Ηλεκτρομαγνητική μελέτη υπόγειων αγωγών

Abstract

The aim of this doctoral thesis is to study electromagnetic compatibility problems dealing with field couplings to underground transmission lines, communication systems or electronic devices. As an overview: (i) we develop expressions for the accurate computation of mutual impedances between two underground conductors of finite length, (ii) we use a modern technique to solve the well-known Pollaczek and Carson formulas for the evaluation of the earth-return impedance for underground and overground conductors, (iii) we present a method for calculating the electromagnetic field generated by a lightning stroke for studying the problem of induced over-voltage on lines and electronic devices both in power and telecommunication systems, (iv) we deal with the computation of the current distribution along a vertical grounding rod. In all cases, our approach is purely electromagnetic with the use of the elementary electric dipoles technique. More specifically: In the first chapter we provide the expressions for the field generated by a vertical or horizontal elementary electric dipole placed in air or in ground. We form the boundary problem of the system dipole and air-ground interface for the calculation of the Hertz vector components generated by the dipole and the calculation of the electromagnetic field. We also provide tables with the cylindrical components of the produced field. In the second chapter we study the problem of the mutual impedance between two underground conductors of finite length and arbitrary position. With the use of the elementary dipoles technique we derive expressions for the accurate calculation of the mutual impedance that have the form of double infinite improper integrals and we evaluate them by using advanced integration algorithms. We then follow an alternative approach which involves the computation of the equivalent Sommerfeld type integrals by using the Discrete Complex Image Method (DCIM). This method allows the transformation of the Sommerfeld integrals to semi-infinite integrals with known analytical solutions. This is possible by approximating the integrand by a sum of complex exponentials. We finally give results of the mutual impedance and carry out comparisons in order to validate our expressions. In the third chapter we deal with the computation of the current distribution along a vertical grounding rod. We derive the mathematical model by applying the elementary dipoles technique and then we use the Method of Moments for solving the electric field integral equation. For the validation of the developed model, we solve the problem with the FEM method by using the software package COMSOL. In the fourth chapter we evaluate the well-known Pollaczek and Carson formulas for the earth-return impedance for underground and overground conductors. The integrals are solved by using again the DCIM method. For the approximation of the integrand with a sum of exponentials we use the Generalized Pencil of Function (GPOF) method (one and two level). The results of the impedance are compared with results derived with numerical integration of the Pollaczek integral and the analytical solution of Carson’s integral. In chapter five we evaluate the electromagnetic field generated by the lightning stroke in an observation point above and underground. The knowledge of the field is very important when we study couplings with power lines or telecommunication conductors. The expressions for the lightning field have the form of semi-infinite improper integrals in frequency domain, and their numerical computation poses a computational challenge. The problem is more demanding in the case of time domain response, were a large number of computations for a frequency range is required, in order to carry out the required inverse Fourier transform. We propose an efficient method for calculating the lightning integrals, based on their numerical calculation along a deformed path of integration. The method is combined with an interpolation technique in order to reduce the number of frequencies required in the Fourier synthesis of the time domain electric field. The result is a very fast and straightforward tool for the calculation of the underground and overground lightning field, without the use of specially developed numerical algorithms or analytical approximations.