Marcos Rubinstein

Lightning Electromagnetic Field Coupling to Overhead Lines: Theory, Numerical Simulations, and Experimental Validation

The evaluation of electromagnetic transients in overhead power lines due to nearby lightning return strokes requires accurate models for the calculation of both the incident lightning electromagnetic pulse (LEMP) and the effects of coupling of this field to the line conductors. Considering also the complexity of distribution networks in terms of their topology and the presence of power system components and protection devices, the implementation of the LEMP-to-transmission-line coupling models into software tools used to represent the transient behavior of the entire network is of crucial importance. This paper reviews the most significant results obtained by the authors concerning the calculation of lightning-induced voltages. First, the theoretical basis of advanced models for the calculation of LEMP-originated transients in overhead power lines is illustrated; then, the relevant experimental validation using: 1) reduced-scale setups with LEMP and nuclear electromagnetic pulse (NEMP) simulators and 2) full-scale setups illuminated by artificially initiated lightning are reported. Finally, the paper presents comparisons between simulations and new experimental data consisting of measured natural lightning-induced voltages on a real distribution network in northern Italy, correlated with data from lightning location systems.

Far-field-current relationship based on the TL model for lightning return strokes to elevated strike objects

New general expressions relating lightning return stroke currents and far radiated electric and magnetic fields are proposed, taking into account the effect of an elevated strike object, whose presence is included as an extension to the transmission line (TL) model. Specific equations are derived for the case of tall and electrically short objects. The derived expressions show that, for tall structures (when the round-trip propagation time from top to bottom within the tower is greater than the current zero-to-peak risetime), the far field is enhanced through a factor with respect to an ideal return stroke initiated at ground level. The enhancement factor can be expressed in terms of the return stroke wavefront speed v, the speed of light in vacuum c, and the current reflection coefficient at the top of the elevated strike object. For typically negative values of this top reflection coefficient, lightning strikes to tall towers result in a significant enhancement of the far electromagnetic field. Expressions relating the far electromagnetic field and the return stroke current are also presented for electrically short towers and for very long return stroke current wavefronts. For the case of return strokes initiated at ground level (h=0), these expressions represent a generalization of the classical TL model, in which the reflections at the ground are now taken into account. We describe also simultaneous measurements of return stroke current and its associated electric and magnetic fields at two distances related with lightning strikes to the 553-m-high Toronto Canadian National (CN) Tower performed during 2000 and 2001. The derived expressions for tall strike objects are tested versus obtained sets of simultaneously measured currents and fields associated with lightning strikes to the CN Tower, and a reasonable agreement is found. Additionally, it is shown that the peak of the electromagnetic field radiated by a lightning strike to a 553-m-high structure is relatively insensitive to the value of the return stroke velocity, in contrast to the lightning strikes to ground.

Determination of reflection coefficients at the top and bottom of elevated strike objects struck by lightning

Reference LRE-ARTICLE-2008-027doi:10.1029/2002JD002973View record in Web of Science Record created on 2008-02-06, modified on 2017-05-10

Statistical Distributions of Lightning Currents Associated With Upward Negative Flashes Based on the Data Collected at the Säntis (EMC) Tower in 2010 and 2011

This paper presents statistical distributions of lightning current parameters based on the lightning current and current-derivative waveforms measured at the Säntis Tower site in 2010 and 2011. The total number of flashes analyzed in this study was 167, which includes nearly 2000 pulses. The statistical distributions refer to upward negative flashes. It is shown that negative flashes are mainly concentrated in the summer months during the convective season. Statistical data on the salient lightning current parameters, namely, peak current, peak current derivative, risetime, pulse charge, pulse duration, interpulse interval, and flash multiplicity are presented and discussed. The obtained data that constitute the largest dataset available to this date for upward negative flashes are also compared with other available statistical distributions.

On the Current Peak Estimates Provided by Lightning Detection Networks for Lightning Return Strokes to Tall Towers

The peak current estimation of lightning detection networks for strikes to tall towers is discussed in this paper. Such systems are sometimes calibrated using return-stroke current data obtained by means of rocket-triggered lightning or instrumented towers of relatively short height. However, for strikes to electrically tall towers, they tend to overestimate the return-stroke current peak. In this case, in fact, the associated radiated electromagnetic fields, from which the return-stroke current is estimated, experience a significant enhancement with respect to the field that would be radiated if the same return stroke was initiated at ground level or on a short tower. Two approaches to correct the current estimates of a lightning detection network for a lightning strike to a tall tower are discussed and applied to the current measurements obtained at the CN Tower in Toronto in the summer of 2005, for which estimates were available from the North American Lightning Detection Network (NALDN). It is shown that correcting the NALDN estimates using the so-called tower factor obtained from theoretical studies results in an excellent estimation of lightning current peaks.

Radiated Fields From Lightning Strikes to Tall Structures: Effect of Upward-Connecting Leader and Reflections at the Return Stroke Wavefront

An extension of the engineering return-stroke models for lightning strikes to tall structures that takes into account the presence of possible reflections at the return-stroke wavefront and the presence of an upward-connecting leader is presented. Based on the approach proposed by Shostak et al., closed-form, iterative solutions for the current distribution along the channel, and the strike object are derived. Simulation results for the magnetic fields are compared with experimental waveforms associated with lightning strikes to the CN Tower (553 m). It is shown that taking into account the reflections at the return-stroke wavefront results in better agreement with the fine structure of the magnetic-field waveforms. Moreover, the obtained results are in better agreement with experimental observations, reproducing both the early narrow undershoot and the far-field zero crossing. The results also suggest that the typical double-peak response of the radiated fields from tall structures might be due to the combined effect of upward-connecting leaders and reflections at the return-stroke wavefront.

Lightning-induced voltages at both ends of a 448-m power-distribution line

Lightning-induced voltages due to return strokes in ground flashes beyond about 5 km were measured simultaneously at both ends of an unenergized 448-m power-distribution line. The measurements represent an extension of an earlier experiment on the same line in which voltages are obtained at only one end of the line. In addition to the induced voltage measurements, the causative lightning electric and magnetic fields are recorded. The voltage and field measurements are made as a function of the lightning direction and of the power-line termination. For both measured and idealized electric fields as inputs to a time-domain transmission-line coupling model, the authors calculate line voltages as a function of the incident angle of the lightning electromagnetic radiation and of the line termination. Measured and predicted voltages calculated from the coupling model with measured fields as inputs show, overall, good agreement in waveshape, but the predicted voltages are about a factor of three larger in amplitude. To the extent that the results can be compared, there is reasonable agreement with the earlier experiments on the same line. >

Lightning electromagnetic fields at very close distances associated with lightning strikes to the Gaisberg tower

In this paper we present and discuss measurements of electric (vertical and radial) and magnetic fields from leaders and return strokes associated with lightning strikes to the 100 m tall Gaisberg tower in Austria obtained in 2007 and 2008. The fields were measured at a distance of about 20 m from the tower. Simultaneously, return stroke currents were also measured at the top of the tower. The data include, for the first time at such close distances, simultaneous records of vertical and horizontal electric fields. The vertical electric field waveforms appeared as asymmetrical V-shaped pulses. The initial, relatively slow, negative electric field change is due to the downward leader, and the following, fast, positive electric field change is due to the upward return stroke phase of the lightning discharge. The horizontal (radial) electric field due to the leader phase has a waveshape similar to that of the vertical electric field. However, the horizontal field due to the return stroke is characterized by a short negative pulse of the order of 1 mu s or so, starting with a fast negative excursion followed by a positive one. The return stroke vertical electric field changes appear to be significantly smaller than similar measurements obtained using triggered lightning. This finding confirms the shadowing effect of the tower, which results in a significant decrease of the electric field at distances of about the height of the tower or less. The vertical and horizontal E field changes due to the return stroke were also found to be larger on average than the leader electric field changes. In a significant number of cases (33%), the vertical electric field waveforms due to the return stroke were characterized by a first peak exceeding the typical late-time flattening due to the electrostatic term. This is in contrast with similar measurements related to triggered lightning which do not exhibit such a first peak. About one quarter of the measured vertical electric field waveforms (18 pulses out of 76) featured an unusual waveform characterized by a positive leader field change followed by a bipolar return stroke field change with a zero crossing time of about 60 mu s.

On the use of transmission line theory to represent a nonuniform vertically-extended object struck by lightning

In this study, we present an experimental validation of the transmission line representation of an elevated object struck by lightning. The experimental results are obtained using a reduced-scale model and injected signals with narrow pulse widths (down to 500 ps). The validation is performed using a reduced scale structure representing the Toronto CN Tower in Canada. Two models consisting, respectively, of 1-section and 3-section uniform transmission lines were considered for the comparison. It is shown that the 3-section model is able to accurately reproduce the obtained experimental data. The overall agreement between the 1-section model and the experimental results is also satisfactory, at least for the early-time response.

On the Measurement and Calculation of Horizontal Electric Fields From Lightning

In this paper, we discuss two issues related to the measurement and calculation of the horizontal electric fields from lightning. On the one hand, there is an inherent difficulty in measuring the horizontal electric field component from lightning because of the overshadowing effect of the vertical electric field component which, depending on the distance to the lightning channel, the ground conductivity, and the height of the observation point can be one to two orders of magnitude larger than the horizontal electric field component. Consequently, even a small tilt of the measuring antenna would result in a noticeable contamination of the measured horizontal waveform. This may explain the fact that data on horizontal electric fields are very scarce. Numerical simulations show that, for a ground conductivity of 0.0025 S/m, the resulting error for a one-degree sensor tilt in the field peak is about 20% for distances ranging from 60 to 500 m. For strikes to a 100-m-tall tower, the resulting errors are found to be slightly smaller (about 10% to 15% for the first peak). The second issue dealt with in this paper is the computation methods of the horizontal electric field. In this regard, some authors have emphasized the importance of taking into account the so-called conduction current in the calculation of nearby horizontal electric fields. We show in this paper that the conducted contribution is automatically taken into account when using the general solutions of Maxwells equations or obtained by exact numerical simulations. In this case, there is no need to consider separately any other contributions because the solution yields the total horizontal electric field, taking into account both the radiation from the channel and the current flowing into the ground. However, a “conducted contribution” needs indeed to be taken into account separately when high-frequency approximate solutions are used for the evaluation of the electric field. At very close distances to the lightning strike location, the current distribution in the ground may be highly nonuniform because of surface arcing and plasma channel formations. Given the random nature of these phenomena, it is virtually impossible to gain detailed knowledge of the current distribution and, hence, to evaluate the resulting horizontal electric field near the strike point. Based on the results and discussion presented in this paper, we recommend taking special care when measuring the horizontal electric field from lightning to minimize the contaminating effect of the vertical electric field. It is important that both components (vertical and horizontal) be measured simultaneously to evaluate possible contamination of the horizontal field.