Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autor(en): Krebs V, Schewe L, Schmidt M
Zeitschrift: European Journal of Operational Research
Jahr der Veröffentlichung: 2018
Band: 271
Heftnummer: 1
Seitenbereich: 165-178
ISSN: 0377-2217
Sprache: Englisch


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-Autoren / FAU-Herausgeber

Krebs, Vanessa
Lehrstuhl für Wirtschaftsmathematik
Schewe, Lars PD Dr.
Lehrstuhl für Wirtschaftsmathematik
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen


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.


Zuletzt aktualisiert 2019-02-01 um 19:10