Efficient and Robust Equilibrium Strategies of Utilities in Day-Ahead Market With Load Uncertainty

We consider the scenario where $N$ utilities strategically bid for electricity in the day-ahead market and balance the mismatch between the committed supply and actual demand in the real-time market, with uncertainty in demand and local renewable generation in consideration. We model the interactions among utilities as a non-cooperative game, in which each utility aims at minimizing its per-unit electricity cost. We show that all utilities bidding according to (net load) prediction is a unique pure strategy Nash Equilibrium with two salient properties. First, it incurs no loss of efficiency; hence, competition among utilities does not increase the social cost. Second, it is robust and (0, $N-1$)-immune. That is, fault behaviors of irrational utilities only help to reduce the costs of other rational utilities. We prove the results hold under the settings of correlated prediction errors and a general class of real-time spot pricing models, which capture the relationship between the spot price, the day-ahead clearing price, and the market-level mismatch. Simulations based on real-world traces corroborate our theoretical findings. Our study highlights a set of sufficient conditions for the market operator to design real-time pricing schemes, so that the interactions among utilities admit a unique, efficient, and robust Nash Equilibrium.