## 2 Object of the Study  
The simulations reported in this paper were performed in the Fazonord software package [33]. We considered a power supply system for a section of mainline railroad, including an external 220 kV network, four traction substations, and three areas between the substations (Figure 1). The simulation was carried out for two scenarios. In the first one, the 220 kV feeder network used standard lines (Figure 2) made of AS-600 wires, and in the second one, the power lines had a compact design (Figure 3). The COHLs investigated here fall into three groups: with coaxial, linear, and sector-shaped arrangements of conductors. We considered eight COHL designs. The coordinates of their conductors are shown in Figure 4.  
Figure 1: Network circuit: TS-traction substation.  
Figure 3: Classification of COHLs.  
Figure 2: Coordinates of the arrangement of conductors of the power line of a standard design.  
Compact power transmission lines are characterized by their unconventional arrangements of conductors and close together placement of phases, which keep the distance  
Figure 4: Coordinates of conductor arrangement for compact transmission lines: (**a**)—with a vertical arrangement of conductors, (**b**)—two-segment coaxial, (**c**)—four-segment coaxial, (**d**)—delta, (**e**)—double coaxial, (**f**)—parabolic, (**g**)—three-segment, (**h**)—concentric.  
between them to a permissible minimum. The distance is subject to technical limitations, which are determined by the following factors:  
* Possible movement of conductors within the span due to wind;
* Non-synchronous galloping;
* Galloping during ice removal;
* Possible overvoltages and constraints on corona discharge.  
Compact power transmission lines are built by bringing phase conductors closer together using in-span spacers made of insulating materials, such as polymer rod insulators. In this case, the distances between phases on the towers do not change.  
Another way of building compact transmission lines is based on the use of special-purpose towers. When selecting the minimum allowable phase distances, switching overvoltages act as the limiting factor. Minimum cross-section values are limited by radio interference and corona losses.  
In terms of their design, the investigated COHLs fall into three groups (Figure 3):  
* Lines with a coaxial arrangement of conductors (Figure 4b,c,e,h);
* Power transmission lines with a linear arrangement of current-conducting parts (Figure 4a,e);
* Sector-shaped COHLs (Figure 4d,g).  
In addition to obviously reducing right-of-way requirements, compact overhead lines lessen the impact of electromagnetic fields on the natural environment, increase the capacity of power transmission lines, and reduce power losses compared to conventional three-phase lines. These factors can be measured in quantitative terms by modeling COHLs using the three-phase frame of reference for different types of compact lines. The results of such modeling, performed in the Fazonord software package, are detailed below. Key differences between the presented findings and the results reported in the literature review of Section 1 include the following: load flow analysis of COHLs was carried out so as to take into account the significant unbalance caused by single-phase traction loads; simulations were performed for a series of load flows corresponding to the movement of traction loads in space.