MFDFA: Efficient Multifractal Detrended Fluctuation Analysis in Python

Gorjão, Leonardo Rydin; Hassan, Galib; Kurths, Jürgen; Witthaut, Dirk

doi:10.48550/arxiv.2104.10470

Cited by 2 publications

(3 citation statements)

References 70 publications

(95 reference statements)

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“…3a the variance of the increment statistics increases in a power-law relation with the incremental lag τ . In order to best describe this-and to retrieve the Hurst exponent H-we employ Detrended Fluctuation Analysis (DFA) of the power-grid frequency recordings [51][52][53]. Recall that DFA studies the scaling of the fluctuations of a time series by studying the local properties of the data, similarly to what increment statistics does.…”

Section: E Amplitude Synchronisationmentioning

confidence: 99%

Phase and amplitude synchronisation in power-grid frequency fluctuations in the Nordic Grid

Gorjão¹,

Vanfretti²,

Witthaut³

et al. 2021

Preprint

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Monitoring and modelling the power grid frequency is key to ensuring stability in the electrical power system. Many tools exist to investigate the detailed deterministic dynamics and especially the bulk behaviour of the frequency. However, far less attention has been paid to its stochastic properties, and there is a need for a cohesive framework that couples both short-time scale fluctuations and bulk behaviour. Moreover, commonly assumed uncorrelated stochastic noise is predominantly employed in modelling in energy systems. In this publication, we examine the stochastic properties of six synchronous power-grid frequency recording with high-temporal resolution of the Nordic Grid from September 2013, focusing on the increments of the frequency recordings. We show that these increments follow non-Gaussian statistics and display spatial and temporal correlations. Furthermore, we report two different physical synchronisation phenomena: a very short timescale phase synchronisation (< 2 s) followed by a slightly larger timescale amplitude synchronisation (2 s-5 s). Overall, these results provide guidance on how to model fluctuations in power systems.

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Section: E Amplitude Synchronisationmentioning

confidence: 99%

Phase and amplitude synchronisation in power-grid frequency fluctuations in the Nordic Grid

Gorjão¹,

Vanfretti²,

Witthaut³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Multifractal detrended fluctuation analysis (MFDFA) [49,62,63] is one of the principal methods to estimate the scaling function ξ(n) of one-dimensional time series. It is well suited for time series with trends, like price time series.…”

Section: Multifractal Detrended Fluctuation Analysismentioning

confidence: 99%

“…To obtain some statistics of the range of Hurst exponents using MFDFA, we estimate the Hurst exponent by fitting the ξ(2) function for various ranges of the snippets within the daily and hourly scale. In this way, the results are presented in a box-and-whiskers plot to best quantify the estimation of the Hurst exponents H [63].…”

Section: E Implementationmentioning

confidence: 99%