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

e obtained analyzing fig. 12. This figure shows
comparison of Bode plots of controllers
designed with different values of desired tower
damping D'.
Figure 12: Bode plots of input-output pole placement
controllers designed to achieve different values of
tower damping D'.
From fig. 12 it becomes clear that increased
tower damping results in high pass controller
behavior. This has a consequence of increased
pitch activity which in turn results in additional
oscillations and finally cancels out the
advantages of proposed design methodology. So
a tradeoff between desired increase in tower
damping and pitch activity has to be made.
6. Full state feedback controller
The input-output pole placement controller
described in section 5 has shown some
promising results but its ability to damp the
tower oscillations is limited. Key cause for this
is the fact that it doesn't use information about
actual tower oscillations but only rotor speed
feedback. Damping of tower oscillations by
addition of tower top speed feedback to PID
controller is proposed in [1]. Tower top speed
measurement can be obtained from tower top
acceleration measured by accelerometers that
are nowadays almost a standard part of wind
turbine control system. In our approach we use
slightly different methodology. Instead of
extended PID controller we use full state
feedback controller designed using pole
placement method. Desired closed loop
behavior is chosen in the same way as for
described pole placement controller. For this
purpose process model (13) has to be rewritten
in the state space form:
x� = A⋅ x+ B⋅u, y = C⋅ x+ D⋅u. (19)
State variables used for system description and
control are rotor speed ω , rotor acceleration
ω� , tower top speed x� t and tower top
acceleration x�� t , while system inputs are wind
speed v w , pitch angle β and generator torque
M g :
⎡ω⎤ ⎢ ⎡ v ⎤ w
� ω
⎥
⎢ ⎥
x = ⎢ ⎥,
u = β
x ⎢ ⎥.
(20)
⎢�⎥ t
⎢ ⎥ ⎢M⎥ g
x ⎣ ⎦
⎣��t ⎦
Rotor speed and tower acceleration are
measured variables while other two states are
derived from them. Using Ackermann's formula
[6] vector of feedback gains for selected states
can be calculated. System with such a controller
was tested in Bladed using the same wind
stepwise change as in sections 4 and 5.
Simulation results are shown in the figures 13-
15. From these figures it can be seen that full
state feedback controller maintains good rotor
speed regulation while at the same time
achieving better damping of the tower
oscillations and practically removing the
oscillatory movement of the tower. The pitch
activity in this case increases considerably so a
tradeoff between tower oscillations' damping and
pitch activity is necessary.
To examine the behavior of three described
controllers in more realistic conditions the
system behavior in 3D turbulent wind field was
simulated in Bladed. Further information about
simulations of 3D turbulent wind fields can be
found in e.g. [7]. Let's just mention here that
turbulent wind field was generated in Bladed
Rotor speed [rpm]
25
24.5
24
23.5
23
22.5
22
0 10 20 30 40 50 60 70
t [s]
Figure 13: Response of rotor speed of the system
controlled with full state feedback controller.