Extended second price auctions for Plug-in Electric Vehicle (PEV) charging in smart distribution grids

Large scale deployment of Plug-in Electric Vehicles (PEVs) in the smart grid environment necessitates the use of appropriate charging control algorithms that handle the additional PEV based load effectively. While ensuring grid stability, these PEV charging control algorithms must ensure that the available energy is delivered to where it is needed the most. In this paper, we explore the question of efficient allocation of energy (charging rates and schedules) to PEVs by the aggregator (electricity utility) through an auction mechanism. Recognizing the practical limitations of the Vickrey-Clark-Groves (VCG) 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 multi-level second price (MSP), 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 progressive second price (PSP), the PEV agents submit a two-dimensional 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.