Page 225 - Wind Energy Handbook

TURBULENCE EFFECTS 199

1500

1250 I ■ I ■ I ■ I ■ I I ■ I ■ I ■ I I ■ ■ I I ■ I ■ ■ ■ I ■ I I ■
Electric power, air density 1225 kg/m 3 (kW) 750 0 ■ ■ ■ ■ ■ ■ ■ ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■ I ■
1000
■

500

250

-250

-500
0 2 4 6 8 10 12 14 16 18 20 22
Hub-height wind speed (m/s)

Figure 4.23 Turbine Power Curve with Error Bars

3
3
U ¼ (U þ U )
2
2
3
U þ 3U U þ 3U U þ U 3

The fluctuations U are assumed symmetrical about U and so the mean values of
3
U and U are zero and hence this simplifies to:
3
3
U ¼ U þ 3U 2 U (4:11)
2
By definition the mean square fluctuation about the mean is just the variance, ó ,
and so Equation (4.11) can be written as

3
2
3
U ¼ U þ 3ó U
Also by definition the turbulence intensity, I is simply ó=U, and hence
2
3
3
U ¼ U (1 þ 3I ) (4:12)
Consequently there is more energy in the wind than indicated by the average value
of the wind speed. Corrections to the power curve have been suggested on the basis