# Quick Calculation of Magnetic Flux Density in Electrical Facilities
## 5 Results and Discussion  
The result of the calculation of the MFD at a height of 20 cm above the upper floor is shown in Figure 12.  
In the 3D graphs of Figure 12, the value of the z-coordinate corresponds to MFD B. In this figure, the points with the greatest MFD have been highlighted. In the original case, these correspond to those that remain above the axis of the tray. It is observed that the highest MFD is 50.27 uT at x=2.5 m and y=2.3 m. This value is higher than 50% of the reference levels in the regulation. The calculation results are also shown in Figure 12, using the proposed optimal alternative of cable arrangement. In this case, the highest MFD 28.85 uT is above the transformer. However, in the area that previously had the highest values, a maximum of 8.53 uT are calculated with the proposed alternative. Therefore, a reduction of 80.03% is obtained near the modified section. To analyze in greater detail the magnetic field in the worst areas, a cut can be made at y=2.3 m or at x=1.2 m to represent the resulting two-dimensional curves by keeping one coordinate fixed. In these two-dimensional graphs, the Y axis values correspond to B and the X axis values correspond to the non-fixed coordinate (x or y). In Figure 13a, this curve is shown for both proposals at y=2.3 m. Similarly, Figure 13b represents these curves at x=1.2 m. As depicted in Figure 13, there is a wide area with larger MFDs in the original scenario than in the proposed alternative. The obtained reductions are quite significant in some areas. On the other hand, these reductions are not so significant in farther areas. Logically, the area above the tray and the cables that go down in triplets has a larger MFD because the conductors are closer to the calculation plane. However, in the original case, there is another important fact to take into account that causes the MFD to be so high. In the original situation, a decompensation takes place because the distances between the conductors of the different phases and the calculation points are not balanced. That is, for a given point in the calculation plane, the distance to the cables of one phase is not very similar to the distance to the cables of the other phases. Thus, one way to reduce the MFD in this studied area is to lay the nine conductors, alternating the different phases, as proposed in this study. Therefore, for a given point in the studied plane, the average distance to the cables of each phase is very similar, since they are better distributed. Consequently, the MFD produced by each phase is compensated with the MFD produced by the others, and the MFD is considerably reduced. Figure 12: MFD on the upper floor in 3D using **(a)** the original layout and **(b)** the proposed alternative. MFD on the upper floor in 2D using **(c)** the original layout and **(d)** the proposed alternative. Figure 13: MFD on the upper floor at a height of 20 cm (z=2.9 m), at y=2.3m **(a)**, and at x=1.2m **(b)** for the original situation (crosses) and for the proposed alternative (circles). In the area above the transformer, the reduction is much smaller because these conductors are farther away from the calculation plane and because the phases are separated and minor changes can be proposed. Additionally, the effect of the transformer is the same in both cases. To verify this, the resulting MFD curves at x=1.2 m are shown in Figure 13b. If the field on the sidewalk next to the main facade is studied, the influence of alternating phases can also be significantly noticed. For this purpose, the MFD is calculated outside at a height of z=1 m, from the coordinate x=0 m, y=2.6 m (a wall thickness of 10 cm has been assumed) to the coordinate x=4 m, y=4 m. Figure 14 shows the MFD for both cases, in 3D and in 2D, highlighting the highest values. In order to represent the 3D graphic, the MFD has been curtailed to a limit value of 100 uT, since in the original case there was a maximum value of 946.7 uT that made it impossible to visualize the shape of the represented surface.