弓网电弧电磁干扰传播的若干理论研究
|
摘要
实验室测试结果显示离线引起接触网—受电弓之间的电弧(弓网电弧)是一个频谱很宽的电磁干扰发射源。一方面铁路地面架设的供电导体：接触网、负馈线和钢轨等供电导体构成的多导体传输线(Multiconductor Transmission Line MTL)为弓网电弧电磁干扰的传播提供了回路,另一方面沿着地面架空MTL传播的弓网电弧电磁干扰也向外辐射电磁波,影响铁路沿线电子敏感设备的正常工作。这些为电磁干扰提供传播路径的MTL都架设的大地之上,大地是一个由固体颗粒、水和空气构成的复杂不均匀混合体,由于长期的沉积作用,明显表现出水平分层特性。由于在分层结构表面吸附表面波(trapped surface wave)的存在,弓网电弧电磁干扰沿分层土壤表面的电磁辐射也发生明显变化,同时也影响了电磁干扰沿架空MTL的传播特性。为了简化分析本文把土壤看成是二层结构,其中下层土壤厚度为无穷大,分别研究了AT变压器、轨道电路和二层土壤对电气化铁路弓网电弧电磁干扰传导和辐射传播的影响。
本文基于多导体传输线理论的时域有限差分法(Finite-Difference Time-Domain FDTD)研究了弓网电弧电磁干扰沿架空多导体的传导干扰传播特性,首先根据研究对象不同分别把架空多导体等值合并为三导体和四导体传输线,计算了多导体的二层土壤自阻抗和互阻抗矩阵,并用矢量匹配法得到了该阻抗值的近似结果。考虑到AT变压器和轨道电路设备对电弧电磁干扰的传导影响较大,介绍了基于试验和矢量匹配法得到等效电路的步骤,并根据它们等效电路的状态变量方程和输出方程,推出了集总元件(AT变压器和轨道电路设备)连接在多导体终端和中间时的FDTD迭代公式。从推出的结果可以看出由于AT变压器和轨道电路设备不是连接在主动线(Active Line)和参考线之间而是连接在主动线和主动线之间,使得FDTD迭代公式中的矩阵不再是对角线矩阵,增加了求解时间。
弓网电弧电磁干扰没有成熟的数学模型,而梯形电压波可以很方便地调节参数模拟不同带宽的干扰源,所以本文基于以上推导的迭代公式以梯形电压波作为弓网电弧电磁干扰源研究了不同带宽电磁干扰源的传播特性；二层土壤通过影响电报方程中的地阻抗而影响电弧电磁干扰的传导,通过改变上层土壤的厚度研究了不同土壤结构对电磁干扰传播的影响；由于弓网电弧的发生位置是随机的,且同时也可能连续发生多个干扰源,本文研究了弓网电弧距AT变压器不同距离和单个、双个电磁干扰源的传播特性。
最后论文研究了二层土壤结构对弓网电弧电磁干扰辐射传播的影响,基于频域麦克斯韦方程推导了架设在二层土壤上无限长导体的场分量积分表达式,根据围道积分理论得出在土壤表面的场,包括直射波、反射波、侧面波和吸附表面波,分析得出该吸附表面波由被积函数的极点留数决定,与上层土壤厚度有很大关系(在一定厚度下吸附表面波占主要成分),且离开地面以后迅速衰减的结论。并指出了电气化铁路电磁干扰测试中由于天线距离地面1—3米,此时吸附表面波几乎已经衰减完,不能反映出地面吸附表面波的情况。分析结果显示,地面电子敏感设备建设仅依据测试结果是不行的,还要参考施工地点大地的电磁特性,最好能测试出贴近地面的电磁干扰值作为一项重要的附加参考指标。
Laboratory test results show that Electro-Magnetic interference of pantograph-catenary arcing, which has a wide frequency specturm, is a powerful interference source. On the one hand, the conductors of traction power:catenary, feeder, rails and so on, constitute the multi-conductor transmission line (MTL). Therefore, the EMI of pantograph-catenary arcing can propagate along the MTL. On the other hand, the electromagnetic wave radiated by the EMI signals through the MTL can affect the normal operation of sensitive electronic equipments along the railway line. All the MTLs are set up above the lossy earth. Due to the long-term deposition, the lossy earth, which composed of a solid particles, water and air, shows obviously characteristics of multi-layer. Because of the trapped surface wave existed in the surface of hierachy, the propagation of EMI signals along the MTLs has undergone a significant change. In order to simplify the analysis, the earth is modelled as two-layer structure, and the lower layer is infinite. This thesis gives an investigation of the influence of auto-transformer, track circuit. Also analysis the propagation characteristic of EMI signals in the two-layer earth structure, which produced by pantograph-catenary arcing.
This thesis presents the propagation characteristic of pantograph-catenary arcing EMI, based on Finite-Difference Time-Domain (FDTD) method of MTL. Firstly, the overhead MTL are equivalent to three or four conductors according to the different research objects. The self and mutual impedance matrix of two-layer soil are calculated, which is approximated by vector matching. Secondly, considering the influence to the electromagnetic wave propagation of EMI signals by the AT transformer and track circuit equipment, the steps to obtain the equivalent circuit is presented. Moreover, according to the state equation and output equation of the equivalent circuits, the FDTD iterative equation of the lumped element connected the MTL terminal and intermediate is deduced. From the results, we can see that the iterative formula is no longer a diagonal matrix, because the auto-transformer and the track circuit equipment is not connected between the the active line and the reference line.
Based on the FDTD iterative formula, the trapezoidal voltage wave as the mathematical model of the pantograph-catenary arc electromagnetic interference sources is adopted. By adjusting the rise and fall times of the trapezoidal, the bandwith of EMI can be tuned. Therefore, the propagation characteristic of EMI with different bandwidth of soure can be analysised. The ground impedance of two-layer earth can affect the propagation characteristic of EMI, and thus, this thesis also disscuss the influence of different depth of two-layered earth on the propagation characteristic. Meanwhile, the propagation characteristic v.s. the distance between the arcing point and the auto-transformer and the number of AT are also analysised.
Finally, the thesis studies the influence of the two-layer earth structure on the propagation charecteristic of EMI. Based on the frequency-domain Maxwell equation, the integral formula of infinitely long wire above the two-layer earth is derived. According to the contour integral theory, the total field in the surface of earth consists of direct wave, reflected wave, lateral wave and trapped surface wave. It is noted that the trapped surface wave is determined by the pole residue of the integrand. Meanwhile, it is demonstrated that the amplitude of trapped surface wave decay rapidly when leaving the ground. Based on the analysis of this thesis, it concluded that when the antenna above the earth1-3meters, the trapped surface wave can be neglected. Therefore, the testing standard of Railway applications-EMC could not show propagation charactersitc of the trapped surface wave. Meanwhile, the analysis results show the test results are not enough when the sensitive electronic equipment is close to the earth. An importamt additional test of electromagnetic interference close to the earth is essential.
本文基于多导体传输线理论的时域有限差分法(Finite-Difference Time-Domain FDTD)研究了弓网电弧电磁干扰沿架空多导体的传导干扰传播特性,首先根据研究对象不同分别把架空多导体等值合并为三导体和四导体传输线,计算了多导体的二层土壤自阻抗和互阻抗矩阵,并用矢量匹配法得到了该阻抗值的近似结果。考虑到AT变压器和轨道电路设备对电弧电磁干扰的传导影响较大,介绍了基于试验和矢量匹配法得到等效电路的步骤,并根据它们等效电路的状态变量方程和输出方程,推出了集总元件(AT变压器和轨道电路设备)连接在多导体终端和中间时的FDTD迭代公式。从推出的结果可以看出由于AT变压器和轨道电路设备不是连接在主动线(Active Line)和参考线之间而是连接在主动线和主动线之间,使得FDTD迭代公式中的矩阵不再是对角线矩阵,增加了求解时间。
弓网电弧电磁干扰没有成熟的数学模型,而梯形电压波可以很方便地调节参数模拟不同带宽的干扰源,所以本文基于以上推导的迭代公式以梯形电压波作为弓网电弧电磁干扰源研究了不同带宽电磁干扰源的传播特性；二层土壤通过影响电报方程中的地阻抗而影响电弧电磁干扰的传导,通过改变上层土壤的厚度研究了不同土壤结构对电磁干扰传播的影响；由于弓网电弧的发生位置是随机的,且同时也可能连续发生多个干扰源,本文研究了弓网电弧距AT变压器不同距离和单个、双个电磁干扰源的传播特性。
最后论文研究了二层土壤结构对弓网电弧电磁干扰辐射传播的影响,基于频域麦克斯韦方程推导了架设在二层土壤上无限长导体的场分量积分表达式,根据围道积分理论得出在土壤表面的场,包括直射波、反射波、侧面波和吸附表面波,分析得出该吸附表面波由被积函数的极点留数决定,与上层土壤厚度有很大关系(在一定厚度下吸附表面波占主要成分),且离开地面以后迅速衰减的结论。并指出了电气化铁路电磁干扰测试中由于天线距离地面1—3米,此时吸附表面波几乎已经衰减完,不能反映出地面吸附表面波的情况。分析结果显示,地面电子敏感设备建设仅依据测试结果是不行的,还要参考施工地点大地的电磁特性,最好能测试出贴近地面的电磁干扰值作为一项重要的附加参考指标。
Laboratory test results show that Electro-Magnetic interference of pantograph-catenary arcing, which has a wide frequency specturm, is a powerful interference source. On the one hand, the conductors of traction power:catenary, feeder, rails and so on, constitute the multi-conductor transmission line (MTL). Therefore, the EMI of pantograph-catenary arcing can propagate along the MTL. On the other hand, the electromagnetic wave radiated by the EMI signals through the MTL can affect the normal operation of sensitive electronic equipments along the railway line. All the MTLs are set up above the lossy earth. Due to the long-term deposition, the lossy earth, which composed of a solid particles, water and air, shows obviously characteristics of multi-layer. Because of the trapped surface wave existed in the surface of hierachy, the propagation of EMI signals along the MTLs has undergone a significant change. In order to simplify the analysis, the earth is modelled as two-layer structure, and the lower layer is infinite. This thesis gives an investigation of the influence of auto-transformer, track circuit. Also analysis the propagation characteristic of EMI signals in the two-layer earth structure, which produced by pantograph-catenary arcing.
This thesis presents the propagation characteristic of pantograph-catenary arcing EMI, based on Finite-Difference Time-Domain (FDTD) method of MTL. Firstly, the overhead MTL are equivalent to three or four conductors according to the different research objects. The self and mutual impedance matrix of two-layer soil are calculated, which is approximated by vector matching. Secondly, considering the influence to the electromagnetic wave propagation of EMI signals by the AT transformer and track circuit equipment, the steps to obtain the equivalent circuit is presented. Moreover, according to the state equation and output equation of the equivalent circuits, the FDTD iterative equation of the lumped element connected the MTL terminal and intermediate is deduced. From the results, we can see that the iterative formula is no longer a diagonal matrix, because the auto-transformer and the track circuit equipment is not connected between the the active line and the reference line.
Based on the FDTD iterative formula, the trapezoidal voltage wave as the mathematical model of the pantograph-catenary arc electromagnetic interference sources is adopted. By adjusting the rise and fall times of the trapezoidal, the bandwith of EMI can be tuned. Therefore, the propagation characteristic of EMI with different bandwidth of soure can be analysised. The ground impedance of two-layer earth can affect the propagation characteristic of EMI, and thus, this thesis also disscuss the influence of different depth of two-layered earth on the propagation characteristic. Meanwhile, the propagation characteristic v.s. the distance between the arcing point and the auto-transformer and the number of AT are also analysised.
Finally, the thesis studies the influence of the two-layer earth structure on the propagation charecteristic of EMI. Based on the frequency-domain Maxwell equation, the integral formula of infinitely long wire above the two-layer earth is derived. According to the contour integral theory, the total field in the surface of earth consists of direct wave, reflected wave, lateral wave and trapped surface wave. It is noted that the trapped surface wave is determined by the pole residue of the integrand. Meanwhile, it is demonstrated that the amplitude of trapped surface wave decay rapidly when leaving the ground. Based on the analysis of this thesis, it concluded that when the antenna above the earth1-3meters, the trapped surface wave can be neglected. Therefore, the testing standard of Railway applications-EMC could not show propagation charactersitc of the trapped surface wave. Meanwhile, the analysis results show the test results are not enough when the sensitive electronic equipment is close to the earth. An importamt additional test of electromagnetic interference close to the earth is essential.
引文
[1]吴积钦,“弓网系统电弧的成因与影响”,中国铁道学会2010年高速铁路接触网系统新技术研讨会,2010,104-108
[2]吴积钦,“弓网系统电弧的产生及其影响”,电气化铁路,2008,第2期：27-29
[3]杨世武,“铁路信号电磁兼容技术”,北京,中国铁道出版社,2010
[4]张林昌,“电化铁道无线电干扰的研究及其进展”,中国电机工程学会城市供电专业委员会城网通讯干扰学术会议,成都,1986
[5]王其平,“电器电弧理论”,北京,机械工业出版社,1989
[6]“电气化铁路的电磁兼容”,http://wenku.baidu.com/view/bdf942e5524de518964b7d2f.html
[7]高宗宝,吴广宁,吕玮,何常红,周利军,“高速电气化铁路中的弓网电弧现象研究综述”,高电压电器,2009,45(3)：104-108
[8]陈立,吴广宁,高国强,朱军,王波,“高速铁路弓网电接触研究综述”,机车电传动,2011年9月,第5期：6-10
[9]李文豪,罗健,张倩,陈维荣,“高速铁路受电弓与接触网关系评价综述”,电气化铁道,2009第4期：40-44
[10]西南交通大学报告,“受电弓与接触网系统.ppt”,http://wenku.baidu.com/view/47b09flfa76e58fafab0034c.html:65
[11]Surajit Midya, "Conducted and Radiated Electromagnetic Interference in Modern Electrified Railways with Emphasis on Pantograph Arcing", Stockholm, Royal Institute of Technology,2009
[12]“国务院公布温州高铁事故原因”,http://money.163.com/11/1228/18/7MCP7DTG00253B0H.html
[13]Bernardo Tellini, Massimo Macucci, Romano Giannetti, Gabriele A. Antonacci, "Conducted and Radiated Interference Measurements in the Line-Pantograph systems", IEEE Transctions on Instrumentation and Measurement, vol.50, No.6, Dec.2001, pp.1661-1664
[14]Surajit Midya, Dierk Bormann, Anders Larsson, Thorsten Schiitte, Rajeev Thottappillil, "Understanding Pantograph Arcing in Electrified Railways-Influence of Various Parameters", IEEE International Symposium on Electromagnetic Compatibility, Aug.2008, pp.18-22
[15]Surajit Midya, Dierk Bormann, Thorsten Schutte, Rajeev Thottappillil, "Pantograph Arcing in Electrified Railways—Mechanismand Influence of Various Parameters—Part Ⅱ:With AC Traction Power Supply", IEEE Transction on Power Delivery, vol.24, no.4 Oct,2009, pp.1940-1950
[16]Surajit Midya, Dierk Bormann, Thorsten Schutte, Rajeev Thottappillil, "Pantograph Arcing in Electrified Railways—Mechanismand Influence of Various Parameters—Part Ⅰ:With DC Traction Power Supply", IEEE Transction on Power Delivery, vol.24, no.4 Oct.2009, pp.1931-1939
[17]闫站伟,“浅析接触线拉弧原因及其预防措施”,郑铁科技通讯,2007第1期,25-27
[18]王万岗,吴广宁,高国强,王波,崔易,刘东来,“高速铁路弓网电弧试验系统”,铁道学报,2012年4月,(34)4：22-27
[19]张博,“弓网离线电弧电磁干扰的机理分析及测试系统界面实现研究”,成都,西南交通大学,2011
[20]雷栋,吴广宁,王万岗,张雪原,何常红,“高速铁路弓网电弧模拟装置的研制”,机车电传动,2009年5月,第3期：42-45
[21]何常红,“弓网电弧模拟系统的研制和试验研究”,成都,西南交通大学,2009
[22]王万岗,吴广宁,赵云云,高国强,王波,“弓网电弧电气特性试验研究”,低压电器,2012第6期：5-11
[23]雷栋,吴广宁,张雪原,王万岗,何常红,“高速铁路弓网电弧抑制方法研究”电气化铁路,2008第5期：1-4
[24]杨志鹏,李华伟,孙忠国,李国国,“基于弓网电弧模拟试验装置的电弧参数测量及分析”,北京交通大学学报,2012年4月,(36)2：111-115
[25]杨志鹏,李华伟,孙忠国,李国国,“基于弓网电弧模拟试验装置的电弧研究”,电气化铁道,2012年第一期：28-31
[26]杨志鹏,“弓网电弧研究及其检测”,北京,北京交通大学,2011
[27]CISPR Publication 16—1-1993, "Specification for radio disturbance and immunity measuring apparatus and methods Part 1. Radio disturbance and immunity measuring apparatus", IEC,1993
[28]国家技术监督局,GB/T15708—-1995,“交流电气化铁道电力机车运行产生的无线电辐射干扰的测量方法”,1995
[29]国家技术监督局,GB/T15709—-1995,“交流电气化铁道接触网无线电辐射干扰测量方法”,1995
[30]A. Jr Banos, "Dipole radiation in the presence of a conducting half-space", Oxford, Pergamon Press,1966
[31]中国国家标准管理委员会,GB/T24338—-2009,“轨道交通电磁兼容”,2009
[32]Taketoshi Nakai, Zenichiro Kawasaki, "On Impulsive Noise from Shinkansen", IEEE Transction on Electromagnetic Compatibility, Vol.EMC-25, No.4,1983, pp.396-404
[33]Nakai, Taketoshi,"Measurement and Analysis of Impulsive Noise from Bullet Trains", IEEE Transction on Electromagnetic Compatibility, Vol.EMC-28, No.4,1986, pp.193-203
[34]沈致君,“弓网离线电弧电磁干扰问题的研究”,北京,北京交通大学,2011,36-38
[35]沙斐,张林昌,“电磁干扰的统计参量APD和NAD的特性及其测量”,北方交通大学学报,1983年11月,第2期：11-27
[36]张林昌,徐坤生,蒋忠涌,“电气化铁道干扰源的特性及测量”,北方交通大学学报,1980年第2期：13-29
[37]周克生,张林昌,“高速电气化铁道无线电噪声预测”,铁道学报,1999年4月,(21)2：54-57
[38]闻映红,“无线电骚扰的统计参量测量法-幅度概率分布(APD)”,测试与测量,2006第1期
[39]陈嵩,“幅度概率分布(APD)统计参量测量方法的研究与APD测量系统的研制”,北京,北京交通大学,2008
[40]http://www.kth. se/en/ees/omskolan/organisation/avdelningar/etk/research/topics/emc/2.18951/emc-of-rail ways-pantograph-arcing-1.47295
[41]张溢强,“电气化铁路无线电干扰传播特性仿真及研究”,北京,北京交通大学,2005
[42]张林昌,蒋守守,“用正弦信号源研究电气化铁道无线电干扰的横向波传播特性”,北方交通大学学报,1993,(17)4：351-355
[43]黄朝晖,张林昌,“电气化铁道无线电干扰横向距离特性的理论分析”,铁道学报-S2,1989,1-9
[44]Stefan Niska, "Measurement and Analysis of Electromagnetic Interferences in the Swedish Railway Systems", Lulea, Lulea University,2008
f45]周克生,张林昌,"The Conversion Factors for Radio Interference from Eletrified Railway Measured with Different Detectors", Proceeding of 12th Symposium and Exhibition on EMC, Wroclaw,1994
[46]Andrea Cozza, "Railway EMC:Assessment of infrastructure Impact", Turin, Politecnico di Torino,2005
[47]http://www.transport-research.info/web/projects/project_details.cfm?ID=37707
[48]I. S. Grashteyn, I. M. Ryzhik, "Table of integrals, series and products", Salt Lake City, Academic Press, 1980
[49]R. Giannetti, M. Macucci, B. Tellini, "EMI Measuements in line-pantograph Contact Discontinutity in Railway Transportation Syatems",11th IMEKO TC-4 Symp.,2001, Libon, pp.25-27
[50]Surajit Midya, Rajeev Thottappillil, "An overview of electromagnetic compatibility challenges in European Rail Traffic Management System", Transportation Research Part C 16,2008, pp.515-534
[51]Anping Dong, Guangning Wu, Guoqiang Gao, Lijun Zhou,Wangang Wang,Bo Wang, Yi Cui, Yang Mingming, "Simulation system of pantograph arcing" 1st International Conference on Electric Power Equipment - Switching Technology, Xi'an,2011, pp.637-641
[52]E.J. Bartlett, M. Vaughan, P.J. Moore,"Investigation into electromagnetic emissions from power system arcs", International Conference and Exhibition on Electromagnetic Compatibility,1999, EMC York 99 pp.47-52
[53]Dierk Bormann, Surajit Midya, Rajeev Thottappillil, "DC components in Pantograph Arcing: Mechanisms and Influence of Various Parameters", International Zurich Symposium on Electromagnetic Compatibility,2007, pp.369-372
[54]Demetrios Klapas, Reuben Hackam, F. A. Benson, "Electric Arc Power Collection High-Speed Trains", Proceedings of the IEEE, Vol.64, No.12,1976, pp.1699-1716
[55]Nelson Theethayi, Rajeev Thottappillil,Yaqing Liu, Raul Montano, "Important parameters that influence crosstalk in multiconductor transmission lines", Electric Power Systems Research, Vol.77, No.8,2007, pp. 896-909
[56]Academic Research Projects, "Theoretical Analysis and Experimental Assessment of the Electromagnetic Emissions of Railway Infrastructure and Rolling Stock" http://docenti.etec.polimi.it/ind31/emcgroup/research_projects.html
[57]金学松,温泽峰,张卫华等,“世界铁路发展状况及其关键力学问题”,第十三届全国结构工程学术会议论文集,2004：96-100
[58]杨飞,“无线电骚扰的幅度概率分布统计模型及其对数字通信系统干扰的算法研究”,北京,北京交通大学,2010
[59]R.J. Hill, "Electric Railway traction Part 6 Electromagnetic Compatibility-disturbance sources and equipment susceptibility", Power Engineering Journal, Tutorial,1997, pp.31-39
[60]R.J. Hill, "Electric Railway traction Part 7 Electromagnetic Interference in traction systems", Power Engineering Journal, Tutorial,1997, pp.259-266
[61]R.J. Hill, D.C. Carpenter, "Modelling of Nolinear Rail Impedance in AC Traction Power Systems", IEEE Transaction on Power Delivery, Vol.6, No.4,1991, pp.1755-1761
[62]D.C. Carpenter, R.J. Hill, "Railroad Track Elctrical Impedance and Adjacent Track Crosstalk Modeling Using the Finite-Element Method of Electromagnetic Systems Analysis", IEEE Transaction on Vehicular Technology, Vol.42 No.4,1993, pp.555-562
[63]R.J. Hill, D.C. Carpenter, "Rail Track Distributed Transmission Line Impedance and Admittance: Theoretical Modeling and Experimental Results", IEEE Transaction on Vehicular Technology, Vol.42 No.2, 1993, pp.225-241
[64]J.R. Carson, "Wave Propagation in overhead wires with a ground return", Bell System Technical Journal, Vol.5,1926, pp.539-554
[65]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, "On the influence of conductor heights and lossy ground in multi-conductor transmission lines for lightning interaction studies in railway overhead traction systems", Electric Power Systems Research, Vol.65, No.1,2004, pp.186-193
[66]J.R. Wait, "Theory of Wave Propagation along a Thin Wire Parallel to an Interface", Radio Science, Vol.7, No.6,1972, pp.675-679
[67]Edward F. Kuester, David C. Chang, Robert G Oslen, "Modal theory of long horizontal wire structures above the earth,1, Excitation", Radio Science, Vol.13, No.4,1978, pp.605-613
[68]Robert G. Oslen, Edward F. Kuester, David C. Chang, "Modal theory of long horizontal wire structures above the earth,2, Properties of discrete modes", Radio Science, Vol.13, No.4,1978, pp.615-623
[69]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil, "A Method for Interfacing Lumped-Circuit Models and Transmission-Line System Models With Application to Railways", IEEE Transction on Electromagnetic Compatibility, Vol.51, No.3,2009, pp.833-841
[70]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil "Indirect Lighting-Inducted Voltages Along a Railway Catenary-Track Multiconductor-Line System With Lumped Components", IEEE Transction on Electromagnetic Compatibility, Vol.53, No.2,2011, pp.537-539
[71]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil, "Modeling Indirect Lighting Strikes for Railway System With Lumped Components and Nolinear Effects ", IEEE Transetion on Electromagnetic Compatibility, Vol.53, No.1,2011, pp.249-252
[72]A. Ametani, "Stratified Earth Effects on Wave Propagation Frequency-Dependent Parameters",IEEE Transction on Power Apparatus and Systems, Vol.PAS-93, No.5,1974, pp.1233-1239
[73]高攸纲,“感性耦合与阻性耦合”,北京,人民邮电版社,1979
[74]Peter Marcus Buff Ⅲ, "Characterization of Propagation on Wires over Lossy Earth", North Carolina, North Carolina State University,2006
[75]Nelson Theethayi, "Electromagnetic Interference in Distributed Outdoor Electrical Systems, with an Emphasis on Lightning Interaction with Electrified Railway Network", Uppsala, Uppsala University,2005
[76]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, Michael Zitnik, Vernon Cooray, Victor Scuka, "A theoretical study on the consequence of a direct lightning strike to electrified railway system in Sweden", Electric Power Systems Research, Vol.74, No.2,2005, pp.267-280
[77]Yaqing Liu, Nelson Theethayi, Rajeev Thottappillil, Raul M. Gonzalez, Michael Zitnik, "An improved model for soil ionization around grounding system and its application to stratified soil", Electric Power Systems Research, Vol.60, No.2-4,2004, pp.203-209
[78]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, "Crosstalk in Multiconductor Transmission Line in the Presence of Finitely Conducting Ground", IEEE International Symposium on Electromagnetic Compatibility,Vol.2,2003, pp.1003-1006
[79]C.R. Paul, "Analysis of Multiconductor Transmission Lines, Second Edition", Wiley-Interscience A John Wiley & Sons, INC., Publication, IEEE Press,2008
[80]Erling D. Sunde, "Earth Conduction Effects in Transmission Systems", D. VAN Nostrand Company, Inc., Toronto/New York/London,1968
[81]E. F. Vance, "Coupling to Cable Shields", A Wiley-Interscience Publication John Wiley & Sons, New York/London/Sydney/Toronto,1978
[82]吕英华,王旭莹译,“EMC分析方法与计算模型”,北京,北京邮电大学出版社,2009
[83]Robert G. Olsen, Jeffrey L. Young, David C. Chang, "Electromagnetic Wave Propagation on a Thin Wire Above Earth", IEEE Transction on Antennas and Propagation, Vol.48, No.9,2000, pp.1413-1419
[84]Magnus Akke, Thomas Biro, "Measurements of the Frequency-Dependent Impedance of a Thin Wire With Ground Return", IEEE Transction on Power Delivery, Vol.20, No.2,2005, pp.1748-1752
[85]A.L. Timotin, "Longitudinal transient parameters of a unifilar line with ground return", Science Technical-Electrotechn., Vol.12,No.4,1967, pp.523-535
[86]D.Orzan, "Time domain low frequency approximation for the off-diagonal terms of the ground impedance matrix", IEEE Transactions on Electromagnetic Compatibility, Vol.39, No.1,1997, pp.64
[87]R. Araneo, S. Celozzi, "Direct time domain analysis of transmission lines above a lossy ground",IEE Proceedings on Science and Measurement Technology, Vol.148, No.2,2001, pp.73-79
[88]F. Rachidi, S.L. Loyka, C.A. Nucci, M. Ianoz, "A new expression for ground transient resistance matrix elements of multiconductor overhead transmission lines", Electric Power Systems Research, Vol.65, No.l, 2003, pp.41-46
[89]A.Semlyen, "Ground Return Parameters of Transmission Lines an Asymptotic Analysis for very High frequencies", IEEE Transactions on Power Apparatus and Systems, Vol.100, No.3,1981, pp.1031-1038.
[90]B.Gustavsen, A.Semlyen, "Rational approximation of frequency domain responses by vector fitting", IEEE Transactions on Power Delivery, Vol.14, No.3,1999, pp.1052-1061.
[91]Lei Liu, Xiang Cui, Lei Qi, "Simulation of Electromagnetic Transients of the Bus Bar in Substation by the Time-Domain Finite-Element Method", IEEE Transactions on Electromagnetic Compatibility, Vol.51, No.4,2009, pp.1017-1025
[92]Tiebing Lu, Lei Qi, Xiang Cui, "Effect of multilayer soil on the switching transient in substations", IEEE Transactions On Magnetics, Vol.42, No.4,2006, pp.843-846
[93]Tiebing Lu,Xiang Cui,Haoliu Yin,Lin Li,"Time-domain analysis of transient electromagnetic field generated by aerial busbars above lossy soil", IEEE Transactions On Magnetics, Vol.38, No.2,2002, pp.773-776
[94]Tiebing Lu, Xiang Cui, Lin Li, "Transient analysis of aerial multi-conductor transmission lines with branch", IEEE Transactions On Magnetics, Vol.37, No.5,2001, pp.3298-3302
[95]齐磊,卢铁兵,张重远,崔翔,“考虑多次土壤时架空线的瞬态分析”,中国电机工程学报,2003年5月,(23)5：66-69
[96]M. Nakagama, K. Iwamoto, "Earth-return impedance for thr multi-layer case", IEEE Transction on Power Apparatus and Systems, Vol. PAS-95, No.2,1976, pp.671-676
[97]李凯,“分层介质中的电磁场和电磁波”,杭州,浙江大学出版社,2010
[98]J.R. Wait, "Electromagnetic Waves in Stratified Media", Oxford/London/New York/Paris, Pergamon Press,1962
[99]Weng Cho Chew, "Waves and Fields in Inhomogeneous Media", New York, Van Nostrand Reinhold, 1990
[100]R.W.P. King, M. Owens,T.T. Wu, "Lateral Electromagnetic Waves, Theory and Application to Communications, Geophysical Exploration, and Remote Sensing", Springer-Verlag,1992
[101]R.M. Sorbello,R.W.P. King,K.M. Lee,L.C.Shen,T.T. Wu, "The horizontal-wire antenna over a dissipative half-space:Generalized Formula and Measurements", IEEE Transaction on Antennas and Propagation, Vol.25, No.6,1977, pp.850-854
[102]D.C. Chang,R.G. Oslen, "Excitation of an infinite Antenna above a Dissipative Earth",Radio Science, Vol.10, No.8-9,1975, pp.823-831
[103]Antonio Orlandi, C.R. Paul, "FDTD Analysis of Lossy, Multiconductor Transmission Lines Terminated in Arbitrary Loads",IEEE Transactions on Electromagnetic Compatibility, Vol.38, No.3,1996, pp.388-399
[104]J. Zenneck, "Propagation of plane eletromagnetic waves along a plane conducting surface and its bearing on the theory of transmission in wireless telegraphy", Ann. Phys.,Vol.23,1907, pp.846-866
[105]R.W.P. King, S.S. Sandier, "The eletromagnetic field of a vertical electric dipole in the presence of a three-layered region", Radio Science, Vol.29, No.1,1994, pp.97-113
[106]J.R. Wait, Comment on "The electromagnetic field of a vertical electric dipole in the presence of a three-layered region" by Ronold W. P. King and Sheldon S. Sandler, Radio Science, Vol.33, No.2,1998, pp.251-253
[107]R.E. Collin, "Some observations about the near zone eletric field of a hertzian dipole above a lossy earth", IEEE Transaction onAntennas and Propagation, Vol.52, No.11,2004, pp.3133-3137
[108]R.E. Collin, "Hertzian dipole radiation over a lossy earth or sea:some early and late 20th century controversies", IEEE Magazine on Antennas and Propagation, Vol.46, No.2,2004, pp.64-79
[109]杨儒贵,“高等电磁理论”,北京,高等教育出版社,2008
[110]梁昆淼,刘法,缪国庆,“数学物理方法”,北京,高等教育出版社,2006
[111]吴命利,“电气化铁道牵引网的统一链式电路模型”,中国电机工程学报,2010年10月,(30)28：52-58
[112]孙铭甫译,“轨道电路的分析与综合”,北京,中国铁道出版社,1981
[113]"Colorado Soil Survey Program" http://www.co.nrcs.usda.gov/technical/soil/soil-surveys/soil-survey-program.html
[114]Frank Olyslager, Daniel De Zutter, "High-frequency transmission line models for a thin wire above a conducting ground", IEEE Transction on Electromagnetic Compatibility, Vol.37, No.2,1995, pp.234-240
[115]B.Gustavsen, "Improving the pole Relocating Properties of Vector Fitting", IEEE Transactions on Power Delivery, Vol.21, No.3,2006, pp.1587-1592
[116]中铁电气化局集团有限公司译,“电气化铁道接触网”,北京,中国电力出版社,2004
[2]吴积钦,“弓网系统电弧的产生及其影响”,电气化铁路,2008,第2期：27-29
[3]杨世武,“铁路信号电磁兼容技术”,北京,中国铁道出版社,2010
[4]张林昌,“电化铁道无线电干扰的研究及其进展”,中国电机工程学会城市供电专业委员会城网通讯干扰学术会议,成都,1986
[5]王其平,“电器电弧理论”,北京,机械工业出版社,1989
[6]“电气化铁路的电磁兼容”,http://wenku.baidu.com/view/bdf942e5524de518964b7d2f.html
[7]高宗宝,吴广宁,吕玮,何常红,周利军,“高速电气化铁路中的弓网电弧现象研究综述”,高电压电器,2009,45(3)：104-108
[8]陈立,吴广宁,高国强,朱军,王波,“高速铁路弓网电接触研究综述”,机车电传动,2011年9月,第5期：6-10
[9]李文豪,罗健,张倩,陈维荣,“高速铁路受电弓与接触网关系评价综述”,电气化铁道,2009第4期：40-44
[10]西南交通大学报告,“受电弓与接触网系统.ppt”,http://wenku.baidu.com/view/47b09flfa76e58fafab0034c.html:65
[11]Surajit Midya, "Conducted and Radiated Electromagnetic Interference in Modern Electrified Railways with Emphasis on Pantograph Arcing", Stockholm, Royal Institute of Technology,2009
[12]“国务院公布温州高铁事故原因”,http://money.163.com/11/1228/18/7MCP7DTG00253B0H.html
[13]Bernardo Tellini, Massimo Macucci, Romano Giannetti, Gabriele A. Antonacci, "Conducted and Radiated Interference Measurements in the Line-Pantograph systems", IEEE Transctions on Instrumentation and Measurement, vol.50, No.6, Dec.2001, pp.1661-1664
[14]Surajit Midya, Dierk Bormann, Anders Larsson, Thorsten Schiitte, Rajeev Thottappillil, "Understanding Pantograph Arcing in Electrified Railways-Influence of Various Parameters", IEEE International Symposium on Electromagnetic Compatibility, Aug.2008, pp.18-22
[15]Surajit Midya, Dierk Bormann, Thorsten Schutte, Rajeev Thottappillil, "Pantograph Arcing in Electrified Railways—Mechanismand Influence of Various Parameters—Part Ⅱ:With AC Traction Power Supply", IEEE Transction on Power Delivery, vol.24, no.4 Oct,2009, pp.1940-1950
[16]Surajit Midya, Dierk Bormann, Thorsten Schutte, Rajeev Thottappillil, "Pantograph Arcing in Electrified Railways—Mechanismand Influence of Various Parameters—Part Ⅰ:With DC Traction Power Supply", IEEE Transction on Power Delivery, vol.24, no.4 Oct.2009, pp.1931-1939
[17]闫站伟,“浅析接触线拉弧原因及其预防措施”,郑铁科技通讯,2007第1期,25-27
[18]王万岗,吴广宁,高国强,王波,崔易,刘东来,“高速铁路弓网电弧试验系统”,铁道学报,2012年4月,(34)4：22-27
[19]张博,“弓网离线电弧电磁干扰的机理分析及测试系统界面实现研究”,成都,西南交通大学,2011
[20]雷栋,吴广宁,王万岗,张雪原,何常红,“高速铁路弓网电弧模拟装置的研制”,机车电传动,2009年5月,第3期：42-45
[21]何常红,“弓网电弧模拟系统的研制和试验研究”,成都,西南交通大学,2009
[22]王万岗,吴广宁,赵云云,高国强,王波,“弓网电弧电气特性试验研究”,低压电器,2012第6期：5-11
[23]雷栋,吴广宁,张雪原,王万岗,何常红,“高速铁路弓网电弧抑制方法研究”电气化铁路,2008第5期：1-4
[24]杨志鹏,李华伟,孙忠国,李国国,“基于弓网电弧模拟试验装置的电弧参数测量及分析”,北京交通大学学报,2012年4月,(36)2：111-115
[25]杨志鹏,李华伟,孙忠国,李国国,“基于弓网电弧模拟试验装置的电弧研究”,电气化铁道,2012年第一期：28-31
[26]杨志鹏,“弓网电弧研究及其检测”,北京,北京交通大学,2011
[27]CISPR Publication 16—1-1993, "Specification for radio disturbance and immunity measuring apparatus and methods Part 1. Radio disturbance and immunity measuring apparatus", IEC,1993
[28]国家技术监督局,GB/T15708—-1995,“交流电气化铁道电力机车运行产生的无线电辐射干扰的测量方法”,1995
[29]国家技术监督局,GB/T15709—-1995,“交流电气化铁道接触网无线电辐射干扰测量方法”,1995
[30]A. Jr Banos, "Dipole radiation in the presence of a conducting half-space", Oxford, Pergamon Press,1966
[31]中国国家标准管理委员会,GB/T24338—-2009,“轨道交通电磁兼容”,2009
[32]Taketoshi Nakai, Zenichiro Kawasaki, "On Impulsive Noise from Shinkansen", IEEE Transction on Electromagnetic Compatibility, Vol.EMC-25, No.4,1983, pp.396-404
[33]Nakai, Taketoshi,"Measurement and Analysis of Impulsive Noise from Bullet Trains", IEEE Transction on Electromagnetic Compatibility, Vol.EMC-28, No.4,1986, pp.193-203
[34]沈致君,“弓网离线电弧电磁干扰问题的研究”,北京,北京交通大学,2011,36-38
[35]沙斐,张林昌,“电磁干扰的统计参量APD和NAD的特性及其测量”,北方交通大学学报,1983年11月,第2期：11-27
[36]张林昌,徐坤生,蒋忠涌,“电气化铁道干扰源的特性及测量”,北方交通大学学报,1980年第2期：13-29
[37]周克生,张林昌,“高速电气化铁道无线电噪声预测”,铁道学报,1999年4月,(21)2：54-57
[38]闻映红,“无线电骚扰的统计参量测量法-幅度概率分布(APD)”,测试与测量,2006第1期
[39]陈嵩,“幅度概率分布(APD)统计参量测量方法的研究与APD测量系统的研制”,北京,北京交通大学,2008
[40]http://www.kth. se/en/ees/omskolan/organisation/avdelningar/etk/research/topics/emc/2.18951/emc-of-rail ways-pantograph-arcing-1.47295
[41]张溢强,“电气化铁路无线电干扰传播特性仿真及研究”,北京,北京交通大学,2005
[42]张林昌,蒋守守,“用正弦信号源研究电气化铁道无线电干扰的横向波传播特性”,北方交通大学学报,1993,(17)4：351-355
[43]黄朝晖,张林昌,“电气化铁道无线电干扰横向距离特性的理论分析”,铁道学报-S2,1989,1-9
[44]Stefan Niska, "Measurement and Analysis of Electromagnetic Interferences in the Swedish Railway Systems", Lulea, Lulea University,2008
f45]周克生,张林昌,"The Conversion Factors for Radio Interference from Eletrified Railway Measured with Different Detectors", Proceeding of 12th Symposium and Exhibition on EMC, Wroclaw,1994
[46]Andrea Cozza, "Railway EMC:Assessment of infrastructure Impact", Turin, Politecnico di Torino,2005
[47]http://www.transport-research.info/web/projects/project_details.cfm?ID=37707
[48]I. S. Grashteyn, I. M. Ryzhik, "Table of integrals, series and products", Salt Lake City, Academic Press, 1980
[49]R. Giannetti, M. Macucci, B. Tellini, "EMI Measuements in line-pantograph Contact Discontinutity in Railway Transportation Syatems",11th IMEKO TC-4 Symp.,2001, Libon, pp.25-27
[50]Surajit Midya, Rajeev Thottappillil, "An overview of electromagnetic compatibility challenges in European Rail Traffic Management System", Transportation Research Part C 16,2008, pp.515-534
[51]Anping Dong, Guangning Wu, Guoqiang Gao, Lijun Zhou,Wangang Wang,Bo Wang, Yi Cui, Yang Mingming, "Simulation system of pantograph arcing" 1st International Conference on Electric Power Equipment - Switching Technology, Xi'an,2011, pp.637-641
[52]E.J. Bartlett, M. Vaughan, P.J. Moore,"Investigation into electromagnetic emissions from power system arcs", International Conference and Exhibition on Electromagnetic Compatibility,1999, EMC York 99 pp.47-52
[53]Dierk Bormann, Surajit Midya, Rajeev Thottappillil, "DC components in Pantograph Arcing: Mechanisms and Influence of Various Parameters", International Zurich Symposium on Electromagnetic Compatibility,2007, pp.369-372
[54]Demetrios Klapas, Reuben Hackam, F. A. Benson, "Electric Arc Power Collection High-Speed Trains", Proceedings of the IEEE, Vol.64, No.12,1976, pp.1699-1716
[55]Nelson Theethayi, Rajeev Thottappillil,Yaqing Liu, Raul Montano, "Important parameters that influence crosstalk in multiconductor transmission lines", Electric Power Systems Research, Vol.77, No.8,2007, pp. 896-909
[56]Academic Research Projects, "Theoretical Analysis and Experimental Assessment of the Electromagnetic Emissions of Railway Infrastructure and Rolling Stock" http://docenti.etec.polimi.it/ind31/emcgroup/research_projects.html
[57]金学松,温泽峰,张卫华等,“世界铁路发展状况及其关键力学问题”,第十三届全国结构工程学术会议论文集,2004：96-100
[58]杨飞,“无线电骚扰的幅度概率分布统计模型及其对数字通信系统干扰的算法研究”,北京,北京交通大学,2010
[59]R.J. Hill, "Electric Railway traction Part 6 Electromagnetic Compatibility-disturbance sources and equipment susceptibility", Power Engineering Journal, Tutorial,1997, pp.31-39
[60]R.J. Hill, "Electric Railway traction Part 7 Electromagnetic Interference in traction systems", Power Engineering Journal, Tutorial,1997, pp.259-266
[61]R.J. Hill, D.C. Carpenter, "Modelling of Nolinear Rail Impedance in AC Traction Power Systems", IEEE Transaction on Power Delivery, Vol.6, No.4,1991, pp.1755-1761
[62]D.C. Carpenter, R.J. Hill, "Railroad Track Elctrical Impedance and Adjacent Track Crosstalk Modeling Using the Finite-Element Method of Electromagnetic Systems Analysis", IEEE Transaction on Vehicular Technology, Vol.42 No.4,1993, pp.555-562
[63]R.J. Hill, D.C. Carpenter, "Rail Track Distributed Transmission Line Impedance and Admittance: Theoretical Modeling and Experimental Results", IEEE Transaction on Vehicular Technology, Vol.42 No.2, 1993, pp.225-241
[64]J.R. Carson, "Wave Propagation in overhead wires with a ground return", Bell System Technical Journal, Vol.5,1926, pp.539-554
[65]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, "On the influence of conductor heights and lossy ground in multi-conductor transmission lines for lightning interaction studies in railway overhead traction systems", Electric Power Systems Research, Vol.65, No.1,2004, pp.186-193
[66]J.R. Wait, "Theory of Wave Propagation along a Thin Wire Parallel to an Interface", Radio Science, Vol.7, No.6,1972, pp.675-679
[67]Edward F. Kuester, David C. Chang, Robert G Oslen, "Modal theory of long horizontal wire structures above the earth,1, Excitation", Radio Science, Vol.13, No.4,1978, pp.605-613
[68]Robert G. Oslen, Edward F. Kuester, David C. Chang, "Modal theory of long horizontal wire structures above the earth,2, Properties of discrete modes", Radio Science, Vol.13, No.4,1978, pp.615-623
[69]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil, "A Method for Interfacing Lumped-Circuit Models and Transmission-Line System Models With Application to Railways", IEEE Transction on Electromagnetic Compatibility, Vol.51, No.3,2009, pp.833-841
[70]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil "Indirect Lighting-Inducted Voltages Along a Railway Catenary-Track Multiconductor-Line System With Lumped Components", IEEE Transction on Electromagnetic Compatibility, Vol.53, No.2,2011, pp.537-539
[71]Ziya Mazloom, Nelson Theethayi, Rajeev Thottappillil, "Modeling Indirect Lighting Strikes for Railway System With Lumped Components and Nolinear Effects ", IEEE Transetion on Electromagnetic Compatibility, Vol.53, No.1,2011, pp.249-252
[72]A. Ametani, "Stratified Earth Effects on Wave Propagation Frequency-Dependent Parameters",IEEE Transction on Power Apparatus and Systems, Vol.PAS-93, No.5,1974, pp.1233-1239
[73]高攸纲,“感性耦合与阻性耦合”,北京,人民邮电版社,1979
[74]Peter Marcus Buff Ⅲ, "Characterization of Propagation on Wires over Lossy Earth", North Carolina, North Carolina State University,2006
[75]Nelson Theethayi, "Electromagnetic Interference in Distributed Outdoor Electrical Systems, with an Emphasis on Lightning Interaction with Electrified Railway Network", Uppsala, Uppsala University,2005
[76]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, Michael Zitnik, Vernon Cooray, Victor Scuka, "A theoretical study on the consequence of a direct lightning strike to electrified railway system in Sweden", Electric Power Systems Research, Vol.74, No.2,2005, pp.267-280
[77]Yaqing Liu, Nelson Theethayi, Rajeev Thottappillil, Raul M. Gonzalez, Michael Zitnik, "An improved model for soil ionization around grounding system and its application to stratified soil", Electric Power Systems Research, Vol.60, No.2-4,2004, pp.203-209
[78]Nelson Theethayi, Yaqing Liu, Raul Montano, Rajeev Thottappillil, "Crosstalk in Multiconductor Transmission Line in the Presence of Finitely Conducting Ground", IEEE International Symposium on Electromagnetic Compatibility,Vol.2,2003, pp.1003-1006
[79]C.R. Paul, "Analysis of Multiconductor Transmission Lines, Second Edition", Wiley-Interscience A John Wiley & Sons, INC., Publication, IEEE Press,2008
[80]Erling D. Sunde, "Earth Conduction Effects in Transmission Systems", D. VAN Nostrand Company, Inc., Toronto/New York/London,1968
[81]E. F. Vance, "Coupling to Cable Shields", A Wiley-Interscience Publication John Wiley & Sons, New York/London/Sydney/Toronto,1978
[82]吕英华,王旭莹译,“EMC分析方法与计算模型”,北京,北京邮电大学出版社,2009
[83]Robert G. Olsen, Jeffrey L. Young, David C. Chang, "Electromagnetic Wave Propagation on a Thin Wire Above Earth", IEEE Transction on Antennas and Propagation, Vol.48, No.9,2000, pp.1413-1419
[84]Magnus Akke, Thomas Biro, "Measurements of the Frequency-Dependent Impedance of a Thin Wire With Ground Return", IEEE Transction on Power Delivery, Vol.20, No.2,2005, pp.1748-1752
[85]A.L. Timotin, "Longitudinal transient parameters of a unifilar line with ground return", Science Technical-Electrotechn., Vol.12,No.4,1967, pp.523-535
[86]D.Orzan, "Time domain low frequency approximation for the off-diagonal terms of the ground impedance matrix", IEEE Transactions on Electromagnetic Compatibility, Vol.39, No.1,1997, pp.64
[87]R. Araneo, S. Celozzi, "Direct time domain analysis of transmission lines above a lossy ground",IEE Proceedings on Science and Measurement Technology, Vol.148, No.2,2001, pp.73-79
[88]F. Rachidi, S.L. Loyka, C.A. Nucci, M. Ianoz, "A new expression for ground transient resistance matrix elements of multiconductor overhead transmission lines", Electric Power Systems Research, Vol.65, No.l, 2003, pp.41-46
[89]A.Semlyen, "Ground Return Parameters of Transmission Lines an Asymptotic Analysis for very High frequencies", IEEE Transactions on Power Apparatus and Systems, Vol.100, No.3,1981, pp.1031-1038.
[90]B.Gustavsen, A.Semlyen, "Rational approximation of frequency domain responses by vector fitting", IEEE Transactions on Power Delivery, Vol.14, No.3,1999, pp.1052-1061.
[91]Lei Liu, Xiang Cui, Lei Qi, "Simulation of Electromagnetic Transients of the Bus Bar in Substation by the Time-Domain Finite-Element Method", IEEE Transactions on Electromagnetic Compatibility, Vol.51, No.4,2009, pp.1017-1025
[92]Tiebing Lu, Lei Qi, Xiang Cui, "Effect of multilayer soil on the switching transient in substations", IEEE Transactions On Magnetics, Vol.42, No.4,2006, pp.843-846
[93]Tiebing Lu,Xiang Cui,Haoliu Yin,Lin Li,"Time-domain analysis of transient electromagnetic field generated by aerial busbars above lossy soil", IEEE Transactions On Magnetics, Vol.38, No.2,2002, pp.773-776
[94]Tiebing Lu, Xiang Cui, Lin Li, "Transient analysis of aerial multi-conductor transmission lines with branch", IEEE Transactions On Magnetics, Vol.37, No.5,2001, pp.3298-3302
[95]齐磊,卢铁兵,张重远,崔翔,“考虑多次土壤时架空线的瞬态分析”,中国电机工程学报,2003年5月,(23)5：66-69
[96]M. Nakagama, K. Iwamoto, "Earth-return impedance for thr multi-layer case", IEEE Transction on Power Apparatus and Systems, Vol. PAS-95, No.2,1976, pp.671-676
[97]李凯,“分层介质中的电磁场和电磁波”,杭州,浙江大学出版社,2010
[98]J.R. Wait, "Electromagnetic Waves in Stratified Media", Oxford/London/New York/Paris, Pergamon Press,1962
[99]Weng Cho Chew, "Waves and Fields in Inhomogeneous Media", New York, Van Nostrand Reinhold, 1990
[100]R.W.P. King, M. Owens,T.T. Wu, "Lateral Electromagnetic Waves, Theory and Application to Communications, Geophysical Exploration, and Remote Sensing", Springer-Verlag,1992
[101]R.M. Sorbello,R.W.P. King,K.M. Lee,L.C.Shen,T.T. Wu, "The horizontal-wire antenna over a dissipative half-space:Generalized Formula and Measurements", IEEE Transaction on Antennas and Propagation, Vol.25, No.6,1977, pp.850-854
[102]D.C. Chang,R.G. Oslen, "Excitation of an infinite Antenna above a Dissipative Earth",Radio Science, Vol.10, No.8-9,1975, pp.823-831
[103]Antonio Orlandi, C.R. Paul, "FDTD Analysis of Lossy, Multiconductor Transmission Lines Terminated in Arbitrary Loads",IEEE Transactions on Electromagnetic Compatibility, Vol.38, No.3,1996, pp.388-399
[104]J. Zenneck, "Propagation of plane eletromagnetic waves along a plane conducting surface and its bearing on the theory of transmission in wireless telegraphy", Ann. Phys.,Vol.23,1907, pp.846-866
[105]R.W.P. King, S.S. Sandier, "The eletromagnetic field of a vertical electric dipole in the presence of a three-layered region", Radio Science, Vol.29, No.1,1994, pp.97-113
[106]J.R. Wait, Comment on "The electromagnetic field of a vertical electric dipole in the presence of a three-layered region" by Ronold W. P. King and Sheldon S. Sandler, Radio Science, Vol.33, No.2,1998, pp.251-253
[107]R.E. Collin, "Some observations about the near zone eletric field of a hertzian dipole above a lossy earth", IEEE Transaction onAntennas and Propagation, Vol.52, No.11,2004, pp.3133-3137
[108]R.E. Collin, "Hertzian dipole radiation over a lossy earth or sea:some early and late 20th century controversies", IEEE Magazine on Antennas and Propagation, Vol.46, No.2,2004, pp.64-79
[109]杨儒贵,“高等电磁理论”,北京,高等教育出版社,2008
[110]梁昆淼,刘法,缪国庆,“数学物理方法”,北京,高等教育出版社,2006
[111]吴命利,“电气化铁道牵引网的统一链式电路模型”,中国电机工程学报,2010年10月,(30)28：52-58
[112]孙铭甫译,“轨道电路的分析与综合”,北京,中国铁道出版社,1981
[113]"Colorado Soil Survey Program" http://www.co.nrcs.usda.gov/technical/soil/soil-surveys/soil-survey-program.html
[114]Frank Olyslager, Daniel De Zutter, "High-frequency transmission line models for a thin wire above a conducting ground", IEEE Transction on Electromagnetic Compatibility, Vol.37, No.2,1995, pp.234-240
[115]B.Gustavsen, "Improving the pole Relocating Properties of Vector Fitting", IEEE Transactions on Power Delivery, Vol.21, No.3,2006, pp.1587-1592
[116]中铁电气化局集团有限公司译,“电气化铁道接触网”,北京,中国电力出版社,2004