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Cover
Title Page
About the Author
Foreword
Preface
Introduction
1 Basic Theories of Power System Relay Protection
1. 1.1 Introduction
2. 1.2 Function of Relay Protection
3. 1.3 Basic Requirements of Relay Protection
4. 1.4 Basic Principles of Relay Protection
5. 1.5 Hierarchical Relay Protection
6. 1.6 Summary
7. References
2 Local Area Conventional Protection
1. 2.1 Introduction
2. 2.2 Transformer Protection
3. 2.3 Transmission Line Protection
4. 2.4 Summary
5. References
3 Local Area Protection for Renewable Energy
1. 3.1 Introduction
2. 3.2 Fault Transient Characteristics of Renewable Energy Sources
3. 3.3 Local Area Protection for Centralized Renewable Energy
4. 3.4 Local Area Protection for Distributed Renewable Energy
5. 3.5 Summary
6. References
4 Topology Analysis
1. 4.1 Introduction
2. 4.2 Topology Analysis for the Inner Substation
3. 4.3 Topology Analysis for Inter‐substation
4. 4.4 False Topology Identification
5. 4.5 Summary
6. References
5 Substation Area Protection
1. 5.1 Introduction
2. 5.2 Substation Area Protection Based on Electrical Information
3. 5.3 Substation Area Protection Based on Operating Signals
4. 5.4 Summary
5. References
6 Wide Area Protection
1. 6.1 Introduction
2. 6.2 Wide Area Protection Using Electrical Information
3. 6.3 Wide Area Protection Using Operating Signals
4. 6.4 Wide Area Tripping Strategy
5. 6.5 Summary
6. References
Appendices
1. Appendix A
2. Appendix B
3. Appendix C
4. Appendix D
5. Appendix E
Index
End User License Agreement

List of Tables

Chapter 02
1. Table 2.1 Parameters of the test transformer.
2. Table 2.2 EPDL simulation cases.
3. Table 2.3 Dynamic simulation results of three model signals under various states.
4. Table 2.4 Parameters of each single‐phase unit of transformer used in the test.
5. Table 2.5 Calculation results of k under different operating states of a two‐winding transformer.
6. Table 2.6 Dynamic simulation results of wave comparison and second harmonic restraint algorithm.
7. Table 2.7 Parameters of each single‐phase unit of transformer used in the test.
8. Table 2.8 Calculation results of B_e in various kinds of states.
9. Table 2.9 Parameters of the test model.
10. Table 2.10 Parameters of the transformer used in the test.
11. Table 2.11 Measured voltage and current.
12. Table 2.12 Simulation results of a phase‐A‐to‐ground fault occurring under different system operating conditions.
13. Table 2.13 Errors of the proposed method for different fault resistance under different conditions.
14. Table 2.14 Simulation results of phase‐A‐to‐ground fault occurring under weak feed conditions.
15. Table 2.15 Measured voltage and measured current in different fault types.
16. Table 2.16 Influence of source impedance in terminal M on the accuracy of the method.
17. Table 2.17 Influence of source impedance in terminal N on the accuracy of the method.
18. Table 2.18 Influence of source impedance in terminal M and N on the accuracy of the method.
19. Table 2.19 Operation status of relay R8 when line 11 is in fault.
20. Table 2.20 Operational status of relay R8 when line 10 is in fault.
21. Table 2.21 Operational status of relay R8 when line 14 is in fault.
22. Table 2.22 Results of fault phase identification at the middle point of the line via different fault resistances.
23. Table 2.23 The influence of fault inception angle on the fault phase identification results.
24. Table 2.24 The influence of fault positions on the fault phase identification results.
25. Table 2.25 Fault type codes.
26. Table 2.26 Results of fault phase identification at the weak‐infeed side.
27. Table 2.27 Simulation results with different fault locations when a three‐phase fault occurs at line MN.
28. Table 2.28 Comparison with other fault phase selection methods.
Chapter 03
1. Table 3.1 Percentage of second harmonic in the stator short circuit current with different terminal voltage drops.
2. Table 3.2 Percentage of second harmonic in the grid‐side short circuit current with different terminal voltage drops.
3. Table 3.3 The main parameters of the DFIG.
4. Table 3.4 Simulation results of adaptive distance protection when a phase‐A‐to‐ground fault occurs at different locations on L₁ via different transition resistances.
5. Table 3.5 Simulation results of the system side when a phase‐A‐to‐ground fault occurs at different locations on L₁ via different transition resistances.
Chapter 04
1. Table 4.1 Nodes in stations.
2. Table 4.2 Circuit breakers and switch status.
3. Table 4.3 Topological bases of Station 3.
4. Table 4.4 Ultimate electrical islands of the system.
5. Table 4.5 Electrical islands in Station 3 after switch status change.
6. Table 4.6 Circuit breakers and switch status in Station 4.
7. Table 4.7 Topological bases of Station 4.
8. Table 4.8 Ultimate electrical islands of Station 4.
9. Table 4.9 Electrical islands in Station 4 after switch status change.
10. Table 4.10 Comparison between computational time of different analysis methods.
11. Table 4.11 Branches and corresponding nodes in the New England 10‐machine, 39‐bus system.
12. Table 4.12 Calculation results of road‐loop equation in the IEEE three‐machine, nine‐bus system.
13. Table 4.13 Calculation results when branch L1 breaks off.
14. Table 4.14 Calculation results after topology information is corrected.
15. Table 4.15 Calculation results after L6 breaks off.
16. Table 4.16 Calculation results after the topology information of L6 is corrected.
17. Table 4.17 Calculation results after undesirable data of node B6 are corrected.
18. Table 4.18 Calculation results after L6 is connected to B2.
19. Table 4.19 Calculation results when all branches are switched on.
20. Table 4.20 Calculation results after L6 breaks off.
21. Table 4.21 Calculation results of the network in Figure 4.13.
22. Table 4.22 Calculation results after undesirable data of the current on branch 29 have been corrected.
23. Table 4.23 Calculation results of the network in Figure 4.14.
24. Table 4.24 Calculation results before undesirable data of the injection current to node 12 are corrected.
25. Table 4.25 Calculation results after undesirable data of the injection current to node 12 have been corrected.
26. Table 4.26 Calculation results after branch 24 breaks off.
27. Table 4.27 Calculation results after topology information of branch 24 is corrected.
Chapter 05
1. Table 5.1 Protection object and boundary circuit breaker numbers for the substation area multi‐component coordinated fusion region.
2. Table 5.2 Protection object and boundary circuit breaker numbers for the bus–transformer fusion region.
3. Table 5.3 Corresponding relationships between numbers i, j and k.
4. Table 5.4 Expected operational status of zone‐II when a fault occurs in different protection sections.
5. Table 5.5 Supporting degree of protection to transformer when CB is switched on and a fault occurs at f₁.
6. Table 5.6 Information fusion degree expectation function value of each component when CB is switched on.
7. Table 5.7 Actual operational status of each protection when CB is switched on and a fault occurs at f₁.
8. Table 5.8 Calculated value of the information fusion degree function of each component when CB is switched on and a fault occurs at f₁.
9. Table 5.9 Calculated value of the information fusion factor of each component when CB is switched on and a fault occurs at f₁.
10. Table 5.10 Calculated values of the information fusion factor of each component when CB is switched off and a fault occurs at f₁.
Chapter 06
1. Table 6.1 PMU placement result.
2. Table 6.2 Topology analysis of the specialized PCRs.
3. Table 6.3 Topology analysis of the generalized PCRs.
4. Table 6.4 The calculated FCFs of branches ①, ② and ③.
5. Table 6.5 Fault distance location simulation results.
6. Table 6.6 Fault location simulation results.
7. Table 6.7 The specialized protection correlation region.
8. Table 6.8 The generalized protection associated area.
9. Table 6.9 Virtual fault locations.
10. Table 6.10 Fault location results.
11. Table 6.11 Case 1 bank.
12. Table 6.12 Case 2 bank.
13. Table 6.13 Distance protection zone‐I operating theoretical value in the case of L₃ fault.
14. Table 6.14 Distance protection zone‐II operating theoretical value in the case of L₃ fault.
15. Table 6.15 Distance protection zone‐III operating theoretical value in the case of L₃ fault.
16. Table 6.16 Typical delay of the elements.
17. Table 6.17 Contribution degree of each distance element to fault line L₈ identification.
18. Table 6.18 Protection fitness expectation function value of each line.
19. Table 6.19 Operating status of each distance element in the case of L₈ fault.
20. Table 6.20 Protection fitness function value of each line.
21. Table 6.21 Distance protection fitting factor of each line.
22. Table 6.22 Distance protection fitting factor of each line.
23. Table 6.23 Distance protection fitting factor of each line.
24. Table 6.24 Set fitting factor of each line.
25. Table 6.25 Expected zone‐I operational status of the protection components when L₃ is in fault.
26. Table 6.26 Expected zone‐II operational status of the protection components when L₃ is in fault.
27. Table 6.27 Expected zone‐III operational status of the protection components when L₃ is in fault.
28. Table 6.28 Line parameters of the 10.5 kV power grid in the Tianjin city distribution network.
29. Table 6.29 Adaptive current protection setting value and operational status of the protection components.
30. Table 6.30 Effectiveness degree of each adaptive current protection component to the identification of fault line L_3.
31. Table 6.31 Adaptive current protection suiting degree, suiting degree expectation and suiting factor of the lines.
32. Table 6.32 Adaptive current protection setting value and operational status of the protection components.
33. Table 6.33 Effectiveness degree of each adaptive current protection component to the identification of fault line L_10.
34. Table 6.34 Adaptive current protection suiting degree, suiting degree expectation and suiting factor of the lines.
35. Table 6.35 Results of sequence criterion for an internal metallic fault.
36. Table 6.36 Results of sequence criterion for an internal fault via high transition resistance.
37. Table 6.37 Results of sequence criterion for an external fault.
38. Table 6.38 Results of sequence criterion for a single‐phase grounding fault with no load at terminal N.
39. Table 6.39 Positive sequence current phasor and T_ci before and after the tripping of breakers.
40. Table 6.40 Positive sequence current phasor and M_ci before and after the tripping of breakers.
41. Table 6.41 Positive sequence current phasor and N_ci before and after the tripping of breakers.

List of Illustrations

Chapter 01
1. Figure 1.1 Double‐source system.
2. Figure 1.2 Operational characteristics of distance protection.
3. Figure 1.3 Constitution mode of hierarchical relay protection in a smart grid.
Chapter 02
1. Figure 2.1 Morphological approach to signal using a flat structuring element. (a) Original signal. (b) Structure element. (c) Dilation transformation. (d) Erosion transformation.
2. Figure 2.2 Processing results of the Electrical Power Dynamic Laboratory testing data by the mathematical morphology method.
3. Figure 2.3 Transformer protection scheme block diagram.
4. Figure 2.4 Connection scheme of EPDL testing system.
5. Figure 2.5 The case of asymmetrical inrush.
6. Figure 2.6 The case of symmetrical inrush.
7. Figure 2.7 The case of an internal fault current.
8. Figure 2.8 The case of inrush due to a light internal fault current.
9. Figure 2.9 The case of simultaneous internal fault current and CT saturation.
10. Figure 2.10 The case of simultaneous asymmetrical inrush current and CT saturation.
11. Figure 2.11 The case of an internal fault current with external shunt capacitance.
12. Figure 2.12 Waveform of the asymmetrical inrush current and its 2B‐spline wavelet transform.
13. Figure 2.13 Waveform of inrush current.
14. Figure 2.14 Inrush currents and their fundamental current amplitudes.
15. Figure 2.15 Connection scheme of the dynamic analogy testing system.
16. Figure 2.16 Current waveforms and their fundamental current amplitudes when switching in a transformer with an internal turn‐turn fault.
17. Figure 2.17 Current waveforms and their fundamental current amplitudes when an internal turn‐to‐turn fault occurs.
18. Figure 2.18 Current waveform and its fundamental current amplitudes under TA saturation at an out‐zone fault.
19. Figure 2.19 The square grids needed to cover the differential current at a certain interval when an internal fault occurs.
20. Figure 2.20 The square grids needed to cover the differential current at a certain interval when the transformer is energized.
21. Figure 2.21 The grille curve (N_d) when an internal fault occurs.
22. Figure 2.22 The grille curve (N_d) when the transformer is energized.
23. Figure 2.23 The g and p when an internal fault occurs. (a) Analysis of the calculated NGCs in the time domain. (b) Analysis of the calculated NGCs in the frequency domain.
24. Figure 2.24 The g and p when the transformer is energized. (a) Analysis of the calculated NGCs in the time domain. (b) Analysis of the calculated NGCs in the frequency domain.
25. Figure 2.25 Experimental system.
26. Figure 2.26 Differential currents and experimental results when the transformer is energized. (a) Differential currents. (b) Calculated NGCs. (c) Analysis of the calculated NGCs in the time domain. (d) Analysis of the calculated NGCs in the frequency domain.
27. Figure 2.27 Differential currents and experimental results when a 6.1% turn‐to‐turn internal fault occurs. (a) Differential currents. (b) Calculated NGCs. (c) Analysis of the calculated NGCs in the time domain. (d) Analysis of the calculated NGCs in the frequency domain.
28. Figure 2.28 Differential currents and experimental results when the transformer is switched with no load and a 6.1% turn‐to‐turn internal fault occurs. (a) Differential currents. (b) Calculated NGCs. (c) Analysis of the calculated NGCs in the time domain. (d) Analysis of the calculated NGCs in the frequency domain.
29. Figure 2.29 Differential currents and experimental results when an external fault occurs with CT saturation. (a) Differential currents. (b) Calculated NGCs. (c) Analysis of the calculated NGCs in the time domain. (d) Analysis of the calculated NGCs in the frequency domain.
30. Figure 2.30 Differential currents and experimental results when an internal fault occurs with CT saturation. (a) Differential currents. (b) Calculated NGCs. (c) Analysis of the calculated NGCs in the time domain. (d) Analysis of the calculated NGCs in the frequency domain.
31. Figure 2.31 Grille definition.
32. Figure 2.32 Electrical Power Dynamic Laboratory test model and parameters.
33. Figure 2.33 The differential current waveform and its results under CT saturation at an out‐zone fault. (a) Differential current. (b) Grille variation curve. (c) Processed grille variation curve.
34. Figure 2.34 The symmetrical inrush current and its results. (a) Differential current. (b) Grille variation curve. (c) Processed grille variation curve.
35. Figure 2.35 The differential current waveform and its results under CT saturation in the case of internal fault. (a) Differential current. (b) Grille variation curve. (c) Processed grille variation curve.
36. Figure 2.36 A two‐winding, single‐phase transformer.
37. Figure 2.37 A two‐winding, three‐phase Δ/Y transformer.
38. Figure 2.38 A three‐winding, three‐phase Y₀/Y/Δ transformer.
39. Figure 2.39 Experimental system.
40. Figure 2.40 Experimental results when the transformer is energized. (a) Line currents. (b) Calculated EILIs. (c) Analysis of the calculated EILIs.
41. Figure 2.41 Experimental results when an external line fault is cleared. (a) Line currents. (b) Calculated EILIs. (c) Analysis of the calculated EILIs.
42. Figure 2.42 Experimental results when the transformer is energized with a 2% turn‐to‐turn internal fault. (a) Line currents. (b) Calculated EILIs. (c) Analysis of the calculated EILIs.
43. Figure 2.43 Experimental results when a 3% turn‐to‐turn internal fault occurs at the secondary side. (a) Line currents at the primary side. (b) Calculated EILIs of the primary windings. (c) Analysis of the calculated EILIs.
44. Figure 2.44 Experimental results when a 3% turn‐to‐turn internal fault occurs at the secondary side. (a) Line currents at the secondary side. (b) Calculated EILIs of the secondary windings. (c) Analysis of the calculated EILIs.
45. Figure 2.45 A two‐winding, single‐phase transformer.
46. Figure 2.46 A two‐terminal network.
47. Figure 2.47 A two‐winding, three‐phase Δ/Y transformer.
48. Figure 2.48 A three‐winding, three‐phase Δ/Y/Y₀ transformer.
49. Figure 2.49 Experimental system.
50. Figure 2.50 Differential currents and experimental results when the transformer is energized. (a) Differential currents. (b) ADOAPs.
51. Figure 2.51 Differential currents and experimental results when the transformer is switched with no load and a turn‐to‐ground fault in phase B. (a) Differential currents. (b) ADOAPs.
52. Figure 2.52 Differential currents and experimental results when the transformer is energized with a 2.4% turn‐to‐turn fault in phase A. (a) Differential currents. (b) ADOAPs.
53. Figure 2.53 Differential currents and experimental results when a turn‐to‐ground internal fault occurs in phase B. (a) Differential currents. (b) ADOAPs.
54. Figure 2.54 Differential currents and experimental results when a 2.4% turn‐to‐turn fault occurs in phase A. (a) Differential currents. (b) ADOAPs.
55. Figure 2.55 Analysis models. (a) Single‐source system. (b) Double‐source system.
56. Figure 2.56 Voltage phasor diagram when a single‐phase‐to‐ground fault occurs in the single‐source system.
57. Figure 2.57 Voltage phasor diagram when a single‐phase‐to‐ground fault occurs in the double‐source system.
58. Figure 2.58 Compound sequence network of a single‐phase‐to‐ground fault.
59. Figure 2.59 Flowchart of the line protection scheme for a single‐phase‐to‐ground fault.
60. Figure 2.60 Simulation results of a phase‐A‐to‐ground fault occurring at 180 km from bus M via different fault resistances (δ = 20°).
61. Figure 2.61 Simulation results of a phase‐A‐to‐ground fault occurring at 180 km from bus M via different fault resistances (δ = −20°).
62. Figure 2.62 Simulation results of a phase‐A‐to‐ground fault occurring via 300 Ω fault resistance at different distances from bus M (δ = 20°).
63. Figure 2.63 Simulation results of a phase‐A‐to‐ground fault occurring via 300 Ω fault resistance at different distances from bus M (δ = −20°).
64. Figure 2.64 Simulation results of a non‐linear HIF at different distances from bus M (δ = 20°).
65. Figure 2.65 Simulation results of non‐linear HIF under different source impedances for bus N (δ = 20°).
66. Figure 2.66 Simulation results of a non‐linear HIF under weak‐infeed conditions at different distances from bus N (δ = −20°).
67. Figure 2.67 Impedance relay with quadrilateral characteristic.
68. Figure 2.68 Voltage and current vector in the case of a double‐source system fault.
69. Figure 2.69 Negative sequence network of fault system.
70. Figure 2.70 Analysis model.
71. Figure 2.71 Negative sequence network.
72. Figure 2.72 Simulation results of the adaptive distance protection for a single‐source power system when a phase‐A‐to‐ground fault occurs via different transition resistances at 70 km away from relay R1. (a) 0 Ω. (b) 10 Ω. (c) 50 Ω. (d) 100 Ω.
73. Figure 2.73 Simulation results of the adaptive distance protection for a single‐source power system when a phase‐A‐to‐ground fault occurs via 100 Ω transition resistance at different points away from relay R1. (a) 5 km. (b) 50 km. (c) 114 km. (d) 126 km.
74. Figure 2.74 Simulation results of the adaptive distance protection for a double‐source power system when a phase‐A‐to‐ground fault occurs via different transition resistances at 200 km away from relay R1. (a) 0 Ω. (b) 50 Ω. (c) 150 Ω. (d) 300 Ω.
75. Figure 2.75 Simulation results of the adaptive distance protection for a double‐source power system when a phase‐A‐to‐ground fault occurs via 300 Ω transition resistance at different points away from relay R1. (a) 50 km. (b) 150 km. (c) 300 km. (d) 340 km.
76. Figure 2.76 Simulation results of the adaptive distance protection when a fault occurs via 300 Ω transition resistance at different distances away from bus N. (a) 0 km. (b) 40 km. (c) 80 km.
77. Figure 2.77 Measured impedance trajectory of the conventional distance protection for a single‐source power system when a phase‐A‐to‐ground fault occurs at 70 km from bus M via different transition resistances.
78. Figure 2.78 Measured impedance trajectory of the conventional distance protection for a double‐source power system when a phase‐A‐to‐ground fault occurs at 200 km from bus M via different transition resistances.
79. Figure 2.79 System diagram of a double‐circuit line.
80. Figure 2.80 The electrical quantity of each sequence network.
81. Figure 2.81 Angle of with fault distance increasing.
82. Figure 2.82 Angle of with fault distance increasing.
83. Figure 2.83 The estimated voltage amplitude of the fault point.
84. Figure 2.84 Phase characteristics analysis of the fault location function when the fault happened at 100 km.
85. Figure 2.85 Simulation model of the double‐circuit lines.
86. Figure 2.86 Influence of fault position and fault type on fault location for the ungrounded inter‐line fault.
87. Figure 2.87 Influence of transition position on fault location for the grounded inter‐two‐line fault.
88. Figure 2.88 Influence of fault position and fault type on fault location for the grounded inter‐three‐line fault.
89. Figure 2.89 Influence of fault position and fault type on fault location for the three‐line fault with single‐phase grounded.
90. Figure 2.90 Influence of transition resistance on fault location for the grounded inter‐two‐line fault.
91. Figure 2.91 Influence of transition resistance and fault type on fault location for the grounded inter‐three‐line fault.
92. Figure 2.92 Influence of transition resistance and fault type on fault location for the three‐line fault with single‐phase grounded.
93. Figure 2.93 Influence of transition resistance and fault point on fault location considering the measuring transformer models. (a) Two‐line, two‐phase inter‐line grounded fault (IBICG). (b) Three‐line, two‐phase inter‐line grounded fault (IBCIIC‐G). (c) Three‐line, three‐phase non‐inter‐line single‐phase grounded fault (IBC‐IIAG).
94. Figure 2.94 Influence of transition resistance and fault point on fault location of the existing method. (a) Two‐line, two‐phase inter‐line grounded fault (IBICG). (b) Three‐line, two‐phase inter‐line grounded fault (IBCIIC‐G). (c) Three‐line, three‐phase non‐inter‐line single‐phase grounded fault (IBC‐IIAG).
95. Figure 2.95 A two‐source power system.
96. Figure 2.96 Voltage and current phasor diagram without fault.
97. Figure 2.97 Three‐phase fault at F.
98. Figure 2.98 Voltage and current phasor diagram in the case of a three‐phase fault.
99. Figure 2.99 Protection operational zone.
100. Figure 2.100 IEEE 10‐machine, 39‐bus system.
101. Figure 2.101 Z_m and Z_set variation diagram of relay R8 when line 11 is in fault.
102. Figure 2.102 k_m variation diagram of relay R8 when line 11 is in fault.
103. Figure 2.103 Z_m and Z_set variation diagram of relay 8 when line 10 is in fault.
104. Figure 2.104 k_m variation diagram of relay 8 when line 10 is in fault.
105. Figure 2.105 Z_m and Z_set variation diagram of relay R8 when line 14 is in fault.
106. Figure 2.106 k_m variation diagram of relay R8 when line 14 is in fault.
107. Figure 2.107 Load impedance region and distance protection zone in the impedance plane.
108. Figure 2.108 Z_m and Z_set variation diagram of relay R6 when line 9 is in fault.
109. Figure 2.109 Model of a dual‐source power system.
110. Figure 2.110 Sequence network of internal fault.
111. Figure 2.111 Flowchart of the fault phase selection method.
112. Figure 2.112 Simulation model of a high‐voltage transmission line.
113. Figure 2.113 FPSFs when a phase‐A‐to‐ground fault occurs via a 300 Ω fault resistance.
114. Figure 2.114 FPSFs when a phase‐B‐to‐C fault occurs via a 300 Ω fault resistance.
115. Figure 2.115 FPSFs when a phase‐BC‐to‐ground fault occurs via a 300 Ω fault resistance.
116. Figure 2.116 FPSFs when a three‐phase fault occurs via a 300 Ω fault resistance.
117. Figure 2.117 Results of fault phase identification with a developing fault.
118. Figure 2.118 FPSFs when TCSC is installed at bus N.
119. Figure 2.119 FPSFs when UPFC is installed on line MN.
120. Figure 2.120 Double high‐voltage transmission line.
121. Figure 2.121 FPSFs when different types of faults occur at F_1.
122. Figure 2.122 Single‐line diagram of the CIGRÉ benchmark HVDC system.
123. Figure 2.123 Phase currents at the relaying point of bus P when line PQ is in fault.
124. Figure 2.124 FPSFs at the relaying point of bus P when line PQ is in fault.
125. Figure 2.125 Phase currents at the relaying point of bus Q when line PQ is in fault.
126. Figure 2.126 FPSFs at the relaying point of bus Q when line PQ is in fault.
127. Figure 2.127 Phase currents at the relaying point of bus M when line MN is in fault.
128. Figure 2.128 FPSFs at the relaying point of bus M when line MN is in fault.
129. Figure 2.129 Phase currents at the relaying point of bus N when line MN is in fault.
130. Figure 2.130 FPSFs at the relaying point of bus N when line MN is in fault.
131. Figure 2.131 Results of traditional fault phase identification method.
Chapter 03
1. Figure 3.1 Equivalent circuit of the DFIG system.
2. Figure 3.2 Low‐voltage operation capability curve of wind turbines.
3. Figure 3.3 Grid fault analysis model.
4. Figure 3.4 Equivalent circuit of the line‐side and the rotor‐side converter under dq coordinates.
5. Figure 3.5 Negative sequence analysis model of a DFIG under asymmetrical grid fault.
6. Figure 3.6 Power grid fault.
7. Figure 3.7 Influence of the DFIG terminal voltage phase jump on the rotor current. (a) Rotor current without considering the phase jump. (b) Rotor current considering the phase jump.
8. Figure 3.8 Influence of DFIG terminal voltage phase jump on the stator current. (a) Stator current without considering the phase jump. (b) Stator current considering the phase jump.
9. Figure 3.9 Influence of DFIG grid‐side converter control on the rotor current. (a) Rotor current without considering the grid‐side converter control. (b) Rotor current considering the grid‐side converter control.
10. Figure 3.10 Influence of DFIG grid‐side converter control on the stator current. (a) Stator current without considering the grid‐side converter control. (b) Stator current considering the grid‐side converter control.
11. Figure 3.11 DFIG rotor current under grid phase‐C short circuit fault. (a) Simulation and calculated values of phase‐A rotor current. (b) Simulation and calculated values of phase‐B rotor current. (c) Simulation and calculated values of phase‐C rotor current.
12. Figure 3.12 DFIG stator current under grid phase‐C short circuit fault. (a) Simulation and calculated values of phase‐A stator current. (b) Simulation and calculated values of phase‐B stator current. (c) Simulation and calculated values of phase‐C stator current.
13. Figure 3.13 DFIG rotor current under grid phase‐AC short circuit fault. (a) Simulation and calculated values of phase‐A rotor current. (b) Simulation and calculated values of phase‐B rotor current. (c) Simulation and calculated values of phase‐C rotor current.
14. Figure 3.14 DFIG stator current under grid phase‐AC short circuit fault (a) Simulation and calculated values of phase‐A stator current. (b) Simulation and calculated values of phase‐B stator current. (c) Simulation and calculated values of phase‐C stator current.
15. Figure 3.15 DFIG fault equivalent network considering the rotor‐side converter control in the case of a three‐phase fault. (a) Fault network. (b) Normal‐operation network. (c) Superimposed network.
16. Figure 3.16 Control model of the grid‐side converter.
17. Figure 3.17 Equivalent circuit of the rotor current component.
18. Figure 3.18 Stator and rotor short circuit currents considering the converter transient regulation. (a) Rotor phase A current. (b) Stator phase A current.
19. Figure 3.19 Comparison between DC bus power difference curve and voltage deviation curve in the case of grid short circuit fault.
20. Figure 3.20 DC bus voltage deviation curves with different terminal voltage drops.
21. Figure 3.21 Percentage of second harmonics in the short circuit currents.
22. Figure 3.22 Variation of positive sequence flux eigenvalues as the crowbar resistance changes. (a) Variation of s₁. (b) Variation of s₂.
23. Figure 3.23 Variation of negative sequence flux eigenvalues as the crowbar resistance changes. (a) Variation of s₃. (b) Variation of s₄.
24. Figure 3.24 Variation of different components of the stator flux as the DFIG rotor speed changes. (a) Positive. (b) Negative.
25. Figure 3.25 RTDS models of DFIG simulation system. (a) RTDS model for the simulation system. (b) RTDS model for a wind turbine DFIG. (c) RTDS model for the electrical part of a DFIG.
26. Figure 3.26 Stator short circuit phase currents in the case of a three‐phase symmetrical fault. (a) Short circuit current of phase A under a symmetrical fault. (b) Variation of stator short circuit current as the crowbar resistance changes under a symmetrical fault. (c) Influence of pre‐fault rotor speed on the stator short circuit current under a symmetrical fault.
27. Figure 3.27 Stator short circuit phase currents in the case of a grid asymmetrical fault. (a) Short circuit current of phase A under a phase‐C‐to‐ground fault. (b) Short circuit current of phase C under a phase‐C‐to‐ground fault. (c) Short circuit current of phase A under a phase‐BC‐to‐ground fault. (d) Short circuit current of phase C under a phase‐BC‐to‐ground fault.
28. Figure 3.28 Variation of short circuit phase currents under a grid asymmetrical fault as the crowbar resistance and pre‐fault rotor speed change. (a) Variation of phase A under a phase‐C‐to‐ground fault as the crowbar resistance changes. (b) Variation of phase C under a phase‐C‐to‐ground fault as the crowbar resistance changes. (c) Variation of phase A under a phase‐BC‐to‐ground fault as the pre‐fault rotor speed changes. (d) Variation of phase C under a phase‐BC‐to‐ground fault as the pre‐fault rotor speed changes.
29. Figure 3.29 Simulation results of stator short circuit current when crowbar resistance varies during a fault. (a) Comparison of resistance changing and unchanging during a symmetrical fault. (b) Comparison of calculation and simulation when resistance changes during a symmetrical fault. (c) Comparison of resistance changing and unchanging during an asymmetrical fault. (d) Comparison of calculation and simulation when resistance changes during an asymmetrical fault.
30. Figure 3.30 Wind farm main wiring diagram and relay protection configuration.
31. Figure 3.31 Adaptive distance protection analysis model.
32. Figure 3.32 Wind farm simulation model.
33. Figure 3.33 Operational curve of the adaptive distance protection on the collector system side when a phase‐A‐to‐ground fault occurs at 25% of L₁ via different transition resistances. (a) 0 Ω. (b) 10 Ω. (c) 20 Ω. (d) 30 Ω.
34. Figure 3.34 Operational curve of the adaptive distance protection on the collector system side when a phase‐A‐to‐ground fault occurs at 55% of L₁ via different transition resistances. (a) 0 Ω. (b) 10 Ω. (c) 20 Ω. (d) 30 Ω.
35. Figure 3.35 Operational curve of the adaptive distance protection on the collector system side when a phase‐A‐to‐ground fault occurs at 75% of L₁ via different transition resistances. (a) 0 Ω. (b) 10 Ω. (c) 20 Ω. (d) 30 Ω.
36. Figure 3.36 Operational curve of the adaptive distance protection on the collector system side when none of the crowbar protection of the wind turbines connected to line L₁ is put into operation. (a) L₁ = 20 km. (b) L₁ = 15 km. (c) L₁ = 10 km. (d) L₁ = 5 km.
37. Figure 3.37 Operational curve of the adaptive distance protection on the collector system side when the crowbar protection of some of the wind turbines connected to line L₁ is put into operation. (a) L₁ = 20 km. (b) L₁ = 15 km. (c) L₁ = 10 km. (d) L₁ = 5 km.
38. Figure 3.38 Operational curve of the adaptive distance protection on the collector system side when the crowbar protection of all the wind turbines connected to line L₁ is put into operation. (a) L₁ = 20 km. (b) L₁ = 15 km. (c) L₁ = 10 km. (d) L₁ = 5 km.
39. Figure 3.39 Operational curves of traditional distance protection when a phase‐A‐to‐ground fault occurs at 4 km from the relaying point via different transition resistances.
40. Figure 3.40 Operational curves of traditional distance protection when a phase‐A‐to‐ground fault occurs via 30 Ω transition resistance at different locations.
41. Figure 3.41 Model of network in normal operating state.
42. Figure 3.42 Model of fault steady‐state network.
43. Figure 3.43 Equivalent model of fault supplementary network.
44. Figure 3.44 Equivalent diagram of wind farm outgoing transmission line.
45. Figure 3.45 Protection operational status when a three‐phase fault occurs at 50% of the protection line. (a) Traditional current pilot differential protection. (b) Proposed current pilot differential protection.
46. Figure 3.46 Protection operational status when a two‐phase fault occurs at 50% of the protection line. (a) Traditional current pilot differential protection. (b) Proposed current pilot differential protection.
47. Figure 3.47 Protection operational status when a two‐phase fault occurs at 90% of the protection line. (a) Traditional current pilot differential protection. (b) Proposed current pilot differential protection.
48. Figure 3.48 An industrial power network fed through source G and protected by R1, R2 and R3.
49. Figure 3.49 An industrial power network fed through source G, DG1 and DG2, and protected by R1, R2 and R3.
50. Figure 3.50 An industrial power network with directional protection devices to ensure the correct fault isolation.
51. Figure 3.51 Norton equivalent model behind R4.
52. Figure 3.52 Thévenin equivalent model behind R4.
53. Figure 3.53 A practical 10 kV distribution system in the Tianjin power network.
54. Figure 3.54 The adaptive primary protection setting and the measured current of R5 when a three‐phase fault occurs in the middle of Section BC.
55. Figure 3.55 The adaptive primary protection setting and the measured current of R5 when a phase‐to‐phase fault occurs in the middle of Section BC.
56. Figure 3.56 The adaptive backup protection setting and the measured current of R5 when a three‐phase fault occurs on Section AB close to bus B.
57. Figure 3.57 The adaptive backup protection setting and the measured current of R5 when a phase‐to‐phase fault occurs on Section AB close to bus B.
58. Figure 3.58 The multiple‐loop control schematic of the DG.
59. Figure 3.59 Schematic diagram of the multi‐loop control system.
60. Figure 3.60 Block diagram of grid‐tied control for inverter.
61. Figure 3.61 Block diagram of inverter control after islanding.
62. Figure 3.62 Schematic diagram of integral sum.
63. Figure 3.63 Flowchart of islanding detection.
64. Figure 3.64 Schematic diagram of islanding detection.
65. Figure 3.65 Simulation results of islanding detection. (a) Power grid voltage. (b) H‐curve. (c) Area between H‐curve and the time axis. (d) Inverter output current. (e) Microgrid frequency. (f) Amplitude of the microgrid voltage.
66. Figure 3.66 Simulation results of islanding detection for open phase. (a) Single-phase open. (b) Two-phase open.
67. Figure 3.67 Simulation results under fault islanding. (a) power grid voltage. (b) H‐curve. (c) Area between H‐curve and the time axis.
68. Figure 3.68 Schematic diagram of islanding detection.
69. Figure 3.69 Negative sequence network of a grid‐tied microgrid.
70. Figure 3.70 Negative sequence network of an islanding microgrid.
71. Figure 3.71 Simulation results of islanding detection. (a) Phase voltage of negative sequence voltage source. (b) Negative sequence voltage contribution factor k. (c) Microgrid voltage. (d) Microgrid frequency.
72. Figure 3.72 Schematic diagram of the simulation results of islanding detection for open phase. (a) Single‐phase breaker open. (b) Two‐phase breaker open.
73. Figure 3.73 Simulation results under islanding fault.
Chapter 04
1. Figure 4.1 Simple connected graph.
2. Figure 4.2 Different types of main electrical wiring. (a) Single‐bus segmented wiring. (b) Double‐bus wiring. (c) Double‐bus segmented wiring. (d) Angular wiring. (e) 3/2 wiring.
3. Figure 4.3 Switch ‘off’ analysis.
4. Figure 4.4 Simple network system example.
5. Figure 4.5 Large power system with multiple plants and stations.
6. Figure 4.6 Plant‐station topology analysis example. (a) Initial topology. (b) Switch ‘off’. (c) Switch ‘on’.
7. Figure 4.7 A simple network.
8. Figure 4.8 New England 10‐machine, 39‐bus system.
9. Figure 4.9 Road‐loop labelled graph of IEEE 9‐bus system.
10. Figure 4.10 Road‐loop labelled graph of system after L6 breaks off.
11. Figure 4.11 Road‐loop labelled graph of system after L6 is connected to B2.
12. Figure 4.12 Road‐loop labelled graph of IEEE 39‐bus system.
13. Figure 4.13 Road‐loop labelled graph of local network in the IEEE 39‐bus system.
14. Figure 4.14 Road‐loop labelled graph of local network with node 6 as the terminal point.
Chapter 05
1. Figure 5.1 Wiring diagram of a typical substation and adjacent power grid.
2. Figure 5.2 Flowchart of the substation area protection scheme.
3. Figure 5.3 Operational scheme of bus–line fusion region C1.
4. Figure 5.4 Operational scheme of bus–transformer fusion region B1.
5. Figure 5.5 Operational scheme of substation area multi‐component coordinated fusion region A1.
6. Figure 5.6 Coping with transformer fault and primary protection of the fault transformer refusing to operate (sectional circuit breakers all switched off).
7. Figure 5.7 Coping with transformer fault and primary protection of the fault transformer refusing to operate (sectional circuit breakers not all switched off).
8. Figure 5.8 Coping with bus fault and primary protection of the fault bus refusing to operate (sectional circuit breaker switched off).
9. Figure 5.9 Coping with bus fault and the primary protection of the faulty bus refusing to operate (sectional circuit breaker switched on).
10. Figure 5.10 Coping with line fault and the primary protection of the faulty line refusing to operate.
11. Figure 5.11 Structure of the substation area.
12. Figure 5.12 Example of division of the transformer by protection zone‐II.
13. Figure 5.13 System used for scheme verification.
14. Figure 5.14 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at f₁.
15. Figure 5.15 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at f₂.
16. Figure 5.16 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at f₃.
17. Figure 5.17 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at the exit of high‐voltage side line L_g3.
18. Figure 5.18 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at the exit of medium‐voltage side line L_z3.
19. Figure 5.19 Information fusion factor considering information loss and error when CB is switched on and a fault occurs at the exit of low‐voltage side line L_d6.
20. Figure 5.20 Information fusion factor considering information loss and error when CB is switched off and a fault occurs at f₁.
21. Figure 5.21 Information fusion factor considering information loss and error when CB is switched off and a fault occurs at the exit of high‐voltage side line L_g1.
Chapter 06
1. Figure 6.1 Fault steady‐state network of a generalized PCR.
2. Figure 6.2 Fault steady‐state expanded network of the generalized PCR.
3. Figure 6.3 10‐generator, 39‐bus New England test system.
4. Figure 6.4 Fault steady‐state differential currents in different PCRs when a single‐phase fault occurs.
5. Figure 6.5 Fault steady‐state differential currents in different PCRs when a three‐phase fault occurs.
6. Figure 6.6 Fault branch.
7. Figure 6.7 Fault model.
8. Figure 6.8 IEEE 9‐bus test system.
9. Figure 6.9 Location function value on different branches.
10. Figure 6.10 Location function value on different branches.
11. Figure 6.11 Branch model in normal operation.
12. Figure 6.12 Fault steady‐state model of branch.
13. Figure 6.13 Fault steady‐state equivalent model of branch.
14. Figure 6.14 Fault matching degree of suspicious branches during single‐phase grounding fault. (a) Metal fault. (b) Fault through 300 Ω resistance.
15. Figure 6.15 Fault matching degree of suspicious branches during two‐phase fault. (a) Metal fault. (b) Fault through 300 Ω resistance.
16. Figure 6.16 Fault matching degree of suspicious branches during two‐phase grounding fault. (a) Metal fault. (b) Fault through 300 Ω resistance.
17. Figure 6.17 Fault matching degree of suspicious branches during three‐phase fault. (a) Metal fault. (b) Fault through 300 Ω resistance.
18. Figure 6.18 Fault fitting degree T (8 and 35).
19. Figure 6.19 Fault fitting degree T (7 and 36).
20. Figure 6.20 Fault fitting degree T (10 and 35).
21. Figure 6.21 Fault fitting degree T (8 and 35).
22. Figure 6.22 Fault fitting degree T (12 and 36).
23. Figure 6.23 Fault fitting degree T (10 and 35).
24. Figure 6.24 Wide area protection system structure.
25. Figure 6.25 Framework of wide area power network.
26. Figure 6.26 Branch coefficient calculation.
27. Figure 6.27 Distance protection zone‐I operating theoretical value calculation.
28. Figure 6.28 Distance protection Zone‐II operating theoretical value calculation.
29. Figure 6.29 Distance protection zone‐III operating theoretical value calculation.
30. Figure 6.30 Flowchart of wide area backup protection algorithm.
31. Figure 6.31 Classification of regions in the IEEE 10‐machine, 39‐bus system.
32. Figure 6.32 Distance protection fitting factor of each line in the case of L₈ fault close to bus 4.
33. Figure 6.33 Guizhou DuYun System.
34. Figure 6.34 Distance protection fitting factor of each line in the case of L₆ fault at the midpoint.
35. Figure 6.35 Regional power grid structure.
36. Figure 6.36 Calculation example of the expected zone‐I operational status.
37. Figure 6.37 Calculation example of the expected zone‐II operational status.
38. Figure 6.38 Calculation example of the expected zone‐III operational status.
39. Figure 6.39 Flowchart of the backup protection algorithm based on adaptive current protection suiting factor.
40. Figure 6.40 A 10.5 kV power grid in the Tianjin city distribution network.
41. Figure 6.41 Adaptive current protection suiting factor of each line when L₃ is in fault.
42. Figure 6.42 IEEE 33‐bus distribution system.
43. Figure 6.43 Adaptive current protection suiting factor of each line when L₁₀ is in fault.
44. Figure 6.44 Adaptive current protection suiting factor of each line when L₂₇ is in fault.
45. Figure 6.45 Sequence network of the fault system. (a) Sequence network in the case of external fault. (b) Sequence network in the case of internal fault.
46. Figure 6.46 Cooperation logic of the sequence criteria.
47. Figure 6.47 Diagram of the differential relay.
48. Figure 6.48 Simulation model.
49. Figure 6.49 Result of criterion when different faults occur at a 40% line length from terminal M. (a) Negative sequence criterion when a single‐phase grounding fault occurs. (b) Negative sequence criterion when a phase‐to‐phase fault occurs. (c) Negative sequence criterion when a phase‐to‐phase grounding fault occurs. (d) Positive sequence criterion when a three‐phase symmetrical fault occurs.
50. Figure 6.50 Criteria results in the case of an out‐of‐zone fault. (a) Negative sequence criterion when a single‐phase grounding fault occurs at the backside of terminal N. (b) Positive sequence criterion when a three‐phase symmetrical fault occurs at the backside of terminal M.
51. Figure 6.51 Results of negative sequence criterion when a single‐phase grounding fault at the backside of terminal N transfers to different types of internal fault at terminal N after 0.03 s. (a) Single‐phase grounding fault transfers to single‐phase grounding fault. (b) Single‐phase grounding fault transfers to phase‐to‐phase grounding fault.
52. Figure 6.52 Results of criterion when a single‐phase grounding fault develops into a phase‐to‐phase grounding fault at the same location after 0.03 s. (a) Forward side of terminal N. (b) Backside of terminal N.
53. Figure 6.53 Result of criterion in the case of an internal fault for channel delay 5 ms. (a) Negative sequence criterion when a single‐phase grounding fault occurs. (b) Negative sequence criterion when a phase‐to‐phase fault occurs. (c) Negative sequence criterion when a phase‐to‐phase grounding fault occurs. (d) Positive sequence criterion when a three‐phase symmetrical fault occurs.
54. Figure 6.54 Result of traditional current differential protection when a single‐phase grounding fault occurs via high fault resistance.
55. Figure 6.55 Results of traditional current differential protection when a single‐phase grounding fault at the backside of terminal N transfers to an internal fault at terminal N after 0.03 s.
56. Figure 6.56 Diagram of a 330 kV local power grid.
57. Figure 6.57 Flowchart of line local backup protection tripping strategy.
58. Figure 6.58 Flowchart of the breaker failure tripping strategy.
59. Figure 6.59 Flowchart for the substation and outlet line remote backup protection tripping strategy.
60. Figure 6.60 Diagram of the New England 10‐machine, 39‐bus system.