Progressive second price auctions with elastic supply for PEV charging in the smart gric

Recent years have seen increasing deployment of Plug-in Electric Vehicles (PEVs) for personal transportation, which can lead to energy cost savings as well as reduce our carbon footprint. However, the bursty nature of PEV demand implies that the aggregate PEV load can impart significant stress on the distribution grid unless PEV charging is coordinated through efficient control mechanisms. In this paper, we study the energy supplier's problem of selling energy to the PEVs — while buying the same from the generators (market) — through an auction. In this context, we analyze the properties of an elastic-supply Progressive Second Price (es-PSP) auction mechanism, which requires each PEV agent to submit a desired energy quantity and a per-unit willingness-to-pay value. We establish that social efficiency is attained at Nash equilibria, and PEV agents acting in self-interest have no incentive to untruthfully declare their willingness-to-pay value for the quantity they choose to declare. We also validate some of our theoretical results through simulations in a specific distribution network scenario.