Damping of Wind Turbine Tower Oscillations through Rotor Speed ...

From (16) and (17) it follows that pitch
controller has a form of :
1 Gw() s −Gm()
s
GPC() s = ⋅ . (18)
G s G () s G () s
( )
SD β
m
It should be noted that the above expression
often needs to be modified to assure that the
controller is causal. Details on this design
method can be found in [6].
The crucial step in controller design using
described method is the choice of model
transfer function Gm. It is important to choose
model transfer that is achievable for the system
in scope and that assures its satisfactory
behavior. One possibility that is very common
in the literature is the use of standard forms
such as Butterworth or binomial form.
However, these forms can be rather difficult to
relate to system physical properties. So another
approach is used in this paper. As previously
said our primary goal is the reduction of tower
oscillations. Tower oscillations can be reduced
if the tower modal damping increases what
would require change in tower structural
parameters such as mass and stiffness
distributions. Our goal is to achieve similar
increase of tower damping by means of pitch
controller actions without change in tower
structural parameters. In that sense as a
controller design objective we set a desired
increase of tower modal damping. In other
words tower modal damping D in the last
expression in (13) is replaced with desired
modal damping D' thus forming system model
with new set of parameters. This model is
linearised and transfer functions (14) and (15)
are calculated. Using calculated transfer
functions PID controller is designed following
the guidelines described in section 4. Having
the controller designed it is possible to calculate
closed loop transfer function (16). This closed
loop transfer function, obtained using system
with increased damping and PID controller is
then regarded as desired model transfer
functions Gm for the real system. In other words
our goal is to design a controller that assures
that real system behaves as its tower damping
has increased. The system response with Pole
placement controller was simulated in Bladed
using previously described full featured model.
Wind used for simulation was the same as in
section 4. Simulation results are given in the
figures 9-11. From these figures it can be seen
that pole placement controller achieves almost
the same regulation of rotor speed as PID
Rotor speed [rpm]
25
24.5
24
23.5
23
22.5
22
0 10 20 30 40 50 60 70
t [s]
Figure 9: Response of rotor speed of the system
controlled with input-output pole placement
controller.
Pitch angle [deg]
16
15
14
13
12
11
10
9
8
7
0 10 20 30 40 50 60 70
t [s]
Figure 10: Response of pitch angle of the system
controlled with input-output pole placement
controller.
Tower top displacement [m]
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
0 10 20 30 40 50 60 70
t [s]
Figure 11: Response of tower top displacement of
the system controlled with input-output pole
placement controller.
controller does. This was to be expected since
the PID controller is the "core" of the pole
placement controller design. At the same time
tower oscillations are more damped. Since the
tower structure remains the same this damping
is achieved by higher pitch control activity than
in the case of PID controller.
The question that naturally appears is the limit
to which extend the tower oscillations can be
damped in this way. Answer to this question can