WIND ENERGY SYSTEMS - Cd3wd

Chapter 7—Asynchronous Loads 7–20
A =
(20 hp)(746 W/hp)
=98.8 m2
(0.9)(0.647)(0.35)(9.05)
3
The rotor diameter for this area is 11.22 m. Since rotors are only available in integer meter lengths,
you select the 11 m rotor. This reduces the area by about 4 percent, which in turn increases the wind
speed necessary to get 20 hp by slightly over 1 percent or to 9.17 m/s, an amount which seems quite
acceptable.
The mechanical angular velocity of the rotor in a wind speed of 9.17 m/s and a tip speed ratio of
8 would be, from Eq. 11,
The turbine rotational speed in r/min is then
ω m = u meλ
= 9.17(8) =13.34 rad/s
r m 5.5
n = 30 (13.34) = 127.4 r/min
π
The pump rotational speed needs to be 1750 r/min at this operating point, so the gear box ratio should
be 1750/127.4 = 13.74:1.
You note from Fig. 7a that the maximum flow rate is 1200 gal/min for a NPSH of 25 ft. This
corresponds to a pump speed of 1900 r/min and an input shaft power of 28 hp according to Fig. 7b.
The wind speed required for this shaft power is, from Eq. 13 and using a 0.9 air density correction,
[
] 1/3
28(746)
u R =
0.647(0.9)(0.35)(π/4)(11) 2 =10.25 m/s
From Fig. 7a, you estimate by extrapolation that water will start to flow at an input shaft power
of about 7.5 hp, which corresponds to a cut-in wind speed of 6.61 m/s. The proposed system will,
therefore, pump water at wind speeds between 6.61 and 10.25 m/s. Higher wind speeds can be used
if a blade pitching mechanism can restrict the shaft speed to less than 1900 r/min so that shaft power
does not increase above 28 hp.
The capacity factor can be determined from Eq. 14 as CF = 0.207. The rated power would be 28
hp, so the average power is (0.207)(28) = 5.79 hp. The average power required by the electric motor
driven pump is 20 hp for three hours averaged over a 24 hour day or 20(3/24) = 2.5 hp. The wind
turbine will have to be shut down over half the time because all the required water has been pumped.
You report to the city commissioner that the system should work satisfactorily if a good speed
control system is used.
We should emphasize that pump characteristics vary significantly with pump design. The
curves in Fig. 7 are only valid for that particular pump and should not be considered a good
representation for all centrifugal pumps. Another pump design may yield a much better load
match for a variable speed wind turbine than the one illustrated. It may be necessary to
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001