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

Grübel J, Huber O, Hümbs L, Klimm M, Schmidt M, Schwartz A (2023)

Publication Type: Journal article, Original article

Publication year: 2023

Journal

Optimization Methods & Software Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

Book Volume: 38

Pages Range: 153-183

Journal Issue: 1

DOI: 10.1080/10556788.2022.2117358

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.

Authors with CRIS profile

Julia Grübel Lehrstuhl für Volkswirtschaftslehre, insbesondere Wirtschaftstheorie Lukas Hümbs Economics - Discrete Optimization - Mathematics (EDOM)

Related research project(s)

Multilevel mixed-integer nonlinear optimization for gas markets (B08) (2018 - 2022) TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) July 1, 2018 - June 30, 2022 MIP techniques for equilibrium models with integer constraints (B07) (2018 - 2022) TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) July 1, 2018 - June 30, 2022 B09 „Strategische Buchungsentscheidungen im Entry-Exit-System“ TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) July 1, 2018 - June 30, 2022 Decomposition methods for mixed-integer optimal control (A05) (2018 - 2022) TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks (TRR 154) July 1, 2018 - June 30, 2022

Involved external institutions

Technische Universität Berlin DE Germany (DE) Technische Universität Dresden DE Germany (DE) Universität Trier DE Germany (DE) Humboldt-Universität zu Berlin DE Germany (DE)

How to cite

APA:

Grübel, J., Huber, O., Hümbs, L., Klimm, M., Schmidt, M., & Schwartz, A. (2023). Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium. Optimization Methods & Software, 38(1), 153-183. https://doi.org/10.1080/10556788.2022.2117358

MLA:

Grübel, Julia, et al. "Nonconvex equilibrium models for energy markets: exploiting price information to determine the existence of an equilibrium." Optimization Methods & Software 38.1 (2023): 153-183.

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