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Locating Partial Discharges in Power Transformers with Convolutional Iterative Filtering^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Work

#### 2.1. UHF Data

#### 2.2. General Approach for Locating PD

#### 2.3. Cumulative Energy Method

#### 2.4. Energy Criterion

## 3. Arrival Time

#### 3.1. Thresholding

#### 3.2. Data Spread

#### 3.3. Low-Pass Filter

#### 3.4. Wavelength Comparison

#### 3.5. Noise Cancellation

#### 3.6. Moving Average

#### 3.7. Envelope

#### 3.8. Convolutional Filter

#### 3.9. CIFT

## 4. Localization

#### 4.1. Multilateration

#### 4.2. Table Lookup

#### 4.3. Consensus Location: Coping with Uncertainty in Lab-Triggered PDs

## 5. Empirical Validation

#### 5.1. Partial Discharge Localization Methods

#### 5.2. Signal Timing Methods

#### 5.3. Additional Validation Tests with Arbitrary PD Locations

## 6. Conclusions

## 7. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sample raw data from UHF. The horizontal axis is time steps (where each step is 0.4 ns) and the vertical axis shows UHF measurements (in V).

**Figure 2.**Two state-of-the-art timing methods. The horizontal axis is time steps and the vertical axis is energy (in V${}^{2}$).

**Figure 3.**Low-pass filter could remove too much of the signal, an illustration with a series of high SNR (channel 1) data. The horizontal axis is time steps (where each step is 0.4 ns) and the vertical axis shows UHF measurements before and after filtering (in V).

**Figure 4.**Filtered version of channel 4 data (low SNR). These two popular filtering techniques produce similar range of values. The horizontal axis is time steps (where each step is 0.4 ns) and the vertical axis shows UHF measurements processed with different techniques (in V).

**Figure 5.**Envelope of two sample data sets. The horizontal axis is time steps (where each step is 0.4 ns) and the vertical axis shows UHF measurements (blue) along with envelope (red) (in V).

**Figure 6.**Savitzky–Golay (SG) filter works considerably better than low-pass filter. The horizontal axis is time steps (where each step is 0.4 ns) and the vertical axis shows UHF measurements processed with different techniques (in V).

**Figure 7.**A heat map of arrival time to sensor 2 (located at the upper left corner) from a cross section of the FDTD mesh for KE20. The two axes are given in FDTD indices. Note that FDTD cell A is closer to sensor 2 than cell B, but the travel time from cell A is longer (green) than from cell B (blue).

**Figure 10.**Signal arrival time of a simulated PD event in DL23. The horizontal axis is time and the vertical axis is the measured voltage (from FDTD simulation). In all cases, CIFT is able to identify the signal arrival time close to the known start time of 5 ns. In a low SNR case, shown in (

**b**), the arrival time computed by the cumulative energy method is nearly 10 ns later than the actual signal start time, while the error of CIFT is only about 3 ns.

**Figure 11.**Localization results of multilateration on PD1 in KE20. The three axes are three dimensions of space (measured in mm).

**Figure 12.**Localization results from FDTD table lookup on PD1 in KE20. The three axes are three dimensions of space (measured in mm). Many PD signals are determined to be from the same location, and there is no obvious outliers. All computed PD locations are well within the bounding box defined by the 500 mm tolerance.

**Figure 13.**Localization results of cumulative energy are usually more than 300 mm away from the actual PD2 locations. The three axes are three dimensions of space (in mm).

**Figure 14.**Localization results of CIFT are largely within 300 mm from the actual PD2 locations. The three axes are three dimensions of space (in mm).

**Figure 15.**Error distribution (histogram) of PD events from DL23. The horizontal axis is the computed error. Each occurance is from one simulated PD event from a FDTD cell. The average error using CIFT with FDTD is about 340 mm, which is close the FDTD mesh size of 300 mm and smaller than other methods tested. All methods have some cases with large errors that require further investigation.

Localization Method | PD | Outliers | Accuracy | Total Hits |
---|---|---|---|---|

Multilateration | PD1 | 2 | 0.4 | 69 |

PD2 | 9 | 0.79 | 196 | |

Table lookup | PD1 | 0 | 1 | 536 |

PD2 | 0 | 1 | 238 |

Timing Method | PD | Outliers | Accuracy | Total Hits |
---|---|---|---|---|

Noise Cancellation | PD1 | 15 | 0 | 52 |

PD2 | 15 | 0 | 30 | |

Wavelength Comparison | PD1 | 13 | 0 | 0 |

PD2 | 12 | 1 | 142 | |

Data Spread | PD1 | 4 | 0.22 | 104 |

PD2 | 13 | 1 | 260 | |

Moving Average | PD1 | 13 | 1 | 206 |

PD2 | 0 | 1 | 216 | |

Threshold w corr | PD1 | 10 | 0.42 | 84 |

PD2 | 2 | 1 | 376 | |

Envelope | PD1 | 10 | 0.92 | 286 |

PD2 | 0 | 0 | 0 | |

Cumulative Energy | PD1 | 0 | 1 | 536 |

PD2 | 0 | 1 | 238 | |

CIFT | PD1 | 0 | 1 | 554 |

PD2 | 0 | 1 | 382 |

Timing Method | PD | Outliers | Accuracy | Total Hits |
---|---|---|---|---|

Cumulative Energy | PD1 | 0 | 0.91 | 292 |

PD2 | 0 | 0.13 | 42 | |

CIFT | PD1 | 0 | 0.95 | 298 |

PD2 | 0 | 0.48 | 154 |

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**MDPI and ACS Style**

Wang, J.; Wu, K.; Sim, A.; Hwangbo, S.
Locating Partial Discharges in Power Transformers with Convolutional Iterative Filtering. *Sensors* **2023**, *23*, 1789.
https://doi.org/10.3390/s23041789

**AMA Style**

Wang J, Wu K, Sim A, Hwangbo S.
Locating Partial Discharges in Power Transformers with Convolutional Iterative Filtering. *Sensors*. 2023; 23(4):1789.
https://doi.org/10.3390/s23041789

**Chicago/Turabian Style**

Wang, Jonathan, Kesheng Wu, Alex Sim, and Seongwook Hwangbo.
2023. "Locating Partial Discharges in Power Transformers with Convolutional Iterative Filtering" *Sensors* 23, no. 4: 1789.
https://doi.org/10.3390/s23041789