Faulty Line Selection Method Based on Comprehensive Dynamic Time Warping Distance in a Flexible Grounding System
Abstract
:1. Introduction
- Able to determine the faulty line or busbar fault under diverse fault conditions;
- Applicable for single-phase grounding fault in distribution network with renewable energy sources connected;
- Applicable for high-resistance grounding fault detection, and the ability to detect transition resistance is up to 5000 Ω;
- Under extreme fault conditions, the faulty line selection accuracy of the method proposed in this paper is higher than that of the existing traditional methods.
2. Materials and Methods
2.1. Transient Current Characteristics of Single-Phase Grounding Fault in Flexible Grounding System
2.2. Faulty Line Selection Method Using CDTW Distance
2.2.1. The Principle of DTW Distance
- (1)
- Boundary conditions
- (2)
- Monotonicity
- (3)
- Continuity
2.2.2. Comprehensive Similarity Coefficient of Waveform
2.2.3. Waveform Processing Method of Transient Zero-Sequence Current
2.2.4. Principle of Faulty Line Selection Method
- (1)
- When the monitored instantaneous value of the zero-sequence voltage of the busbar is greater than the threshold KuUn (Un is the rated voltage of the busbar, and the coefficient Ku is usually set to be 0.35 [21]), the faulty line selection process is started.
- (2)
- The zero-sequence voltage of the busbar and the zero-sequence current of each line are extracted, so the interference of the steady-state component and the unbalanced component is eliminated.
- (3)
- The transient zero-sequence current of the line is projected to the transient zero-sequence voltage of the busbar, and the projection component is calculated by Equation (9).
- (4)
- The top three CDTW distances ci, cm, and cn are selected to form the criterion for faulty line selection, . If the condition of is met, line i is selected as the faulty line; otherwise, the busbar fault is determined.
3. Results and Discussion
3.1. Simulation Model and Parameters
3.2. Fault Simulation Analysis under Diverse Conditions
3.2.1. Line Selection Results under Different Transition Resistance
3.2.2. Line Selection Results under Different Fault Inception Angle
3.2.3. Line Selection Results under Different Fault Distance
3.2.4. Line Selection Results in Case of Busbar Failure
3.2.5. Line Selection Results Considering the Access of Renewable Energy Sources
3.2.6. Line Selection Results Compared with Other Methods
3.3. Field Data Test and Analysis
4. Conclusions
- (1)
- Projecting the transient zero-sequence current of the line on the transient zero-sequence voltage of the busbar by the transient projection method can distinguish the difference between the faulty line and non-faulty line more clearly, which would improve the accuracy of single-phase grounding line selection in the flexible grounding system.
- (2)
- The faulty line selection method proposed in this paper can accurately select the faulty line in spite of different transition resistances, fault inception phase angles, and fault point locations.
- (3)
- A large amount of simulation data shows that the method proposed in this paper has strong adaptability to the occurrence of a high-resistance fault in flexible grounding systems, and the ability to detect transition resistance is up to 5000 Ω.
- (4)
- The field data test also shows the effectiveness of the faulty line selection method based on the CDTW distance proposed in this paper.
- (5)
- The simulation results show that the proposed method is also effective in distribution networks with renewable energy sources connected.
- (6)
- Compared with the methods based on, Wavelet packet energy, Grey relational degree, and Fifth harmonic, the proposed method in this paper is more reliable.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
DTW | Dynamic Time Warping |
Rf | transition resistance at the fault point (ohm) |
L | inductance of the arc suppression coil (H) |
Ci | zero-sequence distributed capacitance of the non-faulty line (F) |
Cn | zero-sequence distributed capacitance of the faulty line (F) |
L0 | equivalent inductance of the arc suppression coil (H) |
R0 | equivalent zero-sequence resistance of the transition resistance (ohm) |
UC0 | zero-sequence voltage of the busbar (V) |
U0 | zero-sequence equivalent voltage at the fault point (V) |
If(0) | zero-sequence current of the faulty line (I) |
ci | comprehensive similarity coefficient |
v | degree of over-compensation |
fN | power frequency (Hz) |
RL | resistive active power loss of the arc suppression coil (ohm) |
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Line Parameters | ||||||
---|---|---|---|---|---|---|
Overhead line | 0.2750 | 0.0054 | 4.6000 | 0.1250 | 0.0096 | 1.3000 |
Cable line | 2.7000 | 0.2800 | 1.0190 | 0.2700 | 0.3990 | 0.2550 |
Transition Resistance/Ω | CDTW Distance of Line 1–5 | Selection Criterion | |||||
---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | |||
0 | B | 104.3 | 108.2 | 482.3 | 113.8 | 106.7 | 482.3 > 222.0 |
A | 16.2 | 16.8 | 973.9 | 17.5 | 18.3 | 973.85 > 35.72 | |
10 | B | 31.1 | 32.4 | 150.8 | 27.8 | 37.5 | 150.8 > 69.9 |
A | 5.5 | 5.7 | 337.5 | 6.0 | 6.2 | 337.52 > 12.18 | |
100 | B | 1.0 | 1.0 | 5.2 | 0.8 | 1.3 | 5.2 > 2.3 |
A | 0.2 | 0.3 | 15.3 | 0.3 | 0.3 | 15.27 > 0.53 | |
1000 | B | 0.01 | 0.01 | 0.06 | 0.01 | 0.01 | 0.06 > 0.02 |
A | 3.1 × 10−3 | 3.2 × 10−3 | 0.2 | 3.0 × 10−3 | 3.2 × 10−3 | 0.194 > 6.4 × 10−3 | |
3000 | B | 1.2 × 10−3 | 1.3 × 10−3 | 6.3 × 10−3 | 9.8 × 10−4 | 1.5 × 10−3 | 6.3 × 10−3 > 2.8 × 10−3 |
A | 3.5 × 10−4 | 3.6 × 10−4 | 0.02 | 3.7 × 10−4 | 3.9 × 10−4 | 0.022 > 7.6 × 10−4 | |
5000 | B | 4.4 × 10−4 | 4.5 × 10−4 | 2.3 × 10−3 | 3.6 × 10−4 | 5.7 × 10−4 | 2.3 × 10−3 > 1.0 × 10−3 |
A | 1.3 × 10−4 | 1.8 × 10−4 | 0.008 | 2.2 × 10−4 | 2.3 × 10−4 | 0.008 > 4.5 × 10−4 |
Fault Inception Phase Angle/Rad | CDTW Distance of Line 1–5 | Selection Criterion | |||||
---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | |||
0 | B | 66.0 | 508.3 | 64.4 | 28.7 | 25.4 | 508.3 > 130.4 |
A | 3.9 | 265.4 | 3.1 | 1.3 | 1.3 | 265.4 > 7.0 | |
B | 958.2 | 6898.2 | 881.3 | 390.8 | 366.1 | 6898.2 > 1839.5 | |
A | 80.7 | 3244.5 | 57.5 | 26.2 | 26.7 | 3244.5 > 138.2 | |
B | 1549.6 | 18,925.0 | 1350.6 | 564.7 | 565.3 | 18,925.0 > 2900.2 | |
A | 146.2 | 6513.3 | 103.7 | 45.6 | 48.0 | 6513.3 > 249.9 | |
B | 1159.3 | 11,190.5 | 978.6 | 400.6 | 423.4 | 11,190.5 > 2137.9 | |
A | 154.3 | 6141.3 | 105.0 | 39.9 | 48.8 | 6141.3 > 259.3 | |
B | 156.5 | 2586.4 | 165.1 | 76.2 | 70.9 | 2586.4 > 321.6 | |
A | 14.8 | 1683.8 | 14.4 | 6.0 | 6.5 | 1683.8 > 29.2 |
Fault Distance/Km | CDTW Distance of Line 1–5 | Selection Criterion | |||||
---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | |||
1 | B | 84.0 | 86.6 | 125.8 | 457.3 | 60.5 | 457.3 > 212.4 |
A | 22.4 | 23.1 | 33.8 | 614.5 | 15.2 | 265.4 > 7.0 | |
5 | B | 138.1 | 142.0 | 208.8 | 649.7 | 85.9 | 649.7 > 350.8 |
A | 32.3 | 33.2 | 49.2 | 782.6 | 23.0 | 782.6 > 82.4 | |
7 | B | 123.6 | 127.1 | 185.4 | 657.9 | 88.6 | 657.9 > 312.5 |
A | 26.9 | 32.6 | 40.7 | 684.1 | 19.2 | 684.1 > 73.3 | |
10 | B | 124.4 | 128.1 | 187.6 | 585.5 | 88.9 | 585.5 > 315.7 |
A | 23.2 | 23.9 | 35.3 | 602.8 | 16.6 | 602.8 > 59.2 | |
12 | B | 100.1 | 103.1 | 150.3 | 520.0 | 71.6 | 520.0 > 253.4 |
A | 18.9 | 19.4 | 28.6 | 521.7 | 13.5 | 521.7 > 48.0 |
Fault Inception Phase Angle/Rad | Transition Resistance /Ω | CDTW Distance of Line 1–5 | Selection Criterion | Line Selection Result | ||||
---|---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | ||||
0 | 0 | 55.5 | 57.2 | 70.4 | 60.7 | 44.7 | 70.4 < 117.9 | Busbar |
10 | 262.5 | 271.3 | 330.4 | 204.3 | 171.8 | 330.4 < 533.8 | Busbar | |
100 | 12.1 | 12.5 | 18.6 | 7.8 | 8.5 | 18.6 < 24.6 | Busbar | |
500 | 0.033 | 0.033 | 0.064 | 0.034 | 0.033 | 0.064 < 0.067 | Busbar |
Fault Inception Phase Angle/Rad | Transition Resistance /Ω | CDTW Distance of Line 1–5 | Selection Criterion | Line Selection Result | ||||
---|---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | ||||
0 | 0 | 17.8 | 18.4 | 961.7 | 24.0 | 23.1 | 961.7 > 47.1 | L3 |
10 | 17.1 | 17.7 | 913.2 | 19.5 | 23.9 | 913.2 > 43.4 | L3 | |
50 | 5.3 | 5.5 | 279.2 | 5.3 | 7.9 | 279.2 > 13.4 | L3 | |
100 | 2.7 | 2.8 | 145.8 | 2.0 | 4.2 | 145.8 > 7.0 | L3 | |
500 | 0.2 | 0.2 | 12.3 | 0.2 | 0.4 | 12.3 > 0.6 | L3 |
Faulty Line Selection Method | Fault Criterion | Feeder Number | Judgement Result | ||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |||
CDTW distance | the value of CDTW distance | 0.02 | 0.87 | 0.02 | 0.01 | 0.01 | L2 |
Wavelet packet energy | relative energy | 0.06 | 0.52 | 0.46 | 0.92 | 0.55 | L4 |
Grey relational degree | the degree of gray correlation of each feeder | 2.37 | 2.52 | 2.91 | 3.11 | 2.32 | L5 |
Fifth harmonic | the magnitude of fifth harmonic component | 0.06 | 0.62 | 0.77 | 1.81 | 0.49 | L4 |
CDTW Distance of Each Line | Selection Criterion | Line Selection Result | ||
---|---|---|---|---|
Line Zhuolan A | Line Zhuolan B | Line Zhuojin B | ||
2.0 × 107 | 60.0 | 60.0 | 2.0 × 107 > 120.0 | Line Zhuolan A |
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He, Y.; Zhang, X.; Wu, W.; Zhang, J.; Bai, W.; Guo, A.; Chen, Y. Faulty Line Selection Method Based on Comprehensive Dynamic Time Warping Distance in a Flexible Grounding System. Energies 2022, 15, 471. https://doi.org/10.3390/en15020471
He Y, Zhang X, Wu W, Zhang J, Bai W, Guo A, Chen Y. Faulty Line Selection Method Based on Comprehensive Dynamic Time Warping Distance in a Flexible Grounding System. Energies. 2022; 15(2):471. https://doi.org/10.3390/en15020471
Chicago/Turabian StyleHe, Yu, Xinhui Zhang, Wenhao Wu, Jun Zhang, Wenyuan Bai, Aiyu Guo, and Yu Chen. 2022. "Faulty Line Selection Method Based on Comprehensive Dynamic Time Warping Distance in a Flexible Grounding System" Energies 15, no. 2: 471. https://doi.org/10.3390/en15020471