27.02.2013 Views

an investigation of dual stator winding induction machines

an investigation of dual stator winding induction machines

an investigation of dual stator winding induction machines

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

When the skewing factor <strong>of</strong> the rotor is considered, the expressions for the turn <strong>an</strong>d<br />

<strong>winding</strong> functions become (3.52) <strong>an</strong>d (3.53) respectively:<br />

⎧<br />

⎪<br />

0<br />

⎪<br />

⎪<br />

1<br />

( θ −θ<br />

i + β )<br />

⎪β<br />

θ ∈[<br />

0,<br />

θi<br />

− β )<br />

θ ∈[<br />

θi<br />

− β,<br />

θi<br />

)<br />

⎪<br />

n ( θ ) = ⎨1<br />

θ ∈[<br />

θ , θ + α − β )<br />

i<br />

i i r<br />

⎪<br />

⎪ 1<br />

( θi<br />

+ α r −θ<br />

) θ ∈[<br />

θi<br />

+ α r − β,<br />

θi<br />

+ α r )<br />

⎪β<br />

⎪<br />

⎪0<br />

θ ∈[<br />

θi<br />

+ α r , 2π<br />

)<br />

⎪⎩<br />

(3.52)<br />

⎧ α r<br />

⎪<br />

−<br />

θ ∈[<br />

0,<br />

θi<br />

− β )<br />

2π<br />

⎪<br />

⎪<br />

1<br />

α r<br />

( θ −θ<br />

i + β ) − θ ∈[<br />

θi<br />

− β , θi<br />

)<br />

⎪β<br />

2π<br />

⎪ α r<br />

N ( ) = ⎨ −<br />

∈[<br />

+ − )<br />

i θ 1<br />

θ θi<br />

, θi<br />

α r β<br />

⎪ 2π<br />

⎪ 1<br />

α r<br />

( θi<br />

+ α r −θ<br />

) − θ ∈[<br />

θi<br />

+ α r − β,<br />

θi<br />

+ α r )<br />

⎪β<br />

2π<br />

⎪ α r ⎪0<br />

−<br />

θ ∈[<br />

θi<br />

+ α r , 2π<br />

)<br />

⎪⎩<br />

2π<br />

(3.53)<br />

where, β = skew factor ⋅α<br />

r .<br />

Substituting the turn function <strong>an</strong>d <strong>winding</strong> function <strong>of</strong> the th<br />

i rotor loop into the<br />

general expression for the self-induct<strong>an</strong>ce given in (3.36), the self-induct<strong>an</strong>ce for the th<br />

i<br />

rotor loop c<strong>an</strong> be determined. Since all the rotor loops have the same self-induct<strong>an</strong>ce<br />

under the uniform air gap condition, its expression is:<br />

107

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!