6 folier pr. side - NTNU

NTNU
NTNU
NTNU
Slide 373
Slide 375
Slide 377
Resulterende pu-modell for
asynkronmaskinen på komponentform
k
k k 1 dψ
sα
k
u sα
= rs
⋅ isα
+ − f k ⋅ ψ sβ
ωn
dt
k
1 dψ
k k
sβ
k
u sβ
= rs
⋅ isβ
+ + f k ⋅ ψ sα
ωn
dt
k
1 dψ
k k
sγ
u sγ
= rs
⋅ isγ
+
ωn
dt
dθ
k
= ωn
⋅ f k
dt
ψ
ψ
k
sα
k
sβ
k
sγ
= x ⋅ i
s
s
sσ
k
sα
k
sβ
k
sγ
h
h
k
rα
+ x ⋅ i
k
rβ
= x ⋅ i + x ⋅ i
ψ = x ⋅ i
k
k k 1 dψ
rα
k
u rα
= rr
⋅ i rα
+ − ( f k − n)
⋅ ψ rβ
ωn
dt
k
1 dψ
k k
rβ
k
u rβ
= rr
⋅ i rβ
+ + ( f k − n)
⋅ ψ rα
ωn
dt
k
1 dψ
k k
rγ
u rγ
= rr
⋅ i rγ
+
ωn
dt
dθr
= ωn
⋅ f r = ωn
⋅ ( f k − n)
dt
k
rα
k
rγ
rσ
k
sα
k
rγ
k
rα
ψ = x h ⋅ i + x r ⋅ i
k
k
ψ rβ
= x h ⋅ i sβ
+ x r ⋅ i
ψ = x ⋅ i
k
rβ
Trondheim 2000
Definisjoner av magnetiseringsstrømmer
■ Sammenheng mellom flukser og magnetiseringsstrømmer:
k
s
h
k
μs
k
r
k
μr
ψ = x ⋅ i ψ = x ⋅ i ψ = x ⋅ iμ
■ Settes inn i uttrykkene for fluksforslyngningene:
k k
k
ψ = x s s ⋅ is
+ x h ⋅ i r
k
k k
ψ = x r h ⋅ i s + x r ⋅ i r
h
k
h
x s = x h + x sσ
= x h + σs
x h = (1+
σs
) ⋅ x h
x r = x h + x rσ
= x h + σr
x h = (1+
σr
) ⋅ x h
k
k k
k k
k
k k k
i μs
= ( 1+
σs
) ⋅ i s + i r i μr
= is
+ ( 1 + σr
) ⋅ i r iμ
= i s + i r
Statororientert modell
■ Aksesystemet og de ������� stator og rotor viklinger er spikret
fast i forhold til ������:
dθ
k
= ωn
⋅ f k ≡ 0
dt
dθ
= ωn
⋅ n
dt
θ r = −θ
■ Settes inn i uttrykkene for fluksforslyngningene:
s
s s 1 dψ
s
s s
s
u s = rs
⋅ is
+
ψ = x s s ⋅ is
+ x h ⋅ i r
ω dt
n
s
s 1 dψ
r
s
0 = rr
⋅ i r + − �⋅
n ⋅ ψ r
ωn
dt
me
=
s T ( is
)
s s s s s
�ψ
= ψ s sα
⋅ isβ
− ψ sβ
⋅ isα
s
s s
ψ = x r h ⋅ i s + x r ⋅ i r
■ For to dimensjonale romvektorer har man at romvektoren i
statorkoordinater lik dens koordinatvektor
s s ⎡1⎤
⎡0⎤
⎡I
a ⎤ s
I s = Ia
a + Ib
b = Ia
⎢ I b = ⎢ = Is
0
⎥ + ⎢
1
⎥
I
⎥
⎣ ⎦ ⎣ ⎦ ⎣ b ⎦
h
k
Trondheim 2000
Trondheim 2000
NTNU
NTNU
NTNU
Slide 374
Slide 376
Slide 378
Ser bort i fra γ-systemet ……….
■ Kan da benytte to-dimensjonale romvektorer:
k
k k 1 dψ
s
k
u s = rs
⋅ i s + + � ⋅ f k ⋅ ψ s
ωn
dt
k
k k 1 dψ
r
k
u r = rr
⋅ i r + + � ⋅ ( f k − n)
⋅ ψ r
ωn
dt
m e =
k T k k k k k
( is
) � ψ = ψ ⋅ i − ψ ⋅ i
dn
Tm
= m e − m L
dt
dθ
k
= ωn
⋅ f k
dt
s
sα
sβ
sβ
sα
2
J ⋅ Ω basis
Tm
=
Sn
dθ
= ωn
⋅ n
dt
k
k
k
k ⎡i
⎤ ⎡ ⎤ ⎡ψ
⎤
sα
k u sα
k sα
i s = ⎢ k ⎥ u s = ⎢ k ⎥ ψ s = ⎢ k ⎥
⎢⎣
i sβ
⎥⎦
⎢⎣
u sβ
⎥⎦
⎢⎣
ψ sβ
⎥⎦
k k
k
ψ = x s s ⋅ is
+ x h ⋅ i r
k
k k
ψ = x r h ⋅ is
+ x r ⋅ i r
θ r = θk
− θ
⎡0 −1⎤
= ⎢ ⎥
⎣1
0 ⎦
Orientering av aksesystem
■ Følgende orienteringer
av aksesystem er vanlig:
➨ Statororientert modell;
dvs. at α k orienteres etter
stator a-fase viklingsakse
a s ; dvs. at f k=0
➨ Rotororientert modell;
dvs. at α k orienteres etter
����� a-fase viklingsakse
a r ; dvs. at f k=n
➨ Romvektor-orientering;
dvs. at α k orienteres etter
en romvektor. Det er
vanlig å benytte
rotorfluksens romvektor;
dvs. at f k= f ψr . Stasjonært
lik f s
k
β
�
s
b
θ�
Rotorfluksorientert modell
■ Aksen α k ”spikres” fast
til rotorfluksvektoren:
s
θk
= ξr
k
dψ
k rβ
ψ rβ
≡ ≡ 0
dt
⇓
r
θr
= ξ r
s r
ξr
= ξr
+ θ
■ Romvektoren i α k -
aksen:
dψ
k rβ
ψ rβ
≡ ≡ 0
dt
k
ψ ≡ ψ
rα
k
r
k
β
s
b
θ�
Trondheim 2000
k
α
Ψr
s
a
Trondheim 2000
k
α
Ψr
s
a
Trondheim 2000