An induction motor model with deep-bar effect and leakage inductance saturation

Contents A two-phase dynamic induction motor model is derived which includes the effects of rotor bar eddy currents and leakage inductance saturation. The model is based on approximate analysis of the air-gap and slot electromagnetic fields which leads directly to lumped circuit equations. New expressions are given for the variation of the zig-zag and slot leakage inductance with saturation. — The model is applied to the calculation of both steady state and dynamic characteristics for a large induction motor.

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Ein Modell des Asynchronmotors mit Hochstabläufer-Effekt und Sättigung der Streuinduktivität

Übersicht Es wird ein zweisträngiges Modell eines Asynchronmotors abgeleitet, das Wirbelströme in den Läuferstäben und die Sättigung der Streuinduktivität berücksichtigt. Grundlage des Modells ist eine angenäherte Analyse der Felder im Luftspalt und in den Nuten, die direkt auf Gleichungen mit konzentrierten Elementen führt. Es werden neue Ausdrücke für die Abhängigkeit der doppeltverketteten und der Nutstreuung von der Sättigung angegeben. Das Modell wird für die Berechnung stationärer und dynamischer Vorgänge bei einem großen Asynchronmotor angewendet.

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List of Symbols A magnetic vector potential - B flux density - G describing function - g air-gap length - H magnetic field intensity - I _Om rotor saturation current - I _r rotor current matrix - l _r ^j current in thejth rotor slot - l _rm amplitude of the fundamental ofI _bir ^j distribution - I _rr rotor harmonic conceptual current matrix - I _s stator current matrix - I _ss stator harmonic conceptual current matrix - i _mne m, nth modal eddy current in thejth rotor slot - i _nb nth harmonic conceptual current at the interface betweenjth rotor slot and slot neck regions - i _n ^rj nth harmonic conceptual current at the opening of thejth rotor slot - i _n ^sj nth harmonic conceptual current at the opening of thejth stator slot - i _Ob rotor zero order conceptual current matrix - i _Oi ^j conceptual current at thejth rotor slot due to daturation of the tooth tips - K _nw nth harmonic winding distribution factor effective length of the motor - L _nc self inductance of the eddy current modei _One ^j - L _r rotor inductance matrix - L _s stator inductance matrix - P _p pole pitch - M _ne mutual inductance betweeni _One ^j andI _r ^j and rotor modal eddy currents - M _ri mutual inductance matrix between rotor winding and rotor conceptual winding due to saturation of the tooth tips - M _rr mutual inductance matrix between rotor winding and rotor conceptual winding - M _rss mutual inductance matrix between rotor winding and stator conceptual winding - M _si mutual inductance matrix between stator winding and rotor conceptual winding due to saturation of the rotor tooth tips - M _sr mutual inductance matrix between stator and rotor windings - M _srr mutual inductance matrix between stator winding and rotor conceptual winding - M _ss mutual inductance matrix between stator winding and stator conceptual winding - N ₁,N ₂ number of stator and rotor slots - R _ne resistance of eddy current modei _One ^j - R _r rotor resistance matrix - R _s stator resistance matrix - s ₁,d ₁ dimensions of a stator slot - s ₂,d ₂ rotor slot opening and rotor slot neck height - s _b ,d _b dimensions of a rotor bar - s _p slot pitch - N _c number of turns per slot - U _s applied voltage matrix - q number of slots per pole phase group - rotor flux linkage matrix - y_s stator flux linkage matrix - , inductance coefficients - O angular position - conductivity of rotor bars - eigenvalues - resistivity of rotor bars