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 resultsMaestrí

Hamiltonian formulation of the full vectorial Helmholtz equation for modeling the interaction between ME composites and optical _ber immersed in electromagnetic _elds from high voltage power systems

TThis thesis deals with the proposal, analytical background and practical implementation of fiber optic based sensors for measuring electrical variables in high voltage systems. The thesis presents the physical and mathematical formulation for each of the sensing principles that were tackled in the proposition and develops the theoretical backgorund for each particular application. Three main contributions should be highlighted from the obtained results: Firstly, the formulation of the interaction characteristics with optical fibers by extending the coupled theory mode through a Hamiltonian formulation of the Helmholtz equation to account for transverse perturbations into the propagation characteristics of propagating light. Secondly, the proposition of a numerical method for predicting the magnetic characteristics of magnetostrictive-powder/epoxy composites with arbitrary shapes. Finally, the proposition of two fiber-based sensor for sensing electric variables (magnetic field and voltage magnitudes) from high voltage systems. Proposed sensors were implemented in practice and their results were contrasted to the theoretical expected performance leading to very good agreements. Future work is proposed based on the main opportunities discovered during the analytical and practical implementation of the sensors.Doctorad

Validation of a non-uniform meshing algorithm for the 3D-FDTD method by means of a two-wire crosstalk experimental set-up

This paper presents an algorithm used to automatically mesh a 3D computational domain in order to solve electromagnetic interaction scenarios by means of the Finite-Difference Time-Domain -FDTD-  Method. The proposed algorithm has been formulated in a general mathematical form, where convenient spacing functions can be defined for the problem space discretization, allowing the inclusion of small sized objects in the FDTD method and the calculation of detailed variations of the electromagnetic field at specified regions of the computation domain. The results obtained by using the FDTD method with the proposed algorithm have been contrasted not only with a typical uniform mesh algorithm, but also with experimental measurements for a two-wire crosstalk set-up, leading to excellent agreement between theoretical and experimental waveforms. A discussion about the advantages of the non-uniform mesh over the uniform one is also presented.interchange-newline" Este trabajo presenta un algoritmo usado para enmallar automáticamente un dominio computacional 3D con el fin de solucionar escenarios de interacción electromagnética por medio del Método de Diferencias Finitas en el Dominio del Tiempo - FDTD. El algoritmo propuesto se ha planteado en una forma matemática general, donde es posible definir funciones convenientes de espaciado aplicadas a la discretización del espacio de simulación. Esto permite la inclusión de objetos pequeños en el método FDTD y el cálculo de variaciones detalladas del campo electromagnético en regiones especificadas del dominio de cálculo. Los resultados obtenidos mediante el método FDTD con el  algoritmo propuesto se han contrastado no sólo con un algoritmo típico de enmallado uniforme, sino también con medidas experimentales para un montaje de diafonía de dos hilos conductores logrando una excelente concordancia entre las formas de onda teóricas y experimentales. Además, se presenta una discusión sobre las ventajas del enmallado no uniforme sobre el uniforme

Validation of a non-uniform meshing algorithm for the 3D-FDTD method by means of a two-wire crosstalk experimental set-up

This paper presents an algorithm used to automatically mesh a 3D computational domain in order to solve electromagnetic interaction scenarios by means of the Finite-Difference Time-Domain -FDTD-  Method. The proposed algorithm has been formulated in a general mathematical form, where convenient spacing functions can be defined for the problem space discretization, allowing the inclusion of small sized objects in the FDTD method and the calculation of detailed variations of the electromagnetic field at specified regions of the computation domain. The results obtained by using the FDTD method with the proposed algorithm have been contrasted not only with a typical uniform mesh algorithm, but also with experimental measurements for a two-wire crosstalk set-up, leading to excellent agreement between theoretical and experimental waveforms. A discussion about the advantages of the non-uniform mesh over the uniform one is also presented.interchange-newline"> Este trabajo presenta un algoritmo usado para enmallar automáticamente un dominio computacional 3D con el fin de solucionar escenarios de interacción electromagnética por medio del Método de Diferencias Finitas en el Dominio del Tiempo - FDTD. El algoritmo propuesto se ha planteado en una forma matemática general, donde es posible definir funciones convenientes de espaciado aplicadas a la discretización del espacio de simulación. Esto permite la inclusión de objetos pequeños en el método FDTD y el cálculo de variaciones detalladas del campo electromagnético en regiones especificadas del dominio de cálculo. Los resultados obtenidos mediante el método FDTD con el  algoritmo propuesto se han contrastado no sólo con un algoritmo típico de enmallado uniforme, sino también con medidas experimentales para un montaje de diafonía de dos hilos conductores logrando una excelente concordancia entre las formas de onda teóricas y experimentales. Además, se presenta una discusión sobre las ventajas del enmallado no uniforme sobre el uniforme

Validation of a non-uniform meshing algorithm for the 3D-FDTD method by means of a two-wire crosstalk experimental set-up

This paper presents an algorithm used to automatically mesh a 3D computational domain in order to solve electromagnetic interaction scenarios by means of the Finite-Difference Time-Domain -FDTD-  Method. The proposed algorithm has been formulated in a general mathematical form, where convenient spacing functions can be defined for the problem space discretization, allowing the inclusion of small sized objects in the FDTD method and the calculation of detailed variations of the electromagnetic field at specified regions of the computation domain. The results obtained by using the FDTD method with the proposed algorithm have been contrasted not only with a typical uniform mesh algorithm, but also with experimental measurements for a two-wire crosstalk set-up, leading to excellent agreement between theoretical and experimental waveforms. A discussion about the advantages of the non-uniform mesh over the uniform one is also presented

Proposición de un método para balanceo de carga en un cluster heterogéneo simulado en ns2

Este trabajo tiene como objetivo principal analizar la importancia que tiene en la actualidad el procesamiento paralelo y distribuido cuando nos enfrentamos a problemas potenciales en ingeniería. Se propone la implementación de un algoritmo que involucre un nuevo método para balancear la carga de trabajo en un cluster heterogéneo teniendo en cuenta la aptitud que tiene cada uno de los nodos para ejecutar ciertas tareas, y así, poder realizar la asignación de la carga de acuerdo a la capacidad de cada nodo minimizando el tiempo de ejecución total