ELECTRIC POWER SYSTEMS ELECTRIC POWER SYSTEMS A CONCEPTUAL INTRODUCTION Alexandra von Meier A JOHN WILEY & SONS, INC., PUBLICATION Copyright # 2006 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the Web at www.copyright.com. 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Title TK1005.M37 2006 621.31–dc22 2005056773 Printed in the United States of America 10987654321 To my late grandfather Karl Wilhelm Clauberg who introduced me to The Joy of Explaining Things &CONTENTS Preface xiii 1. The Physics of Electricity 1 1.1 Basic Quantities 1 1.1.1 Introduction 1 1.1.2 Charge 2 1.1.3 Potential or Voltage 3 1.1.4 Ground 5 1.1.5 Conductivity 5 1.1.6 Current 6 1.2 Ohm’s law 8 1.2.1 Resistance 9 1.2.2 Conductance 10 1.2.3 Insulation 11 1.3 Circuit Fundamentals 11 1.3.1 Static Charge 11 1.3.2 Electric Circuits 12 1.3.3 Voltage Drop 13 1.3.4 Electric Shock 13 1.4 Resistive Heating 14 1.4.1 Calculating Resistive Heating 15 1.4.2 Transmission Voltage and Resistive Losses 17 1.5 Electric and Magnetic Fields 18 1.5.1 The Field as a Concept 18 1.5.2 Electric Fields 19 1.5.3 Magnetic Fields 21 1.5.4 Electromagnetic Induction 24 1.5.5 Electromagnetic Fields and Health Effects 25 1.5.6 Electromagnetic Radiation 26 2. Basic Circuit Analysis 30 2.1 Modeling Circuits 30 vii viii CONTENTS 2.2 Series and Parallel Circuits 31 2.2.1 Resistance in Series 32 2.2.2 Resistance in Parallel 33 2.2.3 Network Reduction 35 2.2.4 Practical Aspects 36 2.3 Kirchhoff’s Laws 37 2.3.1 Kirchhoff’s Voltage Law 38 2.3.2 Kirchhoff’s Current Law 39 2.3.3 Application to Simple Circuits 40 2.3.4 The Superposition Principle 41 2.4 Magnetic Circuits 44 3. AC Power 49 3.1 Alternating Current and Voltage 49 3.1.1 Historical Notes 49 3.1.2 Mathematical Description 50 3.1.3 The rms Value 53 3.2 Reactance 55 3.2.1 Inductance 55 3.2.2 Capacitance 58 3.2.3 Impedance 64 3.2.4 Admittance 64 3.3 Power 66 3.3.1 Definition of Electric Power 66 3.3.2 Complex Power 68 3.3.3 The Significance of Reactive Power 73 3.4 Phasor Notation 75 3.4.1 Phasors as Graphics 75 3.4.2 Phasors as Exponentials 78 3.4.3 Operations with Phasors 80 4. Generators 85 4.1 The Simple Generator 86 4.2 The Synchronous Generator 92 4.2.1 Basic Components and Functioning 92 4.2.2 Other Design Aspects 97 4.3 Operational Control of Synchronous Generators 100 4.3.1 Single Generator: Real Power 100 4.3.2 Single Generator: Reactive Power 101 4.3.3 Multiple Generators: Real Power 107 4.3.4 Multiple Generators: Reactive Power 112 CONTENTS ix 4.4 Operating Limits 115 4.5 The Induction Generator 118 4.5.1 General Characteristics 118 4.5.2 Electromagnetic Characteristics 120 4.6 Inverters 123 5. Loads 127 5.1 Resistive Loads 128 5.2 Motors 131 5.3 Electronic Devices 134 5.4 Load from the System Perspective 136 5.4.1 Coincident and Noncoincident Demand 137 5.4.2 Load Profiles and Load Duration Curve 138 5.5 Single- and Multiphase Connections 140 6. Transmission and Distribution 144 6.1 System Structure 144 6.1.1 Historical Notes 144 6.1.2 Structural Features 147 6.1.3 Sample Diagram 149 6.1.4 Topology 150 6.1.5 Loop Flow 153 6.1.6 Stations and Substations 156 6.1.7 Reconfiguring the System 158 6.2 Three-Phase Transmission 159 6.2.1 Rationale for Three Phases 160 6.2.2 Balancing Loads 163 6.2.3 Delta and Wye Connections 164 6.2.4 Per-Phase Analysis 166 6.2.5 Three-Phase Power 166 6.2.6 D.C. Transmission 167 6.3 Transformers 168 6.3.1 General Properties 168 6.3.2 Transformer Heating 170 6.3.3 Delta and Wye Transformers 172 6.4 Characteristics of Power Lines 175 6.4.1 Conductors 175 6.4.2 Towers, Insulators, and Other Components 179 6.5 Loading 182 6.5.1 Thermal Limits 182 6.5.2 Stability Limit 183 x CONTENTS 6.6 Voltage Control 184 6.7 Protection 188 6.7.1 Basics of Protection and Protective Devices 188 6.7.2 Protection Coordination 192 7. Power Flow Analysis 195 7.1 Introduction 195 7.2 The Power Flow Problem 197 7.2.1 Network Representation 197 7.2.2 Choice of Variables 198 7.2.3 Types of Buses 201 7.2.4 Variables for Balancing Real Power 201 7.2.5 Variables for Balancing Reactive Power 202 7.2.6 The Slack Bus 204 7.2.7 Summary of Variables 205 7.3 Example with Interpretation of Results 206 7.3.1 Six-Bus Example 206 7.3.2 Tweaking the Case 210 7.3.3 Conceptualizing Power Flow 211 7.4 Power Flow Equations and Solution Methods 214 7.4.1 Derivation of Power Flow Equations 214 7.4.2 Solution Methods 217 7.4.3 Decoupled Power Flow 224 7.5 Applications and Optimal Power Flow 226 8. System Performance 229 8.1 Reliability 229 8.1.1 Measures of Reliability 229 8.1.2 Valuation of Reliability 231 8.2 Security 233 8.3 Stability 234 8.3.1 The Concept of Stability 234 8.3.2 Steady-State Stability 236 8.3.3 Dynamic Stability 240 8.3.4 Voltage Stability 249 8.4 Power Quality 250 8.4.1 Voltage 251 8.4.2 Frequency 253 8.4.3 Waveform 255 CONTENTS xi 9. System Operation, Management, and New Technology 259 9.1 Operation and Control on Different Time Scales 260 9.1.1 The Scale of a Cycle 261 9.1.2 The Scale of Real-Time Operation 262 9.1.3 The Scale of Scheduling 264 9.1.4 The Planning Scale 267 9.2 New Technology 268 9.2.1 Storage 268 9.2.2 Distributed Generation 271 9.2.3 Automation 278 9.2.4 FACTS 280 9.3 Human Factors 281 9.3.1 Operators and Engineers 281 9.3.2 Cognitive Representations of Power Systems 282 9.3.3 Operational Criteria 285 9.3.4 Implications for Technological Innovation 291 9.4 Implications for Restructuring 292 Appendix: Symbols, Units, Abbreviations, and Acronyms 298 Index 302 &PREFACE This book is intended to bridge the gap between formal engineering texts and more popularly accessible descriptions of electric power technology. I discovered this gap as a graduate student struggling to understand power systems—especially trans- mission and distribution systems—which had always fascinated me but which now invited serious study in the context of research on implementing solar energy. Although I had studied physics as an undergraduate, I found the subject of power systems difficult and intimidating. The available literature seemed to fall into two categories: easy-to-read, qualitat- ive descriptions of the electric grid for the layperson, on the one hand, and highly technical books and papers, on the other hand, written for professionals and electrical engineering majors.