基于行波固有频率的输电网故障定位方法关键问题研究
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摘要
随着电网的加速建设,高压输电网的枢纽作用日渐凸显,快速准确地进行故障点定位以及时恢复供电,具有重要的社会效益和经济价值。本文使用的基于行波固有频率的故障定位方法较之现有基于时域行波的方法,最大优点是避免了波头识别困难的问题,并能准确计算行波波速。但该方法在输电网实际应用中还存在测量端系统等效阻抗难以准确获取,输电网中多端系统的故障支路定位等问题。
钊对系统等效阻抗对故障定位的影响,本文提出了基于行波固有频率的故障定位中测量端系统等效阻抗识别方法。首先将测量端系统电阻与电感视为待识别参数,利用故障行波多次固有频率信息构造非线性多目标函数,再由Nelder-Mead单纯性搜索算法求解局部最优值,得到满足故障定位要求的等效阻抗。因为目标函数具有多解性,满足局部最优的等效阻抗不代表系统实际阻抗值,但由此能计算正确的故障行波系统端反射角,最终得到准确的故障距离,形成规避系统等效阻抗影响的行波固有频率故障定位改进方法。该方法无需增加其他电气量,且和原有的定位方法计算形式保持一致,具有良好的可移植性。大量仿真试验验证表明定位结果不受故障距离、故障类型和过渡电阻的影响,且迭代算法对迭代初值不敏感。另外,在故障距离计算中能实现对定位结果准确度的评价,显著增加原有方法的可靠性,避免提取错误的固有频率而导致定位失败。
针对输电网通常出现的T型结构,本文提出了基于行波固有频率的故障定位在T型线路的解决方案。本文通过分析在T型线路不同位置发生故障时,母线测量电流所反映的行波传播路径,揭示出故障支路母线所测固有频率具有规律的谐波特性,并进一步数学推导出了故障行波在不同系统边界条件下,于故障点和对应母线间传播的固有频率变化趋势,并以此特性构造故障支路判别判据。在判断故障支路后则提取该支路母线电流,利用现有的单端固有频率定位方法计算故障距离,实现完整的T型线路故障定位。仿真实验验证表明定位结果不受故障距离、故障类型等因素的影响,特别在T节点附近发生单相接地故障时,亦能可靠判断故障支路。故障定位的死区出现在母线附近,这是由行波固有频率定位原理本身引起的。
本文解决了行波固有频率定位方法对准确系统等效阻抗的依赖问题,同时以数学表达式揭示了故障行波的固有频率变化趋势,实现了可靠的T型电线路的故障支路判别和定位,以上改进均为该方法在输电网故障定位的实际应用奠定了一定的理论基础。
With the accelerated construction of power grid, it is becoming increasingly prominent for high-voltage power transmission network being the pivotal role, which has important economic value and social benefits to quickly and accurately locate fault and restore power. In this paper, the fault location algorithm based on natural frequencies of traveling wave, compared with the existing traveling wave method based on the time domain, has most notable advantage in avoiding the difficult problem of wave-head identification, and can accurately calculate the wave velocity. But the practical application of this method in transmission network exists several problems, such as the difficulty to obtain accurate equivalent impedances in local system, and the problem of fault branch location in multiterminal system of transmission network.
In view of the influence of system equivalent impedance to the fault location, this article proposed the impedance identification method of measuring end in fault location based on natural frequencies of traveling wave. Firstly, the local system resistance and inductance are considered as parameters to be identified, then multi-objective nonlinear functions are constructed using multiple natural frequencies of fault traveling wave, again by Nelder-Mead, namely simplex search algorithm, to solve the local optimal value to obtain the equivalent impedance satisfying the requirement of fault location. Because of the multiple solutions in multi-objective functions, the obtained local optimal equivalent impedance is not representative of the actual system impedance value, but it can correctly calculate the reflection angle of fault traveling wave, and finally get accurate fault distance, which make improvements to fault location method based on traveling wave natural frequencies in evading the influence of system equivalent impedance. This method eliminates the need to add other electrical parameters, and consistents on the form of original location algorithm, which has good portability. A large number of simulation experiments verify that the fault location results are not affected by the change of fault distance, fault type and transition resistance, and the iterative algorithm is not sensitive to the initial iterative. In addition, it can realize evaluation of location accuracy during the fault distance calculation, also can significantly increase the reliability of the fault location method based on the natural frequencies of traveling wave, to avoid extract the error natural frequencies.
For T type structure usually appearing in transmission network, this paper presents the fault location based on traveling wave natural frequencies in the T type line solution. In this paper, through the analysis of the wave propagation path reflected by busline current considering different fault positions in T-line, it is revealed that the natural frequencies measured by the fault branch busline has a regular harmonic characteristic. Moreover, further study of the natural frequencies of the spread between the fault point and busline has been proofed by mathematical derivation of the trend of fault generated traveling waves in different system boundary conditions, with which the fault discrimination criterion has been structured. After determining the fault branch, extract the branch busline current, then use the existing single-end fault locating method based on natural frequencies to calculate fault distance, finally the complete T-line fault location method can be achieved. Simulation results show that the location results are not affected by the fault distance and the fault type, especially the fault branch can be reliably determined when single-phase faults near the T-node. Fault location dead zone is near the proximal busline, which is caused by the traveling wave frequencies positioning principle itself.
This article addresses the traveling wave fault location method based on natural frequencies dependent on the accurate system equivalent impedance, meanwhile mathematical expressions are proposed to reveal the trend of natural frequencies of the traveling wave, and to achieve reliable fault branch discrimination and fault location in T-line. These above improvements are laid a theoretical foundation for the practical application of the method for fault location in transmission network.
钊对系统等效阻抗对故障定位的影响,本文提出了基于行波固有频率的故障定位中测量端系统等效阻抗识别方法。首先将测量端系统电阻与电感视为待识别参数,利用故障行波多次固有频率信息构造非线性多目标函数,再由Nelder-Mead单纯性搜索算法求解局部最优值,得到满足故障定位要求的等效阻抗。因为目标函数具有多解性,满足局部最优的等效阻抗不代表系统实际阻抗值,但由此能计算正确的故障行波系统端反射角,最终得到准确的故障距离,形成规避系统等效阻抗影响的行波固有频率故障定位改进方法。该方法无需增加其他电气量,且和原有的定位方法计算形式保持一致,具有良好的可移植性。大量仿真试验验证表明定位结果不受故障距离、故障类型和过渡电阻的影响,且迭代算法对迭代初值不敏感。另外,在故障距离计算中能实现对定位结果准确度的评价,显著增加原有方法的可靠性,避免提取错误的固有频率而导致定位失败。
针对输电网通常出现的T型结构,本文提出了基于行波固有频率的故障定位在T型线路的解决方案。本文通过分析在T型线路不同位置发生故障时,母线测量电流所反映的行波传播路径,揭示出故障支路母线所测固有频率具有规律的谐波特性,并进一步数学推导出了故障行波在不同系统边界条件下,于故障点和对应母线间传播的固有频率变化趋势,并以此特性构造故障支路判别判据。在判断故障支路后则提取该支路母线电流,利用现有的单端固有频率定位方法计算故障距离,实现完整的T型线路故障定位。仿真实验验证表明定位结果不受故障距离、故障类型等因素的影响,特别在T节点附近发生单相接地故障时,亦能可靠判断故障支路。故障定位的死区出现在母线附近,这是由行波固有频率定位原理本身引起的。
本文解决了行波固有频率定位方法对准确系统等效阻抗的依赖问题,同时以数学表达式揭示了故障行波的固有频率变化趋势,实现了可靠的T型电线路的故障支路判别和定位,以上改进均为该方法在输电网故障定位的实际应用奠定了一定的理论基础。
With the accelerated construction of power grid, it is becoming increasingly prominent for high-voltage power transmission network being the pivotal role, which has important economic value and social benefits to quickly and accurately locate fault and restore power. In this paper, the fault location algorithm based on natural frequencies of traveling wave, compared with the existing traveling wave method based on the time domain, has most notable advantage in avoiding the difficult problem of wave-head identification, and can accurately calculate the wave velocity. But the practical application of this method in transmission network exists several problems, such as the difficulty to obtain accurate equivalent impedances in local system, and the problem of fault branch location in multiterminal system of transmission network.
In view of the influence of system equivalent impedance to the fault location, this article proposed the impedance identification method of measuring end in fault location based on natural frequencies of traveling wave. Firstly, the local system resistance and inductance are considered as parameters to be identified, then multi-objective nonlinear functions are constructed using multiple natural frequencies of fault traveling wave, again by Nelder-Mead, namely simplex search algorithm, to solve the local optimal value to obtain the equivalent impedance satisfying the requirement of fault location. Because of the multiple solutions in multi-objective functions, the obtained local optimal equivalent impedance is not representative of the actual system impedance value, but it can correctly calculate the reflection angle of fault traveling wave, and finally get accurate fault distance, which make improvements to fault location method based on traveling wave natural frequencies in evading the influence of system equivalent impedance. This method eliminates the need to add other electrical parameters, and consistents on the form of original location algorithm, which has good portability. A large number of simulation experiments verify that the fault location results are not affected by the change of fault distance, fault type and transition resistance, and the iterative algorithm is not sensitive to the initial iterative. In addition, it can realize evaluation of location accuracy during the fault distance calculation, also can significantly increase the reliability of the fault location method based on the natural frequencies of traveling wave, to avoid extract the error natural frequencies.
For T type structure usually appearing in transmission network, this paper presents the fault location based on traveling wave natural frequencies in the T type line solution. In this paper, through the analysis of the wave propagation path reflected by busline current considering different fault positions in T-line, it is revealed that the natural frequencies measured by the fault branch busline has a regular harmonic characteristic. Moreover, further study of the natural frequencies of the spread between the fault point and busline has been proofed by mathematical derivation of the trend of fault generated traveling waves in different system boundary conditions, with which the fault discrimination criterion has been structured. After determining the fault branch, extract the branch busline current, then use the existing single-end fault locating method based on natural frequencies to calculate fault distance, finally the complete T-line fault location method can be achieved. Simulation results show that the location results are not affected by the fault distance and the fault type, especially the fault branch can be reliably determined when single-phase faults near the T-node. Fault location dead zone is near the proximal busline, which is caused by the traveling wave frequencies positioning principle itself.
This article addresses the traveling wave fault location method based on natural frequencies dependent on the accurate system equivalent impedance, meanwhile mathematical expressions are proposed to reveal the trend of natural frequencies of the traveling wave, and to achieve reliable fault branch discrimination and fault location in T-line. These above improvements are laid a theoretical foundation for the practical application of the method for fault location in transmission network.
引文
[1]Dommel H W, Michels J M. High Speed Relaying Using Travelling Wave Transient Analysis[C]. New York:1978.
[2]Chamia M, Liberman S. Ultra High Speed Relay for EHV/UHV Transmission Lines-Development, Design and Application[J]. IEEE Transactions on Power Apparatus and Systems.1978,6(97):2104-2116.
[3]Christopoulos C, Thomas D W P, Wright A. For The Protection of Major Transmission Lines IEEE Proceedings[J].1988,1(135):63-73.
[4]Johns A T. New ultra High Speed Directional Comparison Technique for the Protection of EHV Transmission Lines[J]. IEE Proceedings.1980,127:228-239.
[5]覃剑,陈祥训,郑健超.行波在输电线上传播的色散研究[J].中国电机工程学报.1999,19(9)：27-30.
[6]Spoor D J, Zhu J. Frequency considerations when employing travelling wave fault location algorithms[C]. UPEC:2004.
[7]Chen Y, Liu D, Xu B, et al. Wide area travelling wave fault location in the transmission network[C]. Proceeding of the China International Conference on Electrieity Distribution(CICED):2010.
[8]Ancell G B, Pahalawaththa N C. Maximum Likelihood Estimation of Fault Location on Transmission Lines Using Travelling Waves.[J]. IEEE Transactions on Power Delivery.1994,9(2): 680-689.
[9]邬林勇,何正友,钱清泉.一种提取行波自然频率的单端故障测距方法[J].中国电机工程学报.2008,28(10)：69-75.
[10]邬林勇,何正友,钱清泉.单端行波故障测距的频域方法[J].中国电机工程学报.2008,28(25)：99-104.
[11]李小鹏,何正友,廖凯.基于行波固有频率的串补线路故障测距方法[J].电网技术.2012,36(6)：71-76.
[12]林圣,武骁,何正友,等.基于行波固有频率的电网故障定位方法[J].电网技术.2013,37(1)：270-275.
[13]廖凯,何正友,李小鹏.基于行波固有频率的高压直流输电线路故障定位[J].电力系统自动化.2013,37(3)：104-109.
[14]李小鹏,何正友,夏璐璐.同杆双回输电线路的固有频率测距算法[J].电力系统自动化.2011,35(12)：47-51.
[15]V C. Fundamental Aspects of Fault Location Algorithms Used in Distance Protection[J]. Generation, Transmission and Distribution, IEE Proceedings C.1986,133(6):359-368.
[16]A W. Accurate Fault Impedance Locating Algorithm[J]. [J]. Generation, Transmission and Distribution, IEE Proceedings C.1983,130(6):311-314.
[17]F Z J, S S J, H W Q, et al. Morphological undecimated wavelet decomposition for fault location on power transmission lines[J]. Circuits and Systems I:Regular Papers, IEEE Transactions on.2006,53(6): 1395-1402.
[18]陈平,葛耀中,索南加乐,等.基于故障开断暂态行波信息的输电线路故障测距研究[J].中国电机工程学报.2000,20(8)：56-59,64.
[19]蒋涛,陆于平.不受波速影响的输电线路单端行波故障测距研究[J].电力自动化设备.2004,24(12)：29-32.
[20]张峰,梁军,张利,等.基于三端行波测量数据的输电线路故障测距新方法[J].电力系统自动化.2008,32(8)：69-72.
[21]黄震,江泰廷,张维锡,等.基于双端行波原理的高压架空线-电缆混合线路故障定位方法[J].电力系统自动化.2010,34(14)：88-91.
[22]李泽文,姚建刚,曾祥君,等.基于整个输电网的电压行波故障定位算法[J].电力系统自动化.2008,32(1)：66-69.
[23]Mora-Florez J, Barrera-Nuez V, Carrillo-Caicedo G. Fault Location in Power Distribution Systems Using a Learning Algorithm for Multivariable Data Analysis[J]. Power Delivery, IEEE Transactions on. 2007,22(3):1715-1721.
[24]Reddy M J, Mohanta D K. Adaptive-neuro-fuzzy inference system approach for transmission line fault classification and location incorporating effects of power swings[J]. Generation, Transmission & Distribution, IET.2008,2(2):235-244.
[25]Salat R, Osowski S. Accurate fault location in the power transmission line using support vector machine approach[J]. Power Systems, IEEE Transactions on.2004,19(2):979-986.
[26]Seung-Jae L, Myeon-Song C, Sang-Hee K, et al. An intelligent and efficient fault location and diagnosis scheme for radial distribution systems[J]. Power Delivery, IEEE Transactions on.2004,19(2): 524-532.
[27]Thukaram D, Khincha H P, Vijaynarasimha H P. Artificial neural network and support vector Machine approach for locating faults in radial distribution systems[J], Power Delivery, IEEE Transactions on.2005,20(2):710-721.
[28]康小宁，索南加乐.基于参数识别的单端电气量频域法故障测距原理[J].中国电机工程学报.2005,25(2)：22-27.
[29]康小宁,索南加乐.求解频域参数方程的双端故障测距原理[J].电力系统自动化.2005,29(10)：16-20.
[30]索南加乐,张怿宁,齐军,等.基于参数识别的时域法双端故障测距原理[J].电网技术.2006,30(8)：65-70.
[31]哈恒旭,王婧,谭雨珍,等.基于微分算子逼近的单端故障测距新原理[J].电力系统自动化.2009,33(3)：69-73,78.
[32]de Morais Pereira C E, Jr. Zanetta L C. Fault location in transmission lines using one-terminal postfault voltage data[J]. Power Delivery, IEEE Transactions on.2004,19(2):570-575.
[33]刘千宽,李永斌,黄少锋.基于双端电气量的同杆平行双回线单线故障测距[J].电网技术.2008,32(3)：27-30.
[34]Izykowski J, Molag R, Rosolowski E, et al. Accurate location of faults on power transmission lines with use of two-end unsynchronized measurements[J]. Power Delivery, IEEE Transactions on.2006, 21(2):627-633.
[35]Kawady T, Stenzel J. A practical fault location approach for double circuit transmission lines using single end data[J]. Power Delivery, IEEE Transactions on.2003,18(4):1166-1173.
[36]Liao Y, Elangovan S. Unsynchronised two-terminal transmission-line fault-location without using line parameters[J]. Generation, Transmission and Distribution,IEE Proceedings-.2006,153(6):639-643.
[37]徐鹏,梁远升,王钢.同杆四同线参数自适应双端故障测距频域算法[J].电力系统自动化.2010,34(9)：59-64.
[38]Zhang Q, Zhang Y, Song W, et al. Fault location of two-parallel transmission line for nonearth fault using one-terminal data[J]. Power Delivery, IEEE Transactions on.1999,14(3):863-867.
[39]曾祥君,尹项根,陈浩,等.新型输电线路故障综合定位系统研究[J].电力系统自动化.2000,24(22)：39-44.
[40]曾祥君,尹项根,陈德树,等.基于整个输电网GPS行波故障定位系统的研究[J].电力系统自动化.1999(10)：8-10.
[41]董新洲,葛耀中,徐丙垠,等.新型输电线路故障测距装置的研制[J].电网技术.1998,22(1)：17-21.
[42]黄子俊,陈允平.基于小波变换模极大值的输电线路单端故障定位[J].电力自动化设备.2005,25(2)：10-14.
[43]马丹丹,王晓茹.基于小波模极大值的单端行波故障测距[J].电力系统保护与控制.2009,37(3)：55-59.
[44]张帆.基于单端暂态行波的接地故障测距与保护研究[D].山东大学,2008.
[45]Mallat S, Hwang W L. Singularity detection and processing with wavelets[J]. Information Theory, IEEE Transactions on.1992,38(2):617-643.
[46]陈平,葛耀中,徐丙垠,等.现代行波故障测距原理及其在实测故障分析中的应用-A型原理[J].继电器.2004,32(2)：13-18.
[47]吴大立,尹项根,张哲,等.行波测距硬件系统的研究与设计[J].继电器.2006,34(8)：20-23,44.
[48]董杏丽.基于小波变换的高压电网行波保护原理与技术的研究[D].西安交通大学,2003.
[49]蔡润溟.小电流接地系统单相接地故障选线和测距方法的研究[D].山东大学,2007.
[50]吴军基,吴伊昂,贺济峰,等.数学形态学在行波滤波中的应用[J].继电器.2005,33(17)：21-26.
[51]束洪春,王超,张杰,等.基于形态学的HVDC线路故障识别与定位方法研究[J].电力自动化设备.2007,27(4)：6-9,18.
[52]蔡秀雯,谭伟璞,杨以涵.基于数学形态学的配电网单端行波故障测距[J].现代电力.2006,23(6)：25-29.
[53]林湘宁,刘沛,高艳.基于故障暂态和数学形态学的超高速线路方向保护[J].中国电机工程学报.2005,25(4)：13-18.
[54]束洪春,程春和,赵文渊,等.形态学与HHT检测相结合的行波波头准确标定方法[J].电力自动化设备.2009,29(7)：1-7,37.
[55]Miano G. Transmission Lines and Lumped Circuits[M]. San Diego, USA:Academic Press,2001.
[56]Swift G W. The Spectra of Fault-Induced Transients[J]. Power Apparatus and Systems, IEEE Transactions on.1979, PAS-98(3):940-947.
[57]蔡新雷,宋国兵,高淑萍,等.利用电流固有频率的VSC-HVDC直流输电线路故障定位[J].中国电机工程学报.2011,31(28)：112-119.
[58]夏璐璐,何正友,李小鹏,等.基于行波固有频率和经验模态分解的混合线路故障测距方法[J].电力系统自动化.2010,34(18)：67-73.
[59]林圣,梅俊涛,陈双,等.基于暂态行波时频特征的输电线路故障检测与选相方法[J].电网技术.2012,36(7)：48-53.
[60]S D, Miano G. Transmission lines and lumped circuits[M]. USA:2001:78-84.
[61]邬林勇.利用故障行波固有频率的单端行波故障测距法[D].西南交通大学,2009.
[62]Rangarao K V, Venkatanarasimhan S. gold-MUSIC:A Variation on MUSIC to Accurately Determine Peaks of the Spectrum[J]. Antennas and Propagation, IEEE Transactions on.2013,61(4): 2263-2268.
[63]刘万超,李玮,孙佳佳,等.基于多分辨形态梯度-相关函数综合测距算法的单端行波故障测距[J].电网技术.2011,35(10)：225-229.
[64]覃剑,葛维春,邱金辉,等.影响输电线路行波故障测距精度的主要因素分析[J].电网技术.2007,31(2)：28-35.
[65]Hart P M. An experimental study of short-circuit currents on a low-voltage system[J]. Industry Applications, IEEE Transactions on.1988,24(5):940-946.
[66]索南加乐,张健康,刘辉,等.故障分量提取及故障选相的新方法[J].电力系统自动化.2003,27(16)：58-61,66.
[67]Due-Son P, Zoubir A M. Analysis of Multicomponent Polynomial Phase Signals[J]. Signal Processing, IEEE Transactions on.2007,55(1):56-65.
[68]索南加乐,刘凯,粟小华,等.基于故障分量综合阻抗的输电线路纵联保护[J].中国电机工程学报.2008,28(31)：54-61.
[69]Izykowski J, Molag R, Rosolowski E, et al. Fault location in three-terminal line with use of limited measurements[C].2005.
[70]Khodadadi M, Shahrtash S M. A New Noncommunication-Based Protection Scheme for Three-Terminal Transmission Lines Employing Mathematical Morphology-Based Filters[J]. Power Delivery, IEEE Transactions on.2013,28(1):347-356.
[71]高厚磊,安艳秋,江世芳.超高压T接线路高精度故障测距算法研究[J].电力系统自动化.2001,25(20)：41-44.
[72]束洪春,司大军,葛耀中,等.T型输电线路电弧故障测距时域方法研究[J].电工技术学报.2002,17(4)：99-103,57.
[73]韦钢,唐斌,肖鸿杰.输电线路不对称故障点定位的新方法[J].电力系统自动化.2001,25(17)：29-38.
[74]Girgis A A, Hart D G, Peterson W L. A new fault location technique for two- and three-terminal lines[J]. Power Delivery, IEEE Transactions on.1992,7(1):98-107.
[75]林圣.基于暂态量的高压输电线路故障分类与定位方法研究[D].西南交通大学,2011.
[76]索南加乐,刘凯,粟小华,等.基于故障分量综合阻抗的输电线路纵联保护[J].中国电机工程学报.2008,28(31)：54-61.
[77]王钢,李海锋,赵建仓,等.基于小波多尺度分析的输电线路直击雷暂态识别[J].中国电机工程学报.2004,24(4)：139-144.
[2]Chamia M, Liberman S. Ultra High Speed Relay for EHV/UHV Transmission Lines-Development, Design and Application[J]. IEEE Transactions on Power Apparatus and Systems.1978,6(97):2104-2116.
[3]Christopoulos C, Thomas D W P, Wright A. For The Protection of Major Transmission Lines IEEE Proceedings[J].1988,1(135):63-73.
[4]Johns A T. New ultra High Speed Directional Comparison Technique for the Protection of EHV Transmission Lines[J]. IEE Proceedings.1980,127:228-239.
[5]覃剑,陈祥训,郑健超.行波在输电线上传播的色散研究[J].中国电机工程学报.1999,19(9)：27-30.
[6]Spoor D J, Zhu J. Frequency considerations when employing travelling wave fault location algorithms[C]. UPEC:2004.
[7]Chen Y, Liu D, Xu B, et al. Wide area travelling wave fault location in the transmission network[C]. Proceeding of the China International Conference on Electrieity Distribution(CICED):2010.
[8]Ancell G B, Pahalawaththa N C. Maximum Likelihood Estimation of Fault Location on Transmission Lines Using Travelling Waves.[J]. IEEE Transactions on Power Delivery.1994,9(2): 680-689.
[9]邬林勇,何正友,钱清泉.一种提取行波自然频率的单端故障测距方法[J].中国电机工程学报.2008,28(10)：69-75.
[10]邬林勇,何正友,钱清泉.单端行波故障测距的频域方法[J].中国电机工程学报.2008,28(25)：99-104.
[11]李小鹏,何正友,廖凯.基于行波固有频率的串补线路故障测距方法[J].电网技术.2012,36(6)：71-76.
[12]林圣,武骁,何正友,等.基于行波固有频率的电网故障定位方法[J].电网技术.2013,37(1)：270-275.
[13]廖凯,何正友,李小鹏.基于行波固有频率的高压直流输电线路故障定位[J].电力系统自动化.2013,37(3)：104-109.
[14]李小鹏,何正友,夏璐璐.同杆双回输电线路的固有频率测距算法[J].电力系统自动化.2011,35(12)：47-51.
[15]V C. Fundamental Aspects of Fault Location Algorithms Used in Distance Protection[J]. Generation, Transmission and Distribution, IEE Proceedings C.1986,133(6):359-368.
[16]A W. Accurate Fault Impedance Locating Algorithm[J]. [J]. Generation, Transmission and Distribution, IEE Proceedings C.1983,130(6):311-314.
[17]F Z J, S S J, H W Q, et al. Morphological undecimated wavelet decomposition for fault location on power transmission lines[J]. Circuits and Systems I:Regular Papers, IEEE Transactions on.2006,53(6): 1395-1402.
[18]陈平,葛耀中,索南加乐,等.基于故障开断暂态行波信息的输电线路故障测距研究[J].中国电机工程学报.2000,20(8)：56-59,64.
[19]蒋涛,陆于平.不受波速影响的输电线路单端行波故障测距研究[J].电力自动化设备.2004,24(12)：29-32.
[20]张峰,梁军,张利,等.基于三端行波测量数据的输电线路故障测距新方法[J].电力系统自动化.2008,32(8)：69-72.
[21]黄震,江泰廷,张维锡,等.基于双端行波原理的高压架空线-电缆混合线路故障定位方法[J].电力系统自动化.2010,34(14)：88-91.
[22]李泽文,姚建刚,曾祥君,等.基于整个输电网的电压行波故障定位算法[J].电力系统自动化.2008,32(1)：66-69.
[23]Mora-Florez J, Barrera-Nuez V, Carrillo-Caicedo G. Fault Location in Power Distribution Systems Using a Learning Algorithm for Multivariable Data Analysis[J]. Power Delivery, IEEE Transactions on. 2007,22(3):1715-1721.
[24]Reddy M J, Mohanta D K. Adaptive-neuro-fuzzy inference system approach for transmission line fault classification and location incorporating effects of power swings[J]. Generation, Transmission & Distribution, IET.2008,2(2):235-244.
[25]Salat R, Osowski S. Accurate fault location in the power transmission line using support vector machine approach[J]. Power Systems, IEEE Transactions on.2004,19(2):979-986.
[26]Seung-Jae L, Myeon-Song C, Sang-Hee K, et al. An intelligent and efficient fault location and diagnosis scheme for radial distribution systems[J]. Power Delivery, IEEE Transactions on.2004,19(2): 524-532.
[27]Thukaram D, Khincha H P, Vijaynarasimha H P. Artificial neural network and support vector Machine approach for locating faults in radial distribution systems[J], Power Delivery, IEEE Transactions on.2005,20(2):710-721.
[28]康小宁，索南加乐.基于参数识别的单端电气量频域法故障测距原理[J].中国电机工程学报.2005,25(2)：22-27.
[29]康小宁,索南加乐.求解频域参数方程的双端故障测距原理[J].电力系统自动化.2005,29(10)：16-20.
[30]索南加乐,张怿宁,齐军,等.基于参数识别的时域法双端故障测距原理[J].电网技术.2006,30(8)：65-70.
[31]哈恒旭,王婧,谭雨珍,等.基于微分算子逼近的单端故障测距新原理[J].电力系统自动化.2009,33(3)：69-73,78.
[32]de Morais Pereira C E, Jr. Zanetta L C. Fault location in transmission lines using one-terminal postfault voltage data[J]. Power Delivery, IEEE Transactions on.2004,19(2):570-575.
[33]刘千宽,李永斌,黄少锋.基于双端电气量的同杆平行双回线单线故障测距[J].电网技术.2008,32(3)：27-30.
[34]Izykowski J, Molag R, Rosolowski E, et al. Accurate location of faults on power transmission lines with use of two-end unsynchronized measurements[J]. Power Delivery, IEEE Transactions on.2006, 21(2):627-633.
[35]Kawady T, Stenzel J. A practical fault location approach for double circuit transmission lines using single end data[J]. Power Delivery, IEEE Transactions on.2003,18(4):1166-1173.
[36]Liao Y, Elangovan S. Unsynchronised two-terminal transmission-line fault-location without using line parameters[J]. Generation, Transmission and Distribution,IEE Proceedings-.2006,153(6):639-643.
[37]徐鹏,梁远升,王钢.同杆四同线参数自适应双端故障测距频域算法[J].电力系统自动化.2010,34(9)：59-64.
[38]Zhang Q, Zhang Y, Song W, et al. Fault location of two-parallel transmission line for nonearth fault using one-terminal data[J]. Power Delivery, IEEE Transactions on.1999,14(3):863-867.
[39]曾祥君,尹项根,陈浩,等.新型输电线路故障综合定位系统研究[J].电力系统自动化.2000,24(22)：39-44.
[40]曾祥君,尹项根,陈德树,等.基于整个输电网GPS行波故障定位系统的研究[J].电力系统自动化.1999(10)：8-10.
[41]董新洲,葛耀中,徐丙垠,等.新型输电线路故障测距装置的研制[J].电网技术.1998,22(1)：17-21.
[42]黄子俊,陈允平.基于小波变换模极大值的输电线路单端故障定位[J].电力自动化设备.2005,25(2)：10-14.
[43]马丹丹,王晓茹.基于小波模极大值的单端行波故障测距[J].电力系统保护与控制.2009,37(3)：55-59.
[44]张帆.基于单端暂态行波的接地故障测距与保护研究[D].山东大学,2008.
[45]Mallat S, Hwang W L. Singularity detection and processing with wavelets[J]. Information Theory, IEEE Transactions on.1992,38(2):617-643.
[46]陈平,葛耀中,徐丙垠,等.现代行波故障测距原理及其在实测故障分析中的应用-A型原理[J].继电器.2004,32(2)：13-18.
[47]吴大立,尹项根,张哲,等.行波测距硬件系统的研究与设计[J].继电器.2006,34(8)：20-23,44.
[48]董杏丽.基于小波变换的高压电网行波保护原理与技术的研究[D].西安交通大学,2003.
[49]蔡润溟.小电流接地系统单相接地故障选线和测距方法的研究[D].山东大学,2007.
[50]吴军基,吴伊昂,贺济峰,等.数学形态学在行波滤波中的应用[J].继电器.2005,33(17)：21-26.
[51]束洪春,王超,张杰,等.基于形态学的HVDC线路故障识别与定位方法研究[J].电力自动化设备.2007,27(4)：6-9,18.
[52]蔡秀雯,谭伟璞,杨以涵.基于数学形态学的配电网单端行波故障测距[J].现代电力.2006,23(6)：25-29.
[53]林湘宁,刘沛,高艳.基于故障暂态和数学形态学的超高速线路方向保护[J].中国电机工程学报.2005,25(4)：13-18.
[54]束洪春,程春和,赵文渊,等.形态学与HHT检测相结合的行波波头准确标定方法[J].电力自动化设备.2009,29(7)：1-7,37.
[55]Miano G. Transmission Lines and Lumped Circuits[M]. San Diego, USA:Academic Press,2001.
[56]Swift G W. The Spectra of Fault-Induced Transients[J]. Power Apparatus and Systems, IEEE Transactions on.1979, PAS-98(3):940-947.
[57]蔡新雷,宋国兵,高淑萍,等.利用电流固有频率的VSC-HVDC直流输电线路故障定位[J].中国电机工程学报.2011,31(28)：112-119.
[58]夏璐璐,何正友,李小鹏,等.基于行波固有频率和经验模态分解的混合线路故障测距方法[J].电力系统自动化.2010,34(18)：67-73.
[59]林圣,梅俊涛,陈双,等.基于暂态行波时频特征的输电线路故障检测与选相方法[J].电网技术.2012,36(7)：48-53.
[60]S D, Miano G. Transmission lines and lumped circuits[M]. USA:2001:78-84.
[61]邬林勇.利用故障行波固有频率的单端行波故障测距法[D].西南交通大学,2009.
[62]Rangarao K V, Venkatanarasimhan S. gold-MUSIC:A Variation on MUSIC to Accurately Determine Peaks of the Spectrum[J]. Antennas and Propagation, IEEE Transactions on.2013,61(4): 2263-2268.
[63]刘万超,李玮,孙佳佳,等.基于多分辨形态梯度-相关函数综合测距算法的单端行波故障测距[J].电网技术.2011,35(10)：225-229.
[64]覃剑,葛维春,邱金辉,等.影响输电线路行波故障测距精度的主要因素分析[J].电网技术.2007,31(2)：28-35.
[65]Hart P M. An experimental study of short-circuit currents on a low-voltage system[J]. Industry Applications, IEEE Transactions on.1988,24(5):940-946.
[66]索南加乐,张健康,刘辉,等.故障分量提取及故障选相的新方法[J].电力系统自动化.2003,27(16)：58-61,66.
[67]Due-Son P, Zoubir A M. Analysis of Multicomponent Polynomial Phase Signals[J]. Signal Processing, IEEE Transactions on.2007,55(1):56-65.
[68]索南加乐,刘凯,粟小华,等.基于故障分量综合阻抗的输电线路纵联保护[J].中国电机工程学报.2008,28(31)：54-61.
[69]Izykowski J, Molag R, Rosolowski E, et al. Fault location in three-terminal line with use of limited measurements[C].2005.
[70]Khodadadi M, Shahrtash S M. A New Noncommunication-Based Protection Scheme for Three-Terminal Transmission Lines Employing Mathematical Morphology-Based Filters[J]. Power Delivery, IEEE Transactions on.2013,28(1):347-356.
[71]高厚磊,安艳秋,江世芳.超高压T接线路高精度故障测距算法研究[J].电力系统自动化.2001,25(20)：41-44.
[72]束洪春,司大军,葛耀中,等.T型输电线路电弧故障测距时域方法研究[J].电工技术学报.2002,17(4)：99-103,57.
[73]韦钢,唐斌,肖鸿杰.输电线路不对称故障点定位的新方法[J].电力系统自动化.2001,25(17)：29-38.
[74]Girgis A A, Hart D G, Peterson W L. A new fault location technique for two- and three-terminal lines[J]. Power Delivery, IEEE Transactions on.1992,7(1):98-107.
[75]林圣.基于暂态量的高压输电线路故障分类与定位方法研究[D].西南交通大学,2011.
[76]索南加乐,刘凯,粟小华,等.基于故障分量综合阻抗的输电线路纵联保护[J].中国电机工程学报.2008,28(31)：54-61.
[77]王钢,李海锋,赵建仓,等.基于小波多尺度分析的输电线路直击雷暂态识别[J].中国电机工程学报.2004,24(4)：139-144.