电力市场模型的严格和Γ-robust对应:完全竞争和纳什-古诺均衡

IF 3.7 4区 管理学 Q2 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Operations Research Perspectives Pub Date : 2021-01-01 DOI:10.1016/j.orp.2021.100197
Anja Kramer , Vanessa Krebs , Martin Schmidt
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引用次数: 13

摘要

本文主要研究电力市场均衡模型的线性互补问题和不确定条件下的优化问题。我们考虑电力市场的完全竞争模型和纳什-古诺模型,并使用严格鲁棒性和Γ-approach来研究它们的鲁棒性。对于经济竞争和鲁棒化的四种组合中的三种,我们推导出具有明确经济解释的算法易于处理的凸优化对偶。在完全竞争的情况下,这个结果对应于两个经典的福利定理,它们也适用于两种被认为是鲁棒的情况,再次产生凸鲁棒问题。利用上述对应物,我们还可以证明鲁棒均衡的存在性,在某些情况下,还可以证明鲁棒均衡的唯一性。令人惊讶的是,在纳什-古诺模型Γ-robustifications的情况下,没有这样一个经济上合理的对应。因此,福利定理的类比在这种情况下不成立。最后,我们提供了一个计算案例研究,说明经济竞争和不确定性模型相结合的不同效果。
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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 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 Γ-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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来源期刊
Operations Research Perspectives
Operations Research Perspectives Mathematics-Statistics and Probability
CiteScore
6.40
自引率
0.00%
发文量
36
审稿时长
27 days
期刊最新文献
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