On Storage and Renewables: A Theory of Sizing and Uncertainty

This paper studies the fundamental problem of sizing energy storage given an uncertainty level of variable resources in a microgrid. A queuing theoretical model is introduced, which provides unique insights on the coupling between energy storage size and uncertainty level of the net load. The proposed model lends itself to 3 levels of details: a random walk model with single uncertainty from one net load, a reflected Brownian motion model with many more uncertain resources, and a model with a collection of Markov-type power producers and consumers. It is shown that the fundamental requirement of energy storage sizing can be approximately derived from the aforementioned 3 queuing theory models. Numerical examples suggest that this approach can be applied to microgrid planning and operation in assessing the optimal size of energy storage , as well as the potential curtailment of renewable energy.