Lightning currents and electromagnetic fields associated with return strokes to elevated strike objects
Lightning currents and electromagnetic fields associated with return strokes to elevated strike objects The aim of this thesis is the modeling of lightning return strokes impacting elevated strike objects such as towers. The theoretical and experimental work done led to the evaluation of the effect of the presence of the strike object on the spatial and temporal distribution of the current along the channel and along the strike object, as well as on the radiated electromagnetic fields associated with that current distribution. The first three chapters of the thesis contain a brief description of the lightning discharge, a review of the relevant experimental data available and an overview of the existing return strokes models for lightning initiated at ground level. The main original contributions of this thesis are presented in Chapters 4 through 6. They consist of experimental and theoretical work as follows. For the purpose of validating our theoretical models versus measurements, we participated, during the summers of 2000 and 2001, in experimental campaigns in Toronto, Canada, where we measured currents and electromagnetic fields associated with lightning strikes to the CN Tower in collaboration with the lightning research group of the University of Toronto. The CN Tower is today's tallest free-standing structure in the world (553 m). The collected data constitute the first simultaneous measurements of lightning current, electric and magnetic fields at two distances from the lightning channel, as well as optical measurements using a fast-speed camera system. The set of measurements obtained in Canada was complemented, in the framework of this thesis, with (a) experimental data of lightning return stroke currents measured simultaneously at two locations at the Peissenberg tower in Germany, provided by Prof. Fridolin Heidler, and (b) measurement results obtained using a reduced-scale model also designed, constructed, and tested in the framework of this thesis. The cumulated data allowed us to characterize the elevated strike object and to validate various theoretical expressions developed in this thesis. We generalized in Chapter 4 the so-called engineering models to include the presence of an elevated strike object. The generalization is based on a distributed-source representation of the return stroke channel, which allowed more general and straightforward formulations of these models, including a self-consistent treatment of the impedance discontinuity at the tower top, as opposed to previous representations implying a lumped current source at the bottom of the channel. We modeled the strike object as a vertically-extended, lossless uniform transmission line, characterized by reflection coefficients at its extremities. Special expressions were also derived for the case of electrically short structures. These expressions can be used to quantify the effect of grounding conditions on the current distribution along the strike object and along the channel. In Chapter 5, using the general expressions for the spatial-temporal distribution of the current in the channel and in the elevated strike object, new expressions for the electric and magnetic fields at far distances were derived. These expressions were evaluated for the cases of electrically-tall and electrically-short structures. For electrically-tall structures, it was found that the presence of the strike object enhances the radiated electric and magnetic field peaks in comparison to return strokes initiated at ground level. The enhancement was quantified through a simple multiplicative factor that depends on the return stroke speed and on the top reflection coefficient associated with the strike object. The mentioned simultaneously measured currents and fields associated with lightning strikes to the CN Tower were used to test the theoretical expressions and a reasonable agreement was found. The derived expressions could find a useful application when lightning currents are measured directly on instrumented towers to calibrate the performance of lightning location systems. In Chapter 6, we analyzed the current into the elevated strike object in the frequency domain, and we derived a closed form expression to evaluate this current taking into account frequencydependent reflection coefficients at the top and at the bottom of the elevated strike object. We derived an expression to calculate the reflection coefficient as a function of frequency at the bottom of the lightning strike object from two currents measured simultaneously at different heights along the strike object. We found that the ground reflection coefficient can be found without prior knowledge of the reflection coefficient at the top of the strike object. We showed that, unless the tower is tall enough that the current injected at the top of the object or its derivative drop to zero before the arrival of reflections, it is impossible, at least under our assumptions, to derive either the reflection coefficient at the top of the strike object or the "undisturbed" current from any number of simultaneous current measurements. We proposed two methods to estimate the top reflection coefficient. The proposed methods were applied to the experimental data obtained on Peissenberg Tower where lightning currents were measured simultaneously at two heights. It was found that the reflection coefficient at ground level can be considered as practically constant over a relatively wide range of frequencies from 100 kHz up to 800 kHz. The estimated top reflection coefficients are in good agreement with values found in the literature. Nevertheless, we found that the estimated values for the top reflection coefficient from the extrapolation method are lower than those found employing the current derivative method. The difference might be due to possible experimental errors and also to the fact that the extrapolation method provides values for the top reflection coefficient calculated from the low-frequency tail of the current waveforms, while the current derivative method uses values associated with the faster parts of the waveform. This observation suggests that the top reflection coefficient is frequency dependent. Finally, a genetic algorithm was applied to extract automatically primary lightning parameters from experimental records obtained on instrumented towers. The algorithm was first tested using theoretical waveforms obtained by assuming values for the ground and top reflection coefficients, and an assumed "undisturbed" current expressed in terms of two Heidler's functions. The algorithm was then applied to the actual, measured lightning return stroke currents obtained at the Peissenberg tower in Germany. The individuals that best satisfied the genetic algorithm's fitness function were selected and compared with the measured waveforms. A good agreement was found.
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