Measurement and Analysis of Overvoltages in Power Systems
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JIANMING LI, Sichuan Electric Power Research Institute (SEPRI), State Grid Corporation of China (SGCC), Sichuan, China
Content
Preface xiii
1 Overvoltage Mechanisms in Power Systems 1
1.1 Electromagnetic Transients and Overvoltage Classification 1
1.1.1 Electromagnetic Transients in Power System 1
1.1.2 Characteristics and Research Methods of Electromagnetic Transients 2
1.1.2.1 Refraction and Reflection of TravellingWaves 4
1.1.2.2 Peterson Principle 5
1.1.2.3 Multiple Refraction and Reflection of TravellingWaves 9
1.1.2.4 Evaluation of Overvoltages Using the Bergeron Method 12
1.2 Overvoltage Classification in Power Systems 14
1.2.1 Overvoltage Classification 14
1.3 Atmospheric Overvoltages 16
1.3.1 Lightning Discharge 16
1.3.2 Lightning Parameters 18
1.3.2.1 Frequency of Lightning Activities -Thunderstorm Days andThunderstorm Hours 18
1.3.2.2 Ground Flash Density 19
1.3.2.3 Lightning Current Amplitude 19
1.3.2.4 Front Time, Front Steepness andWavelength of the Lightning Current 19
1.3.2.5 Lightning CurrentWaveforms for Calculation 19
1.3.3 Induced Lightning Overvoltages 20
1.3.3.1 Induced Lightning Overvoltages on the LineWhen Lightning Strikes the Ground Near the Line 20
1.3.3.2 Induced Overvoltages on the Line When Lightning Strikes the Line Tower 22
1.3.4 Direct Lightning Overvoltages 23
1.3.4.1 Overvoltages Due to Lightning Striking the Tower Top 23
1.3.4.2 Overvoltages Due to Lightning Striking the GroundWire at Midspan 24
1.3.4.3 Overvoltages Due to Shielding Failures 25
1.4 Switching Overvoltages 25
1.4.1 Closing Overvoltages 26
1.4.1.1 Overvoltages Caused by Closing Unloaded Lines 26
1.4.1.2 Overvoltages Caused by Planned Closing 26
1.4.1.3 Overvoltages Caused by Automatic Reclosing 28
1.4.1.4 Factors Influencing Closing Overvoltages 29
1.4.1.5 Measures for Suppressing Closing Overvoltages 30
1.4.2 Opening Overvoltages 30
1.4.2.1 Overvoltages Caused by De-Energizing Unloaded Lines 30
1.4.2.2 Physical Process 31
1.4.2.3 Influencing Factors 33
1.4.2.4 Measures 33
1.4.2.5 Switching Off Unloaded Transformers 34
1.4.2.6 Cause and Physical Process 34
1.4.2.7 Waveform Characteristics 36
1.4.2.8 Influencing Factors 37
1.4.2.9 Restrictive Measures 38
1.4.3 Arc Grounding Overvoltages 38
1.4.3.1 Cause and Formation 39
1.4.3.2 Overvoltage Characteristics andWaveforms 41
1.4.3.3 Influencing Factors 42
1.4.3.4 Restrictive Measures 43
1.4.4 Power System Splitting Overvoltages 44
1.5 Power Frequency Overvoltages 47
1.5.1 Power Frequency Overvoltages due to the Ferranti Effect 48
1.5.2 Power Frequency Voltage Rise Due to Asymmetrical Short-Circuit Faults 51
1.5.3 Power Frequency Voltage Rise Due to Load Rejection 54
1.5.4 PrecautionaryMeasures for Power Frequency Overvoltages 54
1.6 Resonance Overvoltages 55
1.6.1 Linear Resonance Overvoltages 56
1.6.2 Ferro-Resonance Overvoltages 59
1.6.3 Parametric Resonance Overvoltages 62
2 Transducers for Online Overvoltage Monitoring 65
2.1 Overvoltage Transducers at Transformer Bushing Taps 65
2.1.1 Design 65
2.1.1.1 Structural Design of the Main Body 65
2.1.1.2 Protection Unit Design 67
2.1.2 Parameter Setting 68
2.1.2.1 Capacity of Voltage-Dividing Capacitance 68
2.1.2.2 Voltage Rating 69
2.1.3 Feasibility Analysis 70
2.1.3.1 Error Analysis and Dynamic Error Correction 70
2.1.3.2 Impulse Response Characteristics Tests 71
2.2 Gapless MOA Voltage Transducers 72
2.2.1 Design 74
2.2.2 Operating Properties and Feasibility Analysis 75
2.2.2.1 Working in the Small Current Section 75
2.2.2.2 Working in the Large Current Range 76
2.2.3 Analysis of Field Applications 79
2.3 Voltage Transducers for Transmission Lines 81
2.3.1 Structure Design 81
2.3.1.1 Selection of Shielding Materials 82
2.3.1.2 Influence of the Shielding Shell on the Measurement 83
2.3.2 Series-Connection Capacitance Calculation and ANSOFT Field Simulation 84
2.3.2.1 Calculation of the Stray Capacitance C1 84
2.3.2.2 3D Capacitance Simulation Using Ansoft Maxwell 85
2.3.3 Experimental Verification of the Transducer Model 89
2.3.3.1 Result Analysis of the Power Frequency Experiment 89
2.3.3.2 Result Analysis of Lightning Impulse Experiment 92
2.4 Full-Waveform Optical Online Monitoring Technology 93
2.4.1 Pockels Sensing Material Selection and Crystal Design 93
2.4.1.1 Selection of Pockels Sensing Material 93
2.4.1.2 Technical Requirements for BGO Crystals 94
2.4.1.3 Technical Requirements for BGO Transparent Conductive Films 95
2.4.2 Longitudinal and Transverse Electro-Optical Modulation 95
3 Online Overvoltage Monitoring System 99
3.1 Overview 99
3.2 The Structure of OvervoltageMonitoring Systems 102
3.3 Acquisition Devices of OvervoltageMonitoring Systems 103
3.3.1 Design of the Signal Preprocessing Circuit 103
3.3.2 Design of the Trigger Circuit 104
3.3.3 Design of the Protection Unit Control Circuit 105
3.3.4 Selection of the Data Acquisition Card 106
3.3.4.1 Properties 106
3.3.4.2 Data SamplingTheory of the Acquisition Card 107
3.4 Overvoltage Signal Transmission System 109
3.4.1 Overvoltage Signal Transmission and Monitoring in Internal Networks 109
3.4.1.1 Private Communication Networks 109
3.4.1.2 General Structure 110
3.4.1.3 Implementation of Internal Network Monitoring 112
3.4.2 Transmission and Monitoring Based onWireless Public Networks 113
3.4.2.1 GSM Networks - Introduction 113
3.4.2.2 General Structure of Systems Based on GSM Networks 114
3.4.2.3 General Structure of the GPRS-Based Transmission Systems 115
3.4.2.4 10Gb All-Optical Carrier Ethernet (CE) 116
3.4.2.5 InfiniBand Network 120
3.5 OvervoltageWaveform Analysis System 121
3.5.1 Introduction to theWaveform Analysis Software 121
3.5.2 Functions and Interface Design 122
3.5.2.1 Serial Communication Interface 122
3.5.2.2 Data-Loading Interface 122
3.5.2.3 Spectrum Analysis Interface 122
3.5.2.4 Main Interface 122
3.6 Remote Terminal Analysis System for OvervoltageWaveforms 123
3.7 Case Study of Online OvervoltageMeasurements 125
3.7.1 Lightning Overvoltages 125
3.7.1.1 Direct Lightning Overvoltages 125
3.7.1.2 Induced Lightning Overvoltages 127
3.7.2 Power Frequency Overvoltages 128
3.7.3 Resonance Overvoltages 131
3.7.3.1 Case One 131
3.7.3.2 Measuring Methods 132
3.7.3.3 Measurement Results 133
3.7.3.4 Analysis 135
3.7.3.5 Case Two 135
3.7.4 Statistical Analysis of Overvoltages in a 110 kV Substation 137
3.7.4.1 TypicalWaveforms 137
3.7.4.2 Data Statistics and Analysis 138
3.7.4.3 Conclusions 139
3.7.5 Single-Phase Grounding Overvoltages 140
3.7.6 Two-Phase Grounding Overvoltages 141
3.7.7 Intermittent Arc Grounding Overvoltages 141
3.7.8 Case Study: Measurement of Transient Voltages When Energizing CVTs 142
3.7.8.1 Onsite Arrangement 142
3.7.8.2 Measurement Results 143
3.7.9 Case Study: Transient Voltage Measurement When Energizing Unloaded Lines 149
3.8 Statistical Analysis of Overvoltages 151
3.8.1 Statistical Analysis of Phase-to-ground Overvoltages 151
3.8.2 Calculation of Overvoltage Characteristic Values 151
3.8.3 Determination of Insulation Levels of Substation Electrical Equipment 152
3.8.3.1 Case Study of the Overvoltages in the 35 kV System of a Substation 152
4 Wave Process of Incoming Surges and Transient Response Characteristics 155
4.1 Current State of Incoming Surge Research 155
4.2 Wave Process under Complex Conditions 156
4.2.1 Wave Process in Lossless Parallel Multi-Conductor Systems 156
4.2.2 Wave Propagation along Lossy Lines 159
4.2.2.1 Line Loss 159
4.2.2.2 Impact of Line Resistance and Line-to-Ground Conductance 159
4.2.2.3 Impact of Impulse Corona 160
4.2.3 Wave Process on TransformerWindings 162
4.2.3.1 Wave Process in Single-PhaseWindings 162
4.2.3.2 Wave Process in Three-PhaseWindings 166
4.2.3.3 Transfer of Impulse Voltage BetweenWindings 168
4.3 Generation of Lightning Overvoltages on Electrical Equipment 169
4.4 Simulation of Incoming Surges in Substations 172
4.5 Influencing Factors of Substation Incoming Surges 174
4.5.1 Influences of Lightning Stroke Types on Incoming Surges 174
4.5.1.1 Shielding FailureWithout Flashover 176
4.5.1.2 Shielding Failure with Flashover 176
4.5.1.3 Lightning Striking GroundWires (or Transmission Towers)Without Flashover 177
4.5.1.4 Lightning Striking GroundWires (or Transmission Towers) with Flashover 179
4.5.2 Influences of Transmission Lines on OvervoltageWave Propagation 181
4.5.3 Influences of In-Station Equipment on OvervoltageWave Propagation 184
4.5.3.1 Potential Transformers (PT) 184
4.5.3.2 Arresters 184
4.6 TypicalWaveforms of Substation Incoming Surges 187
4.6.1 Short-Front-Short-Tail Surges 187
4.6.2 Short-Front-Long-Tail Surges 192
4.6.3 Long-Front-Long-Tail Surges 192
4.6.4 Long-Front-Short-Tail Surges 192
4.7 Response Characteristics of Lightning Overvoltages Propagating in the Grid 196
4.7.1 Status Quo 196
4.7.2 Research Scheme 197
4.8 Lightning Location System (LLS) 202
4.8.1 Overview and Current Situation 202
4.8.2 Detection Principles 203
4.8.2.1 Typical LLS Locating Methods 204
4.8.2.2 Time of Arrival Method 205
4.8.2.3 Calculation Model for the Lightning Current Peak 207
4.8.2.4 Error Analysis 207
4.8.3 System Structure 208
4.8.4 Applications 208
5 Typical Field Tests andWaveform Analysis in UHVDC Transmission Systems 213
5.1 Waveform Acquisition and Analysis in Typical Tests 213
5.1.1 Classification of Overvoltages in Converter Stations 213
5.1.1.1 Overvoltages from the Substation AC Side 213
5.1.1.2 Overvoltages from the Substation DC Side 213
5.1.1.3 Overvoltages from DC Lines 214
5.1.1.4 Switching Overvoltages in UHVDC Transmission System 214
5.1.2 Overvoltage Test Methods and Principles 216
5.2 Typical Field Tests for the UHVDC Transmission System 219
5.2.1 Disconnecting Converter Transformers 219
5.2.2 Connecting Converter Transformers 221
5.2.3 Converter Valve Deblocking 223
5.2.4 Emergency Switch-Off 223
5.2.5 Simulated Single-Phase Grounding Faults on ac Lines 225
6 Overvoltage Digital Simulation 231
6.1 Overvoltage Digital Simulation Software 231
6.2 Evaluation of Switching Overvoltages 232
6.2.1 Evaluation of Opening Overvoltages 232
6.2.2 Evaluation of Closing Overvoltages 236
6.2.3 Restrictive Measures for Switching Overvoltages 245
6.2.3.1 Overvoltages Caused by Closing or Reclosing Unloaded Lines 247
6.2.3.2 Switching Overvoltages Caused by Disconnecting Unloaded Transformers and Shunt Reactors 247
6.2.3.3 Switching Overvoltages Caused by Asymmetrical Faults and Oscillation Overvoltages Due to System Splitting 248
6.3 Evaluation of Power Frequency Overvoltages 248
6.3.1 Calculation of the Ferranti Effect 248
6.3.1.1 Capacitance Effects of Unloaded Long Lines 249
6.3.2 Evaluation of Asymmetrical Short-circuit Faults 252
6.3.3 Simulation of Asymmetric Grounding Faults 254
6.3.4 Restrictive Measures for Power Frequency Overvoltages 256
6.4 Evaluation of Atmospheric Overvoltages 258
6.4.1 Lightning Parameters 259
6.4.2 Equivalent Circuit of Lightning Discharge 261
6.4.3 Lightning Overvoltages 262
6.4.3.1 Direct Lightning Overvoltages 262
6.4.3.2 Induced Lightning Overvoltages 262
6.4.4 Evaluation of Induced Lightning Overvoltages 262
6.4.5 Evaluation of Direct Lighting Overvoltages 263
6.5 Evaluation of Ferro-Resonance Overvoltages 267
6.5.1 Electromagnetic PT Module 267
6.5.1.1 Acquisition of PT Excitation Characteristic Curve 269
6.5.2 Establishment of Open Delta PT Model 272
6.5.2.1 Establishment of Single-Phase Three-Winding (Y-Y0) PTModel 274
6.5.2.2 Establishment of Three-Phase Three-Winding PT Models 275
6.5.3 Transformer Module 275
6.5.3.1 Calculation Principles ofWinding Parameters 275
6.5.3.2 Calculation of Transformer Excitation Resistance 276
6.5.4 Bus Module 277
6.5.4.1 Line Resistance 277
6.5.4.2 Line Inductance 277
6.5.4.3 Line Capacitance 278
6.5.5 Ferro-Resonance Overvoltage Simulation Results 278
6.6 Evaluation of Very-Fast Transient Overvoltages 280
6.6.1 VFTO Mechanism 280
6.6.2 VFTO Models and Parameters 281
6.6.3 VFTO Simulation and Field Tests 281
6.7 Transient Calculation for UHVDC Transmission Systems 283
6.7.1 PSCAD Models for UHVDC Transmission Components 283
6.7.1.1 Converter Valves 286
6.7.1.2 Converter Transformers 288
6.7.1.3 Line Models 288
6.7.1.4 Equivalent Power Sources 290
6.7.1.5 Other Component Models 291
6.7.2 PSCAD Simulation for UHVDC Systems 292
6.7.2.1 Construction of UHVDC Control Systems 292
6.7.2.2 Simulated System Parameter Settings 292
7 Entity Dynamic Simulation of Overvoltages on Transmission Lines 301
7.1 Overview 301
7.2 Modeling Methods for Transmission Line Lightning Channels 301
7.2.1 Structure of Dynamic Simulation Testbed 303
7.2.2 Structural Diagram 307
7.2.3 Definitions of Parameters 308
7.3 Verification of Simulated Transmission Line Lightning Channels 310
7.4 Dynamic Simulation Testing System 314
7.4.1 System Composition 314
7.4.2 Main Technical Indicators 315
7.4.3 Lightning Types 316
7.4.4 Lightning Signal Acquisition of Dynamic Simulation Testbeds 316
7.4.5 Significance of Modeling 317
8 Overvoltage Pattern Recognition in Power Systems 319
8.1 Selection of Characteristic Values 319
8.2 Time-Domain Characteristic Extraction 320
8.3 Wavelet Transform Analysis 322
8.3.1 Basic Theory 322
8.3.2 Characteristic Extraction Based onWavelet Decomposition 323
8.3.2.1 Selection of Decomposition Scales 323
8.3.2.2 Case Study of Decomposition 324
8.4 Singular Value Decomposition (SVD) Theory 327
8.5 Characteristic Value Selection for Sorters 329
8.5.1 Characteristic Value Selection for First-Level Sorters 329
8.5.2 Characteristic Value Selection for Second-Level Sorters 330
8.6 SVM-Based Transient Overvoltage Recognition System 331
8.6.1 Overview of Support Vector Machine (SVM) 331
8.6.2 Multi-Class SVM 333
8.7 Data Preprocessing 334
8.7.1 Dimension Reduction 334
8.7.2 Normalization 335
8.8 Parameter Selection and Optimization 336
8.8.1 Cross Validation 336
8.8.2 Genetic Algorithm 337
8.8.3 Particle Swarm Optimization Algorithm 337
8.9 Extraction and Modification of FieldWaveform Parameters 342
8.9.1 Innovative Extraction Methods for Practical Lightning Parameters 342
8.9.2 Modification of Practical Lightning Impulse Test Parameters 344
Bibliography 347
Index 351
Chapter 1
Overvoltage Mechanisms in Power Systems
1.1 Electromagnetic Transients and Overvoltage Classification
1.1.1 Electromagnetic Transients in Power System
In the case of system faults or switching operations, the operating parameters of the system will change sharply. The system may transit from one operation state to another, or it may be damaged partially or entirely with operating parameters considerably deviated from the normal values. If countermeasures are not taken, the system is hard to restore to normal operation, which may have dramatic consequences on the national economy and on people's livelihoods.
Changes in operation states cannot be completed instantaneously, so there will be a transition, known as the transient process. Transient processes in power systems are generally divided into the electromagnetic transient process and the electromechanical transient process. The electromagnetic transient process refers to the changing dynamics of the electric field and the magnetic field as well as the corresponding voltage and current of each component in the power system, while the electromechanical transient process refers to the dynamics of mechanical movement of electric machine rotors caused by electromagnetic torque changes in generators and motors.
Although the electromagnetic and electromechanical transient processes take place simultaneously and are interrelated, it is difficult and complicated to perform a unified analysis because a lot of influencing factors have to be taken into account due to the constantly expanding scale and increasingly complex structure of modern power systems. Also, the changing rates of the two processes vary widely. For example, the speed of the rotating machinery such as generators and motors will not change immediately because of the inertia in electromagnetic transient analysis. In this case, the transient process mainly depends on the electromagnetic parameters of each system component; the speed changes of the generator and the motor are therefore generally not considered, so electromechanical transients can be ignored. In electromechanical transient analysis such as the analysis of static stability and transient stability, the rotating machinery speed has already changed, thus the transient process depends on both the electromagnetic and electromechanical parameters (speed and angular displacement). In this case, the electromagnetic transient process is often ignored. Comprehensive consideration of both electromagnetic and electromechanical transients is only necessary when analyzing problems such as sub-synchronous resonance phenomena caused by generator shaftings or calculating transient torque of the generator shafting after major disturbances.
The main purpose of electromagnetic transient analysis is to analyze and calculate transient overvoltages and overcurrents which might occur in the case of system faults or switching operations for reasonable and feasible design of electrical equipment. Generally, the equipment insulation levels are decided by overvoltages arising from power system electromagnetic transients, and standards for high voltage tests are made accordingly, to determine the possibility of the safe operation of existing equipment while restrictive and protective measures are studied at the same time. Electromagnetic transient analysis is also needed for a number of issues including operating principles and operation conditions regarding novel high-speed protection devices, fault location and positioning methods and electromagnetic interferences. In addition, electromagnetic transient calculation and simulation is indispensable for investigating accident causes and finding countermeasures, calculating overvoltage occurrence probability and predicting accident rates, checking equipment actuation performances (such as transient recovery voltage and zero offset of circuit breakers) and examining responses concerning protective relays and automatic safety devices.
1.1.2 Characteristics and Research Methods of Electromagnetic Transients
Electromagnetic transients in power systems are characterized by wide frequency range, including travelling wave process and distributed parameters. To reveal the physical mechanism of the wave process on single-conductor lines, the equivalent circuit of a differential-length line segment is used, as shown in Figure 1.1, where R0, L0, C0 and G0 refers to the resistance, inductance, capacitance and conductivity per unit length, respectively.
Figure 1.1 Equivalent circuit of a differential-length line segment.
In Figure 1.1, the equation for the voltage drop between Nodes and is
1.1.1Applying Kirchhoff's current law, the equation for Node becomes
1.1.2Omitting the second-order infinitely small item (dx)2 gives
1.1.3 1.1.4where u(x,t) and i(x,t) are the binary functions for the circuit with regard to time and space. The sending end of the line can be deemed as the origin of the x-axis, and the positive direction is, by definition, towards the receiving end.
In transient calculation for high-voltage or ultra-high-voltage lines, G0 can be neglected, and R0 is also generally neglected. In this case, lines can be regarded as lossless with distributed parameters. The equivalent circuit of a simplified lossless single-conductor line of a differential length is as shown in Figure 1.2.
Figure 1.2 Equivalent circuit of a simplified lossless single conductor line of a differential length.
The equation for the lossless single-conductor line is given by
1.1.5 1.1.6where signs are based on the precondition that the sending end of the line is the origin of the x-axis, and the positive direction is towards the receiving end.
Solving the above set of partial differential equations using Laplace transformation or by separating variables, we obtain
1.1.7 1.1.8with
1.1.9which refers to the electromagnetic wave velocity, and
1.1.10which refers to the wave (characteristic) impedance of the line.
For overhead transmission lines, the wave velocity ? is close to the speed of light, i.e. , while for cables, the wave velocity ? is ½ - ? of the speed of light, as the capacitance C0 is larger and the dielectric constant of the medium is larger than that of air. For overhead single-conductor lines, Z ~ 500 O; for bundle conductor lines, Z ~ 300 O, and for cables, Z ranges from several to dozens of ohms.
In the above two equations, is the wave travelling along the line in the positive x-direction, usually known as the forward travelling wave voltage, while is the wave travelling along the line in the negative x-direction, usually known as the backward travelling wave voltage. By definition, is the forward travelling wave current and is the backward travelling wave current.
For forward and backward travelling waves, the relations between the voltages and the currents are given by
1.1.11 1.1.12According to Equation (1.1.11) and Equation (1.1.12), the voltages and the currents of travelling waves are related based on the wave impedance .
Three differences between the wave impedance and the resistance are: (1) the wave impedance refers to the ratio between the voltage and current waves propagating in the same direction, which is independent of the line length, while the resistance increases with the line length, (2) from the perspective of power, the wave impedance does not consume energy and only determines how much energy the conductor absorbs or releases, while the resistance converts electric energy to thermal energy, (3) if both the forward and backward travelling waves coexist on lines, the ratio of the total voltage to the total current no longer equals the wave impedance when the two waves meet.
1.1.2.1 Refraction and Reflection of Travelling Waves
In Figure 1.3, two lines with different wave impedances are connected together, where A is the connecting point.
Figure 1.3 Refraction and reflection of travelling waves at point A.
When connecting line Z1 to a dc supply U0, a forward travelling voltage wave is generated u1q = U0, which travels from the closed switch to point A. As the lines Z1 and Z2 have different wave impedances, the travelling wave will be refracted and reflected at point A. Wherever the reflected wave reaches, the voltage is u1q + u1f; wherever the refracted wave reaches, the voltage is u2q. In addition,
1.1.13 1.1.14with
1.1.15 1.1.16In this expression, a and ß are the refraction and reflection coefficients of point A respectively, and a = ß + 1. Besides, 0 = a = 2, which means...
