Lecture20

Lecture20 - 1 ECSE 462 Lecture 20 Small Perturbation...

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Unformatted text preview: 1 ECSE 462 Lecture 20 Small Perturbation Linearization of Induction Machine Equations From Lecture 11, the γ- δ frame electrical equations are: i F i G n i p L i R e m ] [ ] [ ] [ ] [ ω ω + + + = where ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = δ γ δ γ R R S S e e e e e ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = δ γ δ γ R R S S i i i i i ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = R R S S R R R R R ] [ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + + = R R S S M M M M M M M M L l l l l ) ] [ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + + − − = ) ( ) ( ] [ R R M M M M G l l ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + − − + − + − + = ) ( ) ( ) ( ) ( ] [ R R S S M M M M M M M M M F l l l l And the mechanical equation of motion is: ) ( 1 1 γ δ δ γ ω ω R S R S L m m i i i i nM T f p J − = + + In applying small perturbation linearization, the first step is to find the equilibrium operating state. The forcing functions consist of the applied voltages: operating state....
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Lecture20 - 1 ECSE 462 Lecture 20 Small Perturbation...

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