Channel-base Current Research Articles

Properties of Three Types of M-Components and ICC-Pulses From Currents of Negative Upward Lightning Measured at the Peissenberg Tower

Channel base currents from natural lightning have been measured on the new top structure of the Peissenberg Tower, Germany, since 2008. Here, an analysis is given of the impulsive currents, called initial continuous current (ICC)-pulses, that occurred during the ICC, and of the impulsive currents, called M-component currents, that occurred during the continuing current following return strokes. It was found that the M-component currents and the ICC-pulses closely resemble each other. The 45 flashes analyzed were exclusively negative upward lightning containing 60 return strokes and 264 impulsive currents (79 M-components and 185 ICC-pulses). A total of 246 (93.2%) impulsive currents were negative ones, and 18 (6.8%) impulsive currents were positive ones. The majority of 83.7% were pure impulsive currents and the minority of 16.3% were combined impulsive currents composed by two or more pure impulsive currents. For the pure impulsive currents, the analysis revealed three different types of waveforms for both the M-component currents and the ICC-pulses. The currents of the first type have a more or less symmetrical wave shape. For the 27 M-component currents and the 103 ICC-pulses (values in parentheses) of the first type, the geometric mean values are 0.7 (0.5) kA for the peak value, 23.9 (24.7) μs for the 10%-to-90% risetime, 101.0 (96.5) μs for the full width at half-maximum (FWHM), and 94.3 (57.1) mC for the transferred charge. The impulsive currents of the second type have a bipolar wave shape with current reversal. For the 31 M-component currents and the 37 ICC-pulses of the second type, the geometric mean values are 0.9 (0.6) kA for the peak value, 11.8 (16.9) μs for the 10%-to-90% risetime, 60.6 (74.7) μs for the FWHM, and −42.4/58.5 (−34.1/26.5) mC for the negative/positive charge of the bipolar pulses. The impulsive currents of the third type have a wave shape, which exhibits a fast rise to peak and a much longer decay to low current values. For the 5 M-component currents and the 18 ICC-pulses of the third type, the geometric mean values are 1.0 (1.2) kA for the current peak, 1.2 (2.9) μs for the 10%-to-90% risetime, 56.8 (29.0) μs for the FWHM, and 44.8 (24.03) mC for the transferred charge.

Modeling of artificially triggered lightning currents by multi-peaked analytically extended functions

PurposeThis paper aims to present the approximation of lightning currents waveshapes by the multi-peaked analytically extended function (MP-AEF) for the experimentally measured channel-base currents in the artificially triggered lightning discharges. Modified transmission line model of lightning return strokes having the channel current both linearly decaying and sinusoidally changing with height (MTLSIN) is used to calculate the lightning electromagnetic field.Design/methodology/approachMP-AEF’s parameters for the artificially triggered lightning channel-base currents are calculated by using Marquardt least squares method (MLSM). Lightning electromagnetic fields are calculated based on electromagnetic theory relations, thin-wire antenna model of the vertical lightning channel and the assumption of the perfectly conducting ground. MTLSIN model as an engineering model of lightning strokes is used to obtain the electric field results as these are simultaneously measured in rocket-triggered lightning experiments together with the channel-base currents.FindingsMP-AEF approximates multi-peaked pulse waveshapes. Some important function parameters are chosen prior to the approximation procedure, such as current peaks and the corresponding time moments of those peaks, which presents an advantage in comparison to other functions. The desired accuracy of approximation is obtained by choosing an adequate number of function terms. MLSM is used for the estimation of unknown parameters. Using MTLSIN model, the influence of the channel height and return stroke speed on the lightning electromagnetic field waveshape is analyzed in this paper.Research limitations/implicationsMP-AEF may be used for approximation of various multi-peaked waveshapes. It has no errors in the points of maxima which is important for the lightning protection systems design. MTLSIN model may be validated by using simultaneously measured lightning electromagnetic fields at various distances from the channel and for channel heights estimated in the experiments. It is also possible to approximate measured current derivatives by MP-AEF and use them for further computation.Originality/valueMTLSIN model is proposed in this paper for the evaluation of lightning electromagnetic fields induced by artificially triggered lightning discharges. The procedure is based on the approximation of lightning channel-base currents by the multi-peaked analytically extended function previously proposed by the authors. This function may be used not only for representing lightning currents but also for other waveshapes as current derivatives, electric and magnetic fields and their derivatives, which are all important for the lightning protection design. MTLSIN gives lightning electromagnetic fields results which are in better agreement with measured fields than those obtained by other models from literature.

Identifying Lightning Channel-Base Current Function Parameters by Powell Particle Swarm Optimization Method

This paper proposes the Powell (PPSO) method. The particle swarm optimization (PSO) algorithm is combined with the Powell algorithm to identify the parameters of lightning channel-base current function. The method can overcome the problem of premature convergence for PSO algorithm, and improve the analysis accuracy. The Heidler function is used to represent the lightning channel-base current. We have compared the PPSO method and genetic algorithm (GA) on reaching the desired peak value of the current $I_{m}$ and the maximum time rate of change of current ( di / dt )max. The results show that the parameters of Heidler function evaluated by the PPSO method can achieve more accurate values of $I_{m}$ and ( di / dt )max than those evaluated by GA. Also, we have compared the PPSO method, the Nelder–Mead particle swarm optimization (NMPSO) method, and PSO method using the measured channel-base current. The results show that the PPSO method is better than the NMPSO and PSO method to determine the channel-base current function parameters. The PPSO method is an efficient method to identify the channel-base function parameters, which can improve the digitalization of lightning monitoring equipment. This approach is also useful in research related to lightning characteristics and lightning protection.

Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation

Lightning discharge currents waveshapes and their derivatives with multiple peaks are measured in artificially triggered lightning experiments and at instrumented tall towers. Such waveshapes are represented in this paper by the N -peaked analytically extended function ( N P-AEF) and Marquardt least-squares method is applied for the estimation of its nonlinear parameters. Typical channel-base currents of the first negative, subsequent negative strokes, and positive strokes, based on comprehensive measurements by Berger et al. at Monte San Salvatore in Switzerland, are approximated by N P-AEFs and used in the computation of lightning electromagnetic fields. A new attenuation factor introducing nonlinear current attenuation along the channel is applied within the modified transmission line model (MTLSIN). A lightning return stroke is assumed to have a vertical discharge channel at the perfectly conducting ground. In order to validate this model, calculated lightning electromagnetic fields are compared with the typical, as measured by Lin et al. at various distances from the discharges. Lightning currents and their derivatives measured at the tall towers are also approximated by N P-AEFs. For the measured artificially triggered lightning currents, MTLSIN is applied for the calculation of their electromagnetic fields. These are compared with the measured fields of specific lightning strokes, so as to results of other models.

Evaluation of Lightning Current and Return Stroke Velocity Using Measured Far Electric Field Above a Horizontally Stratified Ground

This paper proposed an inverse procedure for evaluating the channel-base current and return stroke velocity using measured far electric fields over a two-layer horizontally stratified ground, where the lightning current along lightning channel adopt the modified transmission line model with linear current decaying with height (MTLL) model. Moreover, the proposed method has been validated using two numbers of measured electric field obtained from triggered lightning, where the velocity is considered to be variable along lightning channel and the average value along lightning channel, respectively. The results show that the evaluated channel-base current is in good agreement with the corresponding measured channel-base current, and the average evaluated return stroke velocity is among 1/3 to 2/3 of the speed of light in free space. Also, we compare the evaluated results using transmission line (TL) model or adopting single-layer soil model. The results both show that the method, which combines the MTLL model and the two-layer stratification soil model, is more suitable to evaluate the channel-base current and return stroke velocity in this paper. The proposed inverse procedure can evaluate the lightning current as well as return stroke velocity, this is useful for studies on lightning characteristics and lightning protection.

Influence of the Return Stroke Current Waveform on the Lightning Performance of Distribution Lines

An accurate evaluation of the lightning performance of overhead power distribution lines, that is, the evaluation of the expected number of annual flashovers, can be obtained by the application of the Monte Carlo method. In order to reduce the computational effort, a simplified waveform of the channel base current is generally assumed, for example, a linearly rising current with flat top. This paper proposes a Monte Carlo approach able to take into account the typical functions adopted to represent the waveform of the lightning current at the channel base (i.e., the Heidler function and the CIGRE function). Moreover, this paper analyzes the effects of different current waveforms on the lightning performance of distribution lines for both direct and indirect strokes.

Characteristics of the initial stage and return stroke currents of rocket‐triggered lightning flashes in southern China

AbstractThis study investigates the initial stage (IS) and return stroke (RS) currents of 50 triggered lightning flashes (TLFs) that were conducted in southern China. The IS of the negative TLFs has a longer duration and larger average current, charge transfer, and action integral than those reported elsewhere, with geometric means (GMs) of 347.9 ms, 132.5 A, 45.1 C, and 10.0 × 103 A2 s, respectively. Two positive TLFs containing no RS have much greater average currents, charge transfers, and action integrals in the IS when compared with the negative TLFs. The RS has a greater peak current (17.2 kA; GM, same to below), charge transfer within 1 ms (1.3 C), and action integral within 1 ms (5.8 × 103 A2 s), and shorter 10% to 90% rise time (0.4 μs) than elsewhere. The peak current is prominently correlated with the rate of rise, charge transfer within 1 ms, and action integral within 1 ms. Furthermore, when the total duration of the RS and any following continuing currents is longer than 40 ms, the peak current, charge transfer within 1 ms, and action integral within 1 ms of the RS are seldom greater than 25 kA, 2.6 C, and 15 × 103 A2 s, respectively. It is indicated that TLFs containing RSs tend to have a longer duration but a smaller charge transfer during the IS than those without RS. The peak current of the RS is weakly correlated with its preceding silence period when there was no channel base current.

An Inversion Method for Evaluating Lightning Current Waveform Based on Time Series Neural Network

An inversion method for evaluating lightning current waveforms from measured electromagnetic field data based on time series neural network (TSNN) is presented in this paper. The back-propagation neural network (BPNN) is also adopted to evaluate the channel-base current using measured electromagnetic field data, and comparisons of inversion results between TSNN and BPNN are presented. The inversion results are in good agreement with corresponding measured channel-base currents. The proposed method can evaluate the channel-base current in areas with complex terrain, and it is useful for studies on lightning-protection in power systems and lightning characteristics

Bidirectional leader development in a preexisting channel as observed in rocket‐triggered lightning flashes

AbstractTwo cases of bidirectional leader, starting almost immediately below a decaying dart or dart‐stepped leader which terminated before reaching the ground, were identified, for the first time, in rocket‐triggered lightning flashes based on high‐speed video, electric field changes, and channel base current, indicating that a bidirectional leader can be excited by a decayed dart leader and propagate in a preexisting discharge channel. The positive end of the bidirectional leader moved upward along the terminated downward dart leader path, and the negative end extended downward along the decayed initial continuous current or preceding stroke path to the ground and culminated in a return stroke. The positive leader propagated with an average speed of 1.3 × 106 m/s and 2.2 × 106 m/s in the two cases, roughly twice as fast as its negative counterpart with speed of 7.8 × 105 m/s and 1.0 × 106 m/s, respectively. The positive end started earlier than the negative end with a preceding time less than 40.3 µs. The bidirectional leader can be regarded as a recoil leader with the positive end retrogressing along a negative leader channel, whose polarity is contrary to the traditional recoil leader with negative leader end retrogressing along an existing positive leader channel. Weak luminosity was continuously observed during the terminated dart leader and bidirectional leader stage, but the channel current was less than the minimum detection capability of 9.3 A.

Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations

Genetic algorithm (GA) is applied for the estimation of two-peaked analytically extended function (2P-AEF) parameters in this paper. 2P-AEF is used for approximation of measured and typical lightning discharge currents. Lightning discharge channel is often modeled as thin-wire vertical antenna at perfectly conducting ground. Engineering lightning stroke models assume that the current along that channel is related to the channel-base current which may be measured at the instrumented tall towers and in triggered lightning experiments. Mathematical modeling of lightning currents is important in verification of lightning strokes models based on simultaneously measured electromagnetic fields at various distances, so as in lightning protection studies, computation of lightning induced effects and simulation of overvoltages in power systems. Typical lightning discharge currents of the first positive, first negative, and subsequent negative strokes are defined by IEC 62305 Standard based on comprehensive measurements. Parameters of 2P-AEF’s approximation of the typical negative first stroke current are determined by GA and compared to approximations obtained by other functions. Measured currents at Monte San Salvatore in Switzerland, at Morro de Cachimbo Station in Brazil, and in rocket-triggered lightning experiments at Camp Blanding in Florida are approximated by 2P-AEFs, and good agreement with experimentally measured waveshapes is obtained.

Influence of current reflections from the ground on corona sheath dynamics during the return stroke

Appearance of an overcompensated positive electric field in most vertical field measurements performed very close to the channel core (0.1m from it) is explained using the extended generalized traveling current source (extended GTCS) return stroke model with current reflections from the ground. As suggested by experiments in triggered lightning conditions or in measurements of simulated return strokes in the laboratory we assumed that the ground reflection coefficient depends on the current magnitude. New effects in the corona sheath due to the reflection of current pulses have been noted and taken into account. We separated the channel-base current into two components. The first current component is fast and with a greater peak value, while the second component is slower and with a lower peak. We analyzed two return strokes with simultaneously measured channel-base currents and close electric waveforms. In the first analyzed case, the first current component, with a peak value of over 15kA, reflects from a perfect ground with the reflection coefficient that equals unity, while the second current component, with a peak value below 15kA, reflects with the reflection coefficient lower than 1. In the second analyzed case, both current components reflect from the ground with the reflection coefficient <1. As a result, for the current component with the reflection coefficient lower than 1 an additional transient negative line charge density appears along the channel core at channel bottom, enhancing the negative radial electric field in the channel sheath. This field forces the overcompensated positive charges to move into the corona sheath, so as to satisfy the boundary condition between the channel core and the ground. Since the transient line charge density is proportional to the channel-base current, it disappears after the cessation of the return stroke, leaving accumulated positive charge in the corona sheath. The excess of positive charge generates the overcompensated positive electric field measured in most horizontal field measurements performed close to the channel core. A new charging function according to the extended GTCS model is calculated, as well as the value of the ground reflection coefficient for both analyzed strokes. The obtained results fit well with data reported in other independent studies performed in natural or laboratory conditions.

Some Developments of the Cooray–Rubinstein Formula in the Time Domain

A rigorous formula representing the counterpart of the Cooray–Rubinstein expression in the time domain has recently been derived by the authors. In this paper, the formula is particularized for the cases of a unit step and a linearly rising channel-base current, waveforms frequently used in lightning performance studies. Furthermore, an approximate kernel of the formula is also presented, allowing a very compact and straightforward solution for the case of linearly rising currents.

On the Lightning Induced Voltage Along Overhead Power Distribution Line

Lightning induced voltage is a major factor that causes interruptions on distribution lines. In this paper, analytical expressions are proposed to evaluate a lightning induced voltage on power lines directly in the time domain without the need to apply any extra conversions. The proposed expressions can consider the widely used current functions and models in contrast to the earlier analytical expressions which had a number of limitations related to the simplification of the channel base current and the current along the lightning channel. The results show that the simulated values based on the proposed method are in good agreement with the previous studies and the proposed expressions can be used for optimizing the insulation and protection level of existing and new lines being designed.

Considering on Lightning Electric Fields in Presence of Ground Reflection at Non-Perfect Ground

Abstract In this paper, general electric field expressions are proposed to consider the effect of channel base ground reflections and ground conductivity on the electric field components due to lightning. The proposed method can support different current models and functions directly in the time domain without the need to apply any extra conversions. The proposed method is applied on a sample of measured channel base current from triggered lightning experiment and the results are discussed accordingly. The results show that the ground reflection and ground conductivity can have an effect on the peak values of the electric fields whereby the electric field components have a great effect on the widely used coupling models.

Assessment and analysis of indirect lightning performance of overhead lines

This paper presents an efficient method for the assessment of the indirect lightning performance of overhead power lines and analyses the influence of some relevant parameters on the flashover rate. The method is based on a formula to calculate the peak value of lightning-induced voltages in overhead lines over a lossy ground, which considers the front-time of the channel-base current. The results of the method are validated by comparison with results available in the literature. The method is then used to investigate the effect of subsequent strokes on the line flashover rate, leading to the conclusion that their contribution is negligible, as long as no correlation is assumed between front-time and peak value of the strokes (first and subsequent). In the following, the method is used to analyze the influence of some parameters on the lightning performance of overhead lines. The results show that the stroke current front-time influence decreases as the soil resistivity increases, and that a higher front-time leads to a lower flashover rate. It is shown that the use of a fixed front-time T=5.63μs for the first strokes leads to results that match well the results obtained from Cigré’s front-time probabilistic distribution. Regarding the return stroke velocity, the results show that, for soils with resistivity higher than 100Ωm, the flashover rate increases as the return stroke velocity increases. The results also show that a relative velocity vr=0.4 leads to flashover rates that match well the results obtained considering some correlations between return stroke velocity and peak current proposed in the literature. The influence of the correlation between current peak value and front-time for first strokes is also analyzed and it is shown that the correlation reduces the flashover rate. It is also shown that considering this correlation for first strokes and not for subsequent strokes increases the contribution of the latter to the flashover rate, especially for good conducting soils.

Computation of lightning electromagnetic pulses using the constrained interpolation profile method

In this paper, a numerical procedure for computing electric and magnetic fields in a three-dimensional space using the constrained interpolation profile (CIP) method is presented. Then, this method is applied to computing electric and magnetic fields, which are generated by a current wave propagating upward along a vertical lightning return-stroke channel. The lightning return-stroke channel is modeled by a phased-current-source array. The spatial and temporal distribution of the lightning return-stroke channel or phase-current-source array is represented by a new simple mathematical function of height, time and channel-base current.

Analytical investigation of parameters effect on lightning-induced overvoltages on overhead lines

The evaluation of induced overvoltages from indirect lightning has been for more years one of the most important problems in designing and coordinating the protection of overhead power lines. In this paper, we discuss a modeling procedure that permits calculation of lightning-induced voltages on overhead lines starting from the channel-base current. The calculation is based on two main points: the calculation of the electromagnetic field radiated by lightning in a given point and a coupling model already presented in the literature based on the transmission line theory for field-to-overhead line coupling calculations.

Use of Genetic Algorithm to Determine Lightning Channel-Base Current-Function Parameters

A genetic algorithm (GA) is applied to calculate the lightning current parameters of the channel-base current function. Heidler's function parameters for subsequent return stroke are tuned for a typical value of Im (≈ 12 kA) for different (di/dt)max and also for a typical value of (di/dt)max (≈ 40 kA/ μs) for different values of Im, using a GA as the tool. This is a first of its kind attempt to show that a GA can be used for identifying Heidler's function parameters (as adopted by IEC Standard 62305-1, 2006) to easily obtain the required lightning current wave shape. The data are thus generated and reported (including the extreme cases) in this paper that are thought to be useful in modeling lightning channel-base currents. Further, this approach will be useful in research related to the radiated lightning electromagnetic pulse and its coupling with nearby objects.

Rocket‐and‐wire triggered lightning in 2012 tropical storm Debby in the absence of natural lightning

AbstractLightning Mapping Array source locations, channel base currents, and electric field waveforms are presented for a lightning flash triggered in the rainbands of 2012 tropical storm Debby. The National Lightning Detection Network reported no natural cloud‐to‐ground discharges within 60 km of the North Florida triggering site for at least 20 h before and 8 h after the triggered flash. Additionally, local electric field mill and wideband antenna networks show no close cloud or cloud‐to‐ground flashes. The triggering rocket was launched with negative charge overhead producing an electric field at the ground of 5 kV m−1 and in coordination with X‐band, dual‐polarimetric radar observations of streamers of enhanced precipitation descending from the melting level as they approached the site. The Debby flash consisted of an initial stage (IS) followed by eleven leader/return stroke sequences. The flash exhibited all the processes of normal triggered and natural cloud‐to‐ground lightning: leader/return stroke sequences, continuing currents, K events, and M components. Additionally, the flash exhibited several exceptional characteristics: three return stroke peak currents greater than 25 kA, one very long, 352 ms, continuing current that transferred about 35 C of charge to ground, and a relatively short, 202 ms, IS containing no initial continuous current pulses. Following a near‐vertical upward positive leader attaining 2.8 km height, the IS branched and propagated horizontally at 3.5 km altitude. The flash, exhibiting strokes and continuing current, then ascended to and propagated horizontally at 5.5 km, extending about 25 km south and 15 km east. The 0°C level was near 4.5 km above sea level. It follows from the above that clouds that are not producing natural lightning can represent a triggered lightning hazard to launch vehicles and aircraft.

Fast evaluation of the lightning electromagnetic field in the time domain with an adaptive piecewise approximation of channel base current

PurposeA fast algorithm is proposed to calculate the lightning electromagnetic field over a perfectly conducting earth surface.Design/methodology/approachThe channel base current is approximated by a number of sub‐domain quadratic functions using the proposed adaptive sampling technique, and the derivative and integral of the channel base current with respect to time can be analytically expressed. With the help of these approximations, the ideal electromagnetic field of the lightning channel can be evaluated along the lightning channel with respect to the height.FindingsThe computational time can be greatly reduced using the proposed approach to evaluate the electromagnetic field of a lightning channel in the time domain.Originality/valueThe adaptive sampling technique is a general‐purposed approach, which can be potentially used in other applications to fit a function with the minimal number of intervals.