Simulation of the process of current distribution in a traction rail network

The article synthesizes a simulation model of a section of a traction rail network, analyzes the norms of permissible asymmetry current, at which a choke-transformer is able to function with a set quality. The simulation of the current distribution process that occurs in the traction rail network during the movement of trains of increased weight and length has been carried out. The graphs of the dependence of the asymmetry current on the traction current consumed by the electric rolling stock have been obtained, and the simulation of the dynamics of changes in the traction current in each of the rail lines has been carried out when the train was moving along a section of the traction rail network. Conclusions about the need to monitor the state of traction rail network elements, the service life of which in heavy traffic conditions is significantly reduced both due to dynamic loads and due to overheating due to the passage of increased traction currents have been made.


Rationale
The main component of the program for the development of heavy traffic on the training ground of the Russian Railways network is trains of increased weight and length. During they pass, there are significant loads on infrastructure facilities. In addition to the increase in axle load from 23 to 27 tf, the current consumed by the traction electric rolling stock also increases. The combination of these factors leads to premature failure of traction rail network elements with inadequate quality control over their condition, the strengthening of which is necessary in conditions of heavy traffic [1,2,3].
Due to the wearing of the elements, their resistance to the traction current increases and, as a consequence, an inequality of resistance of one rail thread appears relative to the other, which leads to the appearance of longitudinal asymmetry of the traction current. The asymmetry current is determined by the formula: where Irl1 is the value of the traction current flowing in the first rail line (A), I rl2 is the value of the traction current flowing in the second rail line (A). The asymmetry current magnetizes the magnetic system of the choke-transformer and at a certain value the signal current in the secondary winding becomes less than the trip relay operating current. It results an armature release [4,5]. The consequence of this is the appearance of a failure of the track chain "false occupied". The movement of trains on the section stops until identification and elimination of the cause of this failure. Due to train downtime, the Russian Railways company suffers financial and image losses.

Simulation model synthesis
To analyse the process of current distribution that occurs in the traction rail network during trains passing, it is necessary to develop its mathematical model. The traction electric rolling stock is replaced by the current source J, and the elements of the traction rail network with the corresponding resistances (Rbtj, Rhc, Rtj, Rwr, Rfr, Rwj, Rfj). It is also necessary to determine the maximum permissible values of the asymmetry current at which the choke-transformer stops converting the signal current and voltage with a set quality.
The document [3] defines the following maximum permissible rates of asymmetry current (see table  1). It shall be noted that the presented standard values are selected in such a way that even if they are slightly exceeded, stable operation of the choke-transformer is ensured.
Since 1990, the manufacturing plants have established the standards of the permissible asymmetry current, presented in table 2 [4].  Thus, in order to obtain the most accurate results during the simulation of the current distribution process in the traction rail network, the values given in Table 3 shall be used.

Simulation in MATLAB-Simulink
The model of a traction rail network section, implemented in the MATLAB-Simulink environment, consists of resistances, the values of which are determined in the paper [6,7,8]. = 18420.8 μOhm, and the total resistance of 10% of the rails, the sole wear of which is within the acceptable limits, will be Rfr1 = Rfr2 = The resistance of the choke jumpers Rbtj1 = Rbtj2 = 81.9 μOhm, however, in the considered case, these values can be ignored during the simulation. Figure 1 shows a block diagram of a simulation model of a traction rail network section.  With a traction current I> 3500 A, the asymmetry current Ia will exceed 520 A, which becomes critical for all types of choke transformers.
The MATLAB-Simulink environment also allows simulating the dynamics of changes in the traction current flowing in each of the rail lines and the asymmetry current when the train is moving (figures 3-6).   The obtained values allow to say that under the given conditions the value of the asymmetry current is more than 435 A, which will cause the failure of DT-0.2 (0.6) -500, DT-0.2 (0.6) -1000 type choketransformers. An increase in the traction current consumed by the electric rolling stock, or a deterioration in the state of the traction rail network elements, will lead to an increase in the asymmetry current to values at which choke-transformers, DT-0.2 (0.4) -1500 that is the most resistant to asymmetry of the traction current will fail.

Findings
In course of the study, a simulation model of a traction rail network section has been prepared. This model allows to simulate the process of current distribution by network elements. The values of the traction current at which the choke transformers installed on the traction rail network sections containing faulty elements will fail are determined. Analysis of the permissible asymmetry currents when the choke-transformer is capable of performing the function of converting the signal current and voltage with a set quality has been carried out [10,11].
At the next stage of the work, the model shall be supplemented with the possibility of analyzing the behaviour of the asymmetry current when the resistance of each of the elements of the traction rail network changes.
The results of the work allow to say that the failure of even several elements of the traction rail network can lead to disruption of the stable operation of the choke transformers and, as a result, to the failure of the rail circuits, which will negatively affect the carrying capacity of the railway.
In the conditions of heavy traffic, special control over the state of the elements of the traction rail network is necessary. In order to do it, it is necessary to develop an automated control systems, a feature of which, shall be the possibility of predictive analytics of ongoing processes (taking into account modern trends in the development of railway transport) [12,13,14]. This will require the creation of a multi-parameter mathematical model, on the basis of which it will be possible to train the system in order to obtain high-precision forecasts of the state of the elements of the traction rail network.