冲击电压下棒—板长空气间隙放电中空间电场的计算研究
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摘要
由于对气体放电理论的研究涉及多学科交叉以及受到测量气体放电过程中各种参数所需的先进仪器的制约,到目前为止,在气体放电理论很不完善的情况下,高电压与绝缘技术研究还是一门以试验为基础的学科。模拟试验和真型试验不仅都存在各自的不足,而且耗费巨大的人力和物力,特别是超特高压输变电系统外绝缘的选择涉及各种复杂环境下的长空气间隙和绝缘子长串的放电特性,如果仍依赖于全电压、全尺寸下各种复杂环境中的试验,不仅很不经济,而且很难找到放电过程的普遍规律。因此,借助有限的实验条件研究结果,采用仿真计算方法对超特高压输变电系统外绝缘放电开展研究,会推动以放电理论为基础的高电压与外绝缘学科从半物理到物理研究的方向发展,而且对超特高压外绝缘的设计提供可靠的理论依据。
本文在国内外已有研究基础上,采用有限元数值计算方法对超-特高压输电系统中面临的空气间隙放电问题建立了仿真模型,并对整个放电物理过程进行了计算研究,其主要结果如下:
①流注起始放电时空间中的各离子浓度达到108个.cm-3,当先导放电形成后,流注头的正离子和电子浓度达到1012个.cm-3,此时,各种空间电荷产生的电场与外加电压产生的电场对总体空间电场的影响作用相当。
②空间电场影响空气电离率а,从而影响到电子和正离子在空间中的浓度分布,离子浓度变化又会影响到空间电场大小,而附着率η、结合率β和解离率γ对电场影响较小,γ过程可忽略。
③在等离子体电晕云模型中,不同电晕云长度对空间电场分布的影响都具有相同规律,其电晕云发展条件是头部电场达到11kV.cm-1,内部最低电场达到3kV.cm-1。
④在外加500kV、250/2500μs操作波时,先导通道内的正离子和电子浓度将达到1013～1015个.cm-3,电场约为1～2kV.cm-1,先导起始时间在400μs左右,并以3×104m.s-1速度从棒电极向板电极传播。间隙击穿时先导通道长度占整个空气间隙长度的3/5。
本文建立的等离子体电晕云模型和先导发展模型都能较好的反映长空气间隙的放电过程。通过对先导放电过程的仿真计算分析,得出了先导起始条件和空气击穿条件。
For the cross of multi-disciplinary and the lack of advanced apparatus to measure the parameters of air discharge, the research on high-voltage and insulation technology was mainly based on experiments. The simulation experiment and real experiment both have many deficiency and will take many human power and financial resources, especially for the external insulation research of the ultra-high voltage (UHV) and extra-high voltage (EHV) which will involve the discharge of long air gap and long insulator string under the complex environment, if the research was developed on the real voltage and real dimension it would cost much but found the rule of discharge. For the reasons above we take the method of emulation to research the external insulation of UHV (EHV) and this will accelerate the discipline of high-voltage and insulation from semi-physical research into physical research.
In this article, the air gap discharge model was established in finite element method (FEM), the whole process of air discharge was calculated and analyzing, the results obtained as follows:
①The space charge density of electrons and irons had to reach 108cm-3 to start the stream discharge and reached 1012cm-3 when the leader discharge starting, at this time the efforts of space charge and applied voltage to the space electric field were correspondence.
②The space electric field influences the ionizing rateаand further influences the space charge density, at the same time the variation of space charge density could change the space electric field distribution in air gap. But the attachment rateη,the association rateβand dissociation constantγhave small influences on electric field distribution.
③In the plasma-corona cloud model, the efforts of different length corona cloud to space electric field are regular just when the electric field in head of the corona reached 11kV.cm-1 and 3kV.cm-1 inner, the corona can develop forward. The humidity of air influences the breakdown voltage deeply and the lower humidness the lower breakdown voltage.
④In the leader development model, when applied 500kV、250/2500μs switching over-voltage, the ion density in the leader channel can reach 1013～1015cm-3 and the electric field reach 1～2kV.cm-1, the time to start leader discharge is about 400μs and the velocity of the leader development is about 3×104m.s-1 from rod electrode to plane electrode. The leader channel takes 3/5 of the whole gap, it’s very approach to the tested value 2/3.
Both of the plasma-corona model and the leader growth model in this article can describe the long air gap discharge process perfectly. By the emulation and calculation of the process of leader discharge, we gained the starting condition of the leader and the breakdown condition of the long air gap.
本文在国内外已有研究基础上,采用有限元数值计算方法对超-特高压输电系统中面临的空气间隙放电问题建立了仿真模型,并对整个放电物理过程进行了计算研究,其主要结果如下:
①流注起始放电时空间中的各离子浓度达到108个.cm-3,当先导放电形成后,流注头的正离子和电子浓度达到1012个.cm-3,此时,各种空间电荷产生的电场与外加电压产生的电场对总体空间电场的影响作用相当。
②空间电场影响空气电离率а,从而影响到电子和正离子在空间中的浓度分布,离子浓度变化又会影响到空间电场大小,而附着率η、结合率β和解离率γ对电场影响较小,γ过程可忽略。
③在等离子体电晕云模型中,不同电晕云长度对空间电场分布的影响都具有相同规律,其电晕云发展条件是头部电场达到11kV.cm-1,内部最低电场达到3kV.cm-1。
④在外加500kV、250/2500μs操作波时,先导通道内的正离子和电子浓度将达到1013～1015个.cm-3,电场约为1～2kV.cm-1,先导起始时间在400μs左右,并以3×104m.s-1速度从棒电极向板电极传播。间隙击穿时先导通道长度占整个空气间隙长度的3/5。
本文建立的等离子体电晕云模型和先导发展模型都能较好的反映长空气间隙的放电过程。通过对先导放电过程的仿真计算分析,得出了先导起始条件和空气击穿条件。
For the cross of multi-disciplinary and the lack of advanced apparatus to measure the parameters of air discharge, the research on high-voltage and insulation technology was mainly based on experiments. The simulation experiment and real experiment both have many deficiency and will take many human power and financial resources, especially for the external insulation research of the ultra-high voltage (UHV) and extra-high voltage (EHV) which will involve the discharge of long air gap and long insulator string under the complex environment, if the research was developed on the real voltage and real dimension it would cost much but found the rule of discharge. For the reasons above we take the method of emulation to research the external insulation of UHV (EHV) and this will accelerate the discipline of high-voltage and insulation from semi-physical research into physical research.
In this article, the air gap discharge model was established in finite element method (FEM), the whole process of air discharge was calculated and analyzing, the results obtained as follows:
①The space charge density of electrons and irons had to reach 108cm-3 to start the stream discharge and reached 1012cm-3 when the leader discharge starting, at this time the efforts of space charge and applied voltage to the space electric field were correspondence.
②The space electric field influences the ionizing rateаand further influences the space charge density, at the same time the variation of space charge density could change the space electric field distribution in air gap. But the attachment rateη,the association rateβand dissociation constantγhave small influences on electric field distribution.
③In the plasma-corona cloud model, the efforts of different length corona cloud to space electric field are regular just when the electric field in head of the corona reached 11kV.cm-1 and 3kV.cm-1 inner, the corona can develop forward. The humidity of air influences the breakdown voltage deeply and the lower humidness the lower breakdown voltage.
④In the leader development model, when applied 500kV、250/2500μs switching over-voltage, the ion density in the leader channel can reach 1013～1015cm-3 and the electric field reach 1～2kV.cm-1, the time to start leader discharge is about 400μs and the velocity of the leader development is about 3×104m.s-1 from rod electrode to plane electrode. The leader channel takes 3/5 of the whole gap, it’s very approach to the tested value 2/3.
Both of the plasma-corona model and the leader growth model in this article can describe the long air gap discharge process perfectly. By the emulation and calculation of the process of leader discharge, we gained the starting condition of the leader and the breakdown condition of the long air gap.
引文
[1] 马乃祥. 长间隙放电. 北京: 中国电力出版社, 1998.122-128.
[2] Bruno La Fontaine, Francois Vidal. The Influence of Electron Density on the Formation of Streamers in Electrical Discharges Triggered with Ultrashort Laser Pulses. IEEE Transactions on plasma science, 1999,27(3): 688-701.
[3] I. Gallimberti, G. Bacchiega, Anne Bondiou-Clergerie. Fundamental Processes in Long Air Gap Discharges. C. R. Physique, 2002,3(12): 1335–1359.
[4] I. Gallimberti. A Computer Model for Streamer Propagation. J.Phys. D. Applied Physics, 1972, 5(3): 2179-2189.
[5] Fran?ois Vidal, Ivo Gallimberti, Farouk A. M. Rizk. Modeling of the Air Plasma Near the Tip of the Positive Leader. IEEE Transactions on Plasma Science, 2002,30(3): 1339~1349.
[6] Woong-Gee Min, Hyeong-Seok Kim. An Investigation of FEM-FCT Method for Streamer Corona Simulation. IEEE Transactions on magnetics, 2000, 36(4): 1280-1285.
[7] F Granget, N Soulemt. Numerical and Experimental Determination of Ionizing Front Velocity in a DC Point-to-plane Corona Discharge. J. Phys. D. Appl. Phys, 1995, 28:1619-1629.
[8] 宁成,李劲,李谦. 正脉冲电晕放电的数值研究. 华中科技大学学报,1996,11:43-46.
[9] G.L Bragliai, J.J Lowkef. Comparison of Monte Carlo and Boltzmann Calculation of Electron Diffusion to Absorbing Electrodes. J. Phys. D: Appl. Phys, 1979, 12: 1831-1839.
[10] Savino Longo. Monte Carlo Models of Electron and Ion Transport in Non-equilibrium Plasmas. Plasma Sources Sci. Technol, 2000,9(10): 468–476.
[11] 冯长根,欧阳吉庭,惠和兴. 用蒙特卡洛法研究分均匀电场的放电特性. 北京理工大学学报,2000,20(2): 155-160.
[12] N.R Pinhao, Z.Donko. Comparison of Kinetic Calculation Techniques for the Analysis of Electron Swarm Transport at Low to Moderate E/N Values, Plasma Sources Sci. Technol, 2004, 13: 719–728.
[13] 王海峰,徐建源,李贵胜. 有限元-模拟电荷法在静电场数值分析中的应用. 沈阳工业大学学报,2000,22(6): 494-498.
[14] 刘晓明,王尔智,曹云东,洪福贤. 采用优化模拟电荷法的三维电场计算. 电工技术学报,2002,15(6): 14-19.
[15] Mohamed El-Bahy. A Numerical Modelling of Microdischarge Threshold in Uniform Electric Fields. J. Phys. D: Appl. Phys, 2005, 38: 103–112.
[16] 杨津基. 长间隙放电. 北京: 科学出版社, 1983,115-120.
[17] M. Abdel.Salam, N.L.Allen. Inception of Corona and Rate of Rise of Voltage in Diverging Electric Field. IEE Proc, 1990, 137(4): 217-220.
[18] M. Ramires, M. Moreno, A. Pigini, etal. Air Density Influence on the Strength of External Insulation under Positive Impulse: Experimental Investigation up to an Altitude of 3000 m a.s.l.. IEEE Trans. on Power Delivery, 1990,5(2): 730~737.
[19] E.Nasser, M.Heiszler. Mathematical-physical Model of the Streamer in Nonuniform Field. J.Appl.Phys, 1974, 45(8): 3396-3401.
[20] D. Gral. Calculation of Corona Discharge in Point to Plane Gaps. Proceeding of the 3rd ISH, Milano, 1979,53: 0-4.
[21] M. S. Abou-Seada, A. R. M. Zaghloul, R. Y. Amer. A Physical Modelm for Formative Time Lag Calculation under Space-charge-stabilized. Proceeding of the 3rd ISH, Milano, 1979, 53:0-1.
[22] M. N. Horenstein. Computation of Corona Space Sharge and V-I Characteristic Using Equipotential Charge Shell. IEEE IA. 1980:1081-1086.
[23] E. O. Selim, R.T. Waters, etal. Space Charge Modeling in Impulse Corona. Proceeding of the 4th ISH. 1983, 41: 0-2.
[24] Yongho Kim, Woo Seok Kang, etal. Experimental and Numerical Analysis of Streamers in Pulsed Corona and Dielectric Barrier Discharges. IEEE Transactions on Plasma Science, 2004, 32(1): 18-24.
[25] Vereshchagin I.P, Beloglovsky A.A, Vinokurov V.N, Sokolova M.V. A Model of Impulse Streamer Corona Formation. Eleventh International Symposium on High Voltage Engineering, 1999, 3: 248-251.
[26] R. T. Waters. Breakdown in Nonuniform Fields. IEE Proc,1981, Vol.128, Pt.A, 4: 319-325.
[27] M. Abdel-Salam. Analysis of the Discharge Development of a Positive Rod-plane Gap in Air. IEEE PAS-95, 1976, 4:1019-1027.
[28] R.T. Waters. A Thermodynamic Model of the Leader in Long Air Gaps. Research on Long Air Gaps Discharge at Renardières 1973 Results, Electra, 1974,35: 124-129.
[29] 孙嘉平. 雷闪放电的机理及其等离子体物理学研究方法(Ⅰ). 雷电与静电, 1985, 1(2): 8-17.
[30] 胡昌信, 孙嘉平. 雷闪放电的机理及其等离子体物理学研究方法(Ⅱ). 雷电与静电, 1986, 2(1): 3-16.
[31] Les Renardières Group. Double Impulse Tests of Long Air Gaps. Proc.IEEE, A 133, 1986: 395-483.
[32] H. Pépin, D. Comtois, F. Vidal, etal. Triggering and Guiding High-voltage Large-scale LeaderDischargeswith Sub-joule Ultrashort Laser Pulses. Phys. Plasmas, 2001,8: 2532-2539.
[33] N. L. Aleksandrov, E. M. Bazelyan. Simulation of Long-streamer Propagation in Air at Atmospheric Pressure. J. Phys. D. Appl. Phys, 1996, 29: 740-752.
[34] R. Morrow, J. J. Lowke. Streamer Propagation in Air. J. Phys. D. Appl. Phys, 1997, (30): 614-627.
[35] G. N. Aleksandrov, B. N. Gorin, etal. Peculiarities of the Development of the Electric Breakdown of Air in Extremely Long Discharge Gap. Soviet Physics-Doklady, 1969, 13: 1246-1249.
[36] J. K. Hepworth, R. C. Klewe, B. A. Tozer. A Moder of Impulse Breakdown in Divergen Field Geometry. J.of Physics D. Applied Physics, 1972, (5):730-740.
[37] L. E. Lline. Corona Cloud Model Predictions of Switching Surge Flashover Voltage vs. Electrode Geometry. IEEE PAS-96, 1977, 2:543-549.
[38] M. M. Kekez, P. Savic. Derivation of the Breakdown Characteristics of a Positive Rod-plane Gap over a Three-decade Range. Proceeding of the 3rd ISH, Milano, 1979, (51):14.
[39] B. Hutzler, D. Hutzler-Barre. Leader Propagation Model for Predetermination of Switching Surge Flashover Voltage of Large Air Gaps. IEEE Trans., Vol. PAS-97, 1978, (4): 1087-1096.
[40] Farouk A. M. Rizk. A Model for Switching Impulse Leader Inception and Breakdown of Long Air-gaps. IEEE Trans. on Power Delivery, 1989, 4(1): 596-606.
[41] C. Menemenlis, G. Harbec. Coefficient of Variation of the Positive-impulse Breakdown of Long Air-gaps. IEEE Trans. Vol. PAS-93, 1974: 916-927.
[42] H. M. Schneider, F. J. Turner. Switching-surge Flashover Characteristics of Long Sphere-plane Gaps for UHV Station Design. IEEE Trans. Vol. PAS-94, 1975, (2): 551-559.
[43] 文习山, 陈慈萱, 解广润. 长间隙放电过程的物理模型. 高电压技术, 1990, (2): 1-6.
[44] 陶振中,张述良. 有限元与近似法. 北京:人民交通出版社,1982.250-255.
[45] 夸克工作室. 有限元分析教学范本FEMLAB与Mathematica. 北京: 清华大学出版社, 2003.31-39.
[46] C. L. Longmire. On the Electromagnetic Pulse Produced by Nuclear Explosions. IEEE Trans. Ant. Propagat, AP-26, 1978:3-13.
[47] X. M. Zhao, J. C. Diels, C. Y.Wang, J. M. Elizondo. Femtosecond Ultraviolet Laser Pulse Induced Lighning Discharges in Gases. IEEE J.Quantum Electron, 1995,31: 599-612.
[48] R. Hegerberg, R. W. Crompton. Diffusion Attachment and Attachment Cooling of Thermal Electrons in Oxygen and Oxygen Mixtures. J. Phys, 1983, 36: 831-844.
[49] 张志劲,司马文霞,蒋兴良等. 超/特高压输电线路雷电绕击防护性能研究. 中国电机工程学报,2005, 25(10): 1-6.
[50] 张海燕,王文端. 长间隙放电的电场测量. 华北电力大学学报, 1996,13(3):55-59.
[51] Castellani A, Anne B. C, Gallimberti I, et al. Laboratory Study of the Bi-leader Process from an Electrically Floating Conductor Part 2: Bi-leader properties. IEE Proc.-Sci Meas. Technol, 1998, 145(5): 193-200.
[52] 俞集辉. 电磁场原理. 重庆:重庆大学出版社, 2003.128-133.
[2] Bruno La Fontaine, Francois Vidal. The Influence of Electron Density on the Formation of Streamers in Electrical Discharges Triggered with Ultrashort Laser Pulses. IEEE Transactions on plasma science, 1999,27(3): 688-701.
[3] I. Gallimberti, G. Bacchiega, Anne Bondiou-Clergerie. Fundamental Processes in Long Air Gap Discharges. C. R. Physique, 2002,3(12): 1335–1359.
[4] I. Gallimberti. A Computer Model for Streamer Propagation. J.Phys. D. Applied Physics, 1972, 5(3): 2179-2189.
[5] Fran?ois Vidal, Ivo Gallimberti, Farouk A. M. Rizk. Modeling of the Air Plasma Near the Tip of the Positive Leader. IEEE Transactions on Plasma Science, 2002,30(3): 1339~1349.
[6] Woong-Gee Min, Hyeong-Seok Kim. An Investigation of FEM-FCT Method for Streamer Corona Simulation. IEEE Transactions on magnetics, 2000, 36(4): 1280-1285.
[7] F Granget, N Soulemt. Numerical and Experimental Determination of Ionizing Front Velocity in a DC Point-to-plane Corona Discharge. J. Phys. D. Appl. Phys, 1995, 28:1619-1629.
[8] 宁成,李劲,李谦. 正脉冲电晕放电的数值研究. 华中科技大学学报,1996,11:43-46.
[9] G.L Bragliai, J.J Lowkef. Comparison of Monte Carlo and Boltzmann Calculation of Electron Diffusion to Absorbing Electrodes. J. Phys. D: Appl. Phys, 1979, 12: 1831-1839.
[10] Savino Longo. Monte Carlo Models of Electron and Ion Transport in Non-equilibrium Plasmas. Plasma Sources Sci. Technol, 2000,9(10): 468–476.
[11] 冯长根,欧阳吉庭,惠和兴. 用蒙特卡洛法研究分均匀电场的放电特性. 北京理工大学学报,2000,20(2): 155-160.
[12] N.R Pinhao, Z.Donko. Comparison of Kinetic Calculation Techniques for the Analysis of Electron Swarm Transport at Low to Moderate E/N Values, Plasma Sources Sci. Technol, 2004, 13: 719–728.
[13] 王海峰,徐建源,李贵胜. 有限元-模拟电荷法在静电场数值分析中的应用. 沈阳工业大学学报,2000,22(6): 494-498.
[14] 刘晓明,王尔智,曹云东,洪福贤. 采用优化模拟电荷法的三维电场计算. 电工技术学报,2002,15(6): 14-19.
[15] Mohamed El-Bahy. A Numerical Modelling of Microdischarge Threshold in Uniform Electric Fields. J. Phys. D: Appl. Phys, 2005, 38: 103–112.
[16] 杨津基. 长间隙放电. 北京: 科学出版社, 1983,115-120.
[17] M. Abdel.Salam, N.L.Allen. Inception of Corona and Rate of Rise of Voltage in Diverging Electric Field. IEE Proc, 1990, 137(4): 217-220.
[18] M. Ramires, M. Moreno, A. Pigini, etal. Air Density Influence on the Strength of External Insulation under Positive Impulse: Experimental Investigation up to an Altitude of 3000 m a.s.l.. IEEE Trans. on Power Delivery, 1990,5(2): 730~737.
[19] E.Nasser, M.Heiszler. Mathematical-physical Model of the Streamer in Nonuniform Field. J.Appl.Phys, 1974, 45(8): 3396-3401.
[20] D. Gral. Calculation of Corona Discharge in Point to Plane Gaps. Proceeding of the 3rd ISH, Milano, 1979,53: 0-4.
[21] M. S. Abou-Seada, A. R. M. Zaghloul, R. Y. Amer. A Physical Modelm for Formative Time Lag Calculation under Space-charge-stabilized. Proceeding of the 3rd ISH, Milano, 1979, 53:0-1.
[22] M. N. Horenstein. Computation of Corona Space Sharge and V-I Characteristic Using Equipotential Charge Shell. IEEE IA. 1980:1081-1086.
[23] E. O. Selim, R.T. Waters, etal. Space Charge Modeling in Impulse Corona. Proceeding of the 4th ISH. 1983, 41: 0-2.
[24] Yongho Kim, Woo Seok Kang, etal. Experimental and Numerical Analysis of Streamers in Pulsed Corona and Dielectric Barrier Discharges. IEEE Transactions on Plasma Science, 2004, 32(1): 18-24.
[25] Vereshchagin I.P, Beloglovsky A.A, Vinokurov V.N, Sokolova M.V. A Model of Impulse Streamer Corona Formation. Eleventh International Symposium on High Voltage Engineering, 1999, 3: 248-251.
[26] R. T. Waters. Breakdown in Nonuniform Fields. IEE Proc,1981, Vol.128, Pt.A, 4: 319-325.
[27] M. Abdel-Salam. Analysis of the Discharge Development of a Positive Rod-plane Gap in Air. IEEE PAS-95, 1976, 4:1019-1027.
[28] R.T. Waters. A Thermodynamic Model of the Leader in Long Air Gaps. Research on Long Air Gaps Discharge at Renardières 1973 Results, Electra, 1974,35: 124-129.
[29] 孙嘉平. 雷闪放电的机理及其等离子体物理学研究方法(Ⅰ). 雷电与静电, 1985, 1(2): 8-17.
[30] 胡昌信, 孙嘉平. 雷闪放电的机理及其等离子体物理学研究方法(Ⅱ). 雷电与静电, 1986, 2(1): 3-16.
[31] Les Renardières Group. Double Impulse Tests of Long Air Gaps. Proc.IEEE, A 133, 1986: 395-483.
[32] H. Pépin, D. Comtois, F. Vidal, etal. Triggering and Guiding High-voltage Large-scale LeaderDischargeswith Sub-joule Ultrashort Laser Pulses. Phys. Plasmas, 2001,8: 2532-2539.
[33] N. L. Aleksandrov, E. M. Bazelyan. Simulation of Long-streamer Propagation in Air at Atmospheric Pressure. J. Phys. D. Appl. Phys, 1996, 29: 740-752.
[34] R. Morrow, J. J. Lowke. Streamer Propagation in Air. J. Phys. D. Appl. Phys, 1997, (30): 614-627.
[35] G. N. Aleksandrov, B. N. Gorin, etal. Peculiarities of the Development of the Electric Breakdown of Air in Extremely Long Discharge Gap. Soviet Physics-Doklady, 1969, 13: 1246-1249.
[36] J. K. Hepworth, R. C. Klewe, B. A. Tozer. A Moder of Impulse Breakdown in Divergen Field Geometry. J.of Physics D. Applied Physics, 1972, (5):730-740.
[37] L. E. Lline. Corona Cloud Model Predictions of Switching Surge Flashover Voltage vs. Electrode Geometry. IEEE PAS-96, 1977, 2:543-549.
[38] M. M. Kekez, P. Savic. Derivation of the Breakdown Characteristics of a Positive Rod-plane Gap over a Three-decade Range. Proceeding of the 3rd ISH, Milano, 1979, (51):14.
[39] B. Hutzler, D. Hutzler-Barre. Leader Propagation Model for Predetermination of Switching Surge Flashover Voltage of Large Air Gaps. IEEE Trans., Vol. PAS-97, 1978, (4): 1087-1096.
[40] Farouk A. M. Rizk. A Model for Switching Impulse Leader Inception and Breakdown of Long Air-gaps. IEEE Trans. on Power Delivery, 1989, 4(1): 596-606.
[41] C. Menemenlis, G. Harbec. Coefficient of Variation of the Positive-impulse Breakdown of Long Air-gaps. IEEE Trans. Vol. PAS-93, 1974: 916-927.
[42] H. M. Schneider, F. J. Turner. Switching-surge Flashover Characteristics of Long Sphere-plane Gaps for UHV Station Design. IEEE Trans. Vol. PAS-94, 1975, (2): 551-559.
[43] 文习山, 陈慈萱, 解广润. 长间隙放电过程的物理模型. 高电压技术, 1990, (2): 1-6.
[44] 陶振中,张述良. 有限元与近似法. 北京:人民交通出版社,1982.250-255.
[45] 夸克工作室. 有限元分析教学范本FEMLAB与Mathematica. 北京: 清华大学出版社, 2003.31-39.
[46] C. L. Longmire. On the Electromagnetic Pulse Produced by Nuclear Explosions. IEEE Trans. Ant. Propagat, AP-26, 1978:3-13.
[47] X. M. Zhao, J. C. Diels, C. Y.Wang, J. M. Elizondo. Femtosecond Ultraviolet Laser Pulse Induced Lighning Discharges in Gases. IEEE J.Quantum Electron, 1995,31: 599-612.
[48] R. Hegerberg, R. W. Crompton. Diffusion Attachment and Attachment Cooling of Thermal Electrons in Oxygen and Oxygen Mixtures. J. Phys, 1983, 36: 831-844.
[49] 张志劲,司马文霞,蒋兴良等. 超/特高压输电线路雷电绕击防护性能研究. 中国电机工程学报,2005, 25(10): 1-6.
[50] 张海燕,王文端. 长间隙放电的电场测量. 华北电力大学学报, 1996,13(3):55-59.
[51] Castellani A, Anne B. C, Gallimberti I, et al. Laboratory Study of the Bi-leader Process from an Electrically Floating Conductor Part 2: Bi-leader properties. IEE Proc.-Sci Meas. Technol, 1998, 145(5): 193-200.
[52] 俞集辉. 电磁场原理. 重庆:重庆大学出版社, 2003.128-133.
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