###### Abstract  
There is a special concern for measuring and simulating low-frequency magnetic fields generated by underground power cables, particularly in human exposure studies. In the present study, an accurate 2D finite element model for computing magnetic fields generated by three-phase underground power cables with solid bonding is proposed. The model is developed in ANSYS Maxwell 2D low-frequency electromagnetic field simulation software for a typical 12/20 kV (medium-voltage) three-phase underground power cable in both trefoil and flat formations, but it can be adapted to any cable system. Model validation is achieved by analytical computations conducted with a software tool based on the Biot-Savart law and the superposition principle. RMS magnetic flux density profiles calculated at various heights above the ground with these two methods correlate very well. This is also true for induced shield currents. The application of the finite element model to multiple three-phase power cables laid together is also considered. magnetic field; underground power cable; solid bonding; finite element model; analytical calculation +
Footnote †: journal: Applied Sciences  
002  
with high magnetic permeability, on the principle of the path of minimum reluctance) and induced current shielding (which is effective only if the shield is a good electrical conductor and thick enough). In addition to high costs and constructive-technological difficulties, these solutions for shielding magnetic fields also have the important disadvantage of increasing the losses produced by line charging currents. That is why they will be applied only on relatively short distances and only in the case of very special requirements [2; 3]. Therefore, as in the case of overhead power lines, it is strongly recommended that through analytical calculations, numerical modeling or actual measurements, to be verified that the low-frequency magnetic field generated by underground power cables at the soil level is (far) below the values considered acceptable by the health regulations. Computations, which can be quite accurate, are often preferable to measurements because they can be performed for any desired scenario, rather than being limited to the particular conditions at the measurement time [4; 5; 6; 7; 8]. A common 2D approach for calculating magnetic fields generated by underground power cables is based on the Biot-Savart law and the superposition principle, assuming that the cables are straight, horizontal, infinitely long and parallel to each other and the effect of the induced shield currents on the magnetic field is negligible [9; 10; 11; 12]. Basically, this is the case for single-point bonding systems and cross-bonding systems, in which the induced shield currents are zero or insignificant. However, when dealing with solid bonding (i.e., the underground power cables operate with their metallic shields bonded and grounded at both ends), the circulating currents induced in shields may achieve the same order as the wire-core currents, which leads to a certain total magnetic field reduction. In some studies, e.g., [13; 14], analytical expressions for the induced shield currents have been obtained under balanced three-phase conditions. It has also been considered the magnetic field reduction. Some 2D finite element method (FEM) models have also been developed for computing magnetic fields from three-phase underground cables with solid bonding. In [15], COMSOL Multiphysics is used to investigate the magnetic field reduction rate for a three-phase cable in flat formation as a function of the distance between cables, the shield diameter, as well as the cross-sectional area of the cable shields. In [16], QuickField was mainly used for predicting underground cable ampacity (for both trefoil and flat formations), while the developed model also allows investigating the magnetic field distribution at the ground surface (only limited results are presented). For a similar purpose (flat formation only), ANSYS Maxwell is used in [17].