Wallace do Couto Boaventura

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.

Lightning induced voltage on an aerial wire above two-layer ground

This paper presents a time-domain method for the calculation of induced voltages on an aerial wire above a soil represented by two horizontal layers. Each layer is assumed to be homogeneous, isotropic, and having its own electrical parameters: resistivity, permittivity and permeability. The horizontal electric field at the surface of the top layer is calculated for an incident azimuthal magnetic field and used for the calculation of the induced voltage, using a methodology previously presented by the authors. A simple line configuration is used in order calculate the voltages induced by typical return-stroke waveforms. The results show that the two layers influence the induced voltage waveform. For the example considered, the induced voltage is initially influenced by the first layer but, as time goes by, it follows the voltage that would be induced if the earth was homogeneous and had the characteristics of the second layer.

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.

Horizontal electric field at the surface of layered earth due to lightning

This paper presents a time-domain method for the calculation of the electric field at the surface of earth due to lightning, when the earth structure is made 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 this layer, after they have propagated in the first layer. The paper also shows that the displacement currents could be neglected during the reflection of the waves, which leads to a simple expression for the reflection coefficient. The results from the method presented in this paper agree with reference results calculated from a frequency-domain expression proposed by Wait.

Transient voltage response of ground electrodes in the time-domain

This paper proposes an alternative and simple methodology to find the transient voltage response of a ground electrode in the time-domain. The methodology uses a parametric modeling approach to obtain a model, in terms of a polynomial ratio, to represent the ground electrode impedance in the frequency-domain. Once this model is obtained, it is used to derive a time domain step response for the electrode impedance, which is further used in the procedure to derive the desired transient voltage response. The proposed approach deals with single wire ground electrodes and also with the typical arrangements used in transmission lines grounding towers, with several coupled electrodes. Comparisons with other methodology and with measured results are presented. An application example is used to demonstrate the proposed methodology usefulness.

Induced voltages on overhead lines in the vicinity of 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 induced voltage, which may be relevant in the assessment of lightning performance of power distribution lines.

Transient ground impedance measurement using a very short current lead

This work describes a system for the measurement of the transient impedance of ground electrodes using a portable impulse generator and a new measuring arrangement. The innovation is the use of a very short current reaction lead, which is possible due to the use of transmission line with very low propagation velocity (3% of the velocity of light). The methodology for obtaining the transient impedance from the measurements is discussed and validated. The experimental results regarding transient impedance measurements for two ground electrodes arrangements are presented. The first arrangement consists of two vertical rods and the second one is an actual 138 kV transmission line tower leg, composed by a vertical electrode in parallel with a horizontal wire. A comparison with calculated values for both cases is also presented.