Auction-based optimal distributed vehicle-to-grid coordinations for frequency regulations

In this paper we proposed a novel auction-based distributed V2G coordination method for frequency regulations of the grid. We define a pair of system signals, with respect to agent bid profiles, which is composed of the system price and a binary valued signal which is equal to one if all of the agents are fully allocated, and equal to zero otherwise. We designed an allocation policy to individual agents with respect to the system parameters, such that the supplied service from an agent is fully accepted 1) if his bid price is not higher than the system price in case the signal equal to one, or 2) if his bid price is lower than the system price by a fixed positive value in case the signal equal to zero. All of the individual agents simultaneously update their own best bid strategy with respect to the pair of system signals; then by adapting the above allocation policy and under certain conditions, we show that the auction system can converge to the social optimal solution. Numerical examples are given to illustrate the main results developed the paper.