一种低存储迭代伽辽金间接边界元方法与其在有界波发生器设计中的应用
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摘要
为了克服间接边界元方法的存储要求高、求解速度慢的问题,提出了一种低存储要求迭代求解的间接边界元求解方法。采用Galerkin方法获得间接边界元方程组的系数,根据物理耦合程度的差异,构造方程组的求解格式。对于空间距离较远的单元,在迭代中直接计算耦合系数。由于不存储这些单元对应的系数,可将方程组的存储从O(N2)降低至O(N)。该方法应用于有界波模拟发生器的电容计算中,数值算例表明:该方法可有效提高设计效率和阻抗匹配的准确性。从理论上讲,该方法实质上是一种基于物理耦合的预条件技术的应用,因此,其可推广应用到电磁场数值计算涉及满阵求解的场合。
In order to overcome the problem of high storage requirement and slow convergence rate of indirect bound-ary element method,a new indirect boundary element method with a low storage requirement is proposed. The coeffi-cients of the indirect boundary element equations are obtained by the Galerkin approach,and the iterative procedureof the equations is constructed according to the difference of the degree of physical coupling. For the coefficients cor-responding to elements with distant spatial distances,they are directly calculated in the iteration. Since these coeffi-cients are not stored,the storage of the system of equations can be reduced from O(N2)to O(N). The method is ap-plied to the capacitance calculation of the bounded wave simulation generator. Numerical examples show that the pro-posed method can effectively improve the design efficiency and accuracy of impedance matching. In theory,themethod in this paper is essentially an application of pre-conditional technology based on physical coupling,so it canbe generalized to the case where the numerical calculation of electromagnetic field involves full-scale solution.
In order to overcome the problem of high storage requirement and slow convergence rate of indirect bound-ary element method,a new indirect boundary element method with a low storage requirement is proposed. The coeffi-cients of the indirect boundary element equations are obtained by the Galerkin approach,and the iterative procedureof the equations is constructed according to the difference of the degree of physical coupling. For the coefficients cor-responding to elements with distant spatial distances,they are directly calculated in the iteration. Since these coeffi-cients are not stored,the storage of the system of equations can be reduced from O(N2)to O(N). The method is ap-plied to the capacitance calculation of the bounded wave simulation generator. Numerical examples show that the pro-posed method can effectively improve the design efficiency and accuracy of impedance matching. In theory,themethod in this paper is essentially an application of pre-conditional technology based on physical coupling,so it canbe generalized to the case where the numerical calculation of electromagnetic field involves full-scale solution.
引文
[1]刘玉,鲁海亮,刘文博,等. 500 kV GIS变电站快速暂态过电压研究[J].电瓷避雷器,2017(2):53-58.LIU Yu,LU Hailiang,LIU Wenbo,et al. The research of very fast transient overvoltage in 500 kV GIS substation[J].Insulators and Surge Arresters,2017(2):53-58.
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[4]王磊. 750 kV变电站GIS设备VFTO特性研究[J].中国电力,48(5):125-132.WANG Lei. Study on VFTO characteristics of GIS in 750 kV substation[J]. Electric Power,2015,48(5):125-132.
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[7] AHMED S,RAJU D,CHATURVEDI S,et al. Modal analysis for a bounded-wave EMP simulator-part I:Effect of test object[J]. IEEE Transactions on Electromagnetic Compatibility,2005,47(1):171-182.
[8]焦其祥,顾畹仪.电磁场与电磁波[M]. 2版.北京:科学出版社,2010:258-261.JIAO Qixiang,GU Wanyi. Field and wave electromagnetics[M]. 2rd ed. Beijing:Science Press,2010:258-261.
[9]大卫K.电磁场与电磁波[M].何亚军,桂良启,译.北京:科学出版社,2010:291-295.DAVIDK. Fieldandwaveelectromagnetics[M]. HEYajun,GUI Liangqi, translate. Beijing:Tsinghua University Press,2010:291-295.
[10]杜雷鸣,谢彦召,王绍飞.平行板传输线特性阻抗仿真计算及解析修正[J].强激光与粒子束,2015,27(8):160-164.DU Leiming,XIE Yanzhao,WANG Shaofei. Simulation computation and analytic modification of characteristic impedance of parallel-plate transmission line[J]. High Power Laser and Particle Beams,2015,27(8):160-164.
[11]胡玉生,李保江. GTEM传输室特性阻抗的三维有限元分析[J].计测技术,2006(2):4-5.HU Yusheng,LI Baojiang. Analysis of the characteristic impedance of GTEM cell by three dimension finite-element method[J]. Measurement Technology,2006(2):4-5.
[12]刘彬,李刚.有限元软件Ansys在传输线特性阻抗计算中的应用[J].现代电子技术,2005,4(5):93-95.LIU Bin,LI Gang. Application of finite element software Ansys to calculate characteristic impedance of transmission line[J]. Modern Electronics Technique,2005,4(5):93-95.
[13]胡玉生,蒋全兴,张本军. EUT对TEM传输室特性阻抗影响的边界元分析[J].东南大学学报(自然科学版),2003,2(2):145-147.HU Yusheng,JIANG Quanxing,ZHANG Benjun. Analysis of the characteristic impedance variation of TEM cell caused by equipment under test by BEM[J]. Journal of Southeast University(Science and Technology),2003,2(2):145-147.
[14]张淮清,王亚伟,付志红.虚边界元法在电磁场计算中的应用[J].电工技术学报,2013,28(2):86-90.ZHANG Weiqing,WANG Yawei,FU Zhihong. Virtual boundary element method in computational electromagnetics[J]. Transactions of China Electrotechnical Society,2013,28(2):86-90.
[15]刘士利,王泽忠,孙静.基于线-面模型的边界元法计算特高压交流变电站设备附近工频电场[J].电工技术学报,2011,26(3):162-167.LIU Shili,WANG Zezhong,SUN Jing. Calculation of power frequency electric field near equipments in UHV substations with BEM based on line-area models[J]. Transactions of China Electrotechnical Society,2011,26(3):162-167.
[16]张淮清,聂鑫,王亚伟,等.径向基函数—虚边界法在电磁计算中的应用[J].电工技术学报,2014,29(4):79-84.ZHANG Weiqing,NIE Xin,WANG Yawei,et al. Application of radial basis function-virtual boundary method in electromagnetic computation[J]. Transactions of China Electrotechnical Society,2014,29(4):79-84.
[17]吴万春,文舸一,刘学观.用复变量边界元法求解任意截面TEM传输线的特性阻抗[J].电子学报,1988,2(2):70-77.WU Wanchun,WEN Keyi,LIU Xueguan. Using complex variable boundary element method to solve the characteristic impedance of TEM transmission line with any section[J].Journal of Electronics,1998,2(2):70-77.
[18]盛剑霓.工程电磁场数值分析[M]. 1版.西安:西安交通大学出版社,1991:276-280.SHENG Jianni. Numerical analysis of engineering electromagnetic[M]. 1rd edition. Xi’an:Xi’an Jiaotong University Press,1991:276-280.
[19]刘士利,王泽忠,孙静. HVDC换流系统屏蔽罩寄生电容提取[J].电工技术学报,2011,26(2):201-206.LIU Shili,WANG Zezhong,SUN Jing. Extraction of parasitic capacitance of shield in HVDC converter stations[J].Transactions of China Electrotechnical Society,2011,26(2):201-206.
[20]李亚莎.高精度快速边界元法及其在绝缘子电场计算中应用研究[D].北京:华北电力大学,2007:19-33.LI Yasha. Research on high precision fast bem and its application in insulator electric field calculation[M]. Beijing:North China Electric Power University,2007:19-33.
[2]陈维江,颜湘莲,王绍武,等.气体绝缘开关设备中特快速瞬态过电压研究的新进展[J].中国电机工程学报,2011,31(31):1-11.CHEN Weijiang,YAN Xianglian,WANG Shaowu,et al.Recent progress in investigation on very fast transient overvoltage in gas insulated switchgear[J]. Proceeding of the CSEE,2011,31(31):1-11.
[3]谷定燮,修木洪,戴敏,等. 1 000 kV GIS变电所VFTO特性研究[J].高电压技术,2007,33(11):27-32.GU Dingxie,XIU Muhong,DAI Min,et al. Study on VFTO of 1 000 kV GIS substation[J]. High Voltage Engineering,2007,33(11):27-32.
[4]王磊. 750 kV变电站GIS设备VFTO特性研究[J].中国电力,48(5):125-132.WANG Lei. Study on VFTO characteristics of GIS in 750 kV substation[J]. Electric Power,2015,48(5):125-132.
[5]刘亚培,林生军,高文胜,等. 800 kV GIS变电站VFTO计算研究[J].高压电器,2017,53(9):143-154.LIU Yapei,LIN Shengjun,GAO Wensheng,et al. Calculation of very fast transient overvoltage for 800 kV GIS Substation[J]. High Voltage Apparatus,2017,53(9):143-148.
[6]陈庆国,邱毓昌,张乔根,等. GIS中快速暂态过电压的实验室模拟[J].高电压技术,2000,26(1):1-2.CHEN Qingguo,QIU Yuchang,ZHANG Qiaogen,et al.Laboratory simulation of very fast transient overvoltage in GIS[J]. High Voltage Engineering,2000,26(1):1-2.
[7] AHMED S,RAJU D,CHATURVEDI S,et al. Modal analysis for a bounded-wave EMP simulator-part I:Effect of test object[J]. IEEE Transactions on Electromagnetic Compatibility,2005,47(1):171-182.
[8]焦其祥,顾畹仪.电磁场与电磁波[M]. 2版.北京:科学出版社,2010:258-261.JIAO Qixiang,GU Wanyi. Field and wave electromagnetics[M]. 2rd ed. Beijing:Science Press,2010:258-261.
[9]大卫K.电磁场与电磁波[M].何亚军,桂良启,译.北京:科学出版社,2010:291-295.DAVIDK. Fieldandwaveelectromagnetics[M]. HEYajun,GUI Liangqi, translate. Beijing:Tsinghua University Press,2010:291-295.
[10]杜雷鸣,谢彦召,王绍飞.平行板传输线特性阻抗仿真计算及解析修正[J].强激光与粒子束,2015,27(8):160-164.DU Leiming,XIE Yanzhao,WANG Shaofei. Simulation computation and analytic modification of characteristic impedance of parallel-plate transmission line[J]. High Power Laser and Particle Beams,2015,27(8):160-164.
[11]胡玉生,李保江. GTEM传输室特性阻抗的三维有限元分析[J].计测技术,2006(2):4-5.HU Yusheng,LI Baojiang. Analysis of the characteristic impedance of GTEM cell by three dimension finite-element method[J]. Measurement Technology,2006(2):4-5.
[12]刘彬,李刚.有限元软件Ansys在传输线特性阻抗计算中的应用[J].现代电子技术,2005,4(5):93-95.LIU Bin,LI Gang. Application of finite element software Ansys to calculate characteristic impedance of transmission line[J]. Modern Electronics Technique,2005,4(5):93-95.
[13]胡玉生,蒋全兴,张本军. EUT对TEM传输室特性阻抗影响的边界元分析[J].东南大学学报(自然科学版),2003,2(2):145-147.HU Yusheng,JIANG Quanxing,ZHANG Benjun. Analysis of the characteristic impedance variation of TEM cell caused by equipment under test by BEM[J]. Journal of Southeast University(Science and Technology),2003,2(2):145-147.
[14]张淮清,王亚伟,付志红.虚边界元法在电磁场计算中的应用[J].电工技术学报,2013,28(2):86-90.ZHANG Weiqing,WANG Yawei,FU Zhihong. Virtual boundary element method in computational electromagnetics[J]. Transactions of China Electrotechnical Society,2013,28(2):86-90.
[15]刘士利,王泽忠,孙静.基于线-面模型的边界元法计算特高压交流变电站设备附近工频电场[J].电工技术学报,2011,26(3):162-167.LIU Shili,WANG Zezhong,SUN Jing. Calculation of power frequency electric field near equipments in UHV substations with BEM based on line-area models[J]. Transactions of China Electrotechnical Society,2011,26(3):162-167.
[16]张淮清,聂鑫,王亚伟,等.径向基函数—虚边界法在电磁计算中的应用[J].电工技术学报,2014,29(4):79-84.ZHANG Weiqing,NIE Xin,WANG Yawei,et al. Application of radial basis function-virtual boundary method in electromagnetic computation[J]. Transactions of China Electrotechnical Society,2014,29(4):79-84.
[17]吴万春,文舸一,刘学观.用复变量边界元法求解任意截面TEM传输线的特性阻抗[J].电子学报,1988,2(2):70-77.WU Wanchun,WEN Keyi,LIU Xueguan. Using complex variable boundary element method to solve the characteristic impedance of TEM transmission line with any section[J].Journal of Electronics,1998,2(2):70-77.
[18]盛剑霓.工程电磁场数值分析[M]. 1版.西安:西安交通大学出版社,1991:276-280.SHENG Jianni. Numerical analysis of engineering electromagnetic[M]. 1rd edition. Xi’an:Xi’an Jiaotong University Press,1991:276-280.
[19]刘士利,王泽忠,孙静. HVDC换流系统屏蔽罩寄生电容提取[J].电工技术学报,2011,26(2):201-206.LIU Shili,WANG Zezhong,SUN Jing. Extraction of parasitic capacitance of shield in HVDC converter stations[J].Transactions of China Electrotechnical Society,2011,26(2):201-206.
[20]李亚莎.高精度快速边界元法及其在绝缘子电场计算中应用研究[D].北京:华北电力大学,2007:19-33.LI Yasha. Research on high precision fast bem and its application in insulator electric field calculation[M]. Beijing:North China Electric Power University,2007:19-33.