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A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

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  • Victor M. Zavala
  • Kibaek Kim
  • Mihai Anitescu
  • John Birge

Abstract

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, 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 converge to the quantile of 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.

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  • Victor M. Zavala & Kibaek Kim & Mihai Anitescu & John Birge, 2015. "A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties," Papers 1510.08335, arXiv.org.
    • Handle: RePEc:arx:papers:1510.08335
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    1. 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.
    2. 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.
    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.
    4. 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.
    5. Philip A. Tominac & Victor M. Zavala, 2020. "Economic Properties of Multi-Product Supply Chains," Papers 2006.03467, arXiv.org, revised Jul 2020.
    6. 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.
    7. Dongwei Zhao & Vladimir Dvorkin & Stefanos Delikaraoglou & Alberto J. Lamadrid L. & Audun Botterud, 2023. "Uncertainty-Informed Renewable Energy Scheduling: A Scalable Bilevel Framework," Papers 2312.03868, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
    13. 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).
    14. 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).
    15. 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.
    16. 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).
    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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