Universität Trier
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We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust equilibrium models is still in its infancy. We contribute to this new field of research by considering Γ-robust electricity market equilibrium models on lossless DC networks with transmission and generation investments. We state the nominal market equilibrium problem as a mixed complementarity problem as well as its variational inequality and welfare optimization counterparts. For the latter, we then derive a Γ-robust formulation and show that it is indeed the counterpart of a market equilibrium problem with robustified player problems. Finally, we present two case studies to gain insights into the general effects of robustification on electricity market models. In particular, our case studies reveal that the transmission system operator tends to act more risk-neutral in the robust setting, whereas generating firms clearly behave more risk-averse.
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.