## 3 Method and Results of Modeling
\begin{table}
\begin{tabular}{c c c c c} \hline
**Transmission Line Design** & \(\mathbf{U_{\text{min}}}\)**, **kV** & **Max(\(\mathbf{k_{2U}}\)), \%** & **Max (\(\mathbf{\Delta P_{\text{TN}}}\)), kW** & **Max (\(\mathbf{\Delta P_{\text{TL}}}\)), MW** \\ \hline Standard power transmission line with & & & & \\ AS-600 conductors & 16.73 & 4.86 & 1015 & 1.18 \\ \hline COHL with a vertical arrangement of & & & & \\ conductors & 16.93 & 3.43 & 906 & 1.37 \\ \hline Coaxial two-segment COHL & 18.24 & 2.1 & 872 & 1.18 \\ \hline Coaxial four-segment COHL & 18.72 & 1.6 & 857 & 1.14 \\ \hline COHL with a delta arrangement & & & & \\ of conductors & 18.41 & 1.64 & 872 & 1.2 \\ \hline Double coaxial COHL & 19.05 & 1.55 & 880 & 1.22 \\ \hline COHL with a parabolic arrangement & & & & \\ of conductors & 18.21 & 2.08 & 871 & 1.22 \\ \hline COHL with a three-segment arrangement & & & & \\ of conductors & 21.98 & 1.02 & 753 & 0.81 \\ \hline COHL with a concentric arrangement & & & & \\ of conductors & 19.76 & 1.37 & 832 & 0.88 \\ \hline \end{tabular} Notes: \(U_{\text{min}}\) is the minimum voltage on the bow collector of the electric locomotive; \(k_{2U}\) is the unbalance ratio at 220 kV buses of TS 4; \(\Delta P_{\text{TN}}\) represents power losses in the TN of the middle inter-substation area; 2; \(\Delta P_{\text{TL}}\) represents losses in the transmission line 1.  
\end{table} 
Table 1: Extreme values of parameters. \begin{table}
\begin{tabular}{c c c c c} \hline
**Transmission Line Design** & \(\mathbf{k_{\text{U220}}}\)**, \%** & \(\mathbf{k_{\text{U27.5}}}\) \%** & \(\mathbf{E_{\text{max}}}\)**, kV/m** & \(\mathbf{H_{\text{max}}}\)**, A/m** \\ \hline Standard power transmission line with AS-600 conductors & 3.17 & 39.74 & 0.52 & 2.39 \\ \hline COHL with a vertical arrangement of conductors & 6.31 & 40.14 & 0.33 & 0.94 \\ \hline Coaxial two-segment COHL & 4.05 & 33.19 & 0.92 & 0.66 \\ \hline Coaxial four-segment COHL & 3.48 & 31.13 & 1.05 & 0.25 \\ \hline COHL with a delta arrangement of conductors & 3.92 & 23.19 & 1.21 & 0.8 \\ \hline Double coaxial COHL & 2.96 & 29.8 & 0.73 & 1.2 \\ \hline COHL with a parabolic arrangement of conductors & 4.64 & 33.8 & 1.21 & 0.78 \\ \hline COHL with a three-segment arrangement of conductors & 2.75 & 23.19 & 2.14 & 0.55 \\ \hline COHL with a concentric arrangement of conductors & 2.68 & 27.87 & 2.01 & 0.22 \\ \hline \end{tabular} Notes: \(k_{\text{U220}}\) is the harmonic distortion at 220 kV buses of TS 4, phase C; \(k_{\text{U27.5}}\) is the harmonic distortion at the 27.5 kV input of TS 4; \(E_{\text{max}}\) is the amplitude of the electric field strength; \(H_{\text{max}}\) is the amplitude of the magnetic field strength.  
\end{table} 
Table 2: Maximum values of parameters. Our analysis of the results thus obtained allows us to conclude that the use of compact power transmission lines (Figure 4) instead of standard overhead lines (Figure 2) in the external power supply system of railroads enabled the following gains:  
* Voltages on bow collectors of electrical rolling stock increased and stabilized (Table 1 and Figure 15). In the computational examples with a standard feeding line, voltage on the bow collector of the first train decreased below the permissible limit, and when using a three-segment COHL design it increased to 22 kV;
* Losses in the traction network were reduced; the maximum reduction took place when using a three-segment COHL design (Table 1 and Figure 17);
* Power quality was improved; negative-sequence unbalance ratios at 220 kV buses of traction substations were reduced (Table 1 and Figure 16);
* Harmonic distortions in the traction network (Table 2 and Figure 19) and at the interfaces with EPS networks (Table 2 and Figure 20) were reduced;
* The maximum amplitudes of the electric field (EF) of all the considered COHLs, except for the line with a vertical arrangement of wires, exceeded similar values for a standard power transmission line. The largest, fourfold, difference took place in the case of a three-segment COHL.