Akihiro Ametani

A generalized formulation of earth-return impedance and admittance for overhead lines above a multi-layer earth is derived. An equivalent homogeneous earth method (EHEM) and a Method of Moments - Surface Admittance Operator (MoM-SO) method with modified earth-return Green function considering an N -layer earth are also proposed. The frequency responses of wave propagation characteristics are evaluated by the newly proposed formulas and compared to those found from existing formulas in software used for the simulation of electromagnetic transients. Transient simulations performed in an electromagnetic transient (EMT) type simulation tool are also presented. It is shown that the proposed generalized formulas, the EHEM and the modified MoM-SO method, are in agreement, validating and verifying the results found in this paper.

This article proposes modified formulas of Carson's and approximate earth-return impedances for overhead lines which can deal with high-frequency displacement currents. The calculated results by the proposed methodology are compared with those calculated by accurate formulas, and a satisfactory accuracy of the proposed methodology is confirmed. The proposed formulas are applied to very-fast transients (VFTs) in a gas-insulated substation, and it is made clear that the proposed formulas with the earth-return admittance cause no numerical instability of electro-magnetic transient (EMT) program simulation, while the original Carson's formula and its approximate one implemented in existing EMT-type programs result in the numerical instability. EMT simulation of VFTs can be easily performed using the proposed simple formulas with the earth-return admittance.

The characteristics of external electromagnetic fields (EEMFs) produced by underground cables in the lossy earth are further investigated and studied. This paper develops an excitation current in the cables with the bi-directional propagation for the calculations of the vectors of EEMFs. By adopting the newly proposed method in this paper, it allows the considerations of the terminating conditions and the lengths of the cable on the calculations of the vectors of EEMFs. Moreover, the vectors of EEMFs are calculated, compared and discussed using various load/source impedances. The effects of lengths of underground cables on the vectors of EEMFs are studied. Also, the frequency-dependent earth models are included into the investigations of the EEMFs. The results presented in this paper are compared and verified with the Numerical Electromagnetics Code.

This paper describes the background of Electromagnetic Transients Program (EMTP) and reviews original EMTP development at Bonneville Power Administration of the US Department of Energy starting from 1966 to 1984. Then, the paper briefly explains the development and present situation of four EMTPs, that is, ATP‐EMTP, EMTP‐RV (now EMTP®), EMTDC/PSCAD and XTAP. In addition, the line/cable parameters and the modeling methods prepared in EMTPs are described, and related problems are explained. Finally, the recent trend and future of electromagnetic transient simulations are discussed. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

In this article, lightning-induced overvoltages due to inclined lightning are investigated by a finite-difference time-domain (FDTD) method for distribution lines of a single conductor and a multiphase line (three-phase conductors with a shield wire, utility poles, groundings, and arresters). The FDTD model is validated in comparison with results of circuit-theory-based analytical and numerical calculation methods. In the single conductor line, the influences of inclined lightning on the induced voltage waveform, peak voltage, and voltage profile along the line are investigated with several combinations of lightning distances, earth resistivities, and lightning current waveforms. The induced voltage is significantly influenced by the lightning inclination toward the line (angle θ). The increased ratio of the peak voltage by the angle θ becomes larger with lower earth resistivity and shorter rise time of the lightning current. While the inclination along the line (angle ϕ) makes only minor differences on the peak voltage, the voltage profile along the line becomes asymmetric. In the multiphase line, the influence of the angle θ on the voltage becomes similar to that in the single conductor line. These results clearly indicate that the lightning inclination should be considered for an accurate evaluation of lightning-induced voltages.

A generalized formulation of electromagnetic fields generated from a multi-phase underground cable is proposed based on a complete solution of Maxwell equations. The lateral electromagnetic field components, the shielding effect of cables and the phase currents at high frequencies of a three phase underground cable are evaluated by the newly derived formulas. The accuracies of the recently developed extended transmission line approach of underground cables are investigated based on the performance of electromagnetic field components. It is also shown that Numerical Electromagnetics Code verifies the results calculated from the new formulas presented in this paper.

“© 20xx IEEE.Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.” DOI: 10.1109/TPWRD.2020.3003250 When a lightning strikes the top of a transmission line tower or shield wires, electromagnetic waves propagate through the tower back and forth, increasing the voltage across insulator strings. ‡is can eventually lead to a back-flƒashover (BF), which may cause damage to equipment or costly power outages. To calculate the over-voltages and predict the probability of a BF, an accurate model of the tower and its grounding system is needed in electromagnetic transient (EMT) type simulators. ‡There are a number of theoretical models for the equivalent circuit of a transmission tower. However, they either are not accurate enough or they are derived for a certain type of transmission tower, which limits their applicability. Numerical electromagnetic analyses have less simplifications compared to the theoretical solutions and are by far less expensive than field measurements. They also have the flexibility to analyze any type of tower. In this paper, the direct method for the measurement of tower impedance is implemented by NEC4 and applied to a 400-kV double circuit tower with all its details. Th‡e process of obtaining the wire network of the tower used in this paper is completely automated and it can be applied to any other type of transmission tower. Th‡e results of the numerical simulations are compared to those obtained with existing tower models. Th‡e developed model in this paper is capable of considering all the details of the tower and including the \eurofinite resistance of the ground and grounding electrodes.

When lightning strikes a transmission line tower or shield wires, electromagnetic waves propagate through the tower back and forth, increasing the voltage across insulator strings. To calculate the over-voltages, an accurate model of the tower and its grounding system is needed in electromagnetic transient (EMT) type simulators. There are a number of theoretical models for the equivalent circuit of a tower. However, they either are not accurate enough or they are derived for a certain type of transmission tower, which limits their applicability. Numerical electromagnetic analyses have less simplifications compared to the theoretical solutions and are less expensive than field measurements. In this paper, the direct method for the measurement of tower impedance is implemented by NEC4 and applied to a 400-kV double circuit tower. The process of obtaining the wire network of the tower used in this paper is completely automated and it can be applied to any other type of transmission tower. The results of the numerical simulations are compared to those obtained with existing tower models. The developed model is capable of considering all the details of the tower and including the finite resistance of the ground and grounding electrodes.

This article discusses formulas for the surge/characteristic impedance of vertical conductors. Calculated results of the surge impedance are compared with measured results on vertical conductors and transmission towers. The accuracy of the available time-domain formulas is not satisfactory except for Hara's formulas, while the frequency-domain formulas show satisfactory accuracy. A two-stair model representing a nonuniform transmission tower is investigated based on ABCD parameters, and an approximate characteristic impedance of the nonuniform tower is derived. The circuit-theory approach and finite-difference time-domain (FDTD) computed results using the two-stair model are shown to give better agreement with measured results on UHV and 500-kV towers than those obtained using a single-conductor approximation (uniform line). The FDTD computed results clearly show the position-dependence of line parameters. Existing time-domain formulas describe only the surge impedance seen from the tower top or from the tower base, and thus, are not applicable to a lightning shielding failure studies involving back-flashover, which require the knowledge of the surge impedances of the upper, middle, and lower parts of the tower.

This article investigates the transient characteristics of earth currents and grounding potential rises (GPRs) produced by lightning strikes directly to the earth and to a vertical conductor with a grounding electrode. Influences of the earth depth and the distance from the lightning channel are discussed based on a field test and finite-difference time-domain (FDTD) computed results. The validity of the FDTD is confirmed in comparison with the field test results. Based on the FDTD results, a large portion of the lightning current is observed to flow along the earth surface during a transient period. The current density is roughly proportional to 1/r2 (r: distance from the lightning base) for the lightning to the earth surface, and 1/Lr for the lightning to a vertical conductor with a grounding electrode of length L. The GPR shows similar characteristics. Electromagnetic field radiated from the lightning to the earth contributes to the peak of the earth-surface current, and it becomes dominant when r is larger than 10 m. The pole grounding of a distribution line nearby the lightning absorbs a portion of the lightning current and, thus, the current density becomes larger toward the distribution pole.