Subsequent Return Strokes Research Articles

Transient Analysis of Grounding Electrodes in Multilayer Soils Using Method of Moments

Grounding electrodes are expected to provide a low-impedance path for faults and lightning transient currents and protect the safety of electrical equipment and nearby people against dangerous induced potentials. In this context, a precise model of the grounding electrodes is needed to represent a certain electrode arrangement buried in stratified soil. This paper computes the grounding impedances of different grounding systems buried in three different soil configurations (homogeneous, 2-layer and 3-layer soil) modeled by its frequency-dependent electrical parameters. A simulation model using a commercial full-wave electromagnetic software FEKO to compute the grounding impedances is presented. Method of Moments(MoM), a frequency-domain numerical method, is employed to compute the grounding impedance in a frequency range of100 Hz to 5 MHz. Next, the developed ground potential rise(GPR) generated by two types of lightning currents (first and subsequent return strokes) injected into these grounding systems is computed. Time-domain GPR of each grounding system is also determined using the Vector Fitting (VF) technique combined with the ATP-software. Results show that GPR waveform is reduced when frequency-dependent soils are employed. This reduction is more pronounced in homogeneous and in 2-layersoils of high and moderated resistivity whereas the 3-layer soil has a minor impact due to the lower soil resistivity

Characteristics of electric field waveforms produced by negative return strokes in Colombia and their comparison with other regions

This paper presents the statistical analysis of several parameters associated with the electric field generated by negative cloud-to-ground (CG) lightning flashes recorded in the Bogota savannah (central province of Colombia), including a comparison with other regions. In this way, this is the first study in Colombia where eleven parameters of the electric field and two more related to the electric field derivative are analyzed in detail. From a measuring campaign carried out during the second semester of 2016, 306 negative cloud-to-ground lightning flashes containing the same number of first return strokes (FRS) and 483 subsequent return strokes (SRS) had been analyzed. These return strokes occurred in the range from 3 to 250 km from the measuring station, in such a way that the waveforms analyzed have static components, radiated components or a combination of both. At first, a total of 64.7% of negative CG flashes were categorized as multiple-stroke flashes, the average multiplicity was 2.6 strokes/flash and the maximum value reported was 13 strokes. For the first and subsequent return strokes analyzed in Colombia, the arithmetic mean (AM) of the initial electric field peak normalized to 100 km (EP_N) were 27.6 V/m and 12.4 V/m, respectively. On the other hand, the average of the peak value of the electric field derivative (dE/dt)P was 5.9 V/m/μs for FRS and 3.6 V/m/μs for SRS. These results are similar to those observed in Florida, Germany, Sweden, Japan, Sri Lanka and Malaysia, where the EP_N and the (dE/dt)P for FRS are larger than those for SRS. Furthermore, as reported in Malaysia and other tropical regions, several electric field parameters in Colombia are affected by the geographical location, the distance with respect to the measuring system and the propagation medium. The above was more evident for some temporal parameters such as zero-to-peak rise time, the 10–90% transition duration, the slow front duration and the fast front duration. After comparing with previous data related to natural and rocket-triggered lightnings measured in different regions (tropical, subtropical and temperate latitudes), additional differences were also observed.

Electric Field Parameters of Natural Negative Cloud-to-Ground Lightning in China

This article presents the electric field characteristics of 1612 single, 912 first, and 2901 subsequent return strokes (RS) in negative lightning in Guangdong Province, China. Statistic parameters of electric field waveforms include risetime, fall time, half-peak width, zero-crossing time, overshoot duration, initial peak, overshoot amplitude, and ratio of initial peak to overshoot (Ep/Eos). The results show that the electric field parameters of single RS are similar to those of the first RS. The difference of the geometric mean (GM) for all the parameters is within 10%, except for the Ep/Eos. The value of Ep/Eos for the first strokes is 14.3% larger than that of the single RS. But the values of these parameters for subsequent RS show significant differences from the single and first RS. The values of overshoot duration for subsequent RS are similar to those of the first RS, while the ratio of initial peak to overshoot is larger. As for the other parameters, the arithmetic mean and GM values are all more than 40% larger than the corresponding values of subsequent RS.

Conduction characteristics of lightning dart leader channel and its influence on the corresponding return stroke discharge intensity

Conductivity characteristics of lightning dart leader channel significantly affect the discharge features of the following return stroke process. Based on spectral quantitative analysis, the electrical conductivity, electron density of the dart leader, and the corresponding subsequent return stroke plasma were investigated, and their changes along the height of the discharge channel were calculated; furthermore, the effects of the conduction characteristics of the dart leader channel on the return stroke discharge intensity were investigated. The results indicated that the electrical conductivity distribution along the height of the return stroke channel was approximately consistent with that of the corresponding dart leader; there was a good linear correlation between the electron density of the dart leader tip as it approaches the ground and the bottom of the return stroke channel. It was inferred that the electron density in the dart leader tip is positively correlated with the discharge intensity of the return stroke.

Electromagnetic Fields Radiated by Lightning Return Stroke Over Lossy Ground With Rock Formation

Electromagnetic fields radiated by a lightning return stroke over lossy ground are calculated by finite difference time domain method in a two-dimensional cylindrical coordinate system. The considered ground model contains a rock formation for which four different geometries are defined: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rectangle</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">triangle</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">circle,</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</i> . Two electrical conductivities that are very low and very high compared to the conductivity of the ground are defined for the rock formation. Different scenarios are examined by computing horizontal electric field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{r}}}$</tex-math></inline-formula> , vertical electric field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{z}}}$</tex-math></inline-formula> , and azimuthal magnetic field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_{\boldsymbol{\varphi }}}$</tex-math></inline-formula> for both conductivities. In addition to the effect of different geometries, effects of spatial averaging, changing position of rock, different return stroke propagation speeds, observation points at different heights and different horizontal range distances are investigated adopting both first and subsequent return stroke currents as the source. The results show that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{z}}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{H}}_{\boldsymbol{\varphi }}}$</tex-math></inline-formula> fields are not much affected by geometry and conductivity change. However, for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{E}}_{\boldsymbol{r}}}$</tex-math></inline-formula> component, performances of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rectangle</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">triangle</i> geometries are close to each other and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</i> one shows closest performance to that of the case when there is no rock inside the ground. On the other hand, the field values decrease as the rock conductivity increases for both stroke types.

Evaluation of Site Errors in LLS Magnetic Direction Finding Caused by Large Hills Using the 3D‐FDTD Technique

AbstractAngle and amplitude estimation errors in magnetic direction finding, called site errors, are important sensor‐specific errors in lightning location systems (LLS). They are known to be caused by nearby cables and overhead lines due to induced currents. Due to the reflection and diffraction of electromagnetic waves, hills and mountains are also expected to generate these effects. In this paper, numerical computations applying the finite‐difference time‐domain (FDTD) method are performed to analyze the impact of hills or mountains on the angle and amplitude estimation of LLS sensors for typical first and subsequent return strokes (RS). The influence of hill size, the distance of sensors to the hill, ground parameters, and sensor bandwidth, are evaluated. The results show that on top of low ridges of only 125 m elevation, up to ±10° angle site error and +50% amplitude site error occur. A key finding is that due to field attenuation caused by lossy ground and sensor bandwidth limitations, there is practically no difference in the angle site errors for first and subsequent RS. For two sensors, the average site errors obtained from real sensor measurements are compared to results from 3D‐FDTD simulations, modeling the real terrain based on a digital elevation model. The simulation results are in good agreement with the observed, average angle site errors.

Leader-chasing behavior in negative artificial triggered lightning flashes

Two special cases of dart leader propagation were observed by the high-speed camera in the leader/return stroke sequences of a classical triggered lightning flash and an altitude-triggered lightning flash, respectively. Different from most of the subsequent return strokes preceded by only one leader, the return stroke in each case was preceded by two leaders occurring successively and competing in the same channel, which herein is named leader-chasing behavior. In one case, the polarity of the latter leader was opposite to that of the former leader and these two combined together to form a new leader, which shared the same polarity with the former leader. In the other case, the latter leader shared the same polarity with the former leader and disappeared after catching up with the former leader. The propagation of the former leader in this case seems not to be significantly influenced by the existence of the latter leader.

Ground Potential Rise in Wind Farms due to Direct Lightning

This paper investigates the ground potential rise (GPR) developed in wind farms subject to direct lightning currents representative of first and subsequent negative downward strokes and return strokes associated with upward negative flashes. The wind farm grounding system is studied considering different numbers of interconnected grounding systems and for distinct values of soil resistivity taking into account frequency-dependent soil parameters. A wideband multiport model of the wind farm grounding system is obtained and implemented in a time-domain electromagnetic transient tool to include the aerial elements in simulations, namely the wind turbine blades and tower. It is shown that interconnecting more wind turbine grounding systems in parallel leads to a significant reduction of the low-frequency grounding resistance, whereas the decrease of the impulse impedance is much lower, especially for low-resistivity soils and negative downward subsequent strokes or negative upward lightning return strokes. It is also shown that the presence of the aerial components significantly affects the GPR in the response to lightning currents representative of negative downward subsequent strokes and return strokes associated with negative upward flashes, which have higher frequency content compared to negative first return strokes. The presence of the aerial components increases the GPR peak.

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.

Characteristics of rocket-triggered positive lightning flashes and propagation properties of their initial upward negative leaders

Twelve lightning flashes are successfully triggered under the positive atmospheric electric field condition. The discharge properties of the flashes, and the propagation characteristics and mechanism of the involving upward negative leaders are investigated. When lightning flashes are triggered, the average ground atmospheric electric field is around 5 kV/m, with a maximum value exceeding 13 kV/m. Except for one special event showing a discharge polarity reversal (from positive to negative) and producing multiple negative return strokes, none of the remaining 11 triggered lightning flashes involves the subsequent return stroke process. The discharge currents of these flashes are generally of the order of several hundred amperes. The successfully triggered lightning flashes start with the initiation and the upward propagation of negative stepped leaders, of which the average two-dimensional velocity is 1.85 × 10&lt;sup&gt;5 &lt;/sup&gt;m/s. For a total of 132 steps captured by the high-speed video camera, the step lengths range from 0.8 m to 8.7 m, with an average of 3.9 m. During the initial stage of the upward negative stepped leader, the current and electromagnetic field present a significant impulsive feature. The mean value of pulse interval, current peak, charge transfer, half-peak-width and current rise time &lt;i&gt;T&lt;/i&gt;&lt;sub&gt;10%–90%&lt;/sub&gt; are 17.9 μs, 81A, 364 μC, 3.1 μs, and 0.9 μs, respectively. The equivalent linear charge density of a single step is 118.5 μC/m. The branching of the leader channel generally takes place together with the stepping process in two ways: the first way is to implement the multiple connections of clustering space stems/space leaders to the leader head within an individual step cycle, and the corresponding current waveform presents a multi-peak structure, with a peak interval of about 2–3 μs (up to 6–7 μs); the second way is to reactivate those previously extinguished space stems/space leaders and to connect them to the lateral surface of the channel.

The Energy, Momentum, and Peak Power Radiated by Negative Lightning Return Strokes

Electromagnetic radiation fields generated by return strokes transport both energy and momentum from the return stroke to outer space. The momentum transported by the radiation field has only a vertical or z component due to azimuthal symmetry (cylindrical symmetry) associated with a vertical return stroke. In this paper, the energy, momentum, and peak power radiated by return strokes as a function of the return stroke current, return stroke speed, and the zero-crossing time of the radiation fields are studied. The results obtained by numerical simulations for the energy, vertical momentum, and the peak power radiated by lightning return strokes (all parameters normalized by dividing them by the square of the radiation field peak at 100 km) are the following: A typical first return stroke generating a radiation field having a 50 μs zero-crossing time will dissipate field normalized energy of about (1.7–2.5) × 103 J/(V/m)2 and field-normalized vertical momentum of approximately (2.3–3.1) × 10−6 Kg m/s/(V/m)2. A radiation field with a zero-crossing time of 70 μs will dissipate about (2.6–3.4) × 103 J/(V/m)2 in field-normalized energy and (3.2–4.3) × 10−6 Kg m/s/(V/m)2 in field-normalized vertical momentum. The results show that, for a given peak radiation field, the radiated energy and momentum increase with increasing zero-crossing time of the radiation field. The normalized peak power generated by a first return stroke radiation field is about 1.2 × 108 W/(V/m)2 and the peak power is generated within about 5–6 μs from the beginning of the return stroke. Conversely, a typical subsequent return stroke generating a radiation field having a 40 μs zero-crossing time will dissipate field-normalized energy of about (6–9) × 102 J/(V/m)2 and field-normalized vertical momentum of approximately (7.5–11) × 10−7 Kg m/s/(V/m)2. The field-normalized peak power generated by a subsequent return stroke radiation field is about 1.26 × 108 W/(V/m)2 and the peak power is generated within about 0.7–0.8 μs from the beginning of the return stroke. In addition to these parameters, the possible upper bounds for the energy and momentum radiated by return strokes are also presented.

Lightning generated electric field over land and sea at Northern Region of Peninsular Malaysia: Measuring Setup

Lightning is the transfer of significant charge between two charged object, it can appear between cloud-to-cloud, cloud-to-air and cloud-to-ground. All lightning activities are correlated with charge movement and therefore, it can be studied using measurement of electrostatic field (slow field changes), radiation field (fast field changes) and magnetic field affiliated with charge movement. The measuring equipment was a parallel flat plate and vertical whip antenna with an analog filter buffer circuit, connected to a digital high speed oscilloscope. In principle, both antenna have a similar measuring operation, with the exclusion of the antennas dimension, mode of transient recoder and the association of circuitry characteristic (decay time constant). This measurement setup are commonly used to perform electric field characterization related to various lightning events such as as preliminary breakdown, stepped leader, return stroke, subsequent return stroke, dart leader, dart-stepped leader, narrow bipolar pulses and cloud activity between strokes, such as regular pulse trains, K and M changes and chaotic pulse trains. The measurement systems are located very close to the sea, with respect in obtaining a perspicuous explaination of lightning propagation effects on sea instead on land. Noise-distorted effects in data captured usually introduce in a noisy environment or when the lightning strike far from the measurement station, thus the data gathered from the measurement need to be filter using MATLAB computer simulation before conducting further analysis. A promising wavelet 1-D technique, then, were used in signal denoising process rather using conventional filtration. In this works, the state of art in measuring vertical component of electric field focalized sea area during the thunderstorm days been demonstrate and explained.

The Damage Effects on Surge Protective Devices Caused by the Ground Potential Rise During the Initial Long Continuous Current Processes of Triggered Lightning Events

Based on the triggered lightning technology, this study carried out observational tests regarding the impulses of ground potential rise (GPR) to surge protective devices (SPD), and emphatically analyzed the impulse and damage effects of the initial long continuous current processes of triggered lightning on the SPDs. The results showed that after the triggered lightning currents were injected into grounding grids, the SPDs with rated flow rates were easily damaged under the joint actions of the initial long continuous currents of the lightning and the subsequent return strokes. It was observed that when the energy flowing through the SPDs had accumulated to a certain level, only the initial long continuous current processes had caused damages to the SPDs. The impulse effects on the SPDs were determined to be closely related to the different waveforms of the initial long continuous current processes. For example, when the long continuous current processes were superimposed by the initial continuous current pulses (ICCP), with fast rising edges and large amplitudes, then the energy passing through the SPDs tended to rapidly increase. This was believed to likely be the most critical factor related to the damages to the SPDs during the long continuous current processes.

Electromagnetic transient modeling of grounding electrodes buried in frequency dependent soil with variable water content

The increasing demand for electricity over the past few decades has been continuously urging for more reliable power systems. Power transmission line networks, due to their vast physical dimensions, are the most critical components of a complex power system concerning the direct lightning strike. Grounding systems are widely used to mitigate the transient overvoltages for the protection of electrical component and human safety. The goal of this paper is to investigate the effect of frequency dependence of soil electrical parameters on the performance of vertical and horizontal grounding electrodes subjected to direct lightning strike, considering a variable water content of soil. Four soil models that take into account the variation of soil water content are reviewed and compared. The numerical simulations are performed using a full-wave electromagnetic model based on the Finite Element Method (FEM) in the frequency range from 1 kHz to 5 MHz and applying different soil models with varying water content. Then, electromagnetic transient (EMT) compatible equivalent circuits of grounding electrodes are developed using Fast Relaxed Vector Fitting (FRVF). Typical first and subsequent return stroke current waveforms measured at two different locations are adopted. The results of this paper demonstrate the importance of considering the variation of soil water content in the transient response of grounding electrodes. Simulation results demonstrate that the frequency dependence of the soil parameters lead to a decrease of the potential rise of the grounding electrodes compared to the case where the soil parameters are assumed constant. The effect of soil water content on the grounding performance is also shown to be dependent on the soil type, value of soil water content, and length of electrode.

Latitude and Topographical Dependence of Lightning Return Stroke Peak Current in Natural and Tower-Initiated Negative Ground Flashes

Experimental data show that the peak currents of first and subsequent lightning return strokes in negative ground flashes increase with decreasing latitude. In this paper, the reason for this dependence of peak return stroke current on latitude is explained using the fact that the height of the charge centers increases with decreasing latitude. Results show that in tropical regions where the height to the negative charge center is about 8 km, the median values of the first and the subsequent return stroke peak currents are about 42 kA and 15 kA, respectively. If the height to the charge center is larger than 8 km, the peak currents will also become larger. For example, if the location of the charge center is increased to about 9 km, the median values of the first and subsequent return stroke peak currents will increase to about 45 kA and 16 kA respectively. The same reasoning shows that, even in the same geographical region, the peak return stroke current may decrease as the elevation of the ground where the lightning strikes take place increases. The results also indicate that the peak subsequent return stroke current in tower-initiated negative lightning flashes decreases as the height of the tower increases. These theoretical predictions are in general agreement with the available experimental data.

Comparisons of optical characteristics of two upward lightning flashes triggered by a nearby positive cloud-to-ground lightning

The propagation characteristics of two upward negative lightning flashes, which were initiated from the tops of two tall grounded structures immediately after the return stroke (RS) initiation of one nearby positive cloud-to-ground (CG) lightning flash, have been investigated and compared based on high-speed video observations. Two upward flashes show significant difference in their propagation characteristics mainly due to the existence of lower cloud layer near the Canton tower. Upward flash initiated from the top of Canton tower produces several large luminous pulses, with the enhanced luminosity mostly concentrating near the lower cloud, and it propagates faster beyond the lower cloud, while the brightness of the other upward flash does not vary much and distributes almost uniformly along the discharge channel. The major reason for these differences might lie in the instantaneous negative charge neutralization inside the lower cloud with the positive charges along the discharge channel, when the positive leader propagates upward across the lower cloud layer. After about 90 ms the upward flash initiated from the tall building produces a dart-leader subsequent RS, but it extinguishes faster than the other one.

Investigation of influence of model hydrometeors on characteristics of electromagnetic radiation impulses registered near to artificial thunderstorm cells

Results of the experimental investigations of the influence of the model hydrometeor arrays on the characteristics of the electromagnetic radiation of the channel discharges between the system of the artificial thunderstorm cells of a negative or positive polarity and the ground have been presented in the paper. Parameters of the impulses of the electromagnetic radiation registered by the wideband plate antennas for the first and subsequent return strokes are under a consideration. Significant influence of the array of the large model hydrometeors on the probability of a subsequent stroke initiation and on the parameters of the corresponding electromagnetic radiation pulses has been established and discussed. Found dependencies between the characteristics of the current impulse of the first and subsequent return strokes from the system of the negative and positive artificial thunderstorm cells and the parameters of the impulses of the corresponding electromagnetic radiation have been analyzed. Comparison of the received results with processes of the electromagnetic radiation of a natural lightning has fulfilled.

Inception of subsequent stepped leaders in negative cloud-to-ground lightning

Time-correlated high-speed video and electric field change data for 139 natural, negative cloud-to-ground (CG)-lightning flashes reveal 615 return strokes (RSs) and 29 upward-illumination (UI)-type strokes. Among 121 multi-stroke flashes, 56% visibly connected to more than one ground location for either a RS or UI-type stroke. The number of separate ground-stroke connection locations per CG flash averaged 1.74, with maximum 6. This study examines the 88 subsequent strokes that involved a subsequent stepped leader (SSL), either reaching ground or intercepting a former leader to ground, in 61 flashes. Two basic modes by which these SSLs begin are described and are termed dart-then-stepped leaders herein. One inception mode occurs when a dart leader deflects from the prior main channel and begins propagating as a stepped leader to ground. In these ‘divert’ mode cases, the relevant interstroke time from the prior RS in the channel to the SSL inception from that path is long, ranging from 105 to 204 ms in four visible cases. The alternative mode of SSL inception occurs when a dart leader reaches the end of a prior unsuccessful branch—of an earlier competing dart leader, stepped leader, or initial leader—then begins advancing as a stepped leader toward ground. In this more common ‘branch’ mode (85% of visible cases), there may be no portion of the subsequent RS channel that is shared with a prior RS channel. These two inception modes, and variations among them, can occur in different subsequent strokes of the same flash.

On the influence of the soil stratification and frequency-dependent parameters on lightning electromagnetic fields

We present an analysis of lightning electromagnetic fields taking into account the soil stratification and frequency dependence of its electrical parameters. Two current waveforms corresponding to typical first and subsequent return strokes are considered for the analysis. Different cases for the soil (homogeneous, 2-layer, frequency-dependent/constant electrical parameters) are considered. The analysis is carried out considering different distance ranges: close (50m), intermediate (5km) and distant (100km). The obtained results confirm that the vertical electric field and the azimuthal magnetic field at close range can be evaluated assuming the ground as a perfectly conducting plane. The impact of the soil stratification and frequency-dependent parameters on the vertical electric field and azimuthal magnetic field appear at intermediate and distant ranges. On the other hand, the horizontal electric field is found to be very sensitive to the ground stratification for all the considered distance ranges. However, at close range, the impact of the soil becomes less significant for observation points that are located at above-ground heights of 10m or higher. It is shown that the three field components are affected more markedly by the soil stratification than by the frequency dependence of its electrical parameters, especially for intermediate and distant ranges (i.e., 5km and 100km). Furthermore, subsequent return stroke fields are more significantly affected by the soil stratification and frequency-dependence compared to first return stroke fields. The impact of the frequency-dependent soil parameters on the considered field components is more noticeable in a poorly conducting soil compared to a good conducting soil. We present also a comparison between simulation results with simultaneous measurements of current and distant vertical electric fields associated with rocket-triggered lightning flashes. It is shown that the computed vertical electric field waveforms for the case of a two-layer soil follow to a much better extent the corresponding experimental waveforms compared a non-stratified ground model. The frequency-dependence of the soil affects slightly the early-time response of the field. However, the late-time response of the field is essentially determined by the soil stratification.

Lightning Parameters of a Tropical Region for Engineering Application: Statistics of 51 Flashes Measured at Morro do Cachimbo and Expressions for Peak Current Distributions

The statistics of lightning currents parameters of 51 negative cloud-to-ground flashes measured at Morro do Cachimbo Station was developed. The data comprising 51 currents of first return strokes and 77 currents of subsequent return strokes measured since 1985 composed the only database obtained in tropical regions with statistical significance. The previous result of median and maximum peak currents of about 40%–50% higher than the counterparts measured at Mount San Salvatore, obtained for 31 flashes, was confirmed. Median peaks of 43.3 and 17.3 kA and maximum peaks of 153 and 65 kA were found for first and subsequent return strokes, respectively. Expressions correlating the peak current and front time were developed for first return strokes. Formulae expressing the probability of peak-current occurrence of first and subsequent return strokes were derived from the respective cumulative distributions for direct application in the assessment of the lightning performance of electrical systems.