IDEAS home Printed from https://ideas.repec.org/p/cor/louvco/2015017.html
   My bibliography  Save this paper

A MIP framework for non-convex uniform price day-ahead electricity auctions

Author

Listed:
  • Madani, M.

    (Université catholique de Louvain, CORE, Belgium)

  • Van Vyve, M.

    (Université catholique de Louvain, CORE, Belgium)

Abstract

It is well-known that a market equilibrium with uniform prices often does not exist in non-convex day-ahead electricity auctions. We consider the case of the non-convex, uniform- price Pan-European day-ahead electricity market ”PCR” (Price Coupling of Regions), with non-convexities arising from so-called complex and block orders. Extending previous results, we propose a new primal-dual framework for these auctions, which has applications in both economic analysis and algorithm design. The contribution here is threefold. First, from the algorithmic point of view, we give a non-trivial exact (i.e. not approximate) linearization of a non-convex ’minimum income condition’ that must hold for complex orders arising from the Spanish market, avoiding the introduction of any auxiliary variables, and allowing us to solve market clearing instances involving most of the bidding products proposed in PCR using off-the-shelf MIP solvers. Second, from the economic analysis point of view, we give the first MILP formulations of optimization problems such as the maximization of the traded volume, or the minimization of opportunity costs of paradoxically rejected block bids. We first show on a toy example that these two objectives are distinct from maximizing welfare. We also recover directly a previously noted property of an alternative market model. Third, we provide numerical experiments on realistic large-scale instances. They illustrate the efficiency of the approach, as well as the economics trade-offs that may occur in practice.

Suggested Citation

  • Madani, M. & Van Vyve, M., 2015. "A MIP framework for non-convex uniform price day-ahead electricity auctions," LIDAM Discussion Papers CORE 2015017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2015017
    as

    Download full text from publisher

    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2015.html
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Meeus, Leonardo & Verhaegen, Karolien & Belmans, Ronnie, 2009. "Block order restrictions in combinatorial electric energy auctions," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1202-1206, August.
    2. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, April.
    3. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9781107001411.
    4. Fleurbaey, Marc & Maniquet, François, 2015. "Optimal taxation theory and principles of fairness," LIDAM Discussion Papers CORE 2015005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. NESTEROV, Yurii, 2015. "Complexity bounds for primal-dual methods minimizing the model of objective function," LIDAM Discussion Papers CORE 2015003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. O'Neill, Richard & Mead, David & Malvadkar, Partha, 2005. "On Market Clearing Prices Higher than the Highest Bid and Other Almost Paranormal Phenomena," The Electricity Journal, Elsevier, vol. 18(2), pages 19-27, March.
    7. 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.
    8. Garci'a-Bertrand, Raquel & Conejo, Antonio J. & Gabriel, Steven, 2006. "Electricity market near-equilibrium under locational marginal pricing and minimum profit conditions," European Journal of Operational Research, Elsevier, vol. 174(1), pages 457-479, October.
    9. VAN VYVE, Mathieu, 2011. "Linear prices for non-convex electricity markets: models and algorithms," LIDAM Discussion Papers CORE 2011050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. O'Neill, Richard P. & Sotkiewicz, Paul M. & Hobbs, Benjamin F. & Rothkopf, Michael H. & Stewart, William R., 2005. "Efficient market-clearing prices in markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 164(1), pages 269-285, July.
    11. Mehdi MADANI & Mathieu VAN VYVE, 2015. "Computationally efficient MIP formulation and algorithms for European day-ahead electricity market auctions," LIDAM Reprints CORE 2808, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. MADANI, Mehdi & VAN VYVE, Mathieu, 2016. "Revisiting Minimum Profit Conditions in Uniform Price Day-Ahead Electricity Auctions," LIDAM Discussion Papers CORE 2016043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. David Fuller, J. & Çelebi, Emre, 2017. "Alternative models for markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 261(2), pages 436-449.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mehdi Madani & Mathieu Van Vyve, 2017. "A MIP framework for non-convex uniform price day-ahead electricity auctions," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 263-284, March.
    2. D'avid Csercsik, 2020. "Strategic bidding via the interplay of minimum income condition orders in day-ahead power exchanges," Papers 2012.07789, arXiv.org.
    3. Csercsik, Dávid, 2021. "Strategic bidding via the interplay of minimum income condition orders in day-ahead power exchanges," Energy Economics, Elsevier, vol. 95(C).
    4. Godin, M. & Hindriks, J., 2015. "A Review of Critical Issues on Tax Design and Tax Administration in a Global Economy and Developing Countries," LIDAM Discussion Papers CORE 2015028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Pestieau, Pierre & Ponthiere, Gregory, 2016. "Longevity Variations And The Welfare State," Journal of Demographic Economics, Cambridge University Press, vol. 82(2), pages 207-239, June.
    6. Samuel Ferey & Pierre Dehez, 2016. "Multiple Causation, Apportionment, and the Shapley Value," The Journal of Legal Studies, University of Chicago Press, vol. 45(1), pages 143-171.
    7. 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.
    8. Jean Hindriks & Yukihiro Nishimura, 2017. "Equilibrium leadership in tax competition models with capital ownership: a rejoinder," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(2), pages 338-349, April.
    9. Queyranne, M. & Wolsey, L.A., 2015. "Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups," LIDAM Discussion Papers CORE 2015036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Christian M. Hafner & Hans Manner & Léopold Simar, 2018. "The “wrong skewness” problem in stochastic frontier models: A new approach," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 380-400, April.
    11. Nermin Elif Kurt & H. Bahadir Sahin & Kurc{s}ad Derinkuyu, 2018. "An Adaptive Tabu Search Algorithm for Market Clearing Problem in Turkish Day-Ahead Market," Papers 1809.10554, arXiv.org.
    12. Jean J. Gabszewicz & Marco A. Marini & Ornella Tarola, 2015. "Alliance Formation in a Vertically Differentiated Market," DIAG Technical Reports 2015-06, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    13. Balandraud, Eric & Queyranne, Maurice & Tardella, Fabio, 2015. "Largest minimally inversion-complete and pair-complete sets of permutations," LIDAM Discussion Papers CORE 2015009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Mouchart, M. & Wunsch, G. & Russo, F., 2015. "The issue of control in multivariate systems A contribution of structural modelling," LIDAM Discussion Papers CORE 2015029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Le Hong Lam & Valentin Ilea & Cristian Bovo, 2020. "New Clearing Model to Mitigate the Non-Convexity in European Day-ahead Electricity Market," Energies, MDPI, vol. 13(18), pages 1-28, September.
    16. Yukihiro Nishimura & Pierre Pestieau, 2016. "Efficient taxation with differential risks of dependence and mortality," Economics Bulletin, AccessEcon, vol. 36(1), pages 52-57.
    17. Gokhan Ceyhan & Nermin Elif Kurt & H. Bahadir Sahin & Kurc{s}ad Derinkuyu, 2017. "Empirical comparison of three models for determining market clearing prices in Turkish day-ahead electricity market," Papers 1712.00235, arXiv.org.
    18. Mouchart, M. & Wunsch, G. & Russo, F., 2015. "The issue of control in multivariate systems, A contribution of structural modelling," LIDAM Discussion Papers ISBA 2015019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Ceyhan, Gökhan & Köksalan, Murat & Lokman, Banu, 2022. "Extensions for Benders cuts and new valid inequalities for solving the European day-ahead electricity market clearing problem efficiently," European Journal of Operational Research, Elsevier, vol. 300(2), pages 713-726.
    20. Dufays, A. & Rombouts, V., 2015. "Sparse Change-Point Time Series Models," LIDAM Discussion Papers CORE 2015032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    Day-ahead electricity market auctions; Non-convexities; Mixed Integer Pro- gramming; Market Coupling; Equilibrium Prices;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cor:louvco:2015017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.