Second Problem. Consider a 64 meter diameter, 1.5 MW wind turbine located at a s

Question

Second Problem. Consider a 64 meter diameter, 1.5 MW wind turbine located at a site with Rayleigh winds averaging 7.5 m/s Problem 7- Using Equation 7.63 calculate the capacity factor. Write answer in format 0.XXX PR CF 0.087V(Rayleigh winds) Problem 8- determine the estimated energy delivered during the year, in MWh Suppose the installed cost of the wind turbine is $1.5 million (1 S/Watt ), and its annual cost is based on a 20-year, 6% loan to cover the capital costs Problem 9- Determine the CRF capital recovery factor. Write answer in format 0.XXXX Problem 10- Determine the annuity to pay the capital cost In addition, consider the annual operation and maintenance cost to be 1 % of the capital cost, Problem 11- What is the cost of electricity from this turbine, in cents/kWh Problem 12- If a farmer is paid 0.1 cents/kWh to put this turbine on his (her) land, what would the annual royalty payment be, in ?/year

Explanation / Answer

Answer:

7. Capacity Factor CF=0.087V-PR/D2

Where V is the velocity of the wind in m/s

PR is the Rated power in MW =1.5MW or 1500KW

D is the turbine diameter in meters

Capacity Factor CF=0.087*7.5-1500/642

Capacity Factor CF= 0.6525-0.366=0.2862

8. Estimated Energy Delivered during the year=Rated Capacity *Number of Hours in year

=1.5MW*8760=13140MWH per Year

9. Capital Recovery Factor=i(1+i)N/(1+i)N-1

Where ‘i’ is the interest rate and N is the number of years

‘i’=0.06 and N=20 years

Capital Recovery Factor=(0.06(1+0.06)20 )/((1+0.06)20-1)=0.086

10. Installed cost of $1.5million=$1500000

With 6% interest and Capital Recovery Factor0.086

Annuity=$1500000*0.086=$129000   for 20 years

11. Annual energy=13140MWH per Year

       Annuity=$129000  

So per unit cost in cents/KWH= Annuity in cents / Annual energy in KWH

=12900000/13140000=0.98 cents/KWH

12.If a farmer is paid 0.1 cents/KWH then Annual royalty payment is

=0.1*13140000=1314000cents

Or $13140 per year

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