# Short-Term Power Load Forecasting Based on an EPT-VMD-TCN-TPA Model
## 4 Experiments
### Classic Experiments  
To verify the accuracy of the prediction model proposed in this paper, we compared SVR, LSTM, CNN-LSTM, LSTM-Attention, BiLSTM, and the EPT-VMD-TCN-TPA prediction model in this paper. We will illustrate that our proposed prediction models are more accurate by the evaluation metrics of the prediction results. These comparative models are related as follows:  
1. SVR prediction model: Support vector regression prediction model. 2. LSTM prediction model [(23)]: A typical recurrent neural network with memory function and gate structure, which can effectively solve the problem of gradient disappearance and gradient explosion due to excessive sequence length in RNN models. 3. CNN-LSTM prediction model [(50)]: By combining CNN and LSTM models, it enables the model to extract features inside the data through the convolution operation of the CNN, while using LSTM models to predict changes in the time series. 4. LSTM-Attention prediction model [(22)]: This model introduces the attention mechanism based on the LSTM model. The attention mechanism assigns more weight to important features, thus strengthening the connection between the whole and the local, and improving the prediction accuracy. 5. BiLSTM prediction model [(25)]: This model is improved on the basis of the LSTM model. Both forward and backward sequence information inputs are available to fully extract the information from the load data. 6. EPT-VMD-TCN-TPA prediction model: Our proposed final model. 7. The prediction effects of the EPT-VMD-TCN-TPA model and the above comparison model on the test set are shown in Figure 19 (only one day is shown), and the prediction error evaluation index data and fit effect data for each model are shown in Table 10.  
As can be seen in Table 10, our proposed EPT-VMD-TCN-TPA model has the lowest MAPE, RMSE, and MAE compared to other comparative models, with 1.25%, 110.2692 MW, and 82.3180 MW, respectively, and the largest fitting index R\({}^{2}\) of 0.9955. It is thus clear that the EPT-VMD-TCN-TPA model can predict the load accurately. Compared with the common LSTM model, the MAPE, RMSE, and MAE of the EPT-VMD-TCN-TPA model are reduced by 64.08%, 65.60%, and 62.96%, respectively, which indicates that the EPT-VMD-TCN-TPA model has a high prediction accuracy. As can be seen in Figure 19, the EPT-VMD-TCN-TPA model has the best prediction effect and the best accuracy for the wave and trough prediction results. Of course, the running time of the EPT-VMD-TCN-TPA model is still the longest, but with the upgrade of hardware devices and parallel computing, the model's running efficiency will be improved significantly. The autocorrelation function (ACF) and partial autocorrelation function (PACF) for the final residuals of all the models in Table 10 are shown in Figure 20. It can be seen in Figure 20 that the classical comparative model has an autocorrelation structure, indicating that it does not predict well. In the previous Figure 18i,j, it is known that the EPT-VMD-TCN-TPA model proposed in this paper has been whitened, which further illustrates the best performance of the model in this paper. Figure 20: ACF and PACF plots of SVR (**a**,**b**), LSTM (**c**,**d**), CNN-LSTM (**e**,**f**), LSTM-Attention (**g**. **h**), BiLSTM (**i**,**j**). In order to verify the performance of the models proposed in this paper with the classical comparison models in Table 10, we performed DM tests for each pair of models. The results of the DM tests are listed in Table 11.  
In Table 11, this DM test table (using the MSE metric) uses the original hypothesis H, which proposes that the column and row models have the same effect. The alternative hypothesis H0 proposes that the column and row models have different effects. The experimental results are \(p\)-values outside the parentheses and DM statistics inside the parentheses.