Calculation of Rail Internal Impedance by Using Finite Elements Methods and Complex Magnetic Permeability

Alberto Dolara,Sonia Leva

doi:10.1155/2009/505246

Alberto Dolara, Sonia Leva

Open Access

https://doi.org/10.1155/2009/505246

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Abstract

The internal parameter of UNI 60 rail is calculated by using finite elements methods. Steel's characterizations by its normal magnetization curve and by complex magnetic permeability are here considered and included into the proposed FEM models. Rail's resistance and internal inductance in function of current and frequency are calculated using both FEM and analytical models. The results obtained at the frequency of 50 Hz are compared with few measurements available, and then they are extended to other frequencies.

Highlights

The railway electric system is usually modeled by a Multiconductor Transmission Line (MTL) [1]
It is known that the hysteresis phenomenon causes time delay between the induction and the magnetic field, and that the loop area represents the energy converted in heat in a cycle
The component of the induction in phase with the magnetic field is associated with the average energy stored in magnetic field; the in-quadrature component is related to hysteresis power loss

Summary

Introduction

The railway electric system is usually modeled by a Multiconductor Transmission Line (MTL) [1]. The characterization of this model by the definition of the resistance, inductance, capacitance, and conductance per unit length (p.u.l.) matrices requires that the electric and magnetic behavior of all the materials must be linear and isotropic. All the elements of these matrices are defined by the spatial position of conductors, their crosssection, and the magnetic and electric properties of the whole system’s materials. For MTL systems with isotropic and linear materials and circular cross-section conductor widely separated, the elements of these matrices can be analytically computed [2]. Rails are the common conductors between traction and signalling circuits and the interface between these circuits and the ground

Results

Discussion

Conclusion