Preface ...................................................... xiii
1 A Combined Electrostatic-Electrodynamic Approach
to Lightning Pre-Stroke Phenomena and Related EMC Problems ... 1
1.1 Preliminary Remarks ..................................... 1
1.2 Thundercloud Electrostatic Modelling .................... 3
1.3 Electric Field at the Plane ............................. 5
1.4 On-Axis Electric Field ................................. 10
1.5 Pre-Stroke Electrostatics .............................. 12
1.6 Pre-Stroke Electrodynamics ............................. 19
1.7 Concluding Remarks ..................................... 22
Appendix A .................................................. 24
A.l On-ground field ........................................ 27
A.2 On-axis field (below the cell bottom) .................. 28
Appendix В .................................................. 28
Appendix С .................................................. 32
C.l Space-charge-free electrostatic solution ............... 32
C.2 Space-charge-free electrodynamic solution .............. 33
C.3 E-field solution including corona ...................... 34
Appendix D .................................................. 37
References .................................................. 40
2 A Reasoned Approach to Lightning Electromagnetics
and Coupling to Nearby Power Transmission Lines ............. 43
2.1 Introduction ........................................... 43
2.2 Remarks on the Pre-Stroke and Stroke-in-Progress
Phases ................................................. 46
2.2.1 Corona activity ................................. 46
2.2.2 Surge current velocity .......................... 48
2.2.3 Earth performances .............................. 49
2.3 Antenna Model .......................................... 50
2.4 Discussion ............................................. 53
2.5 Return-Stroke Current .................................. 57
2.6 Induced Voltage on a Nearby Line ....................... 60
2.6.1 Actual excitation field ......................... 60
2.6.2 Coupling to a nearby line ....................... 62
2.6.3 Example of application and discussion ........... 66
2.7 Concluding Remarks ..................................... 69
Appendix A .................................................. 73
Appendix В .................................................. 74
References .................................................. 76
3 Effects of Geomagnetic Storms on Long Distance AC
Transmission Systems ........................................ 79
3.1 Introduction ........................................... 79
3.2 System Representation .................................. 80
3.2.1 Power transformer and autotransformer
representation .................................. 81
3.2.2 Static VAR compensator representation ........... 83
3.3 Coordinated Compensation Strategy ...................... 84
3.4 Test Results ........................................... 87
3.5 Conclusions ............................................ 90
References .................................................. 90
4 Evaluation of the AC Interferences between
Transmission Lines and Metallic Underground
Structures .................................................. 93
4.1 Introduction ........................................... 93
4.2 System Representation .................................. 97
4.3 Test Results .......................................... 102
4.4 Conclusions ........................................... 107
References ................................................. 107
5 The Crucial Case of Quasistatic Magnetic Field
Penetration into Metallic Enclosures: An Unexplored Model .. 109
5.1 Introduction .......................................... 109
5.2 Unloaded Short Aperture ............................... 113
5.2.1 Preliminary remarks ............................ 113
5.2.2 Concentrated magnetic flux penetration ......... 114
5.2.3 Distributed magnetic field penetration ......... 114
5.3 Loaded Short Aperture and Perforated Sheet ............ 120
Appendix A ................................................. 124
Flux linking a short elliptic aperture ................ 124
Appendix В ................................................. 127
Resistance and inductance of an elliptic aperture
when resulting unfilled, or filled by a continuous
sheet ................................................. 127
Appendix С ................................................. 129
Flux penetration into an aperture blocked by
a sheet of different material ......................... 129
Appendix D ................................................. 130
Some remarks on the notion of flux linkage applied to
a hole ................................................ 130
References ................................................. 131
6 Diakoptic Approach to EMC Problems Involving the Human
Body ....................................................... 133
6.1 Introduction .......................................... 133
6.2 Diakoptic Approach Applied to ELF Electric Field
Exposure of HB ........................................ 135
6.2.1 Evaluation of equivalent capacitances to
earth .......................................... 135
6.2.2 Effective electrostatic heights and
evaluation of the junction currents ............ 140
6.2.3 Earthed person on the plane .................... 141
6.2.4 Person suspended above the earth ............... 145
6.3 Improved HB Model for ESD Applications ................ 146
6.3.1 Preliminary remarks ............................ 146
6.3.2 Evaluation of the serial parameters Ri and
Li ............................................. 147
6.3.3 Transient analysis ............................. 149
6.3.4 Contact discharge mode ......................... 153
6.3.5 Air discharge mode ............................. 159
6.4 Conclusions ........................................... 160
Appendix A ................................................. 161
Sphere above a plane .................................. 161
References ................................................. 162
7 New Power Quality Assessment Criteria for Harmonic
Disturbances ............................................... 165
7.1 Introduction about Power Quality ...................... 166
7.1.1 Different kinds of disturbances ................ 167
7.1.2 Frequency variations ........................... 168
7.1.3 Voltage amplitude variations ................... 168
7.1.4 Waveform variation ............................. 170
7.2 Electromagnetic Compatibility: Standards .............. 171
7.2.1 IEC harmonic standards ......................... 172
7.2.2 IEEE Harmonic standards ........................ 175
7.2.3 Comparison of ГЕС and IEEE standards
harmonic limits ................................ 175
7.3 Harmonic Distortion Level Monitoring .................. 176
7.3.1 Evaluation of the voltage and current
distortion ..................................... 176
7.3.2 The need for new indices ....................... 177
7.4 New Power Quality Assessment Criteria for Supply
Systems under Non-Sinusoidal Conditions ............... 179
7.4.1 Basic assumptions .............................. 179
7.4.2 New criterion for harmonic distortion
evaluation ..................................... 180
7.4.3 Simulation results ............................. 181
7.4.4 Experimental results ........................... 183
7.5 Conclusions ........................................... 188
References ................................................. 188
8 Design of Line Front-End Converter Systems under Real
Line Conditions ............................................ 191
8.1 Introduction .......................................... 191
8.2 Basic Function, Operating Limits and Mathematical
Models ................................................ 194
8.3 Basic Control ......................................... 198
8.3.1 Phase control .................................. 198
8.3.2 AC current control ............................. 199
8.3.3 Two axis-based current control ................. 199
8.3.4 Use of averaging and linearisation ............. 200
8.3.5 The voltage oriented control ................... 201
8.4 Advanced Control Techniques ........................... 202
8.4.1 Sensorless control techniques .................. 202
8.4.2 Direct power control ........................... 204
8.5 Design Criteria for Pi-Based Current Controller ....... 204
8.5.1 Pi-based current control design example ........ 211
8.6 Design Criteria for DC Voltage Control ................ 215
8.6.1 Pi-based voltage control ....................... 215
8.6.2 Pi-based voltage control design example ........ 217
8.7 Non-Ideal Operating Conditions ........................ 219
8.7.1 Delays ......................................... 220
8.7.2 Grid unbalance ................................. 220
8.7.3 Position of the grid sensors ................... 222
8.7.4 Passive damping of the LCL filter .............. 222
8.8 Conclusions ........................................... 223
References ................................................. 223
9 Adjoint Network Theory to Analyse the Power Converters
with Respect to their Line-side Behaviour .................. 225
9.1 Introduction .......................................... 225
9.2 VSC Power Converters Connected to the Line ............ 227
9.3 Modelling of the Current Controlled Voltage Source
Converter with the "Virtual Circuit" Approach ......... 229
9.4 Sensitivity Analysis in the Frequency Domain .......... 233
9.4.1 Basic definitions .............................. 233
9.4.2 Application of the adjoint network ............. 234
9.5 Sensitivity Analysis Based on the Adjoint Circuit:
Case Study ............................................ 236
9.5.1 Sensitivity of the line current with respect
to the transformer inductance .................. 236
9.5.2 Sensitivity of the line current with respect
to the number of sample delays ................. 237
9.5.3 Sensitivity analysis with respect to the LCL
filter ......................................... 239
9.6 Conclusions ........................................... 243
References ................................................. 244
10 Harmonic Load Flow Applications for Industrial Power
Systems Design ............................................. 245
10.1 Introduction .......................................... 245
10.2 Power System Response to Harmonics .................... 247
10.3 Probabilistic Formulation ............................. 253
10.4 Case Study ............................................ 256
10.5 Passive Harmonic Filters .............................. 261
10.6 Minimal Cost Design for Harmonic Reduction ............ 262
10.7 Optimisation Algorithm ................................ 264
10.8 Case Study ............................................ 265
References ................................................. 266
11 Shunt Active Filters to Mitigate Harmonic Propagation in
Distribution Lines ......................................... 269
11.1 Introduction .......................................... 269
11.2 Active Filters ........................................ 270
11.3 Identification of the Polluting Load .................. 272
11.4 Shunt Active Filters (SAFs) ........................... 274
11.4.1 Reference current generation ................... 276
11.4.2 p-q method ..................................... 278
11.4.3 APF AC current control ......................... 280
11.5 Optimisation Methods for SAFs ......................... 283
11.5.1 Introduction to fuzzy control .................. 283
11.5.2 The fuzzy logic applied to the current
control of SAFs ................................ 285
11.5.3 Introduction to the use of Nelder-Mead
optimisation ................................... 285
11.5.4 The Nelder-Mead optimisation of the third
harmonic compensated by an AF .................. 290
11.6 Real-Time Control Implementation ...................... 291
11.6.1 Control code sections .......................... 291
11.6.2 Fuzzy algorithm software implementation ........ 294
11.7 Conclusions ........................................... 296
References ................................................. 296
Index ......................................................... 299
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