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

Tianyu Zhao, Hanling Yi, Minghua Chen, Chenye Wu, Yunjian Xu

Abstract: We consider the scenario where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> 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 noncooperative game, in which each utility aims atminimizing its per-unit electricity cost. We investigate utilities’ optimal bidding strategies and 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, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N-1$</tex-math></inline-formula> ) fault immune. That is, fault behaviors of irrational utilities only help to reduce other rational utilities’ costs. The expected market supply–demand mismatch is minimized simultaneously, which improves the planning and supply-and-demand matching efficiency of the electricity supply chain. 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 article adds new insights to market mechanism design. In particular, we derive a set of fairly general sufficient conditions for the market operator to design real-time pricing schemes so that the interactions among utilities admit the desired equilibrium.