用镜象电流法计算带偏心母线圆环铁芯的磁场

Calculation of H in a Circumferential Iron Core with Eccentric Bus by Setting Mirror Image Currents

母线型和套管型电流互感器主要用于发电机以及超高压电网,具有圆环铁芯线圈结构。计算带偏心母线的圆环铁芯磁场的不对称分布有助于分析母线型和套管型电流互感器的误差特性,从而提出科学的计量方法。磁场求解的场域满足磁势的拉普拉斯方程,可以通过复变函数的保角变换方法把圆环域变换为矩形域并延拓为带状域,结合平面镜象电流方法求解。这种方法物理概念清晰,可以用简单的无穷级数和求解,特别适合使用Matlab工具计算。本文提供了实用的Matlab计算程序,并用此程序计算了样本铁芯的磁场分布,测量了按样本铁芯制造的电流互感器的误差。结果表明磁场计算与分析的结果与实际情况基本一致。

Current transformers in bus type have been mainly used in power plants and ultra high voltage power nets. Their structure is with a circumferential iron core and secondary winding distributed uniformly along circumference. When eccentricity of primary current bus occurs the error characteristics will be changed by asymmetry magnetic field in the core. Circumferential field intensity can be calculated by solving Laplace＇s equation in field domain or by finite-element method. Also the conformal transformation with complex variable theory can give an image of section of line to a circle and it could meet the condition to set mirror image currents before infinite half plane region. The advantage of mirror image currents method is with physical concept rather than that with mathematics. For a certain specimen, field intensity in the core was derived by Matlab program and the error of corresponding current transformer was calibrated. Results show that calculated data are in good agreement with experiment.