| The wide used nonlinear devices to improve the power factor or the reliability of power system have leaded to distortion of the steady-state grid current or voltage waveform, and harmonic wave is the component of the distortion waveform. The serious harmonic pollution causes deterioration of power quality. Therefore, analyzing harmonic waveform accurately becomes one of the most important directions in the research field of the power system, and is of great significance to maintain the stable operation of power system.Fast Fourier transform (FFT) is the most commonly used tools in harmonic analysis. However, it is difficult to achieve synchronous sampling for Fast Fourier transform in practical application, and the spectrum leakage caused by non-integer period truncation reduces the precision of harmonic analysis. Meanwhile, the existing fence effect causes a deviation to the observation of each harmonic signal. The windowed interpolation FFT algorithm can reduce the influence of spectrum leakage and fence effect, and improve the precision of harmonic analysis.The thesis firstly introduces the basic principle of Fast Fourier transform, and discusses the characteristics of several cosine windows. The triple-spectrum-line and four-spectrum-line interpolation algorithm selecting the conventional cosine window are deduced to decrease fence effect on the basis of double-spectrum-line interpolation FFT. The improved algorithm of triple-spectrum-line and four-spectrum-line interpolation FFT are inferred by analyzing phase characteristics of two neighboring frequency spectrums in main lobe of window, thus greatly decreasing calculation burden of the correction formulas of harmonic parameters. Then, the hybrid-convolution window with good side lobe behavior is constructed by hybrid convolution of different cosine windows in order to restrain spectrum leakage. The correction formulas of harmonic parameters are obtained through carrying out discrete spectrum rectification using the least square method. Finally, the calculation results are obtained by analyzing each harmonic signals of power system, inter-harmonic signals and sub-harmonic signals, the harmonic parameters under the condition of fundamental frequency fluctuations using the deduced multispectral-line interpolation FFT, and the hybrid-convolution windowed interpolation FFT algorithm via Matlab software. Compared with related articles, simulation results verifies the accuracy and effectiveness of the algorithm in this thesis. |
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