Chapter 1 Power Quality ......................................... 1
1.1. Introduction ............................................... 1
1.2. Importance of Power Quality ................................ 1
1.3. Common Disturbances in Power Systems ....................... 2
1.4. Short-Duration Voltage Variation ........................... 2
1.5. Long-Duration Voltage Variations ........................... 4
1.6. Transients ................................................. 4
1.6.1. Impulsive Transients ................................ 4
1.6.2. Oscillatory Transients .............................. 5
1.6.3. Voltage Imbalance ................................... 5
1.7. Harmonics .................................................. 6
1.8. Interharmonics ............................................. 6
1.9. DC Offset .................................................. 7
1.10.Notching ................................................... 7
1.11.Noise ...................................................... 7
1.12.Voltage Fluctuations ....................................... 8
1.13.Power Frequency Variations ................................. 8
1.14.Solutions to Power Quality Problems ........................ 8
1.15.Ambiguous Terms ........................................... 10
1.16.CBEMA and ITI Curves ...................................... 10
1.17.Features of Voltages in Power Systems ..................... 11
1.18.Grounding ................................................. 11
1.18.1.Ground Electrodes .................................. 12
1.18.1.1.Ground Rods, Ground Rings, Plates ......... 13
1.18.1.2.Signal Reference Ground (SRG) ............. 14
1.18.2.Single-Point and Multipoint Grounding .............. 14
1.18.3.Ground Loops ....................................... 17
1.18.4.Isolated Ground .................................... 17
1.18.5.Electrochemical Reactions Due to Ground Grids ...... 17
1.19.Reactive Power in Power Systems with Harmonic
Distortion ................................................ 18
1.19.1.Single-Phase Systems ............................... 18
1.20.Reliability ............................................... 20
1.21.Power Quality Data Collection ............................. 20
1.22.Summary ................................................... 21
Appendix ....................................................... 22
References ..................................................... 24
Chapter 2 Static Var Compensators .............................. 27
2.1. Introduction .............................................. 27
2.1.1. Increase in Transient Stability Margin ............. 27
2.1.2. Damping of Power Oscillations ...................... 27
2.1.3. Voltage Support .................................... 29
2.2. Static Var Compensator Systems Versus Synchronous
Condensers, Capacitors, and Reactors ...................... 30
2.3. Shunt and Series Compensation ............................. 31
2.4. Fundamentals of Load Compensation ......................... 31
2.5. Reactive Power Relationships Between Wye- and Delta-
Connected Systems ......................................... 34
2.6. Static Var Compensators for Transmission Systems .......... 39
2.6.1. SVC Using a TCR and an FC .......................... 40
2.6.2. SVC Using a TCR and TSC ............................ 42
2.6.3. STATCOM (SVC Using Self-Commutated Inverters) ...... 42
2.6.4. SVC Using a Saturated Reactor (SR) ................. 43
2.6.5. Comparison of Static Var Systems ................... 46
2.6.6. Specification of SVCs .............................. 46
2.7. A Case Study (Australia): Central Queensland Railway
Project ................................................... 47
2.7.1. Limits for Voltage Unbalance ....................... 48
2.7.2. Three-Phase Power Flow Studies ..................... 49
2.8. Chester-Maine SVC Project ................................. 51
2.9. Conclusions ............................................... 51
References ..................................................... 52
Chapter 3 Control of Static Var Compensators ................... 55
3.1. Introduction .............................................. 55
3.2. Control Systems for SVCs in Transmission System
Applications .............................................. 55
3.2.1. Voltage Regulation ................................. 55
3.2.2. Gain Supervision ................................... 56
3.2.3. Reactive Power Control and Coordination ............ 57
3.2.4. Control Signals for System Transient Stability,
Power Oscillation Damping, and Subsynchronous
Resonance Damping Enhancement ...................... 58
3.3. Control Systems for SVCs in Traction Applications ......... 59
3.3.1. Load Compensation .................................. 59
3.3.2. Voltage Regulation and Balancing ................... 61
3.3.3. Measurement of Sequence Components ................. 62
3.4. Phase-Locked Oscillator Control System .................... 65
3.5. Implementation Details of a Programmable High-Speed
Controller ................................................ 65
3.5.1. Priority Logic ..................................... 66
3.5.2. Detection of Faults ................................ 66
3.5.3. Program Sequence ................................... 67
3.5.4. Special Features of the Programmable High-Speed
Controller ......................................... 67
3.6. Conclusions ............................................... 67
References ..................................................... 68
Chapter 4 Harmonics ............................................ 71
4.1. Converter Harmonics ....................................... 72
4.1.1. Effect of Transformer Connections .................. 74
4.1.2. Harmonics When There Is Overlap in the
Commutation Process ................................ 75
4.1.3. Direct-Voltage Harmonics ........................... 76
4.1.4. Imperfect System Conditions ........................ 77
4.2. Single-Phase Power Supplies ............................... 79
4.3. DC Drives ................................................. 81
4.4. AC Drives ................................................. 81
4.5. Pulse-Width Modulation (PWM) .............................. 82
4.6. Telecontrol Signals ....................................... 84
4.7. Cycloconverters ........................................... 84
4.8. Transformers .............................................. 84
4.8.1. Harmonics in No-Load Exciting Current .............. 84
4.8.2. Harmonics due to Inrush Current .................... 85
4.8.3. DC Magnetization ................................... 85
4.9. Harmonics in Rotating Machines ............................ 86
4.10.Harmonics in Arc Furnace Loads ............................ 87
4.11.Harmonics in a Thyristor-Controlled Reactor ............... 87
4.12.TheK-Factor ............................................... 88
4.13.Conclusions ............................................... 90
References ..................................................... 90
Chapter 5 Utility Harmonic Regulations and Standards ........... 93
5.1. Introduction .............................................. 93
5.2. Undesirable Effects of the Harmonics ...................... 93
5.3. Specification of the Harmonic Limits ...................... 96
5.4. Philosophical Differences between IEEE 519-1992
and IEC 61000-Series Standards ............................ 97
5.5. IEEE 519-1992 ............................................. 97
5.6. IEC 61000-Series Standards ............................... 100
5.6.1. Assessment Procedure (Harmonic Limits) ............ 101
5.6.2. Summation Laws for Combining Harmonics ............ 104
5.7. General Comments on the Standards ........................ 105
5.7.1. Allocation of Harmonic Voltage or Current or
Both Limits to the Customers ...................... 105
5.7.2. Empirical Nature of the Standards ................. 106
5.7.3. Legal Responsibility for Damages due to
Harmonic Problems ................................. 107
5.8. Application of the Standards ............................. 107
5.8.1. Application of Standards—B.C. Hydro's Approach .... 108
5.9. Examples of the Harmonic Studies ......................... 111
5.10.Conclusions .............................................. 111
References .................................................... 112
Appendix—IEC 61000-Series Standards ........................... 113
Chapter 6 Harmonic Filters .................................... 117
6.1. Introduction ............................................. 117
6.2. Undesirable Effects of Harmonics ......................... 117
6.3. Harmonic Sources ......................................... 117
6.4. Types of Filters ......................................... 118
6.4.1. Types of Damped Filters ........................... 118
6.5. AC Network Impedance ..................................... 119
6.5.1. Overhead Lines .................................... 119
6.5.1.1. Line Constants ........................... 120
6.5.2. Underground Cables ................................ 121
6.5.3. Transformers ...................................... 121
6.5.4. Rotating Machines ................................. 122
6.5.5. Passive Loads ..................................... 123
6.5.5.1. Electronic Loads ......................... 123
6.5.6. Norton Equivalents of Residential Loads ........... 123
6.6. Design of Single-Tuned Filters ........................... 124
6.7. Design of Double-Tuned Filters ........................... 127
6.8. Filter Performance Evaluation ............................ 127
6.9. Design of Damped Filters ................................. 129
6.10.Filter Component Ratings ................................. 130
6.10.1. Filter Capacitors ................................ 130
6.10.2. Tuning Reactors .................................. 131
6.11.Outline of Filter Design in Two Queensland (Australia)
Projects ................................................. 132
6.11.1. Transmission SVC Project ......................... 132
6.11.2. Queensland Railway (QR) Project .................. 133
6.12.Conclusions .............................................. 135
References .................................................... 135
Chapter 7 Computational Tools and Programs for the Design
and Analysis of Static Var Compensators and
Filters ............................................. 137
7.1. Introduction ............................................. 137
7.2. Computational Tools ...................................... 137
7.3. Digital Computers ........................................ 138
7.4. Analog Computers ......................................... 139
7.5. Special Problems in the Simulation of Power Electronic
Circuits ................................................. 139
7.5.1. Constant Topology ................................. 139
7.5.2. Varying Topology .................................. 140
7.6. Transient Electrical Network Analyzers ................... 141
7.7. Special-Purpose Simulators ............................... 141
7.8. Computer Programs ........................................ 141
7.8.1. PSS TM E Version 30 ............................... 142
7.8.2. EMTP .............................................. 143
7.8.2.1. Inductance ............................... 143
7.8.2.2. Capacitance .............................. 144
7.8.2.3. Lossless Line ............................ 144
7.8.2.4. Nodal Equations .......................... 146
7.8.2.5. Frequency Scan Facility .................. 146
7.8.3. ATP ............................................... 149
7.8.4. PSCAD/EMTDC ....................................... 149
7.8.5. SuperHarm ......................................... 149
7.8.5.1. SuperHarm Models ......................... 150
7.8.5.2. SuperHarm Solution Procedure ............. 150
7.8.5.3. Support Options .......................... 151
7.8.5.4. Pricing and Availability ................. 151
7.8.6 Three-Phase Power Flow Programs ................. 151
7.8.6.1. Powerlink Program ........................ 151
7.8.6.2. HARMFLO Program .......................... 152
7.9. DADiSP ................................................... 152
7.10.Conclusions .............................................. 153
References .................................................... 154
Chapter 8 Monitoring Power Quality ............................ 155
8.1. Introduction ............................................. 155
8.2. Site Surveys ............................................. 156
8.2.1. Spectrum Analyzers ................................ 157
8.2.2. Special-Purpose Power System Harmonic Analyzers ... 157
8.2.3. Transient-Disturbance Analyzers ................... 157
8.2.4. Combination Disturbance and Harmonic Analyzers .... 158
8.2.5. Flicker Meters .................................... 158
8.3. Transducers .............................................. 158
8.3.1. Measurement of the Frequency Response of
Instrument Transformers ........................... 159
8.3.2. Description of the Instrument Transformers'
Tests ............................................. 162
8.3.3. Summary of the Conclusions from the Tests ......... 164
8.3.3.1. Voltage Transformers ..................... 166
8.4. lEC-Recom mended Measurement Techniques for Harmonics .... 167
8.4.1. Harmonics ......................................... 167
8.4.1.1. RMS Value of a Harmonic Group: Ggn ....... 169
8.4.1.2. RMS Value of a Harmonic Subgroup: Gsgn ... 169
8.4.2. Total Harmonic Distortion (THD) ................... 169
8.4.2.1. Group Total Harmonic Distortion (THDG) ... 170
8.4.2.2. Subgroup Total Harmonic Distortion
(THDS) ................................... 170
8.4.2.3. Partial Weighted Harmonic Distortion
(PWHD) ................................... 170
8.4.3. Tnterharmonics .................................... 170
8.4.3.1. RMS Value of an Interharmonic
Component ................................ 170
8.4.3.2. RMS Value of an Interharmonic Group
(C/gn) ................................... 171
8.4.3.3. RMS Value of an Interharmonic-Centered
Subgroup (Qsg,n) ......................... 171
8.4.4. Relative and Absolute Harmonic Phase Angle
Measurement ....................................... 172
8.5. Necessity for the Measurement of Harmonic Voltages and
Currents ................................................. 173
8.6. Harmonic Monitoring System ............................... 173
8.7. Continuous Harmonic Analysis in Real Time (CHART) ........ 173
8.8. Presentation of Harmonic Measurements .................... 175
8.9. Examples of Projects Needing Harmonic Monitoring in
the Powerlink Queensland System, Australia ............... 177
8.9.1. Aluminum Smelter Project .......................... 177
8.9.2. Central Queensland Railway Electrification
Project ........................................... 178
8.10.Flicker .................................................. 179
8.11.IEC Flicker Meter ........................................ 180
8.11.1.Short-Term Flicker Evaluation ..................... 183
8.11.2.Flicker Standards ................................. 184
8.12.Conclusions .............................................. 185
References .................................................... 185
Chapter 9 Reactors ............................................ 189
9.1. Introduction ............................................. 189
9.2. Losses in the Power System ............................... 189
9.3. Switching Surges ......................................... 190
9.4. Shunt Reactor Installations in EHV Lines ................. 191
9.5. Determination of Shunt Reactor Rating .................... 191
9.6. Choice of Voltage Level for Shunt Reactor Connection ..... 192
9.6.1. Effective Compensation ............................ 192
9.6.2. Influence on Transformers and Generators .......... 192
9.6.3. Switchgear Requirements ........................... 193
9.6.4. Influence on Operation Reliability of the
System ............................................ 193
9.6.5. Influence on Insulation and Overvoltage
Conditions ........................................ 193
9.7. Single-Pole Autoreclosing of Transmission Lines .......... 193
9.7.1. Arc Extinction with Single-Pole Switching ......... 194
9.7.2. Laboratory Tests to Determine the Secondary Arc-
Extinction Time ................................... 195
9.7.3. Choice of Neutral Reactor ......................... 196
9.7.4. Secondary Arc Current and Recovery Voltage ........ 197
9.7.5. Single-Pole Autoreclosing of EHV Lines—Field
Test Results ...................................... 198
9.7.6. Effect of X0/X1 Ratio and Xn on the Secondary
Arc Current and Neutral Voltage ................... 201
9.7.7. Effect of Transposition Phasing of Double-
Circuit Lines ..................................... 206
9.7.8. Selective-Pole Switching of Long Double-Circuit
EHV Line .......................................... 207
9.8. Types of Reactors Based on Their Function ................ 208
9.9. Construction of Reactors ................................. 208
9.9.1. Types of Reactors Based on Their Construction ..... 209
9.9.2. Testing of EHV Reactors ........................... 212
9.10.Conclusions .............................................. 213
References .................................................... 213
Chapter 10 Capacitors ......................................... 215
10.1.Introduction ............................................. 215
10.2.Capacitor Banks .......................................... 216
10.2.1.Fuses ............................................. 217
10.3.Capacitor Bank Connections ............................... 217
10.3.1.Ungrounded Wye-Connected Banks .................... 217
10.3.2.Grounded Wye-Connected Banks ...................... 218
10.3.3.Delta-Connected Banks ............................. 218
10.4.Protection of Capacitor Banks ............................ 218
10.4.1.Protection of Grounded Wye-Connected Capacitor
Banks ............................................. 218
10.5.Capacitor Bank Switching ................................. 226
10.5.1.Evaluation of Different Methods for Mitigating
Remote Overvoltages due to Shunt Capacitor
Energization ...................................... 226
10.5.2.Series Reactors for Capacitors .................... 228
10.5.3.Location of Series Reactors for Capacitors ........ 229
10.5.4.Transient-Free Switching of Capacitors ............ 229
10.6.Series Capacitors ........................................ 230
10.6.1.Protection of Series Capacitors ................... 231
10.6.2.NGH Scheme for Damping Subsynchronous Resonance ... 234
10.6.3.Limitations of Series Capacitor Applications ...... 235
10.6.3.1.Ferroresonance ........................... 235
10.6.3.2.Hunting of Synchronous Motors ............ 236
10.6.3.3.Subsynchronous Resonance ................. 236
10.6.3.4.Self-Excitation of Induction and
Synchronous Machines ..................... 237
10.7.Metal Oxide Varistors (MOVs) ............................. 237
10.7.1.Modeling of MOVs in Computer Simulations .......... 238
10.8.Conclusions .............................................. 239
References .................................................... 240
Chapter 11 Fast Fourier Transforms ............................ 243
11.1.Fourier Series ........................................... 243
11.2.Symmetrical Properties of Waveforms ...................... 245
11.3.Sine Function ............................................ 246
11.4.Discrete Fourier Transform (DFT) ......................... 247
11.5.Fast Fourier Transform (FFT) ............................. 249
11.5.1.Decimation in Time (DIT) .......................... 249
11.5.2.Decimation in Frequency (DIF) ..................... 250
11.5.3.Some Computational Details of FFT Algorithms ...... 252
11.6.Cooley-Tukey Algorithm ................................... 254
11.7.FFT of Two Real Functions Simultaneously ................. 257
11.8.Mixed-Radix FFT .......................................... 258
11.9.Split-Radix FFT .......................................... 259
11.10.FFT Pruning ............................................. 260
11.11.The Convolution Integral ................................ 260
11.12.Auto- and Cross-Correlation Functions ................... 262
11.13.Pitfalls of the Discrete Fourier Transform .............. 262
11.13.1.Aliasing ......................................... 263
11.13.2.Spectral Leakage ................................. 263
11.13.3.The Picket-Fence Effect .......................... 264
11.14.Guidelines for Using FFT for Harmonic Analysis .......... 266
References .................................................... 267
Index ......................................................... 269
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