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Unformatted text preview: Lecture 17 Engineering practice uses many numerical methods and software tools for the analysis. Therefore the emphasis is to make students understand the theory in order to apply the available software tools. This lecture introduces linear analysis of the induction machine by first treating a 2x2 system of transformers. The equations of the equation in the d-q frame is: + + + + + + + + + + = 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 (1) As entries in elements (1,2), (1,4), (2,1) and (2,3) are zeroes, the d-axis and the q-axis of the induction machine are decoupled into those of two independent transformers when the speed , = m , whereupon the entries of (3,2), (3,4), (4,1) and (4,3) are also zeroes. The decoupled equations are: + + + + = Rd Sd R R S S Rd Sd i i p M R Mp Mp p M R e e ) ( ) ( l l (2-a) + + + + = Rq Sq R R S S Rq Sq i i p M R Mp Mp p M R e e ) ( ) ( l l (2-b) Two transformers one aligned along the d-axis and the other aligned along the q-axis. sq-axis sd-axis In order to avoid complicated algebra, it is assumed that the resistances and the leakage inductances of stator are equal to those of the rotor. The subscripts d and q are dropped because the results apply to both axes. The equations of the transformer are: + + + + = R S R S i i p M R Mp Mp p M R e e ) ( ) ( l l (3) which can be put in the form: + = + + R S R S R S e e i i R R i i dt d M M M M l l (4) + + + + + = R S R S R S e e M M M M i i R R M M M M i i dt d 1 1 l l l l (5) The inverted matrix is: + + + = + + l l l l l l M M M M M M M M M 2 1 2 1 (6) Substituting (6) in (5) + + + + + + + = R S R S R S e e M M M M M i i M M M M M R i i dt d l l l l l l l l 2 2 2...
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This note was uploaded on 02/23/2010 for the course ECSE 462 taught by Professor Bon-tekooi during the Spring '09 term at McGill.
- Spring '09