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distribution system modeling and analysis.pdf

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    Contents
    Preface
    The Author
    1. Introduction to Distribution Systems
    2. The Nature of Loads
    3. Approximate Methods of Analysis
    4. Series Impedance of Overhead and Underground Lines
    5. Shunt Admittance of Overhead and Underground Lines
    6. Distribution System Line Models
    7. Regulation of Voltages
    8. Three-Phase Transformer Models
    9. Load Models
    10. Distribution Feeder Analysis
    Appendices
    Index
    Distribution System Modeling and Analysis
    The ELECTRIC POWER ENGINEERING Series The ELECTRIC POWER ENGINEERING Series series editor Leo Grigsy series editor Leo Grigsby Published Titles Electromechanical Systems, Electric Machines, and Applied Mechatronics Sergey E. Lyshevski Electrical Energy Systems Mohamed E. El-Hawary Electric Drives Ion Boldea and Syed Nasar Distribution System Modeling and Analysis William H. Kersting Linear Synchronous Motors: Transportation and Automation Systems Jacek Gieras and Jerry Piech Forthcoming Titles Induction Machine Handbook Ion Boldea and Syed Nasar Power System Operations in a Restructured Business Environment Fred I. Denny and David E. Dismukes Power Quality C. Sankaran
    Distribution System Modeling and Analysis William H. Kersting New Mexico State University Las Cruces, New Mexico Boca Raton London New York Washington, D.C. CRC Press
    0812_frame_FM.fm Page iv Tuesday, July 31, 2001 10:49 AM Library of Congress Cataloging-in-Publication Data Kersting, William H. Distribution system modeling and analysis / William H. Kersting p. cm. -- (Electric power engineering series) Includes bibliographical references and index. ISBN 0-8493-0812-7 (alk. paper) 1. Electric power distribution–Mathematical models. I. Title. II. Series. TK3001 .K423 2001 621.31—dc21 2001035681 CIP This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: used only for identification and explanation, without intent to infringe. Product or corporate names may be trademarks or registered trademarks, and are Visit the CRC Press Web site at www.crcpress.com © 2002 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-0812-7 Library of Congress Card Number 2001035681 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
    0812_frame_FM.fm Page v Tuesday, July 31, 2001 10:49 AM Contents 1 2 ........................................... 1 Introduction to Distribution Systems 1.1 The Distribution System......................................................................2 1.2 Distribution Substations ......................................................................2 1.3 Radial Feeders.......................................................................................5 1.4 Distribution Feeder Map.....................................................................6 1.5 Distribution Feeder Electrical Characteristics..................................8 1.6 Summary................................................................................................9 ..................................................................... 11 The Nature of Loads 2.1 Definitions............................................................................................ 11 Individual Customer Load................................................................13 2.2 2.2.1 Demand ...................................................................................13 2.2.2 Maximum Demand................................................................13 2.2.3 Average Demand....................................................................14 2.2.4 Load Factor .............................................................................14 2.3 Distribution Transformer Loading...................................................15 2.3.1 Diversified Demand...............................................................16 2.3.2 Maximum Diversified Demand...........................................17 2.3.3 Load Duration Curve ............................................................17 2.3.4 Maximum Noncoincident Demand ....................................17 2.3.5 Diversity Factor ......................................................................18 2.3.6 Demand Factor .......................................................................19 2.3.7 Utilization Factor....................................................................19 2.3.8 Load Diversity ........................................................................20 2.4 Feeder Load.........................................................................................20 2.4.1 Load Allocation ......................................................................20 2.4.1.1 Application of Diversity Factors...........................21 2.4.1.2 Load Survey..............................................................21 2.4.1.3 Transformer Load Management............................25 2.4.1.4 Metered Feeder Maximum Demand ....................25 2.4.1.5 What Method to Use? .............................................27 2.4.2 Voltage-Drop Calculations Using Allocated Loads..........27 2.4.2.1 Application of Diversity Factors...........................27 2.4.2.2 Load Allocation Based upon Transformer Ratings................................................31 2.5 Summary..............................................................................................32 Problems.......................................................................................... 33
    0812_frame_FM.fm Page vi Tuesday, July 31, 2001 10:49 AM 3 4 5 drop rise K K ............................................. 39 Approximate Methods of Analysis 3.1 Voltage Drop........................................................................................39 3.2 Line Impedance...................................................................................41 3.3 “K” Factors ..........................................................................................43 Factor.......................................................................43 3.3.1 The 3.3.2 The Factor........................................................................46 3.4 Uniformly Distributed Loads ...........................................................47 3.4.1 Voltage Drop ...........................................................................48 3.4.2 Power Loss ..............................................................................50 3.4.3 The Exact Lumped Load Model..........................................52 3.5 Lumping Loads in Geometric Configurations ..............................55 3.5.1 The Rectangle..........................................................................55 3.5.2 The Triangle ............................................................................60 3.5.3 The Trapezoid .........................................................................65 3.6 Summary..............................................................................................71 References .....................................................................................................71 Problems.......................................................................................... 71 ......... 77 Series Impedance of Overhead and Underground Lines 4.1 Series Impedance of Overhead Lines..............................................77 4.1.1 Transposed Three-Phase Lines.............................................78 4.1.2 Untransposed Distribution Lines ........................................79 4.1.3 Carson’s Equations ................................................................81 4.1.4 Modified Carson’s Equations...............................................83 4.1.5 Primitive Impedance Matrix for Overhead Lines ............85 4.1.6 Phase Impedance Matrix for Overhead Lines ..................86 4.1.7 Sequence Impedances............................................................89 4.2 Series Impedance of Underground Lines.......................................95 4.2.1 Concentric Neutral Cable .....................................................96 4.2.2 Tape-Shielded Cables...........................................................101 4.3 Summary............................................................................................105 References ...................................................................................................105 Problems........................................................................................ 105 ...... 109 Shunt Admittance of Overhead and Underground Lines 5.1 The General Voltage-Drop Equation ............................................. 110 5.2 Overhead Lines................................................................................. 111 5.3 Concentric Neutral Cable Underground Lines ........................... 115 5.4 Tape-Shielded Cable Underground Lines .................................... 119 5.5 Sequence Admittance.......................................................................121 5.6 Summary............................................................................................122 References ...................................................................................................122 Problems........................................................................................ 122
    0812_frame_FM.fm Page vii Tuesday, July 31, 2001 10:49 AM 6 7 8 ............................................. 125 Distribution System Line Models 6.1 Exact Line Segment Model .............................................................125 6.2 The Modified Line Model ...............................................................132 6.3 The Approximate Line Segment Model .......................................136 6.4 Summary............................................................................................141 References ...................................................................................................141 Problems........................................................................................ 141 7.4.1 ............................................................... 145 Regulation of Voltages 7.1 Standard Voltage Ratings ................................................................145 7.2 Two-Winding Transformer Theory................................................147 7.3 The Two-Winding Autotransformer..............................................152 7.3.1 Autotransformer Ratings ....................................................156 7.3.2 Per-Unit Impedance.............................................................158 7.4 Step-Voltage Regulators...................................................................162 Single-Phase Step-Voltage Regulators ..............................163 7.4.1.1 Type A Step-Voltage Regulator............................163 7.4.1.2 Type B Step-Voltage Regulator............................164 7.4.1.3 Generalized Constants ..........................................167 7.4.1.4 The Line Drop Compensator...............................168 7.4.2 Three-Phase Step-Voltage Regulators ...............................174 7.4.2.1 Wye-Connected Regulators..................................175 7.4.2.2 Closed Delta-Connected Regulators...................180 7.4.2.3 Open Delta-Connected Regulators .....................183 7.5 Summary............................................................................................193 References ...................................................................................................194 Problems........................................................................................ 194 ............................................. 199 Three-Phase Transformer Models Introduction.......................................................................................199 8.1 8.2 Generalized Matrices .......................................................................200 8.3 The Delta–Grounded Wye Step-Down Connection....................201 8.3.1 Voltages..................................................................................202 8.3.2 Currents .................................................................................206 8.4 The Ungrounded Wye–Delta Step-Down Connection...............212 8.5 The Grounded Wye–Grounded Wye Connection.......................222 8.6 The Delta–Delta Connection...........................................................224 8.7 The Open Wye–Open Delta Connection ......................................236 8.8 The Thevenin Equivalent Circuit...................................................242 8.9 Summary............................................................................................245 Problems........................................................................................ 245
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