1. [5] The following wind measurements by bin are given for a proposed wind turb

Question

1. [5] The following wind measurements by bin are given for a proposed wind turbine location. Assume the air has a density of 1.15 kg/m. Calculate the total estimated energy available in the wind from the bin data, in k Wh/m2. For bin 16, assume an average wind speed of 16 m/s. Bin Wind Speed (m/s) Hours year Minimum Maximum 0.0 1.0 2.0 3.1 4.1 5.2 6.2 7.2 8.2 9.3 10.3 11.3 12.3 13.4 14.4 And above 4 80 200 501 850 1300 1407 1351 990 641 480 375 291 180 78 32 1 0.0 2 0.0 3 1.0 4 2.0 5 3.1 6 4. 7 5.2 8 6.2 9 7.2 10 8.2 11 9.3 12 10.3 13 11.3 14 12.3 15 13.4 16 14.4

Explanation / Answer

observed bin probability=(hours/yr)/N

fi = observed bin probability or probability density function for the i-th bin (fi is also referred to as frequency).

Bin Wind Speed(m/s) Hours/yr fi (observed) Bin avg. Speed,Ui (m/s) fi.Ui Minimum Maximum 1 0 0 80 0.913242009 0 0 2 0 1 200 2.283105023 0.5 0.011416 3 1 2 501 5.719178082 1.5 0.085788 4 2 3.1 850 9.703196347 2.55 0.247432 5 3.1 4.1 1300 14.84018265 3.6 0.534247 6 4.1 5.2 1407 16.06164384 4.65 0.746866 7 5.2 6.2 1351 15.42237443 5.7 0.879075 8 6.2 7.2 990 11.30136986 6.7 0.757192 9 7.2 8.2 641 7.317351598 7.7 0.563436 10 8.2 9.3 480 5.479452055 8.75 0.479452 11 9.3 10.3 375 4.280821918 9.8 0.419521 12 10.3 11.3 291 3.321917808 10.8 0.358767 13 11.3 12.3 180 2.054794521 11.8 0.242466 14 12.3 13.4 78 0.890410959 12.85 0.114418 15 13.4 14.4 32 0.365296804 13.9 0.050776 16 14.4 and above 4 0.0456621 N=8760 5.49085

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