PDE battery model simplification for SOC and SOH estimator design

Accurate knowledge of the battery state-of-charge (SOC) and state-of-health (SOH) is critical for optimal and safe utilisation of the battery. Although the battery system dynamics contain electrochemical, thermal, electrical, and ageing phenomena, most state estimators resort to equivalent circuit models (ECM). These models are often not accurate and are problematic for SOC estimation during an extended range of operations and do not address SOH dynamics. In this paper, starting from an initial high-fidelity Lithium-ion (Li-ion) battery model consisting of a set of partial differential equations (PDE), a recently proposed framework for PDE battery model simplification is employed and one of these obtained models is used for battery state estimation. Model order reduction techniques are then constructively applied to the simplified PDE battery model and resulted in a computationally efficient ordinary differential equation (ODE) model. Based on this obtained ODE model, an extended Kalman filter (EKF) is designed for the estimation of both SOC and SOH. Simulations over 20 cycles show the designed estimator is capable of simultaneously estimating the battery's SOC in each electrode and SOH.