# Fault Location Method of Distribution Network Based on VGAE-GraphSAGE

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## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement

#### 1.2. Main Contributions

#### 1.3. Paper Organization

## 2. The Overall Process of the Distribution Network Fault Location Method

## 3. Selection of Data Input Features of VGAE

## 4. Extract the Hidden Features of Graph Nodes Based on VGAE

Algorithm 1. The Operation Procedure of the VGAE Model Encoding |

Input: $\mathit{A},\mathit{X},\mathit{D},{\mathit{W}}^{\left(\mathbf{0}\right)},{\mathit{W}}_{\mathit{\mu}}^{\left(\mathbf{1}\right)},{\mathit{W}}_{\mathit{\sigma}}^{\left(\mathbf{1}\right)},\mathit{W},\mathit{B}$Output: $\mathit{Z}$ |

1 $\mu ={\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\tilde{A}{\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\left[Relu\left({\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\tilde{A}{\tilde{D}}^{-{\displaystyle \frac{1}{2}}}X{W}^{\left(0\right)}\right)\right]{W}_{\mu}^{\left(1\right)}$ |

2 $\sigma ={\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\tilde{A}{\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\left[Relu\left({\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\tilde{A}{\tilde{D}}^{-{\displaystyle \frac{1}{2}}}X{W}^{\left(0\right)}\right)\right]{W}_{\sigma}^{\left(1\right)}$ |

3 sampled random number $\epsilon ~N\left(0,1\right)$ |

4 $Z=\mu +\sigma \xb7\epsilon $ |

5 $\tilde{A}=\sigma \left(W\ast Z+B\right)$ |

6 return $Z$ |

## 5. Distribution Network Fault Location Based on GraphSAGE

## 6. Analysis of Numerical Examples

#### 6.1. Data Set Introduction and Experimental Environment Construction

#### 6.2. Evaluation Indicators

#### 6.3. Experimental Results and Analysi

#### 6.3.1. Analysis of the Influence of Feature Extraction on the Model Positioning Effect

#### 6.3.2. Effect Comparison of Feature Extraction Methods

#### 6.3.3. Comparison of Similar Models

#### 6.3.4. Analysis of Model Positioning Effect in the Scenario of Distributed Power Access

#### 6.3.5. Noise Experimental Analysis

## 7. Conclusions and Prospect

#### 7.1. Conclusions

#### 7.2. Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Comparison of the F1 score indicator and the loss function results of the VGAE_GraphSAGE model and the GAE_GraphSAGE model. (

**a**) Comparison of the F1 score indicator; (

**b**) Comparison of loss function results.

**Figure 9.**Comparison of model positioning effects. (

**a**) Comparison of model positioning effects with different fault location settings. (

**b**) Comparison of model positioning effects with different settings of single-phase grounding fault resistance.

**Figure 11.**Temperature curve and irradiation curve of solar panels. (

**a**) Temperature curve of solar panels. (

**b**) Irradiation curve of solar panels.

**Figure 12.**Wind speed curve and operation curve of wind power generation. (

**a**) Wind speed curve of wind power generation. (

**b**) Operation curve of wind power generation.

**Figure 14.**F1 score comparison and accuracy comparison of fault location effects of different models in the “dirty sample” scenario. (

**a**) F1 score comparison of fault location effects. (

**b**) Accuracy comparison of fault location effects.

Method | References | Advantage | Disadvantage |
---|---|---|---|

Impedance Method | [1,2,4] | Simple implementation Low cost | Assumes ideal line models Affected by non-ideal line characteristics Limited accuracy in complex networks |

Traveling Wave Method | [5,6] | Mature technology High accuracy in ideal conditions | Increased complexity Affected by network topology |

Signal Injection Method | [7,8] | Real-time monitoring Effective fault detection | High operation and maintenance costs |

Matrix Algorithms | [9,10] | High detection speed Good accuracy | Poor fault tolerance Less effective with distorted signals |

Genetic Algorithms | [11,12] | Global search capability Handles complex optimizations | Requires careful hyperparameter tuning High computational cost with large populations |

Artificial Neural Networks | [13,14,15] | Simulates complex information processing Improved accuracy with hybrid methods | May not fully leverage network topology Effectiveness depends on training data |

Geometric Deep Learning | [16] | Utilizes graph neural networks to capture molecular interactions High accuracy in drug resistance prediction Effective in small datasets | Limited to specific datasets (e.g., HIV drug interactions) High computational complexity in larger datasets |

Graph Neural Networks for Data Science | [17] | Powerful in analyzing complex, interconnected data structures Applicable to multiple scientific disciplines Effective in modeling complex relationships with graph data | Challenges in visualizing and interpreting large-scale graph data Scalability issues with very large datasets |

Proposed Method | Considering equipment interrelationships Improved VGAE resists noise Explores line correlations in depth Adapts to complex real-world scenarios |

Model | Test Sample Size | Accuracy | F1 Score | Test Time (s) |
---|---|---|---|---|

CNN | 9520 | 86.02% | 85.76% | 21.45 |

FC | 9520 | 75.30% | 72.98% | 34.27 |

GCN | 9520 | 90.04% | 89.76% | 12.39 |

GAT | 9520 | 94.19% | 93.78% | 11.76 |

VGAE_GraphSAGE | 9520 | 97.81% | 97.32% | 13.81 |

Distributed Power Supply Settings | Accuracy | F1 Score |
---|---|---|

All are solar photovoltaic power generation | 95.30% | 94.89% |

All are wind power | 93.02% | 91.71% |

All are energy storage power generation | 96.34% | 96.12% |

Hybrid power generation | 95.07% | 94.62% |

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**MDPI and ACS Style**

Fan, M.; Xia, J.; Zhang, H.; Zhang, X.
Fault Location Method of Distribution Network Based on VGAE-GraphSAGE. *Processes* **2024**, *12*, 2179.
https://doi.org/10.3390/pr12102179

**AMA Style**

Fan M, Xia J, Zhang H, Zhang X.
Fault Location Method of Distribution Network Based on VGAE-GraphSAGE. *Processes*. 2024; 12(10):2179.
https://doi.org/10.3390/pr12102179

**Chicago/Turabian Style**

Fan, Min, Jialu Xia, Huanjiao Zhang, and Xi Zhang.
2024. "Fault Location Method of Distribution Network Based on VGAE-GraphSAGE" *Processes* 12, no. 10: 2179.
https://doi.org/10.3390/pr12102179