The study of the interaction of lightning electromagnetic fields with electrical systems and the design of appropriate protection strategies are generally based on statistical distributions of the lightning current measured at the channel base using either instrumented towers or artificial initiation of lightning using rockets. Recent studies based both on numerical modeling and experimental observations have shown that the presence of the structure struck by (or used to initiate) lightning does affect the current measurement in a way depending upon the geometry of the structure itself, compromising therefore the reliability of the statistics adopted so far for lightning data. The aim of this thesis is to provide new elements (from both theoretical and experimental investigations) to improve the understanding of the electromagnetic consequences of the impact of lightning return strokes to tall structures. Chapter 2 introduces to the phenomenology of cloud-to-ground lightning and the importance of lightning return-stroke modeling. Among the different classes of return-stroke models existing in the literature, the attention is focused in this thesis on the so-called engineering models, which allow describing the current distribution along the channel as a function of the current at the channel base and the return-stroke speed, two quantities for which data can be obtained experimentally. After presenting a review of five engineering return-stroke models describing lightning strikes to ground, the extension of the engineering models to take into account the presence of an elevated strike object is presented and discussed. The original contributions of this thesis, consisting of both theoretical and experimental works, are presented in Chapters 3 through 6. Chapter 3 is devoted to the computation of the electromagnetic field produced by lightning return strokes to elevated strike objects, using the extension of the engineering models to include an elevated strike object presented in the previous chapter. It is shown, for the first time, that the current distribution associated with these extended models exhibits a discontinuity at the return-stroke wavefront which (although not physically conceivable) needs to be taken into account by an additional term in the equations for the electromagnetic field, the so-called "turn-on" term. A general analytical formula describing the "turn-on" term associated with this discontinuity for various engineering models is derived and simulation results illustrating the effect of the "turn-on" term on the radiated electric and magnetic fields are also presented. In the second part of the chapter, dedicated to the investigation of the propagation effects on lightning electromagnetic field traveling along a finitely-conducting ground, the commonly-used assumption of an idealized perfectly-conducting ground is relaxed in order to analyze, for the first time, how the electromagnetic field radiated by a tower-initiated strike is affected while propagating along a soil characterized by a finite conductivity. The results showed that the attenuation of the initial peak of the field radiated by a tower-initiated strike, resulting from the propagation over finitely conducting ground, depends strongly on the risetime of the current, the tower height and the ground conductivity and is, in general, much more important than the attenuation experienced, while propagating along the same finite ground, by the field produced by ground-initiated strikes. Chapter 4 presents a comparison among the predictions obtained using the five extended engineering return-stroke models for lightning strikes to tall structures described in Chapter 2. The spatial-temporal current profiles along the tower-channel axis predicted by the engineering models, as well as the respective predictions for the radiated electric and magnetic fields, calculated at different distances, are compared and discussed. It is shown that the computed electromagnetic fields associated with a strike to a tall tower are generally less model-dependent than those corresponding to a strike to ground, especially as far as the first-peak value is concerned, which is nearly model-insensitive in case of tall-tower strikes. A theoretical analysis is performed in the last part of the chapter with the aim to provide, for the same five engineering models extended to take into account the presence of the tower, expressions relating the return-stroke current and the associated distant radiated electric and magnetic fields. It is demonstrated, in addition, that only one model among the five presented is characterized by simple analytical formulas relating current-peak and far-field peak values, which (being the electromagnetic field peak value nearly independent of the adopted model) become general expressions applicable for any engineering return-stroke model in case of tower-initiated lightning. It was also shown that the peak amplitude of the electromagnetic field radiated by a lightning strike to a tall structure is relatively insensitive to both the values of the top reflection coefficient and the return-stroke speed. This latter result is important, in particular, because, unlike ground-initiated strikes, for which the far-field peak is strongly dependent on the return-stroke speed, far field peaks associated with strikes to tall structures are little sensitive to the return stroke speed. Since in most practical cases the value of the return-stroke speed is unknown, this interesting result suggests a possible calibration procedure for lightning detection systems by means of direct measurement of lightning currents on instrumented towers. Chapter 5 reports on the simultaneous measurements of the return-stroke current and of the electric and magnetic fields at three distances associated with lightning strikes to the Toronto CN Tower (553 m) that have been carried out during the summer of 2005. This is the first time ever that simultaneous records of lightning current and associated electric and magnetic fields at three distances have been obtained. Two propagation paths for the electromagnetic field to the first and to the second field measurement stations (located, respectively, 2.0 km and 16.8 km away from the CN Tower) were along the soil and through the Toronto city, whereas for the third location (50.9 km away) the propagation path was nearly entirely across the fresh water of Lake Ontario. It is shown that the waveforms of the electric and magnetic fields at 16.8 km and 50.9 km exhibit a first zero-crossing about 5 microseconds after the onset of the return-stroke, which is part of a narrow undershoot and which may be attributed to the transient processes along the tower. Effects of propagation (decrease of field amplitude and increase of its risetime) could also be observed in experimental records. It is shown that the fields at 50.9 km are less affected by such attenuation, compared to those at 16.8 km, presumably because the path of propagation was mostly across Lake Ontario. The measured waveforms are compared with the theoretical predictions obtained using five engineering return-stroke models, extended to include the presence of the strike object, finding a reasonable agreement for the magnetic field waveforms at the three considered distances. The overall agreement between the theoretically predicted and the experimentally observed field-peak-to-current-peak ratio is reasonable, although the theoretical expression appears to underestimate the experimentally measured ratio (by about 25 %). This may be due, at least in part, to the enhancement effect of the buildings on which the field measurement antennas were installed. Finally, the directly-measured lightning currents at the tower were correlated and compared with the current-peak estimations provided by the US National Lightning Detection Network (NLDN). It is shown that the NLDN-inferred values overestimate the actual current peaks because the presence of the tall struck object produces an enhanced radiated field at far distances (with respect to strikes to flat ground), which is not included in the algorithm used to infer lightning current peaks from remote field measurements. It is shown in this thesis that correcting the NLDN estimates using the correction factor introduced by the tower results in an excellent estimation of lightning current peaks. This is an important conclusion of this study showing that the estimation of lightning peak currents for tall towers can be greatly improved by considering the tower correction factor. Chapter 6 is devoted to the measurement of electromagnetic fields radiated by lightning. In its first part, the need for guidelines for reporting lightning data obtained experimentally is emphasized. The second part of the chapter presents the design, the construction and preliminary tests of a low-cost, multi-channel lightning field measuring system for the simultaneous measurement of three components of the electromagnetic field radiated by lightning. The proposed system uses one single optical link for the transmission of the three signals, appropriately digitized and multiplexed, lowering considerably the overall cost of the system itself.
EPFL2007
