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Strictly and -robust counterparts of electricity market models

  • This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the -approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable convex optimization counterparts that have a clear-cut economic interpretation. In the case of perfect competition, this result corresponds to the two classic welfare theorems, which also apply in both considered robust cases that again yield convex robustified problems. Using the mentioned counterparts, we can also prove the existence and, in some cases, uniqueness of robust equilibria. Surprisingly, it turns out that there is no such economic sensible counterpart for the case of -robustifications of Nash–Cournot models. Thus, an analog of the welfare theorems does not hold in this case. Finally, we provide a computational case study that illustrates the different effects of the combination of economic competition and uncertainty modeling.

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Author:Anja Kramer, Vanessa Krebs, Martin Schmidt
Parent Title (English):Operations Research Perspectives
Place of publication:Amsterdam
Document Type:Article
Date of completion:2021/10/02
Date of publication:2021/10/02
Publishing institution:Universität Trier
Contributing corporation:The publication was funded by the Open Access Fund of Universität Trier and the German Research Foundation (DFG)
Release Date:2022/03/15
Tag:Electricity market equilibrium models; Linear complementarity problems; Nash–Cournot competition; Perfect competition; Robust optimization
Volume (for the year ...):2021
Issue / no.:Band 8
Number of pages:16
Institutes:Fachbereich 4 / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCC BY: Creative-Commons-Lizenz 4.0 International

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