Synchronous generator induced EMF

Question

I have started studying synchronous generators in more detail of recent and I'm finding it difficult locating helpful information regarding their operation.

• What is the formula that can be used to calculate the induced emf on the stator windings, and how does the rotor rpm affect this induced emf? I am also trying to find an equivalent circuit model of the rotor and stator windings to understand the generators terminal output voltage.

• Also how to calculate the required magnetic field strength of rotor, i.e. the dc field current and voltage, that will produce a desired peak voltage at a given rpm?

• Also how does the synchronous machine's parameters affect these above calculations? Like for example, the rotor and stator resistance and self-inductance (inductive reactance)?

Can anyone help or recommend good books or webpages/videos etc that may prove helpful? I cannot seem to find much info and books are expensive to buy if they will not be off any help.

I have created a basic model in MATLAB Simulink of a synchronous generator and would like to be able to enter machine parameters, measure produced simulated values, and have calculations that produce similar answers.

Thanks guys.

Answer 1

There is a quick but (rather) exact calculation of the emf in this page. You just have to know the number of conductors in series and the flux \$ \phi \$ per pole. To have an idea of \$ \phi \$: $$ \phi \approx k \frac{S \times B_m}{P} $$ where:

• S is the surface of the rotor
• \$ B_m \$ is the maximum of the magnetic field. Let say 1.2T (saturation of standard magnetic materials)
• P: number of poles
• k: depends on the shape of B. Let's say \$ 0.5 < k < 1 \$

You can see easily that the emf is proportional to the frequency, hence to the rotor speed.

The most simple equivalent circuit is given here. You have the emf and an inductance that represents the effect of the statoric current on the external voltage of the generator.

Note however that the full calculation of all the parameters of a rotating machine is not that easy. Some people spent the time of a PhD on this subject. If all you want is a decent set of parameters that could represent a real-world machine, you could try to find the parameters in manufacturers' data (for example: this one).

On a final note: you asked for videos. I love the videos from LearnEngineering (but they deal more with principles than calculations). There is one on synchronous motors.