State estimation for enhanced low dimensional electrochemical models of lithium-ion batteries

Safe and efficient operation of lithium-ion batteries requires an accurate estimation of the internal states. One approach is to design an observer based on an electrochemical model of the battery internal dynamics. However, electrochemical models, and their associated observers, typically require a high dimension to generate accurate variables. In this paper, we explain how to alleviate this limitation by correcting the lithium concentrations generated by a finite-dimensional electrochemical model derived from the spatial discretizations of partial differential equations (PDE). We show that the corrected concentrations asymptotically match those generated by the original PDEs for constant input currents, irrespectively of the order of the considered finite-dimensional model. We then exploit this fact to derive a new state space model for which we design an observer, whose global, robust convergence is supported by a Lyapunov analysis provided a linear matrix inequality holds. The estimated concentrations are then corrected to asymptotically match those of the original PDEs in absence of disturbances for constant currents. Simulation results show improvements both in terms of modeling and estimation accuracy as a result of the proposed corrections.