Wind Energy

Wind turbines convert part of the kinetic energy of moving air into mechanical shaft power and, in most modern systems, electrical power through a generator. The kinetic power available in a wind stream passing through the rotor swept area is P_wind = 0.5ρAv³, where ρ is air density, A = πD²/4 is the rotor swept area, and v is wind speed. The turbine cannot extract all of this power because the air must retain kinetic energy after passing through the rotor. The power coefficient C_p represents the fraction of available wind power converted into rotor power, giving P_turbine = 0.5ρAv³C_p. For an ideal actuator-disk turbine, the Betz limit gives a maximum C_p of 16/27 ≈ 0.593. Real turbines operate below this theoretical limit because of aerodynamic losses, wake rotation, blade drag, tip losses, control limitations, and mechanical and electrical losses. Wind-turbine operation is strongly dependent on wind speed. Below the cut-in speed, the turbine normally remains stopped because the available power is insufficient for useful operation. Between cut-in and rated speed, control systems generally allow power to increase strongly with wind speed. Around rated speed, the turbine reaches its rated power and pitch or other control methods limit additional aerodynamic power. Above the cut-out speed, the turbine is shut down to protect the rotor and drivetrain from excessive loads. The tip-speed ratio λ = ωR/v compares blade tip speed with wind speed and is an important aerodynamic operating parameter. Modern variable-speed turbines control rotor speed to maintain a suitable tip-speed ratio and operate near a high-power-coefficient region over part of their operating range. Because wind power varies with the cube of wind speed, a change in wind speed can produce a much larger change in available power than the same percentage change in air density or rotor area.