List of Figures xiii
List of Tables xxv
Preface xxix
Acknowledgments xxxvii
Chapter 1 Mathematics Used in Electromagnetism 1
1.1 Introduction 1
1.2 Numbers 2
1.3 Mathematical Operations with Vectors 17
1.4 Calculus with Vectors—The Gradient 18
1.5 Divergence, Curl, and Stokes’ Theorem 23
1.6 Maxwell’s Equations 25
Chapter 2 Electrical Safety Aspects of the Resistance Property of Materials 30
2.1 Introduction 30
2.2 Hazards Caused by Electrical Resistance 31
2.3 Resistance and Conductance 38
2.4 Example—Trunk of a Human Body 42
2.5 Example—Limb of a Human Body 43
2.6 Power and Energy Flow 44
2.7 Sheet Resistivity 47
2.8 Example—Square of Dry Skin 48
2.9 Spreading Resistance 48
2.10 Example—Circle of Dry Skin 49
2.11 Particle Conductivity 50
2.12 Examples—Potassium, Sodium, and Chlorine Ions 53
2.13 Cable Resistance 53
Chapter 3 Capacitance Phenomena 59
3.1 Fundamentals of Capacitance 59
3.2 Capacitance and Permittivity 62
3.3 Capacitance in Electrical Circuits 65
3.4 Capacitance of Body Parts 69
3.4.1 Example—Skin Capacitance 69
3.4.2 Example—Capacitance of Trunk and Limb 70
3.5 Electrical Hazards of Capacitance 71
3.6 Capacitance of Cables 72
Chapter 4 Inductance Phenomena 74
4.1 Inductance in Electrical Theory 74
4.2 Inductance of Wires 76
4.3 Example—Inductance of a Conductor 76
4.4 Example—Inductance of Trunk and Limb 77
4.5 Inductors or Reactors 77
4.6 Skin Effect 77
4.7 Cable Inductance 81
4.8 Surge Impedance 83
4.9 Bus Bar Impedance Calculations 84
Chapter 5 Circuit Model of the Human Body 90
5.1 Calculation of Electrical Shock Using the Circuit Model of the Body 90
5.2 Frequency Response of the Human Body 93
Chapter 6 Effect of Current on the Human Body 101
6.1 Introduction to Electrical Shock 101
6.2 Human and Animal Sensitivities to Electric Current 102
6.3 Human Body Impedance 104
6.4 Effects of Various Exposure Conditions 107
6.4.1 Bare Feet, Wet Conditions, and Other Variations 107
6.4.2 Shoes and Other Insulated Objects and the Earth 108
6.5 Current Paths Through the Body 108
6.6 Human Response to Electrical Shock Varies with Exposure Conditions, Current Magnitude, and Duration 113
6.7 Medical Imaging and Simulations 114
Chapter 7 Fundamentals of Ground Grid Design 118
7.1 Introduction to Ground Grid Design 118
7.2 Summary of Ground Grid Design Procedures 119
7.2.1 Site Survey 119
7.2.2 Conductor Sizing 119
7.2.3 Step and Touch Voltages 122
7.2.4 Ground Grid Layout 124
7.2.5 Ground Resistance Calculation 124
7.2.6 Calculation of Maximum Grid Current 125
7.2.7 Calculation of Ground Potential Rise (GPR) 125
7.2.8 Calculation of Mesh Voltage, Em 125
7.2.9 Calculation of Step Voltage, Es 127
7.2.10 Detailed Design 127
7.3 Example Design from IEEE Standard 80 128
Chapter 8 Safety Aspects of Ground Grid Operation and Maintenance 138
8.1 Introduction 138
8.2 Effects of High Fault Currents 138
8.3 Damage or Failure of Grounding Equipment 142
8.3.1 Thermal Damage to Conductors Due to Excessive Short-Circuit Currents 142
8.3.2 Connector Damage Due to Excessive Short-Circuit Stresses 143
8.3.3 Drying of the Soil Resulting in Increased Soil Resistivity 144
8.4 Recommendations 145
Chapter 9 Grounding of Distribution Systems 147
9.1 Stray Currents in Distribution Systems 147
9.2 Three-Phase Multigrounded Neutral Distribution Line 148
9.3 Secondary Systems: 120/240 V Single Phase 154
9.3.1 Example of Stray Currents—Touching a Grounded Conductor 158
9.3.2 Example of Stray Currents—With One Conductor Shorted to Neutral 159
9.4 Remediation of Stray-Current Problems 160
9.5 Grounding and Overvoltages in Distribution Systems 163
9.6 High-Resistance Grounding of Distribution Systems 167
9.6.1 Methods of Determining Charging Current 169
Chapter 10 Arc Flash Hazard Analysis 172
10.1 Introduction to Arc Flash Hazards 172
10.2 Factors Affecting the Severity of Arc Flash Hazards 176
10.3 Example Arc Flash Calculations 179
10.4 Remediation of Arc Flash Hazards 180
10.4.1 Example: Correcting an Arc Flash Problem When a Coordination Problem Requires Replacing Trip Units 180
10.4.2 Example: Correcting a Coordination Problem Without Introducing an Arc Flash Problem 182
10.5 Coordination of Low-Voltage Breaker Instantaneous Trips for Arc Flash Hazard Reduction 185
10.5.1 Hospital #1—Time–Current Curve Examples 189
10.5.2 Hospital #2—Time–Current Curve Examples 194
10.5.3 Hospital #3—Time−Current Curve Examples 200
10.6 Low-Voltage Transformer Secondary Arc Flash Protection using Fuses 205
Chapter 11 Effect of High Fault Currents on Protection and Metering 216
11.1 Introduction 216
11.2 Current Transformer Saturation 217
11.3 Saturation of Low-Ratio CTs 219
11.3.1 AC Saturation 219
11.3.2 DC Saturation 221
11.4 Testing of Current Transformer Saturation 224
11.5 Effect of High Fault Currents on Coordination 228
11.6 Protective Relay Ratings and Settings 230
11.7 Effects of Fault Currents on Protective Relays 232
11.7.1 Examples 233
11.8 Methods for Upgrading Protection Systems 233
11.8.1 Update Short-Circuit Study 233
11.8.2 Update Protective Device Coordination Study 233
Chapter 12 Effects of High Fault Currents on Circuit Breakers 235
12.1 Insufficient Interrupting Capability 236
12.2 High Voltage Air Circuit Breakers 236
12.3 Vacuum Circuit Breakers 237
12.4 SF6 Circuit Breakers 239
12.5 Loss of Interruption Medium 241
12.6 Interrupting Ratings of Switching Devices 242
12.7 Circuit Breakers 243
12.8 Fuses 244
12.9 Case Studies 245
12.9.1 Example: Diablo Canyon 245
12.9.2 Example: Dresden and Quad Cities 248
12.10 Low-Voltage Circuit Breakers 249
12.11 Testing of Low-Voltage Circuit Breakers 251
12.11.1 Testing of Low-Voltage Molded-Case Circuit Breakers According to UL Standard 489 252
12.11.2 Testing of Low-Voltage Molded-Case Circuit Breakers for Use With Uninterruptible Power Supplies According to UL Standard 489 259
12.11.3 Testing of Supplementary Protectors for Use in Electrical Equipment According to UL Standard 1077 261
12.11.4 Testing of Transfer Switch Equipment According to UL Standard 1008 272
12.11.5 Testing of Low-Voltage AC Power Circuit Breakers According to ANSI Standard C37.50-1989 276
12.11.6 Testing of Low-Voltage DC Power Circuit Breakers According to IEEE Standard C37.14-2002 280
12.11.7 Testing of Low-Voltage Switchgear and Controlgear According to IEC Standard 60947-1 284
12.11.8 Testing of Low-Voltage AC and DC Circuit Breakers According to IEC Standard 60947-2 285
12.11.9 Testing of Circuit Breakers Used for Across-the-Line Starters for Motors According to IEC Standard 60947-4-1 288
12.11.10 Testing of Circuit Breakers Used in Households and Similar Installations According to IEC Standard 60898-1 and -2 290
12.11.11 Testing of Circuit Breakers Used in Equipment such as Electrical Appliances According to IEC Standard 60934 293
12.12 Testing of High-Voltage Circuit Breakers 296
Chapter 13 Mechanical Forces and Thermal Effects in Substation Equipment Due To High Fault Currents 299
13.1 Introduction 299
13.2 Definitions 299
13.3 Short-Circuit Mechanical Forces on Rigid Bus Bars 300
13.3.1 Short-Circuit Mechanical Forces on Rigid Bus Bars—Circular Cross Section 300
13.3.2 Short-Circuit Mechanical Forces—Rectangular Cross Section 302
13.4 Dynamic Effects of Short Circuits 302
13.5 Short-Circuit Thermal Effects 304
13.6 Flexible Conductor Buses 305
13.6.1 Conductor Motion During a Fault 307
13.6.2 Pinch Forces on Bundled Conductors 311
13.7 Force Safety Devices 316
13.8 Substation Cable and Conductor Systems 318
13.8.1 Cable Thermal Limits 318
13.8.2 Cable Mechanical Limits 319
13.9 Distribution Line Conductor Motion 319
13.10 Effects of High Fault Currents on Substation Insulators 320
13.10.1 Station Post Insulators for Rigid Bus Bars 320
13.10.2 Suspension Insulators for Flexible Conductor Buses 322
13.11 Effects of High Fault Currents on Gas-Insulated Substations (GIS) 322
Chapter 14 Effect of High Fault Currents on Transmission Lines 325
14.1 Introduction 325
14.2 Effect of High Fault Current on Non-Ceramic Insulators (NCI) 325
14.3 Conductor Motion Due to Fault Currents 328
14.4 Calculation of Fault Current Motion for Horizontally Spaced Conductors 329
14.5 Effect of Conductor Shape 330
14.6 Conductor Equations of Motion 331
14.7 Effect of Conductor Stretch 332
14.8 Calculation of Fault Current Motion for Vertically Spaced Conductors 332
14.9 Calculation Procedure 333
14.10 Calculation of Tension Change with Motion 334
14.11 Calculation of Mechanical Loading on Phase-to-Phase Spacers 335
14.12 Effect of Bundle Pinch on Conductors and Spacers 336
Chapter 15 Lightning and Surge Protection 338
15.1 Surge Voltage Sources and Waveshapes 338
15.2 Surge Propagation, Refraction, and Reflection 343
15.3 Insulation Withstand Characteristics and Protection 346
15.4 Surge Arrester Characteristics 349
15.5 Surge Arrester Application 350
References 352
Index 361
Peter E. Sutherland serves as lead consultant at GE Energy Services, in Schenectady, New York. He has a PhD in Electric Power Engineering from Rensselaer Polytechnic Institute. He is a well-respected industry expert who has taught several courses on the topic. He is a fellow of IEEE.
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