WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–46
Figure 27: Shaft torque output of Sandia 17-m Darrieus in variable-speed operation.
we can argue that the maximum shaft torque varies as the square of the rotational speed. In
Fig. 27, for example, the peak torque in a 12 m/s wind is 10,600 N·m/rad at 60 r/min. The
peak torque in a 6 m/s wind is 2650 N·m/rad at 30 r/min. The peak torque has changed by
a factor of four while the rotational speed has changed by a factor of two.
The turbine torque T m must be opposed by an equal and opposite load torque T L for
the turbine to operate at a steady rotational speed. If T m is greater than T L ,theturbine
will accelerate, while if T m is less than T L the turbine will decelerate. The mathematical
relationship describing this is
T m = T L + I dω m
N · m/rad (51)
dt
where I is the moment of inertia of the turbine, transmission, and generator, all referred to
the turbine shaft.
The relationship between shaft torque and an optimum load torque for the Sandia 17-m
Darrieus turbine is illustrated in Fig. 28. We have assumed a load torque with the optimum
variation
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001