## 5 Discussion  
The results obtained from mathematical calculations of the magnetic field in the selected locations of point M\({}_{i}\) are presented mathematically in Table 1. The mathematical calculation results in Table 1 suggest that the magnetic field strength achieves its maximum values at points M\({}_{6}\) and M\({}_{11}\), and these values are grouped into six categories with six types of conductor transposition. These points of observation are situated near phases B\({}_{1}\) and B\({}_{2}\) and between phases C\({}_{1}\) and C\({}_{2}\) of the double-circuit 400 kV overhead power line conductor system. The observation point M\({}_{8}\) is at the very centre of the 400 kV overhead power line (see Figure 3). At this particular point, the magnetic field strength values are also lower. The obtained analytical results were also verified through a simulation using the software package COMSOL Multiphysics 3.5. The model simulation additionally assessed the marginal and ambient conditions [6]. Results obtained from a finite element method (FEM) simulation of the magnetic field in the selected locations of point M\({}_{i}\) are presented mathematically in Table 2. The FEM simulation results in Table 2 suggest that the magnetic field strength reaches its maximum values at points M\({}_{6}\) and M\({}_{11}\), and these values are also grouped into six categories with six types of conductor transposition. The results of the simulation (see the upper curve of Figure 4) were found to be close to the analytical results; consequently, the proposed methodology can be used to investigate the relevant magnetic field. The assessment of our findings and the obtained results lead us to the following suggestions: the mean error between the analytical findings and simulation results is below 4%. The methodology described here allows the calculation of the magnetic field strength at any point under the three-phase double-circle power transmission line. The graph in Figure 4 shows that as the measurement point M\({}_{i}\) gets farther from the outside phases of the double-circuit 400 kV overhead power line conductor system, the magnetic field strength decreases proportionally. However, at the distance of 12 m from phases B\({}_{1}\) and B\({}_{2}\), the magnetic field strength still exceeds 16 A/m (i.e., \(\mathbf{B}\) is more than 20 uT). The assessment of the calculation results revealed that values of the magnetic field strength exceed the numerical values established in the EU Hygiene Standard HN 104:2011. The regulation on the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Point** & **Distance** & **Group 1** & **Group 2** & **Group 3** & **Group 4** & **Group 5** & **Group 6** \\
**No.** & **[m]** & **[A/m]** & **[A/m]** & **[A/m]** & **[A/m]** & **[A/m]** & **[A/m]** \\ \hline M\({}_{1}\) & 0 & 2.63 & 2.85 & 3.14 & 2.76 & 2.76 & 2.95 \\ M\({}_{2}\) & 5 & 4.51 & 4.66 & 5.23 & 4.75 & 4.94 & 5.42 \\ M\({}_{3}\) & 10 & 8.84 & 9.12 & 9.41 & 8.74 & 9.79 & 9.6 \\ M\({}_{4}\) & 15 & 18.18 & 19.67 & 19.95 & 19.48 & 21.38 & 22.33 \\ M\({}_{5}\) & 20 & 35.72 & 37.05 & 35.63 & 40.38 & 40.85 & 41.8 \\ M\({}_{6}\) & 22 & 39.48 & 41.33 & 38.48 & 46.08 & 44.65 & 47.5 \\ M\({}_{7}\) & 25 & 32.9 & 35.15 & 31.83 & 43.7 & 41.33 & 45.6 \\ M\({}_{8}\) & 30 & 18.8 & 18.53 & 9.5 & 35.63 & 30.88 & 38.0 \\ M\({}_{9}\) & 35 & 37.13 & 31.35 & 31.83 & 43.7 & 41.33 & 45.6 \\ M\({}_{10}\) & 38 & 42.3 & 38.0 & 38.48 & 46.08 & 44.65 & 47.5 \\ M\({}_{11}\) & 40 & 37.6 & 34.2 & 35.63 & 40.38 & 40.85 & 41.8 \\ M\({}_{12}\) & 45 & 19.72 & 18.81 & 19.95 & 19.49 & 21.38 & 22.33 \\ M\({}_{13}\) & 50 & 9.21 & 8.74 & 9.41 & 8.74 & 9.79 & 9.6 \\ M\({}_{14}\) & 55 & 4.8 & 4.37 & 5.23 & 4.75 & 4.94 & 5.42 \\ M\({}_{15}\) & 60 & 3.01 & 2.47 & 3.14 & 2.76 & 2.76 & 2.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The mathematical calculation of the effective values of the magnetic field strength at 1.5 m above the ground.