Analysis of the Leakage Queue: A Queueing Model for Energy Storage Systems with Self-discharge

TL;DR

This paper models energy storage with self-discharge as a queueing system, revealing two operational regimes and providing methods to compute overflow and underflow probabilities, with applications to renewable energy sources.

Contribution

It introduces the leakage queue model for energy storage with self-discharge and analyzes its regimes and probabilistic behavior, a novel approach in this context.

Findings

Stored energy stabilizes below capacity in leakage-dominated regime

Stored energy distribution approximates a normal distribution under certain assumptions

Two methods for calculating overflow and underflow probabilities are validated

Abstract

Energy storage is a crucial component of the smart grid, since it provides the ability to buffer transient fluctuations of the energy supply from renewable sources. 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. In this paper, we investigate the self-discharge phenomenon in energy storage using a queueing system model, which we refer to as leakage queue. When the average net charge is positive, we discover that the leakage queue operates in one of two regimes: a leakage-dominated regime and a capacity-dominated regime. We find that in the leakage-dominated regime, the stored energy stabilizes at a point that is below the storage capacity. Under suitable independence assumptions for energy supply and demand, the stored energy in this regime closely follows a normal distribution. We present two methods for computing probabilities of underflow and overflow at a leakage queue. The methods are validated in a numerical example where the energy supply resembles a wind energy source.