Wind Energy

154 A. Rauh et al.
2000
1500
1000
500
L
6 8 10 12 14 16
U
1200
1000
800
600
400
L
b)
200
U
0
5 6 7 8 9 10 11 12
Fig. 27.1. (a) Schematic power curve as an attractor. (b) 20-s (U, L) trajectory
in relation to the power curve. Horizontal and vertical units are m s −1 and kW,
respectively
2500
2000
1500
1000
500
L
5 10 15 20 25
Fig. 27.2. Cluster of 10 4 one Hz points (2 MW turbine at Tjareborg)
27.2 Power Curve from Measurement Data
An inspection of the point cluster in Fig. 27.2 suggests to define an empirical
power curve by the location where, in a given speed bin, the maximal density of
points L(ti) is found. This extremal property is expected, if the power curve
is an attractor. In previous work [2], the following expectation values were
considered ∆jk := Uj,Lk with the suffix Uj,Lk denoting
the restriction to the speed and power bin Uj and Lk, respectively. For a
given speed bin Uj, the corresponding point on the power curve was defined
by the power bin L k(j) where ∆ jk(j) changes sign. In practice this may cause a
problem, if for a given speed bin there are several locations with sign change.
The maximum principle, on the other hand, should give a unique result after
properly defining the bin sizes:
U