Abstract
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 Gamma -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 Gamma -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.
Highlights
Equilibrium modeling for liberalized electricity markets and solving these models is of great practical relevance today
Similar trilevel models are considered in [1,16,26,27,38] where the first level models decisions of the regulator/operator such as market-design decisions or investment in transmission lines, the second level models generation investment as well as spot-market behavior of market participants, and the third level contains redispatch models as they are used in, e.g., Germany. In many of these studies, bilevel or trilevel problems are cast as mathematical programs with equilibrium constraints (MPECs) or equilibrium problems with equilibrium constraints (EPECs) and are solved by equivalent single-level reformulations of the multilevel problem
Since classical strict robustness is often criticized for its very conservative solutions, we study the concept of robustness as it is proposed in [5,6,52] and as it is applied to market equilibrium models in [39] that we modify here to put emphasis on the relation between uncertainty and long-run decision-making
Summary
Equilibrium modeling for liberalized electricity markets and solving these models is of great practical relevance today. We contribute to the second of the three mentioned fields and consider robustified market equilibrium models with transmission and generation investments. Similar trilevel models are considered in [1,16,26,27,38] where the first level models decisions of the regulator/operator such as market-design decisions or investment in transmission lines, the second level models generation investment as well as spot-market behavior of market participants, and the third level contains redispatch models as they are used in, e.g., Germany In many of these studies, bilevel or trilevel problems are cast as mathematical programs with equilibrium constraints (MPECs) or equilibrium problems with equilibrium constraints (EPECs) and are solved by equivalent single-level reformulations of the multilevel problem.
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