10kV配网单相接地故障小波选线方法研究
|
摘要
由于10kV配网发生单相接地故障时的特征信息不明显,目前常采用稳态电流特征进行选线会产生误选和拒选,而应用故障线路暂态信息进行选线是目前研究的热点。本文在总结国内外10kV配网单相接地故障选线技术的基础上,分析了10kV配网发生单相接地故障时系统暂态零序电流和电压的变化规律,利用Matlab仿真平台并根据典型实小波和复小波变换的特征,分析和比较了实小波和复小波变换及其在单相接地故障选线中的应用,提出可根据各馈线零序电流暂态变化规律及小波多尺度分解的尺度系数的特征值进行选线。
针对馈线数目少的10kV系统选线困难的问题,利用Matlab平台对4回馈线及其以下10kV系统的单相接地故障进行了仿真,采用Db N系列、Sym N系列、Bior Nr.Nd系列和Coif N系列共50种实小波对故障系统暂态零序电流进行小波变换,分析了零序电流小波变换后的特征,首次提出了暂态零序电流低频能量选线方法,并与目前采用的模极大值法和高频能量法进行了比较,结果表明:对于四回线及以下10kV系统,采用模极大值和高频能量法选线时,只有Sym 3、Coif 1、Bior 2.4、Bior 2.6和Bior 4.4等5个小波可实现正确选线;而采用本文提出的低频能量法进行选线时,不仅不受小波基选择的限制,且不受系统回路数的限制,对不接地系统和经消弧线圈接地系统均可实现正确选线。因此,本文提出了10kV系统发生单相接地故障时实小波选线可采用低频能量法。
针对实小波选线存在的问题,采用Morlet 1-0.1、Cgaussian 1和Shannon 1-1等3种复小波对5回馈线10kV系统单相接地故障的暂态零序电压和各线路的暂态零序电流进行了变换,根据复小波变换具有的幅值和相位特征信息,提出了复小波变换的零序暂态电流功率、零序暂态电流能量和零序暂态电流幅值范数的故障选线方法,比较了不同选线判据和不同复小波选线的差异,提出了表征选线方法优劣的显著性指标,结果表明:采用零序暂态电流功率、零序暂态电流能量和零序暂态电流幅值范数进行选线,反映的故障特征突出和明显,具有综合特征;比较而言,采用Morelet复小波对10kV系统进行故障选线具有准确率高、选线可靠且易实现、特征值的显著性指标高等特点,且不受采样频率(3~100kHz)、过渡电阻、故障点位置和线路长度的限制,特别是对二回馈线谐振接地系统单相接地故障选线的显著性系数远高于实小波;而采用Cgaussian复小波和Shannon复小波虽也能实现正确选线,但因其边界效应明显,使信号边界部分严重失真,使用存在局限性。因此,复小波变换不仅可应用于10kV单相接地故障选线,而且对于馈线数少的系统选线具有优势。
Because the characteristic signal of single-phase-grounded fault of 10kV distribution network system is not obvious, the fault detection based on the steady current of the faulted line might be not correct. Therefore, the fault detection based on the transient signal of the fault distribution network has become one of the key techiniques.
Based on the art-of-the-state of the fault detection techniques for the single-phase-grounded fault of 10kV distribution network system, the performance of the transient zero sequence current and voltage in the the single-phase-grounded 10kV distribution network was analyzed in this thesis. Based on the simulating results of the transient zero sequence current and voltage with Matlab Simulink platform and according to the characteristics of both typical real and complex wavelet transform, the author analyzed and compared the applicaions of both the real and the complex wavelet transform in the fault detection of the single-phase-grounded fault of 10kV distribution network system, and proposed a fault detection method according to the performances of both the transient zero currents of all feeders and the scale-coefficients index-values of the multi-scale decomposition in the wavelet transform.
Because of the difficulty for the fault detection of the two to four feeder 10 kV distribution network, based on the simulating results of transient zero sequence current for the single-phase-grounded fault for the four feeder 10kV distribution network and below on Matlab platform, the wavelet transform results of the transient zero sequence current with fifty real wavelets including Db N series, Sym N series, Bior Nr.Nd series and Coif N series, etc. were analyzed. And it put forward a fault detection method based on the transient low-frequency zero-sequence-current(ZSC) energy for the first time which was compared with the fault detection methods based on both the transient high-frequency ZSC energy or the maximun module value . For the four feeder 10kV distribution network and below, the results shows that only five real wavelets such as Sym 3、Coif 1、Bior 2.4、Bior 2.6 and Bior 4.4 can detect the faulted line correctly with the transient high-frequency ZSC energy and the maximun module value correctly, and with the low-frequency high-scale-coefficient of the multi-scale decomposition of wavelet transform, the fault line for both NUS and NES network could be located correctly which is not effected with the real wavelets and the feeder number of the network. Therefore, this paper concluded that the fault detection based on the low frequency energy can used to fault detection of 10kV single-phase-grounded system with the real wavelet transform.
In order to avoiding the disadvantages of the fault detection with real wavelets, both the transient ZSCs of all feeders and the transient zero-sequence-voltage(ZSV) for the single-phase-grounded fault of five feeder 10kV distribution network were transformed with three kinds of complex wavelets such as Morlet 1-0.1, Cgaussian 1 and Shannon 1-1. According to the phase and mulitude performances of the complex wavelet, three kinds of fault detection methods, such as the transient power, the transient energy and transient module eigenvalue methods of ZSC are put forward. With the analyses and conparions of simulated results, the marked indexes of three fault detection methods, which show the stand or fall of a fault detection method, are indicated.
The results show that the three kinds of fault detection methods above based on complex wavelet show a distincting character and a synthetical information. For the three complex wavelets analyszed in this thesis, Morlet wavelet is the best one, and is of a high reliability. Although Cgaussian and Shannon wavelets can select fault line, they are obviously influenced by boundary effection so as to the boundary signal’s distortion. And Morlet wavelet can not be effected by sampling frequency(3~100kHz), transition resistance, fault position, and line’s length. Therefore, the fault detection with complex wavelet has an advantage in the system with two to four feeders, for example, in a single-phase-grounded two feeder NES, its marked factor with Morlet 1-0.1 complex wavelet is greatly higher than that with the real wavelets.
针对馈线数目少的10kV系统选线困难的问题,利用Matlab平台对4回馈线及其以下10kV系统的单相接地故障进行了仿真,采用Db N系列、Sym N系列、Bior Nr.Nd系列和Coif N系列共50种实小波对故障系统暂态零序电流进行小波变换,分析了零序电流小波变换后的特征,首次提出了暂态零序电流低频能量选线方法,并与目前采用的模极大值法和高频能量法进行了比较,结果表明:对于四回线及以下10kV系统,采用模极大值和高频能量法选线时,只有Sym 3、Coif 1、Bior 2.4、Bior 2.6和Bior 4.4等5个小波可实现正确选线;而采用本文提出的低频能量法进行选线时,不仅不受小波基选择的限制,且不受系统回路数的限制,对不接地系统和经消弧线圈接地系统均可实现正确选线。因此,本文提出了10kV系统发生单相接地故障时实小波选线可采用低频能量法。
针对实小波选线存在的问题,采用Morlet 1-0.1、Cgaussian 1和Shannon 1-1等3种复小波对5回馈线10kV系统单相接地故障的暂态零序电压和各线路的暂态零序电流进行了变换,根据复小波变换具有的幅值和相位特征信息,提出了复小波变换的零序暂态电流功率、零序暂态电流能量和零序暂态电流幅值范数的故障选线方法,比较了不同选线判据和不同复小波选线的差异,提出了表征选线方法优劣的显著性指标,结果表明:采用零序暂态电流功率、零序暂态电流能量和零序暂态电流幅值范数进行选线,反映的故障特征突出和明显,具有综合特征;比较而言,采用Morelet复小波对10kV系统进行故障选线具有准确率高、选线可靠且易实现、特征值的显著性指标高等特点,且不受采样频率(3~100kHz)、过渡电阻、故障点位置和线路长度的限制,特别是对二回馈线谐振接地系统单相接地故障选线的显著性系数远高于实小波;而采用Cgaussian复小波和Shannon复小波虽也能实现正确选线,但因其边界效应明显,使信号边界部分严重失真,使用存在局限性。因此,复小波变换不仅可应用于10kV单相接地故障选线,而且对于馈线数少的系统选线具有优势。
Because the characteristic signal of single-phase-grounded fault of 10kV distribution network system is not obvious, the fault detection based on the steady current of the faulted line might be not correct. Therefore, the fault detection based on the transient signal of the fault distribution network has become one of the key techiniques.
Based on the art-of-the-state of the fault detection techniques for the single-phase-grounded fault of 10kV distribution network system, the performance of the transient zero sequence current and voltage in the the single-phase-grounded 10kV distribution network was analyzed in this thesis. Based on the simulating results of the transient zero sequence current and voltage with Matlab Simulink platform and according to the characteristics of both typical real and complex wavelet transform, the author analyzed and compared the applicaions of both the real and the complex wavelet transform in the fault detection of the single-phase-grounded fault of 10kV distribution network system, and proposed a fault detection method according to the performances of both the transient zero currents of all feeders and the scale-coefficients index-values of the multi-scale decomposition in the wavelet transform.
Because of the difficulty for the fault detection of the two to four feeder 10 kV distribution network, based on the simulating results of transient zero sequence current for the single-phase-grounded fault for the four feeder 10kV distribution network and below on Matlab platform, the wavelet transform results of the transient zero sequence current with fifty real wavelets including Db N series, Sym N series, Bior Nr.Nd series and Coif N series, etc. were analyzed. And it put forward a fault detection method based on the transient low-frequency zero-sequence-current(ZSC) energy for the first time which was compared with the fault detection methods based on both the transient high-frequency ZSC energy or the maximun module value . For the four feeder 10kV distribution network and below, the results shows that only five real wavelets such as Sym 3、Coif 1、Bior 2.4、Bior 2.6 and Bior 4.4 can detect the faulted line correctly with the transient high-frequency ZSC energy and the maximun module value correctly, and with the low-frequency high-scale-coefficient of the multi-scale decomposition of wavelet transform, the fault line for both NUS and NES network could be located correctly which is not effected with the real wavelets and the feeder number of the network. Therefore, this paper concluded that the fault detection based on the low frequency energy can used to fault detection of 10kV single-phase-grounded system with the real wavelet transform.
In order to avoiding the disadvantages of the fault detection with real wavelets, both the transient ZSCs of all feeders and the transient zero-sequence-voltage(ZSV) for the single-phase-grounded fault of five feeder 10kV distribution network were transformed with three kinds of complex wavelets such as Morlet 1-0.1, Cgaussian 1 and Shannon 1-1. According to the phase and mulitude performances of the complex wavelet, three kinds of fault detection methods, such as the transient power, the transient energy and transient module eigenvalue methods of ZSC are put forward. With the analyses and conparions of simulated results, the marked indexes of three fault detection methods, which show the stand or fall of a fault detection method, are indicated.
The results show that the three kinds of fault detection methods above based on complex wavelet show a distincting character and a synthetical information. For the three complex wavelets analyszed in this thesis, Morlet wavelet is the best one, and is of a high reliability. Although Cgaussian and Shannon wavelets can select fault line, they are obviously influenced by boundary effection so as to the boundary signal’s distortion. And Morlet wavelet can not be effected by sampling frequency(3~100kHz), transition resistance, fault position, and line’s length. Therefore, the fault detection with complex wavelet has an advantage in the system with two to four feeders, for example, in a single-phase-grounded two feeder NES, its marked factor with Morlet 1-0.1 complex wavelet is greatly higher than that with the real wavelets.
引文
[1]徐青山.电力系统故障诊断及故障恢复[M].北京:中国电力出版社, 2007.
[2]庞清乐,孙同景,钟麦英,等.基于粗糙集理论的配电网故障选线装置研究[J].高电压技术,2007,33(3):37-41.
[3]庞清乐,孙同景,穆健,等.基于神经网络的中性点经消弧线圈接地系统故障选线方法[J].电网技术,2005,29(24):78-81.
[4]张庆超,王振华.基于协同学理论的小电流接地系统单相接地故障选线方法[J].电网技术,2007,31(8):87-92.
[5]郭彦东.基于遗传算法的BP网络在小电流接地选线中的应用[J].自动化技术与应用,2007,26(1):18-20.
[6]俞晓荣,廖培金,彭书涛,等.小波分析在小电流接地系统故障选线中的应用[J].电力系统及其自动化学报,2003,15(4):24-26.
[7]陈祥训.正交紧支复小波的生成及其在电力系统中的应用[J].中国电机工程学报,2000, 20(7): 83-88.
[8]郝玉山,杨以涵,任元恒等.小电流接地微机选线的群体比幅比相原理[J].电力情报,1994, (2): 15-19.
[9]张尔桦,潘贞存,桑在中等.群体比幅原理接地选线保护[J].继电器,1991,(2): 15-17.
[10]檀国彪,涂东明,陈大鹏.基于最大Isinφ或△(Isinφ)原理的微机选线原理[J].中国电力,1995, 28(7): 16-20.
[11]牟龙华.零序电流有功分量方向接地选线保护原理[J].电网技术,1999,23(9): 60-62.
[12]杜丁香,徐玉琴.消弧线圈接地电网有功选线[J].继电器,2002, 30(5):33-36.
[13] D. Griffel, V Leitoff, Y Harmand, et al. A new deal for safety and quality on MV networks [J]. IEEE Transactions on Power Delivery. 1997, 12(4):1428-1433.
[14]何奔腾,胡为进.能量法小电流接地选线原理[J].浙江大学学报(自然科学版),1998, 32(4): 451-456.
[15]束洪春,刘娟,王超,等.谐振接地电网故障暂态能量自适应选线新方法[J].电力系统自动化,2006, 30(11): 72-76.
[16] M. Michalik, W. Rebizant, M. Lukowicz, et al. High-impedance fault detection in distribution networks with use of wavelet-based algorithm[J]. IEEE Transactions on Power Delivery, 2006, 21(4): 1793-1802.
[17] R. Sedighi, M. R. Haghifam, 0. P. Malik, et al. High impedance fault detection based on wavelet transform and statistical pattern recognition[J]. IEEE Transactions on Power Delivery, 2005, 20(4): 2414-2421.
[18] T. M. Lai, L. A. Snider, E. Lo, et al. High-impedance fault detection using discrete wavelet transform and frequency range and RMS conversion[J]. IEEE Transactions on Power Delivery, 2005, 20(1): 397-407.
[19] Shyh-Jier Huang, Cheng-Tao Hsieh. High-impedance fault detection utilizing a Morlet wavelet transform approach[J]. IEEE Transactions on Power Delivery, 1999, 14(4): 1401-1410.
[20] Lazkano, J. Ruiz, E. Aramendi, et al. A new approach to high impedance fault detection using wavelet packet analysis[J]. Proceedings of Ninth International Conference on Harmonics and Quality of Power, 2000, 3:1005-1010.
[21]贾清泉,刘连光,杨以涵等.应用小波检测故障突变特性实现配电网小电流故障选线保护[J].中国电机工程学报,2001, 21(10): 78-82.
[22] M. Sharaf, L. A. Snider, K. Debnath. A neural network based ralaying scheme for distribution system high impedance fault detection[C]. Proceedings of First New Zealand International Two-Stream Conference on Artificial Neural Networks and Expert Systems, 1993, 321-324.
[23] T. M. Lai, L. A. Snider, E. Lo, et al. High impedance faults detection using artificial neural network[C]. Sixth International Conference on Advances in Power System Control, Operation and Management, 2003, 2: 821-826.
[24] L. A. Snider, Yuen Yee Shan. The artificial neural networks based relay algorithm for distribution system high impedance fault detection[C]. Fourth International Conference on Advances in Power System Control, Operation and Management, 1997, 1:100-106.
[25] M. Sharat, L. A. Snider, K. Debnath. A neural network based back error propagation relay algorithm for distribution system high impedance fault detection[C]. 2nd International Conference on Advances in Power System Control, Operation and Management, 1993, 2: 613-620.
[26] F. Ruz, J. A. Fuentes. Fuzzy decision making applied to high impedance fault detection in compensated neutral grounded MV distribution systems[C]. Seventh International Conference on Developments in Power System Protection, 2001:307-310.
[27] DAUBECHIES I. Where do wavelet come from: a personal point of view[J]. IEEE, 1996, 84(4):510-513.
[28] DAUBECHIES I. Ten lectures on wavelets. Philadelphia, PA, USA: SIAM, 1992.
[29]任震等.小波分析及其在电力系统中的应用[M].北京:中国电力出版社, 2003.
[30]尚赵伟,张明新,赵平,等.基于不同复小波变换方法的纹理检索和相似计算[J].计算机研究与发展, 2005, 8(28):51-55.
[31]李冬辉,史临潼.基于小波变换的直流系统接地故障检测中小波基的选择与比较[J].电力系统及其自动化学报,2004,16(6):48-51,87.
[32]林军.小波变换在零序电流暂态高频信号分析中的应用[J].电工技术学报,2004,4(19):89-92.
[33]薛蕙,杨仁刚,郭永芳,等.利用复值小波变换检测轻微的电力系统扰动[J].电网技术, 2004, 9(28):24-27.
[34]董杰,张举,王增平.利用小波变换进行故障选相[J].电力情报, 2002, 1(12):12-14,24.
[35]贾国强.几种复小波在奇异性检测中效果的比较分析[J].人工智能及识别技术, 2006, 11:815-816.
[36]苗友忠,孙雅明,等.基于相电流间相位关联特征的馈线单相接地保护新原理[J].电力系统自动化, 2004, 16(28):101-104.
[37]赵成勇,何明锋.基于复小波变换相位信息的谐波检测算法[J].中国电机工程学报,2005,25(1):38-42.
[38]赵新红,袁洪,车伟等.小波变换在小电流接地电弧故障选线中的应用[J].高电压技术,2005, 10(31): 18-20.
[39]唐炬,许中荣,孙才新,等.应用复小波变换抑制GIS局部放电信号中白噪声干扰的研究[J].中国电机工程学报,2005,25(16):30-34.
[40]苏鹏声,王欢.短窗Morlet复小波用于电力系统信号处理的探讨[J].电力系统自动化,2004,28(9):36-42.
[41]张安安,马文营,杨洪耕.复小波在谐波阻抗估计中的应用[J].四川大学学报(工程科学版),2003, 35(2): 104-107.
[42]张大波,刘志刚,张亚军.复小波研究现状及其在电力系统中的应用进展[J].电力系统自动化,2006, 30(17): 97-104.
[43]张大波.复小波变换在小电流接地故障选线中的应用[D].成都:西南交通大学,2007.
[44]陈生贵,卢继平等.电力系统继电保护[M].重庆:重庆大学出版社, 2003.
[45]桑在中,张慧芬,潘贞存等.用注入法实现小电流接地系统单相接地选线保护[J].电力系统自动化,1996, 20(2): 11-12.
[46]王新超,桑在中.基于“S注入法”的一种故障定位新方法[J].继电器,2001,29(7): 9-12.
[47]曾祥君,尹项根,于永源,等.基于注入变频信号法的经消弧线圈接地系统控制与保护新方法[J].中国电机工程学报,2000, 20(1): 29-32.
[48]唐轶,陈奎,陈庆.小电流接地电网单相接地故障的暂态特性[J].高电压技术,2007,33(11):175-179.
[49]要焕年,曹梅月.电力系统谐振接地[M].北京:中国电力出版社, 2000: 23-78.
[50]高志,余啸海. Matlab小波分析工具箱原理与应用[M].北京:国防工业出版社, 2004.
[51]罗建军等. MATLAB教程[M].北京:电子工业出版社, 2005.
[52]王琦,徐式蕴,赵睿涛等. MATLAB基础与应用实例集粹.北京:人民邮电出版社[M], 2007.
[53]费佩燕,刘曙光.几种常见小波的应用性能分析[J].中国电子学会第七届学术年会论文集, 2001.
[54]和敬涵,范瑜,等.基于对称分量变换的暂态电流极性方向比较保护算法[J].电工技术学报,2007, 22(2): 116-120,136.
[55]和敬涵,张飚,等.解耦变换在电力系统暂态保护中的应用研究[J].北京交通大学学报, 2006, 30(5):101-104.
[56]陈基明.小波分析基础[M].上海:上海大学出版社,2002,12.
[2]庞清乐,孙同景,钟麦英,等.基于粗糙集理论的配电网故障选线装置研究[J].高电压技术,2007,33(3):37-41.
[3]庞清乐,孙同景,穆健,等.基于神经网络的中性点经消弧线圈接地系统故障选线方法[J].电网技术,2005,29(24):78-81.
[4]张庆超,王振华.基于协同学理论的小电流接地系统单相接地故障选线方法[J].电网技术,2007,31(8):87-92.
[5]郭彦东.基于遗传算法的BP网络在小电流接地选线中的应用[J].自动化技术与应用,2007,26(1):18-20.
[6]俞晓荣,廖培金,彭书涛,等.小波分析在小电流接地系统故障选线中的应用[J].电力系统及其自动化学报,2003,15(4):24-26.
[7]陈祥训.正交紧支复小波的生成及其在电力系统中的应用[J].中国电机工程学报,2000, 20(7): 83-88.
[8]郝玉山,杨以涵,任元恒等.小电流接地微机选线的群体比幅比相原理[J].电力情报,1994, (2): 15-19.
[9]张尔桦,潘贞存,桑在中等.群体比幅原理接地选线保护[J].继电器,1991,(2): 15-17.
[10]檀国彪,涂东明,陈大鹏.基于最大Isinφ或△(Isinφ)原理的微机选线原理[J].中国电力,1995, 28(7): 16-20.
[11]牟龙华.零序电流有功分量方向接地选线保护原理[J].电网技术,1999,23(9): 60-62.
[12]杜丁香,徐玉琴.消弧线圈接地电网有功选线[J].继电器,2002, 30(5):33-36.
[13] D. Griffel, V Leitoff, Y Harmand, et al. A new deal for safety and quality on MV networks [J]. IEEE Transactions on Power Delivery. 1997, 12(4):1428-1433.
[14]何奔腾,胡为进.能量法小电流接地选线原理[J].浙江大学学报(自然科学版),1998, 32(4): 451-456.
[15]束洪春,刘娟,王超,等.谐振接地电网故障暂态能量自适应选线新方法[J].电力系统自动化,2006, 30(11): 72-76.
[16] M. Michalik, W. Rebizant, M. Lukowicz, et al. High-impedance fault detection in distribution networks with use of wavelet-based algorithm[J]. IEEE Transactions on Power Delivery, 2006, 21(4): 1793-1802.
[17] R. Sedighi, M. R. Haghifam, 0. P. Malik, et al. High impedance fault detection based on wavelet transform and statistical pattern recognition[J]. IEEE Transactions on Power Delivery, 2005, 20(4): 2414-2421.
[18] T. M. Lai, L. A. Snider, E. Lo, et al. High-impedance fault detection using discrete wavelet transform and frequency range and RMS conversion[J]. IEEE Transactions on Power Delivery, 2005, 20(1): 397-407.
[19] Shyh-Jier Huang, Cheng-Tao Hsieh. High-impedance fault detection utilizing a Morlet wavelet transform approach[J]. IEEE Transactions on Power Delivery, 1999, 14(4): 1401-1410.
[20] Lazkano, J. Ruiz, E. Aramendi, et al. A new approach to high impedance fault detection using wavelet packet analysis[J]. Proceedings of Ninth International Conference on Harmonics and Quality of Power, 2000, 3:1005-1010.
[21]贾清泉,刘连光,杨以涵等.应用小波检测故障突变特性实现配电网小电流故障选线保护[J].中国电机工程学报,2001, 21(10): 78-82.
[22] M. Sharaf, L. A. Snider, K. Debnath. A neural network based ralaying scheme for distribution system high impedance fault detection[C]. Proceedings of First New Zealand International Two-Stream Conference on Artificial Neural Networks and Expert Systems, 1993, 321-324.
[23] T. M. Lai, L. A. Snider, E. Lo, et al. High impedance faults detection using artificial neural network[C]. Sixth International Conference on Advances in Power System Control, Operation and Management, 2003, 2: 821-826.
[24] L. A. Snider, Yuen Yee Shan. The artificial neural networks based relay algorithm for distribution system high impedance fault detection[C]. Fourth International Conference on Advances in Power System Control, Operation and Management, 1997, 1:100-106.
[25] M. Sharat, L. A. Snider, K. Debnath. A neural network based back error propagation relay algorithm for distribution system high impedance fault detection[C]. 2nd International Conference on Advances in Power System Control, Operation and Management, 1993, 2: 613-620.
[26] F. Ruz, J. A. Fuentes. Fuzzy decision making applied to high impedance fault detection in compensated neutral grounded MV distribution systems[C]. Seventh International Conference on Developments in Power System Protection, 2001:307-310.
[27] DAUBECHIES I. Where do wavelet come from: a personal point of view[J]. IEEE, 1996, 84(4):510-513.
[28] DAUBECHIES I. Ten lectures on wavelets. Philadelphia, PA, USA: SIAM, 1992.
[29]任震等.小波分析及其在电力系统中的应用[M].北京:中国电力出版社, 2003.
[30]尚赵伟,张明新,赵平,等.基于不同复小波变换方法的纹理检索和相似计算[J].计算机研究与发展, 2005, 8(28):51-55.
[31]李冬辉,史临潼.基于小波变换的直流系统接地故障检测中小波基的选择与比较[J].电力系统及其自动化学报,2004,16(6):48-51,87.
[32]林军.小波变换在零序电流暂态高频信号分析中的应用[J].电工技术学报,2004,4(19):89-92.
[33]薛蕙,杨仁刚,郭永芳,等.利用复值小波变换检测轻微的电力系统扰动[J].电网技术, 2004, 9(28):24-27.
[34]董杰,张举,王增平.利用小波变换进行故障选相[J].电力情报, 2002, 1(12):12-14,24.
[35]贾国强.几种复小波在奇异性检测中效果的比较分析[J].人工智能及识别技术, 2006, 11:815-816.
[36]苗友忠,孙雅明,等.基于相电流间相位关联特征的馈线单相接地保护新原理[J].电力系统自动化, 2004, 16(28):101-104.
[37]赵成勇,何明锋.基于复小波变换相位信息的谐波检测算法[J].中国电机工程学报,2005,25(1):38-42.
[38]赵新红,袁洪,车伟等.小波变换在小电流接地电弧故障选线中的应用[J].高电压技术,2005, 10(31): 18-20.
[39]唐炬,许中荣,孙才新,等.应用复小波变换抑制GIS局部放电信号中白噪声干扰的研究[J].中国电机工程学报,2005,25(16):30-34.
[40]苏鹏声,王欢.短窗Morlet复小波用于电力系统信号处理的探讨[J].电力系统自动化,2004,28(9):36-42.
[41]张安安,马文营,杨洪耕.复小波在谐波阻抗估计中的应用[J].四川大学学报(工程科学版),2003, 35(2): 104-107.
[42]张大波,刘志刚,张亚军.复小波研究现状及其在电力系统中的应用进展[J].电力系统自动化,2006, 30(17): 97-104.
[43]张大波.复小波变换在小电流接地故障选线中的应用[D].成都:西南交通大学,2007.
[44]陈生贵,卢继平等.电力系统继电保护[M].重庆:重庆大学出版社, 2003.
[45]桑在中,张慧芬,潘贞存等.用注入法实现小电流接地系统单相接地选线保护[J].电力系统自动化,1996, 20(2): 11-12.
[46]王新超,桑在中.基于“S注入法”的一种故障定位新方法[J].继电器,2001,29(7): 9-12.
[47]曾祥君,尹项根,于永源,等.基于注入变频信号法的经消弧线圈接地系统控制与保护新方法[J].中国电机工程学报,2000, 20(1): 29-32.
[48]唐轶,陈奎,陈庆.小电流接地电网单相接地故障的暂态特性[J].高电压技术,2007,33(11):175-179.
[49]要焕年,曹梅月.电力系统谐振接地[M].北京:中国电力出版社, 2000: 23-78.
[50]高志,余啸海. Matlab小波分析工具箱原理与应用[M].北京:国防工业出版社, 2004.
[51]罗建军等. MATLAB教程[M].北京:电子工业出版社, 2005.
[52]王琦,徐式蕴,赵睿涛等. MATLAB基础与应用实例集粹.北京:人民邮电出版社[M], 2007.
[53]费佩燕,刘曙光.几种常见小波的应用性能分析[J].中国电子学会第七届学术年会论文集, 2001.
[54]和敬涵,范瑜,等.基于对称分量变换的暂态电流极性方向比较保护算法[J].电工技术学报,2007, 22(2): 116-120,136.
[55]和敬涵,张飚,等.解耦变换在电力系统暂态保护中的应用研究[J].北京交通大学学报, 2006, 30(5):101-104.
[56]陈基明.小波分析基础[M].上海:上海大学出版社,2002,12.