Uniqueness and multiplicity of market equilibria on DC power flow networks

Vanessa Krebs, Lars Schewe, Martin Schmidt*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 different a posteriori criteria for the uniqueness of a given solution and thereby specify properties of unique solutions.

Original languageEnglish
Pages (from-to)165-178
Number of pages14
JournalEuropean Journal of Operational Research
Volume271
Issue number1
Early online date18 Jun 2018
DOIs
Publication statusPublished - 16 Nov 2018

Keywords

  • DC power flow
  • Market equilibria
  • Multiplicity
  • Networks
  • Uniqueness

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