Transmission Line Return Stroke Model Research Articles

On the use of lumped sources in a nonlinear lightning return stroke model and extension for evaluating strikes to tall objects

The use of lumped current and voltage sources is investigated in a nonlinear return stroke model that includes the dependence of the channel per‐unit‐length resistance on the lightning current and the variation of the channel impedance with height. First, considering the case of lightning strikes to flat ground, it is shown that equivalent channel currents can be obtained regardless of the lumped source type (current or voltage) connected at the channel base. This equivalency is obtained provided the effect of current reflections coming from the upper part of the channel is taken into account in the derivation of the voltage source waveform, which is made according to a procedure proposed by the authors. The nonlinear return stroke model is then extended for evaluating lightning strikes to tall grounded objects. Two different possibilities are considered for selecting the channel impedances in this case. In one approach, the impedance of each channel segment is calculated by considering its total height to ground whereas in the other approach the distance from each channel segment to the excitation point at the tower top is considered. It is shown that currents calculated along a lossy channel are nearly independent of the considered approach, whereas differences of about 10% are expected in the peak values of currents calculated along a 102‐m‐high object. Also, regardless of the selected approach, relatively small errors are observed in the evaluation of the total charge transferred to ground, which is convenient for allowing a consistent comparison between lightning strikes to flat ground and lightning strikes to grounded objects of different heights. Finally, comparisons with results obtained with the transmission line return stroke model show that the nonlinear interaction between the channel resistance and the lightning current has a moderate effect on the predicted tower currents, as opposed to the channel currents, which are greatly affected by such interaction.

Analytical formulation of lightning-induced voltages on multiconductor overhead lines above lossy ground

This paper presents analytical expressions for calculation of lightning-induced voltages (LIV) on multiconductor overhead lines above lossy ground. The transmission-line return-stroke model is used and the propagation effect on the electromagnetic field is approximated by the surface impedance method. Assuming a linear return-stroke current, the standard numerical integrations along the lightning channel and the overhead line are avoided, and the result is a fast and stable formulation that contains only a single convolution integral. The described method applies for distances between 100 m and 10 km and is valid the first few microseconds where the maximum LIV usually occurs. A simplified approach to how to include overhead line losses is also outlined. A model is proposed that can be included in the electromagnetic transients program ATP-EMTP for calculation of LIV in larger and practical systems.

Characteristics of the radiation fields from lightning in Sri Lanka in the tropics

Characteristics of the radiation fields from (1) stepped leader, (2) return strokes, and (3) cloud flashes in the tropics are presented. The separation between the successive leader pulses immediately preceding the return strokes are distributed over the range of 4–40 μs with a mean value of 12 μs. The ratio of the amplitude of the last leader pulse to that of the return stroke is log‐normally distributed with mean and standard deviation of 0.1 and 0.03, respectively. A correlation between the amplitude of the last leader pulse and the return stroke radiation field peak is observed. Consequences of this correlation are interpreted using the transmission line return stroke model. The initial peak of the return stroke radiation field is followed by several subsequent peaks. The time intervals between the successive peaks and their amplitudes are studied and compared with those observed in Florida. The zero crossing time of the first stroke radiation fields are distributed over the range of 40–160 μs, with a mean and standard deviation of 95 μs and 30 μs, respectively. The corresponding values for the subsequent strokes are 15–75 μs, 42 μs, and 14 μs, respectively. The separation between the subsequent strokes are distributed log normally with a mean and standard deviation of 91 ms and 62 ms, respectively. The average number of strokes per flash is 3.2. Characteristics of a particular type of radiation field pulses from cloud flashes are presented. Initial polarity of these pulses is opposite to that of the return strokes. The amplitudes of these pulses are about 0.2–0.5 of the return stroke amplitudes. Total duration of these pulses is about 70 μs, with initial half‐cycle duration of about 10 μs.

Correlated electric and magnetic fields from lightning return strokes

The first broad band (1 kHz to 5 mHz) correlated measurements of electric and magnetic fields from close lightning return strokes are presented. Sample wave forms are shown for the distance range 2-200 km. The transmission line return stroke model is used to find a typical current wave shape and return stroke velocity from the experimental data, and theoretical curves are given of electric and magnetic field as a function of time for 1, 5, 10, and 100 km by using this typical current and velocity.

Currents in Florida lightning return strokes

The transmission line return stroke model is used to derive individual current versus time wave forms from measured electric fields. A total of 98 strokes in 21 flashes at distances less than or equal to 10 km and 63 strokes in 18 flashes at distances between 10 and 32 km are analyzed for current wave shape and magnitude. For the closer strokes, return stroke velocity is also determined from the electric field wave forms. Eighteen detailed current and field wave forms and a statistical distribution of peak currents are presented. Return stroke channel currents are found to exhibit a sharp initial peak which currents measured in tall structures at the base of the lightning channel apparently do not exhibit. A complete discussion of errors is given.

Electric field intensity of the lightning return stroke

From an examination of about 1000 electric field wave forms produced by lightning return strokes in 16 storms at distances between 20 and 100 km from an observation site at the Kennedy Space Center, Florida, a typical return stroke current wave form is derived. For this current wave form, the electric field intensity at distances between 0.5 and 100 km is computed for three values of return stroke velocity. The resultant curves for close lightning are compared with measured field wave forms. The transmission line return stroke model is used in all calculations since, as discussed, the Bruce-Golde model cannot account for the observed electric field characteristics.