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Linear prices for non-convex electricity markets: models and algorithms


  • VAN VYVE, Mathieu

    () (Université catholique de Louvain, CORE and LSM, B-1348 Louvain-la-Neuve, Belgium)


Strict Linear Pricing in non-convex markets is a mathematical impossibility. In the context of electricity markets, two different classes of solutions have been proposed to this conundrum on both sides of the Atlantic. We formally describe these two approaches in a common framework, review and analyze their main properties, and discuss their shortcomings. In US, some orders are not settled at the market price, but at their bidding price, deviating from uniform pricing (all orders are financially settled at the same prices). This creates a disincentive to bid one's own true cost, and creates a missing money problem for the clearing house of the market. In Europe, all accepted orders are in-the-money are settled at the uniform market price. This implies that the welfare-maximizing solution is considered infeasible and also that the optimization problem is much less convex and more difficult to solve. This also creates fairness issues for orders of small volume, and the solution obtained does not implement a Walrasian equilibrium. Based on this analysis we propose a new model that draws on both approaches and retains their best theoretical properties. We also show how the different approaches compare on classical toy problem.

Suggested Citation

  • VAN VYVE, Mathieu, 2011. "Linear prices for non-convex electricity markets: models and algorithms," CORE Discussion Papers 2011050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2011050

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    References listed on IDEAS

    1. Fleurbaey,Marc & Maniquet,François, 2011. "A Theory of Fairness and Social Welfare," Cambridge Books, Cambridge University Press, number 9780521715348, May.
    2. 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.
    3. Herbert Scarf, 1994. "The Allocation of Resources in the Presence of Indivisibilities," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.
    4. Duranton, Gilles & Martin, Philippe & Mayer, Thierry & Mayneris, Florian, 2010. "The Economics of Clusters: Lessons from the French Experience," OUP Catalogue, Oxford University Press, number 9780199592203.
    5. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
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    Cited by:

    1. 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.
    2. Madani, M. & Van Vyve, M., 2015. "A MIP framework for non-convex uniform price day-ahead electricity auctions," CORE Discussion Papers 2015017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. Vazquez, Carlos & Hallack, Michelle & Vazquez, Miguel, 2017. "Price computation in electricity auctions with complex rules: An analysis of investment signals," Energy Policy, Elsevier, vol. 105(C), pages 550-561.

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    electricity markets; non-convexities; pricing;


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