WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–10
Figure 6: Torques or moments existing on a cup-type anemometer.
ThesolutiontoEq.4forastepchangeinwindspeedfromu o to u 1 is
ω (
o
ω =
K 1 u 1 +[K bf + K 1 (u o − u 1 )]e −t/τ
K bf + K 1 u o
rad/s (6)
The time constant τ is given by
τ =
I
K bf + K 1 u o
s (7)
For good bearings, the bearing friction torque is small compared with the aerodynamic
torques and can be neglected. This simplifies the last two equations to the forms
ω = ω o
u 1
u o
+(u o − u 1 ) ω o
u o
e −t/τ rad/s (8)
τ =
I
K 1 u o
s (9)
Equation 8 shows that the angular velocity of a linearized anemometer is directly proportional
to the wind speed when transients have disappeared. Actual commercial anemometers
satisfy this condition quite well. The transient term shows an exponential change in angular
velocity from the equilibrium to the final value. This also describes actual instrumentation
rather well, so Eqs. 8 and 9 are considered acceptable descriptors of anemometer performance
even though several approximations are involved.
Aplotofω following a step change in wind speed is given in Fig. 7. The angular velocity
increases by a factor of 1 - 1/e or 0.63 of the total increase in one time constant τ. In the
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001