Introduction to Wind Turbine Technology - Small Wind Turbines: Analysis, Design, and Application - page 12

Fig. 1.6 Power coefficient
variation with tip speed ratio
for the Vestas V80

0.5

0. 45

0.4

0. 35

0.3

0. 25

0.2

0. 15

0.1

4 6 8 10 12 14 16 18

Tip speed ratio

after Chap. 5 ) to assist in starting. In contrast, the lack of pitch adjustment on small
tribunes makes them rely on the lift generated at high angles of attack, to over-
come the resistive torque of the drive train and generator. Some of these aspects
will be discussed further in Chap. 6 , which highlights the importance of good low
wind speed performance of small turbines. The optimisation method described in
Chap. 7 is a formal procedure to combine good starting performance with high
efficiency of power extraction.
Figure 1.6 shows that k has a major effect on turbine performance. This is
because it controls the angle of attack of the blades. Since the value of C P
determines how much power is extracted at a given wind speed, Fig. 1.6 implies
that a constant speed turbine cannot operate at maximum efficiency over a large
range of wind speed; obviously the turbine's designers have opted to forgo some of
the extractable power for the simplicity of constant speed operation.
Figure 1.6 was generated from the power curve data by using the almost-
constant X of 16.9 rpm for the Vestas V80. The maximum C P is nearly 0.44, but
note that the power listed in Table 1.1 is the output electrical power which is less
than the input aerodynamic power by the product of the efficiencies of the
(mechanical) drivetrain and the (electrical) generator. Estimating the combined
efficiencies as 0.9, indicates that the V47's maximum efficiency is within 20% of
the Betz-Joukowsky 2 limit of 16/27 = 0.593, the supposed maximum efficiency
of this type of turbine ( Chap. 2 ). It is unlikely that any turbine will be able to get
significantly closer to the Betz-Joukowsky limit. Figure 1.6 shows the general
shape of any performance curve: as k increases from zero, C P increases to reach its
maximum at the optimal value of k and then decrease to zero at the ''runaway''
point where X is maximised. For the Vestas V80 the runaway k is probably around
20. Any turbine that loses its electrical load will accelerate towards runaway. The

2 This limit is often called the Betz limit. Okulov and van Kuik [ 12 ] argued convincingly for the
renaming that is followed here.