## 3 Experiments and Results Analysis
### Comparative Analysis of Experimental Results
#### 3.3.1 ISO-NE Dataset  
In order to further elaborate its performance for load forecasting, the proposed model was mainly compared to the hybrid models with VMD decomposition. Tables 2-4 show  
Figure 9: Evolutions in power load in different time horizons for ISO-NE dataset. (**a**) One year, (**b**) one week, (**c**) from 22 to 28 December 2003.  
the maximum, minimum and average values of the MAPE, RMSE and R\({}^{2}\), respectively. Compared with the VCLA, one can find that the VTL reduces the MAPE by 13.6% and the RMSE by 10.4%, due to the large receptive field of TCN. The VCTA model is conducive to the extraction of long-term in-depth features, and improves the performance of load forecasting. For example, the VCTA greatly decreases the MAPE by 48.6% and the RMSE by 48% compared to the VTL. When the VCTA is further stacked with GRU, i.e., VCTGA, one finds that its MAPE and RMSE can further be reduced by 20.8% and 30.8%, respectively. It means that the GRU can enhance the extraction of long-term dependencies. However, the proposed model even outperforms the VCTGA by 17.5% and 7% in terms of the MAPE and RMSE, respectively. This again demonstrates that LSTM has a stronger capability to capture temporal dependencies compared with GRU. Compared with VCTL, one can see that SAM is very important to globally enhance the key features for the proposed model. For example, compared with the VCTL, the proposed model significantly decreases the MAPE by 39% and the RMSE by 49%. Therefore, SAM is extremely important for globally adjusting and retaining key features to improve the superior performance of the proposed model. Additionally, the R\({}^{2}\) of the proposed model increases from 0.04% to 1.02% compared with that of the contrast models and reaches up to 99.9%, which infers that VDM decomposition is indeed effective in improving prediction accuracy, and that the proposed model results can be trusted.  
To further see the deviations between each model and the actual load data, Figure 10 shows the predicted load over 24 h and the actual load data when the MAPE is a maximum and a minimum, respectively. One can find that the VMD-CNN-TCN (VCT)-based hybrid models approximately capture the changing trends in the actual load. However, the VCLA and VTLA models obviously deviate from the actual load. This means that the stacked model based on CNN and TCN plays a critical role in feature extraction for the training model. Similarly, load forecasting during the peak or valley areas is still difficult for the models to accurately predict. However, it can be seen from the subplots that the hybrid model proposed in this article achieves the smallest deviation compared with other VCT-based hybrid models, especially during the turning area. Furthermore, Figure 11 shows bar charts of the RMSE for each model. One can clearly see that the VCTA-based hybrid models are more stable compared with other models, and the proposed model has the best stability among all of these models. At the same time, SAM is also important to improve the stability of the VCT-based models.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **VCLA** & **VTLA** & **VCTA** & **VCTL** & **VCTGA** & **Proposed** \\ \hline Max R\({}^{2}\) (\%) & 99.31 & 99.53 & 99.88 & 99.87 & 99.91 & 99.93 \\ Min R\({}^{2}\) (\%) & 97.90 & 98.27 & 99.51 & 99.32 & 99.80 & 99.87 \\ Average R\({}^{2}\) (\%) & 98.88 & 99.20 & 99.75 & 99.73 & 99.86 & 99.90 \\ \hline