WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–9
Figure 5: Digital representation of analog voltages.
differential equation which is solved easily. Unfortunately the air friction torque is a nonlinear
function of ω, being described by[4]
T af = a o ω 2 + a 1 ω + a 2 (3)
where a o , a 1 ,anda 2 are constants determined from wind tunnel tests. The driving torque T u
is a nonlinear function of wind speed and also varies with ω. This makes Eq. 2 very difficult
to solve exactly. Instead of this exact solution we shall seek analytic insights which might be
available from a simpler and less precise solution.
A linearized equation of motion which is approximately valid for small variations in u and
ω about some equilibrium values u o and ω o is given by[4]
I dω
dt +(K bf + K 1 u o )ω = K 1 ω o u (4)
In this equation, the torques of Eq. 2 have been assumed to be represented by
T u = K 1 ω o u
T af = K 1 u o ω (5)
T bf = K bf ω
If the torque due to the bearing friction is small, then at equilibrium T u and T af have to be
numerically equal, as is evident from Eqs. 2 and 6.
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001