Optimal Control of Plug-In Hybrid Electric Vehicles with Market Impact and Risk Attitude

In this paper, we develop optimal electricity storage control policies to manage charging and discharging activities for plug-in hybrid electric vehicles for the benefit of an energy market participant. We first develop models for both risk-neutral and risk-averse aggregators to participate only in a real-time market. The proposed models capture the impact of the charging and discharging activities on real-time electricity prices. Next, we extend our study to the case in which aggregators participate in both the real-time and day-ahead markets. For each developed model, we analyze the properties of the optimal objective value function, prove the existence and uniqueness of the optimal policy, and explore the corresponding optimal policy structure. Moreover, through numerical studies, we explore insights into how electricity prices are influenced by charging and discharging activities. In particular, we observe that aggregated charging/discharging activities with market-impact consideration could reduce the variance of the real-time electricity prices more efficiently, as compared to individual activities. In addition, considering market impact, an aggregator tends to use less electricity storage. Finally, it is beneficial to let an aggregator control the electricity storage and participate in both the real-time and day-ahead markets, instead of participating only in the real-time market.