A Stochastic-Programming-Based Coupled Constraint Equilibrium Problem Under PV Uncertainty in Day-Ahead Energy Market

In this paper, as for a microgrid system, we establish a game-theoretic framework for modeling the strategic behavior of the energy aggregators (microgrid components) that are connected to solar energy resources. Considering the prediction uncertainty of the solar energy, we model the profit function of each aggregator (market player) with a two-stage stochastic structure. Then, according to the power flow equation, a coupled constraint equilibrium is defined, and some properties are studied. To compute the specific equilibrium, we recast the problem by its Karush-Kuhn-Tucker (KKT) conditions and then reformulate the problem. The numerical simulation illustrates the coupled strategies of the market players and the existence of the coupled constraint equilibrium.