The high variability of renewable energy resources presents significant
challenges to the operation of the electric power grid. Conventional generators
can be used to mitigate this variability but are costly to operate and produce
carbon emissions. Energy storage provides a more environmentally friendly
alternative, but is costly to deploy in large amounts. This paper studies the
limits on the benefits of energy storage to renewable energy: How effective is
storage at mitigating the adverse effects of renewable energy variability? How
much storage is needed? What are the optimal control policies for operating
storage? To provide answers to these questions, we first formulate the power
flow in a single-bus power system with storage as an infinite horizon
stochastic program. We find the optimal policies for arbitrary net renewable
generation process when the cost function is the average conventional
generation (environmental cost) and when it is the average loss of load
probability (reliability cost). We obtain more refined results by considering
the multi-timescale operation of the power system. We view the power flow in
each timescale as the superposition of a predicted (deterministic) component
and an prediction error (residual) component and formulate the residual power
flow problem as an infinite horizon dynamic program. Assuming that the net
generation prediction error is an IID process, we quantify the asymptotic
benefits of storage. With the additional assumption of Laplace distributed
prediction error, we obtain closed form expressions for the stationary
distribution of storage and conventional generation. Finally, we propose a
two-threshold policy that trades off conventional generation saving with loss
of load probability. We illustrate our results and corroborate the IID and
Laplace assumptions numerically using datasets from CAISO and NREL.Comment: 45 pages, 17 figure