A statistical model of cell-to-cell variation in Li-ion batteries for system-level design

Due to manufacturing tolerances, different battery cells exhibit substantial variability among them, which should be carefully assessed and managed, especially when assembling large battery packs. Cell-to-cell variability has been mostly approached from the point of view of the chemical and physical phenomena, but these studies did not provide a practical solution for the system-level design. In this work, we propose a combined cell-to-cell variation model of the capacity and of the internal resistance of a battery cell that accounts for variability effects in the cell manufacturing process. The model is derived from analytical models for a specific type of Li-ion cell provided in the literature, from which we identify what model parameters can be regarded as true random variables. This allows transforming capacity and internal resistance into the functions of random variables, which can be incorporated into an equivalent circuit model that is suitable for the system-level statistical simulations. The proposed model allows us to qualitatively verify some known properties such as the correlation between capacity and internal resistance, and quantitatively assess the amount of variability and its impact on the design of battery packs.