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# lect14 - Lecture 14 EE743 Two-Phase Induction Machines Part...

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Lecture 14 - EE743 Lecture 14 - EE743 Professor: Ali Keyhani Professor: Ali Keyhani Two-Phase Induction Machines Part II

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2 The stator and rotor windings are orthogonal. No coupling exists between as as and bs bs windings or between ar ar and br br windings. The stator and rotor windings are in relative motion, that is, a coupling exists between the stator and rotor windings. Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines
3 This coupling will vary with the position of θ r of the rotor windings relative to the stator windings. We will describe the dynamic equations for the schematic representation of an induction machine depicted in the following figures. Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines

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4 Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines x x x x as as’ br bs ar br’ ar’ bs’ as-axis br-axis bs-axis ar-axis s φ r ϖ r θ r φ T e T L
5 Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines A two-pole two-phase symmetrical induction machine s

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6 The voltage equations are given by, Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines ings rotor wind the of Resistance r ings, rotor wind For the dings stator win the of Resistance r dings, stator win For the r s = + = + = = + = + = br br r br ar ar r ar bs bs s bs as as s as P i r V P i r V P i r V P i r V λ λ λ λ
7 The vector representation of the voltage equations is as follows, Let Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines abr abr r abr abs abs s abs P i r V P i r V λ λ + = + = ( 29 [ ] ( 29 [ ] br ar T abr bs as T abs f f f f f f = =

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8 f f ” can represent voltage, current, or flux linkages. The stator and rotor resistances can be also represented as a vector, Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines [ ] [ ] I r r r r r I r r r r r r r r r r s s s s s = = = = = = 1 0 0 1 0 0 1 0 0 1 0 0
9 The flux linkage equations, in a matrix form are expressed as, Two-Phase Two-Poles Induction Two-Phase Two-Poles Induction Machines Machines ( 29 abr r abs T sr abr abr sr abs s abs br ar bs as brbr brar brbs bras arbr arar arbs aras bsbr bsar bsbs bsas asbr asar asbs asas br ar bs as i L i L i L i L i i i i L L L L L L L L L L L L L L L L + = + = = λ λ λ λ λ λ

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lect14 - Lecture 14 EE743 Two-Phase Induction Machines Part...

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