Das allgemeine Gleichungssystem des K�figl�ufermotors unter Ber�cksichtigung der Oberfelder

Abstract

Tell I : Allgemeine TheorieF. TAEGE~ und E. HOMSIES, Delft l~bersicht: Das System der --auch dynamisch gi~ltigen --SpannungsgleichungeI1 und der Drehmomentgleichung des Kfifig-1/iufermotors wird unter t3erfmksichtigung der Oberfelder aufgestellt, undes werden alle fflr die Berechnung erforderlichen In-duktivit~ten ermittelt. Dutch zwei lineare Transformationen l~tBt sich das Gleichnngssystem weitgehend vereinfachen, tilerdutch wird es m6glich, das Verhalten der lXlaschine einschlieBlich aller Kopplungen der /;'elder und der eventuell auftretenden Unipolarflt~sse zu beschreiben, ohne dab hierffir jeweils beso~ldere physikalische Betrachtungen erforderlich W~iren. Ein einlaches Beispiel, in dem fi~r die Drehmomentberechnung nur das Grundfeld und die dritte tIarmonische berflcksichtigt werden, erl~utert die Amvendung des Gleichungssystems. Contents : The system of the voltage equations and the torque equation of the squirrel cage motor --including the dynamical behaviour --are set up considering the space harmonic fields. The necessary inductances for the analysis of the machine are determined. By the use of two linear transformations the system of equations can be extensively simplified. By this means ~he behaviour of the machine including all harmonic field linkages and the homopoIar fluxes which may occur can be described without the necessity of particular physical considerations. A simple example, ill which are taken into account in the torque calculation only the fundamental and the third harmonic fields, illustrates the application of the system of equations.

Stator current spectrum analysis of a double cage induction motor with rotor asymmetry

“…The magnetic circuit is fully symmetric and linearised, the air-gap between the stator and rotor is assumed to be smooth, and the field density in the air-gap has only a radial component. Under these assumptions, the equations of the circuits on the stator and rotor take a general form, given by (1).…”

“…The matrices with the subscript 𝜎 contain the respective inductances owing to leakages fluxes. Detailed forms of these matrices are not presented here because they are the same as those for classical cage motors and are well known in the literature [1,4,8,9,20]. The resistance matrices, which are essential for modelling the asymmetry of the rotor cages and stator side, are expressed as follows:…”

“…and are the RMS values of the phase voltages. Consequently, it is sufficient to obtain the harmonic balance equations for forced vector u 1 𝑠 = 𝑢 1 𝑠 0 𝑇 . Under these conditions, the vector of the currents in the steady state can be predicted using the following Fourier series:…”

“…This study presents an approach to predict the Fourier spectra of stator currents for a double cage motor at arbitrary damage to bars in the outer and inner cages. The mathematical model of these motors is presented as ordinary differential equations for all circuits on the stator and rotor sides by extending a known circuit model of typical cage motors, considering the higher space harmonics generated by the stator and rotor windings [1,4,6,8,14,20]. The double cage on the rotor increases the number of rotor equations by twice in this model; thus, the number of model equations to be solved for diagnostic signals is rather high.…”

Die Theorie des K�figl�ufermotors unter Ber�cksichtigung der St�nder- und L�ufernutung

“…Fiihrt man analog zu [1] die Gruppentransformarion der Rotorgr~Sgen und die Transformation in symmetrische Komponenten aus, so erh~ilt man schlieglich die Spannungsgleichungen …”