# Current Interruption Transients Calculation

ISBN: 978-1-118-70722-7 January 2014 246 Pages

## Description

Provides an original, detailed and practical description of current interruption transients, origins, and the circuits involved, and how they can be calculated

Current Interruption Transients Calculationis a comprehensive resource for the understanding, calculation and analysis of the transient recovery voltages (TRVs) and related re-ignition or re-striking transients associated with fault current interruption and the switching of inductive and capacitive load currents in circuits.

This book provides an original, detailed and practical description of current interruption transients, origins, and the circuits involved, and how they can be calculated and then analysed using only a hand calculator and a spreadsheet program.

Key features:

• Detailed theory on all of the current interruption cases that can occur on a power system.
• Clear explanation on how to calculate transients, showing how four basic circuits can represent all transients and can be solved in general without any use of the ‘classical’ Laplace transform method.
• Series and parallel RLC circuit theory, followed by the calculation of pole factors using the symmetrical component method to derive the base power frequency components, with results applied to all the relevant transient cases.
• Fault current interruption and inductive and capacitive load current switching cases illustrated using real application examples.

With its practical approach, this book offers engineers the tools they need when analysing circuit breaker applications. It will be of great interest to practicing engineers and electric utility staff involved in circuit breaker design, specification, testing, switchgear application, system operation and planning, and in particular, for engineers using simulation programs for transient calculations. It will also be useful for senior undergraduate and postgraduate electrical power engineering students looking to work in switchgear manufacturers and testing laboratories.

Preface ix

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

Bibliography 7

2 RLC Circuits 8

2.1 General 8

2.2 Series RLC Circuit with Step Voltage Injection 8

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 Travelling Wave Basics 28

2.8 Summary 32

Bibliography 32

3 Pole Factor Calculation 33

3.1 General 33

3.2 Pole Factors: Effectively Earthed Systems 43

3.3 Pole Factors: Non-Effectively Earthed Systems 51

3.4 Alternative Pole Factor Calculation Method 56

3.5 Three-Phase Test Circuit Arrangement 57

3.6 Summary 59

Bibliography 60

4 Terminal Faults 61

4.1 General Considerations 61

4.2 Standard TRV Derivation 63

4.3 Effect of Added Capacitance 72

4.4 Effect of Added Resistance 83

4.5 Effect of Added Inductance 84

4.6 Out-of-Phase Switching 90

4.7 Asymmetrical Currents 91

4.8 Double Earth Faults 99

4.9 Summary 102

Bibliography 103

5 Short-Line Faults 104

5.1 General 104

5.2 Line-Side Voltage Calculation 104

5.3 Effect of Added Capacitance 115

5.4 Discussion 118

Bibliography 119

6.1 General 120

6.2 General Shunt Reactor Switching Case 123

6.3 Shunt Reactors with Isolated Neutrals 130

6.4 Shunt Reactors with Neutral Reactor Earthed Neutrals 135

6.5 Shunt Reactors with Earthed Neutrals 136

6.6 Re-Ignitions 137

6.8 Discussion 139

6.9 Summary 139

Bibliography 140

7.1 General 141

7.2 Shunt Capacitor Banks 141

7.2.1 Energization 141

7.2.2 De-Energization 152

7.2.3 Outrush 159

7.3 Transmission Lines 160

7.4 Cables 163

7.5 Summary 165

Bibliography 166

8 Circuit Breaker Type Testing 167

8.1 Introduction 167

8.2 Circuit Breaker Interrupting Time 167

8.3 Inherent Transient Recovery Voltages 173

8.5 Capacitive Current Switching 175

Bibliography 175

Appendix A: Differential Equations 177

Bibliography 186

Appendix B: Principle of Duality 187

Appendix C: Useful Formulae 190

Appendix D: Euler’s Formula 193

Bibliography 196

Appendix E: Asymmetrical Current-Calculating Areas Under Curves 197

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

Representation 200

Appendix G: Special Case: Interrupting Small Capacitive Currents 207

Bibliography 210

Appendix H: Evolution of Transient Recovery Voltages 211

H.1 Introduction 211

H.2 TRVs: Terminal Faults 212

H.3 Terminal Fault TRV Standardization 218

H.4 Short-Line Fault 220

H.5 Inductive and Capacitive Load Current Switching 221

H.6 Terminal Fault TRV Calculation 221

H.6.1 Pole Factor Calculation 221

H.6.2 Transient Calculation 225

Bibliography 226

Index 231

“It would be of interest to engineers involved with specification, testing, switchgear application, and simulation programs.”  (IEEE Electrical Engineering magazine, 1 May 2015)