电气化铁路钢轨内阻抗计算研究

Study on calculation of internal impedance for railof electric railway

为解决因集肤效应和钢轨横截面不规则造成的钢轨内阻抗计算困难的问题,在把钢轨等效为圆柱形导体的基础上,分别推导出钢轨在电流低、高频时的内阻抗计算公式;根据Rolle平均值定理及Maclaurian近似公式,得到整个频率范围内钢轨内阻抗的计算公式;利用有限元法对钢轨模型进行仿真计算。结果表明:所推导的钢轨内阻抗计算公式能正确地反映钢轨交流电阻和内电感随电流幅值、频率的变化规律。将计算结果同有限元仿真结果对比,相对误差小于6%,验证了该计算公式的正确性,从而为牵引供电系统建模时钢轨内阻抗的计算提供了可靠的理论基础。

In order to deal with the difficulty in calculation of rail internal impedance caused by skin effect and irregular sections of the rail,the rail is taken as a cylindrical conductor at first.Based on that,the formula of internal impedance under the current at both low and high frequency are derived.According to the derived formulae and Rolle's average value theorem as well as Maclaurian approximate formula,the formula adapted to the whole frequency range is obtained.Finite element method is used on the rail model to simulate and calculate the impedance.The result shows that the formula can correctly reflect the change rules of rail alternating current resistance and internal inductance with current amplitude and frequency.The error between the calculation result and the simulation result is less than 6%,which verifies the formula.The research can be a theoretical basis for the calculation of rail internal impedance under the establishment of a traction power supply system model.