Wind Energy

160 K. Kaiser et al.
28.2 Turbulence and Its Impact on Power Curves
Turbulence intensity depends on a number of site specific conditions and has
a wide range of variation. It is related to the standard deviation and can be
expressed as follows:
I = σv
(28.1)
v
with the standard deviation σ of the wind speed and the mean value v.
The numeric error is related to the shape of the ideal power curve. Hence
to quantify the numeric error the power curve in homogeneous flow has to be
known. In general this information is not available, therefore it is impossible
to isolate the numeric error. To eliminate the effects due to turbulence on the
power curve, we need to find a method covering the WTs and anemometers
response and the numeric error at the same time. Within a wind speed bin
the power varies depending on the turbulence intensity [5]. Albers et al. have
shown that the mean power in a bin can be described as:
P (v) =P (¯v)+ 1 d
2
2P (¯v)
dv2 σ2 v (28.2)
with P (v) mean measured power in a bin P (¯v) theoretical power at average
wind speed ¯v in a bin σv standard deviation of the averaged wind speed ¯v.
From (28.2) it can be seen that the measured power in a bin contains two
components, the theoretical power output and a second term, which is related
to the second derivative of the power curve and the turbulence. The second
term will be negative when the power curve is bent to the right and positive
when the power curve is bent to the left. Hence with increasing turbulence
intensity the power output will be underestimated at rated wind speed and
overestimated near cut-in wind speed (Fig. 28.1). The unknown factors of
(28.2) are the ideal power curve at zero turbulence and its second derivative.
Power
I=8%
I=12%
I=16%
Wind Speed
Fig. 28.1. Typical effects of turbulence on power curves