Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Julia Grübel - , Friedrich-Alexander University Erlangen-Nürnberg (Author)
  • Olivier Huber - , Humboldt University of Berlin (Author)
  • Lukas Hümbs - , Friedrich-Alexander University Erlangen-Nürnberg (Author)
  • Max Klimm - , Technical University of Berlin (Author)
  • Martin Schmidt - , Trier University (Author)
  • Alexandra Schwartz - , Chair of Mathematical Optimization (Author)

Abstract

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.

Details

Original languageEnglish
Pages (from-to)153-183
Number of pages31
JournalOptimization Methods and Software
Volume38
Issue number1
Publication statusPublished - 2023
Peer-reviewedYes

External IDs

Scopus 85142150406

Keywords

Library keywords