Extended Second Price Auctions With Elastic Supply for PEV Charging in the Smart Grid

In this paper, we explore the question of efficient allocation of energy, while buying the same from generation companies, to plug-in electric vehicles (PEVs) by aggregator (electricity utility or load serving entities) through auction mechanisms. Recognizing the practical limitations of the Vickrey–Clarke–Groves mechanism, which would be natural to apply in this context, we investigate two practical mechanisms that can be viewed as extensions of second price auction mechanisms and have limited message (bid) complexity. In the first mechanism, the elastic-supply multi-level second price, each PEV agent submits a number of price bids, one for each of a given set of energy levels (energy quantities). In the second mechanism, the elastic-supply progressive second price, the PEV agents submit a 2-D bid indicating the price as well as the desired energy quantity. Taking into account differences across PEV-owners in terms of their willingness-to-pay values and charging time constraints, we analyze the social optimality and incentive compatibility properties of the two auction mechanisms. We also complement our theoretical findings with numerical simulations.