基于管状导体模型钢轨内阻抗计算

Calculation of rail internal impedance based on tubular conductor model

针对钢轨等效管状导体模型在大参数下利用修正Bessel函数表示的内阻抗公式计算其钢轨内阻抗时,出现数值计算不稳定及收敛困难问题,提出引入缩放比例因子,对修正Bessel函数进行缩放,并利用数值积分法计算缩放后的Bessel函数,得到数值计算稳定且精度高的内阻抗计算公式。利用该公式分析电流频率、幅值对钢轨内阻抗的影响规律,同时,使用有限元法对钢轨模型进行仿真计算,验证该计算公式的准确性。研究结果表明:该内阻抗计算公式解决了数值计算不稳定及收敛困难问题,反映了钢轨电阻和内电感随电流幅值、频率的变化规律,钢轨电阻和内电感计算结果与有限元仿真结果的相对误差均在±5%以内,可见该公式计算精度较高,可为牵引供电系统建模时钢轨内阻抗的计算提供可靠的数据支撑。

Aiming at the problem of existing numerical calculation instability and convergence difficulty when calculating the rail internal impedance by using the internal impedance formula expressed by modified Bessel function at large parameters for rail equivalent tubular conductor model, a scaling factor was introduced to scale the modified Bessel function, which was then calculated through the numerical integration method. In this way, a stable and accurate internal impedance formula was obtained. The obtained formula was used to analyze the influence of current frequency and amplitude on rail internal impedance. At the same time, the finite element method was used to simulate the rail model as a way to verify the accuracy of the formula. The results show that the internal impedance formula can solve the problem of numerical calculation instability and convergence difficulty, and correctly reflects the change laws of rail resistance and internal inductance with current amplitude and frequency. The relative errors between the calculated results and simulated results of rail resistance and internal inductance are within ±5%, which proves the improvement in the calculation accuracy of the formula,providing reliable data for the calculation of rail internal impedance in the modeling of traction power supply system.