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Lecture5

# Lecture5 - 1 LECTURE 5 This lecture moves from reluctance...

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1 LECTURE 5 This lecture moves from reluctance machines to induction machines. The formulae of the coupling between winding-x and winding-y which have been developed in chapter 3 will be applied. The resultant equations are simpler because induction machines are round rotor machines with a uniform air-gap. For example, the inductance matrix of the 3-phase reluctance machine is: ° + + ° + + ° + ° + ° + ° + + = ) 240 ( 2 cos ) ( 2 cos 5 . 0 ) 240 ( 2 cos 5 . 0 ) ( 2 cos 5 . 0 ) 120 ( 2 cos ) 120 ( 2 cos 5 . 0 ) 240 ( 2 cos 5 . 0 ) 120 ( 2 cos 5 . 0 ) ( 2 cos )] ( [ d B A d B A d B A d B A d B A d B A d B A d B A d B A d L L L L L L L L L L L L L L L L L L L θ θ θ θ θ θ θ θ θ θ (1) When the saliency is removed by setting b/a=0, 0 ) / ( 5 . 0 . 2 1 3 0 = = a b B LR L B πμ . One reverts to the simpler equation of the round rotor: = A A A A A A A A A S L L L L L L L L L L 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 ] [ (2) where a B LR L A / 2 1 3 0 πμ = Engineers, who work with induction machines, have their set of symbols. The notes will follow them so much as possible. For the present, only two changes are made: Up to now, the average air-gap is given the symbol “a”. It will be changed to “g”. Secondly, a B LR L A / 2 1 3 0 πμ = is changed to g B LR M / 2 1 3 0 πμ = . Therefore, = M M M M M M M M M L S 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 5 . 0 ] [ (3) Recall that in Lecture 3-Appendix, the inductances of the coupling between windings x and y are: )] ( 2 cos [ x d B A xx L L L θ θ + = (3-19) )] ( 2 cos [ y d B A yy L L L θ θ + = (3-20) )] 2 cos( ) (cos( [ y x d B y x A yx xy L L L L θ θ θ θ θ + = = (3-21) When b/a=0 so that 0 ) / ( 5 . 0 .

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Lecture5 - 1 LECTURE 5 This lecture moves from reluctance...

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