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Skalert modell - pu-modell
■ Ønsket form på induktansmatrisen:
⎡x
ad + x sσ
0 0 x ad x ad 0 ⎤
⎢
0 x x 0 0 0 x
⎥
⎢
aq + sσ
aq ⎥
⎢ 0 0 x 0 0 0 ⎥
r
sσ
� = ⎢
⎥
⎢ x ad 0 0 x ad + x fσ
x ad 0 ⎥
⎢ x ad 0 0 x ad x ad + x D 0 ⎥
σ
⎢
⎥
⎢⎣
0 x aq 0 0 0 x aq + x Qσ
⎥⎦
( L + L ) ⋅ ω ⋅ Î
3 / 2 ⋅ ( L − L ) ⋅
3 / 2 ⋅ a0
g
x ad =
Û n
n
n
x aq =
a0
g ωn
⋅ Î n
Û n
Skalert modell - pu-modell
■ For multiplisere med skaleringsmatrisen, samt sette
inn produkt av skelaringsmatrisen og dens inverse:
r
r r r dΨ
r
U = � I + + ω ⋅ � Ψ
dt
r
r r r −1
r −1
dψ
−1
r
u = � u U = � u � �i
i + � u � ψ + n ⋅ ωn
� u � �ψ
ψ
dt
■ Endelig form blir:
r r r 1 dψ
r
u = � i + + n ⋅ � ⋅ ψ
ω dt
n
r
Resulterende pu-modell for
synkronmaskinen
1 dψ
d
u d = rs
⋅ i d + − n ⋅ ψ q
ωn
dt
1 dψ
q
u q = rs
⋅ i q + + n ⋅ ψ d
ωn
dt
1 dψ
0
u 0 = rs
⋅ i 0 +
ωn
dt
ψ d = x d ⋅ i d + x ad ⋅ i f + x ad ⋅ i D
ψ q = x q ⋅ i q + x aq ⋅ i Q
ψ 0 = x aσ
⋅ i 0
x d = x ad + x aσ
x q = x aq + x aσ
dn
Tm
= m e − m L
dt
dθ
= ωn
⋅ n
dt
x f = x ad + x fσ
x D = x ad + x Dσ
x Q = x aq + x Qσ
m e = ψ d ⋅ i q − ψ q ⋅ i d
1 dψ
f
u f = rf
⋅ i f +
ωn
dt
1 dψ
D
0 = rD
⋅ i D +
ωn
dt
1 dψ
Q
0 = rQ
⋅ i Q +
ωn
dt
ψ f = x ad ⋅ i d + x f ⋅ i f + x ad ⋅ i D
ψ D = x ad ⋅ i d + x ad ⋅ i f + x D ⋅ i D
ψ Q = x aq ⋅ i q + x Q ⋅ i Q
℘=
u d ⋅ i d + u q ⋅ i q + 2 ⋅ u 0 ⋅ i 0
J ⋅ Ω mek,
n
Tm
=
Sn
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Skalert modell - pu-modell
■ Valg av basis-verdier for stator viklinger:
I s , basis = Î n U s,
basis = Û n
Û n Û n
Ψs,
basis = =
ω 2π
⋅ f
■ Valg av basis-verdier for de andre viklinger er gitt
av kravene til formen på induktansmatrisen
■ Total 18 basisverdier å velge
−1
Sψ
= diag
−1
Su
= diag
−1
Si
= diag s,
basis
[ Ψs,
basis Ψs,
basis Ψs,
basis Ψf
, basis ΨD,
basis ΨQ,
basis ]
[ Us
, basis Us,
basis Us
, basis U f , basis U D,
basis U Q,
basis ]
[ I I I I I I ]
s,
basis
s,
basis
f , basis
D,
basis
n
Q,
basis
Skalert modell - pu-modell
■ Man får samme basis for effekt i alle viklinger:
3
Sn = ⋅ Û n ⋅ În
= U f , basis ⋅ I f , basis = U D,
basis ⋅ I D,
basis = U Q,
basis ⋅ I
2
■ Skalerte likning for momentet:
Sn
3 Û n ⋅ Î n 3
M basis = M n = = ⋅ p ⋅ = ⋅ p ⋅ Ψn
⋅ Î n
Ω mek,
n 2 ωn
2
⋅ ( Ψ ⋅ I − Ψ ⋅ I )
3
⋅ p
M
d q q d
e
m e = =
2
= ψ d ⋅ i q − ψ q ⋅ id
M 3
n ⋅ p ⋅ Ψn
⋅ Î n
2
Resulterende pu-modell for
Permanent Magnet synkronmaskinen
1 dψ
d
u d = rs
⋅ id
+ − n ⋅ ψ q
ω dt
1 dψ
u 0 = rs
⋅ i 0 +
ω dt
ψ = x ⋅ i + ψ
d
x = x + x
d
e
d
ad
d
d
q
aσ
n
n
m
q
0
d
ψ = x ⋅ i
q
q
m
aq
q
q
q
x = x + x
aσ
q
ψ = x ⋅ i
0
d
aσ
0
m = ψ ⋅ i − ψ ⋅ i = ψ ⋅ i − ( x − x ) ⋅ i ⋅ i
d
q
n
n
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Q,
basis
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1 dψ
q
u q = rs
⋅ i q + + n ⋅ ψ d
ω dt
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