A Highly Accurate Upwind Finite Element Method for Ion-Flow Field Based on the Error Transport Equation
Cheng Qiwen1, Wan Baoquan2, Zhang Jiangong2, Zou Jun1
1. State key Laboratory of Control and Simulation of Power system and Generation Equipment Department of Electrical Engineering Tsinghua University Beijing 100084 China; 2. State Key Laboratory of Power Grid Environmental Protection China Electric Power Research Institute Wuhan 430074 China
Abstract：The upwind Finit element method (FEM) is proposed by Takuma to simulate the ion flow field stably and efficiently. The upwind FEM applies very simple numerical scheme and its drawback is that the corresponding numerical error is large. A correction method based on the error transfer equation is proposed to improve the accuracy of the original upwind FEM. The original continuity equation is corrected by the corresponding error transport equation. Numerical experiments show that the proposed method can improve the conservation property of the ion flow field and the accuracy has been significantly improved. This paper provides a general idea to obtain the high-precision calculation results through the explicit difference formats, which can also be applied to simulate other physics problems.
程启问, 万保权, 张建功, 邹军. 基于误差传递方程的离子流场迎风有限元高精度计算方法[J]. 电工技术学报, 2020, 35(21): 4432-4438.
Cheng Qiwen, Wan Baoquan, Zhang Jiangong, Zou Jun. A Highly Accurate Upwind Finite Element Method for Ion-Flow Field Based on the Error Transport Equation. Transactions of China Electrotechnical Society, 2020, 35(21): 4432-4438.
[1] Maruvada P S, Janischewskyj W. Analysis of corona losses on DC transmission lines: I-unipolar lines[J]. IEEE Transaction on Power Apparatus and Systems, 1969, P45-88(5): 718-731. [2] 田冀焕, 邹军, 刘杰, 等. 高压直流双回输电线路合成电场与离子流计算[J]. 电网技术, 2008, 32(2):61-70. Tian Jihuan, Zou jun, Liu Jie, et al. Calculation of total electric field and ionic current density of double-circuit HVDC transmission lines[J]. Power System Technology, 2008, 32(2): 61-70. [3] 乔骥, 邹军, 袁建生, 等. 采用有限差分求解高压直流输电线路空间离子流场的新方法[J]. 电工技术学报, 2015, 20(6): 85-91. Qiao Ji, Zou Jun, Yuan Jiansheng, et al.A new finite difference based approach for calculating ion flow field of HVDC transmission lines[J]. Transactions of China Electrotechnical Society, 2015, 20(6): 85-91. [4] Qiao Ji, Zhang Pengfei, Zhang Jiangong, et al.An iterative flux tracing method without deutsch assumption for ion-flow field of AC/DC hybrid transmission lines[J]. IEEE Transaction on Magnetics, 2018, 54(3): 1-4 [5] 乔骥, 徐志威, 邹军, 等. 一种消除Deutch假设的高精度迭代特征线方法求解高压直流输电线路离子流场[J]. 电工技术学报, 2018, 33(19): 4419-4425. Qiao Ji, Xu Zhiwei, Zou Jun, et al.A high-accuracy iterative method of characteristics without deutsch assumption for calculating ion-flow field of HVDC overhead lines[J]. Transactions of China Electrotechnical Society, 2018, 33(19): 4419-4425. [6] Liu Jie, Zou Jun, Tian Jihuan, et al.Analysis of electric field, ion flow density, and corona loss of same-tower double-circuit HVDC lines using improved FEM[J]. IEEE Transaction on Power Delivery, 2009, 24(1): 482-483. [7] Li Xin.Numerical analysis of ionized fields associated with HVDC transmission lines including effect of wind [D]. Manitoba: The University of Manitoba, 1997. [8] Takuma T, Ikeda T, Kawamoto T.Calculation of ion flow fields of HVDC transmission lines by the finite element method[J]. IEEE Transaction on Power Systems, 1982, 1(12): 4802-4810. [9] 甄永赞, 崔翔, 卢铁兵, 等. 离子流场中导体充电电位的计算[J]. 中国电机工程学报, 2011, 31(27): 8-13. Zhen Yongzan, Cui Xiang, Lu Tiebing, et al.Calculating charged electric potential of the conductor in ionized field[J]. Proceedings of the CSEE, 2011, 31(27): 8-13. [10] Huang Guodong, Ruan Jiangjun, Du Zhiye, et al.Highly stable upwind FEM for solving ionized field of HVDC transmission line[J]. IEEE Transaction on Magnetics, 2012, 48(2): 719-722. [11] 杨扬, 陆家榆, 杨勇. 基于上流有限元法的同走廊两回±800kV直流线路地面合成电场计算[J]. 电网技术, 2012, 36(4): 22-27. Yang Yang, Lu Jiayu, Yang Yong.Calculation of total electric field at the ground level under double-circuit ±800kV DC transmission lines arranged on same corridor with upstream FEM method[J]. Power System Technology, 2012, 36(4): 22-27. [12] 乔冀, 葛小宁, 邹军. 采用通量线-有限元混合方法求解有风条件下直流输电线路离子流场[J]. 电工技术学报, 2019, 34(5): 910-916. Qiao Ji, Ge Xiaoling, Zou Jun.A flux-tracing hybrid method for calculating ion-flow field of HVDC overhead lines in presence of wind[J]. Transaction of China Electrotechnical Society, 2019, 34(5): 910-916. [13] 袁海燕, 傅正财. 基于有限元法的±800kV特高压直流输电线路离子流场计算[J]. 电工技术学报. 2010, 25(2): 139-146. Yuan Haiyan, Fu Zhengcai.Corona ionized field analysis of ±800kV HVDC transmission lines[J]. Transaction of China Electrotechnical Society, 2010, 25(2): 139-146. [14] Qiao Ji, Zou Jun, Zhang Jiangong, et al.Ion-flow field calculation of HVDC overhead lines using a high-order stabilization technique based on Petrov-Galerkin method[J]. IET Generation, Transmission and Distribution, 2018, 12(5): 1138-1189. [15] 乔骥. 交直流并行线路离子流与混合电场计算方法及应用研究[D]. 北京: 清华大学, 2018. [16] Arthur J B, Zoltan J C, James F.Interfacing the finite-element method with the method of characteristic field models[J]. IEEE Transactions on Industry Applications, 1989, 25(3): 533-538. [17] Tian Yi, Huang Xinbo, Tian Wenchao.Hybrid method of calculation of ion-flow fields of HVDC transmission lines[J]. IEEE Transaction on Dielectrics and Electrical Insulation, 2016, 23(5): 2830-2839. [18] Qin Yuehui.Discrete error transport equation for error estimation in CFD[D]. Michigan: Michigan State University, 2004. [19] Zienkiewicz O C, Zhu J Z.The super convergent patch recovery and a posteriori error estimates. Part 1: the recovery technique[J]. International Journal for Numerical Methods in Engineering, 1992, 33: 1331-1364. [20] Martin M.Generation and measurement of dc electric fields with space charge[J]. Journal of Applied Physics, 1981, 52(5): 3135-3144. [21] Yin Han, Zhang Bo, He Jinliang, et al.Time domain finite volume method for ion-flow field analysis of bipolar high voltage direct current transmission lines[J]. IET Generation, Transmission and Distribution, 2012, 6(8): 785-791.
2020, Vol. 35 
