Damping of Wind Turbine Tower Oscillations through Rotor Speed ...
Damping of Wind Turbine Tower Oscillations through Rotor Speed ...
Damping of Wind Turbine Tower Oscillations through Rotor Speed ...
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<strong>Wind</strong> speed [m/s]<br />
18<br />
17<br />
16<br />
15<br />
14<br />
13<br />
12<br />
0 10 20 30 40 50 60 70<br />
t [s]<br />
Figure 4: <strong>Wind</strong> speed used for simulation in Bladed.<br />
<strong>Rotor</strong> speed [rpm]<br />
25<br />
24.5<br />
24<br />
23.5<br />
23<br />
22.5<br />
22<br />
0 10 20 30 40 50 60 70<br />
t [s]<br />
Figure 5: Response <strong>of</strong> rotor speed <strong>of</strong> the system<br />
controlled with PID controller.<br />
Pitch angle [deg]<br />
16<br />
15<br />
14<br />
13<br />
12<br />
11<br />
10<br />
9<br />
8<br />
7<br />
0 10 20 30 40 50 60 70<br />
t [s]<br />
Figure 6: Response <strong>of</strong> pitch angle <strong>of</strong> the system<br />
controlled with PID controller.<br />
<strong>Tower</strong> top displacement [m]<br />
0.12<br />
0.1<br />
0.08<br />
0.06<br />
0.04<br />
0.02<br />
0<br />
-0.02<br />
-0.04<br />
-0.06<br />
-0.08<br />
0 10 20 30 40 50 60 70<br />
t [s]<br />
Figure 7: Response <strong>of</strong> tower top displacement <strong>of</strong> the<br />
system controlled with PID controller.<br />
While rotor speed and pitch angle behavior is<br />
satisfactory, attention should be paid to the<br />
tower top oscillations shown in fig. 7. It can be<br />
observed that tower top experiences lightly<br />
damped oscillatory behavior. These lasting<br />
oscillations, although small in magnitude,<br />
contribute to material fatigue and can lead to<br />
structure premature failure. So in the following<br />
sections two methods for controller design that<br />
aim at reduction <strong>of</strong> tower top oscillations are<br />
proposed.<br />
5. Input-output pole placement<br />
controller<br />
In this section the pitch controller with inputoutput<br />
structure is designed using well known<br />
pole placement method [6]. As design objective<br />
in this method the desired behavior <strong>of</strong> the<br />
closed loop system has to be chosen. The pitch<br />
controller GPC is then designed to assure that<br />
closed loop system behaves in the chosen<br />
manner. Transfer functions (14) and (15) form<br />
the linearised wind turbine model that can be<br />
described with the principle scheme shown in<br />
fig. 8.<br />
Figure 8: Principle scheme <strong>of</strong> the linearised wind<br />
turbine model.<br />
From the principle scheme given in fig. 8 closed<br />
loop transfer function with respect to wind<br />
speed change can be derived:<br />
G<br />
CL_ w<br />
Δω()<br />
s<br />
Gw() s<br />
= =<br />
. (16)<br />
Δ v () s 1 + G () s G s G () s<br />
w CL PC SD<br />
( )<br />
The pitch controller GPC has to assure that<br />
closed loop transfer function (16) is equal to the<br />
chosen model transfer function Gm:<br />
( ) !<br />
G s = G () s . (17)<br />
CL _ w m<br />
β