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Multifractal Power Network Based on the Two Scales Cantor Set Topology

Siham Lakrih(1*), Jaouad Diouri(2)

(1) University Abelmalik Essaadi, Morocco
(2) University Abelmalik Essaadi, Morocco
(*) Corresponding author


DOI: https://doi.org/10.15866/iree.v16i3.19632

Abstract


This paper proposes a transition from monofractal to multifractal topology to study the dynamic behavior of modern power networks. For this purpose, a multifractal power network is proposed based on the two scales Cantor set topology. The dynamic properties of the proposed network are investigated using the renormalization method, Continuous Wavelet Transform (CWT) and Multifractal Detrended Fluctuation Analysis (MFDFA). Our findings prove that the scale-invariant behavior of the proposed network is governed by two scales factors. The results of CWT indicate that the frequency responses corresponding to the two scales Cantor network exhibit a self-similar behavior. As for the MFDFA results, they revealed that a set of fractal dimensions is required to reproduce the dynamics of the proposed multifractal network.
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Keywords


Multifractal Cantor Network; Continuous Wavelet Transform; Scale Invariance; Renormalization; Self-Similarity; Multifractal Detrended Fluctuation Analysis

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References


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