Engineering Return Stroke Models Research Articles

New Approach to Revise the Spatiotemporal Lightning Current Distribution Models Intended for Tall Objects

In this article, we revised the commonly known engineering return stroke models for elevated objects, by taking into account the relativistic Doppler effect of the return stroke velocity shift. This revised model is applied to calculate the electromagnetic lightning field, struck by the Peissenberg tower using the finite difference time domain method in two-dimensions method. The simulation results are both compared with the results of the experimental measurements and with those obtained from the only two theoretical extending models existing in the literature that consider the presence of towers. Results show that the vertical lightning electric field is in perfect agreement with that measured experimentally, which means that this novel model was able to eliminate the nonphysical aspect of the transmitted current wave velocity from the tower top to the lightning channel observed in the hypothesis of the other authors and to reproduce in a more refined way the experimental measured electric field. The magnetic field behavior presents a concordance in the first peak and a slight difference in the tail waveform with that measured experimentally. These new formulations approximate the reality of the lightning radiation and, thus, allow to improve protection against its harmful effects.

Unification of engineering return stroke models

Engineering models burrow various features from transmission line theory and combine them using empirical data to create models that can predict the electromagnetic fields of lightning return strokes in space and time. At present, engineering models are the most successful in predicting the features of lightning electromagnetic fields in close agreement with the experimental data. Today, most scientists who are interested in lightning protection use engineering models in their studies. A large number of engineering return stroke models exist in the literature. Depending on the assumptions made they can be categorized as Current Propagation models (CP-models), Current Generation models (CG-models) and Current Dissipation models (CD-models). The goal of this paper is to describe the different approximations used in constructing these engineering return stroke models and to show that all these models are a special case of a more general model which we call Current model (C-model). We will show how various return stroke models can be precipitated from the C-model by neglecting different features associated with it.

Modified Transmission Line Model with a Current Attenuation Function Derived from the Lightning Radiation Field—MTLD Model

In return strokes, the parameters that can be measured are the channel base current and the return stroke speed. For this reason, many return stroke models have been developed with these two parameters, among others, as inputs. Here, we concentrate on the current propagation type engineering return stroke models where the return stroke is represented by a current pulse propagating upwards along the leader channel. In the current propagation type return stroke models, in addition to the channel base current and the return stroke speed, the way in which the return stroke current attenuates along the return stroke channel is specified as an input parameter. The goal of this paper is to show that, within the confines of current propagation type models, once the channel base current and the return stroke speed are known, the measured radiation field can be used to evaluate how the return stroke current attenuates along the channel. After giving the mathematics necessary for this inverse transformation, the procedure is illustrated by extracting the current attenuation curve from the typical wave shape of the return stroke current and from the distant radiation field of subsequent return strokes. The derived attenuation curve is used to evaluate both the subsequent and first return stroke electromagnetic fields at different distances. It is shown that all the experimentally observed features can be reproduced by the derived attenuation curve, except for the subsidiary peak and long zero-crossing times. In order to obtain electromagnetic fields of subsequent return strokes that are in agreement with measurements, one has to incorporate the current dispersion into the model. In the case of first return strokes, both current dispersion and reduction in return stroke speed with height are needed to obtain the desired features.

A New Calculation Method of the Lightning Electromagnetic Field Considering Variable Return Stroke Velocity

The article proposes an improved method for the calculation of the electromagnetic field radiated by a lightning return stroke over a perfectly conducting ground. Specifically, the proposed time domain expressions allow a closed-form solution for the field produced by an impulse-current propagating upward along a vertical path with a given velocity. The expressions are valid for a wide class of engineering return stroke models and can be adopted also in case the return stroke velocity varies along the channel. The solution for an arbitrary current waveform can be obtained by the convolution of the current at the channel base with the electromagnetic field due to the impulse-current along the channel. The accuracy and advantages of the method are assessed by the comparison with those obtained by a finite-element method computer model. The expressions are implemented in the LIOV-EMTP-RV code for the calculation of the induced voltages in an overhead distribution line.

Evaluation of an Approximate Channel-Base Current and Its Analytical Function Parameters Based on the Measured Lightning Magnetic Field

In this paper, a new method is proposed for directly evaluating approximate lightning channel-base-current (CBC) parameters ( $I_{m}$ , ( di / dt )max, t FD, and t SD) and analytical function parameters (AFPs) of the CBC based on the measured lightning magnetic fields using a deconvolution and differential evolution (DE) method. This proposed method comprises two sequential steps. The first step is for determining the lightning CBC based on the measured magnetic field using modified transmission line model with exponential current decaying with height (MTLE) through deconvolution, while the second step is for evaluating the AFPs (Heidler's function) corresponding to the lightning CBC obtained from the first step. Data from the measured magnetic field above ground level ( z = 10 m) at different horizontal distances ( r = 9 km, 4.6 km, 2 km, and 50 m) from the lightning channel are considered for testing the proposed method. The sum of two Heidler's functions is used to represent the lightning CBC; and its parameters, namely I 01, I 02, τ 11, τ 12, τ 21, τ 22, n 1 , and n 2 are identified using DE as a tool. Further, this methodology is helpful in the evaluation of the CBC parameters and mathematical modeling of the lightning CBC and the estimation of the lightning current through the channel using data from the measured magnetic field for different engineering return stroke models.

Close electric fields and lightning-induced voltages predicted by a return-stroke model including corona and nonlinear channel resistance

In this paper, a return-stroke model based on nonuniform transmission line theory that includes nonlinear losses and corona is used for calculating close electric fields and lightning-induced voltages on an overhead line. A study is performed to identify the influence of return-stroke corona on close electric fields and line overvoltages considering different model assumptions. It is shown that the consideration of corona affects the attenuation and distortion of the return-stroke current. Close vertical electric fields predicted by the model present waveforms, peak values, and decay with distance that are in agreement with measured data. A simpler case in which the return-stroke speed is artificially set to a prescribed value by controlling the inductance and capacitance of the channel is shown to lead to results that are in agreement with the complete return-stroke model considering nonlinear losses and corona. Similar conclusions apply to popular engineering return-stroke models typically used in lightning-induced voltage calculations provided the return-stroke speed is suitably adjusted. It is also shown that lightning-induced voltages calculated with the considered model are in good agreement with experimental data.

A Novel Procedure to Represent Lightning Return Strokes—Current Dissipation Return Stroke Models

Engineering return stroke models available in the literature can be divided into two categories, namely, current propagation models and current generation models. Based on the theory of pulse propagation along transmission lines in the presence of corona, a third procedure to describe return strokes, which, in fact, is the inverse of current generation models, is introduced. Models based on the new concept are called current dissipation models. In the current generation models, the corona currents generated by the neutralization of the corona sheath travel downward and the cumulative effects of these corona currents generate the return stroke current. In current dissipation models, the return stroke is initiated by a current pulse injected into the core of the leader channel at ground level. This injected current pulse travels upward with speed vc . If the return stroke channel is treated as a transmission line, then this speed is equal to the speed of light. The propagation of this pulse along the central core initiates the neutralization of the corona sheath leading to the release of corona currents into the central core. In contrast to current generation models in which corona currents travel downward, these corona currents travel upward along the core. The speed of propagation of the corona pulses upward along the core is also equal to vc. The corona currents, being of opposite polarity, lead to the dissipation of the injected current pulse. As in the case of current generation models, a current dissipation model can be described completely by any three of the following four parameters. They are: 1) channel base current; 2) spatial variation of the return stroke velocity; 3) spatial variation of the corona decay time constant; and 4) the spatial variation of the positive charge deposited by the return stroke on the leader channel. It is also shown that current propagation models available in the literature are special cases of current dissipation models.

On the Relationship Between the Signature of Close Electric Field and the Equivalent Corona Current in Lightning Return Stroke Models

Engineering return stroke models can be categorized either as current generation (traveling current source type) models or current propagation (transmission line type) models. The current generation models are described among other parameters by a corona current distributed along the channel. Recent studies show that there is equivalence between the models of current generation and current propagation types. Due to this equivalence, any engineering return stroke model of current propagation type can be described in terms of an equivalent corona current per unit channel length. The measurements conducted within 10-500 m from triggered lightning flashes show that the electric field of subsequent return strokes at these distances flattens within 15 mus or so. In this paper, the constraints imposed by this feature on the temporal and spatial variation of the equivalent corona current are investigated. The results show that in order for the close fields to flatten within 15 mus or so, the equivalent corona current, should be bipolar and the corona current wave shape at late times should be identical to that of the longitudinal current time derivative. This is in contrast to most of the engineering models of current generation type, in which the corona current is assumed to be unipolar.

On return stroke currents and remote electromagnetic fields associated with lightning strikes to tall structures: 2. Experiment and model validation

In this paper, simultaneous GPS time‐stamped measurements of the electric and magnetic fields at three distances and of the return stroke current associated with lightning strikes to the Toronto CN Tower (553 m) during the summer of 2005 are presented. The lightning return stroke current was measured using a Rogowski coil installed at a height of 474 m above ground level (AGL). The vertical component of the electric field and the azimuthal component of the magnetic field were measured simultaneously at distances of 2.0 km, 16.8 km, and 50.9 km from the CN Tower. The propagation path from the CN Tower to the first two stations (2.0 and 16.8 km) was along the soil and through the Toronto city, whereas for the third location (50.9 km) the propagation path was nearly entirely across Lake Ontario. The waveforms of the electric and magnetic fields at 16.8 km and 50.9 km exhibit a first zero crossing about 5 μs after the onset of the return stroke. This early zero crossing is part of a narrow undershoot. For fields at 50.9 km the expected zero crossing at about 40 μs is also observed. Metallic beams and other conducting parts in buildings on which electric and magnetic field sensors were located cause an enhancement effect on the measured fields. Although an enhancement can be identified both on the electric and the magnetic fields, the degree of enhancement is actually more significant for the electric field than for the magnetic field. It is shown that the value of the wave impedance (E‐field peak to H‐field peak ratio) could give an estimate of the enhancement effect of the building on the electric field. Propagation effects (decrease of field amplitude and increase of its risetime) can 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 is mostly across Lake Ontario. Measured waveforms are compared with theoretical predictions obtained using the five engineering return stroke models extended to include the presence of the strike object, namely, transmission line (TL), modified transmission line (MTLL and MTLE), Bruce‐Golde (BG), and traveling current source (TCS) models. A reasonable agreement is found with all five engineering models for the magnetic field waveforms at the three considered distances, although the peak values of the computed fields are systematically about 25% lower than measured values. None of the models was able to reproduce the early zero crossing and the narrow undershoot. As far as the electric field is concerned, larger differences have been observed between simulations and measurements. This may be due to the fact that the enhancement effect of the building on the electric field is stronger than that on the magnetic field. The expression relating current and field peaks associated with strikes to tall structures is also tested versus obtained sets of experimental data. The overall agreement between the theoretically predicted and the experimentally observed field‐to‐current ratio is reasonable, although the formula of Bermudez et al. (2005) appears also 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 antennae were installed.

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.

Modification of Engineering Return-Stroke Models to Include Dispersion Effects

Recently, Baba and Ishii (see ibid., vol.44, p.476-7, Aug. 2002) have presented a method to modify the transmission-line (TL) type model to incorporate current distortion. In this brief, we generalize their method, as well as an exponential decay return stroke speed model, to simple engineering return-stroke models, and investigate the influence of dispersion effects on associated electromagnetic fields. Results show that the proposed modification to the models eliminates the inherent discontinuity in the traveling current source (TCS) model and the Bruce-Golde (BG) model at the upward-moving front. In addition, it turns out that an increase in the current risetime with height does not have significant effect on magnetic hump, electric ramp, and distant zero crossing, while a rapid decrease in return stroke speed with height could affect these features.

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.

On the concepts used in return stroke models applied in engineering practice

In this paper, we investigate the similarities between two basic concepts used in engineering return stroke models. In one type, the current propagation (CP) models, the return stroke channel merely acts as a medium for the current propagation with the driving source being at the ground. In the other type, the current generation (CG) models, the current sources (corona current) are assumed to be distributed along the return stroke channel. Our analysis shows that popular CP models, such as transmission line (TL), the modified transmission-line exponential (MTLE) model , and the modified transmission-line linear (MTLL) can be converted to CG models leaving the temporal and spatial variation of the return stroke current the same. In this alternative representation, the equivalent corona currents of the TL, MTLE, and MTLL models are bipolar, indicating initial deposition and subsequent removal of positive charge from the channel. This knowledge is applied to construct a simple CG model which generates electromagnetic fields identical to those obtained with the TL model at short times, but free from the difficulties associated with the latter at longer times.