WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–45
extract significantly more power from the wind for wind speeds above 8 m/s than was possible
at 42 r/min. It would appear that if fixed speed operation is required, that 52.5 r/min is a
good choice for sites with a high percentage of winds between 6 and 10 m/s since the turbine
can deliver nearly the maximum possible shaft power over this wind speed range. A higher
fixed shaft speed would be justified only if there were a significant fraction of wind speeds
above 10 m/s. Increasing the shaft speed above 52.5 r/min would decrease the power output
for wind speeds below 8 m/s, and this would be a significant penalty at many sites.
Suppose now that the load can accept shaft power according to the curve marked Load in
Fig. 26 and that the turbine is free to operate at any speed. The turbine will then operate at
maximum power for any wind speed, so the energy output will be maximized. If this maximum
energy output can be obtained without increasing losses or costs, then we have developed a
system which extracts more energy from the wind at a lower cost per unit of energy.
Variable speed operation requires a load which has a suitable curve of power input versus
rotational speed. The optimum load will have a cubic variation of input power versus rotational
speed. In examining various types of loads, we notice that the input power to pumps
and fans often has a cubic variation with rotational speed. The power input to an electrical
generator connected to a fixed resistance will vary as the square of the rotational speed. The
power input to a generator used to charge batteries will vary even more rapidly than cubic,
as we shall see in Chapter 6. Load curves like the one shown in Fig. 26 are therefore quite
possible, so variable speed operation is possible with several applications.
In addition to the variation of shaft power with rotational speed, we must also examine
the variation of torque with rotational speed. If we take the shaft power curves in Fig. 26 and
divide by the angular velocity at each point, we obtain the torque curves shown in Fig. 27. One
important feature of these curves is that the torque is zero for n = 0, which means that the
Darrieus turbine can not be expected to start without help. The friction in the transmission
and generator produces an opposing torque, and the torque T m must exceed this opposing or
tare torque before the turbine can be accelerated by the power in the wind. The turbine must
be accelerated to some minimum rotational speed by an external power source so that T m
will reach a sufficient value to accelerate the turbine up to operating speed. This particular
machine would need to be accelerated up to perhaps 10 r/min before the wind would be able
to accelerate it to higher speeds.
This external power source is required for reliable starting of any Darrieus turbine. However,
there have been cases where a combination of very low tare torques and strong, gusty
winds allowed a Darrieus turbine to start on its own, sometimes with disastrous consequences.
A Darrieus turbine should have a brake engaged when repairs are being made or at other times
when rotation is not desirable.
The torque rises to a maximum at a particular rotational speed for each wind speed, in
the same manner as the shaft power. The peak torque is reached at a lower rotational speed
than the peak shaft power, as can be seen by a careful comparison of Figs. 26 and 27. From
Eq. 35 and the fact that maximum shaft power varies as the cube of the rotational speed,
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001