51
Subsequently, the mass model has also been further calculated considering the
precise function of wind turbine system to produce energy relating to the rotational
speed of turbine of which the rotor-side inertia J r is
J
d
dt
T T K
t
t
m
l s
t t
ω
ω
= − −
(3.38)
The low-speed shaft torque is calculated as
T B
K
=
−
(
)+
−
(
)
ls
t
l s
l s
t
ls
θ θ
ω ω
(3.39)
The generator inertia J g is driven by the high-speed shaft and braked by the electromagnetic torque T g of the generator:
J
d
dt
T K
T
g
g
hs
g g
g
ω
ω
= −
−
(3.40)
If we assume the ideal gearbox with ratio n, then
n
T
T
=
=
=
ls
hs
g
t
g
ls
ω
ω
θ
θ
(3.41)
where the notations are the same as those of one mass model. K ls is the low-speed
shaft damping coefficient in [Nm/rad/s], ω g is the high-speed shaft angular speed in
[rad/s
2
], T m is the turbine torque in [Nm], T ls is the low-speed shaft torque in [Nm],
J g is the generator rotor moment of inertia in [kg m
2
], and T hs is the high-speed shaft
torque in [Nm]. After eliminating T ls time derivative from (3.39) and using (3.40)
and (3.41), the following dynamical system is derived:
dT
dt
B
K K
J
n
K K
J
B
K
J n
ls
ls
ls l
l
l
ls l
g
ls
g
l s
l
=
−





 +
−


 


 
−
+
ω
ω
1
2 2
2
J
n J J
T
K
J
T
K
nJ
T
g
l g
ls
ls
l
ls
g
g


 


 
+
+
α
(3.42)
where
K ls  = IG/L ls
D ls  = ξD s
ξ
ω
ω
= −






1
2
n
(3.43)
D
K m
s
l s
= 2
(3.44)
Results and Discussion