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Distribution System Modeling and Analysis

 

Distribution System Modeling and Analysis Fourth Edition

William H. Kersting

 

MALAB® is a trademark o Te MathWorks, Inc. and is used with permission. Te MathWorks does not warrant the accuracy o the text or exercises in this book. Tis book’s use or discussion o MALAB® sotware or related products does not constitute endorsement or sponsorship by Te MathW Math Works o a particular part icular pedagogical approach or particular use o the MALAB® M ALAB® sotware. sotwa re. CRC Press aylor & Francis Group 6000 600 0 Broken Broke n Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by aylor & Francis Group, LLC CRC Press is an imprint o aylor & Francis Group, an Inorma business No claim to original U.S. Government works Printed on acid-ree paper International Standard Book Number-13: 978-1-4987-7213-6 (Hardback) Tis book contains inormation in ormation obtained rom authentic authentic and highly hig hly regarded sources. Reasonable Reasonable eorts have been made to publish reliable data and inormation, but the author and publisher cannot assume responsibility or the validity o all materials or the consequences o their use. Te authors and publishers have attempted to trace the copyright holders o all material reproduced in this publication and apologize to copyright holders i permission to publish in this orm has not been obtained. I any copyright material has not been acknowledged please write and let us know so we may rectiy in any uture utu re reprint. reprint. Except as permitted under U.S. Copyright Law, no part o this book may be reprinted, reproduced, transmitted, or utilized in any orm by any electronic, mechanical, or other means, now known or hereater invented, including photocopying, microflming, and recording, or in any inormation storage or retrieval system, without written writ ten permission rom the publishers. For permission to photocopy or use material electronically rom this work, please access www. copyright.com (http://www.copyright.com/) http://www.copyright.com/),, or contact the Copyright Copyrig ht Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-or-proft organization that provides licenses and registration or a variety o users. u sers. For organizations that have been granted a photocopy license by the CCC, a separate system o payment has been b een arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and

are used only or identifcation and explanation without intent to inringe. in ringe. Library of Congress Cataloging‑in‑Publication Data

Names: Kersting, William H., author. itle: Distribution system modeling modeling and analysis / William Wi lliam H. Kersting. Description: Fourth edition. | Boca Raton : aylor & Francis, CRC Press, 2017. Identifers: LCCN 2017010755 | ISBN 9781498772136 (hardback : alk. paper) | ISBN 9781498772143 (ebook) Subjects: LCSH: Electric power distribution--Mathematical distribution--Mathematical models. Classifcation: LCC K3001 .K423 2017 | DDC 333.793/2--dc23 LC record available at https://lccn.loc.gov/2017010755

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Contents

Preace............. ........................... ........................... ........................... ............................ ............................ ............................ ............................ ......................xi ........xi Acknowledgments Acknowl edgments ............ .......................... ............................ ............................ ............................ ............................ ......................... ...........xvii xvii Author Au thor ............. ........................... ........................... ........................... ............................ ............................ ............................ ............................ ................... ..... xix   1. Introduction Introduct ion to Distr Distribution ibution Systems .............. ............................ ............................ ............................1 ..............1 1.1 The Distribution Syst System em ............ .......................... ............................ ............................ ............................ ..................11 1.2 Distribution Substa Substations tions .............. ............................ ............................ ............................ ............................2 ..............2 1.3 Radial Feeders ............. ........................... ............................ ............................ ........................... ........................... ................... .....55 1.4 Distribution Feeder Map............ .......................... ............................ ............................ ............................ ..................66 1.5 Distribution Feeder Electrical Characteristics ............. ........................... ..................... .......88 1.6 Summary ............. ........................... ........................... ........................... ............................ ............................ ............................9 ..............9 Reerence ............ .......................... ............................ ............................ ............................ ........................... ........................... ..........................9 ............9   2. The Nature of Loads ............. ........................... ............................ ............................ ........................... ........................... ................. ... 11 2.1 Denitions ............. ........................... ............................ ............................ ........................... ........................... ........................ .......... 11 2.2 Individual Cust Customer omer Load ............. ........................... ........................... ........................... ........................ ..........13 13 2.2.1 Demand ............. ........................... ............................ ............................ ............................ ............................ ..............13 13 2.2.2 Maximum Demand .............. ............................ ............................ ............................ ..................... ....... 13 2.2.3 Avera verage ge Demand ............. ........................... ............................ ............................ .......................... ............ 14 2.2.4 Load Facto Factorr .............. ............................ ............................ ............................ ............................ ..................... ....... 14 2.3 Distribution Transormer Loading .............. ........................... ........................... ........................ ..........15 15 2.3.1 Divers Diversied ied Demand ............. ........................... ............................ ............................ ..................... ....... 16 2.3.2 Maximum Divers Diversied ied Demand ............. .......................... ........................... ................. ... 16 2.3.3 Load Duration Curve ............. ........................... ............................ ............................ ................... ..... 17 2.3.4 Maximum Noncoincid Noncoincident ent Demand ............ .......................... ........................ .......... 18 2.3.5 Divers Diversity ity Facto Factorr .............. ............................ ............................ ............................ ............................ ..............18 18 2.3.6 Demand Factor ............. .......................... ........................... ............................ ............................ ................. ... 19 2.3.7 Utilization Facto Factorr ............. ........................... ............................ ............................ .......................... ............20 20 2.3.8 Load Divers Diversity ity .............. ........................... ........................... ............................ ............................ ................. ... 20 2.4 Feeder Load Load............. ........................... ............................ ............................ ............................ ........................... ..................... ........20 20 2.4.1 Load Allocation .............. ............................ ............................ ........................... ........................... ................ 21 2.4.1.1 App Application lication o Divers Diversity ity Facto Factors rs............ .......................... ................ 21 2.4.1.2 Load Survey ............. ........................... ............................ ........................... ................... ...... 21 2.4.1.3 Transormer Load Management .............. ..........................25 ............25 2.4.1.4 Metered Feeder Maximum Demand ............. ................... ......26 26 2.4.1.5 What Method to Use Use?? ............. ........................... ............................ ................. ... 27 2.4.2 Voltag oltagee Drop Calculations Using Allocated Loads .......... ..........28 28

2.4.2.1 2.4.2.2  

Application o Divers Application Diversity ity Facto Factors rs............ .......................... ................ 28 Load Allocation Based upon Transormer Ratings ............. ........................... ........................... ................... ...... 32 v

 

 

vi

Contents

2.5 Summary ............. ........................... ........................... ........................... ............................ ............................ .......................... ............33 33 Problems............. ........................... ............................ ............................ ............................ ............................ ............................ ....................... .........33 33   3. Approximate Method of Analysis ............. .......................... ........................... ............................ ..................... .......39 39 3.1 Voltag oltagee Drop .............. ............................ ............................ ............................ ............................ ........................... .................. ..... 39

3.2 3.3

3.4

3.5

Line Impedance .............. ............................ ........................... ........................... ............................ ............................ ..............41 41 “K”” Factors ............ “K .......................... ............................ ............................ ............................ ............................ ....................... .........42 42 3.3.1 K drop Factor ................................... ................................................. ........................... ........................... ................. ...43 43 3.3.2 K rise Facto Factorr ............. ........................... ........................... ........................... ............................ .......................... ............45 45 Uniormly Distributed Loads............. ........................... ............................ ............................ ................... .....47 47 3.4.1 Voltag oltagee Drop ............ .......................... ............................ ............................ ............................ ..................... .......47 47 3.4.2 Po Power wer Loss ............. ........................... ........................... ........................... ............................ ........................ ..........50 50 3.4.3 The Exact Lumped Load Model .............. ............................ ........................... ............... 52 Lumping Lump ing Loads in Geometric Confgurations .............. ............................ ................. ...55 55 3.5.1 The Rectangle ............ .......................... ............................ ............................ ............................ ................... .....55 55 3.5.2 The Triangle ............. ........................... ............................ ............................ ............................ ..................... .......60 60 3.5.3 The Trapezoi rapezoid d ............. .......................... ........................... ............................ ............................ ................... .....65 65

3.6 Summary ........................... ............. ............................ ........................... ........................... ............................ .......................... ............71 71 Problems ........................... ............. ............................ ............................ ............................ ............................ ........................... ....................... ..........71 71 Reerence ............ .......................... ............................ ............................ ............................ ............................ ........................... ....................... .......... 76   4. Series Impedance of Overhead and Underground Lines .........  .....................7 ............777 4.1 Series Impedance o Overhea Overhead d Lines ............ .......................... ............................ ..................... .......77 77 4.1.1 Transposed Three Three-Phase -Phase Lines .............. ............................ ............................ .................. 78 4.1.2 Untransposed Distribution Lines ............ .......................... ............................ ..............79 79 4.1.3 Carson’ Carson’ss Equations ............. ........................... ............................ ............................ ....................... .........81 81 4.1.4 Modifed Carson’ Carson’ss Equations ............. .......................... ........................... ..................... .......83 83 4.1.5 Primitive Impedance Matrix or Overhea Overhead d Lines .............86 4.1.6 Phase Impedance Matrix or Overhea Overhead d Lines ............ ................... .......86 86 4.1.7 Sequence Impedances ............. ........................... ............................ ............................ .................. ....89 89 4.1.8 Parallel Overhea Overhead d Distribution Lines ............ .......................... ..................... .......96 96 4.2 Series Impedance o Und Underground erground Lines ............ .......................... ............................99 ..............99 4.2.1 Concentric Neutral Cable .............. ............................ ............................ ....................... ......... 100 4.2.2 Tape-Shielded Cables .............. ............................ ............................ ............................ .................. 106 4.2.3 Parallel Und Underground erground Distribution Lines ............ ........................ ............ 109 4.3 Summar Summary y ............. ........................... ............................ ............................ ............................ ............................ ....................... ......... 113 Problems ........................................................................................................ 114 WindMil Assignment ............. .......................... ........................... ............................ ............................ ............................ .............. 118 Reerences ............. ........................... ............................ ............................ ............................ ........................... ........................... ................... ..... 119   5. Shunt Admitt Admittance ance of Overhead and Underground Lines .................. ................. 121 5.1 General Volta oltage ge Drop Equation ............ .......................... ............................ ............................ ..............121 121 5.2 Overhea Overhead d Lines .............. ............................ ............................ ........................... ........................... .......................... ............123 123 5.2.1 The Shunt Admittance o Overhea Overhead d Parallel   Lines .............. ............................ ............................ ............................ ............................ ............................ .................. 127

 

Contents

5.3 5.4 5.5 5.6 5.7

vii

Concentric Neutral Cable Und Concentric Underground erground Lines Lines.............. ............................ ................ 130 Tape-Shielded Cable Und Underground erground Lines ............. ........................... ........................ ..........134 134 Sequence Admittance ............ .......................... ............................ ............................ ............................ ................. ... 136 The Shunt Admittance o Parallel Und Underground erground Lines ............. ............... 13 1377 Summary ............. ........................... ........................... ........................... ............................ ............................ ........................ ..........138 138

Problems............. ........................... ............................ ............................ ............................ ............................ ........................... ..................... ........ 138 WindMil Assignment ............ .......................... ............................ ............................ ............................ ........................... ............... 139 Reerences ............. ........................... ........................... ........................... ............................ ............................ ............................ ................... ..... 139   6. Distribution Dist ribution System Line Models .............. ............................ ............................ ............................ ................. ... 141 6.1 Exact Line Segment Model ............. ........................... ........................... ........................... ...................... ........ 141 6.2 The Modifed Line Model ............ .......................... ............................ ............................ ........................ ..........150 150 6.2.1 The Three Three-W -Wire ire Delta Line .............. ........................... ........................... ...................... ........ 150 6.2.2 The Comp Computation utation o Neutral and Ground   Currents............. ........................... ............................ ............................ ............................ .......................... ............ 15 1522 6.3 The App Approximate roximate Line Segment Model............. ........................... ........................... ............... 155 6.4 The Modifed “Ladd “Ladder” er” Iter Iterative ative Techn echnique ique .............. ............................ ................... ..... 160

6.5

The Matrices or Parallel Lines .............. ............................ .......................... ............ 6.5.1General Physically Physi cally Parallel Lines ............. ........................... ............................ .......................... ............ 1163 66 6.5.2 Electrically Parallel Lines ............. ........................... ............................ ........................ .......... 172 6.6 Summary ............. ........................... ............................ ........................... ........................... ............................ ........................ ..........177 177 Problems.............. ........................... ........................... ............................ ............................ ............................ ............................ ..................... ....... 17 1788 WindMil Assignment ............ .......................... ............................ ............................ ............................ ............................ ..............183 183 Reerences ............. ........................... ............................ ........................... ........................... ............................ ............................ ................... ..... 183   7. V Voltage oltage Regu Regulat lation ion ............. ........................... ............................ ............................ ........................... ........................... ................. ... 185 7.1 Standa Standard rd Voltage Rati Ratings ngs.............. ............................ ............................ ........................... ....................... .......... 185 7.2 Twowo-Winding Winding Transormer Theory ............. ........................... ............................ ..................... ....... 18 1877 7.3 Twowo-Winding Winding Au Autotransormer totransormer .............. ............................ ............................ .......................... ............ 192 7.3.1 Au Autotransormer totransormer Ratings ............ .......................... ............................ .......................... ............ 19 1966 7.3.2 Per Per-unit -unit Impedance .............. ............................ ............................ ............................ ................... ..... 199 7.4 StepStep-V Voltag oltagee Regulators ............. ........................... ............................ ............................ .......................... ............202 202 7.4.1 Single-Phase StepStep-V Voltag oltagee Regulators..... Regulators................... .......................... ............204 204 7.4.1.1 Type A Step-V Step-Voltage oltage Regu Regulator lator .......... .................... ................ ...... 204 7.4.1.2 Type B Step-V Step-Voltage oltage Regu Regulator lator ........... ..................... ................ ...... 206 7.4.1.3 Generalized Constants .............. ............................ .......................... ............208 208 7.4.1.4 The Line Drop Compensat Compensator or ............. ........................... ................. ... 209 7.4.2 Three Three-Phase -Phase StepStep-V Voltag oltagee Regulators .............. ............................ ................. ... 21 2166 7.4.2.1 Wy Wye-Connected e-Connected Regulators ............. ........................... ................... ..... 21 2166 7.4.2.2 Closed Delta-Connected Regulators .............. ................. ...226 226 7.4.2.3 Open Delta-Connected Regulators............ .................... ........229 229 7.5 Summary ............. ........................... ........................... ........................... ............................ ............................ ........................ .......... 24 2411 Problems............. ........................... ............................ ............................ ............................ ............................ ........................... ..................... ........ 24 2411 WindMil Assignment ............ .......................... ............................ ............................ ............................ ........................... ............... 247 Reerences ............. ........................... ........................... ........................... ............................ ............................ ............................ ................... ..... 247

 

 

viii

Contents

  8. Thr Three-Phase ee-Phase Transformer Models ............. ........................... ............................ ............................ ................. ... 249

8.1 8.2 8.3

Introduction ............ .......................... ............................ ............................ ............................ ........................... ................... ...... 249 Generalized Matrices......... Matrices....................... ........................... ........................... ............................ ...................... ........250 250 The Delta–Grounded Wy Wyee Step-Down Connection ............ .................... ........ 251 8.3.1 Voltag oltages es ............. ........................... ............................ ............................ ........................... .......................... .............251 251

8.3.2 Currents............. ........................... ............................ ............................ ........................... .......................... .............256 256 8.4 The Delta–Grounded Wy Wyee Step-Up Connection ............. .......................... .............267 267 8.5 The Ungrounded Wy Wye–Delta e–Delta Step-Down Connection ............. ................ ... 269 8.6 The Ungrounded Wy Wye–Delta e–Delta Step-Up Connection ............. ..................... ........ 281 8.7 The Grounded Wy Wye–Delta e–Delta Step-Down Connection ............ .................... ........283 283 8.8 Open Wy Wye– e–Open Open Delta .............. ............................ ............................ ........................... .......................... .............290 290 8.9 The Grounded Wy Wye– e–Grounded Grounded Wy Wyee Connection Connection.............. ........................ ..........296 296 8.10 The Delta–Delta Connection .............. ............................ ............................ ............................ ................. ... 299 8.111 Open Delta–Open Delta 8.1 Delta............. ........................... ........................... ........................... ...........................309 .............309 8.12 Thevenin Equivalent Circuit .............. ............................ ............................ ........................... ................. .... 31 3144 8.13 Summar Summary y ............ .......................... ............................ ............................ ............................ ............................ ........................ .......... 31 3177 Problems............. ........................... ........................... ........................... ............................ ............................ ............................ ...................... ........ 31 3188 WindMil Assignment .............. ............................ ............................ ........................... ........................... ........................... .............323 323 .......................................... ............................ ............................ ........................... ........................... ........................... .............325 325 Wye-Connected Wy e-Connected Loads ............ .......................... ............................ ............................ ............................ ................ 325 9.1.1 Constant Real and Reactive Po Power wer Loads .............. ........................ ..........326 326 9.1.2 Constant Impedance Loads ............ .......................... ............................ ...................... ........ 327 9.1.3 Constant Current Loads.............. ........................... ........................... ........................... .............327 327 9.1.4 Combination Loads .............. ............................ ............................ ........................... ................... ...... 328 Delta-Connected Loads .............. ............................ ............................ ........................... .......................... .............332 332 9.2.1 Constant Real and Reactive Po Power wer Loads .............. ........................ ..........332 332 9.2.2 Constant Impedance Loads ............ .......................... ............................ ...................... ........333 333 9.2.3 Constant Current Loads.............. ............................ ........................... .......................... .............333 333 9.2.4 Combination Loads .............. ............................ ............................ ........................... ................... ......334 334 9.2.5 Line Currents Servi Serving ng a Delta-Connected Load .............334 Two-Phase and Single-Phase Loads .............. ............................ ........................... ................... ......334 334 Shunt Capa Capacitors citors .............. ........................... ........................... ............................ ............................ ........................ ..........334 334 9.4.1 Wy Wye-Connected e-Connected Capaci Capacitor tor Bank .............. ............................ ..........................334 ............334 9.4.2 Delta-Connected Capaci Capacitor tor Bank .............. ............................ ........................ ..........335 335 Three-Phase Induction Machine ............. ........................... ............................ .......................... ............336 336 9.5.1 Induction Machine Model ............ .......................... ............................ ........................ ..........337 337 9.5.2 Symmetrical Compon Component ent Analysis of a Motor ............. ................ ...340 340 9.5.3 Phase Analysis of an Induction Motor ............ .......................... ................. ...346 346 9.5.4 Voltag oltagee and Current Unbalance............. .......................... ........................... ................ 353 9.5.5 Motor Starti Starting ng Current ............. ........................... ........................... ........................... ................ 354 9.5.6 The Equivalent T  Circuit ............... ............................. ............................ ........................ ..........354 354 9.5.7 Comp Computation utation of Slip.............. ............................ ............................ ............................ ................... ..... 36 3611 9.5.8 Induction Generato Generatorr ............. ........................... ............................ ............................ ................... ..... 362

  9. Load Models

9.1

9.2

9.3 9.4

9.5

 

Contents

ix

9.5.9 Induction Machine Thevenin Equivalent Circuit ........... ...........365 365 9.5.10 The Unground Ungrounded ed Wy Wye–Delta e–Delta Transormer Bank   with an Induction Motor............. ........................... ............................ .......................... ............368 368 9.6 Summary ............. ........................... ........................... ........................... ............................ ............................ ........................ ..........375 375 Problems............. ........................... ............................ ............................ ............................ ............................ ........................... ..................... ........ 37 3766 Reerences ............. .......................... ........................... ............................ ............................ ............................ ............................ ................... .....380 380  10. 10. Distribution Dist ribution Feeder Analysi Analysiss ............. ........................... ............................ ............................ .......................... ............381 381 10.1 Po Powerwer-Flow Flow Analysis .............. ........................... ........................... ............................ ............................ ................. ... 381 10.1.1 The Ladder Ladder Iterativ Iterativee Techn Technique ique ............. ........................... ............................ ..............382 382 10.1.1.1 Linear Network Network ............ .......................... ............................ .......................... ............382 382 10.1.1.2 Nonlinear Network Network ............. ........................... ............................ ................... .....383 383 10.1.2 General Feeder ............. ........................... ............................ ............................ ............................386 ..............386 10.1.3 The Unbalanced Three-Phase Distribution Feeder ........ ........387 387 10.1.3.1 Shunt Components Components.............. ............................ ............................ ................... .....388 388 10.1.4 App Applying lying the Ladder Ladder Iterativ Iterativee Techn Technique ique .............. ........................ ..........389 389 10.1.5 Let’ Let’ss Put It All Together Together .............. ............................ ............................ .......................... ............390 390

10.1.6 ............................ .............. ............................ ............................ .......................... ............398 398 10.1.7 Load Loop Allocation Flow .............. ............................ ............................ ............................ ........................... ..................... ........399 399 10.1.7.1 Single-Phase Feeder Feeder .............. ............................ ............................ ................. ... 399 10.1.7.2 IEEE 13 13 Bus Test Test Feeder ............. ........................... ..........................405 ............405 10.1.7.3 Summar Summary y o Loop Flow .............. ............................ ........................ .......... 41 4122 10.1.8 Summar Summary y o Po Powerwer-Flow Flow Studies .............. ............................ ........................ .......... 41 4122 10.2 Short Short-Circuit -Circuit Studies .............. ........................... ........................... ............................ ............................ ................. ... 41 4133 10.2.1 General Short Short-Circuit -Circuit Theory ............. ........................... ............................ ................. ... 41 4133 10.2.2 Specifc Short Circuits ............ .......................... ............................ ............................ ................. ... 41 4177 10.2.3 Backeed Ground Faul Faultt Currents Currents ............. ........................... ..........................422 ............422 10.2.3.1 One Downstrea Downstream m Tr Transormer ansormer Bank ............. ................ ...423 423 10.2.3.2 Comp Complete lete Three-Phase Circuit Analysis ........... ...........426 426 10.2.3.3 Backeed Currents Summary ............ .......................... ................. ...435 435 10.3 Summary ............. ........................... ........................... ........................... ............................ ............................ ........................ ..........435 435 Problems............. ........................... ............................ ............................ ............................ ............................ ........................... ..................... ........436 436 WindMil Assignment .............. ............................ ............................ ............................ ............................ ..........................442 ............442 Reerences ............. .......................... ........................... ............................ ............................ ............................ ............................ ................... .....447 447  11. 11. Center-Tapped Center-Tapped Transfor Transformers mers and a nd Secondaries ........................  .................................... ............449 449 11.1 CenterCenter-T Tapped Single Single-Phase -Phase Tr Tran ansormer sormer Model .......... .................... .............. .... 449 11.1.1 Matrix Equations..... Equations................... ............................ ............................ ............................ ................... .....453 453 11.1.2 CenterCenter-T Tapped Transormer Ser Servi ving ng Loads through a Triplex Secondary S econdary ............. ........................... ............................ ................... .....460 460 11.2 Ungrounded Wye–Delta Tr Tran ansormer sormer Ban Bank k with Center-Tapped Transormer ............................................................466 11.2.1 Basic Transormer Equations ............ .......................... ............................ ................... .....466 466 11.2.2 Summar Summary y.............. ............................ ............................ ........................... ........................... ........................ ..........483 483

 

x

 

Contents

11.3 Open Wy Wye– e–Open Open Delta Transformer Connections .............. ...................... ........484 484 11.3.1 The Leading Open Wy Wye– e–Open Open Delta Connection ..........48 ..........4844 11.3.2 The Lagging Open Wy Wye– e–Open Open Delta Delta Connection .......... ..........485 485 11.3.3 Forward Sw Sweep eep .............. ............................ ............................ ............................ .......................... ............486 486 11.3.4 Backward Sw Sweep eep ............ .......................... ............................ ............................ .......................... ............490 490 11.4 Four-Wire Four-Wire Secondary .............. ............................ ........................... ........................... ............................ ................. ... 493 11.5 Putting It All Together......... ogether....................... ............................ ............................ ............................ ................... ..... 497 11.5.1 Ungrounded Wy Wye–Delta e–Delta Connection .............. ............................ ................. ... 497 11.5.2 Open Wye–Delta Wye–Delta Connections ............ .......................... ............................ ................. ...503 503 11.5.3 Com Comparisons parisons of Volta oltage ge and Curren Currentt Unb Unbalances alances .......... ..............508 508 11.6 Summary ............. ........................... ........................... ........................... ............................ ............................ ........................ ..........508 508 Problems............. ........................... ............................ ............................ ............................ ........................... ........................... ...................... ........509 509 WindMil Homework Assignment ............................ .......................................... ............................ ................... ..... 51 5100 References ............. .......................... ........................... ............................ ............................ ............................ ............................ ................... ..... 51 5111 Appendix A: Conductor Data ............. ........................... ............................ ............................ ........................... ................... ...... 51 5133 Appendix B: Underground Cable Data ............ .......................... ............................ ............................ ................. ... 51 5177 Index ............ .......................... ............................ ............................ ............................ ............................ ........................... ........................... ...................... ........ 51 5199

 

Preface

One o the “hot” topics today is the “smart grid.” At the very start, I want to emphasize that this text is intended to only develop and demonstrate the computer models o all o the physical components o a distribution system. As the text develops the component models, it will become clear that what we we called “load” is the weak link in the overall analysis ana lysis o a distribution system. At present, the only true inormation available or every customer is the energy, in kilowatt hours, consumed during a specied period. This topic is addressed in Chapter 2. The T he problem with load is that it is constantly changing. cha nging. Computer Computer programs can be and have been developed that will very accurately model the components; but without real load data the results o the studies are only as good as the load data used. As the smart smar t grid is developed, developed, more accurate load data will wil l become available, which provide provid or a much more accurate o the operating ditionswill o the distreibution distribution system. system. What needsanalysis to be emphasized i s thatconis the smart grid must have computer programs that will very accurately model all o the physical physical components o the system. The purpose o this t his text is i s to develop the very accurate models o the physical components o a distribution system. In the model developments, it is very important to accurately model the unbalanced nature o the components. Programs used in the modeling o a transmission system make the assumption that the system is a balanced three-phase system. This makes it possible to model only one phase. That is not the case in the modeling o a distribution di stribution system. system. The unbalanced unbala nced nature o the distribution system has to be modeled. This requirement requi rement is made possible by modeling all three phases o every component o the distribution system. The distribution d istribution system computer computer program or pow power-fo er-fow w studies can be run to simulate present loading conditions and or long-range planning o new acilities. For example, the tools provide an opportunity or the distri bution engineer to optimize optimi ze capacitor placement placement to minimi min imize ze power losses. Dierent switching scenarios or normal and emergency conditions can be simulated. Short-circuit studies provide the necessary data or the development o a reliable coordinated protection plan or uses and recloser and relay/ relay /circ circuit uit breake breakers. rs. So what is the problem? Garbage in, garbage out is the answer. Armed with a commercially available computer program, it is possible or the user to prepare incorrect data, and as a result, the program outputs are not correct. Without an understanding o the models and a general “eel” or the operating characteristics o a distribution system, serious design errors and operational procedures may result. The user must ully understand the  xi

 

xiii xi

 Preface

models and analysis techniques o the program. Without this knowledge, the garbage in, garbage ga rbage out out problem becomes very very real. rea l. The purpose o this text is to present the reader a general overall eeling or the operating characteristics o a distribution system and the modeling o each component. Beore using the compu computer ter program, it is extremely ext remely important or the student/engineer to have a “eel” or what the answers should  be. When W hen I was still sti ll teaching, I would bring bri ng up how my generation used us ed a slide rule as our compu computational tational tool. The advantage o using a slide rule was you were orced to know what the “ballpark” “ba llpark” answer a nswer should be. We have have lost that ability owing to hand ha nd calculators and computers, computers, but understanding the  ballpark answer is still still a necessity. necessity. It has been very interesting to receive many questions and comments about previous editions o the text rom undergraduate and graduate students in addition to practicing engineers rom around the world. That gets  back to the need ne ed or the “eel” o the correct correc t answer a nswer.. New students need to study the early chapters o the book in order to develop this “eel.” Practicing engineers will already have the “eel” and perhaps will not need the early chapters 2, and 3). contents In developing o and the book, I have retained (1, most o the o thethe rstourth threeedition editions have added “advanced” topics in the nal our chapters. The advanced topics should be o interest to the practicing engineers. engi neers. This textbook assumes that the reader has a basic understanding o transormers, electric electric machines, mach ines, transmission lines, and symmetrical sym metrical components. components. In many universities, all o these topics are crammed into a one-semester course. For that reason, a quick review o the needed theory is presented as required. There are many example problems throughout the text. These examples are intended to not only demonstrate the application o the models but also teach the “eel” o what the answers should be. The example problems should be studied very careully since they demonstrate the application o the theory just presented. Each chapter has a series o homework problems that will assist the student in applying the models and developing a better understanding o the operating characteristics o the component being modeled. Most o the example and homework problems are very number-intensive. All o the example problems have used a sotware package called “Mathcad” [1]. I have ound this sotware to be a wonderul number-crunching tool used to apply the models and perorm the analysis o a eeder e eder.. Many simple Mathcad routines are display displayed ed in some o the more intensive example example problems. The students are urged to learn how to use this th is powerul tool. The students are also encouraged to write their own computer programs or many o the homework problems. These programs can use Mathcad or the t he more popular MATLAB® [2]. As more components are developed and the eeder becomes more complicated, it becomes necessary to use a sophisticated distribution

 

 Preface

xiii

analysis program. Milsot Utility Solutions has made a student version o “WindMil” [3] available along with a user’s manual. The user’s manual includes instructions and illustration on how to get started using the program. Starting Starti ng in Chapter 4, there is a WindMil assignment a ssignment at the end o the homework problems. A very simple system utilizing all o the major components o the system will evolve as each chapter assignment is completed. In Chapter 10, the data or a small system are given that will allow the student/engineer to match operating criteria. The student version o WindMil and the user’s user’s manual can be downloaded rom the Milsot Utility Solu S olutions tions website homepage. The address is: Milsot Utility Solutions P.O. Box 7526 Abilene, TX 79608 E-mail: support@milso E-mail:  support@milsot.co t.com m Homepage: www.milsot.com Homepage:  www.milsot.com Unortunately, there a tendency on theAlthough part ugh o the student/engineer to  believe the results o aiscompu computer ter program. program. Altho computer compu ter programs programs are a wonderul wonderul tool, it is still stil l the responsibility o the users to study the results and confrm whether or not the results make sense. That is a major concern and one that is addressed throughou t hroughoutt the text. Chapter 1 presents a quick overview o the major components o a distribution system. This is the only section in the text that will present the components inside a substation along with two connection schemes. The importance o the distribution dist ribution eeder map and the data required is presented. Chapter 2 addresses the important question—what is the “load” on the system?? This system Thi s chapter defnes the common terms associated a ssociated with the load. In the past, there was limited knowledge o the load, and many assumptions had to be made. With With the coming o the smart grid, there will be ampl a mplee realtime data to assist in defning the load or a given study. Even with better load data, data, there will wi ll still sti ll be a concern on whether or not the computer computer results make sense. Chapter 3 may seem to be old ashioned and o not much use because it develops dev elops some approximate approximate methods that help in deve developing loping a eel or ballpark answers. It is important that the new students study this chapter in detail; in the process, they will discover ways o evaluating the correctness o computer program results. The major requirement o a distribution system is to supply sae and reliable energy to every customer at a voltage within the ANSI standard is addressed in Chapters 4 and 5. The major goal o planning is to simulate the distribution system under dierent conditions now and into the uture and ensure that t hat all customer voltages voltages are within with in the acceptable ANSI range. Because voltage drop is a major concern, it is extremely important that the

 

xiv

 Preface

impedances o the system components be as accurate as possible. In particular, the impedances o the overhead and underground distribution lines must be computed as accurately as possible. The importance o a detailed eeder map that includes the phase positions or both overhead and underground line is i s emphasized. emphasized. Chapter 6 develops develops the models or overhead and underground lines li nes using the impedances and admittance computed in earlier chapters. The “exact” model along with an approximate approxim ate model is included. The “ladder” (orward/  backward sweep sweep)) iterativ iterativee method used by by many commercial commercial programs and the matrices required or the application o the ladder analysis method are introduced. Methods o modeling parallel distribution lines are included in this chapter chapter.. Chapter 7 addresses the important concept o voltage voltage regulation: How is it possible to maintain maintai n every customer’ c ustomer’ss voltage voltage within with in ANSI A NSI standards when the load is varying varyi ng all o the t he time? The step-voltag step-voltagee regulator is presented as an answer to the question. A model is developed or the application in the ladder technique techn ique.. Chapter 8 is one(closed o the and mostopen) important chapters in the text.inModels or most three-phase transormer connections use today are developed. Again, the models use matrices that are used in the ladder iterative itera tive technique. The importance o phasing phasi ng is emphasized once again. Chapter 9 develops the models or all types o loads on the system. A new term is introduced that helps dene the types o static load models. The term ter m is “ZIP. “ZIP.” Most static models in a distr distribution ibution system can be modeled as constant impedance (Z (Z), constant current (I  (I ), ), or constant complex power (P (P), or a combination o the three. These models are developed or wye and delta connections. A very important model developed is that o an induction machine. mac hine. The T he induction motor is the workhorse o the power system and needs, once again, to be modeled as accurately as possible. Several new sections have been included in this chapter that develop models o the induction machine and associated transormer connection that are useul or power-fow and short-circuit studies. Induction generators are becoming a major source o distributed generation. Chapter 9 shows that an induction machine can be modeled either as a motor or as a generator. Chapter 10 puts everything in the text together or steady-state power-fow and short-circuit studies. The “ladder” iterative technique is introduced in Chapter 4. This chapter goes into detail on the development o the ladder technique starting with the analysis o a linear ladder network that is introduced in most early circuit analysis courses. This moves onto the nonlinear nature o the three-phase unbalanced distribution eeder. The ladder technique is used or power-fow studies. A method or the analysis o shortcircuit conditions on a eeder is introduc i ntroduced ed in this t his chapter c hapter.. Chapter 11 11 introduces the centercenter-tapped tapped transormer that th at is used or providproviding the three-wire service to customers. Models or the various connections

 

 Preface

xv

are introduced that are used in the ladder iterative technique and shortcircuit analysis. The WindMil assignments at the end o Chapters 10 and 11 allow the student/engineer to build and to study and fx the operating characteristics o a small smal l distribution eeder.

References

     

1. Mathcad: www.ptc.com Mathcad: www.ptc.com 2. MATLAB: MATLAB: www.mathworks.com  www.mathworks.com 3. WindMil: WindMil: www.milsot.com  www.milsot.com

 

 Acknowledg  Ackno wledgme ments nts

I want to thank the many students and engineers who have communicated with me via e-mail their questions about some of the contents of the third edition. It has been a pleasure to work with these individuals in helping them to understand better some of the models and applications in the text. Since I am retired, ret ired, it has been a real rea l pleasure to have the opportunity to work with many graduate students working on their research involving distribution systems. I hope that students and practicing engineers will continue to feel free fre e to contact me at bjkersti at [email protected] [email protected].. Special thanks to Wayne Carr, Milsoft Utility Solutions, Inc., for allowing me to make WindMil a major part of the third and fourth editions. Thanks also to the t he many support engineers at Milsoft Mil soft who have guided me in developing the special WindMil assignments. always , I 50 want to thank tha mybeen wife,very Joanne, who hasme been suppo ofAs mealways, for over years. Shenkhas patient with as very I worked worsupportive ked onrtive t he the fourth edition.

 xvii

 

 Author 

William H. Kersting received his BSEE from New Mexico State University (NMSU), Las Cruces, NM and his MSEE from the Illinois Institute of Technology. Prior to attending graduate school and for a year after graduate school, he was employed by El Paso Electric Company as a distribution engineer. He joined the faculty at NMSU in 1962 and served as a professor of electrical engineering and from 1968 as the director of the Electric Utility Management Program until his retirement in 2002. He is currently a consultant for Milsoft Milsof t Utility Solutions. Professor Kersting is a life fellow of the Institute of Electrical and Electronics Electron ics Engineers (IEEE). He received the NMSU Westhafer award for Excellence in Teaching in 1977 and the Edison Electric Institutes’ Power Engineering Education award in 1979. He has been an active member of the IEEE Power

Engineering Education Committee and the Distribution Systems Analysis Subcommittee.

 xix

 

1  Introduction to Distr Distribution ibution Systems Systems The major components o an electric power system are shown in Figure 1.1. O these components, the distribution system has traditionally been characterized as the most unglamorous component. In the latter hal o the 20th century, the design and operation o the generation and transmission components presented many challenges to the practicing engineers and researchers. Power Power plants became larger, and transmission lines li nes crisscrossed the land, orming large interconnected networks. The operation o the large interconnected networks required the development o new analysis and operational techniques. Meanwhile, the distribution systems continued to deliver power to the ultimate user’s meter with little or no analysis. As a direct result, distribution systems were typically over-designed. over-designed. Nowadays, it has become very important and necessary to operate a distribution system at its maximum max imum capacity. capacity. Some o the questions that need to  be answered are as ollows: ollows:          

1. 2. 3. 4.

What is the maximum capaci capacity? ty? How do we determine this capaci How capacity? ty? What are the operating limits that must be satised satised?? What can be done to operat operatee the distribution system within the operating limits li mits?? 5. What can be done to make the distribution system operat operatee more more eciently?

All o these questions can be answered only i the distribution system is modeled very accurately. The purpose o this text is to develop accurate accurate models or all o the major components o a distribution distribut ion system. Once the models have have been developed, analysis techniques or steady-state and short-circuit conditions will be developed.

1.1 The Distribution System The distribution distr ibution system system typically ty pically starts with the distribution substation that is ed by one or more subtransmission lines. In some cases, the distribution 1

 

Distribution System Modeling Modeling and Analysis

2

Interconnected Generation

transmission system

Bulk power

Subtransmission

Distribution

Primary 

substation

network

substation

feeders

FIGURE 1.1

Major power system components.

substation is ed directly rom a high-vo high-voltage ltage transmission line in i n which case, most likely, likely, there is no subtransmission system. This Thi s varies rom company to company compan y. Each distribution di stribution substation will serve ser ve one or more primary primar y eeders. With a rare exception, the eeders are radial, which means that there is only one path or power to fow rom the distribution d istribution substation to the user.

1.2 Distribution Substations A one-line diagram o a very simple distribution substation is shown in Figure 1.2. Although Figure 1.2 displays the simplest o distribution substations, it does illustrate the major components components that will wil l be ound in all substations.  

 

 

1. Hig 1.  High-side h-side and low-side switchi switching ng:: In Figure 1.2, the high-voltage switching is done with a simple switch. Substations that are more extensive may use high-voltage high-voltage circuit breakers (C (CBs Bs)) in a variety variet y o high-voltage bus designs. The low-voltage switching in Figure 1.2 is accomplished with relay-controlled CBs. In many cases, reclosers will be used in place o the relay–CB combination. Some substation designs include a low-voltage bus CB in addition to the CBs or each eeder. As is the case with the high-voltage bus, the low-voltage bus can take on a variety o designs. 2. Voltage transformation transformat ion:: The primary unction  unction o a distribution substation is to reduce the voltage down to the distribution dist ribution voltage level. In Figure 1.2, only one transormer is shown. Other substation designs will call or two or more three-phase transormers. The substation transormers can be three-phase units or three single-phase units connected in a standard connection. There are many ma ny “standard” “standard” distribution tribut ion voltage levels. Some o the common co mmon ones are 34.5, 3 4.5, 23.9 23.9, 14.4, 14.4, 13.2, 12.47 kV kV, and, in older syste systems, ms, 4.1 4.166 kV kV.. 3. Voltage regulation: regulation: Because the load on the eeders vary, the voltage drop between the substation and the user will vary. In order to maintain maintai n the user’ user’ss voltages voltages within withi n an acceptab acceptable le range, the vol voltage tage

 

 Introduction  Introduc tion to t o Distributio Distr ibution n Systems

3

Subtransmission line Disconnect switch Fuse Transformer Voltage regulator

Meters

Circuit breakers Primary feeders FIGURE 1.2

Simple distribution substation.

at the substation needs to vary as the load varies. In Figure 1.2, the voltage is regulated by a “step-type” regulator that will vary the voltage vol tage plus or minus 10% on the low-side low-side bus. Sometimes this unction is accom accomplished plished with a “load tap changing” chang ing” (LTC) (LTC) transormer tra nsormer.. The LTC LTC changes cha nges the taps on the t he low-v low-voltag oltagee windings wi ndings o the transormer as the load varies. Many substation transormers will have “xed taps” on the high-voltage winding. These are used when the source voltage is always either above or below the nominal voltage. The xed tap settings setti ngs can vary the t he voltage voltage plus or minus 5%. Mostly, Mostly, instead o a bus regulator, each eeder will have its own regulator.

 

 

This can be in the orm o a three-phase gang-operated regulator or individual phase regulators that operate independently. Protection:: The substation must be protected against the occurrence 4. Protection o short circuits. In the simple design in Figure 1.2, the only automatic protection against short circuits inside i nside the substation is by way way o the high-side uses on the transormer. As the substation designs  become more comp complex, lex, more extensive protective schemes will be employed to protect the transormer, the high- and low-voltage  buses, and a nd any other piece o equipment equipment.. Individual eeder ee der CBs or reclosers are used use d to provide provide interruption o short circuits that occur outside the substation. 5. Metering 5.  Metering:: Every substation has some orm o metering. This may be as simple as an analog ana log ammeter displaying the present value o substation current as well well as the minimum mi nimum and maximum maxi mum currents that have occurred over a specic time period. Digital recording meters

 

Distribution System Modeling Modeling and Analysis

4

are becoming very common. These meters record the minimum, average, and maximum values o current, voltage, power, power actor, etc., over a specied time range. Typical time ranges are 15 min, 30 min, and 1 h. The T he digital d igital meters may monitor the outpu outputt o each substation transormer and/or the output o each eeder. A more comprehensive substation layout is shown in Figure 1.3. The substation in Figure 1.3 has two LTC transormers, serves our distri bution eeders, ee ders, and a nd is ed rom two substransmission lines. Und Under er normal conditions,, the CBs are in conditions i n the ollowing positions po sitions:: Circuit breakers closed: X , Y , 1, 3, 4, 6 Circuit breakers open: Z, 2, 5 With the breakers in their normal positions, each transormer is served rom a dierent subtransmission line and serves two eeders. I one o the subtransmission lines goes out o service, then breaker X   or Y  is   is opened and  breaker Z is closed. Now both transormers are served rom the same subtransmission line. The transormers are sized such that each transormer can supply all our eeders under an emergency operating condition. For example, i transormer T-1 is out o service, then breakers X , 1, and 4 are opened and breakers 2 and 5 are closed. With that breaker arrangement, all Line 1

Line 2  X 

N.C.

N.C. N.O.

 Z 

T-1

T-2

N.C.

N.O.

N.C.

1

2

3

N.C.

  FD-1

4

N.O.

  FD-3

5

FD-2

N.C.

6

FD-4

FIGURE 1.3

Two-transormer substation with breaker and a hal h al scheme.

Y 

 

 Introduction  Introduc tion to t o Distributio Distr ibution n Systems

5

our eeders are served by transormer T-2. The low-voltage bus arrangement is reerred to as a “breaker and a hal scheme,” because three breakers are required to serve ser ve two eeders. There is an unlimited number o substation congurations possible. It is up to the substation design engineer to create a design that provides the ve  basic unct unctions ions and provid provides es the most reliable service economically possibl possible. e.

1.3 Radial Feeders Radial distribution eeders are characterized by the presence o only one path or power to fow rom the source (“distribution substation”) to each customer.. A typical customer t ypical distribution dist ribution system consists o one or more distribution d istribution substations consisting o one or more “eeders.” Components o the eeder may consist o the ollowing:                

1. 2. 3. 4. 5. 6. 7. 8.

Three -phase primary “main Three-phase “main”” eeder Three-phase, two-phase (“V” phase phase), ), and single-phase laterals Step-type vol voltage tage regulators In-line transormers Shunt capacitor ban banks ks Distribution transormers Secondaries Seconda ries Three-phase, Three -phase, two-phase, and single-phase loads

The loading o a distribution eeder is inherently unbalanced because o the large number o unequal single-phase loads that must be served. An additional unbalance is introduced by the nonequilateral conductor spacings o the three-phase th ree-phase overhead overhead and underground line li ne segments. Because o the nature o the distribution system, conventional conventional power-fow power-fow and short-circuit programs used or transmission system studies are not adequate. adequat e. Such programs display poor convergence convergence characteristics or radial systems. The programs also assume a perectly balanced system so that a single-phase equivalent system is used. I a distribution engineer is to be able to perorm accurate power-fo power-fow w and short-circu short -circuit it studies, it is imperative that the distribution d istribution eeder be modeled as accurately as possible. This means that three-phase models o the major components must be utilized. Three-phase models or the major components will be developed developed in the ollowing chapters. The models will wil l be developed in the “phase rame” rather than applying the method o symmetrical components. Figure 1.4 shows shows a simple “one-line” “one-line” diagram o a three-phase eeder eeder..

 

Distribution System Modeling Modeling and Analysis

6

Fuse Substation

Transformer Voltage regulator Circuit breaker

Single-phase lateral

Node b c

“V” phase lateral b

a

a b

c

c

ree-phase lateral b

Capacitor bank

c ab c

Underground Undergro und cables

Fuse b

c

Distribution transformer

b a

In-line transformer

Secondary  Customers

FIGURE 1.4

Simple distribution eeder.

Figure 1.4 illustrates the major components o a distribution system. The connecting points o the components will be reerred to as “nodes.” Note in the gure that the phasing o the line segments is shown. This is important i the t he most accurate models are to be devel developed. oped.

1.4 Distr Distribution ibution Feeder Map The analysis o a distribution eeder is important to an engineer in order to determine the existing operating conditions o a eeder ee der and to be able to play play the “what i” scenarios o uture changes to the eeder. Beore the engineer can perorm the analysis o a eeder, a detailed map o the eeder must be available. A sample o such a map is shown in Figure 1.5. The map in Figure 1.5 contains most o the ollowing inormation: in ormation:      

1. Lines Line s (o (overhead verhead and underg underground) round) a. Where b. Distances

 

 Introduction  Introduc tion to t o Distributio Distr ibution n Systems

800

7

5 ′  4 75  4 7

50 325

c

50

′

275

50

′

300

′

25 325

50 700

b

50

′

′

50 ′

50   b

300

325

′

a

50

′

 a  c

25 50 50

225 225

450 575 25

′

′

a   3  2

50

M    ′  1  7 5

  b ′

   ′   2 5 0

 b

50

25

25 750 325

′

′

100

275

′

25

b

′

50

b

50 25

500

′

′

650

c

325 300

250

′

250

25

200'

′

3–50

 c  b  a

   ′  2 5 0

a

 c  b  a

   ′  2 5 0

350

  5    ′   3  7

  3 0 0   ′

50

50

′

′

c

  5   ′  4  2

325

25

b

 5   ′   2  2

250

a

225 200

25

50

350

50

c    ′  2 2 5

25

   ′  1  7 5

50 400

′

  ′  2 5 0

abc

′

50

50 275

′

50  n  t i o  s t a  S u  b

 0   ′   3 0

25

  ′  2 0 0

c a

′

′

′

b

250

c

25 325

b

300

25

′

′

b

′

′

′

525

′

25

550

25

  0    ′   1  0

300

   ′   2 5 0

 c  a

a

50

c

50   250

 0   ′   2 5   5   ′   2  7

50

′

′

50

b

 0   ′   2 0

25

400

 a  c

′

375

 0   ′   3 0

3–100

b

′

  5    ′   8  2

   ′  2 5 0

  25

50

b

′

′

300

  0   ′   1  5

   ′   2 0 0

150

   ′  2 0 0

b

 b c b

 

25

25

b  a

3–50

   ′   3 5 0

′

a

  0    ′   2  0

b

′

′

25

50

300

′

′

′

50 250

25 25

50

200

25

a

250

′

 

c b

50 250

a ′

225

  0   ′  6  5

a ′

125 b

800

c

 5   ′   2  7

5 0 ′  35  3

c  b  a

′

50

275 ′

225

′

25 250

b

   ′   3 0 0

3–50 ′

′

b

 b  c  a

325

275

50

 a

25

a

50

3–50

2 5 0  ′

 

100

425

b

50

  0    ′   3  5

    ′   0  0   1  0

′

450

  ′  5 5 0

  5     ′

′

  0    ′

 c   ′  1 7 5

25

b

  5   ′   2  7

350

     ′    7  5   2

b

′

  0    ′   2  5

c

  0   1  0   3 –

  0     ′   2  5

′

c

a  c  b

  0    ′   7  0

  0 c   2

′

a

275

′

′

200

25

 

a

b

50 275

 2 5 0  ′

50

b

 b

′

400

25

 c  a

′

100

50

 c

 b

50

550'

575

 a c

′

 a

5 ′  4 75  4 7

 2 5 0  ′

c

 1 7 5  ′

′

350 275

25

225

50

50

 

a

400

50

′

25

50

50

′

525

 6 7 5 ′

′

25

3-Phase OH

a

3-Phase UG    ′  5 0 0

2-Phase OH

50

1-Phase OH 50

1-Phase transformer kVA 3-Phase transformer bank

3–50 Voltage regulator

FIGURE 1.5

IEEE 123 node test eeder.

 

Distribution System Modeling Modeling and Analysis

8

       

c. Details i. Conductor size sizess (not on thi thiss map map)) ii. Phasing 2. Distribution transormers

                   

a. Location b. kV kVA A rati rating ng c. Phase connection 3. In-line transormers a. Location b. kV kVA A rati rating ng c. Connection 4. Shunt capacitors a. Location b. kvar rating

                   

c. Phase connection 5. Voltage regu regulators lators a. Location b. Phase connection c. Type (not shown on thi thiss map map)) i. Single-phase ii. Three Three-phase -phase 6. Switches a. Location b. Norma Normall open/ open/close close status

1.5 Distribution Feeder Electr Electrical ical Character Characteristics istics Inormation rom the map will dene the physical location o the various devices. Electrical characteristics or each device will have to be determined beore the analysis o the eeder can commence. In order to determine the electrical characteristics, the ollowing data must be available:      

1. Overhead and underg underground round spacings 2. Conductor tables a. Geomet Geometric ric mean radius (GMR (GMR)) (t (t))

 

 Introduction  Introduc tion to t o Distributio Distr ibution n Systems

       

b. Dia Diameter meter (in. (in.)) c. Resistance (Ω/mile) 3. Voltage regu regulators lators a. Pot Potential ential transormer ratios

                   

b. Current transormer ratios c. Compensato Compensatorr setti settings ngs i. Voltage level ii. Bandwid Bandwidth th iii. R and X  settings  settings in volts 4. Tr Tran ansormers sormers a. kV kVA A rati rating ng b. Voltage rating ratingss c. Impedance (R and X ) d. No-load power loss

9

1.6 Summary As the smart grid g rid [1] [1] becomes a reality reality,, it becomes increasingly increa singly more important to be able to accurately model and analyze each component o a distribution system. There are many dierent substation designs possible; however, or the most part, the substation serves one or more radial eeders. Each component o a eeder must be modeled as accurately as possible in order or the analysis ana lysis to have meani meaning. ng. Sometimes Sometimes the most dicult task or the engineer is i s to acquire all o the necessary data. Feeder maps will contain most o the needed data. Addi Additional tional such as standard pole congurations, specic conductors conductors on each li nedata line segment, phasing, three-phase t ransormer transormer connections, andused voltvoltage regulator settings must come rom stored records. The remaining bits o inormation are the values o the loads. Chapter 2 will address the loads in a general sense. Again, when the smart sma rt grid, along with smart meters, becomes becomes a reality real ity,, the load values will become much more accurate, accurate, which in turn tu rn will wi ll make the analysis more accurate. Once all o the data have been acquired, the analysis can commence com mence by utilizing system models o the various devices that will be developed developed in later chapters.

Reference  

1. T Thomas, homas, M. S. and McDonald, J. D. D.,, Power System SCADA and Smart Grids, CRC Press, Boca Raton, FL, 2015. 2015.

 

Introduction to Distribution Systems  

Thomas, M. S. . and McDonald, J. D. , Power System SCADA and Smart Grids, CRC Press, Boca Raton, FL, 2015.10

 

Approximate Method of Analysis  

Glover, J. D. and Sarma, M. , Power System Analysis and Design, 2nd Edition, PWS Publishing Co., Boston, MA, 1994.

 

Series Impedance of Overhead and Underground Lines  

Glover, J. D. and Sarma, M. , Power System Analysis and Design, 2nd Edition, PWS-Kent Publishing, Boston, MA, 1994. Carson, J. R. , Wave propagation in overhead wires with ground return, Bell System Technical Journal, Vol. 5, pp. 539 5   554, 54, 1926. Kron, G. , Tensorial analysis of integrated transmission systems, part I, the six basic reference frames, Transactions of the American Institute of Electrical Engineers, Vol. 71, pp. 814 8   882, 82, 1952.

 

Shunt Admittance of Overhead and Underground Lines  

Glover, J. D. and Sarma, M. , Power System Analysis and Design, 2nd Edition PWS-Kent Publishing, Boston, MA, 1995. T. P., Arnold and Mercier, C. D. (eds), Power Cable Manual, 2nd Edition, Southwire Company, Carrollton, GA, 1997.

 

Distribution System Line Models  

Glover, J. D. and Sarma, M. , Power System Analysis and Design, 2nd Edition PWS-Kent Publishing, Boston, MA, 1995. ANSI/NEMA Standard Publication No. MG1-1978, National Electrical Manufactures Association, Washington, DC.

 

Voltage Regulation  

American Nation Standard for Electric Power S   Systems ystems and Equipment Voltage Ratings (60 Hertz), ANSI C84.1-1995, National Electrical Manufacturers Association, Rosslyn, VA, 1996. IEEE Standard Requirements, Terminology, and Test Code for Step-Voltage and InductionVoltage Regulators, ANSI/IEEE C57.15-1986, Institute of Electrical and Electronic Engineers, New York, 1988.

 

 

Load Models  

Kersting, W. H. and Phillips, W. H. , Phase frame analysis of the effects of voltage unbalance on induction machines, IEEE Transactions on Industry Applications, Vol. 33, pp. 415 4   420, 20, 1997. American national standard for electric power systems and equipment   Vol Voltag tage e rati ratings ngs (60 (60    Hertz), ANSI C84.1-1995 , National Electrical Manufacturers Association, Rosslyn, Virginia, 1996.

   Distribution Feeder Analysis Trevino, C. , Cases of difficult convergence in load-flow problems, IEEE Paper n.71 6   62-PWR, 2-PWR, Presented at the IEEE Summer Power Meeting, Los Angeles, 1970. Kersting, W. H. and Mendive, D. L. , An application of ladder network theory to the solution of three-phase radial load-flow problems, IEEE Conference Paper,Presented at the IEEE Winter Power Meeting, New York, 1976. Radial Test Feeders, IEEE Distribution System Analysis Subcommittee, http://ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html. Kersting, W.H. and Phillips, W. H. , Distribution system short-circuit analysis, 25 th Intersociety Energy Conversion Engineering Conference, Reno, NV, 1990. Kersting, W.H. , The simulation of loop flow in radial distribution analysis programs, IEEE Conference Paper, Presented at the IEEE Rural Electric Power Conference, 2014. Kersting, W. H. and Carr, W. , Grounded wye d   delta elta transformer backfeed short-circuit currents, IEEE Conference Paper, Presented at the IEEE Rural Electric Power Conference, 2016.448

 

Center Tapped Transformers and Secondaries  

Gonen, T. , Electric Power Distribution System Engineering, CRC Press, Boca Raton, FL, 2007. Radial Test Feeders, IEEE Distribution System Analysis Subcommittee , http://ewh.ieee.org/soc/pes/dsacom/testfeeders/index.html.512