Physics-informed equivalent circuit modeling of solid diffusion polarization for low-temperature state of charge estimation in lithium-ion batteries

Accurate state of charge (SOC) estimation is critical for fully utilizing the capacity of lithium-ion batteries (LIBs) in smartphones and preventing unexpected shutdowns. However, sluggish solid-phase diffusion and intensified polarization at low temperatures cause voltage responses to differ from those at room temperature, leading to large SOC estimation errors when using conventional equivalent circuit models (ECMs). To address these limitations, based on the solid-phase diffusion mechanism, this study systematically analyzes the differences in constant-current discharge behavior at low versus room temperatures, and reveals the respective failure mechanisms of conventional ECMs in the high SOC region and the end of discharge (EOD) region. Building on these findings, an improved ECM is proposed, comprising a physically interpretable Voigt element that accurately captures solid-phase diffusion kinetics, and an adaptive resistor R_EOD that accurately captures the sharp increase in solid-phase diffusion polarization and the corresponding steep voltage drop in the EOD region. Moreover, the parameters of the improved ECM evolve dynamically with temperature and SOC, enabling the model to accurately reflect electrochemical dynamics at low temperatures. Experimental results show that, at −10 °C, an extended Kalman filter based on the improved ECM rapidly corrects initial SOC errors of up to 10% across four dynamic profiles used in smartphones, achieving root mean square error below 2%. The improved ECM helps enhance SOC estimation accuracy, robustness, and interpretability with low computational cost, offering strong potential for smartphone battery management systems.