SP16 The state of Indiana especially counties north and east

SP16 The state of Indiana, especially counties north and east of West Lafayette, have conditions ripe for wind farming plenty of wind year around, flat and open land that won\'t decelerate or divert winds, and proximity to our county\'s main electrical grid. The Meadow Lake Wind Farm, located in White County, is the best example. The Meadow Lake Wind Farm was built in four phases, with power generation beginning in October of 2009. Turbines installed to date are 121 Vestas V82 units that each produce 1.65 MW, 66 Acciona Aws 1.5 MW units, 69 GE sle 1.5 MW turbines, and 47 Suzlon S288 turbines rated at 2.1 MW each. The performance map for the Vestas V82 units is provided below. Note that the rotor assembly provides a maximum of 1800 kW to the gearbox, but the generator only supplies a maximum of 1650 kW to the grid. What is the overall efficiency of this device? Report your answer in

Solution

Given data tells us that for the vestas, the amount of energy input to the rotor assembly via the winds is 1800 kW which is supplied to the gearbox. Hence power input = 1800kW

Now. only 160kW is supplied into the grid. Hence the power output = 1650KW

Percentage Efficiency of a system = Work output / Power Input x 100 = 1650/1800 x 100 = 91.67%

Now. it is given that the blade set rotates at 15rpm. Converting it into standard units of radian/sec, we get = 15*2pi/60 = pi/2 rad/sec

Given power grabbed by the rotor blades is 1800 kW

We know that power input = Torque X angular velocity

1800 = Torque * pi/2

Hence, torque = 1145.91 kN-m