应用于电力谐波分析的改进插值算法
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摘要
频谱泄漏是加窗插值傅里叶变换算法测量误差的主要来源,可通过加高阶窗抑制误差,但二次谐波及其他弱谐波的估计精度仍难显著提升,且带来复杂的频谱表达式和频率分辨率的损失。针对上述问题,提出一种改进插值算法。通过加低阶的sine窗函数,将传统离散傅里叶变换(DFT)平移1/2个谱线间隔到Odd-DFT域插值修正。利用相对频偏在所求谐波分量上减去其他分量的长程谱泄漏干扰之和,再进行插值修正,获得更精确的相对频偏。循环迭代若干次,用于抑制频谱泄漏对估计精度的影响。推导了修正公式,给出了算法流程,在不同环境下进行仿真分析,得出合理的迭代次数。研究结果表明,该算法的测量精度较传统加窗方法更高,并且弱谐波的估计精度得到提升,所需的采样时窗更少,提高了测量精度,满足电网测量的需要。
The spectral leakage is the main cause of measurement error in windowed interpolation Fourier transform algorithm and the high-order window could be used to restrain it. However, it is still hard for improving the estimation accuracy of the second harmonic and other weak harmonics significantly. Moreover, it not only causes the loss of frequency resolution but also complicates the spectral expressions. An improved interpolation estimation algorithm is proposed to solve these problems. Using a low-order sine window, the traditional discrete Fourier transform(DFT) is shifted by 1/2 line spacing to the Odd-DFT domain for revision by the interpolated algorithm. The relative frequency offset of harmonics is used to subtract the sum of the long-range spectral leakage interference of other components, and then the interpolated algorithm is performed to obtain the more accurate relative frequency offset. Several iterations of loop are performed to restrain the impact of spectral leakage on estimation accuracy. The correction formula is deduced and the algorithm flow is given. The simulation analysis is carried out under different environments to obtain a reasonable number of iterations. The analysis results show that the measurement accuracy of this algorithm is higher than traditional windowing algorithm, the accuracy of weak harmonics is even more significantly improved and the number of required sampling time window is decreasing as well, which improve the measurement accuracy and meet the requirement of power grid.
The spectral leakage is the main cause of measurement error in windowed interpolation Fourier transform algorithm and the high-order window could be used to restrain it. However, it is still hard for improving the estimation accuracy of the second harmonic and other weak harmonics significantly. Moreover, it not only causes the loss of frequency resolution but also complicates the spectral expressions. An improved interpolation estimation algorithm is proposed to solve these problems. Using a low-order sine window, the traditional discrete Fourier transform(DFT) is shifted by 1/2 line spacing to the Odd-DFT domain for revision by the interpolated algorithm. The relative frequency offset of harmonics is used to subtract the sum of the long-range spectral leakage interference of other components, and then the interpolated algorithm is performed to obtain the more accurate relative frequency offset. Several iterations of loop are performed to restrain the impact of spectral leakage on estimation accuracy. The correction formula is deduced and the algorithm flow is given. The simulation analysis is carried out under different environments to obtain a reasonable number of iterations. The analysis results show that the measurement accuracy of this algorithm is higher than traditional windowing algorithm, the accuracy of weak harmonics is even more significantly improved and the number of required sampling time window is decreasing as well, which improve the measurement accuracy and meet the requirement of power grid.
引文
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[12] 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,2018,33(3):553-562.WANG Baoshuai, XIAO Xia. A high accuracy multi-spectrum-line interpolation algorithm for harmonic analysis[J]. Transactions of China Electrotechnical Society, 2018, 33(3): 553-562.
[13] 陈国志,陈隆道,蔡忠法.基于Nuttall窗插值FFT的谐波分析方法[J].电力自动化设备,2011,31(4):27-31.CHEN Guozhi, CHEN Longdao, CAI Zhongfa. Harmonic analysis based on Nuttall window interpolation FFT[J]. Electric Power Automation Equipment, 2011, 31(4): 27-31.
[14] SCHUSTER S, SCHEIBLHOFER S, STELZER A. The influence of windowing on bias and variance of DFT-based frequency and phase estimation[J]. IEEE Transactions on Instrumentation and Measurement, 2009, 58(6): 1975-1990.
[15] FERREIRA A, SINHA D. Accurate and robust frequency estimation in the ODFT domain[C]// IEEE Workshop on Applications of Signal Process to Audio and Acoustics, October 16, 2005, New York, USA: 203-206.
[16] PRINCEN J, BRADLEY A. Analysis/synthesis filter bank design based on time domain aliasing cancellation[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986, 34(5): 1153-1161.
[17] JACOBSEN E, KOOTSOOKOS P. Fast, accurate frequency estimators[J]. IEEE Signal Processing Magazine, 2007, 24(3): 123-125.
[18] 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.
[19] FERREIRA A J S. Accurate estimation in the ODFT domain of the frequency, phase and magnitude of stationary sinusoids[C]// Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics, October 24, 2001, New York, USA: 47-50.
[20] FERREIRA A J S. An Odd-DFT based approach to time-scale expansion of audio signals[J]. IEEE Transactions on Speech and Audio Processing, 1999, 7(4): 441-453.
[21] DUN Yujie, LIU Guizhong. A fine-resolution frequency estimator in the Odd-DFT domain[J]. IEEE Signal Processing Letters, 2015, 22(12): 2489-2493.
[22] YE Shanglin, SUN Jiadong, ABOUTANIOS E. On the estimation of the parameters of a real sinusoid in noise[J]. IEEE Signal Processing Letters, 2017, 24(5): 638-642.
[23] HORNE J, FLYNN D, LITTLER T, et al. Frequency stability issues for islanded power systems[C]// IEEE PES Power Systems Conference and Exposition, October 10-13, 2004, New York, USA: 299-306.
[24] DUDA K, BARCZENTEWICZL S. Interpolated DFT for sinα(x) windows[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 63(4): 754-760.
[2] SRINIVASAN K. On separating customer and supply side harmonic contributions[J]. IEEE Transactions on Power Delivery, 1996, 11(2): 1003-1012.
[3] GUO Xiaoqiang, GUERRERO J M. Abc-frame complex-coefficient filter and controller based current harmonic elimination strategy for three-phase grid connected inverter[J]. Journal of Modern Power Systems and Clean Energy, 2016, 4(1): 87-93.
[4] 李宁,左培丽,王新刚,等.基于改进DFT和时域准同步的间谐波检测算法[J].电力自动化设备,2017,37(4):170-178.LI Ning, ZUO Peili, WANG Xingang, et al. Inter-harmonic detection based on improved DFT and time-domain quasi-synchronization[J]. Electric Power Automation Equipment, 2017, 37(4): 170-178.
[5] 翟晓军,周波.一种改进的插值FFT谐波分析算法[J].中国电机工程学报,2016,36(11):2952-2958.ZHAI Xiaojun, ZHOU Bo. An improved interpolated FFT algorithm for harmonic analysis[J]. Proceedings of the CSEE, 2016, 36(11): 2952-2958.
[6] 孙仲民,黄俊,杨健维,等.基于切比雪夫窗的电力系统谐波/间谐波高精度分析方法[J].电力系统自动化,2015,39(7):117-123.SUN Zhongmin, HUANG Jun, YANG Jianwei, et al. A high accuracy analysis method for harmonics and inter-harmonics in power systems based on Dolph-Chebyshev windows[J]. Automation of Electric Power Systems, 2015, 39(7): 117-123.
[7] 宋树平,马宏忠,徐刚,等.五项最大旁瓣衰减窗插值电力谐波分析[J].电力系统自动化,2015,39(22):83-89.SONG Shuping, MA Hongzhong, XU Gang, et al. Power harmonic analysis based on 5-term maximum-sidelobe-decay window interpolation[J]. Automation of Electric Power Systems, 2015, 39(22): 83-89.
[8] 张介秋,梁昌洪,陈砚圃.一类新的窗函数-卷积窗及其应用[J].中国科学E辑,2005,35(7):773-784.ZHANG Jieqiu, LIANG Changhong, CHEN Yanpu. A new family of windows-convolution windows and their applications[J]. Science in China Series E-technological Sciences, 2005, 35(7): 773-784.
[9] 曾博,唐求,卿柏元,等.基于Nuttall自卷积窗的改进FFT谱分析方法[J].电工技术学报,2014,29(7):59-65.ZENG Bo, TANG Qiu, QING Baiyuan, et al. Spectral analysis method based on improved FFT by Nuttall self-convolution window[J]. Transactions of China Electrotechnical Society, 2014, 29(7): 59-65.
[10] 邹培源,黄纯,江辉,等.基于全相位谱细化与校正的谐波和间谐波测量方法[J].电网技术,2016,40(8):2496-2502.ZOU Peiyuan, HUANG Chun, JIANG Hui, et al. Method of harmonics and interharmonics measurement based on all-phase spectrum zoom and correction[J]. Power System Technology, 2016, 40(8): 2496-2502.
[11] 张介秋,梁昌洪,陈砚圃,等.提高谐波参量测量精度的谱泄漏相消算法[J].电子学报,2005,33 (9):1614-1617.ZHANG Jieqiu, LIANG Changhong, CHEN Yanpu, et al. Spectral leakage canceling algorithm for improving precision of harmonic analysis[J]. Acta Electronica Sinica, 2005, 33(9): 1614-1617.
[12] 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,2018,33(3):553-562.WANG Baoshuai, XIAO Xia. A high accuracy multi-spectrum-line interpolation algorithm for harmonic analysis[J]. Transactions of China Electrotechnical Society, 2018, 33(3): 553-562.
[13] 陈国志,陈隆道,蔡忠法.基于Nuttall窗插值FFT的谐波分析方法[J].电力自动化设备,2011,31(4):27-31.CHEN Guozhi, CHEN Longdao, CAI Zhongfa. Harmonic analysis based on Nuttall window interpolation FFT[J]. Electric Power Automation Equipment, 2011, 31(4): 27-31.
[14] SCHUSTER S, SCHEIBLHOFER S, STELZER A. The influence of windowing on bias and variance of DFT-based frequency and phase estimation[J]. IEEE Transactions on Instrumentation and Measurement, 2009, 58(6): 1975-1990.
[15] FERREIRA A, SINHA D. Accurate and robust frequency estimation in the ODFT domain[C]// IEEE Workshop on Applications of Signal Process to Audio and Acoustics, October 16, 2005, New York, USA: 203-206.
[16] PRINCEN J, BRADLEY A. Analysis/synthesis filter bank design based on time domain aliasing cancellation[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1986, 34(5): 1153-1161.
[17] JACOBSEN E, KOOTSOOKOS P. Fast, accurate frequency estimators[J]. IEEE Signal Processing Magazine, 2007, 24(3): 123-125.
[18] 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.
[19] FERREIRA A J S. Accurate estimation in the ODFT domain of the frequency, phase and magnitude of stationary sinusoids[C]// Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics, October 24, 2001, New York, USA: 47-50.
[20] FERREIRA A J S. An Odd-DFT based approach to time-scale expansion of audio signals[J]. IEEE Transactions on Speech and Audio Processing, 1999, 7(4): 441-453.
[21] DUN Yujie, LIU Guizhong. A fine-resolution frequency estimator in the Odd-DFT domain[J]. IEEE Signal Processing Letters, 2015, 22(12): 2489-2493.
[22] YE Shanglin, SUN Jiadong, ABOUTANIOS E. On the estimation of the parameters of a real sinusoid in noise[J]. IEEE Signal Processing Letters, 2017, 24(5): 638-642.
[23] HORNE J, FLYNN D, LITTLER T, et al. Frequency stability issues for islanded power systems[C]// IEEE PES Power Systems Conference and Exposition, October 10-13, 2004, New York, USA: 299-306.
[24] DUDA K, BARCZENTEWICZL S. Interpolated DFT for sinα(x) windows[J]. IEEE Transactions on Instrumentation and Measurement, 2014, 63(4): 754-760.