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 chargingand discharging activities for plug-in hybrid electric vehicles for the benefit of an energy mar-ket participant. We first develop models for both risk-neutral and risk-averse aggregators toparticipate only in a real-time market. The proposed models capture the impact of the charg-ing and discharging activities on real-time electricity prices. Next, we extend our study to thecase in which aggregators participate in both the real-time and day-ahead markets. For eachdeveloped model, we analyze the properties of the optimal objective value function, prove theexistence and uniqueness of the optimal policy, and explore the corresponding optimal policystructure. Moreover, through numerical studies, we explore insights on how electricity pricesare influenced by charging and discharging activities. In particular, we observe that aggregatedcharging/discharging activities with market-impact consideration could reduce the variance ofthe real-time electricity prices more efficiently, as compared to individual activities. In addition,with the consideration of market impact, an aggregator tends to use less electricity storage. Fi-nally, it is beneficial to let an aggregator control the electricity storage and participate in boththe real-time and day-ahead markets, instead of participating only in the real-time market.