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Uniqueness and Multiplicity of Market Equilibria on DC Power Flow Networks

  • 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.

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Metadaten
Author:Vanessa Krebs, Lars Schewe, Martin Schmidt
Parent Title (German):European Journal on Operations Research
Document Type:Article
Language:English
Date of Publication (online):2017/10/02
Date of first Publication:2017/10/02
Release Date:2017/10/02
Tag:DC Power Flow; Market Equilibria; Multiplicity; Networks; Uniqueness
Issue:271(1)
Page Number:14
First Page:165
Last Page:178
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:B07
B08