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A new formulation of the European day-ahead electricity market problem and its algorithmic consequences

Author

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  • MADANI, Mehdi

    () (Université catholique de Louvain, Louvain School of Management, Belgium)

  • VAN VYVE, Mathieu

    () (niversité catholique de Louvain, CORE and Louvain School of Management, Belgium)

Abstract

A new formulation of the optimization problem implementing European market rules for non- convex day-ahead electricity markets is presented, that avoids the use of complementarity constraints to express market equilibrium conditions, and also avoids the introduction of auxiliary binary variables to linearise these constraints. Instead, we rely on strong duality theory for linear or convex quadratic optimization problems to recover equilibrium constraints imposed by most of European power exchanges facing indivisible orders. When only so-called stepwise preference curves are considered to describe continuous bids, the new formulation allows to take full advantage of state-of-the-art solvers, and in most cases, an optimal solution together with market clearing prices can be computed for large-scale instances without any further algorithmic work. The new formulation also suggests a very competitive Benders-like decomposition procedure, which helps to handle the case of interpolated preference curves that yield quadratic primal and dual objective functions, and consequently a dense quadratic constraint. This procedure essentially consists in strengthening classical Benders cuts locally. Computational experiments on real data kindly provided by main European power exchanges (Apx-Endex, Belpex and Epex spot) show that in the linear case, both approaches are very efficient, while for quadratic instances, only the decomposition procedure is tractable and shows very good results. Finally, when most orders are block orders, and instances are combinatorially very hard, the new MILP approach is substantially more efficient.

Suggested Citation

  • MADANI, Mehdi & VAN VYVE, Mathieu, 2013. "A new formulation of the European day-ahead electricity market problem and its algorithmic consequences," CORE Discussion Papers 2013074, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2013074
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    File URL: http://uclouvain.be/cps/ucl/doc/core/documents/coredp2013_74web.pdf
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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, January.
    2. Förster, Manuel & Mauleon, Ana & Vannetelbosch, Vincent J., 2016. "Trust and manipulation in social networks," Network Science, Cambridge University Press, vol. 4(02), pages 216-243, June.
    3. Nigar Hashimzade & Jean Hindriks & Gareth D. Myles, 2006. "Solutions Manual to Accompany Intermediate Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582694, January.
    4. VARDAR, N. Baris, 2013. "Imperfect resource substitution and optimal transition to clean technologies," CORE Discussion Papers 2013072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Auctions/bidding; market coupling; equilibrium prices; mixed integer programming; large scale optimization;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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