Magnetic field produced by power lines with complex geometry

Abstract

This paper should be intended as a contribution to the evaluation of the extremely low frequency (ELF) magnetic field produced by power lines in the context of the human exposure to the magnetic field itself; in particular, we consider those situations where the actual geometry of the conductors and the lay-out of the power line(s) have to be taken into account in order to correctly calculate the field. The main implication is that a 3D model of power line has to be used instead of the simpler 2D model which is based on the Biot-Savart law applied to rectilinear and infinite wires. Purpose of this paper is to give operational formulas to be directly applied in all those situations where a 3D evaluation of the magnetic field is needed in order to quantify the environmental impact of one or more power lines on a certain part of the territory.

3d Computation of the Power Lines Magnetic Field

“…Although various 3D algorithms for computation of the power lines magnetic field are based on the Biot-Savart law [25][26][27], there are certain differences between them and algorithm presented herein. In [25][26][27], the exact shape of the catenary is taken into account and in order to compute all the components and the total magnetic flux density, numerical integration of the complex functions have to be done.…”

“…In [25][26][27], the exact shape of the catenary is taken into account and in order to compute all the components and the total magnetic flux density, numerical integration of the complex functions have to be done. This is required for each power line conductor's catenary which leads to long computation time and much more complicated mathematical model then model presented in this paper.…”

“…This is required for each power line conductor's catenary which leads to long computation time and much more complicated mathematical model then model presented in this paper. Therefore, in [26], catenary approximation by a set of straight segments is mentioned as an alternative solution. This approach is used in this paper, and with a simple mathematical model, sufficiently accurate results as it is considered a real catenary form, were obtained.…”

“…Computation of the buried cable lines magnetic field and also different magnetic shielding solutions are presented in [20][21][22][23][24]. In recent years, these 2D models are substituted by more sophisticated 3D models [25][26][27][28], which can take the catenary form of power line conductors into account. Consequently, more accurate results of power frequency magnetic field at any point under complex configurations of overhead power lines can be obtained.…”

Influence of Environmental Conditions on Emf Levels in a Span of Overhead Transmission Lines

“…It was shown that the approximation, which assumes a wire as a straight and horizontal conductor with the height varied at each point and equaled to the height of the catenary or the parabola, provides satisfactory accuracy (5%). In order to calculate EMF distributions, complete integration techniques and approaches with catenary approximation were proposed in [6][7][8][9][10]. In [11], the effect of temperature on EMF levels was calculated using alteration of wire length in the span and the linear expansion temperature coefficient, which does not enable us to take into account ice and wind loads.…”