Extracted Power

From Wind wiki

The power that a turbine actually extracts from the wind is:

P=1/2 C_p μρAv^3

where ρ is the density of the air mass, v is the velocity of the air mass, and A is the area of the cross-section of the air mass. You can see that we have added two things to the original equation of the power in the wind:

C_p = the turbine’s power coefficient

μ = the turbine’s combined mechanical & electrical efficiencies.

C_p must be less than the Betz limit and is determined by the following equation:

C_p=(Q_A Ω)/(1/2 ρAv^3 )=P/P_wind

Where Q_A is the aerodynamic torque, Ω is the rotor angular speed, and P is the mechanical power delivered to the rotor.