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

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Details zur Publikation

Autorinnen und Autoren: Kramer A, Krebs V, Schmidt M
Jahr der Veröffentlichung: 2018
Sprache: Englisch


Abstract

This paper mainly studies two topics: linear complementarity problems
(LCPs) for modeling electricity market equilibria and optimization under
uncertainty. While there have been quite some attempts to deal with uncertain LCPs in a stochastic - i.e., distributional - sense, robust
LCPs have only gained attention very recently. In this paper, 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
particularly means that the two classical welfare theorems also hold in
both considered robust cases. 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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Krebs, Vanessa
Professur für Angewandte Mathematik (Gemischt-ganzzahlige lineare und nichtlineare Optimierung)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen


Zitierweisen

APA:
Kramer, A., Krebs, V., & Schmidt, M. (2018). Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash--Cournot Equilibria.

MLA:
Kramer, Anja, Vanessa Krebs, and Martin Schmidt. Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash--Cournot Equilibria. 2018.

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Zuletzt aktualisiert 2018-17-07 um 10:53