迭代加窗插值FFT谐波分析方法
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摘要
为了提高谐波分析精度,提出了一种基于迭代加窗插值快速傅里叶变换FFT(fast Fourier transform)的谐波分析方法,并给出了统一的谐波频率、幅值及相位的计算公式。通过主瓣拟合,将传统的基于最大旁瓣衰减窗MSDW(maximum sidelobe decay window)的插值FFT方法扩展至其他对称窗,并根据窗函数的主瓣特性选择合适的窗函数进行拟合。最后通过迭代算法计算出谐波的精确频率值。仿真结果表明:在非同步采样的条件下,该算法可精确地实现谐波和间谐波分析。与传统加窗插值FFT方法相比,所提方法不依赖窗函数的类型,针对不同的窗函数具有统一的谐波参数计算公式,通用性强,实现方式灵活。
To improve the accuracy of harmonic analysis,a harmonic analysis approach based on iterative windowed interpolation fast Fourier transform(FFT)is proposed in this paper.Meanwhile,the uniform formulas for harmonic frequency,amplitude,and phase are deduced.Through mainlobe fitting,the traditional interpolation FFT approach based on maximum sidelobe decay window(MSDW)is extended to other symmetrical windows,and appropriate windows are selected to fit according to the mainlobe features of interpolated windows.Finally,an iterative algorithm is performed to calculate the accurate value of harmonic frequency.Simulation results show that the proposed approach can realize harmonic and inter-harmonic analyses accurately under the condition of asynchronous sampling.Compared with the traditional windowed interpolation FFT algorithm,the proposed approach is independent of the types of window function,and it has uniform formulas that can calculate harmonic parameters for different window functions,indicating its universality and feasible realization.
To improve the accuracy of harmonic analysis,a harmonic analysis approach based on iterative windowed interpolation fast Fourier transform(FFT)is proposed in this paper.Meanwhile,the uniform formulas for harmonic frequency,amplitude,and phase are deduced.Through mainlobe fitting,the traditional interpolation FFT approach based on maximum sidelobe decay window(MSDW)is extended to other symmetrical windows,and appropriate windows are selected to fit according to the mainlobe features of interpolated windows.Finally,an iterative algorithm is performed to calculate the accurate value of harmonic frequency.Simulation results show that the proposed approach can realize harmonic and inter-harmonic analyses accurately under the condition of asynchronous sampling.Compared with the traditional windowed interpolation FFT algorithm,the proposed approach is independent of the types of window function,and it has uniform formulas that can calculate harmonic parameters for different window functions,indicating its universality and feasible realization.
引文
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[14]焦新涛,丁康(Jiao Xintao,Ding Kang).加窗频谱分析的恢复系数及其求法(Resetting module and solutions in windowing spectrum analysis)[J].汕头大学学报:自然科学版(Journal of Shantou University:Natural Science),2003,18(3):26-30,38.
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[2]Zhang Fusheng,Geng Zhongxing,Yuan Wei.The algorithm of interpolating windowed FFT for harmonic analysis of electric power system[J].IEEE Trans on Power Delivery,2001,16(2):160-164.
[3]许珉,杨阳,章梦哲,等(Xu Min,Yang Yang,Zhang Mengzhe,et al).一种加三项余弦窗的加窗插值FFT算法(An interpolated FFT algorithm based on three-item cosine window)[J].电力系统保护与控制(Power System Protection and Control),2010,38(17):11-15.
[4]孙仲民,黄俊,杨健维,等(Sun Zhongmin,Huang Jun,Yang Jianwei,et al).基于切比雪夫窗的电力系统谐波/间谐波高精度分析方法(A high accuracy method for harmonic and inter-harmonic in power systems based on Dolph-Chebyshev windows)[J].电力系统自动化(Automation of Electric Power Systems),2015,39(7):117-123.
[5]曾博,滕召胜,高云鹏,等(Zeng Bo,Teng Zhaosheng,Gao Yunpeng,et al).基于Rife-Vincent窗的高准确度电力谐波相量计算方法(An accurate approach for power harmonic phasor calculation based on Rife-Vincent window)[J].电工技术学报(Transactions of China Electrotechnical Society),2009,24(8):154-159.
[6]卿柏元,滕召胜,高云鹏,等(Qing Boyuan,Teng Zhaosheng,Gao Yunpeng,et al).基于Nuttall窗双谱线插值FFT的电力谐波分析方法(An approach for electrical harmonic analysis bases on Nuttall window double-spectrum-line interpolation FFT)[J].中国电机工程学报(Proceedings of the CSEE),2008,28(25):153-158.
[7]Liu Yanhui,Nie Zaiping,Zhao Zhiqin,et al.Generalization of iterative Fourier interpolation algorithms for single frequency estimation[J].Digital Signal Processing,2011,21(1):141-149.
[8]Aboutanios E,Mulgrew B.Iterative frequency estimation by interpolation on Fourier coefficients[J].IEEE Trans on Signal Processing,2005,53(4):1237-1242.
[9]Luo Jiufei,Xie Zhijiang,Xie Ming.Frequency estimation of the weighted real tones or resolved multiple tones by iterative interpolation DFT algorithm[J].Digital Signal Processing,2015,41:118-129.
[10]Belega D,Dallet D.Frequency estimation via weighted multipoint interpolated DFT[J].IET Science,Measurement&Technology,2008,2(1):1-8.
[11]Belega D,Dallet D.Multifrequency signal analysis by Interpolated DFT method with maximum sidelobe decay windows[J].Measurement,2009,42(3):420-426.
[12]Luo Jiufei,Xie Zhijiang,Xie Ming.Interpolated DFT algorithms with zero padding for classic windows[J].Mechanical Systems and Signal Processing,2016,s70-71:1011-1025.
[13]谢长贵,陈平(Xie Changgui,Chen Ping).一种DFT的频率校正算法(DFT interpolation algorithm for frequency estimation)[J].云南大学学报:自然科学版(Journal of Yunnan University:Natural Science),2017,39(2):200-206.
[14]焦新涛,丁康(Jiao Xintao,Ding Kang).加窗频谱分析的恢复系数及其求法(Resetting module and solutions in windowing spectrum analysis)[J].汕头大学学报:自然科学版(Journal of Shantou University:Natural Science),2003,18(3):26-30,38.
[15]Harris F J.On the use of windows for harmonic analysis with the discrete Fourier transform[J].Proceedings of the IEEE,1978,66(1):51-83.
[16]Qian Hao,Zhao Rongxiang,Chen Tong.Interharmonics analysis based on interpolating windowed FFT algorithm[J].IEEE Trans on Power Delivery,2007,22(2):1064-1069.--------