Naoto Nagaoka

Phase domain modeling of frequency-dependent transmission lines by means of an ARMA model

This paper presents a method for time-domain transient calculation in which frequency-dependent transmission lines and cables are modeled in the phase domain rather than in the modal domain. This avoids convolution due to the modal transformation, and possible numerical instability due to mode crossing. In the new approach, time domain convolutions are replaced by an ARMA (auto-regressive moving average) model that minimizes computation and is EMTP-compatible. A fast and stable method to produce the ARMA model is developed, and results are shown to agree well with both rigorous frequency-domain simulations and also field tests.

Modeling of thin wires in a lossy medium for FDTD simulations

An equivalent radius of a thin wire in a lossy medium, represented by the finite-difference time-domain method, is derived using the concept that was proposed to derive an equivalent radius of a thin wire in air. Then, a simple technique to specify an arbitrary radius of a thin wire in a lossy medium is proposed. The proposed technique does not employ locally fine or nonuniform subgrids, but is based on an orthogonal and uniform-spacing Cartesian grid. The validity of the proposed technique is investigated in a transient state, as well as in a quasisteady state, and shown to be satisfactory.

A development of a generalized frequency-domain transient program-FTP

The frequency-domain transient program (FTP) is based on a frequency-time transform method using nodal analysis, admittance parameters, and modal theories. Discontinuous and nonlinear elements are solved as initial condition problems using a piecewise linear approximation. The FTP is used to solve for the transient and steady states of a network composed of an arbitrary interconnection of basic circuit elements. The FTP is structured to be compatible with the Electromagnetic Transients Program (EMTP), so that the same input data and output formats can be used. The present version of the FTP can deal with a network with over a hundred nodes and branches. Comparisons of calculated results obtained with the FTP with results of field tests and calculations by the EMTP confirm the high accuracy and satisfactory efficiency of the FTP. The FTP offers the most accurate or theoretically exact solutions of transients on distributed-parameter lines. >

FDTD Simulation of a Horizontal Grounding Electrode and Modeling of its Equivalent Circuit

Transient responses of a horizontal grounding electrode in three different arrangements of a current lead wire and a voltage reference wire are calculated using the finite-difference time-domain (FDTD) method for solving Maxwells equations. The test arrangement does not significantly influence the transient response of the horizontal grounding electrode. The transient response calculated using the electromagnetic transients program (EMTP) for Sundes equivalent circuit agrees reasonably well with the corresponding response calculated using the FDTD method, except for the initial rising portion of the voltage at the close end (to the excitation point) of the horizontal grounding electrode. The EMTP-calculated response for an equivalent circuit, modified to improve this discrepancy, agrees better with the corresponding FDTD-calculated response

Transient Calculations on Crossbonded Cables

The present paper describes accurate and approximate methods of calculating transients on a crossbonded cable. Calculated results are compared with field test results, and the accuracy of the calculation, which has never been discussed in the previous publications, is proved. It is characteristic to a crossbonded cable that the sheath overvoltage is much greater than that on a noncrossbonded cable. This overvoltage is due to the reflection of a traveling-wave from the crossbonded points. The approximate method of a calculation shows satisfactory results with much smaller computation time in comparison with the accurate method if the number of crossbonding is large.

An Improved Thin Wire Representation for FDTD Computations

We have shown that finite-difference time-domain (FDTD) electromagnetic computations for a conductor system having a radius smaller than 0.15Deltar or larger than 0.65 Deltar (Deltar is the lateral side length of cells employed), modeled using arbitrary-radius-wire representations proposed so far with a time increment determined from the upper limit of Courants stability condition, result in numerical instability. A primary factor causing this numerical instability is that the speed of waves propagating in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light, and therefore, Courants condition is not satisfied there. It is further shown that for these cases, the arbitrary-radius-wire representation can be improved by modifying the material parameters for the axial field components closest to the wire as well as those for the radial electric and circulating magnetic field components. The improved wire representation is effective in representing a wire whose radius ranges from 0.0001Deltar to 0.9Deltar.

Semiconducting Layer impedance and its effect on cable wave-propagation and transient Characteristics

This paper has derived an impedance formula for conductors semiconducting layer based on a conventional circuit theory. The formula is confirmed to be identical to an accurate one derived by solving Maxwells equation. A wave-propagation characteristic and a transient voltage on a cable having the semiconducting layer on the conductors surface are evaluated by applying the derived formula, and are compared with those on a cable with no semiconducting layer. The semiconducting layer increases the conductor impedance, and thus, the attenuation constant is increased, and the propagation velocity and the characteristic impedance are decreased for a coaxial mode by the semiconducting layer, but the inter-phase mode of propagation is not affected. A transient voltage is attenuated more and its oscillating period becomes greater than those on a cable with no semiconducting layer. The effect of the semiconducting layer impedance on the wave-propagation characteristic and the transient voltage is rather minor when the layer thickness is small and the resistivity is high, and the semiconducting layer effect is dominated by its admittance.

Further improvements to a phase-domain ARMA line model in terms of convolution, steady-state initialization, and stability

This paper presents further improvements to a phase-domain ARMA (auto-regressive moving average) line model that is implemented in the ATP version of EMTP. According to the improvement to convolution, each ARMA model, which reproduces the phase-domain frequency dependence of a transmission line, uses its own economical time step considering the frequency characteristic. Linear interpolation is used to allow a different time step for each ARMA model, and this new convolution strategy makes transient calculations more efficient. A steady-state initialization method of the line model is developed, and fault-surge calculations requiring the initialization are demonstrated. Convenient stability criteria of the line model are also presented.

A Simplified Model of Corona Discharge on Overhead Wire for FDTD Computations

A simplified model of corona discharge on overhead wire has been proposed for propagating surge computations using the finite-difference time-domain method. The radial progression of corona streamers from the wire is represented as the radial expansion of cylindrical conducting region whose conductivity is several tens of microsiemens per meter. Two wire radii are considered: 5 and 2 mm, in order to simulate two experimental con- figurations by Noda. The critical electric field on the surface of a 5-mm radius wire for corona initiation is set to E0 = 1.8 or 2.9 MV/m. For a 2-mm radius wire, it is set to E0 = 2.2 MV/m. The critical background electric field necessary for streamer propagation is set to Ecp = 0.5 MV/m for positive voltage application, and Ecn = 1.5 MV/m for negative voltage application. The computed waveform of radial current (including both conduction and displacement currents) agrees well with the corresponding measured waveform. Also, the computed relation between the total charge (charge residing on the wire and emanated corona charge) and applied voltage (qV curve) agrees well with the corresponding measured one, except for relatively low applied voltages. Additionally, the increase of coupling between the energized wire and another one nearby due to corona discharge is well reproduced.

Application of the Partial Element Equivalent Circuit Method to Analysis of Transient Potential Rises in Grounding Systems

This paper presents calculations of lightning transient potential rises in grounding systems. A partial element equivalent circuit (PEEC) method, adopting a modified image method, is employed in this paper. The modified image method in this paper has two options either including or neglecting images of conduction currents along conductors for calculating series impedances. The effect of retardation in the PEEC method is also investigated. Comparisons of simulation results by the proposed method with those by the method of moments, the finite-difference time-domain method, and experimental results collected from the literature show that the PEEC method with the modified image method is quite effective in the evaluation of transient potential rise in a grounding system.