Rafael Alipio

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.

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.

Modeling the Frequency Dependence of Electrical Parameters of Soil

An original semitheoretical causal model was developed to describe the frequency dependence of electrical parameters of soil in the representative frequency range of lightning currents. The expressions of such model, based simply on the measured low-frequency soil resistivity, can be promptly applied to general soils in practical problems. The model allows the user to adopt different levels of conservativeness to take the dispersion of the frequency dependence of soil and eventual uncertainties into account. The comparison of experimental results and those provided by this model denoted its consistency.

Impulse Efficiency of Grounding Electrodes: Effect of Frequency-Dependent Soil Parameters

The effect of frequency-dependent soil resistivity and permittivity on the lightning response of electrodes subjected to representative currents of first and subsequent strokes was analyzed. Expressions for expediting the estimate of the impulse impedance, effective length, and impulse coefficient from the measured low-frequency resistance and soil resistivity that take this frequency dependence into account were proposed for some electrode arrangements of practical interest. The estimates were shown to be consistent with the results simulated using an elaborate model and with experimental results.

Lightning-Induced Voltages Over Lossy Ground: The Effect of Frequency Dependence of Electrical Parameters of Soil

The impact of the frequency dependence of soil resistivity and permittivity on lightning overvoltages induced on overhead lines over lossy ground is investigated. The Visacro-Alipio expressions were implemented on the hybrid electromagnetic model to take this effect into account. Systematic simulations were performed considering representative current waveforms of first and subsequent strokes and different stroke locations near the simulated overhead line. In general, the results indicated that this effect is responsible for a reduction of the induced overvoltage. This reduction increases with increasing soil resistivity and becomes relevant for soil resistivity above 1000 Ω·m.

Transient response of grounding electrodes for the frequency-dependence of soil parameters

This study evaluates the response of a horizontal grounding electrode against impulsive currents whose waveforms and time front is typical of lightning. The electrode is found buried in soil with different resistivity values and whose conductivity and permittivity vary with spectrum frequency of lightning according four formulations exists in literature. It was possible to observe the intense propagation effects responsible for the grounding impedance values significantly different from the resistance at low frequency and also difference according to each formulation, which has decreased the potential, the impedance impulsive and impulsive coefficient compared to traditional data from the technical literature specialist.

How the frequency dependence of soil parameters affects 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, considering low- and high-resistivity soils. 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 for high-resistivity soils and typical currents of subsequent strokes.

Voltage Distribution Along Earth Grounding Grids Subjected to Lightning Currents

This paper applies a rigorous electromagnetic model to determine the transient distribution of potentials along a substation earth grounding grid subjected to lightning currents. The obtained results show that, in the initial period of the transient, equipment pieces that are earth grounded at distinct points of the grid and are electrically linked (for example, by aerial communication cables) experience impulsive loop currents. Such loop currents can cause equipment malfunctions, failures, and damage. A remarkable conclusion of this paper is that such loop currents can reach substantial values even in the case of soils of low resistivity. Some practical aspects are highlighted in order to reduce the risks due to the nonuniform distribution of potentials along earth grounding.

The response grounding electrodes to lightning currents: the effect of frequency-dependent resistivity and permittivity of soil

A methodology to find the variation of soil resistivity ρ and permittivity ϵ in field conditions at the typical range of lightning-current frequencies was proposed and applied in low- and high-resistivity soils. Considering this variation in simulations using the hybrid electromagnetic model HEM was able to practically match results of theoretical and experimental voltage waves developed in response to the impression of impulsive currents with lightning-pattern waveforms to horizontal grounding electrodes buried in the analyzed soils, different from the results obtained with the conventional approach of constant values for ρ and ϵ.