No description available.

In the design of most of the modern systems, lightning threat needs to be considered at the design phase itself. This demands a suitable model and owing to associated complexity, only simplified modeling have been attempted. As a consequence, it does not provide adequate insight into the phenomena. Considering these, a more realistic time-¬ domain electromagnetic model for the return stroke current evolution has been developed by incorporating the following underlying physical processes: (i) excitation formed by the electric field due to charge distribution along the channel, cloud and that induced on ground, (ii) the transient enhancement of series conductance at the bridging regime, which initiates the return stroke,( iii) the non¬linear variation of channel conductance along with (iv) the associated dynamic Electromagnetic Fields(EMFs) that supports the current evolution. The intended modeling begins from the instant of bridging and the pre-¬return stroke charge distribution along the channel is calculated using Charge Simulation Method(CSM). For the calculation of dynamic EMFs, the thin wire Time Domain Electric Field Integral Equation(TD¬EFIE) is employed The transient enhancement of conductance at the bridging/streamer region is emulated using Toepler’s spark law while that along the matured section of the channel is described by first order arc model. The macroscopic physical model developed depicts most of the salient features of current evolution and resulting remote electromagnetic fields in a self¬ consistent manner. The work is not limited by the simplifications adopted for the channel geometry. The strength of the model was exploited for investigating a couple of practically important questions, one of which had divided opinion in the literature. Firstly, analysis showed that the "secondary" current waves generated by successive reflection within struck TGO and that fed by branches do not get reflected at the main wave front. It is shown that the dynamic spatial resistance profile of the channel at the main wave front is primarily responsible for this behavior. Secondly, it is shown that the abrupt change in radii at TGO ¬channel junction is mainly responsible for reflection at the junction. In summary, a novel time-¬domain macroscopic physical model for the first return stroke of a downward cloud¬-to-¬ ground lightning has been successfully developed, which is capable of providing much deeper insight in to the complex phenomena.

In the present PhD work, three sophisticated models based on the "Engineering" modeling approach have been utilized to conveniently describe and thoroughly analyze details of Lightning events at the CN Tower. Both the CN Tower and the Lightning Channel are represented by a number of connected in series Transmission Line sections in order to account for the variations in the shape of the tower and for plasma processes that take place within the Lightning Channel. A sum of two Heidler functions is used to describe the "uncontaminated" Return Stroke current, which is injected at the attachment point between the CN Tower and the Lightning Channel. Reflections and refractions at all points of mismatched impedances are considered until their contribution becomes less than 1% of the originally injected current wave. In the proposed models, the problem with the current discontinuity at the Lightning Channel front, commonly taken care of by introducing a "turn-on" term when computing radiation fields, is uniquely treated by introducing reflected and transmitted components. For the first time, variable speed of propagation of the Return Stroke current front has been considered and its influence upon the predicted current distributions along the whole Lightning Channel path and upon the radiated distant fields analyzed. Furthermore, as another novelty, computation of the electromagnetic field is accomplished in Cartesian Coordinates. This fact permits to relax the requirement on the verticality of the Lightning Channel, normally imposed in Cylindrical Coordinates. Therefore, it becomes possible to study without difficulty the influence of a slanted Lightning Channel upon the surrounding electromagnetic field. Since the proposed sophisticated Five-Section Model has the capability to represent very closely the structure of the CN Tower and to emulate faithfully the shape of, as well as physical processes within the Lightning Channel, it is believed to have the potential of truthfully reproducing observed fields. The developed modeling approach can be easily adapted to study the anticipated radiated fields at tall structures even before construction.

Being one of the most spectacular events in nature, lightning is basically a transient high current electric discharge in the atmosphere, which extends up to kilometres. Cloud to ground discharge is the most hazardous one as far as ground based structures are considered. Among the different phases of a lightning flash, return stroke is considered to be the most energetic phase and is basically responsible for most of the damages. Hence, much emphasis has been given to return stroke modeling. A more realistic modeling of return stroke is very essential to accurately study the interaction of return stroke with the structures on ground. As return stroke is dominated by electromagnetic phenomenon, an electromagnetic model will be the most suitable one. It does not call for any assumption on the mode of wave propagation, as well as, electromagnetic coupling between the different channel portions. There are mainly two approaches adopted for electromagnetic models i.e. frequency domain and time domain approach. Time domain approach is more reliable as it can handle, in principle, the nonlinear processes in the lightning channel. It is also free of numerical frequency domain to time domain inversion problem, which are found to be quite severe. However, most of the previous works on time domain electromagnetic models suffered from following two serious limitations - (i) the initial charge on the channel, which forms the true excitation for the problem, is not considered and (ii) instead of the non-linearly rising conductivity of the channel, a constant resistance is employed. For a realistic simulation of the interaction between the channel and any intercepting system, a time domain model with the above two major aspects being fully represented is very essential. In an earlier work, all these aspects have been fully considered but a domain based numerical modelling was employed. Consequently, it was difficult to consider the down conductor and further the number of unknowns was considerably large. In view of this, the present work is taken up and its scope is defined as to develop a boundary based numerical time domain electromagnetic model in which the initial charge on the channel and the non-linearly evolving channel conductance are fully considered. For the electrical engineering applications, electromagnetic aspects of the lightning phenomena is more important than the other associated physical processes and hence, importance is given only to the electromagnetic aspects. In other words, the light emission, thunder, chemical reactions at the channel etc. are not considered. Also, for most of the electrical engineering applications, the critical portion of current would be the region up to and around the peak and hence, modeling for this regime will be given prime importance. Owing to the complexity of the problem, some simplifying assumptions would be very essential. The literature indicates that these assumptions do not affect the adequate representation of the phenomena. Lightning channel is considered to be vertically straight without any branches. Earth is considered to be perfectly conducting. Explicit reference to dynamically varying channel radius, temperature and the air density is not made. However, it is assumed that the arc equation employed to describe the temporal changes in conductivity would adequately take care of these parameters. Lightning channel is represented by a highly conducting small core, which is surrounded by a weakly conducting corona sheath. The initial charge on the channel is deduced by solving for electrostatic field, with leader portion set to possess an axial gradient of 60 V/cm and the streamer portion to 5 – 10 kV/cm. The radius of the corona sheath is set iteratively by enforcing a gradient of 24 kV/cm up to its radial boundary. As analytical solution for the problem is impractical, suitable numerical solution is sought. Since the spatial extension of this time marching problem is virtually unbound and that the significant conduction is rather solely confined to an extremely small cross section of the channel core, a boundary-based method is selected. Amongst the numerical methods, the present work employs the moment method for the solution of the fields associated with the return strokes. A numerical solution of the Electric Field Integral Equation (EFIE) for thin structures has been developed in the literature. The same approach has been employed in the present work, however, with suitable modifications to suit the lightning problem. The code was written in MATLAB and integrations involved in the EFIE were solved using MATLAB symbolic computation. Before introducing the channel dynamic conductance and the initial charge on the channel, the code developed is validated by comparing the results for a center fed dipole antenna with that given in the literature. Also, NEC (Numeric Electromagnetic Code) simulations for various cases of monopole and dipole antenna were performed. The results from the code developed are shown to have good matching with that obtained from NEC based time domain results. In an earlier work, the dynamic conductance of the return stroke channel core, which is a high current electric arc, was represented by a first order arc equation. The same approach is employed in the present work also. Similarly, the transition from streamer to leader was modeled by Braginskii’s spark law and the same has been considered in the present work. A value of 10-5 S/m was used for minimum value of streamer conductance. For numerical stability, upper (Gmax = 3 S/m) and lower bounds (Gmin = 0.0083 S/m) for the channel conductance are forced. Preliminary simulations were run with and without dynamic channel conductance. The initial charge distribution along the channel formed the excitation. Results clearly show that without the dynamically varying channel conductance, no streamer to leader transition and hence, no return stroke evolution can occur. In other words, the non-linearly evolving channel conductance is mainly responsible for the evolution of the return stroke. In order to consider the charge neutralization by the return stroke, the charge deposited by it is diffused into the corona sheath. A fixed value of the corona sheath conductance is employed and the diffusion process is modeled by an equation derived from the continuity equation. To study the effect of corona sheath, simulations were run with and without corona. From the simulation results it was observed that the corona sheath causes increase in peak value of the stroke current, as well as, time to front and a decrease in the velocity of propagation. For the validation of the model, the basic characteristics of the return stroke current like the current wave shape, temporal variation of stroke current at different heights, velocity of propagation and the vertical electric fields at various radial distances were compared with available field/experimental data. A good agreement was seen and based on this, it is concluded that the present work has successfully developed a boundary based time domain numerical model for the lightning return stroke. Natural lightning being a stochastic process, the values of the parameters associated with it would differ in every event. On other hand, any deterministic model like the one developed in the present work predicts a fixed pattern of the simulated quantities. Therefore, it was felt that some of the model parameters must be permitted to vary so that a range of results could be obtained rather than a single pattern of results. Incidentally, the model parameters like arc time constant, settling value of arc conductivity/gradient, bounds for channel conductivity, streamer gradient, radius of the core etc. are not precisely known for the natural lightning environment. Further, some of them are known to vary within an event. Considering these and that simplicity is very important in already complex model, the above-mentioned parameters are taken as tunable parameters (of course to be varied within the prescribed range) for deducing the return stroke currents with some desired characteristics. A study on the influence of these parameters is made and suggestions are provided. Simulations for the nominal range of stroke currents are made and results are presented. These simulations clearly show the role of cloud potential, which in turn dictates the length of final bridging streamer, on the return stroke currents. The spatio-temporal variation of the current, charge deposited by the return stroke and the channel conductivity are presented which, reveal the dynamic processes leading to the evolution of return stroke current. Subsequently, simulations for two cases of stroke to elevated strike object are attempted. The upward leader was modeled quite similar to the descending one. Many interesting findings are made. In summary, the present work has successfully developed a boundary-based time domain numerical electromagnetic model for the lightning return stroke, wherein, the initial charge deposited on the channel and the non-linearly rising channel conductance have been appropriately considered. Simulation using the model clearly depicts the dynamic evolution of the return stroke. The characteristics of the simulated return strokes are in good agreement with the field data. Some of the parameters of the model are suggested as tunable parameters, which permit simulation of strokes with different characteristics.

In the present PhD work, three sophisticated models based on the "Engineering" modeling approach have been utilized to conveniently describe and thoroughly analyze details of Lightning events at the CN Tower. Both the CN Tower and the Lightning Channel are represented by a number of connected in series Transmission Line sections in order to account for the variations in the shape of the tower and for plasma processes that take place within the Lightning Channel. A sum of two Heidler functions is used to describe the "uncontaminated" Return Stroke current, which is injected at the attachment point between the CN Tower and the Lightning Channel. Reflections and refractions at all points of mismatched impedances are considered until their contribution becomes less than 1% of the originally injected current wave. In the proposed models, the problem with the current discontinuity at the Lightning Channel front, commonly taken care of by introducing a "turn-on" term when computing radiation fields, is uniquely treated by introducing reflected and transmitted components. For the first time, variable speed of propagation of the Return Stroke current front has been considered and its influence upon the predicted current distributions along the whole Lightning Channel path and upon the radiated distant fields analyzed. Furthermore, as another novelty, computation of the electromagnetic field is accomplished in Cartesian Coordinates. This fact permits to relax the requirement on the verticality of the Lightning Channel, normally imposed in Cylindrical Coordinates. Therefore, it becomes possible to study without difficulty the influence of a slanted Lightning Channel upon the surrounding electromagnetic field. Since the proposed sophisticated Five-Section Model has the capability to represent very closely the structure of the CN Tower and to emulate faithfully the shape of, as well as physical processes within the Lightning Channel, it is believed to have the potential of truthfully reproducing observed fields. The developed modeling approach can be easily adapted to study the anticipated radiated fields at tall structures even before construction.

As características das correntes das descargas atmosféricas têm fundamental importância na coordenação de isolamento e nos projetos de equipamentos de sistemas de transmissão e de distribuição de energia. As curvas de distribuição de freqüência cumulativa da CIGRE relativas aos principais parâmetros da primeira e das descargas subseqüentes, freqüentemente utilizadas para avaliar o desempenho das linhas de transmissão e distribuição, se referem a dados obtidos através da medição de correntes de descargas negativas em estruturas elevadas. Entretanto, as correntes medidas nesses objetos podem apresentar distorções associadas às diferenças de impedâncias entre o canal, o objeto e o aterramento. Em outras palavras, a corrente em tais objetos pode variar substancialmente em função do ponto escolhido para medição, bem como apresentar diferenças significativas em relação à corrente no canal da descarga. Essas correntes são denominadas “contaminadas". As curvas da CIGRE relativas às amplitudes, tempos de frente e taxas de crescimento das correntes se referem às correntes “contaminadas", uma vez que as reflexões que ocorrem no topo e na base de objetos elevados não foram levadas em consideração no processo de construção dessas curvas. Assim, o tratamento desses dados necessita ser revisto. Por outro lado, o termo "corrente descontaminada" se refere à corrente que fluiria através do canal da descarga caso os coeficientes de reflexão no topo e na base do objeto fossem iguais a zero. Neste trabalho, por meio de uma ferramenta computacional desenvolvida, diversos aspectos relacionados aos processos de “contaminação" e “descontaminação" de correntes são discutidos, com especial atenção no que se refere às influências dos vários parâmetros do sistema "canal-objeto-aterramento" no comportamento espaço-temporal da corrente. É também apresentada uma discussão acerca das características de uma corrente de descarga medida na base de uma torre de 62,5 m de altura localizada no Instituto de Eletrotécnica e Energia da Universidade de São Paulo. / The characteristics of lightning currents have a fundamental importance on insulation coordination and on the design of transmission and distribution lines equipment. The CIGRE cumulative frequency distribution curves relative to the main parameters of the first and subsequent downward flashes, which are very frequently used for the evaluation of the lightning performance of transmission and distribution lines, refers to data obtained from negative current measurements from tall instrumented structures. However, currents measured on elevated objects may present distortions associated with differences on the impedances of the lightning channel, the strike object and the grounding system. In other words, the current in such objects may, in some circumstances, depend significantly on the measuring point and differ substantially from the current that flows along the lightning channel. These currents are called "contaminated". The curves regarding current magnitudes, front times and rates of rise presented in CIGRE refer to these "contaminated" currents, since the reflections that occur at the base and at the top of elevated strike objects were not taken into account in the processing of the data that led to those curves. The data should, thus, be reviewed. On the other hand, the term “decontaminated" current stands for the current that flows through the lightning channel assuming reflection coefficients at the bottom and at the top of the strike object equal to zero, i.e., the same impedances for the lightning channel, the elevated object and the grounding system. In this work a computer code was developed and several aspects related to the "contamination" and "decontamination" processes are discussed, with emphasis upon the influences of the various parameters of the system "lightning channel - strike object - grounding" on the stroke current. A discussion of the characteristics of a stroke current measured at the bottom of a 62,5 m high mast located at the Instituto de Eletrotécnica e Energia da Universidade de São Paulo is also presented.

As características das correntes das descargas atmosféricas têm fundamental importância na coordenação de isolamento e nos projetos de equipamentos de sistemas de transmissão e de distribuição de energia. As curvas de distribuição de freqüência cumulativa da CIGRE relativas aos principais parâmetros da primeira e das descargas subseqüentes, freqüentemente utilizadas para avaliar o desempenho das linhas de transmissão e distribuição, se referem a dados obtidos através da medição de correntes de descargas negativas em estruturas elevadas. Entretanto, as correntes medidas nesses objetos podem apresentar distorções associadas às diferenças de impedâncias entre o canal, o objeto e o aterramento. Em outras palavras, a corrente em tais objetos pode variar substancialmente em função do ponto escolhido para medição, bem como apresentar diferenças significativas em relação à corrente no canal da descarga. Essas correntes são denominadas “contaminadas”. As curvas da CIGRE relativas às amplitudes, tempos de frente e taxas de crescimento das correntes se referem às correntes “contaminadas”, uma vez que as reflexões que ocorrem no topo e na base de objetos elevados não foram levadas em consideração no processo de construção dessas curvas. Assim, o tratamento desses dados necessita ser revisto. Por outro lado, o termo "corrente descontaminada” se refere à corrente que fluiria através do canal da descarga caso os coeficientes de reflexão no topo e na base do objeto fossem iguais a zero. Neste trabalho, por meio de uma ferramenta computacional desenvolvida, diversos aspectos relacionados aos processos de “contaminação” e “descontaminação” de correntes são discutidos, com especial atenção no que se refere às influências dos vários parâmetros do sistema "canal-objeto-aterramento" no comportamento espaço-temporal da corrente. É também apresentada uma discussão acerca das características de uma corrente de descarga medida na base de uma torre de 62,5 m de altura localizada no Instituto de Eletrotécnica e Energia da Universidade de São Paulo. / The characteristics of lightning currents have a fundamental importance on insulation coordination and on the design of transmission and distribution lines equipment. The CIGRE cumulative frequency distribution curves relative to the main parameters of the first and subsequent downward flashes, which are very frequently used for the evaluation of the lightning performance of transmission and distribution lines, refers to data obtained from negative current measurements from tall instrumented structures. However, currents measured on elevated objects may present distortions associated with differences on the impedances of the lightning channel, the strike object and the grounding system. In other words, the current in such objects may, in some circumstances, depend significantly on the measuring point and differ substantially from the current that flows along the lightning channel. These currents are called "contaminated". The curves regarding current magnitudes, front times and rates of rise presented in CIGRE refer to these "contaminated" currents, since the reflections that occur at the base and at the top of elevated strike objects were not taken into account in the processing of the data that led to those curves. The data should, thus, be reviewed. On the other hand, the term “decontaminated” current stands for the current that flows through the lightning channel assuming reflection coefficients at the bottom and at the top of the strike object equal to zero, i.e., the same impedances for the lightning channel, the elevated object and the grounding system. In this work a computer code was developed and several aspects related to the "contamination" and "decontamination" processes are discussed, with emphasis upon the influences of the various parameters of the system "lightning channel - strike object - grounding" on the stroke current. A discussion of the characteristics of a stroke current measured at the bottom of a 62,5 m high mast located at the Instituto de Eletrotécnica e Energia da Universidade de São Paulo is also presented.

As descargas atmosféricas são reconhecidamente responsáveis por uma parcela expressiva das interrupções não programadas de fornecimento de energia em sistemas elétricos, contribuindo de forma significativa para a composição dos índices de qualidade de energia mesmo no caso de regiões com níveis ceráunicos moderados. No caso de sistemas de distribuição, grande parte dos problemas está relacionada às sobretensões induzidas por descargas próximas às linhas, as quais decorrem dos campos elétrico e magnético, associados à corrente que se propaga ao longo do canal da descarga. O conhecimento das características de tais campos é, portanto, fundamental para a determinação das sobretensões induzidas nas linhas aéreas de energia. Embora a importância do tema tenha propiciado nos últimos anos o desenvolvimento de um grande número de pesquisas a respeito dos campos eletromagnéticos e das tensões induzidas por descargas atmosféricas, na grande maioria dos trabalhos o solo é representado através de um plano condutor perfeito, portanto com condutividade infinita. Embora tal simplificação possa, em geral, ser considerada válida para a indução magnética e para o campo elétrico vertical, ela não é aplicável ao campo elétrico horizontal, em especial no caso de solos com alta resistividade. Este estudo visa avaliar o comportamento dos campos elétrico (vertical e horizontal) e indução magnética gerados por descargas atmosféricas nuvem-terra, levando em consideração os parâmetros da descarga (amplitude, forma de onda e velocidade de propagação da corrente) e os diferentes modelos para representação do canal da descarga. Além do caso de solo perfeitamente condutor, são consideradas situações mais realistas, isto é, verificando-se a influência, nos campos, de parâmetros como a resistividade e permissividade do solo. / The occurrence of lightning discharges causes a significant amount of unscheduled supply interruptions in overhead lines of electricity systems, contributing to decrease quality indicators of these systems, even in the case of regions with moderated ground flash density. Focusing on the distribution systems, great part of the problems are related to the induced voltages due to lightning discharges in the vicinity of overhead lines, which results from the electric and magnetic fields associated with the current propagation along the return stroke channel. The knowledge of the characteristics of lightning electromagnetic fields is, therefore, crutial for determining induced voltages on overhead lines. Although the importance of the assumption has propitiated in the last years the development of a great number of research concerning the lightning electromagnetic fields and induced voltages on overhead lines, in most of the studies the hypothesis of a perfect conducting ground is assumed. While such assumption can be considered valid for magnetic induction field and for the vertical component of the electric field, it doesn’t apply to the horizontal electric field, especially in the case of ground with high resistivity. The aim of this work is to present and to discuss the characteristics of the electric field (vertical and horizontal components) and magnetic induction generated by the cloud-to-ground lightning discharge, taking into account the lightning parameters (amplitude, waveform and propagation speed of the return stroke current) and the different return stroke models. Besides the case of perfect conducting ground, the influences of the ground permittivity and finite conductivity in the calculation of the electromagnetic fields are so considered.

As descargas atmosféricas são reconhecidamente responsáveis por uma parcela expressiva das interrupções não programadas de fornecimento de energia em sistemas elétricos, contribuindo de forma significativa para a composição dos índices de qualidade de energia mesmo no caso de regiões com níveis ceráunicos moderados. No caso de sistemas de distribuição, grande parte dos problemas está relacionada às sobretensões induzidas por descargas próximas às linhas, as quais decorrem dos campos elétrico e magnético, associados à corrente que se propaga ao longo do canal da descarga. O conhecimento das características de tais campos é, portanto, fundamental para a determinação das sobretensões induzidas nas linhas aéreas de energia. Embora a importância do tema tenha propiciado nos últimos anos o desenvolvimento de um grande número de pesquisas a respeito dos campos eletromagnéticos e das tensões induzidas por descargas atmosféricas, na grande maioria dos trabalhos o solo é representado através de um plano condutor perfeito, portanto com condutividade infinita. Embora tal simplificação possa, em geral, ser considerada válida para a indução magnética e para o campo elétrico vertical, ela não é aplicável ao campo elétrico horizontal, em especial no caso de solos com alta resistividade. Este estudo visa avaliar o comportamento dos campos elétrico (vertical e horizontal) e indução magnética gerados por descargas atmosféricas nuvem-terra, levando em consideração os parâmetros da descarga (amplitude, forma de onda e velocidade de propagação da corrente) e os diferentes modelos para representação do canal da descarga. Além do caso de solo perfeitamente condutor, são consideradas situações mais realistas, isto é, verificando-se a influência, nos campos, de parâmetros como a resistividade e permissividade do solo. / The occurrence of lightning discharges causes a significant amount of unscheduled supply interruptions in overhead lines of electricity systems, contributing to decrease quality indicators of these systems, even in the case of regions with moderated ground flash density. Focusing on the distribution systems, great part of the problems are related to the induced voltages due to lightning discharges in the vicinity of overhead lines, which results from the electric and magnetic fields associated with the current propagation along the return stroke channel. The knowledge of the characteristics of lightning electromagnetic fields is, therefore, crutial for determining induced voltages on overhead lines. Although the importance of the assumption has propitiated in the last years the development of a great number of research concerning the lightning electromagnetic fields and induced voltages on overhead lines, in most of the studies the hypothesis of a perfect conducting ground is assumed. While such assumption can be considered valid for magnetic induction field and for the vertical component of the electric field, it doesn’t apply to the horizontal electric field, especially in the case of ground with high resistivity. The aim of this work is to present and to discuss the characteristics of the electric field (vertical and horizontal components) and magnetic induction generated by the cloud-to-ground lightning discharge, taking into account the lightning parameters (amplitude, waveform and propagation speed of the return stroke current) and the different return stroke models. Besides the case of perfect conducting ground, the influences of the ground permittivity and finite conductivity in the calculation of the electromagnetic fields are so considered.

No description available.