Hi everyone!

I follow some electrical drives classes and we have exercises on synchronous machines. When considering no losses nor saturation in a synchronous generator it can be represented like this:

I get more or less the method to solve the exercises but I don't fundamentally understand them because I cannot figure out what the reactance X represents. Is that the inductance of the stator coils? But that seems strange because ‘E’ is representing the e.m.f. generated at the stator coils and not ‘XI’.

I found no clear answer to the physical representation of X and even our assistants of the university seem not able to answer it.

I hope/think that's an easy question for you guys !

 

I believe X is indeed the stator inductance. The (back) emf generated by the stator is not due (mainly) to this inductance but due to the rotation of the rotor magnetic field cutting the stator conductors. This back emf is part of the energy transfer between the rotor and stator by the magnetic field.

 

Ok I guess you're right but here is what I thought about the synchronous machines. You can consider them like a kind of transformer: the rotor field induces voltage across the stator coils. For an ideal transformer, the power is the same at each side of it. So it should be the same for a synchronous machine but it isn't since there is a voltage drop across the reactance X.

According to you, the back emf is created in the conductors? I agree but these are the conductors of the stator coils because they are the one's that undergo the change of magnetic field in the rotor cage. Or maybe I am wrong by making this transformer comparison but it seems to make sense.

 

The synchronous reactance is actually a combination of two factors - the armature winding leakage self-inductance equivalent reactance and the armature reaction equivalent reactance (effectively the fundamental air gap coupled self-inductance). These are based on the fundamental frequency (sinusoidal) air gap flux.

Also, keep in mind the distinction between steady-state and dynamic machine reactances. Transient and sub-transient reactances are other parameters not included in steady-state analysis based on the synchronous parameters.

I doubt your transformer model holds up in this circumstance, but I would need to think this through to elaborate the deficiencies in your assumptions. There is a closer affinity with DC machines.

Subsequent to original posting:

On reflection it would seem one could use the ideal transformer model with one significant distinction. The primary would be driven by an ideal sinusoidal current source rather than an ideal sinusoidal voltage source. Clearly the assumed transformer core must be linear so as to ensure a sinusoidal excitation flux is established in the magnetic circuit. Also a current driven primary ensures the secondary load current mmf is not canceled by the commensurate primary current mmf typical of a loaded (voltage driven) transformer situation.