Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks

Journal article

Publication Details

Author(s): Krebs V, Schewe L, Schmidt M
Journal: European Journal of Operational Research
Publication year: 2018
Volume: 271
Journal issue: 1
Pages range: 165-178
ISSN: 0377-2217
Language: English


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 market outcomes are especially important in more complicated multilevel models for measuring market (in)efficiency. Thus, our findings are important prerequisites for such studies. We show that market equilibria are unique on tree networks under mild assumptions and we also present a priori conditions under which equilibria are unique on cycle networks. On general networks, uniqueness fails to hold and we present simple examples for which multiple equilibria exist. However, we prove a posteriori criteria for the uniqueness of a given solution and characterize situations in which multiple solutions exist.

FAU Authors / FAU Editors

Krebs, Vanessa
Economics - Discrete Optimization - Mathematics (EDOM)
Schewe, Lars PD Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen

How to cite

Krebs, V., Schewe, L., & Schmidt, M. (2018). Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks. European Journal of Operational Research, 271(1), 165-178. https://dx.doi.org/10.1016/j.ejor.2018.05.016

Krebs, Vanessa, Lars Schewe, and Martin Schmidt. "Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks." European Journal of Operational Research 271.1 (2018): 165-178.


Last updated on 2019-02-01 at 19:10