## 5 Results and Discussions  
### Magnetic Fields from the Considered Tefoil and Flat Formations  
Comparisons between FEM simulation results and analytical computation results (lateral profiles of the total RMS magnetic flux density at the height of 1 m above the ground) for the considered trefoil and flat formations are given in Figure 10a,b, respectively. Induced shield currents calculated by both methods are given in Tables 2 and 3, respectively. As it can be seen, the results obtained by the two methods correlate very well. The smallest difference in the RMS magnetic flux density at the cable central axis is obtained for trefoil formation (Figure 10a), namely 2.36 nT. For the three-phase underground power cable in flat formation (Figure 10b), the difference in RMS magnetic flux density at the centerline is 26.49 nT. In both cases, lower values of magnetic flux density have been obtained by numerical simulation. Clearly, these differences are too small for any practical purposes related to magnetic field exposure assessment, but we may assume a slightly different evaluation of the electromagnetic interaction between models (eddy currents in shields are neglected in the analytical model). Figure 9: Example of results obtained by analytical computation (the total RMS magnetic flux density and its transversal components at the height of 1 m above the ground): (**a**) for the three-phase power cable in trefoil formation; (**b**) for the three-phase power cable in flat formation. Decreasing the number of mesh elements to about 620,000 still produces very accurate results in the RMS magnetic flux density (differences below 0.04% at the height of 1 m above the ground, regardless the measurement point), while the computation time reduces from about 25 min to 10 min (Intel(r) Core(tm) i7-12700H Processor, 14 CPU, 16 GB RAM, GeForce RTX 3050 GPU). Doubling and even tripling the number of mesh elements has no significant effect on the calculated RMS magnetic flux density profile at the height of 1 m above the ground. With the setting of Balloon boundary conditions, the distance from the source of magnetic fields (cables) to the outer boundary is not a critical issue, since different dimensions of boundary has almost no effect on the simulation results (for instance, the simulation results obtained by doubling the side \(a\) of the computational domain are virtually identical). If the side \(  
At maximum rated current (319 A), the magnetic field at the central axis of the three-phase power cable in trefoil formation is very low compared to the ICNIRP 1998 limit for general public (100 \(\upmu\)T at 50 Hz) [28], ranging from 4.377 \(\upmu\)T at the ground level (0-m height) to 0.357 \(\upmu\)T at the height of 2 m. At the standard height of 1 m, the RMS magnetic flux density at the centerline is 0.864 \(\upmu\)T (115.74-fold below the ICNIRP reference level), while at the distance of 10 m from the cable axis it falls to only 0.027% of the ICNIRP limit. Much higher exposure levels can be observed for the three-phase power cable in flat formation (maximum rated current of 352 A), in which case the RMS magnetic flux density above the cable axis varies from 19.409 \(\upmu\)T at 0-m height to 1.604 \(\upmu\)T at the height of 2 m. Once again, at the standard height of 1 m, the RMS magnetic flux density at the centerline is 3.876 \(\upmu\)T (25.8-fold below the ICNIRP reference level), falling to 0.122% of the ICNIRP limit at the distance of 10 m from the cable axis. These values should be seen as maximum exposure levels from such common configurations of 12/20 kV three-phase underground power cables. To illustrate the effect of shields on the magnetic field reduction, Figure 12a,b compare vertical profiles of the total RMS magnetic flux density at the central axis of the two analyzed cable structures, obtained by numerical simulation, with solidly bonded and non-bonded shields.