Abstract：Sinusoidal steady-state field exists widely in power transmission and transformation system and other practical engineering. It is very important to carry research to its variation law and maximum. So further study on three dimensional sinusoidal steady-state field is required to compute the maximum and understand the endpoint trajectory of three dimensional field vector. In this paper, analytical formulas for the maximum, the minimum and direction cosine of 3-D sinusoidal steady-state field are deduced based on phasor. It is demonstrated that the endpoint trajectory is an elliptical orbit in three dimensional space by coordinate transformation. The availability of the formulas is verified by comparing the computational results with the measured results.
王泽忠, 刘士利, 黄颖. 三维正弦稳态场矢量最大值的直接计算方法[J]. 电工技术学报, 2012, 27(4): 1-6.
Wang Zezhong, Liu Shili, Huang Ying. Direct Calculation Method for Maximum of 3-D Sinusoidal Steady-State Field Vector. Transactions of China Electrotechnical Society, 2012, 27(4): 1-6.
[1] Harrington R F. Time-harmonic electromagnetic fields[M]. New York: Mc-Graw-Hill, 1961. [2] 陈丕璋, 严烈通, 姚若萍. 电机电磁场理论与计算[M]．北京: 科学出版社, 1986． [3] Singer H, Steinbigler H, Weiss P. A charge simulation method for the calculation of high fields[J]. IEEE Transactions on Power Apparatus and Systems, 1974, (5): 1660-1668. [4] Deno D W. Transmission line field[J]. IEEE Transactions on Power Apparatus and Systems, 1976, (5): 1600-1611. [5] 邵方殷, 李顺元. 用模拟电荷法计算变电站三维空间电场[J]. 中国电机工程学报, 1982, 15(2): 35-46. Shao Fangyin, Li Shunyuan. Calculation of three- dimensional electric field in a substation by means of charge substitution method[J]. Proceedings of the CSEE, 1982, 15(2): 35-46. [6] Hoffmann J N, Pulino P. New developments on the combined application of charge simulation and numerical methods for the computation of electric fields[J]. IEEE Transactions on Power Delivery, 1995, 10(2): 1105-1111. [7] Gomollon A, Palau R. Steady state 3-D-field calculations in three-phase systems with surface charge method[J]. IEEE Transactions on Power Delivery, 2005, 20(2): 919-924. [8] Lee B Y, Park J K, Myung S H, et al. An effective modeling method to analyze electric field around transmission lines and substations using a generalized finite line charge[J]. IEEE Transactions on Power Delivery, 1997, 12(3): 1143-1150. [9] 刘晓明, 王尔智, 曹云东. 采用优化模拟电荷法的三维电场计算[J]. 电工技术学报, 2000, 15(6): 14-17. Liu Xiaoming, Wang Erzhi, Cao Yundong. Computation of three dimension electric field using the optimized charge simulation method[J]. Transaction of China Electrotechnical Society, 2000, 15(6): 14-17. [10] 卢铁兵, 肖刊, 张波, 等. 超高压输电线路铁塔附近的三维工频电场计算[J]. 高电压技术, 2001, 27(3): 24-26. Lu Tiebing, Xiao Kan, Zhang Bo, et al. Calculation of electric field distribution near EHV power towers[J]. High Voltage Engineering, 2001, 27(3): 24-26. [11] 彭迎, 阮江军. 模拟电荷法计算特高压架空线路3维工频电场[J]. 高电压技术, 2006 , 32(12): 69-73. Peng Ying, Ruan Jiangjun. Calculation of three- dimensional harmonic electric field around ultra high voltage overhead line based on the charge simulation method[J]. High Voltage Engineering, 2006, 32(12): 69-73. [12] 俞集辉, 周超. 复杂地势下超高压输电线路的工频电场[J]. 高电压技术, 2006 , 32(1): 18-20, 44. Yu Jihui, Zhou Chao. Power-frequency electric field of EHV transmission lines under condition of complex landscape[J]. High Voltage Engineering, 2006, 32(1): 18-20, 44. [13] 赵志斌, 崔翔, 张波. 应用矩量法计算变电站内的空间电磁场[J]. 中国电机工程学报, 2004, 24(11): 148-153. Zhao Zhibin, Cui Xiang, Zhang Bo. The electromagnetic field calculation in substation by the method of moment[J]. Proceedings of the CSEE, 2004, 24(11): 148-153． [14] Zhang Bo, He Jinliang, Cui Xiang, et al. Electric field calculation for HV insulators on the head of transmission tower by coupling CSM with BEM[J]. IEEE Transactions on Magnetics, 2006, 42(4): 543-546. [15] 卢斌先, 王泽忠, 李成榕, 等．500kV变电站开关操作瞬态电场测量与研究[J]. 中国电机工程学报, 2004, 24(4): 16-19． Lu Binxian, Wang Zezhong, Li Chengrong, et al. Measurements and research of switching operation transient electric field in 500kV substations[J]. Proceedings of the CSEE, 2004, 24(4): 16-19． [16] 饶章权, 郭启贵, 赵殿全. 500kV变电站工频电磁场分布测量[J]. 高电压技术, 2004, 30(9): 41-43. Rao Zhangquan, Guo Qigui, Zhao Dianquan. Measurement of power frequency electromagnetic field in 500kV substation[J]. High Voltage Engineering, 2004, 30(9): 41-43. [17] 梁振光, 董霞, 孟昭敦. 三相传输线产生的旋转电场[J]. 高电压技术, 2006, 32(10): 50-53. Liang Zhenguang, Dong Xia, Meng Zhaodun. Rotary electric field of three-phase transmission lines[J]. High Voltage Engineering, 2006, 32(10): 50-53. [18] 熊汉亮, 龚大德. 超高压变电站空间旋转电场的计算[J]. 天津大学学报, 1993, 26(4): 86-96. Xiong Hanliang, Gong Dade. Calculation of rotary space electric field at superhigh-voltage substation[J]. Journal of Tianjin University, 1993, 26(4): 86-96. [19] 姜常珍. 500kV变电站三相旋转电场的计算[J]. 天津大学学报, 1998, 31(3): 290-295. Jiang Changzhen. Calculation of three-phase rotary electric field at a 500kV voltage substation[J]. Journal of Tianjin University, 1998 , 31(3): 290-295. [20] 王泽忠, 刘士利, 孙静．特高压交流变电站设备附件工频电场计算[J]. 高电压技术, 2010, 36(1): 81-85. Wang Zezhong, Liu Shili, Sun Jing. Calculation of power frequency electric field near equipments in UHV AC substation[J]. High Voltage Engineering, 2010, 36(1): 81-85.
2012, Vol. 27 
