Environmental Engineering Reference
In-Depth Information
concepts of these main three platforms are also possible [
2
]. In June 2009, the
world's first spar buoy supported floating wind turbine was installed off the coast
of Norway in 220-m deep water [
3
].
The floating platform introduces six new degrees of freedom (DOFs) to the
system; these added DOFs, if not taken into account actively or passively, can
negatively affect the power production and turbine structural loading. The load
comparison between land-based and floating turbines shows dramatic increase in
the loading of the floating structure, basically, in tower base fore-aft and side-side
bending moments, blade flap-wise and edge-wise bending moments, and drive-
train torsional loading [
4
]. This overall increase in structural loading is related to
the motion of the platform in the fore-aft direction (platform pitch motion) that
induces the oscillatory wind inflow relative to the rotor, and excites the gyroscopic
yaw moment in combination with the spinning inertia of the rotor. The turbine
motion in the fore-aft direction in combination with the blade pitch control
engaged in the above-rated region results in a servo-induced negative damping to
the pitch motion. Considering, for example, a single DOF model of the floating
wind turbine where the platform pitch angle is the only considered DOF (assuming
rigid body model for tower, blades, drive-train, and platform). The equation of
motion of such simple model could be written as
Jn
þ
C n
þ
Kn
¼
hT
ð
11
:
1
Þ
where n
;
n
;
n are the platform pitch angle, rotational velocity and rotational
acceleration, respectively, J is the inertia term that combines the turbine and
platform pitch inertia in addition to the added inertia due to hydrodynamic radi-
ation in pitch, C is the damping term that combines the damping associated with
the hydrodynamic radiation in pitch and the linearized damping associated with
the hydrodynamic viscous drag in pitch, K is the stiffness term that combines the
hydrostatic restoring in pitch and the linearized hydrostatic restoring in pitch from
all mooring lines, h is the hub height, and T is the aerodynamic rotor thrust.
The aerodynamic rotor thrust depends on the relative wind speed at the hub
height, blade pitch angle b and rotor speed X
r
. Assuming a slow change in hub
translation, and using the first-order Taylor series expansion, then
T
T
0
o
T
oV
x
ð
11
:
2
Þ
with V is the average wind speed over the rotor disk, x is the tower top (hub)
velocity, and T
0
is the aerodynamic thrust over the rotor at the linearization point.
The hub translation and the platform pitch angle are related such as
x
¼
hn
:
ð
11
:
3
Þ
