Consider a wind turbine with a rotor diameter of 40 m and an

Consider a wind turbine with a rotor diameter of 40 m and an efficiency of 36%. During one day the wind is a constant 2 m/s for 22 h and then suddenly increases to 12 m/s for the last two hours of the day. How much percentage of the energy produced during the last two hours with respect to the full energy produced during the whole day? Select one: 95.16 % 75.23 % 84.56 % 56.88 %

Solution

Power output from wind turbine is given by

P_out = (0.5 * pi*D² * Da * eff * V³ )/4

where D = 40 m ; Da = 1.225 Kg/m³ ; eff = 0.3 ; V = 2 m/s for 22 hours and V = 12 m/s for 2 hours

Energy output is E = P_out1 * 22 + P_out2 * 2

E = (0.5 * pi * 40*40*1.225*0.3*2³ )/4 * 22 + (0.5 * pi * 40*40*1.225*0.3*12³ )/4 * 2

E = 40639.642 + 798014.799 = 838654.441

% Energy generated in last 2 hours with respect to total energy is

%e = (798014.799 / 838654.441) * 100 = 95.154 %

option :- A