Lightning Induced Voltages on Overhead Lines above Non-Uniform and Non-Homogeneous Ground

Abstract: lightning induced voltages are one of the most common sources of failures on distribution networks operating in high lightning activity regions. Traditionally, the selection of insulation levels and protecting devices are carried out using statistical analysis based on typical values of resistivity and assuming a homogeneous ground for the whole network. In calculating lightning induced voltages, the effect of the topography and non-homogeneities of the ground have been traditionally neglected. In rural distribution lines, non-homogeneous and non-uniform ground is a common feature. In literature, induced voltages calculations are mainly calculated based on several assumptions that are not valid when more realistic conditions are taken into account. In order to allow a better selection of protective devices and hence contributing to the improvement of some power quality indicators of rural distribution networks, the calculation of lightning induced voltages for distribution lines must be performed including the effects of the non-homogeneous and nonuniform ground. Most of the theoretical approaches proposed for calculating the propagation path effects on the radiated electromagnetic fields for a current dipole above ground, are valid only in the far-field region even when considering irregular and inhomogeneous terrain. Despite some authors have demonstrated the validity of those approaches for flat ground in the near field range calculations, there are valid for some specific cases and geometric symmetry that in some practical cases cannot be assumed. In order to overcome this problem, this thesis presents an extensive application of a full wave solution obtained from the implementation of the Finite Difference Time Domain (FDTD) method including a non-regular mesh. This method is applied to the calculation of lightning induced voltages on an overhead single wire when different ground features such as: homogeneity, inhomogeneity and non-uniformity are present all simultaneously in a simulation scenario. In order to validate the FDTD implementation, some numerical comparisons were made with previous results presented in the literature. The aim of this thesis is to provide new elements related to the effects on lighting induced voltages on overhead lines when different electric and geometric parameters of the surrounding ground are considered. Along this thesis, the lightning induced voltage problem has been analyzed taking into account three involved aspects individually: the return-stroke model, the propagation of the electromagnetic field produced by it, and the resulting induced voltages on the overhead lines once all their models are included into an FDTD simulation. This document has been divided into eight sections. The first section presents a discussion about lightning induced voltages and how they have been addressed in the literature. Throughout this iii section all the involved elements into the lighting induced problem have been addressed and a short discussion about their previous results and conclusions is also presented. In section 2 the scope of the thesis is defined in order to give the reader a brief summary about the objectives that were established in the master thesis proposal. Section 3 presents the FDTD method. In this section most of the theoretical background is presented related to: sources, lumped elements and thin-wire modeling techniques. Next, the FDTD method is formulated for a non-regular mesh and a general formulation for an automatic meshing algorithm is proposed. Finally, a comparison between the FDTD method implementation used in this thesis and some experimental data from a two horizontal wires cross-talk problem is presented. Section 4 deals with the calculation of radiated fields when different propagation paths are present. Homogeneous ground effects on radiated fields were obtained by using the Norton’s approach and the surface impedance concept. Inhomogeneities of the ground conductivity for flat grounds were also analyzed by using the surface impedance concept and the Wait´s formula derived from the compensation theorem; the Wait´s formulas for a mixed-path of two and three section were implemented and compared with some results presented before in literature. Finally,the terrain non-uniformity was addressed by means of the Ott’s integral approach. Despite all of these implemented approaches allow the analysis of radiated fields, they are derived under several assumptions and are valid only for the far field region and a cylindrical symmetry regarding geometry. Then, a comparison between these and the results obtained by means of the FDTD method were performed for different simulation scenarios in order to analyze their validity. In section 5 the lightning return-stroke is modeled by means of an implementation of engineering and electromagnetic models. A discussion about the current distribution along the cannel depending on the return-stroke model is also presented. Besides, a comparison between the antenna theory and the series RL-loaded thin-wire model included into the FDTD method was carried out taking into account the characteristics of apparent propagation velocity and current wave shape along the channel. In section 6 the lightning radiated fields are calculated for different propagation path conditions such as: perfectly conducting ground, homogeneous finitely conductive ground and inhomogeneous conducting ground. For those propagation paths a set of comparisons between the FDTD method and the approximated formulas discussed in section 5 were performed. Lightning induced voltages are analyzed in section 7. In this section the lightning channel and the overhead line are included into the FDTD method. A set of simulations scenarios were proposed in order to evaluate the influence of different ground features on the induced voltages on a single overhead-wire. Important influences on induced voltage waveforms were determined for inhomogeneous and irregular terrains, resulting in changes on polarity and higher induced peak voltages values when compared to those obtained from a flat homogeneous ground. iv In section 8 concluding remarks about the analyzed cases and most critical situations are presented. There is also a future work proposed by the author based on the obtained results