IDEAS home Printed from https://ideas.repec.org/a/nat/natene/v3y2018i2d10.1038_s41560-017-0058-z.html
   My bibliography  Save this article

Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics

Author

Listed:
  • Benjamin Schäfer

    (Technical University of Dresden
    MPIDS)

  • Christian Beck

    (Queen Mary University of London)

  • Kazuyuki Aihara

    (The University of Tokyo)

  • Dirk Witthaut

    (Institute of Energy and Climate Research-Systems Analysis and Technology Evaluation
    University of Cologne)

  • Marc Timme

    (Technical University of Dresden
    MPIDS)

Abstract

Multiple types of fluctuations impact the collective dynamics of power grids and thus challenge their robust operation. Fluctuations result from processes as different as dynamically changing demands, energy trading and an increasing share of renewable power feed-in. Here we analyse principles underlying the dynamics and statistics of power grid frequency fluctuations. Considering frequency time series for a range of power grids, including grids in North America, Japan and Europe, we find a strong deviation from Gaussianity best described as Lévy-stable and q-Gaussian distributions. We present a coarse framework to analytically characterize the impact of arbitrary noise distributions, as well as a superstatistical approach that systematically interprets heavy tails and skewed distributions. We identify energy trading as a substantial contribution to today’s frequency fluctuations and effective damping of the grid as a controlling factor enabling reduction of fluctuation risks, with enhanced effects for small power grids.

Suggested Citation

  • Benjamin Schäfer & Christian Beck & Kazuyuki Aihara & Dirk Witthaut & Marc Timme, 2018. "Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics," Nature Energy, Nature, vol. 3(2), pages 119-126, February.
    • Handle: RePEc:nat:natene:v:3:y:2018:i:2:d:10.1038_s41560-017-0058-z
    DOI: 10.1038/s41560-017-0058-z
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/s41560-017-0058-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1038/s41560-017-0058-z?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. dos Santos, M.A.F. & Menon, L. & Cius, D., 2022. "Superstatistical approach of the anomalous exponent for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Sabarathinam Srinivasan & Suresh Kumarasamy & Zacharias E. Andreadakis & Pedro G. Lind, 2023. "Artificial Intelligence and Mathematical Models of Power Grids Driven by Renewable Energy Sources: A Survey," Energies, MDPI, vol. 16(14), pages 1-56, July.
    3. Davis, Sergio, 2022. "Fluctuating temperature outside superstatistics: Thermodynamics of small systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    4. Santiago Bustamante-Mesa & Jorge W. Gonzalez-Sanchez & Sergio D. Saldarriaga-Zuluaga & Jesús M. López-Lezama & Nicolás Muñoz-Galeano, 2024. "Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection," Energies, MDPI, vol. 17(2), pages 1-20, January.
    5. Todeschini, G. & Coles, D. & Lewis, M. & Popov, I. & Angeloudis, A. & Fairley, I. & Johnson, F. & Williams, A.J. & Robins, P. & Masters, I., 2022. "Medium-term variability of the UK's combined tidal energy resource for a net-zero carbon grid," Energy, Elsevier, vol. 238(PA).
    6. Chen, Xiaodong & Ge, Xinxin & Sun, Rongfu & Wang, Fei & Mi, Zengqiang, 2024. "A SVM based demand response capacity prediction model considering internal factors under composite program," Energy, Elsevier, vol. 300(C).
    7. Haoyao Nie & Xiaohua Nie, 2021. "Adaptive Tracking Method of Distorted Voltage Using IMM Algorithm under Grid Frequency Fluctuation Conditions," Energies, MDPI, vol. 14(23), pages 1-17, November.
    8. Konlechner, Roland & Allagui, Anis & Antonov, Vladimir N. & Yudin, Dmitry, 2023. "A superstatistics approach to the modelling of memristor current–voltage responses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    9. Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    10. Zhou, Hao & Toth, Christopher & Guensler, Randall & Laval, Jorge, 2022. "Hybrid modeling of lane changes near freeway diverges," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 1-14.

    More about this item

    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:nat:natene:v:3:y:2018:i:2:d:10.1038_s41560-017-0058-z. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.nature.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.