The wind measurements in Table 1 are given for a proposed turbine location. You can assume that the density of air is 1.22 kg/m3 , and that the data was observed at the hub height of the proposed turbine.

a. Calculate the total estimated energy available in the wind from the bin data, in [kWh/m2*yr]. (Hint: calculate the power density at each average bin speed and multiply by hours in bin)

b. Calculate the total estimated energy available in the wind, in [kWh/m2*yr], using the average wind speed and the Rayleigh distribution. For Bin #22,assume an average wind speed of 22 m/s. (Hint: the probability of wind being in a bin between U_i,minand _i,max: probability ()_i = (_i.max) (U_i,min), CDF = cumulative distribution function)

c. Calculate the error incurred, compared to (a) when using the Rayleigh distribution under (b).

Wind speed (m/s) max Bin i min hours/yr [kW] 120 U_ E82 power (m/s) 0.00 0.50 1.501 2.50 3.50 348 828 987 1049 1004 908 761 624 503 8.50 9.50 10.50 11.50 1735 357 241 12.50 13.50 14.50 15.50 16.50 17.50 18.50 1957 2050 2050 2050 2050 2050 2050 2050 2050 2050 18 19 20 21 22 16 17 17 18 18 19 19 20 20 no bound 19.50 22.00 Table 1: wind measurements at site. Table 2: turbine power production vs. wind speed Wind speed (m/s) max Bin i min hours/yr [kW] 120 U_ E82 power (m/s) 0.00 0.50 1.501 2.50 3.50 348 828 987 1049 1004 908 761 624 503 8.50 9.50 10.50 11.50 1735 357 241 12.50 13.50 14.50 15.50 16.50 17.50 18.50 1957 2050 2050 2050 2050 2050 2050 2050 2050 2050 18 19 20 21 22 16 17 17 18 18 19 19 20 20 no bound 19.50 22.00 Table 1: wind measurements at site. Table 2: turbine power production vs. wind speed