2009-09-08 The Generation of Electric Energy Part III

2009-09-08 The Generation of Electric Energy Part III - The...

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The Generation of Electric Energy Part III Jovan Ilić ECE 18-418 Fall 2009
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Single Phase Synchronous Machine [2] Graphics from [2]
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ˆ ( ) sin( ) sa s s s ZZ  Graphics from [2] the stator winding distribution [1/m] sa Z
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    00 ˆˆ sin 2 s sa s s s s s s N Z rd Z rd rZ       sin 2 s sa s s N Z r        1 ˆ cos s s n s s n n B B n  Knowing total number of turns find: ˆ s Z Fourier series of the flux density distribution within the air gap: Amount of flux crossing an infinitely small area of the air gap:     s s s s d B lrd 
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        sin 1 cos 22 ss sa s s s s s NN Z rd rd r    The number of turns linked with this flux: Flux linked with the stator:             2 2 2 0 0 0 1 cos cos 2 2 2 s s s s s s sa s s s s s s s s N N N B lrd lr B d lr B d             2 1 0 2 1 0 ˆ cos cos 2 ˆ [cos 1 cos 1 ] 4 s sa s n s n s n s n s n s n s n N lr B n d N lr B n n d 
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Which is zero for 1 n      2 1 1 1 1 0 ˆˆ cos cos 42 s sa s s N lr B d B N lr Finding Fourier coefficient for n=1: 0 1 4 ˆ when 0 2 ff sa NI Bi     1 For 0 the first harmonic is at maximum sr   0 cos when 0 sa s saf f sa N lr M I i  and So, the mutual inductance is:     0 ˆ cos cos saf s f sf lr M N N M mutual inductance between rotor and stator [H] ˆ maximum value of the mutual inductance [H] N number of turns on the stator winding N number of turns on the rotor winding rotor length [m] rotor ra saf saf s f M M l r dius [m] air gap width [m]
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for 0 and stator winding voltage [V] rotor winding voltage [V] stator resistance [ ] sa f sa sa s sa f f f sa sa sa saf f f saf sa f f sa f s i d d v R i v R I dt dt L i M I M i L I vv R 
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2009-09-08 The Generation of Electric Energy Part III - The...

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