电力线路雷电感应过电压的时域积分方程法分析
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摘要
占雷击率90%的感应雷是造成低压输电线路雷害故障次数和线路跳闸率明显增加,高压输电线路绝缘老化的重要原因。并且感应雷电波沿线路的传播分布会严重影响电能质量及二次设备的正常运行。架空输电线路的雷电感应过电压计算是电力线路绝缘设计、采取防雷保护措施的基础计算。
本文首先采用时域近似公式计算方法计算了雷击在空间某点处感应的水平电场:对雷击模型做了基本假设与建模,推导了梯形波在空间某点处感应产生的水平电场的两个分量,叠加得到水平电场,任意电流波形在空间某点感应产生的水平电场用梯形波进行拟合得到。推导过程中考虑了土壤电导率对水平电场的影响,还分析了影响雷电流周围水平电场的因素。
建立雷电水平电场与单根细线导体耦合的时域积分方程,计算得到的雷击在空间某点处感应的水平电场值,可作为入射场的值代入推导得到的时域积分方程中。建立的时域积分方程应用矩量法的思想进行空间和时间离散,得到的线性方程组应用时间步进算法进行求解。在此过程中,本文讨论了基函数权函数选取的原则,及改善时间步进算法后时稳定性的一些方法。
讨论了大地影响及带负载情况下对方程的改造方法,最后采用上述方法对单根及三相架空输电线路带负载情况下的感应过电压进行了一些算例计算,结果显示,与相关文献的结果吻合的很好,证明了方法的可行性。另外,针对工作的不足提出了下一步工作重点与展望。
Most of low-pressure transmission line’s fault and trip and high-pressure transmission line’s insulation aging are caused by lightning induced over voltages, which is 90% of the total lightning. Induction lightning over voltages along the lines will seriously affect the power quality and the normal operation of secondary equipment. The calculation of lightning induced over voltage in overhead transmission lines is the basis of power line insulation and lightning protection design.
Firstly, this paper use an approximate formula method to calculate the horizontal electric field at a point in space. A basic lightning model is built, and according to the modeling assumption, the two components(one due to the return stroke charge and the other due to the return stroke current) generated by a trapezium wave are derived. Superimpose the two components derived the horizontal electric field. Any arbitrary current waveform can be represented by the superposition of a set of trapeziums so we can get the electric induced by any arbitrary current waveform. In the process, we considered the soil conductivity’s influence, and also analysis the factors that impact the electric field.
Then, this paper establish the time domain integral equations of horizontal electric field coupled with a single thin wire. The horizontal electric field can be seen as the incident field in the time domain integral equations. Apply moment method to this equation in space and time discretization. Use time stepping algorithm to solve the obtained linear equations. In this process, the article have discussed the principle to chose the basic functions and weighting functions, and improved the stability of time stepping algorithm.
The impact of the earth and lines under load have been discussed. At last, some calculation samples are presented. The results agree well with relevant literatures, the feasibility of the method is demonstrated. In addition, the lack of job and the aspect are presented.
本文首先采用时域近似公式计算方法计算了雷击在空间某点处感应的水平电场:对雷击模型做了基本假设与建模,推导了梯形波在空间某点处感应产生的水平电场的两个分量,叠加得到水平电场,任意电流波形在空间某点感应产生的水平电场用梯形波进行拟合得到。推导过程中考虑了土壤电导率对水平电场的影响,还分析了影响雷电流周围水平电场的因素。
建立雷电水平电场与单根细线导体耦合的时域积分方程,计算得到的雷击在空间某点处感应的水平电场值,可作为入射场的值代入推导得到的时域积分方程中。建立的时域积分方程应用矩量法的思想进行空间和时间离散,得到的线性方程组应用时间步进算法进行求解。在此过程中,本文讨论了基函数权函数选取的原则,及改善时间步进算法后时稳定性的一些方法。
讨论了大地影响及带负载情况下对方程的改造方法,最后采用上述方法对单根及三相架空输电线路带负载情况下的感应过电压进行了一些算例计算,结果显示,与相关文献的结果吻合的很好,证明了方法的可行性。另外,针对工作的不足提出了下一步工作重点与展望。
Most of low-pressure transmission line’s fault and trip and high-pressure transmission line’s insulation aging are caused by lightning induced over voltages, which is 90% of the total lightning. Induction lightning over voltages along the lines will seriously affect the power quality and the normal operation of secondary equipment. The calculation of lightning induced over voltage in overhead transmission lines is the basis of power line insulation and lightning protection design.
Firstly, this paper use an approximate formula method to calculate the horizontal electric field at a point in space. A basic lightning model is built, and according to the modeling assumption, the two components(one due to the return stroke charge and the other due to the return stroke current) generated by a trapezium wave are derived. Superimpose the two components derived the horizontal electric field. Any arbitrary current waveform can be represented by the superposition of a set of trapeziums so we can get the electric induced by any arbitrary current waveform. In the process, we considered the soil conductivity’s influence, and also analysis the factors that impact the electric field.
Then, this paper establish the time domain integral equations of horizontal electric field coupled with a single thin wire. The horizontal electric field can be seen as the incident field in the time domain integral equations. Apply moment method to this equation in space and time discretization. Use time stepping algorithm to solve the obtained linear equations. In this process, the article have discussed the principle to chose the basic functions and weighting functions, and improved the stability of time stepping algorithm.
The impact of the earth and lines under load have been discussed. At last, some calculation samples are presented. The results agree well with relevant literatures, the feasibility of the method is demonstrated. In addition, the lack of job and the aspect are presented.
引文
[1]文习山,彭向阳,解广润.架空配电线路感应雷过电压的数值计算[J].中国电机工程学报,1998,18(4):299-301.
[2]文武.感应雷电磁干扰及其防护研究[D].武汉大学博士论文,2004.
[3]侯牧武,曾嵘,何金良.感应过电压对输电线路耐雷水平的影响[J].电网技术,2004,28(4):46-49.
[4]文武,李自品,陈玉,裴金勇.多导体配电线路感应雷过电压分析[J].高电压技术,2006,32(8):14-17.
[5]文武,阮江军,陈允平,等.架空传输线在间接雷击作用下负载浪涌的分析[J].中国电机工程学报,2003,23(1):116-120.
[6] C′elio Fonseca Barbosa, Jos′e Osvaldo Saldanha Paulino. 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.
[7] C.A. Nucci,F. Rachidi.Lightning-Induced Overvoltages[J].IEEE Transmission and Distribution Conference,1999.
[8] C.A.Nucci.Lightning-induced voltages on overhead power lines[J].IEEE Transactions on Electromagnetic Compatibility,1993,35(1):75-85.
[9] C.A. Nucci,F. Rachidi,M. Ianoz,et al.Comparison of Two Coupling models for Lightning-Induced Overvoltage Calculations[J].IEEE Transactions on Electromagnetic Compatibility,1995,10(1):330-339.
[10] Marcos Ruhinstein.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.
[11] Vladimir A. Rakov,Martin A. Uman.Review and Evaluation of Lightning Return Stroke Models Including Some Aspects of Their Application[J].IEEE Transactions on Electromagnetic Compatibility,1998,40(4):403-426.
[12] Vernon Cooray.Horizontal Electric Field Above and Underground Produced by Lightning Flashes[J].IEEE Transactions on Electromagnetic Compatibility,2010,52(4):936-943.
[13] F.Rashidi.Formulation of field to transmission line coupling equations in terms of magnetic excitation field[J] . Transactions on Electromagnetic Compatibility,1993,35(3):404-407.
[14] Farhad Rachidi,Carlo Alberto Nucci,Michel Ianoz,Carlo Mazzetti.Influence of a lossy ground on lightning-induced voltages on overhead lines[J].IEEE Transactions on Electromagnetic Compatibility,1996,38(4):250-264.
[15] Carlo Albert0 Nucci,Farhad Rachidi,Michel V.lanoz,et al.Lightning-Induced Voltages on Overhead Lines[J] . IEEE Transactions on Electromagnetic Compatibility,1993,35(1):75-85.
[16] R.Moini , B.Kordi , M.Abedi . The Evaluation of LEMP Effects on Substansmission Line Using the Method of Moment:A Comparison Between TL and MTL Model[J].IEEE Transactions on Electromagnetic Compatibility,1994:127-131.
[17] Abdenbi Mimouni,Zin E. Azzouz,Boualem Ghemri.Lightning Induced Overvoltages on Overhead Lines : Modelling And Experimental Validation[J].Electrical Engineering,2007:146-131.
[18] Federico Delfino,Renato Procopio,Mansueto Rossi,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.
[19] Carlo Alberta Nucci,Farhad Rachidi.On the Contribution of the Electromagnetic Field Components in Field-to-Transmission Line Interaction[J] . IEEE Transactions on Electromagnetic Compatibility,1995,37(4):505-508.
[20] Ashok K.Agrawal,Harold J.Price,Shyam H.Gurbaxani.Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field[J] . IEEE Transactions on Electromagnetic Compatibility,1980,22(2):119-129.
[21] Vernon Cooray,Viktor Scuka.Lightning-Induced Overvoltages in power Lines:Validity of Various Approximations Made in Overvoltage Calculations[J].IEEE Transactions on Electromagnetic Compatibility,1998,40(4):355-363.
[22]汪泉弟,张西鹏,朱蕾蕾.输电线雷击过电压波辐射场模型及数值分析[J].重庆大学学报(自然科学版),2006,29(9):24-43.
[23]陈中明,郑楚韬.配电网架空线路感应雷过电压产生机理与防护[J].广东电力,2008,21(5):19-22.
[24]谢莉,雷银照.架空传输线在电偶极子激励下的瞬态电磁响应[J].电工技术学报,2009,24(4):6-13.
[25]苟晓彤,张露,叶宽,文习山.限制配电线路感应过电压的避雷器布置优化[J].高电压技术,2009,35(2):315-318.
[26]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,1996,25(2):65-73.
[27]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.
[28]杨静,赵阳,袁铁,等.雷电在水平导体中产生感应电压的观测及数值模拟研究[J].物理学报,2008,57(3):1968-1975.
[29]李景禄,吴维宁,杨廷方,等.配电网防雷保护的分析与研究[J].高电压技术,2004,30(4):58-59.
[30]刘杰.应用时域积分方程法分析复杂细线导体的瞬态响应[D].华北电力大学硕士论文,2009.
[31]王湃,夏明耀,周乐柱,等.使用改进的时域积分方程法计算导体目标的瞬态散射[J].电子学报,2005,33(3):488-491.
[32]唐煜,顾长青.一种改进稳定性的时域电场积分方程法[J].微波学报,2008,24(4):31-35.
[33]姜光兴,曹伟,朱洪波.TD-EFIE分析任意几何形状导体的瞬态特性[J].电子学报,2006,34(4):60-64.
[34]何浏.基于时域积分方程的金属目标时域电磁散射数值分析[D].电子科技大学硕士论文,2009.
[35]李琳,李丽娟,高长征,谷雪松.电介质半空间两耦合线天线的时域积分方程法[J].电波科学学报,2008,23(3):411-416.
[36]胡俊,雷霖,王湃,等.任意细线结构瞬态响应的高效求解[J].电子科技大学学报,2004,33(5):496-498.
[37]刘顺坤,陈雨生,孙蓓云,等.时域电场积分方程在求解架空屏蔽电缆蒙皮电流中的应用[J].强激光与粒子束,2005,17(4):637-640.
[38] Jin-Lin Hu,Chi H. Chan,Yuan Xu.A New Temporal Basis Function for the Time-Domain Integral Equation Method[J].IEEE Microwave and wireless components letters,2001,11(11):465-466.
[39] Jin-Lin Hu,Chi H. Chan.Novel Approach to Construct Temporal Bases Functions for Time-Domain Integral Equation Method[J] . Antennas and Propagation Society International Symposium,2001,4:172-175.
[40] Heming Ren , Bihua Zhou , Tongbin Yu , Zhao Wang . Calculation of lighting-induced voltage on an overhead line[J].MAPE 2005,1:748–751.
[41] Rao S M,Sarkar T K,Dianat S A.A novel technique to the solution of transient electromagnetic scattering from thin wires[J].IEEE Transactions on Antennas and Propagation,1986,34 (5):630-634.
[42] Selby A,Dawalibi F.Determination of current distribution in energized conductors for the computation of electromagnetic fields[J].IEEE Transactions On Power Delivery,1994,9(21):l069-l078.
[2]文武.感应雷电磁干扰及其防护研究[D].武汉大学博士论文,2004.
[3]侯牧武,曾嵘,何金良.感应过电压对输电线路耐雷水平的影响[J].电网技术,2004,28(4):46-49.
[4]文武,李自品,陈玉,裴金勇.多导体配电线路感应雷过电压分析[J].高电压技术,2006,32(8):14-17.
[5]文武,阮江军,陈允平,等.架空传输线在间接雷击作用下负载浪涌的分析[J].中国电机工程学报,2003,23(1):116-120.
[6] C′elio Fonseca Barbosa, Jos′e Osvaldo Saldanha Paulino. 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.
[7] C.A. Nucci,F. Rachidi.Lightning-Induced Overvoltages[J].IEEE Transmission and Distribution Conference,1999.
[8] C.A.Nucci.Lightning-induced voltages on overhead power lines[J].IEEE Transactions on Electromagnetic Compatibility,1993,35(1):75-85.
[9] C.A. Nucci,F. Rachidi,M. Ianoz,et al.Comparison of Two Coupling models for Lightning-Induced Overvoltage Calculations[J].IEEE Transactions on Electromagnetic Compatibility,1995,10(1):330-339.
[10] Marcos Ruhinstein.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.
[11] Vladimir A. Rakov,Martin A. Uman.Review and Evaluation of Lightning Return Stroke Models Including Some Aspects of Their Application[J].IEEE Transactions on Electromagnetic Compatibility,1998,40(4):403-426.
[12] Vernon Cooray.Horizontal Electric Field Above and Underground Produced by Lightning Flashes[J].IEEE Transactions on Electromagnetic Compatibility,2010,52(4):936-943.
[13] F.Rashidi.Formulation of field to transmission line coupling equations in terms of magnetic excitation field[J] . Transactions on Electromagnetic Compatibility,1993,35(3):404-407.
[14] Farhad Rachidi,Carlo Alberto Nucci,Michel Ianoz,Carlo Mazzetti.Influence of a lossy ground on lightning-induced voltages on overhead lines[J].IEEE Transactions on Electromagnetic Compatibility,1996,38(4):250-264.
[15] Carlo Albert0 Nucci,Farhad Rachidi,Michel V.lanoz,et al.Lightning-Induced Voltages on Overhead Lines[J] . IEEE Transactions on Electromagnetic Compatibility,1993,35(1):75-85.
[16] R.Moini , B.Kordi , M.Abedi . The Evaluation of LEMP Effects on Substansmission Line Using the Method of Moment:A Comparison Between TL and MTL Model[J].IEEE Transactions on Electromagnetic Compatibility,1994:127-131.
[17] Abdenbi Mimouni,Zin E. Azzouz,Boualem Ghemri.Lightning Induced Overvoltages on Overhead Lines : Modelling And Experimental Validation[J].Electrical Engineering,2007:146-131.
[18] Federico Delfino,Renato Procopio,Mansueto Rossi,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.
[19] Carlo Alberta Nucci,Farhad Rachidi.On the Contribution of the Electromagnetic Field Components in Field-to-Transmission Line Interaction[J] . IEEE Transactions on Electromagnetic Compatibility,1995,37(4):505-508.
[20] Ashok K.Agrawal,Harold J.Price,Shyam H.Gurbaxani.Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field[J] . IEEE Transactions on Electromagnetic Compatibility,1980,22(2):119-129.
[21] Vernon Cooray,Viktor Scuka.Lightning-Induced Overvoltages in power Lines:Validity of Various Approximations Made in Overvoltage Calculations[J].IEEE Transactions on Electromagnetic Compatibility,1998,40(4):355-363.
[22]汪泉弟,张西鹏,朱蕾蕾.输电线雷击过电压波辐射场模型及数值分析[J].重庆大学学报(自然科学版),2006,29(9):24-43.
[23]陈中明,郑楚韬.配电网架空线路感应雷过电压产生机理与防护[J].广东电力,2008,21(5):19-22.
[24]谢莉,雷银照.架空传输线在电偶极子激励下的瞬态电磁响应[J].电工技术学报,2009,24(4):6-13.
[25]苟晓彤,张露,叶宽,文习山.限制配电线路感应过电压的避雷器布置优化[J].高电压技术,2009,35(2):315-318.
[26]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,1996,25(2):65-73.
[27]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.
[28]杨静,赵阳,袁铁,等.雷电在水平导体中产生感应电压的观测及数值模拟研究[J].物理学报,2008,57(3):1968-1975.
[29]李景禄,吴维宁,杨廷方,等.配电网防雷保护的分析与研究[J].高电压技术,2004,30(4):58-59.
[30]刘杰.应用时域积分方程法分析复杂细线导体的瞬态响应[D].华北电力大学硕士论文,2009.
[31]王湃,夏明耀,周乐柱,等.使用改进的时域积分方程法计算导体目标的瞬态散射[J].电子学报,2005,33(3):488-491.
[32]唐煜,顾长青.一种改进稳定性的时域电场积分方程法[J].微波学报,2008,24(4):31-35.
[33]姜光兴,曹伟,朱洪波.TD-EFIE分析任意几何形状导体的瞬态特性[J].电子学报,2006,34(4):60-64.
[34]何浏.基于时域积分方程的金属目标时域电磁散射数值分析[D].电子科技大学硕士论文,2009.
[35]李琳,李丽娟,高长征,谷雪松.电介质半空间两耦合线天线的时域积分方程法[J].电波科学学报,2008,23(3):411-416.
[36]胡俊,雷霖,王湃,等.任意细线结构瞬态响应的高效求解[J].电子科技大学学报,2004,33(5):496-498.
[37]刘顺坤,陈雨生,孙蓓云,等.时域电场积分方程在求解架空屏蔽电缆蒙皮电流中的应用[J].强激光与粒子束,2005,17(4):637-640.
[38] Jin-Lin Hu,Chi H. Chan,Yuan Xu.A New Temporal Basis Function for the Time-Domain Integral Equation Method[J].IEEE Microwave and wireless components letters,2001,11(11):465-466.
[39] Jin-Lin Hu,Chi H. Chan.Novel Approach to Construct Temporal Bases Functions for Time-Domain Integral Equation Method[J] . Antennas and Propagation Society International Symposium,2001,4:172-175.
[40] Heming Ren , Bihua Zhou , Tongbin Yu , Zhao Wang . Calculation of lighting-induced voltage on an overhead line[J].MAPE 2005,1:748–751.
[41] Rao S M,Sarkar T K,Dianat S A.A novel technique to the solution of transient electromagnetic scattering from thin wires[J].IEEE Transactions on Antennas and Propagation,1986,34 (5):630-634.
[42] Selby A,Dawalibi F.Determination of current distribution in energized conductors for the computation of electromagnetic fields[J].IEEE Transactions On Power Delivery,1994,9(21):l069-l078.