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6.11s June 2006 L4

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6.11s Notes for Lecture 4

Analysis of Induction Machines

June 15, 2006

J.L. Kirtley Jr.

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Induction motor stator and rotor windings are coupled together much
like windings of a transformer. But the coupling is dependent on rotor
position:

Stator                 
Rotor

Rotor angle

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Assume currents are of a balanced form

And that the rotor is turning at steady speed:

Note the frequencies will match if

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We can calculate stator flux:

Do some trig and this reduces. And the rotor flux is similar:

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Now: we see that this simplifies if we use complex notation:

So that

Now make a couple of definitions

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And our flux-current relationship becomes simple:

Now we can write voltage equations

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Now we need to look at the internals of the machine: winding self
inductances are of the form:

Note these both have fundamental inductances that have the same permeance and then some leakage inductance. The mutual
inductance has the same permeance as the fundamental of the self indctances:

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6.11s