A Comparison of Double-End Partial Discharge Localization Algorithms in Power Cables
Abstract
:1. Introduction
2. PD Measurement Methods
2.1. Single-End PD Measurement
- TD—Time difference between consecutive pulses;
- L—Cable length.
2.2. Double-End PD Measurement
- v—Propagation velocity of the PD signal that travels along the cable;
- TD—Time difference of the PD signal that arrives at two adjacent sensors;
- L—Total length of the cable.
2.3. Multi-End PD Measurement
- Case 1:
- Case 2:
- tab—Time difference between signal A[n] and signal B[n];
- tcb—Time difference between signal C[n] and signal B[n].
- If tab is less than tcb, then Equation (3) is applied. Otherwise, Equation (4) is applied.
3. Methodology
3.1. PD Localization Algorithm
- A—The magnitude coefficient, assumed to be 0.01;
- ;
- ;
- ;
- ;
- .
- ;
- ε—Effective relative permittivity of the cable dielectric and semiconducting screen layers.
3.2. Maximum Peak Detection Algorithm
- ;
- The time that yields a maximum peak in
3.3. Segmented Correlation (SC) Algorithm
- TSR—Total samples of the reference signal before the signal was cropped;
- TSRcropped—Total samples of the reference signal after the signal was cropped.
3.4. Segmented Correlation Trimmed Mean Data Filtering (SCTM) Algorithm
- ;
- Sn—Estimated PD localization samples that enter the mod class;
- m—Total number of samples that enter the mod class.
4. Result and Discussion
4.1. Maximum PD Estimation Error
4.2. Average PD Estimation Error
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Localization Techniques | Descriptions |
---|---|
Electrical [7,8,9] |
|
Chemical [10] |
|
Acoustic [9,11,12,13,14,15] |
|
Electromagnetic [14,16,17,18,19,20,21,22] |
|
Ultrasonic [23,24] |
|
Ultraviolet [25,26,27,28,29,30,31,32] |
|
Reference signal () | |||
Shifting signal () | |||
Multiplication of signals () | |||
Summation () | |||
Correlation profile |
128.3491 | 1298.874 | 1299.654 | 1300.435 | 1301.215 |
130.6901 | 1298.874 | 1299.654 | 1300.435 | 1301.215 |
1259.857 | 1298.874 | 1299.654 | 1300.435 | 1301.215 |
1264.539 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1294.972 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1295.753 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1296.533 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1296.533 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1301.995 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1302.776 |
1297.313 | 1298.874 | 1299.654 | 1300.435 | 1302.776 |
1298.094 | 1298.874 | 1299.654 | 1300.435 | 1302.776 |
1298.094 | 1298.874 | 1299.654 | 1300.435 | 1302.776 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1302.776 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1303.556 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1303.556 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1304.337 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1304.337 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1305.117 |
1298.094 | 1299.654 | 1299.654 | 1300.435 | 1335.551 |
1298.094 | 1299.654 | 1299.654 | 1301.215 | 1336.331 |
1298.094 | 1299.654 | 1299.654 | 1301.215 | 1866.969 |
1298.094 | 1299.654 | 1299.654 | 1301.215 | 1866.969 |
1298.094 | 1299.654 | 1300.435 | 1301.215 | 1868.53 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 1873.212 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 1879.454 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2467.838 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2470.179 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2472.52 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2472.52 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2473.301 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2475.642 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2476.422 |
1298.874 | 1299.654 | 1300.435 | 1301.215 | 2502.174 |
SNR (dB) | MPD | SC | SCTM |
---|---|---|---|
4 | 0.1068 | 0.0102 | 0.0102 |
2 | 1.6490 | 0.0102 | 0.0102 |
0 | 1.6675 | 0.0288 | 0.0102 |
−2 | 1.6880 | 0.0288 | 0.0102 |
−4 | 1.6880 | 0.0492 | 0.0102 |
−6 | 1.7066 | 0.0492 | 0.0102 |
−8 | 1.7456 | 0.0678 | 0.0102 |
−10 | 1.7660 | 0.0883 | 0.0102 |
−12 | 1.8050 | 0.1273 | 0.0102 |
−14 | 1.8440 | 0.1273 | 0.0288 |
−16 | 58.7111 | 58.5160 | 0.0288 |
−18 | 59.9021 | 58.6925 | 0.0492 |
SNR (dB) | MPD | SC | SCTM |
---|---|---|---|
4 | 0.0254 | 0.0102 | 0.0102 |
2 | 0.0367 | 0.0102 | 0.0102 |
0 | 0.0415 | 0.0113 | 0.0102 |
−2 | 0.1757 | 0.0127 | 0.0102 |
−4 | 0.2784 | 0.0134 | 0.0102 |
−6 | 0.3301 | 0.0167 | 0.0102 |
−8 | 0.4655 | 0.0204 | 0.0102 |
−10 | 0.5844 | 0.0215 | 0.0102 |
−12 | 0.5996 | 0.0257 | 0.0102 |
−14 | 0.7645 | 0.0391 | 0.0104 |
−16 | 1.3236 | 0.6343 | 0.0117 |
−18 | 3.1409 | 4.1756 | 0.0182 |
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Abu Bakar, A.; Yii, C.C.; Fern, C.K.; Hou Pin, Y.; Lago, H.; Rohani, M.N.K.H. A Comparison of Double-End Partial Discharge Localization Algorithms in Power Cables. Energies 2023, 16, 1817. https://doi.org/10.3390/en16041817
Abu Bakar A, Yii CC, Fern CK, Hou Pin Y, Lago H, Rohani MNKH. A Comparison of Double-End Partial Discharge Localization Algorithms in Power Cables. Energies. 2023; 16(4):1817. https://doi.org/10.3390/en16041817
Chicago/Turabian StyleAbu Bakar, Asfarina, Chai Chang Yii, Chin Kui Fern, Yoong Hou Pin, Herwansyah Lago, and Mohamad Nur Khairul Hafizi Rohani. 2023. "A Comparison of Double-End Partial Discharge Localization Algorithms in Power Cables" Energies 16, no. 4: 1817. https://doi.org/10.3390/en16041817