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In this paper, a static non-cooperative game formulation of the problem ofdistributed charging in electrical vehicle (EV) networks is proposed. Thisformulation allows one to model the interaction between several EV which areconnected to a common residential distribution transformer. Each EV aims atchoosing the time at which it starts charging its battery in order to minimizean individual cost which is mainly related to the total power delivered by thetransformer, the location of the time interval over which the chargingoperation is performed, and the charging duration needed for the considered EVto have its battery fully recharged. As individual cost functions are assumedto be memoryless, it is possible to show that the game of interest is always anordinal potential game. More precisely, both an atomic and nonatomic versionsof the charging game are considered. In both cases, equilibrium analysis isconducted. In particular, important issues such as equilibrium uniqueness andefficiency are tackled. Interestingly, both analytical and numerical resultsshow that the efficiency loss due to decentralization (e.g., when costfunctions such as distribution network Joule losses or life of residentialdistribution transformers when no thermal inertia is assumed) induced bycharging is small and the corresponding "efficiency", a notion close to thePrice of Anarchy, tends to one when the number of EV increases.

Charging Games in Networks of Electrical Vehicles