Question

2. A wind turbine has the maximum power output at the rated speed of 12 m/s and a rotor diameter of 82 meters. The cut-in and cut-out speeds for this type of wind turbine are 4 m/s and 23 m/s, respectively. The table below shows the annual wind data near a potential site for setting up a wind farm using this type of wind turbine and the power coefficient of the wind turbine at the specific wind speed. The air density is 1.22 kg/m'. Power coefficient 7 Wind speed (m/s) O 5 10 15 I 0. 25 0.5 0.25 0.1 Hours 1190 3 000 2400 1700 400 50 20 25 30 (a). What is the maximum power output of this wind turbine? (b). What is the average power output if the wind turbine is installed at this site? (c). What is the capacity factor of the wind turbine at this site?

Answer 1

To find average wind power output from turbine:

The cut in speed is 4m/s and cut out speed is 20 m/s. i.e. Power is produced

4>V<23

Also, power coefficient is the ratio of actual power output from turbine to the available wind power.

From the data given, it can be observed that for given speed limits, total duration of turbine operation = 3000+2400+1700+400=7500 hours.

So;

=

Wind speed: 5 m/s

n = 0.25 = PAV3 = {(1.22)(5281.702)(53) Pr = 100.682 kW

Since the velocity of 5m/s is available for 3000 hrs out of 7500 hrs;

(PT)v=5m/s = 3000 + (100.682) = 40.273 kW

Similarly calculating for other velocities;

(PT)v=10m/s = 40" (1610.919) = 515.494 kW

(PT)v=15m/s = 770 (2718.426) = 616.176 kW

$(P_T)_{V=20m/s}=\frac{400}{7500} (2557.471)=136.398 \, kW$

Therefore, average power output;

Pave = 40.273+515.494 + 616.176 + 136.398 = 1308.341 kW

Maximum power output is given at rated speed 12 m/s.

Pmax = 1mar (5pavated

Area of flow across the turbine;

$A=\frac{\pi}{4} D^2 = \frac{\pi}{4} (82^3)=5281.702 \, m^2$

The maximum power coefficient or Betz limit;

$\eta_{max} = \frac{16}{27}$

So;

MY 79T+667€ = ((71)(702*1879)(771);) si = roup

Capacity factor is the ratio of average power output to the maximum power output at rated speed.

$CF=\frac{P_{avg}}{P_{max}}=\frac{1308.341}{3299.162}=0.396$