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

¹ Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
henrion@wias-berlin.de
² Institute of Information Theory and Automation, 18208 Praha 8, Czech Republic
outrata@utia.cas.cz
³ Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany
surowiec@math.hu-berlin.de

Received: 6 September 2009
Revised: 16 June 2010
Revised: 4 November 2010

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.