On the Battery Recharge Time in a Stochastic Energy Harvesting System

Systems with energy harvesting capability from stochastic sources have been widely studied in the literature. However, the determination of the recharge time of such systems has not received as much attention as it deserves. Here, we examine the recharge time of a battery/super-capacitor when the energy arrival is discrete stochastic. We consider the cases when the energy storage system is modeled as a linear and a nonlinear system. The energy arrival is assumed to be a Poisson process, or more generally, a renewal process; while the energy packet size may assume any distribution with finite mean and variance. We obtain formulas for the distribution and the expected value of the recharge time. Monte-Carlo simulations verify the obtained formulas.