基于Blackman自乘-卷积窗的FFT谐波检测算法
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摘要
电网中存在的大量谐波严重影响着电力系统的安全稳定运行,快速傅里叶变换(Fast Fourier Transform,FFT)算法被广泛应用于电网谐波的检测,由于存在频谱泄漏和栅栏效应导致谐波参数检测的误差较大,通过加窗函数和插值算法可以提高FFT算法的精度。对窗函数进行自乘和卷积运算可以改善旁瓣性能,以Blackman窗作为母窗,进行自乘和卷积运算,提出了Blackman自乘-卷积窗,该窗函数具有较优的主瓣和旁瓣性能。结合三谱线插值算法,推导出频率、幅值、相位的插值修正公式。采用Blackman自乘-卷积窗和其他余弦窗对含弱幅值信号的复杂信号进行对比仿真,验证了Blackman自乘-卷积窗三谱线插值算法在检测弱幅值信号时依然具有很高的精度,对含白噪声的信号进行仿真,验证了该算法对谐波信号参数检测的相对误差较小,抗干扰能力强。
The existence of a large number of harmonics in the power network seriously affects the safe and stable operation of the power system. Fast Fourier transform algorithm is widely used in the detection of harmonic in the power grid.Because of the spectrum leakage and fence effect,the error of harmonic parameter detection is large. The precision of FFT algorithm can be improved by window function and interpolation algorithm. The sidelobe performance of window function is improved by multiplication and convolution. The Blackman self-multiplication convolution window is obtained by multiplying and convolution of Blackman window. The window function has better main lobe and sidelobe performance. The interpolation correction formula of frequency,amplitude and phase is derived by using the interpolation algorithm of triplespectral-line. It is verified that the triple-spectral-line interpolation algorithm of Blackman self-multiplication convolution window still has high accuracy in detecting weak amplitude signal through using the proposed window function and other windows simulate the complex signal with weak amplitude signal. The simulation of the signal with white noise verifies that the algorithm has small relative error and strong anti-jamming ability to the harmonic signal parameter detection.
The existence of a large number of harmonics in the power network seriously affects the safe and stable operation of the power system. Fast Fourier transform algorithm is widely used in the detection of harmonic in the power grid.Because of the spectrum leakage and fence effect,the error of harmonic parameter detection is large. The precision of FFT algorithm can be improved by window function and interpolation algorithm. The sidelobe performance of window function is improved by multiplication and convolution. The Blackman self-multiplication convolution window is obtained by multiplying and convolution of Blackman window. The window function has better main lobe and sidelobe performance. The interpolation correction formula of frequency,amplitude and phase is derived by using the interpolation algorithm of triplespectral-line. It is verified that the triple-spectral-line interpolation algorithm of Blackman self-multiplication convolution window still has high accuracy in detecting weak amplitude signal through using the proposed window function and other windows simulate the complex signal with weak amplitude signal. The simulation of the signal with white noise verifies that the algorithm has small relative error and strong anti-jamming ability to the harmonic signal parameter detection.
引文
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[18]温和,滕召胜,王永,等.改进加窗插值FFT动态谐波分析算法及应用[J].电工技术学报,2012,27(12):270-277.Wen He,Teng Zhaosheng,Wang Yong,et al.Improved windowed interpolation FFT algorithm and application for power harmonic analysis[J].Transactions of China Electrotechnical Society,2012,27(12):270-277.
[2]Zhang J,Li G,Xu C,et al.Study of harmonic analysis based on improved discrete Fourier transform[C]//Industrial Electronics and Applications.IEEE,2016:2541-2545.
[3]Wen H,Guo S,Teng Z,et al.Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach[J].IEEETransactions on Power Systems,2014,29(2):765-774.
[4]温和.新型窗函数与改进FFT谐波分析方法及应用研究[D].湖南大学,2009.Wen He.Study on new windows and improved FFT-based harmonic analysis methods and applications[D].Changsha:Hunan University,2009.
[5]牛胜锁,梁志瑞,张建华,等.基于三谱线插值FFT的电力谐波分析算法[J].中国电机工程学报,2012,32(16):130-136.Niu Shengsuo,Liang Zhirui,Zhang Jianhua,et al.An Algorithm for E-lectrical Harmonic Analysis Based on Triple-spectrum-line Interpolation FFT[J].Proceedings of the Csee,2012,32(16):130-136.
[6]王刘旺,黄建才,等.基于加汉宁窗的FFT高精度谐波检测改进算法[J].电力系统保护与控制,2012,(24):28-33.Wang Liuwang,Huang Jiancai,et al.An improved precise algorithm for harmonic analysis based on Hanning-windowed FFT[J].Power System Protection&Control,2012,(24):28-33.
[7]Lobos T,Rezmer J.Real-time determination of power system frequency[J].Instrumentation&Measurement IEEE Transactions on,1997,46(4):877-881.
[8]Qian H,Zhao R,Chen T.Interharmonics Analysis Based on Interpolating Windowed FFT Algorithm[J].IEEE Transactions on Power Delivery,2007,22(2):1064-1069.
[9]Nuttall A H.Some windows with very good sidelobe behavior[J].A-coustics Speech&Signal Processing IEEE Transactions on,1981,29(1):84-91.
[10]刘冬梅,郑鹏,何怡刚,等.几种谐波检测加窗插值FFT算法的比较[J].电测与仪表,2013,50(12):51-55.Liu Dongmei,Zheng Peng,He Yigang,et al.Analysis and comparison of several harmonic detection methods with windowed and interpolation FFT[J].Electrical Measurement&Instrumentation,2013,50(12):51-55.
[11]Yao W,Teng Z,Tang Q,et al.Measurement of power system harmonic based on adaptive Kaiser self-convolution window[J].Iet Generation Transmission&Distribution,2015,10(2):390-398.
[12]张俊敏,刘开培,等.基于乘法窗函数的插值FFT的谐波分析方法[J].电力系统保护与控制,2016,(13):1-5.Zhang Junmin,Liu Kaipei,et al.An algorithm for harmonic analysis based on multiplication window function[J].Power System Protection&Control,2016,(13):1-5.
[13]柳坤,张俊敏,田微.基于互乘法窗函数的谐波分析方法[J].电测与仪表,2016,53(24):19-23.Liu Kun,Zhang Junmin,Tian Wei,et al.An algorithm for harmonic analysis based on mutual-multiplication window function[J].Electrical Measurement&Instrumentation,2016,53(24):19-23.
[14]刘涛,庄双勇,陈晓伟,等.基于四阶Hanning自乘窗FFT三峰插值的电能计量新算法[J].电测与仪表,2017,54(21):1-6.Liu Tao,Zhuang Shuangyong,Chen Xiaowei,et al.A new algorithm for electric energy measurement based on Hanning self multiplicationconvolution window triple-spectrum-line interpolation FFT[J].Power System Protection&Control,2017,54(21):1-6.
[15]陈坚,汪伟,王少华,等.基于Hanning自相乘窗的电力谐波FFT分析方法[J].电力系统保护与控制,2016,(19):114-121.Chen Jian,Wang Wei,Wang Shaohua,et al.An approach for electrical harmonic FFT analysis based on Hannning self-multiply window[J].Power System Protection&Control,2016,(19):114-121.
[16]温和,滕召胜,等.Hanning自卷积窗及其在谐波分析中的应用[J].电工技术学报,2009,24(2):164-169.Wen He,Teng Zhaosheng,et al.Hanning self-convolution window and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):467-476.
[17]刘清蝉,曹敏,李波,等.基于Hanning自卷积窗和三谱线插值的谐波无功功率测量方法[J].电测与仪表,2017,54(20):82-86.Liu Qingchan,Cao Min,Li Bo,et al.A method of harmonic reactive power measurement based on Hanning self-convolution window and triple-spectrum-line interpolation[J].Electrical Measurement&Instrumentation,2017,54(20):82-86.
[18]温和,滕召胜,王永,等.改进加窗插值FFT动态谐波分析算法及应用[J].电工技术学报,2012,27(12):270-277.Wen He,Teng Zhaosheng,Wang Yong,et al.Improved windowed interpolation FFT algorithm and application for power harmonic analysis[J].Transactions of China Electrotechnical Society,2012,27(12):270-277.