Analysis of a Queueing Model for Energy Storage Systems with Self-discharge

This article presents an analysis of a recently proposed queueing system model for energy storage with discharge. Even without a load, energy storage systems experience a reduction of the stored energy through self-discharge. In some storage technologies, the rate of self-discharge can exceed 50% of the stored energy per day. We consider a queueing model, referred to as leakage queue, where, in addition to an arrival and a service process, there is a leakage process that reduces the buffer content by a factor ɣ ( 0 < ɣ < 1) in each time slot. When the average drift is positive, we discover that the leakage queue operates in one of two regimes, each with distinct characteristics. In one of the regimes, the stored energy always stabilizes at a point that lies below the storage capacity, and the stored energy closely follows a Gaussian distribution. In the other regime, the storage system behaves similar to a conventional finite capacity system. For both regimes, we derive expressions for the probabilities of underflow and overflow. In particular, we develop a new martingale argument to estimate the probability of underflow in the second regime. The methods are validated in a numerical example where the energy supply resembles a wind energy source.