Auctioning game based Demand Response scheduling in smart grid

Abstract

Matching demand to supply is one of the key features of smart grid infrastructure. Transforming conventional static customers into active participants who interact with the electrical utility in real time is the central idea of Demand Response (DR)\Demand Side Management (DSM) in smart grid. In this paper, we decouple utility cost minimization and customer social welfare maximization into two stages. Since the utility is usually more risk averse than risk neutral in real life, this decoupling approach is more realistic than the usually adopted optimization setup, in which the two objectives are combined in a single weighted sum. With a block processing model introduced, in the first stage a convex optimization problem is formulated to minimize utility's generation cost and delay operation cost. An optimal load demand scheduling solution, of the form of water-filling, is derived analytically. Based on the optimal load profile generated in this first stage, repeated Vickrey auctions over time intervals are adopted to allocate load demands among customers while maximizing the social welfare. Despite the fact that truthful bidding is a weakly dominant strategy for all customers in the auctioning game, collusive equilibria do exist and jeopardize utility's profit severely. Analysis on the structure of the Bayesian Nash equilibrium solutions shows that by introducing a positive reserve price the Vickrey auction can be made to be more robust against such collusion by customers. Moreover the corresponding Bayesian Nash equilibrium is essentially unique and guarantees the basic profit of the utility. We further discuss how customers' valuations and bidding strategies change over time for the repeated Vickrey auction model. Simulation results emphasizing the influences of reserve price and time interval size on utility's profit is also presented.