## 6 Conclusions  
The main achievements of this study are the development and validation of a simple and yet effective FEM model, based on ANSYS Maxwell (2D), for computing and analyzing low-frequency magnetic fields generated by three-phase underground cable systems with solid bonding. Comparisons to analytical computations based on the Biot-Savart law and the superposition principle, for both trefoil and flat formations of cables, revealed a very good agreement between results (for instance, at the standard height of 1 m above the ground, the differences in the RMS magnetic flux density at the central axis of the analyzed cable formations are only 2.36 nT and 26.49 nT, respectively).  
The effect of cable shields on the magnetic field reduction has also been investigated. At maximum rated current (under balanced loading conditions), the magnetic field reduction rate due to induced shield currents is clearly better for flat cable formation, but the remaining magnetic field is significantly higher than for trefoil cable configuration. A similar situation has also been observed for an arrangement of two adjacent three-phase power cables, first laid in flat formation and then laid in trefoil formation. However, in both cases investigated here, the highest magnetic field reduction rate (due to induced shield currents) is not obtained for the optimum (low magnetic field) phasing of the two circuits.  
The proposed FEM model can be adapted to calculate magnetic field distributions for any cable layout, as well as for various types of cable groups, taking into account influencing factors such as cable spacing, burial depth, phase sequence, magnetic permeability of soil. Generally, it may be used as an accurate tool for determining the worst-case magnetic field exposure levels produced by three-phase underground power cables close to the ground surface and for optimizing cable layout and location to mitigate magnetic field problems.  
Conceptualization, E.L., S.V. and A.S.; methodology, E.L. and S.V.; software, E.L. and S.V.; validation, E.L., S.V. and A.S.; formal analysis, E.L., S.V. and A.S.; investigation, E.L., S.V. and A.S.; resources, E.L., S.V. and A.S.; data curation, E.L., S.V. and A.S.; writing--original draft preparation, E.L., S.V. and A.S.; writing--review and editing, E.L. and A.S., visualization, E.L. and S.V.; supervision, E.L. and A.S. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sequence No.**} & \multicolumn{2}{c}{**Phase Sequence**} & \multirow{2}{*}{**Magnetic Field Reduction Rate at 1 m**} \\ \cline{2-2} \cline{4-4}  & **Left Circuit** & & **Right Circuit** & **above the Ground** \\ \hline
1 & ABC & A\({}^{\prime}\)B\({}^{\prime}\)C\({}^{\prime}\) & 1.45\% \\
2 & ABC & A\({}^{\prime}\)C\({}^{\prime}\)B\({}^{\prime}\) & 1.77\% \\
3 & ABC & B\({}^{\prime}\)A\({}^{\prime}\)C\({}^{\prime}\) & 2.16\% \\
4 & ABC & B\({}^{\prime}\)C\({}^{\prime}\)A\({}^{\prime}\) & 1.62\% \\
5 & ABC & C\({}^{\prime}\)A\({}^{\prime}\)B\({}^{\prime}\) & 1.52\% \\
6 & ABC & C\({}^{\prime}\)B\({}^{\prime}\)A\({}^{\prime}\) & 0.20\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Magnetic field reduction rate due to the shields for the arrangement of two horizontally laid three-phase power cables with solid bonding.  
**Funding:** This research received no external funding. The APC was funded by \"[PERSON]\" Technical University of Iasi.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.