# A Power System Timing Data Recovery Method Based on Improved VMD and Attention Mechanism Bi-Directional CNN-GRU

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## Abstract

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## 1. Introduction

## 2. Power System Time Series Missing Data Recovery Model Structure

- The mode number k in the VMD technique is ascertained via the dual-threshold filtration method. Subsequently, the acquired k value and VMD methodology are employed to disintegrate the time-series data bilaterally, yielding k modal numbers.
- A CNN-GRU forecasting model is erected for each component, incorporating a dual attention mechanism. The input coding assay incorporates a feature attention mechanism to excavate the correlation between the time series data and the corresponding feature quantity. On the other hand, the output coding assay integrates a temporal attention mechanism to unearth the pertinent relationship between temporal data and missing data on time scales.
- The data of each component are superimposed and reconstructed to complete the data recovery results on one side.
- The data on either side of the absent data within the power system possess excellent completeness; hence, both sides of the missing data are individually modeled. Subsequently, the ultimate data restoration outcome is attained by incorporating the data restoration results of one side through adaptive weight allocation. The results are then scrutinized.

## 3. Decomposition of Quantitative Time Series Data Based on Improved VMD

## 4. Dual Attention Model

#### 4.1. CNN-GRU Neural Network

#### 4.2. Attentional Mechanisms

## 5. Example Analysis

#### 5.1. Data Pre-Processing and Error Indicators

#### 5.2. Model Configuration

#### 5.3. Data Set Comparison

#### 5.3.1. Reconstructed Data Length of 32 Sampling Time Points Reconstruction Effect Comparison

#### 5.3.2. Reconstructed Data Length of 128 Sampling Time Points Reconstruction Effect Comparison

#### 5.3.3. Reconstructing Data Error Distribution Analysis

#### 5.3.4. 128 Sample Points Reconstruction Results Compared to 32 Sample Points Reconstruction Results

## 6. Conclusions

- The model in this paper has strong data reconstruction capability, especially for fitting data mutations.
- This model has better performance in long time series data reconstruction compared to other models.
- This model has a more outstanding effect on data reconstruction with drastic changes compared to other models in this paper and has broader application potential.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A3.**Results of reconstructing 128 temporal sampling points of photovoltaic power generation with different models.

Literature | Main Technical Means | Advantage | Disadvantages |
---|---|---|---|

[12] | A new method for detecting bad data in power systems using temporal correlation and statistical consistency of measurements is proposed. The method uses three innovative matrices to capture measurement correlation and statistical consistency, and it applies projection statistics to detect bad data. | The computational requirements are not large, and the data categories with high similarity in the power system can be more effectively detected and reconstructed for bad data. | The reconstruction is less effective for data with high dimensionality and complexity, complex change trends, and difficulty in finding patterns. |

[13] | In the case of a small amount of synchronous phase volume data missing and using a Lagrangian interpolation polynomial approach to adaptively estimate incomplete and missing data. | Fast computation, practical, good for reconstructing data with small amount of 1D data. | The method has a small range and cannot be used once the missing data becomes long or the data are not one-dimensional. |

[14,15,16] | The core idea is to take advantage of the similarity between the data column where the missing data are located and the complete data column and use this similarity to reconstruct the data through further data processing. | The performance is highly correlated with the degree of data similarity, and the deeper the similarity between the data, the better the method refactoring and vice versa. Supported by explicit mathematical principles. | Large differences between data can seriously affect the effectiveness of data reconstruction, and the larger the amount of data, the more patterns in the data and performance degradation. |

[17] | A shallow coder is used to learn the data features and to complement the data by the data structure after the weighting process. | It also has better adaptability for complex data and has a more outstanding reconfiguration effect. | Poor reconfiguration for complex, variable data. |

[18,19] | Ref. [18] learns the features of temporal data through a positive and negative GRU network. Ref. [19] then learn the features of the data using generative adversarial networks. | It also has better adaptability for complex data and has a more outstanding reconfiguration effect. | The mathematical mechanism is not clear. The algorithms take longer to compute and are more demanding on computational resources. |

**Figure A5.**Error results of reconstructing 128 wind power generation time sampling points with different models.

**Figure A6.**Error results of reconstructing 128 photovoltaic power generation time sampling points with different models.

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**Figure 1.**Power system timing data recovery model based on improved VMD and double radial GRU with a triple attention mechanism.

**Figure 7.**Results of reconstructing 32 photovoltaic power time sampling points with different models.

**Figure 9.**Error results of reconstructing 32 wind power generation time sampling points with different models.

**Figure 10.**Error results of reconstructing 32 photovoltaic power generation time sampling points with different models.

Load Data Set | Wind Power Dataset | Photovoltaic Power Dataset | ||
---|---|---|---|---|

Model of this paper | MAE/(e-2) | 1.96 | 5.38 | 4.48 |

MSE/(e-4) | 5.97 | 37.29 | 31 | |

One-sided modeling | MAE/(e-2) | 2.9 | 9.58 | 8.28 |

MSE/(e-4) | 11.6 | 74.06 | 61.7 | |

LSTM | MAE/(e-2) | 2.27 | 8.25 | 6.87 |

MSE/(e-4) | 7.49 | 61.68 | 51.4 | |

CNN | MAE/(e-2) | 2.48 | 8.54 | 7.12 |

MSE/(e-4) | 8.57 | 65.04 | 54.2 | |

Seq2seq | MAE/(e-2) | 2.14 | 7.12 | 5.84 |

MSE/(e-4) | 6.57 | 44.09 | 36.7 | |

MLP | MAE/(e-2) | 2.85 | 8.54 | 7.21 |

MSE/(e-4) | 7.98 | 59.46 | 49.8 |

Model of This Paper | Load Data Set | Wind Power Dataset | Photovoltaic Power Dataset | |
---|---|---|---|---|

MAE/(e-2) | 2.74 | 9.95 | 6.97 | |

One-sided modeling | MSE/(e-4) | 11.14 | 83.53 | 64.48 |

MAE/(e-2) | 4.09 | 16.77 | 13.33 | |

LSTM | MSE/(e-4) | 21.46 | 165.89 | 125.25 |

MAE/(e-2) | 3.28 | 20.54 | 10.85 | |

CNN CNN | MSE/(e-4) | 15.22 | 108.56 | 114.11 |

MAE/(e-2) | 3.59 | 21.26 | 10.96 | |

Seq2seq | MSE/(e-4) | 17.22 | 101.46 | 123.58 |

MAE/(e-2) | 3.08 | 12.67 | 9.46 | |

MLP | MSE/(e-4) | 13.25 | 106.7 | 81.11 |

MAE/(e-2) | 4.29 | 15.79 | 11.82 |

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**MDPI and ACS Style**

Xie, K.; Liu, J.; Liu, Y. A Power System Timing Data Recovery Method Based on Improved VMD and Attention Mechanism Bi-Directional CNN-GRU. *Electronics* **2023**, *12*, 1590.
https://doi.org/10.3390/electronics12071590

**AMA Style**

Xie K, Liu J, Liu Y. A Power System Timing Data Recovery Method Based on Improved VMD and Attention Mechanism Bi-Directional CNN-GRU. *Electronics*. 2023; 12(7):1590.
https://doi.org/10.3390/electronics12071590

**Chicago/Turabian Style**

Xie, Kangmin, Jichun Liu, and Youbo Liu. 2023. "A Power System Timing Data Recovery Method Based on Improved VMD and Attention Mechanism Bi-Directional CNN-GRU" *Electronics* 12, no. 7: 1590.
https://doi.org/10.3390/electronics12071590