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Lecture18 - Lecture 18 Induction Machine Torque Transients...

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Lecture 18 Induction Machine Torque Transients at Zero Speed From (28) of Lecture 29, the solutions of the stator and rotor currents of the d-phase are of the form: } ) cos( ) cos( ) exp( 0 0 ) 2 exp( { 1 1 1 1 2 1 ) ( ) ( 2 2 1 1 2 1 + + + + = ϑ ω ϑ ω t Q t Q C C t R t l M R t i t i SS SS Rd Sd l (1) and the q-phase are: } ) cos( ) cos( ) exp( 0 0 ) 2 exp( { 1 1 1 1 2 1 ) ( ) ( 2 4 1 3 4 3 + + + + = ϑ ω ϑ ω t Q t Q C C t R t l M R t i t i SS SS Rq Sq l (2) In general, the currents of (1) and (2) can be organized in the form: + + + + + + + = ) 4 4 3 3 2 2 1 1 4 3 2 1 4 3 2 1 cos( ) cos( ) cos( ) cos( ) exp( ) 2 exp( η ω η ω η ω η ω t I t I t I t I E E E E t R D D D D t M R i i i i Rq Rd Sq Sd l l (3) From (3), all the currents are characterized by three terms based on the time variations: ) 2 exp( t M R l + , ) exp( t R l and the line frequency t ω cos . As the torque equation ) ( Rd Sq Rq Sd e i i i i nM T = is obtained from the products of currents, there are altogether 6 characteristic terms.
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