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Uniqueness and multiplicity of market equilibria on DC power flow networks

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  • Krebs, Vanessa
  • Schewe, Lars
  • Schmidt, Martin
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.

Suggested Citation

  • Krebs, Vanessa & Schewe, Lars & Schmidt, Martin, 2018. "Uniqueness and multiplicity of market equilibria on DC power flow networks," European Journal of Operational Research, Elsevier, vol. 271(1), pages 165-178.
    • Handle: RePEc:eee:ejores:v:271:y:2018:i:1:p:165-178
    DOI: 10.1016/j.ejor.2018.05.016
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    References listed on IDEAS

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    2. Lars Schewe & Martin Schmidt, 2020. "The impact of potential-based physics models on pricing in energy networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 1003-1029, September.
    3. Ratha, Anubhav & Pinson, Pierre & Le Cadre, Hélène & Virag, Ana & Kazempour, Jalal, 2023. "Moving from linear to conic markets for electricity," European Journal of Operational Research, Elsevier, vol. 309(2), pages 762-783.
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    5. Veronika Grimm & Lars Schewe & Martin Schmidt & Gregor Zöttl, 2019. "A multilevel model of the European entry-exit gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 223-255, April.
    6. Egerer, Jonas & Grimm, Veronika & Kleinert, Thomas & Schmidt, Martin & Zöttl, Gregor, 2021. "The impact of neighboring markets on renewable locations, transmission expansion, and generation investment," European Journal of Operational Research, Elsevier, vol. 292(2), pages 696-713.
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    8. Skolfield, J. Kyle & Escobedo, Adolfo R., 2022. "Operations research in optimal power flow: A guide to recent and emerging methodologies and applications," European Journal of Operational Research, Elsevier, vol. 300(2), pages 387-404.
    9. Bobo, Lucien & Mitridati, Lesia & Taylor, Josh A. & Pinson, Pierre & Kazempour, Jalal, 2021. "Price-region bids in electricity markets," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1056-1073.
    10. Ambrosius, Mirjam & Grimm, Veronika & Kleinert, Thomas & Liers, Frauke & Schmidt, Martin & Zöttl, Gregor, 2020. "Endogenous price zones and investment incentives in electricity markets: An application of multilevel optimization with graph partitioning," Energy Economics, Elsevier, vol. 92(C).
    11. Egerer, Jonas & Grimm, Veronika & Grübel, Julia & Zöttl, Gregor, 2022. "Long-run market equilibria in coupled energy sectors: A study of uniqueness," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1335-1354.
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