WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–28
by the Weibull parameters c =9m/sandk = 2.3. You work for a wind farm company that plans to
build wind machines of the same size as the MOD-2 (rotor diameter 91.5 m) but optimized for this
site, if necessary. You know that the MOD-2 has a rated power of 2500 kW at a rated wind speed of
12.4 m/s at hub height. You conservatively estimate that u c =0.5u R and u F =2u R .
a) What is the optimum rated wind speed?
b) What is the capacity factor of your optimized turbine?
c) What are the average power and yearly energy production values for your optimized turbine?
d) What would be the capacity factor, average power, and yearly energy production of the MOD-2
turbine used in that wind regime without modification?
e) Should you recommend building the MOD-2 on this site without modification?
From Fig. 17 we see that the normalized power is greatest at u R /c =1.6fork =2.3andu c =
0.5u R . The optimum rated wind speed is then
The capacity factor is, from Eq. 30,
u R =1.6(9) = 14.4 m/s
CF = exp[−(1.6/2)2.3 ] − exp(−1.6) 2.3
(1.6) 2.3 − (1.6/2) 2.3 − exp{−[2(1.6)] 2.3 }
=
0.550 − 0.052
2.948 − 0.599 − 5 × 10 − 7
= 0.212
The rated power, assuming all efficiencies remain the same, will just be in the ratio of the cube of the
wind speeds.
The average power is
P eR = 2500
( ) 3 14.4
= 3900 kW
12.4
The yearly energy production is then
P e,ave =(CF)P eR =(0.212)(3900) = 830 kW
W = 830(8760) = 7, 270, 000 kWh
The same computations for the unmodified MOD-2 in that wind regime yield the following results:
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001