Limits on the Benefits of Energy Storage for Renewable Integration

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.

💡 Research Summary

This paper investigates the fundamental limits of using energy storage to mitigate the variability of renewable generation in a power system. The authors consider a single‑bus model with stochastic net renewable generation (the difference between renewable output and load) and formulate the power‑flow problem as an infinite‑horizon average‑cost stochastic program. Two objective functions are studied: (i) minimizing the long‑term average conventional (fossil‑fuel) generation, which reflects environmental cost, and (ii) minimizing the long‑term average loss‑of‑load probability, which reflects reliability.

For an arbitrary net‑renewable process, the authors prove that simple stationary policies are optimal for both objectives. The optimal policy for the environmental cost never uses conventional generation to charge the storage; it charges the storage with any excess renewable energy and, when a deficit occurs, discharges the storage first and only then resorts to conventional generation. Conversely, the reliability‑oriented optimal policy keeps the storage as full as possible, using conventional generation only to replenish the storage when its state of charge falls below a lower threshold. These results are formalized in Theorems 1 and 2 and illustrated with CAISO load data and NREL wind simulations.

The paper then extends the analysis to multi‑timescale operation (day‑ahead, hour‑ahead, minute‑ahead, real‑time). In each timescale the net generation is decomposed into a deterministic forecast and a stochastic residual (prediction error). Assuming the residuals are independent and identically distributed (IID), the authors model the residual power‑flow as another infinite‑horizon dynamic program. Under the IID assumption they derive asymptotic benefits: as storage capacity grows, the reduction in fast‑ramping conventional generation approaches the round‑trip efficiency of the storage (Proposition 1), and the average loss‑of‑load probability can be driven to zero (Proposition 4).

Empirically, the authors find that wind forecast errors are well approximated by a Laplace distribution. With this additional assumption they obtain closed‑form stationary distributions for the stored energy and conventional generation (Propositions 2 and 3). The analysis shows that most of the possible reduction in conventional generation can be achieved with relatively modest storage (on the order of a few gigawatt‑hours), while a dramatic reduction in loss‑of‑load probability (by an order of magnitude) is possible with even smaller storage.

To bridge the two extreme policies, the paper proposes a two‑threshold control law. The storage state of charge is kept between an upper threshold S_H and a lower threshold S_L. When the state exceeds S_H, conventional generation is used to avoid further charging; when it falls below S_L, conventional generation is used to charge the storage. By weighting the environmental and reliability costs with a parameter λ∈