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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
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    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. 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.
    3. 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.
    4. Davis, Sergio, 2022. "Fluctuating temperature outside superstatistics: Thermodynamics of small systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    5. 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.
    6. 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).
    7. 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).
    8. Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    9. 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.

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