Solving discretely-constrained MPEC problems with applications in electric power markets

Many of the European energy markets are characterized by dominant players that own a large share of their respective countries' generation capacities. In addition to that, there is a significant lack of cross-border transmission capacity. Combining both facts justifies the assumption that these dominant players are able to influence the market outcome of an internal European energy market due to strategic behavior. In this paper, we present a mathematical formulation in order to solve a Stackelberg game for a network-constrained energy market using integer programming. The strategic player is the Stackelberg leader and the independent system operator (including the decisions of the competitive fringe firms) acts as follower. We assume that there is one strategic player which results in a mathematical program with equilibrium constraints (MPEC). This MPEC is reformulated as mixed-integer linear program (MILP) by using disjunctive constraints and linearization. The MILP formulation gives the opportunity to solve the problems reliably and paves the way to add discrete constraints to the original MPEC formulation which can be used in order to solve discretely-constrained mathematical programs with equilibrium constraints (DC-MPECs). We report computational results for a small illustrative network as well as a stylized Western European grid with realistic data. (author)