Vernon Cooray

Horizontal fields generated by return strokes

Horizontal fields generated by return strokes play an important role in the interaction of lightning-generated electromagnetic fields with overhead power lines. In many of the recent investigations on the interaction of lightning electromagnetic fields with power lines, the horizontal field was calculated by employing the expression for the tilt of the electric field of a plane wave propagating over the finitely conducting Earth. In this paper we show that the horizontal field generated by return strokes over the finitely conducting ground can be obtained to a high accuracy by using the expression for the surface impedance of the finitely conducting Earth. The method is suitable to calculate horizontal fields generated by return strokes at distances as close as 200 m. At these close ranges the use of the wave tilt expression can cause large errors.

A simplified physical model to determine the lightning upward connecting leader inception

In this paper, a generalized leader inception model is proposed. It is based on an iterative geometrical analysis of the background potential distribution of an earthed structure to simulate the first meters of propagation of an upward connecting leader. By assuming a static field approach, the leader stabilization fields and the striking distances were computed for a lightning rod and for a building. The obtained results were compared with the existing leader inception criteria. Furthermore, in order to validate the model, the leader inception condition was computed for a triggered lightning experiment. Excellent agreement with the experimental results was obtained. The present model has several advantages in comparison with the existing leader inception criteria. One of them is related to the fact that the proposed model can be used to analyze the effect of the space charge on the upward leader inception.

A self-consistent upward leader propagation model

The knowledge of the initiation and propagation of an upward moving connecting leader in the presence of a downward moving lightning stepped leader is a must in the determination of the lateral attraction distance of a lightning flash by any grounded structure. Even though different models that simulate this phenomenon are available in the literature, they do not take into account the latest developments in the physics of leader discharges. The leader model proposed here simulates the advancement of positive upward leaders by appealing to the presently understood physics of that process. The model properly simulates the upward continuous progression of the positive connecting leaders from its inception to the final connection with the downward stepped leader (final jump). Thus, the main physical properties of upward leaders, namely the charge per unit length, the injected current, the channel gradient and the leader velocity are self-consistently obtained. The obtained results are compared with an altitude triggered lightning experiment and there is good agreement between the model predictions and the measured leader current and the experimentally inferred spatial and temporal location of the final jump. It is also found that the usual assumption of constant charge per unit length, based on laboratory experiments, is not valid for lightning upward connecting leaders.

Lightning-induced overvoltages in power lines: validity of various approximations made in overvoltage calculations

The validity of different approximations used in the calculation of induced overvoltages in power lines are investigated. These approximations are as follows: (1) neglect the distortions introduced by the finitely conducting ground on the electromagnetic (EM) fields; (2) the horizontal electric field at ground level is calculated by using the wavetilt approximation, which is valid for radiation fields and for grazing incidence; (3) the horizontal field at the line height is obtained by adding the horizontal field calculated at ground level to the horizontal field at the line height calculated over a perfectly conducting ground; (4) the transmission line equations derived by assuming that the ground is perfectly conducting are used with the horizontal field present over a finitely conducting ground as a source term in calculating the induced overvoltages; and (5) the propagation effects on the transients as they propagate along the line are either neglected or modeled by replacing the line impedance due to the ground by a constant resistance. The results presented show that in the calculation of induced overvoltages the approximation (3) is justified and approximation (2) is justified if the interest is to estimate the peak value of the induced overvoltage. Approximation (4) is probably justified for short lines and/or for highly conducting grounds. But it can introduce significant errors if the line is long and ground conductivity is low. Approximations (1) and (5) may lead to significant errors in the peak value, risetime, and derivative of the lightning-induced overvoltages.

Concepts of lightning return stroke models

Return stroke models have been reviewed according to the assumptions they make and their underlying concepts. We have investigated the roots of the modern concepts used to describe return stroke related phenomena and illustrated their developments and deviations from the original idea. We discuss the return stroke models in two categories in accordance with the direction of the charge transfer along the channel. We show that all the models that we have considered can be described by two general sets of mathematical equations. The validation and comparison of models in reproducing measured lightning parameters are discussed. We also show the different methods employed by return stroke models to estimate the return stroke speed and discuss possible improvements that could be introduced into return stroke models in the future.

Comparison of preliminary breakdown pulses observed in Sweden and in Sri Lanka

Abstract In this paper we have analysed breakdown pulse trains preceding the first return stroke in 47 negative cloud-to-ground (CG) lightning flashes observed in Sri Lanka (tropics) and that in 41 negative CG flashes recorded in Sweden (temperate regions). In the data obtained in Sri Lanka, breakdown pulses could be detected only in nine flashes. In other flashes either these pulses are absent or, if they are present, their amplitudes should be below the background noise level. From the nine flashes with breakdown pulse trains, we obtained the following results. The ratio between the maximum breakdown pulse amplitude and the return stroke amplitude (BP\RS ratio), as a percentage, is 16.5%. The time duration between the most active part of the pulse train and the return stroke (BP\RS separation), is 11.9 ms and the ratio between the noise amplitude and the return stroke amplitude (N\RS ratio), as a percentage, for all 47 flashes, is 5.0%. In the flashes observed in Sweden, breakdown pulses are detectable in all records. In this data, the BP\RS ratio, as a percentage, is 101.4%, the BP\RS separation is 13.8 ms and the N\RS ratio, as a percentage, is 3.7%. All the above values are arithmetic means. Most of the pulses of breakdown pulse trains observed in both countries are bipolar in nature with the initial polarity the same as that of the succeeding return stroke.

Horizontal Electric Field Above- and Underground Produced by Lightning Flashes

The horizontal electric field both at points above and below ground in the vicinity of lightning return strokes were evaluated by numerical solution of Sommerfelds integrals. Results are presented for ground conductivities in the range of 0.01-0.0001 S/m. The results are compared with the following approximate procedures used in the literature to calculate horizontal electric fields: 1) the surface impedance approximation; 2) the quasi-static approximation frequently used in lightning protection standards; and 3) Coorays simplified formula for the computation of underground electric field. Based on this comparison, the distance range in which these approximations are valid is obtained. The results obtained show that: 1) The surface impedance approximation can generate correct horizontal electric field when the distance to the point of observation is larger than about 50, 200, and 500 m for ground conductivities of 0.01, 0.001, and 0.0001 S/m, respectively. 2) It is necessary to include propagation effects in the magnetic field that is being used as an input in the surface impedance expression when it is being used to calculate the horizontal electric field. 3) Cooray-Rubinstein approximation gives exact results when it is being used to calculate the horizontal electric field aboveground generated by cloud flashes. 4) Coorays simplified formula connecting the surface horizontal electric field to the underground one gives accurate results, provided that the horizontal electric field at the surface of the ground, which is used as an input, is calculated accurately and the depth of the point of observation is kept much less than the distance to the point of strike.

Propagation effects on the lightning-generated electromagnetic fields for homogeneous and mixed sea-land paths

The influences of the path of propagation on the shape and amplitude of the electric fields and electric field derivatives generated by lightning return strokes were investigated. Results are presented for the cases where (1) both the lightning return stroke and the point of observation are located over finitely conducting, homogeneous ground and (2) the lightning return stroke is located over sea and the point of observation is located over land at some distance from the sea-land boundary. For propagation paths over finitely conducting ground the electric field derivative can decrease significantly in propagation distances as small as 1000 m. When the path of propagation is partly over sea and partly over land, the propagation effects on the electric radiation field derivative are significant unless the width of the land portion of the propagation path is less than a few tens of meters.

Time dependent evaluation of the lightning upward connecting leader inception

The evaluation of the upward connecting leader inception from a grounded structure has generally been performed neglecting the effect of the propagation of the downward stepped leader. Nevertheless, field observations suggest that the space charge produced by streamer corona and aborted upward leaders during the approach of the downward lightning leader can influence significantly the initiation of stable upward positive leaders. Thus, a physical leader inception model is developed, which takes into account the electric field variations produced by the descending leader during the process of inception. Also, it accounts for the shielding effect produced by streamer corona and unstable leaders formed before the stable leader inception takes place. The model is validated by comparing its predictions with the results obtained in long gap experiments and in an altitude triggered lightning experiment. The model is then used to estimate the leader inception conditions for free standing rods as a function of tip radius and height. It is found that the rod radius slightly affects the height of the downward leader tip necessary to initiate upward leaders. Only an improvement of about 10% on the lightning attractiveness can be reached by using lightning rods with an optimum radius. Based on the obtained results, the field observations of competing lightning rods are explained. Furthermore, the influence of the average stepped leader velocity on the inception of positive upward leaders is evaluated. The results obtained show that the rate of change of the background electric field produced by a downward leader descent largely influences the conditions necessary for upward leader initiation. Estimations of the leader inception conditions for the upper and lower limit of the measured values of the average downward lightning leader velocity differ by more than 80%. In addition, the striking distances calculated taking into account the temporal change of the background field are significantly larger than the ones obtained assuming a static downward leader field. The estimations of the present model are also compared with the existing leader inception models and discussed.

Propagation of lightning generated transient electromagnetic fields over finitely conducting ground

Abstract This paper elucidates the propagation effects on lightning generated electric fields. The mathematics of the problem is described and a simple procedure that can be used to predict the propagation effect is outlined together with its experimental confirmation. This procedure is used to analyse the propagation effects, over distances less than about 300 km, on the radiation fields of negative first return strokes, positive first return strokes and subsequent return strokes in triggered lightning flashes. From the results, empirical equations that can be used to correct for the propagation effects are extracted. The results show that the attenuation due to propagation effects of the initial peak amplitudes may differ in negative and positive return strokes and that the data from triggered lightning flashes should be applied with caution in correcting for the propagation effects of natural lightning flashes.