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A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

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  • Victor M. Zavala

    (Department of Chemical and Biological Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706)

  • Kibaek Kim

    (Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439)

  • Mihai Anitescu

    (Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, Illinois 60439)

  • John Birge

    (Booth School of Business, University of Chicago, Chicago, Illinois 60637)

Abstract

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives. We extend and analyze a previously proposed stochastic clearing formulation in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price bounded price distortions, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities equal a quantile of their real-time counterparts. The undesired effects of price distortions suggest that stochastic settings provide significant benefits over deterministic ones that go beyond social surplus improvements. We propose additional metrics to evaluate these benefits.

Suggested Citation

  • Victor M. Zavala & Kibaek Kim & Mihai Anitescu & John Birge, 2017. "A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties," Operations Research, INFORMS, vol. 65(3), pages 557-576, June.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:3:p:557-576
    DOI: 10.1287/opre.2016.1576
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    1. Javad Khazaei & Golbon Zakeri & Shmuel S. Oren, 2017. "Single and Multisettlement Approaches to Market Clearing Under Demand Uncertainty," Operations Research, INFORMS, vol. 65(5), pages 1147-1164, October.
    2. Mete Şeref Ahunbay & Martin Bichler & Johannes Knörr, 2023. "Challenges in Designing Electricity Spot Markets," NBER Chapters, in: New Directions in Market Design, National Bureau of Economic Research, Inc.
    3. Bjørndal, Endre & Bjørndal, Mette & Midthun, Kjetil & Tomasgard, Asgeir, 2016. "Stochastic Electricity Dispatch: A challenge for market design," Discussion Papers 2016/11, Norwegian School of Economics, Department of Business and Management Science.
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    5. 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.
    6. Hohl, Cody & Lo Prete, Chiara & Radhakrishnan, Ashish & Webster, Mort, 2023. "Intraday markets, wind integration and uplift payments in a regional U.S. power system," Energy Policy, Elsevier, vol. 175(C).
    7. López-Flores, Francisco Javier & Hernández-Pérez, Luis Germán & Lira-Barragán, Luis Fernando & Rubio-Castro, Eusiel & Ponce-Ortega, José M., 2022. "Optimal Profit Distribution in Interplant Waste Heat Integration through a Hybrid Approach," Energy, Elsevier, vol. 253(C).
    8. Ordoudis, Christos & Delikaraoglou, Stefanos & Kazempour, Jalal & Pinson, Pierre, 2020. "Market-based coordination of integrated electricity and natural gas systems under uncertain supply," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1105-1119.
    9. Philip A. Tominac & Victor M. Zavala, 2020. "Economic Properties of Multi-Product Supply Chains," Papers 2006.03467, arXiv.org, revised Jul 2020.
    10. Bjørndal, Endre & Bjørndal, Mette & Midthun, Kjetil & Zakeri, Golbon, 2016. "Congestion Management in a Stochastic Dispatch Model for Electricity Markets," Discussion Papers 2016/12, Norwegian School of Economics, Department of Business and Management Science.
    11. Anna Schwele & Christos Ordoudis & Pierre Pinson & Jalal Kazempour, 2021. "Coordination of power and natural gas markets via financial instruments," Computational Management Science, Springer, vol. 18(4), pages 505-538, October.
    12. Bjørndal, Endre & Bjørndal, Mette & Midthun, Kjetil & Tomasgard, Asgeir, 2018. "Stochastic electricity dispatch: A challenge for market design," Energy, Elsevier, vol. 150(C), pages 992-1005.
    13. Laur, Arnaud & Nieto-Martin, Jesus & Bunn, Derek W. & Vicente-Pastor, Alejandro, 2020. "Optimal procurement of flexibility services within electricity distribution networks," European Journal of Operational Research, Elsevier, vol. 285(1), pages 34-47.
    14. 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.
    15. Morales, J.M. & Muñoz, M.A. & Pineda, S., 2023. "Prescribing net demand for two-stage electricity generation scheduling," Operations Research Perspectives, Elsevier, vol. 10(C).
    16. Yankai Cao & Carl D. Laird & Victor M. Zavala, 2016. "Clustering-based preconditioning for stochastic programs," Computational Optimization and Applications, Springer, vol. 64(2), pages 379-406, June.
    17. Zhang, Weiqi & Zavala, Victor M., 2022. "Remunerating space–time, load-shifting flexibility from data centers in electricity markets," Applied Energy, Elsevier, vol. 326(C).

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