On Birth–Death Processes of Battery Energy Storage Systems

Abstract

Battery technology is becoming more diverse; sodium-sulfur batteries that can operate at high temperatures and high-energy-density lead-acid or lithium-ion batteries for electric vehicles have been developed. However, these chemical battery types differ in their cycle lives. In this study, a theoretical stochastic process method was used to model the charge–discharge behavior and cycle life of batteries to increase the efficiency of battery storage systems. The developed modeling methodology represents the charging and discharging behavior of a battery using the birth and death rates of the birth–death process. However, the countable state space of the birth–death process generally cannot be used for a continuous representation of remaining energy. Hence, a Markov kernel was used to construct a positive real representation system for the remaining energy in a battery.