Lagging or leading synchronous generator

[tim9000]

Hi,
It has been a long time since I studied synchronous machines and I am trying to understand the mechanism of how the armature excitation can result in the generator being lagging or leading. So please correct me if I say something like it's axiomatic but its really erroneous.

Now, according to wiki:
https://upload.wikimedia.org/wikipe...r.svg/330px-V_curve_synchronous_motor.svg.png

"the stator of the machine is connected to a three-phase supply of voltage Vs (assumed to be constant)...the rotor is excited with a DC current (Ie)...The rotating electromagnet induces a three-phase voltage (Vg) in the stator windings...If the machine is considered to be ideal, with no mechanical, magnetic, or electrical losses, its equivalent circuit will be an AC generator in series with the winding inductance (L) of the stator. The magnitude of Vg depends on the excitation current (Ie)...If Ie is critically adjusted to a value Ie0, Vg will be equal and opposite to Vs, and the current in the stator (Is) will be zero...If, Ie is increased above Ie₀, Vg will exceed Vs, and the difference is accounted for by a voltage (Vl) appearing across the stator inductance L: Vl = I_s x Xl where Xl is the stator reactance. Now the stator current (I_s) is no longer zero. Since the machine is ideal, Vg, Vl and Vs will all be in phase, and Is will be entirely reactive (i.e. in phase quadrature). Viewed from the supply side of the machine's terminals, a negative reactive current will flow out of the terminals, and the machine will therefore appear as a capacitor, the magnitude of whose reactance will fall as Ir increases above Is₀. If Ie is adjusted to be less than Ie₀, Vs will exceed Vg, and a positive reactive current will flow into the machine. The machine will then appear as an inductor whose reactance falls as Ie is reduced further."

So the mechanism underlying this operation is that all current to and from the stator coils passes through (ideally) just an inductor:
http://www.eeeguide.com/wp-content/uploads/2016/01/Circuit-Model-of-Synchronous-Machine-9.jpg

So is it just the direction of this current (through the stator/armature inductance) which determines if the VARs is + or - ?

I don't understand how you can have an armature voltage less than the source voltage (as is the case for an under excited generator) and still be pushing current back out onto the bus. Or how if you have an over-excited motor if the armature voltage is induced to be greater than the source voltage, how is any current coming into the stator to keep the rotor spinning?

http://machineryequipmentonline.com...roubleshooting-and-maintenance-0171_thumb.jpg

Thanks

 

[anorlunda]

I didn't follow your verbal narrative, but I think this PF Insights article will answer your question.
https://www.physicsforums.com/insights/ac-power-analysis-part-2-network-analysis/

 

[jim hardy]

Is this old thread of any help ?
https://www.physicsforums.com/threads/voltage-and-reactive-power-relationship.876346/#post-5503690