Silverio Visacro

HEM: a model for simulation of lightning-related engineering problems

This paper presents the assumptions and formulation of a hybrid electromagnetic model, developed for general application in numerical solutions of lightning current-related problems. Results provided by this model show very good agreement with experimental data for the transient response of a transmission-line tower to impulsive currents.

A Comprehensive Approach to the Grounding Response to Lightning Currents

This paper is intended to present a comprehensive and objective approach to the behavior of grounding electrodes when subjected to lightning currents

Frequency Dependence of Soil Parameters: Experimental Results, Predicting Formula and Influence on the Lightning Response of Grounding Electrodes

An experimental methodology was applied to determine the frequency dependence of the soil resistivity and permittivity under field conditions. A large number of soils of low-frequency resistivity ranging from 50 to 9100 .m were tested and showed strong variation of both parameters in the Hz frequency interval. Simplified expressions were proposed to predict this frequency dependence. The response of grounding electrodes subjected to lightning currents was simulated using an electromagnetic model under the assumption of variation of soil parameters given by such expressions and obtained from measurements. The results were very similar, though quite different from those obtained under the assumption of constant values for soil resistivity and permittivity.

The Response of Grounding Electrodes to Lightning Currents: The Effect of Frequency-Dependent Soil Resistivity and Permittivity

A methodology is proposed and applied to determine the variation of soil resistivity and permittivity in the typical range of lightning current frequency components. The response of horizontal electrodes buried in high- and low-resistivity soils subjected to currents with lightning waveform patterns was measured and also simulated, taking this variation into account. The waves of the simulated and measured grounding potential rise are nearly the same but are quite different from the simulated waves considering the conventional assumption of constant values for soil resistivity and permittivity.

Analytical Representation of Single- and Double-Peaked Lightning Current Waveforms

An analytical representation for first and subsequent stroke currents is proposed, and simple application examples are given. The waveforms are able to reproduce the characteristic concave profile at the front of first stroke currents, including or not a second peak that is usually observed in the data available from direct measurements on actual lightning. They also reproduce, with good accuracy, median parameters describing lightning currents measured at short instrumented towers. The proposed waveforms have the advantage of using a sum of Heidler functions that last over the entire time of analysis. This avoids the use of separate functions to characterize the front and the tail of the synthesized currents and makes the proposed waveforms suitable for lightning computational analysis.

Frequency Dependence of Soil Parameters: Effect on the Lightning Response of Grounding Electrodes

Quantities related to the response of grounding electrodes subject to lightning currents are simulated under the assumption of constant and frequency-dependent soil resistivity and permittivity for 100-4000 Ω·m soils, using an accurate electromagnetic model. It was found that the frequency dependence of soil parameters is responsible for decreasing the grounding potential rise of electrodes and, thus, their impulse impedance and their impulse coefficient. This effect is more pronounced with increasing soil resistivity and for typical currents of subsequent strokes. The reduction of these quantities is negligible for soils of 300 Ω·m and below. It is considerable for soils above 500 Ω·m and is very significant above 1000 Ω·m. Reductions of around 23%, 30%, 40%, and 52% are found, respectively, for soils of 600, 1000, 2000, and 4000 Ω·m and typical subsequent stroke currents. Lower values, around 8%, 11%, 18%, and 28%, are found for first stroke currents.

Response of Grounding Electrodes to Impulsive Currents: An Experimental Evaluation

Experimental results for the transient behavior of grounding electrodes are presented to clarify fundamental aspects of the grounding response to lightning currents. It is shown that for fast current waves, the value of impulsive grounding impedance ZP of short electrodes is smaller than its low-frequency resistance R LF while electrodes longer than the effective length have a resistance value smaller than impulsive impedance. The values found for the ratio ZP/R LF in the experiments are lower than those resulting from numerical simulation for electrodes shorter than the effective length.

Revision, extension, and validation of Jordan's formula to calculate the surge impedance of vertical conductors

Jordans formula to calculate the surge impedance of vertical conductors is revised and extended to take into account systems with multiple conductors. Experimental data and the hybrid electromagnetic model are applied in order to validate the derived expressions. Additionally, Jordans formula is successfully used in the representation of an actual tower as a multiconductor vertical system. The obtained results indicate the usefulness of the derived expressions if an engineering analysis of direct strikes over elevated strike objects is required

Calculation of Lightning-Induced Voltages on Overhead Distribution Lines Including Insulation Breakdown

This paper investigates the influence of considering actual insulation volt-time curves both in the calculation of lightning-induced voltages and in the estimation of the number of flashovers an overhead wire may experience per year due to nearby lightning strokes. The flashover mechanism is modeled according with the integration method, which is used as a reference for comparisons with the simplified 1.5 CFO flashover criterion traditionally used in the estimation of the lightning performance of overhead distribution lines. Sensitivity analysis show the dependence of flashovers on the shape and front time of the assumed channel-base current. The obtained results suggest that the simplified 1.5 CFO flashover criterion is likely to underestimate the number of flashovers an overhead line may experience per year due to nearby lightning strokes. This result is confirmed by statistical analyses considering a Monte Carlo-based approach. It is also shown that more realistic flashover rate estimates can be obtained in the statistical analysis of lightning-induced voltages provided a reduced threshold level (1.2 CFO in the particular case evaluated in this paper) is considered instead of the 1.5 CFO level traditionally used in this type of study.

Evaluation of Lightning-Induced Voltages Over a Lossy Ground by the Hybrid Electromagnetic Model

In this paper, the hybrid electromagnetic model is applied to calculate lightning-induced voltages over a lossy ground. Results provided by this model are compared with experimental data obtained from a reduced-scale model and with results simulated by the numerical electromagnetics code. Good agreement is achieved in all cases.