Please can you explain why the output voltage of a wind turbine generator is proportional to the angular speed?

E=N d(flux)/dt.  d(flux)dt is directly related to angular velocity.

Faraday's Law states that the voltage produced in a coil, moving relative to a magnetic field, is directly proportional to the number of turns in the coil times the change in magnetic flux per unit time.

V = -n (dB/dt)

In a rotating machine, obviously the number of turns in the coil is a constant. Also, the magnetic field in permanent magnet generators can be considered a constant for this purpose.

What changes when a wind turbine rotor speeds up (or slows down) is the rate of change of magnetic flux per unit time. When the rotor speeds up, the dt in the denominator becomes smaller (it takes less time for the rotor to move a fixed angle). Therefore, the voltage must increase as the speed increases. Conversely, as the rotor slows down, it takes more time for the rotor to move a some fixed angle and the dt in the denominator becomes larger, causing the voltage to drop. If the rotor is stationary then it effectively takes an infinite amount of time for the rotor to move a given angle. If dt becomes infinity, obviously, V becomes zero.


For the pedants out there:
I am aware that I played a little loose with dt vs. delta t, but for the purposes here I think it illustrates the point well enough