HANDBOOK OF ELECTRIC POWER CALCULATIONS H. Wayne Beaty Third Edition M C GRAW-HILL New York San Francisco Washington, D.C. Auckland Bogotá Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Copyright © 2001, 1997, 1984 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be repro- duced or distributed in any form or by any means, or stored in a data base or re- trieval system, without the prior written permission of the publisher. 1234567890 DOC/DOC 909876543210 P/N 0-07-136299-1 Part of ISBN 0-07-136298-3 The sponsoring editor for this book was Stephen Chapman and the production supervisor was Sherri Souffrance. It was set in Times Roman by Progressive Publishing Alternatives. Printed and bound by R. R. Donnelley & Sons Company. McGraw-Hi l l Information contained in this work has been obtained by The McGraw-Hill Companies, Inc. (“McGraw-Hill”) from sources believed to be reliable. However, neither McGraw-Hill nor its authors guarantees the accuracy or completeness of any information published herein and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. This book is printed on recycled, acid-free paper containing a minimum of 50% recycled, de-inked fiber. CONTRIBUTORS Amick, Charles L. Lighting Consultant. ( SECTION 20: LIGHTING DESIGN ) Chowdhury, Badrul H. Associate Professor, Electrical and Computer Engineering, University of Missouri-Rolla. ( SECTION 11: LOAD - FLOW ANALYSIS IN POWER SYSTEMS ) Galli, Anthony W. Project Engineer, Newport News Shipbuilding. ( SECTION 1: BASIC NETWORK ANALYSIS ) Hollander, Lawrence J. Dean of Engineering Emeritus, Union College. ( SECTION 3: DC MOTORS AND GENERATORS ; SECTION 6: SINGLE - PHASE MOTORS ; SECTION 10: ELECTRIC - POWER NETWORKS ; SECTION 13: SHORT - CIRCUIT COMPUTATIONS ) Ilic, Marija Senior Research Scientist, Electrical Engineering and Computer Science, Massachu- setts Institute of Technology. ( SECTION 12: POWER SYSTEMS CONTROL ) Khan, Shahriar Electrical Design Engineer, Schlumberger Ltd. ( SECTION 2: INSTRUMENTATION ) Liu, Yilu (Ellen) Associate Professor, Electrical Engineering Department, Virginia Tech Univer- sity. ( SECTION 4: TRANSFORMERS ) Mazzoni, Omar S. President, Systems Research International, Inc. ( SECTION 7: SYNCHRONOUS MACHINES ) Migliaro, Marco W. Chief Electrical and I&C Engineer, Nuclear Division, Florida Power & Light. ( SECTION 7: SYNCHRONOUS MACHINES ) Oraee, Hashaam Professor, Electrical & Computer Engineering, Worcester Polytechnic Insti- tute. ( SECTION 5: THREE - PHASE INDUCTION MOTORS ) Rivas, Richard A. Associate Professor, Universidad Simón Bolívar. ( SECTION 9: OVERHEAD TRANSMISSION LINES AND UNDERGROUND CABLES ) Robertson, Elizabeth President, Lyncole XIT Grounding. ( SECTION 14: SYSTEM GROUNDING ) Sauer, Peter W. Professor, Electrical Engineering, University of Illinois at Urbana-Champaign. ( SECTION 16: POWER SYSTEM STABILITY ) Schneider, Alexander W., Jr. Senior Engineer, Mid-America Interconnected Network. ( SECTION 16: POWER SYSTEM STABILITY ) Shaalan, Hesham Assistant Professor, Georgia Southern University. ( SECTION 8: GENERATION OF ELECTRIC POWER ; SECTION 17: COGENERATION ) Sheble, Gerald B. Professor, Iowa State University. ( SECTION 19: ELECTRIC ENERGY ECONOMIC METHODS ) Stocking, David R. Lyncole XIT Grounding. ( SECTION 14: SYSTEM GROUNDING ) vii PREFACE The Handbook of Electric Power Calculations provides detailed step-by-step calculation procedures commonly encountered in electrical engineering. The Handbook contains a wide array of topics and each topic is written by an authority on the subject. The treat- ment throughout the Handbook is practical with very little emphasis on theory. Each of the 20 Sections follows this format: • Clear statement of the problem. • Step-by-step calculation procedure. • Inclusion of suitable graphs and illustrations to clarify the procedure. • Use of SI and USCS equivalents. This relatively simple, yet comprehensive format adds greatly to the use of the Hand- book by the engineer or technician. Arithmetic and algebra are employed in the solution of the majority of the problems. Each section contains a list of references or a bibliogra- phy that is pertinent to the subject matter. This edition also includes a CD that has calculation procedures available for inclusion of other parameters, which will allow you to calculate problems with your specific num- bers inserted. Grateful acknowledgment is given to each of the authors for their contribution to this 3rd edition of the Handbook. H. Wayne Beaty ix CONTENTS Section 1. Basic Network Analysis 1.1 Section 2. Instrumentation 2.1 Section 3. dc Motors and Generators 3.1 Section 4. Transformers 4.1 Section 5. Three-Phase Induction Motors 5.1 Section 6. Single-Phase Motors 6.1 Section 7. Synchronous Machines 7.1 Section 8. Generation of Electric Power 8.1 Section 9. Overhead Transmission Lines and Underground Cables 9.1 Section 10. Electric-Power Networks 10.1 Section 11. Load-Flow Analysis in Power Systems 11.1 Section 12. Power-Systems Control 12.1 Section 13. Short-Circuit Computations 13.1 Section 14. System Grounding 14.1 v Section 15. Power-System Protection 15.1 Section 16. Power System Stability 16.1 Section 17. Cogeneration 17.1 Section 18. Stationary Batteries 18.1 Section 19. Electric Energy Economic Methods 19.1 Section 20. Lighting Design 20.1 Index I.1 vi CONTENTS SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding Series-Parallel dc Network Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Branch-Current Analysis of a dc Network . . . . . . . . . . . . . . . . . . . . . . 1.6 Mesh Analysis of a dc Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Nodal Analysis of a dc Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8 Direct-Current Network Solution Using Superposition Theorem . . . . . . . . 1.9 Direct-Current Network Solution Using Thevenin’s Theorem . . . . . . . . . . 1.10 Direct-Current Network Solution Using Norton’s Theorem . . . . . . . . . . . . 1.11 Balanced dc Bridge Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.12 Unbalanced dc Bridge Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.13 Analysis of a Sinusoidal Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.14 Analysis of a Square Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.16 Analysis of an Offset Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.17 Circuit Response to a Nonsinusoidal Input Consisting of a dc Voltage in a Series with an ac Voltage . . . . . . . . . . . . . . . . . . . . . 1.18 Steady-State ac Analysis of a Series RLC Circuit . . . . . . . . . . . . . . . . . . 1.19 Steady-State ac Analysis of a Parallel RLC Circuit . . . . . . . . . . . . . . . . . 1.20 Analysis of a Series-Parallel ac Network . . . . . . . . . . . . . . . . . . . . . . . 1.22 Analysis of Power in an ac Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.23 Analysis of Power Factor and Reactive Factor . . . . . . . . . . . . . . . . . . . 1.24 Power-Factor Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.25 Maximum Power Transfer in an ac Circuit . . . . . . . . . . . . . . . . . . . . . . 1.26 Analysis of a Balanced Wye-Wye System . . . . . . . . . . . . . . . . . . . . . . 1.27 Analysis of a Balanced Delta-Delta System . . . . . . . . . . . . . . . . . . . . . 1.27 Response of an Integrator to a Rectangular Pulse . . . . . . . . . . . . . . . . . 1.30 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.31 SERIES-PARALLEL DC NETWORK ANALYSIS A direct-current circuit (network) contains 19 resistors arranged as shown in Fig. 1.1. Compute the current through and the voltage drop across each resistor in this circuit. 1.1 Calculation Procedure 1. Label the Circuit Label all the sections. Mark the direction of current through each resistor (Fig. 1.2). The equivalent resistance of the series-parallel combination of resistors can be found by successive applications of the rules for combining series resistors and paral- lel resistors. 2. Combine All Series Resistors In a series circuit, the total or equivalent resistance R EQS seen by the source is equal to the sum of the values of the individual resistors: R EQS ϭ R 1 ϩ R 2 ϩ R 3 ϩ иии ϩ R N . Calculate the series equivalent of the elements connected in series in sections DE, CG, and GF: R EQS (section DE) ϭ R 13 ϩ R 14 ϭ 200 ϩ 40 ϭ 240 ⍀, R EQS (section CG) ϭ R 7 ϩ R 8 ϭ 200 ϩ 400 ϭ 600 ⍀, and R EQS (section GF) ϭ R 10 ϩ R 11 ϭ 400 ϩ 200 ϭ 600 ⍀. Replace the series elements included in sections DE, CG, and GF by their equiva- lent values (Fig. 1.3). 3. Combine All Parallel Resistors In the case of a parallel circuit of two unequal resistors in parallel, the total or equivalent resistance R EQP can be found from the following product-over-sum equation: R EQP ϭ R 1 ʈR 2 ϭ R 1 R 2 /(R 1 ϩ R 2 ), where ʈ stands for in parallel with. The equivalent parallel resistance is always less than the smaller of the two resistors. In section CG, R 5 ʈR 6 ϭ (1000 ϫ 1500)/(1000 ϩ 1500) ϭ 600 ⍀. Section CG now consists of two 600-⍀ resistors in parallel. In a case of a circuit of N equal resistors in 1.2 HANDBOOK OF ELECTRIC POWER CALCULATIONS FIGURE 1.1 A series-parallel dc circuit to be analyzed. 39495_01_p1.1-1.31 7/28/00 2:03 PM Page 1.2 Copyright (C) 2000 by The McGraw-Hill Companies, Inc. All rights reserved. Use of this product is subject to the terms of its License Agreement. Click here to view. BASIC NETWORK ANALYSIS 1.3 FIGURE 1.2 Labeling the circuit of Fig. 1.1. FIGURE 1.3 Series elements replaced by their equivalent values. 39495_01_p1.1-1.31 7/28/00 2:03 PM Page 1.3 this product is subject to the terms of its License Agreement. Click here to view. parallel, the total, or equivalent, resistance R EQP can be determined from the following equation: R EQP ϭ R/N, where R is the resistance of each of the parallel resistors and N is the number of resistors connected in parallel. For section CG, R CG ϭ 600/2 ϭ 300 ⍀; for section BC, R BC ϭ 100/3 ϭ 33 1 / 3 ⍀; for section EF, R EF ϭ 104/2 ϭ 52 ⍀; for section GF, R GF ϭ 600/2 ϭ 300 ⍀. In a circuit of three or more unequal resistors in parallel, the total, or equivalent resis- tance R EQP is equal to the inverse of the sum of the reciprocals of the individual resistance values: R EQP ϭ 1/(1/R 1 ϩ 1/R 2 ϩ 1/R 3 ϩ иии ϩ 1/R N ). The equivalent parallel resistance is always less than the smallest-value resistor in the parallel combination. Calculate the equivalent resistance of the elements connected in parallel in sec- tion DE: R 15 ʈR 16 ʈR 17 ϭ 1/(1/100 ϩ 1/200 ϩ 1/600) ϭ 60 ⍀. Calculate R DE : R DE ϭ 240ʈ60 ϭ (240)(60)/(240 ϩ 60) ϭ 48 ⍀. Replace all parallel elements by their equiva- lent values (Fig. 1.4). 4. Combine the Remaining Resistances to Obtain the Total Equivalent Resistance Combine the equivalent series resistances of Fig. 1.4 to obtain the simple series- parallel circuit of Fig. 1.5: R AB ϩ R BC ϭ R AC ϭ R EQS ϭ 20 ϩ 33 1 / 3 ϭ 53 1 / 3 ⍀, R CG ϩ R GF ϭ R CF ϭ R EQS ϭ 300 ϩ 300 ϭ 600 ⍀, R CD ϩ R DE ϩ R EF ϭ R CF ϭ R EQS ϭ 20 ϩ 48 ϩ 52 ϭ 120 ⍀. Calculate the total equivalent resistance R EQT : R EQT ϭ 53 1 / 3 ϩ (600 ʈ 120) ϭ 153 1 / 3 ⍀. The final reduced circuit is illustrated in Fig. 1.6. 5. Compute the Total Line Current in Fig. 1.6 Using Ohm’s Law I 1 ϭ E/R EQT , where I 1 ϭ total line current, E ϭ line voltage (power-supply voltage), and R EQT ϭ line resistance or total equivalent resistance seen by power supply. Substitut- ing values yields: I 1 ϭ E/R EQT ϭ 460/153 1 / 3 ϭ 3 A. 1.4 HANDBOOK OF ELECTRIC POWER CALCULATIONS FIGURE 1.4 Parallel elements replaced by their equivalent values. FIGURE 1.5 Circuit of Fig. 1.4 reduced to a sim- ple series-parallel configuration. FIGURE 1.6 Final reduced circuit of Fig. 1.1. 39495_01_p1.1-1.31 7/28/00 2:03 PM Page 1.4 this product is subject to the terms of its License Agreement. Click here to view. . The Handbook of Electric Power Calculations provides detailed step-by-step calculation procedures commonly encountered in electrical engineering. The Handbook. two 600-⍀ resistors in parallel. In a case of a circuit of N equal resistors in 1.2 HANDBOOK OF ELECTRIC POWER CALCULATIONS FIGURE 1.1 A series-parallel