Multidimensional Statistical Model of Relationships Between Battery Cell-to-Cell and Pack Variations Considering Parametric Correlation

Cell-to-cell variations of Li-ion batteries directly weaken the pack performance, which is mainly reflected in the variations of pack capacity and resistance. Pack capacity-resistance statistics can quantify these pack variations. However, various cell distributions pose tremendous difficulties in obtaining pack statistics. Moreover, the pack parameter correlations are important elements of multidimensional pack statistics, but there is a lack of effective methods to obtain them. This study first innovatively quantifies irregular cell 2-D distributions by the Gaussian mixture model. Then, the 2-D pack statistical models for any pack configurations are groundbreakingly developed through theoretical derivations. Based on these models, the capacity-resistance 2-D distribution of numerous packs, including their parameter correlation coefficients, can be obtained quickly and accurately. These models also consider different pack equalizations and are verified through Monte Carlo simulation. The errors of these models are less than 1% for most of the module statistics over the range of 100 series and parallel cell numbers. The results show that the capacity-resistance distributions of parallel modules and actively equalized series modules are close to the 2-D Gauss distribution although the cell parameter distribution is irregular. The capacity-resistance correlation coefficients of parallel modules and actively equalized series modules are the same as those of cells. The series–parallel packs inherit the module distribution characteristics. It has significant applications for pack configuration optimization, pack capacity rapid estimation, and equalization selection.