Current Interruption Transients Calculation (Hardcover, 2)

Preface to the Second Edition ix

Preface to First Edition xi

1 Introduction 1

1.1 Background 1

1.2 Short-Circuit Rating Basis for High-Voltage Circuit Breakers 2

1.3 Current Interruption Terminology 4

Further Reading 7

2 RLC Circuits 9

2.1 General 9

2.2 Series RLC Circuit with Step Voltage Injection 9

2.3 Source-Free Series RLC Circuit with Precharged Capacitor 15

2.4 Source-Free Parallel RLC Circuit with Precharged Capacitor 18

2.5 Parallel RLC Circuit with Ramp Current Injection 21

2.6 Alternative Equations 27

2.7 Traveling Wave Basics 28

2.8 Summary 34

References 34

Further Reading 34

3 Pole Factor Calculation 35

3.1 General 35

3.2 Pole Factors: Effectively Earthed Systems 44

3.3 Pole Factors: Non-Effectively Earthed Systems 52

3.4 Alternative Pole Factor Calculation Method 56

3.5 Three-Phase Test Circuit Arrangement 59

3.6 Summary 60

Further Reading 61

4 Terminal Faults 63

4.1 General Considerations 63

4.2 Standard TRV Derivation 65

4.3 Effect of Added Capacitance 73

4.4 Effect of Added Resistance 85

4.5 Effect of Series Reactors 88

4.6 Out-of-Phase Switching 96

4.7 Asymmetrical Currents 97

4.8 Double Earth Faults 105

4.9 Summary 108

Further Reading 109

5 Short Line Faults 111

5.1 General 111

5.2 Line Side Voltage Calculation 111

5.3 Effect of Added Capacitance 119

5.4 Discussion 122

Further Reading 123

6 Inductive Load Switching 125

6.1 General 125

6.2 General Shunt Reactor Switching Case 128

6.3 Shunt Reactors with Isolated Neutrals 135

6.4 Shunt Reactors with Neutral Reactor Earthed Neutrals 139

6.5 Shunt Reactors with Earthed Neutrals 140

6.6 Reignitions 141

6.7 Unloaded Transformer Switching 142

6.8 Discussion 143

6.9 Summary 143

Further Reading 146

7 Capacitive Load Switching 147

7.1 General 147

7.2 Shunt Capacitor Banks 147

7.2.1 Energization 147

7.2.1.1 Inrush Current 148

7.2.1.2 Limiting Inrush Current 154

7.2.2 De-Energization 156

7.2.2.1 General Considerations 156

7.2.2.2 Recovery Voltages 156

7.2.2.3 Reignitions and Restrikes 157

7.2.3 Outrush 163

7.3 Transmission Lines 164

7.4 Cables 167

7.5 Special Case: Interrupting Small Capacitance Currents 170

7.6 Summary 173

References 174

Further Reading 174

8 Circuit Breaker Type Testing 175

8.1 Introduction 175

8.2 Circuit Breaker Interrupting Time 175

8.3 Inherent Transient Recovery Voltages 182

8.4 Inductive Load Switching 182

8.5 Capacitive Current Switching 183

Further Reading 183

Appendix A: Differential Equations 185

Appendix B: Principle of Duality 195

Appendix C: Useful Formulae 201

Appendix D: Euler’s Formula 205

Appendix E: Asymmetrical Current-Calculating Areas Under Curves 209

Appendix F: Shunt Reactor Switching – First-Pole-to-Clear Circuit Representation 213

Appendix G: Special Case: Generator Circuit Breakers TRVs 219

Appendix H: Evolution of Transient Recovery Voltages 239

Appendix I: Equation Plotting Using Excel 261

Index 277