vii
Contents
Abstract iii
Acknowledgements v
Contents vii
List of Figures xiii
List of Tables xix
List of Abbreviations xxiii
Introduction 1
I Theory 7
1 Travelling waves 11
1.1 Overview . . . 12
1.2 Transmission lines . . . 13
1.2.1 Lumped element models . . . 13
1.2.2 Distributed parameter models . . . 14
1.2.3 Modal analysis . . . 15
1.2.4 Line parameters . . . 16
1.2.5 Non homogeneous lines . . . 18
1.3 Transmission line equations . . . 18
1.3.1 Time domain . . . 18
1.3.2 Frequency domain . . . 19
1.4 The lossless line . . . 21
1.4.1 Propagation speed . . . 22
1.4.2 Characteristic impedance . . . 23
1.4.3 General solution . . . 23
1.5 Reflections . . . 24
1.5.1 Reflections on line junctions . . . 24
1.5.2 Reflections on line terminations . . . 26
1.5.3 Lattice diagram . . . 27
1.6 Attenuation and distortion . . . 28
1.7 The impact of substation measurement . . . 29
1.7.1 Transformers bandwidth . . . 29
1.7.2 Secondary cable ringing . . . 30
2 Simulation tools 33 2.1 Power system model . . . 34
2.1.1 Overhead lines . . . 34
2.1.2 Measurement transformers . . . 35
2.1.3 Neglected effects . . . 36
2.2 Illustration of TWs properties . . . 37
2.2.1 Wave propagation and reflection . . . 37
2.2.2 Attenuation and distortion . . . 40
2.2.3 Typical propagation speed in overhead lines . . . 40
2.3 Discussion . . . 41
3 Algorithms based on travelling waves 43 3.1 Fault location algorithms . . . 44
3.1.1 Passive two-ended (Type D) . . . 44
3.1.2 Passive single-end (Type A) . . . 45
3.1.3 Active single end (Type E) . . . 46
3.2 Non homogeneous lines . . . 47
3.2.1 Updated type-D algorithm . . . 48
3.2.2 Example . . . 49
3.3 Practical considerations . . . 50
3.3.1 Technical requirements . . . 50
3.3.2 Propagation speed . . . 51
3.3.3 Measurement transducers . . . 51
3.3.4 Signal processing . . . 52
3.3.5 In this project . . . 52
4 Travelling wave fault location based on Pattern recognition 55 4.1 Theoretical development . . . 56
4.1.1 Starting equations . . . 57
4.1.2 Building the signals . . . 58
4.1.3 Pattern recognition . . . 59
ix
4.2 Basic principle illustration . . . 60
4.3 Practical challenges and solutions . . . 61
4.3.1 Big data transfer -SReduced . . . 62
4.3.2 Unreliable voltages -SI . . . 62
4.3.3 Attenuation and reflections - Correction factor . . . 63
4.3.4 Secondary cable ringing - notch filter . . . 63
4.3.5 Line parameters knowledge . . . 65
4.3.6 Distortion . . . 65
4.4 Algorithm description . . . 66
4.4.1 Pre-computations . . . 66
4.4.2 Define the value of the parameters . . . 66
4.4.3 Apply the pattern recognition algorithm . . . 67
4.5 Discussion . . . 67
II Results 69
5 Substation measurements 73 5.1 Lightning impulse . . . 745.1.1 Definition . . . 74
5.1.2 Single stage generator circuit . . . 75
5.1.3 Multi-stage generator circuit . . . 77
5.1.4 Current impulse . . . 78
5.2 Test set-up . . . 78
5.2.1 Lightning current impulse generator . . . 79
5.2.2 Equipment description . . . 80
5.3 Test results . . . 81
5.3.1 Records . . . 81
5.3.2 CT transfer function . . . 83
5.4 Notch filter . . . 84
5.4.1 Notch filter design . . . 85
5.4.2 Results . . . 85
5.5 Discussion . . . 86
6 Measurement campaign 89 6.1 Measurement campaign description . . . 91
6.1.1 Monitored line . . . 91
6.1.2 Measurement systems . . . 92
6.1.3 Useful records acquired . . . 94
6.2 Records . . . 95
6.2.1 Event 1: Line energizing of substation A . . . 95
6.2.2 Event 2: Line energizing of substation B . . . 96
6.2.3 Event 3: Single phase to ground fault (2-ended) . . . 97
6.2.4 Event 4: Single phase to ground fault (1-ended) . . . 99
6.3 Propagation speed . . . 100
6.4 Fault record analysis . . . 101
6.4.1 Impact of the voltage transformers . . . 101
6.4.2 Reflections on the T-junction . . . 103
6.4.3 Reflections on the CT secondary cabling . . . 103
6.4.4 Fault location . . . 103
6.4.5 Notch filter . . . 106
6.5 Discussion . . . 109
7 Simulation models 111 7.1 Current measurement system . . . 112
7.1.1 EMTP model . . . 113
7.1.2 Parameters sensitivity . . . 114
7.1.3 Discussion . . . 116
7.2 Power system . . . 116
7.2.1 Model . . . 116
7.2.2 Results . . . 118
7.3 Case studies . . . 119
7.3.1 Effect of topology - Bergeron models . . . 119
7.3.2 Effect of wave properties - No outside reflections . . . . 120
7.3.3 Complete overhead lines . . . 121
7.4 Discussion . . . 123
8 Pattern recognition algorithm 125 8.1 Algorithm parameters . . . 126
8.1.1 Impact of usingSI . . . 127
8.1.2 Impact of the correlation window . . . 130
8.1.3 Impact of the measurement system and notch filter . . . 133
8.1.4 Discussion . . . 134
8.2 Algorithm performance . . . 136
8.2.1 Complete simulation models . . . 136
8.2.2 Application to the fault record . . . 137
8.3 Discussion . . . 138
xi
Conclusion 141
A List of reports and publications 145
B Simulation models 147
C Measurement tools 153
D Measurement campaign and lab tests 159
D.1 Measurement campaign description . . . 159 D.2 HV laboratory tests . . . 164
Bibliography 167
