An efficient game for vehicle-to-grid coordination problems in smart grids

Emerging plug-in electric vehicles (PEVs), as distributed energy sources, are promising to provide vehicle-to-grid (V2G) services for power grids, like frequency and voltage regulations, by coordinating their active and reactive power rates. However, due to the autonomy of PEVs, it is challenging how to efficiently schedule the coordination behaviours among these units in a distributed way. In this paper, we formulate the underlying coordination problems as a novel class of Vickrey–Clarke–Groves style (VCG-style) auction games where players, power grids and PEVs do not report a full cost or valuation function but only a multidimensional bid signal: the maximum active and reactive power quantities that a power grid wants and the maximum per unit prices it is willing to pay, and the maximum active and reactive power quantities that a PEV can provide and the minimum per unit prices it asks for. We show the existence of the efficient Nash equilibrium (NE) for the underlying auction games, though there may exist other inefficient NEs. In order to deal with large-scale PEVs, we design games with aggregator players each of which submits bid profiles representing the overall utility for a collection of PEVs, and extend the so-called quantised-progressive second price mechanism to the underlying auction games to implement the efficient NE.