w — cut-off where Pm is the power extracted from the wind; p is the air density; Cp is the performance coefficient; X is the tip-speed ratio (vt/vw), the ratio between blade tip speed, vt (m/s), and wind speed at hub height upstream of the rotor, vw (m/s); Awt=nR2 is the area covered by the wind turbine rotor, R is the radius of the rotor; Vw denotes the wind speed; and ^ is the blade pitch angle; Vcut-ln and Vcut-offt are the cut-in and cut-off wind speed of wind turbine; Vrated is the wind speed at which the mechanical power output will be the rated power. When Vw is higher than Vrated and lower than Vcut-off, with a pitch angle control system, the mechanical power output of wind turbine will keep constant as the rated power. It is known that the performance coefficient Cp is not a constant. Usually the majority of wind turbine manufactures supply the owner with a Cp curve. The curve expresses Cp as a function of the turbine's tip-speed ratio X. However, for the purpose of power system
Pm stability analysis of large power systems, numerous researches have shown that Cp can be assumed constant. Fig. 1 (Akhmatov, 2002) gives the curves of performance coefficient Cp with changing of rotational speed of wind turbine at different wind speed conditions (f is fixed). According to Fig. 1, by adjusting the rotational speed of the rotor to its optimized value (Dm-cpt, the optimal performance coefficient Cpmax can be reached.
In this chapter, we assume that for any wind speed at the range of Vcut-in < Vw<Vmted, the rotational speed of rotor can be controlled to its optimized value, therefore the Cpmax can be kept constant.
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