A Hybrid Electrochemical Multi-Particle Model for Li-ion Batteries

Physics-based models have proven to be effective tools for predicting the electrochemical behavior of Li-ion batteries. Among the various physics-based models, the Doyle-Fuller-Newman (DFN) model has emerged as the most widely employed. In response to certain limitations of the DFN model, the multiple particle-Doyle-Fuller-Newman (MP-DFN) model was introduced. The MP-DFN model utilizes multiple electrode particle sizes, addressing internal concentration heterogeneities and more realistically simulate diffusion processes in the electrodes. However, the model requires relatively high computational cost. This work introduces the Padé approximation for the MP-DFN model, resulting in the simplified MP-DFN model, leading to a faster simulation time. However, depending on battery design and operation conditions, this solution shows to have lower accuracy compared to the MP-DFN. To overcome these challenges, this study also introduces a hybrid MP-DFN model. This model uses a novel approach aimed at striking a balance between accuracy and computational speed. The hybrid MP-DFN model integrates both the finite difference method (FDM) and Padé approximation to effectively address the challenges posed by multiple particle sizes within the electrodes. The choice between FDM or the approximations for a specific particle in the electrode is determined by the scaled diffusion length.