换流阀屏蔽系统表面电场对称多极子曲面边界元法研究
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摘要
为确保柔性直流换流阀运行时不发生电晕现象,需要合理设计屏蔽系统,控制表面电场,但是屏蔽系统结构复杂,数值求解存在较大困难。为准确快速地计算表面电场,提出了对称多极子曲面边界元法。通过多极子方法加速基于坐标变换的曲面边界元,提高计算速度减少内存占用。通过镜像法将封闭的阀厅问题转换为多平面对称问题,同时利用多极展开系数的对称关系和紧致二叉树结构,进一步加快计算速度。使用球模型和实际屏蔽系统模型,与有限元方法对比验证了该算法的计算精度;与不同方法比较验证了该算法在计算效率上的提升效果。最后应用该算法研究了±160 kV换流阀屏蔽系统表面电场,地面、墙壁对于屏蔽系统表面电场影响明显,随着距离的减小影响变大。此方法可以快速准确地计算屏蔽系统表面电场,是优化设计的有效工具。
In order to ensure that the corona phenomenon does not occur during the operation of a flexible DC converter valve, it is necessary to design a shielding system to control the surface electric field. However, the shielding system has a complex structure and it is difficult to solve numerically.Consequently, we proposed a symmetric multipole curved boundary element method to calculate the surface electric field accurately and quickly. To increase the calculation speed and reduce the memory occupation, the fast multipole method was used to accelerate the curved boundary element method based on coordinate transformation. The mirror image method was used to convert the closed valve hall problem into multi-plane symmetry problem. Besides, the symmetric relation of multipole expansion coefficients and the binary tree structure with tight bounds were used to further speed up the calculation. The sphere model and shielding system model were used to verify the accuracy by comparison of finite element method, and the improvement effect of this method in computational efficiency was verified by comparison of different methods. The surface electric field of ±160 kV converter valve shielding system was studied. The influence of the valve hall on the surface electric field of the shielding system is obvious, and it becomes more remarkabe as the distance decreases. This method can quickly and accurately calculate the surface electric field, which is an effective tool for optimal design.
In order to ensure that the corona phenomenon does not occur during the operation of a flexible DC converter valve, it is necessary to design a shielding system to control the surface electric field. However, the shielding system has a complex structure and it is difficult to solve numerically.Consequently, we proposed a symmetric multipole curved boundary element method to calculate the surface electric field accurately and quickly. To increase the calculation speed and reduce the memory occupation, the fast multipole method was used to accelerate the curved boundary element method based on coordinate transformation. The mirror image method was used to convert the closed valve hall problem into multi-plane symmetry problem. Besides, the symmetric relation of multipole expansion coefficients and the binary tree structure with tight bounds were used to further speed up the calculation. The sphere model and shielding system model were used to verify the accuracy by comparison of finite element method, and the improvement effect of this method in computational efficiency was verified by comparison of different methods. The surface electric field of ±160 kV converter valve shielding system was studied. The influence of the valve hall on the surface electric field of the shielding system is obvious, and it becomes more remarkabe as the distance decreases. This method can quickly and accurately calculate the surface electric field, which is an effective tool for optimal design.
引文
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[7]石雨鑫,王泽忠,刘丽平.针对换流阀屏蔽系统表面电场的多极子边界元算法研究[J].中国电机工程学报,2018,38(9):2799-2807.SHI Yuxin,WANG Zezhong,LIU Liping.Research on fast multipole boundary element method for electrostatic field of converter valve shielding system[J].Proceedings of the CSEE,2018,38(9):2799-2807.
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[11]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,2007:35-64.LI Yasha.Research on high precision fast BEM and its application in insulator electric field calculation[D].Beijing,China:North China Electric Power University,2007:35-64.
[12]BAPAT M S,SHEN L,LIU Y.Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems[J].Engineering Analysis with Boundary Elements,2009,33(8/9):1113-1123.
[13]YASUDA Y,HIGUCHI K,OSHIMA T,et al.Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems[J].Engineering Analysis with Boundary Elements,2012,36(10):1493-1501.
[14]袁建生,李中新.求解多层媒质中点源电场问题的复镜像法[J].清华大学学报,1999,39(5):51-53.YUAN Jiansheng,LI Zhongxin.Complex image method for calculating electrostatic field in multilayer media[J].Journal of Tsinghua University,1999,39(5):51-53.
[15]URAGO M,KOYAMA T,TAKAHASHI K,et al.Fast multipole boundary element method using the binary tree structure with tight bounds:application to a calculation of an electrostatic force for the manipulation of a metal micro particle[J].Engineering Analysis with Boundary Elements,2003,37(8):835-844.
[16]杨虎,尹文禄,赵菲,等.高阶矢量有限元方法中的稀疏矩阵技术[J].微波学报,2011,27(2):13-18.YANG Hu,YIN Wenlu,ZHAO Fei,et al.Sparse matrix technology in higher order vector FEM[J].Journal of Microwaves,2011,27(2):13-18.
[17]BAKER A H,JESSUP E R,KOLEV T V.A simple strategy for varying the restart parameter in GMRES(m)[J].Journal of Computational and Applied Mathematics,2009,230(2):751-761.
[18]QIN X,ZHANG J,LI G,et al.An element implementation of the boundary face method for 3D potential problems[J].Engineering Analysis with Boundary Elements,2010,34(11):934-943.
[2]习贺勋,汤广福,曹均正,等.特高压直流换流阀电磁场与电磁兼容研究进展[J].中国电机工程学报,2012,32(22):1-6.XI Hexun,TANG Guangfu,CAO Junzheng,et al.Research progress of electromagnetic field and electromagnetic compatibility of UHVDCconverter valves[J].Proceedings of the CSEE,2012,32(22):1-6.
[3]齐磊,王星星,李超,等.±1 100 kV特高压直流换流阀绝缘型式试验下的电场仿真及优化[J].高电压技术,2015,41(4):1262-1271.QI Lei,WANG Xingxing,LI Chao,et al.Electric field simulation and optimization of±1 100 kV HVDC converter valve in insulation type test[J].High Voltage Engineering,2015,41(4):1262-1271.
[4]杜志叶,朱琳,阮江军,等.基于瞬时电位加载法的±800 k V特高压阀厅金具表面电场求解[J].高电压技术,2014,40(6):1809-1815.DU Zhiye,ZHU Lin,RUAN Jiangjun,et al.Surface electric field calculation of fittings inside±800 k V valve hall using electrostatic field instantaneous load method[J].High Voltage Engineering,2014,40(6):1809-1815.
[5]王泽忠,樊亮,夏天,等.基于边界元法的输电杆塔上分裂导线表面电场数值计算简明电磁场数值计算[J].高电压技术,2017,43(12):3835-3842.WANG Zezhong,FAN Liang,XIA Tian,et al.Numerical calculation of bundle conductor surface electric field on transmission tower based on boundary element method[J].High Voltage Engineering,2017,43(12):3835-3842.
[6]刘士利,王洋,张力丹,等.±800 kV特高压直流受端分层接入方式下低端阀厅金具结构设计[J].电工技术学报,2017,32(14):238-245.LIU Shili,WANG Yang,ZHANG Lidan,et al.Structure design of±800 kV UHVDC receiving end low voltage valve hall fittings for hierarchical connection[J].Transactions of China Electrotechnical Society,2017,32(14):238-245.
[7]石雨鑫,王泽忠,刘丽平.针对换流阀屏蔽系统表面电场的多极子边界元算法研究[J].中国电机工程学报,2018,38(9):2799-2807.SHI Yuxin,WANG Zezhong,LIU Liping.Research on fast multipole boundary element method for electrostatic field of converter valve shielding system[J].Proceedings of the CSEE,2018,38(9):2799-2807.
[8]LIU Y J.Fast multipole boundary element method-theory and applications in engineering[M].Cambridge,UK:Cambridge University Press,2009:47-65.
[9]郭卫,黄文武,文习山,等.应用快速多极子边界元法的块状土壤结构地网接地参数算法研究[J].中国电机工程学报,2014,34(9):1436-1445.GUO Wei,HUANG Wenwu,WEN Xishan,et al.A study of grounding parameters of grounding grid in soil with massive texture by using fast multipole boundary method[J].Proceedings of the CSEE,2014,34(9):1436-1445.
[10]张占龙,邓军,李德文,等.多介质工频电场分析的快速多极子边界元法[J].电机与控制学报,2010,14(4):80-85.ZHANG Zhanlong,DENG Jun,LI Dewen,et al.Fast multi-pole boundary element method analysis for power frequency electric field distribution of multi-medium[J].Electric Machines and Control,2010,14(4):80-85.
[11]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,2007:35-64.LI Yasha.Research on high precision fast BEM and its application in insulator electric field calculation[D].Beijing,China:North China Electric Power University,2007:35-64.
[12]BAPAT M S,SHEN L,LIU Y.Adaptive fast multipole boundary element method for three-dimensional half-space acoustic wave problems[J].Engineering Analysis with Boundary Elements,2009,33(8/9):1113-1123.
[13]YASUDA Y,HIGUCHI K,OSHIMA T,et al.Efficient technique in low-frequency fast multipole boundary element method for plane-symmetric acoustic problems[J].Engineering Analysis with Boundary Elements,2012,36(10):1493-1501.
[14]袁建生,李中新.求解多层媒质中点源电场问题的复镜像法[J].清华大学学报,1999,39(5):51-53.YUAN Jiansheng,LI Zhongxin.Complex image method for calculating electrostatic field in multilayer media[J].Journal of Tsinghua University,1999,39(5):51-53.
[15]URAGO M,KOYAMA T,TAKAHASHI K,et al.Fast multipole boundary element method using the binary tree structure with tight bounds:application to a calculation of an electrostatic force for the manipulation of a metal micro particle[J].Engineering Analysis with Boundary Elements,2003,37(8):835-844.
[16]杨虎,尹文禄,赵菲,等.高阶矢量有限元方法中的稀疏矩阵技术[J].微波学报,2011,27(2):13-18.YANG Hu,YIN Wenlu,ZHAO Fei,et al.Sparse matrix technology in higher order vector FEM[J].Journal of Microwaves,2011,27(2):13-18.
[17]BAKER A H,JESSUP E R,KOLEV T V.A simple strategy for varying the restart parameter in GMRES(m)[J].Journal of Computational and Applied Mathematics,2009,230(2):751-761.
[18]QIN X,ZHANG J,LI G,et al.An element implementation of the boundary face method for 3D potential problems[J].Engineering Analysis with Boundary Elements,2010,34(11):934-943.