State of Charge Estimation for Lithium-Ion Batteries Under Wide Temperature Ranges Using Error Feedforward of Sparrow-Optimized Back Propagation Neural Network

Accurate state of charge (SOC) estimation for lithium-ion batteries (LIBs) is essential. To overcome the susceptibility of conventional data-driven models to local optima and terminal divergence under complex conditions, this paper proposes a novel joint estimation algorithm. Using a second-order resistor–capacitor (RC) model, the slime mould algorithm (SMA) identifies parameters offline at temperature chamber setpoints of 0 °C, 25 °C, and 45 °C for a modified extended Kalman filter (MEKF). Subsequently, a backpropagation (BP) neural network optimized by the sparrow search algorithm (SSA) is introduced to perform feedforward compensation for nonlinear residuals, addressing the error accumulation caused by the randomness of initial network weights, collectively constituting the proposed SSA-BP-MEKF algorithm. Validation at 0 °C, 25 °C, and 45 °C under the Dynamic Stress Test (DST), US06, Federal Urban Driving Schedule (FUDS), and Beijing Dynamic Stress Test (BJDST) demonstrates that the maximum absolute error (MaxAE) remains within 2.21% at 25 °C. At 0 °C and 45 °C, the algorithm effectively suppresses the local divergence of conventional BP compensation, restricting the MaxAE for the demanding BJDST cycle to 2.65% and 1.49%, respectively. Ultimately, the proposed approach significantly enhances estimation accuracy and robustness in complex operating environments.