Estimation of Li-ion degradation test sample sizes required to understand cell-to-cell variability

Ageing of lithium-ion batteries results in irreversible reduction in performance. Intrinsic variability between cells, caused by manufacturing differences, occurs at all stages of life and increases with age. Researchers need to know the minimum number of cells they should test to give an accurate representation of population variability, since testing many cells is expensive. In this paper, empirical capacity versus time ageing models were fitted to various degradation datasets assuming that the model parameters could be drawn from a distribution describing a larger population. Using a hierarchical Bayesian approach, we estimated the number of cells required to be tested. Depending on the complexity of the ageing model, models with 1, 2 or 3 parameters respectively required data from at least 9, 11 or 13 cells for a consistent fit. This implies that researchers will need to test at least these numbers of cells at each test point in their experiment to capture manufacturing variability.