# Quick Calculation of Magnetic Flux Density in Electrical Facilities
## 1 Introduction
As demonstrated in this paper, the MFD values that these facilities can produce on neighboring premises can be significantly higher than the threshold values of 0.4 \(\mu\)T. Therefore, extending an epidemiological analysis to these areas affected by the DTSs could considerably increase the number of people included in epidemiological studies. The study of the magnetic fields produced by electrical installations can have a certain complexity. Due to this reason, sometimes, very simplified models are used for these studies. As a result of this simplification, only an indicative value can be provided, with a considerable margin of error (the fact that MFD is a vector quantity must be taken into account). Usually, actual values of MFD are considerably lower than the practical limit of 100 \(\mu\)T (1 G) that the regulation establishes for the general public at 50 Hz [10; 11]. Therefore, an approximate calculation, even with a 100% error, can be used to justify this limit not being reached. The situation would be very different if the precautionary principle had been applied and that limit had been set at a lower value, like in Italy (3 \(\mu\)T is the limit for certain cases) and some other countries in Europe [25]. The tendency to reduce the size of DTSs, for example, in order to minimize their environmental impact [26], does not usually take into account aspects related to the emission of magnetic fields. In fact, the magnetic field is often reduced by shielding techniques [27], instead of studying the expected field before its execution and assessing other cheaper solutions. An example of a study of a shielding for a building located under high-voltage overhead lines is shown in [25]. However, the MFD in facilities is usually below the limits set by the regulation, as in [28]. An accurate calculation of the expected MFD produced by an electrical facility can provide useful information for several reasons:  
* It increases the knowledge of this topic. * It would provide guidance for the development of future standards. * It enables the identification of the best installation practices and the rejection of inadequate assemblies. * It facilitates the detection of overexposure in workers or the general population. * The monitoring of exposure levels related to epidemiological studies can be carried out. Nevertheless, given the complexity of this calculation, approximate prediction methods from the analysis of experimental measures are developed in some works [29]. For example, a simplistic numerical method for MFD prediction in open air type substations is shown in [30]. For this reason, in the Department of Electrical Engineering of the Universitat Politecnica de Valencia, a software has been developed for the calculation of the MFDs produced by the electric currents in the facilities (CRMag(r)). This program has been designed to be easy to use by engineering firms when developing the projects of facilities. With this program, the geometric arrangement of conductors, their grouping, and so on, can be easily taken into account. This allows engineers to study optimal solutions that may provide significant reductions in MFDs. Thus, the influence of these facilities on neighboring premises, or on their environment, can be studied and minimized. The use of this type of software facilitates obtaining sufficient information about the influence of electrical installations on adjacent premises. This process is much simpler than measurement campaigns carried out by other researchers [31]. In addition, the information is more complete and reaches areas that are difficult access to carry out the measurements. Likewise, the simulation allows us to take into account scenarios that differ from the particular situation of the moment in which the measurement is carried out. To demonstrate the usefulness of CRMag(r), this paper includes a real case study of the expected magnetic field around a facility and the analysis of possible modifications in order to reduce the commission produced in neighboring premises.