4 The wind
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4.3.2 Yield calculation from distribution function and turbine
power curve
If both, the wind speed distribution h(v) – to be inserted in 1/(m/s) - and the power
curve P(v) are given analytically, the yield is calculated in analogy to equation
(4.19) as the integral
dvvPvhTE )()(
0
³
f
(4.20)
In reality, the procedure is always a numerical integration (summation, see above)
since the turbine’s power curve is determined by measurement (cf. Fig. 4-26), and
the sections between the measuring points of the power curve are linearised for the
integration.
The specific annual energy yield, per square meter of the rotor swept area, for
an idealized modern speed-variable wind turbine, calculated depending on the
annual mean wind speed at hub height and using a Rayleigh distribution, is shown
in Fig.s 15-23 and 15-24.
In general, the power curves are given for a standard air density of 1.225 kg/m³.
The energy yield calculation for a particular site has to consider that the wind
power is proportional to the air density, which itself depends according to the ideal
gas equation from the ambient temperature and the atmospheric pressure. With
increasing temperature (tropical zones) the air density decreases, as well with the
increasing altitude of the site above sea level.
For the yield calculation of a single wind turbine the energy shares of all wind
classes and wind directions are summed up, Fig. 4-25. But if a wind farm is
planned, the yield calculation is done sector by sector, Fig. 4-22, in order to con-
sider the shading by other wind turbines (wind farm effects).
4.3.3 Power curve measurement
The power curve of a wind turbine shows the output of electric power depending
on the wind speed. Power curves are either calculated from the design data for
rotor and drive train, or they are measured on the real machine standing in the wind.
The measured power curve is determined from the simultaneous measurement of
the wind speed at hub height and the produced power, Fig. 4-26. The averaging
interval is usually 10 minutes [4]. It is assumed that the wind speed measured with
the measuring mast is the same as the wind speed at hub height at the position of
the wind turbine. To assure this, the distance between turbine and measuring mast
should not be too large, on one hand. On the other, the mast should not be placed