Ideal Wind Power calculations

previous Theory of Wind Energy

In Theory, Wind power (P) is calculated by the following general equation (the proof for which will be derived in the following section):

Where
C_p is the power coefficient
ρ is the density of the oncoming air
A swept area of the rotor
V is the velocity of the wind
The actual power is further reduced by two more inefficiencies, due to the gear box losses and the generator efficiency.
The value of the ideal power is limited by what is know as Betz coefficient with a value of C_p = 0.59 as the highest possible conversion efficiency possible.

In practice, most wind turbines have efficiencies well below 0.5, depending on the type, design and operational conditions.

In the operational output range, wind power generated increases with wind speed cubed. In other words, at a wind speed of 5 m/s, the power output is proportional with 5 cubed = 125, whereas at a wind speed of 10 m/s, the power output is proportional to 1000. This shows that doubling the speed from 5 to 10 m/s resulted in a power increase of 8 folds. This highlights the importance of location when it comes to install wind turbines. The effect of the rotor diameter affect the power output in a square manner, i.e, doubling the rotor diameter results in increasing the power output by four times.

On the other hand, since power generated is related to wind speed by a cubic ratio. That means if your turbine is rated at producing 1KW at 12m/s then it will produce 125W at 6m/s and 15W at 3m/s.
next Theory of Wind Turbines