Taku Noda

Thin wire representation in finite difference time domain surge simulation

Simulation of very fast surge phenomena in a three-dimensional structure requires a method based on Maxwells equations such as the finite difference time domain (FDTD) method or the method of moments (MoM), because circuit-equation-based methods cannot handle the phenomena. This paper presents a method of thin wire representation for the FDTD method that is suitable for the three-dimensional surge simulation. The thin wire representation is indispensable to simulate electromagnetic surges on wires or steel flames of which the radius is smaller than a discretized space step used in the FDTD simulation. Comparisons between calculated and laboratory-test results are presented to show the accuracy of the proposed thin wire representation, and the development of a general surge analysis program based on the FDTD method is also described in the present paper.

Identification of a multiphase network equivalent for electromagnetic transient calculations using partitioned frequency response

This paper presents an algorithm for identifying a multiphase network equivalent for electromagnetic (EM) transient calculations. Conventional rational fitting methods intrinsically get into ill condition because the s/sup n/ terms in the rational function take a wide range of values which cannot be accurately treated within machine arithmetic accuracy. The proposed algorithm averts the ill conditioning by partitioning the given frequency response into sections along the frequency axis. Rational fitting is applied to each section of the frequency response to identify the poles, and then the corresponding residue matrices are obtained by a standard least-squares procedure using the entire frequency response. Adaptive weighting, column scaling, and iteration step adjustment are utilized to facilitate the rational fitting. The proposed identification algorithm is applied to obtain a reduced-order equivalent of a 500-kV power network, and the equivalent is used in a switching transient simulation to demonstrate its performance.

Dynamic System Equivalents: A Survey of Available Techniques

This paper presents a brief review of techniques available for reducing large systems to smaller equivalents. The paper is divided into High Frequency Equivalents, Low Frequency Equivalents, and Wide-band Equivalents.

Accurate modeling of core-type distribution transformers for electromagnetic transient studies

This paper proposes a model of core-type distribution transformers for electromagnetic transient studies. The model accurately reproduces not only the impedance characteristics seen from each terminal of a core-type distribution transformer but also the surge-transfer characteristics between the primary and secondary sides in a wide range of frequency. Because of this capability, the proposed model enables the accurate evaluation of overvoltages on distribution lines including consumer-side overvoltages. A 10 kVA transformer is modeled, and transient-simulation results agree well with laboratory-test ones.

Numerical Integration by the 2-Stage Diagonally Implicit Runge-Kutta Method for Electromagnetic Transient Simulations

This paper proposes applying the 2-Stage Diagonally Implicit Runge-Kutta (2S-DIRK) method of numerical integration to the calculation of electromagnetic transients (EMTs) in a power system. The accuracy and the numerical stability of 2S-DIRK are almost the same as those of the trapezoidal method, while 2S-DIRK does not produce sustained numerical oscillation due to a sudden change of an inductor current or a capacitor voltage unlike the trapezoidal method. Firstly, this paper reviews the 2S-DIRK integration scheme and derives the 2S-DIRK formulas of inductors and capacitors for both linear and nonlinear cases. Then, analytical comparisons of 2S-DIRK with the trapezoidal, backward Euler, and Gear-Shichman methods are carried out, and numerical examples which verify the analytical comparisons are shown. Finally, 2S-DIRK is compared with CDA (Critical Damping Adjustment) implemented in EMTP (Electro-Magnetic Transients Program) for some simulation cases.

Three-Dimensional FDTD Calculation of Lightning-Induced Voltages on a Multiphase Distribution Line With the Lightning Arresters and an Overhead Shielding Wire

To suppress the lightning-induced voltages on a distribution line, lightning arresters and/or overhead shielding wire can be installed, and the effectiveness of these countermeasures are usually studied by simulations. Traditionally, field-to-transmission line coupling techniques based on the distributed-parameter circuit theory are used for the calculation of the lightning-induced voltages. Recently, the finite-difference time-domain (FDTD) method that directly and numerically solves Maxwells equations was applied to the calculation of the lightning-induced voltages. Compared with the conventional methods, the FDTD-based calculation is advantageous in terms of the modeling of inhomogeneous ground parameters, 3-D structures, and grounding systems. But, in the previous works, the distribution line was simulated simply by a single-phase line. Moreover, the representation of lightning arresters in the FDTD method was not yet established. This paper proposes a technique to incorporate the lightning arresters in the FDTD-based lightning overvoltage calculations. In this technique, the voltage-current relationships of the lightning arresters are represented by piecewise linear curves, which can be obtained directly from the data sheets or measured results. For validation purpose, the lightning-induced voltages on a three-phase distribution line equipped with the lightning arresters and a multipoint-grounded overhead shielding wire are calculated by the proposed method, and the results are compared with those obtained by the conventional method and a very good agreement is found.

A Numerical Simulation of Transient Electromagnetic Fields for Obtaining the Step Response of a Transmission Tower Using the FDTD Method

This letter presents a numerical simulation of transient electromagnetic fields using the finite-difference time-domain (FDTD) method for obtaining the step response of a 500-kV transmission tower. The purpose of this simulation is to reproduce the result of a field test which has been carried out for obtaining the step response of the tower as fundamental data for lightning overvoltage studies. From the comparison between the calculated and measured results, the accuracy of the FDTD method, when applied to lightning overvoltage studies, is examined. The simulation carried out in this letter takes into account the following items that have been ignored or oversimplified in the existing simulations. One is the resistivity of the ground soil, and the other is the detailed structures of the arms, the lattice elements, and the foundations. The calculated result obtained closely reproduces the field-test result.

A Time-Domain Harmonic Power-Flow Algorithm for Obtaining Nonsinusoidal Steady-State Solutions

Steady-state simulation plays a vital role in power system analysis and design. Over the past 25 plus years, various steady-state methods have been proposed. Most of these methods only deal with how to obtain steady-state waveforms of a system in an efficient manner. Only a few of them also take power-flow constraints into account. The majority of these “power-flow” methods are implemented in the frequency domain, which inevitably suffers from harmonic truncation errors. Moreover, the problem of model incompatibility will rise when they are used for the steady-state initialization of a time-domain electromagnetic transient (EMT) program. This paper presents a harmonic power-flow method, which is implemented entirely in the time domain. The proposed method essentially extends a time-domain steady-state method, called “shooting method” to include the power-flow constraints and to account for aggregate loads in the power-flow calculations.

Entirely harmonic domain calculation of multiphase nonsinusoidal steady state

This paper proposes an algorithm for obtaining the periodic steady-state solution of a multiphase network including nonlinear, switching, and frequency dependent elements. Unlike existing methods which deal with nonlinear and switching elements in the time domain, the approach presented is entirely in the harmonic domain. The method will be used for the harmonic analysis of power systems and for steady-state initialization in electromagnetic transient analysis. The algorithm takes rigorously into account the inter-harmonic couplings in the Jacobian matrix of the proposed Newton-Raphson iteration process so that a quadratic convergence rate is achieved. Linear, nonlinear, switching, and frequency dependent elements are modeled in a modular approach, and any network topology can be handled by extending the Modified Nodal Equations approach to the harmonic domain case. First the algorithm is described and then applied to a test case to demonstrate its computational performance.

A double logarithmic approximation of Carson's ground-return impedance

This paper proposes a simple closed-form formula of the ground-return impedance of horizontal parallel wires above a lossy ground plane. It is derived by a double logarithmic approximation of the integral term with a semi-infinite interval in Carsons ground-return impedance formula. The proposed double logarithmic approximation gives better accuracy compared to a similar approximation proposed by Pizarro and Eriksson, and this is achieved by an advanced optimization technique used for determining the coefficients in the double logarithmic approximation and also by incorporating an additional variable which minimizes errors. In this paper, it is shown, using practical examples, that the derived formula gives more accurate results compared with other existing approximate formulas. It is also shown that a graphical interpretation of the double logarithmic approximation is to replace a homogeneous lossy ground with a pair of perfectly conducting return planes located at different complex depths.