A multi-leader-common-follower game formulation has been recently used by many authors to model deregulated electricity markets. In our work, we first propose a model for the case of electricity market with thermal losses on transmission and with production bounds, a situation for which we emphasize several formulations based on different types of revenue functions of producers. Focusing on a problem of one particular producer, we provide and justify an MPCC reformulation of the producer’s problem. Applying the generalized differential calculus, the so-called M-stationarity conditions are derived for the reformulated electricity market model. Finally, verification of suitable constraint qualification that can be used to obtain first order necessary optimality conditions for the respective MPCCs are discussed.
Accepté le :
DOI : 10.1051/ro/2015009
Mots-clés : Deregulated electricity market, production bounds, mathematical program with complementarity constraints, M-stationarity, calmness
@article{RO_2016__50_1_19_0,
author = {Aussel, Didier and \v{C}ervinka, Michal and Marechal, Matthieu},
title = {Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {19--38},
publisher = {EDP-Sciences},
volume = {50},
number = {1},
year = {2016},
doi = {10.1051/ro/2015009},
mrnumber = {3460660},
zbl = {1333.91045},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ro/2015009/}
}
TY - JOUR AU - Aussel, Didier AU - Červinka, Michal AU - Marechal, Matthieu TI - Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 19 EP - 38 VL - 50 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2015009/ DO - 10.1051/ro/2015009 LA - en ID - RO_2016__50_1_19_0 ER -
%0 Journal Article %A Aussel, Didier %A Červinka, Michal %A Marechal, Matthieu %T Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 19-38 %V 50 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2015009/ %R 10.1051/ro/2015009 %G en %F RO_2016__50_1_19_0
Aussel, Didier; Červinka, Michal; Marechal, Matthieu. Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 19-38. doi : 10.1051/ro/2015009. http://archive.numdam.org/articles/10.1051/ro/2015009/
, and , Spot electricity market with transmission losses. J. Ind. Manag. Optim. 9 (2013) 275–290. | DOI | MR | Zbl
J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer Ser. Oper. Res. Fin. Engr. Springer-Verlag, New York (2000). | MR | Zbl
M. Červinka, Hierarchal Structures in Equilibrium Problems. Ph.D. thesis, Charles University in Prague and Academy of Sciences of the Czech Republic (2008).
, and , On the computation of relaxed pessimistic solutions to MPECs. Optim. Methods Softw. 28 (2013) 186–206. | DOI | MR | Zbl
COSMOS description, CWE Market Coupling algorithm. Version 1.1 (2011).
, A bundle algorithm applied to bilevel programming problems with non-unique lower level solutions. Comput. Optim. Appl. 15 (2000) 145–166. | DOI | MR | Zbl
and , Is bilevel programming a special case of a mathematical program with complementarity constraints? Math. Program. A 131 (2012) 37–48. | DOI | MR | Zbl
and , Monopolistic competition in electricity networks with resistance losses. Econom. Theory 44 (2010) 101–121. | DOI | MR | Zbl
J.F. Escobar and A. Jofré, Equilibrium analysis of electricity auctions (2014).
F. Facchinei and J.-S. Pang, Finite-dimensional variational inequalities and complementarity problems. In vol. I. Springer Series Oper. Res. Springer-Verlag, New York (2003). | MR | Zbl
and , Competition in the British electricity spot market. J. Political Economy 100 (1992) 929–953. | DOI
, and , On the calmness of a class of multifunctions. SIAM J. Optim. 13 (2002) 603–618. | DOI | MR | Zbl
, and , Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market. ESAIM: COCV 18 (2012) 295–317. | Numdam | MR | Zbl
J.-B. Hiriart-Urruty and C. Lemaréchal, Convex analysis and minimization algorithms. I. Fundamentals. In vol. 305. Springer-Verlag, Berlin (1993). | MR
and , Strategic Gaming Analysis for Electric Power Systems: An MPEC Approach. IEEE Trans. Power Systems 15 (2000) 638–645. | DOI
and , Using EPECs to model bilevel games in restructured electricity markets with locational prices. Oper. Res. 55 (2007), 809–827. | DOI | MR | Zbl
and , On metric and calmness qualification conditions in subdifferential calculus. Set-Valued Anal. 16 (2008) 199–227. | DOI | MR | Zbl
and , Supply function equilibria in oligopoly under uncertainty. Econometrica 57 (1989) 1243–1277. | DOI | MR | Zbl
and , Solving multi-leader-common-follower games. Optim. Methods Softw. 25 (2010) 601–623. | DOI | MR | Zbl
and , New results on Approximate Solutions in Two-Level Optimization. Optimization 20 (1989) 819–836. | DOI | MR | Zbl
Z.-Q. Luo, J.-S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1997). | MR | Zbl
, Sensitivity analysis in nonsmooth optimization. In Theoretical Aspects of Industrial Design. D.A. Field and V. Komkov. SIAM Proc. Appl. Math. 58 (1992) 32–46. | MR | Zbl
B.S. Mordukhovich, Variational Analysis and Generalized Differentiation. Applications. In vol. 2. Springer Verlag, Berlin (2006). | MR | Zbl
RTE Balancing mechanism webpage: http://clients.rte-france.com/lang/an/visiteurs/vie/viemecanisme.jsp
, A generalized mathematical program with equilibrium constraints. SIAM J. Control Optim. 38 (2000) 1623–1638. | DOI | MR | Zbl
, A note on a class of equilibrium problems with equilibrium constraints. Kybernetika 40 (2004) 585–594. | MR | Zbl
J.V. Outrata, M. Kočvara and J. Zowe,, Nonsmooth Approach to Optimization Problems with Equilibrium Constraints. Kluwer, Dordrecht (1998). | MR | Zbl
and , Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Manag. Sci. 1 (2005) 21–56. | DOI | MR | Zbl
, Some continuity properties of polyhedral multifunctions. Math. Program. Stud. 14 (1976) 206–214. | MR | Zbl
, Strongly regular generalized equations. Math. Oper. Res. 5 (1980) 43–62. | DOI | MR | Zbl
R.T. Rockafellar and R.J.-B. Wets, Variational Analysis, Vol. 317 of A Series of Comprehensive Studies in Mathematics. Springer, Berlin, Heidelberg (1998). | Zbl
M. Saguan, J.-M. Glachant and P. Dessante, Risk management and optimal hedging in electricity forward markets coupled with a balancing mechanism. Vols. 1 and 2 of 9th International Conference on Probabilistic Methods Applied to Power Systems (2006) 917–922.
T. Surowiec, Explicit Stationarity Conditions and Solution Characterization for Equilibrium Problems with Equilibrium Constraints. Ph.D. thesis, Humboldt University in Berlin (2009).
and , Necessary optimality conditions for optimization problems with variational inequality constraints. Math. Oper. Res. 22 (1997) 977–997. | DOI | MR | Zbl
Cité par Sources :
