Abstract
The high variability of renewable energy is a major obstacle toward its increased penetration. Energy storage can help reduce the power imbalance due to the mismatch between the available renewable power and the load. How much can storage reduce this power imbalance? How much storage is needed to achieve this reduction? This paper presents a simple analytic model that leads to some answers to these questions. Considering the multitimescale grid operation, we formulate the power imbalance problem for each timescale as an infinite horizon stochastic control problem and show that a greedy policy minimizes the average magnitude of the residual power imbalance. Observing from the wind power data that in shorter timescales the power imbalance can be modeled as an iid zero-mean Laplace distributed process, we obtain closed form expressions for the minimum cost and the stationary distribution of the stored power. We show that most of the reduction in the power imbalance can be achieved with relatively small storage capacity. In longer timescales, the correlation in the power imbalance cannot be ignored. As such, we relax the iid assumption to a weakly dependent stationary process and quantify the limit on the minimum cost for arbitrarily large storage capacity.
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