Mixed integer parametric bilevel programming for optimal strategic bidding of energy producers in day-ahead electricity markets with indivisibilities

We address the problem of finding the optimal bidding strategy of an energy producer that participates in a single-period day-ahead electricity market, assuming full knowledge of the market's parameters. The problem is formulated as a mixed integer bilevel optimization model, with the producer maximizing his individual profit, at the upper level, and an independent system operator clearing the market at the minimum total system bid-cost, at the lower level. The model utilizes discrete variables to represent the commitment of the production units, which prohibits the application of typical methodologies for finding its optimal solution, such as the substitution of the lower level problem by its first-order KKT optimality conditions. We develop an exact algorithm for the solution of the problem that utilizes important findings from the theory of parametric integer programming, and we report experimental results demonstrating its efficiency on random problem instances. We conclude with a discussion on several computational issues pertaining to the behaviour of this algorithm, and an outline of how the theory developed in the present work can be modified to fit alternative market designs