Avaliação dos limites de aplicação da teoria de linhas de transmissão para o cálculo de transitórios eletromagnéticos em cabos subterrâneos utilizando o FDTD

Abstract

This thesis evaluates the validity of transmission line theory for calculating of electromagnetic transients on underground cable systems. Using a rigorous methodology based on the solution of Maxwell's equations with the three-dimensional (3D) Finite Difference Time-Domain (FDTD) method, it is investigated the validity of formulations developed from transmission line theory to calculate the impedance and admittance associated with the ground return. It is demonstrated that the transmission line theory can be used to simulate electromagnetic transients on underground cables even if the cable length is less than 100 m and the soil resistivity reaches 1000 Ωm, in which case the validity of this approach would be, in principle, questionable. The errors verified with using transmission line theory are compatible with engineering applications, but this approach has the advantage of presenting greater computational efficiency and being easier to implement than the solution strategy via FDTD. It is demonstrated the importance of the ground-return admittance for the simulation of electromagnetic transients on underground cables, especially for high-resistivity soils and short cable lengths. Furthermore, it is confirmed that the expression proposed by Pollaczek, traditionally used in electromagnetic transients calculation programs, is not rigorous enough to characterize the ground-return parameters for multiconductor underground cable systems. Finally, a closed-form approximation is proposed for the calculation of the ground-return admittance of underground cable systems that avoids the calculation of improper integrals present in more rigorous expressions available in the literature. A range of analyses is performed to evaluate and validate this approximation. Lastly, it is shown that the proposed approximation, despite its simplicity, leads to results compatible with those obtained through more complete formulations for the calculation of transients on underground cables using transmission line theory and the FDTD method, but more efficiently and without significant loss of accuracy.