Distribution System Modeling and Analysis (Electric Power Engineering Series)

329 Pages·2001·4.54 MB·English

by  William H. Kersting

Distribution
System
Modeling
and
Analysis
ThThee E ELLEECCTTRRIICC PPOOWWEERR EENNGGIINNEEEERRIINNGG SSeerireises
sseerrieiess eeddiittoorr LLeeoo GGrriiggssbyy
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
CRC Press
Boca Raton London New York Washington, D.C.
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
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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 Introduction to Distribution Systems...........................................1
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
2 The Nature of Loads.....................................................................11
2.1 Definitions............................................................................................11
2.2 Individual Customer Load................................................................13
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
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3 Approximate Methods of Analysis.............................................39
3.1 Voltage Drop........................................................................................39
3.2 Line Impedance...................................................................................41
3.3 “K” Factors..........................................................................................43
3.3.1 The K Factor.......................................................................43
drop
3.3.2 The K Factor........................................................................46
rise
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
4 Series Impedance of Overhead and Underground Lines.........77
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
5 Shunt Admittance of Overhead and Underground Lines......109
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
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6 Distribution System Line Models.............................................125
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 Regulation of Voltages...............................................................145
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
7.4.1 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
8 Three-Phase Transformer Models .............................................199
8.1 Introduction.......................................................................................199
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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9 Load Models.................................................................................251
9.1 Wye-Connected Loads.....................................................................252
9.1.1 Constant Real and Reactive Power Loads.......................252
9.1.2 Constant Impedance Loads................................................253
9.1.3 Constant Current Loads......................................................253
9.1.4 Combination Loads..............................................................254
9.2 Delta-Connected Loads...................................................................257
9.2.1 Constant Real and Reactive Power Loads.......................257
9.2.2 Constant Impedance Loads................................................258
9.2.3 Constant Current Loads......................................................258
9.2.4 Combination Loads..............................................................258
9.2.5 Line Currents Serving a Delta-Connected Load.............259
9.3 Two-Phase and Single-Phase Loads..............................................259
9.4 Shunt Capacitors...............................................................................259
9.4.1 Wye-Connected Capacitor Bank........................................259
9.4.2 Delta-Connected Capacitor Bank......................................260
9.5 The Three-Phase Induction Motor.................................................261
References...................................................................................................266
Problems........................................................................................266
10 Distribution Feeder Analysis.....................................................269
10.1 Power-Flow Analysis.....................................................................269
10.1.1 The Ladder Iterative Technique.....................................270
10.1.1.1 Linear Network................................................270
10.1.1.2 Nonlinear Network..........................................271
10.1.2 The General Feeder..........................................................274
10.1.3 The Unbalanced Three-Phase Distribution Feeder.....276
10.1.3.1 Series Components..........................................276
10.1.3.2 Shunt Components..........................................278
10.1.4 Applying the Ladder Iterative Technique....................279
10.1.5 Putting It All Together.....................................................279
10.1.6 Load Allocation.................................................................289
10.1.7 Summary of Power-Flow Studies..................................289
10.2 Short-Circuit Studies......................................................................290
10.2.1 General Theory..................................................................290
10.2.2 Specific Short Circuits......................................................293
10.3 Summary..........................................................................................298
References...................................................................................................299
Problems........................................................................................299
Appendix A..........................................................................................303
Appendix B..........................................................................................307
Index.....................................................................................................309
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Preface
In the last 40 years many papers and textbooks devoted to the computer
modeling and analysis of large power system networks have been written.
For the most part the models and analysis techniques have been developed
for large interconnected transmission systems and synchronous generators.
Little, if any, attention was devoted to the distribution system and its major
components. As a result, the distribution engineer has not had the same
number of tools as the systems engineer to analyze the distribution system
under steady-state (power-flow) and fault (short-circuit) conditions. Without
these tools the distribution engineer has been left in the dark (no pun inten-
ded) as to the operating characteristics of distribution feeders. A lot of “seat
of the pants” engineering has had to take place in order to keep the lights on.
In recent years more attention has been devoted to the computer modeling
and analysis of distribution systems. Computer programs are now available
so that the distribution engineer can develop a real feel for how the distri-
bution system is operating. With the tools, power-flow studies can be run to
simulate present loading conditions and to help with the long-range plan-
ning of new facilities. The tools also provide an opportunity for the distri-
bution engineer to do such things as optimize capacitor placement in order
to minimize losses. Different switching scenarios for normal and emergency
conditions can be simulated, and short-circuit studies provide the necessary
data for the development of a reliable coordinated protection plan for fuses,
reclosers, and relay/circuit breakers. In short, the distribution engineer now
has the needed tools.
So what is the problem? “Garbage in, garbage out” is the answer. Armed
with a commercially available computer program, it is possible for a user to
prepare incorrect data that will lead to results that do not make any sense.
Without an understanding of the models and a general “feel” for the operating
characteristics of a distribution system, serious design errors and operational
procedures may result. The user must fully understand the models and
analysis techniques of the program.
Most power systems textbooks and courses are limited to the modeling
and analysis of balanced three-phase systems. The models and analyses
assume a balance so that only a single-phase equivalent model is required.
While this works fine for interconnected systems, it is not sufficient for the
modeling and analysis of a distribution system. A distribution system is
inherently unbalanced, and therefore three-phase models of all the compo-
nents must be employed. There is a significant difference between the com-
puter programs developed for interconnected system studies and the
programs developed for distribution systems. The data requirements for the