Wind Energy

25 Wind Farm Power Fluctuations 141
the wind turbine under test. For the present study, only wind measurements
in the height 80±5 m are used.
25.3 PSDs
The PSD of the wind speed in 80 m height is measured, based on data acquired
in only 3 months, from 7 July to 9 October 2003. A total of 1787 h data,
corresponding to 74 full days, has been acquired and saved in that period.
Met mast 5 has been selected for the PSD estimation, and only data in the
wind direction sector from 120 to 330 deg has been used to ensure that wake
effects from wind turbines are not included.
To obtain values of the PSD for low frequencies, the PSDs are based on
time series of 32768 s length, i.e. more than 9 h.
Figure 25.2 shows the resulting measured PSDs for data sectors with 9 h
mean wind speed (7±1) m s −1 and (14±2) m s −1 , respectively. For comparison,
also a Kaimal spectrum [3] is shown. It is seen that the Kaimal spectrum
is valid for the higher frequencies, but the measured spectrum has much
more energy at low frequencies. To represent this low-frequency energy, a low
frequency spectrum has been added, shown as Kaimal + LF.
The Kaimal spectrum is normalised on the well known form
n · SKai(n) =u 2 52.5 · n
∗ ·
,
(1 + 33 · n) 5/3
(25.1)
where n is a dimensionless frequency, expressed by height above ground z,
mean wind speed V0 and frequency in Hz, f according to (25.2):
n = z
· f. (25.2)
Wind speed PSD [(m/s) 2 ]
10 1
10 0
10 −1
10 −2
10−5 10−4 10−3 10−2 10−1 100 10−3 Frequency [Hz]
Measured
Kaimal
Kaimal+LF
V0
Wind speed PSD [(m/s) 2 ]
10 1
10 0
10 −1
10 −2
Measured
Kaimal
Kaimal+LF
10−3 10−5 10−4 10−3 10−2 10−1 100 Frequency [Hz]
Fig. 25.2. Measured PSD of wind speed time series with 7 m s −1 (left) and 14 m s −1
(right) mean wind speed compared to Kaimal spectrum and to Kaimal + proposed
low frequency spectrum