Does the rotation speed of a synchronous machine affect the voltages induced?

Question

We know that synchronous generator are the go to for power generation. They essentially need an excitation current for the rotor and an external force to rotate it. This would induce a voltage in the 3 stator windings that has a frequency proportional to its rotation speed. The thing that I don't really understand is how do these machines produce a voltage amplitude that is independent of its rotation speed while Faraday's law clearly states that the EMF produced is dependant on the rate of variation of the flux. (So let say, I increase the rotation speed consequently the frequency will increase but will that affect my voltage?) Additionally, how do these generator provide sine waves, wouldn't that require a variation of the number of wire turns in each slot of the stator?

Thank you :)

Answer 1

The voltage induced is defined as the change in magnetic flux with respect to time (Faraday’s law). Which if you differentiate Faraday’s law you’ll find you that it’s directly proportional to angular velocity. Therefore increasing the frequency of rotation does increase the induced voltage. What really happens is that generators are locked at a specific rotational frequency, they always produce the same voltage, though not the same current. This is very important in order to not overpower the grid (if it’s being connected to the grid). The more power that is consumed the harder it is to rotate the generator, more torque is required. So if you intend to have the same voltage while under heavy use, you need to push the generator harder.

They produce sine waves because they are rotating at a constant angular velocity. The induced voltage changes as \$\cos(\theta)\$ (Faraday’s law).