Page 213 - Wind Energy Handbook

ESTIMATION OF ENERGY CAPTURE 187

The tip speed of the rotor will be 3:7 3 13 m=s ¼ 48:1m=s and so the rotational
speed will be 48:1=24:6 rad=s ¼ 1:96 rad=s, which is 1:96 3 60=2ð rev=min ¼
18:7 rev=min.
The power versus wind-speed curve for the turbine can then be obtained from
Figure 4.15.
1
3
Power (electrical) ¼ (K P 3 3 1:225 kg=m 3 (48:1m=s) 3
2
3
2
3 1:92 3 10 m 10 3 1000 W) 3 0:9
Wind speed ¼ 48:1m=s=º
To determine the energy capture of the turbine over a time period T multiply the
power by f(u) 3 T (Equation 4.4); because f(u) is the proportion of time T spent at
a normalized wind speed u.

äT
f(u)äu ¼ (4:5)
T
and
ð
1
f(u)du ¼ 1 (4:6)
0

Plot power against u and integrate over the operational wind-speed range of the
turbine to give the energy capture.
The operational speed range will be between the cut-in speed and the cut-out
speed. The cut-in speed is determined by the transmission losses and is the wind
speed at which the turbine begins to generate power. The cut-in speed is usually

600

400

P (kW)

200

0
0 5 10 15 20 25
U (m/s)
Figure 4.16 Power versus Wind Speed