## 1 Introduction
It should be pointed out that one-dimensional (1D) CNNs can overcome the overfitting problem due to there being fewer learnable parameters. Furthermore, the temporal convolutional network (TCN) developed from CNN has a unique dilated convolutional module to obtain a large receptive field with fewer layers [22], which is conducive to extracting nonlinear features of time series. Although the TCN has better predictive performance in time series compared with LSTM and CNN [23; 24], it cannot learn the dependency of long-range positions inside the sequence and extract internal correlations of input. In addition, self-attention mechanism (SAM) focuses on capturing internal correlations of input features and can effectively deal with long time series, which helps the training model to identify key features. For instance, a novel model based on bidirectional LSTM, XGBoost and SAM was proposed for power load forecasting in [25]. An improved LSTM optimized with SAM was used to predict the concentration of air pollutants in [26]. A new model based on SAM and multi-task learning was developed to predict ultra-short-term photovoltaic power generation in [27]. These experimental results mentioned above indicate that SAM has the capability to select key information from complex features and avoid irrelevant information during model training. Although these deep learning methods improve the prediction accuracy, single models cannot fully extract the input features, especially in-depth features. Therefore, scholars are increasingly focusing on hybrid models, which combine the advantages of each single model [28]. For example, a hybrid approach combining singular spectrum analysis-based decomposition and ANN for day-ahead hourly load forecasting was proposed in [29]. A TCN-LSTM hybrid model was used to forecast weather on meteorological data in [30]. A day-ahead load forecasting model based on CNN and TCN was conducted to achieve superior performance in [31]. A hybrid model based on TCN combined with attention mechanism was proposed to fully exploit the nonlinear relationships between load data and external factors in [32]. Although the above hybrid models improved the prediction performances in various aspects, the raw load data were directly fed into the training models without being smoothed and denoised in advance, which cannot be conducive to further enhancing the accuracy of STLF. In order to avoid the effects of nonlinear patterns and dynamics of load data on the forecasting accuracy, decomposition methods have been used to decompose the load data into multiple smoothing and stable sub-series at different frequency bands. For instance, [PERSON] et al. [33] decomposed the load data into a series of sub-signals using wavelet decomposition (WD). The sub-signals were predicted by different models according to their frequencies. [PERSON] et al. [34] used empirical mode decomposition (EMD) to decompose load signals into multiple intrinsic mode functions (IMFs) to weaken the nonlinearity and dynamics of the load data. [PERSON] et al. [35] proposed a hybrid model for carbon price forecasting based on EMD and evolutionary least squares to support vector regression. An ensemble empirical mode decomposition (EEMD) was used to decompose load data into different frequency components in [36]. The low- and high-frequency components were predicted via multivariable linear regression LSTM. However, WD cannot meet the requirements of complex and dynamic load series in time-frequency analysis [33]. In addition, EMD and EEMD have the disadvantages of mode aliasing and end effect, and lack the support of mathematical theory [37]. Then, a variational mode decomposition (VMD) algorithm with a solid mathematical model was used as an alternative to overcome their drawbacks mentioned above. VMD has good data decomposition accuracy, and obtains a group of stable sub-signals without noise interference [38]. A hybrid model based on VMD and LSTM for short-term load forecasting was proposed in [39].