Numerical analysis of steady-state operation of three-phase induction machines by an approximate frequency domain technique1

Abstract

An approximate frequency domain technique is applied to determine the initial values for the transient time-stepping numerical scheme required to take time dependent phenomena like induced voltages, eddy currents and slot ripples in induction machines into account. Using the initial conditions obtained, the steady-state operation of the motor is obtained much faster than by assuming zero initial values. This procedure is employed to the current-fed and voltage-fed 2-D induction motor models and, additionally, to the 2-D multislice FEM model of the 1 MW squirrel cage induction motor.Numerische Analyse des station€ aren Betriebszustands einer dreiphasigen Asynchronmaschine mit Hilfe einer Vorabsch€ atzung im Frequenzbereich.Eine Vorabsch€ atzung im Frequenzbereich wird angewandt, um die notwendigen Startwerte f€ ur die transiente Analyse im Zeitschrittverfahren zu ermitteln. Die transiente Analyse erlaubt es, zeitlich ver€ anderliche Vorg€ ange, wie induzierte Spannungen, Wirbelstr€ ome und Oberwellenmomente, zu erfassen. Mit den Startwerten aus der Frequenzbereichs-Analyse kann der station€ are Betriebszustand deutlich schneller erreicht werden als bei der Annahme aller Startwerte mit null. Die Anwendung der Methode wird an einem Strom-und Spannungs-gespeisten 2-D-Asynchronmaschinen-Modell sowie an einem 2-D-Mehr-Schichten-Modell eines K€ afigl€ aufers gezeigt. IntroductionThe efficient analysis of an induction motors steady-state operation under arbitrary load conditions with the effects of the time-varying electrical variables as well as those due to rotor movement considered is a very challenging engineering task. Using time-harmonic finite element (FE) analysis in order to simulate the motors steadystate operation is not sufficient, since motional eddy current effects are not included in the time-harmonic approach. Therefore, the time-harmonic analysis often fails in torque computation e.g. when motor operation at lower speed is under consideration whereby the torque characteristic is affected by the asynchronous crawling tendencies. To include these transient phenomena in the analysis, a transient FE time-stepping numerical procedure is required. When such a procedure is started with zero initial conditions, a huge computational effort is needed to reach the steady-state solution. This approach is often referred to as the brute force method. A previous work using this direct method at the induction motor analysis has been published by the authors in (Stermecki et al., 2006). The brute force method becomes especially unsuitable when larger electromagnetic devices are to be analyzed. To avoid the cumbersome time-stepping through the transient phenomena, it is much more recommendable to start the solution procedure with non-zero initial conditions. These can be provided using the combination of an electric equivalent circuit analysis and an initial linear

Accounting for Magnetic Saturation Effects in Complex Multi-harmonic Model of Induction Machine

“…The application of the above-mentioned approach essentially involves the problem of modeling the nonlinearity of the magnetic materials. Taking this into account in the monoharmonic field models based on the use of the complex magnetic vector potential method is not a new task and it has been described to date in several works, including [10][11][12][13][14][15][16]. They propose several different methods of defining the so-called effective magnetic permeability based, among others, on the development of nonlinear waveforms in the Fourier series [14,16], averaging the magnetic reluctivity [10,15,16] or equivalence of energy stored in ferromagnetic components [10][11][12][13].…”

“…Taking this into account in the monoharmonic field models based on the use of the complex magnetic vector potential method is not a new task and it has been described to date in several works, including [10][11][12][13][14][15][16]. They propose several different methods of defining the so-called effective magnetic permeability based, among others, on the development of nonlinear waveforms in the Fourier series [14,16], averaging the magnetic reluctivity [10,15,16] or equivalence of energy stored in ferromagnetic components [10][11][12][13]. However, analyzing the conclusions drawn in the mentioned works, it is not possible to clearly state which method of defining the effective magnetic permeability will be most appropriate when using the multi-harmonic model with a strong coupling, as proposed by Garbiec et al Some of them assume the sinusoidal variation of the magnetic flux density in calculating the effective magnetic permeability (which facilitates the calculations using the magnetic vector potential) [12][13][14][15], while others assume that it should be determined assuming sinusoidal variation of the magnetic field strength, or that it is insignificant for the accuracy of the calculations [10,11,14].…”

OVE Nachrichten

“…To avoid the cumbersome time-stepping through the transient phenomena, it is advisable to start the solution procedure with non-zero initial conditions. In [1][2], the method of fictitious materials has been applied in a harmonic finite element procedure in order to take the non-linearity into account and to compute initial conditions as close as possible to the steady-state solution. This method has been found to substantially improve the speed of the analysis.…”

Accelerating the Time-Stepping Finite-Element Analysis of Induction Machines in Transient-Magnetic Solutions

“…At present, the nonlinear B-H property of the magnetic core can be partly considered in TH solutions of some packages e.g. Altair Flux, ANSYS Maxwell, JMAG, and FEMM, by an equivalent curve based on the energetic equivalence method [26]- [28]. By applying this method, accurate scalar values (e.g.…”