ELECTRICAL POWER SYSTEMS, Study notes of Electrical Engineering

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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

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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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

Case Study: The Problem of Arcing Faults in Low-Voltage

 - CHAPTER 1 Introduction List of Symbols, Units, and Notation xix - Industry Heed the Call? Case Study: The Future Beckons: Will the Electric Power - 1.1 History of Electric Power Systems - 1.2 Present and Future Trends - 1.3 Electric Utility Industry Structure - 1.4 Computers in Power System Engineering - 1.5 PowerWorld Simulator 

• CHAPTER 2 Fundamentals - Case Study: Making Microgrids Work - 2.1 Phasors - 2.2 Instantaneous Power in Single-Phase AC Circuits - 2.3 Complex Power - 2.4 Network Equations - 2.5 Balanced Three-Phase Circuits - 2.6 Power in Balanced Three-Phase Circuits - Single-Phase Systems 2.7 Advantages of Balanced Three-Phase Versus
  • CHAPTER 3 Power Transformers - Case Study: PJM Manages Aging Transformer Fleet - 3.1 The Ideal Transformer - 3.2 Equivalent Circuits for Practical Transformers - 3.3 The Per-Unit System - 3.4 Three-Phase Transformer Connections and Phase Shift - Two-Winding Transformers 3.5 Per-Unit Equivalent Circuits of Balanced Three-Phase - 3.6 Three-Winding Transformers - 3.7 Autotransformers - 3.8 Transformers with O¤-Nominal Turns Ratios
  • 6.4 The Power-Flow Problem
  • 6.5 Power-Flow Solution by Gauss–Seidel
  • 6.6 Power-Flow Solution by Newton–Raphson
  • 6.7 Control of Power Flow
  • 6.8 Sparsity Techniques
  • 6.9 Fast Decoupled Power Flow
  • 6.10 The ‘‘DC’’ Power Flow
  • 6.11 Power-Flow Modeling of Wind Generation
  • Design Projects 1–5
• CHAPTER 7 Symmetrical Faults - Power Distribution Systems
  • 7.1 Series R–L Circuit Transients
    • Synchronous Machine 7.2 Three-Phase Short Circuit—Unloaded
  • 7.3 Power System Three-Phase Short Circuits
  • 7.4 Bus Impedance Matrix
  • 7.5 Circuit Breaker and Fuse Selection
  • Design Project 4 (continued )
• CHAPTER 8 Symmetrical Components
  • Case Study: Circuit Breakers Go High Voltage
  • 8.1 Definition of Symmetrical Components
  • 8.2 Sequence Networks of Impedance Loads
  • 8.3 Sequence Networks of Series Impedances
  • 8.4 Sequence Networks of Three-Phase Lines
  • 8.5 Sequence Networks of Rotating Machines
    • Two-Winding Transformers 8.6 Per-Unit Sequence Models of Three-Phase
    • Three-Winding Transformers 8.7 Per-Unit Sequence Models of Three-Phase
  • 8.8 Power in Sequence Networks
• CHAPTER 9 Unsymmetrical Faults
  • Case Study: Fires at U.S. Utilities
  • 9.1 System Representation
  • 9.2 Single Line-to-Ground Fault
  • 9.3 Line-to-Line Fault
  • 9.4 Double Line-to-Ground Fault
  • 9.5 Sequence Bus Impedance Matrices
  • Design Project 4 (continued )
  • Design Project
• CHAPTER 10 System Protection - Case Study: The Future of Power Transmission - 10.1 System Protection Components - 10.2 Instrument Transformers - 10.3 Overcurrent Relays - 10.4 Radial System Protection - 10.5 Reclosers and Fuses - 10.6 Directional Relays - 10.7 Protection of Two-Source System with Directional Relays - 10.8 Zones of Protection - 10.9 Line Protection with Impedance (Distance) Relays - 10.10 Di¤erential Relays - 10.11 Bus Protection with Di¤erential Relays - 10.12 Transformer Protection with Di¤erential Relays - 10.13 Pilot Relaying - 10.14 Digital Relaying
• CHAPTER 11 Transient Stability - Case Study: Real-Time Dynamic Security Assessment - 11.1 The Swing Equation - Equivalents 11.2 Simplified Synchronous Machine Model and System - 11.3 The Equal-Area Criterion - 11.4 Numerical Integration of the Swing Equation - 11.5 Multimachine Stability - 11.6 A Two-Axis Synchronous Machine Model - 11.7 Wind Turbine Machine Models - 11.8 Design Methods for Improving Transient Stability
  • CHAPTER 12 Power System Controls - with Major Power System Disturbances Case Study: Overcoming Restoration Challenges Associated
    • 12.1 Generator-Voltage Control
    • 12.2 Turbine-Governor Control
    • 12.3 Load-Frequency Control
    • 12.4 Economic Dispatch
    • 12.5 Optimal Power Flow
• CHAPTER 13 Transmission Lines: Transient Operation - Case Study: VariSTAR^8 Type AZE Surge Arresters - Case Study: Change in the Air - 13.1 Traveling Waves on Single-Phase Lossless Lines - 13.2 Boundary Conditions for Single-Phase Lossless Lines
  • 13.3 Bewley Lattice Diagram
    • and Lumped RLC Elements 13.4 Discrete-Time Models of Single-Phase Lossless Lines
  • 13.5 Lossy Lines
  • 13.6 Multiconductor Lines
  • 13.7 Power System Overvoltages
  • 13.8 Insulation Coordination
• CHAPTER 14 POWER DISTRIBUTION
  • Case Study: The Path of the Smart Grid
  • 14.1 Introduction to Distribution
  • 14.2 Primary Distribution
  • 14.3 Secondary Distribution
  • 14.4 Transformers in Distribution Systems
  • 14.5 Shunt Capacitors in Distribution Systems
  • 14.6 Distribution Software
  • 14.7 Distribution Reliability
  • 14.8 Distribution Automation
  • 14.9 Smart Grids
  • Appendix
  • Index

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 incor- porate 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 pri- marily the units of the MKS (meter–kilogram–second) system. However, CGS (centimeter–gram–second) units are often accepted as SI units, espe- cially 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 ex- tremely di‰cult to convert all values to SI, it also encroaches upon the intel- lectual 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, ex- amples, and references, therefore, remains in FPS units. For readers unfamil- iar with the relationship between the FPS and the SI systems, conversion ta- bles 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

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 pack- age, able to handle power systems of any size. PowerWorld Simulator is now used throughout the power industry, with a range of users encompassing uni- versities, utilities of all sizes, government regulators, power marketers, and consulting firms. In integrating PowerWorld Simulator with the text, our design philoso- phy 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 in- cludes 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 im- mediate feedback on whether they understand the solution process. The inter- active and visual design of PowerWorld Simulator also makes it an excellent tool for instructors to use for in-class demonstrations. With numerous exam- ples utilizing PowerWorld Simulator instructors can easily demonstrate many of the text topics. Additional PowerWorld Simulator functionality is in- troduced in the text problems and design projects. The text is intended to be fully covered in a two-semester or three- quarter course o¤ered to seniors and first-year graduate students. The orga- nization of chapters and individual sections is flexible enough to give the instructor su‰cient latitude in choosing topics to cover, especially in a one- semester course. The text is supported by an ample number of worked exam- ples 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 neces- sary, 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

xiv PREFACE

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 (pre- viously 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, load- frequency 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.

ADDITIONAL RESOURCES

Companion websites for this book are available for both students and in- structors. These websites provide useful links, figures, and other support ma- terial. The Student Companion Site includes a link to download the free stu- dent version of PowerWorld. The Instructor Companion Site includes access to the solutions manual and PowerPoint slides. Through the Instructor Com- panion Site, instructors can also request access to additional support mate- rial, including a printed solutions manual. To access the support material described here along with all additional course materials, please visit www.cengagebrain.com. At the cengage- brain.com home page, search for the ISBN of your title (from the back cover of your book) using the search box at the top of the page. This will take you to the product page where these resources can be found.

ACKNOWLEDGMENTS

The material in this text was gradually developed to meet the needs of classes taught at universities in the United States and abroad over the past 30 years. The original 13 chapters were written by the first author, J. Duncan Glover, Failure Electrical LLC, who is indebted to many people who helped during the planning and writing of this book. The profound influence of earlier texts written on power systems, particularly by W. D. Stevenson, Jr., and the de- velopments made by various outstanding engineers are gratefully acknowl- edged. Details of sources can only be made through references at the end of each chapter, as they are otherwise too numerous to mention. Chapter 14 (Power Distribution) was a collaborative e¤ort between Dr. Glover (Sections 14.1–14.7) and Co-author Thomas J. Overbye (Sections 14.8 & 14.9). Professor Overbye, University of Illinois at Urbana-Champaign,

PREFACE xv

at Urbana–Champaign; R. Ramakumar, Oklahoma State University; Teodoro C. Robles, Milwaukee School of Engineering, Ronald G. Schultz, Cleveland State University; Stephen A. Sebo, Ohio State University; Raymond Shoults, University of Texas at Arlington, Richard D. Shultz, University of Wisconsin at Platteville; Charles Slivinsky, University of Missouri–Columbia; John P. Stahl, Ohio Northern University; E. K. Stanek, University of Missouri–Rolla; Robert D. Strattan, University of Tulsa; Tian-Shen Tang, Texas A&M University–Kingsville; S. S. Venkata, University of Washington; Francis M. Wells, Vanderbilt University; Bill Wieserman, University of Pennsylvania– Johnstown; Stephen Williams, U.S. Naval Postgraduate School; and Salah M. Yousif, California State University–Sacramento.

First Edition: Frederick C. Brockhurst, Rose-Hulman Institute of Technology; Bell A. Cogbill. Northeastern University; Saul Goldberg, California Polytechnic State University; Mack Grady, University of Texas at Austin; Leonard F. Grigsby, Auburn University; Howard Hamilton, University of Pittsburgh; William F. Horton, California Polytechnic State University; W. H. Kersting, New Mexico State University; John Pavlat, Iowa State University; R. Ramakumar, Oklahoma State University; B. Don Russell, Texas A&M; Sheppard Salon, Rensselaer Polytechnic Institute; Stephen A. Sebo, Ohio State University; and Dennis O. Wiitanen, Michigan Technological University. In conclusion, the objective in writing this text and the accompanying software package will have been fulfilled if the book is considered to be student-oriented, comprehensive, and up to date, with consistent notation and necessary detailed explanation at the level for which it is intended.

J. Duncan Glover Mulukutla S. Sarma Thomas J. Overbye

PREFACE xvii

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