Regression Equilibrium in Electricity Markets

Renewable power producers participating in electricity markets build forecasting models independently, relying on their own data, model and feature preferences. In this paper, we argue that in renewable-dominated markets, such an uncoordinated approach to forecasting results in substantial opportunity costs for stochastic producers and additional operating costs for the power system. As a solution, we introduce Regression Equilibrium--a welfare-optimal state of electricity markets under uncertainty, where profit-seeking stochastic producers do not benefit by unilaterally deviating from their equilibrium forecast models. While the regression equilibrium maximizes the private welfare, i.e., the average profit of stochastic producers across the day-ahead and real-time markets, it also aligns with the socially optimal, least-cost dispatch solution for the system. 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 for computing the regression equilibrium: centralized optimization and a decentralized ADMM-based algorithm that preserves the privacy of regression datasets.