Theoretical Performance Bound and Its Experimental Validation of Battery Capacity Estimates in Rechargeable Batteries

Capacity of a battery is a salient indicator of aging. Accurate estimation of capacity will help in evaluating the state of health (SOH), predicting its remaining useful life (RUL), and in determining a suitable second use application for the retired battery. The existing methods in the literature employ slow discharge, standard C-rate discharge, or curve-based approaches to estimate the battery capacity. A major drawback of these methods is that the quality of the estimate is not known. The Cramer–Rao lower bound (CRLB) defines the theoretical minimum error variance of an unbiased estimator. This article discusses several real-world uncertainties that influence the capacity estimation in batteries. Such uncertainties are taken into consideration in deriving the CRLB for the estimated capacity. Based on the performance analysis of the obtained estimates, approaches are proposed to improve the accuracy of capacity estimation. The derived performance limits help one to choose the method that best fits the quality of capacity estimation in a given application. Experimental data obtained from cylindrical Li-ion battery cells are used to demonstrate the theoretically derived quality of performance reported in this article.