Strategic behavior in power markets under uncertainty

We consider a setting of a two settlement power market where firms compete in the forward market and an uncertain real-time market. A recourse-based framework is proposed where firms make simultaneous bids in the forward market and take recourse in the real-time market contingent on the realization of uncertainty. The market participants include both generation firms as well as the independent system operator (ISO), the latter of which is assumed to maximize wheeling revenue. The resulting stochastic game-theoretic problem is seen to be a Nash game with coupled strategy sets, often referred to as a generalized Nash game. In general, the primal variational conditions of such problems are given by quasi-variational inequality. Yet, the associated complementarity problem in a primal-dual space admits a monotonicity property that allows us to derive an appropriate existence statement. Computation of equilibria is complicated by the challenge arising from the size of the sample-space. We present a distributed iterative regularization technique that is shown to scale well with the size of the sample-space. Finally, the paper concludes with the application of this model on an electrical network and provides insights on market design and operation.