Nonconvex Equilibrium Models for Energy Markets: Exploiting Price Information to Determine the Existence of an Equilibrium

Submission Status:under review
  • Motivated by examples from the energy sector, we consider market equilibrium problems (MEPs) involving players with nonconvex strategy spaces or objective functions, where the latter are assumed to be linear in market prices. We propose an algorithm that determines if an equilibrium of such an MEP exists and that computes an equilibrium in case of existence. Three key prerequisites have to be met. First, appropriate bounds on market prices have to be derived from necessary optimality conditions of some players. Second, a technical assumption is required for those prices that are not uniquely determined by the derived bounds. Third, nonconvex optimization problems have to be solved to global optimality. We test the algorithm on well-known instances from the power and gas literature that meet these three prerequisites. There, nonconvexities arise from considering the transmission system operator as an additional player besides producers and consumers who, e.g., switches lines or faces nonlinear physical laws. Our numerical results indicate that equilibria often exist, especially for the case of continuous nonconvexities in the context of gas market problems.

Download full text files

Export metadata

Metadaten
Author:Julia Grübel, Olivier Huber, Lukas Hümbs, Max Klimm, Martin Schmidt, Alexandra Schwartz
Document Type:Preprint
Language:English
Date of Publication (online):2021/05/31
Date of first Publication:2021/05/31
Release Date:2021/05/31
Tag:Energy markets; Equilibrium computation; Existence; Nonconvex games; Perfect competition
Page Number:29
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Technische Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Universität Trier
Subprojects:A05
A07
B02
B07
B08
B09
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International