2007-12-07Buch DOI: 10.18452/3009
On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
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.