Introduction to Modern Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 79

where
l = tip-speed ratio
W = rotor speed (rad/s)
R = rotor radius, from axis to tip (m)
Two basic physical processes limit the maximum rotor power coeficient of an unducted
wind turbine. First, a rotor increases the upwind static pressure, reducing the mass low rate
through its swept area and the wind energy available for conversion. Second, a rotor converts
some of the linear kinetic energy of the wind to rotational kinetic energy in its wake, which
is no longer available for conversion to mechanical energy. Figure 2-17 is a typical graph of
rotor power coeficient vs. tip-speed ratio and illustrates the effects of these two limiting pro-
cesses. The irst or retardation process limits the rotor power coeficient at all tip-speed ra-
tios to 0.593 (16/27), which is referred to as the Betz or, more-accurately, the Lanchester-Betz
limit [Bergey 1980]. The second or wake rotation process reduces the maximum rotor power
coeficient further, but this is important only if the tip-speed ratio is less than about 3.
Figure 2-17. Sample variations of HAWT and VAWT rotor power coeficients with tip-
speed ratio. Power coeficients are limited by retardation and wake rotation effects.
The design rotor power coeficients of the Mod-5B HAWT [Boeing 1988] and the 34-m
VAWT [Dodd 1990] are also shown in Figure 2-17. These are typical of modern wind
turbine rotors which have a small number of slender blades designed to operate at higher tip-
speed ratios. As such, their power coeficients are not signiicantly affected by wake rotation
losses.
For a HAWT with blade pitch control, when the wind speed exceeds the rated wind
speed power is limited to the maximum permitted through the power train. In Figure 2-17,