State of energy estimation during electric vehicle charging based on hybrid machine learning models

With the rapid growth of electric vehicle (EV) adoption, accurately estimating the energy state of lithium-ion batteries (LIBs) has become a critical task in battery management systems (BMS). The state of energy (SOE), which reflects the available energy, provides more practical value than the traditional state of charge (SOC) in improving charging safety, optimizing energy scheduling, and enhancing user experience. However, SOE estimation during charging remains challenging due to current fluctuations and nonlinear battery dynamics. This study proposes a hybrid SOE estimation framework, named LTGPR, which integrates a long short-term memory (LSTM) network, Transformer, and Gaussian process regression (GPR). In this framework, LSTM captures temporal dependencies, Transformer models global feature interactions, and GPR performs refined regression with uncertainty quantification. This combination leverages the sequence modeling capabilities of deep networks and the generalization robustness of probabilistic models. Extensive experiments conducted on real-world EV charging datasets covering four vehicles and multiple charging intervals demonstrate that the proposed method achieves consistent and superior performance. The mean absolute error (MAE) and root mean square error (RMSE) of the SOE estimation remain below 1%.