## CONTENTS

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

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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

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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

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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

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

## 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

it an immediate hit as an educational tool, but a funny thing happened—its

interactive and graphical design also appealed to engineers doing analysis of

real power systems. To meet the needs of a growing group of users,

PowerWorld Simulator was commercialized in 1996 by the formation of

PowerWorld Corporation. Thus while retaining its appeal for education, over

the years PowerWorld Simulator has evolved into a top-notch analysis package,

able to handle power systems of any size. PowerWorld Simulator is now

used throughout the power industry, with a range of users encompassing universities,

utilities of all sizes, government regulators, power marketers, and

consulting firms.

In integrating PowerWorld Simulator with the text, our design philosophy

has been to use the software to extend, rather than replace, the fully

worked examples provided in previous editions. Therefore, except when the

problem size makes it impractical, each PowerWorld Simulator example includes

a fully worked hand solution of the problem along with a PowerWorld

Simulator case. This format allows students to simultaneously see the details

of how a problem is solved and a computer implementation of the solution.

The added benefit from PowerWorld Simulator is its ability to easily extend

the example. Through its interactive design, students can quickly vary example

parameters and immediately see the impact such changes have on the

solution. By reworking the examples with the new parameters, students get immediate

feedback on whether they understand the solution process. The interactive

and visual design of PowerWorld Simulator also makes it an excellent

tool for instructors to use for in-class demonstrations. With numerous examples

utilizing PowerWorld Simulator instructors can easily demonstrate many

of the text topics. Additional PowerWorld Simulator functionality is introduced

in the text problems and design projects.

The text is intended to be fully covered in a two-semester or threequarter

course o¤ered to seniors and first-year graduate students. The organization

of chapters and individual sections is flexible enough to give the

instructor su‰cient latitude in choosing topics to cover, especially in a onesemester

course. The text is supported by an ample number of worked examples

covering most of the theoretical points raised. The many problems to be

worked with a calculator as well as problems to be worked using a personal

computer have been expanded in this edition.

As background for this course, it is assumed that students have had

courses in electric network theory (including transient analysis) and ordinary

di¤erential equations and have been exposed to linear systems, matrix algebra,

and computer programming. In addition, it would be helpful, but not necessary,

to have had an electric machines course.

After an introduction to the history of electric power systems along

with present and future trends, Chapter 2 on fundamentals orients the students

to the terminology and serves as a brief review. The chapter reviews phasor

concepts, power, and single-phase as well as three-phase circuits.

Chapters 3 through 6 examine power transformers, transmission-line

parameters, steady-state operation of transmission lines, and power flows

including the Newton–Raphson method. These chapters provide a basic

understanding of power systems under balanced three-phase, steady-state,

normal operating conditions.

Chapters 7 through 10, which cover symmetrical faults, symmetrical

components, unsymmetrical faults, and system protection, come under the

general heading of power system short-circuit protection. Chapter 11 (previously

Chapter 13) examines transient stability, which includes the swing

equation, the equal-area criterion, and multi-machine stability with modeling

of wind-energy systems as a new feature. Chapter 12 (previously Chapter 11)

covers power system controls, including turbine-generator controls, loadfrequency

control, economic dispatch, and optimal power flow, with reactive/

pitch control of wind generation as a new feature. Chapter 13 (previously

Chapter 12) examines transient operation of transmission lines including

power system overvoltages and surge protection. The final and new Chapter 14

introduces power distribution.