Abstract
The article considers the methodology of forming the matrix of A-parameters of a rail line, represented by a multi-pole equivalent circuit. It is shown that when using a four-pole equivalent circuit of a rail line in case of violation of the equipotentiality of the circuit, it is impossible to take into account the flow of current along bypass paths, along the earth path, and the influence of adjacent track circuits. A multi-pole equivalent circuit of a rail line is represented as a 2x4 pole, in the rail lines of which self-induction EMF sources are included, and an earth path is used as the second wire. An equivalent multi-pole of equivalent circuit is represented by two groups of poles – at the input and output of the rail line, including one common (ground). The parameters of all elements of the equivalent multi-pole circuit are presented in the form of matrices, which makes it possible to analyze the state of the rail lines when changing the primary parameters of the rail multi-pole in a wide range. Using Kirchhoff's laws and solving a system of ordinary differential equations, the A-parameters of a rail multi-pole are obtained.
Highlights
In the analysis and synthesis of track circuits, one of the main tasks is to determine the dependencies between the complex amplitudes of the input and output electrical parameters of rail line (RL), depending on the class of its states
When modeling the asymmetric mode with the simulation of the asymmetry of one rail connected to the contact-line supports, using the matrix A-parameters of the rail line obtained by the developed method, the possibility of analyzing the asymmetric states of the rail lines was confirmed
One of the approaches to solving the problem is to consider a rail line, which is a line with distributed parameters, as a multi-pole
Summary
In the analysis and synthesis of track circuits, one of the main tasks is to determine the dependencies between the complex amplitudes of the input and output electrical parameters of RL, depending on the class of its states. These dependences are determined by the state equations of four-pole rail line equivalent circuits (Bruin et al, 2017). The analysis of established and transition modes in homogeneous long lines, which include rail lines in the absence of external and mutual influences, is based on the so-called telegraph equations. The solution of these hyperbolic partial derivatives differential equations is carried out using the Dalembert method and the Fourier method. The first method is based on the superposition of incident and reflected waves on each other and describes the physical processes in the lines well, but it is difficult to take into account the waves attenuation when implementing it. The second approach is based on the representation of the phenomena of summed standing waves, it is less "physical", but more convenient for practical calculations
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