## 1 Introduction
The authors reported the results of preliminary research on the benefits of COILs in terms of increased transmission capacity. Based on those studies, they proposed a concept of a flexible compact AC transmission system. Study [23] investigated the outage rate caused by lightning strikes on compact power transmission lines. To that end, design differences between compact and conventional power transmission lines were taken into consideration. Article [24] dealt with the magnetic field analysis of a 150 kV compact transmission line. The results indicated that the maximum magnetic field density around the 150 kV compact transmission line was 8.25 uT, which met the WHO standard (100 uT). In [25], methods for lightning protection of compact overhead power lines are presented. Article [26] discusses the engineering aspects of a new configuration of transmission line. The line was of a compact delta design, differing significantly from the standard flat horizontal configuration. Article [27] details the testing of the first small-scale 500 kV transmission line in China. A number of tests were conducted to investigate its characteristics. The electrical parameters, including positive and negative sequence impedances, matched the design values. In [28], it was shown that large-power compact overhead 500 kV transmission lines will contribute to significant economic gains. In [29; 30; 31; 32], several models of 500 kV compact transmission lines were described, including single-circuit and double-circuit ones. The results of the calculations confirmed that the application of COHLs can reduce the maximum surface field gradients as well as reduce the surge impedance, which leads to a significant increase in transfer capacity. The main characteristics of COHLs are reported in [30]. On the basis of the above review, we can conclude that the relevance of the study of load flows and electromagnetic fields of COHLs has been well-established. In the future, it will be possible to use COHLs in the networks feeding traction substations of mainline AC railroads. Against the backdrop of digitalization and the use of power in the transport sector, computer technologies should be utilized to assess the effectiveness of such engineering solutions. This can be implemented based on the integrated modeling of electric power systems and power supply systems of railroads using the three-phase (ABC) frame of reference [33]. Below are the results of research aimed at developing digital models of COHLs and determining the effectiveness of utilizing such transmission lines in 220 kV electrical networks that power traction substations. This study contributes to the existing literature by providing the following:  
* We propose original models of power systems and power supply systems for AC railroads, with such models enabling quantitative evaluation of efficacy and the application of COHLs for supplying power to traction substations;
* The approach adopted for the creation of these models stands apart from other approaches in that it is system-based and treats COHLs as inseparable from the power flows of a complex power system. * In contrast to traditional methods based on a single-line representation, our models were built using the three-phase (ABC) reference frame, which provides the most adequate modeling of power system load flows with single-phase traction loads that create significant imbalances in the electrical networks that feed them. * Dynamics changes in traction loads were captured by simulating the movement of trains along real-world rail track profiles.