Lightning-induced Voltages Research Articles

誘導雷サージ解析のための解析式を用いた配電線等価回路

This paper proposes an equivalent circuit at a transition point of distribution line for lightning-induced voltage analysis. The lightning-induced voltages caused by a piecewise linearly varying lightning current are expressed by analytical formulas. The equivalent circuit is represented by resistors and current sources, which are known from past history and given by the lightning-induced voltage on an infinite-length line. Transient voltages and currents at the transition point are accurately obtained in small computation time using the equivalent circuit. Thus, the proposed equivalent circuit is very convenient for analyzing the lightning induced effect in complicated electric power networks. This paper presents an example of EMTP data cards to use the proposed equivalent circuit in the EMTP.

Lightning-Induced Voltages in the Presence of Nearby Buildings: FDTD Simulation Versus Small-Scale Experiment

In this paper, we have computed lightning-induced voltages on overhead distribution lines in the presence of nearby buildings using the 3-D finite-difference time-domain method. In the simulations, four-conductor lines with surge arresters and pole transformers are considered. It appears that the presence of nearby buildings causes reduction of lightning induced voltages, as expected. The observed trend is in general agreement with that reported from the small-scale experiment by Piantini et al.

On the Effects of Channel Tortuosity in Lightning-Induced Voltages Assessment

We present a study on lightning-induced voltages on overhead lines produced by tortuous lightning channels, by using a recently developed tool called CiLIV (Andreotti et al. 2015). CiLIV, initially developed for straight and vertical channels, is here extended to account for tortuosity. High-resolution stereoscopic images of six triggered lightning channels have been 3-D digitized and used as input data for CiLIV. The result is that tortuosity, usually ignored in lightning-induced voltage assessment, can instead play a significant role: an attempt is made in characterizing and quantifying these effects. It is shown that, in contrast to other lightning parameters, like channel-base peak current, which are log-normally distributed and generate log-normally distributed induced voltages too, tortuosity generates normally distributed induced voltages. It is also shown that these voltages can deviate up to 23% (relative standard deviation) from the mean value.

Induced voltages on overhead transmission lines because of nearby included lightning channel

The power system networks can be adversely affected by indirect coupling with the cloud-to-ground lightning return stroke. In most computations of lightning-induced voltages on overhead transmission lines, the overhead transmission lines are considered as straight lines and the return stroke channel is assumed to be a straight and a vertical channel. However, in reality, the line is not straight and is not parallel to the ground level because of the sag produced by its weight. In addition, the lightning channel is most often inclined. This study studies the effect of conductors’ sag as well as the inclination angle of the lightning channel on the lightning-induced voltage on the three-phase power lines because of inclined lightning channel. This study has been evolved, formulated and applied on Egyptian 500 kV three-phase transmission line. Moreover, the effect of the ground conductivity on induced overvoltages in case of sagged transmission lines is considered. It can be observed that, taking into account the effects of the ground conductivity, the presence of the ground wire and the sag of the transmission lines reduce the values of the calculated induced voltages.

Indirect Lightning Performance of Aerial Distribution Lines Considering the Induced-Voltage Waveform

This paper shows that the wave-shape parameters of lightning-induced voltages (front-time and time-to-half value) are influenced by the ground resistivity, the line length, and the distance between the flash and the line. In general, these parameters increase with the ground resistivity, the line length, and the distance from the flash. The probabilistic distribution of the waveshape parameters are presented, considering different values of line length and ground resistivity. The effect of the induced voltage waveform on the indirect lightning performance of aerial distribution lines is evaluated using the disruptive effect (DE) method as a flashover criterion. The resulting flashover rates differ significantly from those obtained when only the peak value is used as flashover criterion. The use of a correction factor to multiply the line critical flashover when using the peak value as a flashover criterion is investigated.

3-D FDTD Simulation of the Lightning-Induced Waves on Overhead Lines Considering the Vertically Stratified Ground

In this paper, we have employed the 3-D finite-difference time-domain technique to analyze the influence of the vertically stratified conducting ground (mixed path) on the lightning-induced voltages of the overhead line at 60 and 200 m from the lightning strike point by using decomposing method. In order to analyze the effect range caused by mixed path, we assumed that the mixed path has much different conductivities with 100:1 ratio. When the conductivity near the strike point (0.1 S/m) is larger than that near the overhead line section (0.001 S/m), the induced voltage clearly increases with the increase of the closest distance from the center of the line to the interface between the two media ( dl ). However, for strike point with a less conducting earth (0.001 S/m) than the overhead line section (0.1 S/m), when dl is less than 30 m, the influence of the stratification should be considered; when dl is larger than 30 m, it can just be regarded as a homogeneous soil with the conductivity of 0.1 S/m equal to that near the overhead line. For the smaller ratio of conductivities of the mixed path, its effect on the induced voltages decreases.

Design and construction of a Reduced Scale Model to Measure Lightning Induced Voltages over an Inclined Terrain

<p>In this paper is presented the design and construction of a reduce scale model indented to be used for measuring Lightning induced voltages on overhead lines placed over an inclined terrain. Here we present technical details of the source developed for achieve a fast impulse that represent a lightning. The experiment, although, is a first approximation to the phenomenal, is useful for validate numerical methods which are more flexible for future. Additionally, several simulations are done by means of the FDTD method with the aim to show the expected measurements of the reduced scale model.</p>

Lightning-induced voltages caused by lighting strike to tall objects considering the effect of frequency dependent soil

In this paper we have analyzed the effect of frequency dependent soil (FDS) on the lightning-induced voltages caused by lightning subsequent return stroke for strike to tall objects ranging from 100m to 300m. It is found that the effect of FDS on the induced voltages peak can be approximately ignored when the low frequency conductivity (LFC) is equal to or larger than 0.01S/m, and with the decrease of LFC, the effect of FDS on the lightning induced voltages is more obvious. Compared with the constant LFC, the induced voltage peak becomes less for FDS. For example, for a constant LFC of 0.001S/m, the ratio of the induced voltages peak value for FDS to that for LFC is 83.2% at the line center and 66.8% at the line end for strike to 300-m-tall object, respectively. By using the decomposition method, we divide the lightning induced voltages into two components named by the incident induced waves (Vi) related with the vertical field and scattered induced waves (Vs) related with horizontal field, and it is found that FDS results into a less initial peak of tangential horizontal field along the overhead line and further results into a less induced voltage. Also, compared FDS with LFC, the FDS reduces the disparity of lightning induced voltages caused by different tall objects. For example, for the constant LFC, the induced voltage peak for strike to 300-m-tall object is 1.69 times larger than that for strike to 50-m-tall object. However, for the case of FDS, the corresponding ratio is about 1.2.

FDTD Computation of Lightning-Induced Voltages on Multiconductor Lines With Surge Arresters and Pole Transformers

In this paper, lightning-induced voltages on multiconductor lines with surge arresters and pole transformers have been computed using the 3-D finite-difference time-domain method. This method uses a subgrid model, in which spatial discretization is fine (cell side length is 0.5 m) in the vicinity of overhead wires and coarse (cell side length is 5 m) in the rest of the computational domain. In the simulations, four-conductor lines with surge arresters and pole transformers are considered. The 1-cm-radius overhead conductors are represented by placing a wire having an equivalent radius of about 0.12 m (≈ 0.23 × 0.5 m) in the center of an artificial rectangular prism having a cross-sectional area of 1 m × 1 m (2 cells × 2 cells) and the modified (relative to air) constitutive parameters: lower electric permittivity and higher magnetic permeability. The computed lightning-induced voltage waveforms agree reasonably well with the corresponding ones measured in the small-scale experiment of Piantini et al. (2007).

A New Tool for Calculation of Lightning-Induced Voltages in Power Systems—Part I: Development of Circuit Model

In this paper, we present a new tool for lightning-induced voltage calculations. The tool, a circuit model which can be integrated into power systems simulators, is based on the theory developed by Andreotti (2001, 2009, 2013). In Part II, the accuracy, stability, and efficiency of the new tool are demonstrated via comparison with other solutions/codes found in the literature and with experimental data.

The Effect of an Ocean-Land Mixed Propagation Path on the Lightning Electromagnetic Fields and Their Induced Voltages on Overhead Lines

We use a full-wave approach based on the finite-element method solution to Maxwell's equations for the evaluation of the effect of an ocean-land mixed propagation path on the above-ground lightning electromagnetic fields and their induced voltages on overhead lines. Two cases of normal and oblique strikes are studied. For normal strike, it is shown that neither the vertical electric field nor the azimuthal magnetic field is affected by the considered mixed propagation path. For an oblique strike, however, the azimuthal magnetic field is slightly affected when the observation point is close to the ocean-land interface (i.e., 5 m or so), while the vertical electric field remains unchanged. For both normal and oblique strikes, at moderate and far distances from the channel base and when the observation point is located in the vicinity of the ocean-land interface, the radial electric field is markedly affected by this interface. For the calculation of lightning-induced voltages, two cases, namely, the ocean-side and the river-crossing transmission lines are studied. For the ocean-side transmission line, as the overhead line gets closer to the ocean, the induced voltages on the line midpoint decrease while increasing behavior is observed in the voltages induced on the line terminations. For the river-crossing transmission line, the lightning-induced voltages along the line experience a significant change in terms of their peak values and waveshapes. In some cases, the enhancement in induced voltages can be as high as a factor of 2 with respect to that obtained by assuming a homogeneous propagation path characterized by the electrical properties of the land.

A New Tool for Calculation of Lightning-Induced Voltages in Power Systems—Part II: Validation Study

In the companion paper (Part I), a new tool for lightning-induced voltage calculations, called CiLIV, has been presented. In this paper (Part II), predictions made with the new tool are compared to experimental data and to outputs of analytical procedures/numerical codes found in the literature.

Lightning-Induced Voltages Over Lossy Ground: The Effect of Frequency Dependence of Electrical Parameters of Soil

The impact of the frequency dependence of soil resistivity and permittivity on lightning overvoltages induced on overhead lines over lossy ground is investigated. The Visacro-Alipio expressions were implemented on the hybrid electromagnetic model to take this effect into account. Systematic simulations were performed considering representative current waveforms of first and subsequent strokes and different stroke locations near the simulated overhead line. In general, the results indicated that this effect is responsible for a reduction of the induced overvoltage. This reduction increases with increasing soil resistivity and becomes relevant for soil resistivity above 1000 Ω·m.

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.

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.

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.

Calculation of Lightning Flashover Rates of Overhead Distribution Lines Considering Direct and Indirect Strokes

This paper presents a procedure for evaluation of lightning performance of overhead distribution lines. Because both voltages from direct strokes and nearby strokes may cause flashovers in distribution lines, flashover rates due to them need to be analyzed. The procedure is implemented in electromagnetic transient program, and the Monte Carlo method is used to take into account the random nature of lightning parameters. The lightning-induced voltages are calculated with an equivalent circuit derived from Agrawal formula. The influence of insulation level and spacing between surge arresters on lightning flashover rates is analyzed with the procedure. For a line with low-insulation level about 150 kV above high conductivity ground or with high-insulation level about 300 kV above low conductivity ground, the spacing between arresters is best less than 400 m. But for a line with low-insulation level above low conductivity ground, it is better to reduce the spacing to 200 m.

A Comparison Between Analytical Solutions for Lightning-Induced Voltages Calculation

An exact closed form solution for the calculation of lightning-induced voltages on overhead lines has been recently proposed by A. Andreotti et al. (2012). Predictions of this exact formulation are compared here to those based on approximate analytical solutions proposed in the literature. DOI: http://dx.doi.org/10.5755/j01.eee.20.5.2967

Evaluation of Lightning-Induced Voltages on Multiconductor Overhead Lines Located Above A Lossy Dispersive Ground

The paper presents a comprehensive study on the effect of soil dispersion (i.e., frequency dependence of soil conductivity and relative permittivity) on the lightning-induced voltages on single/multiconductor overhead distribution lines. For this aim, a full-wave approach based on the finite-element method is utilized. The soil dispersion is incorporated into the model using available analytical formulae obtained from experimental data. It is shown that for soils characterized by relatively moderate and low resistivity values (less than 1000 Ω.m), lightning-induced voltages are not significantly affected by the soil dispersion property. In the analyses, two different integration paths are used for obtaining the induced voltages by integrating the total vertical component of the electric field. It is shown that the soil dispersion effect on the induced voltages is negligible if the integration path continues vertically from the conductor surface to a point well below the ground surface at which the electric field vanishes. However, the soil dispersion for poorly conducting soils can markedly change the induced voltages if the integration path is considered as a vertical path between the conductor surface and the ground surface.

An Approximate Formula for Estimating the Peak Value of Lightning-Induced Overvoltage Considering the Stratified Conducting Ground

In this paper, we present an improved and extended approximate formula for estimating the peak value of lightning-induced voltages in an overhead line, considering the horizontally stratified conducting ground. The approximate formula proposed in this paper is based on the return stroke transmission-line model (TL) and a trapezoidal lightning return stroke current waveform with the typical representative front time of 3.8 μs and the return stroke velocity of 120 m/ μs according to CIGRÉ and the IEEE Standard 1410 Guide. The extended approximate formula is validated by using the 2-D finite-different time-domain method and Agrawal field-line coupling model. The results show that the proposed approximate formula in this paper is simple and suitable for estimating the lightning-induced voltage peak value considering the horizontally stratified ground with satisfied accuracy.