AC power systems handbook

AC power systems handbook

AC Power Systems Handbook Third Edition Jerry C Whitaker Technical Press Morgan Hill, California Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business © 2007 by Taylor & Francis Group, LLC 4034_Discl.fm Page Friday, August 25, 2006 10:06 AM Published in 2007 by CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group No claim to original U.S Government works Printed in the United States of America on acid-free paper 10 International Standard Book Number-10: 0-8493-4034-9 (Hardcover) International Standard Book Number-13: 978-0-8493-4034-5 (Hardcover) Library of Congress Card Number 2006042620 This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400 CCC is a not-for-profit organization that provides licenses and registration for a variety of users For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe Library of Congress Cataloging-in-Publication Data Whitaker, Jerry C AC power systems / Jerry C Whitaker. 3rd ed p cm Includes bibliographical references and index ISBN 0-8493-4034-9 (alk paper) Electric power distribution Alternating current Handbooks, manuals, etc Electric power systems Protection Handbooks, manuals, etc I Title TK3141.W45 2006 621.319’13 dc22 2006042620 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com Taylor & Francis Group is the Academic Division of Informa plc © 2007 by Taylor & Francis Group, LLC and the CRC Press Web site at http://www.crcpress.com For Jenny and Andy, very special people v © 2007 by Taylor & Francis Group, LLC   Table of Contents Preface xvii About the Author xix Chapter AC Power Systems 1.1 Introduction 1.1.1 Defining Terms 1.1.2 Power Electronics 1.2 AC Circuit Analysis 1.2.1 Power Relationship in AC Circuits 1.2.2 Complex Numbers 1.2.3 Phasors 1.2.4 Per Unit System 1.3 Elements of the AC Power System 1.3.1 Transmission Circuits 1.3.1.1 Types of Conductors 1.3.1.2 Overhead Conductors 1.3.1.3 Underground Cables 10 1.3.1.4 Skin Effect 10 1.3.2 Dielectrics and Insulators 11 1.3.2.1 Insulating Liquids 12 1.3.2.2 Insulating Solids 13 1.3.3 Control and Switching Systems 14 1.3.3.1 Fault Protection Devices 15 1.3.3.2 Lightning Arrester 16 1.4 Utility AC Power System Architecture 16 1.4.1 Power Distribution 18 1.4.2 Distribution Substations 18 1.4.2.1 Breaker Schemes 20 1.4.3 Voltage Analysis 22 1.4.4 High-Voltage DC Transmission 22 1.4.4.1 AC vs DC Transmission 24 1.4.4.2 DC Circuit Breakers 25 1.4.5 Utility Company Interfacing 26 1.4.5.1 Phase-to-Phase Balance 27 1.4.6 Load Fault Protection 27 1.4.6.1 Fuses 28 1.4.6.2 Circuit Breakers 28 1.4.6.3 Semiconductor Fuses 28 vii © 2007 by Taylor & Francis Group, LLC Chapter Chapter Chapter 1.4.6.4 Application Considerations 29 1.4.6.5 Transient Currents 29 1.4.6.6 Delay-Trip Considerations 30 1.4.7 Measuring AC Power 31 1.4.7.1 Digital Measurement Techniques 32 1.5 References 33 1.6 Bibliography 34 Power-Generation Systems 2.1 Introduction 35 2.2 Fundamental Concepts 35 2.2.1 Operating Principles 35 2.2.2 Control Techniques 39 2.3 Power-Generating Systems 40 2.3.1 Fossil Fuel Power Plants 40 2.3.2 Nuclear Power Plants 44 2.3.3 Hydroelectric Power Plants 45 2.4 References 48 2.5 Bibliography 48 Power Factor 3.1 Introduction 49 3.2 Fundamental Principles 49 3.3 PF Correction Techniques 52 3.3.1 On-Site Power Factor Correction 53 3.3.2 Shunt Reactors 55 3.3.3 Unwanted Resonance Conditions 55 3.3.4 Series Capacitor Compensation 56 3.3.5 Static Compensation Devices 57 3.4 References 58 3.5 Bibliography 58 Power Transformers 4.1 Introduction 59 4.2 Inductive Properties 59 4.2.1 Coils 60 4.2.2 The Toroid 61 4.2.3 Circuit Description of Self-Inductance 61 4.2.4 Magnetic Materials 62 4.3 Basic Principles of the Transformer 62 4.3.1 Counter-Electromotive Force 68 4.3.2 Full Load Percent Impedance 68 4.3.3 Design Considerations 69 4.3.4 The Ideal Transformer 71 4.3.5 Application Considerations 72 4.4 Transformer Failure Modes 75 4.4.1 Thermal Considerations 76 viii © 2007 by Taylor & Francis Group, LLC Chapter Chapter 4.4.1.1 Life Expectancy and Temperature 76 4.4.2 Voltage Considerations 76 4.4.3 Mechanical Considerations 77 4.4.3.1 Dry-Type and Liquid-Filled Transformers 77 4.4.3.2 Insulation Materials 78 4.4.3.3 Insulating Liquids 78 4.4.3.4 Cooling 79 4.5 References 79 4.6 Bibliography 79 Capacitors 5.1 Introduction 81 5.2 Basic Principles 81 5.2.1 Series and Parallel Connections 85 5.2.2 Practical Capacitors 86 5.3 Capacitor Failure Modes 86 5.3.1 Electrolytic Capacitors 86 5.3.1.1 Mechanical Failure 88 5.3.1.2 Temperature Cycling 89 5.3.1.3 Electrolyte Failures 89 5.3.2 Capacitor Life Span 90 5.3.3 Tantalum Capacitor 91 5.4 References 91 5.5 Bibliography 92 Semiconductors 6.1 Introduction 93 6.2 Semiconductor Failure Modes 93 6.2.1 Device Ruggedness 93 6.2.2 Forward Bias Safe Operating Area 94 6.2.3 Reverse Bias Safe Operating Area 94 6.2.4 Power-Handling Capability 95 6.2.5 Semiconductor Derating 95 6.2.6 Failure Mechanisms 96 6.2.6.1 Avalanche Breakdown 96 6.2.6.2 Alpha Multiplication 96 6.2.6.3 Punch-Through 96 6.2.6.4 Thermal Runaway 97 6.3 MOSFET Devices 97 6.3.1 Safe Operating Area 97 6.3.2 MOSFET Failure Modes 101 6.3.3 Breakdown Effects 101 6.3.3.1 Thermal Second Breakdown 102 6.3.3.2 Metallization Failure 102 6.3.3.3 Polarity Reversal 102 6.4 Thyristor Components 103 6.4.1 Failure Modes 104 6.4.2 Application Considerations 104 ix © 2007 by Taylor & Francis Group, LLC 6.5 Chapter Chapter ESD Failure Modes 104 6.5.1 Failure Mechanisms 105 6.5.1.1 Latent Failures 107 6.5.1.2 Case in Point 107 6.6 Semiconductor Development 107 6.6.1 Failure Analysis 108 6.6.2 Chip Protection 111 6.7 Effects of Arcing 111 6.7.1 Insulation Breakdown 112 6.8 References 112 6.9 Bibliography 112 Rectifier and Filter Circuits 7.1 Introduction 115 7.2 Power Rectifiers 116 7.2.1 Operating Rectifiers in Series 116 7.2.2 Operating Rectifiers in Parallel 117 7.2.3 Silicon Avalanche Rectifiers 118 7.2.4 Single-Phase Rectifier Configurations 119 7.2.4.1 Half-Wave Rectifier 119 7.2.4.2 Full-Wave Rectifier 120 7.2.4.3 Bridge Rectifier 121 7.2.4.4 Voltage Multiplier 122 7.2.5 Polyphase Rectifier Circuits 122 7.3 Power Supply Filter Circuits 125 7.3.1 Inductive Input Filter 125 7.3.2 Capacitive Input Filter 127 7.4 References 129 7.5 Bibliography 129 Power Electronics 8.1 Introduction 131 8.2 Thyristor Devices 131 8.2.1 Thyristor Servo Systems 132 8.2.1.1 Inductive Loads 133 8.2.1.2 Applications 134 8.2.1.3 Triggering Circuits 137 8.2.1.4 Control Flexibility 139 8.2.2 Gate Turn-Off Thyristor 139 8.2.3 Reverse-Conducting Thyristor 139 8.2.4 Asymmetrical Silicon-Controlled Rectifier 140 8.2.5 Fusing 140 8.3 Power Transistors 140 8.3.1 Power MOSFET 141 8.3.1.1 Rugged MOSFET 141 8.3.2 Insulated-Gate Bipolar Transistor 142 8.3.3 MOS-Controlled Thyristor 143 8.4 References 143 x © 2007 by Taylor & Francis Group, LLC 8.5 Bibliography 143 Chapter Origins of AC Line Disturbances 9.1 Introduction 145 9.2 Naturally Occurring Disturbances 145 9.2.1 Sources of Atmospheric Energy 145 9.2.2 Characteristics of Lightning 147 9.2.2.1 Cloud-to-Cloud Activity 149 9.2.3 Lightning Protection 150 9.2.3.1 Protection Area 151 9.2.4 Electrostatic Discharge 153 9.2.4.1 Triboelectric Effect 154 9.2.5 EMP Radiation 155 9.2.6 Coupling Transient Energy 156 9.3 Equipment-Caused Transient Disturbances 157 9.3.1 Utility System Faults 158 9.3.2 Switch Contact Arcing 158 9.3.3 Telephone System Transients 159 9.3.4 Nonlinear Loads and Harmonic Energy 161 9.3.4.1 Harmonic Sources 164 9.3.5 Carrier Storage 165 9.3.6 Transient-Generated Noise 166 9.3.6.1 ESD Noise 166 9.3.6.2 Contact Arcing 166 9.3.6.3 SCR Switching 166 9.4 References 167 9.5 Bibliography 167 Chapter 10 Power Disturbance Characterization 10.1 Introduction 169 10.2 Standards of Measurement 170 10.2.1 Assessing the Threat 173 10.2.2 Fundamental Measurement Techniques 173 10.2.2.1 Root-Mean-Square 173 10.2.2.2 Average-Response Measurement 174 10.2.2.3 Peak-Response Measurement 174 10.2.2.4 Meter Accuracy 176 10.2.3 Digital Measurement Instruments 177 10.2.4 Digital Monitor Features 178 10.3 Reliability Considerations 179 10.4 References 179 10.5 Bibliography 179 Chapter 11 Power System Protection Methods 11.1 Introduction 181 11.2 The Key Tolerance Envelope 181 11.3 Assessing the Lightning Hazard 183 11.4 FIPS Publication 94 184 11.5 Protection Alternatives 185 xi © 2007 by Taylor & Francis Group, LLC 11.5.1 Specifying System-Protection Hardware 187 11.6 References 189 11.7 Bibliography 189 Chapter 12 Motor-Generator Set 12.1 Introduction 191 12.2 System Configuration 191 12.2.1 Motor Design Considerations 194 12.2.1.1 Single-Shaft Systems 195 12.2.2 Flywheel Considerations 196 12.2.3 Maintenance Considerations 197 12.2.4 Motor-Generator UPS 197 12.2.5 Kinetic Battery Storage System 199 12.3 References 201 12.4 Bibliography 201 Chapter 13 Uninterruptible Power Systems 13.1 Introduction 203 13.2 UPS Configuration 203 13.2.1 Power-Conversion Methods 205 13.2.1.1 Ferroresonant Inverter 205 13.2.1.2 Delta Magnetic Inverter 206 13.2.1.3 Inverter-Fed L/C Tank 207 13.2.1.4 Quasi-Square Wave Inverter 207 13.2.1.5 Step Wave Inverter 209 13.2.1.6 Pulse-Width Modulation Inverter 209 13.2.1.7 Phase Modulation Inverter 209 13.2.2 Redundant Operation 209 13.2.3 Output Transfer Switch 212 13.2.4 Battery Supply 213 13.3 References 213 13.4 Bibliography 213 Chapter 14 Power Conditioning Devices 14.1 Introduction 215 14.2 Ferroresonant Transformer 215 14.2.1 Magnetic-Coupling-Controlled Voltage Regulator 216 14.3 Isolation Transformer 217 14.3.1 Tap-Changing Regulator 219 14.3.1.1 Variable Ratio Regulator 220 14.3.2 Variable Voltage Transformer 221 14.3.2.1 Brush Type 222 14.3.2.2 Induction Type 222 14.4 Line Conditioner 222 14.4.1 Hybrid Transient Suppressor 224 14.4.2 Active Power-Line Conditioner 224 14.4.2.1 Application Considerations 226 14.5 References 226 14.6 Bibliography 226 xii © 2007 by Taylor & Francis Group, LLC 388 AC Power Systems Handbook To Convert barrels (U.S., liquid) barrels (oil) bars bars bars bars bars baryl bolt (U.S cloth) Btu Btu Btu Btu Btu Btu Btu Btu Btu Btu/hr Btu/hr Btu/hr Btu/hr Btu/min Btu/min Btu/min Btu/min Btu/sq ft/min bucket (br dry) bushels bushels bushels bushels bushels bushels bushels calories, gram (mean) candle/sq cm candle/sq in centares (centiares) Centigrade centigrams centiliter centiliter centiliter centiliter centimeter centimeter centimeter centimeter centimeter centimeter centimeter centimeter centimeter-dynes centimeter-dynes centimeter-dynes centimeter-grams centimeter-grams centimeter-grams © 2007 by Taylor & Francis Group, LLC Into gallons gallons (oil) atmospheres dynes/sq cm kg/sq m pounds/sq ft pounds/sq in dyne/sq cm meters liter-atmosphere ergs foot-pounds gram-calories horsepower-hr joules kilogram-calories kilogram-meters kilowatt-hr foot-pounds/s gram-calories/s horsepower-hr watts foot-lb/s horsepower kilowatts watts watts/sq in cubic cm cubic ft cubic in cubic m liters pecks pints (dry) quarts (dry) Btu (mean) Lamberts Lamberts sq meters Fahrenheit grams ounce fluid (U.S.) cubic in drams liters feet inches kilometers meters miles millimeters mils yards cm-grams meter-kg pound-ft cm-dynes meter-kg pound-ft Multiply by 31.5 42.0 0.9869 104 1.020 × 104 2,089 14.50 1.000 36.576 10.409 1.0550 × 1010 778.3 252.0 3.931 × 10–4 1,054.8 0.2520 107.5 2.928 × 10–4 0.2162 0.0700 3.929 × 10–4 0.2931 12.96 0.02356 0.01757 17.57 0.1221 1.818 × 104 1.2445 2,150.4 0.03524 35.24 4.0 64.0 32.0 3.9685 × 10–3 3.142 0.4870 1.0 (C˚ × 9/5) + 32 0.01 0.3382 0.6103 2.705 0.01 3.281 × 10–2 0.3937 10–5 0.01 6.214 × 10–6 10.0 393.7 1.094 × 10–2 1.020 × 10–3 1.020 × 10–8 7.376 × 10–8 980.7 10–5 7.233 × 10–5 389 Units Conversion Table To Convert centimeters of mercury centimeters of mercury centimeters of mercury centimeters of mercury centimeters of mercury centimeters/sec centimeters/sec centimeters/sec centimeters/sec centimeters/sec centimeters/sec centimeters/sec centimeters/sec/sec centimeters/sec/sec centimeters/sec/sec centimeters/sec/sec chain chain chains (surveyor’s or Gunter’s) circular mils circular mils circular mils circumference cord feet cords coulomb coulombs coulombs/sq cm coulombs/sq cm coulombs/sq in coulombs/sq in coulombs/sq meter coulombs/sq meter cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic centimeters cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet cubic feet/min cubic feet/min cubic feet/min cubic feet/min cubic feet/sec cubic feet/sec cubic in cubic in cubic in © 2007 by Taylor & Francis Group, LLC Into atmospheres feet of water kg/sq meter pounds/sq ft pounds/sq in feet/min feet/sec kilometers/hr knots meters/min miles/hr miles/min feet/sec/sec km/hr/sec meters/sec/sec miles/hr/sec in meters yards sq cm sq mils sq in radians cubic feet cord feet statcoulombs faradays coulombs/sq in coulombs/sq meter coulombs/sq cm coulombs/sq meter coulombs/sq cm coulombs/sq in cubic feet cubic in cubic meters cubic yards gallons (U.S liq.) liters pints (U.S liq.) quarts (U.S liq.) bushels (dry) cubic cm cubic in cubic meters cubic yards gallons (U.S liq.) liters pints (U.S liq.) quarts (U.S liq.) cubic cm/sec gallons/sec liters/sec pounds of water/min million gal/day gallons/min cubic cm cubic feet cubic meters Multiply by 0.01316 0.4461 136.0 27.85 0.1934 1.9686 0.03281 0.036 0.1943 0.6 0.02237 3.728 × 10–4 0.03281 0.036 0.01 0.02237 792.00 20.12 22.00 5.067 × 10–6 0.7854 7.854 × 10–7 6.283 16 2.998 × 109 1.036 × 10–5 64.52 104 0.1550 1,550 10–4 6.452 × 10–4 3.531 × 10–5 0.06102 10–6 1.308 × 10–6 2.642 × 10–4 0.001 2.113 × 10–3 1.057 × 10–3 0.8036 28,320.0 1,728.0 0.02832 0.03704 7.48052 28.32 59.84 29.92 472.0 0.1247 0.4720 62.43 0.646317 448.831 16.39 5.787 × 10–4 1.639 × 10–5 390 AC Power Systems Handbook To Convert cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic in cubic yards cubic yards cubic yards cubic yards cubic yards cubic yards cubic yards cubic yards cubic yards/min cubic yards/min cubic yards/min Dalton days decigrams deciliters decimeters degrees (angle) degrees (angle) degrees (angle) degrees/sec degrees/sec degrees/sec dekagrams dekaliters dekameters drams (apothecaries or troy) drams (apothecaries or troy) drams (U.S., fluid or apothecaries) drams drams drams dyne/cm dyne/sq cm dyne/sq cm dyne/sq cm dynes dynes dynes dynes dynes dynes dynes/sq cm ell ell © 2007 by Taylor & Francis Group, LLC Into cubic yards gallons liters mil-feet pints (U.S liq.) quarts (U.S liq.) bushels (dry) cubic cm cubic feet cubic in cubic yards gallons (U.S liq.) liters pints (U.S liq.) quarts (U.S liq.) cubic cm cubic feet cubic in cubic meters gallons (U.S liq.) liters pints (U.S liq.) quarts (U.S liq.) cubic ft/sec gallons/sec liters/sec grams seconds grams liters meters quadrants radians seconds radians/sec revolutions/min revolutions/sec grams liters meters ounces (avdp.) ounces (troy) cubic cm grams grains ounces erg/sq millimeter atmospheres in of mercury at 0°C in of water at 4°C grams joules/cm joules/meter (newtons) kilograms poundals pounds bars cm in Multiply by 2.143 × 10–5 4.329 × 10–3 0.01639 1.061 × 105 0.03463 0.01732 28.38 106 35.31 61,023.0 1.308 264.2 1,000 2,113 1,057 7.646 × 105 27.0 46,656.0 0.7646 202.0 764.6 1,615.9 807.9 0.45 3.367 12.74 1.650 × 10–24 86,400 0.1 0.1 0.1 0.01111 0.01745 3,600 0.01745 0.1667 2.778 × 10–3 10 10 10 0.1371429 0.125 3.6967 1.7718 27.3437 0.0625 0.01 9.869 × 10–7 2.953 × 10–5 4.015 × 10–4 1.020 × 10–3 10–7 10–5 1.020 × 10–6 7.233 × 10–5 2.248 × 10–6 10–6 114.30 45 391 Units Conversion Table To Convert em, pica em, pica erg/sec ergs ergs ergs ergs ergs ergs ergs ergs ergs ergs ergs ergs/sec ergs/sec ergs/sec ergs/sec ergs/sec ergs/sec farad faraday/sec faradays faradays fathom fathoms feet feet feet feet feet feet feet feet of water feet of water feet of water feet of water feet of water feet of water feet/min feet/min feet/min feet/min feet/min feet/sec feet/sec feet/sec feet/sec feet/sec feet/sec feet/sec/sec feet/sec/sec feet/sec/sec feet/sec/sec feet/100 feet foot-candle foot-pounds foot-pounds foot-pounds © 2007 by Taylor & Francis Group, LLC Into in cm Dyne-cm/sec Btu dyne-centimeters foot-pounds gram-calories gram-cm horsepower-hr joules kg-calories kg-meters kilowatt-hr watt-hr Btu/min ft-lb/min ft-lb/sec horsepower kg-calories/min kilowatts microfarads ampere (absolute) ampere-hr coulombs meters feet centimeters kilometers meters miles (naut.) miles (stat.) millimeters mils atmospheres in of mercury kg/sq cm kg/sq meter pounds/sq ft pounds/sq in cm/sec feet/sec km/hr meters/min miles/hr cm/sec km/hr knots meters/min miles/hr miles/min cm/sec/sec km/hr/sec meters/sec/sec miles/hr/sec per centigrade lumen/sq meter Btu ergs gram-calories Multiply by 0.167 0.4233 1.000 9.480 × 10–11 1.0 7.367 × 10–8 0.2389 × 10–7 1.020 × 10–3 3.7250 × 10–14 10–7 2.389 × 10–11 1.020 × 10–8 0.2778 × 10–13 0.2778 × 10–10 5,688 × 10–9 4.427 × 10–6 7.3756 × 10–8 1.341 × 10–10 1.433 × 10–9 10–10 106 9.6500 × 104 26.80 9.649 × 104 1.828804 6.0 30.48 3.048 × 10–4 0.3048 1.645 × 10–4 1.894 × 10–4 304.8 1.2 × 104 0.02950 0.8826 0.03048 304.8 62.43 0.4335 0.5080 0.01667 0.01829 0.3048 0.01136 30.48 1.097 0.5921 18.29 0.6818 0.01136 30.48 1.097 0.3048 0.6818 1.0 10.764 1.286 × 10–3 1.356 × 107 0.3238 392 AC Power Systems Handbook To Convert foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds foot-pounds/min foot-pounds/min foot-pounds/min foot-pounds/min foot-pounds/min foot-pounds/sec foot-pounds/sec foot-pounds/sec foot-pounds/sec foot-pounds/sec furlongs furlongs furlongs gallons gallons gallons gallons gallons gallons gallons (liq Br Imp.) gallons (U.S.) gallons of water gallons/min gallons/min gallons/min gausses gausses gausses gausses gilberts gilberts/cm gilberts/cm gilberts/cm gills gills gills (British) grade grains grains (troy) grains (troy) grains (troy) grains (troy) grains/Imp gal grains/U.S gal grains/U.S gal gram-calories gram-calories gram-calories gram-calories gram-calories gram-calories gram-calories/sec gram-centimeters gram-centimeters © 2007 by Taylor & Francis Group, LLC Into hp-hr joules kg-calories kg-meters kilowatt-hr Btu/min foot-pounds/sec horsepower kg-calories/min kilowatts Btu/hr Btu/min horsepower kg-calories/min kilowatts miles (U.S.) rods feet cubic cm cubic feet cubic in cubic meters cubic yards liters gallons (U.S liq.) gallons (Imp.) pounds of water cubic ft/sec liters/sec cubic ft/hr lines/sq in webers/sq cm webers/sq in webers/sq meter ampere-turns amp-turns/cm amp-turns/in amp-turns/meter liters pints (liq.) cubic cm radian drams (avdp.) grains (avdp.) grams ounces (avdp.) pennyweight (troy) parts/million parts/million pounds/million gal Btu ergs foot-pounds horsepower-hr kilowatt-hr watt-hr Btu/hr Btu ergs Multiply by 5.050 × 10–7 1.356 3.24 × 10–4 0.1383 3.766 × 10–7 1.286 × 10–3 0.01667 3.030 × 10–5 3.24 × 10–4 2.260 × 10–5 4.6263 0.07717 1.818 × 10–3 0.01945 1.356 × 10–3 0.125 40.0 660.0 3,785.0 0.1337 231.0 3.785 × 10–3 4.951 × 10–3 3.785 1.20095 0.83267 8.3453 2.228 × 10–3 0.06308 8.0208 6.452 10–8 6.452 × 10–8 10–4 0.7958 0.7958 2.021 79.58 0.1183 0.25 142.07 0.01571 0.03657143 1.0 0.06480 2.0833 × 10–3 0.04167 14.286 17.118 142.86 3.9683 × 10–3 4.1868 × 107 3.0880 1.5596 × 10–6 1.1630 × 10–6 1.1630 × 10–3 14.286 9.297 × 10–8 980.7 393 Units Conversion Table To Convert gram-centimeters gram-centimeters gram-centimeters grams grams grams grams grams grams grams grams grams grams grams/cm grams/cubic cm grams/cubic cm grams/cubic cm grams/liter grams/liter grams/liter grams/liter grams/sq cm hand hectares hectares hectograms hectoliters hectometers hectowatts henrys horsepower horsepower horsepower horsepower horsepower horsepower horsepower (boiler) horsepower (boiler) horsepower, metric (542.5 ft lb./sec) horsepower (550 ft lb./sec) horsepower-hr horsepower-hr horsepower-hr horsepower-hr horsepower-hr horsepower-hr horsepower-hr horsepower-hr hours hours hundredweights (long) hundredweights (long) hundredweights (short) hundredweights (short) hundredweights (short) hundredweights (short) in in in © 2007 by Taylor & Francis Group, LLC Into joules kg-calories kg-meters dynes grains joules/cm joules/meter (newtons) kilograms milligrams ounces (avdp.) ounces (troy) poundals pounds pounds/in pounds/cubic ft pounds/cubic in pounds/mil-foot grains/gal pounds/1,000 gal pounds/cubic ft parts/million pounds/sq ft cm acres sq feet grams liters meters watts millihenrys Btu/min foot-lb/min foot-lb/sec kg-calories/min kilowatts watts Btu/hr kilowatts horsepower (550 ft lb./sec) horsepower, metric (542.5 ft lb./sec) Btu ergs foot-lb gram-calories joules kg-calories kg-meters kilowatt-hr days weeks pounds tons (long) ounces (avdp.) pounds tons (metric) tons (long) centimeters meters miles Multiply by 9.807 × 10–5 2.343 × 10–8 10–5 980.7 15.43 9.807 × 10–5 9.807 × 10–3 0.001 1,000 0.03527 0.03215 0.07093 2.205 × 10–3 5.600 × 10–3 62.43 0.03613 3.405 × 10–7 58.417 8.345 0.062427 1,000.0 2.0481 10.16 2.471 1.076 × 105 100 100 100 100 1,000 42.44 33,000 550 10.68 0.7457 745.7 33.479 9.803 0.9863 1.014 2,547 2.6845 × 1013 1.98 × 106 641,190 2.684 × 106 641.1 2.737 × 105 0.7457 4.167 × 10–2 5.952 × 10–3 112 0.05 1,600 100 0.0453592 0.0446429 2.540 2.540 × 10–2 1.578 × 10–5 394 AC Power Systems Handbook To Convert in in in in of mercury in of mercury in of mercury in of mercury in of mercury in of mercury in of water (at 4°C) in of water (at 4°C) in of water (at 4°C) in of water (at 4°C) in of water (at 4°C) in of water (at 4°C) international ampere international Volt international volt international volt joules joules joules joules joules joules joules/cm joules/cm joules/cm joules/cm joules/cm kilogram-calories kilogram-calories kilogram-calories kilogram-calories kilogram-calories kilogram-calories kilogram-calories kilogram meters kilogram meters kilogram meters kilogram meters kilogram meters kilogram meters kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms kilograms/cubic meter kilograms/cubic meter kilograms/cubic meter kilograms/cubic meter kilograms/meter kilograms/sq cm kilograms/sq cm kilograms/sq cm © 2007 by Taylor & Francis Group, LLC Into millimeters mils yards atmospheres feet of water kg/sq cm kg/sq meter pounds/sq ft pounds/sq in atmospheres in of mercury kg/sq cm ounces/sq in pounds/sq ft pounds/sq in amperes (absolute) volts (absolute) joules (absolute) joules Btu ergs foot-pounds kg-calories kg-meters watt-hr grams dynes joules/meter (newtons) poundals pounds Btu foot-pounds hp-hr joules kg-meters kilojoules kilowatt-hr Btu ergs foot-pounds joules kg-calories kilowatt-hr dynes grams joules/cm joules/meter (newtons) poundals pounds tons (long) tons (short) grams/cubic cm pounds/cubic ft pounds/cubic in pounds/mil-foot pounds/ft dynes atmospheres feet of water Multiply by 25.40 1,000.0 2.778 × 10–2 0.03342 1.133 0.03453 345.3 70.73 0.4912 2.458 × 10–3 0.07355 2.540 × 10–3 0.5781 5.204 0.03613 0.9998 1.0003 1.593 × 10–19 9.654 × 104 9.480 × 10–4 107 0.7376 2.389 × 10–4 0.1020 2.778 × 10–4 1.020 × 104 107 100.0 723.3 22.48 3.968 3,088 1.560 × 10–3 4,186 426.9 4.186 1.163 × 10–3 9.294 × 10–3 9.804 × 107 7.233 9.804 2.342 × 10–3 2.723 × 10–6 980,665 1,000.0 0.09807 9.807 70.93 2.205 9.842 × 10–4 1.102 × 10–3 0.001 0.06243 3.613 × 10–5 3.405 × 10–10 0.6720 980,665 0.9678 32.81 395 Units Conversion Table To Convert kilograms/sq cm kilograms/sq cm kilograms/sq cm kilograms/sq meter kilograms/sq meter kilograms/sq meter kilograms/sq meter kilograms/sq meter kilograms/sq meter kilograms/sq mm kilolines kiloliters kilometers kilometers kilometers kilometers kilometers kilometers kilometers kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr kilometers/hr/sec kilometers/hr/sec kilometers/hr/sec kilometers/hr/sec kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatt-hr kilowatts kilowatts kilowatts kilowatts kilowatts kilowatts knots knots knots knots knots knots league light year light year lines/sq cm lines/sq in lines/sq in lines/sq in lines/sq in links (engineer’s) © 2007 by Taylor & Francis Group, LLC Into in of mercury pounds/sq ft pounds/sq in atmospheres bars feet of water in of mercury pounds/sq ft pounds/sq in kg/sq meter maxwells liters centimeters feet in meters miles millimeters yards cm/sec feet/min feet/sec knots meters/min miles/hr cm/sec/sec feet/sec/sec meters/sec/sec miles/hr/sec Btu ergs foot-lb gram-calories horsepower-hr joules kg-calories kg-meters pounds of water raised from 62° to 212°F Btu/min foot-lb/min foot-lb/sec horsepower kg-calories/min watts feet/hr kilometers/hr nautical miles/hr statute miles/hr yards/hr feet/sec miles (approx.) miles kilometers gausses gausses webers/sq cm webers/sq in webers/sq meter in Multiply by 28.96 2,048 14.22 9.678 × 10–5 98.07 × 10–6 3.281 × 10–3 2.896 × 10–3 0.2048 1.422 × 10–3 106 1,000 1,000 105 3,281 3.937 × 104 1,000 0.6214 104 1,094 27.78 54.68 0.9113 0.5396 16.67 0.6214 27.78 0.9113 0.2778 0.6214 3,413 3.600 × 1013 2.655 × 106 859,850 1.341 3.6 × 106 860.5 3.671 × 105 22.75 56.92 4.426 × 104 737.6 1.341 14.34 1,000.0 6,080 1.8532 1.0 1.151 2,027 1.689 3.0 5.9 × 1012 9.4637 × 1012 1.0 0.1550 1.550 × 10–9 10–8 1.550 × 10–5 12.0 396 AC Power Systems Handbook To Convert links (surveyor’s) liters liters liters liters liters liters liters liters liters liters/min liters/min lumen lumen lumens/sq ft lumens/sq ft lux maxwells maxwells megalines megohms megohms meter-kilograms meter-kilograms meter-kilograms meters meters meters meters meters meters meters meters meters meters/min meters/min meters/min meters/min meters/min meters/min meters/sec meters/sec meters/sec meters/sec meters/sec meters/sec meters/sec/sec meters/sec/sec meters/sec/sec meters/sec/sec microfarad micrograms microhms microhms microliters microns miles (naut.) miles (naut.) miles (naut.) © 2007 by Taylor & Francis Group, LLC Into in bushels (U.S dry) cubic cm cubic feet cubic in cubic meters cubic yards gallons (U.S liq.) pints (U.S liq.) quarts (U.S liq.) cubic ft/sec gal/sec spherical candle power watts foot-candles lumen/sq meter foot-candles kilolines webers maxwells microhms ohms cm-dynes cm-grams pound-feet centimeters feet in kilometers miles (naut.) miles (stat.) millimeters yards varas cm/sec feet/min feet/sec km/hr knots miles/hr feet/min feet/sec kilometers/hr kilometers/min miles/hr miles/min cm/sec/sec ft/sec/sec km/hr/sec miles/hr/sec farads grams megohms ohms liters meters feet kilometers meters Multiply by 7.92 0.02838 1,000 0.03531 61.02 0.001 1.308 × 10–3 0.2642 2.113 1.057 5.886 × 10–4 4.403 × 10–3 0.07958 0.001496 1.0 10.76 0.0929 0.001 10–8 106 1012 106 9.807 × 107 105 7.233 100 3.281 39.37 0.001 5.396 × 10–4 6.214 × 10–4 1,000 1.094 1.179 1,667 3.281 0.05468 0.06 0.03238 0.03728 196.8 3.281 3.6 0.06 2.237 0.03728 100 3.281 3.6 2.237 10–6 10–6 10–12 10–6 10–6 × 10–6 6,080.27 1.853 1,853 397 Units Conversion Table To Convert miles (naut.) miles (naut.) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles (statute) miles/hr miles/hr miles/hr miles/hr miles/hr miles/hr miles/hr miles/hr miles/hr/sec miles/hr/sec miles/hr/sec miles/hr/sec miles/min miles/min miles/min miles/min miles/min mil-feet milliers milligrams milligrams milligrams/liter millihenrys milliliters millimeters millimeters millimeters millimeters millimeters millimeters millimeters millimeters millimicrons million gal/day mils mils mils mils mils miner’s inches minims (British) minims (U.S., fluid) minutes (angles) minutes (angles) minutes (angles) minutes (angles) myriagrams myriameters myriawatts nepers © 2007 by Taylor & Francis Group, LLC Into miles (statute) yards centimeters feet in kilometers meters miles (naut.) yards cm/sec feet/min feet/sec km/hr km/min knots meters/min miles/min cm/sec/sec feet/sec/sec km/hr/sec meters/sec/sec cm/sec feet/sec km/min knots/min miles/hr cubic in kilograms grains grams parts/million henrys liters centimeters feet in kilometers meters miles mils yards meters cubic ft/sec centimeters feet in kilometers yards cubic ft/min cubic cm cubic cm degrees quadrants radians seconds kilograms kilometers kilowatts decibels Multiply by 1.1516 2,027 1.609 × 105 5,280 6.336 × 104 1.609 1,609 0.8684 1,760 44.70 88 1.467 1.609 0.02682 0.8684 26.82 0.1667 44.70 1.467 1.609 0.4470 2,682 88 1.609 0.8684 60 9.425 × 10–6 1,000 0.01543236 0.001 1.0 0.001 0.001 0.1 3.281 × 10–3 0.03937 10–6 0.001 6.214 × 10–7 39.37 1.094 × 10–3 x 10–9 1.54723 2.540 × 10–3 8.333 × 10–5 0.001 2.540 × 10–8 2.778 × 10–5 1.5 0.059192 0.061612 0.01667 1.852 × 10–4 2.909 × 10–4 60 10 10 10 8.686 398 AC Power Systems Handbook To Convert Newton ohms (international) ohms ohms ounces ounces ounces ounces ounces ounces ounces ounces (fluid) ounces (fluid) ounces (troy) ounces (troy) ounces (troy) ounces (troy) ounces (troy) ounces/sq in ounces/sq in parsec parsec parts/million parts/million parts/million pecks (British) pecks (British) pecks (U.S.) pecks (U.S.) pecks (U.S.) pecks (U.S.) pennyweights (troy) pennyweights (troy) pennyweights (troy) pennyweights (troy) pints (dry) pints (liq.) pints (liq.) pints (liq.) pints (liq.) pints (liq.) pints (liq.) pints (liq.) pints (liq.) Planck’s quantum poise poundals poundals poundals poundals poundals poundals pound-feet pound-feet pound-feet pounds pounds pounds pounds © 2007 by Taylor & Francis Group, LLC Into dynes ohm (absolute) megohms microhms drams grains grams pounds ounces (troy) tons (long) tons (metric) cubic in liters grains grams ounces (avdp.) pennyweights (troy) pounds (troy) dynes/sq cm pounds/sq in miles kilometers grains/U.S gal grains/Imp gal pounds/million gal cubic in liters bushels cubic in liters quarts (dry) grains ounces (troy) grams pounds (troy) cubic in cubic cm cubic feet cubic in cubic meters cubic yards gallons liters quarts (liq.) erg-second gram/cm sec dynes grams joules/cm joules/meter (newtons) kilograms pounds cm-dynes cm-grams meter-kg drams dynes grains grams Multiply by × 105 1.0005 10–6 106 16.0 437.5 28.349527 0.0625 0.9115 2.790 × 10–5 2.835 × 10–5 1.805 0.02957 480.0 31.103481 1.09714 20.0 0.08333 4,309 0.0625 19 × 1012 3.084 × 1013 0.0584 0.07016 8.345 554.6 9.091901 0.25 537.605 8.809582 24.0 0.05 1.55517 4.1667 × 10–3 33.60 473.2 0.01671 28.87 4.732 × 10–4 6.189 × 10–4 0.125 0.4732 0.5 6.624 × 10–27 1.00 13,826 14.10 1.383 × 10–3 0.1383 0.01410 0.03108 1.356 × 107 13,825 0.1383 256 44.4823 × 104 7,000 453.5924 399 Units Conversion Table To Convert pounds pounds pounds pounds pounds pounds pounds pounds pounds (avdp.) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds (troy) pounds of water pounds of water pounds of water pounds of water/min pounds/cubic ft pounds/cubic ft pounds/cubic ft pounds/cubic ft pounds/cubic in pounds/cubic in pounds/cubic in pounds/cubic in pounds/ft pounds/in pounds/mil-foot pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq ft pounds/sq in pounds/sq in pounds/sq in pounds/sq in pounds/sq in quadrants (angle) quadrants (angle) quadrants (angle) quadrants (angle) quarts (dry) quarts (liq.) quarts (liq.) quarts (liq.) quarts (liq.) quarts (liq.) quarts (liq.) quarts (liq.) radians radians radians radians © 2007 by Taylor & Francis Group, LLC Into joules/cm joules/meter (newtons) kilograms ounces ounces (troy) poundals pounds (troy) tons (short) ounces (troy) grains grams ounces (avdp.) ounces (troy) pennyweights (troy) pounds (avdp.) tons (long) tons (metric) tons (short) cubic ft cubic in gallons cubic ft/sec grams/cubic cm kg/cubic meter pounds/cubic in pounds/mil-foot gm/cubic cm kg/cubic meter pounds/cubic ft pounds/mil-foot kg/meter gm/cm gm/cubic cm atmospheres feet of water inches of mercury kg/sq meter pounds/sq in atmospheres feet of water in of mercury kg/sq meter pounds/sq ft degrees minutes radians seconds cubic in cubic cm cubic feet cubic in cubic meters cubic yards gallons liters degrees minutes quadrants seconds Multiply by 0.04448 4.448 0.4536 16.0 14.5833 32.17 1.21528 0.0005 14.5833 5,760 373.24177 13.1657 12 240 0.822857 3.6735 × 10–4 3.7324 × 10–4 4.1143 × 10–4 0.01602 27.68 0.1198 2.670 × 10–4 0.01602 16.02 5.787 × 10–4 5.456 × 10–9 27.68 2.768 × 104 1,728 9.425 × 10–6 1.488 178.6 2.306 × 106 4.725 × 10–4 0.01602 0.01414 4.882 6.944 × 10–3 0.06804 2.307 2.036 703.1 144 90 5,400.0 1.571 3.24 x 105 67.20 946.4 0.03342 57.75 9.464 × 10–4 1.238 × 10–3 0.25 0.9463 57.30 3,438 0.6366 2.063 × 105 400 AC Power Systems Handbook To Convert radians/sec radians/sec radians/sec radians/sec/sec radians/sec/sec radians/sec/sec revolutions revolutions revolutions revolutions/min revolutions/min revolutions/min revolutions/min/min revolutions/min/min revolutions/min/min revolutions/sec revolutions/sec revolutions/sec revolutions/sec/sec revolutions/sec/sec revolutions/sec/sec rod rod rods rods (surveyors’ meas.) scruples seconds (angle) seconds (angle) seconds (angle) seconds (angle) slug slug sphere square centimeters square centimeters square centimeters square centimeters square centimeters square centimeters square centimeters square feet square feet square feet square feet square feet square feet square feet square feet square in square in square in square in square in square in square kilometers square kilometers square kilometers square kilometers square kilometers © 2007 by Taylor & Francis Group, LLC Into degrees/sec revolutions/min revolutions/sec revolutions/min/min revolutions/min/sec revolutions/sec/sec degrees quadrants radians degrees/sec radians/sec revolutions/sec radians/sec/sec revolutions/min/sec revolutions/sec/sec degrees/sec radians/sec revolutions/min radians/sec/sec revolutions/min/min revolutions/min/sec chain (Gunter’s) meters feet yards grains degrees minutes quadrants radians kilogram pounds steradians circular mils sq feet sq in sq meters sq miles sq millimeters sq yards acres circular mils sq cm sq in sq meters sq miles sq millimeters sq yards circular mils sq cm sq feet sq millimeters sq mils sq yards acres sq cm sq feet sq in sq meters Multiply by 57.30 9.549 0.1592 573.0 9.549 0.1592 360 4.0 6.283 6.0 0.1047 0.01667 1.745 × 10–3 0.01667 2.778 × 10–4 360.0 6.283 60 6.283 3,600 60.0 0.25 5.029 16.5 5.5 20 2.778 × 10–4 0.01667 3.087 × 10–6 4.848 × 10–6 14.59 32.17 12.57 1.973 × 105 1.076 × 10–3 0.1550 0.0001 3.861 × 10–11 100.0 1.196 × 10–4 2.296 × 10–5 1.833 × 108 929.0 144.0 0.09290 3.587 × 10–8 9.290 × 104 0.1111 1.273 × 106 6.452 6.944 × 10–3 645.2 106 7.716 × 10–4 247.1 1010 10.76 × 106 1.550 × 109 106 401 Units Conversion Table To Convert square kilometers square kilometers square meters square meters square meters square meters square meters square meters square meters square miles square miles square miles square miles square miles square millimeters square millimeters square millimeters square millimeters square mils square mils square mils square yards square yards square yards square yards square yards square yards square yards temperature (°C) + 273 temperature (°C) + 17.78 temperature (°F) + 460 temperature (°F) – 32 tons (long) tons (long) tons (long) tons (metric) tons (metric) tons (short) tons (short) tons (short) tons (short) tons (short) tons (short) tons (short) tons (short)/sq ft tons (short)/sq ft tons of water/24 hr tons of water/24 hr tons of water/24 hr volt (absolute) volts/in watt-hours watt-hours watt-hours watt-hours watt-hours watt-hours watt-hours watt-hours © 2007 by Taylor & Francis Group, LLC Into sq miles sq yards acres sq cm sq feet sq in sq miles sq millimeters sq yards acres sq feet sq km sq meters sq yards circular mils sq cm sq feet sq in circular mils sq cm sq in acres sq cm sq feet sq in sq meters sq miles sq millimeters absolute temperature (°C) temperature (°F) absolute temperature (°F) temperature (°C) kilograms pounds tons (short) kilograms pounds kilograms ounces ounces (troy) pounds pounds (troy) tons (long) tons (metric) kg/sq meter pounds/sq in pounds of water/hr gallons/min cubic ft/hr statvolts volts/cm Btu ergs foot-pounds gram-calories horsepower-hr kilogram-calories kilogram-meters kilowatt-hr Multiply by 0.3861 1.196 × 106 2.471 × 10–4 104 10.76 1,550 3.861 × 10–7 106 1.196 640.0 27.88 × 106 2.590 2.590 × 106 3.098 × 106 1,973 0.01 1.076 × 10–5 1.550 × 10–3 1.273 6.452 × 10–6 10–6 2.066 × 10–4 8,361 9.0 1,296 0.8361 3.228 × 10–7 8.361 × 105 1.0 1.8 1.0 5/9 1,016 2,240 1.120 1,000 2,205 907.1848 32,000 29,166.66 2,000 2,430.56 0.89287 0.9078 9,765 2,000 83.333 0.16643 1.3349 0.003336 0.39370 3.413 3.60 × 1010 2,656 859.85 1.341 × 10–3 0.8605 367.2 0.001 402 AC Power Systems Handbook To Convert watts (international) watts watts watts watts watts watts watts watts watts watts (Abs.) watts (Abs.) webers webers webers/sq in webers/sq in webers/sq in webers/sq in webers/sq meter webers/sq meter webers/sq meter webers/sq meter yards yards yards yards yards yards © 2007 by Taylor & Francis Group, LLC Into watts (absolute) Btu/hr Btu/min ergs/sec foot-lb/min foot-lb/sec horsepower horsepower (metric) kg-calories/min kilowatts Btu (mean)/min joules/sec maxwells kilolines gausses lines/sq in webers/sq cm webers/sq meter gausses lines/sq in webers/sq cm webers/sq in centimeters kilometers meters miles (naut.) miles (stat.) millimeters Multiply by 1.0002 3.4129 0.05688 107 44.27 0.7378 1.341 × 10–3 1.360 × 10–3 0.01433 0.001 0.056884 108 105 1.550 × 107 108 0.1550 1,550 104 6.452 × 104 10–4 6.452 × 10–4 91.44 9.144 × 10–4 0.9144 4.934 × 10–4 5.682 × 10–4 914.4 ... AM 24 AC Power Systems Handbook + + Idc AC system AC system Idc − − (a) Idc AC system AC system Idc (b) Line AC system AC system Line Breaker (c) Figure 1.16 Two-terminal dc transmission systems: ... integrated with a reactor, which is generally an air-core design A back-to-back dc system is used to tie two asynchronous ac systems (systems that are not in synchronism) The two ac systems can be... AM 23 AC Power Systems AC system AC system Converter building Figure 1.15 The back-to-back system of dc transmission (From [9] Used with permission.) synchronized with their neighboring systems