A fuzzy extended PI observer for state of charge estimation of LiFePO₄ batteries across broad temperature ranges

Accurate state of charge (SOC) estimation for LiFePO₄ (LFP) batteries across broad temperature ranges is a critical challenge. This study proposes an adaptive fuzzy extended proportional–integral (PI) observer framework to enhance SOC estimation accuracy and robustness under these demanding conditions. First, a temperature-compensated capacity model (TCCM) is proposed to enhance the Ampere-hour (Ah) integral method for better temperature-dependent capacity description, which motivates revised SOC definitions to provide more physically meaningful state representations (SOC_T and SOC_S) across temperatures. Second, to account for the effect of hysteresis on SOC assessment, a temperature-adaptive open-circuit voltage (OCV) tracking model is developed by incorporating the second-order equivalent circuit model (ECM) with temperature-dependent hysteresis compensation. Third, to minimize errors from model uncertainty when fusing the enhanced Ah integral method and OCV tracker, a fuzzy extended PI observer is employed to intelligently adjust its gains based on real-time conditions for adaptive SOC estimation. Experimental validation using demanding dynamic profiles at temperatures from −10 °C to 10 °C demonstrates the framework's effectiveness. The results demonstrate that the proposed framework can accurately provide physically meaningful states across broad temperature ranges, with error of SOC_T consistently below 2.5% across all tested conditions and SOC_S showing end-point errors of 3%, ensuring performance for real-world EV applications.