Environmental Engineering Reference
In-Depth Information
Fig. 4.1 Power coefficient
C P for a 5 MW variable-
speed variable-pitch wind
turbine [ 6 ]
0.5
0.4
0.3
0.2
0.1
0
−10
0
15
10
10
20
5
30
0
λ
β
Fig. 4.2 Two-mass model
describing the first drive-train
mode
T sh
T g
T r
K s
Ω r
B s
Ω
g
J g
J t
the purpose of this work that the torque reference of the power converter coincides
with the electrical torque T g imposed to the wind rotor. That is, it can be assumed
that T g is a control input.
The pitch actuator is a highly nonlinear mechanic and hydraulic system [ 5 ]. For
control-oriented purposes, it is usually modeled as a first-order low-pass filter with
saturation in the amplitude b and rate of change b. The pitch system is showed in
Fig. 4.3 . In the linear zone, the pitch actuator dynamics can be described by
b ¼ 1
s b þ 1
s b r ;
ð 4 : 4 Þ
where s is the time constant and b r the pitch angle command.
The drive-train dynamics (Eq. 4.3 ) is highly nonlinear. This nonlinearity comes
mainly from the aerodynamic torque (Eq. 4.2 ). For optimal control design, a linear
representation of the system dynamics is necessary. With this aim, the aerody-
namic torque is linearized around the operating point:
T r ð V ; b ; X r Þ¼ B r ð V ; b ; X r Þ X r þ k V ð V ; b ; X r Þ V þ k b ð V ; b ; X r Þ b ;
ð 4 : 5 Þ
 
Search WWH ::




Custom Search