Joint estimation of state of charge and state of energy for lithium-ion batteries based on the iTransformer deep learning network

Lithium-ion batteries are the core energy storage devices in electric vehicles. Accurate estimation of the state of charge (SOC) and state of energy (SOE) of lithium-ion batteries is critical to ensure their safe and healthy operation. Most existing methods focus on state estimation under constant temperatures. However, during actual charging and discharging processes, battery temperature continuously fluctuates. To address the challenge of accurately estimating SOC and SOE under varying environmental temperatures (such as high and low temperatures), we propose a deep learning network model based on the Inverted Transformer (iTransformer), named iTransformer-SQL-AdamP. During training, the smoothed quadratic loss (SQL) function is incorporated to dynamically adjust the gradient, reducing noise interference, while the Adaptive Moment Estimation with Projection (AdamP) optimizer is employed to further enhance estimation accuracy. SOC and SOE estimations were conducted under different conditions at − 20 °C, − 10 °C, 0 °C, 10 °C, 25 °C, and 45 °C to validate the model’s efficacy. In the LA92 cycle at 0 °C, the lowest MAE for SOC and SOE were 0.416% and 0.395%, respectively, with R² coefficients approaching 1, demonstrating significant estimation accuracy. The predictive validation results show that the proposed network exhibits strong generalization ability, high estimation accuracy, and robustness. Therefore, this network provides a novel method for joint estimation of battery SOC and SOE across a wide range of temperatures, offering excellent predictive performance.