External Circuit Equations Research Articles

A generalized external circuit model for electrostatic particle-in-cell simulations

A fully self-consistent second order accuracy model for coupling a generalized external circuit and a one-dimensional bounded electrode-driven plasma was proposed in this paper. The plasma was embedded in the circuit as a non-linear element with a potential difference. Based on Kirchhoff's voltage law and the definition of current, the problem of solving the generalized external circuit was transformed into an initial value problem of a set of first-order ordinary differential equations which can be discretized numerically by the second-order backward differential formula. The charge conservation equation at the electrode plate was coupled to the above equation, and the voltage, current, and surface charge density at the next moment were solved by a differential equation solver. Dirichlet boundary conditions of Poisson's equation were obtained through the surface charge density σ0 of the generalized external circuit equation and the plasma density ρ of the Particle-in-Cell (PIC) model. The spatial distribution of plasma potential was solved by using the second-order central difference scheme. The obtained potential at the electrode plate can be used as the Robin boundary condition of the system of generalized external circuit equations. In this model, the loose coupling between the generalized external circuit and plasma was realized by the boundary condition, and the system was fully self-consistent based on the charge conservation law and energy conservation law. We simulated the capacitively coupled plasmas (CCP) under different external circuits as the example and verified the performance of the model. This model can be used to study the influence of different external circuit structures and parameters on plasma discharge, and can be used for any plasma sources driven by electrodes, like CCP, some vacuum electronic devices, and Z-Pinches.

Stator Shape Design Method for Improving Power Density in PM Motor

In this paper, we propose a stator shape design method for improving power density in a small permanent magnet motor. In order to calculate iron loss correctly, we analyze a motor by using 2-D finite element method (FEM) in which an E&S model is introduced. Moreover, external circuit equations are solved coupled with equations in electromagnetic field by FEM to calculate copper loss correctly. It is possible to calculate power density correctly by evaluating loss and weight of a motor correctly whether stator shape is changed. As a result, we show that our analysis technique is useful as a shape design method of a motor’s stator for improving power density.

Generation of VUV radiation in Lyman and Werner bands of pulsed space discharge in hydrogen mixtures with helium

A self-consistent numerical model for the self-sustained high-current pulsed discharge is constructed based on the solution of the equations of the population of H2 electronic and vibrational states. The model accounts for electronic, ion-molecular, and vibrational kinetics, electron attachment to and detachment from the H2 molecule, Lyman and Werner band emission, and their radiation trapping. The equations of electron-vibrational kinetics are solved simultaneously with the Boltzmann equation for the electron energy distribution function and the external electrical circuit equations.

Analysis of internal winding short circuit faults in power transformers using transient finite element method coupling with external circuit equations

SUMMARYInterturn short circuit faults are the leading cause of power transformer failures. If not quickly detected, these faults usually develop into more serious faults, which would result in irreversible damage to the transformer, unexpected outages, and consequential costs. The aim of this research is to obtain a better understanding of the physical behavior of the power transformers in the presence of interturn faults as well as to discover the best indicators for detection of interturn short circuit faults. To this end, a time stepping finite element model of power transformer has been developed to analyze the transient behavior of a real power transformer when the transformer is working under winding short circuit fault conditions. The transient model, coupled with external circuit equations, allows us to simulate the dynamic behavior of the transformer with the real power supply and external loads connections. The FEM computations show the ability of the electromagnetic flux inside the transformer, transformer terminal currents, and circulating current in the shorted turns as useful monitoring parameters for transformer fault detection. Copyright © 2013 John Wiley & Sons, Ltd.

３次元ＶＭＳＷ法を用いた希土類永久磁石の残留磁化分布の評価

This paper presents results obtained from a numerical simulation of the magnetizing Nd-Fe-B magnets by using the three-dimensional Variable Magnetization and Stoner-Wohlfarth (VMSW) method combined with the finite element method (FEM) and external circuit equations. The initial magnetization curves of rare-earth permanent magnets measured with a magnetizer were used in the simulation. The calculated results were compared with the measured results to verify the numerical method of the simulating magnetizing process.

Modeling and Characterization of Transformers Internal Faults Using Finite Element and Discrete Wavelet Transforms

This paper investigates the behavior of three phase transformers with internal faults under sinusoidal and nonsinusoidal operating conditions. The terminal behavior of the transformer was investigated by coupling the finite element transformer's physical model with external electric circuit equations. Two types of internal faults were modeled turn-to-ground faults, and turn-to-turn faults with and without arcing. A discrete wavelet transforms (DWT) procedure was then used to extract the feature of the transformer fault currents. The key advantages of the DWT are its ability to provide a local representation of the current signal for normal and faulty modes, as well as its applicability to handle nonstationary fault signals. This characterization gives us an efficient way to design and evaluate detection algorithms for transformers internal faults and the system they operate in

Finite element analysis of a single-phase grid-connected induction generator with the Steinmetz connection

The Steinmetz connection enables a three-phase induction generator (IG) to operate satisfactorily on a single-phase grid by using only a capacitance phase converter. This paper presents a finite element analysis of this mode of IG operation. A time-stepping, two-dimensional (2-D) finite element method (FEM) is employed in the solver, with the external circuit equations coupled to the set of simultaneous equations formulated with the nodal magnetic vector potentials as the variables. A detailed rotor circuit model that accounts for the current density distribution as well as the end-ring parameters is also presented. Generator performance computed using FEM is compared with that computed using the method of symmetrical components and that obtained experimentally on a small induction machine. The results indicate that FEM gives an accurate prediction of the line current and the output power of the IG.

Transient analysis of superconducting generator under the three phases of sudden grounding fault condition

This paper presents 2-D transient analysis of 30 kV A superconducting AC generator (SCG) using the finite element method (FEM). The compensated 2-D model obtained by lengthening the airgap of the original 2-D model is proposed for the efficient transient analysis. The performance of SCG is analyzed by taking into account the rotation, external circuit equations, and eddy current effect of the damper. The eddy current losses occurring in the dampers are analyzed during the transient state under the three phases of sudden grounding fault condition in the armature. Moving line technique is introduced to carry out the dynamic FEM analysis efficiently without remesh of the total elements.

Two-dimensional electrical modeling of asymmetric radio-frequency discharges for geometry effect analysis. Comparison with experiments

A self-consistent two-dimensional particle model coupled to the external circuit equations was developed in an asymmetrical configuration for the self-bias voltage calculation and the reactor design study. An intermediate modeling was performed in one and two symmetrical geometries. The one-dimensional model is used to optimize the computing time which is reduced by a factor of 10 by using some optimization techniques. It is also used to validate the charged particle and basic data choices. We have shown that the consideration of only two charged particle species (electron and H3+ positive ion) is sufficient in the present hydrogen radio-frequency discharge modeling. Computational results (i.e., power density and self-bias voltage) are in good agreement with experimental results. A strong gradient of the plasma parameters (such as electric field, potential, charged particle densities and energies) was observed in the periphery of the driven electrode. Furthermore, the present two-dimensional asymmetric model shows that the interelectrode distance increase (from 1.7 up to 3.7 cm) can lead to reducing the plasma heterogeneity due to the geometrical electric field.

Time domain simulation of magnetic systems with a general moving geometry

A method based on a hybrid finite element-boundary element formulation for time domain analysis of magnetic field problems is presented. The problem domain is allowed to contain several objects moving relatively to each other. The relative movement can be a prescribed function or the movement can be part of the simulated solution. Simple external circuit equations are added to the field equations. Only 2D problems are treated. Simulations including a direct on-line start of an induction motor are presented.

Simultaneous Potential and Circuit Solution for Two-Dimensional Bounded Plasma Simulation Codes

An algorithm for coupling external circuit elements to be bounded two-dimensional electrostatic plasma simulation codes is developed. In general, the external circuit equations provide a mixture of Dirichlet and Neumann boundary conditions for the Poisson equation, which is solved each time step for the internal plasma potential. We rewrite the coupling between the plasma and the external circuit parameters as an algebraic or ordinary differential equation for the potential on the boundary. This scheme allows decomposition of the field solve into a Laplace solver with boundary conditions (e.g., applied potentials) and a Poisson solver with zero boundary conditions. We present the details of the external circuit coupling to an explicit electrostatic planar two-dimensional particle-in-cell code called PDP2, and discuss briefly how the coupling can be done in an implicit electrostatic code. The decomposition replaces the iterative coupling with a direct coupling and reduces the amount of computational time spent in the field solver. We use PDP2 to simulate a dually excited capacitively coupled RF discharge and show how such a system can be used as a plasma processing tool with separate control over ion flux and ion bombarding energy.

Circuit theoretical approach to couple two-dimensional finite element models with external circuit equations

This paper presents a new method to couple two-dimensional finite element models with circuit equations. The method is based on handling of the finite element model as a circuit theoretical multiport element. This multiport element is treated in the same way as ordinary nonlinear circuit elements within the Newton-Raphson iteration of the circuit equations. The method has been utilized in a simulator program for analyzing power electronic drives in the time domain. The electrical machine is modeled by the two-dimensional finite element method. The power electronic circuit and the connections of the windings of the machine may have an arbitrary topology which is given by a net-list file (SPICE-type input file). The applicability of the method is investigated with two example cases which are verified by measurements. According to tests, the method proposed provides an effective and reliable way to construct simulators including finite element modeling.

Armature current and magnetic force at rotor dampers in superconducting generator on sudden three‐phase short circuit

AbstractThe important design factor of a superconducting generator is estimating the electromagnetic forces at the rotor dampers on a sudden three‐phase short‐circuit. In this paper, the armature current and electromagnetic forces on such a short‐circuit are simulated directly by two‐dimensional transient analysis, considering the following complex terms: 1 induced current by the speed electromotive force caused by the rotor rotation; the connection of three‐phase windings; and 3 the resistance and reactance at the armature coil‐end.The speed electromotive force is considered by using the combination method, which is FEM combined with BEM at the air gap. The connection of the armature winding and the effect of the armature coil‐end are considered by using the analysis combined with the external circuit equations. Moreover, the effect of the Röbel transposition of the armature winding is approximately considered.As a result of analysis, the electromagnetic forces at the rotor dampers can be calculated with a high accuracy.

Analysis of Armature Current and Magnetic Force at Rotor Dampers in Superconducting Generator on Sudden 3-Phase Short-Circuit.

The important design factor of superconducting generator is the estimation of the electromagnetic forces at the rotor dampers on sudden three-phase short-circuit. In this paper, the armature current and electromagnetic forces on sudden three-phase short-circuit are directly simulated by two-dimensional transient analysis, considering the following complex terms.(1) Induced current by the speed electromotive force caused by the rotor rotation. (2) The connection of three-phase windings. (3) The resistance and reactance at the armature coil-end.The speed electromotive force is considered by using the combination method, which is FEM combined with BEM at the air gap. The connection of the armature winding and the effect of the armature coil-end are considered by using the analysis combined with the external circuit equations. Moreover, the effect of the Roebel-transposition of the armature winding is approximately considered.By the authors, analysis, the electromagnetic forces at the rotor dampers can be calculated with a high accuracy.

Stable calculation for power device simulation with inductive load circuit: application of an integral method

The integral method for the device simulation, taking into account the external circuit equations, is discussed. One feature of this method is the combination of the integral circuit equation and the Dirichlet boundary condition of the device simulator. It can give a stable and precise calculation with less accumulated error even if the circuit equation includes a time-differential term, e.g. L ∗ dI/ dt ( where L = inductance and I = current) . Application examples for power devices are also given.

Transient shielding effect of slitted electrothermal shield of superconducting generator

An electrothermal shield with direct axis directional slits is proposed for application to a superconducting alternator with quick-response excitation system. Using the finite element method combined with external circuit equations, short-circuit characteristics due to slitting effects are investigated by comparing three cases, conventional electrothermal shield (CES), slitted electrothermal shield (SES), and no electrothermal shield (NES) models, under three phase fault and line to line fault, respectively. The field current variations, flux densities in the vicinity of superconducting field winding, and the eddy currents of the SES model are computed and then compared with those of the CES and NES models. It is expected that the superconducting alternators with SES could adopt the quick-response excitation system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two-dimensional modeling of the formation of spheromak configurations

A reduced set of two-dimensional magnetohydrodynamic equations has been derived describing the axisymmetric time evolution of a stable plasma evolving slowly due to resistive diffusion and changing boundary conditions. The equations are restricted to low b but allow changing topology. They are integrated in time to demonstrate a possible spheromak formation method. External circuit equations are integrated simultaneously with the plasma equations to determine the electromagnetic boundary conditions self-consistently. The effects of a finite conductivity vacuum chamber are included.

Switching properties of highly doped Gunn devices in resistive circuits

The switching behaviour of Gunn devices in the doping range between 7 × 10 14 cm −3 and 5 × 10 15 cm −3 acting in resistive circuits is investigated by numerical methods. Carrier transport equations including diffusion are solved for the device in combination with external circuit equations. The switching time is below 100 psec down to less than 10 psec depending on load and doping. The current pulse amplitude is about 40% of the peak current.