Abstract
A power grid harmonic signal is characterized as having both nonlinear and nonstationary features. A novel multifractal detrended fluctuation analysis (MFDFA) algorithm combined with the empirical mode decomposition (EMD) theory and template movement is proposed to overcome some shortcomings in the traditional MFDFA algorithm. The novel algorithm is used to study the multifractal feature of harmonic signals at different frequencies. Firstly, the signal is decomposed and the characteristics of wavelet transform multiresolution analysis are employed to obtain the components at different frequency bands. After this, the local fractal characteristic of the components is studied by utilizing the novel MFDFA algorithm. The experimental results show that the harmonic signals exhibit obvious multifractal characteristics and that the multifractal intensity is related to the signal frequency. Compared with the traditional MFDFA algorithm, the proposed method is more stable in curve fitting and can extract the multifractal features more accurately.
Highlights
With a large number of nonlinear electrical equipment and electronic devices being applied in the power system, more and more harmonics are appearing in the power grid
To solve the above-mentioned problem, this paper proposes a new multifractal detrended fluctuation analysis (MFDFA) algorithm based on empirical mode decomposition (EMD) and template movement
The multifractal characteristics of harmonic signals are analyzed by the new algorithm and a new method for determining the harmonic signals’ characteristics is obtained
Summary
With a large number of nonlinear electrical equipment and electronic devices being applied in the power system, more and more harmonics are appearing in the power grid. Fourier transform (FT) [19], etc These methods ignore the self-similarity that exists in the time-domain waveform and the trend of harmonics, i.e., the so-called fractal characteristics [20]. To solve the shortcomings of the periodic trend affecting the Hurst index estimation in MFDFA, Fourier transform and MFDFA were combined to analyze the fluctuations in a high-frequency power load [31]. The above-mentioned various methods can effectively describe the nonlinear system, especially the multifractal features of time series, but the analysis of time-series signals requires the process of detrending. The multifractal characteristics of harmonic signals are analyzed by the new algorithm and a new method for determining the harmonic signals’ characteristics is obtained. The multifractal characteristics of the harmonic components are determined by the novel MFDFA algorithm.
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