6 folier pr. side - NTNU
6 folier pr. side - NTNU
6 folier pr. side - NTNU
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<strong>NTNU</strong><br />
<strong>NTNU</strong><br />
<strong>NTNU</strong><br />
Slide 397<br />
Slide 399<br />
Slide 401<br />
Transformasjon for 3-fase viklinger<br />
■ Finner da Park-transformasjonen:<br />
⎡ cos θk<br />
k ⎢<br />
�ss<br />
= ⋅ ⎢−<br />
sin θ<br />
3<br />
⎢<br />
⎣<br />
1/<br />
2<br />
0<br />
0<br />
cos( θ<br />
⎤<br />
k −120<br />
) cos( θ k − 240 )<br />
0<br />
⎥<br />
− sin( θk<br />
−120<br />
) − sin( θk<br />
− 240 ) ⎥<br />
1/<br />
2<br />
1/<br />
2 ⎥<br />
⎦<br />
2 0<br />
k<br />
■ Den inverse Park-transformasjonen:<br />
⎡ cos θk<br />
− sin θ k 1⎤<br />
−k<br />
⎢<br />
0<br />
0<br />
�<br />
⎥<br />
ss =<br />
⎢<br />
cos( θk<br />
−120<br />
) − sin( θk<br />
−120<br />
) 1<br />
⎥<br />
0<br />
0<br />
⎢⎣<br />
cos( θ − 240 ) − sin( θ − 240 ) 1⎥<br />
k<br />
k ⎦<br />
Ser bort i fra γ-systemet ……….<br />
■ Kan da benytte to-dimensjonale romvektorer:<br />
k<br />
k k 1 dψ<br />
s<br />
k<br />
u s = rs<br />
⋅ i s + + � ⋅ f k ⋅ ψ s<br />
ωn<br />
dt<br />
k<br />
k k 1 dψ<br />
r<br />
k<br />
u r = rr<br />
⋅ i r + + � ⋅ ( f k − n)<br />
⋅ ψ r<br />
ωn<br />
dt<br />
m e =<br />
k T k k k k k<br />
( is<br />
) � ψ = ψ ⋅ i − ψ ⋅ i<br />
dn<br />
Tm<br />
= m e − m L<br />
dt<br />
dθ<br />
k<br />
= ωn<br />
⋅ f k<br />
dt<br />
s<br />
sα<br />
sβ<br />
sβ<br />
sα<br />
2<br />
J ⋅ Ω basis<br />
Tm<br />
=<br />
Sn<br />
dθ<br />
= ωn<br />
⋅ n<br />
dt<br />
k<br />
k<br />
k<br />
k ⎡i<br />
⎤ ⎡ ⎤ ⎡ψ<br />
⎤<br />
sα<br />
k u sα<br />
k sα<br />
i s = ⎢ k ⎥ u s = ⎢ k ⎥ ψ s = ⎢ k ⎥<br />
⎢⎣<br />
i sβ<br />
⎥⎦<br />
⎢⎣<br />
u sβ<br />
⎥⎦<br />
⎢⎣<br />
ψ sβ<br />
⎥⎦<br />
k k<br />
k<br />
ψ = x s s ⋅ is<br />
+ x h ⋅ i r<br />
k<br />
k k<br />
ψ = x r h ⋅ is<br />
+ x r ⋅ i r<br />
θ r = θk<br />
− θ<br />
⎡0 −1⎤<br />
= ⎢ ⎥<br />
⎣1<br />
0 ⎦<br />
Statororientert modell<br />
■ Aksesystemet og de ������� stator og rotor viklinger er spikret<br />
fast i forhold til ������:<br />
dθ<br />
k<br />
= ωn<br />
⋅ f k ≡ 0<br />
dt<br />
dθ<br />
= ωn<br />
⋅ n<br />
dt<br />
■ Settes inn i uttrykkene for fluksforslyngningene:<br />
s<br />
s s 1 dψ<br />
s<br />
s s<br />
s<br />
u s = rs<br />
⋅ is<br />
+<br />
ψ = x s s ⋅ is<br />
+ x h ⋅ i r<br />
ω dt<br />
n<br />
s<br />
s 1 dψ<br />
r<br />
s<br />
0 = rr<br />
⋅ i r + − �⋅<br />
n ⋅ ψ r<br />
ωn<br />
dt<br />
me<br />
=<br />
s T ( is<br />
)<br />
s s s s s<br />
�ψ<br />
= ψ s sα<br />
⋅ isβ<br />
− ψ sβ<br />
⋅ isα<br />
�<br />
θ r = −θ<br />
s<br />
s s<br />
ψ = x r h ⋅ i s + x r ⋅ i r<br />
■ For to dimensjonale romvektorer har man at romvektoren i<br />
statorkoordinater lik dens koordinatvektor<br />
s s ⎡1⎤<br />
⎡0⎤<br />
⎡I<br />
a ⎤ s<br />
I s = Ia<br />
a + Ib<br />
b = Ia<br />
⎢ I b = ⎢ = Is<br />
0<br />
⎥ + ⎢<br />
1<br />
⎥<br />
I<br />
⎥<br />
⎣ ⎦ ⎣ ⎦ ⎣ b ⎦<br />
Trondheim 2000<br />
Trondheim 2000<br />
Trondheim 2000<br />
<strong>NTNU</strong><br />
<strong>NTNU</strong><br />
<strong>NTNU</strong><br />
Slide 398<br />
Transformasjon for 3-fase rotor viklinger<br />
i en asynkronmaskin<br />
■ Finner da Park-transformasjonen:<br />
0<br />
0<br />
⎡ cosθ<br />
⎤<br />
r cos( θr<br />
−120<br />
) cos( θr<br />
− 240 )<br />
k 2 ⎢<br />
0<br />
0 ⎥<br />
�rr<br />
= ⋅ ⎢−<br />
sin θr<br />
− sin( θr<br />
−120<br />
) − sin( θr<br />
− 240 )<br />
3<br />
⎥<br />
⎢<br />
⎥<br />
⎣<br />
1/<br />
2 1/<br />
2<br />
1/<br />
2<br />
⎦<br />
■ Den inverse Park-transformasjonen:<br />
⎡ cos θr<br />
− sin θr<br />
1⎤<br />
−k<br />
⎢<br />
0<br />
0<br />
�<br />
⎥<br />
rr =<br />
⎢<br />
cos( θr<br />
−120<br />
) − sin( θr<br />
−120<br />
) 1<br />
⎥<br />
0<br />
0<br />
⎢⎣<br />
cos( θ − 240 ) − sin( θ − 240 ) 1⎥<br />
r<br />
r ⎦<br />
k<br />
−k<br />
k ⎡�<br />
⎤<br />
⎡ ⎤<br />
ss �<br />
−k<br />
�ss<br />
�<br />
� = ⎢ ⎥<br />
� =<br />
k<br />
⎢<br />
−k<br />
⎥<br />
⎣ � �rr<br />
⎦<br />
⎣ � �rr<br />
⎦<br />
Slide 400<br />
Slide 402<br />
Orientering av aksesystem<br />
■ Følgende orienteringer<br />
av aksesystem er vanlig:<br />
➨ Statororientert modell;<br />
dvs. at α k orienteres etter<br />
stator a-fase viklingsakse<br />
a s ; dvs. at f k=0<br />
➨ Rotororientert modell;<br />
dvs. at α k orienteres etter<br />
����� a-fase viklingsakse<br />
a r ; dvs. at f k=n<br />
➨ Romvektor-orientering;<br />
dvs. at α k orienteres etter<br />
en romvektor. Det er<br />
vanlig å benytte<br />
rotorfluksens romvektor;<br />
dvs. at f k= f ψr . Stasjonært<br />
lik f s<br />
k<br />
β<br />
s<br />
b<br />
θ�<br />
Rotorfluksorientert modell<br />
■ Aksen α k ”spikres” fast<br />
til rotorfluksvektoren:<br />
s<br />
θk<br />
= ξr<br />
k<br />
dψ<br />
k rβ<br />
ψ rβ<br />
≡ ≡ 0<br />
dt<br />
⇓<br />
r<br />
θr<br />
= ξ r<br />
s r<br />
ξr<br />
= ξr<br />
+ θ<br />
■ Romvektoren i α k -<br />
aksen:<br />
dψ<br />
k rβ<br />
ψ rβ<br />
≡ ≡ 0<br />
dt<br />
k<br />
ψ ≡ ψ<br />
rα<br />
k<br />
r<br />
k<br />
β<br />
s<br />
b<br />
θ�<br />
Trondheim 2000<br />
k<br />
α<br />
Ψr<br />
s<br />
a<br />
Trondheim 2000<br />
k<br />
α<br />
Ψr<br />
s<br />
a<br />
Trondheim 2000