## 4 Conclusions  
In order to globally extract in-depth features from load data with nonlinear patterns and dynamics, a novel model needs to be developed to achieve greater accuracy in load forecasting to ensure the reliable and economic operations of an electric grid. This study proposed a new hybrid model based on VMD and deep TCN-based networks with SAM for STLF. The load data were decomposed into multiple sub-series that were reshaped into a feature matrix, along with external factors. A three-layer 1D-CNN network was used as a deep network to extract in-depth features, thus avoiding the over-fitting and gradient vanishing of the training model. The TCN extracted the long-term temporal dependencies, and LSTM further enhanced the extraction of temporal features. These features were globally adjusted via SAM to obtain important features. The load forecast was eventually obtained from the fully connected layer. The effectiveness and generalization of the proposed model were validated on two real-world datasets, ISO-NE and GEFCom2012. Compared with other benchmarking models, the experimental results demonstrated that the proposed model improved the prediction accuracy by 17% to 71% in terms of the MAPE and 7% to 70% in terms of the RMSE for the ISO-NE dataset, or by 15% to 53% in terms of the MAPE and 12% to 43% in terms of the RMSE for the GEFCom2012 dataset. Moreover, the R\({}^{2}\) of the proposed model achieved up to 99.9% for the ISO-NE dataset and 99.83% for the GEFCom2012 dataset. Therefore, the proposed model can be effective in globally extracting the in-depth features from load data and external factors to obtain greater accuracy for load forecasting. In future research, we would like to further optimize the deep learning techniques to reduce their computational costs and achieve greater prediction accuracies. Moreover, future research could improve the TCN-based models to better adapt to complex time \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Study** & **Year** & **Method** & **Dataset** & **Forecast Horizon** & **MAPE (\%)** & **RMSE (MW)** \\ \hline [PERSON] et al. [31] & 2021 & CNN–TCN & Guangzhou, China & 24 h & 2.39 & 378.29 \\ \hline [PERSON] et al. [32] & 2022 & SAM–TCN & Chongqing, China & 1 h & 5.35 & 52.14 \\ \hline [PERSON] et al. [16] & 2022 & \begin{tabular}{c} EMD–CNN– \\ SAM–LSTM \\ \end{tabular} & ISO-NE & 1 h & 0.75 & 168.19 \\ \hline [PERSON] et al. [57] & 2017 & Parallel CNN–RNN & GEFCom2012 & 1 h & 1.405 & - \\ \hline [PERSON] et al. [58] & 2018 & RH–ANN & GEFCom2012 & 24 h & 4.90 & - \\ \hline [PERSON] et al. [59] & 2016 & Sister model & \begin{tabular}{c} ISO-NE \\ GEFCom2012 \\ \end{tabular} & 1 h & (2.10–5.44) & - \\ \hline Proposed model & - & VCTLA & \
\begin{tabular}{c} ISO-NE \\ GEFCom2012 \\ \end{tabular} & 1 h &
\begin{tabular}{c} 0.47 \\ 0.89 \\ \end{tabular} & 102.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of the proposed model with state-of-the-art models. series, and then apply these models to other areas such as wind speed, photovoltaic power and integrated energy systems. Conceptualization, Q.X. and M.L. ; methodology, Q.X. and M.L. ; software, Q.X. and Y.L. ; validation, C.Z. and S.D. ; formula analysis, M.L. and Q.X. ; writing--original draft preparation, M.L. and Q.X. ; writing--review and editing, M.L. and Y.L. ; data curation, Q.X. and Y.L. ; supervision, C.Z. and S.D. ; funding acquisition, M.L. and S.D. All authors have read and agreed to the published version of the manuscript. This research was supported in part by the National Natural Science Foundation of China under grant 62065012, and in part by the Natural Science Foundation of Jiangxi Province of China under grant 20212 BAB202031, and in part by the Interdisciplinary Innovation Fund of Natural Science, Nanchang University under grant 9167-28220007-YB2111, and in part by the Innovation Fund Designated for Graduate Students of Jiangxi Province of China under grant YC2022-S132. Not applicable.