Research On Characteristics Of Window Functions And The Window And Interpolated FFT Algorithms

With massive applications of the power electronic equipments in power system,the harmonic pollutions has gone from bad to worse. It has a dramatic effect on power quality,the secruity and economical operation of power system.Therefore,the accurate measurement of the harmonic content in power system is very important to prevent the harmonic hazards and maintain the safe operation of power grids.Fourier transform (FFT) algorithm is usually used as the primary method of harmonic analysis because of its easily implemented on a microcomputer.It caused fence effect and spectral leakage to carry out fast fourier transform on non-synchronous sampling sequence.On account of that it gives measurement errors and can not meet the required of the accurate measurement on harmonics.Therefore we takes the windows and interpolated FFT algorithms.Adding window function on the signal can reduce the error caused by the spectral leakage.Meanwhile,the error which is caused by the fence effect can be reduced by interpolation algorithm.To reduce spectrum leakage,it should choose the window with the small peak sidelobes and fast decay.By comparing the characteristics of the windows,it proposed the windows and interpolated FFT algorithms based on the 3-term Exact-Blackman window and the 4-term Nuttall(â… ) window.The paper gives the correction formula for frequency and complex amplitude by taking the window and interpolated FFT algorithm based on the 3-term Exact-Blackman window for example.To compare with the other windows and interpolated FFT algorithms,it concluded that the window and interpolated FFT algorithm based on the 3-term Exact-Blackman window required minimum sampling period and least observation time. It has the simplest formula and the minimum calculated amount of the window and interpolated FFT algorithm based on the 4-term Nuttall(â… ) window. Meanwhile, the sidelobe has the maximum rate of decay of the 4-term Nuttall(â… ) window. With the increase of the sampling period, the window and interpolated FFT algorithm based on the 4-term Nuttall(â… ) window gets the highest calculation precision. The amplitude ratio is N polynomial of the frequency offset,and the complex amplitude correction factor has N polynomial as well as trigonometric function. So it gets a lot of calculated amount. In order to reduce the computational complexity, The effective form of cubic spline function is adopted to calculate correction factor for frequency and complex amplitude.The computing method has a high calculation precision as well as it effectively enhance the computation speed of the windows and interpolated FFT algorithms based on the 3-term Exact-Blackman window and the 4-term Nuttall(â… ) window.Based on the new algorithm, it takes advantage of the platform of MATLAB to develop a computer program for Simulation. Simulation results show that this new algorithms has high precision with less calculations. It also has good results when the power frequency fluctuates greatly.It provides a powerful means for the measurement of power system harmonic.