Regression Equilibrium in Electricity Markets

In two-stage electricity markets, renewable power producers enter the day-ahead market with a forecast of future power generation and then reconcile any forecast deviation in the real-time market at a penalty. The choice of the forecast model is thus an important strategy decision for renewable power producers as it affects financial performance. In electricity markets with large shares of renewable generation, the choice of the forecast model impacts not only individual performance but also outcomes for other producers. In this paper, we argue for the existence of a competitive regression equilibrium in two-stage electricity markets in terms of the parameters of private forecast models informing the participation strategies of renewable power producers. In our model, renewables optimize the forecast against the day-ahead and real-time prices, thereby maximizing the average profits across the day-ahead and real-time markets. By doing so, they also implicitly enhance the temporal cost coordination of day-ahead and real-time markets. We base the equilibrium analysis on the theory of variational inequalities, providing results on the existence and uniqueness of regression equilibrium in energy-only markets. We also devise two methods to compute regression equilibrium: centralized optimization and a decentralized ADMM-based algorithm.