Geodesic
Deregulated electricity markets with thermal losses and production bounds: models and optimality conditions
Aussel, Didier1  ; Červinka, Michal2, 3 ; Marechal, Matthieu4 
1 University of Perpignan, Lab. PROMES, UPR CNRS 8521, Rambla de la Thermodynamique, Technosud, 66100 Perpignan, France.
2 The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodarenskou vezi 4, 182 08 Prague, Czech Republic.
3 Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Opletalova 26, 110 00 Prague, Czech Republic.
4 Centro de Modelamiento Matematico, Santiago, Chile.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 19-38

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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.

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Accepté le :
DOI : 10.1051/ro/2015009
Classification : 91B26, 90C30, 49J53
Keywords: Deregulated electricity market, production bounds, mathematical program with complementarity constraints, M-stationarity, calmness

Aussel, Didier 1 ; Červinka, Michal 2, 3 ; Marechal, Matthieu 4

1 University of Perpignan, Lab. PROMES, UPR CNRS 8521, Rambla de la Thermodynamique, Technosud, 66100 Perpignan, France.
2 The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodarenskou vezi 4, 182 08 Prague, Czech Republic.
3 Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Opletalova 26, 110 00 Prague, Czech Republic.
4 Centro de Modelamiento Matematico, Santiago, Chile. 
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     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},
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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

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