基于主瓣宽度多谱线插值的高精度快速谐波分析算法
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摘要
根据窗函数的主瓣宽度提出了一种多谱线插值算法,结合采样率最终确定参与插值的谱线根数。根据窗函数的主瓣内任意相邻两根谱线之间的相位差为π这一规律,提出了一种快速算法,说明无论采用多少根谱线参与运算,计算某次谐波参数仅需要1次求模运算,大大降低了计算复杂度,节约了计算时间。利用不同阶次的Hanning自乘法窗仿真实验表明,多谱线插值算法在拟合阶次较低的情况下,该算法的精度比常用双谱线和三谱线更高,且大大节约了计算量。
This paper has induced multi-spectrum-line interpolation algorithm based on main-lobe width. At the same time, we have proved that the phase difference of any two adjacent spectrum lines isπ. According to this rule, this paper has induced a rapid algorithm so that square root is only calculated one time when we analyze some harmonic parameters. Based on the different order's hanning selfmultiplication windows, the simulation results have shown that the multi-spectrum-line interpolation algorithm has higher precision than double/triple-spectrum-line interpolation algorithm especially when the order of polynomial is lower than two others if obtaining same precision and the rapid algorithm can save calculation amount greatly.
This paper has induced multi-spectrum-line interpolation algorithm based on main-lobe width. At the same time, we have proved that the phase difference of any two adjacent spectrum lines isπ. According to this rule, this paper has induced a rapid algorithm so that square root is only calculated one time when we analyze some harmonic parameters. Based on the different order's hanning selfmultiplication windows, the simulation results have shown that the multi-spectrum-line interpolation algorithm has higher precision than double/triple-spectrum-line interpolation algorithm especially when the order of polynomial is lower than two others if obtaining same precision and the rapid algorithm can save calculation amount greatly.
引文
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[6]周俊,王小海,祈才君.基于Blackman窗函数的插值FFT在电网谐波信号分析中的应用[J].浙江大学学报:理学版,2006,33(6):650-653.Zhou Jun,Wang Xiaohai,Qi Caijun.Estimation of electrical harmonic parameters by using the interpolated FFT algorithm based on Blackman window[J].Journal of Zhejiang University:Science Edition,2006,33(6):650-653.
[7]许珉,张鸿博.基于Blackman-Harris窗的加窗FFT插值修正算法[J].郑州大学学报:工学版,2005,26(4):99-101.Xu Min,Zhang Hongbo.The correction algorithm based on the Blackman-Harris windows and interpolated FFT[J].Journal of Zhengzhou University:Engineering Science,2005,26(4):99-101.
[8]卿柏元,滕召胜,高云鹏,等.基于Nuttall窗双谱线插值FFT的电力谐波分析方法[J].中国电机工程学报,2008,28(10):153-158.Qin Baiyuan,Teng Zhaosheng,Gao Yunpeng,et al.An approach for electrical harmonic analysis based on Nuttall window double-spectrum-line interpolation FFT[J].Proceedings of the CSEE,2008,28(10):153-158.
[9]曾博,滕召胜,温和,等.莱夫-文森特窗插值FFT谐波分析方法[J].中国电机工程学报,2009,29(10):115-120.Zeng Bo,Teng Zhaosheng,Wen He,et al.Harmonic analysis based on Rife-Vincent window interpolated FFT[J].Proceedings of the CSEE,2009,29(10):115-120.
[10]He Wen,Zhaosheng Teng,Si Yuguo.Triangular selfconvolution window with desirable side lobe behaviors for harmonic analysis of power system[J].IEEE Transactions on Instrumentation&Measurement,2010,59(3):543-552.
[11]Zeng Bo.Parameter estimation of power system signals based on cosine self-convolution window with desirable Side-Lobe behaviors[J].IEEE Transactions on power delivery,2011,26(1):250-257.
[12]Wen He,Teng Zhaosheng,Guo Siyu,et al.Hanning self-convolution window and its application to harmonic analysis[J].Science in China,2009,52(2):467-476.
[13]周念成,楼晓轩,王强钢,等.电网电压不平衡下三相光伏发电系统的谐波电流抑制[J].电工技术学报,2015,30(16):246-254.Zhou Niancheng,Lou Xiaoxuan,Wang Qianggang,et al.Harmonic currents suppression for three-phase photovoltaic power generation system under unbalanced grid voltage conditions[J].Transactions of China Electrotechnical Society,2015,30(16):246-254.
[14]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,2013,27(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,2013,27(12):270-277.
[15]温和,金冉,蒙娟,等.电压不平衡度的加窗FFT快速测量方法[J].电工技术学报,2017,32(6):275-283.Wen He,Jin Ran,Meng Juan,et al.Fast measurement method of voltage unbalance factor based on Window FFT[J].Transactions of China Electrotechnical Society,2017,32(6):275-283.
[16]张俊敏,刘开培,汪立,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,2016,44(13):1-5.Zhang Junmin,Liu Kaipei,Wang Li,et al.An algorithm for harmonic analysis based on multiplication window function[J].Power System Protection and Control,2016,44(13):1-5.
[17]温和,滕召胜,卿柏元.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,Qing Baiyuan.Hanning selfconvolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[18]孙仲民,何正友,臧天磊.一种混合卷积窗及其在谐波分析中的应用[J].电工技术学报,2016,31(16):207-214.Sun Zhongmin,He Zhengyou,Zang Tianlei.A kind of hybrid convolution window and its application in Harmonic analysis[J].Transactions of China Electrotechnical Society,2016,31(16):207-214.
[19]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.An algorithm for harmonic analysis based on mutual-multiplication window function[J].Electrical Measurement&Instrumentation,2016,53(24):19-23.
[20]Agrez D.Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal[J].IEEE Transactions on Instrumentation and Measurement,2002,51(2):287-292.
[21]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 electrical harmonic analysis based on triple-spectrum-line interpolation FFT[J].Proceeding of the CSEE,2012,32(16):130-136.
[22]黄冬梅,龚仁喜,焦凤昌,等.莱夫-文森特窗三谱线插值的电力谐波分析[J].电力系统保护与控制,2014,42(2):28-34.Huang Dongmei,Gong Renxi,Jiao Fengchang,et al.Power harmonic analysis based on Rife-Vincent window and triple-spectral-line interpolation[J].Power System Protection and Control,2014,42(2):28-34.
[23]张俊敏,刘开培,汪立,等.基于四谱线插值FFT的谐波分析快速算法[J].电力系统保护与控制,2017,1(45):139-147.Zhang Junmin,Liu Kaipei,Wang Li,et al.A rapid algorithm for Harmonic analysis based on fourspectrum-line interpolation FFT[J].Power System Protection and Control,2017,45(1):139-147.
[24]蔡晓峰,张鸿博,鲁改凤.应用三谱线插值FFT分析电力谐波的改进算法[J].电力系统保护与控制,2015,43(2):33-39.Cai Xiaofeng,Zhang Hongbo,Lu Gaifeng.Improvement algorithm for harmonic analysis of power system using triple-spectrum-line interpolation algorithm based on window FFT[J].Power System Protection and Control,2015,43(2):33-39.
[25]张俊敏,刘宗方,陈勉.一种基于Hanning自乘法窗函数和四插值的谐波分析方法[J].中南民族大学学报(自然科学版),2016,35(1):132-135.Zhang Junmin,Liu Zongfang,Chen Mian.A harmonic analysis method based on Hamming selfmultiplication window functions and four-spectrumline-interpolation[J].Journal of South-Central University for Nationalities(Natural Science Edition),2016,35(1):132-135.
[26]张俊敏,刘开培,汪立,等.基于Hanning自乘法窗函数的高精度谐波分析[J].智能电网,2016,4(5):473-477.Zhang Junmin,Liu Kaipei,Wang Li,et al.Highprecision harmonic analysis based on Hanning selfmultiplication window functions[J].Smart Grid,2016,4(5):473-477.
[2]王保帅,肖霞.一种用于谐波分析的高精度多谱线插值算法[J].电工技术学报,2017,32(15):22-31.Wang Baoshuai,Xiao Xia.A high accuracy multispectrum-line interpolation algorithm for harmonic analysis[J].Transactions of China Electrotechnical Society,2017,32(15):22-31.
[3]Chang G W,Chen C I,Liu Y J,et al.Measuring power system harmonics and interharmonics by an improved fast Fourier transform-based algorithm[J].IET Generation,Transmission&Distribution,2008,2(2):193-201.
[4]庞浩,李东霞,俎云霄,等.应用FFT进行电力系统谐波分析的改进算法[J].中国电机工程学报,2003,23(6):50-54.Pang Hao,Li Dongxia,Zu Yunxiao,et al.An improved algorithm for harmonic analysis of power system using FFT technique[J].Proceedings of the CSEE,2003,23(6):50-54.
[5]Grandke T.Interpolation algorithms for discrete Fourier transform of weighed signals[J].IEEE Transactions on Instrumentation and Measurement,1983,32(2):350-355.
[6]周俊,王小海,祈才君.基于Blackman窗函数的插值FFT在电网谐波信号分析中的应用[J].浙江大学学报:理学版,2006,33(6):650-653.Zhou Jun,Wang Xiaohai,Qi Caijun.Estimation of electrical harmonic parameters by using the interpolated FFT algorithm based on Blackman window[J].Journal of Zhejiang University:Science Edition,2006,33(6):650-653.
[7]许珉,张鸿博.基于Blackman-Harris窗的加窗FFT插值修正算法[J].郑州大学学报:工学版,2005,26(4):99-101.Xu Min,Zhang Hongbo.The correction algorithm based on the Blackman-Harris windows and interpolated FFT[J].Journal of Zhengzhou University:Engineering Science,2005,26(4):99-101.
[8]卿柏元,滕召胜,高云鹏,等.基于Nuttall窗双谱线插值FFT的电力谐波分析方法[J].中国电机工程学报,2008,28(10):153-158.Qin Baiyuan,Teng Zhaosheng,Gao Yunpeng,et al.An approach for electrical harmonic analysis based on Nuttall window double-spectrum-line interpolation FFT[J].Proceedings of the CSEE,2008,28(10):153-158.
[9]曾博,滕召胜,温和,等.莱夫-文森特窗插值FFT谐波分析方法[J].中国电机工程学报,2009,29(10):115-120.Zeng Bo,Teng Zhaosheng,Wen He,et al.Harmonic analysis based on Rife-Vincent window interpolated FFT[J].Proceedings of the CSEE,2009,29(10):115-120.
[10]He Wen,Zhaosheng Teng,Si Yuguo.Triangular selfconvolution window with desirable side lobe behaviors for harmonic analysis of power system[J].IEEE Transactions on Instrumentation&Measurement,2010,59(3):543-552.
[11]Zeng Bo.Parameter estimation of power system signals based on cosine self-convolution window with desirable Side-Lobe behaviors[J].IEEE Transactions on power delivery,2011,26(1):250-257.
[12]Wen He,Teng Zhaosheng,Guo Siyu,et al.Hanning self-convolution window and its application to harmonic analysis[J].Science in China,2009,52(2):467-476.
[13]周念成,楼晓轩,王强钢,等.电网电压不平衡下三相光伏发电系统的谐波电流抑制[J].电工技术学报,2015,30(16):246-254.Zhou Niancheng,Lou Xiaoxuan,Wang Qianggang,et al.Harmonic currents suppression for three-phase photovoltaic power generation system under unbalanced grid voltage conditions[J].Transactions of China Electrotechnical Society,2015,30(16):246-254.
[14]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,2013,27(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,2013,27(12):270-277.
[15]温和,金冉,蒙娟,等.电压不平衡度的加窗FFT快速测量方法[J].电工技术学报,2017,32(6):275-283.Wen He,Jin Ran,Meng Juan,et al.Fast measurement method of voltage unbalance factor based on Window FFT[J].Transactions of China Electrotechnical Society,2017,32(6):275-283.
[16]张俊敏,刘开培,汪立,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,2016,44(13):1-5.Zhang Junmin,Liu Kaipei,Wang Li,et al.An algorithm for harmonic analysis based on multiplication window function[J].Power System Protection and Control,2016,44(13):1-5.
[17]温和,滕召胜,卿柏元.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,Qing Baiyuan.Hanning selfconvolution windows and its application to harmonic analysis[J].Transactions of China Electrotechnical Society,2009,24(2):164-169.
[18]孙仲民,何正友,臧天磊.一种混合卷积窗及其在谐波分析中的应用[J].电工技术学报,2016,31(16):207-214.Sun Zhongmin,He Zhengyou,Zang Tianlei.A kind of hybrid convolution window and its application in Harmonic analysis[J].Transactions of China Electrotechnical Society,2016,31(16):207-214.
[19]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.An algorithm for harmonic analysis based on mutual-multiplication window function[J].Electrical Measurement&Instrumentation,2016,53(24):19-23.
[20]Agrez D.Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal[J].IEEE Transactions on Instrumentation and Measurement,2002,51(2):287-292.
[21]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 electrical harmonic analysis based on triple-spectrum-line interpolation FFT[J].Proceeding of the CSEE,2012,32(16):130-136.
[22]黄冬梅,龚仁喜,焦凤昌,等.莱夫-文森特窗三谱线插值的电力谐波分析[J].电力系统保护与控制,2014,42(2):28-34.Huang Dongmei,Gong Renxi,Jiao Fengchang,et al.Power harmonic analysis based on Rife-Vincent window and triple-spectral-line interpolation[J].Power System Protection and Control,2014,42(2):28-34.
[23]张俊敏,刘开培,汪立,等.基于四谱线插值FFT的谐波分析快速算法[J].电力系统保护与控制,2017,1(45):139-147.Zhang Junmin,Liu Kaipei,Wang Li,et al.A rapid algorithm for Harmonic analysis based on fourspectrum-line interpolation FFT[J].Power System Protection and Control,2017,45(1):139-147.
[24]蔡晓峰,张鸿博,鲁改凤.应用三谱线插值FFT分析电力谐波的改进算法[J].电力系统保护与控制,2015,43(2):33-39.Cai Xiaofeng,Zhang Hongbo,Lu Gaifeng.Improvement algorithm for harmonic analysis of power system using triple-spectrum-line interpolation algorithm based on window FFT[J].Power System Protection and Control,2015,43(2):33-39.
[25]张俊敏,刘宗方,陈勉.一种基于Hanning自乘法窗函数和四插值的谐波分析方法[J].中南民族大学学报(自然科学版),2016,35(1):132-135.Zhang Junmin,Liu Zongfang,Chen Mian.A harmonic analysis method based on Hamming selfmultiplication window functions and four-spectrumline-interpolation[J].Journal of South-Central University for Nationalities(Natural Science Edition),2016,35(1):132-135.
[26]张俊敏,刘开培,汪立,等.基于Hanning自乘法窗函数的高精度谐波分析[J].智能电网,2016,4(5):473-477.Zhang Junmin,Liu Kaipei,Wang Li,et al.Highprecision harmonic analysis based on Hanning selfmultiplication window functions[J].Smart Grid,2016,4(5):473-477.