Variational Methods for Equilibrium Problems Applied to Electricity Markets

This paper focuses on the study of an economic equilibrium problem for an electricity market model in a multistage-stochastic framework, where,stage by stage, the uncertainty evolves with continuity. We analyze the point of view of a finite number of power companies in a sequence of competitive markets.Each of them produces electricity, both with conventional and renewable-based plants, participates in the trade in the spot markets that open after the uncertainty is revealed, and signs bilateral and forward contracts. Moreover, we capture the risk attitude of each power company by considering a suitable coherent risk measure in the problem’s formulation. In order to prove the existence of at least one equilibrium solution, we introduce a suitable quasi-variational inequality formulation. In this light, we also investigate suitable regularity properties of the involved superdifferential operator in the presence of certain parameter perturbations in Banach spaces.