WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–32
The shaft diameters are then computed from Eq. 37.
√
2(54, 650)
D L = 2 3 π(55 × 10 6 ) =0.172 m
√
2(1140)
D H = 2 3 π(55 × 10 6 ) =0.0473 m
It can be seen that the low speed shaft is rather substantial in size. This adds to the mass and
cost of the turbine and should be held to a minimum length for this reason.
Torque at the rotor shaft will vary significantly as the rotor goes by the tower. This will be
smoothed out somewhat by the inertia and damping of the system but will still appear in the
electrical power output curve. Fig. 19 illustrates this situation for the MOD-0 wind turbine
in a 15 m/s wind[7]. The system losses have been subtracted from the power input curve,
so the areas under the input and output curves are the same. The actual aerodynamic rotor
input power is rather difficult to measure, so its curve is theoretically developed. It shows the
input power decreasing to 40 kW as a blade goes by the tower and increasing to 120 kW as
the blade clears the tower. The torque will follow the same pattern since the rotor rotational
speed is fixed. The output power is considerably damped, but still shows a variation of about
18 kW for a stiff steel shaft, 16 kW for a flexible elastomeric shaft and 14 kW for a fluid
coupling. The system lag is such that the output power is at a peak when the rotor power is
at a minimum.
A power variation of this magnitude can be a major problem to a utility. It can affect
voltage levels, causing lights to flicker. It can cause utility control equipment such as voltage
regulators to cycle excessively. Careful attention must be given to the design of the drive train
in order to hold this variation to a minimum.
This power flow variation can also be minimized by placing several wind turbines in a wind
farm in parallel operation. The larger wind turbines normally use synchronous generators, to
be discussed in the next chapter. One feature of synchronous generators in parallel is that
they all turn at exactly the same speed, and the angular positions of their shafts vary only
slightly with individual power flows. If fixed gearing is used, and there are no drive train
components like vee-belts or fluid couplings which allow slip, each rotor in the wind farm can
be at a different angular position. A collection of 18 turbines with a 10 o angular position
difference between individual rotors would be expected to have a much smoother net output
than the output of any one turbine.
The torque and power variation for a Darrieus turbine is even more pronounced than that
for a horizontal axis turbine. Figure 20 shows the aerodynamic torque for the Sandia 17-m
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001