Vanessa Krebs 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 … Read more
We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-robustified LCPs for … Read more
We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storages allow for shifting produced electricity from one time period to a later one. Due to this, multiple market equilibria may occur even if classical uniqueness assumptions for the case without storages are satisfied. For models containing storage operators, … Read more
Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems. Specific examples are game-theoretic settings like the bimatrix game or energy market models like for electricity or natural gas. While optimization under uncertainties is rather well-developed, the field of equilibrium models represented by complementarity problems under uncertainty … Read more
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 … Read more
We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a … Read more
We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation. The firms face fluctuating demand and decide on their production, which is constrained by given capacities. Today, uniqueness of such … Read more