## 5 Conclusions  
The presented work is devoted to the study of the influence of conductive structures on the electromagnetic fields of the traction network.  
In the presence of a metal structure, the EMF becomes three-dimensional and the modeling problem is significantly complicated. The methodology for solving it is based on the following main provisions:  
* Current-carrying parts are represented as rectilinear segments that are located in space in accordance with the structure of the object; some elements, in particular grounding devices, can be located underground. To use the quasi-stationary zone equations, the dimensions of the set of objects should not exceed several hundred meters.
* The analyzed network can include power transmission lines and traction networks, transformers, loads, sets of short conductors, which are modeled in the same way as power transmission line wires for calculating the mode; due to the smallness of their resistance, this approach does not distort the network mode.
* The potentials and currents of short wires are determined by calculating the mode in phase coordinates.  
The analysis of the results of modeling, performed on the basis of the Fazonord software package according to the technique described in the article, showed that the presence of a metal overpass significantly changes the nature of the distribution of EMF strengths in space, especially in the immediate vicinity of it. These changes must be taken into account when determining the influence of EMF on the operation of communication systems and electronic devices located near the railway infrastructure. Unlike the plane-parallel EMF created by the traction network in the spans between supports, the field in this situation becomes three-dimensional. The technology for determining the strengths presented in the article was based on the use of the concept of conductor segments of limited length, some of which can be located underground. To be able to apply the equations of the quasi-stationary zone, the dimensions of the set of objects formed by these conductors did not exceed several hundred meters. The technique is universal and can be used to model the EMF of almost any conductive structures. It can be used in the practice of designing and operating traction power supply systems when developing measures to improve electromagnetic safety conditions.  
The described method of determining EMF is distinguished by the following features:* Systematicity--consisting in the possibility of modeling electromagnetic fields taking into account the properties and characteristics of a complex STE and the power supply electric power system;
* Universality--ensuring the modeling of power transmission lines and traction networks of various designs;
* Adequacy to the external environment--achieved by taking into account the profile of the underlying surface, underground communications, metal structures, artificial structures of railway transport, such as galleries, bridges, and tunnels;
* Complexity--ensured by combining the calculations of the mode and the determination of EMF strengths.  
Conceptualization, I.I. and A.K.; Methodology, A.K. and K.S.; Software, E.V.; Validation, A.B. and Y.V.; Formal analysis, I.I., K.S. and A.B.; Data curation, I.I., A.K. and A.B.; Writing--original draft, A.K., K.S. and E.V.; Writing--review & editing, I.I., E.V., I.B. and Y.V.; Visualization, Y.V.; Project administration, I.B.; Funding acquisition, I.B. All authors have read and agreed to the published version of the manuscript.  
This study is financed by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project No BG-RRP-2.013-0001-C01.  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.