基于贝塞尔函数修正的异型长导体阻抗计算实用方法  

A Practical Method for Impedance Calculation of Special-shaped Long Conductor Based on Bessel Function Modification

作　　者：张文仁 ZHANG Wen-ren(Lanzhou Railway Design Institute Co.,Ltd.,China Railway First Survey and Design Institute Group,Lanzhou 730000,China)

机构地区：[1]中铁第一勘察设计院集团兰州铁道设计院有限公司

出　　处：《兰州交通大学学报》2019年第6期50-55,共6页Journal of Lanzhou Jiaotong University

摘　　要：异型长导体的阻抗通常用简化计算得到,将异型长导体截面直接按几何尺寸换算等效为圆截面的长导体,再按圆截面的长导体计算阻抗.计算结果与实测数据误差较大.为此,从导体的电流密度入手,依据麦可斯韦方程和复变量贝塞尔函数的近似解法,并利用贝塞尔函数中变量绝对值的两种特殊条件,重新推理圆柱型长导体的阻抗计算方法,得到了圆柱型长导体简化计算公式.基于电磁理论先把异型长导体等效为管型长导体.设定管型长导体与圆柱型长导体两个导体截面总电流相等且外表面处电流密度相等,继而把管型长导体等效为圆柱型长导体,将异型长导体的特殊结构简化为圆柱型长导体,进而按等效圆柱型长导体计算阻抗.实例计算结果与实测数据误差符合工程要求,具有实用价值.The impedance of a special-shaped long conductor is usually obtained by simplified calculation.The cross-section of a special-shaped long conductor is directly converted into a long conductor with circular cross-section according to its geometrical size,and then the impedance is calculated according to the long conductor with circular cross-section.The error between the calculated results and the measured data is large.In this paper,starting with the current density of conductors,according to the approximate solution of McCosway equation and Bessel function of complex variables,the impedance calculation method of long cylindrical conductors is re-reasoned,and the simplified calculation formula of long cylindrical conductors is obtained by using two special conditions of absolute value of variables in Bessel function.Based on the electromagnetic theory,the special-shaped long conductor is first equivalent to the tubular long conductor.It is assumed that the total cross-sectional current of the two conductors is equal and the current density at the outer surface is equal.Then the tube-shaped long conductor is equivalent to the cylindrical long conductor.The special structure of the special-shaped long conductor is simplified to the cylindrical long conductor,and the impedance is calculated according to the equivalent cylindrical long conductor.The error between the calculated results and the measured data in this paper meets the engineering requirements and has practical value.

关 键 词：圆柱导体 贝塞尔函数 阻抗计算 等效半径 内阻抗 

分 类 号：TM751[电气工程—电力系统及自动化]