Comparative Analysis of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling

Electrochemical models provide insights into the battery internal states and have become powerful tools for battery design and management. These models consist of partial differential equations (PDEs) that are solved numerically. In this paper, we compare two spatial discretization methods commonly used to numerically solve the governing PDEs in the context of Lithium ion batteries, namely finite difference method (FDM) and finite volume method (FVM) in terms of model accuracy and mass conservation guarantee. First, we provide the mathematical details to carry out the spatial discretization for both FDM and FVM to solve the battery single particle model (SPM). SPM parameters are identified from experimental data, and sensitivity analysis is conducted to study parameter identifiability under different current input profiles, followed by model accuracy and mass conservation analysis of the two numerical schemes. Leveraging the third order Hermite extrapolation approach, an enhanced FVM scheme is proposed in this paper to improve the model accuracy of standard FVM which relies on linear extrapolation. This paper shows that the FVM scheme with Hermite extrapolation leads to accurate and robust control-oriented battery model while guaranteeing mass conservation and high accuracy.