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

Assessment of induced voltages in common and differential‐mode for a PV module due to nearby lightning strikes

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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