Uma contribuição à análise de sistemas de aterramento em meios horizontalmente estratificados

Abstract

The main aim of this work is to develop an equation for the calculation of electric potential in heterogeneous soils. The proposed equation is applied in the study of grounding systems for short-circuit current conduction problems at industrial frequency. Initially, a model for grounding systems in homogeneous soil is proposed, calculating electric potential, electric field and grounding resistance. The equipotentiality condition for the electrodes is then adopted and the system current distribution is determined. The homogeneous soil model is used as the calculation basis for the heterogeneous soil. For the proposed heterogeneous soil model, it is applied the boundary conditions at the interface among different materials and the electric potential is assumed to be zero at an infinite distance from the source. As for the calculation of the potential function in the heterogeneous soil it is necessary the solution of an integral involving Bessel polynomials. For so, two solutions are proposed. The first one is made for a generic point and is rooted on an integration quadrature formula for highly oscillatory functions involving Bessel polynomials. The second solution proposed is limited to points located on the soil surface and is based on the Lipschitz identity, where the characteristic heterogeneous soil functions are expanded into Chebyshev series, for the application of such mathematical identity. All the equation developed is initially made for a point current source and then generalized for a linear trajectory in the three-dimensional space. The representation of the coordinates for each conductor in the space is purposely made the same way as in the drawing software (CAD) available, thus allowing the reading of CAD files for the simulation of generic grounding system configuration. The results of resistance and distribution of potentials on the surface for various configurations are compared with experimental, analytical and numerical reference values available in the literature.