Analysis of interconnection of permanent magnet generators to the ...

2. MATHEMATICAL MODEL OF PM
GENERATOR
x = x = x
ak d
f k d
a d
⎡ψ
d
⎢
⎢ψ
⎢
⎣ψ
f
v
v
k d
⎡ψ
q
⎢
⎣ψ
⎤ ⎡ x
⎥ ⎢
⎥ = ⎢x
⎥ ⎢
⎦ ⎣
x
k q
d
a d
a d
⎤ ⎡ x
⎥ = ⎢
⎦ ⎣
x
1
dψ
q
a k q
x
x
x
a d
k d
a d
x
x
ω
a k q
k q
x
x
x
a d
a d
f
⎤
⎥ ⋅
⎦
d
d = ⋅ − ⋅ψ
q
ω0
dt ω0
q
1 dψ
q ω
= ⋅ − ⋅ψ
d
dt ω
ω0
0
⎤ ⎡ i
⎥ ⎢
⎥ ⋅ ⎢i
⎥ ⎢
⎦ ⎣
i
⎡ i
⎢
⎣
i
q
k q
a
⎤
⎥
⎦
d
k d
f
+ r ⋅ i
a
d
+ r ⋅ i
q
⎤
⎥
⎥
⎥
⎦
v
v
v
f
=
1
ω 0
dψ
f
⋅
dt
1 dψ
⋅
ω dt
+ r
f
⋅ i
k d
k d = + rk
d ⋅ ik
d
0
1 dψ
k
⋅
ω dt
q
k q = + rk
q ⋅ ik
q
0
T
e
= ψ ⋅ i −ψ
⋅ i
d
2H
dω
⋅ = T e + T m
dt
ω 0
q
q
d
f
= 0
= 0
⎡ψ
d
⎢
⎣ψ
k d
⎡ψ
q
⎢
⎣ψ
k q
ψ = x
−ψ
0 ⎤ ⎡ x
⎥ =
−ψ
⎢
0 ⎦ ⎣
x
−ψ
0 ⎤ ⎡ x
⎥ =
−ψ
⎢
0 ⎦ ⎣
x
⋅ i
0 a d f 0
d
a d
q
a q
x
x
x
x
a d
k d
a q
k q
⎤
⎥ ⋅
⎦
⎡ i
⎢
⎣
i
⎤ ⎡ i
⎥ ⋅ ⎢
⎦ ⎣
i
d
k d
q
k q
⎤
⎥
⎦
⎤
⎥
⎦
CLASSICAL MACHINE
PERMANENT MAGNET MACHINE
09. 09. 2009. DEMSEE 2009 4