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The high variability of renewable energy resources presents significantchallenges to the operation of the electric power grid. Conventional generatorscan be used to mitigate this variability but are costly to operate and producecarbon emissions. Energy storage provides a more environmentally friendlyalternative, but is costly to deploy in large amounts. This paper studies thelimits on the benefits of energy storage to renewable energy: How effective isstorage at mitigating the adverse effects of renewable energy variability? Howmuch storage is needed? What are the optimal control policies for operatingstorage? To provide answers to these questions, we first formulate the powerflow in a single-bus power system with storage as an infinite horizonstochastic program. We find the optimal policies for arbitrary net renewablegeneration process when the cost function is the average conventionalgeneration (environmental cost) and when it is the average loss of loadprobability (reliability cost). We obtain more refined results by consideringthe multi-timescale operation of the power system. We view the power flow ineach timescale as the superposition of a predicted (deterministic) componentand an prediction error (residual) component and formulate the residual powerflow problem as an infinite horizon dynamic program. Assuming that the netgeneration prediction error is an IID process, we quantify the asymptoticbenefits of storage. With the additional assumption of Laplace distributedprediction error, we obtain closed form expressions for the stationarydistribution of storage and conventional generation. Finally, we propose atwo-threshold policy that trades off conventional generation saving with lossof load probability. We illustrate our results and corroborate the IID andLaplace assumptions numerically using datasets from CAISO and NREL.

Limits on the Benefits of Energy Storage for Renewable Integration