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The power coefficient [9] C P (= P/P wind) is the dimensionless ratio of the extractable power P to the kinetic power P wind available in the undistributed stream. [ citation needed ] It has a maximum value C P max = 16/27 = 0.593 (or 59.3%; however, coefficients of performance are usually expressed as a decimal, not a percentage).
Whereas the streamtube area is reduced by a propeller, it is expanded by a wind turbine. For either application, a highly simplified but useful approximation is the Rankine–Froude "momentum" or "actuator disk" model (1865, [1] 1889 [2]). This article explains the application of the "Betz limit" to the efficiency of a ground-based wind turbine.
Betz was able to show that the optimum axial induction factor is one third. The optimum axial induction factor was then used to find the maximum coefficient of power. This maximum coefficient is the Betz limit. Betz was able to show that the maximum coefficient of power of a wind turbine is 16/27.
Power rating Deployment status Deployment date Wind farms Notes and references Mingyang Wind Power: MySE 22MW 22 Concept Rotor diameter of over 310 m and swept area of 75,438 m 2. [3] Mingyang Wind Power: MySE18.X-20MW 18.X to 20 MW Prototype Rotor diameter of 260-292 meters. [4] [5] [6] Dongfang Electric: DEW-18 MW-260 18 Prototype June 2024
The maximum theoretical power output of a wind machine is thus 16 ⁄ 27 times the rate at which kinetic energy of the air arrives at the effective disk area of the machine. If the effective area of the disk is A, and the wind velocity v, the maximum theoretical power output P is:
An example of a wind turbine, this 3 bladed turbine is the classic design of modern wind turbines Wind turbine components : 1-Foundation, 2-Connection to the electric grid, 3-Tower, 4-Access ladder, 5-Wind orientation control (Yaw control), 6-Nacelle, 7-Generator, 8-Anemometer, 9-Electric or Mechanical Brake, 10-Gearbox, 11-Rotor blade, 12-Blade pitch control, 13-Rotor hub
By extension, the efficiency of the wind turbine is a function of the tip-speed ratio. Ideally, one would like to have a turbine operating at the maximum value of C p at all wind speeds. This means that as the wind speed changes, the rotor speed must change as well such that C p = C p max.
For a wind farm, the capacity factor is determined by the availability of wind, the swept area of the turbine and the size of the generator. Transmission line capacity and electricity demand also affect the capacity factor. Typical capacity factors of current wind farms are between 25 and 45%. [12]