# Interpretable Detection of Partial Discharge in Power Lines with Deep Learning

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Preprocessing

#### 2.2. Temporal Convolutional Neural Network

#### 2.3. Pulse Activation Maps (PAM)

## 3. Experiments

#### 3.1. Datasets

#### 3.2. Network Architecture and Training

#### 3.3. Threshold Setting

- (i)
- Baseline: Round the output (threshold $th=0.5$).
- (ii)
- ‘1=3’-Phase Classification: Round the prediction of the three phases. If one phase is estimated as damaged, the whole power line (the three phases) is considered as being damaged.
- (iii)
- 1-Phase Optimized Threshold: Infer the threshold $t{h}_{v}$ with cross-validation, and consider each phase independently.
- (iv)
- Proposed 3-Phase Global threshold: Using the threshold $t{h}_{v}$ devised in (iii), apply the 3-Phase Global threshold, ${G}_{t{h}_{v}}=3\xb7t{h}_{v}$, to the sum of the output values for the three phases.

#### 3.4. Evaluation Metrics

## 4. Results

#### 4.1. Results on the Test Dataset

#### 4.2. Ablation Study

## 5. Discussion

#### 5.1. Results Analysis

#### 5.2. Note on the MCC for Imbalanced Datatset

#### 5.3. Pulse Activation Maps (PAM)

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Graphical Abstract: (

**1**) The raw data: three phases over one period. (

**2**) For each phase, the signal is filtered to remove the utility frequency ${f}_{\mathrm{ut}}$. (

**3**) Extracted w samples of pulses identified with a maximum filter. The windows start 1/8th before the identified peak. (

**4**) For each phase, the pulse collection is fed to a deep 1D convolution neural network. (

**5**) The outputs of the three phases are considered together to label the powerline. (

**6**) Thanks to the Global Average Pooling (GAP) Layer, the Pulse Activation Map can be displayed for further diagnostics.

**Figure 2.**MCC: Colormap of the MCC. From colormap to top, $\mathrm{TP}$$=95\%$, MCC, and its derivative as a function of $\mathrm{TN}$. From colormap to right, $\mathrm{TN}$$=95\%$, MCC, and its derivative as a function of $\mathrm{TP}$.

**Figure 3.**PAM: For $\mathrm{TP}$ (3

**upper left**), $\mathrm{FN}$ (2

**upper right**), $\mathrm{TN}$ (3

**lower left**), and $\mathrm{FP}$ (2

**lower right**). The color mapping is symmetric around 0 (white), from dark-blue (strongly negative) to dark-red (strongly positive). Note the the actual values matter little as the decision of the network only depends on whether the map is positive or negative in average.

**Figure 4.**Pulse Activation: Some typical pulses with their activation (same color-map as in Figure 3). Upper row: pulses positively activated. Lower row left, the tail is rather considered as distinctive by the network. Lower row, right, strongly negatively activated pulses (the last one appears to be noise). The Y-axes are independent.

**Table 1.**Results on the test dataset (evaluated online) for our four proposed decision rules and for ${N}_{p}$ set to 200 and 150.

Settings | Kaggle VSB Test Data | |||
---|---|---|---|---|

${\mathit{N}}_{\mathit{p}}=\mathbf{150}$, $\mathit{w}=\mathbf{40}$ | ${\mathit{N}}_{\mathit{p}}=\mathbf{200}$, $\mathit{w}=\mathbf{40}$ | |||

MCC Private | Rank * | MCC Private | Rank * | |

(i) Baseline | 0.580 | 1054 | 0.629 | 272 |

(ii) ‘1 = 3’ | 0.656 | 118 | 0.704 | 4 |

(iii) 1-Phase Opt. | 0.631 | 245 | 0.658 | 65 |

(iv) 3-Phase (our) | 0.665 | 46 | 0.704 | 4 |

**Table 2.**Ablation study and impact of the decision rules on the proposed model with ${N}_{p}=200$ and $w=40$.

Methods | MCC | Acc. | Precision | Recall | |
---|---|---|---|---|---|

(1) | (i) Baseline | 0.710 | 0.959 | 0.772 | 0.695 |

(ii) ‘1 = 3’ | 0.802 | 0.963 | 0.687 | 0.979 | |

(iii) 1-Phase Opt. | 0.727 | 0.953 | 0.669 | 0.844 | |

(iv) 3-Phase (our) | 0.817 | 0.967 | 0.726 | 0.957 | |

(2) | w/o $GAP$-(i) | 0.583 | 0.944 | 0.712 | 0.525 |

w/o $GAP$-(ii) | 0.722 | 0.952 | 0.656 | 0.851 | |

w/o $GAP$-(iii) | 0.598 | 0.945 | 0.709 | 0.553 | |

w/o $GAP$-(iv) | 0.616 | 0.955 | 0.683 | 0.610 | |

(3) | w/o $FC$-(i) | 0.643 | 0.952 | 0.784 | 0.567 |

w/o $FC$-(ii) | 0.751 | 0.959 | 0.702 | 0.851 | |

w/o $FC$-(iii) | 0.701 | 0.954 | 0.700 | 0.745 | |

w/o $FC$-(iv) | 0.775 | 0.966 | 0.772 | 0.816 | |

(STL + SVM) ${}^{\u2020}$ | 0.779 ${}^{\u25b9}$ | 0.963 ${}^{\u25b9}$ | 0.73 ${}^{\u25b9}$/0.68 * | 0.88 * | |

(LSTM) ${}^{\u2020\phantom{\rule{-1.42262pt}{0ex}}\u2020}$ | 0.344 ${}^{\u25b9}$ | 0.765 ${}^{\u25b9}$ | 0.23 ${}^{\u25b9}$/0.79 * | 0.81 * |

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**MDPI and ACS Style**

Michau, G.; Hsu, C.-C.; Fink, O. Interpretable Detection of Partial Discharge in Power Lines with Deep Learning. *Sensors* **2021**, *21*, 2154.
https://doi.org/10.3390/s21062154

**AMA Style**

Michau G, Hsu C-C, Fink O. Interpretable Detection of Partial Discharge in Power Lines with Deep Learning. *Sensors*. 2021; 21(6):2154.
https://doi.org/10.3390/s21062154

**Chicago/Turabian Style**

Michau, Gabriel, Chi-Ching Hsu, and Olga Fink. 2021. "Interpretable Detection of Partial Discharge in Power Lines with Deep Learning" *Sensors* 21, no. 6: 2154.
https://doi.org/10.3390/s21062154