Environmental Engineering Reference
In-Depth Information
˙
β
β
β
1
τ
1
s
r
Fig. 4.3 Pitch actuator model
where
ð V ; b ; X r Þ
ð V ; b ; X r Þ
B r ð V ; b ; X r Þ¼ o T r
oX r
k V ð V ; b ; X r Þ¼ o T r
oV
;
;
ð V ; b ; X r Þ
k b ð V ; b ; X r Þ¼ o T r
ob
;
The bar over the variables denotes the corresponding values at the operating
point, whereas the hat denotes deviations with respect to the operating point.
Substituting the linearized expression of the aerodynamic torque (Eq. 4.5 )in
the two-mass model (Eq. 4.3 ) and adding the linear model of the pitch system, the
wind turbine becomes described, locally around a given operating point, by
2
3
0
1
1 = N g
0
4
5
ð B r ð V ; b ; X r Þ B s Þ= J r
k b ð V ; b ; X r Þ= J r
K s = J r
B s = J r N g
x ¼
x
K s = J g N g
B s = J g N g
B s = J g N g
0
0
0
0
1 = s
ð 4 : 6 Þ
2
3
0
0
0
2
4
3
5 ;
V
T g
b r
4
k V ð V ; b ; X r Þ= J r
5
0
0
þ
0
1 = J g
0
0
0
1 = s
where x ¼½ H X r X g b T is the state. The signal V is the wind speed acting as
disturbance, and T g and b r are the control inputs.
4.3 Objectives and Control Scheme
A wind turbine normally works in different operating modes along the wind speed
range [ 2 ]. These operating modes are illustrated in the power-wind speed curve of
Fig. 4.4 . The control objectives in these regions are substantially different. Below
rated wind speed V N (region 1), the objective is to capture as much energy as
possible. In this case, the pitch angle is kept constant at its optimum value, whereas
the rotational speed is varied in proportion to the wind speed by properly
 
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