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Power system analysis and design
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POWER SYSTEM ANALYSIS
AND DESIGN
FIFTH EDITION, SI
J. DUNCAN GLOVER
FAILURE ELECTRICAL, LLC
MULUKUTLA S. SARMA
NORTHEASTERN UNIVERSITY
THOMAS J. OVERBYE
UNIVERSITY OF ILLINOIS
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Power System Analysis and Design,
Fifth Edition, SI
J. Duncan Glover, Mulukutla S. Sarma,
and Thomas J. Overbye
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Christopher M. Shortt
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c 2012, 2008 Cengage Learning
ALL RIGHTS RESERVED. No part of this work covered by the copyright
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Copyright Act, without the prior written permission of the publisher.
Library of Congress Control Number: 2011924686
ISBN-13: 978-1-111-42579-1
ISBN-10: 1-111-42579-5
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TO LOUISE, TATIANA & BRENDAN, ALISON & JOHN, LEAH, OWEN,
ANNA, EMILY & BRIGID
Dear Lord! Kind Lord!
Gracious Lord! I pray
Thou wilt look on all I love,
Tenderly to-day!
Weed their hearts of weariness;
Scatter every care
Down a wake of angel-wings
Winnowing the air.
Bring unto the sorrowing
All release from pain;
Let the lips of laughter
Overflow again;
And with all the needy
O divide, I pray,
This vast treasure of content
That is mine to-day!
James Whitcomb Riley
CONTENTS
Preface to the SI Edition xii
Preface xiii
List of Symbols, Units, and Notation xix
CHAPTER 1 Introduction 1
Case Study: The Future Beckons: Will the Electric Power
Industry Heed the Call? 2
1.1 History of Electric Power Systems 10
1.2 Present and Future Trends 17
1.3 Electric Utility Industry Structure 21
1.4 Computers in Power System Engineering 22
1.5 PowerWorld Simulator 24
CHAPTER 2 Fundamentals 31
Case Study: Making Microgrids Work 32
2.1 Phasors 46
2.2 Instantaneous Power in Single-Phase AC Circuits 47
2.3 Complex Power 53
2.4 Network Equations 58
2.5 Balanced Three-Phase Circuits 60
2.6 Power in Balanced Three-Phase Circuits 68
2.7 Advantages of Balanced Three-Phase Versus
Single-Phase Systems 74
CHAPTER 3 Power Transformers 90
Case Study: PJM Manages Aging Transformer Fleet 91
3.1 The Ideal Transformer 96
3.2 Equivalent Circuits for Practical Transformers 102
3.3 The Per-Unit System 108
3.4 Three-Phase Transformer Connections and Phase Shift 116
3.5 Per-Unit Equivalent Circuits of Balanced Three-Phase
Two-Winding Transformers 121
3.6 Three-Winding Transformers 126
3.7 Autotransformers 130
3.8 Transformers with O¤-Nominal Turns Ratios 131
vii
CHAPTER 4 Transmission Line Parameters 159
Case Study: Transmission Line Conductor Design Comes of Age 160
Case Study: Six Utilities Share Their Perspectives on Insulators 164
4.1 Transmission Line Design Considerations 169
4.2 Resistance 174
4.3 Conductance 177
4.4 Inductance: Solid Cylindrical Conductor 178
4.5 Inductance: Single-Phase Two-Wire Line and Three-Phase
Three-Wire Line with Equal Phase Spacing 183
4.6 Inductance: Composite Conductors, Unequal Phase Spacing,
Bundled Conductors 185
4.7 Series Impedances: Three-Phase Line with Neutral Conductors
and Earth Return 193
4.8 Electric Field and Voltage: Solid Cylindrical Conductor 199
4.9 Capacitance: Single-Phase Two-Wire Line and Three-Phase
Three-Wire Line with Equal Phase Spacing 201
4.10 Capacitance: Stranded Conductors, Unequal Phase Spacing,
Bundled Conductors 204
4.11 Shunt Admittances: Lines with Neutral Conductors
and Earth Return 207
4.12 Electric Field Strength at Conductor Surfaces
and at Ground Level 212
4.13 Parallel Circuit Three-Phase Lines 215
CHAPTER 5 Transmission Lines: Steady-State Operation 233
Case Study: The ABCs of HVDC Transmission Technologies 234
5.1 Medium and Short Line Approximations 248
5.2 Transmission-Line Di¤erential Equations 254
5.3 Equivalent p Circuit 260
5.4 Lossless Lines 262
5.5 Maximum Power Flow 271
5.6 Line Loadability 273
5.7 Reactive Compensation Techniques 277
CHAPTER 6 Power Flows 294
Case Study: Future Vision 295
Case Study: Characteristics of Wind Turbine Generators
for Wind Power Plants 305
6.1 Direct Solutions to Linear Algebraic Equations:
Gauss Elimination 311
6.2 Iterative Solutions to Linear Algebraic Equations:
Jacobi and Gauss–Seidel 315
6.3 Iterative Solutions to Nonlinear Algebraic Equations:
Newton–Raphson 321
viii CONTENTS
6.4 The Power-Flow Problem 325
6.5 Power-Flow Solution by Gauss–Seidel 331
6.6 Power-Flow Solution by Newton–Raphson 334
6.7 Control of Power Flow 343
6.8 Sparsity Techniques 349
6.9 Fast Decoupled Power Flow 352
6.10 The ‘‘DC’’ Power Flow 353
6.11 Power-Flow Modeling of Wind Generation 354
Design Projects 1–5 366
CHAPTER 7 Symmetrical Faults 379
Case Study: The Problem of Arcing Faults in Low-Voltage
Power Distribution Systems 380
7.1 Series R–L Circuit Transients 382
7.2 Three-Phase Short Circuit—Unloaded
Synchronous Machine 385
7.3 Power System Three-Phase Short Circuits 389
7.4 Bus Impedance Matrix 392
7.5 Circuit Breaker and Fuse Selection 400
Design Project 4 (continued ) 417
CHAPTER 8 Symmetrical Components 419
Case Study: Circuit Breakers Go High Voltage 421
8.1 Definition of Symmetrical Components 428
8.2 Sequence Networks of Impedance Loads 433
8.3 Sequence Networks of Series Impedances 441
8.4 Sequence Networks of Three-Phase Lines 443
8.5 Sequence Networks of Rotating Machines 445
8.6 Per-Unit Sequence Models of Three-Phase
Two-Winding Transformers 451
8.7 Per-Unit Sequence Models of Three-Phase
Three-Winding Transformers 456
8.8 Power in Sequence Networks 459
CHAPTER 9 Unsymmetrical Faults 471
Case Study: Fires at U.S. Utilities 472
9.1 System Representation 473
9.2 Single Line-to-Ground Fault 478
9.3 Line-to-Line Fault 483
9.4 Double Line-to-Ground Fault 485
9.5 Sequence Bus Impedance Matrices 492
Design Project 4 (continued ) 512
Design Project 6 513
CONTENTS ix
CHAPTER 10 System Protection 516
Case Study: The Future of Power Transmission 518
10.1 System Protection Components 525
10.2 Instrument Transformers 526
10.3 Overcurrent Relays 533
10.4 Radial System Protection 537
10.5 Reclosers and Fuses 541
10.6 Directional Relays 545
10.7 Protection of Two-Source System with Directional Relays 546
10.8 Zones of Protection 547
10.9 Line Protection with Impedance (Distance) Relays 551
10.10 Di¤erential Relays 557
10.11 Bus Protection with Di¤erential Relays 559
10.12 Transformer Protection with Di¤erential Relays 560
10.13 Pilot Relaying 565
10.14 Digital Relaying 566
CHAPTER 11 Transient Stability 579
Case Study: Real-Time Dynamic Security Assessment 581
11.1 The Swing Equation 590
11.2 Simplified Synchronous Machine Model and System
Equivalents 596
11.3 The Equal-Area Criterion 598
11.4 Numerical Integration of the Swing Equation 608
11.5 Multimachine Stability 613
11.6 A Two-Axis Synchronous Machine Model 621
11.7 Wind Turbine Machine Models 625
11.8 Design Methods for Improving Transient Stability 632
CHAPTER 12 Power System Controls 639
Case Study: Overcoming Restoration Challenges Associated
with Major Power System Disturbances 642
12.1 Generator-Voltage Control 652
12.2 Turbine-Governor Control 657
12.3 Load-Frequency Control 663
12.4 Economic Dispatch 667
12.5 Optimal Power Flow 680
CHAPTER 13 Transmission Lines: Transient Operation 690
Case Study: VariSTAR8 Type AZE Surge Arresters 691
Case Study: Change in the Air 695
13.1 Traveling Waves on Single-Phase Lossless Lines 707
13.2 Boundary Conditions for Single-Phase Lossless Lines 710
x CONTENTS
13.3 Bewley Lattice Diagram 719
13.4 Discrete-Time Models of Single-Phase Lossless Lines
and Lumped RLC Elements 724
13.5 Lossy Lines 731
13.6 Multiconductor Lines 735
13.7 Power System Overvoltages 738
13.8 Insulation Coordination 745
CHAPTER 14 POWER DISTRIBUTION 757
Case Study: The Path of the Smart Grid 759
14.1 Introduction to Distribution 770
14.2 Primary Distribution 772
14.3 Secondary Distribution 780
14.4 Transformers in Distribution Systems 785
14.5 Shunt Capacitors in Distribution Systems 795
14.6 Distribution Software 800
14.7 Distribution Reliability 801
14.8 Distribution Automation 804
14.9 Smart Grids 807
Appendix 814
Index 818
CONTENTS xi
PREFACE TO THE SI EDITION
This edition of Power System Analysis and Design has been adapted to incorporate the International System of Units (Le Syste`me International d’Unite´s
or SI) throughout the book.
LE SYSTE`ME INTERNATIONAL D’UNITE´S
The United States Customary System (USCS) of units uses FPS (foot–
pound–second) units (also called English or Imperial units). SI units are primarily the units of the MKS (meter–kilogram–second) system. However,
CGS (centimeter–gram–second) units are often accepted as SI units, especially in textbooks.
USING SI UNITS IN THIS BOOK
In this book, we have used both MKS and CGS units. USCS units or FPS
units used in the US Edition of the book have been converted to SI units
throughout the text and problems. However, in case of data sourced from
handbooks, government standards, and product manuals, it is not only extremely di‰cult to convert all values to SI, it also encroaches upon the intellectual property of the source. Also, some quantities such as the ASTM grain
size number and Jominy distances are generally computed in FPS units and
would lose their relevance if converted to SI. Some data in figures, tables, examples, and references, therefore, remains in FPS units. For readers unfamiliar with the relationship between the FPS and the SI systems, conversion tables have been provided inside the front and back covers of the book.
To solve problems that require the use of sourced data, the sourced
values can be converted from FPS units to SI units just before they are to be
used in a calculation. To obtain standardized quantities and manufacturers’
data in SI units, the readers may contact the appropriate government agencies
or authorities in their countries/regions.
INSTRUCTOR RESOURCES
A Printed Instructor’s Solution Manual in SI units is available on request. An
electronic version of the Instructor’s Solutions Manual, and PowerPoint
slides of the figures from the SI text are available through http://login.
cengage.com.
The readers’ feedback on this SI Edition will be highly appreciated and
will help us improve subsequent editions.
The Publishers
xii
PREFACE
The objective of this book is to present methods of power system analysis and
design, particularly with the aid of a personal computer, in su‰cient depth
to give the student the basic theory at the undergraduate level. The approach
is designed to develop students’ thinking processes, enabling them to reach a
sound understanding of a broad range of topics related to power system
engineering, while motivating their interest in the electrical power industry.
Because we believe that fundamental physical concepts underlie creative
engineering and form the most valuable and permanent part of an engineering
education, we highlight physical concepts while giving due attention to mathematical techniques. Both theory and modeling are developed from simple beginnings so that they can be readily extended to new and complex situations.
This edition of the text features new Chapter 14 entitled, Power Distribution. During the last decade, major improvements in distribution reliability
have come through automated distribution and more recently through the
introduction of ‘‘smart grids.’’ Chapter 14 introduces the basic features of primary and secondary distribution systems as well as basic distribution components including distribution substation transformers, distribution transformers,
and shunt capacitors. We list some of the major distribution software vendors
followed by an introduction to distribution reliability, distribution automation,
and smart grids.
This edition also features the following: (1) wind-energy systems modeling in the chapter on transient stability; (2) discussion of reactive/pitch control
of wind generation in the chapter on powers system controls; (3) updated case
studies for nine chapters along with four case studies from the previous edition
describing present-day, practical applications and new technologies; (4) an
updated PowerWorld Simulator package; and (5) updated problems at the end
of chapters.
One of the most challenging aspects of engineering education is giving
students an intuitive feel for the systems they are studying. Engineering systems are, for the most part, complex. While paper-and-pencil exercises can
be quite useful for highlighting the fundamentals, they often fall short in
imparting the desired intuitive insight. To help provide this insight, the book
uses PowerWorld Simulator to integrate computer-based examples, problems,
and design projects throughout the text.
PowerWorld Simulator was originally developed at the University of
Illinois at Urbana–Champaign to teach the basics of power systems to
nontechnical people involved in the electricity industry, with version 1.0 introduced in June 1994. The program’s interactive and graphical design made
xiii