A fractal model for the lightning induced current on a transmission line

This article presents a model of a tortuous lightning channel, and a study of the consequent electromagnetic coupling to a transmission line. We analyse the fractal dimension of the induced current on the line, compared with the fractal dimension of the lightning channel and the impinging electromagnetic field on the line. This comparison confirms our previous studies pointing out that the channel fractal dimension and the electromagnetic field fractal dimension are related (in particular, for typical lightning parameters they are the same). A comparison of simulated fields and line currents with experimental measurements is also attempte

How Lightning Tortuosity Affects the Electromagnetic Fields by Augmenting Their Effective Distance

A novel approach for developing the electromagnetic fields from a lightning return stroke which follows a tortuous path will be presented. The proposed model is unique in that it recognizes that the symmetrical tortuosity of lightning directly impacts the observable distance r, which in turn, alters the resulting electromagnetic fields. In the literature, lightning return stroke models typically employ the assumption that the cloud-to-ground path is straight. Although this assumption yields fairly consistent results across an array of varying approaches, it does not account for lightning\u27s natural physical appearance. Furthermore, straight-line models only account for the cloud-to-ground discharges and do not address branching and/or cloud-to-cloud discharges which are far more common. In reality, the steps which make up the lightning channel\u27s initial descent are staggered or tortuous with respect to each other. Given this fact, the upward traveling current wavefront which follows this prescribed path will exhibit the same characteristics. In doing so, each current segment, which forms along its respective step, induces electromagnetic fields with angular aggregates that propagate outward from their origin. This, in turn, will generate spatial points where there are fields of higher and lower intensities. The results presented in this paper will show how the effective observable distance due to symmetrical tortuosity alters the resulting electromagnetic fields. Furthermore, it will be shown that as the observable distance r is increased, results from the proposed model closely resemble the straight-line model which strongly suggests that symmetrical tortuosity is only influential at relatively close distances

ON THE INFLUENCE OF CHANNEL TORTUOSITY ON ELECTRIC FIELDS GENERATED BY LIGHTNING RETURN STROKES AT CLOSE DISTANCE

In this paper the results of the estimated electric field associated with tortuous lightning paths at close distance (50 m to 500 m) are shown. Such results are compared with experimental data available in the literature and are illustrated along with a quantitative analysis of the field waveforms and their frequency spectra. The limits of the usual straight-vertical channel assumption and the influence of tortuosity at different azimuth and distances from the lightning channel base are also highlighted

Lightning return stroke current from a new distributed circuit model and electromagnetic fields generated by tortuous lightning channels

Ph.DNUS-SUPELEC JOINT PH.D. PROGRAMM

Fractal modeling of lightning

A program has been developed that portrays the fractal modeling of lightning, which subsequently calculates the fields from a fractal antenna. Nodal currents are weighted with branch length. The Hausdorff dimension for various growth parameters η, agree with those in the literature. Electric fields in the far zone have been calculated by weighting the branch currents with an overall damped sinusoidal current. The current waveform for each element is evaluated at retarded times based upon the speed the discharge propagates along the fractal. At scale lengths of 100 m an interference pattern becomes noticeable. We have investigated the slope of the power spectrum for spider lightning. For f \u3c fthreshold the slope is between -1.6 to -2.6 with a standard deviation of ~ 2. In the case of channel lightning this slope would be -2. For f \u3e fthreshold the average slope varies between -3.4 and -3.5. In the case of channel lightning this slope would be -4. The lesser slope is attributed to more interference between radiating elements in this model. For f \u3e fthreshold the slope appears to be independent of the growth parameter. Observations show for inter-cloud lightning the threshold frequency is 50 kHz, with zero slope for f \u3c fthreshold and -1.6 slope for f \u3e fthreshold

Modeling of pv module and dc/dc converter assembly for the analysis of induced transient response due to nearby lightning strike

Photovoltaic (PV) systems are subject to nearby lightning strikes that can contribute to extremely high induced overvoltage transients. Recently, the authors introduced a 3D semi-analytical method to study the electromagnetic transients caused by these strikes in a PV module. In the present paper we develop an improved model of the PV module that: (a) takes into account high-frequency effects by modelling capacitive and inductive couplings; (b) considers the electrical insulation characteristics of the module; (c) includes the connection to a DC/DC converter. The whole process involves three major steps, i.e., the magnetic-field computation, the evaluation of both common-mode-and differential-mode-induced voltages across the PV module, and the use of the calculated voltages as input to a lumped equivalent circuit of the PV module connected to the DC/DC converter. In such a framework, the influence of the PV operating condition on the resulting electrical stresses is assessed; moreover, the relevance or insignificance of some parameters, such as the module insulation or the frame material, is demonstrated. Finally, results show that the induced overvoltage are highly dependent both on the grounding of the conducting parts and on the external conditions such as lightning current waveforms and lightning channel (LC) geometry

Modeling of pv module and dc/dc converter assembly for the analysis of induced transient response due to nearby lightning strike

Photovoltaic (PV) systems are subject to nearby lightning strikes that can contribute to extremely high induced overvoltage transients. Recently, the authors introduced a 3D semi-analytical method to study the electromagnetic transients caused by these strikes in a PV module. In the present paper we develop an improved model of the PV module that: (a) takes into account high-frequency effects by modelling capacitive and inductive couplings; (b) considers the electrical insulation characteristics of the module; (c) includes the connection to a DC/DC converter. The whole process involves three major steps, i.e., the magnetic-field computation, the evaluation of both common-mode-and differential-mode-induced voltages across the PV module, and the use of the calculated voltages as input to a lumped equivalent circuit of the PV module connected to the DC/DC converter. In such a framework, the influence of the PV operating condition on the resulting electrical stresses is assessed; moreover, the relevance or insignificance of some parameters, such as the module insulation or the frame material, is demonstrated. Finally, results show that the induced overvoltage are highly dependent both on the grounding of the conducting parts and on the external conditions such as lightning current waveforms and lightning channel (LC) geometry

The influence of ground conductivity on the structure of RF radiation from return strokes

The combination of the finite conductivity of the Earth plus the propagation of the return stroke current up the channel which results in an apparent time delay between the fast field changes and RF radiation for distant observers is shown. The time delay predicted from model return strokes is on the order of 20 micro and the received signal has the characteristics of the data observed in Virginia and Florida. A piecewise linear model for the return stroke channel and a transmission line model for current propagation on each segment was used. Radiation from each segment is calculated over a flat Earth with finite conductivity using asymptotics approximations for the Sommerfeld integrals. The radiation at the observer is processed by a model AM radio receiver. The output voltage was calculated for several frequencies between HF-UHF assuming a system bandwidth (300 kHz) characteristic of the system used to collect data in Florida and Virginia. Comparison with the theoretical fast field changes indicates a time delay of 20 microns

Lightning Return-Stroke Current Waveforms Aloft, from Measured Field Change, Current, and Channel Geometry

Three-dimensional reconstructions of six rocket-triggered lightning channels are derived from stereo photographs. These reconstructed channels are used to infer the behavior of the current in return strokes above the ground from current waveforms measured at the channel base and electric-field-change waveforms measured at a range of 5.2 kilometers for 24 return strokes in these channels. Streak photographs of 14 of the same strokes are analyzed to determine the rise times, propagation speeds, and amplitudes of relative light intensity for comparison with the electrical inferences. Results include the following: 1) The fine structure of the field-change waveforms that were radiated by these subsequent return strokes can be explained, in large part, by channel geometry. 2) The average 10 - 90% rise time of the stroke current increased by about a factor of seven in our sample, from an observed 0.31 plus or minus 0.17 microseconds at the surface to an inferred 2.2 plus or minus 0.5 microcseconds at 1 kilometer path length above the surface. 3) The three-dimensional propagation speed of the current front averaged 1.80 plus or minus 0.24 X 10(exp 8) meters per second over channel lengths typically greater than 1 kilometer. 4) Assuming that the measured current was entirely due to the return stroke forced an unreasonably large and abrupt reduction in inferred current amplitude over the first few tens of meters above the surface, especially in cases when the leader was bright relative to its stroke. Therefore, a significant fraction of the current at the surface was probably due to the leader, at least in such cases. 5) Peak return-stroke currents decreased by approximately 37 plus or minus 12% from 100 meters to 1 kilometer of path length above the surface. Because of uncertainty about how to partition the measured current between leader and return stroke, we are unable to infer the variation of current amplitude near the ground

Lightning Induced Overvoltages Caused by Non-Vertical Lightning and Earth Current Behavior

RÉSUMÉ Les surtensions induites par la foudre deviennent un sujet important dans le domaine des réseaux de distribution. Une évaluation précise des tensions induites est très essentielle pour la protection contre la foudre. Un problème des évaluations existantes est qu'un canal de foudre vertical et une terre parfaitement conductrice, qui ne sont pas réalistes, sont supposés dans la plupart des cas. Ces hypothèses nécessitent des recherches plus approfondies pour une évaluation précise de la tension induite. L'objectif principal de cette thèse est de révéler et résumer (1) les influences de la foudre non verticale sur les surtensions induites par la foudre dans les réseaux de distribution et (2) le comportement du courant de foudre dans une terre avec pertes, pour une évaluation précise des tensions induites. Pour (1), les circuits du modèle FDTD pour représenter la foudre non verticale sont construits et les influences de la foudre non verticale sur les tensions induites sont étudiées avec diverses conditions telles que la forme d'onde du courant de foudre, la géométrie du canal de foudre, l'état de la terre et la distribution ligne, etc. De plus, le mécanisme des changements est discuté en comparaison avec une formule analytique. Il est clair que l'inclinaison de la foudre vers la ligne augmente considérablement les tensions induites. Les tensions atteignent plus de deux fois plus que celles du boîtier vertical. L'inclinaison le long de la ligne ne montre que des différences mineures sur la tension de crête alors qu'elle rend le profil de tension le long de la ligne asymétrique. Des tendances similaires sont observées même lorsque l'on suppose une ligne triphasée réaliste avec mises à la terre et parafoudres. Les connaissances acquises dans cette thèse indiquent clairement que les influences de la foudre non verticale doivent être prises en compte pour une évaluation précise des surtensions induites par la foudre. Pour (2), les circuits du modèle FDTD sont validés par rapport aux résultats expérimentaux dans des articles publiés, et les influences de la distance de la foudre, de la position de la foudre sur la ligne, de la structure de mise à la terre, de la position du fil neutre, etc. sont étudiées par la FDTD. Il est confirmé que le couplage électromagnétique foudre-terre influence le courant de surface de la terre et l'augmentation du potentiel de terre (GPR) qui en résulte pendant une période transitoire, et donc l'inclinaison de la foudre rend le courant et le GPR différents du cas vertical.----------ABSTRACT Lightning induced overvoltages are becoming one of the most important topics in the field of distribution networks. An accurate evaluation of the induced voltages is essential for the design of lightning protection. One problem of existing evaluations is that a vertical lightning channel and a perfectly conducting earth, which are not realistic, are assumed in most cases. These assumptions require further careful investigations for an accurate induced-voltage evaluation. The main objective of this thesis is to reveal and summarize (1) the influences of non-vertical lightning on the lightning induced overvoltages in the distribution systems and (2) lightning current behavior in a lossy earth, for an accurate evaluation of the induced voltages. For (1), FDTD model circuits to represent the non-vertical lightning are built and influences of the non-vertical lightning on the induced voltages are investigated with various conditions such as lightning current waveform, lightning-channel geometry, earth condition, and distribution-line configuration etc. In addition, the mechanism of the changes is discussed in comparison with an analytical formula. It is made clear that lightning inclination toward the line significantly increases the induced voltages. The voltages reach values that are more than two times larger than those of the vertical case. The inclination along the line shows only minor differences on the peak voltage while it makes the voltage profile along the line asymmetric. Similar trends are observed even when a realistic three-phase line with groundings and arresters is assumed. The knowledge obtained in this thesis clearly indicates that the influences of non-vertical lightning should be considered for an accurate evaluation of lightning induced overvoltages. For (2), FDTD model circuits are validated in comparison with experimental results in published papers, and influences of lightning distance, lightning-struck position to the line, grounding structure, neutral wire position etc. are investigated by FDTD. It is confirmed that lightning-to-earth electromagnetic coupling influences the earth surface current and resulting ground potential rise (GPR) in a transient period, and thus the lightning inclination makes the current and GPR different from the vertical case. The coupling effect should be considered for accurate earth current and GPR studies. When there is a distribution line nearby, a large portion of lightning current flows into the nearby line via its groundings. Although the current itself does not make a large difference to the induced voltage, it would cause lightning surge problems in the line