 894 17.1.13 Control of HVDC Transmission Links. . . . . . . . . . . . . . 897 17.2 Small-Signal Stability Enhancement. . . . . . . . . . . . . . . . . . . . . . . . 899 17.2.1 Power System Stabilizers. . . . . . . . . . . . . . . . . . . . . . . . . 899 17.2.2 Supplementary Control of Static Var Compensators. . . . 912 17.2.3 Supplementary Control of HVDC Transmission Links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933 00_Kundur_FM_i-xxii.indd 14 05/04/22 4:57 PM

Preface to the First Edition This book is concerned with understanding, modeling, analyzing, and mitigating power system stability and control problems. Such problems constitute very important considerations in the planning, design, and operation of modem power systems. The complexity of power systems is continually increasing because of the growth in interconnections and use of new technologies. At the same time, financial and regulatory constraints have forced utilities to operate the systems nearly at stability limits. These two factors have created new types of stability problems. Greater reliance is, therefore, being placed on the use of special control aids to enhance system security, facilitate economic design, and provide greater flexibility of system operation. In addition, advances in computer technology, numerical analysis, control theory, and equipment modeling have contributed to the development of improved analytical tools and better system design procedures. The primary motivation for writing this book has been to describe these new developments and to provide a comprehensive treatment of the subject. The text presented in this book draws together material on power system stability and control from many sources: graduate courses I have taught at the University of Toronto since 1979, several EPRI research projects (RP1208, RP2447, RP3040, RP3141, RP4000, RP849, and RP997) with which I have been closely associated, and a vast number of technical papers published by the IEEE, IEE, and CIGRE. This book is intended to meet the needs of practicing engineers associated with the electric utility industry as well as those of graduate students and researchers. Books on this subject are at least 15 years old; some well-known books are 30 to 40 years old. In the absence of a comprehensive text, courses on power system stability often tend to address narrow aspects of the subject with emphasis on special analytical techniques. Moreover, both the teaching staff and students do not have ready access to information on the practical aspects. Since the subject requires an understanding of a wide range of areas, practicing engineers just entering this field are faced with the formidable task of gathering the necessary information from widely scattered sources. This book attempts to fill the gap by providing the necessary fundamentals, explaining the practical aspects, and giving an integrated treatment of the latest developments in modeling techniques and analytical tools. It is divided into three parts. Part I provides general background information in two chapters. Chapter 1 describes xv 00_Kundur_FM_i-xxii.indd 15 05/04/22 4:57 PM

xvi Preface to the First Edition the structure of modem power systems and identifies different levels of control. Chapter 2 introduces the stability problem and provides basic concepts, definitions, and classification. Part II of the book, comprising Chapters 3 to 11, is devoted to equipment characteristics and modeling. System stability is affected by the characteristics of every major element of the power system. A knowledge of the physical characteristics of the individual elements and their capabilities is essential for the understanding of system stability. The representation of these elements by means of appropriate mathematical models is critical to the analysis of stability. Chapters 3 to 10 are devoted to generators, excitation systems, prime movers, ac and dc transmission, and system loads. Chapter 11 describes the principles of active power and reactive power control and develops models for the control equipment. Part III, comprising Chapters 12 to 17, considers different categories of power system stability. Emphasis is placed on physical understanding of many facets of the stability phenomena. Methods of analysis along with control measures for mitigation of stability problems are described in detail. The notions of power system stability and power system control are closely related. The overall controls in a power system are highly distributed in a hierarchical structure. System stability is strongly influenced by these controls. In each chapter, the theory is developed from simple beginnings and is gradually evolved so that it can be applied to complex practical situations. This is supplemented by a large number of illustrative examples. Wherever appropriate, historical perspectives and past experiences are highlighted. Because this is the first edition, it is likely that some aspects of the subject may not be adequately covered. It is also likely that there may be some errors, typographical or otherwise. I welcome feedback on such errors as well as suggestions for improvements in the event that a second edition should be published. I am indebted to many people who assisted me in the preparation of this book. Baofu Gao and Sainath Moorty helped me with many of the calculations and computer simulations included in the book. Kip Morison, Solomon Yirga, Meir Klein, Chi Tang, and Deepa Kundur also helped me with some of the results presented. Atef Morched, Kip Morison, Ernie Neudorf, Graham Rogers, David Wong, Hamid Hamadanizadeh, Behnam Danai, Saeed Arabi, and Lew Rubino reviewed various chapters of the book and provided valuable comments. David Lee reviewed Chapters 8 and 9 and provided valuable comments and suggestions. I have worked very closely with Mr. Lee for the last 22 years on a number of complex power system stability-related problems; the results of our joint effort are reflected in various parts of the book. Carson Taylor reviewed the manuscript and provided many helpful suggestions for improving the text. In addition, many stimulating discussions I have had with Mr. Taylor, Dr. Charles Concordia, and with Mr. Yakout Mansour helped me develop a better perspective of current and future needs of power system stability analysis. Patti Scott and Christine Hebscher edited the first draft of the manuscript. Janet Kibblewhite edited the final draft and suggested many improvements. I am deeply indebted to Lei Wang and his wife, Xiaolu Meng, for their outstanding work in the preparation of the manuscript, including the illustrations. I wish to take this opportunity to express my gratitude to Mr. Paul L. Dandeno for the encouragement he gave me and the confidence he showed in me during the early 00_Kundur_FM_i-xxii.indd 16 05/04/22 4:57 PM

Preface to the First Edition xvii part of my career at Ontario Hydro. It is because of him that I joined the electric utility industry and then ventured into the many areas of power system dynamic performance covered in this book. I am grateful to the Electric Power Research Institute for sponsoring this book. In particular, I am thankful to Dr. Neal Balu and Mr. Mark Lauby for their inspiration and support. Mark Lauby also reviewed the manuscript and provided many helpful suggestions. I wish to express my appreciation to Liz Doherty and Patty Jones for helping me with the correspondence and other business matters related to this book. Finally, I wish to thank my wife, Geetha Kundur, for her unfailing support and patience during the many months I worked on this book. Prabha Shankar Kundur 00_Kundur_FM_i-xxii.indd 17 05/04/22 4:57 PM

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Preface To quote Dr. Kundur from the Preface to the first edition, most books on power system stability “address narrow aspects of the subject with emphasis on general analytical techniques” and the practicing engineers just entering this field have no access to a source that can quickly provide information on the practical aspects. This book fills that gap “by providing the necessary fundamentals, explaining the practical aspects, and giving an integrated treatment of” modeling, techniques, and analytical tools. In that respect, this book is unique in meeting “the needs of practicing engineers associated with the electric utility industry as well as those of graduate students and researchers.” The primary objective of the book has been maintained in preparing this second edition as there is still no single book on the market specifically devoted to that objective. Although significant new developments in the structure and operation of the power systems have taken place over the past 25 to 30 years, the fundamentals of theory and practice remain the same. Details of new advances in technology are available in specialized books specifically devoted to these developments. Therefore, keeping in tune with the basic objective of the book, major revisions to incorporate these specialized developments have been intentionally avoided. Revisions and changes made, though many, are subtle and may not be self-evident. This is also in accord with the opinions of the reviewers obtained before starting to prepare the revised edition. Some of the reviewers even recommended that absolutely no changes be made. I wish to convey my sincere thanks to the staff, in particular, Lara Zoble, at McGrawHill, for the excellent cooperation and help received during the entire period of preparing this edition of the book. It was a labor of love, though certainly not made easy by the challenges faced in accessing relevant and necessary material due to the restrictions during the COVID-19 epidemic. Finally, I wish to convey my heartfelt thanks to my wife, Margareta Malik, for the patience and support during the preparation of this edition. Om Parkash Malik xix 00_Kundur_FM_i-xxii.indd 19 05/04/22 4:57 PM

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PART I General Background CHAPTER 1 General Characteristics of Modern Power Systems CHAPTER 2 Introduction to the Power System Stability Problem 01-Kundur_ch01_p001-018.indd 1 07/04/22 10:35 AM

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3 CHAPTER 1 General Characteristics of Modern Power Systems Electricity has become all pervasive in the present-day world. A power grid is dedicated to serve a variety of consumers, both large and small, with electrical energy. Development of the power grid is aimed at providing the consumers with electrical energy as economically as possible, and with an acceptable degree of reliability and quality of supply. The term “grid” denotes the entire electric system infrastructure that is also commonly known as “electric power system,” and the two terms “grid” and “power system” are often used interchangeably [1]. With the increased importance of electricity, power system stability plays a very important role in system resilience, that is, the ability to withstand disruptive events and maintain continuity of supply. A general description of electric power systems beginning with a historical sketch of their evolution is given in this introductory chapter. The basic characteristics and structure of modern power systems are then identified. The performance requirements of a properly designed power system and the various levels of controls used to meet these requirements are also described. In addition to providing general background information, this chapter and the next lay the groundwork for the remainder of the book. 1.1 Evolution of Electric Power Systems The commercial use of electricity began in the late 1870s when arc lamps were used for lighthouse illumination and street lighting. The first complete electric power system (comprising a steam-engine-driven dc generator, cable, fuse, meter, and loads)—the historic Pearl Street Station in New York City built by Thomas Edison—began operation in September 1882. This was a dc system supplying power to 59 customers within an area roughly 1.5 km in radius. The load, which consisted entirely of incandescent lamps, was supplied at 110 V through an underground cable system. Within a few years, similar systems were in operation in many large cities in various parts of the world. With the development of motors by Frank Sprague in 1884, motor loads were added to such systems. This was the beginning of what would develop into one of the largest industries in the world. 01-Kundur_ch01_p001-018.indd 3 07/04/22 10:35 AM

4 Part I: General Background In spite of the initial widespread use of dc systems, limitations of the dc systems were becoming increasingly apparent by 1886. They could deliver power only a short distance from the generators. To keep transmission power losses (RI2 ) and voltage drops to acceptable levels, voltage levels had to be high for long-distance power transmission. Such high voltages were not acceptable for generation and consumption of power. Therefore, a convenient means for voltage transformation became a necessity. With the new developments in ac voltage transformation, more ac systems started to be deployed instead of the dc systems. Development of the transformer and ac transmission by L. Gaulard and J.D. Gibbs of Paris, France, led to ac electric power systems. George Westinghouse secured rights to these developments in the United States. In 1886, William Stanley, an associate of Westinghouse, developed and tested a commercially practical transformer and ac distribution system for 150 lamps at Great Barrington, Massachusetts. In 1889, the first ac transmission line in North America, a single-phase line transmitting power at 4,000 V, was put into operation in Oregon between Willamette Falls and Portland, a distance of 21 km. With the development of polyphase systems by Nikola Tesla, the ac system became even more attractive. By 1888, Tesla held several patents on ac motors, generators, transformers, and transmission systems. Westinghouse bought the patents to these early inventions, and they formed the basis of the present-day ac systems. In the 1890s, there was considerable controversy over whether the electric utility industry should be standardized on dc or ac. There were passionate arguments between Edison, who advocated dc, and Westinghouse, who was in favor of ac. By the turn of the century, the ac system had won out over the dc system for the following reasons: • Voltage levels can be easily transformed in ac systems, thus providing the flexibility for use of different voltages for generation, transmission, and consumption. • AC generators are much simpler than dc generators. • AC motors are much simpler and cheaper than dc motors. The first three-phase line in North America went into operation in 1893—a 2,300 V, 12-km line in southern California. Around this time, ac was chosen at Niagara Falls because dc was not practical for transmitting power to Buffalo, about 30 km away. This decision ended the ac versus dc controversy and established victory for the ac system. In the early period of ac power transmission, frequency was not standardized. Many different frequencies of 25, 50, 60, 125, and 133 Hz were in use. This posed a problem for interconnection. Eventually, 60 Hz was adopted as standard in North America, although 50 Hz is also in use in many other parts of the world. The increasing need for transmitting larger amounts of power over longer distances created an incentive to use progressively higher voltage levels. The early ac systems used 12, 44, and 60 kV (RMS line-to-line). This rose to 165 kV in 1922, 220 kV in 1923, 287 kV in 1935, 330 kV in 1953, and 500 kV in 1965. Hydro Quebec energized its first 735-kV line in 1966, and 765 kV was introduced in the United States in 1969. By 2015, voltages as high as 1,100 kV were in use in certain parts of the world. To avoid the proliferation of an unlimited number of voltages, the industry has standardized voltage levels. The standards are 115, 138, 161, and 230 kV for the 01-Kundur_ch01_p001-018.indd 4 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 5 high-voltage (HV) class, and 345, 500, and 765 kV for the extra-high-voltage (EHV) class [2,3]. With the development of mercury arc valves in the early 1950s, high-voltage dc (HVDC) transmission systems became viable in special situations. The HVDC transmission is attractive for transmission of large blocks of power over long distances. The crossover point beyond which dc transmission may become a competitive alternative to ac transmission is around 500 km for overhead lines and 50 km for underground or submarine cables. HVDC transmission also provides an asynchronous link between systems where ac interconnection would be impractical because of system stability considerations or because the nominal frequencies of the systems are different. The first modern commercial application of HVDC transmission occurred in 1954 when the Swedish mainland and the island of Gotland were interconnected by a 96-km submarine cable. With the advent of thyristor valve converters, HVDC transmission became even more attractive. The first application of an HVDC system using thyristor valves was at Eel River, Canada, in 1972—a back-to-back scheme providing an asynchronous tie between the power systems of the provinces of Quebec and New Brunswick. With the cost and size of conversion equipment decreasing and its reliability increasing, there has been a steady increase in the use of HVDC transmission. The progress in the level of technology in power systems has led to many programs using available new technology (e.g., flexible ac transmission system [FACTS], fast controllers, communication systems, etc.) to improve power system characteristics, in particular, reliability, security, and stability [4]. Power system reliability: In general, system reliability is specified by the overall ability of the system to perform its function. In a power system, the basic aspect of identifying its reliability is the power system adequacy. It relates to the presence of sufficient facilities within the system to satisfy the consumer load demand, that is, it is necessary to generate sufficient energy and to use both transmission and distribution networks with sufficient power transfer capacity to enable the system to transport the energy to the load points. Therefore, adequacy is associated with static conditions excluding contingencies and is evaluated by identifying suitable indices such as the following: · Expected frequency and duration of failure: It identifies the expected frequency of encountering a deficiency and the expected duration of the deficiencies. · Loss of energy expectation: It identifies the expected energy that will not be supplied by generating station when the load demand exceeds the available generating capacity. · Outage time of consumer load points: It is the annual time of unavailability of feeding load points with energy. Power system security: The term “security” refers to the degree of risk in the ability of electric power systems to withstand without serious consequences of a preselected set of sudden disturbances such as short-circuits or unanticipated loss of system elements. From a control perspective, security is the degree of risk in the ability of a power system to reach a steady-state operating point without violating system operating constraints, mainly, thermal limits of transmission lines and bus voltage limits. These constraints 01-Kundur_ch01_p001-018.indd 5 07/04/22 10:35 AM

6 Part I: General Background are referred to as security constraints when referred to the post-contingency scenarios and can be written as the following: and 1 loss min max P P P P P P i N Gi D Gi Gi Gi g ∑ = + ≤ ≤ = (1.1) and       branch V V min m V S ax max S j k j j ≤ ≤ j jk j ≤ ∀ k − (1.2) where PGi Generated real power at bus # i PD Total system demand Ploss Total real power loss in the transmission network Vj Voltage magnitude at bus # j Sjk Apparent power (MVA) flow in branch j–k Ng Number of generators Power system stability: It commonly pertains to rotor angle stability. Stability phenomena are characterized by generator rotor oscillations under a sever perturbation and can be analyzed by solving nonlinear dynamic equations describing the transient behavior of the system under a set of credible contingencies. Interconnection of neighboring utilities usually leads to improved system security and economy of operation. Improved security results from the mutual emergency assistance that the utilities can provide. Improved economy results from the need for less generating reserve capacity in each system. In addition, the interconnection permits the utilities to make economic transfers and thus take advantage of the most economical sources of power. These benefits have been recognized from the beginning and interconnections continue to grow. Almost all electric utilities in the United States and Canada are now part of one interconnected system. The result is a very large system of enormous complexity. The design of such a system and its secure operation are indeed challenging problems. 1.2 Structure of the Power System Electric power systems vary in size and structural components. However, they all have the same basic characteristics: • Comprised of three-phase ac systems operating essentially at constant voltage and frequency. Generation and transmission facilities use three-phase equipment. Industrial loads are invariably three-phase; single-phase residential and commercial loads are distributed equally among the phases so as to effectively form a balanced three-phase system. • Prime movers convert the primary sources of energy (fossil, nuclear, and hydraulic) to mechanical energy that is, in turn, converted to electrical energy by synchronous generators running at fixed speed. • Transmit power over significant distances to consumers spreads over a wide area. This requires a transmission system comprising subsystems operating at different voltage levels. 01-Kundur_ch01_p001-018.indd 6 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 7 The basic elements of a power system are illustrated in Fig. 1.1. Electric power is produced at generating stations (GS) and transmitted to consumers through a complex network of individual components, including transmission lines, transformers, and switching devices. 500 kV 22 kV 24 kV GS 500 kV 230 kV GS GS 20 kV Tie line to neighboring system Transmission substation Bulk power system Subtransmission and distribution system Industrial customer Industrial customer Distribution substation Distribution transformer 3-phase primary feeder 120/240 V Single-phase secondary feeder Residential Commercial Small GS 12.47 kV Transmission system (500 kV) Transmission system (230 kV) To subtransmission and distribution 230 kV Tie line 345 kV 500 kV 115 kV Subtransmission 115 kV Figure 1.1 Basic elements of a power system. 01-Kundur_ch01_p001-018.indd 7 07/04/22 10:35 AM

8 Part I: General Background It is common practice to classify the transmission network into the following subsystems: 1. Transmission system 2. Subtransmission system 3. Distribution system The transmission system interconnects all major generating stations and main load centers in the system. It forms the backbone of the integrated power system and operates at the highest voltage levels (typically, 230 kV and above). The generator voltage, usually in the range of 11 to 35 kV, is stepped up to the transmission voltage level, and power is transmitted to transmission substations where the voltages are stepped down to the subtransmission level (typically, 69–to 138 kV). The generation and transmission subsystems are often referred to as the bulk power system. The subtransmission system transmits power in smaller quantities from the transmission substations to the distribution substations. Large industrial customers are commonly supplied directly from the subtransmission system. In some systems, there is no clear demarcation between the subtransmission and transmission circuits. As the system expands and higher-voltage levels become necessary for transmission, the older transmission lines are often relegated to the subtransmission function. The distribution system represents the final stage in the transfer of power to the individual customers. The primary distribution voltage is typically between 4.0 and 34.5 kV. Small industrial customers are supplied by primary feeders at this voltage level. The secondary distribution feeders supply residential and commercial customers at 120/240 V. Small generating plants located near the load are often connected to the subtransmission or distribution system directly. Interconnections to neighboring power systems are usually formed at the transmission system level. The overall system thus consists of multiple generating sources and several layers of transmission networks. This provides a high degree of structural redundancy that enables the system to withstand unusual contingencies without service disruption to the consumers. Nowadays, electricity has become all pervasive in the world. This has been accomplished by continued growth in load demand and, therefore, necessitates further development of the power system to meet load requirements. Consequently, the conventional power system infrastructure has become: · Large scale · Multi-input/multi-output · Distributed over large geographical areas and then, the energy needs to be routed through long distances, resulting in increased transmission losses · Complex with many interconnections · Represented by tremendous number of nonlinear differential equations · Costly due to the investments needed to expand generation, transmission, and distribution systems and keeping a desired level of reliability, security, and stability In addition, very large part of generation is based on fossil fuel (coal, oil, and natural gas) as source. Various factors, such as inflation and increase in fuel prices, led to a 01-Kundur_ch01_p001-018.indd 8 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 9 rapid increase in consumer tariffs as well as adverse effect on the environment. Their combined effects introduce considerable uncertainty in predicting the future. However, it is beneficial to empower every consumer in a new energy economy based on renewable sources to conserve energy and become an energy producer by installing renewable energy generation sources. These are major issues in satisfying system adequacy as it creates a reduction in forecast demand, improves system security and stability, and reduces greenhouse gas emissions. Distributed generation (DG) including renewable energy sources (e.g., wind, solar, photovoltaic, tidal, micro-hydro) and nonrenewable energy sources (e.g., fuel cells, diesel generators, microgas turbines) can be interconnected together to form what is called a “microgrid” (MG), which can operate in isolation or, in turn, can be connected to utility distribution system. Therefore, power system planning and configuration have to be modified to recognize this new scenario [5,6]. Microgrids are small distribution systems encompassing a group of electricity consumers (industrial, commercial, and residential) connected to a number of distributed generators and storage units that can be interfaced by power electronics. They can operate in isolation or, in turn, can be connected to utility distribution system. Therefore, power system planning and configuration have to be modified to recognize this new scenario [5,6]. MG technologies help electric system evolve into one that is more efficient, less polluting, lower chances of transmission congestion, reduced energy and power loss, and more flexible to provide energy consumers want and need. MGs can help make better use of energy generated, stored, and used at a local level, for example, local generation and islanding operation. In addition, in future each home-user can become an autonomous entity with the capability not only of demanding but also injecting power into the grid when the generated power exceeds the local needs [7,8]. Therefore, utility companies have been motivated to encourage local connection of renewable energy sources (RESs) at the distribution level. This can modernize the conventional power systems into multiple, interconnected distribution systems, that is, MGs. It is not a simple proposition to move from the centralized system that has developed over the past more than 130 years to one that is distributed. Implementing distributed generation comes with challenges as the present electric power infrastructure is not designed to meet problems pertaining to operational capability and quality of supply of electricity generation when using RESs such as wind and solar that are intermittent and unpredictable. 1.3 Power System Control The function of an electric power system is to convert energy from one of the naturally available forms to the electrical form and to transport it to the points of consumption. Energy is seldom consumed in the electrical form but is rather converted to other forms such as heat, light, and mechanical energy. The advantage of the electrical form of energy is that it can be transported and controlled with relative ease and with a high degree of efficiency and reliability. A properly designed and operated power system should, therefore, meet the following fundamental requirements: 1. The system must be able to meet the continually changing load demand for active and reactive power. Unlike other types of energy, electricity cannot be conveniently stored in sufficient quantities. Therefore, adequate “spinning” reserve of active and reactive power should be maintained and appropriately controlled at all times. 01-Kundur_ch01_p001-018.indd 9 07/04/22 10:35 AM

10 Part I: General Background 2. The system should supply energy at minimum cost and with minimum ecological impact. 3. The “quality” of power supply must meet certain minimum standards with regard to the following factors: (a) Constancy of frequency (b) Constancy of voltage (c) Level of reliability Several levels of control involving a complex array of devices are used to meet the above requirements. These are depicted in Fig. 1.2, which identifies the various Figure 1.2 Subsystems of a power system and associated controls. System Generation Control Load frequency control with economic allocation Transmission Controls Reactive power and voltage control, HVDC transmission, and associated controls Generating Unit Controls Supplementary control Prime mover and control Excitation system and control Generator Shaft power Field current Schedule Frequency Tie fiows Generator power Other generating units and associated controls Frequency Electrical power Voltage Speed Speed/Power Tie fiows Generator power 01-Kundur_ch01_p001-018.indd 10 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 11 subsystems of a power system and the associated controls. In this overall structure, controllers operate directly on individual system elements. In a generating unit, these consist of prime mover controls and excitation controls. The prime mover controls are concerned with speed regulation and control of energy supply system variables such as boiler pressure, temperature, and flows. The function of the excitation control is to regulate generator voltage and reactive power output. The desired MW outputs of the individual generating units are determined by the system-generation control. The primary purpose of the system-generation control is to balance the total system generation against system load and losses so that the desired frequency and power interchange with neighboring systems (tie flows) are maintained. The transmission controls include power and voltage control devices, such as static var compensators, synchronous condensers, switched capacitors and reactors, tapchanging transformers, phase-shifting transformers, and HVDC transmission controls. The controls described above contribute to the satisfactory operation of the power system by maintaining system voltages, frequency, and other system variables within their acceptable limits. They also have a profound effect on the dynamic performance of the power system and on its ability to cope with disturbances. The control objectives are dependent on the operating state of the power system. Under normal conditions, the control objective is to operate as efficiently as possible with voltages and frequency close to nominal values. When an abnormal condition develops, new objectives must be met to restore the system to normal operation. Major system failures are rarely the result of a single catastrophic disturbance causing collapse of an apparently secure system. Such failures are usually brought about by a combination of circumstances that stress the network beyond its capability. Severe natural disturbances (such as a tornado, severe storm, or freezing rain), equipment malfunction, human error, and inadequate design combine to weaken the power system and eventually lead to its breakdown. This may result in cascading outages that must be contained within a small part of the system if a major blackout is to be prevented. 1.3.1 Operating States of a Power System and Control Strategies [9,10] For the purpose of analyzing power system security and designing appropriate control systems, it is helpful to conceptually classify the system operating conditions into five states: normal, alert, emergency, in extremis, and restorative. These operating states and the ways in which transition can take place from one state to another is depicted in Fig. 1.3. In the normal state, all system variables are within the normal range and no equipment is being overloaded. The system operates in a secure manner and is able to withstand a contingency without violating any of the constraints. The system enters the alert state if the security level falls below a certain limit of adequacy, or if the possibility of a disturbance increases because of adverse weather conditions such as the approach of severe storms. In this state, all system variables are still within the acceptable range and all constraints are satisfied. However, the system has been weakened to a level where a contingency may cause an overloading of equipment that places the system in an emergency state. If the disturbance is very severe, the in extremis (or extreme emergency) state may result directly from the alert state. Preventive action, such as generation shifting (security dispatch) or increased reserve, can be taken to restore the system to the normal state. If the restorative steps do not succeed, the system remains in the alert state. 01-Kundur_ch01_p001-018.indd 11 07/04/22 10:35 AM

12 Part I: General Background The system enters the emergency state if a sufficiently severe disturbance occurs when the system is in the alert state. In this state, voltages at many buses are low and/or equipment loadings exceed short-term emergency ratings. The system is still intact and may be restored to the alert state by initiating emergency control actions: fault clearing, excitation control, fast-valving, generation tripping, generation run-back, HVDC modulation, and load curtailment. If the above measures are not applied or are ineffective, the system is in extremis; the result is cascading outages and possibly a shutdown of a major portion of the system. Control actions, such as load shedding and controlled system separation, are aimed at saving as much of the system as possible from a widespread blackout. The restorative state represents a condition in which control action is being taken to reconnect all the facilities and to restore system load. The system transits from this state to either the alert state or the normal state, depending on the system conditions. Characterization of the system conditions into the five states as described above provides a framework in which control strategies can be developed and operator actions identified to deal effectively with each state. For a system that has been disturbed and that has entered a degraded operating state, power system controls assist the operator in returning the system to a normal state. If the disturbance is small, power system controls by themselves may be able to achieve this task. However, if the disturbance is large, it is possible that operator actions such as generation rescheduling or element switching may be required for a return to the normal state. The philosophy that has evolved to cope with the diverse requirements of system control comprises a hierarchical structure as shown in Fig. 1.4. In this structure, there are controllers operating directly on individual system elements such as excitation systems, prime movers, boilers, transformer tap changers, and dc converters. There is usually some form of overall plant controller that coordinates the controls of closely linked elements. The plant controllers are, in turn, supervised by system controllers at the operating centers. The system-controller actions are coordinated by pool-level master controllers. The overall control system is thus highly distributed and relies on Figure 1.3 Power system operating states. Normal Restorative Alert In extremis Emergency 01-Kundur_ch01_p001-018.indd 12 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 13 many different types of telemetering and control signals. Supervisory Control and Data Acquisition (SCADA) systems provide information to indicate the system status. State estimation programs filter monitored data and provide an accurate picture of the system’s condition. The human operator is an important link at various levels in this control hierarchy and at key locations on the system. The primary function of the operator is to monitor system performance and manage resources so as to ensure economic operation while maintaining the required quality and reliability of power supply. During system emergencies, the operator plays a key role by coordinating related information from diverse sources and developing corrective strategies to restore the system to a more secure state of operation. 1.4 Design and Operating Criteria for Stability For reliable service, a bulk electricity system must remain intact and be capable of withstanding a wide variety of disturbances. Therefore, it is essential that the system be designed and operated so that the more probable contingencies can be sustained with no loss of load (except that connected to the faulted element) and thus the most adverse possible contingencies do not result in uncontrolled, widespread, and cascading power interruptions. The November 1965 blackout in the northeastern part of the United States and Ontario, Canada, had a profound impact on the electric utility industry, particularly in North America. Many questions were raised relating to design concepts and planning criteria. These led to the formation of the National Electric Reliability Council in 1968 that, over the years, has evolved into North American Electric Reliability Corporation (NERC), “a not-for-profit international regulatory authority whose mission is to assure the effective and efficient reduction of risks to the reliability and security of the grid” [11]. Its purpose is to develop and enforce reliability standards that augment the reliability and adequacy of bulk power supply in the electricity systems of North America. NERC encompasses six regional organizations and spans the continental Figure 1.4 Power system control hierarchy. Pool control center To other systems System control center To other systems Transmission plant Power plant Distribution center Generating units 01-Kundur_ch01_p001-018.indd 13 07/04/22 10:35 AM

14 Part I: General Background United States, Canada, and the northern portion of Baja California, Mexico. “NERC provides industry-wide perspective and oversight, and the Regional Entities have unique features and activities that serve the needs of their regional constituents while ensuring that industry follows NERC Reliability Standards” [11]. Since differences exist in geography, load pattern, and power sources, criteria for the various regions differ to some extent [12]. Design and operating criteria play an essential role in preventing major system disturbances following severe contingencies. These criteria ensure that, for all frequently occurring contingencies, the system will, at worst, transit from the normal state to the alert state, rather than to a more severe state such as the emergency state or the in extremis state. When the alert state is entered following a contingency, operators can take action to return the system to the normal state. An illustrative example of design and operating criteria related to system stability that gives an indication of the types of contingencies considered for stability assessment is given below. 1.4.1 Normal Design Contingencies The criteria require that the stability of the bulk power system be maintained during and after the most severe of the contingencies specified below, with due regard to reclosing facilities. These contingencies are selected on the basis that they have a significant probability of occurrence given the large number of elements comprising the power system. The normal design contingencies may include the following: · A permanent three-phase fault on any generator, transmission circuit, transformer or bus section, with normal fault clearing and with due regard to reclosing facilities · Simultaneous permanent phase-to-ground faults on different phases of each of two adjacent transmission circuits on a multiple-circuit tower, cleared in normal time · A permanent phase-to-ground fault on any transmission circuit, transformer, or bus section with delayed clearing because of malfunction of circuit breakers, relay, or signal channel · Loss of any element without a fault · A permanent phase-to-ground fault on a circuit breaker, cleared in normal time · Simultaneous permanent loss of both poles of a dc bipolar facility It is required that, following any of the above contingencies, the stability of the system be maintained, and voltages and line and equipment loadings be within applicable limits. These requirements apply under the following two basic conditions: 1. All facilities in service. 2. A critical generator, transmission circuit, or transformer out of service, assuming that the area generation and power flows are adjusted between outages using 10-minute reserve. 01-Kundur_ch01_p001-018.indd 14 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 15 1.4.2 Extreme Contingency Assessment The extreme contingency assessment recognizes that the interconnected bulk power system can be subjected to events that exceed in severity the normal design contingencies. The objective is to determine the effects of extreme contingencies on system performance in order to obtain an indication of system strength and to determine the extent of a widespread system disturbance even though extreme contingencies do have very low probabilities of occurrence. After an analysis and assessment of extreme contingencies, measures are to be utilized, where appropriate, to reduce the frequency of occurrence of such contingencies or to mitigate the consequences that are indicated as a result of simulating for such contingencies. The extreme contingencies include the following: · Loss of the entire capability of a generating station · Loss of all lines emanating from a generating station, switching station, or substation · Loss of all transmission circuits on a common right-of-way · A permanent three-phase fault on any generator, transmission circuit, transformer, or bus section, with delayed fault clearing and with due regard to reclosing facilities · The sudden dropping of a large-load or major-load center · The effect of severe power swings arising from disturbances outside the interconnected systems · Failure or misoperation of a special protection system, such as a generation rejection, load rejection, or transmission cross-tripping scheme 1.4.3 Renewable Energy Sources The extreme contingencies mentioned above are being exacerbated by new developments such as cyber-attacks and penetration of RESs with input from intermittent sources of energy. Digital transformation of the electrical grid raises a big concern about security against unauthorized access or hacking. The uncertainty surrounding the forecast of availability of uncontrolled variable sources, such as solar and wind, over a reasonable period of time adds an additional layer that the system must be responsive to. Thus, the system must be made resilient against both natural contingencies and cyber security disruptions. One possibility is to harden the system against such contingencies by strong physical components and improved security measures at a significant investment. The other approach to sustain the impact of such contingencies is to make the network more flexible and reconfigurable by including energy storage, microgrids, distributed generation, and load management. High penetration of RESs combined with their intermittent nature can adversely affect the stability of the system because of their intermittent nature and difficulty to forecast with good accuracy. This drawback can be mitigated by applying suitable controls. For example, most RESs are inverter-based. The start-up times of these sources can be significantly shorter than the conventional generating plants. The grid forming inverter control can provide black-start functionality and frequency and voltage regulation. Also, fault current contribution and inrush current can be managed [13]. 01-Kundur_ch01_p001-018.indd 15 07/04/22 10:35 AM

16 Part I: General Background Deployment of RESs and MGs in large interconnected systems requires its own unique consideration and will not be discussed here. 1.4.4 System Design for Stability The design of a large interconnected system to ensure stable operation at minimum cost is a very complex problem. However, the economic gains to be realized through the solution to this problem are enormous. From the control theory point of view, the power system is a very high-order multivariable process, operating in a constantly changing environment. Because of the high dimensionality and complexity of the system, it is essential to make simplifying assumptions and to analyze specific problems using the right degree of detail of system representation. This requires a good grasp of the characteristics of the overall system as well as those of its individual elements. The power system is a highly nonlinear system whose dynamic performance is influenced by a wide array of devices with different response rates and characteristics. System stability must be viewed not as a single problem, but rather in terms of its different aspects. Different forms of power system stability problems are described in Chap. 2. Characteristics of virtually every major element of the power system have an effect on system stability. A knowledge of these characteristics is essential for the understanding and study of power system stability. Therefore, equipment characteristics and modeling will be discussed in Part II. Intricacies of the physical aspects of various categories of system stability, methods of their analysis, and special measures to enhance stability performance of the power system will be presented in Part III. References 1. O.P. Malik, “Evolution of Power Systems into Smarter Grids,” Journal of Control, Automation and Power Systems, Vol. 24(1-1), pp. 139–147, April 2013. 2. H.M. Rustebakke (editor), Electric Utility Systems and Practices, John Wiley & Sons, 1983. 3. C.A. Gross, Power System Analysis, 2nd ed., John Wiley & Sons, 1986. 4. Seyed Ali Arefifar, Yasser Abdel-Radi, and I. Mohamed, “DG Mix, Reactive Sources and Energy Storage Units for Optimizing Microgrid Reliability and Supply Security,” IEEE Trans. on Smart Grid, Vol. 5(4), pp. 1835–1844, July 2014. 5. Charles Smith, “Wind and Solar Energy-Variable Generation Across the Land,” IEEE Power and Energy Magazine, Vol. 13(6), November/December 2015. 6. V. Krishnan, J. Ho, et. al., “Co-optimization of Transmission and Other Supply Resources—Concept, Review and Modeling Approaches,” Energy Systems, Springer-Verlag, Berlin, pp. 1–36, August 2015. 7. A.K. Basu, S.P. Chowdhury, et. al., “Reliability Study of a Micro-grid Power System”, 43rd International Universities Power Engineering Conference, Padova, pp. 1–4, 2008. 8. R. Ahshan, M.T. Iqbal, et. al., “Micro-Grid System Based on Renewable Power Generation Systems,” 23rd Canadian Conference on Electrical and Computer Engineering, Calgary, AB, pp. 1–4, May 2010. 9. L.H. Fink and K. Carlsen, “Operating under Stress and Strain,” IEEE Spectrum, pp. 48–53, March 1978. 01-Kundur_ch01_p001-018.indd 16 07/04/22 10:35 AM

Chapter 1: General Characteristics of Modern Power Systems 17 10. EPRI Report EL 6360-L, “Dynamics of Interconnected Power Systems: A Tutorial for System Dispatchers and Plant Operators,” Final Report of Project 2473-15, prepared by Power Technologies Inc., May 1989. 11. IEEE Special Publication 77 CH 1221-1-PWR, Symposium on Reliability Criteria for System Dynamic Performance, 1977. 12. North American Reliability Corporation, https://www.nerc.com. Accessed April 20, 2021. 13. Y. Wang, C. Chen, J. Wang, and R. Baldick, “Research on Resilience of Power Systems under Natural Disasters: A Review,” IEEE Trans. on Power Systems, Vol. 31(2), pp. 1604–1631, 2017, DOI: 10.1109/TP-WRS.2015.2429656. 01-Kundur_ch01_p001-018.indd 17 07/04/22 10:35 AM

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