Page 453 - Wind Energy Handbook

GEARBOX 427

o
where S (r i , r k , n) is the rotationally sampled cross spectrum of the wind speed
u
fluctuations at a pair of points, j and k, on the rotor (see Section 5.7.5) and (d p=du) j
is the rate of change with wind speed of the power generated by the blade elements
at r j on all N blades if the pitch does not change. The summations are carried out
over the whole rotor, and give ó P ¼ 0:213(dP=du)ó u ¼ 91 kW for the example two-
bladed machine operating at 40.4 r.p.m. in a 20 m/s mean wind with 16.5 percent
turbulence intensity. Here dP=du is the rate of change of turbine power with wind
if the pitch does not change. The standard deviation of the power fluctuations for a
three-bladed machine of similar size would be about one third less.

7.4.3 Drive-train dynamics

All wind turbines experience aerodynamic torque fluctuations at blade-passing
frequency and multiples thereof because of the ‘gust slicing’ phenomenon, and
these fluctuations will inevitably interact with the dynamics of the drive train,
modifying the torques transmitted. The resulting drive train torque fluctuations can
be assessed by dynamic analysis of a drive train model consisting of the following
elements connected in series:

• a body with rotational inertia and damping (representing the turbine rotor),
• a torsional spring (representing the gearbox),
• a body with rotational inertia (representing the generator rotor),
• a torsional damper (modelling the resistance produced by slip on an the
induction generator), and
• a body of infinite rotational inertia rotating at constant speed (the mechanical
equivalent of the electrical grid).
The inertias, spring stiffness and damping must all be referred to the same shaft.

7.4.4 Braking loads

Most turbines have the mechanical brake located on the high-speed shaft, with the
result that braking loads are transmitted through the gearbox. If, as is usually the
case, the mechanical brake is one of the two independent braking systems required,
then it must be capable of decelerating the rotor to a standstill from an overspeed,
e.g., after a grid loss. This typically requires a torque of about three times rated
torque.
The mechanical brake is only required to act alone during emergency shut-
downs, which are comparatively rare. During normal shut-downs the rotor is
decelerated to a much lower speed by aerodynamic braking, so the duration of
mechanical braking is much less, but the braking torque is the same, unless there is
provision for two different braking torque levels.
Figure 7.26 is a typical record of low-speed shaft torque during a normal shut-