Environmental Engineering Reference
In-Depth Information
pitch actuator. The rotor diameter is 126 m, the hub height is 90 m, it has a gear
box ratio of 97, the rated wind speed is 11.3 m/s, the cut-out wind speed is 25 m/s
and the rated rotor rotational speed is 12.1 rpm, so the nominal generator speed is
1,173 rpm. The family of linear models of this wind turbine is obtained in different
operating points from the wind turbine non-linear model using the linearization
tool of this software. Twelve operating points are defined according to wind speeds
from 3 to 25 m/s. Once the non-linear model has been linearized, a modal analysis
of the structural and non-structural modes of the wind turbine is essential to carry
out a good control system. For example, the most important modes of the Upwind
wind turbine in the operating points with wind speeds of 11 and 19 m/s are
represented in Table
5.1
. The 1P non-structural mode is related to the rotor
rotational speed, which nominal value is 0.2 Hz for this wind turbine.
The plants of the family of linear models are expressed by the state-space matrices
(Eq.
5.1
) and they have different inputs and outputs. The inputs u(t) are the collective
pitch angle b(t), the individual pitch angle in each blade b
1
(t), b
2
(t), b
3
(t), the
generator torque control T(t) and the disturbance input w(t) caused by the wind speed.
The outputs y(t) are the sensorized measurements used to design the controller. The
outputs used in the different designs shown in this chapter are the generator speed
w
g
(t), the tower top fore-aft acceleration a
Tfa
(t), the tower top side-to-side acceler-
ation a
Tss
(t) and the bending flapwise M
flap
(t) and the bending edgewise
M
edge
(t) moments in the blade roots. Due to the non-linear model complexity, and the
number of modes taken into account, the order of the linear models is 55.
x
ð
t
Þ¼
A
x
x
ðÞþ
B
u
u
ðÞþ
B
w
w
ðÞ
y
ð
t
Þ¼
C
x
x
ðÞþ
D
u
u
ðÞþ
D
w
w
ðÞ
ð
5
:
1
Þ
Figure
5.3
shows the SISO family of linear plants of the Upwind wind turbine
model which relates the collective pitch angle control signal to the measured
generator speed. Three operating points in the above rated zone are presented to
demonstrate the differences between them for wind speeds of 13, 19 and 25 m/s
due the non-linearities of the wind turbine in this control zone.
5.2.2 Baseline Control Strategy
The baseline control strategy to regulate the electric power production for the
Upwind 5 MW wind turbine developed in this chapter is based on the ABCD curve
shown in Fig.
5.1
and the control loops explained in [
10
]. This strategy is named C1
and it is used to be compared with the robust controllers described in next sections. In
the below rated zone, the generator torque control depends on the generator speed
measurement (Eq.
5.2
). The generator torque T
br
is proportional to the square of the
generator speed by a constant K
opt,
where K
opt
is 2.14 Nm/(rad/s
2
) for the Upwind
model. In this way, the wind turbine works with the optimum power coefficient value.
