Wind Energy

30 Uncertainty of Wind Energy Estimation 169
at Kékestető (9) was only 3.42 m s −1 , and at Siófok (5) 3.04 m s −1 but contrarily
in Pápa (4) it was significantly larger (2.93 m s −1 ) than the long term
average (see Table 30.1 for long term averages of each station).
30.3 The Uncertainty of the Power Law Wind Profile
Estimation
Two common methods for the estimation of wind profile include (1) the
Monin–Obukhov similarity theory and (2) the power law profile approximation.
The similarity theory, however, has large error above the surface
layer [10].
The scope of this section is the analysis of the power-law estimation. The
independent variables of the power law wind profile formula are the wind speed
(Ur) of the reference level (zr) and the stability dependent exponent (p). The
numerical value of the exponent is 1/7 over homogeneous terrain with short
vegetation, which is the most common first guess. Dependence on stability
(e.g., Pasquill categories) can be assumed through the daily variation of the
exponent p. In the daytime convective surface layer its value ranges between
0.07 and 0.1, while by extreme stable stratification p = 0.3–0.5 is suggested.
The first derivative of the formula for the wind speed at a certain height
(U(z) =Ur(z/zr) p ) with respect to p gives an expression for the sensitivity
of the exponential wind profile to p: δU/U =ln(z/zr)δp.
In addition, sensitivity for the wind energy (which is proportional to the
cube of wind speed) is three times larger! An error of δp = ±0.1 results in a
20% error at 80 m in the wind speed and 60% in the wind energy! In case of
special tower measurements for energy estimation purpose (usually at 10 and
40 m in Hungary) the profile fitting can be done with higher accuracy (as z0
is higher).
30.4 Inter-Annual Variability of Wind Energy
Extensive wind-energy measurements were initiated in 2001 in Hungary. Let us
consider the wind statistics for the period 2001–2003. Year 2001 was especially
windy, while year 2003 was calm in Hungary and in the whole Carpathian
Basin. The average at Siófok (5) for example in 2001 and 2003 was 3.31 and
2.27 m s −1 , respectively. Note that in the data series for Budapest (7) no such
significant variability was found, perhaps due to the urban effects.
Let us demonstrate this variability through a practical example! Calculations
have been done for a proposed wind farm on the Balaton Highlands.
Continuous wind data were generated from discrete wind measurements
(station Szentkirályszabadja, 10) by extrapolating the wind speed in the
interval Ur ± 0.5 ms −1 for each observation. This continuous data set could
be extrapolated smoothly with the power law wind profile to the upper levels.