Abstract：In order to reduce the influence of the fast Fourier transform on spectrum leakage, caused by non-synchronous sampling, and to improve the accuracy of harmonic analysis, a multi-spectrum-line interpolation algorithm with high precision was proposed. By analyzing the possibility of spectral distribution near the discrete frequency point of the windowed signal, paper used six spectral lines near the peak spectral line to calculate the harmonic information, fully considered the harmonic information of these lines. And different correction formula was given, based on different leakage conditions respectively. The multi-spectrum-line interpolation algorithm and the fitting process of correction formula was deduced in detail. Then the numerical simulation and experimental platform were set up, and studied the influences of fundamental frequency fluctuation and the non-integer harmonics on the accuracy of algorithm. Simulation and experimental results demonstrate that the proposed multi-spectrum-line interpolation algorithm is effective and has excellent accuracy.
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. Transactions of China Electrotechnical Society, 2018, 33(3): 553-562.
[1] 李得民, 何怡刚. 基于Nuttall窗四谱线插值FFT的电力谐波分析[J]. 电力系统保护与控制, 2016, 44(3): 64-71. Li Demin, He Yigang.Harmonic analysis of power system based on Nuttall window four-spectrum-line interpolation FFT[J]. Power System Protection and Control, 2016, 44(3): 64-71. [2] 郝柱, 顾伟, 褚建新, 等. 基于四谱线插值FFT的电网谐波检测方法[J]. 电力系统保护与控制, 2014, 42(19): 107-113. Hao Zhu, Gu Wei, Chu Jianxin, et al.A power network harmonic detection method based on the four-spectrum-line interpolation FFT[J]. Power System Protection and Control, 2014, 42(19): 107-113. [3] 金涛, 陈毅阳, 游胜强. 基于Nuttall窗-5点变换的改进FFT介质损角测量算法[J]. 电工技术学报, 2015, 30(2): 7-15. Jin Tao, Chen Yiyang, You Shengqiang.An improved FFT algorithm for dielectric loss angle based on Nuttall window and five-point polynomial transform[J]. Transactions of China Electrotechnical Society, 2015, 30(2): 7-15. [4] 曾博, 滕召胜. 纳托尔自卷积窗加权电力谐波分析方法[J]. 电网技术, 2011, 35(8): 134-139. Zeng Bo, Teng Zhaosheng.A Nuttall self-convolution window-based approach to weighted analysis on power system harmonic[J]. Power System Technology, 2011, 35(8): 134-139. [5] 刘闯, 潘岱栋, 蔡国伟, 等. 适合低压配电网分布式发电的抗谐波干扰型增强锁相环路技术[J]. 电工技术学报, 2016, 31(10): 185-192. Liu Chuang, Pan Daidong, Cai Guowei, et al.Enhanced phased-locked loop technology with anti harmonic interference capability for distributed generation in low-voltage distribution[J]. Transactions of China Electrotechnical Society, 2016, 31(10): 185-192. [6] 翟瑞淼, 英超, 任国臣, 等. 基于Nuttall窗的三峰插值谐波算法分析[J]. 电力系统保护与控制, 2015, 43(10): 38-43. Zhai Ruimiao, Ying Chao, Ren Guochen, et al.An approach for harmonic analysis based on Nuttall window and triple-spectral-line interpolation[J]. Power System Protection and Control, 2015, 43(10): 38-43. [7] 潘文, 钱俞寿, 周鹗. 基于加窗插值FFT的电力谐波测量理论(|)窗函数研究[J]. 电工技术学报, 1994, 9(1): 50-54. Pan Wen, Qian Yushou, Zhou E.Power harmonics measurement based on windows and interpolated FFT(|)study of windows[J]. Transactions of China Electrotechnical Society, 1994, 9(1): 50-54. [8] 谢明, 丁康. 频谱分析的校正方法[J].振动工程学报, 1994, 7(2): 172-178. Xie Ming, Ding Kang.Rectifying technique of spectrum analysis[J]. Journal of Vibration Engineering, 1994, 7(2): 172-178. [9] 潘文, 钱俞寿, 周鹗. 基于加窗插值FFT的电力谐波测量理论(‖)双插值FFT理论[J].电工技术学报,1994, 9(2): 53-56. Pan Wen, Qian Yushou, Zhou E.Power harmonics measurement based on windows and interpolated FFT(‖)dual interpolated FFT algorithms[J]. Transactions of China Electrotechnical Society, 1994, 9(2): 53-56. [10] 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(25): 153-158. Qing 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(25): 153-158. [11] 高云鹏, 滕召胜, 卿柏元, 等. 基于Kaiser窗双谱线插值FFT的谐波分析方法[J]. 仪器仪表学报, 2010, 31(2): 287-292. Gao Yunpeng, Teng Zhaosheng, Qing Baiyuan, et al.Harmonic analysis based on Kaiser window double spectrum line interpolation FFT[J]. Chinese Joumal of Scientific Instrument, 2010, 31(2): 287-292. [12] 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. [13] 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 self-convolution windows and its application to harmonic analysis[J]. Transactions of China Electrotechnical Society, 2009, 24(2): 164-169. [14] 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. [15] 曾博, 唐求, 卿柏元. 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.Spectral analysis method based on improved FFT by nuttall self-convolution window[J]. Transactions of China Electrotechnical Society, 2014, 29(7): 59-65. [16] 曾博, 滕召胜, 高云鹏, 等. 基于Rife-Vincent窗的高准确度电力谐波相量计算方法[J]. 电工技术学报, 2009, 24(8): 154-159. Zeng Bo, Teng Zhaosheng, Gao Yunpeng.et al.An accurate approach for power harmonic phasor calculation based on Rife-Vincent window[J]. Transactions of China Electrotechnical Society, 2009, 24(8): 154-159. [17] 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-1ine interpolation FFT[J]. Proceedings of the CSEE, 2012, 32(16): 130-136. [18] 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. [19] 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. [20] 刘宏友, 李莉, 彭峰. Matlab 6基础及应用[M]. 重庆:重庆大学出版社, 2002.
2018, Vol. 33 
