45
From stator side the equation is
λ
λ
d
d
d
q
sq
d
d
d
L i
L i
L i
L i
L L L
L L L
V
Ri
s
s s
m r
s
s
m r
s
l s
m
r
l r
m
s
s s
=
+
=
+
= +
= +
=
+
d d
dt
V
Ri
d
dt
d
q
q
q
λ
λ
s
s
s s
s
=
+
(3.11)
From rotor side the equation is
λ
λ
λ ω λ
d
d
d
q
q
q
d
d
d
q
q
L i
L i
L i
L i
V
Ri
d
dt
V
R
r
r r
m s
r
r r
m s
r
r r
r
r
r
r
r
=
+
=
+
=
+
+
= i i
d
dt
q
q
d
r
r
r
r
+
−
λ ω λ
(3.12)
For the air gap flux linkage, the equations are
λ
λ
d
d
d
q
q
q
L i i
L i i
m
m
s
r
r
m
r
s
=
+
(
)
=
+
(
)
(3.13)
where R s , R r , L m , L ls , L lr , ω r , i d , i q , V d , V q , λ d , and λ q are the stator winding
resistance, motor winding resistance, magnetizing inductance, stator leakage inductance, rotor leakage inductance, electrical rotor angular speed, current, voltage, and
fluxes, respectively, of the d–q model, respectively [20, 21]. Simply, the net wind energy
power considering the torque of turbine (T t ) in terms of rotational speed is calculated as
P
AC
R
w
p
opt
opt
,
=
( )


 


 
1
2
3
ρ
λβ
ω
λ
(3.14)
T
AC
R
t
p
opt
opt
,
=
( )


 


 
1
2
3
ρ
λβ λ
ω
(3.15)
Materials and Simulation