Question

Question 2: [27 miks (a) In the North coast of Oman, on the Al-Batina region - Sohar, the wind has a most peculiar behavior as shown in Figure Q2 a (i). At precisely 06:00, there is a short interval with absolutely no wind. Local peasants set their digital watches by this lull. Wind velocity then builds up linearly with time, reaching exactly 8 m/s at 22: 00. It then decays, again Iinearly; to the moming lull. To simplify the graph we redrew the velocity vs time diagram of the Figure Q2a (i). The result is shown in the Figure Q2a (i). It consists of displacing the 06:00 to 22:00 wind speed rise so that it occurs between 00:00 and 16:00 and of reversing the 22:00 to 06:00 wind decline so that it looks like a speed rise from 00:00 to 08:00. A 45 kW vertical-axis windmill area is 1125 m2 and its overal with 30 m high wings was installed in Sohar. The swept efficiency is 0.4. This includes the efficiency of the generator. [4 Marks] (i) What is the verage power gen erated? (ii) What is the peak power? [2 Marks] d outout nower 20 8 kW (m/s) v (m/s) V LICI 0 12 t (h) 18 24 8 4 v t/2 V = 0 16 >8 t (h) V 2 Figure Q22

Answer 1

The available power in a stream of wind of the same cross-sectional area as the wind turbine can easily be shown to be

If the wind speed V is in meters per second, the density ρ is in kilograms per cubic meter and the rotor swept area A is in meter then the available power is in watts.

In the formula of available power, all factors remain constant except wind velocity, and average wind velocity can be found from the graph.

Average wind velocity = Sum of area of 2 triangles/24hours

1 x8 x 16 x 8 x 8)/24 2

=4 m/s

Assuming average density of air to be 1.225 kg/m³

Available wind power = 0.5*1.225*4*4*4*1125=44.1kW

Average wind power generated by windmill=windmill efficiency*avaiable power=0.4*44.1=17.64kW

Peak power generated by windmill = Power corresponding to peak wind speed=0.4*0.5*1.225*8*8*8*1125 = 141.12kW