A sensitivity study of HV and EHV lightning performance shows that surge response characteristics of towers and lines are as important as the footing response. Tower travel time has a very large sensitivity for taller double-circuit lines. Existing methods for analysis of tower and line response have considerable uncertainty. This uncertainty is resolved by extensions to travelling- wave analysis combined with experimental verification. New equations for tower surge impedance and tower travel time are proposed to deal with the most common situation of a midspan stroke to the skywire.

Lightning Surge Response Of Transmission Towers

[1] The widely used transmission-line (TL) model of lightning return stroke in a vertical channel is most rigorously represented by a vertical phased array of current sources that produce a spherical transverse electromagnetic (TEM) wave in the case of return-stroke speed v equal to the speed of light c. If the radius of the lightning channel were equal to zero, the equivalent representation could be obtained by applying a hypothetical infinitesimal source of pure spherical TEM wave at the bottom of the channel. A non-zero-radius vertical wire above ground excited by a practical source at its bottom end cannot support unattenuated current waves, and the associated electromagnetic field structure is non-TEM.

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On the transmission line model for lightning return stroke representation

It is known from both theory and numerical simulations that a current pulse suffers apparent attenuation as it propagates along a vertical perfect conductor of uniform, nonzero thickness (e.g., a cylinder) above perfectly conducting ground, excited at its bottom by a lumped source. The associated electromagnetic field structure is non-transverse electromagnetic (TEM), particularly near the source region. On the other hand, it has been shown analytically by Thottappillil et al. (2001, 2004) that no attenuation occurs and the electromagnetic field structure is pure transverse electromagnetic (TEM) if the conductor thickness and source size are assumed to be infinitesimal. The goal of this paper is to examine the mechanism of current attenuation as it propagates along a nonzero thickness conductor, based on the scattering theory and on a nonuniform transmission line approximation. In applying the scattering theory, we decompose the "total" current in the conductor into two components that we refer to as the "incident" and "scattered" currents. The "incident" current serves as a reference (no attenuation), specified disregarding the interaction of resultant electric and magnetic fields with the conductor, while the "scattered" current, found here using the finite-difference time-domain (FDTD) method, can be viewed as a correction to account for that interaction. The scattered current modifies the incident current so that the resultant total current pulse appears attenuated. Thus, the current attenuation is likely to be due to field scattering that does not occur in the case of zero thickness conductor. The attenuation of the total current pulse is accompanied by the lengthening of its tail, such that the total charge transfer is independent of height. Approximation of the vertical conductor above ground by a nonuniform transmission line whose characteristic impedance increases with increasing height is shown to reasonably reproduce the current pulse attenuation predicted by the scattering theory. In this approximation, the apparent current attenuation with height can be attributed to waves reflected back to the source. The results have important implications for development and interpretation of lightning models.

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On the mechanism of attenuation of current waves propagating along a vertical perfectly conducting wire above ground: application to lightning

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.

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

This paper presents a new approach to model a transmission tower for lightning performance studies. It consists of representing each part of the tower by equivalent vertical and/or horizontal transmission lines as required. While horizontal line parameters are obtained from standard line formulas, specific expressions are derived for the parameters of vertical lines. Moreover, mutual coupling between any two parallel vertical transmission lines is taken into account. Transient waveforms obtained using the proposed method are compared with experimental data obtained using a reduced-scale model and field experiments. The agreement between simulated results and experimental measurements is satisfactory.

Nonuniform transmission tower model for lightning transient studies

The conventional traveling-wave technique is extended to nonuniform lines by attributing distributed reflection and refraction coefficients to each point on the line. Analytical expressions are derived giving the variations in voltage and current wave fronts as they travel along a nonuniform line as well as variations in the voltage and current and their respective ratio Z(t) = E/I at a fixed position of the line caused by the continuous generation of reflections along the line. It is shown that the ratio Z(t), representing the so-called transient surge impedance of a given position of a nonuniform line, depends not only on time and the function expressing the conventional surge impedance of the line but also on the shape of the current wave, a fact which considerably reduces the usefulness of Z(t) in solving nonuniform line problems.

Zhu Tong Chun

Papers

Wave Propagation on Nonuniform Lines