# sync generator phase diagram

#### Ledwardz

Joined Oct 31, 2010
37
hey, i'm after a bit of help with another past exam paper question which is on the attachment along with the phase diagram i am using.

ok so im a little confused. First off are the reactances in the question supposed to be stator leakage and magnetising reactance or what? in which case is Xs= 13.05 if this is correct it says per phase and there are 3 phases so do i multiply this by 3?
which gives Xs = 39.15 ohms?

Assuming that is correct i put the values given in the question onto the phase diagram and using the cosine rule derived that jXsI = 2029 V

meaning i could say I= 2029 / Xs = 51A for 3 phase and 155A / phase?
however considering the question is worth 12 marks i am beginning to think this is wrong.

i am also guessing that the axis current is the phase current?

anyways, any help is appreciated. cheers, Lee.

#### jegues

Joined Sep 13, 2010
733
I don't see any attachement.

Did you forget to attach it?

#### Ledwardz

Joined Oct 31, 2010
37
hmmm..... i must not of waited enough time for the files to upload.
its question B on the attachment.

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#### t_n_k

Joined Mar 6, 2009
5,455
This may help .....

And the reactances are leakage.

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Joined Dec 26, 2010
2,148
For future reference, the title "sync generator" is a bit confusing: prefer "synchronous...". Many people reading this may will have more experience in electronics than in power engineering, and may associate "sync generator" with video devices or oscilloscopes. A Google search on this phrase will show this.

#### Ledwardz

Joined Oct 31, 2010
37
This may help .....

And the reactances are leakage.
thanks for the help.

I'm still a little confused tho. I assume or at least the picture in my head is a stator with a rotating magnetic field created by 3 electro magnetic pole pairs spaced 120 degrees mechanically apart. The question asks me to consider 1 phase but gives 2 reactances? If they are both leakage reactance is it the reactance on the north pole and then the reactance on the south pole?

I thought the synchronous machine rotor field was produced by a DC generator attached to the shaft meaning when the generator turns this produced a back emf which created a field current and excites the rotor but if this were the case there would be no rotor reactance because it doesn't rely on frequency or AC?

when i look at the phase diagram i see that Id.Xd = Ed
but how can this be the case when the rotor current is DC?

now i think about it the field current creates the flux which is proportional somehow to the voltage induced on the stator windings. okay now im really confused.

The other reactance must be the losses from the stator windings which is IqXq = jXsI ?

i suppose im trying to ask is Id the rotor or stator current and is Xd the stator or rotor leakage reactance (if the rotor can have a leakage reactance) ?

and my final question is why on your phase diagram is the voltage 90 out of phase? the only phase diagram i have seen like that is a unity power one???

anyways, thanks for all the help!
Lee.

#### t_n_k

Joined Mar 6, 2009
5,455
Sorry I need to be more careful. The reactance terms include both leakage and magnetizing components. Leakage reactance is essentially independent of steady-state rotor position in relation to the synchronous armature mmf wave.

The steady-state direct & quadrature synchronous magnetizing reactances arise from a consideration of the synchronous armature current mmf / flux relationship adjacent to either a rotor pole face midpoint axis or an inter-pole gap midpoint axis. The effective magnetic reluctance differs on the two axes in a salient pole machine. For mathematical convenience the total stator mmf is resolved (per phase) into two components 90° electrically displaced. It's a somewhat simplistic view but suffices for (steady-state) analysis and more importantly differentiates this case from the non-salient round rotor machine analysis.

In the same manner the two component (DQ) model leads one to propose the 'existence' of two current components (direct and quadrature) which themselves are in quadrature and when added as vectors equate to the actual armature current - magnitude and phase.

With respect to the 90 degree phase offset of the Q axis vector component it would seem reasonable that the quadrature reactance voltage drop vector should be just so displaced with respect to the rotor field induced internal armature emf vector.

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#### t_n_k

Joined Mar 6, 2009
5,455
Also a second apology - my vector diagram is incorrect as I have shown the displacement angle δ as 30° which is not the case.

I was obviously not thinking very straight with my initial post.

#### t_n_k

Joined Mar 6, 2009
5,455
After some fiddling with equations I have the displacement angle as ~18.52°. Hope that might now be of some help.

There are a couple of curious matters in relation to the whole question part b.

1. The phasor diagram you attached to your post #3 is normally applied to a round rotor generator and is not applicable to the two axis (D-Q) model for a salient pole machine.

2. The solution of the problem in this case can only be done using numerical techniques and is therefore beyond the scope of a exam situation where the necessary numerical method can't be easily applied without the right 'tools'.

I wouldn't spend too much time on trying to solve it as a typical exam question. It is probably better to consult your professor regarding the 'approved' solution if that is convenient.

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#### Ledwardz

Joined Oct 31, 2010
37
sorry for the late reply. I will have a look on the weekend when i get a bit of time and try to catch my lecturer in the meantime. Thanks for all the help, It is much appreciated.

I am beginning to wonder if this was part of the syllabus last year which may have changed.........

#### Ledwardz

Joined Oct 31, 2010
37
yip it turns out i don't need to know about this....... i wasted loads of time trying to figure this out too. i suppose at least i learnt something..... once again thanks for your help and i suppose sorry for wasting your time too.

#### t_n_k

Joined Mar 6, 2009
5,455
No problem - it was an interesting question.