Global sensitivity analysis and uncertainty quantification of Lead-Acid battery

Lead-acid batteries are one of the most important electrochemical energy storage devices which used in variety application due to their lower price, high rate discharge, recycling and deep cycling. But improvement of energy density of Lead-acid battery has become a research concern in nowadays. Improvement of this type of battery has significant dependency on determining of its effective parameters. But the most effective physical properties involved in battery performance and energy density may not be exactly known, possibly because of intrinsic variability which cannot be measured directly in practice. Thus, in the simulation process, some uncertainties are unavoidable. Quantification and understanding of these uncertainties are required to evaluate the differences between the actual system behavior and numerical predictions. To this end, in this paper effect of these uncertainties on energy density of Lead-acid battery are quantified and propagated through its governing equations. Finally all the uncertainties roll up to evaluate convenient range of cell voltage. Also a global sensitivity analysis based on Sobol indices is carried out to determine the most effective parameters. Frequently, the uncertain model parameters are denoted by random variables/processes which are known as probabilistic techniques. In this case, traditional methods such as Monte Carlo sampling (MCS) [1] and perturbation-based methods [2,3] is not suitable choice because MCS has low converging rate and perturbation-based methods have restriction on range of variation of the parameters of interest. In this paper, stochastic spectral methods [1,2] based on polynomial chaos (PC) expansions [1] are chosen because it can be implemented without any limitation. Moreover this method has higher rate of converging and accuracy [1]. In the present study, the coefficients of PC-expansion are calculated non-intrusively. Non-intrusive methods depend on individual 203 realizations to recognize the stochastic model reaction to random inputs. Despite of intrusive methods, non-intrusive methods have less computational effort and easily can be implemented in complex physics such as lead-acid batteries. Lead-acid battery is simulated using finite volume method. Results agree well respect to previous studies at different discharge rates. The numerical results show that the proposed UQ method can accurately compute the variability in the output quantity of interest such as cell voltage and energy density. The obtained numerical results can be used to design more efficient batteries.