IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v17y2023i4d10.1007_s11579-023-00348-6.html
   My bibliography  Save this book

A mean field model for the development of renewable capacities

Author

Listed:
  • Clémence Alasseur

    (Laboratoire de Finance des Marchés de l’énergie)

  • Matteo Basei

    (Laboratoire de Finance des Marchés de l’énergie)

  • Charles Bertucci

    (UMR7641 École Polytechnique)

  • Alekos Cecchin

    (Università di Padova)

Abstract

We propose a model based on a large number of small competitive producers of renewable energies, to study the effect of subsidies on the aggregate level of capacity, taking into account a cannibalization effect. We first derive a model to explain how long-time equilibrium can be reached on the market of production of renewable electricity and compare this equilibrium to the case of monopoly. Then we consider the case in which other capacities of production adjust to the production of renewable energies. The analysis is based on a master equation and we get explicit formulae for the long-time equilibria. We also provide new numerical methods to simulate the master equation and the evolution of the capacities. Thus we find the optimal subsidies to be given by a central planner to the installation and the production in order to reach a desired equilibrium capacity.

Suggested Citation

  • Clémence Alasseur & Matteo Basei & Charles Bertucci & Alekos Cecchin, 2023. "A mean field model for the development of renewable capacities," Mathematics and Financial Economics, Springer, volume 17, number 5, February.
    • Handle: RePEc:spr:mathfi:v:17:y:2023:i:4:d:10.1007_s11579-023-00348-6
    DOI: 10.1007/s11579-023-00348-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-023-00348-6
    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/s11579-023-00348-6?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. Bhagwat, Pradyumna C. & Richstein, Jörn C. & Chappin, Emile J.L. & de Vries, Laurens J., 2016. "The effectiveness of a strategic reserve in the presence of a high portfolio share of renewable energy sources," Utilities Policy, Elsevier, vol. 39(C), pages 13-28.
    2. René Aïd & Roxana Dumitrescu & Peter Tankov, 2021. "The entry and exit game in the electricity markets: A mean-field game approach," Post-Print hal-03215763, HAL.
    3. Meus, Jelle & Van den Bergh, Kenneth & Delarue, Erik & Proost, Stef, 2019. "On international renewable cooperation mechanisms: The impact of national RES-E support schemes," Energy Economics, Elsevier, vol. 81(C), pages 859-873.
    4. Brown, David P., 2018. "Capacity payment mechanisms and investment incentives in restructured electricity markets," Energy Economics, Elsevier, vol. 74(C), pages 131-142.
    5. López Prol, Javier & Steininger, Karl W. & Zilberman, David, 2020. "The cannibalization effect of wind and solar in the California wholesale electricity market," Energy Economics, Elsevier, vol. 85(C).
    6. René Aïd & Luciano Campi & Adrien Nguyen Huu & Nizar Touzi, 2009. "A Structural Risk-Neutral Model Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 925-947.
    7. René Aïd & Matteo Basei & Huyen Pham, 2020. "A McKean-Vlasov approach to distributed electricity generation development," Post-Print hal-03714163, HAL.
    8. M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298, October.
    9. Bublitz, Andreas & Keles, Dogan & Zimmermann, Florian & Fraunholz, Christoph & Fichtner, Wolf, 2019. "A survey on electricity market design: Insights from theory and real-world implementations of capacity remuneration mechanisms," Energy Economics, Elsevier, vol. 80(C), pages 1059-1078.
    10. René Aïd & Matteo Basei & Huyên Pham, 2020. "A McKean–Vlasov approach to distributed electricity generation development," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 269-310, April.
    Full references (including those not matched with items on IDEAS)

    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. Cl'emence Alasseur & Heythem Farhat & Marcelo Saguan, 2019. "A Principal-Agent approach to Capacity Remuneration Mechanisms," Papers 1911.12623, arXiv.org, revised Sep 2020.
    2. Sirin, Selahattin Murat & Uz, Dilek & Sevindik, Irem, 2022. "How do variable renewable energy technologies affect firm-level day-ahead output decisions: Evidence from the Turkish wholesale electricity market," Energy Economics, Elsevier, vol. 112(C).
    3. Wieger Hinderks & Andreas Wagner & Ralf Korn, 2018. "A structural Heath-Jarrow-Morton framework for consistent intraday, spot, and futures electricity prices," Papers 1803.08831, arXiv.org, revised Jan 2019.
    4. Yiakoumi, Despina & Rouaix, Agathe & Phimister, Euan, 2022. "Evaluating capacity auction design for electricity: An experimental analysis," Energy Economics, Elsevier, vol. 115(C).
    5. repec:dui:wpaper:1504 is not listed on IDEAS
    6. Ren'e Aid & Ofelia Bonesini & Giorgia Callegaro & Luciano Campi, 2021. "A McKean-Vlasov game of commodity production, consumption and trading," Papers 2111.04391, arXiv.org.
    7. Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    8. Sam Howison & Daniel Schwarz, 2010. "Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach," Papers 1011.3736, arXiv.org, revised May 2015.
    9. Andreas Wagner, 2014. "Residual Demand Modeling and Application to Electricity Pricing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    10. Rene Carmona & Michael Coulon & Daniel Schwarz, 2012. "Electricity price modeling and asset valuation: a multi-fuel structural approach," Papers 1205.2299, arXiv.org.
    11. Kallabis, Thomas & Pape, Christian & Weber, Christoph, 2016. "The plunge in German electricity futures prices – Analysis using a parsimonious fundamental model," Energy Policy, Elsevier, vol. 95(C), pages 280-290.
    12. Coulon, Michael & Powell, Warren B. & Sircar, Ronnie, 2013. "A model for hedging load and price risk in the Texas electricity market," Energy Economics, Elsevier, vol. 40(C), pages 976-988.
    13. S. Oliveira, Fernando & William-Rioux, Bertrand & Pierru, Axel, 2023. "Capacity expansion in liberalized electricity markets with locational pricing and renewable energy investments," Energy Economics, Elsevier, vol. 127(PB).
    14. Rai, Alan & Nunn, Oliver, 2020. "On the impact of increasing penetration of variable renewables on electricity spot price extremes in Australia," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 67-86.
    15. Tolis, Athanasios I. & Rentizelas, Athanasios A., 2011. "An impact assessment of electricity and emission allowances pricing in optimised expansion planning of power sector portfolios," Applied Energy, Elsevier, vol. 88(11), pages 3791-3806.
    16. Wieger Hinderks & Ralf Korn & Andreas Wagner, 2020. "Unifying the theory of storage and the risk premium by an unobservable intrinsic electricity price," Papers 2011.03987, arXiv.org.
    17. Woo, C.K. & Milstein, I. & Tishler, A. & Zarnikau, J., 2019. "A wholesale electricity market design sans missing money and price manipulation," Energy Policy, Elsevier, vol. 134(C).
    18. Zhang, Yuanyuan & Zhao, Huiru & Li, Bingkang, 2022. "Research on the design and influence of unit generation capacity adequacy guarantee mechanism in the power market," Energy, Elsevier, vol. 248(C).
    19. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    20. Markus Hess, 2020. "Pricing electricity forwards under future information on the stochastic mean-reversion level," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 751-767, December.
    21. Simone Göttlich & Ralf Korn & Kerstin Lux, 2019. "Optimal control of electricity input given an uncertain demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 301-328, December.

    More about this item

    Keywords

    Energy transition; Mean field equilibrium; Master equation; Optimal incentives;
    All these keywords.

    JEL classification:

    • G38 - Financial Economics - - Corporate Finance and Governance - - - Government Policy and Regulation
    • Q48 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Government Policy

    Statistics

    Access and download statistics

    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:mathfi:v:17:y:2023:i:4:d:10.1007_s11579-023-00348-6. 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.