  The paper considers a bidirectional power flow model of the electric vehicles
(EVs) in a charging station. The EVs can inject energies 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. A
proper compensation needs to be paid to the users to participate in the V2G
service. We propose a menu-based pricing scheme, where the charging station
selects a price for each arriving user 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 contracts or rejects all depending on their utilities. The
charging station can serve users using a combination of the renewable energy
and the conventional energy bought from the grid. We show that though there
exists a profit maximizing price which maximizes the social welfare, it
provides no surplus to the users if the charging station is aware of the
utilities of the users. If the charging station is not aware of the exact
utilities, the social welfare maximizing price may not maximize the expected
profit. In fact, it can give a zero profit. We propose a pricing strategy which
provides a guaranteed fixed profit to the charging station and it also
maximizes the expected profit for a wide range of utility functions. Our
analysis shows that 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.
