Enhanced Battery State Estimation: Part 1 - Electrolyte Lithium-ion Concentration Observer

This paper introduces backstepping closed-loop observers designed to estimate the concentration of lithium ions in the electrolyte within the negative electrode, positive electrode, and separator. The battery model employed is the Single Particle Model with electrolyte (SPMe) dynamics. Partial Differential Equation (PDE) backstepping observers are proposed to estimate electrolyte lithium concentration in the negative and positive electrodes, followed by a separator observer based on these results. The electrolyte lithium concentration observers for the positive and negative electrodes require the concentration at the boundaries. As direct measurement of this concentration is challenging, an alternative measurable parameter will be identified for indirect calculation. While Part 1 of this study operates independently, Part 2 complements it by conducting reverse sensitivity analysis to determine the most appropriate measurable parameter. The convergence of the estimation error for the designed observers is ensured through Lyapunov stability analysis. A simulation on a LiFePO4 battery cell under an Urban Dynamometer Driving Schedule (UDDS) current profile is included to confirm the theoretical aspects and the convergence of the state estimation error.