Constrained ensemble Kalman filter for distributed electrochemical state estimation of lithium-ion batteries

This article proposes a novel model-based estimator for distributed electrochemical states of lithium-ion (Li-ion) batteries. Through systematic simplifications of a high-order electrochemical-thermal coupled model consisting of partial differential-algebraic equations, a reduced-order battery model is obtained, which features an equivalent circuit form and captures local state dynamics of interest inside the battery. Based on the physics-based equivalent circuit model, a constrained ensemble Kalman filter (EnKF) is pertinently designed to detect internal variables, such as the local concentrations, overpotential, and molar flux. To address slow convergence issues due to weak observability of the battery model, the Li-ion's mass conservation is judiciously considered as a constraint in the estimation algorithm. The estimation performance is comprehensively examined under a wide operating range. It demonstrates that the proposed EnKF-based nonlinear estimator is able to accurately reproduce the physically meaningful state variables at a low computational cost and is significantly superior to its prevalent benchmarks for online applications.