Page 398 - Wind Energy Handbook

372 CONCEPTUAL DESIGN OF HORIZONTAL-AXIS TURBINES

In the variable-speed case, the dynamics may be quite simple: the drive train may
be modelled as a rotor and a generator inertia, separated by a torsional spring.
Typically the natural frequency of this resonant system is quite high, of the order of
3–4 Hz. However, this mode is subject to very little damping, especially above
rated where the generator torque is held constant. (Below rated the torque will be
varied as a function of rotational speed, thus providing a small amount of
damping.) There is very little aerodynamic damping from the rotor, and this mode
of vibration can potentially generate very large gearbox torque oscillations. Chapter
8 explains how the control system can be used to damp this mode by appropriate
control of the generator torque, but it is important to ensure that the resonant
frequency does not coincide with a significant forcing frequency such as 6P, which
can make it very difficult to achieve sufficient damping through the control system.
In the fixed-speed case, the directly-coupled induction generator provides a lot of
damping since the air-gap torque increases steeply with generator speed. The
torque–slip curve completely changes the dynamics compared to the variable-
speed case, resulting in a much lower first mode frequency, typically closer to 1 Hz.
The damping factor is strongly dependent on the generator slip: a generator with
0.5% rated slip can give a peak dynamic magnification of perhaps 2 to 5 at the
resonant frequency, whereas with 2 percent slip the peak magnification may be no
more than 1 to 1.5. The position of the peak with respect to blade-passing frequency
is critical: if the blade-passing frequency is close to the peak, very large gearbox
torque and electrical power oscillations will occur at this frequency. Pitch control
may further exacerbate these.
With a two-bladed turbine the blade-passing frequency tends to be closer to the
resonant peak; with a three-bladed turbine the blade-passing frequency is typically
higher, where the dynamic magnification is much lower. Nevertheless, even for
three-bladed turbines it is not uncommon for power and torque oscillations at the
blade passing frequency to be as large as 50–100 percent during pitch controlled
operation in high winds.
The use of a high-slip generator greatly improves the situation, but there are two
main drawbacks. First, each 1 percent of slip corresponds to 1 percent of extra
losses, which significantly reduces the energy yield below rated wind speed.
Second, these extra losses equate with heat dissipation in the generator, making it
more difficult to keep the generator cool, especially in large machines.
An alternative to high generator slip which has occasionally been used is a fluid
coupling between the gearbox and the generator. This is also a device which
generates a torque proportional to slip speed, and it suffers from the same draw-
backs as a high-slip generator.
Another technique which has sometimes been used is to reduce the resonant
frequency by introducing additional torsional flexibility into the drive train. This
can be done by means of a quill shaft, a flexible low-speed coupling, or flexible
mounts for the gearbox or even for the whole bedplate. The frequency reduction is,
however, accompanied by a further loss of damping, and it may therefore be
necessary to incorporate additional mechanical damping with the torsional flex-
ibility, which is not always easy to engineer. Torsional flexibility in the high-speed
shaft is not usually practical because of the large angular movement required to
achieve the necessary flexibility: half a revolution may be necessary, compared to