Power of a Wind Turbine and the Moment of Inertia I am trying to calculate the power of a wind turbine that is a relatively complicated object and then I use the sensors to measure the angular velocity of the turbine to plug in the relation for rotational kinetic energy $E = 1/2 (w.I.w)$ and the amount of time needed to reach the highest rpm from stationary point so that later I can use in P=E/t.
I have the matrix for I from the output of a computational software and my guess is that the final relation would be $P=(I_{zz}w_{z}^2)/2t$.
Am I doing it wrong? Because a device (which I am not certain of its accuracy) shows a different numerical value than what I get.
Any thought would be greatly appreciated.
 A: No, you are not doing it correctly.
The quantity you have as $E = \frac{1}{2} w^2 I $ is the kinetic energy in the turning of a thing with angular velocity $w$ and angular inertia $I$. That is, it is the amount of energy in the rotational motion of the rotor of the turbine.
If you had the time it took to go from zero to that energy, that might give you some indication of the power of the turbine.  Suppose it took $T$ seconds for the turbine to get from zero to normal speed, then the power going into speeding up the turbine is just $P = E / T$ where the E is the energy from the previous paragraph.
However, that is unlikely to be a good estimate of the power the turbine could output in normal use. The turbine during this speeding-up phase will be interacting quite differently with wind as compared to when it is at full speed. The blades of the turbine will be designed to have some optimum wind speed, for example. At that speed (or close to it) the turbine will output more power. Below that it won't be very efficient. Above that it may be damaged by the excessive forces on the turbine. The blades will also have optimum turning speed to take advantage of this wind speed.
You usually want to know what the turbine's electrical output will be. In other words, you want the amount of energy per second that the turbine can produce and stay at constant speed. It will depend on a bunch of other things such  as the wind speed, the effective area of the turbine, the shape and efficiency of the blades, and the efficiency of the generator in the turbine.
Those things are quite complicated in general. I expect that in the usual case there are measured coefficients for any given wind turbine. So the result will be that the turbine has an ideal turbine speed and a rated maximum power at each wind speed. This information will be determined for each design of wind turbine on the basis of some combination of measurements and quite detailed calculations.
