State estimation for lithium-ion batteries based on electrolyte–electrode PDE observers

Abstract

Accurate information about the states of an electrochemical battery model facilitates a deeper understanding of battery behavior and enables performance enhancement. This paper first proposes backstepping Partial Differential Equation (PDE) observers for lithium concentration in the electrolyte phase within the negative electrode, positive electrode, and separator. Reverse sensitivity analysis is conducted to identify the most suitable measurable parameter for obtaining the electrolyte lithium concentration at the boundaries, which is used in the design of the electrolyte-phase observer. Subsequently, enhanced observers for the solid-phase lithium concentration in the negative and positive electrodes are developed. The proposed solid-phase observer enables more accurate State-of-Charge (SoC) estimation by leveraging the closed-loop electrolyte-phase observer. Simulations of the reverse sensitivity analysis and state observers are performed on a commercial cylindrical lithium iron phosphate (${\text{LiFePO}}_4$) cell to validate the effectiveness of the proposed approach.