190
energy [49, 50]. Hence, the functional mechanism of the gearbox of this PMSG
plays a vital role in converting the electric energy to DC current and it is quantified
by the d–q synchronous voltage equation as
V
Ri L
di
dt
L i
d
d
d
q
q q
= −
−
+
s
ω
V
Ri L
di
dt
L i
q
q
q
q
d d
= −
−
−
+
s
m
ω
ωλ
(10.31)
The electronic torque is given by
T
i
L L i i
q
d
q
d q
e =
+
−
(
)
1 5
. ρ λ
(10.32)
where L q represents the q axis inductance, L d is considered as the d axis inductor, i q
represents the q axis current, i d represents the d axis current, V q represents the q axis
voltage, V d denotes the d axis voltage, ω r represents the angular speed of rotor, λ
represents the amplitude of flux induced, and p is the number of pairs of poles.
Then the electronic torque is simplified by the following equation which demonstrates the dynamic modeling of wind energy as
V
V
V
V
R pL
p L
R pL
p L
pL
L
R
q
d
q
d
s
s
r
r
s
s
m
s
s
m
m
r m
=
+
+
−
0
0
0
0
ω
r r
r
r r
r m
m
r r
r
r
s
s
r
r
+
−
+
pL
L
L
p L
L
R pL
i
i
i
i
q
d
q
d
ω
ω
ω
(10.33)
where the stator side is expressed as
λ
λ
d
d
d
q
q
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 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
=
+
(10.34)
It is further simplified as
10 Zero-Emission Vehicles
energy [49, 50]. Hence, the functional mechanism of the gearbox of this PMSG
plays a vital role in converting the electric energy to DC current and it is quantified
by the d–q synchronous voltage equation as
V
Ri L
di
dt
L i
d
d
d
q
q q
= −
−
+
s
ω
V
Ri L
di
dt
L i
q
q
q
q
d d
= −
−
−
+
s
m
ω
ωλ
(10.31)
The electronic torque is given by
T
i
L L i i
q
d
q
d q
e =
+
−
(
)
1 5
. ρ λ
(10.32)
where L q represents the q axis inductance, L d is considered as the d axis inductor, i q
represents the q axis current, i d represents the d axis current, V q represents the q axis
voltage, V d denotes the d axis voltage, ω r represents the angular speed of rotor, λ
represents the amplitude of flux induced, and p is the number of pairs of poles.
Then the electronic torque is simplified by the following equation which demonstrates the dynamic modeling of wind energy as
V
V
V
V
R pL
p L
R pL
p L
pL
L
R
q
d
q
d
s
s
r
r
s
s
m
s
s
m
m
r m
=
+
+
−
0
0
0
0
ω
r r
r
r r
r m
m
r r
r
r
s
s
r
r
+
−
+
pL
L
L
p L
L
R pL
i
i
i
i
q
d
q
d
ω
ω
ω
(10.33)
where the stator side is expressed as
λ
λ
d
d
d
q
q
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 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
=
+
(10.34)
It is further simplified as
10 Zero-Emission Vehicles