提出一种基于时频原子方法的间谐波分析方法。将信号分解成一系列时频原子，其中每个原子都来自于冗余的时频原子库，选择的原子可以最好地匹配信号结构。将分解后原子的Wigner-Ville分布相加得到时频能量分布图，相对于Wigner-Ville分布及Cohen类分布，该时频能量分布图不含有交叉项，其时频图更清晰。分别在有噪声干扰和无噪声干扰的情况下对时变的间谐波信号进行分析，均可有效提取出各次谐波和间谐波的时频信息，为间谐波分析提供了新的途径。

A new method to analyze inter-harmonics by time-frequency atom is proposed. In this method, a signal is decomposed into a series of time-frequency atoms and each atom is selected from a redundant time-frequency atom dictionary, the selected atom can best match to signal structure. Adding the Wigner-Ville distribution of the decomposed atoms, the time-frequency energy distribution map is obtained. Different from Wigner-Ville distribution and Cohen’s class distributions, this time-frequency energy distribution map does not contain interference terms, thus its time-frequency map is clearer. The time-varying inter-harmonic signals are analyzed by the proposed method under noisy and noise-free conditions respectively. Analysis results show that using the proposed method the time-frequency information of harmonic and inter-harmonic can be effectively extracted.

国家自然科学基金资助项目(50877014)

[1] 林海雪．电力系统中的间谐波问题[J]．供用电，2001，18(3)：6-9． Lin Haixue．Interharmonics in electrical power system[J]．Distribution and Utilization，2001，18(3)：6-9(in Chinese)． [2] 祈才君，王小海．基于插值FFT算法的间谐波参数估计[J]．电工技术学报，2003，18(1)：92-95． Qi Caijun，Wang Xiaohai．Interharmonics estimation based on interpolation FFT algorithm[J]．Transactions of China Electrotechnical Society，2003，18(1)：92-95(in Chinese)． [3] 钱昊，赵荣祥．基于插值FFT算法的间谐波分析[J]．中国电机工程学报，2005，25(21)：87-91． Qian Hao，Zhao Rongxiang．Interharmonics analysis based on interpolation FFT algorithm[J]．Proceedings of the CSEE，2005，25(21)：87-91(in Chinese)． [4] 张伏生，耿中行，葛耀中．电力系统谐波分析的高精度FFT算法[J]．中国电机工程学报，1999，19(3)：63-66． Zhang Fusheng，Geng Zhongxing，Ge Yaozhong．FFT algorithm with high accuracy for harmonic analysis in power system[J]．Proceedings of the CSEE，1999，19(3)：63-66(in Chinese)． [5] 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(in Chinese)． [6] 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(in Chinese)． [7] 马秉伟，刘会金，周莉，等．一种基于自回归模型的间谐波谱估计的改进算法[J]．中国电机工程学报，2005，25(15)：79-83． Ma Bingwei，Liu Huijin，Zhou Li，et al．An improved algorithm of interharmonics spectral estimation based on AR mode[J]．Proceedings of the CSEE，2005，25(15)：79-83(in Chinese)． [8] 王志群，朱守真，周双喜．基于Pisarenko谐波分解的间谐波估算方法[J]．电网技术，2004，28(15)：72-77． Wang Zhiqun，Zhu Shouzhen，Zhou Shuangxi．Inter-harmonics estimation by Pisarenko harmonic decomposition method[J]．Power System Technology，2004，28(15)：72-77(in Chinese)． [9] 沈睿佼，杨洪耕．基于特征空间求根法的非整数次谐波估计方法[J]．中国电机工程学报，2006，26(24)：72-76． Shen Ruijiao，Yang Honggeng．A new method for non-integer harmonics measurement based on root-eigenspace method [J]．Proceedings of the CSEE，2006，26(24)：72-76(in Chinese)． [10] 蔡忠法，陈隆道．基于AR谱估计和Adaline神经元的间谐波分析[J]．电力系统自动化，2007，31(17)：78-82． Cai Zhongfa，Chen Longdao．Inter-harmonic analysis based on AR spectral estimation and Adaline neural network[J]．Automation of Electric Power Systems，2007，31(17)：78-82(in Chinese)． [11] 李晶，裴亮，郁道银，等．一种用于电力系统谐波与间谐波分析的超分辨率算法[J]．中国电机工程学报，2006，26(15)：35-39． Li Jing，Pei Liang，Yu Daoyin，et al．A super-resolution algorithm for harmonic and inter-harmonic analysis in power system [J]．Proceedings of the CSEE，2006，26(15)：35-39(in Chinese)． [12] 薛蕙，杨仁刚．利用Morlet连续小波变换实现非整次谐波的检测 [J]．电网技术，2002，26(12)：41-44． Xue Hui，Yang Rengang．Morlet wavelet based detection of noninteger harmonics[J]．Power System Technology，2002，26(12)：41-44(in Chinese)． [13] 薛蕙，杨仁刚，罗红．利用小波包变换实现电力系统谐波分析[J]．电网技术，2004，28(5)：41-45． Xue Hui，Yang Rengang，Luo Hong．Power system harmonics analysis using wavelet packet transform[J]．Power System Technology，2004，28(5)：41-45(in Chinese)． [14] 乐叶青，徐政．平滑伪Wigner-Ville分布在电力系统谐波和电压变动检测中的应用[J]．继电器，2006，34(16)：39-43． Le Yeqing，Xu Zheng．Application of smoothed pseudo Wigner-Ville distribution in detecting harmonics and short duration voltage variations[J]．Relay，2006，34(16)：39-43(in Chinese)． [15] 张宇辉，金国彬，李天云．基于自适应最优核时频分布理论的间谐波分析新方法[J]．中国电机工程学报，2006，26(18)：84-89． Zhang Yuhui，Jin Guobin，Li Tianyun．A novel approach to interharmonics analysis based on adaptive optimal kernel time- frequency distribution[J]．Proceedings of the CSEE，2006，26(18)：84-89(in Chinese)． [16] Mallat S G，Zhang Zhifeng．Matching pursuits with time-frequency dictionaries[J]．IEEE Trans on Signal Processing，1993，41(12)：3397-3415． [17] Zhang Gexiang，Rong Haina．Quantum-inspired genetic algorithm based time-frequency atom decomposition[J]．Lecture Notes in Computer Science，2007，4490：243-250． [18] Zhang Gexiang，Rong Haina．Improved quantum-inspired genetic algorithm based time-frequency analysis of radar emitter signals [J]．Lecture Notes in Artificial Intelligence，2007，4481：484-491． [19] Tropp J A．Greed is good：Algorithmic results for sparse approximation[J]．IEEE Trans on Information Theory，2004，50(10)：2231-2242． [20] Mallat S．信号处理的小波导论[M]．杨力华，戴道清，黄文良，等译．北京：机械工业出版社，2002：50．