A tridimensional approach for magnetic field calculation in power systems

Abstract

This paper presents the basis and application of a three-dimensional magnetic field computational method for electric power systems. The main application of the software is the evaluation of the environmental impact of transmission and distribution power systems, which produces a growing public concern. An advantage of this method is to depict in quality and quantity the magnetic field density due to geometrically complex three phase installations such as overhead power lines or power substations, including underground cables. The routines were programmed using Fortran and Matlab softwares, making use of the advantages of each of them. The calculation begins with the data upload of the electric system. The system?s characteristics comprise the spatial coordinates (beginning and end of each conductor, eventually sag at midspan) and the electrical parameters (rms current and phase angle) of conductors in the whole system. The next input data are the spatial coordinates of the magnetic field calculation points of interest. The program makes use of the Biot?Savart?s law for the physical model, vector algebra for space analysis and phasors for time relationships between the three-phase systems. The numerical calculation subroutines allow to achieve the resultant magnetic field in space due to the specific preloaded scenario. All these routines were tested with several examples, some of them theoretical and most of them real life cases, namely some overhead power lines and power substations, where on-site measurements have verified the computation method. In all cases, the results obtained by the software were compared with the measured values in real cases and the achieved results were pretty satisfactory. As a conclusion, an useful tool for the magnetic field calculation in power systems was accomplished that has the advantages of not needing the discretization of the whole domain surrounding the conductor and, as opposite of many commercially available softwares, allows 3-D magnetic field calculation with a moderate computation time and quite good graphical results.