Power Systems Grounding (eBook)

Md. Abdus Salam obtained his PhD in Electrical Engineering, in 2000 from the University Teknologi Malaysia. Currently, he is working as a Faculty member in the Department of Electrical and Electronic Engineering, Faculty of Engineering at the Institut Teknologi Brunei (Our National Engineering and Technology University), Negara Brunei Darussalam. His research interests include power system modelling for on-line control, insulator pollution studies, grounding systems and renewable energy. He has published a large number of referred journal and conference papers. He is a senior member of IEEE, member of IET and working as a reviewer of IEEE Transactions on Power Delivery, IEEE Transactions on Dielectrics and Electrical Insulation, IET Generation, Transmission and Distribution, Journal of Electrostatics, Elsevier Science etc.Quazi M. Rahman obtained his PhD degree from the University of Calgary, Canada in 2002. Currently, he is serving as a faculty member in the Department of Electrical and Computer Engineering, at the University of Western Ontario, London, Canada. He is a licensed professional engineer in the province of Ontario, Canada and a senior member of the IEEE. He is a contributing author of a number of refereed journals and proceeding papers, and book chapters in the areas of wireless communications. His research interest includes Spread Spectrum and MIMO systems, OFDM systems; channel estimation and detection in the physical layer of wireless mobile, satellite communications and grounding systems. Also, he is involved in the study of software applications.

Preface 7
Contents 9
1 Power Analysis 13
1.1 Introduction 13
1.2 Instantaneous Power 13
1.3 Average and Apparent Power 15
1.4 Power Factor 18
1.5 Complex Power and Reactive Power 19
1.6 Complex Power Balance 23
1.7 Power Factor Correction 25
1.8 Three-Phase System 29
1.9 Naming Phases and Phase Sequence 30
1.10 Star Connection 31
1.11 Voltage and Current Relations for Y-Connection 32
1.12 Delta or Mesh Connection 36
1.13 Voltage and Current Relations for Delta-Connection 36
1.14 Three-Phase Power Calculation 39
1.15 Measurement of Three-Phase Power 44
1.16 Power Factor Measurement 45
1.17 Series Resonance 48
1.18 Parallel Resonance 50
Exercise Problems 53
References 59
2 Transformer: Principles and Practices 60
2.1 Introduction 60
2.2 Working Principle of Transformer 60
2.3 Flux in a Transformer 61
2.4 Ideal Transformer 62
2.5 E.M.F. Equation of Transformer 63
2.6 Turns Ratio of Transformer 64
2.7 Rules for Referring Impedance 67
2.8 Equivalent Circuit of a Transformer 69
2.8.1 Exact Equivalent Circuit 69
2.8.2 Approximate Equivalent Circuit 71
2.9 Polarity of a Transformer 73
2.10 Three-Phase Transformer 75
2.11 Transformer Vector Group 76
2.12 Voltage Regulation of a Transformer 84
2.13 Efficiency of a Transformer 87
2.14 Iron and Copper Losses 87
2.15 Condition for Maximum Efficiency 89
2.16 Transformer Tests 91
2.16.1 Open Circuit Test 92
2.16.2 Short Circuit Test 93
2.17 Autotransformer 96
2.18 Parallel Operation of a Single-Phase Transformer 98
2.19 Three-Phase Transformer Connections 99
2.19.1 Wye-Wye Connection 99
2.19.2 Wye-Delta Connection 100
2.19.3 Delta-Wye Connection 101
2.19.4 Delta-Delta Connection 102
2.20 Instrument Transformers 105
Exercise Problems 106
References 110
3 Symmetrical and Unsymmetrical Faults 111
3.1 Introduction 111
3.2 Symmetrical Faults 111
3.3 Unsymmetrical Faults 112
3.4 Symmetrical Components 112
3.5 Representation of Symmetrical Components 114
3.6 Complex Power in Symmetrical Components 119
3.7 Sequence Impedances of Power System Equipment 121
3.8 Zero Sequence Models 125
3.9 Classification of Unsymmetrical Faults 130
3.10 Sequence Network of an Unloaded Synchronous Generator 131
3.11 Single Line-to-Ground Fault 134
3.12 Line-to-Line Fault 139
3.13 Double Line-to-Ground Fault 144
Exercise Problems 157
References 161
4 Grounding System Parameters and Expression of Ground Resistance 162
4.1 Introduction 162
4.2 Objectives of Grounding System 162
4.3 Grounding Symbols and Classification 163
4.4 Ungrounded Systems 164
4.5 Grounded Systems 171
4.5.1 Solidly Grounded System 171
4.5.2 Resistance Grounding 176
4.5.3 Reactance Grounding 178
4.5.4 Voltage Transformer Grounding 179
4.6 Resonant Grounding 180
4.7 Ground Resistance 184
4.8 Electric Potential 185
4.9 Ground Resistance with Hemisphere 186
4.10 Ground Resistance with Sphere Electrode 189
4.11 Ground Resistance with Cylindrical Rod 191
4.12 Ground Resistance with Circular Plate 200
4.13 Ground Resistance with Conductor Type Electrode 205
Exercise Problems 209
References 210
5 Soil Resistivity 211
5.1 Introduction 211
5.2 Soil Resistance and Resistivity 211
5.3 Types of Soil 213
5.4 Permeability and Permittivity of Soil 215
5.5 Influence of Different Factors on Soil Resistivity 216
5.6 Current Density of Soil 218
5.7 Continuity of Earth Current 220
5.8 Current Density at Soil Interface 223
5.9 Derivation of Poisson’s and Laplace’s Equations 227
5.10 Uniqueness Theorem 230
5.11 Solutions of Laplace’s Equation 232
5.11.1 One Dimension Solution 232
5.11.2 Two-Dimension Solution 234
5.12 Solution of Laplace’s Equation in Cylindrical Coordinates 241
5.13 Spherical Coordinate System 243
5.14 Solution of Poisson’s Equation 250
5.15 Numerical Solution of Laplace’s Equation 251
Exercise Problems 257
References 257
6 Soil Resistivity Measurement 259
6.1 Introduction 259
6.2 Two-Pole Method 259
6.3 Four-Pole Equal Method 260
6.4 Derivation of Resistivity 262
6.5 Lee’s Partitioning Method 269
6.6 Sided Probe System 271
6.7 Schlumberger Method 273
6.8 Different Terms in Grounding System 276
6.9 Touch and Step Potentials 277
Exercise Problems 282
References 283
7 Ground Resistance Measurement 284
7.1 Introduction 284
7.2 Types of Electrodes 284
7.3 Two-Pole Method 286
7.4 Three-Pole Method 287
7.5 Fall of Potential Method 288
7.6 The 62 % Method 289
7.7 Derivation of 62 % Method 290
7.8 Position of Probes 293
7.9 Clamp-on Method 295
7.10 Slope Method 297
7.11 Ammeter-Voltmeter Method 299
7.12 Ammeter-Wattmeter Method 300
7.13 Wheatstone Bridge Method 300
7.14 Bridge Method 302
7.15 Potentiometer Method 303
7.16 Measurement of Touch and Step Potentials 305
7.17 Application Example 1: Measurement of Ground Resistance at Telephone Exchange 306
7.18 Application Example 2: Measurement of Ground Resistance at Residential Area 308
7.19 Ground Resistance Measuring Equipment 309
References 312
Index 313