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

Published online by Cambridge University Press:  19 January 2011

René Henrion ,
Jiří Outrata  and
Thomas Surowiec
René Henrion
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. henrion@wias-berlin.de
Jiří Outrata
Affiliation:
Institute of Information Theory and Automation, 18208 Praha 8, Czech Republic; outrata@utia.cas.cz
Thomas Surowiec
Affiliation:
Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany; surowiec@math.hu-berlin.de
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Abstract

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.

Keywords

Equilibrium problems with equilibrium constraintsEPECM-stationary solutionselectricity spot marketcalmness
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 2 , April 2012 , pp. 295 - 317
Copyright
© EDP Sciences, SMAI, 2011

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