José Osvaldo Saldanha Paulino

An Approximate Time-Domain Formula for the Calculation of the Horizontal Electric Field from Lightning

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 Sommerfelds integrals and the Cooray-Rubinsteins formula. The comparison is favorable for a wide range of distances from the lightning channel and values of earths 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.

A time-domain formula for the horizontal electric field at the earth surface in the vicinity of lightning

This paper presents a time-domain formula for the calculation of the horizontal electric field in the vicinity of the lightning channel. The formula is based on the incident azimuthal magnetic field, so that it does not depend on the assumptions considered in the calculation of the magnetic field, such as return stroke model or propagation effects. The application of the formula with the magnetic field calculated from perfectly conducting earth provided results that agreed very well with results from Sommerfeld integrals, even in the vicinity of the lightning channel, where the Cooray-Rubinstein formula does not hold. The deviations of the results of the formula with respect to the Sommerfeld integrals are on the order of a few percent, which is the same order of magnitude as the deviations involved in the numerical evaluation of Sommerfeld integrals.

An Approximate Formula for the Peak Value of Lightning-Induced Voltages in Overhead Lines

An approximate formula is proposed to estimate the peak value of lightning induced voltages in an infinite line, considering the soil resistivity. The formula is derived from results of a computer code for lightning induced voltage calculation. The code is based on Ruscks formulation for the vertical electric field, for a perfect conducting earth, and the formulation for the horizontal electric field for finitely conducting earth proposed by Barbosa and Paulino. The electromagnetic field coupling with the line is carried out using the model proposed by Agrawal. The results are compared with experimental data from Barker for validation purposes. The paper also presents an extension of the methodology proposed in IEEE Std.1410 Guide to include the effect of the soil finite conductivity in the assessment of the lightning performance of distribution lines due to nearby strikes. The annual indirect lightning induced voltage flashover rates obtained with IEEE Std. 1410 method are compared with the approximate formula results.

Measured and Modeled Horizontal Electric Field From Rocket-Triggered Lightning

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.

Time-Domain Analysis of Rocket-Triggered Lightning-Induced Surges on an Overhead Line

This paper presents the results of simultaneous measurements of a return stroke current from rocket-triggered lightning 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 proposed 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.

A Time-Domain Method for the Horizontal Electric Field Calculation at the Surface of Two-Layer Earth Due to Lightning

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.

The Peak Value of Lightning-Induced Voltages in Overhead Lines Considering the Ground Resistivity and Typical Return Stroke Parameters

This paper presents an approximate formula for the peak value of lightning-induced voltages in an overhead line, considering the ground resistivity and a trapezoidal lightning return stroke current waveform with typical parameters 3.8-μ s front time and 120-m/μ s velocity. It presents an improvement in a formula previously proposed by the authors. The formula is used with a probabilistic approach, and the results are compared with theoretical and experimental results available in the literature. The results show that the proposed formula, although very simple, is in good agreement with results obtained using complete formulations and experimental data.

Effect of the Surface Impedance on the Induced Voltages in Overhead Lines From Nearby Lightning

This paper presents the calculation results of lightning-induced voltages on overhead lines using two different formulations for the horizontal electric field at the earth surface. The first one is a time-domain equation equivalent to the surface impedance contained in the Cooray-Rubinstein formula, while the second one is an improved equation that provides more accurate results in the vicinity of lightning. The induced voltages are calculated for a strike in the vicinity of the line (50 m) and the results show that, for good-conducting earth, the two formulations are equivalent. However, for poor-conducting earth, the second expression provides a higher and longer induced voltage. Based on the calculation results, a limiting condition for the use of these equations is proposed.

Lightning-Induced Current in a Cable Buried in the First Layer of a Two-Layer Ground

This paper analyzes the effect of a two-layer ground on the current induced in the shield of a buried cable due to lightning flashes. Each layer is assumed to be horizontal, homogeneous, isotropic, and having its own electrical parameters: conductivity, permittivity, and permeability. The inducing horizontal electric field is calculated for the incident azimuthal magnetic field and it is used for the calculation of the induced current. The calculation method is validated by comparing its results with results published in the literature. The currents induced in the shield of a buried cable by typical return-stroke current waveforms are calculated. The results show that the induced current waveform is initially determined by the first layer but, for later times, it follows the current that would be induced if the ground was homogeneous and had the characteristics of the second layer.

Calculation of lightning-induced voltages with RUSCK's method in EMTP: Part I: Comparison with measurements and Agrawal's coupling model

This paper discusses the computation of lightning-induced voltages on a transmission line with a phase and neutral conductor, using an implementation of Rusck’s theory in the Electromagnetic Transients Program EMTP. The results obtained are compared with measurements and with equations for the estimation of the maximum induced voltage, for an experimental distribution line subjected to rocket triggered lightning flashes. In this comparison, good agreement is found among the EMTP-RUSCK method, measurements on the experimental line, and the equation for the estimation of the maximum induced voltage based on the Agrawal coupling model.