| The voltage fluctuation and flicker is one of the key factors to influence power quality. The premise of managing voltage fluctuation and flicker is to detect the signal accurately and quickly. This paper provided a detailed analysis of the voltage flicker waveform signals. According to the characteristics of flicker signals, the complex wavelet was created and then transformed to extract fluctuation signals and some important conclusions were obtained.In the biorthogonal filter group, the orthogonality of low-pass filtering and high-pass filtering was abandoned, which could realize perfect performance filter with linear-phase and compactly supported wavelet function. On the basis of biorthogonal wavelet and the theory of fully recoverable filter group, compactly supported biorthogonal real wavelet was generated into compactly supported biorthogonal complex wavelet with linear-phase by lifting scheme. The influence of trigonometric polynomial coefficient on its phase frequency characteristics during the lifting process was analyzed in theory. By adjusting the trigonometric polynomial coefficient during the lifting process, the complex wavelet with certain vanishing moment and symmetry was created. Thus, the complex wavelet could match with power frequency voltage signal waveform and then it was characterized by linear-phase.In the paper, the envelope curve was extracted from complex wavelets with linear-phase and the relevant theories were elaborated. The simulation analyses were conducted in sine wave with signal-frequency flicker signal, multi-frequency flicker signal and rectangular pulse signal respectively. Moreover, the influences of power frequency voltage frequency shift on analysis results were also discussed. Shift invariance were detected by fluctuation voltage. In this way, the sampling frequency and voltage flicker signal did not require synchronization, which could provide a facility for designing sampling circuit. The signals were projected into two orthogonal spaces by biorthogonal wavelets with linear-phase. The filter was characterized by undistorted transmission. Furthermore, the correction factor was only concerned with complex wavelet decomposition scale and signal sampling frequency, which could lead to shift invariant in extracting flicker envelope curve. The complex wavelet coefficient did not need reconstructing. This method had the characteristics of less calculation and preferable simulation results. When the fluctuation voltage signal was being analyzed by frequency spectrum, interpolation FFT algorithm was adopted to calculate the amplitude and frequency of flicker signal. Compared with FFT algorithm, better results were obtained. |
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