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The purpose of the article is to develop an equation to accurately represent OCV as a function of SoC with reduced computational burden. Dependency of open circuit voltage (OCV) on state of charge (SoC) is often represented by either a look-up table or an equation developed by regression analysis. The accuracy is increased by either a larger data set for the look-up table or using a higher order equation for the regression analysis. Both of them increase the memory requirement in the controller. In this paper, Gaussian exponential regression methodology is proposed to represent OCV and SoC relationships accurately, with reduced memory requirement.

Incremental OCV test under constant temperature provides a data set of OCV and SoC. This data set is subjected to polynomial, Gaussian and the proposed Gaussian exponential equations. The unknown coefficients of these equations are obtained by least residual algorithm and differential evolution–based fitting algorithms for charging, discharging and average OCV.

Root mean square error (RMSE) of the proposed equation for differential evolution–based fitting technique is 35% less than second-order Gaussian and 74% less than a fifth-order polynomial equation for average OCV with a 16.66% reduction in number of coefficients, thereby reducing memory requirement.

The knee structure in the OCV and SoC relationship is accurately represented by Gaussian first-order equation, and the exponential equation can accurately describe the linear relation. Therefore, this paper proposes a Gaussian exponential equation that accurately represents the OCV as a function of SoC. The results obtained from the proposed regression methodology are compared with the polynomial and Gaussian regression in terms of RMSE, mean average, variance and number of coefficients.