Calculation Of The Frequency-dependent Internal Impedance Parameters Of Conductors In Traction Network

The multi-conductor system of electrified railway traction network has its particularity.It is significant to research the electrical parameters of traction network wires for mastering the electrical performance of traction power supply system.In this paper,starting from the calculation of the internal impedance of general circular conductors,the internal impedance theoretical calculation formula and numerical calculation of solid circular conductors are briefly described for most of the overhead circular conductors in the traction network,and then the numerical oscillation problem caused by Bessel function with large parameters in the numerical calculation process and the solution are described.However,the contact wire and rail track used in the traction network have a specific cross-section,and the rail also has ferromagnetic nonlinearity.In view of the internal impedance calculation of the contact wire,based on the finite element method,the internal frequency-dependent impedance parameters and equivalent radius of different contact wires are proposed.By using the finite element software(ANSYS Maxwell),aiming at existing electrified railway lines are widely used in several kinds of contact wires,the calculation results shows the ac resistance and internal inductance change with frequency curve(0~10MHz),and two types of nominal cross-section of the equivalent radius of contact line.Aiming at the internal impedance problem of rail,this paper presents a finite element method based on incremental permeability to calculate the frequency-dependent impedance of the rail in transient state.By analyzing the magnetization characteristics of the rail under the steady state large current signal as the theoretical basis.The local hysteresis curve of the rail under transient small current signal was further studied.According to the magnetization mechanism and definition of incremental permeability,the incremental permeability curve of large current signal superimposed with transient signal was calculated and incorporated into the finite element ANSYS Maxwell model.In order to reflect the difference of the impedance characteristics between the high-frequency transient signal and the low-frequency large current signal propagating on the rail,the frequency-dependent impedance curves of the rail under the large current signal are calculated for comparison.The results show that the incremental magnetic field caused by the superposition of large ac signal with small signal disturbance in the transient condition will affect the internal impedance value of the P60 rail,and the values of the ac resistance and internal inductance of the rail with frequency variation(0~10MHz)calculated under the incremental magnetic field are both greater than the values of thefrequency variation impedance under the steady-state ac large signal.