Modeling and bayes estimation of battery lifetime for smart grids under an Inverse Gaussian model

An efficient use of many power systems, from smart grids to mobile devices, requires a careful assessment of the lifetime of the employed batteries. In this paper, a stochastic method for estimating the probability distributions of the battery lifetime is illustrated, which is in particular focused on smart grid applications. The method is based upon a Poisson random process for describing the current load, as motivated by the intermittent supply capability of renewable resources, and uses an advanced battery model, with a proper stochastic input, for deducing the battery lifetime. Extensive numerical experiments performed by means of such battery model and laboratory tests have shown that the best fitting reliability model of a generic battery is the Inverse Gaussian model. This model is thoroughly discussed in the paper and, in order to address the problem of the parameter estimation of such reliability model, a novel practical Bayes approach is proposed, based upon an Inverted Generalized Gamma Distribution. Then, the feasibility and efficiency of such estimation method is illustrated by extensive stochastic simulations. An insight on some key aspects on reliability model identification closes the paper