POWER QUALITY IN POWER SYSTEMS AND ELECTRICAL MACHINES This page intentionally left blank POWER QUALITY IN POWER SYSTEMS AND ELECTRICAL MACHINES Second Edition MOHAMMAD A.S. MASOUM EWALD F. FUCHS AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an imprint of Elsevier Academic Press is an imprint of Elsevier 125 London Wall, London, EC2Y 5AS, UK 525 B Street, Suite 1800, San Diego, CA 92101-4495, USA 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK Copyright © 2015, 2008 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. For information on all Academic Press publications visit our website at http://store.elsevier.com/ ISBN: 978-0-12-800782-2 Printed in The United States of America 08 09 10 11 12 9 8 7 6 5 4 3 2 1 CONTENTS Preface xi Acknowledgments xiii 1. Introduction to Power Quality 1 1.1 Definition of power quality 4 1.2 Causes of disturbances in power systems 4 1.3 Classification of power quality issues 7 1.4 Formulations and measures used for power quality 20 1.5 Effects of poor power quality on power system devices 57 1.6 Standards and guidelines referring to power quality 57 1.7 Harmonic modeling philosophies 65 1.8 Power quality improvement techniques 67 1.9 Summary 89 1.10 Problems 90 References 101 Additional bibliography 104 2. Harmonic Models of Transformers 105 2.1 Sinusoidal (linear) modeling of transformers 108 2.2 Harmonic losses in transformers 109 2.3 Derating of single-phase transformers 118 2.4 Nonlinear harmonic models of transformers 128 2.5 Ferroresonance of power transformers 145 2.6 Effects of solar-geomagnetic disturbances on power systems and transformers 161 2.7 Grounding 165 2.8 Measurement of derating of three-phase transformers 179 2.9 Summary 194 2.10 Problems 195 References 201 Additional bibliography 205 3. Modeling and Analysis of Induction Machines 207 3.1 Complete sinusoidal equivalent circuit of a three-phase induction machine 211 3.2 Magnetic fields of three-phase machines for the calculation of inductive machine parameters 219 v vi Contents 3.3 Steady-state stability of a three-phase induction machine 225 3.4 Spatial (space) harmonics of a three-phase induction machine 229 3.5 Time harmonics of a three-phase induction machine 233 3.6 Fundamental and harmonic torques of an induction machine 236 3.7 Measurement results for three- and single-phase induction machines 242 3.8 Inter- and subharmonic torques of three-phase induction machines 260 3.9 Interaction of space and time harmonics of three-phase induction machines 268 3.10 Conclusions concerning induction machine harmonics 272 3.11 Voltage-stress winding failures of ac motors fed by variable-frequency, voltage- and current-source pwm inverters 272 3.12 Nonlinear harmonic models of three-phase induction machines 293 3.13 Static and dynamic rotor eccentricity of three-phase induction machines 297 3.14 Operation of three-phase machines within a single-phase power system 297 3.15 Classification of three-phase induction machines 298 3.16 Summary 300 3.17 Problems 300 References 308 Additional bibliography 312 4. Modeling and Analysis of Synchronous Machines 313 4.1 Sinusoidal state-space modeling of a synchronous machine in the time domain 317 4.2 Steady-state, transient, and subtransient operation 322 4.3 Harmonic modeling of a synchronous machine 384 4.4 Summary 411 4.5 Problems 411 References 424 Additional bibliography 427 5. Interaction of Harmonics with Capacitors 429 5.1 Application of capacitors to power-factor correction 431 5.2 Application of capacitors to reactive power compensation 443 5.3 Application of capacitors to harmonic filtering 444 5.4 Power quality problems associated with capacitors 448 5.5 Frequency and capacitance scanning 470 5.6 Harmonic constraints for capacitors 473 5.7 Equivalent circuits of capacitors 478 5.8 Summary 482 5.9 Problems 483 References 487 Contents vii 6. Lifetime Reduction of Transformers and Induction Machines 489 6.1 Rationale for relying on the worst-case conditions 492 6.2 Elevated temperature rise due to voltage harmonics 492 6.3 Weighted-harmonic factors 493 6.4 Exponents of weighted-harmonic factors 508 6.5 Additional losses or temperature rises versus weighted-harmonic factors 510 6.6 Arrhenius plots 512 6.7 Reaction rate equation 512 6.8 Decrease of lifetime due to an additional temperature rise 514 6.9 Reduction of lifetime of components with activation energy E¼1.1 eV due to harmonics of the terminal voltage within residential or commercial utility systems 515 6.10 Possible limits for harmonic voltages 517 6.11 Probabilistic and time-varying nature of harmonics 524 6.12 The cost of harmonics 525 6.13 Temperature as a function of time 525 6.14 Various operating modes of rotating machines 528 6.15 Summary 561 6.16 Problems 562 References 569 7. Power System Modeling under Nonsinusoidal Operating Conditions 573 7.1 Overview of a modern power system 575 7.2 Power system matrices 578 7.3 Fundamental power flow 594 7.4 Newton-based harmonic power flow 623 7.5 Classification of harmonic power flow techniques 659 7.6 Summary 671 7.7 Problems 671 References 679 8. Impact of Poor Power Quality on Reliability, Relaying and Security 681 8.1 Reliability indices 684 8.2 Degradation of reliability and security due to poor power quality 687 8.3 Tools for detecting poor power quality 720 8.4 Tools for improving reliability and security 739 8.5 Load shedding and load management 755 8.6 Energy-storage methods 755 8.7 Matching the operation of intermittent renewable power plants with energy storage 756 8.8 Summary 757 8.9 Problems 758 References 771 Additional bibliography 778 viii Contents 9. The Roles of Filters in Power Systems and Unified Power Quality Conditioners 779 9.1 Types of nonlinear loads 782 9.2 Classification of filters employed in power systems 785 9.3 Passive filters as used in power systems 786 9.4 Active filters 810 9.5 Hybrid power filters 813 9.6 Block diagram of active filters 818 9.7 Control of filters 820 9.8 Compensation devices at fundamental and harmonic frequencies 842 9.9 Unified power quality conditioner (UPQC) 848 9.10 The UPQC control system 854 9.11 UPQC control using the park (DQO) transformation 855 9.12 UPQC control based on the instantaneous real and imaginary power theory 859 9.13 Performance of the UPQC 872 9.14 Summary 882 References 885 10. Optimal Placement and Sizing of Shunt Capacitor Banks in the Presence of Harmonics 887 10.1 Reactive power compensation 890 10.2 Common types of distribution shunt capacitor banks 893 10.3 Classification of capacitor allocation techniques for sinusoidal operating conditions 897 10.4 Optimal placement and sizing of shunt capacitor banks in the presence of harmonics 921 10.5 Summary 957 References 957 11. Power Quality Solutions for Renewable Energy Systems 961 11.1 Energy conservation and efficiency 964 11.2 Photovoltaic and thermal solar (power) systems 975 11.3 Horizontal – and vertical-axes wind power (WP) plants 990 11.4 Complementary control of renewable plants with energy storage plants 1024 11.5 AC transmission lines versus DC lines 1055 11.6 Fast-charging stations for electric cars 1055 11.7 Off-shore renewable plants 1056 11.8 Metering 1056 11.9 Other renewable energy plants 1057 11.10 Production of automotive fuel from wind, water, and CO2 1058 11.11 Water efficiency 1058 Contents ix 11.12 Village with 2,600 inhabitants achieves energy independence 1058 11.13 Summary 1060 11.14 Problems 1060 References 1078 Appendix 1 1085 Appendix 2 1091 Appendix 3 1101 Appendix 4 1103 Index 1105