# Quick Calculation of Magnetic Flux Density in Electrical Facilities
## 3 Materials and Methods
### Comparison between the Measurement and Simulation of the MFD  
The measurement of the MFD produced by low frequency variable currents can be done with electromagnetic field (EMF) meters. These devices use scanning coils or Hall-effect devices. Hall-effect devices can also be used in magnetometers, which allow us to measure a static magnetic field. EMF meters can perform measurements in one direction or in three orthogonal directions. Using CRMag(r), the circuit depicted in Figure 2, with an electric current of 7.69 A, has been simulated, calculating the MFD in a horizontal plane at 2.5 cm in height above the X-Y plane. The simulation results are represented in Figure 3.  
The values calculated at points 1 to 16 indicated in Figure 3 are shown in Table 1, together with the values measured at the same points using a 3-axis meter (3D H / E fieldmeter ESM-100 Maschek). Figure 4 shows the results of the measurements (in blue) and those obtained by the simulation (in orange) in these points. In Table 2, some technical data about the mentioned field meter are shown. Table 1 and Figure 4 demonstrate the high level of accuracy achieved when using the developed software. The differences are due to small inaccuracies in the placement of the probe and the finite size of the probe, which makes the measured value an average of the MFD in a small region, but not a point value. Therefore, in studies of the EMF produced by electric currents, the calculation results can be used with a high level of confidence instead of the measured data. The measurement requires more time, especially in the case where the user wants to get a complete view of the MFDs in a large area and not just a specific value. In addition, simulation allows the users to calculate MFDs in hard-to-reach areas or vary the values of the electric current in the conductors at their convenience, thus allowing them to analyze multiple scenarios, whereas measurements are representative only of the existing conditions in the circuits at the moment when the measurement is made. Figure 2: (**a**) Simulated and measured circuit and (**b**) its 3D representation. Figure 4: Representation of simulation and measurement results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Sensor** & **CRMag®** & **Error** \\ \hline
1 & 12.87 & 13.09 & 1.71\% \\
2 & 14.08 & 14.22 & 0.99\% \\
3 & 16.56 & 16.70 & 0.85\% \\
4 & 22.00 & 22.38 & 1.73\% \\
5 & 36.20 & 37.40 & 3.31\% \\
6 & 5.22 & 5.16 & \(-\)1.11\% \\
7 & 2.11 & 2.07 & \(-\)2.13\% \\
8 & 1.17 & 1.17 & \(-\)0.09\% \\
9 & 0.75 & 0.75 & 0.60\% \\
10 & 13.07 & 13.27 & 1.53\% \\
11 & 14.61 & 14.86 & 1.71\% \\
12 & 19.10 & 19.33 & 1.20\% \\
13 & 33.80 & 34.33 & 1.57\% \\
14 & 7.39 & 7.23 & \(-\)2.15\% \\
15 & 2.91 & 2.97 & 1.92\% \\
16 & 1.62 & 1.65 & 1.54\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of simulation and measurement results. Figure 3: Simulation of the test circuit. Another important aspect to highlight the advantage of simulation in these studies is that it allows the user to analyze the effect of possible modifications of the facilities and thereby choose the arrangements or designs that have less influence on the environment. The case study described in detail in Section 4 shows some possibilities that simulation offers in the design stage of a new facility as well as in the study of the influence of existing facilities on nearby premises. Since the described case study corresponds to a DTS, it is necessary to include the effect of the transformer to simulate the MFD. For this reason, the authors have made MFD measurements in several DTSs in order to achieve a simple model, but accurate enough to be used in CRMag@and avoid the use of complex finite element models. Figure 5 shows a 630 kVA transformer. Figure 6 indicates the points where MFD measurements have been made, at a height of 1m above the ground.