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

Author

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  • 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
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    References listed on IDEAS

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    1. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, April.
    2. 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.
    3. 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.
    4. 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.
    5. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9780521171960, October.
    6. 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.
    7. 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).
    8. 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.
    9. 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).
    10. 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).
    11. 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).
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    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.

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    More about this item

    Keywords

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

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