Observability and State Estimation Accuracy Analysis of LiFePO\(_4\) Batteries with Hysteresis Model
摘要
Lithium iron phosphate (LFP) batteries provide high stability but present significant challenges for state of charge (SOC) estimation due to their flat open-circuit voltage (OCV) characteristics. Traditional equivalent circuit models (ECMs) often suffer from rank deficiency in the observability matrix within these regions. This study analyzes and proves how voltage hysteresis contributes to SOC observability via non-linear state coupling. Through the formulation of a non-linear ECM that couples hysteresis dynamics with SOC, the system’s observability rank is derived using Lie derivatives. The inclusion of hysteresis eliminates rank deficiency, maintaining local observability even in the flat OCV region. Experimental validation using an Extended Kalman Filter (EKF) with 230 Ah LFP cells under a UDDS profile confirms that the hysteresis-based model offers superior SOC estimation performance and aligns with theoretical predictions. This research establishes a solid theoretical framework for utilizing hysteresis as a robust solution to observability issues in LFP battery systems.