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Slide 403
Slide 405
Slide 407
Hvordan bestemmes vinkelen til rotorfluksen?
■ Denne er gitt av rotorfluksens frekvens:
s
dξ
r
= ωn
⋅ f k = ωn
⋅ f ψr
dt
■ La oss finne et utrykk for f k :
k
k 1 dψ
rα
k
0 = rr
⋅ i rα
+ − ( f k − n)
⋅ ψ rβ
ωn
dt
k
d
k 1 ψ rβ
k
0 = rr
⋅ i rβ
+ + ( f k − n)
⋅ ψ rα
ωn
dt
■ Fra øvre likning:
ψr
1 dψ
r
0 = rr
⋅ i rα
+
ωn
dt
■ Fra nedre likning:
ψr
rr
⋅ i rβ
f k = f ψr
= − + n
ψ r
Moment
■ Moment utrykket for den transformerte modell:
k T k k T ⎛ k x k
k T
h ⎞ x h
( is
) � ψ = ( is
) �⎜
x ⋅ is
+ ψ ⎟ = ⋅ ( is
)
m e = s ⎜ σ
⎝ x r
r ⎟
⎠ x r
k
�ψ
r
x h k k k k x h ψr
1
ψr
m e = ⋅ ( ψ rα
⋅ isβ
− ψ rβ
⋅ i sα
) = ⋅ ψ r ⋅ isβ
= ⋅ ψ r ⋅ isβ
x r
x r 1 + σ r
■ Her har vi benyttet :
k
k x h k
ψ = x s σ ⋅ i s + ψ x = σ ⋅ x
r
σ s
x r
1
ψr
m e = ⋅ ψ r ⋅ isβ
1 + σ r
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2
x h
1
σ = 1 - = 1 −
x s ⋅ x r ( 1 + σs
) ⋅ ( 1 + σ r )
Den fullstendige rotorfluksorienterte modell
ψr
di sα
1 ψr
ψr
1 − σ ωn
ψr
= − ⋅ i f i
u
" sα
+ ωn
⋅ ψr
⋅ sβ
+ ⋅ ψ r + ⋅ sα
dt T
T x x
s
σ ⋅ r ⋅ h
σ
ψr
di sβ
1 ψr
ψr
1 − σ
ωn
= − ⋅ i s − ωn
⋅ f r ⋅ i s − ⋅ ωn
⋅ n ⋅ ψ r + ⋅ u
" β
ψ α
dt T
x h
x
s
σ ⋅
σ
dψ
r 1 x h ψr
= − ⋅ ψ r + ⋅ i sα
dt T T
r
r
s
ψr
dξ
⎛ rr
⋅ x h ⋅ i ⎞
r
s
n f r n ( f r n) ⎜
β
= ω ⋅
n
+ n⎟
ψ = ω ⋅ + = ω ⋅
dt
⎜ x ⎟
⎝ rψ
r ⎠
dn 1 ⎛ 1
= ⋅
dt T ⎜ ⋅ ψ
m ⎝1
+ σr
dθ
= ωn
⋅ n
dt
r
ψr
⎞
⋅ i s − m L ⎟
β
⎠
ψr
sβ
Trondheim 2000
Trondheim 2000
NTNU
NTNU
NTNU
Slide 404
Slide 406
Slide 408
Eliminasjon av rotorstrømmer…..
■ Fra fluksforslyngningslikningene:
k
k
k
ψ rα
= x h ⋅ i sα
+ x r ⋅ i rα
= ψ r
k
k
k
ψ rβ
= x h ⋅ i sβ
+ x r ⋅ i rβ
= 0
■ Utrykket for f k blir da:
rr
⋅ x h ⋅ isrβ
f k = f ψr
= + n
x ⋅ ψ
■ For rotorfluksens amplitude:
d
r
ψr
ψ r 1 x h ψr
= − ⋅ ψ r + ⋅ i sα
dt Tr
Tr
r
k
k − ψ r + x h ⋅ isα
⇒ - i rα
=
x r
k x h k
⇒ − i rβ
= ⋅ i sβ
x r
x r
Tr
=
ω ⋅ r
Spenningsbalanse i stator
n
r
Trondheim 2000
■ Da man skal ha indre statorstrømregulatorer ønskes statorstrøm
og rotorfluks som tilstandsvariable
■ Eliminerer så statorflukser og rotorstrømmer fra
spenningslikningen ved hejlp av følgende sammenhenger:
k
s
k
s ⋅ is
k
r
■ Spenningsbalanse i stator:
h
k
r
k
h ⋅ is
ψ = x + x ⋅ i ψ = x + x ⋅ i
ψr
disα
1 ψr
ψr
1−
σ ωn
ψr
= − ⋅ i
" sα
+ ωn
⋅ f ψr
⋅ isβ
+ ⋅ ψ r + ⋅ u sα
dt T
σ ⋅ T
s
r ⋅ x h x σ
ψr
disβ
1 ψr
ψr
1−
σ
ωn
ψr
= − ⋅ i
" sβ
− ωn
⋅ f ψr
⋅ i sα
− ⋅ ωn
⋅ n ⋅ ψ r + ⋅ u sβ
dt T
σ ⋅ x
s
h
x σ
r
k
r
" x σ
Ts
=
’
ωn
⋅ rs
2
’ ⎛ x h ⎞
rs
= rs
+
⎜ ⋅ rr
x ⎟
⎝ r ⎠
2
x h
1
x σ = σ ⋅ x s σ = 1 - = 1 −
x s ⋅ x r ( 1 + σ s ) ⋅ ( 1 + σ r )
Hva skal reguleres ?
■ Vi har to uavhengige komponenter av statorspenningen:
➨ Styrer momentet
➨ Styrer fluksens amplitude
■ Hvilken fluksamplitude ?
➨ Stator ψs ➨ Luftgapsfluks ψ h
➨ Rotor ψ r
Trondheim 2000
Trondheim 2000