|edoc-Server der Humboldt-Universität zu Berlin|
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|
Stochastic Programming E-Print Series |
|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)|
|Metadata export: To export the complete metadata set as Endote or Bibtex format please click to the appropriate link.||Endnote Bibtex|
|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 . 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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