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Moving from linear to conic markets for electricity

Author

Listed:
  • Ratha, Anubhav
  • Pinson, Pierre
  • Le Cadre, Hélène
  • Virag, Ana
  • Kazempour, Jalal

Abstract

We propose a new forward electricity market framework that admits heterogeneous market participants with second-order cone strategy sets, who accurately express the nonlinearities in their costs and constraints through conic bids, and a network operator facing conic operational constraints. In contrast to the prevalent linear-programming-based electricity markets, we highlight how the inclusion of second-order cone constraints improves uncertainty-, asset-, and network-awareness of the market, which is key to the successful transition towards an electricity system based on weather-dependent renewable energy sources. We analyze our general market-clearing proposal using conic duality theory to derive efficient spatially-differentiated prices for the multiple commodities, comprised of energy and flexibility services. Under the assumption of perfect competition, we prove the equivalence of the centrally-solved market-clearing optimization problem to a competitive spatial price equilibrium involving a set of rational and self-interested participants and a price setter. Finally, under common assumptions, we prove that moving towards conic markets does not incur the loss of desirable economic properties of markets, namely market efficiency, cost recovery, and revenue adequacy. Our numerical studies focus on the specific use case of uncertainty-aware market design and demonstrate that the proposed conic market brings advantages over existing alternatives within the linear programming market framework.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:309:y:2023:i:2:p:762-783
    DOI: 10.1016/j.ejor.2022.12.025
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    1. Wenqing Chen & Melvyn Sim & Jie Sun & Chung-Piaw Teo, 2010. "From CVaR to Uncertainty Set: Implications in Joint Chance-Constrained Optimization," Operations Research, INFORMS, vol. 58(2), pages 470-485, April.
    2. Mitridati, Lesia & Kazempour, Jalal & Pinson, Pierre, 2020. "Heat and electricity market coordination: A scalable complementarity approach," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1107-1123.
    3. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    4. Nemirovski, Arkadi, 2012. "On safe tractable approximations of chance constraints," European Journal of Operational Research, Elsevier, vol. 219(3), pages 707-718.
    5. 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.
    6. Geoffrey Pritchard & Golbon Zakeri & Andrew Philpott, 2010. "A Single-Settlement, Energy-Only Electric Power Market for Unpredictable and Intermittent Participants," Operations Research, INFORMS, vol. 58(4-part-2), pages 1210-1219, August.
    7. 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.
    8. Roger E. Bohn & Michael C. Caramanis & Fred C. Schweppe, 1984. "Optimal Pricing in Electrical Networks over Space and Time," RAND Journal of Economics, The RAND Corporation, vol. 15(3), pages 360-376, Autumn.
    9. 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.
    10. DE WOLF, Daniel & SMEERS, Yves, 2000. "The gas transmission problem solved by an extension of the simplex algorithm," LIDAM Reprints CORE 1489, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Charles C. Holt & Franco Modigliani & Herbert A. Simon, 1955. "A Linear Decision Rule for Production and Employment Scheduling," Management Science, INFORMS, vol. 2(1), pages 1-30, October.
    12. Burak Kocuk & Santanu S. Dey & X. Andy Sun, 2016. "Strong SOCP Relaxations for the Optimal Power Flow Problem," Operations Research, INFORMS, vol. 64(6), pages 1177-1196, December.
    13. 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.
    14. Jae Ho Kim & Warren B. Powell, 2011. "Optimal Energy Commitments with Storage and Intermittent Supply," Operations Research, INFORMS, vol. 59(6), pages 1347-1360, December.
    15. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    16. Steven Chu & Arun Majumdar, 2012. "Opportunities and challenges for a sustainable energy future," Nature, Nature, vol. 488(7411), pages 294-303, August.
    17. Anthony Papavasiliou, 2018. "Analysis of distribution locational marginal prices," LIDAM Reprints CORE 3045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-127, January.
    19. Erick Delage & Yinyu Ye, 2010. "Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems," Operations Research, INFORMS, vol. 58(3), pages 595-612, June.
    20. Conrado Borraz-Sánchez & Russell Bent & Scott Backhaus & Hassan Hijazi & Pascal Van Hentenryck, 2016. "Convex Relaxations for Gas Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 645-656, November.
    21. repec:inm:orijoo:v:3:y:2021:i:4:p:350-372 is not listed on IDEAS
    22. Ximing Cai & Daene C. McKinney & Leon S. Lasdon & David W. Watkins, 2001. "Solving Large Nonconvex Water Resources Management Models Using Generalized Benders Decomposition," Operations Research, INFORMS, vol. 49(2), pages 235-245, April.
    23. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    Full references (including those not matched with items on IDEAS)

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