摘要
钢轨内阻抗存在非线性频变特性,若在地铁牵引供电系统直流短路暂态建模中将其视为固定不变的常量,则必然会导致暂态计算误差增大,给后续的故障测距带来不利的影响。为了确定钢轨频变内阻抗,将钢轨等效为长直实心圆柱导体模型,推导了用Bessel函数表示的内阻抗解析公式。针对大参数条件下,因Bessel级数表达式的局限性而导致内阻抗公式计算结果不可靠的问题,提出采用指数逼近的Prony方法对Bessel函数进行近似,得到易于编程且准确度高的内阻抗计算修正公式,同时使用有限元法对钢轨进行涡流场仿真分析,给出了适用于不同频段钢轨内阻抗计算的模型半径。研究结果表明:修正后的内阻抗计算公式避免了大参数下的数值计算问题,能正确反映钢轨电阻和内电感随电流频率(0~500 Hz)、电流幅值(300~10000 A)变化的非线性规律。当电流幅值在300~10000 A范围变化时,不同频率下钢轨电阻和内电感计算结果与有限元仿真结果之间的Pearson相关系数均在0.9998以上,相对误差均在±5%以内,验证了所提方法的精确性和有效性,可为地铁牵引供电系统直流短路暂态计算中钢轨阻抗建模提供可靠的数据基础。
The internal impedance of rail exhibits non-linear freuqnecy-dependent charcateristics.If it is treated as a constant value in the transient modeling of the DC short circuit in the subway traction power supply system,it will inevitably lead to an increase in transient calculation errors,adversely affecting the subsequent fault distance measurement.To determine the frequency-dependent internal impedance of rail,the rail is modeled as long straight cylindrical conductor,and the analytical formula of internal impedance expressed by Bessel function is derived.As for the unreliable calculation result of inetrnal impedance formula due to the limitation of Bessel series expression,a Prony method with expotential approximation is proposed to approximate Bessel function.An internal impedance calculation correction formula with ease of programming and high accuracy is obtained.At the same time,the finite-element method is used to simulate the eddy current field of rail and the radii of model suitable for calculating rail internal impedance in different frequency bands is given.The results of research show that the modified internal impedance calculation formula can not only avoid the numerical calculation problem of large parameters,but also correctly reflect the non-linear variations of rail resistance and internal inductance with current frequency(0-500 Hz)and amplitude(300-10000 A).When the current amplitude varies from 300 A to 10000 A,the Pearson correlation coefficients between the calculated results and simulated results of rail resiatance and internal inductace under different frequencies are all above 0.9998,and the relative errors are all within±5%,which verify the accuracy and effectiveness of the proposed method,providing reliable data for rail impedance modeling in DC short-circuit transient calculation of metro traction power supply system.
作者
华敏
陈剑云
钟汉华
HUA Min;CHEN Jianyun;ZHONG Hanhua(State Key Laboratory of Performance Monitoring and Protecting of Rail Transportation Infrastructure,East China Jiaotong University,Nanchang 330013,China)
出处
《高压电器》
北大核心
2025年第9期175-183,共9页
High Voltage Apparatus
基金
国家自然科学基金(52362052)
江西省教育厅科学技术研究项目(GJJ2200660)。
关键词
钢轨内阻抗
大参数
BESSEL函数
PRONY方法
频变特性
有限元
rail internal impedance
large parameters
Bessel function
Prony method
frequency-dependent characteristics
finite-element method
作者简介
华敏(1991-),男,硕士,主要研究方向为轨道交通电气化与自动化(E-mail:772629093@qq.com);通信作者:陈剑云(1962-),男,博士,教授,主要研究方向为轨道交通供电系统运行与保护(E-mail:tiger984@163.com)。
