WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–52
(b) What is the average torque in the high speed shaft?
8. Assume that a wind turbine rated at 100 kW can be adequately modeled by the model
turbine of Fig. 16, a rated wind speed of 7.7 m/s, a cut-in speed of 4.3 m/s, and a furling
speed of 17.9 m/s. Determine the capacity factor and the monthly energy production
in kWh (in a 30 day month) for sites where:
(a) c =5.0andk =1.6
(b) c =6.5andk =2.0
(c) c =8.0andk =2.4
9. A Sandia 17-m Darrieus is located at a site with wind characteristics c =7m/sand
k = 2.6. Which configuration produces more energy each year, the 42 r/min machine
rated at 25 kW in an 11 m/s wind speed, or the 52.5 r/min machine rated at 60 kW
in a 15.5 m/s wind speed? Assume u c = 5 m/s and 6.5 m/s respectively and that the
furling speed is 20 m/s.
10. You are designing a wind turbine for which the cut-in wind speed is one-half the rated
wind speed. What is the rated wind speed for which yearly energy production is maximized
for
(a) c =6m/sandk =1.4
(b) c =6m/sandk =2.0
(c) c =8m/sandk =2.6
11. You are designing the low speed shaft for a horizontal axis turbine which has to transmit
50 kW of mechanical power at a rotational speed of 95 r/min. Solid steel shafts are available
in half-inch increments starting at 2 inches outside diameter. The recommended
maximum stress is 55 MPa. What size shaft should you specify?
12. An elastomeric shaft 2 m in length is used to deliver 100 kW of mechanical power to a
generator at 1800 r/min. The shaft diameter is 0.05 m and the shear modulus G is 0.9
GPa.
(a) What is the total twist θ in the shaft?
(b) What is the total energy stored in the shaft?
13. The generator of the previous problem is receiving 100 kW of mechanical power when
it suddenly loses electrical load at time t =0. TheinertiaI of the generator can be
assumed to be 3.6 kg·m 2 .
(a) Findanexpressionforθ as a function of time.
(b) How long does it take for θ to change π/2 radians?
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001