高铁牵引供电系统的宽频建模与时域计算方法的研究与应用
|
摘要
牵引供电系统和贯通线是高速铁路系统中重要的基础设施,随着我国高速铁路的发展和高速铁路、客运专线在我国的快速建设,对供电系统的可靠性提出了更高的要求。运行数据表明,雷击故障是影响高速铁路供电系统可靠性的重要因素之一,须加以有效解决。本文结合“十一五”国家“科技支撑计划”重点项目“中国高速列车关键技术研究及装备研制”的“高速列车牵引供电技术”课题(2009BAG12A09)和国家自然科学基金项目“变电站关键设备分数阶无源宽频建模方法的研究”(51177048),重点研究了高速铁路接触网系统、高速铁路综合接地系统和10kV贯通线电缆的宽频建模与时域计算方法,对高速铁路接触网和10kV贯通线电缆的感应雷和直击雷过电压进行了计算与分析,对接触网线路耐雷水平及故障跳闸率进行了评估,提出了雷电防护措施建议。本文主要研究成果如下：
1.提出了计算架空线路雷电感应过电压的改进DEPACT (Delay Extraction-based Passive Compact Transmission Line macromodeling algorithm, DEPACT)时域宏模型,该方法与现有的架空线雷电感应过电压时域计算方法相比,分段数少,可有效提高计算雷电感应过电压的计算速度。该方法无需在模域可直接在相域进行求解,所建立的模型能直接嵌入通用的电磁瞬态仿真软件,因此在处理端接复杂集中参数网络或非线性设备等问题时十分简便。
2.基于部分单元等效电路法和开路抑制原理,建立了高速铁路高架桥综合接地系统的宽频多口模型,并给出了相应的时域求解方法。结合接触网线路的多导体传输线模型,实现了接触网线路感应雷和直击雷过电压的计算与分析,并对接触网架空线路的故障跳闸率进行了评估,提出了雷电防护措施建议。
3.提出了外部电磁场激励下的多导体传输线时域有限元法,总结出了有关系数矩阵元素的送值表,并对该方法的数值稳定性进行了讨论,证明了该方法具有无条件稳定的优点,通过与现有方法的计算结果进行比较,验证了本文计算方法的正确性。
4.将分数阶拟合方法和分数阶系统的数值解法相结合,提出了一种通用的电气设备宽频建模方法。通过研究分数阶系统的无源性质,提出了一种适用于分数阶电路系统的无源判据,丰富了电网络理论。与现有的整数阶宽频建模方法相比,本文方法可计及频变效应固有的非整数阶次幂特性,仅需较低的拟合阶数就可获得较高的计算精度,所建立的模型更为简洁。
5.基于本文提出的分数阶宽频建模方法,建立了电缆的分数阶宽频模型,并验证了模型的正确性。利用该模型,实现了高速铁路10kV贯通线感应雷和直击雷过电压的计算与分析,给出了雷电防护措施建议。
Traction power supply system and railway cable continuous power line are the important infrastructures and play a decisive role of the high-speed railway system. The operating data indicates that the lightning failure is one of the important factors that affect the reliability of the power supply system of the high-speed railway. Supported by the Eleventh Five-Year Plan for National Science and Technology (Grant No.2009BAG12A09) and the National Natural Science Foundation of China (Grant No.51177048), the wideband modeling method and the time domain calculational method of the catenary multi-conductor system, the integrated grounding system and the lOkV railway cable continuous power line in high-speed railway are studied, the indirect and direct lightning overvoltages and the flash-over rate are calculated. The main innovative achievements are presented as follows:
1. The improved Delay Extraction-Based Passive Compact Transmission Line (DEPACT) macromodeling algorithm for calculating the induced voltages of the overhead transmission line is proposed. Compared with the existing methods, the segmentation number of the transmission lines can be effectively reduced and the operating efficiency can be raised. Furthermore, because the improved model can be solved in the phase domain instead of in the modal domain, it can be embedded into the circuit simulation software, which provides a conveninet and efficient way for calculating the lightning induced ovrevoltages of the overhead transmission lines.
2. Based on the partial element equivalent circuit (PEEC) method, the integrated grounding system of the rail transit viaduct is modeled and the time domain calculational method is also derived. Combined with the multi-conductor transmission lines model of the catenary, the indirect and direct lightning overvoltages are calculated, the flash-over rates of the catenary are evaluated, and an effective lightning protection measure is put forward.
3. An efficient time domain finite element method for the transient response of MTLs with frequency-dependent parameters excited by an external electromagnetic field is presented and a value-delivery table to form the coefficient matrices is generalized. The stability condition of this method is also studied and the conclusion is archived that the method proposed in this paper is unconditionally stable for any temporal step. The method is verified to be correct by comparing the results with the existing method.
4. Combined with the fractional identification method and numeric solution to the fractional order differential equation, a general wideband modeling method is proposed. Comparing with the existing wideband modeling method, the orders of the model can be reduced effectively. Considering the indispensability of the passivity verification of a system for the transient simulation, a passivity verification method for the fractional order state-space system is studied and a practical criterion is proposed in this paper.
5. A novel wideband model of the cable is presented based on the fractional order wideband modeling method and the model is verified by comparing with the results of the existing method. The indirect and the direct lightning overvolages of the lOkV railway cable continuous power line are computed and analyzed, and the lightning protection measures are put forward.
1.提出了计算架空线路雷电感应过电压的改进DEPACT (Delay Extraction-based Passive Compact Transmission Line macromodeling algorithm, DEPACT)时域宏模型,该方法与现有的架空线雷电感应过电压时域计算方法相比,分段数少,可有效提高计算雷电感应过电压的计算速度。该方法无需在模域可直接在相域进行求解,所建立的模型能直接嵌入通用的电磁瞬态仿真软件,因此在处理端接复杂集中参数网络或非线性设备等问题时十分简便。
2.基于部分单元等效电路法和开路抑制原理,建立了高速铁路高架桥综合接地系统的宽频多口模型,并给出了相应的时域求解方法。结合接触网线路的多导体传输线模型,实现了接触网线路感应雷和直击雷过电压的计算与分析,并对接触网架空线路的故障跳闸率进行了评估,提出了雷电防护措施建议。
3.提出了外部电磁场激励下的多导体传输线时域有限元法,总结出了有关系数矩阵元素的送值表,并对该方法的数值稳定性进行了讨论,证明了该方法具有无条件稳定的优点,通过与现有方法的计算结果进行比较,验证了本文计算方法的正确性。
4.将分数阶拟合方法和分数阶系统的数值解法相结合,提出了一种通用的电气设备宽频建模方法。通过研究分数阶系统的无源性质,提出了一种适用于分数阶电路系统的无源判据,丰富了电网络理论。与现有的整数阶宽频建模方法相比,本文方法可计及频变效应固有的非整数阶次幂特性,仅需较低的拟合阶数就可获得较高的计算精度,所建立的模型更为简洁。
5.基于本文提出的分数阶宽频建模方法,建立了电缆的分数阶宽频模型,并验证了模型的正确性。利用该模型,实现了高速铁路10kV贯通线感应雷和直击雷过电压的计算与分析,给出了雷电防护措施建议。
Traction power supply system and railway cable continuous power line are the important infrastructures and play a decisive role of the high-speed railway system. The operating data indicates that the lightning failure is one of the important factors that affect the reliability of the power supply system of the high-speed railway. Supported by the Eleventh Five-Year Plan for National Science and Technology (Grant No.2009BAG12A09) and the National Natural Science Foundation of China (Grant No.51177048), the wideband modeling method and the time domain calculational method of the catenary multi-conductor system, the integrated grounding system and the lOkV railway cable continuous power line in high-speed railway are studied, the indirect and direct lightning overvoltages and the flash-over rate are calculated. The main innovative achievements are presented as follows:
1. The improved Delay Extraction-Based Passive Compact Transmission Line (DEPACT) macromodeling algorithm for calculating the induced voltages of the overhead transmission line is proposed. Compared with the existing methods, the segmentation number of the transmission lines can be effectively reduced and the operating efficiency can be raised. Furthermore, because the improved model can be solved in the phase domain instead of in the modal domain, it can be embedded into the circuit simulation software, which provides a conveninet and efficient way for calculating the lightning induced ovrevoltages of the overhead transmission lines.
2. Based on the partial element equivalent circuit (PEEC) method, the integrated grounding system of the rail transit viaduct is modeled and the time domain calculational method is also derived. Combined with the multi-conductor transmission lines model of the catenary, the indirect and direct lightning overvoltages are calculated, the flash-over rates of the catenary are evaluated, and an effective lightning protection measure is put forward.
3. An efficient time domain finite element method for the transient response of MTLs with frequency-dependent parameters excited by an external electromagnetic field is presented and a value-delivery table to form the coefficient matrices is generalized. The stability condition of this method is also studied and the conclusion is archived that the method proposed in this paper is unconditionally stable for any temporal step. The method is verified to be correct by comparing the results with the existing method.
4. Combined with the fractional identification method and numeric solution to the fractional order differential equation, a general wideband modeling method is proposed. Comparing with the existing wideband modeling method, the orders of the model can be reduced effectively. Considering the indispensability of the passivity verification of a system for the transient simulation, a passivity verification method for the fractional order state-space system is studied and a practical criterion is proposed in this paper.
5. A novel wideband model of the cable is presented based on the fractional order wideband modeling method and the model is verified by comparing with the results of the existing method. The indirect and the direct lightning overvolages of the lOkV railway cable continuous power line are computed and analyzed, and the lightning protection measures are put forward.
引文
[1]翟铁久.新型高压真空间隙避雷器研究[J].铁道机车车辆,2012,32(3)：129-131
[2]苏冬冬.京沪高铁接触网防雷问题的探讨[J].上海铁道科技,2011(4)：52-53
[3]李学伟.高速铁路概论[M].北京：中国铁道出版社,2012.5
[4]陈纪纲.无砟轨道线路接触网防雷技术研究[J].铁道工程学报,2007,S1：422-425
[5]刘明光.接触网受雷击过电压影响及其分析计算[J].铁道学报,1997,03：48-51
[6]于增.接触网防雷技术研究[J].铁道工程学报,2002,01：89-94
[7]范海江,罗健.铁路客运专线接触网防雷研究[J].铁道工程学报,2008,119(8)：80-83
[8]周歧斌,边晓燕,傅正财.香港地区电气化铁路直流电力牵引系统电力电缆的雷电过电压分析[J].中国铁道科学,2009,30(4)：91-95
[9]李康,刘家军,卓元志,等.高速电气化铁路接触网防雷研究[J].电网与清洁能源,2012,28(7)：39-45
[10]张鹏远.电气化铁道牵引网的防雷保护研究[D].硕士论文,西南交通大学,四川,中国,2010
[11]赵海军,陈维江,王彦利,等.城市轨道交通架空接触网雷电防护[J].电气化铁道,2008,28(5)：23-27
[12]Theethayi N, Liu Y, Montano R, et al. A theoretical study on the consequence of a direct lightning strike to electrified railway system in Sweden[J]. Electric power systems research,2005,74(2):267-280
[13]Theethayi N, Liu Y, Montano R, et al. Modeling direct lightning attachment to electrified railway system in Sweden[C].2003 IEEE Power Tech Conference Proceedings, Bologna,2003:4-7
[14]Theethayi N. Electromagnetic interference in distributed outdoor electrical systems, with an emphasis on lightning interaction with electrified railway network[D]. PhD Thesis, Uppsala University, Uppsala, Sweden,2005
[15]Filippone F, Mariscotti A, Pozzobon P. The internal impedance of traction rails for DC railways in the 1-100 kHz frequency range[J]. IEEE Transactions on Instrumentation and Measurement,2006,55(5):1616-1619
[16]Ferrari P, Pozzobon P. Railway lines models for impedance evaluation [C], Harmonics and Quality of Power Proceedings,1998. Proceedings.8th International Conference On. IEEE,1998,2:641-646
[17]Carpenter D C, Hill R J. FEM applied to railroad track electrical impedance and adjacent track crosstalk modelling[C]. Railroad Conference,1991, Proceedings of the 1991 IEEE/ASME Joint. IEEE,1991:87-95
[18]Hill R. J. and Carpenter D. C.. Rail track distributed transmission line impedance and admittance:theoretical modeling and experimental results[J]. IEEE Transactions on Vehicular Technology,1993,42(2):225-241
[19]Mariscotti A, Pozzobon P. Measurement of the internal impedance of traction rails at 50 Hz[J]. IEEE Transactions on Instrumentation and Measurement,2000,49(2): 294-299
[20]Mariscotti A, Pozzobon P. Measurement of the internal impedance of traction rails at audio frequency [J]. IEEE Transactions on Instrumentation and Measurement, 2004,53(3):792-797
[21]Wang Y J, Wang J H. Modeling of frequency-dependent impedance of the third rail used in traction power systems[J]. IEEE Transactions on Power Delivery,2000, 15(2):750-755
[22]Wang Y J, Tsai Y L. Calculation of the frequency-dependent impedance of rail tracks using a four-parameter equivalent tubular conductor model [J]. IEEE Transactions on Power Delivery,2004,19(3):1142-1147
[23]Wagner K W. Elektromagnetische Ausgleichsvorgange in Freileitungen und Kabeln[M]. B. G. Teubner,1908
[24]V. Aigner. Induzierte Blitzuberspannunen und ihre beziehung zumruck wartigen[J]. Uberschlag,1935, ETZ 56:497-500
[25]Wagner C F, McCann G D. Induced voltages on transmission lines[J]. Transactions of the American Institute of Electrical Engineers,1942,61(12):916-930
[26]S. Szpor. A new theory of the induced overvoltages[R]. CIGRE Report 308,1948.
[27]Lundholm R. Induced overvoltage-surges on transmission lines and their bearing on the lightning performance at medium voltage networks [M]. Gumperts Forlag, 1957
[28]Rusck S. Induced-lightning overvoltages on power transmission lines with special reference to the overvoltage protection of low voltage networks[M]. Transactions of Royal Institute of Technology,1958
[29]Piantini A, Janiszewski J M. Lightning-induced voltages on overhead lines—Application of the extended rusck model [J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(3):548-558
[30]Silva J P, Araujo A E A, Paulino J O S. Calculation of lightning-induced voltages with Rusck's method in EMTP—part Ⅱ:effects of lightning parameter variations[J]. Electric Power Systems Research,2002,61(2):133-137
[31]Darveniza M. A practical extension of Rusck's formula for maximum lightning-induced voltages that accounts for ground resistivity [J]. IEEE Transactions on Power Delivery,2007,22(1):605-612
[32]Chowdhuri P, Gross E T B. Voltage surges induced on overhead lines by lightning strokes[C]. Proceedings of the Institution of Electrical Engineers. IET Digital Library,1967,114(12):1899-1907
[33]Liew A C, Mar S C. Extension of the Chowdhuri-Gross model for lightning induced voltage on overhead lines[J]. IEEE Transactions on Power Delivery,1986, 1(2):240-247
[34]Hoidalen H K. Analytical formulation of lightning-induced voltages on multiconductor overhead lines above lossy ground[J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(1):92-100
[35]Taylor C, Satterwhite R, Harrison Jr C. The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field[J]. IEEE Transactions on Antennas and Propagation,1965,13(6):987-989
[36]Agrawal A K, Price H J, Gurbaxani S H. Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field [J]. IEEE Transactions on Electromagnetic Compatibility,1980 (2):119-129
[37]Rachidi F. Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field[J]. IEEE Transactions on Electromagnetic Compatibility 1993,35(3):404-407
[38]Master M J, Uman M A. Lightning induced voltages on power lines:Theory [J]. IEEE Transactions on Power Apparatus and Systems,1984 (9):2502-2518
[39]Georgiadis N, Rubinstein M, Uman M A, et al. Lightning-induced voltages at both ends of a 448-m power-distribution line[J]. IEEE Transactions on Electromagnetic Compatibility,1992,34(4):451-460
[40]Barker P P, Short T A, Eybert-Berard A R, et al. Induced voltage measurements on an experimental distribution line during nearby rocket triggered lightning flashes [J]. IEEE Transactions on Power Delivery,1996,11(2):980-995
[41]Michishita K, Ishii M, Asakawa A, et al. Voltage induced on a test distribution line by negative winter lightning strokes to a tall structure[J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(1):135-140
[42]Ishii M, Michishita K, Hongo Y, et al. Lightning-induced voltage on an overhead wire dependent on ground conductivity [J]. IEEE Transactions on Power Delivery, 1994,9(1):109-118
[43]Nucci C A, Borghetti A, Piantini A, et al. Lightning-induced voltages on distribution overhead lines:comparison between experimental results from a reduced-scale model and most recent approaches[C]. Proceedings of the 24th International Conference on Lightning Protection,1998:314-320
[44]Nucci C A, Rachidi F, Ianoz M V, et al. Lightning-induced voltages on overhead lines[J]. IEEE Transactions on Electromagnetic Compatibility,1993,35(1): 75-86
[45]K. Agrawal, H. J. Price, and S. H. Gurbaxani. Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field. IEEE Transactions on Electromagnetic Compatibility,1980,22(2):119-129
[46]齐磊.多导体传输线的时域有限差分法研究[D].硕士论文,华北电力大学,河北,中国,2002
[47]卢铁兵.变电站瞬态电磁环境数值预测方法的研究[D].博士论文,华北电力大学,河北,中国,2001
[48]Clayton R.P. Analysis of Multiconductor Transmission Lines[M]. New York:John Wiley and Sons Press,1994
[49]Cooray V. Calculating lightning-induced overvoltages in power lines:A comparison of two coupling models[J]. IEEE Transactions on Electromagnetic Compatibility,1994,36(3):179-182
[50]Nucci C A, Rachidi F, Ianoz M, et al. Comparison of two coupling models for lightning-induced overvoltage calculations[J]. IEEE Transactions on Power Delivery,1995,10(1):330-339
[51]P. Santt. Deuxieme campagne de caracterisation du nouveau moyen d'essaia 1'I.E.M.N du LEHT:l'antetine "Strip-Line", lere partie[J]. EdF, Direction des Etudes et Researches,1990, HM82-1367A
[52]Rachidi F, Nucci C A, Ianoz M, et al. Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields[J]. IEEE Transactions on Power Delivery,1997,12(3):1404-1411
[53]Rachidi F, Nucci C A, Ianoz M. Transient analysis of multiconductor lines above a lossy ground[J]. IEEE Transactions on Power Delivery,1999,14(1):294-302
[54]Paolone M, Nucci C A, Rachidi F. A new finite difference time domain scheme for the evaluation of lightning induced overvoltages on multiconductor overhead lines[C]. Proceeding of the 5th International Conference on Power System Transient,2001:596-602
[55]Paolone M. Modeling of lightning-induced voltages on distribution networks for the solution of power quality problems, and relevant implementation in a transient program[D]. PhD Thesis, Department of Electrical Engineering Bologna, University of Bologna, Italy,2001
[56]Nucci C A. Lightning-induced voltages on distribution systems:influence of ground resistivity and system topology[J]. Journal of Lightning Research,2007,1: 148-157
[57]Nucci C A. The lightning induced over-voltage (LIOV) code[C].2000 IEEE Power Engineering Society Winter Meeting,2000:2417-2418
[58]H(?)idalen H. K.. Lightning-induced overvoltages in low-voltage systems[D]. PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1997
[59]Hoidalen H. K. Calculation of lightning-induced overvoltages using MODELS[C]. Proceedings of the International Conference on Power Systems Transients,1999: 359-64
[60]H(?)idalen H K. Calculation of lightning-induced voltages in MODELS including lossy ground effects [C]. Proceedings of the International Conference on Power System Transient (IPST2003), New Orleans,2003:1-6
[61]Borghetti A, Gutierrez J A, Nucci C A, et al. Software tools for the calculation of lightning-induced voltages on complex distribution systems[C]. Proceeding of the 26th International Conference on Lightning Protection.2002:2-6
[62]Montano R, Theethayi N, Cooray V. An Efficient implementation of the Agrawal et al. model for lightning-Induced voltage calculations using circuit simulation software[J]. IEEE Transactions on Circuits and Systems I:Regular Papers,2008, 55(9):2959-2965
[63]Baum C E, Liu T K, Tesche F M. On the analysis of general multiconductor transmission-line networks[J]. Interaction Note.1978,350:467-547
[64]Sheshyekani K, Hesamedin Sadeghi S H, Moini R, et al. Analysis of transmission lines with arrester termination, considering the frequency-dependence of grounding systems[J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(4): 986-994
[65]Tesche F M. Development and use of the BLT equation in the time domain as applied to a coaxial cable[J]. IEEE Transactions on Electromagnetic Compatibility, 2007,49(1):3-11
[66]Tesche F M. On the analysis of a transmission line with nonlinear terminations using the time-dependent BLT equation [J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(2):427-433
[67]Pokharel R K, Ishii M, Baba Y. Numerical electromagnetic analysis of lightning-induced voltage over ground of finite conductivity [J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(4):651-656
[68]Silveira F H, Visacro S, Herrera J, et al. Evaluation of lightning-induced voltages over a lossy ground by the hybrid electromagnetic model [J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(1):156-160
[69]Yutthagowith P, Ametani A, Nagaoka N, et al. Lightning-Induced voltage over lossy ground by a hybrid electromagnetic circuit model method with Cooray-Rubinstein formula[J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(4):975-985
[70]Baba Y, Rakov V A. Voltages induced on an overhead wire by lightning strikes to a nearby tall grounded object[J]. IEEE Transactions on Electromagnetic Compatibility,2006,48(1):212-224
[71]A.Taflove. Computational electrodynamics-the finite-difference time-domain method[M].2nd edition, Artech House,2000
[72]李福寿.电力系统过电压计算[M].北京：水利电力出版社,1998
[73]文习山,彭向阳,解广润.架空配电线路感应雷电过电压的数值计算[J].中国电机工程学报,1998,18(4)：299-301
[74]何平,蓝磊,文习山,等.关于架空线路感应过电压的计算问题[J].高电压技术,1999,25(2)：65-68
[75]莫付江,陈允平,阮江军.架空输电线路雷击感应过电压耦合机理及计算方法分析[J].电网技术,2005,29(6)：72-77
[76]文武.感应雷电磁干扰及其防护研究[D].博士论文,武汉大学,湖北,中国,2004.
[77]王希,王顺超,何金良,等.10kV配电线路的雷电感应过电压特性[J].高电压技术,2011,37(3)：599-605
[78]王希,王顺超,何金良,等.安装避雷器后10kV配电线路的雷电感应过电压特性[J].电网技术,2012,36(7)：149-154
[79]Morched A, Gustavsen B, Tartibi M. A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables[J]. IEEE Transactions on Power Delivery,1999,14(3):1032-1038
[80]张喜乐,梁贵书,董华英,等.变压器绕组的特快速暂态建模[J].电工技术学报,2007,22(3)：55-59
[81]张重远,徐志钮,律方成,等.电压互感器的高频无源电路模型[J].电工技术学报,2012,27(4)：77-82
[82]Gustavsen B, Semlyen A. Rational approximation of frequency domain responses by vector fitting[J]. IEEE Transactions on Power Delivery,1999,14(3):1052-1061
[83]Semlyen A, Gustavsen B. Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices[J]. Circuits, Systems and Signal Processing,2000,19(6):549-566
[84]Gustavsen B, Semlyen A. Enforcing passivity for admittance matrices approximated by rational functions[J]. IEEE Transactions on Power Systems,2001, 16(1):97-104
[85]Gustavsen B. Computer code for rational approximation of frequency dependent admittance matrices[J]. IEEE Transactions on Power Delivery,2002,17(4): 1093-1098
[86]Semlyen A, Gustavsen B. A robust approach for system identification in the frequency domain[J]. IEEE Transactions on Power Delivery,2004,19(3): 1167-1173
[87]Elwakil A S. Fractional-order circuits and systems:An emerging interdisciplinary research area[J]. IEEE Circuits and Systems Magazine,2010,10(4):40-50
[88]Vorperian V. A fractal model of anomalous losses in ferromagnetic materials[C]. Power Electronics Specialists Conference,1992. PESC'92 Record.,23rd Annual IEEE. IEEE,1992:1277-1283
[89]Mahon P J, Paul G L, Keshishian S M, et al. Measurement and modelling of the high-power performance of carbon-based supercapacitors[J]. Journal of power sources,2000,91(1):68-76
[90]Cugnet M, Sabatier J, Laruelle S, et al. On lead-acid-battery resistance and cranking-capability estimation[J]. IEEE Transactions on Industrial Electronics, 2010,57(3):909-917
[91]周激流,蒲亦非,廖科.分数阶微积分原理及其在现代信号分析与处理中的应用[M].北京：科学出版社,2010
[92]Tenreiro Machado J A, Jesus I S, Galhano A, et al. Fractional order electromagnetics[J]. Signal Processing,2006,86(10):2637-2644
[93]Monje C A, Chen Y, Vinagre B M, et al. Fractional-order systems and controls: fundamentals and applications[M]. Springer,2010
[94]汪纪锋.分数阶系统控制性能分析[M].北京：电子工业出版社,2010
[95]姚舜才,潘宏侠.粒子群优化同步电机分数阶鲁棒励磁控制器[J].中国电机工程学报,2010,30(21)：91-97
[96]高心.分数阶动力学系统的混沌、控制和同步的研究[D].博士论文,电子科技大学,西安,2005
[97]Kamath A K, Gandhi J R, Bohra A S, et al. Modeling of transformer characteristics using fractional order transfer functions[C]. IEEE International Conference on Control and Automation,2009:2123-2128
[98]Riu D, Guerin P, Retiere N. Transformer modelling by half-order systems[J]. EPE'03. Toulouse,2003
[99]朱呈祥,邹云.分数阶控制研究综述[J].控制与决策,2009,24(2)：161-169.
[100]Mansouri R, Bettayeb M, Djamah T, et al. Vector Fitting fractional system identification using particle swarm optimization[J]. Applied Mathematics and Computation,2008,206(2):510-520
[101]Radwan A G, Soliman A M, Elwakil A S, et al. On the stability of linear systems with fractional-order elements[J]. Chaos, Solitons & Fractals,2009,40(5): 2317-2328
[102]Brune O. Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency[D]. PhD Thesis, Massachusetts Institute of Technology,1931
[103]Brian D. O. Anderson, Sumeth Vongpanitlerd. Network Analysis and Synthesis-A Modern Systems Theory Approach [M]. Prentice-Hall, Inc, Englewood Cliffs, New Jersey,1973
[104]Bakshi A. V., Bakshi U. A.. Network Theory[M]. Pune:Technical Publications, 2008
[105]Wing O. Classical circuit theory[M]. Berlin:Springer,2008
[106]Ametani A. A general formulation of impedance and admittance of cables[J]. IEEE Transactions on Power Apparatus and Systems,1980 (3):902-910
[107]Wedepohl L M, Wilcox D J. Transient analysis of underground power-transmission systems. System-model and wave-propagation characteristics[C]. Proceedings of the Institution of Electrical Engineers,1973,120(2):253-260
[108]吴维韩,张芳榴.电力系统过电压数值计算[M].北京：科学技术出版社,1989
[109]Tesche F M, Ianoz M, Karlsson T. EMC analysis methods and computational models[M]. Wiley-Interscience,1996
[110]Agrawal A K, Scott L D, Fowles H M. Experimental characterization of multiconductor transmission lines in the frequency domain[J]. IEEE Transactions on Electromagnetic Compatibility,1979 (1):20-27
[111]李莉,万里兮.多导体传输线互耦实验研究[J].电波科学学报,1999,14(2)：166-171
[112]齐磊.变电站瞬态电磁场对二次电缆耦合机理的研究[D].博士论文,华北电力大学,河北,中国,2006
[113]Marti J R. Accuarte modelling of frequency-dependent transmission lines in electromagnetic transient simulations[J]. IEEE Transactions on Power Apparatus and Systems,1982 (1):147-157
[114]Marti L. Simulation of transients in underground cables with frequency dependent modal transformation matrix[J]. IEEE Transactions on Power Delivery,1988, 3(3):1099-1110
[115]Noda T, Nagaoka N, Ametani A. Phase domain modeling of frequency-dependent transmission lines by means of an ARMA model [J]. IEEE Transactions on Power Delivery,1996,11(1):401-411
[116]B Gustavsen, A Semlyen. Simulation of transmission lines transients using vector fitting and modal decomposition[J]. IEEE Transactions on Power Delivery,1998, 13(2):605-614
[117]Petrache E, Rachidi F, Paolone M, et al. Lightning induced disturbances in buried cables-Part I:Theory[J]. IEEE Transactions on Electromagnetic Compatibility, 2005,47(3):498-508
[118]Paolone M, Petrache E, Rachidi F, et al. Lightning induced disturbances in buried cables-Part II:Experiment and model validation[J]. IEEE Transactions on Electromagnetic Compatibility,2005,47(3):509-520
[119]Yang B, Zhou B H, Chen B, et al. Numerical Study of Lightning-Induced Currents on Buried Cables and Shield Wire Protection Method[J]. IEEE Transactions on Electromagnetic Compatibility,2012,54(2):323-331
[120]Henriksen T, Gustavsen B, Balog G, et al. Maximum lightning overvoltage along a cable protected by surge arresters[J]. IEEE Transactions on Power Delivery,2005, 20(2):859-866
[121]Sarajcev P. Assessment of lightning stroke incidence to underground power cables[C]. Software, Telecommunications and Computer Networks (SoftCOM), 2010 International Conference on. IEEE,2010:102-106
[122]Bruce C E R, Golde R H. The lightning discharge [J]. Journal of the Institution of Electrical Engineers-Part II:Power Engineering,1941,88(6):487-520
[123]张明霞.雷电电磁场计算方法及沿地表传播特性的研究[D].博士论文,华北电力大学,北京,中国,2009
[124]Moini R, Rakov V A, Uman M A, et al. An antenna theory model for the lightning return stroke[C]. Proceeding 12th International Zurich Symposium Electromagnetic Compatibility,1997:149-152
[125]M.A.Uman, D.K.Melain, E.P.Krider. The electromagnetic radiation from a finite antenna. American Journal of physics.1975,43(1):33-35
[126]Uman M A, McLain D K. Magnetic field of lightning return stroke [J]. Journal of Geophysical Research,1969,74(28):6899-6910
[127]Rakov V A, Dulzon A A. Calculated electromagnetic fields of lightning return stroke[J]. Tekh. Elektrodinam,1987,1:87-89
[128]Nucci C A, Mazzetti C, Rachidi F, et al. On lightning return stroke models for LEMP calculations[C].19th International Conference on Lightning Protection, Graz,1988:223-228
[129]Rachidi F, Nucci C A. On the Master, Uman, Lin, Standler and the modified transmission line lightning return stroke current models[J]. Journal of Geophysical Research,1990,95(D12):20389-20393
[130]Heidler F. Traveling current source model for LEMP calculation[C]. Proc.6th Int. Zurich Symp. Electromagn. Compat.1985:157-162
[131]A. Sommerfeld. Uber die Ausbreitung derWellen in der drahtlosen Telegraphie[J]. Annata Physics.,1909,28(4):665-736
[132]A. Sommerfeld. Partial Differential Equations in Physics[M]. NewYork:Academic, 1949 [33]Cooray V. Horizontal fields generated by return strokes[J]. Radio Science,1992, 27(4):529-537
[134]Rubinstein M. An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate, and long range[J]. IEEE Transactions on Electromagnetic Compatibility,1996,38(3):531-535
[135]Cooray V. Some considerations on the Cooray-Rubinstein formulationused in deriving the horizontal electric field of lightning return strokes [J]. IEEE Transactions on Electromagnetic Compatibility,2002,44(4):560-566
[136]Barbosa C F, Paulino J O S. An approximate time-domain formula for the calculation of the horizontal electric field from lightning[J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(3):593-601
[137]Nakhla N M, Dounavis A, Achar R, et al. DEPACT:Delay extraction-based passive compact transmission-line macromodeling algorithm[J]. IEEE Transactions on Advanced Packaging,2005,28(1):13-23
[138]Takashima T. Calculation of Complex Fields in Conducting Media[J]. IEEE Transactions on Electric Insulation,1982, V El-15(1):1-7.
[139]黄红瑕.复杂媒质中瞬态电磁场快速算法的研究[D].博士论文,华北电力大学,河北,中国,2011
[140]Ruehii A E. Inductance calculations in a complex integrated circuit environment [J]. IBM Journal of Research and Development,1972,16(5):470-481
[141]Yang K, Yin W Y, Shi J, et al. A study of on-chip stacked multiloop spiral inductors[J]. IEEE Transactions on Electron Devices,2008,55(11):3236-3245
[142]Restle P J, Ruehli A E, Walker S G, et al. Full-wave PEEC time-domain method for the modeling of on-chip interconnects[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,2001,20(7):877-886
[143]Milsom R F, Scott K J, Clark G, et al. FACET-a CAE system for RF analogue simulation including layout[C]. Design Automation,1989.26th Conference on. IEEE,1989:622-625
[144]Wang S, He J, Zhang B, et al. A time-domain multiport model of thin-wire system for lightning transient simulation[J]. IEEE Transactions on Electromagnetic Compatibility,2010,52(1):128-135
[145]Ruehii A E, Pinello W P, Cangellaris A C. Comparison of differential and common mode response for short transmission line using PEEC models[C]. Electrical Performance of Electronic Packaging, IEEE 5th Topical Meeting.1996:169-171
[146]Wang S, He J, Zhang B, et al. Time-Domain Simulation of Small Thin-Wire Structures Above and Buried in Lossy Ground Using Generalized Modified Mesh Current Method[J]. IEEE Transactions on Power Delivery,2011,26(1):369-377
[147]Yutthagowith P, Ametani A, Nagaoka N, et al. Application of the partial element equivalent circuit method to analysis of transient potential rises in grounding systems[J]. IEEE Transactions on Electromagnetic Compatibility,2011,53(3): 726-736
[148]Clayton R. Paul. Inductance:Loop and Partial[M]. New Jersey:John Willy & Sons, 2011:195-245
[149]De Conti A, Visacro S, Soares A, et al. Revision, extension, and validation of Jordan's formula to calculate the surge impedance of vertical conductors[J]. IEEE Transactions on Electromagnetic Compatibility,2006,48(3):530-536
[150]Grcev L D. Computer analysis of transient voltages in large grounding systems[J]. IEEE Transactions on Power Delivery,1996,11(2):815-823
[151]Mousa A, Srivastava K D. A revised electrogeometric model for the termination of lightning strokes on ground objects[C]. NOAA, International Aerospace and Ground Conference on Lightning and Static Electricity,1988:342-352
[152]IEEE Working Group on the Lightning Performance of Distribution Lines. IEEE Std.1410-2004 Guide for improving the lightning performance of electric power overhead distribution lines [S]. Transmission and Distribution Committee of the IEEE Power Engineering Society,2004
[153]电力工业部电力科学研究院高压研究所.DL/T 620-1997交流电气装置的过电压保护与绝缘配合[S].北京：行业标准-电力(CN-DL),1997
[154]Brayton R K, Gustavson F G, Hachtel G D. A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas[Jj. Proceedings of the IEEE,1972,60(1):98-108
[155]杨华中,罗嵘,汪蕙.电子电路的计算机辅助分析与设计方法(第2版)[M].北京：清华大学出版社,2008
[156]Levy E C. Complex curve fitting[J]. IRE Transactions on Automatic Control,1959, AC-4:37-44
[157]Kilbas, Anatoly A, Srivastava, Hari M, et al. Theory and applications of fractional differential equations[M]. Amsterdam and Boston:Elsevier Press,2006
[158]Podlubny I. Fractional differential equations[M]. New York:Academic Press,1999
[159]GB/T 12706.2-2008,额定电压1kV(Um=1.2kV)到35kV(Um=40.5kV)挤包绝缘电力电缆及附件第2部分：额定电压6kV(Um=7.2kV)到30kV(Um=36kV)电缆[S].北京：国家标准,2008
[160]GB50217-2007.电力工程电缆设计规范[S].北京：国家标准,2008
[161]Delfino F, Procopio R, Rossi M, et al. An algorithm for the exact evaluation of the underground lightning electromagnetic fields[J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(2):401-411
[2]苏冬冬.京沪高铁接触网防雷问题的探讨[J].上海铁道科技,2011(4)：52-53
[3]李学伟.高速铁路概论[M].北京：中国铁道出版社,2012.5
[4]陈纪纲.无砟轨道线路接触网防雷技术研究[J].铁道工程学报,2007,S1：422-425
[5]刘明光.接触网受雷击过电压影响及其分析计算[J].铁道学报,1997,03：48-51
[6]于增.接触网防雷技术研究[J].铁道工程学报,2002,01：89-94
[7]范海江,罗健.铁路客运专线接触网防雷研究[J].铁道工程学报,2008,119(8)：80-83
[8]周歧斌,边晓燕,傅正财.香港地区电气化铁路直流电力牵引系统电力电缆的雷电过电压分析[J].中国铁道科学,2009,30(4)：91-95
[9]李康,刘家军,卓元志,等.高速电气化铁路接触网防雷研究[J].电网与清洁能源,2012,28(7)：39-45
[10]张鹏远.电气化铁道牵引网的防雷保护研究[D].硕士论文,西南交通大学,四川,中国,2010
[11]赵海军,陈维江,王彦利,等.城市轨道交通架空接触网雷电防护[J].电气化铁道,2008,28(5)：23-27
[12]Theethayi N, Liu Y, Montano R, et al. A theoretical study on the consequence of a direct lightning strike to electrified railway system in Sweden[J]. Electric power systems research,2005,74(2):267-280
[13]Theethayi N, Liu Y, Montano R, et al. Modeling direct lightning attachment to electrified railway system in Sweden[C].2003 IEEE Power Tech Conference Proceedings, Bologna,2003:4-7
[14]Theethayi N. Electromagnetic interference in distributed outdoor electrical systems, with an emphasis on lightning interaction with electrified railway network[D]. PhD Thesis, Uppsala University, Uppsala, Sweden,2005
[15]Filippone F, Mariscotti A, Pozzobon P. The internal impedance of traction rails for DC railways in the 1-100 kHz frequency range[J]. IEEE Transactions on Instrumentation and Measurement,2006,55(5):1616-1619
[16]Ferrari P, Pozzobon P. Railway lines models for impedance evaluation [C], Harmonics and Quality of Power Proceedings,1998. Proceedings.8th International Conference On. IEEE,1998,2:641-646
[17]Carpenter D C, Hill R J. FEM applied to railroad track electrical impedance and adjacent track crosstalk modelling[C]. Railroad Conference,1991, Proceedings of the 1991 IEEE/ASME Joint. IEEE,1991:87-95
[18]Hill R. J. and Carpenter D. C.. Rail track distributed transmission line impedance and admittance:theoretical modeling and experimental results[J]. IEEE Transactions on Vehicular Technology,1993,42(2):225-241
[19]Mariscotti A, Pozzobon P. Measurement of the internal impedance of traction rails at 50 Hz[J]. IEEE Transactions on Instrumentation and Measurement,2000,49(2): 294-299
[20]Mariscotti A, Pozzobon P. Measurement of the internal impedance of traction rails at audio frequency [J]. IEEE Transactions on Instrumentation and Measurement, 2004,53(3):792-797
[21]Wang Y J, Wang J H. Modeling of frequency-dependent impedance of the third rail used in traction power systems[J]. IEEE Transactions on Power Delivery,2000, 15(2):750-755
[22]Wang Y J, Tsai Y L. Calculation of the frequency-dependent impedance of rail tracks using a four-parameter equivalent tubular conductor model [J]. IEEE Transactions on Power Delivery,2004,19(3):1142-1147
[23]Wagner K W. Elektromagnetische Ausgleichsvorgange in Freileitungen und Kabeln[M]. B. G. Teubner,1908
[24]V. Aigner. Induzierte Blitzuberspannunen und ihre beziehung zumruck wartigen[J]. Uberschlag,1935, ETZ 56:497-500
[25]Wagner C F, McCann G D. Induced voltages on transmission lines[J]. Transactions of the American Institute of Electrical Engineers,1942,61(12):916-930
[26]S. Szpor. A new theory of the induced overvoltages[R]. CIGRE Report 308,1948.
[27]Lundholm R. Induced overvoltage-surges on transmission lines and their bearing on the lightning performance at medium voltage networks [M]. Gumperts Forlag, 1957
[28]Rusck S. Induced-lightning overvoltages on power transmission lines with special reference to the overvoltage protection of low voltage networks[M]. Transactions of Royal Institute of Technology,1958
[29]Piantini A, Janiszewski J M. Lightning-induced voltages on overhead lines—Application of the extended rusck model [J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(3):548-558
[30]Silva J P, Araujo A E A, Paulino J O S. Calculation of lightning-induced voltages with Rusck's method in EMTP—part Ⅱ:effects of lightning parameter variations[J]. Electric Power Systems Research,2002,61(2):133-137
[31]Darveniza M. A practical extension of Rusck's formula for maximum lightning-induced voltages that accounts for ground resistivity [J]. IEEE Transactions on Power Delivery,2007,22(1):605-612
[32]Chowdhuri P, Gross E T B. Voltage surges induced on overhead lines by lightning strokes[C]. Proceedings of the Institution of Electrical Engineers. IET Digital Library,1967,114(12):1899-1907
[33]Liew A C, Mar S C. Extension of the Chowdhuri-Gross model for lightning induced voltage on overhead lines[J]. IEEE Transactions on Power Delivery,1986, 1(2):240-247
[34]Hoidalen H K. Analytical formulation of lightning-induced voltages on multiconductor overhead lines above lossy ground[J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(1):92-100
[35]Taylor C, Satterwhite R, Harrison Jr C. The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field[J]. IEEE Transactions on Antennas and Propagation,1965,13(6):987-989
[36]Agrawal A K, Price H J, Gurbaxani S H. Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field [J]. IEEE Transactions on Electromagnetic Compatibility,1980 (2):119-129
[37]Rachidi F. Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field[J]. IEEE Transactions on Electromagnetic Compatibility 1993,35(3):404-407
[38]Master M J, Uman M A. Lightning induced voltages on power lines:Theory [J]. IEEE Transactions on Power Apparatus and Systems,1984 (9):2502-2518
[39]Georgiadis N, Rubinstein M, Uman M A, et al. Lightning-induced voltages at both ends of a 448-m power-distribution line[J]. IEEE Transactions on Electromagnetic Compatibility,1992,34(4):451-460
[40]Barker P P, Short T A, Eybert-Berard A R, et al. Induced voltage measurements on an experimental distribution line during nearby rocket triggered lightning flashes [J]. IEEE Transactions on Power Delivery,1996,11(2):980-995
[41]Michishita K, Ishii M, Asakawa A, et al. Voltage induced on a test distribution line by negative winter lightning strokes to a tall structure[J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(1):135-140
[42]Ishii M, Michishita K, Hongo Y, et al. Lightning-induced voltage on an overhead wire dependent on ground conductivity [J]. IEEE Transactions on Power Delivery, 1994,9(1):109-118
[43]Nucci C A, Borghetti A, Piantini A, et al. Lightning-induced voltages on distribution overhead lines:comparison between experimental results from a reduced-scale model and most recent approaches[C]. Proceedings of the 24th International Conference on Lightning Protection,1998:314-320
[44]Nucci C A, Rachidi F, Ianoz M V, et al. Lightning-induced voltages on overhead lines[J]. IEEE Transactions on Electromagnetic Compatibility,1993,35(1): 75-86
[45]K. Agrawal, H. J. Price, and S. H. Gurbaxani. Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field. IEEE Transactions on Electromagnetic Compatibility,1980,22(2):119-129
[46]齐磊.多导体传输线的时域有限差分法研究[D].硕士论文,华北电力大学,河北,中国,2002
[47]卢铁兵.变电站瞬态电磁环境数值预测方法的研究[D].博士论文,华北电力大学,河北,中国,2001
[48]Clayton R.P. Analysis of Multiconductor Transmission Lines[M]. New York:John Wiley and Sons Press,1994
[49]Cooray V. Calculating lightning-induced overvoltages in power lines:A comparison of two coupling models[J]. IEEE Transactions on Electromagnetic Compatibility,1994,36(3):179-182
[50]Nucci C A, Rachidi F, Ianoz M, et al. Comparison of two coupling models for lightning-induced overvoltage calculations[J]. IEEE Transactions on Power Delivery,1995,10(1):330-339
[51]P. Santt. Deuxieme campagne de caracterisation du nouveau moyen d'essaia 1'I.E.M.N du LEHT:l'antetine "Strip-Line", lere partie[J]. EdF, Direction des Etudes et Researches,1990, HM82-1367A
[52]Rachidi F, Nucci C A, Ianoz M, et al. Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields[J]. IEEE Transactions on Power Delivery,1997,12(3):1404-1411
[53]Rachidi F, Nucci C A, Ianoz M. Transient analysis of multiconductor lines above a lossy ground[J]. IEEE Transactions on Power Delivery,1999,14(1):294-302
[54]Paolone M, Nucci C A, Rachidi F. A new finite difference time domain scheme for the evaluation of lightning induced overvoltages on multiconductor overhead lines[C]. Proceeding of the 5th International Conference on Power System Transient,2001:596-602
[55]Paolone M. Modeling of lightning-induced voltages on distribution networks for the solution of power quality problems, and relevant implementation in a transient program[D]. PhD Thesis, Department of Electrical Engineering Bologna, University of Bologna, Italy,2001
[56]Nucci C A. Lightning-induced voltages on distribution systems:influence of ground resistivity and system topology[J]. Journal of Lightning Research,2007,1: 148-157
[57]Nucci C A. The lightning induced over-voltage (LIOV) code[C].2000 IEEE Power Engineering Society Winter Meeting,2000:2417-2418
[58]H(?)idalen H. K.. Lightning-induced overvoltages in low-voltage systems[D]. PhD Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1997
[59]Hoidalen H. K. Calculation of lightning-induced overvoltages using MODELS[C]. Proceedings of the International Conference on Power Systems Transients,1999: 359-64
[60]H(?)idalen H K. Calculation of lightning-induced voltages in MODELS including lossy ground effects [C]. Proceedings of the International Conference on Power System Transient (IPST2003), New Orleans,2003:1-6
[61]Borghetti A, Gutierrez J A, Nucci C A, et al. Software tools for the calculation of lightning-induced voltages on complex distribution systems[C]. Proceeding of the 26th International Conference on Lightning Protection.2002:2-6
[62]Montano R, Theethayi N, Cooray V. An Efficient implementation of the Agrawal et al. model for lightning-Induced voltage calculations using circuit simulation software[J]. IEEE Transactions on Circuits and Systems I:Regular Papers,2008, 55(9):2959-2965
[63]Baum C E, Liu T K, Tesche F M. On the analysis of general multiconductor transmission-line networks[J]. Interaction Note.1978,350:467-547
[64]Sheshyekani K, Hesamedin Sadeghi S H, Moini R, et al. Analysis of transmission lines with arrester termination, considering the frequency-dependence of grounding systems[J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(4): 986-994
[65]Tesche F M. Development and use of the BLT equation in the time domain as applied to a coaxial cable[J]. IEEE Transactions on Electromagnetic Compatibility, 2007,49(1):3-11
[66]Tesche F M. On the analysis of a transmission line with nonlinear terminations using the time-dependent BLT equation [J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(2):427-433
[67]Pokharel R K, Ishii M, Baba Y. Numerical electromagnetic analysis of lightning-induced voltage over ground of finite conductivity [J]. IEEE Transactions on Electromagnetic Compatibility,2003,45(4):651-656
[68]Silveira F H, Visacro S, Herrera J, et al. Evaluation of lightning-induced voltages over a lossy ground by the hybrid electromagnetic model [J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(1):156-160
[69]Yutthagowith P, Ametani A, Nagaoka N, et al. Lightning-Induced voltage over lossy ground by a hybrid electromagnetic circuit model method with Cooray-Rubinstein formula[J]. IEEE Transactions on Electromagnetic Compatibility,2009,51(4):975-985
[70]Baba Y, Rakov V A. Voltages induced on an overhead wire by lightning strikes to a nearby tall grounded object[J]. IEEE Transactions on Electromagnetic Compatibility,2006,48(1):212-224
[71]A.Taflove. Computational electrodynamics-the finite-difference time-domain method[M].2nd edition, Artech House,2000
[72]李福寿.电力系统过电压计算[M].北京：水利电力出版社,1998
[73]文习山,彭向阳,解广润.架空配电线路感应雷电过电压的数值计算[J].中国电机工程学报,1998,18(4)：299-301
[74]何平,蓝磊,文习山,等.关于架空线路感应过电压的计算问题[J].高电压技术,1999,25(2)：65-68
[75]莫付江,陈允平,阮江军.架空输电线路雷击感应过电压耦合机理及计算方法分析[J].电网技术,2005,29(6)：72-77
[76]文武.感应雷电磁干扰及其防护研究[D].博士论文,武汉大学,湖北,中国,2004.
[77]王希,王顺超,何金良,等.10kV配电线路的雷电感应过电压特性[J].高电压技术,2011,37(3)：599-605
[78]王希,王顺超,何金良,等.安装避雷器后10kV配电线路的雷电感应过电压特性[J].电网技术,2012,36(7)：149-154
[79]Morched A, Gustavsen B, Tartibi M. A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables[J]. IEEE Transactions on Power Delivery,1999,14(3):1032-1038
[80]张喜乐,梁贵书,董华英,等.变压器绕组的特快速暂态建模[J].电工技术学报,2007,22(3)：55-59
[81]张重远,徐志钮,律方成,等.电压互感器的高频无源电路模型[J].电工技术学报,2012,27(4)：77-82
[82]Gustavsen B, Semlyen A. Rational approximation of frequency domain responses by vector fitting[J]. IEEE Transactions on Power Delivery,1999,14(3):1052-1061
[83]Semlyen A, Gustavsen B. Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices[J]. Circuits, Systems and Signal Processing,2000,19(6):549-566
[84]Gustavsen B, Semlyen A. Enforcing passivity for admittance matrices approximated by rational functions[J]. IEEE Transactions on Power Systems,2001, 16(1):97-104
[85]Gustavsen B. Computer code for rational approximation of frequency dependent admittance matrices[J]. IEEE Transactions on Power Delivery,2002,17(4): 1093-1098
[86]Semlyen A, Gustavsen B. A robust approach for system identification in the frequency domain[J]. IEEE Transactions on Power Delivery,2004,19(3): 1167-1173
[87]Elwakil A S. Fractional-order circuits and systems:An emerging interdisciplinary research area[J]. IEEE Circuits and Systems Magazine,2010,10(4):40-50
[88]Vorperian V. A fractal model of anomalous losses in ferromagnetic materials[C]. Power Electronics Specialists Conference,1992. PESC'92 Record.,23rd Annual IEEE. IEEE,1992:1277-1283
[89]Mahon P J, Paul G L, Keshishian S M, et al. Measurement and modelling of the high-power performance of carbon-based supercapacitors[J]. Journal of power sources,2000,91(1):68-76
[90]Cugnet M, Sabatier J, Laruelle S, et al. On lead-acid-battery resistance and cranking-capability estimation[J]. IEEE Transactions on Industrial Electronics, 2010,57(3):909-917
[91]周激流,蒲亦非,廖科.分数阶微积分原理及其在现代信号分析与处理中的应用[M].北京：科学出版社,2010
[92]Tenreiro Machado J A, Jesus I S, Galhano A, et al. Fractional order electromagnetics[J]. Signal Processing,2006,86(10):2637-2644
[93]Monje C A, Chen Y, Vinagre B M, et al. Fractional-order systems and controls: fundamentals and applications[M]. Springer,2010
[94]汪纪锋.分数阶系统控制性能分析[M].北京：电子工业出版社,2010
[95]姚舜才,潘宏侠.粒子群优化同步电机分数阶鲁棒励磁控制器[J].中国电机工程学报,2010,30(21)：91-97
[96]高心.分数阶动力学系统的混沌、控制和同步的研究[D].博士论文,电子科技大学,西安,2005
[97]Kamath A K, Gandhi J R, Bohra A S, et al. Modeling of transformer characteristics using fractional order transfer functions[C]. IEEE International Conference on Control and Automation,2009:2123-2128
[98]Riu D, Guerin P, Retiere N. Transformer modelling by half-order systems[J]. EPE'03. Toulouse,2003
[99]朱呈祥,邹云.分数阶控制研究综述[J].控制与决策,2009,24(2)：161-169.
[100]Mansouri R, Bettayeb M, Djamah T, et al. Vector Fitting fractional system identification using particle swarm optimization[J]. Applied Mathematics and Computation,2008,206(2):510-520
[101]Radwan A G, Soliman A M, Elwakil A S, et al. On the stability of linear systems with fractional-order elements[J]. Chaos, Solitons & Fractals,2009,40(5): 2317-2328
[102]Brune O. Synthesis of a finite two-terminal network whose driving-point impedance is a prescribed function of frequency[D]. PhD Thesis, Massachusetts Institute of Technology,1931
[103]Brian D. O. Anderson, Sumeth Vongpanitlerd. Network Analysis and Synthesis-A Modern Systems Theory Approach [M]. Prentice-Hall, Inc, Englewood Cliffs, New Jersey,1973
[104]Bakshi A. V., Bakshi U. A.. Network Theory[M]. Pune:Technical Publications, 2008
[105]Wing O. Classical circuit theory[M]. Berlin:Springer,2008
[106]Ametani A. A general formulation of impedance and admittance of cables[J]. IEEE Transactions on Power Apparatus and Systems,1980 (3):902-910
[107]Wedepohl L M, Wilcox D J. Transient analysis of underground power-transmission systems. System-model and wave-propagation characteristics[C]. Proceedings of the Institution of Electrical Engineers,1973,120(2):253-260
[108]吴维韩,张芳榴.电力系统过电压数值计算[M].北京：科学技术出版社,1989
[109]Tesche F M, Ianoz M, Karlsson T. EMC analysis methods and computational models[M]. Wiley-Interscience,1996
[110]Agrawal A K, Scott L D, Fowles H M. Experimental characterization of multiconductor transmission lines in the frequency domain[J]. IEEE Transactions on Electromagnetic Compatibility,1979 (1):20-27
[111]李莉,万里兮.多导体传输线互耦实验研究[J].电波科学学报,1999,14(2)：166-171
[112]齐磊.变电站瞬态电磁场对二次电缆耦合机理的研究[D].博士论文,华北电力大学,河北,中国,2006
[113]Marti J R. Accuarte modelling of frequency-dependent transmission lines in electromagnetic transient simulations[J]. IEEE Transactions on Power Apparatus and Systems,1982 (1):147-157
[114]Marti L. Simulation of transients in underground cables with frequency dependent modal transformation matrix[J]. IEEE Transactions on Power Delivery,1988, 3(3):1099-1110
[115]Noda T, Nagaoka N, Ametani A. Phase domain modeling of frequency-dependent transmission lines by means of an ARMA model [J]. IEEE Transactions on Power Delivery,1996,11(1):401-411
[116]B Gustavsen, A Semlyen. Simulation of transmission lines transients using vector fitting and modal decomposition[J]. IEEE Transactions on Power Delivery,1998, 13(2):605-614
[117]Petrache E, Rachidi F, Paolone M, et al. Lightning induced disturbances in buried cables-Part I:Theory[J]. IEEE Transactions on Electromagnetic Compatibility, 2005,47(3):498-508
[118]Paolone M, Petrache E, Rachidi F, et al. Lightning induced disturbances in buried cables-Part II:Experiment and model validation[J]. IEEE Transactions on Electromagnetic Compatibility,2005,47(3):509-520
[119]Yang B, Zhou B H, Chen B, et al. Numerical Study of Lightning-Induced Currents on Buried Cables and Shield Wire Protection Method[J]. IEEE Transactions on Electromagnetic Compatibility,2012,54(2):323-331
[120]Henriksen T, Gustavsen B, Balog G, et al. Maximum lightning overvoltage along a cable protected by surge arresters[J]. IEEE Transactions on Power Delivery,2005, 20(2):859-866
[121]Sarajcev P. Assessment of lightning stroke incidence to underground power cables[C]. Software, Telecommunications and Computer Networks (SoftCOM), 2010 International Conference on. IEEE,2010:102-106
[122]Bruce C E R, Golde R H. The lightning discharge [J]. Journal of the Institution of Electrical Engineers-Part II:Power Engineering,1941,88(6):487-520
[123]张明霞.雷电电磁场计算方法及沿地表传播特性的研究[D].博士论文,华北电力大学,北京,中国,2009
[124]Moini R, Rakov V A, Uman M A, et al. An antenna theory model for the lightning return stroke[C]. Proceeding 12th International Zurich Symposium Electromagnetic Compatibility,1997:149-152
[125]M.A.Uman, D.K.Melain, E.P.Krider. The electromagnetic radiation from a finite antenna. American Journal of physics.1975,43(1):33-35
[126]Uman M A, McLain D K. Magnetic field of lightning return stroke [J]. Journal of Geophysical Research,1969,74(28):6899-6910
[127]Rakov V A, Dulzon A A. Calculated electromagnetic fields of lightning return stroke[J]. Tekh. Elektrodinam,1987,1:87-89
[128]Nucci C A, Mazzetti C, Rachidi F, et al. On lightning return stroke models for LEMP calculations[C].19th International Conference on Lightning Protection, Graz,1988:223-228
[129]Rachidi F, Nucci C A. On the Master, Uman, Lin, Standler and the modified transmission line lightning return stroke current models[J]. Journal of Geophysical Research,1990,95(D12):20389-20393
[130]Heidler F. Traveling current source model for LEMP calculation[C]. Proc.6th Int. Zurich Symp. Electromagn. Compat.1985:157-162
[131]A. Sommerfeld. Uber die Ausbreitung derWellen in der drahtlosen Telegraphie[J]. Annata Physics.,1909,28(4):665-736
[132]A. Sommerfeld. Partial Differential Equations in Physics[M]. NewYork:Academic, 1949 [33]Cooray V. Horizontal fields generated by return strokes[J]. Radio Science,1992, 27(4):529-537
[134]Rubinstein M. An approximate formula for the calculation of the horizontal electric field from lightning at close, intermediate, and long range[J]. IEEE Transactions on Electromagnetic Compatibility,1996,38(3):531-535
[135]Cooray V. Some considerations on the Cooray-Rubinstein formulationused in deriving the horizontal electric field of lightning return strokes [J]. IEEE Transactions on Electromagnetic Compatibility,2002,44(4):560-566
[136]Barbosa C F, Paulino J O S. An approximate time-domain formula for the calculation of the horizontal electric field from lightning[J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(3):593-601
[137]Nakhla N M, Dounavis A, Achar R, et al. DEPACT:Delay extraction-based passive compact transmission-line macromodeling algorithm[J]. IEEE Transactions on Advanced Packaging,2005,28(1):13-23
[138]Takashima T. Calculation of Complex Fields in Conducting Media[J]. IEEE Transactions on Electric Insulation,1982, V El-15(1):1-7.
[139]黄红瑕.复杂媒质中瞬态电磁场快速算法的研究[D].博士论文,华北电力大学,河北,中国,2011
[140]Ruehii A E. Inductance calculations in a complex integrated circuit environment [J]. IBM Journal of Research and Development,1972,16(5):470-481
[141]Yang K, Yin W Y, Shi J, et al. A study of on-chip stacked multiloop spiral inductors[J]. IEEE Transactions on Electron Devices,2008,55(11):3236-3245
[142]Restle P J, Ruehli A E, Walker S G, et al. Full-wave PEEC time-domain method for the modeling of on-chip interconnects[J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,2001,20(7):877-886
[143]Milsom R F, Scott K J, Clark G, et al. FACET-a CAE system for RF analogue simulation including layout[C]. Design Automation,1989.26th Conference on. IEEE,1989:622-625
[144]Wang S, He J, Zhang B, et al. A time-domain multiport model of thin-wire system for lightning transient simulation[J]. IEEE Transactions on Electromagnetic Compatibility,2010,52(1):128-135
[145]Ruehii A E, Pinello W P, Cangellaris A C. Comparison of differential and common mode response for short transmission line using PEEC models[C]. Electrical Performance of Electronic Packaging, IEEE 5th Topical Meeting.1996:169-171
[146]Wang S, He J, Zhang B, et al. Time-Domain Simulation of Small Thin-Wire Structures Above and Buried in Lossy Ground Using Generalized Modified Mesh Current Method[J]. IEEE Transactions on Power Delivery,2011,26(1):369-377
[147]Yutthagowith P, Ametani A, Nagaoka N, et al. Application of the partial element equivalent circuit method to analysis of transient potential rises in grounding systems[J]. IEEE Transactions on Electromagnetic Compatibility,2011,53(3): 726-736
[148]Clayton R. Paul. Inductance:Loop and Partial[M]. New Jersey:John Willy & Sons, 2011:195-245
[149]De Conti A, Visacro S, Soares A, et al. Revision, extension, and validation of Jordan's formula to calculate the surge impedance of vertical conductors[J]. IEEE Transactions on Electromagnetic Compatibility,2006,48(3):530-536
[150]Grcev L D. Computer analysis of transient voltages in large grounding systems[J]. IEEE Transactions on Power Delivery,1996,11(2):815-823
[151]Mousa A, Srivastava K D. A revised electrogeometric model for the termination of lightning strokes on ground objects[C]. NOAA, International Aerospace and Ground Conference on Lightning and Static Electricity,1988:342-352
[152]IEEE Working Group on the Lightning Performance of Distribution Lines. IEEE Std.1410-2004 Guide for improving the lightning performance of electric power overhead distribution lines [S]. Transmission and Distribution Committee of the IEEE Power Engineering Society,2004
[153]电力工业部电力科学研究院高压研究所.DL/T 620-1997交流电气装置的过电压保护与绝缘配合[S].北京：行业标准-电力(CN-DL),1997
[154]Brayton R K, Gustavson F G, Hachtel G D. A new efficient algorithm for solving differential-algebraic systems using implicit backward differentiation formulas[Jj. Proceedings of the IEEE,1972,60(1):98-108
[155]杨华中,罗嵘,汪蕙.电子电路的计算机辅助分析与设计方法(第2版)[M].北京：清华大学出版社,2008
[156]Levy E C. Complex curve fitting[J]. IRE Transactions on Automatic Control,1959, AC-4:37-44
[157]Kilbas, Anatoly A, Srivastava, Hari M, et al. Theory and applications of fractional differential equations[M]. Amsterdam and Boston:Elsevier Press,2006
[158]Podlubny I. Fractional differential equations[M]. New York:Academic Press,1999
[159]GB/T 12706.2-2008,额定电压1kV(Um=1.2kV)到35kV(Um=40.5kV)挤包绝缘电力电缆及附件第2部分：额定电压6kV(Um=7.2kV)到30kV(Um=36kV)电缆[S].北京：国家标准,2008
[160]GB50217-2007.电力工程电缆设计规范[S].北京：国家标准,2008
[161]Delfino F, Procopio R, Rossi M, et al. An algorithm for the exact evaluation of the underground lightning electromagnetic fields[J]. IEEE Transactions on Electromagnetic Compatibility,2007,49(2):401-411