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Equilibrium prices supported by dual price functions in markets with non-convexities

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  • Bjørndal, Mette
  • Jörnsten, Kurt

Abstract

The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start-up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price functions that are the basis for integer programming duality.

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  • Bjørndal, Mette & Jörnsten, Kurt, 2008. "Equilibrium prices supported by dual price functions in markets with non-convexities," European Journal of Operational Research, Elsevier, vol. 190(3), pages 768-789, November.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:3:p:768-789
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    2. Araoz, Veronica & Jörnsten, Kurt, 2011. "Semi-Lagrangean approach for price discovery in markets with non-convexities," European Journal of Operational Research, Elsevier, vol. 214(2), pages 411-417, October.
    3. Arribas, I. & Urbano, A., 2018. "Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 83-94.
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    5. George Liberopoulos & Panagiotis Andrianesis, 2016. "Critical Review of Pricing Schemes in Markets with Non-Convex Costs," Operations Research, INFORMS, vol. 64(1), pages 17-31, February.
    6. Izabela Żółtowska & Eugeniusz Toczyłowski, 2009. "A compensation-based pricing scheme in markets with non-convexities," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(4), pages 125-140.
    7. An, Qingxian & Tao, Xiangyang & Chen, Xiaohong, 2023. "Nested frontier-based best practice regulation under asymmetric information in a principal–agent framework," European Journal of Operational Research, Elsevier, vol. 306(1), pages 269-285.
    8. Izabela Zoltowska & Eugeniusz Toczylowski, 2009. "A compensation-based pricing scheme in marketswith non-convexities," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 125-140.
    9. Hassan Shavandi & Mehrdad Pirnia & J. David Fuller, 2018. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Papers 1809.09734, arXiv.org.
    10. Johannes Knorr & Martin Bichler & Teodora Dobos, 2024. "Zonal vs. Nodal Pricing: An Analysis of Different Pricing Rules in the German Day-Ahead Market," Papers 2403.09265, arXiv.org, revised Apr 2024.
    11. Kuang, Xiaolong & Lamadrid, Alberto J. & Zuluaga, Luis F., 2019. "Pricing in non-convex markets with quadratic deliverability costs," Energy Economics, Elsevier, vol. 80(C), pages 123-131.
    12. David Fuller, J. & Çelebi, Emre, 2017. "Alternative models for markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 261(2), pages 436-449.
    13. Hacopian Dolatabadi, Sarineh & Latify, Mohammad Amin & Karshenas, Hamidreza & Sharifi, Alimorad, 2022. "On pricing issues in electricity markets in the presence of externalities," Energy, Elsevier, vol. 246(C).
    14. Vazquez, Carlos & Hallack, Michelle & Vazquez, Miguel, 2017. "Price computation in electricity auctions with complex rules: An analysis of investment signals," Energy Policy, Elsevier, vol. 105(C), pages 550-561.
    15. Morales, Juan M. & Zugno, Marco & Pineda, Salvador & Pinson, Pierre, 2014. "Electricity market clearing with improved scheduling of stochastic production," European Journal of Operational Research, Elsevier, vol. 235(3), pages 765-774.
    16. Madani, Mehdi & Van Vyve, Mathieu, 2015. "Computationally efficient MIP formulation and algorithms for European day-ahead electricity market auctions," European Journal of Operational Research, Elsevier, vol. 242(2), pages 580-593.
    17. Brown, Gardner & Patterson, Trista & Cain, Nicholas, 2011. "The devil in the details: Non-convexities in ecosystem service provision," Resource and Energy Economics, Elsevier, vol. 33(2), pages 355-365, May.
    18. Wang, Yi & Yang, Zhifang & Yu, Juan & Liu, Sixu, 2023. "Pricing in non-convex electricity markets with flexible trade-off of pricing properties," Energy, Elsevier, vol. 274(C).
    19. Knaut, Andreas & Obermüller, Frank & Weiser, Florian, 2017. "Tender Frequency and Market Concentration in Balancing Power Markets," EWI Working Papers 2017-4, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI).
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    21. Shavandi, Hassan & Pirnia, Mehrdad & Fuller, J. David, 2019. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Applied Energy, Elsevier, vol. 240(C), pages 251-264.
    22. Xin Shi & Alberto J. Lamadrid L. & Luis F. Zuluaga, 2021. "Revenue Adequate Prices for Chance-Constrained Electricity Markets with Variable Renewable Energy Sources," Papers 2105.01233, arXiv.org.

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