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β
=
90
0
max
β
β
Ki
1
s
Re
f
P
K
+
Re
f
τ
P
s
β =
0
0
min
P
Fig. 6.
Pitch angle controller
2.5
Wind Generator Model
Most wind farms are made of induction generators because they are cheap and robust.
The dq stator and rotor voltage equations model in generating mode are as follows
[14, 15].
v
=−
r i
−
ωλ
−
p
λ
(19)
qs
s qs
qs
qs
v
=−
r i
+
ωλ
−
p
λ
(20)
ds
s ds
qs
ds
(
)
v
=−
r i
−
ωωλ
−
−
p
λ
(21)
qr
r qr
r
qr
qr
(
)
v
=−
r i
+
ωωλ
−
−
p
λ
(22)
dr
r dr
r
qr
dr
()
d
dt
.
where
r
,
r
are the stator and rotor speed resistance,
p
is
term.
The equation presented in (19)-(22) is a fifth order model. Third order model is
obtained by neglecting the transient term in the stator voltage equation. The stator and
rotor flux equations are
λ
=+
Li
L i
(23)
qs
s qs
m qr
λ
=+
Li
L i
(24)
ds
s ds
m dr
λ
=+
Li
L i
(25)
qr
r qr
m qs
λ
=+
Li
L i
(26)
dr
r dr
m ds
where
L
,
L
,
L
are the stator, rotor and magnetizing inductance respectively.
ds
i
,
qs
i
i
and
q
i
are the stator and rotor d-axis and q-axis current.
The electromechanical torque,
dr
T
developed by the induction generator in pu can
be derived as (27)
1
(
)
T
=
λλ
−
λλ
(27)
e
qs
dr
qr
ds
σ
where
L
LL
2
σ =−
1
m
rs
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