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The paper considers a bidirectional power flow model of the electric vehicles (EVs) in a charging station. The EVs can inject energy by discharging via a vehicle-to-grid (V2G) service, which can enhance the profits of the charging station. However, frequent charging and discharging degrade battery life. We propose a menu-based pricing scheme, where the charging station selects a price for each arriving user (EV owner) for the amount of battery utilization, the total energy, and the time (deadline) that the EV will stay. The user can accept one of the menus or rejects all. The user reaches its decision based on the utilities. The charging utilizes its own limited renewable energy, and the conventional energy bought from the grid to serve the users. We show that there exists a prior-free pricing mechanism, which maximizes the ex-post social welfare for a myopic scenario. It selects a lower price for the menu containing a higher V2G service. However, the prior free pricing mechanism does not necessarily maximizes the expected profit. We show that the pricing strategy, which sets the price for a menu at a fixed value greater than the marginal cost of serving the menu, maximizes the expected profit for a wide class of utility functions. In the menu-based pricing, when the harvested renewable energy is small the users have higher incentives for the V2G service. We, numerically, show that the charging station's profit and the user's surplus both increase as V2G service is efficiently utilized by the pricing mechanism.

Menu-Based Pricing for Charging of Electric Vehicles With Vehicle-to-Grid Service