Given a WT with the following parameters, calculate the annual energy production assuming a Rayleigh PDF:

\(C_{p}=C_{p \max }=0.40\left(C_{p}\right.\) value assumed maximum and constant for all wind speeds)

Rated power \(=3000 \mathrm{~kW}=3.0 \mathrm{MW}\)

Annual average wind speed \(=7.0 \mathrm{~m} / \mathrm{s}\)

Rated wind speed \(=12.5 \mathrm{~m} / \mathrm{s}\)

Cut-out wind speed \(=25 \mathrm{~m} / \mathrm{s}\)

Rotor radius \(=45.0 \mathrm{~m}\)

Area \(=6361.73 \mathrm{~m}^{2}\)

Air density \(=1.20 \mathrm{~kg} / \mathrm{m}^{3}\)

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Wind Speed (m/s) Power (kW) Probability (%) # of Hours/Year Energy (kWh) 123 in 1.5 12.2 41.2 4 97.7 5 190.9 6 329.8 7 523.7 8 781.7 9 1113.0 10 1526.8 11 2032.2 12 2638.3 13 3000.0 14 3000.0 15 3000.0 16 3000.0 17 3000.0 18 3000.0 19 3000.0 20 3000.0 21 3000.0 22 3000.0 23 3000.0 24 3000.0 25 3000.0 Total: Total: kWh MWh