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Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

  • 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 Γ-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 classical 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 Γ-robustifications of Nash–Cournot models. Thus, an analogue 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 (German):Operations Research Perspectives
Document Type:Article
Language:English
Date of Publication (online):2018/07/12
Date of first Publication:2018/07/13
Release Date:2018/07/13
Tag:Electricity market equilibrium models; Linear complementarity problems; Nash-Cournot competition; Perfect competition; Robust optimization
Issue:89(2)
Page Number:33
First Page:100197
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Universität Trier
Subprojects:A05
B08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International