Short-Term Power Load Forecasting Based on Feature Filtering and Error Compensation under Imbalanced Samples
Abstract
:1. Introduction
- Constructing an error compensation model and using the prediction results of the errors to compensate for the original results can effectively improve the overall prediction accuracy.
- By expanding the minority sample data, the imbalance of the load data is alleviated, and the accuracy of the prediction results in the minority sample area can be effectively improved.
- Improvements to GRU ensure prediction accuracy while simplifying the model’s structure and improving the overall operational efficiency.
2. Data Processing Methods
2.1. Feature Selection Process Based on Kernel Principal Component Analysis
- Standardization of data. Find the kernel matrix K and use the radial basis kernel function to complete the mapping of the original data from data space to feature space.
- The centralized kernel matrix is used to correct the kernel matrix , where is the matrix of with 1/N for each element.
- Calculate the eigenvalues of the matrix The eigenvalues determine the magnitude of the variance. Arrange the eigenvalues in descending order to obtain the arranged eigenvector .
- Schmitt orthogonalization and unitization of the eigenvectors to obtain the master sequence
- Calculate the contribution of each feature value , and select the first t principal components as the retained features if > p, according to the set requirement p.
2.2. Sample Expansion Methods Based on the Synthesis of a Small Number of Probability Distributions
- 1.
- Conducting sample screening
- 2.
- Select a few samples and synthesize
3. Modelling and Improvement of Main Algorithm
3.1. Error Compensation Model
3.2. Optimizing VMD with WOA
3.3. Feature Extraction Using Temporal Convolutional Networks
3.4. Improved Gated Recurrent Unit
4. Results and Discussions
4.1. Experimental Background and Evaluation Indicators
4.2. Feature Filtering Process
4.3. SyMProD-Based Sample Expansion
4.4. Experimental Results and Analysis
4.4.1. Algorithm Vertical Improvement Comparison Experiments
4.4.2. Algorithm Cross-Sectional Comparison Experiments
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Serial Number | Features | Contribution Rate | Whether to Retain (Threshold 0.5) |
---|---|---|---|
1 | Average temperature | 0.854 | Yes |
2 | Humidity | 0.843 | Yes |
3 | Wind speed | 0.732 | Yes |
4 | Date Type | 0.712 | Yes |
5 | Precipitation | 0.665 | Yes |
6 | Illumination | 0.547 | Yes |
7 | Pneumatic pressure | 0.331 | No |
8 | Air visibility | 0.318 | No |
9 | Air density | 0.201 | No |
Main Algorithm Runtime | Total Running Time (Including Time Consumed for Reference Adjustment) | |
---|---|---|
Method 1 | VMD: 16 min GRU: 141 min | 201 min |
Method 2 | VMD: 16 min TCN: 47 min GRU: 101 min | 208 min |
Method 3 | WOA-VMD: 23 min TCN: 69 min IGRU: 77 min | 189 min |
Method 4 | WOA-VMD: 23 min TCN: 71 min IGRU: 94 min | 188 min |
Method in this paper | WOA-VMD: 23 min TCN: 67 min IGRU: 80 min | 170 min |
Appendix B
Appendix C
- Experimental software: Python 3.8; Pycharm 2018
- Experimental environment: PyTorch; Keras; Tensorflow
- Computer configuration:
- CPU: Intel i5 4200U
- GPU: NVIDIA GT740M
- RAM: 16 GB
- Operating system: Windows 10 Professional Edition
- Empirical mode decomposition (EMD)
- Variational mode decomposition (VMD)
- Whale optimization algorithm (WOA)
- Long-short-term-memory (LSTM)
- Gated recurrent unit (GRU)
- Synthetic minority based on probabilistic distribution (SyMProD)
- Kernel principal component analysis (KPCA)
- Mean envelope entropy (MEE)
- Temporal convolutional networks (TCN)
- Mean absolute error (MAE)
- Mean absolute percentage error (MAPE)
- Root mean square error (RMSE)
- Extreme gradient boost (XGBoost)
- Light gradient boost machine (LightGBM)
- Least squares support vector machine (LSSVM)
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Algorithm Used | Algorithm Settings | |
---|---|---|
Method 1 | VMD-GRU algorithm | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
Method 2 | VMD-TCN-GRU algorithm | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
Method 3 | WOA-VMD-TCN-improved GRU algorithm | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
Method 4 | WOA-VMD-TCN-improved GRU algorithm (for minority sample expansion) | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
Method in this paper | WOA-VMD-TCN-improved GRU algorithm (for minority sample expansion and feature screening to construct error compensation models) | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
MAE/kW | MAPE/% | RMSE/kW | |
---|---|---|---|
Method 1 | 263.393 | 4.13 | 417.397 |
Method 2 | 250.305 | 3.87 | 302.359 |
Method 3 | 194.916 | 3.18 | 310.693 |
Method 4 | 108.373 | 1.72 | 177.442 |
Method in this paper | 61.779 | 0.97 | 84.637 |
MAE/kW | MAPE/% | RMSE/kW | |
---|---|---|---|
Method 1 | 599.462 | 8.98 | 936.248 |
Method 2 | 441.105 | 6.61 | 479.568 |
Method 3 | 318.029 | 4.73 | 416.602 |
Method 4 | 128.223 | 1.92 | 297.485 |
Method in this paper | 38.586 | 0.58 | 45.825 |
Algorithm Used | Algorithm-Related Settings | |
---|---|---|
Method 1 | Extreme gradient boost (XGBoost)algorithm | Number of trees: 100 Maximum tree depth: 20 Leaf nodes: 40 |
Method 2 | Light gradient boost machine (LightGBM) algorithm | Number of trees: 100 Maximum tree depth: 20 Leaf nodes: 40 |
Method 3 | Least squares support vector machine (LSSVM) algorithm | Kernel function: RBF Learning rate: 0.01 |
Method 4 | LSTM algorithm | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
Method in this paper | WOA-VMD-TCN-improved GRU algorithm (method in this paper) | Neurons: 128 Activation function: RELU Learning rate: 0.01 Training style: Adam |
MAE/kW | MAPE/% | RMSE/kW | |
---|---|---|---|
Method 1 | 124.053 | 2.53 | 153.771 |
Method 2 | 98.312 | 1.82 | 123.594 |
Method 3 | 94.052 | 1.79 | 119.776 |
Method 4 | 86.351 | 1.57 | 108.573 |
Method in this paper | 50.561 | 0.96 | 67.511 |
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Wan, Z.; Li, H. Short-Term Power Load Forecasting Based on Feature Filtering and Error Compensation under Imbalanced Samples. Energies 2023, 16, 4130. https://doi.org/10.3390/en16104130
Wan Z, Li H. Short-Term Power Load Forecasting Based on Feature Filtering and Error Compensation under Imbalanced Samples. Energies. 2023; 16(10):4130. https://doi.org/10.3390/en16104130
Chicago/Turabian StyleWan, Zheng, and Hui Li. 2023. "Short-Term Power Load Forecasting Based on Feature Filtering and Error Compensation under Imbalanced Samples" Energies 16, no. 10: 4130. https://doi.org/10.3390/en16104130