Lithium-ion batteries SOE estimation via SSA-optimized transformer coupled with extended Kalman filter

State of Energy (SOE) represents one of the most critical state parameters in battery management systems. Due to its inherent nonlinear characteristics, accurate estimation of SOE remains a significant challenge in this domain. This research proposes a novel lithium-ion battery SOE estimation methodology that integrates a Transformer network optimized by sparrow search algorithm (SSA-Transformer) with extended Kalman filter (EKF). The SSA algorithm, characterized by its unique producer-scout mechanism and defensive awareness behavior simulation, exhibits superior performance in global search capability and convergence efficiency. In comparison with the conventional particle swarm optimization (PSO) algorithm, SSA demonstrates enhanced capability to escape local optima and accelerated convergence rates, while simultaneously reducing the complexity of manual parameter tuning. The proposed SSA-Transformer-EKF methodology has been validated under various temperature conditions through neural network (NN) and Urban Dynamometer Driving Schedule (UDDS) operational profiles, with mean absolute error (MAE) and root mean square error (RMSE) constrained within 0.6% and 0.8% respectively, thus achieving high-precision real-time estimation. Relative to traditional Transformer and comparable algorithms, the proposed SSA-Transformer-EKF algorithm exhibits superior SOE prediction performance, with average RMSE and MAE values of 0.518% and 0.422%, respectively. Furthermore, at elevated temperatures of 45 °C, the algorithm maintains robust performance with average RMSE and MAE values of 0.523% and 0.442%, further substantiating that the SSA-Transformer-EKF model possesses exceptional fitting capability and generalization performance across diverse operational conditions.