Cálculo de parâmetros externos unitários de sistemas de transmissão subterrâneos por meio do método dos elementos finitos

Abstract

This work proposes an application of the Finite Element Method (FEM) for the evaluation of ground return impedances and admittances per unit of length (pul) in underground cable system when ducts and tunnels are considered. To infer the adequacy of using FEM for that matter, initially, it is considered a conventional con guration, i.e., underground cables in direct contact with soil. The results of the per-unit length parameters are then compared with those obtained using analytical expressions and considering a frequency range from 10 Hz up to 10 MHz. Two distinct formulations were considered when evaluating the pul impedance. For lower frequencies, a quasi-static form was used, i.e., neglecting electromagnetic wave propagation. For higher frequencies, the complete form of Maxwell's equations was considered, which includes propagation e ects. An applicability criterion was then established which implies in di erent dimensions for the external domain depending on the formulation. For the pul admittance evaluation, super cial charge method was applied regardless of the frequency range. Single-phase and multiphase cases were analyzed. For some con gurations, propagation parameters, i.e., characteristic admittance and propagation function were evaluated. It was found that ducts and tunnels have little e ect on impedances, but they cause an increase of shunt pul conductance at higher frequencies and that ducts decreases the shunt pul capacitance modulus at lower frequencies. For the propagation parameters, it was found that the tunnel e ects are essentially limited to higher frequencies, while ducts have a more pronounced impact on both propagation parameters in all frequency range.