Abstract：Aiming at the limitations of Shannon wavelet energy entropy (WEE), a novel approach to detect power harmonics, based on Tsallis wavelet packet singularity entropy (WPSE) and power spectral density (PSD) analysis, is proposed. By means of Shannon entropy theory and Mallat algorithm, the shortcomings of Shannon WEE applied to characterize complexity and frequency features of power harmonics are discussed in detail. After analyzing the relations and differences between Tsallis entropy and Shannon entropy, Nonextensive Tsallis WPSE algorithm is provided by combining Tsallis entropy with wavelet packet transform(WPT). According to the complexity of power harmonics calculated by Tsallis WPSE, the harmonics are analyzed in different time stages by PSD. The theoretical analysis and simulation results indicate that the proposed approach is valid to characterize the complexity of harmonics. In addition, the frequency and power of harmonics are measured precisely.
陈继开, 李浩昱, 杨世彦, 寇宝泉. Tsallis小波包奇异熵与功率谱分析在电力谐波检测的应用[J]. 电工技术学报, 2010, 25(8): 193-199.
Chen Jikai, Li Haoyu, Yang Shiyan, Kou Baoquan. Application of Wavelet Packet Singularity Entropy and PSD in Power Harmonics Detection. Transactions of China Electrotechnical Society, 2010, 25(8): 193-199.
[1] 周念成, 谭桂华, 何建森, 等. 基于统计方法的电网谐波状态估计误差分析[J]. 电工技术学报, 2009, 24(6)：109-114. Zhou Niancheng, Tan Guihua, He Jiansen, et al. Error analysis in harmonic state estimation of power system based on the statistical approach[J]. Transactions of China Electro-technical Society, 2009, 24(6)：109-114. [2] 郭创新, 朱传柏, 曹一家, 等. 电力系统故障诊断的研究现状与发展趋势[J]．电力系统自动化, 2006, 30(8)：98-102. Guo Chuangxin, Zhu Chuanbai, Cao Yijia, et al. State of arts of fault diagnosis of power systems[J]. Automation of Electric Power Systems, 2006, 30(8): 98-102. [3] 周林, 夏雪, 万蕴杰, 等．基于小波变换的谐波测量方法综述[J]．电工技术学报, 2006, 21(9)：67-74． Zhou Lin, Xia Xue, Wan Yunjie, et al． Harmonic detection based on wavelet transform [J]. Transactions of China Electrotechnical Society, 2006, 21(9)：67-74． [4] 黄文清, 戴瑜兴, 全慧敏. 基于Daubechies小波的谐波分析算法[J]. 电工技术学报, 2006, 21(6)： 45-48. Huang Wenqing, Dai Yuxing, Quan Huimin. Harmonic estimation method based on Daubechies wavelet[J]. Transactions of China Electro-technical Society, 2006, 21(6)：45-48. [5] 冯鹏, 魏彪, 米德伶, 等．基于抗混叠轮廓波变换系数分布模型的去噪算法研究[J]．仪器仪表学报, 2009, 30(11)：2361-2365． Feng Peng, Wei Biao, Mi Deling, et al．Novel denoising algorithm based on coefficient distribution model of non-aliasing contourlet transform[J]. Chinese Journal of Scientific Instrument, 2009, 30(11)：2361-2365． [6] 何正友, 蔡玉梅, 钱清泉．小波熵理论及其在电力系统故障检测中的应用研究[J]．中国电机工程学报, 2005, 25(5)：23-43． He Zhengyou, Cai Yumei, Qian Qingquan． A study of wavelet entropy theory and its application in electric power system fault detection [J]．Proceedings of the CSEE, 2005, 25(5)：23-43． [7] 何正友, 刘志刚, 钱清泉．小波熵理论及其在电力系统中应用的可行性探讨[J]．电网技术, 2004, 28(21)：17-21． He Zhengyou, Liu Zhigang, Qian Qingquan. Study on wavelet entropy theory and adaptabibility of its application in power system [J]. Power System Technology, 2004, 28(21)：17-21． [8] 李庚银, 王洪磊, 周明．基于改进小波能熵和支持向量机的短时电能质量扰动识别[J]．电工技术学报, 2009, 24(4)：161-167． Li Gengyin, Wang Honglei, Zhou Ming. Short-time power quality disturbances identification based on improved wavelet energy entropy and SVM[J]. Transactions of China Electro-technical Society, 2009, 24(4)：161-167． [9] Suyari H. Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy[J]. IEEE Transactions on Information Theory, 2004, 50(8)：1783-1787． [10] Tsallis C. Possible generalization of Boltzmann- Gibbs statistics [J]．Journal of Statistical Physics, 1988, 52(1-2)：479-487． [11] Plastino A, Tsallis C. Variational method in generalized statistical mechanics[J]. Journal of Physics A: Math. Gen, 1993, 26(18)：893-896． [12] 曹克非, 王参军. Tsallis熵与非广延统计力学[J]．云南大学学报(自然科学版), 2005, 27 (6)：514-520． Cao Kefei, Wang Canjun. Tsallis entropy and nonextensive statistical mechanics[J]. Journal of Yunnan University, 2005, 27(6)：514-520． [13] Tsallis C, Mendes R S, Plastino A R．The role of constraints within generalized nonextensive statistics[J]. Physica A, 1998, 261(3)：534-554. [14] 王刚, 黄海, 谢洪波, 等．心室纤颤和心动过速的小波非广度熵分析[J]．哈尔滨工业大学学报, 2008, 40(3)：458-461． Wang Gang, Huang Hai, Xie Hongbo, et al. Tsallis multiresolution entropy analysis of ventricular fibrillation and ventricular tachycardia[J]．Journal of Harbin Institute of Technology, 2008, 40(3)：458-461． [15] 何正友, 符玲, 麦瑞坤, 等．小波奇异熵及其在高压输电线路故障选相中的应用[J]．中国电机工程学报, 2007, 27(1)：31-35． He Zhengyou, Fu Ling, Mai Ruikun, et al．Study on wavelet singular entropy and its application to faulty phase selection in HV transmission lines [J]. Proceedings of the CSEE, 2007, 27(1)：31-35． [16] Golub G H, Vanloan C F．矩阵计算[M]．袁亚湘, 译. 北京：科学出版社, 2001．
2010, Vol. 25 
