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Unformatted text preview: Lecture 11 Transformation from d-q frame to - frame In Lecture 10, one notes that in the induction machine the magnetic fluxes produced by the currents of the stator and the rotor rotate around the air-gap at the same angular velocity , the synchronous velocity of the supply frequency. The d-q frame axes of the stator and the rotor coincide and are stationary. Their voltages and currents are at the same frequency . The objective of transforming to the - frame is to view the magnetic fluxes as stationary. This is by rotating the axes frame at the same angular velocity . The - frame axes of the stator and the rotor coincide because they have been coinciding in the d-q frame. The voltages and currents associated with the rotating - frame windings are constant voltages and currents. Having the voltages and currents time-invariant is an important reason for the transformation. The rotational transformation, which is applied to both the stator and the rotor d-q windings, is = t t t t t C dq cos sin sin cos )] ( [ (1) The complete transformation is: = R S dq dq R dq S dq e e C C e e )] ( [ )] ( [ (2) = R S dq dq R dq S dq i i C C i i )] ( [ )] ( [ (3) Substituting (2) and (3) in the equations in the d-q frame: + + + + + + + + + + = Rq Rd Sq Sd R R m R m m R R R m S S S S Rq Rd Sq Sd i i i i p M R n M Mp Mn n M p M R Mn Mp Mp p M R Mp p M R e e e e ) ( ) ( ) ( ) ( ) ( ) ( l l l l l l (4) the resultant - frame equations are:...
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- Spring '09