A Comparative Study of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling

Lithium-ion battery (LIB) with high specific energy density and long cycle life is one widely used energy storage technology. In order to ensure longevity and safety of the battery system, a battery management system (BMS) that relies on battery model is required. With the development of BMS technique, more attention has been given to electrochemical models that provide insights into the battery internal states. In general, battery electrochemical models consist of partial differential equations (PDEs) describing the thermodynamic and electrochemical process inside the cell, and those PDEs can only be solved numerically due to their complexity. Existing battery simulation software utilize numerical methods such as finite difference method (FDM), finite volume method (FVM), and finite element method (FEM) to solve PDEs in battery models. However, there are little discussions for the selection of a specific numerical methods. In our recent study 1, we compare two spatial discretization methods commonly used to numerically solve the governing PDEs of LIB electrochemical models, namely FDM and FVM, in terms of model accuracy and mass conservation guarantee. First, we provide the mathematical details of the spatial discretization process for both FDM and FVM to solve the battery single particle model (SPM), this result has not been shown in any publication before. Second, we propose a new Hermite extrapolation based FVM scheme leading to higher accuracy when compared to the normally used linear extrapolation based FVM scheme. Then, SPM parameters are identified using experimental data, and a comprehensive parameter sensitivity analysis is conducted under different current input profiles to study parameter identifiability. Finally, model accuracy and mass conservation analysis of the FDM and FVM schemes are presented. Our study shows that the FVM scheme with Hermite extrapolation leads to accurate and robust control-oriented battery model while guaranteeing mass conservation and high accuracy. Also, the proposed new FVM scheme can be extended to solve other battery models, such as SPM model with electrolyte and Doyle-Fuller-Newman model. Moreover, we provide findings of mass conservation analysis for FDM and FVM schemes, which we hope can facilitate BMS model selection. References 1 Xu, L.; Cooper, J.; Allam, A.; Onori, S., "Comparative Analysis of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling," Journal of The Electrochemical Society, 2023. 10.1149/1945-7111/ad1293