Farhad Rachidi

Influence of a lossy ground on lightning-induced voltages on overhead lines

A comprehensive study on the effect of a lossy ground on the induced voltages on overhead power lines by a nearby lightning strike is presented. The ground conductivity plays a role in both the evaluation of the lightning radiated fields and of the line parameters. To be calculated by means of a rigorous theory, both fields and line constants need important computation time, which, for the problem of interest, is still prohibitive. The aim of this paper is to discuss and analyze the various simplified approaches and techniques that have been proposed for the calculation of the fields and the line constants when the ground cannot be assumed as a perfectly conducting plane. Regarding the radiated electromagnetic field, it is shown that the horizontal electric field, the component which is most affected by the ground finite conductivity, can be calculated in an accurate way using the Cooray-Rubinstein simplified formula. The presence of an imperfectly conducting ground is included in the coupling equations by means of two additional terms: the longitudinal ground impedance and the transverse ground admittance, which are both frequency-dependent. The latter can generally be neglected for typical overhead lines, due to its small contribution to the overall transverse admittance of the line. Regarding the ground impedance, a comparison between several simplified expressions used in the literature is presented and the validity limits of these expressions are established. It is also shown that for typical overhead lines the wire impedance can be neglected as regard to the ground impedance.

Lightning-induced voltages on overhead lines

A modeling procedure that permits calculation of lightning-induced voltages on overhead lines starting from the channel-base current is discussed. The procedure makes use of a coupling model already presented in the literature, based on transmission line theory, for field-to-overhead line coupling calculations. Both models are discussed and compared with experimental results. The hypothesis of perfect conducting ground, used to analyze the voltages induced on an overhead line by a nearby lightning return stroke with a striking point equidistant from the line terminations, and the limits of its validity are determined. A comparison shows that peak value and maximum front steepness of the induced voltages calculated using other lightning return-stroke models differ. It is also shown that another coupling model used in the power-lightning literature by several other authors may result in a less accurate estimation of the induced voltages. >

Current and electromagnetic field associated with lightning-return strokes to tall towers

An analysis of electric and magnetic fields radiated by lightning first and subsequent return strokes to tall towers is presented. The contributions of the various components of the fields, namely, static, induction, and radiation for the electric field, and induction and radiation for the magnetic field are illustrated and discussed. It is shown in particular that the presence of a tower tends, in general, to increase substantially the electric and magnetic field peaks and their derivatives. This increase is mainly caused by the presence of two oppositely propagating current wavefronts originating from the tower top and by the very high propagation velocity of current pulses within the tower, and depends essentially on the wavefront steepness of the channel-base current. Because of the last factor, the increase of the field magnitudes is found to be significantly higher for subsequent return strokes, which are characterized by much faster risetimes compared to first return strokes. The presented results are consistent with experimental observations of current in lightning strokes to the Toronto CN Tower and of the associated electric and magnetic fields measured 2 km away. These findings partially explain the fact that subsequent return strokes characterized by lower current peaks but higher front steepnesses and return stroke speeds may result in higher field peaks. The results obtained have important implications in electromagnetic (EM) compatibility. It is found that lightning strokes to tall metallic objects lead to increased EM field disturbances. Also, subsequent return strokes are to be considered an even more important source of EM interference than first return strokes. Indeed, EM fields from subsequent strokes are characterized by faster fronts and additionally, they may reach greater peaks than first strokes. Lastly, findings of this study emphasize the difficulty of extracting reliable lightning return stroke current information from remote EM field measurements using oversimplified formulae.

Formulation of the field-to-transmission line coupling equations in terms of magnetic excitation field

Different formulations of the field-to-transmission-line coupling equations are reviewed and discussed. An equivalent formulation is derived in which the source terms (or forcing functions) are expressed in terms of the magnetic excitation field. This formulation is particularly useful for evaluating field-to-transmission-line coupling when the exciting field is determined experimentally, since only the measurement of the electric field-generally easier to measure than the electric field-is necessary. >

Mitigation of lightning-induced overvoltages in medium Voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters: modeling and experimental validation

In this paper, we investigate the effect of periodically-grounded shielding wires and surge arresters on the attenuation of lightning-induced voltages. We discuss the adequacy of the commonly made simplification of assuming the shielding wire at ground potential, instead of being treated as one of the conductors of the multiconductor system. We also compare then the mitigation effect of shielding wires with that achievable by the insertion of surge arresters along the line. The computation results are first validated by means of calculations obtained by other authors referring to a simple line configuration, and then by means of experimental results obtained using a reduced-scale line model illuminated by a nuclear electromagnetic pulse (NEMP) simulator. One of the main conclusions is that the effectiveness of shielding wires and surge arresters depends mostly on the spacing between two adjacent grounding points or surge arresters.

Overview of Recent Progress in Lightning Research and Lightning Protection

This review paper, prepared for this second special issue on lightning of the IEEE Transactions on Electromagnetic Compatibility, summarizes major publications on lightning and lightning protection since the first special issue published in November 1998, i.e., during the last decade. The review is organized in the following five sections: lightning discharge-observations, lightning discharge-modeling, lightning occurrence characteristics/lightning locating systems, lightning electromagnetic pulse and lightning-induced effects, and protection against lightning-induced effects.

Electromagnetic field coupling to a line of finite length: theory and fast iterative solutions in frequency and time domains

A system of integral-differential equations for evaluating currents and voltages induced by external electromagnetic fields on a finite-length horizontal wire above a perfectly conducting ground is derived under the thin wire approximation. Based on perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zeroth iteration term is determined by using the transmission line (TL) approximation. The method can be applied both in the frequency and in the time domains. The proposed iterative procedure converges rapidly to the exact analytical solution for the case of an infinite line, and to the NEC solution for a line of finite length. Moreover, with only one iteration, an excellent approximation to the exact solution can be obtained. The method is applied to assess the validity of the TL approximation for plane wave coupling to an overhead line of finite length. It is shown that the resulting errors for the early-time response are generally higher than those corresponding to infinite lines.

A Review of Field-to-Transmission Line Coupling Models With Special Emphasis to Lightning-Induced Voltages on Overhead Lines

We discuss the transmission line (TL) theory and its application to the problem of lightning electromagnetic field coupling to TLs. We start with the derivation of the general field-to-TL coupling equations for the case of a single-wire line above a perfectly conducting ground. The derived equations are solely based on the thin-wire approximation and they do take into account high-frequency radiation effects. Under the TL approximation, the general equations reduce to the Agrawal et al. field-to-TL coupling equations. After a short discussion on the underlying assumptions of the TL theory, three seemingly different but completely equivalent approaches that have been proposed to describe the coupling of electromagnetic fields to TLs are presented. The derived equations are then extended to deal with the presence of losses and multiple conductors and expressions for the line parameters, including the ground impedance and admittance, are presented. The time-domain representation of the field-to-TL coupling equations, which allows for a straightforward treatment of nonlinear phenomena as well as the variation in the line topology, is also described. Solution methods in the frequency domain and in the time domain are given and application examples with reference to lightning-induced voltages are presented and discussed. Specifically, the effects of ground losses and corona are illustrated and discussed. When the traveling voltage and current waves are originated from lumped excitation sources located at a specific location along a TL (direct lightning strike), both the corona phenomenon and ground losses result, in general, in an attenuation and dispersion of propagating surges along TLs. However, when distributed sources representing the action of the electromagnetic field from a nearby lightning illuminating the line are present, ground losses and corona phenomenon could result in important enhancement of the induced voltage magnitude.

Lightning induced disturbances in buried Cables-part I: theory

In this paper, we present a review of theoretical methods to compute lightning induced currents and voltages on buried cables. The evaluation of such induced disturbances requires the calculation of the electric field produced by lightning along the cable path. We show that the Coorays simplified formula is capable of predicting accurately the horizontal electric field penetrating the ground, at distances as close as 100 m. Regarding the parameters of the buried cable, a comparison of several approximations of the ground impedance is presented. We show that the Pollaczek expression corresponds to the Sunde general expression, when the displacement current is neglected. The analysis shows also that all the proposed approximations provide very similar results for the considered range of frequencies (up to 30 MHz). Most of the approximate formulas neglect the contribution of the displacement current and, therefore, predict values for the ground impedance which tend to infinity at higher frequencies. This corresponds in the time domain to a singularity of the ground transient resistance at t=0. By analogy to the Sunde approximation for the ground impedance of overhead lines, we propose a logarithmic approximation for the ground impedance of a buried cable. In addition, unlike most of the considered approximations, the proposed formula has an asymptotic behavior at high frequencies; therefore, the corresponding transient ground resistance in the time domain has no singularity at t=0. It is also demonstrated that within the frequency range of interest, the wire impedance can be neglected, due to its small contribution to the overall longitudinal impedance of the line. The ground admittance, however, can play an important role at high frequencies (1 MHz or so) especially in the case of poor ground conductivity. The ground admittance needs to be taken into account in the calculation of lightning induced currents and voltages on buried cables. This is in contrast with the case of overhead lines in which its contribution is generally negligible, even in the MHz range. We also investigate the time-domain representation of field-to-transmission line coupling equations. The coupling model includes the effect of ground admittance which appears in terms of an additional convolution integral. An analytical expression for the ground transient resistance in the time domain is also proposed which is shown to be sufficiently accurate and nonsingular. Finally, we present a time domain solution of field-to-buried cable coupling equations using the point-centered finite difference time domain (FDTD) method, and a frequency domain solution using Greens functions. In our companion paper (Part II), we compare both solutions to experimental waveforms obtained using triggered lightning.

Comparison of two coupling models for lightning-induced overvoltage calculations

The two coupling models most frequently used in the power-lightning literature for the calculation of lightning-induced overvoltages, namely the model by Chowdhuri and Gross (1967) and the model by Agrawal, Price and Gurbaxani (1980), are compared and discussed. It is shown that the Chowdhuri-Gross model is incomplete: the source term due to the contribution of the magnetic induction is missing. The authors investigate how much the lack of the source term affects the accuracy of the calculated overvoltages. Experimental tests of the two models using a short line illuminated by a NEMP simulator support the theoretical conclusion. >