Synchronous generator reactance (Sub, transient, SS)

[EEstudent90]

Hi

I know that when studying fault conditions for synchronous machines you have three reactances: Sub, transient and steady state reactance. Where the magnitude of the reactances are (from smallest to largest) in the same order as previously listed.

However, I have tried searching - hoping to understand why it is as it is, but have not succeeded.

How is the magnetic flux affecting the synchronous reactance during transient conditions? (I assume that flux plays an important role here, not sure tho.)Best regards

 

[anorlunda]

There are specific windings added called Amortisseur (French for damper) associated with the subtransient reactance.
http://www.electrotechnik.net/2010/11/amortisseur-windings.html

I read a story (sorry, can't remember the title) about the genius generator designer who intuited what was needed to damp oscillations, and he did that without analytic tools. He just pointed at the blueprint and said, "Add short circuited windings here." (Could it have been Tesla?)

 

[EEstudent90]

Thanks.I found this image while doing some more research, but with little explanation (at least for me). Image (a) is sub-transient, (b) transient and (c) steady state.

Based on this image, we can observe that the flux from the stator does not return via the rotor and therefore has a high reluctance path through the air (i.e. low impedance).

Similarly in (b), the flux now return now in a small part of the rotor, still there is some flux outside the rotor, but the reluctance path is nevertheless reduced.

In (c), most of the flux return via the rotor.So now I need to understand how the flux produced by the stator currents are "not allowed" to return via the rotor as shown in image (a) and (b).

I assume the damper/amortisseur windings have an impact, since you mentioned it. However, based on the image above, I can not see any flux lines around the damper windings, trying to prevent any flux from return via the rotor? Have they maybe ignored it in the drawing?

 

[jim hardy]

I assume the damper/amortisseur windings have an impact, since you mentioned it. However, based on the image above, I can not see any flux lines around the damper windings, trying to prevent any flux from return via the rotor? Have they maybe ignored it in the drawing?

Try sketching in some damper winding currents and their MMF. Think Lenz... will their MMF will oppose changing _edit: change in rotor flux ?

There are tremedous opposing MMF's during a fault.

 

[EEstudent90]

Think Lenz... will their MMF will oppose changing in rotor flux ?

Ah, in the pdf where I found the picture in post #3 they wrote:

"Induced rotor currents keep armature reaction flux out of rotor core – to maintain rotor flux linkages constant"
​

I did not fully understand why the rotor flux linkages wanted to maintain constant, but I suppose its because of Lenz.

Because, of the changing flux (due to fault) in stator, currents will be induced in the damper windings. And using Lenz, these currents will set up their own flux, working against the flux created by the currents in stator, and this will try to keep the flux in the rotor constant.

Right?

 

[jim hardy]

Because, of the changing flux (due to fault) in stator, currents will be induced in the damper windings. And using Lenz, these currents will set up their own flux, working against the flux created by the currents in stator, and this will try to keep the flux in the rotor constant.

Right?

I think you have it right.
We think about this in slightly different ways -
i think of current as making MMF not flux, and flux as ∑MMF's / Reluctance.
If you think instead of currents making their own individual fluxes and add them (superposition?) we'll probably arrive at the same answer provided we both are rigorous in our thinking..

We each got where we are walking in our own shoes - so stick with what is comfortable and works for you.

What I'm saying is - I believe you have the concept correct . That substantial rotor flux can't disappear all at once.
That's why even an induction motor will briefly contribute current to a nearby fault..

And - you discovered that you already knew it - all i did was hint at Lenz.

Good Job !

old jim

 

[jim hardy]

I read a story (sorry, can't remember the title) about the genius generator designer who intuited what was needed to damp oscillations, and he did that without analytic tools. He just pointed at the blueprint and said, "Add short circuited windings here." (Could it have been Tesla?)

Maybe..
http://magazine.ieee-pes.org/septemberoctober-2013/history-9/

from this book on Google

page 826 (794 of the e-book)
Ahh, my old buddy* Silvanus P Thompson is mentioned.

old books are fun.
S P Thompson's "Calculus made Easy" is a classic, still in print.
https://www.amazon.com/dp/1484024850/?tag=pfamazon01-20

* virtual buddy - I'm not that old. He was of my great grandparents' generation.. His 1901 textbook helped me with a LOT of basics .

1899 Electrical Engineer is at
https://play.google.com/books/reade...c=frontcover&output=reader&hl=en&pg=GBS.PA826
sign-in to Google required. Finally there's something worth signing up for !old jim

 

[anorlunda]

@jim hardy

 

[jim hardy]

Thanks @anorlunda ... I'm STILL reaping rewards from that old book !Aha ! Found their US patent ...

http://pdfpiw.uspto.gov/.piw?PageNum=0&docid=00529272&IDKey=019E7468A4A6 &HomeUrl=http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1%26Sect2=HITOFF%26d=PALL%26p=1%26u=%252Fnetahtml%252FPTO%252Fsrchnum.htm%26r=1%26f=G%26l=50%26s1=0,529,272.PN.%26OS=PN/0,529,272%26RS=PN/0,529,272

 

[anorlunda]

And here they are in modern practice.

 

[Babadag]

Let's explain this more intuitive [I hope so].
In a generator there are 3 windings connected through magnetic field [without direct [galvanic] contact:
the stator main winding connected with the load [or grid] where the short-circuit occurs, the amortisseur or damper winding and the excitation connected with d.c. supply system-the last two are installed on the rotor.
The stator main winding produces a rotating magnetic field opposing to the rotor poles rotating field exerting the mechanical load on the prime mover.
In a steady state the rotor poles and the stator rotating magnetic field rotate synchronously-the same velocity then no variable magnetic field will be connected with damper and excitation windings.
If a short-circuit occurs, for a short time the rotor velocity will decrease a bit up to the time when the prime mover will overcome the new load and return the synchronization. The rotating magnetic field all this time will determine an a.c. EMF in both damper and excitation windings-like the current in the rotor of an induction motor. Both these currents decrease in time since the rotor velocity returns. The damping current decreases faster.
This current presences will determine an increase in the short-circuit current of the stator.
The reactance is the voltage divided by current.
If both currents are present the subtransient current is maximum and the x" will be minimum.
After damper current extinguishes only excitation part stays active and the current will be less so x' will be more.
If no damping and no excitation a.c. current exists the current will be less and the reactance is the maximum.

 

[jim hardy]

If a short-circuit occurs, for a short time the rotor velocity will decrease a bit

But - Does not the rotor actually pull ahead, because the flux linking stator is reduced by the short circuit's collapsing the voltage?
Damper windings oppose collapse of flux (by Lenz's Law) on their own time constant(subtransient)
Field windings do the same on their time constant (transient)
finally Armature Reaction determines steady state current , Zsynchronous...

?

 

[Babadag]

Thank you, jim hardy . It depends on if the short-circuit location is close or not –I think-and if it is located on generator terminals you are right. Actually will be an "oscillation" of the rotor forward and backward and the damper will act in order to "damp“ it. I think also the damper winding time constant [T=L/R] is shorter than field winding time constant. Of course the rotor steel itself could act as a damper also.

 

[anorlunda]

Actually will be an "oscillation" of the rotor forward and backward and the damper will act in order to "damp“ it.

If you are talking about rotor angle swings following a fault, then the exciter and the prime mover and the other machines on the grid also have important influences in addition to the generator. It makes no sense to pick just one of those influences and name that as the main cause.

 

[Babadag]

You are right, anorlunda. It is very difficult to take all the parameters into consideration. I tried to sketch only an intuitive explanation.