A wind farm is going to be built at a site that has an avera

A wind farm is going to be built at a site that has an average wind speed of approximately 7.2 m/s. Each wind turbine in the farm is rated at 2 MW with 120 meter diameter blades, and an overall efficiency of 42%. The density of air is 1.2 kg/m^3. If the desired annual energy yield of this wind farm is expected to be approximately 250 GWh, calculate the following: a) How many wind turbines are required to achieve this energy yield? (round your answer appropriately) b) What is the capacity factor of this wind farm? An unknown source has claimed that a wind turbine with 100 m diameter blades can output 1.5 MW with a wind velocity of 7.5 m/s. Assuming the density of air is 1.2 kg/m^3 answer the following: a) What is the wind turbine\'s efficiency? b) Is the estimated efficiency theoretically possible? Why or why not?

Solution

a) Let us calculate the yeild required 250 GWh annually

Yeild required per hour = 250 x 10^9 W / (365x24) = 28.5 MW

Yeild per wind turbine = 1/2 x density of air x cross section of blades x velocity³

= 1/2 x 1.2 * pi ( 60)² x 7.2³

   = 703.55 Watts

No of turbines required = 28.5 / (0.0070355x 0.42) = 9644 turbines are required

b) capacity factor of a wind farm is already given as avg output generated by rated output =28.5 MW / (9644 x 2) = 0.14%

2) Power generated = 1/2 x density of air x cross section of blades x velocity³

   ⁼ 552.2 Watts.

Efficiency = 1.5 MW / 552.2 watts = 0.36%

b) Yes it is possible, and it is realisitic in nature.