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