Wind Energy

32 Handling Systems Driven by Different Noise Sources 181
Gaussian distributed around V with variance σ2 = β/2α and the difference
between the actual and the “real” power decays exponentially. The factor κ
(inverse relaxation time) is just a constant in this approach but might well be
extended to a more complex function as proposed by [4]. For different mean
velocities V and defining
Pr(u) =
� au 3 , u < urated,
Prated, u≥ urated,
(32.7)
the corresponding wind speed and the resulting power output time series can
be reconstructed by integration of (32.6). Prated and urated denote the turbinespecific
rated power and the corresponding rated velocity.
In a first step we apply the IEC-norm to determine the power curve from
the time series. As can be seen from Fig. 32.1 the resulting power curve differs
significantly from the real one, the more the larger the turbulence intensity.
This means that although the evolution of the power is purely deterministic
the standard averaging procedure is – as a matter of principle – not able to
reproduce the correct power curve.
Therefore we suggest in a second step to calculate the drift coefficient
according to (32.5) and to search for its zero crossings D (1)
P (u, P )=0asa
new procedure for the evaluation of the “real” power curve. The power curve is
reconstructed well by this approach even for very large turbulence intensities
such as ζ = 30% as also shown in Fig. 32.1.
P(u)/P rated
100%
50%
0 0 5
P(u) real
(10%)
(20%)
(30%)
D (1) (u,P) = 0
10 15
u [m/s]
Fig. 32.1. The “real” power curve is indicated by a thick solid line. Theopen symbols
represent the reconstructed curves according to the IEC-standard for turbulence
intensities of ζ = 10% (dashed line with circles), ζ = 20% (dashed line with triangles),
and ζ = 30% (dashed line with diamonds). The filled squares represent the
zero crossings of D (1)
P
(u, P )=0forζ = 30%