Hybrid VMD–LSTM–transformer model with Bayesian optimization for electricity load forecasting

Electricity load forecasting constitutes a critical component in optimizing energy resource allocation and grid management. However, the proliferation of flexible load integration has increased temporal volatility, seasonal variations, and non-linear dynamics within electricity consumption patterns, substantially limiting the predictive capabilities of contemporary deep learning models. To address this challenge, this study proposes a hybrid model integrating Variational Mode Decomposition (VMD), the Transformer mechanism, and Bayesian Optimization (BO) for enhanced electricity load forecasting. In the proposed model, electricity load data are first decomposed into intrinsic mode functions through VMD. Then, these decomposed components are processed using Long Short-Term Memory (LSTM) network, with Transformer architecture employed to provide the attention mechanism for enhanced temporal feature extraction. In addition, the parameters of the prediction model are optimized using the BO algorithm. Finally, the proposed model’s performance is evaluated using established statistical metrics including Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and R 2 . Moreover, comprehensive comparative analyses are carried out against baseline models as well as versions integrated with VMD, Transformer, and BO. Upon examining the results, it was observed that the proposed hybrid model achieved the lowest error rates among all models, with MAE 544.12, RMSE 788.80, and R 2 0.9828. These findings demonstrate the efficacy of the proposed model managing the inherent complexities of electricity load time series, thereby validating the strategic integration of decomposition techniques, recurrent networks, and attention mechanisms for robust forecasting performance.