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

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 e...

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Bibliographic Details
Published in:Optimization methods & software 2023-01, Vol.38 (1), p.153-183
Main Authors: Grübel, Julia, Huber, Olivier, Hümbs, Lukas, Klimm, Max, Schmidt, Martin, Schwartz, Alexandra
Format: Article
Language:English
Subjects:
91-08
Algorithms
Energy markets
Equilibrium
equilibrium computation
existence
Market prices
Mathematical analysis
nonconvex games
Operators (mathematics)
Optimization
perfect competition
Players
Pricing
Switches
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Summary: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.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2022.2117358