作者：熊德智1,2, 肖宇1,2, 胡军华1,2, 黄瑞1,2, 温和2,3, 温乐鹏2,3
作者单位：1. 国网湖南省电力有限公司, 湖南 长沙 410004;
2. 智能电气量测与应用技术湖南省重点实验室, 湖南 长沙 410004;
3. 湖南大学电气与信息工程学院, 湖南 长沙 410082
关键词：频率估计;傅里叶变换;频谱插值;窗函数
摘要：
针对电力系统信号频率估计的高准确性要求，该文提出一种基于矩形窗的三点复频域插值频率估计方法。所提出的方法首先采用矩形窗对信号加权处理，然后进行离散傅里叶变换，最后选择离散频谱中幅度最大的三根谱线进行复频域插值，得到频率估计结果。该方法同时考虑离散频谱中的正、负频谱，消除短程和长程频谱泄漏对频率估计误差的影响。采用主瓣最窄的矩形窗进行加窗，能最大程度地减少白噪声对频率估计误差的影响。仿真和实验结果表明：在不同周期和噪声强度情况下，所提出的方法均可以实现对信号频率的准确估计。在与已有的加窗插值傅里叶变换方法相比，该文所提出的插值算法抗噪性更好、频率估计误差更小，适用于对电力系统信号频率的准确估计。
Rectangular window three-point interpolation Fourier transform high-precision frequency estimation method
XIONG Dezhi1,2, XIAO Yu1,2, HU Junhua1,2, HUANG Rui1,2, WEN He2,3, WEN Lepeng2,3
1. State Grid Hunan Electric Power Corporation Limited, Changsha 410004, China;
2. Hunan Province Key Laboratory of Intelligent Electrical Measurement and Application Technology, Changsha 410004, China;
3. College of Electrical and Information Engineering, Hunan University, Changsha 410082, China
Abstract: Aiming at the high accuracy requirement of power system signal frequency estimation, this paper proposes a three-point complex frequency domain interpolation frequency estimation method based on rectangular window. The proposed method first uses a rectangular window to weight the signal, then performs discrete Fourier transform, and finally selects the three spectral lines with the largest amplitude in the discrete spectrum for complex frequency domain interpolation to obtain the frequency estimation result. This method simultaneously considers the positive and negative spectrum in the discrete spectrum to eliminate the influence of short-range and long-range spectral leakage on the frequency estimation error. The rectangular window with the narrowest main lobe is used for windowing, which can minimize the influence of white noise on the frequency estimation error. Simulation and experimental results show that the proposed method can achieve accurate estimation of signal frequency under different periods and noise intensities. Compared with the existing Fourier transform method of windowed interpolation, the interpolation algorithm proposed in this paper has better anti-noise and smaller frequency estimation error. So it is suitable for accurate estimation of power system signal frequency.
Keywords: frequency estimation;Fourier transform;spectral interpolation;window function
2023, 49(9):57-62 收稿日期: 2021-12-06;收到修改稿日期: 2022-02-09
基金项目:
作者简介: 熊德智（1979-），男，湖南长沙市人，高级工程师，主要从事电能计量与电气测量研究
参考文献
[1] WEN H, ZHANG J H, MENG Z, et al. Harmonic estimation using symmetrical interpolation FFT based on triangular self-convolution window[J]. IEEE Transactions on Industrial Informatics, 2015, 11(1): 16-26
[2] 舒骁骁, 祝君剑, 朱亮, 等. 计及噪声影响的高准确度迭代滤波电网频率测量方法[J]. 中国测试, 2020, 46(7): 54-59, 132
[3] HAUER J F, DEMEURE C J. Initial results in Prony analysis of power system response signals[J]. IEEE Transactions on Power Systems, 1990, 5(1): 80-89
[4] SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas and Propagation, 1986, 34(3): 276-280
[5] WANG X C, TANG F, WANG X R, et al. Estimation of electromechanical modes under ambient condition via random decrement technique and TLS-ESPRIT algorithm[C]//2014 International Conference on Power System Technology (Powercon), 2014.
[6] BELEGA D, PETRI D. Accuracy analysis of the multicycle synchrophasor estimator provided by the interpolated DFT algorithm[J]. IEEE Transactions on Instrumentation and Measurement, 2013, 62(5): 942-953
[7] WEN H, LI C C, TANG L. Novel three-point interpolation DFT method for frequency measurement of sine-wave[J]. IEEE Transactions on Industrial Informatics, 2017, 13(5): 2333-2338
[8] BORKOWSKI J, KANIA D, MROCZKA J. Interpolated-DFT-based fast and accurate frequency estimation for the control of power[J]. IEEE Transactions on Industrial Electronics, 2014, 61(12): 7026-7034
[9] BELEGA D, PETRI D, DALLET D. Frequency estimation of a sinusoidal signal via a three-point interpolated DFT method with high image component interference rejection capability[J]. Digital Signal Processing, 2014, 24: 162-169
[10] 张金平, 李建立, 段晨. 计及负频率影响的新能源发电低频间谐波检测方法[J]. 电测与仪表, 2020, 57(2): 95-100
[11] 李恺, 向鑫, 卜文彬, 等. 基于频谱分辨率自适应的双插值DFT谐波分析方法[J]. 电测与仪表, 2021, 58(5): 92-97
[12] 陈向群, 高云鹏, 李典卿, 等. 基于Blackman-Nuttall窗改进FFT校正的新型三相动态谐波电能表设计[J]. 电测与仪表, 2020, 57(9): 132-139
[13] BELEGA D, DALLET D, PETRI D. Statistical description of the sine-wave frequency estimator provided by the interpolated DFT method[J]. Measurement, 2012, 45(1): 109-117
[14] WEN H, LI C C, YAO W X. Power system frequency estimation of sine-wave corrupted with noise by windowed three-point interpolated DFT[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 5163-5172
