  Electric storage units constitute a key element in the emerging smart grid
system. In this paper, the interactions and energy trading decisions of a
number of geographically distributed storage units are studied using a novel
framework based on game theory. In particular, a noncooperative game is
formulated between storage units, such as PHEVs, or an array of batteries that
are trading their stored energy. Here, each storage unit's owner can decide on
the maximum amount of energy to sell in a local market so as to maximize a
utility that reflects the tradeoff between the revenues from energy trading and
the accompanying costs. Then in this energy exchange market between the storage
units and the smart grid elements, the price at which energy is traded is
determined via an auction mechanism. The game is shown to admit at least one
Nash equilibrium and a novel proposed algorithm that is guaranteed to reach
such an equilibrium point is proposed. Simulation results show that the
proposed approach yields significant performance improvements, in terms of the
average utility per storage unit, reaching up to 130.2% compared to a
conventional greedy approach.
