IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v70y2018i2d10.1007_s10898-017-0595-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0595-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-017-0595-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, September.
    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. 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.
    4. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    5. 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.
    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. Michael Herty & Sonja Steffensen & Anna Thunen, 2018. "Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response," Papers 1808.07941, arXiv.org, revised Apr 2020.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2021. "A Local Variation Method for Bilevel Nash Equilibrium Problems," CSEF Working Papers 620, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    3. Wenting Zhao & Jun Lv & Xilong Yao & Juanjuan Zhao & Zhixin Jin & Yan Qiang & Zheng Che & Chunwu Wei, 2019. "Consortium Blockchain-Based Microgrid Market Transaction Research," Energies, MDPI, vol. 12(20), pages 1-22, October.

    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. Ioan Alexandru Puiu & Raphael Andreas Hauser, 2022. "A fundamental Game Theoretic model and approximate global Nash Equilibria computation for European Spot Power Markets," Papers 2208.14164, arXiv.org.
    2. Huifu Xu & Dali Zhang, 2013. "Stochastic Nash equilibrium problems: sample average approximation and applications," Computational Optimization and Applications, Springer, vol. 55(3), pages 597-645, July.
    3. Benjamin Heymann & Alejandro Jofré, 2016. "Mechanism Design and Auctions for Electricity Network," Working Papers hal-01315844, HAL.
    4. Dali Zhang & Huifu Xu & Yue Wu, 2010. "A two stage stochastic equilibrium model for electricity markets with two way contracts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 1-45, February.
    5. Tsimopoulos, Evangelos G. & Georgiadis, Michael C., 2021. "Nash equilibria in electricity pool markets with large-scale wind power integration," Energy, Elsevier, vol. 228(C).
    6. Christos N. Dimitriadis & Evangelos G. Tsimopoulos & Michael C. Georgiadis, 2021. "A Review on the Complementarity Modelling in Competitive Electricity Markets," Energies, MDPI, vol. 14(21), pages 1-27, November.
    7. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Cambridge Working Papers in Economics 1421, Faculty of Economics, University of Cambridge.
    8. Wang, Lu & Gu, Wei & Wu, Zhi & Qiu, Haifeng & Pan, Guangsheng, 2020. "Non-cooperative game-based multilateral contract transactions in power-heating integrated systems," Applied Energy, Elsevier, vol. 268(C).
    9. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    10. Ming Hu & Masao Fukushima, 2011. "Variational Inequality Formulation of a Class of Multi-Leader-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 455-473, December.
    11. Holmberg, Pär & Philpott, Andrew, 2012. "Supply Function Equilibria in Networks with Transport Constraints," Working Paper Series 945, Research Institute of Industrial Economics, revised 10 Aug 2015.
    12. Benjamin Heymann & Alejandro Jofré, 2016. "Mechanism design and allocation algorithms for network markets with piece-wise linear costs and externalities," Working Papers hal-01416411, HAL.
    13. Ming Hu & Masao Fukushima, 2012. "Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints," Computational Optimization and Applications, Springer, vol. 52(2), pages 415-437, June.
    14. David P. Brown & David E. M. Sappington, 2022. "Vertical integration and capacity investment in the electricity sector," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(1), pages 193-226, February.
    15. David Pozo & Enzo Sauma & Javier Contreras, 2017. "Basic theoretical foundations and insights on bilevel models and their applications to power systems," Annals of Operations Research, Springer, vol. 254(1), pages 303-334, July.
    16. Brown, David P. & Sappington, David E.M., 2020. "Load-Following Forward Contracts," Working Papers 2020-14, University of Alberta, Department of Economics, revised 31 Dec 2021.
    17. A. Downward & G. Zakeri & A. B. Philpottt, 2010. "On Cournot Equilibria in Electricity Transmission Networks," Operations Research, INFORMS, vol. 58(4-part-2), pages 1194-1209, August.
    18. Yi Tang & Jing Ling & Tingting Ma & Ning Chen & Xiaofeng Liu & Bingtuan Gao, 2017. "A Game Theoretical Approach Based Bidding Strategy Optimization for Power Producers in Power Markets with Renewable Electricity," Energies, MDPI, vol. 10(5), pages 1-16, May.
    19. Keles, Dogan & Dehler-Holland, Joris & Densing, Martin & Panos, Evangelos & Hack, Felix, 2020. "Cross-border effects in interconnected electricity markets - an analysis of the Swiss electricity prices," Energy Economics, Elsevier, vol. 90(C).
    20. Aghamohammadloo, Hossein & Talaeizadeh, Valiollah & Shahanaghi, Kamran & Aghaei, Jamshid & Shayanfar, Heidarali & Shafie-khah, Miadreza & Catalão, João P.S., 2021. "Integrated Demand Response programs and energy hubs retail energy market modelling," Energy, Elsevier, vol. 234(C).

    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:spr:jglopt:v:70:y:2018:i:2:d:10.1007_s10898-017-0595-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.