Environmental Engineering Reference
In-Depth Information
1000
35
30
800
25
600
20
15
400
10
200
0
5
3
5
7
9 1 3 5 7 9 1 3 5
Fig. 11.2 Rotor thrust over operating regions, maximum at rated wind speed and blade pitch
angle active in full load region
Using Eqs. (
11.2
) and (
11.3
) in the equation of motion (
11.1
) then
x
þ
K
J
h
2
x
þ
h
2
þ
o
T
C
h
2
x
¼
T
0
ð
11
:
4
Þ
oV
An interesting result obtained from this simple model is the dependency of the
damping term on the thrust sensitivity to wind speed
oT
oV
. Using a closed-loop blade-
pitch speed-regulation controller along with the 5 MW mounted on the barge
platform as an example, the sensitivity of the closed loop could be ''ideally''
estimated from the slope of the steady-state thrust versus wind speed response
presented in Fig.
11.2
. The maximum negative slope can be found directly above
the rated wind speed; moreover, the maximum thrust over the rotor is at the rated
wind speed [
5
]. The decrease in thrust sensitivity in the full load region is due to
the engagement of the pitch control loop in this region (Fig.
11.2
). This control
loop changes the blade pitch angle such as to adapt the rotor aerodynamic effi-
ciency with the above-rated wind speeds, which in turn will also affects the
damping term in Eq. (
11.4
).
The negative damping of the platform pitch motion affects the turbine perfor-
mance, as this motion induces the oscillatory wind inflow relative to the rotor, and
in combination with the spinning inertia of the rotor it excites the gyroscopic yaw
moment which turns the turbine away from the wind. Several publications
explored the negative damping behavior and suggested some guidelines for con-
troller design to avoid it, yet, the most interesting result is presented by Larsen and
Hansen which states that, to avoid negative damping implied by a conventional
controller, the controller frequency should be less than the natural frequency of the
floating wind turbine, and the decreased performance of controlling power and
rotational speed can be compensated by a nonlinear gain on the pitch regulator [
6
].
Using this result, Jonkman updated the baseline gain-scheduled proportional
integral (GSPI) controller developed originally for land-based turbines to suit the
new conditions of floating platforms [
5
]. Other methods to stabilize platform
