  An important scenario for smart grids which encompass distributed electrical
networks is given by the simultaneous presence of aggregators and individual
consumers. In this work, an aggregator is seen as an entity (a coalition) which
is able to manage jointly the energy demand of a large group of consumers or
users. More precisely, the demand consists in charging an electrical vehicle
(EV) battery. The way the EVs user charge their batteries matters since it
strongly impacts the network, especially the distribution network costs (e.g.,
in terms of Joule losses or transformer ageing). Since the charging policy is
chosen by the users or the aggregators, the charging problem is naturally
distributed. It turns out that one of the tools suited to tackle this
heterogenous scenario has been introduced only recently namely, through the
notion of composite games. This paper exploits for the first time in the
literature of smart grids the notion of composite game and equilibrium. By
assuming a rectangular charging profile for an EV, a composite equilibrium
analysis is conducted, followed by a detailed analysis of a case study which
assumes three possible charging periods or time-slots. Both the provided
analytical and numerical results allow one to better understand the
relationship between the size (which is a measure) of the coalition and the
network sum-cost. In particular, a social dilemma, a situation where everybody
prefers unilaterally defecting to cooperating, while the consequence is the
worst for all, is exhibited.

Computer Science and Game Theory;Optimization and Control