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


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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Fig. 1: Fluctuations in frequency around the reference frequency of 50 Hz.
Fig. 2: Non-Gaussian nature of the frequency distribution.
Fig. 3: Decay of the autocorrelation of the frequency dynamics.
Fig. 4: Inverse correlation time of different regions.
Fig. 5: Noise amplitudes for European and American grids.
Fig. 6: Superimposed Gaussian distributions leading to heavy tails.
Fig. 7: Self-consistency test of superstatistics.


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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.

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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.

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Correspondence to Benjamin Schäfer.

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

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Schäfer, B., Beck, C., Aihara, K. et al. Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics. Nat Energy 3, 119–126 (2018).

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