Revenue- and network-constrained market clearing via bilevel programming

This paper addresses a practical network-constrained auction model wherein generation offers include terms related to revenues from selling energy. The resulting revenue-constrained model is a particular instance of price-based market clearing in which locational market-clearing prices become decision variables of the optimization process. As an additional major complicating factor, producer revenues are formulated as bilinear and highly nonconvex products of prices and power outputs. Consequently, the use of conventional unit-commitment-based approaches relying on mixed-integer linear programming or Lagrangian relaxation is precluded, being only heuristics available. Under a standard marginal pricing scheme, this paper presents a novel and exact technique based on bilevel programming. In the upper level, generation is scheduled with the goal of maximizing the declared social welfare while taking into account that locational marginal prices are determined by an optimal power flow in the lower level. Based on Karush-Kuhn-Tucker optimality conditions, duality theory, and integer algebra results, the bilinear bilevel program is transformed into an equivalent single-level mixed-integer program with no bilinear terms. Numerical results illustrate the effective performance of the proposed approach and its superiority over the heuristic currently implemented in the Iberian electricity market.