Volume 18, Number 2, April-June 2012
|Page(s)||295 - 317|
|Published online||19 January 2011|
Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market∗
Weierstrass Institute for Applied Analysis and
2 Institute of Information Theory and Automation, 18208 Praha 8, Czech Republic
3 Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany
Revised: 16 June 2010
Revised: 4 November 2010
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.
Mathematics Subject Classification: 90C30 / 49J53
Key words: Equilibrium problems with equilibrium constraints / EPEC / M-stationary solutions / electricity spot market / calmness
© EDP Sciences, SMAI, 2011
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