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This paper discusses the back-flashover (BFO) phenomena in a high-voltage (HV) vertical double-circuit transmission line by means of numerical simulations. The single- and multiphase BFOs are analyzed considering 24 cases of AC-voltage angles and nonlinear characteristic of flashovers, taking advantage of the circuit analysis method in time domain. The models used in circuit analysis are the TEM-delay model, which can take into account the non-TEM characteristics of tower and line, and the conventional models. Prior to the BFO analysis, the characteristics of circuit models are compared and discussed with the numerical electromagnetic analysis results. In BFO analysis, it is clarified that the occurrence probability of the multiphase BFO is heavily depending on the bias AC-voltages. The relation of measured BFO phases and AC-voltages are well explained by the TEM-delay model with the valid lightning current magnitude. The conventional circuit models could have underestimated the occurrence of BFOs in HV transmission lines. The analysis and discussions shown in this paper can be utilized for advanced evaluation of lightning performance of transmission lines that considers the seriousness of lightning accidents. [ABSTRACT FROM AUTHOR]

Most of the literatures dealing with time domain simulation of grounding system response to lightning surges use an electrostatic approach. In this approach frequency dependence of soil electrical parameters and plane-wave propagation constant are not included. In this paper, based on Hybrid Electromagnetic Method and simplification of it, a new method is developed to include frequency dependent parameters of soil in time domain simulation. Since only one convolution is used, the simulation time is significantly reduced. The consistency of the developed formulation while the plane-wave propagation constant is ignored is investigated through comparisons with experimental results and precise frequency domain approaches. Simulations results show ignoring both effects simultaneously can lead to high levels of error (140%), whereas the error significantly reduces when frequency dependence of soil parameters is considered. The developed model exhibits errors of about 2% to 25% compared to the results of models that take into account both effects. However, simulation results showed all these errors to be conservative. Due to neglecting propagation constant, the model is more suitable for lightning studies of grounding system with short length. [ABSTRACT FROM AUTHOR]

The accurate assessment of lightning-induced over-voltages is essential for proper insulation coordination studies. In this paper, a novel machine learning based Gaussian process regression model is developed for the prediction of lightning-induced over-voltages considering wide range of ground resistivity and permittivity. The lightning-induced over-voltages have been computed using two-dimensional finite-difference time-domain technique associated with Agrawal field to line coupling model. To account for the input space variability, seven predictor variables namely: resistivity, permittivity, return stroke velocity, distance from flashpoint, return stroke peak current, front-time, and height of an overhead line are considered to determine the response variable, that is, lightning-induced over-voltages. Accordingly, the training of the Gaussian process regression model is carried out using lightning-induced over-voltages obtained from two-dimensional finite-difference time-domain technique for both first and the subsequent strokes. The estimation accuracy of model is appraised using root mean squared error indicating that the exponential kernel function has the least error than other kernel types for describing the covariance. The predictive performance is evaluated by corroborating the predictions from the model against the random test cases generated from two-dimensional finite-difference time-domain technique. The predicted results showed a good agreement with those obtained from finite-difference time-domain technique. [ABSTRACT FROM AUTHOR]

Seven decades have passed since the Schumann resonances (SRs) were identified. Since then, their research interest has increased, currently being a topic of significance. Nonetheless, the papers that study their nature from the frequency perspective are in clear majority regarding those who focus on the time domain. To fill this gap in the literature and further characterize the SRs, a method to perform statistical analysis on the SRs signal in the time domain has been developed. For any given segment of data, the analysis performs a maximum likelihood estimation (MLE) of the statistical parameters from a group of previously selected distributions. After that, the best fit among the target distributions is selected through the application of Akaike information criterion (AIC). The method is tested by analyzing a month’s worth of data, showing the general analysis’ results and discussing the relationship between the chosen target distributions and common aspects between the time segments fitted to them. The reliability of the method’s results is also discussed by looking at different aspects of the analysis. Special emphasis is put over the results being correlated with lightning activity. This correlation highlights the usefulness of the method, given the well-established relationship between lightning and SRs. [ABSTRACT FROM AUTHOR]

The Cooray–Rubinstein formula (C–R formula) has been widely used to calculate the horizontal electric field generated by a lightning return stroke over the lossy ground. To evaluate the time-domain C–R formula by a recursive convolution, an alternative method is proposed in this paper, where the formulation in terms of the “step response” corresponding to the ground surface impedance, denoted as $k_{\varepsilon }(t)$ , is evaluated by the numerical inverse Laplace transform (NILT). Considering the good performance of Talbot's method for the NILT, Talbot's method is adopted to express $k_{\varepsilon }(t)$ in terms of a series of exponential functions, which can avoid the tedious piecewise approximation used by the available method and make the recursive convolution easier to program. In addition, some key formulae for the recursive convolution with complex poles and residues are presented in this paper. Numerical examples are provided to validate the proposed method. [ABSTRACT FROM AUTHOR]

This paper analyses the inherent difficulties in measuring the horizontal electric field from lightning and proposes some solutions to mitigate the contamination effect of the overwhelming vertical electric field. The analysis is carried out with a set of time-domain equations for the calculation of the electromagnetic fields from lightning. As these equations are scattered in several publications, in this paper they are compiled and presented in a harmonized form. Moreover, one new expression for the vertical electric field slightly below the ground surface is presented. It is shown that the horizontal electric field at the surface of lossy ground can be measured with minimum disturbance caused by the vertical electric field if the field sensor is placed slightly below the ground surface. This paper also shows that the horizontal electric field above the ground surface could be measured with the help of a pair of field sensors conveniently arranged so that the influence of the vertical electric field on the measurement is cancelled. [ABSTRACT FROM AUTHOR]

In this paper, we study the effect of overhead shielding wires on the lightning-induced voltages of two typical multiconductor lines configurations at distances from 50 to 1000 m from the lightning channel, considering perfect and lossy ground, respectively, by using the 2-D finite-difference time-domain method and Agrawal field-line coupling model. The results show that the effect of overhead shielding wires on the lightning-induced voltages is closely related to the finite ground conductivity (σ) and the observation distance (d) from the lightning channel. For the ground conductivity ranging from 0.1 to 0.001 S/m, the values of shielding factor (SF) range about from 0.7 to 0.8 for vertical configuration, and range about from 0.6 to 0.7 for horizontal configuration, within distances from 50 to 1000 m from the lightning channel. Also, we have compared the SF values predicted by using Rusck simplified formula with ours in this paper, and it is noted that the Rusck simplified formula underestimates the SF values and the errors may be above 10% under poor ground conductivities of 0.001 S/m when distances larger than 500 m. [ABSTRACT FROM AUTHOR]

This paper analyzes three time-domain expressions for the surface impedance, which allows the calculation of the horizontal electric field produced by a lightning return stroke. They are the expression obtained by Barbosa and Paulino directly in the time domain, the expression obtained by Andreotti et al. as a time-domain counterpart of the Cooray–Rubinstein formula, and an approximate expression derived independently from the two former expressions. The analysis is carried out by comparing the kernels of the expressions and by comparing the lightning-induced voltages (LIVs) on an aerial line. The results show that the two former expressions provide almost identical LIVs, while the approximate one provides peak values from 5% to 7% lower than those provided by the other expressions. A detailed discussion of the results is included in the paper. [ABSTRACT FROM AUTHOR]

Voltage and current waveforms of transmission lines struck by lightning are calculated for use in back flashover analysis. Calculation by using equivalent circuits is the general practice, however, there are limited experimental results for reference to evaluate validity of developed equivalent circuits under various line conditions. Calculation results by numerical electromagnetic analysis can be used as references if they are proved reliable. In this paper, the voltage rises at a model of a 154 kV transmission line hit by lightning is calculated by Method of Moments (MoM) and FDTD for comparison. They solve Maxwell's equations by using different algorithms, so, if the calculated results by these methods reasonably agree under various line conditions, the results of these numerical analyses are regarded reliable. The calculated voltage and current waveforms by the two numerical methods agree well under a variety of footing resistance of transmission towers, thus the authors conclude that the calculated results by FDTD or MoM can be employed as references to evaluate validity of circuit models for back flashover analyses. Thus, the results calculated by circuit analysis are compared with those calculated by FDTD. The multistory tower model (Ishii model) better reproduces the voltage waveforms in a wide range of the footing resistance than simple circuit models of a tower, and can be easily tuned for further accuracy. [ABSTRACT FROM AUTHOR]

This paper investigates lightning surges on a distribution line reported using a finite-difference time-domain (FDTD) method. FDTD simulation results show a satisfactory agreement with measured lightning currents when lightning strikes ground nearby a distribution line. The current and voltage characteristics along the line, which were not measured in the test, are calculated by the FDTD simulation. Parametric analysis shows that lightning currents and voltages are dependent on the lightning position, distance from the lightning to the nearest pole, and pole grounding resistance. A large portion of phase-wire voltage is induced by the lightning channel current, and correspondingly, a large portion of phase-wire current is produced by the induced voltage. When the lightning channel is inclined, the peak current and voltage vary by +10% to −10% depending on the inclined angle. The effect of neutral wire position in the line is also investigated, and the induced voltage at the nearest pole to the lightning can be effectively suppressed by installing two neutral wires above and under the phase wires. EMTP simulation results agree qualitatively well with the measurement and FDTD results. [ABSTRACT FROM AUTHOR]

This paper presents a study performed on time, frequency, and energy correlations of transient voltages generated by the cloud to cloud discharges. It revealed that the energy embedded in transient voltages have been lumped over few segments of time domain voltage profile than uniquely scattering over the time span. The study further determined that the energy concentration becomes higher in and around the vicinity of the time domain voltage maxima or minima, and such high energy-concentrated segments confined to a minute time span in comparison to the total time span of the transient voltage. The study also established that there is a small time lead or lag between the time domain voltage maxima or minima and the time of energy maximize. Moreover, the analysis deduced that the time lead or time lag phenomenon, is not sensitive to the orientation of the time domain voltage profile, but fuelled by the pulse type. The response time of surge protective devices can become crucial if the stipulated clamping voltages of the protection devices fall close to local peaks of the transient voltages. [ABSTRACT FROM AUTHOR]

This paper analyzes the effect of lightning strikes to an oblique cone-shaped mountain on the lightning-induced voltages on the power distribution line. The lightning-generated electromagnetic fields are calculated by using a three-dimensional finite-difference time-domain method in Cartesian coordinates, and the lightning-induced voltages are computed by means of Agrawal coupling model. The simulation results are presented for an oblique cone-shaped mountain with different inclining angles, and for different relative positions of the distribution line placed over nonflat lossy terrain. It is found that, when lightning strikes the top of an oblique cone-shaped mountain, the lightning-induced voltages are closely related with the mountain inclining angles where the distribution line is located above as well as the other mountain inclining angles; in general, the peak values of induced voltages increase with increasing inclining angles. For example, for the constant angle β = 45° (the inclining angle where the line is located above), the induced voltages at the close end of line for α = 26.6°, 45°, and 63.4° (the inclining angle opposite to angle β) is increased by 24%, 60%, and 106% as compared with that for flat ground, respectively. [ABSTRACT FROM AUTHOR]

This paper evaluates the lightning-induced voltages of two typical multiconductor lines configurations with or without shielding wires over lossy ground for striking the cone-shaped mountain top, by means of a cylindrical two-dimensional finite-difference time-domain method and Agrawal coupling model. It is found that the lightning-induced voltages both for the vertical and the horizontal configurations can be enhanced obviously for striking to the cone-shaped mountain, compared with the case of flat terrain, especially for the lower finite ground conductivity. The larger mountain inclining angle results in the higher peak values of lightning-induced voltages, which can be explained by the enhancement of lightning electromagnetic fields due to wave reflection of the transition between mountain terrain and flat ground. Moreover, the shielding wires can effectively reduce the voltages induced at both ends of the phase lines. [ABSTRACT FROM AUTHOR]

Electromagnetic (EM) fields triggered by lightning strikes are likely to display non-negligible variability in practice, with an apparent effect on various quantities of interest, such as induced voltages on transmission lines. This paper investigates the stochastic properties of lightning-generated fields, when the latter are affected by random ground parameters and/or nondeterministic lightning base current. In essence, the EM components are represented herein by truncated series of orthogonal polynomials, according to the generalized polynomial-chaos theory, and their expansion coefficients are computed via a regression approach. The necessary samplings of the random spaces are constructed with either tensor-based or sparse grids, and their performance is validated and compared. It is shown that reliable calculations of the expectation can be conducted with low-order polynomial approximations, while at least third-order expansions are required for the standard deviation. In addition, we conclude that nontrivial variability is induced in lightning-produced pulses, when variations of the considered stochastic parameters are taken into account. [ABSTRACT FROM AUTHOR]

To study the lightning return-stroke process, this paper proposed a new inversion algorithm for evaluating the average return-stroke velocity. As the Gaussian function covers a frequency range wider than the typical channel-base current, the main step of this method was to treat the channel-base current representing using the Gaussian function and the corresponding azimuthal magnetic field at close distance as the inputs and outputs, respectively, to establish the transfer functions. We have verified the proposed method using the azimuthal magnetic field with/without noises at different distances from the lightning channel. In addition, we compared the evaluated results using different return-stroke models including the transmission line (TL) model, the modified TL model with linear (MTLL) current decay with height, and the modified TL model with exponential (MTLE) current decay with height. The evaluated results are in agreement with the simulated return-stroke velocity, indicating the effectiveness and robustness of this method for predicting the return-stroke velocity. The proposed inversion method is effective in estimating the return-stroke velocity, which can be applied in lightning physics research. [ABSTRACT FROM AUTHOR]

This paper presents an improved analytical expression for the calculation of the lightning horizontal electric field considering high values of ground resistivity, which is validated by comparing its results with published results obtained with other methods. The expression is used to calculate lightning-induced voltages in overhead power distribution lines and its results showed that conducted currents injected into the ground by the lightning flash should be considered in the assessment of power line outages, whenever the ground resistivity is higher than 1000 Ω·m. The results also show that, for very high values of ground resistivity, the line length and the ground permittivity affect the lightning-induced voltage peak value, whereas the line height, the return stroke velocity, and the stroke current front-time have negligible effects. [ABSTRACT FROM AUTHOR]

This paper presents the computed lightning-radiated vertical electric field and azimuthal magnetic field at the ground level at observing distances ranging from 0.3 to 50 km from the lightning channel for striking the cone-shaped mountain top, by using the two-dimensional finite-difference time-domain method in cylindrical coordinate systems. It is found that the mountain height and the inclination angle have a significant effect on the lightning-radiated electromagnetic field both for the close and far observing distances. For the lightning-radiated vertical electric field, the enhancement of the far field beyond several kilometers (mainly radiation field component) is due to the reflection process in the transition between the mountain terrain and the flat ground, but the reduction of close field near the mountain terrain (mainly quasi-electrostatic field component) is due to the shadowing effect, but not due to such reflection. For the lightning-radiated azimuthal magnetic field, the field values for different mountain terrains, including the mountain height and inclination angle, increase both for close and far observing distances. [ABSTRACT FROM AUTHOR]

The evaluation of the ground admittance of an underground insulated conductor with a homogeneous nonmagnetic earth is of great significance when the electromagnetic compatibility is concerned. To evaluate the ground admittance efficiently, researchers proposed that the ground impedance of the conductor should be evaluated first and the ground admittance is related to the ground impedance through the wave number in the soil. There are several approximated analytical expressions for the evaluation of the ground impedance with a homogeneous earth and this fact makes the ground admittance easy to obtain. The characteristic of the approximated ground admittance evaluation approach is examined in this paper. Numerical examples illustrate that at frequencies with which the burial depth is much larger than the skin depth in the soil, the ground admittance and the ground impedance of the buried cable are well-related through the wave number in the soil. However, at other frequencies, the approximated approach fails to evaluate the ground admittance accurately. This paper also reveals that the discrepancy of the ground admittance will lead to a noticeable difference in the lightning induced voltage on buried cables. [ABSTRACT FROM PUBLISHER]

The paper addresses the important issue of evaluating the overvoltages produced on a power system by a lightning event. First, the theoretical formulation of the problem in the time domain is presented. Then its numerical solution together with its implementation is described. Finally, a PSCAD-EMTDC interface and platform is developed, which allows us to model a realistic network, automatically distinguish between direct and indirect strokes and account for power network precontingency conditions. The obtained results are compared with a frequency-domain solution for a simple case in order to validate the finite-difference time-domain method adopted to solve the coupling equations and the interface with PSCAD. The comparison with the well-known LIOV code for a more complex case is used as a general validation of the overall tool. In a companion paper, the developed platform will be used to evaluate the lightning performance of a portion of the Italian MV distribution network. [ABSTRACT FROM PUBLISHER]

This paper analyzes the influence of the radial electric field radiated by return strokes on the lightning performance of an overhead distribution line. The calculation of the lightning electromagnetic pulse (LEMP) over a finitely conducting ground is performed by solving the Sommerfeld integral for the radial component of the electric field. The proposed method uses a trapezoidal scheme in which nodes are equidistant in logarithmic scale. The method is implemented in the LIOV-EMTP (lightning induced overvoltages-electromagnetic transient program) code that solves the field-to-multiconductor line coupling equations and calculates the lightning induced voltages in distribution networks having complex and realistic configuration. The results obtained by the proposed method for the LEMP calculation are compared with those obtained by using the Cooray–Rubinstein formula, which is the most commonly adopted approximation. Finally, the peak-amplitude probability distributions of the induced voltages obtained by using the two approaches are presented. It is shown that for ground conductivity values larger than 0.001 S/m, the Cooray–Rubinstein formula provides results in agreement with the accurate solution, while it significantly underestimates the lightning performance for lower conductivities and for lines with a high insulation level. [ABSTRACT FROM AUTHOR]

Lightning surge propagation on telecommunication towers is essential to lightning protection design. Analysis of very fast surges in a telecommunication tower requires a full-wave solution of Maxwell's equations. This paper proposes a full-wave time domain partial element equivalent circuit (PEEC) method considering the effect of ground to evaluate the surge currents and voltages on vertical structures. The PEEC of the formulation is provided by using the method of image. This method can take into account the attenuation of the lighting surges, and has the potential to be implemented as a new type of solution for general lightning surge analysis. The proposed method is validated numerically with the finite-difference time domain method, and is used to analyze the surge propagation on cables mounted on two typical grounded telecommunication towers. The simulation shows that both the location of cable installations and the type of towers have a significant influence on the lightning protection performance. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the study of electromagnetic (EM) field waveforms generated by a lightning strike to a tower located on a trapezoidal mountain. The latter has a height of 500 m and a steepness angle of slope of 45°. The EM field components are calculated at six points and in three directions from the tower. Among these six points, four of them are placed on a flat ground and located at close distances from the mountain bottom while the other two points are located on the mountain at close distances from the tower. Also, because of the three-dimensional (3-D) geometry of the problem being treated, the computation is performed in three dimensions by using the finite-difference time-domain (FDTD) method. In this computation, the lightning channel is represented by the transmission line model extended to include a tall strike object. To evaluate the influence of the presence of mountain on the EM field waveforms, a comparison between the results obtained in the presence and absence of the mountain has been done. On the other hand, the ground conductivity effect on the EM field components has been also studied. At the end of this study, we show that the trapezoidal mountain shadowing effect causes a reduction of the vertical electric field calculated on a flat ground at close distances from the mountain bottom, while the field is enhanced on the top of the mountain. The same conclusion is drawn for the azimuthal magnetic field. Furthermore, the initial peaks of the vertical electric field and the azimuthal magnetic field, above the ground, have been attenuated because of the finite conductivity of ground. The horizontal electric fields above the ground are characterized by oscillations due to the presence of tower and mountain. The underground horizontal electric field and azimuthal magnetic field have the same waveforms as those obtained above the ground but with smaller magnitudes. Thus, the underground vertical electric is initially bipolar and then essentially zero. Finally, the 3-D-FDTD developed program was validated (see the Appendix). [ABSTRACT FROM AUTHOR]

Cooray–Rubinstein formula has been extensively used for the evaluation of the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. Considering the good characteristics of the formulation in terms of “step response” kernel $K_{\varepsilon }(t)$ corresponding to the ground surface impedance, proposed by Andreotti et al. recently, a new method for evaluating the Cooray–Rubinstein formula in the time domain is proposed in this paper. In this method, $K_{\varepsilon }(t)$ is first expressed by an integral of exponential function based on the integral formula of the modified Bessel function of the first kind, and then approximated by a piecewise exponential function using the Gauss numerical integration. Finally, taking advantage of the piecewise recursive convolution, the time-domain Cooray–Rubinstein formula for evaluating the lightning horizontal electric field can be calculated accurately and efficiently. The validity and efficiency of the proposed method are demonstrated by the comparisons with the methods in other literature. [ABSTRACT FROM AUTHOR]

In this paper, we present an analysis of electromagnetic fields generated by a lightning return stroke to a tall tower in presence of a horizontally stratified two-layer ground. The electromagnetic fields are evaluated at a distance of 50 m from the tower for two observation points above and below the ground surface, by using the finite-difference time-domain method. The developed numerical model is validated using available experimental data obtained at the CN Tower in Toronto. To illustrate and discuss the effect of the soil stratification on the electromagnetic fields, we adopt two different cases characterized, respectively, by an upper layer less conductive than the lower level, and vice versa. The obtained results show, for the considered distance range (50 m), that the electromagnetic fields above ground at such close distance are nearly insensitive to the ground stratification. However, the underground electromagnetic fields are markedly affected by the properties of the soil layers. In the presence of a lower layer of higher conductivity, the horizontal electric field is characterized by a faster rise time, a significant decrease in amplitude and a bipolar wave-shape compared to that in the case of a homogeneous ground with the upper-layer characteristics. On the other hand, the presence of a lower layer with lower conductivity results in an increase of the peak value of the underground horizontal electric field. [ABSTRACT FROM AUTHOR]

In this paper, we thoroughly review all analytical solutions (both exact and approximate) presented to date in the literature for evaluation of voltages induced on a lossless horizontal conductor, placed over an infinite-conductivity ground, and excited by an external field produced by either a step function or a linearly rising current, moving unattenuated and undistorted along a vertical lightning channel. We also obtain the exact analytical solution for the step-function current case in the time domain via development in the s-domain. To date, there had been three attempts to obtain such solution, all of which yielding incorrect results. [ABSTRACT FROM AUTHOR]

Installing lightning arresters is an effective way to protect distribution lines from lightning-induced voltages. Spacing effectiveness of lightning arresters is one of the main concerns in the industry. Different separation distances of arresters have been proposed in the literature. In these studies, the simulations are made with simplified circuit models, which are not sufficient to support their conclusions. This paper presents a hybrid finite-difference time-domain (FDTD) SPICE method for analyzing lightning-induced overvoltages on a distribution line with arresters being installed. The FDTD method gives a full-wave solution of the induced voltages. To handle nonlinear lightning arresters, this FDTD method is integrated with a circuit solver SPICE. A diode-based model for the arrester is proposed using a SPICE subcircuit and is coupled to the FDTD domain as a connecting port. For the verification purpose, the method is compared with the results obtained in the rocket-triggered lightning experiment, in which no arresters were installed. Lightning-induced overvoltages on the distribution line with different arrester spacing arrangements are analyzed finally. Efficient arrester spacing under both first and subsequent strokes is investigated. [ABSTRACT FROM AUTHOR]

The protective effect of a shield wire against direct lightning flashes to a buried power cable has been clarified in this paper. The finite-difference time-domain (FDTD) method is used in the investigation. The FDTD model considers a 1-km-long insulated cable protected by a shield wire, and a lightning strike right above them. The model has been validated by comparing its results with experimental results available in the literature. The computed results show that the presence of the shield wire can effectively prevent the cable from being directly struck by the lightning flash. The voltage across the cable insulation at the striking point depends on the ground resistivity (the higher the resistivity, the higher the voltage), but this dependence is not linear. It is also shown that the soil surface ionization is relevant to the current delivered to the shield wire and to the voltage developed across the cable insulation. On the other hand, the soil ionization around the shield wire has negligible effects. The intrinsic resistance of the shield wire does not influence significantly the peak voltage across the cable insulation, but it influences its duration (the higher the intrinsic resistance, the longer the voltage duration). [ABSTRACT FROM PUBLISHER]

At lightning discharge, the grounding systems’ transient behavior is influenced by time-dependent nonlinear behavior and frequency-dependent effects. These effects are related to complex phenomena arising from the soil ionization surrounding the conductors at high current and to the fast risetime of the impulse current, respectively. Most of the performed investigations were either focused on soil ionization effects or frequency-dependent effects. This paper proposes a model that incorporates both aspects including the mutual coupling and air–soil interface effects, giving a more realistic representation of the grounding systems behavior. Based on the transmission line approach, the model can compute the grounding systems transient response buried in uniform and nonuniform soil. The model is applied to horizontal, vertical electrodes, and grounding grid subjected to impulse currents of variable magnitudes and shapes. The model results are validated against published measurement results obtained with low-current and high-current impulses. The time-domain transient potential and transient impedances show good agreement with experimental results. Other impulse impedance parameters used for the grounding systems analysis are reproduced quite accurately. As an application, the impulse impedance of a horizontal electrode and a grounding grid buried in two-layer soil is discussed when the upper layer depth and the resistivity of soil layers are varied. [ABSTRACT FROM PUBLISHER]

This paper discusses the influence of stroke current propagation velocity on the characteristics of lightning horizontal electric fields, considering different types of soil and distances to the stroke location. The MTLE model is adopted for the determination of the current distribution along the return stroke channel, whereas the effect of the finite-ground conductivity is taken into account by using the modified Cooray–Rubinstein approximation. This paper also discusses the effect of the propagation velocity on each of the horizontal electric field components. The results show that the horizontal electric field is strongly influenced by the stroke current propagation velocity even for the case of good conductive ground and observation points relatively close to the stroke location. Regardless of the ground conductivity, the peak value of the static component decreases and the negative peak of the radiation component increases with the propagation velocity. Therefore, for short distances to the lightning channel, the absolute peak value of the horizontal electric field tends to decrease as the velocity increases, while for distances of few kilometers or larger its behavior is just the opposite, i.e., the amplitude increases with the propagation velocity. [ABSTRACT FROM PUBLISHER]

Models of one or several extremely simple transmission towers (pylons) are usually used for analyzing the influence of lightning strikes on power network. Models of more complex transmission towers with transmission lines, ground wires and even lightning channel are required. In this paper, first of all, the reason why one only focuses on the magnetic field at the observation points is briefly explained. Secondly, a method used to get the time-domain results from the frequency-domain results by Antenna Design Framework Electromagnetic Satellite (ADF?EMS) software is established and its validity is proved. Thirdly, the effects of the lightning channels with different geometries are discussed. Finally, this paper comes up with a complex multi-tower system under the following fault types of lightning strikes, 1) direct lightning strikes to the edge phase wire without flashover, 2) direct lightning strikes to the edge phase wire with flashover, 3) lightning strikes to the top of the tower without flashover, and 4) lightning strikes to the top of the tower with back flashover. The magnetic field waveforms from these fault types are very important for the follow-up activity to achieve the fault type identification of lightning strikes in the observation system automatically. [ABSTRACT FROM PUBLISHER]

In this paper, we present a new solution for the evaluation of the horizontal electric field in the presence of finitely conducting ground in the time domain. The solution is general, numerically robust, and overcomes the problems related to previously proposed approaches. [ABSTRACT FROM PUBLISHER]

In this paper, a hybrid approach of the constrained interpolation profile (CIP) method and the transmission line modeling (TLM) method has been proposed for analyzing lightning electromagnetic fields and surges in the three-dimensional Cartesian coordinate system. The TLM method is employed locally in the working space for representing thin-wire conductors, and the CIP method is used for computing fields in the rest of the working space. Waveforms of lightning electromagnetic fields and surges computed using the CIP-TLM hybrid method agree well with corresponding ones computed using exact analytical expressions or with the finite-difference time-domain method. [ABSTRACT FROM PUBLISHER]

It is essential that the insulation system of the overhead distribution lines should be properly designed to ensure their immunity against lightning-induced overvoltages (LIOVs) caused by nearby return strokes. Therefore, accurate calculation of the peak values of LIOVs is important for the insulation design. In this paper, a formula is proposed to calculate the peak values of LIOVs for both first and subsequent strokes. The typical waveforms of the first and subsequent return strokes are adopted for this study considering a wide range of ground resistivity, from 0.25 to 20 k $\Omega $m. The 2-D finite-difference time-domain method associated with the Agrawal coupling model is employed for the calculation of LIOVs. In addition, the effect of ground permittivity on the peak values of LIOVs is also investigated. Finally, the proposed formula is applied to calculate the annual number of flashovers per 100 km of the overhead line. [ABSTRACT FROM AUTHOR]

The Cooray–Rubinstein formula is most widely used to evaluate the horizontal electric field generated by a lightning return stroke over a lossy ground. In this paper, a new method for fast evaluation of the Cooray–Rubinstein formula in time domain is proposed, by means of approximating the integral form of the modified Bessel function of the first kind using Gauss numerical integral. In the proposed method, the integral form of the modified Bessel function of the first kind is expressed by a summation of exponential functions, and a recursive convolution is achieved, which makes the calculation of the Cooray–Rubinstein formula in time domain much more efficient. Besides, the residues and poles due to the expression of the kernel function K( s) can be obtained directly for any ground conductivity and permittivity which makes the method proposed very simple and easy to program. The numerical examples demonstrate the validity and efficiency of the proposed method. [ABSTRACT FROM PUBLISHER]

An efficient approach to evaluate the radiated electromagnetic field of a lightning channel over a horizontally stratified conducting ground is proposed in this paper. The electromagnetic field component produced by a lightning channel, expressed in the form of generalized Sommerfeld integral (GSI) with a complicated integrand, is calculated along a newly proposed path in the complex plane. Due to the change of the integration path, the integrand in the GSI turns out to decay dramatically fast and without any oscillation at all. As explained in this paper, the larger horizontal distance will become the benefit to achieve a quicker convergence, which is just opposite to the case that the integration path is along the real axis. The validity of the proposed methodology is justified by the extensive comparison with the results in other publications. As a matter of fact, the methodology in this paper can be generalized to evaluate stratified conducting ground with any number of layers. [ABSTRACT FROM AUTHOR]

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 ~\mus and the return stroke velocity of 120 m/ \mus 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. [ABSTRACT FROM AUTHOR]

An improved finite difference time-domain (FDTD) method based on the telegraph equations of transmission lines is proposed. The original time-domain simulation method that resembles the well-established FDTD scheme based on the Maxwell's equations has been used in this paper to tackle the modeling problems of buried and overhead transmission lines. In this paper, a group of time domain responses of the ground impedance or ground admittance can be extracted analytically by means of a correlation between the ground impedance and the ground admittance. Thanks to the analytical technique, the accuracy of this time-domain solution is improved significantly. As a result, the application of this time-domain algorithm can be greatly expanded beyond the modeling of common transmission lines. By combining with the shunt and series connection difference equations, the method can be used to analyze an entire buried grounding network. Because the correlation between the ground impedance and the ground admittance is related to the propagation constant of electromagnetic waves, the analytical technique makes the propagation velocity unchanged during the iterative calculation. Therefore, the improved FDTD method allows the grounding network to be analyzed more accurately and efficiently. [ABSTRACT FROM PUBLISHER]

This paper presents a time-domain method for the calculation of the horizontal electric field at the earth surface due to lightning, when the earth structure is made up of two parallel horizontal layers of finitely conducting earth. The method is based on the assessment of the electric field at the surface considering the earth as homogeneous and with the electrical parameters of the first layer. The contribution of the second layer is considered by computing the waves reflected from the boundary between the layers, after they have propagated through the first layer. The paper also shows that the displacement currents could be neglected during the wave reflection, which leads to a simple expression for the reflection coefficient. The results from the method presented in this paper agree with results calculated using a known frequency-domain expression. [ABSTRACT FROM PUBLISHER]

The analysis of the impact of the frequency dependence of electrical parameters of soil on the lightning response of electrical systems has often been based on frequency-domain approaches. In this paper, a causal time-domain field formulation including the frequency dependence of soil parameters is proposed. The consistency of the developed formulation is proved considering a canonical electromagnetic problem and also comparisons with experimental results. The proposed formulation is useful for application of techniques such as the finite-difference time-domain method in problems involving dispersive soils. [ABSTRACT FROM PUBLISHER]

Wind power plants are one of the most widespread sources of electric energy during the last few decades. Wind towers are quite often exposed to lightning strikes due to their tall height and long blades. In this paper, the lightning-induced voltages (LIVs) on a three-phase overhead line are computed for both first and subsequent strokes to a nearby grounded wind tower using the three-dimensional finite-difference time-domain method with homogeneous and horizontally stratified grounds. The horizontal electric fields are computed on the line and on the ground surface considering the transient grounding and characteristic impedances of the struck wind tower. The impact of the existence of wind tower on LIVs and horizontal electric fields is illustrated by removing the tower (i.e., return stroke to the ground surface). Finally, the influence of ground permittivity on the peak values of LIVs is investigated. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss how to replace a time-demanding computer code having both quantitative and qualitative variables with a surrogate model based on Kriging technique. The recourse to a predictive model is motivated by a challenging electromagnetic compatibility problem of maximum lightning-induced current in electronic equipment connected to a large industrial site. The technical aspects of the incorporation of qualitative variables via specific correlation functions are detailed. The accuracy of the built surrogate model is statistically validated. The application of the resulting metamodel to the uncertainty analysis of induced currents will be also investigated. [ABSTRACT FROM PUBLISHER]

This paper presents the results of a radiated electromagnetic field due to lightning strike to a tall tower sitting on a mountainous terrain when considering both the first and subsequent return strokes. A cone-shaped ground with finite conductivity represents the mountainous terrain; and a cylindrical two-dimensional finite-difference time-domain (FDTD) scheme is used to determine the lightning-generated electromagnetic fields. The return stroke channel is modeled using the antenna theory model with fixed inductive loading which is appropriately incorporated into the FDTD algorithm. Simulation results are presented for different values of the cone angle and height, and for different values of the tower height. It is shown that when the first and subsequent return strokes hit a tower on a cone-shaped ground, the radiated electric and magnetic fields experience an enhancement in their amplitudes as compared to the case where the tower sits on a flat ground. Also, the current reflections from the tower base, influencing the current distribution along the tower and radiated electromagnetic field waveforms, depend on the cone angle and height, as well as the tower height. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical formula for calculating lightning-induced voltages on an infinitely long overhead line generated by a lightning stroke departing from an arbitrary altitude. A calculation method of the lightning-induced voltages to consider various engineering return-stroke models that can account for the variation of both current amplitude and velocity in a lightning channel is proposed. The lightning stroke is divided into a number of segments, and the analytical formula of the lightning-induced voltage is applied to each segment. This paper discusses the influence of parameters of return-stroke models on lightning-induced voltages. The proposed method is applied to a case of lightning strike to a tall stack. [ABSTRACT FROM AUTHOR]

This paper presents the results of simultaneous measurements of a return stroke current from rocket-triggered light- fling and the current induced on a nearby 2600-m-long line. The experimental data are compared with the results of calculations using time-domain equations and show good agreement. The induced current is calculated using the equation for the vertical electric field for perfect conducting earth proposed by Rusck and the equation for the horizontal electric field for finitely conducting earth pro- posed by Barbosa and Paulino. The coupling between the electric fields and the line is carried out using the model proposed by Agrawal. The paper also compares the results of the calculations with results available in the literature, and discusses the effect of line length and earth resistivity on the induced voltages. [ABSTRACT FROM AUTHOR]

This paper presents the results of experiments carried out with rocket-triggered lightning and the related theoretical analysis. It describes the test setup and presents the electric field waveform recorded at the earth surface alongside with the simultaneous measurement of the lightning return stroke current at the channel base. The relevant parameters that allow the validation of a model to correlate the two waveforms are presented, i.e., the return stroke velocity, the distance from the lightning channel base, and the earth parameters (resistivity and permittivity). A theoretical analysis is also presented, which models the phenomenon by the superposition of an induced and a conducted component, providing results that are in good agreement with the measurements. Finally, the paper presents a discussion about the range of validity of the theoretical model and analyzes the behavior of the two components of the electric field [ABSTRACT FROM AUTHOR]

Recently, applications of 3-D numerical electromagnetic analysis have been increasing either for lightning electromagnetic impulse (LEMP) studies or lightning surge analyses on transmission and distribution lines. This paper is mainly concerned with the use of time- and frequency-domain codes for electromagnetic analysis of lightning surges. The thin-wire in time-domain (TWTD) code and numerical electromagnetic code (NEC-2) in the frequency domain based on the method of moments are chosen for comparative studies. The accuracy of TWTD code in the analysis of lightning surge characteristics of a double-circuit transmission tower is first investigated by comparing the computed results with the measured results on a reduced-scale tower model, computed results by NEC-2 on a full-scale tower model, and those computed by electromagnetic transients program. In the latter part of the paper, a switch model is combined with the TWTD code, and its applicability in analyzing the lightning surge characteristics of a transmission tower equipped with a surge arrester or in analyzing lightning-induced voltage on an overhead line is demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents an approximate formula to calculate the horizontal electric field from lightning, considering finitely conducting earth. The formula is represented by an analytical expression in the time domain, which is useful for the calculation of lightning-induced voltages on power and telecommunication lines, without the need of domain transformations. The paper also compares the results of the formula with the results obtained from frequency-domain techniques, namely the numerical calculation of Sommerfeld's integrals and the Cooray-Rubinstein's formula. The comparison is favorable for a wide range of distances from the lightning channel and values of earth's conductivity. The horizontal electric field calculated by the formula is composed of two components of opposed polarities, one due to the return stroke charge and the other due to the return stroke current, resulting in an electric field with a bipolar wave shape. The charge component prevails in the region close to the lightning channel, while the current component prevails in the region far from it. [ABSTRACT FROM AUTHOR]

This paper comments on the recently published article entitled “Time-Domain Modeling of Grounding Systems’ Impulse Response Incorporating Nonlinear and Frequency-Dependent Aspects.” Some formulas used for time-domain simulation of grounding system behavior subjected to lightning in the referred paper are discussed. Afterward, some corrections made to the formulas are presented. [ABSTRACT FROM AUTHOR]

The general integral expressions for the elements of the ground impedance matrix do not have an analytical inverse transform in the time domain. Therefore, the ground transient resistance of a multiconductor line is commonly evaluated in the time domain by means of approximated expressions in order to avoid the numerical inverse fast Fourier transform burden. In this paper, we propose a new analytical approach for calculating the transient ground resistance in the time domain that stands on the very accurate Sunde logarithmic expression for the ground impedance matrix of an overhead multiconductor line. The proposed analytical approach is adopted for calculating lightning induced voltages in a multiconductor overhead line. The results show that the proposed analytical formula is in perfect agreement with the numerical inverse Fourier transform of the general Sunde expression and, therefore, is more accurate than the approximated expressions available in the literature. [ABSTRACT FROM AUTHOR]

It is important for the proper insulation design of the distribution system that lightning-induced overvoltages ( LIOVs) are accurately computed. This paper investigates the impact of ground resistivity, considering wide range up to 20 kΩm, on LIOVs impinging an overhead line due to nearby return stroke using the three-dimensional finite difference time domain (3-D FDTD) method. The investigation considers two values of both ground permittivity as well as the rise rate of lightning current. Subsequently, it is inferred that the influence of both ground permittivity and rise rate of lightning current on the peak values of LIOVs depends on the ground resistivity. Furthermore, horizontal conduction and displacement current densities are also calculated on the ground surface under the line to analyze the behavior of ground surface impedance. Consequently, it is deduced that the behavior of the impedance changes from inductive to capacitive at high values of ground resistivity, thus increasing the time to the peak value of LIOVs. The peak values of LIOVs computed using the 3-D FDTD method are compared with those calculated using Darveniza's formula. It has been revealed that this formula considerably underestimates the peak values of LIOVs at high values of ground resistivity. Thereby, an interpretation is presented for the reason of this underestimation from an electromagnetic perspective. Accordingly, Darveniza's formula is appropriately modified to improve the computation accuracy. [ABSTRACT FROM AUTHOR]