Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market

Henrion, René; Outrata, Jiří; Surowiec, Thomas

ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 2, pp. 295-317.

We consider an equilibrium problem with equilibrium constraints (EPEC) arising from the modeling of competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called M-stationarity conditions are derived. This first requires a structural analysis of the problem, e.g., verifying constraint qualifications. Second, the calmness property of a certain multifunction has to be verified in order to justify using M-stationarity conditions. Third, for stating the stationarity conditions, the coderivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlement example serves as an illustration.

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