$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

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 $$\Gamma $$ 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 $$\Gamma $$ 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.

Affinely Adjustable Robust Linear Complementarity Problems

“…Following the idea of studying less conservative notions of robustness, the concept of Γ-robustness has been applied to LCPs in [20] for the case of ℓ 1 -and box-uncertainty sets and in [19] for the case of ellipsoidal uncertainties. Applications of Γ-robust LCPs in the area of power markets or traffic equilibrium problems can be found in [8,18,19]. To the best of our knowledge, the given and rather short list of papers on robust LCPs is complete.…”