Power system analysis and design solution PDF

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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

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Power System Analysis and Design, Fifth Edition, SI J. Duncan Glover, Mulukutla S. Sarma, and Thomas J. Overbye Publisher, Global Engineering: Christopher M. Shortt Acquisitions Editor: Swati Meherishi

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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

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CONTENTS Preface to the SI Edition xii Preface xiii List of Symbols, Units, and Notation CHAPTER 1

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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 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

47

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 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

116

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CONTENTS

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 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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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

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CONTENTS

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 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 Case 13.1 13.2

Study: VariSTAR8 Type AZE Surge Arresters 691 Study: Change in the Air 695 Traveling Waves on Single-Phase Lossless Lines 707 Boundary Conditions for Single-Phase Lossless Lines 710

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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 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9

Study: The Path of the Smart Grid 759 Introduction to Distribution 770 Primary Distribution 772 Secondary Distribution 780 Transformers in Distribution Systems 785 Shunt Capacitors in Distribution Systems 795 Distribution Software 800 Distribution Reliability 801 Distribution Automation 804 Smart Grids 807

Appendix 814 Index 818

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P R E FA C E TO T H E S I E D I T I O N 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

P R E F A C E 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

xiv

PREFACE

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

PREFACE

xv

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, i...