Wind Energy

142 P. Sørensen et al.
A spectrum SLF(n) for the low frequency fluctuations has been estimated,
and a new spectrum SWS(n) (shown in Fig. 25.2) is defined as the sum of the
Kaimal spectrum and the low-frequency spectrum, i.e.
n · SWS(n) =n · SKai(n)+n · SLF(n). (25.3)
The low frequency spectrum is estimated based on all measurements from
5ms −1 to above. The result of this estimate is given in (25.4).
n · SLF(n) =u 2 ∗ ·
0.0105 · n−2/3
. (25.4)
1 + (125 · n) 2
It is worth noticing in Fig. 25.2 that the new spectrum fits quite well for high
frequencies for 7 m s −1 as well as 14 m s −1 , which indicates that it is reasonable
to use all time series with wind speeds above 5 m s −1 in the estimation of the
normalised spectrum, and then apply the estimated normalised spectrum to
any mean wind speed.
25.4 Coherence
The coherence analysis presented here is based on all data logged form July
2003 to September 2005. It is necessary to base the coherence analysis on more
data than the PSD analysis, because the coherence depends strongly on the
wind direction, and therefore only small wind direction sectors can be used.
The Davenport type coherence function [4] between the two points r and
c can be defined in the square root form
drc
−arc
V f
γ(f,drc,V0) =e 0 , (25.5)
where arc is the decay factor. Schlez and Infield [5] suggest a decay factor,
which depends on the inflow angle αrc shown in Fig. 25.3. The figure shows
that αrc = 0 corresponds to points separated in the longitudinal direction,
whereas αrc = 90 deg corresponds to points separated in the lateral direction.
With any other inflow angles αrc, the decay factor can be expressed according
to
�
arc = (along cos αrc) 2 +(alat sin αrc) 2 , (25.6)
where along and alat are the decay factors for separations in the longitudinal
and the lateral directions, respectively. Using our definition of coherence decay
factors in (25.5) and (25.6), the recommendation of Schlez and Infield can be
rewritten as to use the decay factors
along = (15 ± 5) · σ
, (25.7)
V0