Show all steps The moment of inertia of the rotor of a variable-speed wind-turbi
ID: 1332410 • Letter: S
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The moment of inertia of the rotor of a variable-speed wind-turbine-generator is 7500 kg-m2. As a result of reduction in wind speed, it is required to lower the rotor speed from 100 RPM to 95 RPM in 5 seconds to maintain maximum rotor efficiency (maximum energy capture.) Calculate the decelerating power as a result of the change in the rotor speed. Calculate the resulting torque that produces torsional stress on the rotor blades. Repeat parts a) and b) when the rotor speed is reduced from 100 to 95 RPM in one second. Draw conclusion about control of rate of change of rotor speed of variable speed wind turbines for their safe operation in the long run.Explanation / Answer
(b)the torque produces on the rotr blades is
T = I alpha= I ( wf - wi/ t) = 7500 kg m^2 ( 95( 2pi/60 ) - 100( 2 pi/ 60)/5) = -775 Nm^2
(a) the power is
P = T w= -775 Nm^2( 95( 2pi/60 ) - 100( 2 pi/ 60)) = 400.41 W
(c)
T = I alpha= I ( wf - wi/ t) = 7500 kg m^2 ( 95( 2pi/60 ) - 100( 2 pi/ 60)/1) = -3870 Nm^2
P = T w= -775 Nm^2( 95( 2pi/60 ) - 100( 2 pi/ 1)) = 399.9 W