Elevated Strike Object Research Articles

An Extension of the Guided Wave M‐Component Model Taking Into Account the Presence of a Tall Strike Object

AbstractWe present in this paper an extension of the guided‐wave M‐component model of Rakov et al. considering the presence of a vertically elevated strike object. The tall object is represented as a lossless, uniform transmission line. Expressions for the current distribution along the channel and along the strike object are derived. Simulation results for the electric field at close (100 m), intermediate (15 km), and far (100 km) distance ranges are presented, considering fast and slow M‐component currents. The results show that, for very tall structures and fast M‐component waves, the presence of a tall strike object can result in a sharp peak superimposed on the M‐component electric field at intermediate and far distance ranges (e.g., 15 and 100 km). At close distances, the electric field of a fast M‐component is characterized by an initial negative excursion followed by a polarity change. It is shown that the presence of the tower results in a decrease of the negative initial excursion of the field. For slow M‐component waveforms or for moderately tall structures, the presence of the tall strike object can be disregarded in the M‐component field calculations. A discussion on the influence of the M‐wave channel height and velocity on the electric fields for fast M‐component currents is also presented. The study suggests a noticeable effect of the M‐wave velocity on the electric fields at all distance ranges. The variations of the wave velocity and channel length affect the time of appearance of the superimposed sharp peak on the electric fields. However, the sharp peak magnitude, which is due to the presence of the tower, is independent of the channel length and wave velocity. It is determined by the injected current and the reflection coefficients from the ground and tower top.

Electromagnetic Environment in the Vicinity of a Tall Tower Struck by Lightning—A Review—

In this paper, an overview of recent theoretical investigations and experimental characterization of the electromagnetic fields in the vicinity of a tower struck by lightning is presented. The presence of an elevated strike object has been included in two classes of return-stroke models, namely the engineering models and the electromagnetic or Antenna-Theory (AT) models. Extensions of engineering models based on distributed-source and lumped-source representations are described. The adequacy of the representation of the tall structure as an ideal uniform transmission line is discussed. Different approaches and assumptions for the computation of electromagnetic fields are summarized. Finally, recent progress in the characterization of electromagnetic fields radiated by lightning to tall structures is presented.

On return stroke currents and remote electromagnetic fields associated with lightning strikes to tall structures: 1. Computational models

In this paper, analytical expressions relating far fields and currents associated with lightning strikes to tall towers are derived. The derived equations are general and can be used with any engineering model. It is shown that the far field can be decomposed into three terms, namely (1) contribution of the main return stroke pulse along the lightning channel, (2) contribution of the multiple‐reflection process along the elevated strike object, including the contribution of upward propagating pulses transmitted into the channel, and (3) contribution of the so‐called “turn‐on” terms, associated with the current discontinuity at the return stroke wavefront. This discontinuity is associated with neglecting reflections at the upward moving front. It is also shown that only the first term is model‐dependent and that the far field–current relationship does not significantly depend on the adopted engineering model. It is therefore possible to use the analytical equation relating the current peak and the associated distant electric or magnetic fields, derived by Bermudez et al. (2005) for the transmission line (TL) model, for any engineering model extended to include a tall strike object. It is also shown that the peak amplitude of the electromagnetic field radiated by a lightning strike to a tall structure is relatively insensitive both to the value of the return stroke speed and the top reflection coefficient. These results and findings of this paper emphasize the key differences between return strokes initiated at ground level (or from short strike objects) and those striking tall towers: (1) The electromagnetic field from lightning strikes to tall towers is largely determined by the tower and only to a lesser extent by the channel, (2) electromagnetic fields associated with tall strike objects are less model‐sensitive than those corresponding to a strike to ground; in particular, the early time response of the field is nearly model‐independent, and (3) unlike ground‐initiated strikes, for which the far field peak is strongly dependent on the return stroke speed (proportional according to the TL model), far field peaks associated with strikes to tall strike objects are little sensitive to the return stroke speed. This is a particularly interesting result when lightning currents are measured directly on instrumented towers to calibrate the performance of lightning location systems, since in most practical cases the value of the return stroke speed is unknown. Note that points (2) and (3) can be considered as corollaries of point (1).

Return stroke current profiles and electromagnetic fields associated with lightning strikes to tall towers: Comparison of engineering models

In this paper, we compare five engineering return stroke models, extended to include the presence of an elevated strike object, namely the Bruce–Golde (BG) model, the transmission line (TL) model, the traveling current source (TCS) model, and the two modified TL models (MTLL and MTLE). The model-predicted current profile along the channel and along the strike object, as well as radiated electric and magnetic fields at different distances are presented and discussed. The comparison is made assuming the same ‘undisturbed current’ (that is the idealized current that would be measured at the tower top if the current reflection coefficients at its both extremities were equal to zero) and the same return-stroke speed. Except for the case of very close (50 m) electric field, it is found that the computed electromagnetic fields associated with a strike to a 168-m tall tower are less model-dependent than those corresponding to a strike to flat ground.

Determination of lightning currents from far electromagnetic fields: Effect of a strike object

We discuss in this paper the influence of the presence of an elevated strike object on the peak of the lightning return stroke current determined from remote field measurements. We develop analytical expressions relating the lightning return stroke channel-base current and the far electromagnetic field for different specific cases, namely, (1) ground-initiated return strokes (classical transmission line (TL) model), (2) ground-initiated return strokes including possible reflections at ground level, (3) tall strike objects for which the current's zero-to-peak time is smaller than the travel time along the object, and (4) electrically short strike objects. It is shown that for tall structures, the field enhancement relative to a return stroke initiated at ground level is expressed through a factor equal to k tall = [ 1 + c / v ( 1 - 2 ρ t ) ] / ( 1 - ρ t ) , where v and c are the return stroke front speed and the speed of light in vacuum, respectively, and ρ t is the top reflection coefficient. For very short towers and/or very slow return stroke current wavefronts, when the condition t f ⪢ h / c applies, expressions relating the far electromagnetic field and the return stroke current were also derived. For case (2), return strokes initiated at ground level, the field enhancement relative to a return stroke initiated at ground level, case (1), is expressed through a factor equal to k short = ( 1 + ( c / v ) ρ ch – g ) / ( 1 + ρ ch – g ) , where ρ ch–g represents the reflection coefficient between the lightning channel and the grounding impedance.

Revision, Extension, and Validation of Jordan's Formula to Calculate the Surge Impedance of Vertical Conductors

Jordan's formula to calculate the surge impedance of vertical conductors is revised and extended to take into account systems with multiple conductors. Experimental data and the hybrid electromagnetic model are applied in order to validate the derived expressions. Additionally, Jordan's formula is successfully used in the representation of an actual tower as a multiconductor vertical system. The obtained results indicate the usefulness of the derived expressions if an engineering analysis of direct strikes over elevated strike objects is required

Far-Field–Current Relationship Based on the TL Model for Lightning Return Strokes to Elevated Strike Objects

New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike object, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed v, the speed of light in vacuum c, and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electromagnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level (h=0), these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground.

Electromagnetic field radiated by lightning to tall towers: Treatment of the discontinuity at the return stroke wave front

Recently, engineering return stroke models were extended to take into account the presence of an elevated strike object, which was modeled as an ideal uniform transmission line. We show in this paper that the current distribution associated with these extended models exhibits a discontinuity at the return stroke wave front, which cannot be considered to be physically plausible. This discontinuity arises from the fact that the current injected into the tower from its top is reflected back and forth at its ends and portions of it are transmitted into the channel; these transmitted pulses, which are supposed to travel at the speed of light, catch up with the return stroke wave front traveling at a lower speed, and no current is allowed to flow in the leader region above the front. This discontinuity needs to be carefully treated when calculating the radiated electromagnetic field through an additional term in the electromagnetic field equations, the so‐called “turn‐on” term. We additionally derive a general analytical formula describing the turn‐on term associated with this discontinuity for various engineering models. We present simulation results illustrating the effect of the turn‐on term on the radiated electric and magnetic fields for an elevated strike object of height h = 168 m, corresponding to the Peissenberg tower in Germany. Finally, possible modifications to engineering models are suggested in order to eliminate this discontinuity.

Currents and radiated electromagnetic fields in lightning strikes to tall structures

The paper presents recent developments in the study of lightning discharges - electrical transient components of a thunderstorm - striking elevated objects. In the computation of lightning return stroke currents, we analyze the disturbance introduced by the elevated strike object. A new methodology in lightning return strike modeling is proposed, and applied in the computation of lightning electromagnetic fields at far distances. We compared the resulting expressions with experimentally-measured lightning currents and electromagnetic fields observed at the CN Tower Research Center in Toronto, and found a reasonable agreement. The expressions can be used to calibrate the performance of lightning location systems in cases where lightning currents are measured directly on instrumented towers.

Determination of reflection coefficients at the top and bottom of elevated strike objects struck by lightning

In this paper, we present an analysis of lightning return stroke currents along an elevated strike object. We derive closed form expressions, both in the frequency domain and in the time domain, to calculate the lightning current at any height along a strike object taking into account reflections at the top and at the bottom. The frequency dependence of reflection coefficients is taken into account. We also derive an expression to calculate the reflection coefficient as a function of frequency at the bottom of the lightning strike object from two currents measured at different heights along the strike object. We show that, if the current and its time derivative overlap with reflections at the top or bottom of the strike object, it is impossible to derive the reflection coefficient at the top of the strike object exactly from any number of simultaneous current measurements. We propose an extrapolation method to estimate this reflection coefficient. We propose a second method to calculate the top reflection coefficient from just one current derivative measurement if the current derivative and its reflections do not overlap significantly. We apply the proposed methodology to experimental data obtained on Peissenberg Tower (Germany) consisting of lightning currents measured at two heights. The results suggest that the reflection coefficient at ground level can be considered as practically constant in the frequency range 100 kHz to 800 kHz. Although the estimated ground and top reflection coefficients are in good overall agreement with values found in the literature, the estimated values for the top reflection coefficient from the extrapolation method are somewhat lower than those found employing the current derivative method; the differences are discussed.

On the influence of elevated strike objects on directly measured and indirectly estimated lightning currents

The knowledge of lightning current parameters comes essentially from direct measurements obtained using instrumented towers or triggered lightning, and from measurements of lightning electromagnetic fields assuming empirical or theoretical relations between fields and currents (indirect estimation). In this paper, the effects of an elevated strike object on both the direct and indirect estimation of the current parameters is examined. The authors first give the expressions which allow for what they call the 'decontamination' of measured lightning currents from the tower reflections, assuming the tower as a perfectly conducting strike object. They show that even though the reflections might not be discernible in experimental recordings for tower heights as those used in Berger et al.'s and Garbagnati and Lo Piparo's investigations, the peak current might be significantly affected. They then extend the transmission line (TL) return-stroke model of Uman and McLain, by taking into account the presence of an elevated strike object and the multiple reflections at the bottom and at the top of it. In general, radiated fields calculated considering and neglecting the presence of the strike object differ. It is shown that relatively short strike objects, such as triggered lightning launching structures, may not appreciably affect the calculated field peak values and overall wave shapes, but could affect the field derivatives.