Estimation of lithium-ion concentrations in both electrodes of a lithium-ion battery cell

For control and estimation tasks in battery management systems, the benchmark Li-ion cell electrochemical pseudotwo- dimensional (P2D) model is often reduced to the Single Particle Model (SPM). The original SPM consists of two electrodes approximated as spherical particles with spatially distributed Li-ion concentration. However, the Li-ion concentration states in these two-electrode models are known to be weakly observable from the voltage output. This has led to the prevalent use of reduced models in literature that generally approximate Li-ion concentration states in one electrode as an algebraic function of that in the other electrode. In this paper, we remove such approximations and show that the addition of the thermal model to the electrochemical SPM essentially leads to observability of the Li-ion concentration states in both electrodes from voltage and temperature measurements. Then, we propose an estimation scheme based on this SPM coupled with lumped thermal dynamics that estimates the Li-ion concentrations in both electrodes. Moreover, these Li-ion concentration estimates also enable the estimation of the cell capacity. The estimation scheme consists of a sliding mode observer cascaded with an Unscented Kalman filter (UKF). Simulation studies are included to show the effectiveness of the proposed scheme.