Frequency Dependence Of Soil Parameters Research Articles

Comparison of Different Approaches for Incorporating Frequency Dependence of Soil Parameters in Time Domain Simulation of Grounding System

Comparison of Different Approaches for Incorporating Frequency Dependence of Soil Parameters in Time Domain Simulation of Grounding System

FDTD-based computational model applied to assess the influence of the frequency dependence of soil parameters on the lightning response of grounding electrodes for typical parameters of first and subsequent return stroke currents

This paper considers an evaluation of the influence of the frequency-dependence of soil parameters on the lightning response of horizontal grounding electrodes by means of the finite-difference time domain (FDTD) electromagnetic model. The FDTD simulations assumed the soil modeled as a multipole Debye medium and the response of grounding electrodes due to lightning return stroke currents with typical front time parameters of negative first and subsequent strokes was assessed. The results in terms of the ground potential rise (GPR) and grounding impulse impedance (ZP), were compared to those provided by the application of the Hybrid Electromagnetic Model (HEM), a frequency domain model widely applied for lightning related problems, and revealed the top quality of the modeled approach in FDTD. The largest percentage variations of the calculated impulse impedance compared to HEM were around 6 % and 10 % for first and subsequent stroke currents, respectively.

New Approaches to Represent the Frequency Dependence of Soil Parameters on the Time-Domain Hybrid Electromagnetic Model (HEM-TD)

New Approaches to Represent the Frequency Dependence of Soil Parameters on the Time-Domain Hybrid Electromagnetic Model (HEM-TD)

Evaluation of the transmission tower and frequency-dependent soil parameters influence on the grounding potential rise waveforms

In this paper, the influence of the transmission tower and the frequency-dependent soil parameters on the grounding potential rise (GPR) waveform is evaluated. This evaluation is performed using a physically consistent electromagnetic model that determines the transient behavior of the grounding system submitted by lightning, together with the Alternative Transients Program for the representation of aerial elements (tower, phase cables and shield wires). This model was developed in the frequency domain and, in this way, allows the inclusion of frequency-dependence of soil electrical parameters. In this sense, three formulations of the dependence in question are considered, widely disseminated in the literature, and determined through systematic measurement processes. The results illustrate that the concomitant inclusion of the tower and the frequency-dependence substantially modifies the GPR waveforms, when compared with those in which isolated grounding is considered, especially for soils with high resistivity values and for first return strokes. This is of most importance when evaluating personal safety criteria in the transmission tower vicinity. In these situations, the GPR waveforms should be determined by considering the presence of the tower and not only with the isolated grounding, since the transient step and touch voltages are directly associated with GPR.

The Impact of Transmission Line Modeling on Lightning Overvoltage

In most of the work that investigates the backflashover phenomenon due to direct lightning strikes, using EMT-type simulators, transmission lines are represented by the J. Marti model and the ground effect is computed employing J. R. Carson’s formulations. Thus, the ground displacement current is neglected, the line voltage definition corresponds to the wire potential formulation, and soil resistivity is considered frequency-independent. These considerations can lead to erroneous measurements of the occurrences of the backflashover phenomenon in the insulator strings of transmission line. In this sense, this paper presents a systematic sensitivity analysis study of lightning overvoltage in insulator strings considering more physically consistent models of the transmission line, which consider the displacement current, ground admittance correction, rigorous voltage definition, and frequency-dependent soil parameters. According to the results, for the case study, transmission line parameters modeling can present a maximum percentual difference of around 71.54%, considering the frequency range of first strokes. This difference leads to a percent difference of around 5.25% in the maximum overvoltage across the insulator strings. These differences confirm that the occurrence or not of backflashover in the insulator strings, including the disruption time, are sensitive to the line model considered.

Experimental analysis of horizontal grounding wires buried in high-resistivity soils subjected to impulse currents

• Experimental response of grounding wires in high-resistivity soils is presented. • Grounding impulse impedance is lower than resistance for higher resistivities. • Experiments show relevant influence of frequency dependence of soil parameters. • Influence of increasing the front-time on impedance depends on electrode length. This paper presents experimental results of the ground potential rise (GPR) developed by grounding wires buried in high-resistivity soils and subjected to impulse currents. A large experimental dataset is presented, comprising grounding wire lengths ranging from 10 m to 50 m, buried in soils of resistivities between around 1100 Ωm to 1600 Ωm, and subjected to impulse currents with front-time ranging from around 1.2 μs to 7 μs. The experimental results further confirmed some important aspects regarding the lightning response of grounding electrodes buried in high-resistivity soils, namely the influence of the frequency dependence of soil parameters and the value of impulse impedance lower than the grounding resistance for electrodes shorter than effective length. Comparison between experimental and simulated results reinforces the need to consider the frequency-dependence of soil parameters for obtaining accurate results of the lightning response of grounding systems buried in poor conducting soils.

Influence of a lossy ground on the lightning performance of overhead transmission lines

• Accurate lossy ground representation impacts lightning overvoltages simulation. • Carson's classic formulation may lead to inaccuracies for high-resistivity soils. • Accurate lossy ground representation in simulations leads to higher TLs outage rate. • An increase up to 15% in TL outages was found when ground is accurately represented. This paper investigates the impact of incorporating both displacement currents and frequency-dependent soil parameters in the calculation of the ground-return impedance for the determination of the backflashover rate of 138 kV and 230 kV overhead transmission lines due to direct lightning strikes. This is done by considering the Sunde's formulation for calculating the ground-return impedance, which is incorporated in a time-domain simulator using an alternative implementation of Marti's transmission line model. The obtained results show that the peak of the lightning overvoltages computed considering Sunde's formula, along with frequency-dependent soil parameters, leads to higher amplitudes in comparison with those simulated using the classical Carson's formula, which neglects the frequency dependence of soil parameters and assumes conductive currents in the soil much larger than displacement currents. This effect is more pronounced in high-resistivity soils and leads to an increase in the line backflashover rate within 4-6%, 7-12% and 9-15% for 1000 Ωm, 5000 Ωm and 10000 Ωm soils, respectively, considering 138 kV and 230 kV lines, and assuming a typical median first stroke lightning current. Analyses performed with slow and fast first stroke currents confirm the trend of increase of the backflashover rate with the consideration of Sunde's formula.

An Electrostatic Approach for Simulation of Grounding Systems Lightning Response in Time Domain

Most of the literatures dealing with time domain simulation of grounding system response to lightning surges use an electrostatic approach. In this approach frequency dependence of soil electrical parameters and plane-wave propagation constant are not included. In this paper, based on Hybrid Electromagnetic Method and simplification of it, a new method is developed to include frequency dependent parameters of soil in time domain simulation. Since only one convolution is used, the simulation time is significantly reduced. The consistency of the developed formulation while the plane-wave propagation constant is ignored is investigated through comparisons with experimental results and precise frequency domain approaches. Simulations results show ignoring both effects simultaneously can lead to high levels of error (140%), whereas the error significantly reduces when frequency dependence of soil parameters is considered. The developed model exhibits errors of about 2% to 25% compared to the results of models that take into account both effects. However, simulation results showed all these errors to be conservative. Due to neglecting propagation constant, the model is more suitable for lightning studies of grounding system with short length.

Assessment of Frequency-Dependent Parameters of Stratified Soils for Lightning Response of Earth Electrodes

Typically, the frequency dependence of soil parameters is predicted by models or formulas that assume a uniform soil, although it usually presents a stratified structure. This work develops analytical expressions that allow to evaluating of the errors associated with the uniform soil hypothesis, in comparison with the hypothesis of a two-layered soil, taking as reference a field methodology for measuring the variation of soil parameters with frequency. The results suggest that in the case of a stratified soil, the frequency dependence of its parameters can be considered individually for each layer.

Evaluation of the lightning performance of grounding electrodes using FDTD-based computational model: Influence of absorbing boundary conditions and representation of the frequency-dependence of soil parameters

• Lightning response of grounding electrodes is assessed using FDTD. • The effect of absorbing boundary conditions is shown. • Liao's 3rd order and CPML lead to results better than those of Liao's 2nd order. • Modeling the soil as a Debye medium leads to results closer to those of HEM model. • 6 poles are enough to represent the frequency-dependence of soil parameters. This work evaluates the influence of the absorbing boundary conditions (ABC) and the representation of frequency-dependent soil parameters on the assessment of the lightning performance of grounding electrodes using FDTD-based computational model. The results in terms of grounding potential rise (GPR), grounding impulse impedance (Z P ), and low-frequency grounding resistance (R LF ) showed a better agreement with those calculated by the HEM model when Liao's 3rd order and Convolutional perfect matched layer (CPML) boundary conditions were assumed. The increase of the simulation space contributed to improve the results related to Liao's 2nd order but demanding a longer computation time. Despite the observed improvement, they are still far from those provided by the other ABC. Modeling the soil as a Debye medium to consider frequency-dependent soil parameters leaded to lightning response of grounding electrodes very close to that provided by the HEM model. In terms of Z P , the largest percentage difference was about 6%. Also, the work indicated that the adoption of 6 poles identified by the MATLAB function invfreqs was enough to represent the frequency-dependence of soil parameters, contributing to decrease the computation time.

Implementation of Radiation and Soil Losses in VFTO Simulation by Frequency-Domain TL Model

Transmission line (TL) models are widely used within the simulation of the very fast transient over-voltages (VFTO) for gas-insulated substations (GISs); however, due to quasi-TEM approximation and model complexity, energy losses related to bushing radiation and frequency-dependent soil parameters are either not available or simply neglected, limiting the simulation accuracy of TL models. In this study, a new frequency-domain TL model is proposed, enabling the model to consider the influences of both radiation and soil losses in a VFTO simulation. Derived from the radiation power of a line antenna model, the radiation resistance of a “lossy” TL is put forward as an equivalent of the radiation loss for GIS bushing. For the soil loss, the Sunde approximation formula and the L-S soil dispersion expression are involved, and the parameters of the overhead busbar are also analyzed. The model gets validation by the measured VFTO generated at a full-scale 1100 kV GIS testing circuit. By considering radiation loss to suppress high-frequency response and soil loss to improve low-frequency response accuracy, the calculated and measured waveforms have the best consistency, which may greatly help assess the risk of insulation breakdown and the level of very fast transient disturbance in GISs.

Improving Grounding System for Oil Tanks Using Finite Element Method, Taking into Account the Frequency Dependence of Soil Parameters

This work was devoted to the development of a simulation model of the grounding and lightning protection system for oil tanks, taking into account the frequency dependence of soil parameters, where we, based on the equations mentioned in previous studies, designed a grounding model for an oil tank taking into account the frequency dependence of soil parameters by using the finite elements method. and for different configurations, where it was observed that the grounding potential rise GPR was significantly reduced at high frequencies, especially in the case of high soil resistivity, the percentage of decrease in the grounding potential rise in the case of dry soil for the studied site 1266.65 Ω.m and for wet soil 596.27 Ω.m, respectively, 22.8% and 23.8%, respectively. and it was pointed out the necessity of conducting soil resistivity measurements before the tank construction process, and the need to use the network configuration of the oil tank grounding model in some cases where the soil resistivity is high and it is difficult to eliminate the effect of lightning current with the typical design mentioned in NFPA 780 for tank grounding.

Computation of Lightning-Induced Voltages Considering Ground Impedance of Multi-Conductor Line for Lossy Dispersive Soil

Soil conductivity and permittivity have a substantial influence on lightning-electromagnetic transients in power system. In this paper, lightning-induced voltages are computed on a multi-conductor overhead line due to nearby first and subsequent return strokes. Besides, this study considers the longitudinal complex inductance of the line due to the penetration depth of electromagnetic fields through finitely conducting ground as well as the frequency dependent soil parameters using the finite-difference time-domain method. Various case studies in light of variations of return stroke velocity, line height, and soil conductivity are explored for thoughtful investigations. The obtained results reveal that the influence of this complex inductance on peak values of lightning induced voltages changes with varying the return stroke velocity. Also, the frequency dependence of soil parameters markedly impacts the computed lightning-induced voltages particularly for poor soil conductivity.

Transmission Line Dynamic Circuit Model for Effective Length of Ground Electrode Under Lightning Transients

The effective length of the ground electrode is one of the primary research interests of lightning grounding system design. In this article, using a practical numerical analysis, a new expression for estimating the effective length of the simple ground electrode is proposed. A new dynamic circuit model based on the transmission line is developed to derive the expression. The model considers the soil ionization, frequency-dependent soil parameters, mutual reactance, and skin effect. Several rigorous impulse test simulations are performed on different electrode lengths, soil properties, and lightning currents to estimate the effective length of ground electrode numerically. A new expression is arrived at using the curve-fitting and optimization technique from the relationships of the effective length with soil resistivity, impulse rise time, and current. The proposed dynamic model and the expression to obtain the effective length are validated by published results.

Implementation of Modal Domain Transmission Line Models in the ATP Software

Electromagnetic Transients Program make extensive use of transmission line models for the simulation of electromagnetic transients. This paper proposes a circuit representation of the modal transformation, more specifically Clarke’s matrix. The arrangement of ideal transformers we propose allows modal transformation to be directly implemented in software such as Alternative Transient Program - Electromagnetic Transients Program. We combined the proposed circuit with single-phase transmission line models that consider frequency independent and frequency dependent parameters to represent transposed three-phase transmission lines. The main advantage of the proposed approach is that it allows the implementation of new transmission line models without depending on models provided in applications. To show this capability, we included the frequency dependence of soil parameters in the simulations. Results show that the proposed model is accurate both in the frequency domain and in the time domain.

Global optimization algorithms for particle swarm optimization to the derivation of horizontal multilayered soil models considering the frequency dependence of soil parameters

AbstractThe frequency dependence of soil parameters has been confirmed by many experiments. Most of them are done by the measurement of soil sample in laboratories. Although some studies are based on field measurement, only homogeneous ground or two‐layer model are considered. The study of frequency dependence of soil parameters with considering multilayered model is lacking. The frequency dependence of the horizontally multilayered soil model is studied by the inversion of soil parameters in the frequency domain. The inversion of frequency domain soil parameters is translated into an optimization problem. The model parameters are determined by spectral induced polarization data, and particle swarm optimization is applied to optimizing model parameters. The performances of three different methods to trap particles inside boundaries are compared. In order to improve the computational efficiency of the inversion program, parallel computing is combined with particle swarm optimization to solve the optimization problem. The execution time of the developed algorithm before and after the application of parallel computing is compared. The performances of other two optimization algorithms, simulated annealing and genetic algorithm, are compared with that of particle swarm optimization. So it would be more clear which optimization algorithm should be selected among these three commonly used algorithms when dealing with the inversion problem of soil parameters. The accuracy of the proposed method is verified by a numerical simulation experiment. Then, this method is applied to interpreting field data, and the frequency dependence of soil parameters can be observed from the inversion results.

Computation of ground potential rise and grounding impedance of simple arrangement of electrodes buried in frequency-dependent stratified soil

Grounding electrodes are used to provide a low-impedance dissipation path for the excess lightning or fault currents. Several studies have been dedicated to the computation of the grounding impedance of different electrode arrangements considering either the frequency dependence of soil parameters (resistivity ρ and relative permittivity εr) or the multi-layer nature of soil. This paper aims at the calculation of the grounding impedance and the ground potential rise (GPR) of simple electrode arrangements (vertical and cross electrodes) due to the injection of first and subsequent lightning currents in various configurations of soil, considering a frequency-dependent stratified soil.A frequency-domain full-wave electromagnetic solver based on the Method of Moment (MoM) that employs a stratified medium Green’s function is used to compute the grounding impedance in a frequency range of 100Hz to 10MHz. The transient GPRs are computed using the equivalent circuit of the grounding system, obtained through the application of the Vector Fitting (VF) technique and recursive convolution method.The simulation results show that considering the frequency dependence of the soil parameters has no effect on the low-frequency grounding impedance up to ≈10kHz. However, the frequency dependence of soil parameters leads to a considerable variation of the grounding impedance at higher frequencies especially for soils of higher resistivity. Furthermore, it is shown that considering the layers of soil has a more significant impact on the GPR of the vertical electrode than that of the cross electrode.

Bare versus insulated conductors for improving the lightning response of interconnected wind turbine grounding systems

This paper investigates the lightning response of a pair of interconnected wind turbine grounding systems assuming their connection to be performed by a bare or insulated underground conductor. Typical first and subsequent stroke current waveforms are injected at one of the grounding systems and the transient response is studied for different soil resistivities considering frequency-dependent soil parameters. The ground potential rise (GPR) at the current injection point and the voltages transferred to the adjacent grounding system are calculated. GPR peak reductions are obtained using either a bare or insulated conductor, but the former is more effective. It is shown that when the wind turbine grounding systems are interconnected by a bare conductor, the GPR peak reduction is essentially due to the interconnecting wire. On the other hand, when the interconnection is made through an insulated conductor, the GPR reduction is related to the current that is partly diverted to the adjacent tower, especially for high resistivity soils. For an insulated interconnecting conductor and first lightning return-stroke currents, the adjacent grounding system also contributes to the GPR peak decrease.

Extension of Vance's closed-form approximation to calculate the ground admittance of multiconductor underground cable systems

In this paper, Vance's closed-form approximation for the ground admittance of a single underground cable is extended to represent three-phase underground cable systems. The proposed methodology considers Sunde's expression for the ground-return impedance calculation. The accuracy of the proposed extension is investigated taking as reference the generalized formulas of Xue et al. considering frequency-dependent soil parameters according to the Alipio-Visacro model. It is shown that the agreement between the approximate and generalized formulations is improved as the frequency increases. More importantly, it is shown that both methodologies lead to transient waveforms in good agreement for different types of excitation, different values of soil resistivity, and usual underground cable system configurations.

Ground Potential Rise in Wind Farms due to Direct Lightning

This paper investigates the ground potential rise (GPR) developed in wind farms subject to direct lightning currents representative of first and subsequent negative downward strokes and return strokes associated with upward negative flashes. The wind farm grounding system is studied considering different numbers of interconnected grounding systems and for distinct values of soil resistivity taking into account frequency-dependent soil parameters. A wideband multiport model of the wind farm grounding system is obtained and implemented in a time-domain electromagnetic transient tool to include the aerial elements in simulations, namely the wind turbine blades and tower. It is shown that interconnecting more wind turbine grounding systems in parallel leads to a significant reduction of the low-frequency grounding resistance, whereas the decrease of the impulse impedance is much lower, especially for low-resistivity soils and negative downward subsequent strokes or negative upward lightning return strokes. It is also shown that the presence of the aerial components significantly affects the GPR in the response to lightning currents representative of negative downward subsequent strokes and return strokes associated with negative upward flashes, which have higher frequency content compared to negative first return strokes. The presence of the aerial components increases the GPR peak.