Numerically Efficient Algorithm for Solving Pseudo 2-Dimensional Li-Ion Cell Model
Authors: Han Sangwoo 
Published: February 2020

Vehicle electrification is gaining momentum and the number of electric vehicle (EV) lineup from each car manufacturer is expected grow significantly within a few years. In every EV, the battery management system (BMS) plays an important role in providing optimal performance while ensuring safety of each battery pack. Tasks related to battery performance include determining state-of-charge (SOC), state-of-power (SOP), state-of-health (SOH), cell balancing, and battery charging. Safety related functions include making sure cells operate within specified static and dynamic voltage window and temperature range, derating power, detecting faulty cells, and warning the user if necessary. The BMS utilizes an RC circuit model to model a Li-ion cell because of its robustness and low computation cost among other benefits. Because an equivalent circuit model such as the RC model is not a physics-based model, it can never be a prognostic model to predict battery SOH and avoid any safety risk even before it occurs. A physics-based pseudo-2D (P2D) Li-ion cell model, on the other hand, is more capable and versatile. For example, the model can provide Li+ plating potential during fast charging and incorporate various physics-based degradation mechanisms such as evolution of the solid electrolyte interphase (SEI) layer and diffusion-induced mechanical stress. Despite its usefulness, its use in the battery management system (BMS) is limited mainly due to its computational complexity. To avoid the high computation cost associated with a full-order model, many researchers have demonstrated the use of a single particle reduced-order model (SP-ROM) for BMS applications.1-3 One drawback associated with the single particle modeling approach is that it forces to use the average current density in the calculation because only one particle is involved for each electrode domain. The single particle model (SPM) would be appropriate for simulating drive cycles or low current applications where the development of transient current distribution within a cell is insignificant. Under a continuous or high-pulse electrical load, however, the model may fail to predict accurate cell voltage. To address this issue, a multi-particle reduced-order modeling approach is proposed here. In this approach, the charge-transfer reaction kinetics and charge balance governing equations are solved first, and the mass balance governing equations are solved in sequence to minimize computational cost associated with iteratively solving mass balance partial differential equations (PDEs). To solve PDEs, a finite volume method is adopted. The use of the multiple particle modeling approach combined with either linear or nonlinear charge-transfer reaction kinetics enables to closely match cell voltage and current distributions predicted by a full-order model. Moreover, the multi-particle reduced-order model approach maintains computation cost like that of an SPM. The model is validated against a full-order model implemented in COMSOL Multiphysics.

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