Generally, a wind turbine converts the captured wind energy into mechanical power output. The expression is
Pm=Cp Pw=0. 5CpρA1vw3 （1-1）
In the formula: Pm represents the output power of the wind turbine (W); Cp is the phoenix energy utilization coefficient (a parameter that characterizes the ability of the wind turbine to capture wind energy); ρ represents the air density (kg/m³); A1=πR2, represents the swept area of the wind turbine blade (㎡), where R is the radius of the wind turbine blade (m); vw represents the wind speed (m/s).
It can be seen from formula (1-1) that the power of the wind turbine is affected by factors such as ρ, vw, R, and Cp. Under normal circumstances, since ρ and vw cannot be controlled, and the blade radius R is fixed, the maximum wind energy capture can only be achieved by controlling Cp.
Generally, people call the wind speed corresponding to the ideal wind turbine power as the “design wind speed”, and use this as the basis for determining the power of the wind turbine. Of course, the actual output power of a wind turbine will be affected by many factors, and it is generally not stable. In fact, the wind turbine can only be started when the torque acting on the wind turbine reaches a certain value. This torque is usually called the “minimum torque”. There are two main factors that determine the torque received by the wind turbine: one is the installation angle of the wind turbine impeller, and the other is the wind speed. For a given wind turbine, its installation angle is certain, so it must correspond to a minimum working wind speed, which is called the cut-in wind speed. The standard output power of a wind turbine is called rated power or normal power, and the wind speed corresponding to this power is called rated wind speed. In order to prevent wind turbines from being damaged due to high power, each wind turbine has a maximum wind speed called cut-out wind speed. If the wind speed reaches the cut-out wind speed, the wind turbine will automatically stop. The wind speed between the cut-in wind speed and the cut-out wind speed is called the effective wind speed, and the corresponding wind energy is called the effective wind energy. In order to facilitate research and control, people have defined the effective wind power density, which specifically refers to the average wind speed power density during the effective wind energy phase.
In theory, as long as the rated power is increased, the wind turbine can convert high-speed wind energy with greater energy into mechanical energy. However, the rated power of the generator supporting the wind turbine must be considered.
In short, it is impossible for a wind turbine to work with the best power factor and tip speed ratio at any wind speed. At a fixed rated speed, the Cp value has nothing to do with λ and is determined by the wind speed v.