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SPEPS Preprint

Author(s): Rene Henrion, WIAS
Werner Römisch, Humboldt-University
Title: On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
Date of Acceptance: 07.12.2007
Submission Date: 02.07.2007
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Keywords (eng): electricity market, bidding, noncooperative games, equilibrium constraint, EPEC, optimality condition, co-derivative, random demand
Appeared in: Applications of Mathematics 52 (2007)
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Abstract (eng):
Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata [17]. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived (Proposition 3.2). Later the co-derivative formula is used for verifying constraint qualifications and for identifying M-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.
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