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On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity

Author

Listed:
  • Elisabetta Allevi

    (Università degli Studi di Brescia)

  • Didier Aussel

    (University of Perpignan Via Domitia)

  • Rossana Riccardi

    (Università degli Studi di Brescia)

Abstract

We consider a model of pay-as-clear electricity market based on a Equilibrium Problem with Complementarity Constraints approach where the producers are playing a noncooperative game parameterized by the decisions of regulator of the market (ISO). In the proposed approach the bids are assumed to be convex quadratic functions of the production quantity. The demand is endogenously determined. The ISO problem aims to maximize the total welfare of the market. The demand being elastic, this total welfare take into account at the same time the willingness to pay of the aggregated consumer, as well as the cost of transactions. The market clearing will determine the market price in a pay-as-clear way. An explicit formula for the optimal solution of the ISO problem is obtained and the optimal price is proved to be unique. We also state some conditions for the existence of equilibria for this electricity market with elastic demand. Some numerical experiments on a simplified market model are also provided.

Suggested Citation

  • Elisabetta Allevi & Didier Aussel & Rossana Riccardi, 2018. "On an equilibrium problem with complementarity constraints formulation of pay-as-clear electricity market with demand elasticity," Journal of Global Optimization, Springer, vol. 70(2), pages 329-346, February.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0595-9
    DOI: 10.1007/s10898-017-0595-9
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    References listed on IDEAS

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    1. Steven A. Gabriel & Antonio J. Conejo & J. David Fuller & Benjamin F. Hobbs & Carlos Ruiz, 2013. "Complementarity Modeling in Energy Markets," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4419-6123-5, April.
    2. Juan Escobar & Alejandro Jofré, 2010. "Monopolistic competition in electricity networks with resistance losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 101-121, July.
    3. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    4. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    5. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
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