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

Nature Energyvolume 3pages119126 (2018) | Download Citation


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.

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We gratefully acknowledge support from the Federal Ministry of Education and Research (BMBF grant no. 03SF0472A-F to M.T. and D.W.), the Helmholtz Association (via the joint initiative “Energy System 2050—a Contribution of the Research Field Energy” and grant no. VH-NG-1025 to D.W.), the Göttingen Graduate School for Neurosciences and Molecular Biosciences (DFG grant GSC 226/2) to B.S., the EPSRC via grant EP/N013492/1 to C.B., the JST CREST, grant nos JPMJCR14D2 and JPMJCR15K1, to K.A. and the Max Planck Society to M.T.

Author information

Author notes

  1. Dirk Witthaut and Marc Timme contributed equally to this work.


  1. Chair for Network Dynamics, cfaed and Institute for Theoretical Physics, Technical University of Dresden, Dresden, Germany

    • Benjamin Schäfer
    •  & Marc Timme
  2. Network Dynamics, MPIDS, Göttingen, Germany

    • Benjamin Schäfer
    •  & Marc Timme
  3. School of Mathematical Sciences, Queen Mary University of London, London, UK

    • Christian Beck
  4. Institute of Industrial Science, The University of Tokyo, Meguro-ku, Tokyo, Japan

    • Kazuyuki Aihara
  5. Forschungszentrum Jülich, Institute of Energy and Climate Research-Systems Analysis and Technology Evaluation, Jülich, Germany

    • Dirk Witthaut
  6. Institute for Theoretical Physics, University of Cologne, Köln, Germany

    • Dirk Witthaut


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B.S., D.W. and M.T. conceived and designed the research. B.S. acquired the data, performed the data analysis and formulated stochastic predictions. All authors contributed to discussing the results and writing the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Benjamin Schäfer.

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  1. Supplementary Information

    Supplementary Notes 1–6, Supplementary Tables 1–2, Supplementary Figures 1–16 and Supplementary References.

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