At a given sea level location, the wind statistics, taken over a period of one y

Question

At a given sea level location, the wind statistics, taken over a period of one year and measured at a an anemometer height of 10 m above the ground, are as follows: The velocity is constant in each range (to simplify the problem). Although the wind varies with the l/7th power of height, assume that the velocity of the windmill sees is that at its center. The windmill characteristics are: If h is the height of the tower and M is the mass of the windmill on top of the tower, then the cost, CT, of the tower is CT = 0.05hm How big must the swept area of the windmill be so that the average delivered power is 10 kW? How big is the peak power delivered - that is, the rated power of the generator? Be sure to place the windmill at the most economic height. How tall will the tower be? Neglecting operating costs and assuming an 18% yearly cost of the capital invested, what is the cost of the MWh?

Explanation / Answer

efficiency of windmill = 0.7

Cost = $150/m^2

Weight = 100 kg/m^2

Ct = 0.05hM

a) Power = 10 kW =(n) *W*A*V

10000 = 0.7*100*A*8.42

Area = 16.96 m^2

b) Peak power = 0.7*100* 16.96 * 25 = 29691 W = 29.6 kW

c)Cost = 16.96 * 150 = $2544

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