# Fault Location Method of Multi-Terminal Transmission Line Based on Fault Branch Judgment Matrix

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## Abstract

**:**

## 1. Introduction

## 2. Improved Double-Ended Traveling Wave Localization Method Based on Line Mode Component

#### 2.1. Decoupling of Three-Phase Transmission Lines

#### 2.2. Main Errors of Double-Ended Traveling Wave Ranging

- Traveling wave velocity: In actual working conditions, the transmission line environment affects line parameters, making it difficult to determine the wave speed. Therefore, wave speed cannot be accurately calculated in practical applications, leading to large-ranging errors.
- Wave head capture accuracy: First arrival time of fault traveling wave at both ends of the line is a primary factor affecting the positioning accuracy. The error mainly consists of the synchronization error of the sampling clock and the extraction error of the faulty traveling wave head.
- Arc sag, ambient temperature, load current, and other factors on the line length.

#### 2.3. Improved Double-Ended Traveling Wave Ranging Method Based on the Line Mode Component

## 3. Traveling Wave Head Detection Algorithm Based on CEEMDAN-TEO

#### 3.1. Selection of IMFs

#### 3.2. Demodulation of TEO

#### 3.3. Simulation Verification

#### 3.4. Algorithm Adaptation Analysis

#### 3.4.1. Different Transition Resistance

#### 3.4.2. Different Fault Types

## 4. Research on Multi-Branch Line Fault Ranging Technology Based on Fault Branch Judgment Matrix

#### 4.1. T-Type Transmission Line Fault Branch Judgment Method

#### 4.1.1. Fault Occurred on The Branch Line

#### 4.1.2. T-Node Failure

#### 4.2. Multi-Terminal Transmission Line Fault Location Method

#### 4.2.1. Branch Line Failure

#### 4.2.2. T-Node Failure

#### 4.2.3. T-T Inter-Node Failure

#### 4.3. Fault Distance Calculation

#### 4.4. Simulation Verification

#### 4.4.1. Branch Line Failure

#### 4.4.2. T-Node Failure

#### 4.4.3. T-T Failure

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**The comparative experimental results of this paper and Raphael et al. [19].

Transition Resistance /Ω | In This Paper Positioning Results/km | Positioning Error/m | Relative Error/% | Reference [19] Positioning Results/km | Positioning Error/m | Relative Error/% |
---|---|---|---|---|---|---|

0 | 49.921 | 79 | 0.158 | 49.837 | 163 | 0.326 |

10 | 49.912 | 88 | 0.176 | 50.198 | 198 | 0.396 |

50 | 50.096 | 96 | 0.192 | 50.241 | 241 | 0.482 |

200 | 50.111 | 111 | 0.222 | 49.764 | 236 | 0.472 |

500 | 49.846 | 154 | 0.308 | 49.743 | 257 | 0.514 |

1000 | 49.824 | 176 | 0.352 | 50.346 | 346 | 0.692 |

2000 | 50.251 | 251 | 0.502 | 50.428 | 428 | 0.856 |

Fault Type | In This Paper Positioning Results/km | Positioning Error/m | Relative Error/% | Reference [19] Positioning Results/km | Positioning Error/m | Relative Error/% |
---|---|---|---|---|---|---|

Ag | 80.124 | 124 | 0.155 | 79.703 | 297 | 0.371 |

AB | 79.824 | 176 | 0.220 | 80.367 | 367 | 0.459 |

BC | 80.192 | 192 | 0.240 | 80.344 | 344 | 0.430 |

ABg | 80.137 | 137 | 0.171 | 79.641 | 359 | 0.449 |

BCg | 79.845 | 155 | 0.194 | 79.639 | 361 | 0.451 |

ABC | 80.131 | 131 | 0.163 | 80.369 | 369 | 0.461 |

Line Parameters | r/(Ω/km) | r/(Ω/km) | g/(S/km) |
---|---|---|---|

Positive sequence parameters | 0.035 | 0.43 | 1 × 10^{−7} |

Zero sequence parameters | 0.3 | 1.21 | 1 × 10^{−7} |

Measurement Point Name | M_{1} | N_{1} | N_{2} | N_{3} | M_{2} |
---|---|---|---|---|---|

α-mode | 1120 | 1437 | 1273 | 276 | 1405 |

β-mode | 1023 | 1356 | 1103 | 291 | 1312 |

**Table 5.**Sampling numbers that the initial wave arrives at each measurement when the fault occurs on a T node.

Measurement Point Name | M_{1} | N_{1} | N_{2} | N_{3} | M_{2} |
---|---|---|---|---|---|

α-mode | 720 | 1054 | 903 | 710 | 1056 |

β-mode | 687 | 984 | 921 | 690 | 1145 |

**Table 6.**Sampling numbers that the initial wave arrives at each measurement when the fault occurs on a T node.

Measurement Point Name | M_{1} | N_{1} | N_{2} | N_{3} | M_{2} |
---|---|---|---|---|---|

α-mode | 864 | 956 | 1047 | 1123 | 1187 |

β-mode | 793 | 902 | 1103 | 1082 | 1097 |

**Table 7.**The results of the method presented in this paper are obtained under different experimental conditions.

Fault Point | Fault Type | Beginning | Actual Failure Distance/km | Calculation of Faults Distance/km | Positioning Error/m |
---|---|---|---|---|---|

N2-T2 | Bg | N2 | 40 | 40.134 | 134 |

ABg | N2 | 40 | 40.087 | 87 | |

BC | N2 | 40 | 39.921 | 79 | |

ABC | N2 | 40 | 40.104 | 104 | |

T2 node | Bg | N2 | 100 | 100.094 | 94 |

ABg | N2 | 100 | 99.961 | 39 | |

BC | N2 | 100 | 100.145 | 145 | |

ABC | N2 | 100 | 100.109 | 109 | |

T1-T2 | Bg | N2 | 110 | 110.036 | 36 |

1 | ABg | N2 | 110 | 110.127 | 127 |

BC | N2 | 110 | 109.934 | 66 | |

ABC | N2 | 110 | 109.947 | 53 |

**Table 8.**The results of reference [20] under different experimental conditions.

Fault Point | Fault Type | Beginning | Actual Failure Distance/km | Calculation of Faults Distance/km | Positioning Error/m |
---|---|---|---|---|---|

N2-T2 | Bg | N2 | 40 | 40.376 | 376 |

ABg | N2 | 40 | 40.341 | 341 | |

BC | N2 | 40 | 39.795 | 205 | |

ABC | N2 | 40 | 40.267 | 267 | |

T2 node | Bg | N2 | 100 | 100.401 | 401 |

ABg | N2 | 100 | 99.654 | 346 | |

BC | N2 | 100 | 100.317 | 317 | |

ABC | N2 | 100 | 100.397 | 397 | |

T1-T2 | Bg | N2 | 110 | 110.295 | 295 |

1 | ABg | N2 | 110 | 110.364 | 364 |

BC | N2 | 110 | 109.629 | 371 | |

ABC | N2 | 110 | 109.713 | 287 |

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## Share and Cite

**MDPI and ACS Style**

Yang, Y.; Zhang, Q.; Wang, M.; Wang, X.; Qi, E.
Fault Location Method of Multi-Terminal Transmission Line Based on Fault Branch Judgment Matrix. *Appl. Sci.* **2023**, *13*, 1174.
https://doi.org/10.3390/app13021174

**AMA Style**

Yang Y, Zhang Q, Wang M, Wang X, Qi E.
Fault Location Method of Multi-Terminal Transmission Line Based on Fault Branch Judgment Matrix. *Applied Sciences*. 2023; 13(2):1174.
https://doi.org/10.3390/app13021174

**Chicago/Turabian Style**

Yang, Yongsheng, Qi Zhang, Minzhen Wang, Xinheng Wang, and Entie Qi.
2023. "Fault Location Method of Multi-Terminal Transmission Line Based on Fault Branch Judgment Matrix" *Applied Sciences* 13, no. 2: 1174.
https://doi.org/10.3390/app13021174