Bayesian and Robust Nash Equilibria in Hydrodominated Systems Under Uncertainty

In this paper, we model strategic interaction of multiple producers in hydrodominated power systems under uncertainty as an equilibrium problem with equilibrium constraints (EPEC), reformulated as a stochastic mixed-integer linear program with disjunctive constraints. We model strategic hydropower producers who can affect the market price by submitting strategic bids in quantity, price, and ramp rate. The bids are submitted to the system operator who minimizes the dispatch cost. We take into account the hydrospecific constraints and uncertainty in the system. Solving the problem results in finding Nash equilibria. We discuss two types of Nash equilibria under uncertainty: Bayesian and robust Nash equilibria. Large EPEC instances can be solved using a decomposition method-Modified Benders Decomposition Approach. This method eliminates the problem of tuning the disjunctive parameter and reduces the memory requirements, resulting in improved computation time.