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This paper quantifies and discusses the increase in induced voltage on a sheath due to changes in duct banks in terms of type and dimensions along an underground transmission line, guaranteeing the ampacity required for a project. The four most common duct banks in double-circuit underground transmission lines with phase transposition were considered in this study, along with two special cross-bonding techniques: continuous cross-bonding (CCB) and sectionalized cross-bonding (SCB). These techniques aim to reduce sheath currents and enhance the distribution of the induced voltage on the sheath. The analysis considers two distinct scenarios in which the profile of the induced voltage is calculated: the first one accounts for underground obstructions, intersections with important traffic avenues, and ground with high excavation costs that force changes in the duct bank dimensions and configuration, which is the most exact and realistic case. The second one solely considers one typical configuration of a duct bank along the route. This last scenario is normally applied to calculate the induced voltage when an underground transmission design is required. The results show that when installing cables at a greater depth, it is imperative to increase the distance between them to guarantee the ampacity. The induced voltage on the sheath will rise as the distance increases. Furthermore, the results reveal that instead of calculating the induced voltage by considering the scenario that is exact and most like a real case, it is enough to calculate following the second scenario and then add a scaling factor according to each duct bank configuration.

Adequate soil modeling is fundamental to assessing the grounding impedance of the grounding system and the transient responses in power systems. This paper aims to investigate three soil models with electrical parameters varying with frequency and water content, namely Smith-Longmire, Scott, and Messier models, and their impact on the ground potential rise (GPR) waveforms of vertical grounding rods. Besides that, the transient induced voltages across the string of insulators induced are also investigated for lightning currents representative first, and subsequent return strokes are employed. The harmonic grounding impedance (HGI) is calculated for rods of 3, 15, and 30 m buried in frequency-dependent (FD) soil model using commercial electromagnetic software (FEKO) with the Method of Moments (MoM) for a range of 100 Hz to 10 MHz. Simulation results show a significant modification of the calculated HGI beyond a particular frequency. The induced transient GPR waveforms show a notable reduction in their voltage peaks when the FD soil model is compared with those computed using the frequency-independent (FI) soil model. Finally, a backflashover analysis is carried out that demonstrates its dependence on the rod length, water content, and the specific soil model employed.

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.

This work presents a transmission line model for simulating electromagnetic transients directly in the time domain. For this purpose, the exact equivalent $\pi $ -circuit is used, which represents the line taking into account its distributed and frequency-dependent parameters. The admittances that constitute the exact equivalent $\pi $ -circuit are approximated by rational functions using the vector fitting technique. Then, for each admittance, an electrical circuit is synthesized, consisting of an association of discrete elements (resistors, inductors, and capacitors) aiming at modeling the transmission line, thus allowing its use in any circuit simulation software and the eventual connection of nonlinear elements. From the simulation results, it is reasonable to state that the proposed model is a feasible representation, which aggregates the same features of the exact equivalent $\pi $ -circuit directly in the time domain, not only in steady state, but mainly during transients and also without the need for using convolutions, as well as inverse Laplace or Fourier transforms.

Several approaches to calculate the ground-return impedance and admittance matrices are proposed in the literature. Carson’s approach assumes a lossy ground modeled by frequency-independent conductivity where displacement currents and non-perfectly conducting ground effects are neglected. However, Nakagawa’s approach considers both characteristics and also the frequency-dependent (FD) soil electrical parameters that can be incorporated into his formulations. This paper investigates the influence of Nakagawa’s approach and Carson’s approach on the transient responses using the ATP tool. First, the performances of the Bode’s method and Vector Fitting (VF) technique for approximating the characteristic impedance $\boldsymbol {Z}_{\text {c}}$ ( $s$ ) and propagation $\boldsymbol {H}$ ( $s$ ) are also investigated for the JMarti’s line model. Then, lightning-induced voltages (LIVs) developed for a lightning striking at the shield wire of an overhead transmission line (OHTL) on a high-resistive FD soil are investigated. Results demonstrated a much higher accuracy using the VF for approximating $\boldsymbol {Z}_{\text {c}}$ ( $s$ ) and $\boldsymbol {H}$ ( $s$ ) than Bode’s method. Transient voltages on the OHTL calculated with Nakagawa’s approach showed notable differences compared to those obtained with Carson’s approach. The voltage peaks are reduced when Nakagawa’s approach is utilized, especially when transmission lines are located on high-resistive soils.

This paper presents a novel three-phase transmission line model for electromagnetic transient simulations that are executed directly within the time domain. This model relies on distributed and frequency-dependent parameters, as well as employs modal transformation for its implementation. The single-phase model of the exact equivalent π-circuit is utilized for each propagation mode. This model combines discrete components, such as resistors, inductors, and capacitors, to accurately emulate the transmission line behavior via linear circuit elements. This model can be seamlessly integrated into various electrical circuit simulation software, thus allowing easy utilization and incorporating time-varying elements to analyze transmission lines. The JMarti model, which comes by default in the Alternative Transient Program, and the numerical Laplace transform method implemented in MATLAB were utilized to validate the proposed solution across various scenarios. An advantage of this model is its independence from the prior calculation of travel time and its exemption from convolutions, inverse Laplace transforms, and Fourier transforms, thus streamlining the simulation process.

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.

This paper proposes an alternative multiconductor transmission line model that combines the folded line equivalent with the modal transformation. The folded line equivalent decomposes the nodal admittance matrix of a transmission line into its open-circuit and short-circuit contributions. These contributions are fitted to rational functions, which are associated with Norton equivalent circuits based on their state space models. The proposed model uses an orthogonal matrix to transform voltages and currents from the phase domain to the folded line equivalent domain and vice versa. Because the transformation matrix is orthogonal, we represent it using ideal transformers in simulation software. First, we use a circuit representation of Clarke’s matrix to decompose a transmission line into its modes. Then, each mode is decomposed into its open-circuit and short-circuit contributions using a circuit implementation of the proposed matrix. The proposed approach can accurately represent short lines in simulations with time steps equal to or greater than the propagation time of the transmission line. We compare the results obtained with the proposed approach to those obtained with power systems computer-aided design/electromagnetic transients including the DC universal line model.

This article investigates the influence of four causal frequency-dependent (FD) soil models and their impact on the responses of a multiphase overhead transmission line (OHTL) with ground wires, generated by a lightning strike. The FD models proposed by Longmire-Smith (LS), Messier (M), Portela (P) and Alípio-Visacro (AV) are considered. The ground-return impedance and admittance matrices are computed with the Nagakawa approach for both frequency-constant and FD soil models. The frequency-domain modal voltages and time-domain transient voltages are assessed in this work. Modal decomposition technique is used to study the attenuation constant, propagation velocity and voltages for each propagation mode. Simulations are carried out in a frequency range of 100 Hz to 10 MHz, for OHTLs with lengths of 1 and 10 km, on soils of 700 and 4000 Ω·m. Simulation results demonstrated that the Portela (P) model has resulted in more significant variation in the ground-return impedance and admittance, constant attenuation and propagation velocity in which a pronounced variation, especially at the high frequencies, is seen. On the other hand, Longmire-Smith (LS) and Messier (M) have produced similar results in both frequency and time domains. Additionally, the Alípio-Visacro (AV) model has produced intermediate responses, being the model recommended by CIGRÈ WG C4.33. Time-domain induced voltage waveforms obtained with the Portela (P) model has shown pronounced differences, especially at the peak values, for the high-resistive soil. This study demonstrates the importance of considering the FD soil models to assess the transient responses adequately, especially when OHTLs are on high-resistive soils.

This paper evaluates the influence of frequency-dependent soil conductivity and permittivity in the transient responses of single- and double-circuit transmission lines including the ground wires subjected to lightning strikes. We use Nakagawa’s approach to compute the ground-return impedance and admittance matrices where the frequency-dependent soil is modeled using Alípio and Visacro’s model. We compare some elements of these matrices with those calculated by Carson’s approach which assumes the frequency constant. Results show that a significant difference can be obtained in high resistive soils for these elements in impedance and admittance matrices. Then, we compute the transient responses for single- and double-circuit lines with ground wires located above soils of 500, 1000, 5000, and 10,000 Ω·m considering the frequency constant and frequency-dependent parameters generated for two lightning strikes (subsequent stroke and Gaussian pulse). We demonstrate that the inclusion of frequency dependence of soil results in an expressive reduction of approximately 26.15% and 42.75% in the generated voltage peaks in single- and double-circuit lines located above a high-resistive soil. These results show the impact of the frequency-dependent soils that must be considered for a precise transient analysis in power systems.