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with no restriction on pitch actuation. However, we may want to minimize pitch actuation in
addition to generator speed error or particular loads of interest. It is possible that additional
preview time may be useful in meeting this combined objective. This topic is currently under
investigation.
10.4 Blade Effective Wind Speed
Before analyzing lidar measurement error in depth, it is important to define the wind speed
quantities that are of interest for blade pitch control. For collective pitch control, the effective
wind speed experienced by the rotor is often calculated by integrating the wind speeds across
the entire rotor disk using the formula:
1
⎛
⎞
urotor =
⎜
⎝
2π
R
0
0
2π
R
0
u 3 (r,φ)CP (r)rdrdφ
⎟
⎠
0
CP (r)rdrdφ
3
, (229)
where CP (r) is the radially-dependent coefficient of power and R is the rotor radius (Schlipf
et al., 2012b). The resulting urotor is the uniform wind speed that would produce the same
power as the actual distribution of wind speeds across the rotor disk. Note that Eq. (229) is
only a function of the u component of wind, which is perpendicular to the rotor plane (see
Fig. 133), rather than also including the horizontal v and vertical w components. Because u
has a significantly greater impact on the turbine’s aerodynamics than v or w, the calculation
ofeffective wind speeds at the turbine is performed solelyforthe u component.Section 10.4.1
describes the relative importance of the u, v, and w wind speed components in further detail.
For individual pitch control, the effective wind speeds experienced by each individual blade
are ofinterest, ratherthan a rotoraveraged quantity.The bladeeffective wind speedused here
is a weighted sum of wind speeds along the blade span such that wind speeds at each location
are weighted according to their contribution to overall aerodynamic torque. Aerodynamic
torque δQ(r) produced by a segment of the blade with spanwise thickness δr at radial
distance r along the blade can be described using the radially dependent coefficient of torque
CQ(r) as
δQ(r) = ρπr 2 u 2 (r)CQ(r)δr, (230)
where ρ is the air density and u(r) is the u component of the wind speed at radial distance
r along the blade (Moriarty and Hansen 2005; WT Perf 2012). Although other weighting
variables could be chosen for the definition of blade effective wind speed, aerodynamic torque
is used here because it is directly related to the power generated by the turbine.
Using Eq. (230), the torque-based blade effective wind speed is given by
1
⎛ ⎞
ublade =
⎜
⎝
R
u 2 (r)CQ(r)r 2 dr
CQ(r)r 2 ⎟
⎠
dr
0
R
0
2
. (231)
A linearized form of Eq. (231) is used to calculate blade effective wind speed by integrating
the wind speeds along the blade using the linear weighting function
CQ(r)r
Wb(r) =
2
. (232)
R
0
CQ(r)r 2 dr
A linear blade effective wind speed is used because of its simplicity and because the statistics
of a linear combination of wind speeds are generally easy to calculate. Figure 137 illustrates
the blade effective weighting function Wb(r) calculated using WT Perf (2012) for the NREL
5-MW turbine model at the rated wind speed U = 11.4 m/s, and two above-rated wind
speeds (13 m/s and 15 m/s). In above-rated conditions, the weighting curves change with
wind speed because the steady-state blade pitch angle increases as wind speed increases
(Jonkman et al., 2009).
200 DTU Wind Energy-E-Report-0029(EN)