A Copula-based battery pack consistency modeling method and its application on the energy utilization efficiency estimation

Abstract The consistency of battery cells directly influences the maximum available energy and the efficiency of the battery pack, and the energy utilization efficiency (EUE) is a key parameter for the balancing of batteries. Therefore, this paper focuses on the consistency modeling and state estimation of battery packs. In this study, a Copula-based battery pack consistency modeling method is developed. The proposed method shows superiority compared with two existing methods, because it can describe the statistical characteristics of the battery consistency parameters, and the dependence structure between parameters. The squared Euclidean distances between the marginal empirical cumulative distribution functions of the test data and that of the proposed model for capacity, resistance, and SOC are 0.029, 0.169, and 0.025, respectively. The errors of the correlation coefficients between the proposed model and the test data are within 0.12. Then the framework of battery pack EUE estimation using the consistency model is proposed. The accuracy of the proposed method is verified based on the test results of a battery pack with 95 cells connected in-series. The EUE estimation error is within 0.6% at various discharge current rates. The EUE estimation results could provide support for the performance evaluation and balancing of battery packs.